LMFDB - Embedded newform 387.2.y.c.10.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [387,2,Mod(10,387)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(387, base_ring=CyclotomicField(42))

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

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

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

chi := DirichletCharacter("387.10");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 387 = 3^{2} \cdot 43 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	387.y (of order $21$, degree $12$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$3.09021055822$
Analytic rank:	$0$
Dimension:	$36$
Relative dimension:	$3$ over $\Q(\zeta_{21})$
Twist minimal:	no (minimal twist has level 43)
Sato-Tate group:	$\mathrm{SU}(2)[C_{21}]$

Embedding invariants

Embedding label			10.1
Character	$\chi$	$=$	387.10
Dual form			387.2.y.c.271.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.581275 - 2.54673i) q^{2} +(-4.34603 + 2.09294i) q^{4} +(-2.95419 + 0.445272i) q^{5} +(-0.339884 - 0.588696i) q^{7} +(4.59900 + 5.76696i) q^{8} +O(q^{10})$	\(q+(-0.581275 - 2.54673i) q^{2} +(-4.34603 + 2.09294i) q^{4} +(-2.95419 + 0.445272i) q^{5} +(-0.339884 - 0.588696i) q^{7} +(4.59900 + 5.76696i) q^{8} +(2.85118 + 7.26470i) q^{10} +(1.98321 + 0.955063i) q^{11} +(-0.884105 + 2.25266i) q^{13} +(-1.30168 + 1.20779i) q^{14} +(5.99853 - 7.52192i) q^{16} +(2.49942 + 0.376727i) q^{17} +(-0.122786 + 1.63846i) q^{19} +(11.9071 - 8.11809i) q^{20} +(1.27950 - 5.60586i) q^{22} +(-0.0324711 + 0.0221384i) q^{23} +(3.75109 - 1.15706i) q^{25} +(6.25084 + 0.942162i) q^{26} +(2.70925 + 1.84713i) q^{28} +(-5.57974 + 5.17724i) q^{29} +(8.56546 + 2.64209i) q^{31} +(-9.35164 - 4.50351i) q^{32} +(-0.493428 - 6.58434i) q^{34} +(1.26621 + 1.58778i) q^{35} +(-5.57614 + 9.65816i) q^{37} +(4.24410 - 0.639696i) q^{38} +(-16.1542 - 14.9889i) q^{40} +(-0.555724 - 2.43478i) q^{41} +(-6.51074 + 0.781227i) q^{43} -10.6180 q^{44} +(0.0752553 + 0.0698267i) q^{46} +(-7.92075 + 3.81443i) q^{47} +(3.26896 - 5.66200i) q^{49} +(-5.12713 - 8.88045i) q^{50} +(-0.872336 - 11.6405i) q^{52} +(2.23834 + 5.70320i) q^{53} +(-6.28403 - 1.93837i) q^{55} +(1.83186 - 4.66750i) q^{56} +(16.4284 + 11.2007i) q^{58} +(-2.97714 + 3.73321i) q^{59} +(-4.87717 + 1.50441i) q^{61} +(1.74982 - 23.3497i) q^{62} +(-1.75166 + 7.67453i) q^{64} +(1.60876 - 7.04845i) q^{65} +(0.194013 - 2.58893i) q^{67} +(-11.6510 + 3.59386i) q^{68} +(3.30762 - 4.14763i) q^{70} +(7.71099 + 5.25726i) q^{71} +(-1.43804 + 3.66406i) q^{73} +(27.8380 + 8.58689i) q^{74} +(-2.89557 - 7.37780i) q^{76} +(-0.111819 - 1.49212i) q^{77} +(3.10044 + 5.37012i) q^{79} +(-14.3715 + 24.8921i) q^{80} +(-5.87772 + 2.83056i) q^{82} +(-3.97087 - 3.68443i) q^{83} -7.55150 q^{85} +(5.77411 + 16.1270i) q^{86} +(3.61296 + 15.8294i) q^{88} +(-7.30600 - 6.77898i) q^{89} +(1.62662 - 0.245174i) q^{91} +(0.0947861 - 0.164174i) q^{92} +(14.3185 + 17.9548i) q^{94} +(-0.366830 - 4.89500i) q^{95} +(-0.852010 - 0.410306i) q^{97} +(-16.3198 - 5.03398i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q + 10 q^{2} - 18 q^{4} + 17 q^{5} + 6 q^{7} - 18 q^{8}+O(q^{10}) $ 36 * q + 10 * q^2 - 18 * q^4 + 17 * q^5 + 6 * q^7 - 18 * q^8	$ 36 q + 10 q^{2} - 18 q^{4} + 17 q^{5} + 6 q^{7} - 18 q^{8} - 7 q^{10} + 4 q^{11} - 18 q^{14} - 10 q^{16} + 10 q^{17} + 10 q^{19} + 3 q^{20} - 3 q^{22} - 4 q^{23} - 2 q^{25} + 15 q^{26} + 20 q^{28} - 9 q^{29} + 40 q^{31} - 48 q^{32} - 42 q^{34} - 11 q^{35} - 19 q^{37} + 21 q^{38} - 97 q^{40} + 28 q^{41} - 8 q^{43} - 14 q^{44} - 61 q^{46} + 30 q^{47} + 6 q^{49} + 3 q^{50} - 8 q^{52} + 24 q^{53} + 14 q^{55} - 39 q^{56} + 64 q^{58} + q^{59} - 14 q^{61} - 33 q^{62} + 48 q^{64} - 38 q^{65} + 66 q^{67} - 66 q^{68} + 47 q^{70} + 33 q^{71} + 29 q^{73} + 40 q^{74} - 39 q^{76} + 27 q^{77} - 17 q^{79} - 8 q^{80} - 54 q^{82} + 23 q^{83} - 56 q^{85} + 45 q^{86} - 17 q^{88} + 19 q^{89} - 13 q^{91} + 18 q^{92} + 44 q^{94} - q^{95} - 31 q^{97} + 5 q^{98}+O(q^{100}) $ 36 * q + 10 * q^2 - 18 * q^4 + 17 * q^5 + 6 * q^7 - 18 * q^8 - 7 * q^10 + 4 * q^11 - 18 * q^14 - 10 * q^16 + 10 * q^17 + 10 * q^19 + 3 * q^20 - 3 * q^22 - 4 * q^23 - 2 * q^25 + 15 * q^26 + 20 * q^28 - 9 * q^29 + 40 * q^31 - 48 * q^32 - 42 * q^34 - 11 * q^35 - 19 * q^37 + 21 * q^38 - 97 * q^40 + 28 * q^41 - 8 * q^43 - 14 * q^44 - 61 * q^46 + 30 * q^47 + 6 * q^49 + 3 * q^50 - 8 * q^52 + 24 * q^53 + 14 * q^55 - 39 * q^56 + 64 * q^58 + q^59 - 14 * q^61 - 33 * q^62 + 48 * q^64 - 38 * q^65 + 66 * q^67 - 66 * q^68 + 47 * q^70 + 33 * q^71 + 29 * q^73 + 40 * q^74 - 39 * q^76 + 27 * q^77 - 17 * q^79 - 8 * q^80 - 54 * q^82 + 23 * q^83 - 56 * q^85 + 45 * q^86 - 17 * q^88 + 19 * q^89 - 13 * q^91 + 18 * q^92 + 44 * q^94 - q^95 - 31 * q^97 + 5 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/387\mathbb{Z}\right)^\times$.

$n$	$46$	$173$
$\chi(n)$	$e\left(\frac{5}{21}\right)$	$1$

Coefficient data

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

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

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

$2$	−0.581275	−	2.54673i	−0.411024	−	1.80081i	−0.579348	−	0.815080i	$-0.696693\pi$
$2$	−0.581275	−	2.54673i	−0.411024	−	1.80081i	0.168324	−	0.985732i	$-0.446164\pi$
$3$		0			0
$3$		0			0
$4$	−4.34603	+	2.09294i	−2.17301	+	1.04647i
$5$	−2.95419	+	0.445272i	−1.32115	+	0.199132i	−0.771483	−	0.636250i	$-0.780485\pi$
$5$	−2.95419	+	0.445272i	−1.32115	+	0.199132i	−0.549670	+	0.835382i	$0.685246\pi$
$6$		0			0
$7$	−0.339884	−	0.588696i	−0.128464	−	0.222506i	0.794618	−	0.607110i	$-0.207671\pi$
$7$	−0.339884	−	0.588696i	−0.128464	−	0.222506i	−0.923082	+	0.384604i	$0.874338\pi$
$8$	4.59900	+	5.76696i	1.62599	+	2.03893i
$9$		0			0
$10$	2.85118	+	7.26470i	0.901624	+	2.29730i
$11$	1.98321	+	0.955063i	0.597960	+	0.287962i	0.708278	−	0.705934i	$-0.249473\pi$
$11$	1.98321	+	0.955063i	0.597960	+	0.287962i	−0.110318	+	0.993896i	$0.535187\pi$
$12$		0			0
$13$	−0.884105	+	2.25266i	−0.245207	+	0.624776i	−0.999495	−	0.0317667i	$-0.989887\pi$
$13$	−0.884105	+	2.25266i	−0.245207	+	0.624776i	0.754289	+	0.656543i	$0.227982\pi$
$14$	−1.30168	+	1.20779i	−0.347890	+	0.322795i
$15$		0			0
$16$	5.99853	−	7.52192i	1.49963	−	1.88048i
$17$	2.49942	+	0.376727i	0.606199	+	0.0913697i	0.444967	−	0.895547i	$-0.353215\pi$
$17$	2.49942	+	0.376727i	0.606199	+	0.0913697i	0.161231	+	0.986917i	$0.448453\pi$
$18$		0			0
$19$	−0.122786	+	1.63846i	−0.0281690	+	0.375890i	0.965248	+	0.261336i	$0.0841629\pi$
$19$	−0.122786	+	1.63846i	−0.0281690	+	0.375890i	−0.993417	+	0.114554i	$0.963456\pi$
$20$	11.9071	−	8.11809i	2.66250	−	1.81526i
$21$		0			0
$22$	1.27950	−	5.60586i	0.272790	−	1.19517i
$23$	−0.0324711	+	0.0221384i	−0.00677069	+	0.00461618i	−0.566701	−	0.823924i	$-0.691780\pi$
$23$	−0.0324711	+	0.0221384i	−0.00677069	+	0.00461618i	0.559930	+	0.828540i	$0.310828\pi$
$24$		0			0
$25$	3.75109	−	1.15706i	0.750217	−	0.231411i
$26$	6.25084	+	0.942162i	1.22589	+	0.184773i
$27$		0			0
$28$	2.70925	+	1.84713i	0.511999	+	0.349075i
$29$	−5.57974	+	5.17724i	−1.03613	+	0.961389i	−0.999280	−	0.0379317i	$-0.987923\pi$
$29$	−5.57974	+	5.17724i	−1.03613	+	0.961389i	−0.0368507	+	0.999321i	$0.511733\pi$
$30$		0			0
$31$	8.56546	+	2.64209i	1.53840	+	0.474534i	0.944087	−	0.329698i	$-0.106947\pi$
$31$	8.56546	+	2.64209i	1.53840	+	0.474534i	0.594316	+	0.804232i	$0.297423\pi$
$32$	−9.35164	−	4.50351i	−1.65315	−	0.796116i
$33$		0			0
$34$	−0.493428	−	6.58434i	−0.0846222	−	1.12920i
$35$	1.26621	+	1.58778i	0.214028	+	0.268383i
$36$		0			0
$37$	−5.57614	+	9.65816i	−0.916712	+	1.58779i	−0.112336	+	0.993670i	$0.535833\pi$
$37$	−5.57614	+	9.65816i	−0.916712	+	1.58779i	−0.804376	+	0.594121i	$0.797500\pi$
$38$	4.24410	−	0.639696i	0.688485	−	0.103772i
$39$		0			0
$40$	−16.1542	−	14.9889i	−2.55420	−	2.36995i
$41$	−0.555724	−	2.43478i	−0.0867894	−	0.380249i	0.912815	−	0.408373i	$-0.133904\pi$
$41$	−0.555724	−	2.43478i	−0.0867894	−	0.380249i	−0.999604	+	0.0281239i	$0.991047\pi$
$42$		0			0
$43$	−6.51074	+	0.781227i	−0.992878	+	0.119136i
$43$	−6.51074	+	0.781227i	−0.992878	+	0.119136i
$44$	−10.6180			−1.60072
$45$		0			0
$46$	0.0752553	+	0.0698267i	0.0110958	+	0.0102954i
