LMFDB - Embedded newform 287.2.f.a.50.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [287,2,Mod(50,287)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(287, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([0, 3]))

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

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

chi := DirichletCharacter("287.50");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 287 = 7 \cdot 41 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	287.f (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:	$2.29170653801$
Analytic rank:	$0$
Dimension:	$40$
Relative dimension:	$20$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			50.1
Character	$\chi$	$=$	287.50
Dual form			287.2.f.a.155.20

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.46506i q^{2} +(0.589206 + 0.589206i) q^{3} -4.07653 q^{4} -2.39319i q^{5} +(1.45243 - 1.45243i) q^{6} +(0.707107 + 0.707107i) q^{7} +5.11877i q^{8} -2.30567i q^{9} +O(q^{10})$	\(q-2.46506i q^{2} +(0.589206 + 0.589206i) q^{3} -4.07653 q^{4} -2.39319i q^{5} +(1.45243 - 1.45243i) q^{6} +(0.707107 + 0.707107i) q^{7} +5.11877i q^{8} -2.30567i q^{9} -5.89935 q^{10} +(-2.82633 - 2.82633i) q^{11} +(-2.40191 - 2.40191i) q^{12} +(1.13710 + 1.13710i) q^{13} +(1.74306 - 1.74306i) q^{14} +(1.41008 - 1.41008i) q^{15} +4.46503 q^{16} +(-0.138947 + 0.138947i) q^{17} -5.68363 q^{18} +(-3.97298 + 3.97298i) q^{19} +9.75589i q^{20} +0.833263i q^{21} +(-6.96707 + 6.96707i) q^{22} +5.45301 q^{23} +(-3.01601 + 3.01601i) q^{24} -0.727338 q^{25} +(2.80302 - 2.80302i) q^{26} +(3.12613 - 3.12613i) q^{27} +(-2.88254 - 2.88254i) q^{28} +(-7.02439 - 7.02439i) q^{29} +(-3.47593 - 3.47593i) q^{30} +8.21214 q^{31} -0.769023i q^{32} -3.33058i q^{33} +(0.342514 + 0.342514i) q^{34} +(1.69224 - 1.69224i) q^{35} +9.39914i q^{36} +3.00778 q^{37} +(9.79364 + 9.79364i) q^{38} +1.33997i q^{39} +12.2502 q^{40} +(5.88037 - 2.53401i) q^{41} +2.05404 q^{42} +5.73417i q^{43} +(11.5216 + 11.5216i) q^{44} -5.51790 q^{45} -13.4420i q^{46} +(3.40136 - 3.40136i) q^{47} +(2.63082 + 2.63082i) q^{48} +1.00000i q^{49} +1.79293i q^{50} -0.163737 q^{51} +(-4.63542 - 4.63542i) q^{52} +(6.37251 + 6.37251i) q^{53} +(-7.70611 - 7.70611i) q^{54} +(-6.76393 + 6.76393i) q^{55} +(-3.61952 + 3.61952i) q^{56} -4.68181 q^{57} +(-17.3155 + 17.3155i) q^{58} +3.77743 q^{59} +(-5.74823 + 5.74823i) q^{60} -9.77967i q^{61} -20.2434i q^{62} +(1.63036 - 1.63036i) q^{63} +7.03436 q^{64} +(2.72129 - 2.72129i) q^{65} -8.21008 q^{66} +(-4.86163 + 4.86163i) q^{67} +(0.566423 - 