LMFDB - Embedded newform 549.2.bl.b.361.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [549,2,Mod(73,549)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(549, base_ring=CyclotomicField(30))

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

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

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

chi := DirichletCharacter("549.73");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 549 = 3^{2} \cdot 61 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	549.bl (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:	$4.38378707097$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$4$ over $\Q(\zeta_{15})$
Twist minimal:	no (minimal twist has level 61)
Sato-Tate group:	$\mathrm{SU}(2)[C_{15}]$

Embedding invariants

Embedding label			361.3
Character	$\chi$	$=$	549.361
Dual form			549.2.bl.b.73.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.94561 - 0.866241i) q^{2} +(1.69676 - 1.88444i) q^{4} +(1.20434 + 0.255990i) q^{5} +(0.404506 + 3.84862i) q^{7} +(0.352600 - 1.08519i) q^{8} +O(q^{10})$	\(q+(1.94561 - 0.866241i) q^{2} +(1.69676 - 1.88444i) q^{4} +(1.20434 + 0.255990i) q^{5} +(0.404506 + 3.84862i) q^{7} +(0.352600 - 1.08519i) q^{8} +(2.56491 - 0.545189i) q^{10} +1.98434 q^{11} +(2.72937 - 4.72741i) q^{13} +(4.12084 + 7.13751i) q^{14} +(0.276104 + 2.62696i) q^{16} +(-3.60066 + 3.99894i) q^{17} +(0.472909 - 4.49943i) q^{19} +(2.52586 - 1.83515i) q^{20} +(3.86075 - 1.71892i) q^{22} +(-2.24547 - 6.91085i) q^{23} +(-3.18283 - 1.41709i) q^{25} +(1.21521 - 11.5620i) q^{26} +(7.93884 + 5.76791i) q^{28} +(0.207283 + 0.359024i) q^{29} +(-2.26627 - 1.00901i) q^{31} +(3.95380 + 6.84819i) q^{32} +(-3.54143 + 10.8994i) q^{34} +(-0.498045 + 4.73858i) q^{35} +(-5.96555 + 4.33423i) q^{37} +(-2.97749 - 9.16378i) q^{38} +(0.702446 - 1.21667i) q^{40} +(3.12409 - 2.26979i) q^{41} +(-1.69649 - 1.88414i) q^{43} +(3.36695 - 3.73937i) q^{44} +(-10.3553 - 11.5007i) q^{46} +(-1.97577 - 3.42213i) q^{47} +(-7.80121 + 1.65820i) q^{49} -7.42009 q^{50} +(-4.27744 - 13.1646i) q^{52} +(-0.927961 + 2.85597i) q^{53} +(2.38981 + 0.507970i) q^{55} +(4.31911 + 0.918056i) q^{56} +(0.714292 + 0.518963i) q^{58} +(1.34010 - 0.596653i) q^{59} +(1.71348 + 7.61997i) q^{61} -5.28333 q^{62} +(9.35082 + 6.79377i) q^{64} +(4.49725 - 4.99470i) q^{65} +(5.93084 + 1.26064i) q^{67} +(1.42631 + 13.5705i) q^{68} +(3.13575 + 9.65085i) q^{70} +(8.53723 - 1.81465i) q^{71} +(-6.01044 + 1.27756i) q^{73} +(-7.85214 + 13.6003i) q^{74} +(-7.67650 - 8.52561i) q^{76} +(0.802678 + 7.63697i) q^{77} +(-6.05353 - 6.72312i) q^{79} +(-0.339951 + 3.23442i) q^{80} +(4.11208 - 7.12233i) q^{82} +(-4.66057 + 2.07502i) q^{83} +(-5.36009 + 3.89433i) q^{85} +(-4.93282 - 2.19623i) q^{86} +(0.699678 - 2.15339i) q^{88} +(6.45373 + 4.68891i) q^{89} +(19.2980 + 8.59204i) q^{91} +(-16.8331 - 7.49459i) q^{92} +(-6.80846 - 4.94664i) q^{94} +(1.72135 - 5.29776i) q^{95} +(4.08831 + 1.82023i) q^{97} +(-13.7417 + 9.98393i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + 10 q^{2} - 10 q^{4} - 2 q^{5} + q^{7} + 4 q^{8}+O(q^{10}) $ 32 * q + 10 * q^2 - 10 * q^4 - 2 * q^5 + q^7 + 4 * q^8	$ 32 q + 10 q^{2} - 10 q^{4} - 2 q^{5} + q^{7} + 4 q^{8} + 15 q^{10} + 18 q^{11} - 11 q^{14} + 6 q^{16} + 24 q^{17} + 9 q^{19} + 4 q^{20} + q^{22} + 2 q^{23} + 28 q^{25} - 16 q^{26} + 4 q^{28} + 4 q^{29} - 11 q^{31} - 34 q^{32} + 18 q^{34} + 58 q^{35} - 14 q^{37} + 24 q^{38} - 60 q^{40} - 11 q^{41} + 40 q^{43} - 29 q^{44} - 89 q^{46} - 40 q^{47} + q^{49} + 56 q^{50} - 67 q^{52} - 17 q^{53} - 60 q^{55} + 102 q^{56} + 73 q^{58} + 11 q^{59} - 55 q^{61} + 74 q^{62} + 6 q^{64} - 59 q^{65} - 13 q^{67} + 3 q^{68} + 44 q^{70} - 63 q^{71} - 46 q^{73} + 10 q^{74} + 55 q^{76} + 31 q^{77} - 49 q^{79} - 74 q^{80} + 39 q^{82} - 39 q^{83} + 21 q^{85} - 74 q^{86} + 70 q^{88} - 32 q^{89} + 70 q^{91} - 77 q^{92} - 64 q^{94} - 47 q^{95} + 37 q^{97} - 127 q^{98}+O(q^{100}) $ 32 * q + 10 * q^2 - 10 * q^4 - 2 * q^5 + q^7 + 4 * q^8 + 15 * q^10 + 18 * q^11 - 11 * q^14 + 6 * q^16 + 24 * q^17 + 9 * q^19 + 4 * q^20 + q^22 + 2 * q^23 + 28 * q^25 - 16 * q^26 + 4 * q^28 + 4 * q^29 - 11 * q^31 - 34 * q^32 + 18 * q^34 + 58 * q^35 - 14 * q^37 + 24 * q^38 - 60 * q^40 - 11 * q^41 + 40 * q^43 - 29 * q^44 - 89 * q^46 - 40 * q^47 + q^49 + 56 * q^50 - 67 * q^52 - 17 * q^53 - 60 * q^55 + 102 * q^56 + 73 * q^58 + 11 * q^59 - 55 * q^61 + 74 * q^62 + 6 * q^64 - 59 * q^65 - 13 * q^67 + 3 * q^68 + 44 * q^70 - 63 * q^71 - 46 * q^73 + 10 * q^74 + 55 * q^76 + 31 * q^77 - 49 * q^79 - 74 * q^80 + 39 * q^82 - 39 * q^83 + 21 * q^85 - 74 * q^86 + 70 * q^88 - 32 * q^89 + 70 * q^91 - 77 * q^92 - 64 * q^94 - 47 * q^95 + 37 * q^97 - 127 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/549\mathbb{Z}\right)^\times$.

$n$	$245$	$307$
$\chi(n)$	$1$	$e\left(\frac{13}{15}\right)$

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 $

$2$	1.94561	−	0.866241i	1.37575	−	0.612525i	0.420224	−	0.907421i	$-0.361952\pi$
$2$	1.94561	−	0.866241i	1.37575	−	0.612525i	0.955529	+	0.294896i	$0.0952850\pi$
$3$		0			0
$3$		0			0
$4$	1.69676	−	1.88444i	0.848379	−	0.942220i
$5$	1.20434	+	0.255990i	0.538595	+	0.114482i	0.469175	−	0.883105i	$-0.344552\pi$
$5$	1.20434	+	0.255990i	0.538595	+	0.114482i	0.0694209	+	0.997587i	$0.477885\pi$
$6$		0			0
$7$	0.404506	+	3.84862i	0.152889	+	1.45464i	0.754735	+	0.656029i	$0.227765\pi$
$7$	0.404506	+	3.84862i	0.152889	+	1.45464i	−0.601846	+	0.798612i	$0.705568\pi$
$8$	0.352600	−	1.08519i	0.124663	−	0.383673i
$9$		0			0
$10$	2.56491	−	0.545189i	0.811097	−	0.172404i
$11$	1.98434			0.598301			0.299151	−	0.954206i	$-0.403297\pi$
$11$	1.98434			0.598301			0.299151	+	0.954206i	$0.403297\pi$
$12$		0			0
$13$	2.72937	−	4.72741i	0.756991	−	1.31115i	−0.187387	−	0.982286i	$-0.560002\pi$
$13$	2.72937	−	4.72741i	0.756991	−	1.31115i	0.944378	−	0.328862i	$-0.106665\pi$
$14$	4.12084	+	7.13751i	1.10134	+	1.90758i
$15$		0			0
$16$	0.276104	+	2.62696i	0.0690260	+	0.656739i
$17$	−3.60066	+	3.99894i	−0.873288	+	0.969885i	−0.999756	−	0.0220861i	$-0.992969\pi$
$17$	−3.60066	+	3.99894i	−0.873288	+	0.969885i	0.126468	+	0.991971i	$0.459636\pi$
$18$		0			0
$19$	0.472909	−	4.49943i	0.108493	−	1.03224i	−0.795868	−	0.605470i	$-0.792985\pi$
$19$	0.472909	−	4.49943i	0.108493	−	1.03224i	0.904361	−	0.426769i	$-0.140348\pi$
$20$	2.52586	−	1.83515i	0.564800	−	0.410351i
$21$		0			0
$22$	3.86075	−	1.71892i	0.823115	−	0.366474i
$23$	−2.24547	−	6.91085i	−0.468213	−	1.44101i	−0.854896	−	0.518800i	$-0.826379\pi$
$23$	−2.24547	−	6.91085i	−0.468213	−	1.44101i	0.386683	−	0.922213i	$-0.373621\pi$
$24$		0			0
$25$	−3.18283	−	1.41709i	−0.636567	−	0.283418i
$26$	1.21521	−	11.5620i	0.238323	−	2.26749i
$27$		0			0
$28$	7.93884	+	5.76791i	1.50030	+	1.09003i
$29$	0.207283	+	0.359024i	0.0384914	+	0.0666691i	0.884629	−	0.466295i	$-0.154411\pi$
$29$	0.207283	+	0.359024i	0.0384914	+	0.0666691i	−0.846138	+	0.532964i	$0.821078\pi$
$30$		0			0
$31$	−2.26627	−	1.00901i	−0.407035	−	0.181224i	0.192998	−	0.981199i	$-0.438179\pi$
$31$	−2.26627	−	1.00901i	−0.407035	−	0.181224i	−0.600033	+	0.799976i	$0.704846\pi$
$32$	3.95380	+	6.84819i	0.698940	+	1.21060i
$33$		0			0
$34$	−3.54143	+	10.8994i	−0.607350	+	1.86923i
$35$	−0.498045	+	4.73858i	−0.0841849	+	0.800966i
$36$		0			0
$37$	−5.96555	+	4.33423i	−0.980730	+	0.712542i	−0.957872	−	0.287196i	$-0.907277\pi$
$37$	−5.96555	+	4.33423i	−0.980730	+	0.712542i	−0.0228586	+	0.999739i	$0.507277\pi$
$38$	−2.97749	−	9.16378i	−0.483013	−	1.48656i
$39$		0			0
$40$	0.702446	−	1.21667i	0.111067	−	0.192373i
$41$	3.12409	−	2.26979i	0.487902	−	0.354481i	−0.316475	−	0.948601i	$-0.602499\pi$
$41$	3.12409	−	2.26979i	0.487902	−	0.354481i	0.804377	+	0.594120i	$0.202499\pi$
$42$		0			0
$43$	−1.69649	−	1.88414i	−0.258712	−	0.287329i	0.599770	−	0.800172i	$-0.295259\pi$
$43$	−1.69649	−	1.88414i	−0.258712	−	0.287329i	−0.858482	+	0.512844i	$0.828592\pi$
$44$	3.36695	−	3.73937i	0.507586	−	0.563732i
$45$		0			0
$46$	−10.3553	−	11.5007i	−1.52680	−	1.69568i
$47$	−1.97577	−	3.42213i	−0.288195	−	0.499169i	0.685184	−	0.728370i	$-0.259722\pi$