$47$	−7.92075	+	3.81443i	−1.15536	+	0.556392i	−0.910640	−	0.413202i	$-0.864410\pi$
$47$	−7.92075	+	3.81443i	−1.15536	+	0.556392i	−0.244720	+	0.969594i	$0.578696\pi$
$48$		0			0
$49$	3.26896	−	5.66200i	0.466994	−	0.808857i
$50$	−5.12713	−	8.88045i	−0.725085	−	1.25588i
$51$		0			0
$52$	−0.872336	−	11.6405i	−0.120971	−	1.61425i
$53$	2.23834	+	5.70320i	0.307460	+	0.783395i	0.998182	+	0.0602746i	$0.0191976\pi$
$53$	2.23834	+	5.70320i	0.307460	+	0.783395i	−0.690722	+	0.723120i	$0.742707\pi$
$54$		0			0
$55$	−6.28403	−	1.93837i	−0.847338	−	0.261369i
$56$	1.83186	−	4.66750i	0.244793	−	0.623721i
$57$		0			0
$58$	16.4284	+	11.2007i	2.15716	+	1.47072i
$59$	−2.97714	+	3.73321i	−0.387590	+	0.486023i	−0.936901	−	0.349596i	$-0.886319\pi$
$59$	−2.97714	+	3.73321i	−0.387590	+	0.486023i	0.549311	+	0.835618i	$0.314890\pi$
$60$		0			0
$61$	−4.87717	+	1.50441i	−0.624458	+	0.192620i	−0.590806	−	0.806814i	$-0.701190\pi$
$61$	−4.87717	+	1.50441i	−0.624458	+	0.192620i	−0.0336523	+	0.999434i	$0.510714\pi$
$62$	1.74982	−	23.3497i	0.222227	−	2.96542i
$63$		0			0
$64$	−1.75166	+	7.67453i	−0.218958	+	0.959317i
$65$	1.60876	−	7.04845i	0.199543	−	0.874253i
$66$		0			0
$67$	0.194013	−	2.58893i	0.0237025	−	0.316288i	−0.972733	−	0.231928i	$-0.925497\pi$
$67$	0.194013	−	2.58893i	0.0237025	−	0.316288i	0.996435	−	0.0843595i	$-0.0268844\pi$
$68$	−11.6510	+	3.59386i	−1.41289	+	0.435820i
$69$		0			0
$70$	3.30762	−	4.14763i	0.395337	−	0.495737i
$71$	7.71099	+	5.25726i	0.915126	+	0.623922i	0.926615	−	0.376012i	$-0.122705\pi$
$71$	7.71099	+	5.25726i	0.915126	+	0.623922i	−0.0114889	+	0.999934i	$0.503657\pi$
$72$		0			0
$73$	−1.43804	+	3.66406i	−0.168310	+	0.428846i	−0.989996	−	0.141093i	$-0.954938\pi$
$73$	−1.43804	+	3.66406i	−0.168310	+	0.428846i	0.821687	+	0.569940i	$0.193033\pi$
$74$	27.8380	+	8.58689i	3.23610	+	0.998206i
$75$		0			0
$76$	−2.89557	−	7.37780i	−0.332145	−	0.846292i
$77$	−0.111819	−	1.49212i	−0.0127429	−	0.170042i
$78$		0			0
$79$	3.10044	+	5.37012i	0.348827	+	0.604186i	0.986041	−	0.166501i	$-0.0532469\pi$
$79$	3.10044	+	5.37012i	0.348827	+	0.604186i	−0.637215	+	0.770686i	$0.719914\pi$
$80$	−14.3715	+	24.8921i	−1.60678	+	2.78303i
$81$		0			0
$82$	−5.87772	+	2.83056i	−0.649085	+	0.312583i
$83$	−3.97087	−	3.68443i	−0.435860	−	0.404419i	0.431490	−	0.902118i	$-0.357988\pi$
$83$	−3.97087	−	3.68443i	−0.435860	−	0.404419i	−0.867350	+	0.497699i	$0.834179\pi$
$84$		0			0
$85$	−7.55150			−0.819075
$86$	5.77411	+	16.1270i	0.622638	+	1.73902i
$87$		0			0
$88$	3.61296	+	15.8294i	0.385143	+	1.68742i
$89$	−7.30600	−	6.77898i	−0.774435	−	0.718570i	0.190320	−	0.981722i	$-0.439048\pi$
$89$	−7.30600	−	6.77898i	−0.774435	−	0.718570i	−0.964754	+	0.263152i	$0.915238\pi$
$90$		0			0
$91$	1.62662	−	0.245174i	0.170517	−	0.0257012i
$92$	0.0947861	−	0.164174i	0.00988213	−	0.0171163i
$93$		0			0
$94$	14.3185	+	17.9548i	1.47684	+	1.85190i
$95$	−0.366830	−	4.89500i	−0.0376359	−	0.502217i
$96$		0			0
$97$	−0.852010	−	0.410306i	−0.0865085	−	0.0416603i	0.390129	−	0.920760i	$-0.372430\pi$
$97$	−0.852010	−	0.410306i	−0.0865085	−	0.0416603i	−0.476638	+	0.879100i	$0.658145\pi$
$98$	−16.3198	−	5.03398i	−1.64855	−	0.508509i
$99$		0			0
$100$	−13.8807	+	12.8794i	−1.38807	+	1.28794i
$101$	12.0268	+	8.19971i	1.19671	+	0.815901i	0.986820	−	0.161824i	$-0.0517378\pi$
$101$	12.0268	+	8.19971i	1.19671	+	0.815901i	0.209888	+	0.977725i	$0.432690\pi$
$102$		0			0
$103$	−0.475530	−	0.0716747i	−0.0468554	−	0.00706231i	0.125573	−	0.992084i	$-0.459923\pi$
$103$	−0.475530	−	0.0716747i	−0.0468554	−	0.00706231i	−0.172428	+	0.985022i	$0.555161\pi$
$104$	−17.0570	+	5.26139i	−1.67258	+	0.515922i
$105$		0			0
$106$	13.2234	−	9.01559i	1.28437	−	0.875671i
$107$	0.415643	−	1.82105i	0.0401817	−	0.176047i	−0.950855	−	0.309636i	$-0.899793\pi$
$107$	0.415643	−	1.82105i	0.0401817	−	0.176047i	0.991037	+	0.133588i	$0.0426500\pi$
$108$		0			0
$109$	3.78562	−	2.58100i	0.362597	−	0.247214i	−0.368293	−	0.929710i	$-0.620058\pi$
$109$	3.78562	−	2.58100i	0.362597	−	0.247214i	0.730890	+	0.682495i	$0.239105\pi$
$110$	−1.28375	+	17.1305i	−0.122401	+	1.63333i
$111$		0			0
$112$	−6.46693	−	0.974732i	−0.611067	−	0.0921035i
$113$	−8.37826	+	10.5060i	−0.788161	+	0.988322i	0.211779	+	0.977318i	$0.432074\pi$
$113$	−8.37826	+	10.5060i	−0.788161	+	0.988322i	−0.999939	+	0.0110047i	$0.996497\pi$
$114$		0			0
$115$	0.0860681	−	0.0798595i	0.00802589	−	0.00744694i
$116$	13.4141	−	34.1785i	1.24546	−	3.17339i
$117$		0			0
$118$	11.2380	+	5.41195i	1.03454	+	0.498210i
$119$	−0.627734	−	1.59944i	−0.0575443	−	0.146621i
$120$		0			0
$121$	−3.83742	−	4.81197i	−0.348856	−	0.437452i
$122$	6.66631	+	11.5464i	0.603539	+	1.04536i
$123$		0			0
$124$	−42.7555	+	6.44435i	−3.83956	+	0.578720i
$125$	2.89227	−	1.39284i	0.258692	−	0.124580i
$126$		0			0
$127$	0.0467262	+	0.204721i	0.00414628	+	0.0181660i	0.976959	−	0.213428i	$-0.0684630\pi$
$127$	0.0467262	+	0.204721i	0.00414628	+	0.0181660i	−0.972812	+	0.231594i	$0.925606\pi$
$128$	−0.195885			−0.0173140
$129$		0			0
$130$	−18.8857			−1.65638
$131$	−2.11433	−	9.26347i	−0.184730	−	0.809353i	−0.979338	−	0.202231i	$-0.935181\pi$
$131$	−2.11433	−	9.26347i	−0.184730	−	0.809353i	0.794608	−	0.607122i	$-0.207676\pi$
$132$		0			0
$133$	1.00629	−	0.484604i	0.0872564	−	0.0420205i
$134$	−6.70608	+	1.01078i	−0.579317	+	0.0873180i
$135$		0			0
$136$	9.32226	+	16.1466i	0.799377	+	1.38456i
$137$	−3.69528	−	4.63374i	−0.315709	−	0.395887i	0.598504	−	0.801120i	$-0.295762\pi$
$137$	−3.69528	−	4.63374i	−0.315709	−	0.395887i	−0.914214	+	0.405233i	$0.867191\pi$
$138$		0			0
$139$	3.99725	+	10.1848i	0.339043	+	0.863866i	0.994118	+	0.108303i	$0.0345416\pi$
$139$	3.99725	+	10.1848i	0.339043	+	0.863866i	−0.655075	+	0.755563i	$0.727363\pi$
$140$	−8.82610	−	4.25042i	−0.745941	−	0.359226i
$141$		0			0
$142$	8.90664	−	22.6937i	0.747429	−	1.90442i
$143$	−3.90480	+	3.62312i	−0.326536	+	0.302981i
$144$		0			0
$145$	14.1783	−	17.7790i	1.17744	−	1.47647i
$146$	10.1673	+	1.53247i	0.841451	+	0.126828i
$147$		0			0
$148$	4.02015	−	53.6451i	0.330454	−	4.40960i
$149$	8.61865	−	5.87610i	0.706068	−	0.481389i	−0.156275	−	0.987714i	$-0.549949\pi$
$149$	8.61865	−	5.87610i	0.706068	−	0.481389i	0.862343	+	0.506325i	$0.168996\pi$
$150$		0			0
$151$	−2.08440	+	9.13237i	−0.169626	+	0.743181i	0.816522	+	0.577315i	$0.195899\pi$
$151$	−2.08440	+	9.13237i	−0.169626	+	0.743181i	−0.986148	+	0.165867i	$0.946958\pi$
$152$	−10.0137	+	6.82719i	−0.812215	+	0.553759i
$153$		0			0
$154$	−3.73502	+	1.15210i	−0.300977	+	0.0928390i
$155$	−26.4804	−	3.99128i	−2.12696	−	0.320587i
$156$		0			0
$157$	−5.96209	−	4.06488i	−0.475827	−	0.324413i	0.301548	−	0.953451i	$-0.402497\pi$
$157$	−5.96209	−	4.06488i	−0.475827	−	0.324413i	−0.777375	+	0.629038i	$0.783449\pi$
$158$	11.8740	−	11.0175i	0.944649	−	0.876506i
$159$		0			0
$160$	29.6318	+	9.14019i	2.34260	+	0.722596i
$161$	0.0240692	+	0.0115911i	0.00189692	+	0.000913507i
$162$		0			0
$163$	−0.580643	−	7.74814i	−0.0454795	−	0.606881i	−0.972655	−	0.232254i	$-0.925390\pi$
$163$	−0.580643	−	7.74814i	−0.0454795	−	0.606881i	0.927176	−	0.374627i	$-0.122229\pi$
$164$	7.51104	+	9.41855i	0.586514	+	0.735465i
$165$		0			0
$166$	−7.07510	+	12.2544i	−0.549134	+	0.951128i
$167$	−11.5269	+	1.73741i	−0.891981	+	0.134445i	−0.579012	−	0.815319i	$-0.696562\pi$
$167$	−11.5269	+	1.73741i	−0.891981	+	0.134445i	−0.312969	+	0.949763i	$0.601324\pi$
$168$		0			0
$169$	5.23683	+	4.85907i	0.402833	+	0.373774i
$170$	4.38950	+	19.2317i	0.336659	+	1.47500i
$171$		0			0
$172$	26.6608	−	17.0218i	2.03287	−	1.29790i
$173$	5.35127			0.406849			0.203425	−	0.979091i	$-0.434793\pi$
$173$	5.35127			0.406849			0.203425	+	0.979091i	$0.434793\pi$
$174$		0			0
$175$	−1.95609	−	1.81498i	−0.147866	−	0.137200i
$176$	19.0803	−	9.18856i	1.43823	−	0.692614i
$177$		0			0
$178$	−13.0175	+	22.5469i	−0.975699	+	1.68996i
$179$	7.01753	+	12.1547i	0.524515	+	0.908487i	0.999593	+	0.0285427i	$0.00908666\pi$
$179$	7.01753	+	12.1547i	0.524515	+	0.908487i	−0.475078	+	0.879944i	$0.657580\pi$
$180$		0			0
$181$	−1.45930	−	19.4730i	−0.108469	−	1.44742i	−0.740283	−	0.672296i	$-0.765308\pi$
$181$	−1.45930	−	19.4730i	−0.108469	−	1.44742i	0.631814	−	0.775120i	$-0.282311\pi$
