LMFDB - Embedded newform 975.2.o.p.551.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [975,2,Mod(476,975)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(975, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 0, 1]))

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

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

chi := DirichletCharacter("975.476");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 975 = 3 \cdot 5^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	975.o (of order $4$, degree $2$, 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:	$7.78541419707$
Analytic rank:	$0$
Dimension:	$40$
Relative dimension:	$20$ over $\Q(i)$
Twist minimal:	no (minimal twist has level 195)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			551.8
Character	$\chi$	$=$	975.551
Dual form			975.2.o.p.476.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.483812 - 0.483812i) q^{2} +(-1.53965 - 0.793397i) q^{3} -1.53185i q^{4} +(0.361045 + 1.12876i) q^{6} +(1.24531 + 1.24531i) q^{7} +(-1.70875 + 1.70875i) q^{8} +(1.74104 + 2.44311i) q^{9} +O(q^{10})$	\(q+(-0.483812 - 0.483812i) q^{2} +(-1.53965 - 0.793397i) q^{3} -1.53185i q^{4} +(0.361045 + 1.12876i) q^{6} +(1.24531 + 1.24531i) q^{7} +(-1.70875 + 1.70875i) q^{8} +(1.74104 + 2.44311i) q^{9} +(0.387103 - 0.387103i) q^{11} +(-1.21537 + 2.35852i) q^{12} +(0.874878 - 3.49780i) q^{13} -1.20499i q^{14} -1.41028 q^{16} +6.75010 q^{17} +(0.339668 - 2.02434i) q^{18} +(1.33304 - 1.33304i) q^{19} +(-0.929314 - 2.90536i) q^{21} -0.374570 q^{22} +1.69635 q^{23} +(3.98660 - 1.27516i) q^{24} +(-2.11555 + 1.26900i) q^{26} +(-0.742237 - 5.14287i) q^{27} +(1.90763 - 1.90763i) q^{28} +3.85370i q^{29} +(4.06109 - 4.06109i) q^{31} +(4.09981 + 4.09981i) q^{32} +(-0.903130 + 0.288877i) q^{33} +(-3.26578 - 3.26578i) q^{34} +(3.74248 - 2.66702i) q^{36} +(2.36718 + 2.36718i) q^{37} -1.28988 q^{38} +(-4.12215 + 4.69126i) q^{39} +(-5.72121 - 5.72121i) q^{41} +(-0.956036 + 1.85526i) q^{42} -11.7392i q^{43} +(-0.592985 - 0.592985i) q^{44} +(-0.820713 - 0.820713i) q^{46} +(-5.99016 + 5.99016i) q^{47} +(2.17133 + 1.11891i) q^{48} -3.89841i q^{49} +(-10.3928 - 5.35551i) q^{51} +(-5.35811 - 1.34018i) q^{52} +8.81372i q^{53} +(-2.12908 + 2.84728i) q^{54} -4.25585 q^{56} +(-3.11005 + 0.994786i) q^{57} +(1.86446 - 1.86446i) q^{58} +(-1.30531 + 1.30531i) q^{59} -1.16343 q^{61} -3.92960 q^{62} +(-0.874290 + 5.21056i) q^{63} -1.14652i q^{64} +(0.576707 + 0.297183i) q^{66} +(4.66845 - 4.66845i) q^{67} -10.3402i q^{68} +(-2.61178 - 1.34588i) q^{69} +(0.915921 + 0.915921i) q^{71} +(-7.14967 - 1.19966i) q^{72} +(-8.11348 - 8.11348i) q^{73} -2.29054i q^{74} +(-2.04202 - 2.04202i) q^{76} +0.964126 q^{77} +(4.26403 - 0.275341i) q^{78} -3.85408 q^{79} +(-2.93755 + 8.50710i) q^{81} +5.53597i q^{82} +(-11.9347 - 11.9347i) q^{83} +(-4.45059 + 1.42357i) q^{84} +(-5.67957 + 5.67957i) q^{86} +(3.05751 - 5.93334i) q^{87} +1.32293i q^{88} +(5.99694 - 5.99694i) q^{89} +(5.44533 - 3.26635i) q^{91} -2.59855i q^{92} +(-9.47471 + 3.03059i) q^{93} +5.79622 q^{94} +(-3.05949 - 9.56505i) q^{96} +(-1.03487 + 1.03487i) q^{97} +(-1.88610 + 1.88610i) q^{98} +(1.61970 + 0.271772i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q + 12 q^{6} + 16 q^{7}+O(q^{10}) $ 40 * q + 12 * q^6 + 16 * q^7	$ 40 q + 12 q^{6} + 16 q^{7} - 64 q^{16} - 4 q^{18} - 16 q^{19} - 12 q^{21} + 8 q^{24} + 24 q^{27} - 32 q^{28} + 32 q^{31} + 4 q^{33} - 16 q^{34} - 32 q^{37} - 8 q^{39} - 8 q^{42} - 40 q^{46} - 8 q^{48} - 32 q^{54} + 36 q^{57} - 24 q^{58} + 8 q^{61} - 8 q^{63} - 48 q^{66} + 32 q^{67} - 132 q^{72} + 64 q^{73} + 16 q^{76} + 12 q^{78} + 40 q^{79} + 72 q^{81} + 124 q^{84} - 16 q^{87} + 8 q^{91} + 108 q^{93} - 32 q^{94} - 76 q^{96} - 24 q^{97} - 20 q^{99}+O(q^{100}) $ 40 * q + 12 * q^6 + 16 * q^7 - 64 * q^16 - 4 * q^18 - 16 * q^19 - 12 * q^21 + 8 * q^24 + 24 * q^27 - 32 * q^28 + 32 * q^31 + 4 * q^33 - 16 * q^34 - 32 * q^37 - 8 * q^39 - 8 * q^42 - 40 * q^46 - 8 * q^48 - 32 * q^54 + 36 * q^57 - 24 * q^58 + 8 * q^61 - 8 * q^63 - 48 * q^66 + 32 * q^67 - 132 * q^72 + 64 * q^73 + 16 * q^76 + 12 * q^78 + 40 * q^79 + 72 * q^81 + 124 * q^84 - 16 * q^87 + 8 * q^91 + 108 * q^93 - 32 * q^94 - 76 * q^96 - 24 * q^97 - 20 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/975\mathbb{Z}\right)^\times$.

$n$	$301$	$326$	$352$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$-1$	$1$

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 $

$2$	−0.483812	−	0.483812i	−0.342107	−	0.342107i	0.515052	−	0.857159i	$-0.327773\pi$
$2$	−0.483812	−	0.483812i	−0.342107	−	0.342107i	−0.857159	+	0.515052i	$0.827773\pi$
$3$	−1.53965	−	0.793397i	−0.888917	−	0.458068i
$3$	−1.53965	−	0.793397i	−0.888917	−	0.458068i
$4$		−	1.53185i		−	0.765926i
$5$		0			0
$5$		0			0
$6$	0.361045	+	1.12876i	0.147396	+	0.460813i
$7$	1.24531	+	1.24531i	0.470683	+	0.470683i	0.902135	−	0.431453i	$-0.141999\pi$
$7$	1.24531	+	1.24531i	0.470683	+	0.470683i	−0.431453	+	0.902135i	$0.641999\pi$
$8$	−1.70875	+	1.70875i	−0.604135	+	0.604135i
$9$	1.74104	+	2.44311i	0.580347	+	0.814369i
$10$		0			0
$11$	0.387103	−	0.387103i	0.116716	−	0.116716i	−0.646337	−	0.763053i	$-0.723700\pi$
$11$	0.387103	−	0.387103i	0.116716	−	0.116716i	0.763053	+	0.646337i	$0.223700\pi$
$12$	−1.21537	+	2.35852i	−0.350846	+	0.680845i
$13$	0.874878	−	3.49780i	0.242647	−	0.970115i
$13$	0.874878	−	3.49780i	0.242647	−	0.970115i
$14$		−	1.20499i		−	0.322047i
$15$		0			0
$16$	−1.41028			−0.352569
$17$	6.75010			1.63714			0.818570	−	0.574407i	$-0.194767\pi$
$17$	6.75010			1.63714			0.818570	+	0.574407i	$0.194767\pi$
$18$	0.339668	−	2.02434i	0.0800606	−	0.477142i
$19$	1.33304	−	1.33304i	0.305821	−	0.305821i	−0.537465	−	0.843286i	$-0.680618\pi$
$19$	1.33304	−	1.33304i	0.305821	−	0.305821i	0.843286	+	0.537465i	$0.180618\pi$
$20$		0			0
$21$	−0.929314	−	2.90536i	−0.202793	−	0.634003i
$22$	−0.374570			−0.0798586
$23$	1.69635			0.353713			0.176856	−	0.984237i	$-0.443407\pi$
$23$	1.69635			0.353713			0.176856	+	0.984237i	$0.443407\pi$
$24$	3.98660	−	1.27516i	0.813761	−	0.260291i
$25$		0			0
$26$	−2.11555	+	1.26900i	−0.414894	+	0.248871i
$27$	−0.742237	−	5.14287i	−0.142844	−	0.989745i
$28$	1.90763	−	1.90763i	0.360508	−	0.360508i
$29$			3.85370i			0.715614i	0.933796	+	0.357807i	$0.116475\pi$
$29$			3.85370i			0.715614i	−0.933796	+	0.357807i	$0.883525\pi$
$30$		0			0
$31$	4.06109	−	4.06109i	0.729393	−	0.729393i	−0.241106	−	0.970499i	$-0.577510\pi$
$31$	4.06109	−	4.06109i	0.729393	−	0.729393i	0.970499	+	0.241106i	$0.0775102\pi$
$32$	4.09981	+	4.09981i	0.724751	+	0.724751i
$33$	−0.903130	+	0.288877i	−0.157215	+	0.0502869i
$34$	−3.26578	−	3.26578i	−0.560076	−	0.560076i
$35$		0			0
$36$	3.74248	−	2.66702i	0.623747	−	0.444503i
$37$	2.36718	+	2.36718i	0.389163	+	0.389163i	0.874389	−	0.485226i	$-0.161263\pi$
$37$	2.36718	+	2.36718i	0.389163	+	0.389163i	−0.485226	+	0.874389i	$0.661263\pi$
$38$	−1.28988			−0.209247
$39$	−4.12215	+	4.69126i	−0.660072	+	0.751202i
$40$		0			0
$41$	−5.72121	−	5.72121i	−0.893502	−	0.893502i	0.101349	−	0.994851i	$-0.467684\pi$
$41$	−5.72121	−	5.72121i	−0.893502	−	0.893502i	−0.994851	+	0.101349i	$0.967684\pi$
$42$	−0.956036	+	1.85526i	−0.147520	+	0.286273i
$43$		−	11.7392i		−	1.79021i	−0.445853	−	0.895106i	$-0.647100\pi$
$43$		−	11.7392i		−	1.79021i	0.445853	−	0.895106i	$-0.352900\pi$
$44$	−0.592985	−	0.592985i	−0.0893958	−	0.0893958i
$45$		0			0
$46$	−0.820713	−	0.820713i	−0.121008	−	0.121008i
$47$	−5.99016	+	5.99016i	−0.873755	+	0.873755i	−0.992879	−	0.119124i	$-0.961991\pi$
$47$	−5.99016	+	5.99016i	−0.873755	+	0.873755i	0.119124	+	0.992879i	$0.461991\pi$
$48$	2.17133	+	1.11891i	0.313405	+	0.161501i
$49$		−	3.89841i		−	0.556916i
$50$		0			0
$51$	−10.3928	−	5.35551i	−1.45528	−	0.749922i
$52$	−5.35811	−	1.34018i	−0.743036	−	0.185850i
$53$			8.81372i			1.21066i	0.795976	+	0.605328i	$0.206958\pi$
$53$			8.81372i			1.21066i	−0.795976	+	0.605328i	$0.793042\pi$
$54$	−2.12908	+	2.84728i	−0.289731	+	0.387466i
$55$		0			0
$56$	−4.25585			−0.568712