$47$	−1.97577	−	3.42213i	−0.288195	−	0.499169i	−0.973379	+	0.229201i	$0.926389\pi$
$48$		0			0
$49$	−7.80121	+	1.65820i	−1.11446	+	0.236885i
$50$	−7.42009			−1.04936
$51$		0			0
$52$	−4.27744	−	13.1646i	−0.593174	−	1.82560i
$53$	−0.927961	+	2.85597i	−0.127465	+	0.392298i	−0.994342	−	0.106224i	$-0.966124\pi$
$53$	−0.927961	+	2.85597i	−0.127465	+	0.392298i	0.866877	+	0.498522i	$0.166124\pi$
$54$		0			0
$55$	2.38981	+	0.507970i	0.322242	+	0.0684947i
$56$	4.31911	+	0.918056i	0.577166	+	0.122680i
$57$		0			0
$58$	0.714292	+	0.518963i	0.0937911	+	0.0681432i
$59$	1.34010	−	0.596653i	0.174467	−	0.0776776i	−0.317645	−	0.948210i	$-0.602892\pi$
$59$	1.34010	−	0.596653i	0.174467	−	0.0776776i	0.492111	+	0.870532i	$0.336225\pi$
$60$		0			0
$61$	1.71348	+	7.61997i	0.219389	+	0.975637i
$61$	1.71348	+	7.61997i	0.219389	+	0.975637i
$62$	−5.28333			−0.670983
$63$		0			0
$64$	9.35082	+	6.79377i	1.16885	+	0.849221i
$65$	4.49725	−	4.99470i	0.557815	−	0.619516i
$66$		0			0
$67$	5.93084	+	1.26064i	0.724568	+	0.154012i	0.555409	−	0.831577i	$-0.312562\pi$
$67$	5.93084	+	1.26064i	0.724568	+	0.154012i	0.169159	+	0.985589i	$0.445895\pi$
$68$	1.42631	+	13.5705i	0.172966	+	1.64566i
$69$		0			0
$70$	3.13575	+	9.65085i	0.374794	+	1.15350i
$71$	8.53723	−	1.81465i	1.01318	−	0.215359i	0.328737	−	0.944422i	$-0.393377\pi$
$71$	8.53723	−	1.81465i	1.01318	−	0.215359i	0.684447	+	0.729063i	$0.260044\pi$
$72$		0			0
$73$	−6.01044	+	1.27756i	−0.703469	+	0.149527i	−0.545739	−	0.837955i	$-0.683751\pi$
$73$	−6.01044	+	1.27756i	−0.703469	+	0.149527i	−0.157730	+	0.987482i	$0.550418\pi$
$74$	−7.85214	+	13.6003i	−0.912793	+	1.58100i
$75$		0			0
$76$	−7.67650	−	8.52561i	−0.880554	−	0.977955i
$77$	0.802678	+	7.63697i	0.0914736	+	0.870314i
$78$		0			0
$79$	−6.05353	−	6.72312i	−0.681075	−	0.756411i	0.299169	−	0.954200i	$-0.403290\pi$
$79$	−6.05353	−	6.72312i	−0.681075	−	0.756411i	−0.980245	+	0.197789i	$0.936624\pi$
$80$	−0.339951	+	3.23442i	−0.0380077	+	0.361619i
$81$		0			0
$82$	4.11208	−	7.12233i	0.454103	−	0.786530i
$83$	−4.66057	+	2.07502i	−0.511565	+	0.227763i	−0.646251	−	0.763125i	$-0.723664\pi$
$83$	−4.66057	+	2.07502i	−0.511565	+	0.227763i	0.134686	+	0.990888i	$0.456997\pi$
$84$		0			0
$85$	−5.36009	+	3.89433i	−0.581383	+	0.422400i
$86$	−4.93282	−	2.19623i	−0.531920	−	0.236826i
$87$		0			0
$88$	0.699678	−	2.15339i	0.0745860	−	0.229552i
$89$	6.45373	+	4.68891i	0.684093	+	0.497023i	0.874713	−	0.484641i	$-0.161050\pi$
$89$	6.45373	+	4.68891i	0.684093	+	0.497023i	−0.190620	+	0.981664i	$0.561050\pi$
$90$		0			0
$91$	19.2980	+	8.59204i	2.02299	+	0.900691i
$92$	−16.8331	−	7.49459i	−1.75497	−	0.781365i
$93$		0			0
$94$	−6.80846	−	4.94664i	−0.702239	−	0.510206i
$95$	1.72135	−	5.29776i	0.176607	−	0.543539i
$96$		0			0
$97$	4.08831	+	1.82023i	0.415105	+	0.184817i	0.603653	−	0.797247i	$-0.293711\pi$
$97$	4.08831	+	1.82023i	0.415105	+	0.184817i	−0.188548	+	0.982064i	$0.560378\pi$
$98$	−13.7417	+	9.98393i	−1.38812	+	1.00853i
$99$		0			0
$100$	−8.07092	+	3.59340i	−0.807092	+	0.359340i
$101$	2.32112	−	4.02029i	0.230960	−	0.400034i	−0.727131	−	0.686499i	$-0.759147\pi$
$101$	2.32112	−	4.02029i	0.230960	−	0.400034i	0.958091	+	0.286465i	$0.0924801\pi$
$102$		0			0
$103$	0.0983275	−	0.935524i	0.00968850	−	0.0921799i	−0.988609	−	0.150506i	$-0.951910\pi$
$103$	0.0983275	−	0.935524i	0.00968850	−	0.0921799i	0.998298	+	0.0583262i	$0.0185763\pi$
$104$	−4.16777	−	4.62877i	−0.408683	−	0.453889i
$105$		0			0
$106$	0.668509	+	6.36044i	0.0649313	+	0.617780i
$107$	−9.70753	−	10.7813i	−0.938462	−	1.04227i	−0.999027	−	0.0441038i	$-0.985957\pi$
$107$	−9.70753	−	10.7813i	−0.938462	−	1.04227i	0.0605646	−	0.998164i	$-0.480710\pi$
$108$		0			0
$109$	−0.198787	+	0.344309i	−0.0190404	+	0.0329789i	−0.875389	−	0.483420i	$-0.839394\pi$
$109$	−0.198787	+	0.344309i	−0.0190404	+	0.0329789i	0.856348	+	0.516399i	$0.172728\pi$
$110$	5.08967	−	1.08184i	0.485281	−	0.103150i
$111$		0			0
$112$	−9.99846	+	2.12524i	−0.944766	+	0.200816i
$113$	1.84819	+	5.68814i	0.173863	+	0.535095i	0.999580	−	0.0289897i	$-0.00922900\pi$
$113$	1.84819	+	5.68814i	0.173863	+	0.535095i	−0.825717	+	0.564085i	$0.809229\pi$
$114$		0			0
$115$	−0.935197	−	8.89781i	−0.0872076	−	0.829725i
$116$	1.02827	+	0.218565i	0.0954722	+	0.0202933i
$117$		0			0
$118$	2.09047	−	2.32170i	0.192444	−	0.213730i
$119$	−16.8469	−	12.2400i	−1.54435	−	1.12204i
$120$		0			0
$121$	−7.06239			−0.642036
$122$	9.93450	+	13.3412i	0.899427	+	1.20785i
$123$		0			0
$124$	−5.74674	+	2.55861i	−0.516073	+	0.229770i
$125$	−8.45092	−	6.13995i	−0.755873	−	0.549174i
$126$		0			0
$127$	−2.51029	−	0.533579i	−0.222752	−	0.0473475i	0.0951833	−	0.995460i	$-0.469656\pi$
$127$	−2.51029	−	0.533579i	−0.222752	−	0.0473475i	−0.317936	+	0.948112i	$0.602990\pi$
$128$	8.60845	+	1.82978i	0.760887	+	0.161731i
$129$		0			0
$130$	4.42327	−	13.6134i	0.387947	−	1.19398i
$131$	4.15159	+	12.7773i	0.362726	+	1.11636i	0.951393	+	0.307980i	$0.0996531\pi$
$131$	4.15159	+	12.7773i	0.362726	+	1.11636i	−0.588667	+	0.808376i	$0.700347\pi$
$132$		0			0
$133$	17.5079			1.51813
$134$	12.6311	−	2.68483i	1.09116	−	0.231934i
$135$		0			0
$136$	3.07002	+	5.31743i	0.263252	+	0.455966i
$137$	−9.39015	−	10.4288i	−0.802255	−	0.890994i	0.193681	−	0.981065i	$-0.437957\pi$
$137$	−9.39015	−	10.4288i	−0.802255	−	0.890994i	−0.995935	+	0.0900705i	$0.971291\pi$
$138$		0			0
$139$	3.86611	−	4.29375i	0.327919	−	0.364191i	−0.556530	−	0.830827i	$-0.687868\pi$
$139$	3.86611	−	4.29375i	0.327919	−	0.364191i	0.884449	+	0.466637i	$0.154534\pi$
$140$	8.08451	+	8.97876i	0.683266	+	0.758844i
$141$		0			0
$142$	15.0382	−	10.9259i	1.26198	−	0.916880i
$143$	5.41600	−	9.38079i	0.452909	−	0.784461i
$144$		0			0
$145$	0.157731	+	0.485447i	0.0130989	+	0.0403142i
$146$	−10.5873	+	7.69212i	−0.876211	+	0.636605i
$147$		0			0
$148$	−1.95450	+	18.5959i	−0.160659	+	1.52857i
$149$	−7.04785	+	21.6911i	−0.577383	+	1.77700i	0.0505360	+	0.998722i	$0.483907\pi$
$149$	−7.04785	+	21.6911i	−0.577383	+	1.77700i	−0.627919	+	0.778279i	$0.716093\pi$
$150$		0			0
$151$	−5.55147	−	9.61543i	−0.451772	−	0.782492i	0.546724	−	0.837313i	$-0.315875\pi$
$151$	−5.55147	−	9.61543i	−0.451772	−	0.782492i	−0.998496	+	0.0548206i	$0.982541\pi$
$152$	−4.71599	−	2.09969i	−0.382517	−	0.170308i
$153$		0			0
$154$	8.17715	+	14.1632i	0.658934	+	1.14131i
$155$	−2.47106	−	1.79533i	−0.198480	−	0.144204i
$156$		0			0
$157$	−0.905118	+	8.61162i	−0.0722363	+	0.687282i	0.897147	+	0.441731i	$0.145636\pi$
$157$	−0.905118	+	8.61162i	−0.0722363	+	0.687282i	−0.969384	+	0.245551i	$0.921031\pi$
$158$	−17.6016	−	7.83676i	−1.40031	−	0.623459i
$159$		0			0
$160$	3.00864	+	9.25965i	0.237854	+	0.732040i
$161$	25.6889	−	11.4374i	2.02457	−	0.901397i
$162$		0			0
$163$	−16.0936	+	11.6927i	−1.26055	+	0.915842i	−0.998785	−	0.0492895i	$-0.984304\pi$
$163$	−16.0936	+	11.6927i	−1.26055	+	0.915842i	−0.261764	+	0.965132i	$0.584304\pi$
$164$	1.02355	−	9.73845i	0.0799260	−	0.760445i
$165$		0			0
$166$	−7.27019	+	8.07436i	−0.564276	+	0.626692i
$167$	−1.18071	−	11.2337i	−0.0913660	−	0.869290i	−0.940198	−	0.340628i	$-0.889360\pi$
$167$	−1.18071	−	11.2337i	−0.0913660	−	0.869290i	0.848832	−	0.528662i	$-0.177306\pi$
$168$		0			0
$169$	−8.39894	−	14.5474i	−0.646072	−	1.11903i
$170$	−7.05520	+	12.2200i	−0.541109	+	0.937229i
$171$		0			0
$172$	−6.42908			−0.490213
$173$	9.25127	−	1.96642i	0.703361	−	0.149504i	0.157672	−	0.987492i	$-0.449601\pi$
$173$	9.25127	−	1.96642i	0.703361	−	0.149504i	0.545689	+	0.837988i	$0.316268\pi$
$174$		0			0
$175$	4.16636	−	12.8227i	0.314947	−	0.969307i
$176$	0.547885	+	5.21277i	0.0412984	+	0.392928i
$177$		0			0
$178$	16.6181	+	3.53230i	1.24558	+	0.264757i
$179$	−1.16770	+	1.29686i	−0.0872777	+	0.0969317i	−0.785202	−	0.619240i	$-0.787441\pi$
$179$	−1.16770	+	1.29686i	−0.0872777	+	0.0969317i	0.697924	+	0.716172i	$0.254107\pi$
$180$		0			0
$181$	20.1978	−	8.99263i	1.50129	−	0.668417i	0.518827	−	0.854879i	$-0.326369\pi$
$181$	20.1978	−	8.99263i	1.50129	−	0.668417i	0.982462	+	0.186462i	$0.0597023\pi$
$182$	44.9892			3.33482
$183$		0			0
$184$	−8.29135			−0.611246
$185$	−8.29404	+	3.69275i	−0.609790	+	0.271496i
$186$		0			0