$182$	−1.56991	−	4.00007i	−0.116369	−	0.296505i
$183$		0			0
$184$	−0.277006	−	0.0854450i	−0.0204212	−	0.00629909i
$185$	12.1724	−	31.0149i	0.894936	−	2.28026i
$186$		0			0
$187$	4.59707	+	3.13423i	0.336171	+	0.229198i
$188$	26.4404	−	33.1553i	1.92837	−	2.41810i
$189$		0			0
$190$	−12.2530	+	3.77956i	−0.888929	+	0.274198i
$191$	−0.651998	+	8.70031i	−0.0471769	+	0.629533i	0.922634	+	0.385676i	$0.126032\pi$
$191$	−0.651998	+	8.70031i	−0.0471769	+	0.629533i	−0.969811	+	0.243857i	$0.921587\pi$
$192$		0			0
$193$	4.33067	−	18.9739i	0.311729	−	1.36577i	−0.539945	−	0.841700i	$-0.681555\pi$
$193$	4.33067	−	18.9739i	0.311729	−	1.36577i	0.851674	−	0.524072i	$-0.175588\pi$
$194$	−0.549688	+	2.40834i	−0.0394653	+	0.172909i
$195$		0			0
$196$	−2.35677	+	31.4490i	−0.168341	+	2.24635i
$197$	22.2716	−	6.86986i	1.58678	−	0.489458i	0.629110	−	0.777317i	$-0.283420\pi$
$197$	22.2716	−	6.86986i	1.58678	−	0.489458i	0.957673	+	0.287859i	$0.0929434\pi$
$198$		0			0
$199$	−11.7392	+	14.7205i	−0.832169	+	1.04351i	0.166181	+	0.986095i	$0.446856\pi$
$199$	−11.7392	+	14.7205i	−0.832169	+	1.04351i	−0.998351	+	0.0574120i	$0.981715\pi$
$200$	23.9239	+	16.3111i	1.69168	+	1.15337i
$201$		0			0
$202$	13.8916	−	35.3952i	0.977410	−	2.49040i
$203$	4.94428	+	1.52511i	0.347020	+	0.107042i
$204$		0			0
$205$	2.72585	+	6.94536i	0.190382	+	0.485085i
$206$	0.0938777	+	1.25271i	0.00654077	+	0.0872805i
$207$		0			0
$208$	11.6410	+	20.1628i	0.807160	+	1.39804i
$209$	−1.80835	+	3.13215i	−0.125086	+	0.216655i
$210$		0			0
$211$	−14.0286	+	6.75583i	−0.965770	+	0.465090i	−0.849188	−	0.528091i	$-0.822908\pi$
$211$	−14.0286	+	6.75583i	−0.965770	+	0.465090i	−0.116582	+	0.993181i	$0.537194\pi$
$212$	−21.6643	−	20.1016i	−1.48791	−	1.38058i
$213$		0			0
$214$	−4.87933			−0.333544
$215$	18.8861	−	5.20694i	1.28802	−	0.355110i
$216$		0			0
$217$	−1.35587	−	5.94045i	−0.0920424	−	0.403264i
$218$	−8.77359	−	8.14071i	−0.594223	−	0.551358i
$219$		0			0
$220$	31.3675	−	4.72788i	2.11479	−	0.318754i
$221$	−3.05839	+	5.29729i	−0.205730	+	0.356334i
$222$		0			0
$223$	−11.3004	−	14.1702i	−0.756730	−	0.948909i	0.243048	−	0.970014i	$-0.421853\pi$
$223$	−11.3004	−	14.1702i	−0.756730	−	0.948909i	−0.999777	+	0.0211054i	$0.993281\pi$
$224$	0.527271	+	7.03594i	0.0352297	+	0.470108i
$225$		0			0
$226$	31.6261	+	15.2303i	2.10374	+	1.01311i
$227$	−23.8281	−	7.34998i	−1.58152	−	0.487836i	−0.625279	−	0.780402i	$-0.715015\pi$
$227$	−23.8281	−	7.34998i	−1.58152	−	0.487836i	−0.956245	+	0.292566i	$0.905491\pi$
$228$		0			0
$229$	−0.350174	+	0.324914i	−0.0231402	+	0.0214709i	−0.691658	−	0.722225i	$-0.743119\pi$
$229$	−0.350174	+	0.324914i	−0.0231402	+	0.0214709i	0.668518	+	0.743696i	$0.266929\pi$
$230$	−0.253410	−	0.172772i	−0.0167094	−	0.0113923i
$231$		0			0
$232$	−55.5181	−	8.36801i	−3.64494	−	0.549387i
$233$	10.0428	−	3.09778i	0.657924	−	0.202943i	0.0522233	−	0.998635i	$-0.483369\pi$
$233$	10.0428	−	3.09778i	0.657924	−	0.202943i	0.605700	+	0.795693i	$0.292893\pi$
$234$		0			0
$235$	21.7009	−	14.7954i	1.41561	−	0.965147i
$236$	5.12535	−	22.4556i	0.333632	−	1.46174i
$237$		0			0
$238$	−3.70846	+	2.52839i	−0.240384	+	0.163891i
$239$	−0.952467	+	12.7098i	−0.0616099	+	0.822127i	0.877733	+	0.479149i	$0.159055\pi$
$239$	−0.952467	+	12.7098i	−0.0616099	+	0.822127i	−0.939343	+	0.342978i	$0.888564\pi$
$240$		0			0
$241$	4.44144	+	0.669439i	0.286098	+	0.0431224i	0.290524	−	0.956868i	$-0.406171\pi$
$241$	4.44144	+	0.669439i	0.286098	+	0.0431224i	−0.00442537	+	0.999990i	$0.501409\pi$
$242$	−10.0242	+	12.5700i	−0.644380	+	0.808027i
$243$		0			0
$244$	18.0477	−	16.7458i	1.15539	−	1.07204i
$245$	−7.13598	+	18.1822i	−0.455901	+	1.16162i
$246$		0			0
$247$	−3.58235	−	1.72517i	−0.227940	−	0.109770i
$248$	24.1557	+	61.5477i	1.53389	+	3.90828i
$249$		0			0
$250$	−5.22840	−	6.55620i	−0.330673	−	0.414651i
$251$	−1.16008	−	2.00931i	−0.0732233	−	0.126827i	0.827089	−	0.562071i	$-0.189995\pi$
$251$	−1.16008	−	2.00931i	−0.0732233	−	0.126827i	−0.900312	+	0.435245i	$0.856662\pi$
$252$		0			0
$253$	−0.0855406	+	0.0128932i	−0.00537789	+	0.000810586i
$254$	0.494208	−	0.237998i	0.0310094	−	0.0149333i
$255$		0			0
$256$	3.61719	+	15.8479i	0.226074	+	0.990496i
$257$	−0.450674			−0.0281123			−0.0140561	−	0.999901i	$-0.504474\pi$
$257$	−0.450674			−0.0281123			−0.0140561	+	0.999901i	$0.504474\pi$
$258$		0			0
$259$	7.58095			0.471057
$260$	7.76024	+	33.9998i	0.481269	+	2.10858i
$261$		0			0
$262$	−22.3626	+	10.7692i	−1.38156	+	0.665326i
$263$	7.56220	−	1.13982i	0.466305	−	0.0702842i	0.0883127	−	0.996093i	$-0.471853\pi$
$263$	7.56220	−	1.13982i	0.466305	−	0.0702842i	0.377993	+	0.925809i	$0.376614\pi$
$264$		0			0
$265$	−9.15195	−	15.8517i	−0.562200	−	0.973759i
$266$	−1.81909	−	2.28106i	−0.111535	−	0.139861i
$267$		0			0
$268$	4.57527	+	11.6576i	0.279479	+	0.712102i
$269$	−20.2042	−	9.72982i	−1.23187	−	0.593238i	−0.299277	−	0.954166i	$-0.596745\pi$
$269$	−20.2042	−	9.72982i	−1.23187	−	0.593238i	−0.932593	+	0.360929i	$0.882460\pi$
$270$		0			0
$271$	−2.35324	+	5.99596i	−0.142949	+	0.364229i	−0.984360	−	0.176167i	$-0.943630\pi$
$271$	−2.35324	+	5.99596i	−0.142949	+	0.364229i	0.841411	+	0.540396i	$0.181725\pi$
$272$	17.8266	−	16.5406i	1.08089	−	1.00292i
$273$		0			0
$274$	−9.65292	+	12.1044i	−0.583154	+	0.731252i
$275$	8.54425	+	1.28784i	0.515238	+	0.0776596i
$276$		0			0
$277$	−1.04050	+	13.8845i	−0.0625177	+	0.834240i	0.874515	+	0.484999i	$0.161180\pi$
$277$	−1.04050	+	13.8845i	−0.0625177	+	0.834240i	−0.937033	+	0.349242i	$0.886439\pi$
$278$	23.6145	−	16.1001i	1.41631	−	0.965621i
$279$		0			0
$280$	−3.33335	+	14.6044i	−0.199206	+	0.872777i
$281$	5.10601	−	3.48122i	0.304599	−	0.207672i	−0.401368	−	0.915917i	$-0.631465\pi$
$281$	5.10601	−	3.48122i	0.304599	−	0.207672i	0.705967	+	0.708245i	$0.250513\pi$
$282$		0			0
$283$	−1.04493	+	0.322319i	−0.0621148	+	0.0191599i	−0.325657	−	0.945488i	$-0.605585\pi$
$283$	−1.04493	+	0.322319i	−0.0621148	+	0.0191599i	0.263542	+	0.964648i	$0.415109\pi$
$284$	−44.5153	−	6.70960i	−2.64150	−	0.398142i
$285$		0			0
$286$	11.4969	+	7.83845i	0.679825	+	0.463497i
$287$	−1.24447	+	1.15469i	−0.0734585	+	0.0681595i
$288$		0			0
$289$	−10.1396	−	3.12764i	−0.596444	−	0.183979i
$290$	−53.5199	−	25.7738i	−3.14280	−	1.51349i
$291$		0			0
$292$	−1.41890	−	18.9339i	−0.0830346	−	1.10802i
$293$	−11.3840	−	14.2751i	−0.665059	−	0.833958i	0.328824	−	0.944391i	$-0.393348\pi$
$293$	−11.3840	−	14.2751i	−0.665059	−	0.833958i	−0.993884	+	0.110433i	$0.964776\pi$
$294$		0			0
$295$	7.13272	−	12.3542i	0.415283	−	0.719292i
$296$	−81.3429	+	12.2605i	−4.72796	+	0.712625i
$297$		0			0
$298$	−19.9747	−	18.5338i	−1.15710	−	1.07363i
$299$	−0.0211625	−	0.0927191i	−0.00122386	−	0.00536209i
$300$		0			0
$301$	2.67280	+	3.56731i	0.154057	+	0.205617i
$302$	24.4693			1.40805
$303$		0			0
$304$	11.5879	+	10.7520i	0.664610	+	0.616668i
$305$	13.7382	−	6.61597i	0.786648	−	0.378830i
$306$		0			0
$307$	−9.05158	+	15.6778i	−0.516601	+	0.894779i	0.483213	+	0.875503i	$0.339470\pi$
$307$	−9.05158	+	15.6778i	−0.516601	+	0.894779i	−0.999814	+	0.0192762i	$0.993864\pi$
$308$	3.60887	+	6.25075i	0.205635	+	0.356170i
$309$		0			0
$310$	5.22768	+	69.7586i	0.296912	+	3.96202i
$311$	6.32352	+	16.1121i	0.358574	+	0.913631i	0.990364	+	0.138491i	$0.0442253\pi$
$311$	6.32352	+	16.1121i	0.358574	+	0.913631i	−0.631790	+	0.775140i	$0.717679\pi$
$312$		0			0
$313$	6.21930	+	1.91840i	0.351535	+	0.108434i	0.465494	−	0.885051i	$-0.345877\pi$
$313$	6.21930	+	1.91840i	0.351535	+	0.108434i	−0.113958	+	0.993486i	$0.536353\pi$
$314$	−6.88656	+	17.5467i	−0.388631	+	0.990216i
$315$		0			0
$316$	−24.7139	−	16.8497i	−1.39027	−	0.947868i
$317$	−8.24997	+	10.3451i	−0.463365	+	0.581041i	−0.957532	−	0.288326i	$-0.906901\pi$
$317$	−8.24997	+	10.3451i	−0.463365	+	0.581041i	0.494168	+	0.869367i	$0.335473\pi$
$318$		0			0
$319$	−16.0104	+	4.93854i	−0.896409	+	0.276505i
$320$	1.75748	−	23.4520i	0.0982463	−	1.31101i
$321$		0			0
$322$	0.0155286	−	0.0680354i	0.000865377	−	0.00379147i
$323$	−0.924148	+	4.04896i	−0.0514210	+	0.225290i
$324$		0			0
$325$	−0.709895	+	9.47289i	−0.0393779	+	0.525462i
$326$	−19.3949	+	5.98254i	−1.07419	+	0.331342i
$327$		0			0
$328$	11.4855	−	14.4024i	0.634182	−	0.795240i