$57$	−3.11005	+	0.994786i	−0.411936	+	0.131763i
$58$	1.86446	−	1.86446i	0.244816	−	0.244816i
$59$	−1.30531	+	1.30531i	−0.169937	+	0.169937i	−0.786952	−	0.617015i	$-0.788342\pi$
$59$	−1.30531	+	1.30531i	−0.169937	+	0.169937i	0.617015	+	0.786952i	$0.288342\pi$
$60$		0			0
$61$	−1.16343			−0.148961			−0.0744807	−	0.997222i	$-0.523730\pi$
$61$	−1.16343			−0.148961			−0.0744807	+	0.997222i	$0.523730\pi$
$62$	−3.92960			−0.499060
$63$	−0.874290	+	5.21056i	−0.110150	+	0.656469i
$64$		−	1.14652i		−	0.143315i
$65$		0			0
$66$	0.576707	+	0.297183i	0.0709877	+	0.0365807i
$67$	4.66845	−	4.66845i	0.570341	−	0.570341i	−0.361882	−	0.932224i	$-0.617866\pi$
$67$	4.66845	−	4.66845i	0.570341	−	0.570341i	0.932224	+	0.361882i	$0.117866\pi$
$68$		−	10.3402i		−	1.25393i
$69$	−2.61178	−	1.34588i	−0.314421	−	0.162025i
$70$		0			0
$71$	0.915921	+	0.915921i	0.108700	+	0.108700i	0.759365	−	0.650665i	$-0.225510\pi$
$71$	0.915921	+	0.915921i	0.108700	+	0.108700i	−0.650665	+	0.759365i	$0.725510\pi$
$72$	−7.14967	−	1.19966i	−0.842597	−	0.141381i
$73$	−8.11348	−	8.11348i	−0.949611	−	0.949611i	0.0491790	−	0.998790i	$-0.484340\pi$
$73$	−8.11348	−	8.11348i	−0.949611	−	0.949611i	−0.998790	+	0.0491790i	$0.984340\pi$
$74$		−	2.29054i		−	0.266270i
$75$		0			0
$76$	−2.04202	−	2.04202i	−0.234236	−	0.234236i
$77$	0.964126			0.109872
$78$	4.26403	−	0.275341i	0.482806	−	0.0311762i
$79$	−3.85408			−0.433617			−0.216809	−	0.976214i	$-0.569565\pi$
$79$	−3.85408			−0.433617			−0.216809	+	0.976214i	$0.569565\pi$
$80$		0			0
$81$	−2.93755	+	8.50710i	−0.326395	+	0.945234i
$82$			5.53597i			0.611346i
$83$	−11.9347	−	11.9347i	−1.31000	−	1.31000i	−0.921412	−	0.388586i	$-0.872964\pi$
$83$	−11.9347	−	11.9347i	−1.31000	−	1.31000i	−0.388586	−	0.921412i	$-0.627036\pi$
$84$	−4.45059	+	1.42357i	−0.485599	+	0.155325i
$85$		0			0
$86$	−5.67957	+	5.67957i	−0.612443	+	0.612443i
$87$	3.05751	−	5.93334i	0.327800	−	0.636121i
$88$			1.32293i			0.141024i
$89$	5.99694	−	5.99694i	0.635674	−	0.635674i	−0.313811	−	0.949485i	$-0.601606\pi$
$89$	5.99694	−	5.99694i	0.635674	−	0.635674i	0.949485	+	0.313811i	$0.101606\pi$
$90$		0			0
$91$	5.44533	−	3.26635i	0.570826	−	0.342406i
$92$		−	2.59855i		−	0.270918i
$93$	−9.47471	+	3.03059i	−0.982481	+	0.314258i
$94$	5.79622			0.597835
$95$		0			0
$96$	−3.05949	−	9.56505i	−0.312258	−	0.976229i
$97$	−1.03487	+	1.03487i	−0.105075	+	0.105075i	−0.757690	−	0.652615i	$-0.773672\pi$
$97$	−1.03487	+	1.03487i	−0.105075	+	0.105075i	0.652615	+	0.757690i	$0.273672\pi$
$98$	−1.88610	+	1.88610i	−0.190525	+	0.190525i
$99$	1.61970	+	0.271772i	0.162786	+	0.0273141i
$100$		0			0
$101$	18.2471			1.81565			0.907826	−	0.419347i	$-0.137741\pi$
$101$	18.2471			1.81565			0.907826	+	0.419347i	$0.137741\pi$
$102$	2.43709	+	7.61921i	0.241308	+	0.754415i
$103$			3.65487i			0.360125i	0.983655	+	0.180063i	$0.0576300\pi$
$103$			3.65487i			0.360125i	−0.983655	+	0.180063i	$0.942370\pi$
$104$	4.48192	+	7.47182i	0.439488	+	0.732672i
$105$		0			0
$106$	4.26418	−	4.26418i	0.414174	−	0.414174i
$107$		−	14.9588i		−	1.44612i	−0.690786	−	0.723060i	$-0.742735\pi$
$107$		−	14.9588i		−	1.44612i	0.690786	−	0.723060i	$-0.257265\pi$
$108$	−7.87811	+	1.13700i	−0.758072	+	0.109408i
$109$	5.41443	−	5.41443i	0.518609	−	0.518609i	−0.398542	−	0.917150i	$-0.630484\pi$
$109$	5.41443	−	5.41443i	0.518609	−	0.518609i	0.917150	+	0.398542i	$0.130484\pi$
$110$		0			0
$111$	−1.76652	−	5.52275i	−0.167670	−	0.524196i
$112$	−1.75623	−	1.75623i	−0.165948	−	0.165948i
$113$			5.56044i			0.523083i	0.965192	+	0.261541i	$0.0842308\pi$
$113$			5.56044i			0.523083i	−0.965192	+	0.261541i	$0.915769\pi$
$114$	1.98597	+	1.02339i	0.186003	+	0.0958493i
$115$		0			0
$116$	5.90330			0.548107
$117$	10.0687	−	3.95239i	0.930851	−	0.365398i
$118$	1.26305			0.116273
$119$	8.40596	+	8.40596i	0.770573	+	0.770573i
$120$		0			0
$121$			10.7003i			0.972755i
$122$	0.562879	+	0.562879i	0.0509607	+	0.0509607i
$123$	4.26946	+	13.3478i	0.384964	+	1.20353i
$124$	−6.22098	−	6.22098i	−0.558661	−	0.558661i
$125$		0			0
$126$	2.94392	−	2.09794i	0.262265	−	0.186899i
$127$		−	0.0349646i		−	0.00310261i	−0.999999	−	0.00155130i	$-0.999506\pi$
$127$		−	0.0349646i		−	0.00310261i	0.999999	−	0.00155130i	$-0.000493796\pi$
$128$	7.64492	−	7.64492i	0.675722	−	0.675722i
$129$	−9.31386	+	18.0743i	−0.820039	+	1.59135i
$130$		0			0
$131$		−	1.11950i		−	0.0978111i	−0.998803	−	0.0489056i	$-0.984427\pi$
$131$		−	1.11950i		−	0.0978111i	0.998803	−	0.0489056i	$-0.0155733\pi$
$132$	0.442516	+	1.38346i	0.0385161	+	0.120415i
$133$	3.32010			0.287889
$134$	−4.51730			−0.390235
$135$		0			0
$136$	−11.5342	+	11.5342i	−0.989054	+	0.989054i
$137$	2.58611	−	2.58611i	0.220946	−	0.220946i	−0.587950	−	0.808897i	$-0.700065\pi$
$137$	2.58611	−	2.58611i	0.220946	−	0.220946i	0.808897	+	0.587950i	$0.200065\pi$
$138$	0.612459	+	1.91476i	0.0521359	+	0.162995i
$139$	16.6867			1.41535			0.707673	−	0.706540i	$-0.249745\pi$
$139$	16.6867			1.41535			0.707673	+	0.706540i	$0.249745\pi$
$140$		0			0
$141$	13.9753	−	4.47017i	1.17694	−	0.376456i
$142$		−	0.886267i		−	0.0743739i
$143$	−1.01534	−	1.69268i	−0.0849071	−	0.141549i
$144$	−2.45535	−	3.44546i	−0.204612	−	0.287121i
$145$		0			0
$146$			7.85079i			0.649736i
$147$	−3.09299	+	6.00219i	−0.255105	+	0.495052i
$148$	3.62618	−	3.62618i	0.298070	−	0.298070i
$149$	−16.9396	−	16.9396i	−1.38775	−	1.38775i	−0.830030	−	0.557719i	$-0.811677\pi$
$149$	−16.9396	−	16.9396i	−1.38775	−	1.38775i	−0.557719	−	0.830030i	$-0.688323\pi$
$150$		0			0
$151$	−5.21274	−	5.21274i	−0.424207	−	0.424207i	0.462442	−	0.886649i	$-0.346973\pi$
$151$	−5.21274	−	5.21274i	−0.424207	−	0.424207i	−0.886649	+	0.462442i	$0.846973\pi$
$152$			4.55568i			0.369514i
$153$	11.7522	+	16.4912i	0.950109	+	1.33324i
$154$	−0.466456	−	0.466456i	−0.0375881	−	0.0375881i
$155$		0			0
$156$	7.18631	+	6.31452i	0.575366	+	0.505566i
$157$	13.0314			1.04002			0.520008	−	0.854161i	$-0.325929\pi$
$157$	13.0314			1.04002			0.520008	+	0.854161i	$0.325929\pi$
$158$	1.86465	+	1.86465i	0.148343	+	0.148343i
$159$	6.99278	−	13.5700i	0.554563	−	1.07617i
$160$		0			0
$161$	2.11248	+	2.11248i	0.166487	+	0.166487i
$162$	5.53706	−	2.69461i	0.435032	−	0.211709i
$163$	−3.83399	−	3.83399i	−0.300301	−	0.300301i	0.540830	−	0.841132i	$-0.318110\pi$
$163$	−3.83399	−	3.83399i	−0.300301	−	0.300301i	−0.841132	+	0.540830i	$0.818110\pi$
$164$	−8.76404	+	8.76404i	−0.684357	+	0.684357i
$165$		0			0
$166$			11.5483i			0.896318i
$167$	−9.06688	+	9.06688i	−0.701616	+	0.701616i	−0.964757	−	0.263141i	$-0.915242\pi$
$167$	−9.06688	+	9.06688i	−0.701616	+	0.701616i	0.263141	+	0.964757i	$0.415242\pi$
$168$	6.55251	+	3.37658i	0.505537	+	0.260509i
$169$	−11.4692	−	6.12029i	−0.882244	−	0.470792i
$170$		0			0
$171$	5.57765	+	0.935885i	0.426534	+	0.0715689i
$172$	−17.9827			−1.37117
$173$	4.63904			0.352700			0.176350	−	0.984328i	$-0.443571\pi$
$173$	4.63904			0.352700			0.176350	+	0.984328i	$0.443571\pi$
$174$	−4.34988	+	1.39136i	−0.329764	+	0.105479i
$175$		0			0
$176$	−0.545923	+	0.545923i	−0.0411505	+	0.0411505i
$177$	3.04535	−	0.974090i	0.228902	−	0.0732171i
$178$	−5.80278			−0.434936
$179$	13.2894			0.993298			0.496649	−	0.867951i	$-0.334564\pi$
$179$	13.2894			0.993298			0.496649	+	0.867951i	$0.334564\pi$
$180$		0			0
$181$			23.3132i			1.73286i	0.499299	+	0.866429i	$0.333591\pi$
$181$			23.3132i			1.73286i	−0.499299	+	0.866429i	$0.666409\pi$
$182$	−4.21481	−	1.05422i	−0.312423	−	0.0781439i
$183$	1.79127	+	0.923059i	0.132414	+	0.0682345i
$184$	−2.89864	+	2.89864i	−0.213690	+	0.213690i
$185$		0			0
$186$	6.05021	+	3.11774i	0.443623	+	0.228604i
$187$	2.61299	−	2.61299i	0.191080	−	0.191080i
$188$	9.17605	+	9.17605i	0.669232	+	0.669232i
$189$	5.48014	−	7.32877i	0.398622	−	0.533090i
$190$		0			0
$191$			6.40782i			0.463654i	0.972757	+	0.231827i	$0.0744703\pi$
$191$			6.40782i			0.463654i	−0.972757	+	0.231827i	$0.925530\pi$
$192$	−0.909647	+	1.76524i	−0.0656481	+	0.127395i
$193$	16.1130	+	16.1130i	1.15984	+	1.15984i	0.984509	+	0.175332i	$0.0561000\pi$