$187$	−7.14493	+	7.93525i	−0.522489	+	0.580283i
$188$	−9.80120	−	2.08331i	−0.714826	−	0.151941i
$189$		0			0
$190$	−1.24007	−	11.7985i	−0.0899641	−	0.855951i
$191$	1.26390	−	3.88989i	0.0914528	−	0.281463i	−0.894860	−	0.446347i	$-0.852725\pi$
$191$	1.26390	−	3.88989i	0.0914528	−	0.281463i	0.986313	+	0.164884i	$0.0527249\pi$
$192$		0			0
$193$	20.8189	−	4.42519i	1.49858	−	0.318532i	0.615641	−	0.788027i	$-0.288897\pi$
$193$	20.8189	−	4.42519i	1.49858	−	0.318532i	0.882935	+	0.469494i	$0.155564\pi$
$194$	9.53101			0.684287
$195$		0			0
$196$	−10.1120	+	17.5145i	−0.722285	+	1.25103i
$197$	−0.463455	−	0.802727i	−0.0330198	−	0.0571919i	0.849043	−	0.528323i	$-0.177179\pi$
$197$	−0.463455	−	0.802727i	−0.0330198	−	0.0571919i	−0.882063	+	0.471131i	$0.843846\pi$
$198$		0			0
$199$	2.90050	+	27.5964i	0.205611	+	1.95626i	0.282635	+	0.959227i	$0.408791\pi$
$199$	2.90050	+	27.5964i	0.205611	+	1.95626i	−0.0770244	+	0.997029i	$0.524542\pi$
$200$	−2.66008	+	2.95432i	−0.188096	+	0.208902i
$201$		0			0
$202$	1.03344	−	9.83256i	0.0727128	−	0.691816i
$203$	−1.29790	+	0.942979i	−0.0910946	+	0.0661841i
$204$		0			0
$205$	4.34350	−	1.93385i	0.303363	−	0.135066i
$206$	−0.619082	−	1.90534i	−0.0431335	−	0.132751i
$207$		0			0
$208$	13.1723	+	5.86468i	0.913334	+	0.406642i
$209$	0.938413	−	8.92840i	0.0649114	−	0.617590i
$210$		0			0
$211$	1.39195	+	1.01131i	0.0958255	+	0.0696213i	0.634666	−	0.772786i	$-0.281138\pi$
$211$	1.39195	+	1.01131i	0.0958255	+	0.0696213i	−0.538841	+	0.842408i	$0.681138\pi$
$212$	3.80738	+	6.59458i	0.261492	+	0.452918i
$213$		0			0
$214$	−28.2263	−	12.5671i	−1.92951	−	0.859072i
$215$	−1.56082	−	2.70342i	−0.106447	−	0.184372i
$216$		0			0
$217$	2.96657	−	9.13018i	0.201384	−	0.619797i
$218$	−0.0885071	+	0.842089i	−0.00599446	+	0.0570334i
$219$		0			0
$220$	5.01217	−	3.64156i	0.337921	−	0.245514i
$221$	9.07708	+	27.9364i	0.610590	+	1.87920i
$222$		0			0
$223$	7.37302	−	12.7704i	0.493734	−	0.855172i	−0.506240	−	0.862393i	$-0.668965\pi$
$223$	7.37302	−	12.7704i	0.493734	−	0.855172i	0.999974	+	0.00722039i	$0.00229834\pi$
$224$	−24.7567	+	17.9868i	−1.65413	+	1.20179i
$225$		0			0
$226$	8.52315	+	9.46592i	0.566952	+	0.629664i
$227$	4.20101	−	4.66570i	0.278831	−	0.309673i	−0.587420	−	0.809282i	$-0.699856\pi$
$227$	4.20101	−	4.66570i	0.278831	−	0.309673i	0.866251	+	0.499609i	$0.166523\pi$
$228$		0			0
$229$	−1.22133	−	1.35642i	−0.0807077	−	0.0896350i	0.701438	−	0.712730i	$-0.252542\pi$
$229$	−1.22133	−	1.35642i	−0.0807077	−	0.0896350i	−0.782146	+	0.623095i	$0.785875\pi$
$230$	−9.52717	−	16.5015i	−0.628203	−	1.08808i
$231$		0			0
$232$	0.462697	−	0.0983493i	0.0303776	−	0.00645695i
$233$	11.4021			0.746974			0.373487	−	0.927635i	$-0.378162\pi$
$233$	11.4021			0.746974			0.373487	+	0.927635i	$0.378162\pi$
$234$		0			0
$235$	−1.50346	−	4.62717i	−0.0980748	−	0.301843i
$236$	1.14948	−	3.53772i	0.0748245	−	0.230286i
$237$		0			0
$238$	−43.3802	−	9.22074i	−2.81192	−	0.597692i
$239$	−5.69764	−	1.21107i	−0.368549	−	0.0783376i	0.0199141	−	0.999802i	$-0.493661\pi$
$239$	−5.69764	−	1.21107i	−0.368549	−	0.0783376i	−0.388464	+	0.921464i	$0.626994\pi$
$240$		0			0
$241$	14.0356	+	10.1975i	0.904113	+	0.656876i	0.939519	−	0.342497i	$-0.111273\pi$
$241$	14.0356	+	10.1975i	0.904113	+	0.656876i	−0.0354063	+	0.999373i	$0.511273\pi$
$242$	−13.7406	+	6.11773i	−0.883282	+	0.393263i
$243$		0			0
$244$	17.2668	+	9.70029i	1.10539	+	0.620998i
$245$	−9.81975			−0.627361
$246$		0			0
$247$	−19.9799	−	14.5162i	−1.27129	−	0.923647i
$248$	−1.89406	+	2.10356i	−0.120273	+	0.133576i
$249$		0			0
$250$	−21.7609	−	4.62541i	−1.37628	−	0.292537i
$251$	0.530194	+	5.04446i	0.0334656	+	0.318403i	0.998430	+	0.0560213i	$0.0178415\pi$
$251$	0.530194	+	5.04446i	0.0334656	+	0.318403i	−0.964964	+	0.262382i	$0.915492\pi$
$252$		0			0
$253$	−4.45578	−	13.7135i	−0.280133	−	0.862160i
$254$	−5.34625	+	1.13638i	−0.335454	+	0.0713029i
$255$		0			0
$256$	−4.27763	+	0.909238i	−0.267352	+	0.0568274i
$257$	10.8484	−	18.7901i	0.676707	−	1.17209i	−0.299259	−	0.954172i	$-0.596740\pi$
$257$	10.8484	−	18.7901i	0.676707	−	1.17209i	0.975967	−	0.217920i	$-0.0699271\pi$
$258$		0			0
$259$	−19.0939	−	21.2059i	−1.18644	−	1.31767i
$260$	−1.78147	−	16.9496i	−0.110482	−	1.05117i
$261$		0			0
$262$	19.1456	+	21.2633i	1.18282	+	1.31365i
$263$	−0.0382994	+	0.364395i	−0.00236164	+	0.0224695i	−0.995639	−	0.0932870i	$-0.970263\pi$
$263$	−0.0382994	+	0.364395i	−0.00236164	+	0.0224695i	0.993278	+	0.115757i	$0.0369292\pi$
$264$		0			0
$265$	−1.84868	+	3.20200i	−0.113563	+	0.196697i
$266$	34.0635	−	15.1660i	2.08857	−	0.929889i
$267$		0			0
$268$	12.4388	−	9.03732i	0.759821	−	0.552042i
$269$	18.8038	+	8.37201i	1.14649	+	0.510450i	0.889939	−	0.456080i	$-0.150747\pi$
$269$	18.8038	+	8.37201i	1.14649	+	0.510450i	0.256551	+	0.966531i	$0.417414\pi$
$270$		0			0
$271$	−10.0125	+	30.8152i	−0.608215	+	1.87189i	−0.135248	+	0.990812i	$0.543183\pi$
$271$	−10.0125	+	30.8152i	−0.608215	+	1.87189i	−0.472967	+	0.881080i	$0.656817\pi$
$272$	−11.4992	−	8.35465i	−0.697240	−	0.506575i
$273$		0			0
$274$	−27.3034	−	12.1563i	−1.64946	−	0.734387i
$275$	−6.31583	−	2.81199i	−0.380859	−	0.169569i
$276$		0			0
$277$	−3.40946	−	2.47712i	−0.204855	−	0.148836i	0.480628	−	0.876925i	$-0.340409\pi$
$277$	−3.40946	−	2.47712i	−0.204855	−	0.148836i	−0.685483	+	0.728089i	$0.740409\pi$
$278$	3.80251	−	11.7029i	0.228059	−	0.701895i
$279$		0			0
$280$	4.96665	+	2.21130i	0.296814	+	0.132150i
$281$	2.97726	−	2.16310i	0.177608	−	0.129040i	−0.495429	−	0.868648i	$-0.664989\pi$
$281$	2.97726	−	2.16310i	0.177608	−	0.129040i	0.673037	+	0.739608i	$0.264989\pi$
$282$		0			0
$283$	18.0382	−	8.03111i	1.07226	−	0.477400i	0.206801	−	0.978383i	$-0.433695\pi$
$283$	18.0382	−	8.03111i	1.07226	−	0.477400i	0.865457	+	0.500983i	$0.167028\pi$
$284$	11.0660	−	19.1669i	0.656648	−	1.13735i
$285$		0			0
$286$	2.41140	−	22.9429i	0.142589	−	1.35664i
$287$	9.99926	+	11.1053i	0.590238	+	0.655525i
$288$		0			0
$289$	−1.24977	−	11.8907i	−0.0735157	−	0.699455i
$290$	0.727398	+	0.807857i	0.0427143	+	0.0474390i
$291$		0			0
$292$	−7.79079	+	13.4940i	−0.455921	+	0.789679i
$293$	1.67272	−	0.355547i	0.0977212	−	0.0207713i	−0.158792	−	0.987312i	$-0.550760\pi$
$293$	1.67272	−	0.355547i	0.0977212	−	0.0207713i	0.256513	+	0.966541i	$0.417426\pi$
$294$		0			0
$295$	1.76667	−	0.375518i	0.102860	−	0.0218635i
$296$	2.60001	+	8.00201i	0.151123	+	0.465107i
$297$		0			0
$298$	5.07732	+	48.3075i	0.294121	+	2.79838i
$299$	−38.7992	−	8.24702i	−2.24381	−	0.476937i
$300$		0			0
$301$	6.56510	−	7.29128i	0.378406	−	0.420263i
$302$	−19.1303	−	13.8989i	−1.10082	−	0.799794i
$303$		0			0
$304$	11.9504			0.685401
$305$	0.112976	+	9.61564i	0.00646901	+	0.550590i
$306$		0			0
$307$	15.9872	−	7.11797i	0.912439	−	0.406244i	0.103833	−	0.994595i	$-0.466889\pi$
$307$	15.9872	−	7.11797i	0.912439	−	0.406244i	0.808606	+	0.588351i	$0.200222\pi$
$308$	15.7534	+	11.4455i	0.897632	+	0.652168i
$309$		0			0
$310$	−6.36290	−	1.35248i	−0.361389	−	0.0768155i
$311$	14.4204	+	3.06514i	0.817704	+	0.173808i	0.597730	−	0.801697i	$-0.296069\pi$
$311$	14.4204	+	3.06514i	0.817704	+	0.173808i	0.219974	+	0.975506i	$0.429403\pi$
$312$		0			0
$313$	−3.98839	+	12.2750i	−0.225437	+	0.693825i	0.772810	+	0.634638i	$0.218851\pi$
$313$	−3.98839	+	12.2750i	−0.225437	+	0.693825i	−0.998247	+	0.0591867i	$0.981149\pi$
$314$	5.69873	+	17.5389i	0.321598	+	0.989777i
$315$		0			0
$316$	−22.9407			−1.29052
$317$	−14.3518	+	3.05057i	−0.806078	+	0.171337i	−0.592481	−	0.805584i	$-0.701851\pi$
$317$	−14.3518	+	3.05057i	−0.806078	+	0.171337i	−0.213598	+	0.976922i	$0.568518\pi$
$318$		0			0
$319$	0.411319	+	0.712426i	0.0230295	+	0.0398882i
$320$	9.52239	+	10.5757i	0.532318	+	0.591199i
$321$		0			0
$322$	40.0730	−	44.5056i	2.23318	−	2.48020i
$323$	16.2901	+	18.0920i	0.906408	+	1.00667i
$324$		0			0
$325$	−15.3863	+	11.1788i	−0.853478	+	0.620088i
$326$	−21.1832	+	36.6903i	−1.17323	+	2.03209i
$327$		0			0
$328$	−1.36160	−	4.19057i	−0.0751816	−	0.231385i
$329$	12.3713	−	8.98825i	0.682050	−	0.495538i
$330$		0			0
$331$	−0.117148	+	1.11458i	−0.00643901	+	0.0612631i	−0.997270	−	0.0738473i	$-0.976472\pi$