$329$	4.93767	+	3.36645i	0.272223	+	0.185598i
$330$		0			0
$331$	−3.89417	+	9.92219i	−0.214043	+	0.545373i	−0.997060	−	0.0766279i	$-0.975585\pi$
$331$	−3.89417	+	9.92219i	−0.214043	+	0.545373i	0.783017	+	0.622001i	$0.213680\pi$
$332$	24.9688	+	7.70186i	1.37034	+	0.422695i
$333$		0			0
$334$	11.1250	+	28.3461i	0.608735	+	1.55103i
$335$	0.579625	+	7.73456i	0.0316683	+	0.422584i
$336$		0			0
$337$	15.8233	+	27.4068i	0.861953	+	1.49295i	0.870042	+	0.492978i	$0.164092\pi$
$337$	15.8233	+	27.4068i	0.861953	+	1.49295i	−0.00808906	+	0.999967i	$0.502575\pi$
$338$	9.33070	−	16.1613i	0.507523	−	0.879056i
$339$		0			0
$340$	32.8191	−	15.8048i	1.77986	−	0.857137i
$341$	14.4637	+	13.4204i	0.783255	+	0.726754i
$342$		0			0
$343$	−9.20263			−0.496895
$344$	−34.4482	−	33.9543i	−1.85732	−	1.83069i
$345$		0			0
$346$	−3.11056	−	13.6283i	−0.167225	−	0.732659i
$347$	24.8966	+	23.1007i	1.33652	+	1.24011i	0.947843	+	0.318738i	$0.103259\pi$
$347$	24.8966	+	23.1007i	1.33652	+	1.24011i	0.388679	+	0.921373i	$0.372932\pi$
$348$		0			0
$349$	34.7537	−	5.23828i	1.86032	−	0.280399i	0.879589	−	0.475735i	$-0.157818\pi$
$349$	34.7537	−	5.23828i	1.86032	−	0.280399i	0.980736	+	0.195336i	$0.0625799\pi$
$350$	−3.48525	+	6.03664i	−0.186295	+	0.322672i
$351$		0			0
$352$	−14.2451	−	17.8628i	−0.759267	−	0.952091i
$353$	−0.821043	−	10.9561i	−0.0436997	−	0.583132i	−0.975477	−	0.220101i	$-0.929361\pi$
$353$	−0.821043	−	10.9561i	−0.0436997	−	0.583132i	0.931777	−	0.363030i	$-0.118258\pi$
$354$		0			0
$355$	−25.1206	−	12.0974i	−1.33326	−	0.642066i
$356$	45.9401	+	14.1706i	2.43482	+	0.751042i
$357$		0			0
$358$	26.8757	−	24.9370i	1.42043	−	1.31796i
$359$	11.5329	+	7.86296i	0.608681	+	0.414991i	0.828053	−	0.560650i	$-0.189449\pi$
$359$	11.5329	+	7.86296i	0.608681	+	0.414991i	−0.219372	+	0.975641i	$0.570401\pi$
$360$		0			0
$361$	16.1183	+	2.42944i	0.848331	+	0.127865i
$362$	−48.7442	+	15.0356i	−2.56194	+	0.790254i
$363$		0			0
$364$	−6.55623	+	4.46996i	−0.343640	+	0.234289i
$365$	2.61673	−	11.4646i	0.136966	−	0.600087i
$366$		0			0
$367$	23.0999	−	15.7492i	1.20580	−	0.822104i	0.217719	−	0.976011i	$-0.430138\pi$
$367$	23.0999	−	15.7492i	1.20580	−	0.822104i	0.988085	+	0.153908i	$0.0491859\pi$
$368$	−0.0282555	+	0.377043i	−0.00147292	+	0.0196547i
$369$		0			0
$370$	−86.0622	−	12.9718i	−4.47416	−	0.674371i
$371$	2.59667	−	3.25613i	0.134813	−	0.169050i
$372$		0			0
$373$	−0.876784	+	0.813537i	−0.0453982	+	0.0421234i	−0.702546	−	0.711639i	$-0.747953\pi$
$373$	−0.876784	+	0.813537i	−0.0453982	+	0.0421234i	0.657147	+	0.753762i	$0.271763\pi$
$374$	5.30989	−	13.5294i	0.274568	−	0.699587i
$375$		0			0
$376$	−58.4252	−	28.1361i	−3.01305	−	1.45101i
$377$	−6.72950	−	17.1465i	−0.346587	−	0.883089i
$378$		0			0
$379$	20.5142	+	25.7239i	1.05374	+	1.32135i	0.944925	+	0.327288i	$0.106135\pi$
$379$	20.5142	+	25.7239i	1.05374	+	1.32135i	0.108817	+	0.994062i	$0.465294\pi$
$380$	11.8392	+	20.5061i	0.607338	+	1.05194i
$381$		0			0
$382$	22.5364	−	3.39681i	1.15306	−	0.173796i
$383$	−0.101772	+	0.0490107i	−0.00520029	+	0.00250433i	−0.436482	−	0.899713i	$-0.643776\pi$
$383$	−0.101772	+	0.0490107i	−0.00520029	+	0.00250433i	0.431282	+	0.902217i	$0.358061\pi$
$384$		0			0
$385$	0.994730	+	4.35820i	0.0506962	+	0.222114i
$386$	−50.8388			−2.58763
$387$		0			0
$388$	4.56161			0.231580
$389$	−3.94066	−	17.2652i	−0.199800	−	0.875379i	−0.971056	−	0.238854i	$-0.923228\pi$
$389$	−3.94066	−	17.2652i	−0.199800	−	0.875379i	0.771256	−	0.636525i	$-0.219629\pi$
$390$		0			0
$391$	−0.0894991	+	0.0431005i	−0.00452617	+	0.00217969i
$392$	47.6865	−	7.18758i	2.40853	−	0.363028i
$393$		0			0
$394$	−30.4416	−	52.7264i	−1.53363	−	2.65632i
$395$	−11.5504	−	14.4838i	−0.581166	−	0.728759i
$396$		0			0
$397$	3.79333	+	9.66525i	0.190382	+	0.485085i	0.993912	−	0.110179i	$-0.0351425\pi$
$397$	3.79333	+	9.66525i	0.190382	+	0.485085i	−0.803530	+	0.595264i	$0.797047\pi$
$398$	44.3128	+	21.3399i	2.22120	+	1.06967i
$399$		0			0
$400$	13.7977	−	35.1560i	0.689886	−	1.75780i
$401$	26.5760	−	24.6589i	1.32714	−	1.23141i	0.374532	−	0.927214i	$-0.377803\pi$
$401$	26.5760	−	24.6589i	1.32714	−	1.23141i	0.952610	−	0.304194i	$-0.0983870\pi$
$402$		0			0
$403$	−13.5245	+	16.9592i	−0.673704	+	0.844798i
$404$	−69.4301	−	10.4649i	−3.45428	−	0.520649i
$405$		0			0
$406$	1.01006	−	13.4783i	0.0501282	−	0.668915i
$407$	−20.2828	+	13.8286i	−1.00538	+	0.685457i
$408$		0			0
$409$	4.39223	−	19.2436i	0.217182	−	0.951535i	−0.742367	−	0.669993i	$-0.766297\pi$
$409$	4.39223	−	19.2436i	0.217182	−	0.951535i	0.959549	−	0.281542i	$-0.0908458\pi$
$410$	16.1035	−	10.9792i	0.795295	−	0.542223i
$411$		0			0
$412$	2.21668	−	0.683755i	0.109208	−	0.0336862i
$413$	3.20960	+	0.483770i	0.157934	+	0.0238048i
$414$		0			0
$415$	13.3713	+	9.11638i	0.656370	+	0.447506i
$416$	18.4127	−	17.0845i	0.902758	−	0.837637i
$417$		0			0
$418$	9.02789	+	2.78474i	0.441569	+	0.136206i
$419$	13.3314	+	6.42007i	0.651282	+	0.313641i	0.730193	−	0.683241i	$-0.239430\pi$
$419$	13.3314	+	6.42007i	0.651282	+	0.313641i	−0.0789110	+	0.996882i	$0.525144\pi$
$420$		0			0
$421$	1.94811	+	25.9957i	0.0949450	+	1.26695i	0.817617	+	0.575762i	$0.195295\pi$
$421$	1.94811	+	25.9957i	0.0949450	+	1.26695i	−0.722672	+	0.691191i	$0.757086\pi$
$422$	25.3598	+	31.8001i	1.23449	+	1.54801i
$423$		0			0
$424$	−22.5960	+	39.1374i	−1.09736	+	1.90068i
$425$	9.81144	−	1.47884i	0.475925	−	0.0717341i
$426$		0			0
$427$	2.54331	+	2.35985i	0.123079	+	0.114201i
$428$	2.00495	+	8.78425i	0.0969128	+	0.424603i
$429$		0			0
$430$	−24.2387	−	45.0711i	−1.16889	−	2.17352i
$431$	−22.7264			−1.09469			−0.547345	−	0.836907i	$-0.684362\pi$
$431$	−22.7264			−1.09469			−0.547345	+	0.836907i	$0.684362\pi$
$432$		0			0
$433$	8.63794	+	8.01484i	0.415113	+	0.385169i	0.859896	−	0.510470i	$-0.170529\pi$
$433$	8.63794	+	8.01484i	0.415113	+	0.385169i	−0.444782	+	0.895639i	$0.646719\pi$
$434$	−14.3406	+	6.90608i	−0.688371	+	0.331502i
$435$		0			0
$436$	−11.0506	+	19.1402i	−0.529227	+	0.916647i
$437$	−0.0322860	−	0.0559211i	−0.00154445	−	0.00267507i
$438$		0			0
$439$	−1.27757	−	17.0480i	−0.0609753	−	0.813659i	−0.940930	−	0.338601i	$-0.890046\pi$
$439$	−1.27757	−	17.0480i	−0.0609753	−	0.813659i	0.879955	−	0.475058i	$-0.157573\pi$
$440$	−17.7218	−	45.1543i	−0.844852	−	2.15265i
$441$		0			0
$442$	15.2685	+	4.70972i	0.726250	+	0.224019i
$443$	−14.5169	+	36.9885i	−0.689719	+	1.75738i	−0.0375580	+	0.999294i	$0.511958\pi$
$443$	−14.5169	+	36.9885i	−0.689719	+	1.75738i	−0.652161	+	0.758081i	$0.726137\pi$
$444$		0			0
$445$	24.6018	+	16.7732i	1.16624	+	0.795127i
$446$	−29.5192	+	37.0159i	−1.39777	+	1.75275i
$447$		0			0
$448$	5.11333	−	1.57725i	0.241582	−	0.0745181i
$449$	1.53481	−	20.4806i	0.0724321	−	0.966539i	−0.836060	−	0.548638i	$-0.815147\pi$
$449$	1.53481	−	20.4806i	0.0724321	−	0.966539i	0.908492	−	0.417901i	$-0.137234\pi$
$450$		0			0
$451$	1.22326	−	5.35943i	0.0576009	−	0.252366i
$452$	14.4238	−	63.1946i	0.678436	−	2.97242i
$453$		0			0
$454$	−4.86778	+	64.9561i	−0.228456	+	3.04854i
$455$	−4.69618	+	1.44858i	−0.220161	+	0.0679105i
$456$		0			0
$457$	13.7826	−	17.2829i	0.644724	−	0.808458i	−0.346861	−	0.937917i	$-0.612752\pi$
$457$	13.7826	−	17.2829i	0.644724	−	0.808458i	0.991585	+	0.129458i	$0.0413238\pi$
$458$	1.03102	+	0.702936i	0.0481763	+	0.0328460i
$459$		0			0
$460$	−0.206913	+	0.527207i	−0.00964739	+	0.0245812i
$461$	−4.74602	−	1.46395i	−0.221044	−	0.0681831i	0.182255	−	0.983251i	$-0.441660\pi$
$461$	−4.74602	−	1.46395i	−0.221044	−	0.0681831i	−0.403299	+	0.915068i	$0.632137\pi$
$462$		0			0
$463$	−14.6914	−	37.4330i	−0.682766	−	1.73966i	−0.672928	−	0.739708i	$-0.734964\pi$
$463$	−14.6914	−	37.4330i	−0.682766	−	1.73966i	−0.00983742	−	0.999952i	$-0.503131\pi$
$464$	5.47256	+	73.0262i	0.254057	+	3.39016i
$465$		0			0
$466$	−13.7268	−	23.7756i	−0.635884	−	1.10138i
$467$	9.69685	−	16.7954i	0.448717	−	0.777200i	−0.549586	−	0.835437i	$-0.685215\pi$
$467$	9.69685	−	16.7954i	0.448717	−	0.777200i	0.998303	+	0.0582371i	$0.0185479\pi$
$468$		0			0
$469$	−1.59003	+	0.765719i	−0.0734208	+	0.0353576i
$470$	−50.2942	−	46.6662i	−2.31990	−	2.15255i
$471$		0			0
$472$	−35.2211			−1.62118
$473$	−13.6583	−	4.66882i	−0.628008	−	0.214673i
$474$		0			0