$193$	16.1130	+	16.1130i	1.15984	+	1.15984i	0.175332	+	0.984509i	$0.443900\pi$
$194$	1.00136			0.0718936
$195$		0			0
$196$	−5.97179			−0.426556
$197$	11.3286	+	11.3286i	0.807127	+	0.807127i	0.984198	−	0.177071i	$-0.0566622\pi$
$197$	11.3286	+	11.3286i	0.807127	+	0.807127i	−0.177071	+	0.984198i	$0.556662\pi$
$198$	−0.652142	−	0.915115i	−0.0463457	−	0.0650344i
$199$		−	23.0814i		−	1.63620i	−0.575079	−	0.818098i	$-0.695029\pi$
$199$		−	23.0814i		−	1.63620i	0.575079	−	0.818098i	$-0.304971\pi$
$200$		0			0
$201$	−10.8917	+	3.48384i	−0.768242	+	0.245731i
$202$	−8.82815	−	8.82815i	−0.621147	−	0.621147i
$203$	−4.79904	+	4.79904i	−0.336827	+	0.336827i
$204$	−8.20386	+	15.9202i	−0.574385	+	1.11464i
$205$		0			0
$206$	1.76827	−	1.76827i	0.123201	−	0.123201i
$207$	2.95341	+	4.14436i	0.205276	+	0.288053i
$208$	−1.23382	+	4.93286i	−0.0855500	+	0.342032i
$209$		−	1.03205i		−	0.0713884i
$210$		0			0
$211$	−9.04618			−0.622765			−0.311382	−	0.950285i	$-0.600792\pi$
$211$	−9.04618			−0.622765			−0.311382	+	0.950285i	$0.600792\pi$
$212$	13.5013			0.927274
$213$	−0.683508	−	2.13689i	−0.0468332	−	0.146417i
$214$	−7.23723	+	7.23723i	−0.494727	+	0.494727i
$215$		0			0
$216$	10.0562	+	7.51958i	0.684237	+	0.511643i
$217$	10.1146			0.686625
$218$	−5.23913			−0.354839
$219$	6.05470	+	18.9291i	0.409139	+	1.27911i
$220$		0			0
$221$	5.90551	−	23.6105i	0.397248	−	1.58821i
$222$	−1.81731	+	3.52663i	−0.121970	+	0.236692i
$223$	−12.2488	+	12.2488i	−0.820241	+	0.820241i	−0.986142	−	0.165901i	$-0.946947\pi$
$223$	−12.2488	+	12.2488i	−0.820241	+	0.820241i	0.165901	+	0.986142i	$0.446947\pi$
$224$			10.2111i			0.682256i
$225$		0			0
$226$	2.69021	−	2.69021i	0.178950	−	0.178950i
$227$	−10.5073	−	10.5073i	−0.697394	−	0.697394i	0.266454	−	0.963848i	$-0.414148\pi$
$227$	−10.5073	−	10.5073i	−0.697394	−	0.697394i	−0.963848	+	0.266454i	$0.914148\pi$
$228$	1.52387	+	4.76414i	0.100920	+	0.315513i
$229$	−4.44578	−	4.44578i	−0.293785	−	0.293785i	0.544788	−	0.838574i	$-0.316610\pi$
$229$	−4.44578	−	4.44578i	−0.293785	−	0.293785i	−0.838574	+	0.544788i	$0.816610\pi$
$230$		0			0
$231$	−1.48442	−	0.764935i	−0.0976674	−	0.0503290i
$232$	−6.58501	−	6.58501i	−0.432327	−	0.432327i
$233$	17.6896			1.15888			0.579441	−	0.815014i	$-0.303271\pi$
$233$	17.6896			1.15888			0.579441	+	0.815014i	$0.303271\pi$
$234$	−6.78357	−	2.95914i	−0.443456	−	0.193445i
$235$		0			0
$236$	1.99954	+	1.99954i	0.130159	+	0.130159i
$237$	5.93393	+	3.05781i	0.385450	+	0.198626i
$238$		−	8.13381i		−	0.527236i
$239$	4.70800	+	4.70800i	0.304535	+	0.304535i	0.842785	−	0.538250i	$-0.180914\pi$
$239$	4.70800	+	4.70800i	0.304535	+	0.304535i	−0.538250	+	0.842785i	$0.680914\pi$
$240$		0			0
$241$	13.7965	+	13.7965i	0.888710	+	0.888710i	0.994399	−	0.105689i	$-0.0337048\pi$
$241$	13.7965	+	13.7965i	0.888710	+	0.888710i	−0.105689	+	0.994399i	$0.533705\pi$
$242$	5.17693	−	5.17693i	0.332786	−	0.332786i
$243$	11.2723	−	10.7673i	0.723119	−	0.690723i
$244$			1.78220i			0.114093i
$245$		0			0
$246$	4.39223	−	8.52346i	0.280038	−	0.543436i
$247$	−3.49647	−	5.82896i	−0.222475	−	0.370888i
$248$			13.8788i			0.881303i
$249$	8.90626	+	27.8441i	0.564411	+	1.76455i
$250$		0			0
$251$	−5.80617			−0.366482			−0.183241	−	0.983068i	$-0.558659\pi$
$251$	−5.80617			−0.366482			−0.183241	+	0.983068i	$0.558659\pi$
$252$	7.98181	+	1.33928i	0.502807	+	0.0843670i
$253$	0.656662	−	0.656662i	0.0412840	−	0.0412840i
$254$	−0.0169163	+	0.0169163i	−0.00106142	+	0.00106142i
$255$		0			0
$256$	−9.69045			−0.605653
$257$	−8.29597			−0.517488			−0.258744	−	0.965946i	$-0.583309\pi$
$257$	−8.29597			−0.517488			−0.258744	+	0.965946i	$0.583309\pi$
$258$	13.2507	−	4.23839i	0.824952	−	0.263870i
$259$			5.89575i			0.366344i
$260$		0			0
$261$	−9.41500	+	6.70944i	−0.582774	+	0.415304i
$262$	−0.541627	+	0.541627i	−0.0334618	+	0.0334618i
$263$			10.8718i			0.670383i	0.942150	+	0.335191i	$0.108801\pi$
$263$			10.8718i			0.670383i	−0.942150	+	0.335191i	$0.891199\pi$
$264$	1.04961	−	2.03684i	0.0645988	−	0.125359i
$265$		0			0
$266$	−1.60630	−	1.60630i	−0.0984888	−	0.0984888i
$267$	−13.9911	+	4.47522i	−0.856243	+	0.273879i
$268$	−7.15137	−	7.15137i	−0.436839	−	0.436839i
$269$		−	21.6607i		−	1.32068i	−0.750968	−	0.660339i	$-0.770413\pi$
$269$		−	21.6607i		−	1.32068i	0.750968	−	0.660339i	$-0.229587\pi$
$270$		0			0
$271$	−3.57577	−	3.57577i	−0.217213	−	0.217213i	0.590110	−	0.807323i	$-0.299084\pi$
$271$	−3.57577	−	3.57577i	−0.217213	−	0.217213i	−0.807323	+	0.590110i	$0.799084\pi$
$272$	−9.51951			−0.577205
$273$	−10.9754	+	0.708715i	−0.664262	+	0.0428934i
$274$	−2.50238			−0.151174
$275$		0			0
$276$	−2.06169	+	4.00086i	−0.124099	+	0.240824i
$277$		−	17.4880i		−	1.05075i	−0.850870	−	0.525377i	$-0.823924\pi$
$277$		−	17.4880i		−	1.05075i	0.850870	−	0.525377i	$-0.176076\pi$
$278$	−8.07321	−	8.07321i	−0.484199	−	0.484199i
$279$	16.9922	+	2.85115i	1.01730	+	0.170694i
$280$		0			0
$281$	−3.48513	+	3.48513i	−0.207906	+	0.207906i	−0.803377	−	0.595471i	$-0.796965\pi$
$281$	−3.48513	+	3.48513i	−0.207906	+	0.207906i	0.595471	+	0.803377i	$0.296965\pi$
$282$	−8.92415	−	4.59871i	−0.531426	−	0.273849i
$283$			9.47252i			0.563083i	0.959549	+	0.281541i	$0.0908457\pi$
$283$			9.47252i			0.563083i	−0.959549	+	0.281541i	$0.909154\pi$
$284$	1.40306	−	1.40306i	0.0832561	−	0.0832561i
$285$		0			0
$286$	−0.327703	+	1.31017i	−0.0193775	+	0.0774720i
$287$		−	14.2493i		−	0.841112i
$288$	−2.87834	+	17.1542i	−0.169608	+	1.01082i
$289$	28.5639			1.68023
$290$		0			0
$291$	2.41439	−	0.772272i	0.141534	−	0.0452714i
$292$	−12.4287	+	12.4287i	−0.727332	+	0.727332i
$293$	15.2096	−	15.2096i	0.888556	−	0.888556i	−0.105828	−	0.994384i	$-0.533749\pi$
$293$	15.2096	−	15.2096i	0.888556	−	0.888556i	0.994384	+	0.105828i	$0.0337494\pi$
$294$	4.40035	−	1.40750i	0.256634	−	0.0820873i
$295$		0			0
$296$	−8.08986			−0.470214
$297$	−2.27814	−	1.70350i	−0.132191	−	0.0988470i
$298$			16.3912i			0.949516i
$299$	1.48410	−	5.93348i	0.0858275	−	0.343142i
$300$		0			0
$301$	14.6189	−	14.6189i	0.842622	−	0.842622i
$302$			5.04397i			0.290248i
$303$	−28.0941	−	14.4772i	−1.61396	−	0.831693i
$304$	−1.87996	+	1.87996i	−0.107823	+	0.107823i
$305$		0			0
$306$	2.29280	−	13.6645i	0.131070	−	0.781148i
$307$	8.64829	+	8.64829i	0.493584	+	0.493584i	0.909433	−	0.415850i	$-0.136516\pi$
$307$	8.64829	+	8.64829i	0.493584	+	0.493584i	−0.415850	+	0.909433i	$0.636516\pi$
$308$		−	1.47690i		−	0.0841541i
$309$	2.89976	−	5.62722i	0.164962	−	0.320121i
$310$		0			0
$311$	1.51624			0.0859779			0.0429890	−	0.999076i	$-0.486312\pi$
$311$	1.51624			0.0859779			0.0429890	+	0.999076i	$0.486312\pi$
$312$	−0.972464	−	15.0599i	−0.0550550	−	0.852600i
$313$	−0.929202			−0.0525216			−0.0262608	−	0.999655i	$-0.508360\pi$
$313$	−0.929202			−0.0525216			−0.0262608	+	0.999655i	$0.508360\pi$
$314$	−6.30473	−	6.30473i	−0.355796	−	0.355796i
$315$		0			0
$316$			5.90388i			0.332119i
$317$	−15.3001	−	15.3001i	−0.859342	−	0.859342i	0.131919	−	0.991261i	$-0.457886\pi$
$317$	−15.3001	−	15.3001i	−0.859342	−	0.859342i	−0.991261	+	0.131919i	$0.957886\pi$
$318$	−9.94853	+	3.18215i	−0.557886	+	0.178446i
$319$	1.49178	+	1.49178i	0.0835236	+	0.0835236i
$320$		0			0
$321$	−11.8683	+	23.0313i	−0.662421	+	1.28548i
$322$		−	2.04408i		−	0.113912i
$323$	8.99818	−	8.99818i	0.500672	−	0.500672i
$324$	13.0316	+	4.49990i	0.723979	+	0.249994i
$325$		0			0
$326$			3.70986i			0.205470i
$327$	−12.6321	+	4.04053i	−0.698558	+	0.223442i
$328$	19.5522			1.07959
$329$	−14.9192			−0.822523
$330$		0			0
$331$	22.1751	−	22.1751i	1.21885	−	1.21885i	0.250818	−	0.968034i	$-0.419300\pi$
$331$	22.1751	−	22.1751i	1.21885	−	1.21885i	0.968034	−	0.250818i	$-0.0806997\pi$
$332$	−18.2821	+	18.2821i	−1.00336	+	1.00336i
$333$	−1.66192	+	9.90465i	−0.0910727	+	0.542771i
$334$	8.77333			0.480055
$335$		0			0
$336$	1.31059	+	4.09737i	0.0714986	+	0.223530i
$337$			1.11379i			0.0606718i	0.999540	+	0.0303359i	$0.00965769\pi$
$337$			1.11379i			0.0606718i	−0.999540	+	0.0303359i	$0.990342\pi$
$338$	2.58785	+	8.50999i	0.140761	+	0.462883i