$331$	−0.117148	+	1.11458i	−0.00643901	+	0.0612631i	0.990831	+	0.135110i	$0.0431389\pi$
$332$	−3.99761	+	12.3034i	−0.219398	+	0.675236i
$333$		0			0
$334$	−12.0283	−	20.8336i	−0.658158	−	1.13996i
$335$	6.82002	+	3.03647i	0.372617	+	0.165900i
$336$		0			0
$337$	9.71207	+	16.8218i	0.529050	+	0.916342i	0.999426	+	0.0338755i	$0.0107850\pi$
$337$	9.71207	+	16.8218i	0.529050	+	0.916342i	−0.470376	+	0.882466i	$0.655882\pi$
$338$	−28.9426	−	21.0280i	−1.57427	−	1.14377i
$339$		0			0
$340$	−1.75614	+	16.7085i	−0.0952398	+	0.906146i
$341$	−4.49706	−	2.00222i	−0.243530	−	0.108426i
$342$		0			0
$343$	−1.16653	−	3.59021i	−0.0629867	−	0.193853i
$344$	−2.64284	+	1.17667i	−0.142492	+	0.0634416i
$345$		0			0
$346$	16.2960	−	11.8397i	0.876076	−	0.636507i
$347$	2.93642	−	27.9382i	0.157635	−	1.49980i	−0.574423	−	0.818559i	$-0.694774\pi$
$347$	2.93642	−	27.9382i	0.157635	−	1.49980i	0.732059	−	0.681242i	$-0.238560\pi$
$348$		0			0
$349$	−7.40721	+	8.22654i	−0.396499	+	0.440356i	−0.908028	−	0.418909i	$-0.862412\pi$
$349$	−7.40721	+	8.22654i	−0.396499	+	0.440356i	0.511529	+	0.859266i	$0.329079\pi$
$350$	−3.00147	−	28.5571i	−0.160435	−	1.52644i
$351$		0			0
$352$	7.84569	+	13.5891i	0.418177	+	0.724304i
$353$	−5.25836	+	9.10774i	−0.279874	+	0.484756i	−0.971353	−	0.237640i	$-0.923626\pi$
$353$	−5.25836	+	9.10774i	−0.279874	+	0.484756i	0.691479	+	0.722397i	$0.256959\pi$
$354$		0			0
$355$	10.7462			0.570351
$356$	19.7864	−	4.20572i	1.04868	−	0.222903i
$357$		0			0
$358$	−1.14849	+	3.53468i	−0.0606995	+	0.186814i
$359$	−1.23915	−	11.7897i	−0.0653997	−	0.622236i	−0.977305	−	0.211836i	$-0.932056\pi$
$359$	−1.23915	−	11.7897i	−0.0653997	−	0.622236i	0.911906	−	0.410400i	$-0.134611\pi$
$360$		0			0
$361$	−1.43641	−	0.305319i	−0.0756007	−	0.0160694i
$362$	31.5072	−	34.9923i	1.65598	−	1.83915i
$363$		0			0
$364$	48.9353	−	21.7874i	2.56491	−	1.14197i
$365$	−7.56564			−0.396004
$366$		0			0
$367$	−8.31934			−0.434266			−0.217133	−	0.976142i	$-0.569671\pi$
$367$	−8.31934			−0.434266			−0.217133	+	0.976142i	$0.569671\pi$
$368$	17.5345	−	7.80687i	0.914050	−	0.406961i
$369$		0			0
$370$	−12.9382	+	14.3693i	−0.672623	+	0.747023i
$371$	−11.3669	−	2.41611i	−0.590140	−	0.125438i
$372$		0			0
$373$	0.790781	+	7.52378i	0.0409451	+	0.389567i	0.995733	+	0.0922793i	$0.0294153\pi$
$373$	0.790781	+	7.52378i	0.0409451	+	0.389567i	−0.954788	+	0.297287i	$0.903918\pi$
$374$	−7.02740	+	21.6281i	−0.363378	+	1.11836i
$375$		0			0
$376$	−4.41032	+	0.937443i	−0.227445	+	0.0483449i
$377$	2.26300			0.116551
$378$		0			0
$379$	10.9280	−	18.9278i	0.561333	−	0.972257i	−0.436048	−	0.899923i	$-0.643622\pi$
$379$	10.9280	−	18.9278i	0.561333	−	0.972257i	0.997381	−	0.0723332i	$-0.0230445\pi$
$380$	−7.06261	−	12.2328i	−0.362304	−	0.627530i
$381$		0			0
$382$	−0.910524	−	8.66305i	−0.0465864	−	0.443240i
$383$	−20.8527	+	23.1592i	−1.06552	+	1.18338i	−0.0831307	+	0.996539i	$0.526492\pi$
$383$	−20.8527	+	23.1592i	−1.06552	+	1.18338i	−0.982390	+	0.186842i	$0.940175\pi$
$384$		0			0
$385$	−0.988290	+	9.40296i	−0.0503679	+	0.479219i
$386$	36.6721	−	26.6439i	1.86656	−	1.35614i
$387$		0			0
$388$	10.3670	−	4.61569i	0.526305	−	0.234326i
$389$	7.42504	+	22.8519i	0.376465	+	1.15864i	0.942485	+	0.334248i	$0.108482\pi$
$389$	7.42504	+	22.8519i	0.376465	+	1.15864i	−0.566021	+	0.824391i	$0.691518\pi$
$390$		0			0
$391$	35.7212	+	15.9041i	1.80650	+	0.804306i
$392$	−0.951244	+	9.05048i	−0.0480451	+	0.457118i
$393$		0			0
$394$	−1.59706	−	1.16033i	−0.0804585	−	0.0584566i
$395$	−5.56943	−	9.64654i	−0.280229	−	0.485370i
$396$		0			0
$397$	−1.19276	−	0.531050i	−0.0598628	−	0.0266526i	0.376587	−	0.926381i	$-0.377098\pi$
$397$	−1.19276	−	0.531050i	−0.0598628	−	0.0266526i	−0.436450	+	0.899729i	$0.643764\pi$
$398$	29.5484	+	51.1793i	1.48113	+	2.56538i
$399$		0			0
$400$	2.84383	−	8.75242i	0.142192	−	0.437621i
$401$	−2.08242	+	19.8129i	−0.103991	+	0.989410i	0.810756	+	0.585384i	$0.199056\pi$
$401$	−2.08242	+	19.8129i	−0.103991	+	0.989410i	−0.914747	+	0.404026i	$0.867610\pi$
$402$		0			0
$403$	−10.9555	+	7.95965i	−0.545733	+	0.396498i
$404$	−3.63763	−	11.1955i	−0.180979	−	0.556995i
$405$		0			0
$406$	−1.70836	+	2.95896i	−0.0847843	+	0.146851i
$407$	−11.8377	+	8.60058i	−0.586772	+	0.426315i
$408$		0			0
$409$	−7.27309	−	8.07759i	−0.359631	−	0.399411i	0.535993	−	0.844222i	$-0.319937\pi$
$409$	−7.27309	−	8.07759i	−0.359631	−	0.399411i	−0.895624	+	0.444811i	$0.853271\pi$
$410$	6.77557	−	7.52503i	0.334622	−	0.371635i
$411$		0			0
$412$	−1.59610	−	1.77265i	−0.0786343	−	0.0873322i
$413$	2.83837	+	4.91620i	0.139667	+	0.241910i
$414$		0			0
$415$	−6.14408	+	1.30596i	−0.301601	+	0.0641073i
$416$	43.1656			2.11637
$417$		0			0
$418$	−5.90836	−	18.1841i	−0.288987	−	0.889412i
$419$	11.5266	−	35.4752i	0.563111	−	1.73308i	−0.110388	−	0.993889i	$-0.535209\pi$
$419$	11.5266	−	35.4752i	0.563111	−	1.73308i	0.673499	−	0.739188i	$-0.264791\pi$
$420$		0			0
$421$	10.1823	+	2.16431i	0.496254	+	0.105482i	0.449238	−	0.893412i	$-0.351695\pi$
$421$	10.1823	+	2.16431i	0.496254	+	0.105482i	0.0470162	+	0.998894i	$0.485029\pi$
$422$	3.58422	+	0.761849i	0.174477	+	0.0370862i
$423$		0			0
$424$	2.77207	+	2.01403i	0.134624	+	0.0978100i
$425$	17.1271	−	7.62549i	0.830788	−	0.369891i
$426$		0			0
$427$	−28.6333	+	9.67687i	−1.38566	+	0.468296i
$428$	−36.7881			−1.77822
$429$		0			0
$430$	−5.37856	−	3.90775i	−0.259377	−	0.188449i
$431$	12.8860	−	14.3113i	0.620695	−	0.689352i	−0.348031	−	0.937483i	$-0.613150\pi$
$431$	12.8860	−	14.3113i	0.620695	−	0.689352i	0.968726	+	0.248131i	$0.0798164\pi$
$432$		0			0
$433$	−15.3817	−	3.26947i	−0.739195	−	0.157121i	−0.177100	−	0.984193i	$-0.556671\pi$
$433$	−15.3817	−	3.26947i	−0.739195	−	0.157121i	−0.562096	+	0.827072i	$0.690005\pi$
$434$	−2.13714	−	20.3335i	−0.102586	−	0.976040i
$435$		0			0
$436$	0.311537	+	0.958812i	0.0149199	+	0.0459188i
$437$	−32.1568	+	6.83514i	−1.53827	+	0.326969i
$438$		0			0
$439$	22.8168	−	4.84986i	1.08899	−	0.231471i	0.371772	−	0.928324i	$-0.378750\pi$
$439$	22.8168	−	4.84986i	1.08899	−	0.231471i	0.717214	+	0.696853i	$0.245417\pi$
$440$	1.39389	−	2.41429i	0.0664512	−	0.115097i
$441$		0			0
$442$	41.8601	+	46.4903i	1.99108	+	2.21132i
$443$	1.49567	+	14.2304i	0.0710616	+	0.676106i	0.970835	+	0.239749i	$0.0770650\pi$
$443$	1.49567	+	14.2304i	0.0710616	+	0.676106i	−0.899773	+	0.436357i	$0.856268\pi$
$444$		0			0
$445$	6.57214	+	7.29910i	0.311549	+	0.346011i
$446$	3.28273	−	31.2331i	0.155442	−	1.47893i
$447$		0			0
$448$	−22.3642	+	38.7358i	−1.05661	+	1.83010i
$449$	−7.26491	+	3.23455i	−0.342852	+	0.152648i	−0.570938	−	0.820994i	$-0.693420\pi$
$449$	−7.26491	+	3.23455i	−0.342852	+	0.152648i	0.228085	+	0.973641i	$0.426753\pi$
$450$		0			0
$451$	6.19927	−	4.50403i	0.291912	−	0.212087i
$452$	13.8549	+	6.16860i	0.651680	+	0.290146i
$453$		0			0
$454$	4.13191	−	12.7167i	0.193920	−	0.596825i
$455$	21.0419	+	15.2878i	0.986458	+	0.716703i
$456$		0			0
$457$	−29.4136	−	13.0958i	−1.37591	−	0.612595i	−0.420343	−	0.907365i	$-0.638090\pi$
$457$	−29.4136	−	13.0958i	−1.37591	−	0.612595i	−0.955568	+	0.294770i	$0.904757\pi$
$458$	−3.55122	−	1.58110i	−0.165938	−	0.0738801i
$459$		0			0
$460$	−18.3542	−	13.3351i	−0.855769	−	0.621752i
$461$	−9.73046	+	29.9473i	−0.453193	+	1.39478i	0.420052	+	0.907500i	$0.362012\pi$
$461$	−9.73046	+	29.9473i	−0.453193	+	1.39478i	−0.873244	+	0.487283i	$0.837988\pi$
$462$		0			0
$463$	14.0725	+	6.26547i	0.654004	+	0.291181i	0.706789	−	0.707425i	$-0.250143\pi$
$463$	14.0725	+	6.26547i	0.654004	+	0.291181i	−0.0527851	+	0.998606i	$0.516810\pi$
$464$	−0.885908	+	0.643650i	−0.0411272	+	0.0298807i
$465$		0			0
$466$	22.1840	−	9.87693i	1.02765	−	0.457540i
$467$	−12.3112	+	21.3237i	−0.569696	+	0.986743i	0.426900	+	0.904299i	$0.359606\pi$
$467$	−12.3112	+	21.3237i	−0.569696	+	0.986743i	−0.996596	+	0.0824437i	$0.973728\pi$
$468$		0			0
$469$	−2.45266	+	23.3355i	−0.113253	+	1.07753i
$470$	−6.93339	−	7.70031i	−0.319813	−	0.355189i
$471$		0			0
$472$	−0.174962	−	1.66465i	−0.00805326	−	0.0766216i
$473$	−3.36641	−	3.73878i	−0.154788	−	0.171909i
$474$		0			0
$475$	−7.88128	+	13.6508i	−0.361618	+	0.626341i