0.566423i) q^{68} +(3.21294 + 3.21294i) q^{69} +(-4.17147 - 4.17147i) q^{70} +(1.91160 + 1.91160i) q^{71} +11.8022 q^{72} -6.30345i q^{73} -7.41437i q^{74} +(-0.428552 - 0.428552i) q^{75} +(16.1960 - 16.1960i) q^{76} -3.99703i q^{77} +3.30312 q^{78} +(-1.26491 - 1.26491i) q^{79} -10.6856i q^{80} -3.23315 q^{81} +(-6.24650 - 14.4955i) q^{82} -5.53161 q^{83} -3.39682i q^{84} +(0.332527 + 0.332527i) q^{85} +14.1351 q^{86} -8.27762i q^{87} +(14.4673 - 14.4673i) q^{88} +(5.88812 + 5.88812i) q^{89} +13.6020i q^{90} +1.60810i q^{91} -22.2293 q^{92} +(4.83864 + 4.83864i) q^{93} +(-8.38456 - 8.38456i) q^{94} +(9.50808 + 9.50808i) q^{95} +(0.453113 - 0.453113i) q^{96} +(4.75113 - 4.75113i) q^{97} +2.46506 q^{98} +(-6.51659 + 6.51659i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q + 4 q^{3} - 36 q^{4} + 8 q^{6}+O(q^{10}) $ 40 * q + 4 * q^3 - 36 * q^4 + 8 * q^6	$ 40 q + 4 q^{3} - 36 q^{4} + 8 q^{6} - 32 q^{10} - 8 q^{11} + 16 q^{12} + 16 q^{13} - 8 q^{15} + 28 q^{16} + 20 q^{17} - 12 q^{18} - 20 q^{19} + 4 q^{22} + 16 q^{23} - 12 q^{24} - 40 q^{25} - 20 q^{26} - 20 q^{27} - 12 q^{29} + 4 q^{30} + 32 q^{34} + 4 q^{35} - 16 q^{38} + 64 q^{40} + 16 q^{41} + 32 q^{42} + 8 q^{44} + 72 q^{45} - 24 q^{47} - 40 q^{48} - 64 q^{51} - 96 q^{52} + 8 q^{53} + 52 q^{54} - 8 q^{55} - 88 q^{57} - 36 q^{58} + 48 q^{59} + 52 q^{60} - 8 q^{63} - 84 q^{64} - 44 q^{65} + 56 q^{66} + 40 q^{67} - 60 q^{68} + 28 q^{69} - 8 q^{70} + 20 q^{71} + 80 q^{72} - 20 q^{75} - 4 q^{76} + 12 q^{78} - 12 q^{79} + 16 q^{81} - 52 q^{82} + 40 q^{83} + 8 q^{85} + 80 q^{86} + 96 q^{88} - 8 q^{89} - 20 q^{92} - 64 q^{93} + 52 q^{94} + 68 q^{96} - 60 q^{97} - 4 q^{98} - 36 q^{99}+O(q^{100}) $ 40 * q + 4 * q^3 - 36 * q^4 + 8 * q^6 - 32 * q^10 - 8 * q^11 + 16 * q^12 + 16 * q^13 - 8 * q^15 + 28 * q^16 + 20 * q^17 - 12 * q^18 - 20 * q^19 + 4 * q^22 + 16 * q^23 - 12 * q^24 - 40 * q^25 - 20 * q^26 - 20 * q^27 - 12 * q^29 + 4 * q^30 + 32 * q^34 + 4 * q^35 - 16 * q^38 + 64 * q^40 + 16 * q^41 + 32 * q^42 + 8 * q^44 + 72 * q^45 - 24 * q^47 - 40 * q^48 - 64 * q^51 - 96 * q^52 + 8 * q^53 + 52 * q^54 - 8 * q^55 - 88 * q^57 - 36 * q^58 + 48 * q^59 + 52 * q^60 - 8 * q^63 - 84 * q^64 - 44 * q^65 + 56 * q^66 + 40 * q^67 - 60 * q^68 + 28 * q^69 - 8 * q^70 + 20 * q^71 + 80 * q^72 - 20 * q^75 - 4 * q^76 + 12 * q^78 - 12 * q^79 + 16 * q^81 - 52 * q^82 + 40 * q^83 + 8 * q^85 + 80 * q^86 + 96 * q^88 - 8 * q^89 - 20 * q^92 - 64 * q^93 + 52 * q^94 + 68 * q^96 - 60 * q^97 - 4 * q^98 - 36 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/287\mathbb{Z}\right)^\times$.