$339$	4.41164	−	8.56113i	0.239607	−	0.464977i
$340$		0			0
$341$		−	3.14412i		−	0.170264i
$342$	−2.24574	−	3.15132i	−0.121436	−	0.170404i
$343$	13.5719	−	13.5719i	0.732813	−	0.732813i
$344$	20.0594	+	20.0594i	1.08153	+	1.08153i
$345$		0			0
$346$	−2.24442	−	2.24442i	−0.120661	−	0.120661i
$347$			14.9572i			0.802946i	0.915871	+	0.401473i	$0.131502\pi$
$347$			14.9572i			0.802946i	−0.915871	+	0.401473i	$0.868498\pi$
$348$	−9.08901	−	4.68366i	−0.487222	−	0.251071i
$349$	8.13022	+	8.13022i	0.435201	+	0.435201i	0.890393	−	0.455192i	$-0.150430\pi$
$349$	8.13022	+	8.13022i	0.435201	+	0.435201i	−0.455192	+	0.890393i	$0.650430\pi$
$350$		0			0
$351$	−18.6381	−	1.90318i	−0.994827	−	0.101584i
$352$	3.17410			0.169180
$353$	14.0281	+	14.0281i	0.746638	+	0.746638i	0.973846	−	0.227208i	$-0.0729598\pi$
$353$	14.0281	+	14.0281i	0.746638	+	0.746638i	−0.227208	+	0.973846i	$0.572960\pi$
$354$	−1.94465	−	1.00210i	−0.103357	−	0.0532610i
$355$		0			0
$356$	−9.18642	−	9.18642i	−0.486879	−	0.486879i
$357$	−6.27297	−	19.6115i	−0.332001	−	1.03795i
$358$	−6.42958	−	6.42958i	−0.339814	−	0.339814i
$359$	−14.0085	+	14.0085i	−0.739341	+	0.739341i	−0.972451	−	0.233109i	$-0.925110\pi$
$359$	−14.0085	+	14.0085i	−0.739341	+	0.739341i	0.233109	+	0.972451i	$0.425110\pi$
$360$		0			0
$361$			15.4460i			0.812947i
$362$	11.2792	−	11.2792i	0.592822	−	0.592822i
$363$	8.48959	−	16.4747i	0.445588	−	0.864698i
$364$	−5.00356	−	8.34145i	−0.262258	−	0.437211i
$365$		0			0
$366$	−0.420050	−	1.31322i	−0.0219564	−	0.0686433i
$367$	26.2282			1.36910			0.684549	−	0.728966i	$-0.259999\pi$
$367$	26.2282			1.36910			0.684549	+	0.728966i	$0.259999\pi$
$368$	−2.39232			−0.124708
$369$	4.01667	−	23.9384i	0.209099	−	1.24618i
$370$		0			0
$371$	−10.9758	+	10.9758i	−0.569835	+	0.569835i
$372$	4.64242	+	14.5138i	0.240698	+	0.752508i
$373$	−6.83702			−0.354007			−0.177004	−	0.984210i	$-0.556640\pi$
$373$	−6.83702			−0.354007			−0.177004	+	0.984210i	$0.556640\pi$
$374$	−2.52839			−0.130740
$375$		0			0
$376$		−	20.4714i		−	1.05573i
$377$	13.4795	+	3.37151i	0.694227	+	0.173642i
$378$	−6.19711	+	0.894389i	−0.318745	+	0.0460024i
$379$	−24.8881	+	24.8881i	−1.27842	+	1.27842i	−0.336864	+	0.941553i	$0.609366\pi$
$379$	−24.8881	+	24.8881i	−1.27842	+	1.27842i	−0.941553	+	0.336864i	$0.890634\pi$
$380$		0			0
$381$	−0.0277408	+	0.0538332i	−0.00142121	+	0.00275796i
$382$	3.10018	−	3.10018i	0.158619	−	0.158619i
$383$	−7.76391	−	7.76391i	−0.396717	−	0.396717i	0.480356	−	0.877073i	$-0.340507\pi$
$383$	−7.76391	−	7.76391i	−0.396717	−	0.396717i	−0.877073	+	0.480356i	$0.840507\pi$
$384$	−17.8360	+	5.70504i	−0.910188	+	0.291134i
$385$		0			0
$386$		−	15.5914i		−	0.793579i
$387$	28.6801	−	20.4384i	1.45789	−	1.03894i
$388$	1.58526	+	1.58526i	0.0804796	+	0.0804796i
$389$	6.30333			0.319591			0.159796	−	0.987150i	$-0.448916\pi$
$389$	6.30333			0.319591			0.159796	+	0.987150i	$0.448916\pi$
$390$		0			0
$391$	11.4505			0.579078
$392$	6.66141	+	6.66141i	0.336452	+	0.336452i
$393$	−0.888208	+	1.72364i	−0.0448042	+	0.0869460i
$394$		−	10.9618i		−	0.552247i
$395$		0			0
$396$	0.416315	−	2.48114i	0.0209206	−	0.124682i
$397$	24.3714	+	24.3714i	1.22317	+	1.22317i	0.966500	+	0.256665i	$0.0826236\pi$
$397$	24.3714	+	24.3714i	1.22317	+	1.22317i	0.256665	+	0.966500i	$0.417376\pi$
$398$	−11.1670	+	11.1670i	−0.559753	+	0.559753i
$399$	−5.11179	−	2.63416i	−0.255910	−	0.131873i
$400$		0			0
$401$	−8.82040	+	8.82040i	−0.440470	+	0.440470i	−0.892170	−	0.451700i	$-0.850818\pi$
$401$	−8.82040	+	8.82040i	−0.440470	+	0.440470i	0.451700	+	0.892170i	$0.350818\pi$
$402$	6.95506	+	3.58401i	0.346887	+	0.178754i
$403$	−10.6519	−	17.7578i	−0.530609	−	0.884580i
$404$		−	27.9518i		−	1.39066i
$405$		0			0
$406$	4.64367			0.230461
$407$	1.83269			0.0908430
$408$	26.9099	−	8.60746i	1.33224	−	0.426133i
$409$	−10.2362	+	10.2362i	−0.506149	+	0.506149i	−0.913342	−	0.407193i	$-0.866508\pi$
$409$	−10.2362	+	10.2362i	−0.506149	+	0.506149i	0.407193	+	0.913342i	$0.366508\pi$
$410$		0			0
$411$	−6.03352	+	1.92989i	−0.297612	+	0.0951945i
$412$	5.59872			0.275829
$413$	−3.25103			−0.159973
$414$	0.576195	−	3.43398i	0.0283185	−	0.168771i
$415$		0			0
$416$	17.9271	−	10.7535i	0.878951	−	0.527233i
$417$	−25.6916	−	13.2392i	−1.25812	−	0.648325i
$418$	−0.499318	+	0.499318i	−0.0244224	+	0.0244224i
$419$		−	39.8238i		−	1.94552i	−0.231818	−	0.972759i	$-0.574467\pi$
$419$		−	39.8238i		−	1.94552i	0.231818	−	0.972759i	$-0.425533\pi$
$420$		0			0
$421$	−11.1187	+	11.1187i	−0.541893	+	0.541893i	−0.924084	−	0.382190i	$-0.875170\pi$
$421$	−11.1187	+	11.1187i	−0.541893	+	0.541893i	0.382190	+	0.924084i	$0.375170\pi$
$422$	4.37665	+	4.37665i	0.213052	+	0.213052i
$423$	−25.0637	−	4.20550i	−1.21864	−	0.204478i
$424$	−15.0605	−	15.0605i	−0.731400	−	0.731400i
$425$		0			0
$426$	−0.703162	+	1.36454i	−0.0340683	+	0.0661122i
$427$	−1.44883	−	1.44883i	−0.0701136	−	0.0701136i
$428$	−22.9146			−1.10762
$429$	0.220304	+	3.41170i	0.0106364	+	0.164718i
$430$		0			0
$431$	−5.22718	−	5.22718i	−0.251784	−	0.251784i	0.569917	−	0.821702i	$-0.306975\pi$
$431$	−5.22718	−	5.22718i	−0.251784	−	0.251784i	−0.821702	+	0.569917i	$0.806975\pi$
$432$	1.04676	+	7.25286i	0.0503623	+	0.348954i
$433$			2.96201i			0.142345i	0.997464	+	0.0711727i	$0.0226741\pi$
$433$			2.96201i			0.142345i	−0.997464	+	0.0711727i	$0.977326\pi$
$434$	−4.89357	−	4.89357i	−0.234899	−	0.234899i
$435$		0			0
$436$	−8.29411	−	8.29411i	−0.397216	−	0.397216i
$437$	2.26130	−	2.26130i	0.108173	−	0.108173i
$438$	6.22880	−	12.0875i	0.297624	−	0.577562i
$439$			21.3756i			1.02020i	0.860114	+	0.510101i	$0.170392\pi$
$439$			21.3756i			1.02020i	−0.860114	+	0.510101i	$0.829608\pi$
$440$		0			0
$441$	9.52424	−	6.78729i	0.453535	−	0.323204i
$442$	−14.2802	+	8.56588i	−0.679239	+	0.407437i
$443$		−	20.6824i		−	0.982650i	−0.870976	−	0.491325i	$-0.836513\pi$
$443$		−	20.6824i		−	0.982650i	0.870976	−	0.491325i	$-0.163487\pi$
$444$	−8.46004	+	2.70604i	−0.401496	+	0.128423i
$445$		0			0
$446$	11.8522			0.561220
$447$	12.6412	+	39.5210i	0.597910	+	1.86928i
$448$	1.42777	−	1.42777i	0.0674559	−	0.0674559i
$449$	−29.1294	+	29.1294i	−1.37470	+	1.37470i	−0.521375	+	0.853328i	$0.674581\pi$
$449$	−29.1294	+	29.1294i	−1.37470	+	1.37470i	−0.853328	+	0.521375i	$0.825419\pi$
$450$		0			0
$451$	−4.42939			−0.208572
$452$	8.51778			0.400643
$453$	3.89002	+	12.1616i	0.182769	+	0.571401i
$454$			10.1671i			0.477166i
$455$		0			0
$456$	3.61446	−	7.01415i	0.169263	−	0.328468i
$457$	2.59392	−	2.59392i	0.121338	−	0.121338i	−0.643830	−	0.765168i	$-0.722656\pi$
$457$	2.59392	−	2.59392i	0.121338	−	0.121338i	0.765168	+	0.643830i	$0.222656\pi$
$458$			4.30184i			0.201012i
$459$	−5.01018	−	34.7149i	−0.233855	−	1.62035i
$460$		0			0
$461$	18.1031	+	18.1031i	0.843144	+	0.843144i	0.989266	−	0.146123i	$-0.0466794\pi$
$461$	18.1031	+	18.1031i	0.843144	+	0.843144i	−0.146123	+	0.989266i	$0.546679\pi$
$462$	0.348093	+	1.08826i	0.0161948	+	0.0506306i
$463$	−19.7500	−	19.7500i	−0.917862	−	0.917862i	0.0790114	−	0.996874i	$-0.474824\pi$
$463$	−19.7500	−	19.7500i	−0.917862	−	0.917862i	−0.996874	+	0.0790114i	$0.974824\pi$
$464$		−	5.43478i		−	0.252303i
$465$		0			0
$466$	−8.55842	−	8.55842i	−0.396461	−	0.396461i
$467$	−2.98569			−0.138161			−0.0690807	−	0.997611i	$-0.522007\pi$
$467$	−2.98569			−0.138161			−0.0690807	+	0.997611i	$0.522007\pi$
$468$	−6.05448	−	15.4238i	−0.279868	−	0.712963i
$469$	11.6273			0.536900
$470$		0			0
$471$	−20.0637	−	10.3391i	−0.924488	−	0.476398i
$472$		−	4.46090i		−	0.205330i
$473$	−4.54428	−	4.54428i	−0.208946	−	0.208946i
$474$	−1.39150	−	4.35031i	−0.0639136	−	0.199816i
$475$		0			0
$476$	12.8767	−	12.8767i	0.590202	−	0.590202i
$477$	−21.5329	+	15.3450i	−0.985922	+	0.702601i
$478$		−	4.55557i		−	0.208367i
$479$	4.61160	−	4.61160i	0.210710	−	0.210710i	−0.593859	−	0.804569i	$-0.702396\pi$
$479$	4.61160	−	4.61160i	0.210710	−	0.210710i	0.804569	+	0.593859i	$0.202396\pi$
$480$		0			0
$481$	10.3509	−	6.20893i	0.471962	−	0.283103i
$482$		−	13.3498i		−	0.608067i
$483$	−1.57644	−	4.92851i	−0.0717305	−	0.224255i