$476$	−51.6506	+	10.9787i	−2.36740	+	0.503206i
$477$		0			0
$478$	−12.1344	+	2.57926i	−0.555017	+	0.117972i
$479$	2.73131	+	8.40611i	0.124797	+	0.384085i	0.993864	−	0.110609i	$-0.0352802\pi$
$479$	2.73131	+	8.40611i	0.124797	+	0.384085i	−0.869067	+	0.494694i	$0.835280\pi$
$480$		0			0
$481$	4.20746	+	40.0313i	0.191844	+	1.82527i
$482$	36.1412	+	7.68206i	1.64619	+	0.349908i
$483$		0			0
$484$	−11.9832	+	13.3087i	−0.544690	+	0.604939i
$485$	4.45774	+	3.23874i	0.202416	+	0.147064i
$486$		0			0
$487$	−14.6614			−0.664373			−0.332187	−	0.943214i	$-0.607786\pi$
$487$	−14.6614			−0.664373			−0.332187	+	0.943214i	$0.607786\pi$
$488$	8.87330	+	0.827345i	0.401675	+	0.0374522i
$489$		0			0
$490$	−19.1054	+	8.50627i	−0.863094	+	0.384274i
$491$	−21.4615	−	15.5927i	−0.968545	−	0.703689i	−0.0134259	−	0.999910i	$-0.504274\pi$
$491$	−21.4615	−	15.5927i	−0.968545	−	0.703689i	−0.955120	+	0.296220i	$0.904274\pi$
$492$		0			0
$493$	−2.18207	−	0.463813i	−0.0982754	−	0.0208891i
$494$	−51.4476	−	10.9355i	−2.31474	−	0.492013i
$495$		0			0
$496$	2.02490	−	6.23199i	0.0909206	−	0.279825i
$497$	10.4372	+	32.1225i	0.468174	+	1.44089i
$498$		0			0
$499$	15.8024			0.707412			0.353706	−	0.935357i	$-0.384921\pi$
$499$	15.8024			0.707412			0.353706	+	0.935357i	$0.384921\pi$
$500$	−25.9095	+	5.50724i	−1.15871	+	0.246291i
$501$		0			0
$502$	5.40127	+	9.35527i	0.241070	+	0.417546i
$503$	23.2485	+	25.8201i	1.03660	+	1.15126i	0.988315	+	0.152427i	$0.0487088\pi$
$503$	23.2485	+	25.8201i	1.03660	+	1.15126i	0.0482846	+	0.998834i	$0.484625\pi$
$504$		0			0
$505$	3.82456	−	4.24760i	0.170190	−	0.189016i
$506$	−20.5484	−	22.8213i	−0.913487	−	1.01453i
$507$		0			0
$508$	−5.26486	+	3.82514i	−0.233590	+	0.169713i
$509$	13.6496	−	23.6418i	0.605009	−	1.04791i	−0.387042	−	0.922062i	$-0.626503\pi$
$509$	13.6496	−	23.6418i	0.605009	−	1.04791i	0.992050	−	0.125843i	$-0.0401636\pi$
$510$		0			0
$511$	−7.34810	−	22.6151i	−0.325061	−	1.00043i
$512$	−21.7749	+	15.8204i	−0.962324	+	0.699170i
$513$		0			0
$514$	4.83011	−	45.9555i	0.213047	−	2.02701i
$515$	0.357904	−	1.10151i	0.0157711	−	0.0485385i
$516$		0			0
$517$	−3.92060	−	6.79067i	−0.172428	−	0.298653i
$518$	−55.5186	−	24.7185i	−2.43935	−	1.08607i
$519$		0			0
$520$	−3.83447	−	6.64150i	−0.168153	−	0.291249i
$521$	−11.2871	−	8.20059i	−0.494499	−	0.359274i	0.312413	−	0.949946i	$-0.398863\pi$
$521$	−11.2871	−	8.20059i	−0.494499	−	0.359274i	−0.806912	+	0.590672i	$0.798863\pi$
$522$		0			0
$523$	1.81900	−	17.3067i	0.0795395	−	0.756768i	−0.879958	−	0.475051i	$-0.842430\pi$
$523$	1.81900	−	17.3067i	0.0795395	−	0.756768i	0.959498	−	0.281717i	$-0.0909038\pi$
$524$	31.1223	+	13.8565i	1.35958	+	0.605325i
$525$		0			0
$526$	0.241138	+	0.742146i	0.0105141	+	0.0323591i
$527$	12.1951	−	5.42959i	0.531225	−	0.236516i
$528$		0			0
$529$	−24.1104	+	17.5172i	−1.04828	+	0.761617i
$530$	−0.823096	+	7.83124i	−0.0357530	+	0.340167i
$531$		0			0
$532$	29.7066	−	32.9926i	1.28795	−	1.43041i
$533$	−2.20340	−	20.9640i	−0.0954399	−	0.908050i
$534$		0			0
$535$	−8.93123	−	15.4693i	−0.386131	−	0.668798i
$536$	3.45925	−	5.99159i	0.149417	−	0.258797i
$537$		0			0
$538$	43.8371			1.88995
$539$	−15.4803	+	3.29043i	−0.666782	+	0.141729i
$540$		0			0
$541$	10.2665	−	31.5970i	0.441391	−	1.35846i	−0.445003	−	0.895529i	$-0.646798\pi$
$541$	10.2665	−	31.5970i	0.441391	−	1.35846i	0.886394	−	0.462932i	$-0.153202\pi$
$542$	7.21305	+	68.6276i	0.309827	+	2.94781i
$543$		0			0
$544$	−41.6218	−	8.84698i	−1.78452	−	0.379311i
$545$	−0.327546	+	0.363777i	−0.0140305	+	0.0155825i
$546$		0			0
$547$	−40.2659	+	17.9275i	−1.72165	+	0.766527i	−0.724647	+	0.689120i	$0.757997\pi$
$547$	−40.2659	+	17.9275i	−1.72165	+	0.766527i	−0.997000	+	0.0774068i	$0.975336\pi$
$548$	−35.5853			−1.52013
$549$		0			0
$550$	−14.7240			−0.627833
$551$	1.71343	−	0.762867i	0.0729945	−	0.0324992i
$552$		0			0
$553$	23.4261	−	26.0173i	0.996177	−	1.10637i
$554$	−8.77927	−	1.86609i	−0.372995	−	0.0792826i
$555$		0			0
$556$	−1.53146	−	14.5709i	−0.0649485	−	0.617944i
$557$	−12.3150	+	37.9017i	−0.521803	+	1.60594i	0.248749	+	0.968568i	$0.419981\pi$
$557$	−12.3150	+	37.9017i	−0.521803	+	1.60594i	−0.770552	+	0.637377i	$0.780019\pi$
$558$		0			0
$559$	−13.5375	+	2.87748i	−0.572573	+	0.121704i
$560$	−12.5855			−0.531836
$561$		0			0
$562$	3.91881	−	6.78757i	0.165305	−	0.286316i
$563$	−12.7079	−	22.0107i	−0.535573	−	0.927639i	−0.999135	−	0.0415751i	$-0.986762\pi$
$563$	−12.7079	−	22.0107i	−0.535573	−	0.927639i	0.463563	−	0.886064i	$-0.346571\pi$
$564$		0			0
$565$	0.769736	+	7.32355i	0.0323830	+	0.308104i
$566$	28.1384	−	31.2508i	1.18274	−	1.31357i
$567$		0			0
$568$	1.04099	−	9.90437i	0.0436790	−	0.415578i
$569$	−11.2939	+	8.20552i	−0.473466	+	0.343993i	−0.798791	−	0.601609i	$-0.794527\pi$
$569$	−11.2939	+	8.20552i	−0.473466	+	0.343993i	0.325324	+	0.945602i	$0.394527\pi$
$570$		0			0
$571$	−20.0858	+	8.94279i	−0.840566	+	0.374244i	−0.781420	−	0.624005i	$-0.785504\pi$
$571$	−20.0858	+	8.94279i	−0.840566	+	0.374244i	−0.0591457	+	0.998249i	$0.518838\pi$
$572$	−8.48790	−	26.1231i	−0.354897	−	1.09226i
$573$		0			0
$574$	29.0745	+	12.9448i	1.21355	+	0.540306i
$575$	−2.64633	+	25.1781i	−0.110359	+	1.05000i
$576$		0			0
$577$	26.6247	+	19.3440i	1.10840	+	0.805301i	0.982411	−	0.186731i	$-0.0597893\pi$
$577$	26.6247	+	19.3440i	1.10840	+	0.805301i	0.125990	+	0.992032i	$0.459789\pi$
$578$	−12.7318	−	22.0521i	−0.529573	−	0.917247i
$579$		0			0
$580$	1.18243	+	0.526451i	0.0490977	+	0.0218597i
$581$	−9.87120	−	17.0974i	−0.409526	−	0.709320i
$582$		0			0
$583$	−1.84139	+	5.66722i	−0.0762626	+	0.234712i
$584$	−0.732886	+	6.97295i	−0.0303271	+	0.288543i
$585$		0			0
$586$	2.94647	−	2.14073i	0.121717	−	0.0884328i
$587$	−7.85604	−	24.1784i	−0.324253	−	0.997949i	−0.971777	−	0.235903i	$-0.924195\pi$
$587$	−7.85604	−	24.1784i	−0.324253	−	0.997949i	0.647523	−	0.762046i	$-0.275805\pi$
$588$		0			0
$589$	−5.61171	+	9.71977i	−0.231227	+	0.400496i
$590$	3.11196	−	2.26097i	0.128117	−	0.0930828i
$591$		0			0
$592$	−13.0329	−	14.4745i	−0.535650	−	0.594900i
$593$	−13.7052	+	15.2211i	−0.562804	+	0.625057i	−0.955635	−	0.294553i	$-0.904829\pi$
$593$	−13.7052	+	15.2211i	−0.562804	+	0.625057i	0.392831	+	0.919611i	$0.371496\pi$
$594$		0			0
$595$	−17.1560	−	19.0537i	−0.703327	−	0.781124i
$596$	28.9170	+	50.0858i	1.18449	+	2.05159i
$597$		0			0
$598$	−82.6319	+	17.5640i	−3.37907	+	0.718243i
$599$	−24.3177			−0.993593			−0.496797	−	0.867867i	$-0.665490\pi$
$599$	−24.3177			−0.993593			−0.496797	+	0.867867i	$0.665490\pi$
$600$		0			0
$601$	−6.20409	−	19.0942i	−0.253070	−	0.778870i	−0.994204	−	0.107513i	$-0.965711\pi$
$601$	−6.20409	−	19.0942i	−0.253070	−	0.778870i	0.741133	−	0.671358i	$-0.234289\pi$
$602$	6.45711	−	19.8729i	0.263172	−	0.809961i
$603$		0			0
$604$	−27.5392	−	5.85364i	−1.12055	−	0.238181i
$605$	−8.50549	−	1.80790i	−0.345797	−	0.0735015i
$606$		0			0
$607$	−0.0186590	−	0.0135565i	−0.000757344	−	0.000550243i	0.587407	−	0.809292i	$-0.300149\pi$
$607$	−0.0186590	−	0.0135565i	−0.000757344	−	0.000550243i	−0.588164	+	0.808742i	$0.700149\pi$
$608$	32.6827	−	14.5513i	1.32546	−	0.590133i
$609$		0			0
$610$	8.54927	+	18.6104i	0.346150	+	0.753513i
$611$	−21.5704			−0.872646
$612$		0			0
$613$	−33.7387	−	24.5126i	−1.36269	−	0.990056i	−0.998268	−	0.0588237i	$-0.981265\pi$
$613$	−33.7387	−	24.5126i	−1.36269	−	0.990056i	−0.364427	−	0.931232i	$-0.618735\pi$
$614$	24.9390	−	27.6976i	1.00646	−	1.11778i
$615$		0			0
$616$	8.57060	+	1.82174i	0.345319	+	0.0733999i
$617$	4.43511	+	42.1972i	0.178551	+	1.69880i	0.606572	+	0.795028i	$0.292544\pi$
$617$	4.43511	+	42.1972i	0.178551	+	1.69880i	−0.428021	+	0.903769i	$0.640789\pi$
$618$		0			0
$619$	0.767447	+	2.36196i	0.0308463	+	0.0949351i	0.965294	−	0.261164i	$-0.0841064\pi$
$619$	0.767447	+	2.36196i	0.0308463	+	0.0949351i	−0.934448	+	0.356099i	$0.884106\pi$
$620$	−7.57598	+	1.61033i	−0.304259	+	0.0646722i
$621$		0			0
$622$	30.7115	−	6.52794i	1.23142	−	0.261747i
$623$	−15.4352	+	26.7346i	−0.618400	+	1.07110i
$624$		0			0
$625$	3.05042	+	3.38784i	0.122017	+	0.135514i
$626$	2.87326	+	27.3373i	0.114839	+	1.09262i
$627$		0			0