$n$	$206$	$211$
$\chi(n)$	$1$	$e\left(\frac{3}{4}\right)$

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 $

$2$		−	2.46506i		−	1.74306i	−0.490341	−	0.871531i	$-0.663128\pi$
$2$		−	2.46506i		−	1.74306i	0.490341	−	0.871531i	$-0.336872\pi$
$3$	0.589206	+	0.589206i	0.340178	+	0.340178i	0.856434	−	0.516256i	$-0.172675\pi$
$3$	0.589206	+	0.589206i	0.340178	+	0.340178i	−0.516256	+	0.856434i	$0.672675\pi$
$4$	−4.07653			−2.03826
$5$		−	2.39319i		−	1.07027i	−0.844768	−	0.535133i	$-0.820262\pi$
$5$		−	2.39319i		−	1.07027i	0.844768	−	0.535133i	$-0.179738\pi$
$6$	1.45243	−	1.45243i	0.592952	−	0.592952i
$7$	0.707107	+	0.707107i	0.267261	+	0.267261i
$7$	0.707107	+	0.707107i	0.267261	+	0.267261i
$8$			5.11877i			1.80976i
$9$		−	2.30567i		−	0.768558i
$10$	−5.89935			−1.86554
$11$	−2.82633	−	2.82633i	−0.852170	−	0.852170i	0.138230	−	0.990400i	$-0.455859\pi$
$11$	−2.82633	−	2.82633i	−0.852170	−	0.852170i	−0.990400	+	0.138230i	$0.955859\pi$
$12$	−2.40191	−	2.40191i	−0.693373	−	0.693373i
$13$	1.13710	+	1.13710i	0.315375	+	0.315375i	0.846988	−	0.531613i	$-0.178414\pi$
$13$	1.13710	+	1.13710i	0.315375	+	0.315375i	−0.531613	+	0.846988i	$0.678414\pi$
$14$	1.74306	−	1.74306i	0.465853	−	0.465853i
$15$	1.41008	−	1.41008i	0.364081	−	0.364081i
$16$	4.46503			1.11626
$17$	−0.138947	+	0.138947i	−0.0336997	+	0.0336997i	−0.723756	−	0.690056i	$-0.757586\pi$
$17$	−0.138947	+	0.138947i	−0.0336997	+	0.0336997i	0.690056	+	0.723756i	$0.257586\pi$
$18$	−5.68363			−1.33964
$19$	−3.97298	+	3.97298i	−0.911464	+	0.911464i	−0.996388	−	0.0849230i	$-0.972936\pi$
$19$	−3.97298	+	3.97298i	−0.911464	+	0.911464i	0.0849230	+	0.996388i	$0.472936\pi$
$20$			9.75589i			2.18148i
$21$			0.833263i			0.181833i
$22$	−6.96707	+	6.96707i	−1.48538	+	1.48538i
$23$	5.45301			1.13703			0.568515	−	0.822673i	$-0.307518\pi$
$23$	5.45301			1.13703			0.568515	+	0.822673i	$0.307518\pi$
$24$	−3.01601	+	3.01601i	−0.615640	+	0.615640i
$25$	−0.727338			−0.145468
$26$	2.80302	−	2.80302i	0.549718	−	0.549718i
$27$	3.12613	−	3.12613i	0.601625	−	0.601625i
$28$	−2.88254	−	2.88254i	−0.544749	−	0.544749i
$29$	−7.02439	−	7.02439i	−1.30440	−	1.30440i	−0.925397	−	0.378999i	$-0.876268\pi$
$29$	−7.02439	−	7.02439i	−1.30440	−	1.30440i	−0.378999	−	0.925397i	$-0.623732\pi$
$30$	−3.47593	−	3.47593i	−0.634615	−	0.634615i
$31$	8.21214			1.47494			0.737472	−	0.675377i	$-0.236019\pi$
$31$	8.21214			1.47494			0.737472	+	0.675377i	$0.236019\pi$
$32$		−	0.769023i		−	0.135945i