$484$	16.3913			0.745058
$485$		0			0
$486$	−10.6630	−	0.244328i	−0.483685	−	0.0110829i
$487$	−22.7100	+	22.7100i	−1.02909	+	1.02909i	−0.0295239	+	0.999564i	$0.509399\pi$
$487$	−22.7100	+	22.7100i	−1.02909	+	1.02909i	−0.999564	+	0.0295239i	$0.990601\pi$
$488$	1.98801	−	1.98801i	0.0899928	−	0.0899928i
$489$	2.86112	+	8.94488i	0.129384	+	0.404501i
$490$		0			0
$491$	−32.8134			−1.48085			−0.740423	−	0.672141i	$-0.765375\pi$
$491$	−32.8134			−1.48085			−0.740423	+	0.672141i	$0.765375\pi$
$492$	20.4469	−	6.54019i	0.921819	−	0.294854i
$493$			26.0128i			1.17156i
$494$	−1.12849	+	4.51175i	−0.0507732	+	0.202993i
$495$		0			0
$496$	−5.72725	+	5.72725i	−0.257161	+	0.257161i
$497$			2.28121i			0.102326i
$498$	9.16235	−	17.7803i	0.410575	−	0.796753i
$499$	0.358414	−	0.358414i	0.0160448	−	0.0160448i	−0.699039	−	0.715084i	$-0.746389\pi$
$499$	0.358414	−	0.358414i	0.0160448	−	0.0160448i	0.715084	+	0.699039i	$0.246389\pi$
$500$		0			0
$501$	21.1535	−	6.76618i	0.945067	−	0.302291i
$502$	2.80909	+	2.80909i	0.125376	+	0.125376i
$503$		−	1.20071i		−	0.0535371i	−0.999642	−	0.0267685i	$-0.991478\pi$
$503$		−	1.20071i		−	0.0535371i	0.999642	−	0.0267685i	$-0.00852171\pi$
$504$	−7.40961	−	10.3975i	−0.330050	−	0.463141i
$505$		0			0
$506$	−0.635401			−0.0282470
$507$	12.8027	+	18.5227i	0.568587	+	0.822623i
$508$	−0.0535606			−0.00237637
$509$	16.5736	+	16.5736i	0.734613	+	0.734613i	0.971530	−	0.236917i	$-0.0761368\pi$
$509$	16.5736	+	16.5736i	0.734613	+	0.734613i	−0.236917	+	0.971530i	$0.576137\pi$
$510$		0			0
$511$		−	20.2076i		−	0.893931i
$512$	−10.6015	−	10.6015i	−0.468524	−	0.468524i
$513$	−7.84510	−	5.86623i	−0.346369	−	0.259000i
$514$	4.01369	+	4.01369i	0.177036	+	0.177036i
$515$		0			0
$516$	27.6871	+	14.2675i	1.21886	+	0.628090i
$517$			4.63762i			0.203962i
$518$	2.85243	−	2.85243i	0.125329	−	0.125329i
$519$	−7.14250	−	3.68061i	−0.313521	−	0.161561i
$520$		0			0
$521$			24.5938i			1.07747i	0.842474	+	0.538736i	$0.181098\pi$
$521$			24.5938i			1.07747i	−0.842474	+	0.538736i	$0.818902\pi$
$522$	7.80120	+	1.30898i	0.341449	+	0.0572924i
$523$	38.6626			1.69060			0.845299	−	0.534294i	$-0.179422\pi$
$523$	38.6626			1.69060			0.845299	+	0.534294i	$0.179422\pi$
$524$	−1.71491			−0.0749161
$525$		0			0
$526$	5.25989	−	5.25989i	0.229342	−	0.229342i
$527$	27.4127	−	27.4127i	1.19412	−	1.19412i
$528$	1.27366	−	0.407396i	0.0554291	−	0.0177296i
$529$	−20.1224			−0.874887
$530$		0			0
$531$	−5.46161	−	0.916415i	−0.237014	−	0.0397690i
$532$		−	5.08590i		−	0.220502i
$533$	−25.0170	+	15.0063i	−1.08361	+	0.649994i
$534$	8.93424	+	4.60391i	0.386622	+	0.199231i
$535$		0			0
$536$			15.9544i			0.689126i
$537$	−20.4611	−	10.5438i	−0.882960	−	0.454998i
$538$	−10.4797	+	10.4797i	−0.451812	+	0.451812i
$539$	−1.50909	−	1.50909i	−0.0650010	−	0.0650010i
$540$		0			0
$541$	−1.35568	−	1.35568i	−0.0582854	−	0.0582854i	0.677363	−	0.735649i	$-0.263123\pi$
$541$	−1.35568	−	1.35568i	−0.0582854	−	0.0582854i	−0.735649	+	0.677363i	$0.763123\pi$
$542$			3.46000i			0.148620i
$543$	18.4967	−	35.8942i	0.793768	−	1.54037i
$544$	27.6741	+	27.6741i	1.18652	+	1.18652i
$545$		0			0
$546$	5.65292	+	4.96715i	0.241923	+	0.212574i
$547$	−19.9892			−0.854675			−0.427338	−	0.904092i	$-0.640548\pi$
$547$	−19.9892			−0.854675			−0.427338	+	0.904092i	$0.640548\pi$
$548$	−3.96154	−	3.96154i	−0.169229	−	0.169229i
$549$	−2.02557	−	2.84238i	−0.0864493	−	0.121310i
$550$		0			0
$551$	5.13714	+	5.13714i	0.218850	+	0.218850i
$552$	6.76266	−	2.16311i	0.287838	−	0.0920682i
$553$	−4.79952	−	4.79952i	−0.204096	−	0.204096i
$554$	−8.46092	+	8.46092i	−0.359470	+	0.359470i
$555$		0			0
$556$		−	25.5615i		−	1.08405i
$557$	−9.29058	+	9.29058i	−0.393655	+	0.393655i	−0.875988	−	0.482333i	$-0.839789\pi$
$557$	−9.29058	+	9.29058i	−0.393655	+	0.393655i	0.482333	+	0.875988i	$0.339789\pi$
$558$	−6.84160	−	9.60044i	−0.289628	−	0.406419i
$559$	−41.0614	−	10.2704i	−1.73671	−	0.434390i
$560$		0			0
$561$	−6.09622	+	1.94995i	−0.257383	+	0.0823268i
$562$	3.37230			0.142252
$563$	−43.3391			−1.82653			−0.913263	−	0.407370i	$-0.866446\pi$
$563$	−43.3391			−1.82653			−0.913263	+	0.407370i	$0.866446\pi$
$564$	−6.84764	−	21.4081i	−0.288338	−	0.901446i
$565$		0			0
$566$	4.58292	−	4.58292i	0.192634	−	0.192634i
$567$	−14.2521	+	6.93581i	−0.598533	+	0.291277i
$568$	−3.13016			−0.131339
$569$	−7.47436			−0.313342			−0.156671	−	0.987651i	$-0.550076\pi$
$569$	−7.47436			−0.313342			−0.156671	+	0.987651i	$0.550076\pi$
$570$		0			0
$571$		−	20.1324i		−	0.842516i	−0.906941	−	0.421258i	$-0.861589\pi$
$571$		−	20.1324i		−	0.842516i	0.906941	−	0.421258i	$-0.138411\pi$
$572$	−2.59293	+	1.55535i	−0.108416	+	0.0650325i
$573$	5.08395	−	9.86580i	0.212385	−	0.412150i
$574$	−6.89400	+	6.89400i	−0.287750	+	0.287750i
$575$		0			0
$576$	2.80107	−	1.99614i	0.116711	−	0.0831725i
$577$	−12.5798	+	12.5798i	−0.523705	+	0.523705i	−0.918688	−	0.394983i	$-0.870750\pi$
$577$	−12.5798	+	12.5798i	−0.523705	+	0.523705i	0.394983	+	0.918688i	$0.370750\pi$
$578$	−13.8195	−	13.8195i	−0.574817	−	0.574817i
$579$	−12.0244	−	37.5925i	−0.499716	−	1.56229i
$580$		0			0
$581$		−	29.7247i		−	1.23319i
$582$	−1.54175	−	0.794478i	−0.0639075	−	0.0329322i
$583$	3.41182	+	3.41182i	0.141303	+	0.141303i
$584$	27.7278			1.14739
$585$		0			0
$586$	−14.7172			−0.607962
$587$	−0.511868	−	0.511868i	−0.0211270	−	0.0211270i	0.696464	−	0.717591i	$-0.254755\pi$
$587$	−0.511868	−	0.511868i	−0.0211270	−	0.0211270i	−0.717591	+	0.696464i	$0.754755\pi$
$588$	9.19446	+	4.73800i	0.379173	+	0.195392i
$589$		−	10.8272i		−	0.446127i
$590$		0			0
$591$	−8.45397	−	26.4301i	−0.347750	−	1.08719i
$592$	−3.33838	−	3.33838i	−0.137207	−	0.137207i
$593$	13.2208	−	13.2208i	0.542911	−	0.542911i	−0.381470	−	0.924381i	$-0.624582\pi$
$593$	13.2208	−	13.2208i	0.542911	−	0.542911i	0.924381	+	0.381470i	$0.124582\pi$
$594$	0.278020	+	1.92636i	0.0114073	+	0.0790397i
$595$		0			0
$596$	−25.9490	+	25.9490i	−1.06291	+	1.06291i
$597$	−18.3127	+	35.5372i	−0.749489	+	1.45444i
$598$	−3.58871	+	2.15266i	−0.146753	+	0.0880290i
$599$			32.7474i			1.33802i	0.743253	+	0.669011i	$0.233282\pi$
$599$			32.7474i			1.33802i	−0.743253	+	0.669011i	$0.766718\pi$
$600$		0			0
$601$	11.3682			0.463718			0.231859	−	0.972749i	$-0.425519\pi$
$601$	11.3682			0.463718			0.231859	+	0.972749i	$0.425519\pi$
$602$	−14.1456			−0.576533
$603$	19.5335	+	3.27756i	0.795465	+	0.133473i
$604$	−7.98515	+	7.98515i	−0.324911	+	0.324911i
$605$		0			0
$606$	6.58803	+	20.5965i	0.267620	+	0.836675i
$607$	17.5226			0.711221			0.355610	−	0.934634i	$-0.384273\pi$
$607$	17.5226			0.711221			0.355610	+	0.934634i	$0.384273\pi$
$608$	10.9304			0.443288
$609$	11.1964	−	3.58130i	0.453701	−	0.145121i
$610$		0			0
$611$	15.7117	+	26.1930i	0.635628	+	1.05966i
$612$	25.2621	−	18.0026i	1.02116	−	0.727714i
$613$	−22.5157	+	22.5157i	−0.909399	+	0.909399i	−0.996224	−	0.0868247i	$-0.972328\pi$
$613$	−22.5157	+	22.5157i	−0.909399	+	0.909399i	0.0868247	+	0.996224i	$0.472328\pi$
$614$		−	8.36829i		−	0.337717i
$615$		0			0
$616$	−1.64745	+	1.64745i	−0.0663777	+	0.0663777i
$617$	3.20157	+	3.20157i	0.128891	+	0.128891i	0.768609	−	0.639719i	$-0.220949\pi$
$617$	3.20157	+	3.20157i	0.128891	+	0.128891i	−0.639719	+	0.768609i	$0.720949\pi$
$618$	−4.12545	+	1.31957i	−0.165950	+	0.0530811i
$619$	6.99088	+	6.99088i	0.280987	+	0.280987i	0.833503	−	0.552515i	$-0.186332\pi$
$619$	6.99088	+	6.99088i	0.280987	+	0.280987i	−0.552515	+	0.833503i	$0.686332\pi$
$620$		0			0
$621$	−1.25909	−	8.72409i	−0.0505256	−	0.350086i
$622$	−0.733573	−	0.733573i	−0.0294136	−	0.0294136i
$623$	14.9361			0.598401
$624$	5.81337	−	6.61597i	0.232721	−	0.264851i
$625$		0			0
$626$	0.449559	+	0.449559i	0.0179680	+	0.0179680i
$627$	−0.818826	+	1.58900i	−0.0327008	+	0.0634584i
$628$		−	19.9621i		−	0.796576i
$629$	15.9787	+	15.9787i	0.637114	+	0.637114i
$630$		0			0
$631$	19.6866	+	19.6866i	0.783711	+	0.783711i	0.980455	−	0.196744i	$-0.0630369\pi$
$631$	19.6866	+	19.6866i	0.783711	+	0.783711i	−0.196744	+	0.980455i	$0.563037\pi$