$628$	14.6923	+	16.3175i	0.586287	+	0.651138i
$629$	4.14762	−	39.4619i	0.165376	−	1.57345i
$630$		0			0
$631$	−8.73991	+	15.1380i	−0.347930	+	0.602633i	−0.985882	−	0.167444i	$-0.946449\pi$
$631$	−8.73991	+	15.1380i	−0.347930	+	0.602633i	0.637951	+	0.770077i	$0.279782\pi$
$632$	−9.43035	+	4.19866i	−0.375119	+	0.167014i
$633$		0			0
$634$	−25.2805	+	18.3674i	−1.00402	+	0.729461i
$635$	−2.88664	−	1.28522i	−0.114553	−	0.0510023i
$636$		0			0
$637$	−13.4534	+	41.4053i	−0.533044	+	1.64054i
$638$	1.41740	+	1.02980i	0.0561153	+	0.0407702i
$639$		0			0
$640$	9.89906	+	4.40735i	0.391295	+	0.174216i
$641$	−35.5364	−	15.8218i	−1.40360	−	0.624925i	−0.441415	−	0.897303i	$-0.645523\pi$
$641$	−35.5364	−	15.8218i	−1.40360	−	0.624925i	−0.962190	+	0.272378i	$0.912190\pi$
$642$		0			0
$643$	−7.93799	−	5.76729i	−0.313044	−	0.227440i	0.420158	−	0.907451i	$-0.361975\pi$
$643$	−7.93799	−	5.76729i	−0.313044	−	0.227440i	−0.733201	+	0.680012i	$0.761975\pi$
$644$	22.0347	−	67.8159i	0.868289	−	2.67232i
$645$		0			0
$646$	47.3663	+	21.0888i	1.86360	+	0.829729i
$647$	29.8155	−	21.6622i	1.17217	−	0.851629i	0.180900	−	0.983502i	$-0.442099\pi$
$647$	29.8155	−	21.6622i	1.17217	−	0.851629i	0.991267	+	0.131873i	$0.0420990\pi$
$648$		0			0
$649$	2.65922	−	1.18396i	0.104384	−	0.0464746i
$650$	−20.2522	+	35.0778i	−0.794356	+	1.37586i
$651$		0			0
$652$	−5.27278	+	50.1671i	−0.206498	+	1.96470i
$653$	−14.6834	−	16.3076i	−0.574607	−	0.638166i	0.383852	−	0.923395i	$-0.374597\pi$
$653$	−14.6834	−	16.3076i	−0.574607	−	0.638166i	−0.958460	+	0.285228i	$0.907931\pi$
$654$		0			0
$655$	1.72906	+	16.4509i	0.0675599	+	0.642790i
$656$	6.82520	+	7.58016i	0.266479	+	0.295955i
$657$		0			0
$658$	16.2836	−	28.2041i	0.634803	−	1.09951i
$659$	−1.97929	+	0.420712i	−0.0771023	+	0.0163886i	−0.246301	−	0.969193i	$-0.579215\pi$
$659$	−1.97929	+	0.420712i	−0.0771023	+	0.0163886i	0.169199	+	0.985582i	$0.445882\pi$
$660$		0			0
$661$	38.0775	−	8.09362i	1.48104	−	0.314805i	0.604685	−	0.796465i	$-0.293299\pi$
$661$	38.0775	−	8.09362i	1.48104	−	0.314805i	0.876358	+	0.481660i	$0.159966\pi$
$662$	0.737575	+	2.27002i	0.0286667	+	0.0882270i
$663$		0			0
$664$	0.608476	+	5.78927i	0.0236135	+	0.224667i
$665$	21.0854	+	4.48183i	0.817656	+	0.173798i
$666$		0			0
$667$	2.01571	−	2.23868i	0.0780488	−	0.0866819i
$668$	−23.1726	−	16.8359i	−0.896576	−	0.651400i
$669$		0			0
$670$	15.8994			0.614247
$671$	3.40013	+	15.1206i	0.131261	+	0.583725i
$672$		0			0
$673$	−30.4872	+	13.5738i	−1.17519	+	0.523230i	−0.899033	−	0.437881i	$-0.855729\pi$
$673$	−30.4872	+	13.5738i	−1.17519	+	0.523230i	−0.276161	+	0.961111i	$0.589062\pi$
$674$	33.4676	+	24.3156i	1.28912	+	0.936603i
$675$		0			0
$676$	−41.6647	−	8.85610i	−1.60249	−	0.340619i
$677$	23.8568	+	5.07092i	0.916892	+	0.194891i	0.642108	−	0.766615i	$-0.278060\pi$
$677$	23.8568	+	5.07092i	0.916892	+	0.194891i	0.274784	+	0.961506i	$0.411394\pi$
$678$		0			0
$679$	−5.35164	+	16.4706i	−0.205377	+	0.632085i
$680$	2.33613	+	7.18986i	0.0895864	+	0.275719i
$681$		0			0
$682$	−10.4839			−0.401450
$683$	12.9711	−	2.75710i	0.496326	−	0.105497i	0.0470542	−	0.998892i	$-0.485017\pi$
$683$	12.9711	−	2.75710i	0.496326	−	0.105497i	0.449272	+	0.893395i	$0.351683\pi$
$684$		0			0
$685$	−8.63923	−	14.9636i	−0.330088	−	0.571729i
$686$	−5.37960	−	5.97465i	−0.205394	−	0.228113i
$687$		0			0
$688$	4.48115	−	4.97682i	0.170842	−	0.189739i
$689$	10.9686	+	12.1819i	0.417870	+	0.464092i
$690$		0			0
$691$	6.43016	−	4.67178i	0.244615	−	0.177723i	−0.458722	−	0.888580i	$-0.651693\pi$
$691$	6.43016	−	4.67178i	0.244615	−	0.177723i	0.703337	+	0.710857i	$0.251693\pi$
$692$	11.9916	−	20.7700i	0.455851	−	0.789557i
$693$		0			0
$694$	−18.4881	−	56.9004i	−0.701797	−	2.15991i
$695$	5.75524	−	4.18143i	0.218309	−	0.158611i
$696$		0			0
$697$	−2.17206	+	20.6658i	−0.0822727	+	0.782772i
$698$	−7.28536	+	22.4220i	−0.275755	+	0.848687i
$699$		0			0
$700$	−17.0944	−	29.6083i	−0.646107	−	1.11909i
$701$	20.9030	+	9.30662i	0.789495	+	0.351506i	0.761552	−	0.648103i	$-0.224438\pi$
$701$	20.9030	+	9.30662i	0.789495	+	0.351506i	0.0279432	+	0.999610i	$0.491104\pi$
$702$		0			0
$703$	16.6804	+	28.8913i	0.629112	+	1.08965i
$704$	18.5552	+	13.4811i	0.699326	+	0.508090i
$705$		0			0
$706$	−2.34121	+	22.2751i	−0.0881125	+	0.838335i
$707$	16.4115	+	7.30686i	0.617217	+	0.274803i
$708$		0			0
$709$	12.4938	+	38.4519i	0.469214	+	1.44409i	0.853604	+	0.520922i	$0.174412\pi$
$709$	12.4938	+	38.4519i	0.469214	+	1.44409i	−0.384390	+	0.923171i	$0.625588\pi$
$710$	20.9080	−	9.30882i	0.784662	−	0.349354i
$711$		0			0
$712$	7.36394	−	5.35022i	0.275975	−	0.200508i
$713$	−1.88427	+	17.9276i	−0.0705663	+	0.671394i
$714$		0			0
$715$	8.92407	−	9.91119i	0.333741	−	0.370657i
$716$	0.462554	+	4.40091i	0.0172865	+	0.164470i
$717$		0			0
$718$	−12.6236	−	21.8647i	−0.471109	−	0.815985i
$719$	−5.40177	+	9.35614i	−0.201452	+	0.348925i	−0.948996	−	0.315287i	$-0.897899\pi$
$719$	−5.40177	+	9.35614i	−0.201452	+	0.348925i	0.747544	+	0.664212i	$0.231233\pi$
$720$		0			0
$721$	3.64025			0.135570
$722$	−3.05918	+	0.650248i	−0.113851	+	0.0241997i
$723$		0			0
$724$	17.3247	−	53.3198i	0.643866	−	1.98162i
$725$	−0.150977	−	1.43645i	−0.00560715	−	0.0533484i
$726$		0			0
$727$	36.8424	+	7.83110i	1.36641	+	0.290440i	0.831995	−	0.554782i	$-0.187199\pi$
$727$	36.8424	+	7.83110i	1.36641	+	0.290440i	0.534415	+	0.845222i	$0.320532\pi$
$728$	16.1285	−	17.9125i	0.597762	−	0.663882i
$729$		0			0
$730$	−14.7198	+	6.55366i	−0.544803	+	0.242562i
$731$	13.6430			0.504606
$732$		0			0
$733$	2.42808			0.0896831			0.0448416	−	0.998994i	$-0.485722\pi$
$733$	2.42808			0.0896831			0.0448416	+	0.998994i	$0.485722\pi$
$734$	−16.1862	+	7.20655i	−0.597442	+	0.265999i
$735$		0			0
$736$	38.4487	−	42.7016i	1.41724	−	1.57400i
$737$	11.7688	+	2.50154i	0.433510	+	0.0921453i
$738$		0			0
$739$	−0.144334	−	1.37325i	−0.00530942	−	0.0505158i	0.991546	−	0.129753i	$-0.0414183\pi$
$739$	−0.144334	−	1.37325i	−0.00530942	−	0.0505158i	−0.996856	+	0.0792369i	$0.974752\pi$
$740$	−7.11422	+	21.8953i	−0.261524	+	0.804888i
$741$		0			0
$742$	−24.2085	+	5.14567i	−0.888722	+	0.188904i
$743$	33.5407			1.23049			0.615245	−	0.788336i	$-0.289057\pi$
$743$	33.5407			1.23049			0.615245	+	0.788336i	$0.289057\pi$
$744$		0			0
$745$	−14.0407	+	24.3192i	−0.514410	+	0.890985i
$746$	8.05596	+	13.9533i	0.294950	+	0.510868i
$747$		0			0
$748$	2.83029	+	26.9284i	0.103486	+	0.984600i
$749$	37.5664	−	41.7217i	1.37265	−	1.52448i
$750$		0			0
$751$	2.83605	−	26.9833i	0.103489	−	0.984633i	−0.812373	−	0.583139i	$-0.801824\pi$
$751$	2.83605	−	26.9833i	0.103489	−	0.984633i	0.915862	−	0.401494i	$-0.131509\pi$
$752$	8.44427	−	6.13512i	0.307931	−	0.223725i
$753$		0			0
$754$	4.40292	−	1.96031i	0.160345	−	0.0713901i
$755$	−4.22439	−	13.0013i	−0.153741	−	0.473167i
$756$		0			0
$757$	3.14580	+	1.40060i	0.114336	+	0.0509057i	0.463107	−	0.886302i	$-0.346734\pi$
$757$	3.14580	+	1.40060i	0.114336	+	0.0509057i	−0.348771	+	0.937208i	$0.613401\pi$
$758$	4.86553	−	46.2924i	0.176724	−	1.68142i
$759$		0			0
$760$	−5.14214	−	3.73598i	−0.186525	−	0.135518i
$761$	−13.2840	−	23.0085i	−0.481543	−	0.834057i	0.518233	−	0.855240i	$-0.326590\pi$
$761$	−13.2840	−	23.0085i	−0.481543	−	0.834057i	−0.999776	+	0.0211827i	$0.993257\pi$
$762$		0			0
$763$	−1.40553	−	0.625781i	−0.0508835	−	0.0226548i
$764$	−5.18574	−	8.98196i	−0.187613	−	0.324956i
$765$		0			0
$766$	−20.5096	+	63.1222i	−0.741043	+	2.28070i
$767$	0.837019	−	7.96371i	0.0302230	−	0.287553i
$768$		0			0
$769$	11.1719	−	8.11685i	0.402869	−	0.292701i	−0.367840	−	0.929889i	$-0.619903\pi$
$769$	11.1719	−	8.11685i	0.402869	−	0.292701i	0.770708	+	0.637188i	$0.219903\pi$
$770$	6.22240	+	19.1506i	0.224240	+	0.690139i
$771$		0			0
$772$	26.9856	−	46.7405i	0.971233	−	1.68223i
$773$	−10.7009	+	7.77468i	−0.384885	+	0.279636i	−0.763356	−	0.645978i	$-0.776450\pi$
$773$	−10.7009	+	7.77468i	−0.384885	+	0.279636i	0.378471	+	0.925613i	$0.376450\pi$
$774$		0			0
$775$	5.78332	+	6.42302i	0.207743	+	0.230722i
$776$	3.41684	−	3.79478i	0.122657	−	0.136225i
$777$		0			0
$778$	34.2415	+	38.0290i	1.22762	+	1.36341i