$475$	1.43522	+	6.28809i	0.0658523	+	0.288518i
$476$	6.07568	+	5.63741i	0.278478	+	0.258390i
$477$		0			0
$478$	32.9221	−	4.96220i	1.50582	−	0.226966i
$479$	1.26895	−	2.19788i	0.0579796	−	0.100424i	−0.835579	−	0.549371i	$-0.814867\pi$
$479$	1.26895	−	2.19788i	0.0579796	−	0.100424i	0.893558	+	0.448947i	$0.148201\pi$
$480$		0			0
$481$	−16.8267	−	21.1000i	−0.767230	−	0.962076i
$482$	−0.876815	−	11.7003i	−0.0399378	−	0.532933i
$483$		0			0
$484$	26.7487	+	12.8815i	1.21585	+	0.585522i
$485$	2.69969	+	0.832745i	0.122587	+	0.0378130i
$486$		0			0
$487$	−0.530064	+	0.491827i	−0.0240195	+	0.0222868i	−0.692091	−	0.721810i	$-0.743310\pi$
$487$	−0.530064	+	0.491827i	−0.0240195	+	0.0222868i	0.668072	+	0.744097i	$0.267120\pi$
$488$	−31.1060	−	21.2077i	−1.40810	−	0.960027i
$489$		0			0
$490$	50.4531	+	7.60459i	2.27924	+	0.343540i
$491$	4.96897	−	1.53273i	0.224247	−	0.0691709i	−0.180596	−	0.983557i	$-0.557803\pi$
$491$	4.96897	−	1.53273i	0.224247	−	0.0691709i	0.404842	+	0.914386i	$0.367326\pi$
$492$		0			0
$493$	−15.8965	+	10.8381i	−0.715943	+	0.488122i
$494$	−2.31121	+	10.1261i	−0.103986	+	0.455595i
$495$		0			0
$496$	71.2538	−	48.5800i	3.19939	−	2.18131i
$497$	0.474089	−	6.32628i	0.0212658	−	0.283773i
$498$		0			0
$499$	−0.153922	−	0.0232000i	−0.00689050	−	0.00103858i	0.145596	−	0.989344i	$-0.453490\pi$
$499$	−0.153922	−	0.0232000i	−0.00689050	−	0.00103858i	−0.152487	+	0.988306i	$0.548728\pi$
$500$	−9.65474	+	12.1067i	−0.431773	+	0.541426i
$501$		0			0
$502$	−4.44285	+	4.12237i	−0.198294	+	0.183990i
$503$	7.28863	−	18.5711i	0.324984	−	0.828046i	−0.671241	−	0.741239i	$-0.734239\pi$
$503$	7.28863	−	18.5711i	0.324984	−	0.828046i	0.996225	−	0.0868067i	$-0.0276662\pi$
$504$		0			0
$505$	−39.1804	−	18.8683i	−1.74350	−	0.839628i
$506$	0.0825580	+	0.210354i	0.00367015	+	0.00935140i
$507$		0			0
$508$	−0.631541	−	0.791927i	−0.0280201	−	0.0351361i
$509$	9.32749	+	16.1557i	0.413434	+	0.716089i	0.995263	−	0.0972228i	$-0.0309959\pi$
$509$	9.32749	+	16.1557i	0.413434	+	0.716089i	−0.581829	+	0.813311i	$0.697663\pi$
$510$		0			0
$511$	2.64578	−	0.398788i	0.117043	−	0.0176413i
$512$	37.9049	−	18.2540i	1.67518	−	0.806722i
$513$		0			0
$514$	0.261966	+	1.14775i	0.0115548	+	0.0506249i
$515$	1.43672			0.0633094
$516$		0			0
$517$	−19.3515			−0.851079
$518$	−4.40662	−	19.3067i	−0.193616	−	0.848286i
$519$		0			0
$520$	48.0468	−	23.1381i	2.10699	−	1.01467i
$521$	13.8523	−	2.08790i	0.606880	−	0.0914724i	0.161589	−	0.986858i	$-0.448338\pi$
$521$	13.8523	−	2.08790i	0.606880	−	0.0914724i	0.445291	+	0.895386i	$0.353100\pi$
$522$		0			0
$523$	16.1137	+	27.9097i	0.704602	+	1.22041i	0.966835	+	0.255401i	$0.0822076\pi$
$523$	16.1137	+	27.9097i	0.704602	+	1.22041i	−0.262234	+	0.965004i	$0.584459\pi$
$524$	28.5768	+	35.8342i	1.24838	+	1.56542i
$525$		0			0
$526$	−7.29854	−	18.5964i	−0.318231	−	0.810840i
$527$	20.4133	+	9.83055i	0.889219	+	0.428225i
$528$		0			0
$529$	−8.40228	+	21.4087i	−0.365316	+	0.930811i
$530$	−35.0501	+	32.5218i	−1.52248	+	1.41265i
$531$		0			0
$532$	−3.35912	+	4.21220i	−0.145636	+	0.182622i
$533$	5.97606	+	0.900747i	0.258852	+	0.0390157i
$534$		0			0
$535$	−0.417024	+	5.56479i	−0.0180295	+	0.240587i
$536$	15.8225	−	10.7876i	0.683428	−	0.465953i
$537$		0			0
$538$	−13.0351	+	57.1103i	−0.561981	+	2.46220i
$539$	11.8906	−	8.10687i	0.512164	−	0.349188i
$540$		0			0
$541$	−24.2850	+	7.49094i	−1.04409	+	0.322061i	−0.768928	−	0.639336i	$-0.779209\pi$
$541$	−24.2850	+	7.49094i	−1.04409	+	0.322061i	−0.275167	+	0.961396i	$0.588733\pi$
$542$	16.6380	+	2.50777i	0.714663	+	0.107718i
$543$		0			0
$544$	−21.6771	−	14.7792i	−0.929398	−	0.633652i
$545$	−10.0342	+	9.31037i	−0.429818	+	0.398813i
$546$		0			0
$547$	5.19488	+	1.60241i	0.222117	+	0.0685141i	0.403816	−	0.914840i	$-0.367683\pi$
$547$	5.19488	+	1.60241i	0.222117	+	0.0685141i	−0.181699	+	0.983354i	$0.558160\pi$
$548$	25.7579	+	12.4044i	1.10032	+	0.529889i
$549$		0			0
$550$	−1.68678	−	22.5085i	−0.0719245	−	0.959766i
$551$	−7.79761	−	9.77790i	−0.332189	−	0.416552i
$552$		0			0
$553$	2.10758	−	3.65043i	0.0896233	−	0.155232i
$554$	35.9650	−	5.42085i	1.52801	−	0.230310i
$555$		0			0
$556$	−38.6884	−	35.8976i	−1.64075	−	1.52240i
$557$	9.31439	+	40.8090i	0.394664	+	1.72913i	0.647896	+	0.761729i	$0.275649\pi$
$557$	9.31439	+	40.8090i	0.394664	+	1.72913i	−0.253233	+	0.967405i	$0.581494\pi$
$558$		0			0
$559$	3.99633	−	15.3572i	0.169027	−	0.649539i
$560$	19.5385			0.825653
$561$		0			0
$562$	−11.8337	−	10.9801i	−0.499176	−	0.463168i
$563$	−25.0303	+	12.0540i	−1.05490	+	0.508013i	−0.879211	−	0.476432i	$-0.841930\pi$
$563$	−25.0303	+	12.0540i	−1.05490	+	0.508013i	−0.175690	+	0.984446i	$0.556216\pi$
$564$		0			0
$565$	20.0729	−	34.7673i	0.844474	−	1.46267i
$566$	1.42825	+	2.47381i	0.0600339	+	0.103982i
$567$		0			0
$568$	5.14439	+	68.6471i	0.215854	+	2.88037i
$569$	9.42162	+	24.0059i	0.394975	+	1.00638i	0.980639	+	0.195825i	$0.0627386\pi$
$569$	9.42162	+	24.0059i	0.394975	+	1.00638i	−0.585664	+	0.810554i	$0.699166\pi$
$570$		0			0
$571$	38.3172	+	11.8193i	1.60353	+	0.494622i	0.962131	−	0.272588i	$-0.0878797\pi$
$571$	38.3172	+	11.8193i	1.60353	+	0.494622i	0.641395	+	0.767211i	$0.278356\pi$
$572$	9.38740	−	23.9187i	0.392507	−	1.00009i
$573$		0			0
$574$	3.66408	+	2.49812i	0.152936	+	0.104270i
$575$	−0.0961865	+	0.120614i	−0.00401126	+	0.00502996i
$576$		0			0
$577$	19.2792	−	5.94684i	0.802603	−	0.247570i	0.133799	−	0.991009i	$-0.457282\pi$
$577$	19.2792	−	5.94684i	0.802603	−	0.247570i	0.668805	+	0.743438i	$0.266806\pi$
$578$	−2.07139	+	27.6408i	−0.0861584	+	1.14970i
$579$		0			0
$580$	−24.4089	+	106.942i	−1.01353	+	4.44054i
$581$	−0.819374	+	3.58991i	−0.0339934	+	0.148935i
$582$		0			0
$583$	−1.00782	+	13.4484i	−0.0417395	+	0.556976i
$584$	−27.7441	+	8.55791i	−1.14806	+	0.354129i
$585$		0			0
$586$	−29.7375	+	37.2897i	−1.22845	+	1.54042i
$587$	−9.57940	−	6.53112i	−0.395384	−	0.269568i	0.349266	−	0.937024i	$-0.386431\pi$
$587$	−9.57940	−	6.53112i	−0.395384	−	0.269568i	−0.744650	+	0.667455i	$0.767383\pi$
$588$		0			0
$589$	−5.38070	+	13.7098i	−0.221708	+	0.564902i
$590$	−35.6090	−	10.9839i	−1.46600	−	0.452201i
$591$		0			0
$592$	39.1992	+	99.8781i	1.61108	+	4.10496i
$593$	−0.913090	−	12.1843i	−0.0374961	−	0.500351i	−0.984060	−	0.177835i	$-0.943091\pi$
$593$	−0.913090	−	12.1843i	−0.0374961	−	0.500351i	0.946564	−	0.322516i	$-0.104528\pi$
$594$		0			0
$595$	2.56663	+	4.44554i	0.105222	+	0.182249i
$596$	−25.1586	+	43.5760i	−1.03054	+	1.78494i
$597$		0			0
$598$	−0.223830	+	0.107791i	−0.00915307	+	0.00440789i
$599$	7.00317	+	6.49799i	0.286142	+	0.265501i	0.810163	−	0.586204i	$-0.199378\pi$
$599$	7.00317	+	6.49799i	0.286142	+	0.265501i	−0.524022	+	0.851705i	$0.675569\pi$
$600$		0			0
$601$	−9.69294			−0.395383			−0.197692	−	0.980264i	$-0.563344\pi$
$601$	−9.69294			−0.395383			−0.197692	+	0.980264i	$0.563344\pi$
$602$	7.53137	−	8.88049i	0.306956	−	0.361942i
$603$		0			0
$604$	−10.0546	−	44.0521i	−0.409116	−	1.79245i
$605$	13.4791	+	12.5068i	0.548003	+	0.508472i
$606$		0			0
$607$	1.91366	−	0.288437i	0.0776729	−	0.0117073i	−0.110091	−	0.993922i	$-0.535114\pi$
$607$	1.91366	−	0.288437i	0.0776729	−	0.0117073i	0.187764	+	0.982214i	$0.439876\pi$
$608$	8.52710	−	14.7694i	0.345819	−	0.598977i
$609$		0			0
$610$	−24.8348	−	31.1418i	−1.00553	−	1.26090i
$611$	−1.58985	−	21.2151i	−0.0643186	−	0.858272i
$612$		0			0
$613$	−14.0264	−	6.75474i	−0.566519	−	0.272821i	0.128623	−	0.991694i	$-0.458944\pi$
$613$	−14.0264	−	6.75474i	−0.566519	−	0.272821i	−0.695142	+	0.718872i	$0.744659\pi$
$614$	45.1886	+	13.9388i	1.82366	+	0.562526i
$615$		0			0
$616$	8.09072	−	7.50709i	0.325984	−	0.302469i
$617$	−17.3090	−	11.8011i	−0.696835	−	0.475094i	0.162367	−	0.986730i	$-0.448087\pi$
$617$	−17.3090	−	11.8011i	−0.696835	−	0.475094i	−0.859202	+	0.511636i	$0.829039\pi$
$618$		0			0
$619$	−45.0405	−	6.78876i	−1.81033	−	0.272863i	−0.845165	−	0.534506i	$-0.820498\pi$
$619$	−45.0405	−	6.78876i	−1.81033	−	0.272863i	−0.965165	+	0.261643i	$0.915736\pi$
$620$	123.438	−	38.0756i	4.95740	−	1.52915i
$621$		0			0
$622$	37.3574	−	25.4699i	1.49790	−	1.02125i
$623$	−1.50757	+	6.60507i	−0.0603993	+	0.264627i
$624$		0			0
$625$	−24.1410	+	16.4591i	−0.965642	+	0.658363i