$632$	6.58566	−	6.58566i	0.261963	−	0.261963i
$633$	13.9279	+	7.17722i	0.553586	+	0.285269i
$634$			14.8048i			0.587973i
$635$		0			0
$636$	−20.7873	−	10.7119i	−0.824270	−	0.424755i
$637$	−13.6359	−	3.41063i	−0.540272	−	0.135134i
$638$		−	1.44348i		−	0.0571479i
$639$	−0.643038	+	3.83235i	−0.0254382	+	0.151605i
$640$		0			0
$641$	7.99599			0.315822			0.157911	−	0.987453i	$-0.449524\pi$
$641$	7.99599			0.315822			0.157911	+	0.987453i	$0.449524\pi$
$642$	16.8848	−	5.40080i	0.666390	−	0.213153i
$643$	15.0350	−	15.0350i	0.592922	−	0.592922i	−0.345498	−	0.938420i	$-0.612290\pi$
$643$	15.0350	−	15.0350i	0.592922	−	0.592922i	0.938420	+	0.345498i	$0.112290\pi$
$644$	3.23600	−	3.23600i	0.127516	−	0.127516i
$645$		0			0
$646$	−8.70685			−0.342566
$647$	−5.28617			−0.207821			−0.103910	−	0.994587i	$-0.533136\pi$
$647$	−5.28617			−0.207821			−0.103910	+	0.994587i	$0.533136\pi$
$648$	−9.51698	−	19.5561i	−0.373862	−	0.768235i
$649$			1.01058i			0.0396687i
$650$		0			0
$651$	−15.5730	−	8.02491i	−0.610353	−	0.314521i
$652$	−5.87311	+	5.87311i	−0.230009	+	0.230009i
$653$		−	26.0947i		−	1.02116i	−0.859829	−	0.510581i	$-0.829430\pi$
$653$		−	26.0947i		−	1.02116i	0.859829	−	0.510581i	$-0.170570\pi$
$654$	8.06643	+	4.15671i	0.315422	+	0.162540i
$655$		0			0
$656$	8.06848	+	8.06848i	0.315021	+	0.315021i
$657$	5.69621	−	33.9480i	0.222230	−	1.32444i
$658$	7.21809	+	7.21809i	0.281390	+	0.281390i
$659$			10.5160i			0.409646i	0.978799	+	0.204823i	$0.0656618\pi$
$659$			10.5160i			0.409646i	−0.978799	+	0.204823i	$0.934338\pi$
$660$		0			0
$661$	−19.9999	−	19.9999i	−0.777907	−	0.777907i	0.201567	−	0.979475i	$-0.435397\pi$
$661$	−19.9999	−	19.9999i	−0.777907	−	0.777907i	−0.979475	+	0.201567i	$0.935397\pi$
$662$	−21.4571			−0.833955
$663$	−27.8249	+	31.6665i	−1.08063	+	1.22982i
$664$	40.7867			1.58283
$665$		0			0
$666$	5.59604	−	3.98793i	0.216842	−	0.154529i
$667$			6.53721i			0.253122i
$668$	13.8891	+	13.8891i	0.537386	+	0.537386i
$669$	28.5771	−	9.14070i	1.10485	−	0.353400i
$670$		0			0
$671$	−0.450366	+	0.450366i	−0.0173862	+	0.0173862i
$672$	8.10143	−	15.7215i	0.312520	−	0.606469i
$673$		−	0.230805i		−	0.00889689i	−0.999990	−	0.00444844i	$-0.998584\pi$
$673$		−	0.230805i		−	0.00889689i	0.999990	−	0.00444844i	$-0.00141599\pi$
$674$	0.538863	−	0.538863i	0.0207562	−	0.0207562i
$675$		0			0
$676$	−9.37538	+	17.5691i	−0.360592	+	0.675734i
$677$			41.4875i			1.59449i	0.603654	+	0.797247i	$0.293711\pi$
$677$			41.4875i			1.59449i	−0.603654	+	0.797247i	$0.706289\pi$
$678$	−6.27638	+	2.00757i	−0.241043	+	0.0771004i
$679$	−2.57746			−0.0989138
$680$		0			0
$681$	7.84109	+	24.5140i	0.300471	+	0.939379i
$682$	−1.52116	+	1.52116i	−0.0582483	+	0.0582483i
$683$	−31.7789	+	31.7789i	−1.21599	+	1.21599i	−0.246960	+	0.969026i	$0.579432\pi$
$683$	−31.7789	+	31.7789i	−1.21599	+	1.21599i	−0.969026	+	0.246960i	$0.920568\pi$
$684$	1.43364	−	8.54414i	0.0548165	−	0.326693i
$685$		0			0
$686$	−13.1325			−0.501400
$687$	3.31767	+	10.3722i	0.126577	+	0.395724i
$688$			16.5555i			0.631174i
$689$	30.8286	+	7.71092i	1.17448	+	0.293763i
$690$		0			0
$691$	25.0328	−	25.0328i	0.952293	−	0.952293i	−0.0466196	−	0.998913i	$-0.514845\pi$
$691$	25.0328	−	25.0328i	0.952293	−	0.952293i	0.998913	+	0.0466196i	$0.0148449\pi$
$692$		−	7.10633i		−	0.270142i
$693$	1.67858	+	2.35546i	0.0637641	+	0.0894767i
$694$	7.23648	−	7.23648i	0.274693	−	0.274693i
$695$		0			0
$696$	4.91408	+	15.3631i	0.186268	+	0.582338i
$697$	−38.6187	−	38.6187i	−1.46279	−	1.46279i
$698$		−	7.86699i		−	0.297770i
$699$	−27.2357	−	14.0349i	−1.03015	−	0.530847i
$700$		0			0
$701$	−27.4234			−1.03577			−0.517883	−	0.855451i	$-0.673280\pi$
$701$	−27.4234			−1.03577			−0.517883	+	0.855451i	$0.673280\pi$
$702$	8.09654	+	9.93810i	0.305584	+	0.375090i
$703$	6.31112			0.238028
$704$	−0.443822	−	0.443822i	−0.0167272	−	0.0167272i
$705$		0			0
$706$		−	13.5739i		−	0.510859i
$707$	22.7233	+	22.7233i	0.854596	+	0.854596i
$708$	−1.49216	−	4.66502i	−0.0560789	−	0.175322i
$709$	−0.997734	−	0.997734i	−0.0374707	−	0.0374707i	0.688123	−	0.725594i	$-0.258435\pi$
$709$	−0.997734	−	0.997734i	−0.0374707	−	0.0374707i	−0.725594	+	0.688123i	$0.758435\pi$
$710$		0			0
$711$	−6.71010	−	9.41592i	−0.251649	−	0.353125i
$712$			20.4945i			0.768066i
$713$	6.88901	−	6.88901i	0.257996	−	0.257996i
$714$	−6.45334	+	12.5232i	−0.241510	+	0.468669i
$715$		0			0
$716$		−	20.3574i		−	0.760793i
$717$	−3.51336	−	10.9840i	−0.131209	−	0.410205i
$718$	13.5550			0.505867
$719$	−13.8518			−0.516585			−0.258292	−	0.966067i	$-0.583160\pi$
$719$	−13.8518			−0.516585			−0.258292	+	0.966067i	$0.583160\pi$
$720$		0			0
$721$	−4.55144	+	4.55144i	−0.169505	+	0.169505i
$722$	7.47295	−	7.47295i	0.278115	−	0.278115i
$723$	−10.2957	−	32.1879i	−0.382900	−	1.19708i
$724$	35.7124			1.32724
$725$		0			0
$726$	−12.0780	+	3.86330i	−0.448258	+	0.143380i
$727$		−	36.0915i		−	1.33856i	−0.743010	−	0.669280i	$-0.766603\pi$
$727$		−	36.0915i		−	1.33856i	0.743010	−	0.669280i	$-0.233397\pi$
$728$	−3.72335	+	14.8861i	−0.137996	+	0.551715i
$729$	−25.8982	+	7.63446i	−0.959191	+	0.282758i
$730$		0			0
$731$		−	79.2408i		−	2.93083i
$732$	1.41399	−	2.74396i	0.0522626	−	0.101420i
$733$	−13.0564	+	13.0564i	−0.482248	+	0.482248i	−0.905849	−	0.423601i	$-0.860766\pi$
$733$	−13.0564	+	13.0564i	−0.482248	+	0.482248i	0.423601	+	0.905849i	$0.360766\pi$
$734$	−12.6895	−	12.6895i	−0.468378	−	0.468378i
$735$		0			0
$736$	6.95471	+	6.95471i	0.256354	+	0.256354i
$737$		−	3.61434i		−	0.133136i
$738$	−13.5250	+	9.63836i	−0.497861	+	0.354793i
$739$	12.8744	+	12.8744i	0.473592	+	0.473592i	0.903075	−	0.429483i	$-0.141304\pi$
$739$	12.8744	+	12.8744i	0.473592	+	0.473592i	−0.429483	+	0.903075i	$0.641304\pi$
$740$		0			0
$741$	0.758645	+	11.7486i	0.0278695	+	0.431597i
$742$	10.6204			0.389889
$743$	20.7742	+	20.7742i	0.762133	+	0.762133i	0.976708	−	0.214575i	$-0.0688366\pi$
$743$	20.7742	+	20.7742i	0.762133	+	0.762133i	−0.214575	+	0.976708i	$0.568837\pi$
$744$	11.0114	−	21.3685i	0.403697	−	0.783405i
$745$		0			0
$746$	3.30783	+	3.30783i	0.121108	+	0.121108i
$747$	8.37893	−	49.9364i	0.306569	−	1.82708i
$748$	−4.00271	−	4.00271i	−0.146354	−	0.146354i
$749$	18.6283	−	18.6283i	0.680663	−	0.680663i
$750$		0			0
$751$		−	14.1702i		−	0.517080i	−0.966001	−	0.258540i	$-0.916759\pi$
$751$		−	14.1702i		−	0.517080i	0.966001	−	0.258540i	$-0.0832413\pi$
$752$	8.44779	−	8.44779i	0.308059	−	0.308059i
$753$	8.93946	+	4.60660i	0.325772	+	0.167874i
$754$	−4.89034	−	8.15270i	−0.178096	−	0.296904i
$755$		0			0
$756$	−11.2266	−	8.39477i	−0.408308	−	0.305315i
$757$	27.8108			1.01080			0.505400	−	0.862885i	$-0.331345\pi$
$757$	27.8108			1.01080			0.505400	+	0.862885i	$0.331345\pi$
$758$	24.0823			0.874710
$759$	−1.53202	+	0.490035i	−0.0556089	+	0.0177871i
$760$		0			0
$761$	−3.88054	+	3.88054i	−0.140669	+	0.140669i	−0.773935	−	0.633265i	$-0.781714\pi$
$761$	−3.88054	+	3.88054i	−0.140669	+	0.140669i	0.633265	+	0.773935i	$0.281714\pi$
$762$	0.0394665	−	0.0126238i	0.00142972	−	0.000457313i
$763$	13.4853			0.488200
$764$	9.81584			0.355125
$765$		0			0
$766$			7.51254i			0.271439i
$767$	3.42372	+	5.70769i	0.123623	+	0.206093i
$768$	14.9199	+	7.68838i	0.538375	+	0.277430i
$769$	−22.5865	+	22.5865i	−0.814491	+	0.814491i	−0.985304	−	0.170813i	$-0.945361\pi$
$769$	−22.5865	+	22.5865i	−0.814491	+	0.814491i	0.170813	+	0.985304i	$0.445361\pi$
$770$		0			0
$771$	12.7729	+	6.58200i	0.460004	+	0.237045i
$772$	24.6828	−	24.6828i	0.888353	−	0.888353i
$773$	25.7487	+	25.7487i	0.926116	+	0.926116i	0.997452	−	0.0713367i	$-0.0227265\pi$
$773$	25.7487	+	25.7487i	0.926116	+	0.926116i	−0.0713367	+	0.997452i	$0.522726\pi$
$774$	−23.7642	−	3.98744i	−0.854185	−	0.143325i
$775$		0			0
$776$		−	3.53666i		−	0.126959i
$777$	4.67767	−	9.07739i	0.167811	−	0.325650i
$778$	−3.04962	−	3.04962i	−0.109334	−	0.109334i
$779$	−15.2532			−0.546504
$780$		0			0
$781$	0.709112			0.0253740
$782$	−5.53990	−	5.53990i	−0.198106	−	0.198106i
$783$	19.8191	−	2.86036i	0.708275	−	0.102221i
$784$			5.49784i			0.196351i