$779$	−8.73533	−	15.1300i	−0.312976	−	0.542090i
$780$		0			0
$781$	16.9408	−	3.60087i	0.606189	−	0.128849i
$782$	83.2763			2.97796
$783$		0			0
$784$	−6.50996	−	20.0356i	−0.232498	−	0.715557i
$785$	−3.29455	+	10.1396i	−0.117588	+	0.361897i
$786$		0			0
$787$	13.7088	+	2.91390i	0.488666	+	0.103869i	0.445654	−	0.895205i	$-0.352971\pi$
$787$	13.7088	+	2.91390i	0.488666	+	0.103869i	0.0430124	+	0.999075i	$0.486305\pi$
$788$	−2.29906	−	0.488681i	−0.0819007	−	0.0174085i
$789$		0			0
$790$	−19.1922	−	13.9439i	−0.682826	−	0.496102i
$791$	−21.1439	+	9.41386i	−0.751790	+	0.334718i
$792$		0			0
$793$	40.6995	+	12.6974i	1.44528	+	0.450898i
$794$	−2.78066			−0.0986819
$795$		0			0
$796$	56.9252	+	41.3586i	2.01766	+	1.46592i
$797$	6.51823	−	7.23922i	0.230887	−	0.256426i	−0.616557	−	0.787310i	$-0.711473\pi$
$797$	6.51823	−	7.23922i	0.230887	−	0.256426i	0.847445	+	0.530884i	$0.178140\pi$
$798$		0			0
$799$	20.7989	+	4.42095i	0.735814	+	0.156402i
$800$	−2.87981	−	27.3995i	−0.101817	−	0.968720i
$801$		0			0
$802$	13.1112	+	40.3521i	0.462972	+	1.42488i
$803$	−11.9268	+	2.53511i	−0.420887	+	0.0894622i
$804$		0			0
$805$	33.8660	−	7.19843i	1.19362	−	0.253711i
$806$	−14.4202	+	24.9765i	−0.507929	+	0.879758i
$807$		0			0
$808$	−3.54436	−	3.93641i	−0.124690	−	0.138482i
$809$	3.66154	+	34.8372i	0.128733	+	1.22481i	0.847969	+	0.530045i	$0.177825\pi$
$809$	3.66154	+	34.8372i	0.128733	+	1.22481i	−0.719237	+	0.694765i	$0.755508\pi$
$810$		0			0
$811$	−11.7247	−	13.0216i	−0.411711	−	0.457251i	0.501247	−	0.865304i	$-0.332875\pi$
$811$	−11.7247	−	13.0216i	−0.411711	−	0.457251i	−0.912958	+	0.408053i	$0.866208\pi$
$812$	−0.425233	+	4.04582i	−0.0149227	+	0.141980i
$813$		0			0
$814$	−15.5813	+	26.9876i	−0.546125	+	0.945917i
$815$	−22.3753	+	9.96213i	−0.783773	+	0.348958i
$816$		0			0
$817$	−9.27985	+	6.74220i	−0.324661	+	0.235880i
$818$	−21.1477	−	9.41558i	−0.739413	−	0.329208i
$819$		0			0
$820$	3.72564	−	11.4663i	0.130105	−	0.400422i
$821$	−10.2058	−	7.41496i	−0.356185	−	0.258784i	0.395274	−	0.918563i	$-0.370650\pi$
$821$	−10.2058	−	7.41496i	−0.356185	−	0.258784i	−0.751459	+	0.659780i	$0.770650\pi$
$822$		0			0
$823$	−37.3573	−	16.6325i	−1.30219	−	0.579774i	−0.365790	−	0.930698i	$-0.619201\pi$
$823$	−37.3573	−	16.6325i	−1.30219	−	0.579774i	−0.936404	+	0.350924i	$0.885868\pi$
$824$	−0.980552	−	0.436570i	−0.0341591	−	0.0152086i
$825$		0			0
$826$	9.78097	+	7.10629i	0.340323	+	0.247259i
$827$	3.64368	−	11.2141i	0.126703	−	0.389952i	−0.867504	−	0.497429i	$-0.834277\pi$
$827$	3.64368	−	11.2141i	0.126703	−	0.389952i	0.994208	+	0.107477i	$0.0342773\pi$
$828$		0			0
$829$	12.6123	+	5.61538i	0.438045	+	0.195030i	0.613896	−	0.789387i	$-0.289601\pi$
$829$	12.6123	+	5.61538i	0.438045	+	0.195030i	−0.175852	+	0.984417i	$0.556268\pi$
$830$	−10.8227	+	7.86315i	−0.375661	+	0.272934i
$831$		0			0
$832$	57.6388	−	25.6624i	1.99826	−	0.889685i
$833$	21.4585	−	37.1671i	0.743491	−	1.28776i
$834$		0			0
$835$	1.45374	−	13.8314i	0.0503087	−	0.478655i
$836$	−15.2328	−	16.9177i	−0.526837	−	0.585112i
$837$		0			0
$838$	−8.30383	−	79.0056i	−0.286851	−	2.72920i
$839$	−7.79560	−	8.65789i	−0.269134	−	0.298903i	0.593395	−	0.804912i	$-0.297787\pi$
$839$	−7.79560	−	8.65789i	−0.269134	−	0.298903i	−0.862529	+	0.506008i	$0.831121\pi$
$840$		0			0
$841$	14.4141	−	24.9659i	0.497037	−	0.860893i
$842$	21.6856	−	4.60941i	0.747334	−	0.158851i
$843$		0			0
$844$	4.26755	−	0.907095i	0.146895	−	0.0312235i
$845$	−6.39117	−	19.6700i	−0.219863	−	0.676668i
$846$		0			0
$847$	−2.85678	−	27.1805i	−0.0981601	−	0.933931i
$848$	−7.75872	−	1.64917i	−0.266436	−	0.0566326i
$849$		0			0
$850$	26.7172	−	29.6725i	0.916392	−	1.01776i
$851$	43.3487	+	31.4947i	1.48597	+	1.07962i
$852$		0			0
$853$	−18.2376			−0.624444			−0.312222	−	0.950009i	$-0.601073\pi$
$853$	−18.2376			−0.624444			−0.312222	+	0.950009i	$0.601073\pi$
$854$	−47.3266	+	43.6307i	−1.61948	+	1.49301i
$855$		0			0
$856$	−15.1226	+	6.73304i	−0.516881	+	0.230130i
$857$	−40.7310	−	29.5928i	−1.39134	−	1.01087i	−0.995716	−	0.0924606i	$-0.970527\pi$
$857$	−40.7310	−	29.5928i	−1.39134	−	1.01087i	−0.395629	−	0.918411i	$-0.629473\pi$
$858$		0			0
$859$	−49.8985	−	10.6063i	−1.70252	−	0.361881i	−0.748848	−	0.662741i	$-0.769393\pi$
$859$	−49.8985	−	10.6063i	−1.70252	−	0.361881i	−0.953668	+	0.300860i	$0.902726\pi$
$860$	−7.74278	−	1.64578i	−0.264027	−	0.0561206i
$861$		0			0
$862$	12.6740	−	39.0066i	0.431678	−	1.32857i
$863$	−9.13512	−	28.1150i	−0.310963	−	0.957046i	−0.977384	−	0.211470i	$-0.932175\pi$
$863$	−9.13512	−	28.1150i	−0.310963	−	0.957046i	0.666421	−	0.745575i	$-0.267825\pi$
$864$		0			0
$865$	11.6450			0.395943
$866$	−32.7588	+	6.96311i	−1.11319	+	0.236616i
$867$		0			0
$868$	−12.1717	−	21.0820i	−0.413135	−	0.715571i
$869$	−12.0123	−	13.3410i	−0.407488	−	0.452561i
$870$		0			0
$871$	22.1470	−	24.5968i	0.750424	−	0.833430i
$872$	0.303549	+	0.337125i	0.0102795	+	0.0114165i
$873$		0			0
$874$	−56.6437	+	41.1540i	−1.91600	+	1.39206i
$875$	20.2119	−	35.0080i	0.683286	−	1.18349i
$876$		0			0
$877$	−1.77511	−	5.46322i	−0.0599411	−	0.184480i	0.916602	−	0.399800i	$-0.130920\pi$
$877$	−1.77511	−	5.46322i	−0.0599411	−	0.184480i	−0.976543	+	0.215320i	$0.930920\pi$
$878$	40.1914	−	29.2007i	1.35639	−	0.985477i
$879$		0			0
$880$	−0.674578	+	6.41818i	−0.0227400	+	0.216357i
$881$	10.8991	−	33.5439i	0.367199	−	1.13012i	−0.581393	−	0.813623i	$-0.697492\pi$
$881$	10.8991	−	33.5439i	0.367199	−	1.13012i	0.948593	−	0.316500i	$-0.102508\pi$
$882$		0			0
$883$	20.2089	+	35.0028i	0.680083	+	1.17794i	0.974955	+	0.222401i	$0.0713896\pi$
$883$	20.2089	+	35.0028i	0.680083	+	1.17794i	−0.294872	+	0.955537i	$0.595277\pi$
$884$	68.0461	+	30.2961i	2.28864	+	1.01897i
$885$		0			0
$886$	15.2369	+	26.3911i	0.511895	+	0.886628i
$887$	18.8828	+	13.7192i	0.634023	+	0.460644i	0.857792	−	0.513998i	$-0.171836\pi$
$887$	18.8828	+	13.7192i	0.634023	+	0.460644i	−0.223769	+	0.974642i	$0.571836\pi$
$888$		0			0
$889$	1.03811	−	9.87699i	0.0348172	−	0.331264i
$890$	19.1096	+	8.50814i	0.640555	+	0.285194i
$891$		0			0
$892$	−11.5549	−	35.5624i	−0.386887	−	1.19072i
$893$	−16.3320	+	7.27147i	−0.546529	+	0.243330i
$894$		0			0
$895$	−1.73828	+	1.26293i	−0.0581043	+	0.0422153i
$896$	−3.55997	+	33.8708i	−0.118930	+	1.13154i
$897$		0			0
$898$	−11.3328	+	12.5863i	−0.378179	+	0.420011i
$899$	−0.107500	−	1.02280i	−0.00358533	−	0.0341122i
$900$		0			0
$901$	−8.07957	−	13.9942i	−0.269170	−	0.466216i
$902$	8.15977	−	14.1331i	0.271691	−	0.470582i
$903$		0			0
$904$	6.82439			0.226976
$905$	26.6269	−	5.65973i	0.885109	−	0.188136i
$906$		0			0
$907$	0.499891	−	1.53850i	0.0165986	−	0.0510852i	−0.942414	−	0.334448i	$-0.891450\pi$
$907$	0.499891	−	1.53850i	0.0165986	−	0.0510852i	0.959013	+	0.283363i	$0.0914501\pi$
$908$	−1.66413	−	15.8331i	−0.0552260	−	0.525441i
$909$		0			0
$910$	54.1821	+	11.5168i	1.79612	+	0.381777i
$911$	24.3368	−	27.0288i	0.806314	−	0.895503i	−0.189956	−	0.981793i	$-0.560834\pi$
$911$	24.3368	−	27.0288i	0.806314	−	0.895503i	0.996270	+	0.0862900i	$0.0275012\pi$
$912$		0			0
$913$	−9.24817	+	4.11755i	−0.306070	+	0.136271i
$914$	−68.5715			−2.26814
$915$		0			0
$916$	−4.62840			−0.152927
$917$	−47.4955	+	21.1464i	−1.56844	+	0.698315i
$918$		0			0
$919$	11.4978	−	12.7696i	0.379277	−	0.421230i	−0.523037	−	0.852310i	$-0.675201\pi$
$919$	11.4978	−	12.7696i	0.379277	−	0.421230i	0.902313	+	0.431081i	$0.141868\pi$
$920$	−9.98557	−	2.12250i	−0.329214	−	0.0699767i
$921$		0			0
$922$	7.00988	+	66.6946i	0.230858	+	2.19647i
$923$	14.7227	−	45.3119i	0.484604	−	1.49146i
$924$		0			0
$925$	25.1293	−	5.34140i	0.826247	−	0.175624i
$926$	32.8069			1.07810
$927$		0			0
$928$	−1.63911	+	2.83902i	−0.0538064	+	0.0931954i
$929$	11.5819	+	20.0604i	0.379990	+	0.658162i	0.991060	−	0.133415i	$-0.0425942\pi$
$929$	11.5819	+	20.0604i	0.379990	+	0.658162i	−0.611071	+	0.791576i	$0.709261\pi$
$930$		0			0
$931$	3.77168	+	35.8852i	0.123612	+	1.17609i
$932$	19.3465	−	21.4865i	0.633717	−	0.703814i
$933$		0			0
$934$	−5.48140	+	52.1520i	−0.179357	+	1.70647i
$935$	−10.6362	+	7.72768i	−0.347842	+	0.252722i
$936$		0			0