$626$	1.27053	−	16.9540i	0.0507805	−	0.677618i
$627$		0			0
$628$	34.4190	+	5.18782i	1.37347	+	0.207017i
$629$	−17.5756	+	22.0391i	−0.700785	+	0.878757i
$630$		0			0
$631$	7.91485	−	7.34390i	0.315085	−	0.292356i	−0.506737	−	0.862101i	$-0.669148\pi$
$631$	7.91485	−	7.34390i	0.315085	−	0.292356i	0.821822	+	0.569745i	$0.192958\pi$
$632$	−16.7103	+	42.5773i	−0.664702	+	1.69363i
$633$		0			0
$634$	31.1418	+	14.9971i	1.23680	+	0.595611i
$635$	−0.229194	−	0.583977i	−0.00909530	−	0.0231744i
$636$		0			0
$637$	9.86448	+	12.3697i	0.390845	+	0.490104i
$638$	21.8836	+	37.9035i	0.866379	+	1.50061i
$639$		0			0
$640$	0.578682	−	0.0872223i	0.0228744	−	0.00344776i
$641$	−5.95986	+	2.87012i	−0.235400	+	0.113363i	−0.547866	−	0.836566i	$-0.684560\pi$
$641$	−5.95986	+	2.87012i	−0.235400	+	0.113363i	0.312465	+	0.949929i	$0.398845\pi$
$642$		0			0
$643$	−8.62182	−	37.7747i	−0.340012	−	1.48969i	−0.799046	−	0.601270i	$-0.794662\pi$
$643$	−8.62182	−	37.7747i	−0.340012	−	1.48969i	0.459035	−	0.888418i	$-0.348195\pi$
$644$	−0.128865			−0.00507799
$645$		0			0
$646$	10.8488			0.426840
$647$	5.10650	+	22.3730i	0.200757	+	0.879575i	0.970477	+	0.241193i	$0.0775387\pi$
$647$	5.10650	+	22.3730i	0.200757	+	0.879575i	−0.769720	+	0.638382i	$0.779604\pi$
$648$		0			0
$649$	−9.46973	+	4.56038i	−0.371720	+	0.179011i
$650$	24.5376	−	3.69844i	0.962443	−	0.145065i
$651$		0			0
$652$	18.7399	+	32.4584i	0.733910	+	1.27117i
$653$	−17.8010	−	22.3217i	−0.696606	−	0.873516i	0.300159	−	0.953889i	$-0.402960\pi$
$653$	−17.8010	−	22.3217i	−0.696606	−	0.873516i	−0.996765	+	0.0803731i	$0.974389\pi$
$654$		0			0
$655$	10.3709	+	26.4246i	0.405224	+	1.03249i
$656$	−21.6478	−	10.4250i	−0.845204	−	0.407029i
$657$		0			0
$658$	5.70330	−	14.5318i	0.222338	−	0.566507i
$659$	12.3638	−	11.4720i	0.481627	−	0.446884i	−0.401611	−	0.915810i	$-0.631550\pi$
$659$	12.3638	−	11.4720i	0.481627	−	0.446884i	0.883237	+	0.468926i	$0.155359\pi$
$660$		0			0
$661$	5.61134	−	7.03640i	0.218256	−	0.273684i	−0.660635	−	0.750707i	$-0.729713\pi$
$661$	5.61134	−	7.03640i	0.218256	−	0.273684i	0.878891	+	0.477023i	$0.158284\pi$
$662$	27.5327	+	4.14989i	1.07009	+	0.161290i
$663$		0			0
$664$	2.98594	−	39.8446i	0.115877	−	1.54627i
$665$	−2.75699	+	1.87968i	−0.106911	+	0.0728910i
$666$		0			0
$667$	0.0665643	−	0.291637i	0.00257738	−	0.0112922i
$668$	46.4601	−	31.6760i	1.79760	−	1.22558i
$669$		0			0
$670$	19.3609	−	5.97206i	0.747978	−	0.230721i
$671$	−11.1093	−	1.67445i	−0.428868	−	0.0646415i
$672$		0			0
$673$	−9.88152	−	6.73710i	−0.380904	−	0.259696i	0.357698	−	0.933837i	$-0.383562\pi$
$673$	−9.88152	−	6.73710i	−0.380904	−	0.259696i	−0.738603	+	0.674141i	$0.764514\pi$
$674$	60.6002	−	56.2287i	2.33423	−	2.16585i
$675$		0			0
$676$	−32.9291	−	10.1573i	−1.26650	−	0.390665i
$677$	−39.1303	−	18.8442i	−1.50390	−	0.724240i	−0.512944	−	0.858422i	$-0.671445\pi$
$677$	−39.1303	−	18.8442i	−1.50390	−	0.724240i	−0.990957	+	0.134182i	$0.957159\pi$
$678$		0			0
$679$	0.0480386	+	0.641031i	0.00184355	+	0.0246005i
$680$	−34.7293	−	43.5492i	−1.33181	−	1.67004i
$681$		0			0
$682$	25.7707	−	44.6362i	0.986812	−	1.70921i
$683$	−7.26911	+	1.09564i	−0.278145	+	0.0419236i	−0.286633	−	0.958040i	$-0.592536\pi$
$683$	−7.26911	+	1.09564i	−0.278145	+	0.0419236i	0.00848853	+	0.999964i	$0.497298\pi$
$684$		0			0
$685$	12.9798	+	12.0435i	0.495934	+	0.460159i
$686$	5.34926	+	23.4366i	0.204236	+	0.894815i
$687$		0			0
$688$	−33.1785	+	53.6595i	−1.26492	+	2.04575i
$689$	−14.8263			−0.564838
$690$		0			0
$691$	0.0567156	+	0.0526244i	0.00215756	+	0.00200193i	0.681251	−	0.732050i	$-0.261436\pi$
$691$	0.0567156	+	0.0526244i	0.00215756	+	0.00200193i	−0.679093	+	0.734052i	$0.737627\pi$
$692$	−23.2568	+	11.1999i	−0.884090	+	0.425755i
$693$		0			0
$694$	44.3595	−	76.8330i	1.68386	−	2.91654i
$695$	−16.3436	−	28.3080i	−0.619950	−	1.07378i
$696$		0			0
$697$	−0.471738	−	6.29491i	−0.0178684	−	0.238437i
$698$	−33.5420	−	85.4636i	−1.26958	−	3.23484i
$699$		0			0
$700$	12.2999	+	3.79400i	0.464891	+	0.143400i
$701$	2.64824	−	6.74761i	0.100023	−	0.254854i	−0.872099	−	0.489329i	$-0.837242\pi$
$701$	2.64824	−	6.74761i	0.100023	−	0.254854i	0.972122	+	0.234475i	$0.0753371\pi$
$702$		0			0
$703$	−15.1399	−	10.3222i	−0.571011	−	0.389309i
$704$	−10.8036	+	13.5473i	−0.407175	+	0.510581i
$705$		0			0
$706$	−27.4249	+	8.45946i	−1.03215	+	0.318376i
$707$	0.739433	−	9.86704i	0.0278092	−	0.371088i
$708$		0			0
$709$	4.06410	−	17.8060i	0.152630	−	0.668717i	−0.839484	−	0.543384i	$-0.817143\pi$
$709$	4.06410	−	17.8060i	0.152630	−	0.668717i	0.992115	−	0.125333i	$-0.0400000\pi$
$710$	−16.2070	+	71.0074i	−0.608237	+	2.66486i
$711$		0			0
$712$	5.49382	−	73.3099i	0.205890	−	2.74741i
$713$	−0.336622	+	0.103834i	−0.0126066	+	0.00388862i
$714$		0			0
$715$	9.92223	−	12.4421i	0.371070	−	0.465307i
$716$	−55.9375	−	38.1375i	−2.09048	−	1.42527i
$717$		0			0
$718$	13.3211	−	33.9416i	0.497139	−	1.26669i
$719$	−23.5212	−	7.25534i	−0.877194	−	0.270578i	−0.176724	−	0.984260i	$-0.556550\pi$
$719$	−23.5212	−	7.25534i	−0.877194	−	0.270578i	−0.700470	+	0.713682i	$0.747026\pi$
$720$		0			0
$721$	0.119430	+	0.304304i	0.00444782	+	0.0113329i
$722$	−3.18202	−	42.4612i	−0.118423	−	1.58024i
$723$		0			0
$724$	47.0979	+	81.5760i	1.75038	+	3.03175i
$725$	−14.9397	+	25.8763i	−0.554847	+	0.961023i
$726$		0			0
$727$	−31.0316	+	14.9441i	−1.15090	+	0.554244i	−0.909304	−	0.416133i	$-0.863385\pi$
$727$	−31.0316	+	14.9441i	−1.15090	+	0.554244i	−0.241596	+	0.970377i	$0.577671\pi$
$728$	8.89475	+	8.25313i	0.329662	+	0.305881i
$729$		0			0
$730$	−30.7184			−1.13694
$731$	−16.5674	−	0.500154i	−0.612767	−	0.0184989i
$732$		0			0
$733$	−6.10947	−	26.7673i	−0.225658	−	0.988674i	−0.953136	−	0.302542i	$-0.902165\pi$
$733$	−6.10947	−	26.7673i	−0.225658	−	0.988674i	0.727478	−	0.686131i	$-0.240692\pi$
$734$	−53.5365	−	49.6746i	−1.97607	−	1.83352i
$735$		0			0
$736$	0.403359	−	0.0607965i	0.0148680	−	0.00224099i
$737$	2.85736	−	4.94909i	0.105252	−	0.182302i
$738$		0			0
$739$	−26.8699	−	33.6938i	−0.988425	−	1.23945i	−0.970872	−	0.239600i	$-0.922984\pi$
$739$	−26.8699	−	33.6938i	−0.988425	−	1.23945i	−0.0175538	−	0.999846i	$-0.505588\pi$
$740$	12.0104	+	160.268i	0.441511	+	5.89156i
$741$		0			0
$742$	−9.80186	−	4.72033i	−0.359838	−	0.173289i
$743$	24.3219	+	7.50232i	0.892284	+	0.275233i	0.706800	−	0.707414i	$-0.250138\pi$
$743$	24.3219	+	7.50232i	0.892284	+	0.275233i	0.185485	+	0.982647i	$0.440614\pi$
$744$		0			0
$745$	−22.8446	+	21.1967i	−0.836963	+	0.776588i
$746$	2.58151	+	1.76005i	0.0945160	+	0.0644399i
$747$		0			0
$748$	−26.5388	−	4.00008i	−0.970354	−	0.146257i
$749$	−1.21331	+	0.374258i	−0.0443335	+	0.0136751i
$750$		0			0
$751$	28.1091	−	19.1645i	1.02572	−	0.699322i	0.0711949	−	0.997462i	$-0.477319\pi$
$751$	28.1091	−	19.1645i	1.02572	−	0.699322i	0.954522	+	0.298140i	$0.0963664\pi$
$752$	−18.8210	+	82.4603i	−0.686332	+	3.00702i
$753$		0			0
$754$	−39.7558	+	27.1051i	−1.44782	+	0.987108i
$755$	2.09133	−	27.9068i	0.0761112	−	1.01563i
$756$		0			0
$757$	−0.383633	−	0.0578234i	−0.0139434	−	0.00210163i	0.142067	−	0.989857i	$-0.454625\pi$
$757$	−0.383633	−	0.0578234i	−0.0139434	−	0.00210163i	−0.156010	+	0.987755i	$0.549863\pi$
$758$	53.5876	−	67.1968i	1.94639	−	2.44070i
$759$		0			0
$760$	26.5422	−	24.6276i	0.962789	−	0.893337i
$761$	2.93530	−	7.47902i	0.106405	−	0.271114i	−0.867748	−	0.497004i	$-0.834434\pi$
$761$	2.93530	−	7.47902i	0.106405	−	0.271114i	0.974153	+	0.225889i	$0.0725288\pi$
$762$		0			0
$763$	−2.80609	−	1.35134i	−0.101587	−	0.0489219i
$764$	−15.3756	−	39.1764i	−0.556270	−	1.41735i
$765$		0			0
$766$	0.183974	+	0.230697i	0.00664727	+	0.00833541i
$767$	−5.77756	−	10.0070i	−0.208616	−	0.361333i
$768$		0			0
$769$	−20.3218	+	3.06301i	−0.732821	+	0.110455i	−0.504843	−	0.863211i	$-0.668450\pi$
$769$	−20.3218	+	3.06301i	−0.732821	+	0.110455i	−0.227978	+	0.973666i	$0.573212\pi$
$770$	10.5210	−	5.06663i	0.379149	−	0.182589i
$771$		0			0
$772$	20.8900	+	91.5250i	0.751847	+	3.29406i
$773$	20.6462			0.742592			0.371296	−	0.928515i	$-0.378914\pi$
$773$	20.6462			0.742592			0.371296	+	0.928515i	$0.378914\pi$
$774$		0			0
$775$	35.1868			1.26395
$776$	−1.55217	−	6.80051i	−0.0557197	−	0.244124i
$777$		0			0
$778$	−41.6792	+	20.0716i	−1.49427	+	0.719603i