$785$		0			0
$786$	1.26364	−	0.404190i	0.0450726	−	0.0144170i
$787$	19.7231	+	19.7231i	0.703054	+	0.703054i	0.965065	−	0.262011i	$-0.0843856\pi$
$787$	19.7231	+	19.7231i	0.703054	+	0.703054i	−0.262011	+	0.965065i	$0.584386\pi$
$788$	17.3537	−	17.3537i	0.618200	−	0.618200i
$789$	8.62564	−	16.7387i	0.307081	−	0.595915i
$790$		0			0
$791$	−6.92447	+	6.92447i	−0.246206	+	0.246206i
$792$	−3.23205	+	2.30327i	−0.114846	+	0.0818431i
$793$	−1.01786	+	4.06943i	−0.0361451	+	0.144510i
$794$		−	23.5823i		−	0.836906i
$795$		0			0
$796$	−35.3573			−1.25321
$797$	−27.0871			−0.959474			−0.479737	−	0.877412i	$-0.659268\pi$
$797$	−27.0871			−0.959474			−0.479737	+	0.877412i	$0.659268\pi$
$798$	1.19871	+	3.74758i	0.0424338	+	0.132663i
$799$	−40.4342	+	40.4342i	−1.43046	+	1.43046i
$800$		0			0
$801$	25.0921	+	4.21025i	0.886585	+	0.148762i
$802$	8.53483			0.301375
$803$	−6.28151			−0.221670
$804$	5.33672	+	16.6845i	0.188212	+	0.588416i
$805$		0			0
$806$	−3.43792	+	13.7450i	−0.121096	+	0.484145i
$807$	−17.1856	+	33.3499i	−0.604960	+	1.17397i
$808$	−31.1797	+	31.1797i	−1.09690	+	1.09690i
$809$			12.8814i			0.452886i	0.974024	+	0.226443i	$0.0727097\pi$
$809$			12.8814i			0.452886i	−0.974024	+	0.226443i	$0.927290\pi$
$810$		0			0
$811$	−37.1318	+	37.1318i	−1.30387	+	1.30387i	−0.378116	+	0.925758i	$0.623428\pi$
$811$	−37.1318	+	37.1318i	−1.30387	+	1.30387i	−0.925758	+	0.378116i	$0.876572\pi$
$812$	7.35143	+	7.35143i	0.257985	+	0.257985i
$813$	2.66843	+	8.34244i	0.0935858	+	0.292582i
$814$	−0.886676	−	0.886676i	−0.0310780	−	0.0310780i
$815$		0			0
$816$	14.6567	+	7.55275i	0.513087	+	0.264399i
$817$	−15.6489	−	15.6489i	−0.547485	−	0.547485i
$818$	9.90483			0.346314
$819$	17.4606	+	7.61669i	0.610122	+	0.266149i
$820$		0			0
$821$	−10.6744	−	10.6744i	−0.372540	−	0.372540i	0.495861	−	0.868402i	$-0.334852\pi$
$821$	−10.6744	−	10.6744i	−0.372540	−	0.372540i	−0.868402	+	0.495861i	$0.834852\pi$
$822$	3.85279	+	1.98538i	0.134382	+	0.0692482i
$823$			22.6990i			0.791236i	0.918415	+	0.395618i	$0.129470\pi$
$823$			22.6990i			0.791236i	−0.918415	+	0.395618i	$0.870530\pi$
$824$	−6.24527	−	6.24527i	−0.217564	−	0.217564i
$825$		0			0
$826$	1.57289	+	1.57289i	0.0547277	+	0.0547277i
$827$	−13.2802	+	13.2802i	−0.461799	+	0.461799i	−0.899245	−	0.437446i	$-0.855883\pi$
$827$	−13.2802	+	13.2802i	−0.461799	+	0.461799i	0.437446	+	0.899245i	$0.355883\pi$
$828$	6.34855	−	4.52419i	0.220627	−	0.157226i
$829$		−	11.0522i		−	0.383858i	−0.981409	−	0.191929i	$-0.938526\pi$
$829$		−	11.0522i		−	0.383858i	0.981409	−	0.191929i	$-0.0614743\pi$
$830$		0			0
$831$	−13.8750	+	26.9254i	−0.481317	+	0.934033i
$832$	−4.01030	−	1.00307i	−0.139032	−	0.0347750i
$833$		−	26.3147i		−	0.911749i
$834$	6.02465	+	18.8352i	0.208617	+	0.652209i
$835$		0			0
$836$	−1.58095			−0.0546783
$837$	−23.8999	−	17.8713i	−0.826102	−	0.617724i
$838$	−19.2672	+	19.2672i	−0.665575	+	0.665575i
$839$	−2.03658	+	2.03658i	−0.0703107	+	0.0703107i	−0.741388	−	0.671077i	$-0.765832\pi$
$839$	−2.03658	+	2.03658i	−0.0703107	+	0.0703107i	0.671077	+	0.741388i	$0.265832\pi$
$840$		0			0
$841$	14.1490			0.487897
$842$	10.7587			0.370771
$843$	8.13098	−	2.60079i	0.280046	−	0.0895759i
$844$			13.8574i			0.476992i
$845$		0			0
$846$	10.0915	+	14.1608i	0.346952	+	0.486858i
$847$	−13.3252	+	13.3252i	−0.457859	+	0.457859i
$848$		−	12.4298i		−	0.426840i
$849$	7.51547	−	14.5844i	0.257930	−	0.500534i
$850$		0			0
$851$	4.01557	+	4.01557i	0.137652	+	0.137652i
$852$	−3.27340	+	1.04703i	−0.112145	+	0.0358708i
$853$	26.1501	+	26.1501i	0.895364	+	0.895364i	0.995022	−	0.0996578i	$-0.0317748\pi$
$853$	26.1501	+	26.1501i	0.895364	+	0.895364i	−0.0996578	+	0.995022i	$0.531775\pi$
$854$			1.40192i			0.0479726i
$855$		0			0
$856$	25.5608	+	25.5608i	0.873651	+	0.873651i
$857$	21.8580			0.746653			0.373327	−	0.927700i	$-0.378217\pi$
$857$	21.8580			0.746653			0.373327	+	0.927700i	$0.378217\pi$
$858$	1.54403	−	1.75720i	0.0527124	−	0.0599900i
$859$	3.08718			0.105333			0.0526666	−	0.998612i	$-0.483228\pi$
$859$	3.08718			0.105333			0.0526666	+	0.998612i	$0.483228\pi$
$860$		0			0
$861$	−11.3054	+	21.9390i	−0.385287	+	0.747679i
$862$			5.05794i			0.172274i
$863$	16.2854	+	16.2854i	0.554363	+	0.554363i	0.927697	−	0.373334i	$-0.121786\pi$
$863$	16.2854	+	16.2854i	0.554363	+	0.554363i	−0.373334	+	0.927697i	$0.621786\pi$
$864$	18.0418	−	24.1278i	0.613793	−	0.820845i
$865$		0			0
$866$	1.43306	−	1.43306i	0.0486973	−	0.0486973i
$867$	−43.9784	−	22.6625i	−1.49358	−	0.769659i
$868$		−	15.4941i		−	0.525904i
$869$	−1.49193	+	1.49193i	−0.0506101	+	0.0506101i
$870$		0			0
$871$	−12.2450	−	20.4136i	−0.414905	−	0.691688i
$872$			18.5038i			0.626619i
$873$	−4.33004	−	0.726546i	−0.146550	−	0.0245899i
$874$	−2.18809			−0.0740133
$875$		0			0
$876$	28.9966	−	9.27491i	0.979705	−	0.313370i
$877$	9.53726	−	9.53726i	0.322050	−	0.322050i	−0.527503	−	0.849553i	$-0.676872\pi$
$877$	9.53726	−	9.53726i	0.322050	−	0.322050i	0.849553	+	0.527503i	$0.176872\pi$
$878$	10.3418	−	10.3418i	0.349018	−	0.349018i
$879$	−35.4848	+	11.3502i	−1.19687	+	0.382833i
$880$		0			0
$881$	45.3231			1.52697			0.763487	−	0.645823i	$-0.223486\pi$
$881$	45.3231			1.52697			0.763487	+	0.645823i	$0.223486\pi$
$882$	−7.89171	−	1.32417i	−0.265728	−	0.0445870i
$883$			39.8456i			1.34091i	0.741949	+	0.670456i	$0.233902\pi$
$883$			39.8456i			1.34091i	−0.741949	+	0.670456i	$0.766098\pi$
$884$	−36.1678	−	9.04637i	−1.21645	−	0.304263i
$885$		0			0
$886$	−10.0064	+	10.0064i	−0.336171	+	0.336171i
$887$		−	3.65752i		−	0.122807i	−0.998113	−	0.0614037i	$-0.980442\pi$
$887$		−	3.65752i		−	0.122807i	0.998113	−	0.0614037i	$-0.0195577\pi$
$888$	12.4555	+	6.41847i	0.417981	+	0.215390i
$889$	0.0435418	−	0.0435418i	0.00146034	−	0.00146034i
$890$		0			0
$891$	2.15599	+	4.43026i	0.0722284	+	0.148419i
$892$	18.7634	+	18.7634i	0.628244	+	0.628244i
$893$			15.9703i			0.534425i
$894$	13.0047	−	25.2367i	0.434943	−	0.844041i
$895$		0			0
$896$	19.0406			0.636101
$897$	−6.99260	+	7.95800i	−0.233476	+	0.265710i
$898$	28.1863			0.940590
$899$	15.6502	+	15.6502i	0.521963	+	0.521963i
$900$		0			0
$901$			59.4935i			1.98202i
$902$	2.14299	+	2.14299i	0.0713539	+	0.0713539i
$903$	−34.1067	+	10.9094i	−1.13500	+	0.363043i
$904$	−9.50142	−	9.50142i	−0.316012	−	0.316012i
$905$		0			0
$906$	4.00188	−	7.76595i	0.132953	−	0.258006i
$907$			22.0580i			0.732422i	0.930532	+	0.366211i	$0.119345\pi$
$907$			22.0580i			0.732422i	−0.930532	+	0.366211i	$0.880655\pi$
$908$	−16.0956	+	16.0956i	−0.534152	+	0.534152i
$909$	31.7689	+	44.5796i	1.05371	+	1.47861i
$910$		0			0
$911$		−	9.96697i		−	0.330220i	−0.986275	−	0.165110i	$-0.947202\pi$
$911$		−	9.96697i		−	0.330220i	0.986275	−	0.165110i	$-0.0527980\pi$
$912$	4.38603	−	1.40292i	0.145236	−	0.0464554i
$913$	−9.23989			−0.305796
$914$	−2.50993			−0.0830212
$915$		0			0
$916$	−6.81027	+	6.81027i	−0.225018	+	0.225018i
$917$	1.39412	−	1.39412i	0.0460380	−	0.0460380i
$918$	−14.3715	+	19.2194i	−0.474330	+	0.634336i
$919$	44.1088			1.45502			0.727508	−	0.686100i	$-0.240679\pi$
$919$	44.1088			1.45502			0.727508	+	0.686100i	$0.240679\pi$
$920$		0			0
$921$	−6.45380	−	20.1769i	−0.212660	−	0.664850i
$922$		−	17.5169i		−	0.576890i
$923$	4.00503	−	2.40239i	0.131827	−	0.0790756i
$924$	−1.17177	+	2.27391i	−0.0385483	+	0.0748060i
$925$		0			0
$926$			19.1106i			0.628013i
$927$	−8.92924	+	6.36328i	−0.293275	+	0.208997i
$928$	−15.7994	+	15.7994i	−0.518642	+	0.518642i
$929$	13.0994	+	13.0994i	0.429776	+	0.429776i	0.888552	−	0.458776i	$-0.151712\pi$
$929$	13.0994	+	13.0994i	0.429776	+	0.429776i	−0.458776	+	0.888552i	$0.651712\pi$
$930$		0			0
$931$	−5.19675	−	5.19675i	−0.170317	−	0.170317i
$932$		−	27.0978i		−	0.887618i
$933$	−2.33447	−	1.20298i	−0.0764272	−	0.0393838i
$934$	1.44451	+	1.44451i	0.0472659	+	0.0472659i
$935$		0			0
$936$	−10.4512	+	23.9586i	−0.341610	+	0.783110i
$937$	−23.1567			−0.756496			−0.378248	−	0.925704i	$-0.623473\pi$
$937$	−23.1567			−0.756496			−0.378248	+	0.925704i	$0.623473\pi$
$938$	−5.62543	−	5.62543i	−0.183677	−	0.183677i