$937$	2.44613	−	1.08909i	0.0799116	−	0.0355789i	−0.366392	−	0.930461i	$-0.619407\pi$
$937$	2.44613	−	1.08909i	0.0799116	−	0.0355789i	0.446303	+	0.894882i	$0.352740\pi$
$938$	15.4422	+	47.5263i	0.504207	+	1.55179i
$939$		0			0
$940$	−11.2706	−	5.01801i	−0.367608	−	0.163669i
$941$	−5.08037	+	48.3365i	−0.165615	+	1.57572i	0.524108	+	0.851652i	$0.324399\pi$
$941$	−5.08037	+	48.3365i	−0.165615	+	1.57572i	−0.689723	+	0.724073i	$0.742268\pi$
$942$		0			0
$943$	−22.7012	−	16.4934i	−0.739254	−	0.537099i
$944$	1.93739	+	3.35565i	0.0630566	+	0.109217i
$945$		0			0
$946$	−9.78840	−	4.35808i	−0.318248	−	0.141693i
$947$	27.8693	+	48.2710i	0.905630	+	1.56860i	0.820070	+	0.572263i	$0.193935\pi$
$947$	27.8693	+	48.2710i	0.905630	+	1.56860i	0.0855598	+	0.996333i	$0.472732\pi$
$948$		0			0
$949$	−10.3652	+	31.9008i	−0.336468	+	1.03554i
$950$	−3.50903	+	33.3862i	−0.113848	+	1.08319i
$951$		0			0
$952$	−19.2229	+	13.9663i	−0.623018	+	0.452649i
$953$	8.35678	+	25.7195i	0.270703	+	0.833137i	0.990325	+	0.138771i	$0.0443151\pi$
$953$	8.35678	+	25.7195i	0.270703	+	0.833137i	−0.719622	+	0.694366i	$0.755685\pi$
$954$		0			0
$955$	2.51794	−	4.36119i	0.0814785	−	0.141125i
$956$	−11.9497	+	8.68196i	−0.386481	+	0.280795i
$957$		0			0
$958$	12.5958	+	13.9890i	0.406951	+	0.451965i
$959$	36.3382	−	40.3576i	1.17342	−	1.30322i
$960$		0			0
$961$	−16.6252	−	18.4641i	−0.536295	−	0.595616i
$962$	42.8628	+	74.2406i	1.38195	+	2.39361i
$963$		0			0
$964$	43.0315	−	9.14664i	1.38595	−	0.294593i
$965$	26.2057			0.843593
$966$		0			0
$967$	−6.20814	−	19.1067i	−0.199640	−	0.614430i	−0.999891	−	0.0147641i	$-0.995300\pi$
$967$	−6.20814	−	19.1067i	−0.199640	−	0.614430i	0.800251	−	0.599666i	$-0.204700\pi$
$968$	−2.49020	+	7.66404i	−0.0800380	+	0.246332i
$969$		0			0
$970$	11.4785	+	2.43984i	0.368554	+	0.0783385i
$971$	20.4636	+	4.34968i	0.656710	+	0.139588i	0.524202	−	0.851594i	$-0.324364\pi$
$971$	20.4636	+	4.34968i	0.656710	+	0.139588i	0.132508	+	0.991182i	$0.457697\pi$
$972$		0			0
$973$	18.0889	+	13.1423i	0.579902	+	0.421323i
$974$	−28.5254	+	12.7003i	−0.914013	+	0.406945i
$975$		0			0
$976$	−19.5442	+	6.60515i	−0.625595	+	0.211426i
$977$	−60.1275			−1.92365			−0.961824	−	0.273669i	$-0.911763\pi$
$977$	−60.1275			−1.92365			−0.961824	+	0.273669i	$0.911763\pi$
$978$		0			0
$979$	12.8064	+	9.30439i	0.409294	+	0.297369i
$980$	−16.6617	+	18.5047i	−0.532240	+	0.591112i
$981$		0			0
$982$	−55.2628	−	11.7465i	−1.76351	−	0.374845i
$983$	−3.48984	−	33.2036i	−0.111309	−	1.05903i	−0.897490	−	0.441035i	$-0.854612\pi$
$983$	−3.48984	−	33.2036i	−0.111309	−	1.05903i	0.786182	−	0.617996i	$-0.212055\pi$
$984$		0			0
$985$	−0.352665	−	1.08539i	−0.0112369	−	0.0345835i
$986$	−4.64722	+	0.987797i	−0.147998	+	0.0314579i
$987$		0			0
$988$	−61.2561	+	13.0204i	−1.94882	+	0.414233i
$989$	−9.21161	+	15.9550i	−0.292912	+	0.507339i
$990$		0			0
$991$	−20.1793	−	22.4114i	−0.641018	−	0.711922i	0.331838	−	0.943337i	$-0.392331\pi$
$991$	−20.1793	−	22.4114i	−0.641018	−	0.711922i	−0.972855	+	0.231414i	$0.925665\pi$
$992$	−2.05051	−	19.5093i	−0.0651038	−	0.619421i
$993$		0			0
$994$	48.1326	+	53.4567i	1.52667	+	1.69554i
$995$	−3.57121	+	33.9778i	−0.113215	+	1.07717i
$996$		0			0
$997$	18.2499	−	31.6097i	0.577979	−	1.00109i	−0.417732	−	0.908570i	$-0.637175\pi$
$997$	18.2499	−	31.6097i	0.577979	−	1.00109i	0.995711	−	0.0925188i	$-0.0294918\pi$
$998$	30.7453	−	13.6887i	0.973224	−	0.433307i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	549.2.bl.b.361.3		32
3.2	odd	2		61.2.i.a.56.2	yes	32
12.11	even	2		976.2.bw.c.849.1		32
61.12	even	15	inner	549.2.bl.b.73.3		32
183.77	odd	30		3721.2.a.j.1.4		16
183.134	odd	30		61.2.i.a.12.2	✓	32
183.167	odd	30		3721.2.a.l.1.13		16
732.683	even	30		976.2.bw.c.561.1		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
61.2.i.a.12.2	✓	32	183.134	odd	30
61.2.i.a.56.2	yes	32	3.2	odd	2
549.2.bl.b.73.3		32	61.12	even	15	inner
549.2.bl.b.361.3		32	1.1	even	1	trivial
976.2.bw.c.561.1		32	732.683	even	30
976.2.bw.c.849.1		32	12.11	even	2
3721.2.a.j.1.4		16	183.77	odd	30
3721.2.a.l.1.13		16	183.167	odd	30

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:	\( N \)	\(=\)	\( 549 = 3^{2} \cdot 61 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	549.bl (of order \(15\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(1.94561 - 0.866241i) q^{2} +(1.69676 - 1.88444i) q^{4} +(1.20434 + 0.255990i) q^{5} +(0.404506 + 3.84862i) q^{7} +(0.352600 - 1.08519i) q^{8} +O(q^{10})\)	\(q+(1.94561 - 0.866241i) q^{2} +(1.69676 - 1.88444i) q^{4} +(1.20434 + 0.255990i) q^{5} +(0.404506 + 3.84862i) q^{7} +(0.352600 - 1.08519i) q^{8} +(2.56491 - 0.545189i) q^{10} +1.98434 q^{11} +(2.72937 - 4.72741i) q^{13} +(4.12084 + 7.13751i) q^{14} +(0.276104 + 2.62696i) q^{16} +(-3.60066 + 3.99894i) q^{17} +(0.472909 - 4.49943i) q^{19} +(2.52586 - 1.83515i) q^{20} +(3.86075 - 1.71892i) q^{22} +(-2.24547 - 6.91085i) q^{23} +(-3.18283 - 1.41709i) q^{25} +(1.21521 - 11.5620i) q^{26} +(7.93884 + 5.76791i) q^{28} +(0.207283 + 0.359024i) q^{29} +(-2.26627 - 1.00901i) q^{31} +(3.95380 + 6.84819i) q^{32} +(-3.54143 + 10.8994i) q^{34} +(-0.498045 + 4.73858i) q^{35} +(-5.96555 + 4.33423i) q^{37} +(-2.97749 - 9.16378i) q^{38} +(0.702446 - 1.21667i) q^{40} +(3.12409 - 2.26979i) q^{41} +(-1.69649 - 1.88414i) q^{43} +(3.36695 - 3.73937i) q^{44} +(-10.3553 - 11.5007i) q^{46} +(-1.97577 - 3.42213i) q^{47} +(-7.80121 + 1.65820i) q^{49} -7.42009 q^{50} +(-4.27744 - 13.1646i) q^{52} +(-0.927961 + 2.85597i) q^{53} +(2.38981 + 0.507970i) q^{55} +(4.31911 + 0.918056i) q^{56} +(0.714292 + 0.518963i) q^{58} +(1.34010 - 0.596653i) q^{59} +(1.71348 + 7.61997i) q^{61} -5.28333 q^{62} +(9.35082 + 6.79377i) q^{64} +(4.49725 - 4.99470i) q^{65} +(5.93084 + 1.26064i) q^{67} +(1.42631 + 13.5705i) q^{68} +(3.13575 + 9.65085i) q^{70} +(8.53723 - 1.81465i) q^{71} +(-6.01044 + 1.27756i) q^{73} +(-7.85214 + 13.6003i) q^{74} +(-7.67650 - 8.52561i) q^{76} +(0.802678 + 7.63697i) q^{77} +(-6.05353 - 6.72312i) q^{79} +(-0.339951 + 3.23442i) q^{80} +(4.11208 - 7.12233i) q^{82} +(-4.66057 + 2.07502i) q^{83} +(-5.36009 + 3.89433i) q^{85} +(-4.93282 - 2.19623i) q^{86} +(0.699678 - 2.15339i) q^{88} +(6.45373 + 4.68891i) q^{89} +(19.2980 + 8.59204i) q^{91} +(-16.8331 - 7.49459i) q^{92} +(-6.80846 - 4.94664i) q^{94} +(1.72135 - 5.29776i) q^{95} +(4.08831 + 1.82023i) q^{97} +(-13.7417 + 9.98393i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 10 q^{2} - 10 q^{4} - 2 q^{5} + q^{7} + 4 q^{8}+O(q^{10}) \) 32 * q + 10 * q^2 - 10 * q^4 - 2 * q^5 + q^7 + 4 * q^8	\( 32 q + 10 q^{2} - 10 q^{4} - 2 q^{5} + q^{7} + 4 q^{8} + 15 q^{10} + 18 q^{11} - 11 q^{14} + 6 q^{16} + 24 q^{17} + 9 q^{19} + 4 q^{20} + q^{22} + 2 q^{23} + 28 q^{25} - 16 q^{26} + 4 q^{28} + 4 q^{29} - 11 q^{31} - 34 q^{32} + 18 q^{34} + 58 q^{35} - 14 q^{37} + 24 q^{38} - 60 q^{40} - 11 q^{41} + 40 q^{43} - 29 q^{44} - 89 q^{46} - 40 q^{47} + q^{49} + 56 q^{50} - 67 q^{52} - 17 q^{53} - 60 q^{55} + 102 q^{56} + 73 q^{58} + 11 q^{59} - 55 q^{61} + 74 q^{62} + 6 q^{64} - 59 q^{65} - 13 q^{67} + 3 q^{68} + 44 q^{70} - 63 q^{71} - 46 q^{73} + 10 q^{74} + 55 q^{76} + 31 q^{77} - 49 q^{79} - 74 q^{80} + 39 q^{82} - 39 q^{83} + 21 q^{85} - 74 q^{86} + 70 q^{88} - 32 q^{89} + 70 q^{91} - 77 q^{92} - 64 q^{94} - 47 q^{95} + 37 q^{97} - 127 q^{98}+O(q^{100}) \) 32 * q + 10 * q^2 - 10 * q^4 - 2 * q^5 + q^7 + 4 * q^8 + 15 * q^10 + 18 * q^11 - 11 * q^14 + 6 * q^16 + 24 * q^17 + 9 * q^19 + 4 * q^20 + q^22 + 2 * q^23 + 28 * q^25 - 16 * q^26 + 4 * q^28 + 4 * q^29 - 11 * q^31 - 34 * q^32 + 18 * q^34 + 58 * q^35 - 14 * q^37 + 24 * q^38 - 60 * q^40 - 11 * q^41 + 40 * q^43 - 29 * q^44 - 89 * q^46 - 40 * q^47 + q^49 + 56 * q^50 - 67 * q^52 - 17 * q^53 - 60 * q^55 + 102 * q^56 + 73 * q^58 + 11 * q^59 - 55 * q^61 + 74 * q^62 + 6 * q^64 - 59 * q^65 - 13 * q^67 + 3 * q^68 + 44 * q^70 - 63 * q^71 - 46 * q^73 + 10 * q^74 + 55 * q^76 + 31 * q^77 - 49 * q^79 - 74 * q^80 + 39 * q^82 - 39 * q^83 + 21 * q^85 - 74 * q^86 + 70 * q^88 - 32 * q^89 + 70 * q^91 - 77 * q^92 - 64 * q^94 - 47 * q^95 + 37 * q^97 - 127 * q^98

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