$779$	4.05754	−	0.611576i	0.145377	−	0.0219120i
$780$		0			0
$781$	10.2715	+	17.7907i	0.367542	+	0.636602i
$782$	0.161789	+	0.202877i	0.00578557	+	0.00725487i
$783$		0			0
$784$	−22.9802	−	58.5526i	−0.820721	−	2.09116i
$785$	19.4231	+	9.35367i	0.693240	+	0.333847i
$786$		0			0
$787$	12.2749	−	31.2760i	0.437553	−	1.11487i	−0.526739	−	0.850027i	$-0.676586\pi$
$787$	12.2749	−	31.2760i	0.437553	−	1.11487i	0.964292	−	0.264840i	$-0.0853192\pi$
$788$	−82.4146	+	76.4696i	−2.93590	+	2.72412i
$789$		0			0
$790$	−30.1724	+	37.8350i	−1.07348	+	1.34611i
$791$	9.03247	+	1.36143i	0.321158	+	0.0484068i
$792$		0			0
$793$	0.923008	−	12.3167i	0.0327770	−	0.437378i
$794$	22.4098	−	15.2788i	0.795296	−	0.542223i
$795$		0			0
$796$	20.2098	−	88.5450i	0.716318	−	3.13840i
$797$	−19.2517	+	13.1256i	−0.681930	+	0.464932i	−0.854082	−	0.520138i	$-0.825880\pi$
$797$	−19.2517	+	13.1256i	−0.681930	+	0.464932i	0.172152	+	0.985070i	$0.444928\pi$
$798$		0			0
$799$	−21.2343	+	6.54991i	−0.751215	+	0.231719i
$800$	−40.2896	−	6.07268i	−1.42445	−	0.214702i
$801$		0			0
$802$	−78.2477	−	53.3483i	−2.76302	−	1.88380i
$803$	−6.35134	+	5.89319i	−0.224134	+	0.207966i
$804$		0			0
$805$	−0.0762661	−	0.0235250i	−0.00268803	−	0.000829146i
$806$	51.0520	+	24.5854i	1.79823	+	0.865982i
$807$		0			0
$808$	8.02366	+	107.068i	0.282271	+	3.76665i
$809$	−11.8573	−	14.8686i	−0.416882	−	0.522753i	0.528406	−	0.848992i	$-0.322790\pi$
$809$	−11.8573	−	14.8686i	−0.416882	−	0.522753i	−0.945287	+	0.326239i	$0.894219\pi$
$810$		0			0
$811$	−4.29128	+	7.43271i	−0.150687	+	0.260998i	−0.931480	−	0.363792i	$-0.881482\pi$
$811$	−4.29128	+	7.43271i	−0.150687	+	0.260998i	0.780793	+	0.624790i	$0.214815\pi$
$812$	−24.6799	+	3.71990i	−0.866096	+	0.130543i
$813$		0			0
$814$	47.0076	+	43.6166i	1.64761	+	1.52876i
$815$	5.16536	+	22.6309i	0.180935	+	0.792726i
$816$		0			0
$817$	−0.480587	−	10.7635i	−0.0168136	−	0.376568i
$818$	−51.5614			−1.80280
$819$		0			0
$820$	−26.3828	−	24.4797i	−0.921329	−	0.854868i
$821$	−24.0723	+	11.5926i	−0.840130	+	0.404585i	−0.803904	−	0.594758i	$-0.797248\pi$
$821$	−24.0723	+	11.5926i	−0.840130	+	0.404585i	−0.0362253	+	0.999344i	$0.511533\pi$
$822$		0			0
$823$	−5.12770	+	8.88144i	−0.178740	+	0.309588i	−0.941449	−	0.337154i	$-0.890536\pi$
$823$	−5.12770	+	8.88144i	−0.178740	+	0.309588i	0.762709	+	0.646742i	$0.223869\pi$
$824$	−1.77362	−	3.07200i	−0.0617869	−	0.107018i
$825$		0			0
$826$	−0.633630	−	8.45521i	−0.0220468	−	0.294194i
$827$	12.9951	+	33.1111i	0.451886	+	1.15139i	0.957451	+	0.288597i	$0.0931888\pi$
$827$	12.9951	+	33.1111i	0.451886	+	1.15139i	−0.505565	+	0.862789i	$0.668716\pi$
$828$		0			0
$829$	−18.5452	−	5.72042i	−0.644100	−	0.198678i	−0.0445390	−	0.999008i	$-0.514182\pi$
$829$	−18.5452	−	5.72042i	−0.644100	−	0.198678i	−0.599561	+	0.800329i	$0.704658\pi$
$830$	15.4446	−	39.3522i	0.536090	−	1.36593i
$831$		0			0
$832$	−15.7395	−	10.7310i	−0.545668	−	0.372030i
$833$	10.3035	−	12.9202i	0.356996	−	0.447659i
$834$		0			0
$835$	33.2791	−	10.2652i	1.15167	−	0.355243i
$836$	1.30374	−	17.3972i	0.0450907	−	0.601694i
$837$		0			0
$838$	8.60099	−	37.6834i	0.297116	−	1.30175i
$839$	9.15974	−	40.1315i	0.316229	−	1.38549i	−0.527879	−	0.849320i	$-0.677013\pi$
$839$	9.15974	−	40.1315i	0.316229	−	1.38549i	0.844109	−	0.536172i	$-0.180130\pi$
$840$		0			0
$841$	2.16248	−	28.8563i	0.0745684	−	0.995046i
$842$	65.0717	−	20.0720i	2.24252	−	0.691726i
$843$		0			0
$844$	46.8293	−	58.7220i	1.61193	−	2.02130i
$845$	−17.6342	−	12.0228i	−0.606634	−	0.413596i
$846$		0			0
$847$	−1.52851	+	3.89458i	−0.0525202	+	0.133819i
$848$	56.3258	+	17.3742i	1.93424	+	0.596633i
$849$		0			0
$850$	−9.46935	−	24.1275i	−0.324796	−	0.827567i
$851$	−0.0327530	−	0.437058i	−0.00112276	−	0.0149822i
$852$		0			0
$853$	−12.0504	−	20.8719i	−0.412598	−	0.714640i	0.582575	−	0.812777i	$-0.302045\pi$
$853$	−12.0504	−	20.8719i	−0.412598	−	0.714640i	−0.995173	+	0.0981366i	$0.968712\pi$
$854$	4.53154	−	7.84885i	0.155066	−	0.268582i
$855$		0			0
$856$	12.4135	−	5.97801i	0.424283	−	0.204324i
$857$	18.3284	+	17.0062i	0.626085	+	0.580922i	0.928077	−	0.372388i	$-0.121461\pi$
$857$	18.3284	+	17.0062i	0.626085	+	0.580922i	−0.301992	+	0.953311i	$0.597651\pi$
$858$		0			0
$859$	49.1887			1.67830			0.839148	−	0.543904i	$-0.183054\pi$
$859$	49.1887			1.67830			0.839148	+	0.543904i	$0.183054\pi$
$860$	−71.1816	+	62.1569i	−2.42727	+	2.11953i
$861$		0			0
$862$	13.2103	+	57.8780i	0.449944	+	1.97133i
$863$	−18.6697	−	17.3230i	−0.635525	−	0.589681i	0.295184	−	0.955440i	$-0.404619\pi$
$863$	−18.6697	−	17.3230i	−0.635525	−	0.589681i	−0.930710	+	0.365759i	$0.880809\pi$
$864$		0			0
$865$	−15.8086	+	2.38277i	−0.537510	+	0.0810166i
$866$	15.3906	−	26.6574i	0.522995	−	0.905854i
$867$		0			0
$868$	18.3256	+	22.9796i	0.622013	+	0.779980i
$869$	1.02002	+	13.6112i	0.0346017	+	0.461728i
$870$		0			0
$871$	5.66045	+	2.72593i	0.191797	+	0.0923646i
$872$	32.2946	+	9.96156i	1.09363	+	0.337341i
$873$		0			0
$874$	−0.123649	+	0.114729i	−0.00418249	+	0.00388078i
$875$	−1.80299	−	1.22926i	−0.0609523	−	0.0415566i
$876$		0			0
$877$	44.1742	+	6.65819i	1.49166	+	0.224831i	0.843687	−	0.536835i	$-0.180380\pi$
$877$	44.1742	+	6.65819i	1.49166	+	0.224831i	0.647970	+	0.761666i	$0.275618\pi$
$878$	−42.6742	+	13.1632i	−1.44018	+	0.444238i
$879$		0			0
$880$	−52.2752	+	35.6406i	−1.76220	+	1.20145i
$881$	−2.11123	+	9.24989i	−0.0711291	+	0.311637i	−0.997960	−	0.0638421i	$-0.979665\pi$
$881$	−2.11123	+	9.24989i	−0.0711291	+	0.311637i	0.926831	+	0.375479i	$0.122522\pi$
$882$		0			0
$883$	14.5862	−	9.94471i	0.490865	−	0.334666i	−0.292461	−	0.956278i	$-0.594474\pi$
$883$	14.5862	−	9.94471i	0.490865	−	0.334666i	0.783326	+	0.621611i	$0.213522\pi$
$884$	2.20496	−	29.4232i	0.0741609	−	0.989609i
$885$		0			0
$886$	102.638	+	15.4702i	3.44819	+	0.519731i
$887$	25.0000	−	31.3490i	0.839419	−	1.05260i	−0.158452	−	0.987367i	$-0.550650\pi$
$887$	25.0000	−	31.3490i	0.839419	−	1.05260i	0.997870	−	0.0652308i	$-0.0207784\pi$
$888$		0			0
$889$	0.104637	−	0.0970887i	0.00350940	−	0.00325625i
$890$	28.4165	−	72.4040i	0.952523	−	2.42699i
$891$		0			0
$892$	78.7692	+	37.9333i	2.63739	+	1.27010i
$893$	−5.27726	−	13.4462i	−0.176597	−	0.449961i
$894$		0			0
$895$	−26.1433	−	32.7826i	−0.873873	−	1.09580i
$896$	0.0665782	+	0.115317i	0.00222422	+	0.00385247i
$897$		0			0
$898$	−53.0507	+	7.99611i	−1.77033	+	0.266834i
$899$	−61.4718	+	29.6032i	−2.05020	+	0.987323i
$900$		0			0
$901$	3.44601	+	15.0979i	0.114803	+	0.502986i
$902$	−14.3601			−0.478139
$903$		0			0
$904$	−99.1194			−3.29666
$905$	12.9818	+	56.8771i	0.431530	+	1.89066i
$906$		0			0
$907$	−27.1369	+	13.0684i	−0.901065	+	0.433930i	−0.826273	−	0.563269i	$-0.809543\pi$
$907$	−27.1369	+	13.0684i	−0.901065	+	0.433930i	−0.0747914	+	0.997199i	$0.523829\pi$
$908$	118.941	−	17.9274i	3.94718	−	0.594942i
$909$		0			0
$910$	6.41892	+	11.1179i	0.212785	+	0.368555i
$911$	24.7828	+	31.0766i	0.821090	+	1.02961i	0.998962	+	0.0455601i	$0.0145072\pi$
$911$	24.7828	+	31.0766i	0.821090	+	1.02961i	−0.177872	+	0.984054i	$0.556921\pi$
$912$		0			0
$913$	−4.35621	−	11.0994i	−0.144169	−	0.367338i
$914$	−52.0263	−	25.0546i	−1.72088	−	0.828731i
$915$		0			0
$916$	0.841842	−	2.14498i	0.0278153	−	0.0708721i
$917$	−4.73474	+	4.39319i	−0.156355	+	0.145076i
$918$		0			0
$919$	−0.240240	+	0.301251i	−0.00792478	+	0.00993736i	−0.785778	−	0.618509i	$-0.787737\pi$
$919$	−0.240240	+	0.301251i	−0.00792478	+	0.00993736i	0.777853	+	0.628446i	$0.216309\pi$
$920$	0.856374	+	0.129078i	0.0282338	+	0.00425556i
$921$		0			0
$922$	−0.969555	+	12.9378i	−0.0319306	+	0.426084i
$923$	−18.6602	+	12.7223i	−0.614207	+	0.418759i
$924$		0			0
$925$	−9.74154	+	42.6805i	−0.320300	+	1.40333i
$926$	−86.7921	+	59.1739i	−2.85217	+	1.94457i
$927$		0			0
$928$	75.4954	−	23.2873i	2.47826	−	0.764442i
$929$	37.8857	+	5.71035i	1.24299	+	0.187350i	0.737419	−	0.675435i	$-0.236044\pi$
$929$	37.8857	+	5.71035i	1.24299	+	0.187350i	0.505570	+	0.862786i	$0.331282\pi$
$930$		0			0
$931$	8.87561	+	6.05129i	0.290886	+	0.198323i
$932$	−37.1627	+	34.4819i	−1.21730	+	1.12949i
$933$		0			0
$934$	−48.4100	−	14.9325i	−1.58402	−	0.488607i
$935$	−14.9762	−	7.21216i	−0.489774	−	0.235863i