$939$	1.43065	+	0.737227i	0.0466874	+	0.0240585i
$940$		0			0
$941$	14.3573	+	14.3573i	0.468035	+	0.468035i	0.901277	−	0.433242i	$-0.142631\pi$
$941$	14.3573	+	14.3573i	0.468035	+	0.468035i	−0.433242	+	0.901277i	$0.642631\pi$
$942$	4.70492	+	14.7092i	0.153294	+	0.479253i
$943$	−9.70515	−	9.70515i	−0.316043	−	0.316043i
$944$	1.84085	−	1.84085i	0.0599145	−	0.0599145i
$945$		0			0
$946$			4.39716i			0.142964i
$947$	−0.485543	+	0.485543i	−0.0157780	+	0.0157780i	−0.714952	−	0.699174i	$-0.753551\pi$
$947$	−0.485543	+	0.485543i	−0.0157780	+	0.0157780i	0.699174	+	0.714952i	$0.253551\pi$
$948$	4.68412	−	9.08990i	0.152133	−	0.295226i
$949$	−35.4776	+	21.2810i	−1.15165	+	0.690811i
$950$		0			0
$951$	11.4178	+	35.6960i	0.370246	+	1.15752i
$952$	−28.7274			−0.931061
$953$	29.1833			0.945339			0.472670	−	0.881240i	$-0.343290\pi$
$953$	29.1833			0.945339			0.472670	+	0.881240i	$0.343290\pi$
$954$	17.8420	+	2.99374i	0.577655	+	0.0969259i
$955$		0			0
$956$	7.21196	−	7.21196i	0.233252	−	0.233252i
$957$	−1.11324	−	3.48039i	−0.0359860	−	0.112505i
$958$	−4.46230			−0.144170
$959$	6.44102			0.207991
$960$		0			0
$961$		−	1.98485i		−	0.0640273i
$962$	−8.01186	−	2.00394i	−0.258313	−	0.0646098i
$963$	36.5459	−	26.0438i	1.17768	−	0.839251i
$964$	21.1342	−	21.1342i	0.680687	−	0.680687i
$965$		0			0
$966$	−1.62177	+	3.14717i	−0.0521796	+	0.101259i
$967$	−14.9051	+	14.9051i	−0.479316	+	0.479316i	−0.904913	−	0.425597i	$-0.860064\pi$
$967$	−14.9051	+	14.9051i	−0.479316	+	0.479316i	0.425597	+	0.904913i	$0.360064\pi$
$968$	−18.2842	−	18.2842i	−0.587675	−	0.587675i
$969$	−20.9932	+	6.71491i	−0.674398	+	0.215714i
$970$		0			0
$971$			46.0892i			1.47907i	0.673116	+	0.739537i	$0.264955\pi$
$971$			46.0892i			1.47907i	−0.673116	+	0.739537i	$0.735045\pi$
$972$	−16.4939	−	17.2675i	−0.529043	−	0.553856i
$973$	20.7801	+	20.7801i	0.666179	+	0.666179i
$974$	21.9747			0.704116
$975$		0			0
$976$	1.64075			0.0525192
$977$	11.8734	+	11.8734i	0.379864	+	0.379864i	0.871053	−	0.491189i	$-0.163438\pi$
$977$	11.8734	+	11.8734i	0.379864	+	0.379864i	−0.491189	+	0.871053i	$0.663438\pi$
$978$	2.94339	−	5.71188i	0.0941193	−	0.182646i
$979$		−	4.64287i		−	0.148387i
$980$		0			0
$981$	22.6548	+	3.80129i	0.723312	+	0.121366i
$982$	15.8755	+	15.8755i	0.506607	+	0.506607i
$983$	8.05185	−	8.05185i	0.256814	−	0.256814i	−0.566943	−	0.823757i	$-0.691874\pi$
$983$	8.05185	−	8.05185i	0.256814	−	0.256814i	0.823757	+	0.566943i	$0.191874\pi$
$984$	−30.1036	−	15.5127i	−0.959668	−	0.494527i
$985$		0			0
$986$	12.5853	−	12.5853i	0.400798	−	0.400798i
$987$	22.9704	+	11.8369i	0.731155	+	0.376772i
$988$	−8.92911	+	5.35607i	−0.284073	+	0.170399i
$989$		−	19.9138i		−	0.633221i
$990$		0			0
$991$	52.2270			1.65905			0.829523	−	0.558473i	$-0.188612\pi$
$991$	52.2270			1.65905			0.829523	+	0.558473i	$0.188612\pi$
$992$	33.2994			1.05726
$993$	−51.7355	+	16.5482i	−1.64178	+	0.525141i
$994$	1.10368	−	1.10368i	0.0350065	−	0.0350065i
$995$		0			0
$996$	42.6531	−	13.6431i	1.35151	−	0.432297i
$997$	28.9060			0.915462			0.457731	−	0.889091i	$-0.348662\pi$
$997$	28.9060			0.915462			0.457731	+	0.889091i	$0.348662\pi$
$998$	−0.346810			−0.0109781
$999$	10.4171	−	13.9311i	0.329582	−	0.440761i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	975.2.o.p.551.8		40
3.2	odd	2	inner	975.2.o.p.551.13		40
5.2	odd	4		975.2.n.q.824.13		40
5.3	odd	4		975.2.n.r.824.8		40
5.4	even	2		195.2.o.a.161.13	yes	40
13.8	odd	4	inner	975.2.o.p.476.13		40
15.2	even	4		975.2.n.q.824.8		40
15.8	even	4		975.2.n.r.824.13		40
15.14	odd	2		195.2.o.a.161.8	yes	40
39.8	even	4	inner	975.2.o.p.476.8		40
65.8	even	4		975.2.n.q.749.8		40
65.34	odd	4		195.2.o.a.86.8	✓	40
65.47	even	4		975.2.n.r.749.13		40
195.8	odd	4		975.2.n.q.749.13		40
195.47	odd	4		975.2.n.r.749.8		40
195.164	even	4		195.2.o.a.86.13	yes	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
195.2.o.a.86.8	✓	40	65.34	odd	4
195.2.o.a.86.13	yes	40	195.164	even	4
195.2.o.a.161.8	yes	40	15.14	odd	2
195.2.o.a.161.13	yes	40	5.4	even	2
975.2.n.q.749.8		40	65.8	even	4
975.2.n.q.749.13		40	195.8	odd	4
975.2.n.q.824.8		40	15.2	even	4
975.2.n.q.824.13		40	5.2	odd	4
975.2.n.r.749.8		40	195.47	odd	4
975.2.n.r.749.13		40	65.47	even	4
975.2.n.r.824.8		40	5.3	odd	4
975.2.n.r.824.13		40	15.8	even	4
975.2.o.p.476.8		40	39.8	even	4	inner
975.2.o.p.476.13		40	13.8	odd	4	inner
975.2.o.p.551.8		40	1.1	even	1	trivial
975.2.o.p.551.13		40	3.2	odd	2	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 975 = 3 \cdot 5^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	975.o (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.483812 - 0.483812i) q^{2} +(-1.53965 - 0.793397i) q^{3} -1.53185i q^{4} +(0.361045 + 1.12876i) q^{6} +(1.24531 + 1.24531i) q^{7} +(-1.70875 + 1.70875i) q^{8} +(1.74104 + 2.44311i) q^{9} +O(q^{10})\)	\(q+(-0.483812 - 0.483812i) q^{2} +(-1.53965 - 0.793397i) q^{3} -1.53185i q^{4} +(0.361045 + 1.12876i) q^{6} +(1.24531 + 1.24531i) q^{7} +(-1.70875 + 1.70875i) q^{8} +(1.74104 + 2.44311i) q^{9} +(0.387103 - 0.387103i) q^{11} +(-1.21537 + 2.35852i) q^{12} +(0.874878 - 3.49780i) q^{13} -1.20499i q^{14} -1.41028 q^{16} +6.75010 q^{17} +(0.339668 - 2.02434i) q^{18} +(1.33304 - 1.33304i) q^{19} +(-0.929314 - 2.90536i) q^{21} -0.374570 q^{22} +1.69635 q^{23} +(3.98660 - 1.27516i) q^{24} +(-2.11555 + 1.26900i) q^{26} +(-0.742237 - 5.14287i) q^{27} +(1.90763 - 1.90763i) q^{28} +3.85370i q^{29} +(4.06109 - 4.06109i) q^{31} +(4.09981 + 4.09981i) q^{32} +(-0.903130 + 0.288877i) q^{33} +(-3.26578 - 3.26578i) q^{34} +(3.74248 - 2.66702i) q^{36} +(2.36718 + 2.36718i) q^{37} -1.28988 q^{38} +(-4.12215 + 4.69126i) q^{39} +(-5.72121 - 5.72121i) q^{41} +(-0.956036 + 1.85526i) q^{42} -11.7392i q^{43} +(-0.592985 - 0.592985i) q^{44} +(-0.820713 - 0.820713i) q^{46} +(-5.99016 + 5.99016i) q^{47} +(2.17133 + 1.11891i) q^{48} -3.89841i q^{49} +(-10.3928 - 5.35551i) q^{51} +(-5.35811 - 1.34018i) q^{52} +8.81372i q^{53} +(-2.12908 + 2.84728i) q^{54} -4.25585 q^{56} +(-3.11005 + 0.994786i) q^{57} +(1.86446 - 1.86446i) q^{58} +(-1.30531 + 1.30531i) q^{59} -1.16343 q^{61} -3.92960 q^{62} +(-0.874290 + 5.21056i) q^{63} -1.14652i q^{64} +(0.576707 + 0.297183i) q^{66} +(4.66845 - 4.66845i) q^{67} -10.3402i q^{68} +(-2.61178 - 1.34588i) q^{69} +(0.915921 + 0.915921i) q^{71} +(-7.14967 - 1.19966i) q^{72} +(-8.11348 - 8.11348i) q^{73} -2.29054i q^{74} +(-2.04202 - 2.04202i) q^{76} +0.964126 q^{77} +(4.26403 - 0.275341i) q^{78} -3.85408 q^{79} +(-2.93755 + 8.50710i) q^{81} +5.53597i q^{82} +(-11.9347 - 11.9347i) q^{83} +(-4.45059 + 1.42357i) q^{84} +(-5.67957 + 5.67957i) q^{86} +(3.05751 - 5.93334i) q^{87} +1.32293i q^{88} +(5.99694 - 5.99694i) q^{89} +(5.44533 - 3.26635i) q^{91} -2.59855i q^{92} +(-9.47471 + 3.03059i) q^{93} +5.79622 q^{94} +(-3.05949 - 9.56505i) q^{96} +(-1.03487 + 1.03487i) q^{97} +(-1.88610 + 1.88610i) q^{98} +(1.61970 + 0.271772i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q + 12 q^{6} + 16 q^{7}+O(q^{10}) \) 40 * q + 12 * q^6 + 16 * q^7	\( 40 q + 12 q^{6} + 16 q^{7} - 64 q^{16} - 4 q^{18} - 16 q^{19} - 12 q^{21} + 8 q^{24} + 24 q^{27} - 32 q^{28} + 32 q^{31} + 4 q^{33} - 16 q^{34} - 32 q^{37} - 8 q^{39} - 8 q^{42} - 40 q^{46} - 8 q^{48} - 32 q^{54} + 36 q^{57} - 24 q^{58} + 8 q^{61} - 8 q^{63} - 48 q^{66} + 32 q^{67} - 132 q^{72} + 64 q^{73} + 16 q^{76} + 12 q^{78} + 40 q^{79} + 72 q^{81} + 124 q^{84} - 16 q^{87} + 8 q^{91} + 108 q^{93} - 32 q^{94} - 76 q^{96} - 24 q^{97} - 20 q^{99}+O(q^{100}) \) 40 * q + 12 * q^6 + 16 * q^7 - 64 * q^16 - 4 * q^18 - 16 * q^19 - 12 * q^21 + 8 * q^24 + 24 * q^27 - 32 * q^28 + 32 * q^31 + 4 * q^33 - 16 * q^34 - 32 * q^37 - 8 * q^39 - 8 * q^42 - 40 * q^46 - 8 * q^48 - 32 * q^54 + 36 * q^57 - 24 * q^58 + 8 * q^61 - 8 * q^63 - 48 * q^66 + 32 * q^67 - 132 * q^72 + 64 * q^73 + 16 * q^76 + 12 * q^78 + 40 * q^79 + 72 * q^81 + 124 * q^84 - 16 * q^87 + 8 * q^91 + 108 * q^93 - 32 * q^94 - 76 * q^96 - 24 * q^97 - 20 * q^99

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