$936$		0			0
$937$	3.22968	+	43.0971i	0.105509	+	1.40792i	0.759051	+	0.651031i	$0.225663\pi$
$937$	3.22968	+	43.0971i	0.105509	+	1.40792i	−0.653542	+	0.756890i	$0.726718\pi$
$938$	2.87433	+	3.60429i	0.0938501	+	0.117684i
$939$		0			0
$940$	−63.3469	+	109.720i	−2.06615	+	3.57867i
$941$	19.7415	−	2.97555i	0.643553	−	0.0970001i	0.180846	−	0.983511i	$-0.442116\pi$
$941$	19.7415	−	2.97555i	0.643553	−	0.0970001i	0.462707	+	0.886511i	$0.346878\pi$
$942$		0			0
$943$	0.0719473	+	0.0667573i	0.00234292	+	0.00217392i
$944$	10.2225	+	44.7876i	0.332713	+	1.45771i
$945$		0			0
$946$	−3.95104	+	37.4978i	−0.128459	+	1.21916i
$947$	58.8426			1.91213			0.956064	−	0.293159i	$-0.0947066\pi$
$947$	58.8426			1.91213			0.956064	+	0.293159i	$0.0947066\pi$
$948$		0			0
$949$	−6.98252	−	6.47883i	−0.226662	−	0.210312i
$950$	15.1798	−	7.31023i	0.492499	−	0.237175i
$951$		0			0
$952$	6.33697	−	10.9759i	0.205382	−	0.355732i
$953$	1.59117	+	2.75598i	0.0515429	+	0.0892749i	0.890646	−	0.454698i	$-0.150253\pi$
$953$	1.59117	+	2.75598i	0.0515429	+	0.0892749i	−0.839103	+	0.543973i	$0.816919\pi$
$954$		0			0
$955$	−1.94788	−	25.9927i	−0.0630320	−	0.841103i
$956$	−22.4613	−	57.2305i	−0.726451	−	1.85097i
$957$		0			0
$958$	−6.33502	−	1.95409i	−0.204675	−	0.0631339i
$959$	−1.47190	+	3.75033i	−0.0475300	+	0.121104i
$960$		0			0
$961$	40.7731	+	27.7986i	1.31526	+	0.896729i
$962$	−43.9551	+	55.1179i	−1.41717	+	1.77707i
$963$		0			0
$964$	−20.7037	+	6.38625i	−0.666822	+	0.205687i
$965$	−4.34506	+	57.9808i	−0.139872	+	1.86647i
$966$		0			0
$967$	−8.07351	+	35.3724i	−0.259627	+	1.13750i	0.662026	+	0.749481i	$0.269697\pi$
$967$	−8.07351	+	35.3724i	−0.259627	+	1.13750i	−0.921652	+	0.388017i	$0.873160\pi$
$968$	10.1022	−	44.2605i	0.324696	−	1.42259i
$969$		0			0
$970$	0.551515	−	7.35945i	0.0177081	−	0.236298i
$971$	−9.37157	+	2.89075i	−0.300748	+	0.0927684i	−0.441457	−	0.897283i	$-0.645538\pi$
$971$	−9.37157	+	2.89075i	−0.300748	+	0.0927684i	0.140709	+	0.990051i	$0.455062\pi$
$972$		0			0
$973$	4.63716	−	5.81482i	0.148661	−	0.186415i
$974$	1.56067	+	1.06404i	0.0500070	+	0.0340942i
$975$		0			0
$976$	−17.9398	+	45.7100i	−0.574240	+	1.46314i
$977$	−41.6328	−	12.8420i	−1.33195	−	0.410852i	−0.454597	−	0.890697i	$-0.650217\pi$
$977$	−41.6328	−	12.8420i	−1.33195	−	0.410852i	−0.877353	+	0.479845i	$0.840693\pi$
$978$		0			0
$979$	−8.01497	−	20.4218i	−0.256160	−	0.652684i
$980$	−7.04099	−	93.9555i	−0.224916	−	3.00130i
$981$		0			0
$982$	−6.79178	−	11.7637i	−0.216734	−	0.375395i
$983$	4.07894	−	7.06494i	0.130098	−	0.225336i	−0.793616	−	0.608419i	$-0.791804\pi$
$983$	4.07894	−	7.06494i	0.130098	−	0.225336i	0.923714	+	0.383082i	$0.125137\pi$
$984$		0			0
$985$	−62.7354	+	30.2118i	−1.99891	+	0.962627i
$986$	36.8419	+	34.1843i	1.17329	+	1.08865i
$987$		0			0
$988$	19.1797			0.610187
$989$	0.194116	−	0.169505i	0.00617252	−	0.00538994i
$990$		0			0
$991$	9.71748	+	42.5751i	0.308686	+	1.35244i	0.856632	+	0.515928i	$0.172553\pi$
$991$	9.71748	+	42.5751i	0.308686	+	1.35244i	−0.547946	+	0.836514i	$0.684590\pi$
$992$	−68.2024	−	63.2826i	−2.16543	−	2.00922i
$993$		0			0
$994$	−16.3869	+	2.46993i	−0.519762	+	0.0783415i
$995$	28.1251	−	48.7142i	0.891627	−	1.54434i
$996$		0			0
$997$	28.0427	+	35.1644i	0.888121	+	1.11367i	0.992874	+	0.119170i	$0.0380234\pi$
$997$	28.0427	+	35.1644i	0.888121	+	1.11367i	−0.104753	+	0.994498i	$0.533405\pi$
$998$	0.0303868	+	0.405484i	0.000961878	+	0.0128354i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	387.2.y.c.10.1		36
3.2	odd	2		43.2.g.a.10.3	✓	36
12.11	even	2		688.2.bg.c.225.3		36
43.13	even	21	inner	387.2.y.c.271.1		36
129.20	even	42		1849.2.a.o.1.17		18
129.23	odd	42		1849.2.a.n.1.2		18
129.56	odd	42		43.2.g.a.13.3	yes	36
516.443	even	42		688.2.bg.c.529.3		36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
43.2.g.a.10.3	✓	36	3.2	odd	2
43.2.g.a.13.3	yes	36	129.56	odd	42
387.2.y.c.10.1		36	1.1	even	1	trivial
387.2.y.c.271.1		36	43.13	even	21	inner
688.2.bg.c.225.3		36	12.11	even	2
688.2.bg.c.529.3		36	516.443	even	42
1849.2.a.n.1.2		18	129.23	odd	42
1849.2.a.o.1.17		18	129.20	even	42

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:	\( N \)	\(=\)	\( 387 = 3^{2} \cdot 43 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	387.y (of order \(21\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.581275 - 2.54673i) q^{2} +(-4.34603 + 2.09294i) q^{4} +(-2.95419 + 0.445272i) q^{5} +(-0.339884 - 0.588696i) q^{7} +(4.59900 + 5.76696i) q^{8} +O(q^{10})\)	\(q+(-0.581275 - 2.54673i) q^{2} +(-4.34603 + 2.09294i) q^{4} +(-2.95419 + 0.445272i) q^{5} +(-0.339884 - 0.588696i) q^{7} +(4.59900 + 5.76696i) q^{8} +(2.85118 + 7.26470i) q^{10} +(1.98321 + 0.955063i) q^{11} +(-0.884105 + 2.25266i) q^{13} +(-1.30168 + 1.20779i) q^{14} +(5.99853 - 7.52192i) q^{16} +(2.49942 + 0.376727i) q^{17} +(-0.122786 + 1.63846i) q^{19} +(11.9071 - 8.11809i) q^{20} +(1.27950 - 5.60586i) q^{22} +(-0.0324711 + 0.0221384i) q^{23} +(3.75109 - 1.15706i) q^{25} +(6.25084 + 0.942162i) q^{26} +(2.70925 + 1.84713i) q^{28} +(-5.57974 + 5.17724i) q^{29} +(8.56546 + 2.64209i) q^{31} +(-9.35164 - 4.50351i) q^{32} +(-0.493428 - 6.58434i) q^{34} +(1.26621 + 1.58778i) q^{35} +(-5.57614 + 9.65816i) q^{37} +(4.24410 - 0.639696i) q^{38} +(-16.1542 - 14.9889i) q^{40} +(-0.555724 - 2.43478i) q^{41} +(-6.51074 + 0.781227i) q^{43} -10.6180 q^{44} +(0.0752553 + 0.0698267i) q^{46} +(-7.92075 + 3.81443i) q^{47} +(3.26896 - 5.66200i) q^{49} +(-5.12713 - 8.88045i) q^{50} +(-0.872336 - 11.6405i) q^{52} +(2.23834 + 5.70320i) q^{53} +(-6.28403 - 1.93837i) q^{55} +(1.83186 - 4.66750i) q^{56} +(16.4284 + 11.2007i) q^{58} +(-2.97714 + 3.73321i) q^{59} +(-4.87717 + 1.50441i) q^{61} +(1.74982 - 23.3497i) q^{62} +(-1.75166 + 7.67453i) q^{64} +(1.60876 - 7.04845i) q^{65} +(0.194013 - 2.58893i) q^{67} +(-11.6510 + 3.59386i) q^{68} +(3.30762 - 4.14763i) q^{70} +(7.71099 + 5.25726i) q^{71} +(-1.43804 + 3.66406i) q^{73} +(27.8380 + 8.58689i) q^{74} +(-2.89557 - 7.37780i) q^{76} +(-0.111819 - 1.49212i) q^{77} +(3.10044 + 5.37012i) q^{79} +(-14.3715 + 24.8921i) q^{80} +(-5.87772 + 2.83056i) q^{82} +(-3.97087 - 3.68443i) q^{83} -7.55150 q^{85} +(5.77411 + 16.1270i) q^{86} +(3.61296 + 15.8294i) q^{88} +(-7.30600 - 6.77898i) q^{89} +(1.62662 - 0.245174i) q^{91} +(0.0947861 - 0.164174i) q^{92} +(14.3185 + 17.9548i) q^{94} +(-0.366830 - 4.89500i) q^{95} +(-0.852010 - 0.410306i) q^{97} +(-16.3198 - 5.03398i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q + 10 q^{2} - 18 q^{4} + 17 q^{5} + 6 q^{7} - 18 q^{8}+O(q^{10}) \) 36 * q + 10 * q^2 - 18 * q^4 + 17 * q^5 + 6 * q^7 - 18 * q^8	\( 36 q + 10 q^{2} - 18 q^{4} + 17 q^{5} + 6 q^{7} - 18 q^{8} - 7 q^{10} + 4 q^{11} - 18 q^{14} - 10 q^{16} + 10 q^{17} + 10 q^{19} + 3 q^{20} - 3 q^{22} - 4 q^{23} - 2 q^{25} + 15 q^{26} + 20 q^{28} - 9 q^{29} + 40 q^{31} - 48 q^{32} - 42 q^{34} - 11 q^{35} - 19 q^{37} + 21 q^{38} - 97 q^{40} + 28 q^{41} - 8 q^{43} - 14 q^{44} - 61 q^{46} + 30 q^{47} + 6 q^{49} + 3 q^{50} - 8 q^{52} + 24 q^{53} + 14 q^{55} - 39 q^{56} + 64 q^{58} + q^{59} - 14 q^{61} - 33 q^{62} + 48 q^{64} - 38 q^{65} + 66 q^{67} - 66 q^{68} + 47 q^{70} + 33 q^{71} + 29 q^{73} + 40 q^{74} - 39 q^{76} + 27 q^{77} - 17 q^{79} - 8 q^{80} - 54 q^{82} + 23 q^{83} - 56 q^{85} + 45 q^{86} - 17 q^{88} + 19 q^{89} - 13 q^{91} + 18 q^{92} + 44 q^{94} - q^{95} - 31 q^{97} + 5 q^{98}+O(q^{100}) \) 36 * q + 10 * q^2 - 18 * q^4 + 17 * q^5 + 6 * q^7 - 18 * q^8 - 7 * q^10 + 4 * q^11 - 18 * q^14 - 10 * q^16 + 10 * q^17 + 10 * q^19 + 3 * q^20 - 3 * q^22 - 4 * q^23 - 2 * q^25 + 15 * q^26 + 20 * q^28 - 9 * q^29 + 40 * q^31 - 48 * q^32 - 42 * q^34 - 11 * q^35 - 19 * q^37 + 21 * q^38 - 97 * q^40 + 28 * q^41 - 8 * q^43 - 14 * q^44 - 61 * q^46 + 30 * q^47 + 6 * q^49 + 3 * q^50 - 8 * q^52 + 24 * q^53 + 14 * q^55 - 39 * q^56 + 64 * q^58 + q^59 - 14 * q^61 - 33 * q^62 + 48 * q^64 - 38 * q^65 + 66 * q^67 - 66 * q^68 + 47 * q^70 + 33 * q^71 + 29 * q^73 + 40 * q^74 - 39 * q^76 + 27 * q^77 - 17 * q^79 - 8 * q^80 - 54 * q^82 + 23 * q^83 - 56 * q^85 + 45 * q^86 - 17 * q^88 + 19 * q^89 - 13 * q^91 + 18 * q^92 + 44 * q^94 - q^95 - 31 * q^97 + 5 * q^98

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