$33$		−	3.33058i		−	0.579779i
$34$	0.342514	+	0.342514i	0.0587406	+	0.0587406i
$35$	1.69224	−	1.69224i	0.286040	−	0.286040i
$36$			9.39914i			1.56652i
$37$	3.00778			0.494477			0.247238	−	0.968955i	$-0.420477\pi$
$37$	3.00778			0.494477			0.247238	+	0.968955i	$0.420477\pi$
$38$	9.79364	+	9.79364i	1.58874	+	1.58874i
$39$			1.33997i			0.214567i
$40$	12.2502			1.93692
$41$	5.88037	−	2.53401i	0.918360	−	0.395747i
$41$	5.88037	−	2.53401i	0.918360	−	0.395747i
$42$	2.05404			0.316946
$43$			5.73417i			0.874453i	0.899351	+	0.437227i	$0.144039\pi$
$43$			5.73417i			0.874453i	−0.899351	+	0.437227i	$0.855961\pi$
$44$	11.5216	+	11.5216i	1.73695	+	1.73695i
$45$	−5.51790			−0.822560
$46$		−	13.4420i		−	1.98191i
$47$	3.40136	−	3.40136i	0.496139	−	0.496139i	−0.414095	−	0.910234i	$-0.635902\pi$
$47$	3.40136	−	3.40136i	0.496139	−	0.496139i	0.910234	+	0.414095i	$0.135902\pi$
$48$	2.63082	+	2.63082i	0.379726	+	0.379726i
$49$			1.00000i			0.142857i
$50$			1.79293i			0.253559i
$51$	−0.163737			−0.0229278
$52$	−4.63542	−	4.63542i	−0.642817	−	0.642817i
$53$	6.37251	+	6.37251i	0.875332	+	0.875332i	0.993047	−	0.117716i	$-0.0375572\pi$
$53$	6.37251	+	6.37251i	0.875332	+	0.875332i	−0.117716	+	0.993047i	$0.537557\pi$
$54$	−7.70611	−	7.70611i	−1.04867	−	1.04867i
$55$	−6.76393	+	6.76393i	−0.912048	+	0.912048i
$56$	−3.61952	+	3.61952i	−0.483678	+	0.483678i
$57$	−4.68181			−0.620121
$58$	−17.3155	+	17.3155i	−2.27364	+	2.27364i
$59$	3.77743			0.491779			0.245890	−	0.969298i	$-0.420920\pi$
$59$	3.77743			0.491779			0.245890	+	0.969298i	$0.420920\pi$
$60$	−5.74823	+	5.74823i	−0.742093	+	0.742093i
$61$		−	9.77967i		−	1.25216i	−0.779760	−	0.626079i	$-0.784659\pi$
$61$		−	9.77967i		−	1.25216i	0.779760	−	0.626079i	$-0.215341\pi$
$62$		−	20.2434i		−	2.57092i
$63$	1.63036	−	1.63036i	0.205406	−	0.205406i
$64$	7.03436			0.879295
$65$	2.72129	−	2.72129i	0.337535	−	0.337535i
$66$	−8.21008			−1.01059
$67$	−4.86163	+	4.86163i	−0.593943	+	0.593943i	−0.938694	−	0.344751i	$-0.887963\pi$
$67$	−4.86163	+	4.86163i	−0.593943	+	0.593943i	0.344751	+	0.938694i	$0.387963\pi$
$68$	0.566423	−	0.566423i	0.0686888	−	0.0686888i
$69$	3.21294	+	3.21294i	0.386793	+	0.386793i
$70$	−4.17147	−	4.17147i	−0.498586	−	0.498586i
$71$	1.91160	+	1.91160i	0.226866	+	0.226866i	0.811382	−	0.584516i	$-0.198716\pi$
$71$	1.91160	+	1.91160i	0.226866	+	0.226866i	−0.584516	+	0.811382i	$0.698716\pi$
$72$	11.8022			1.39090
$73$		−	6.30345i		−	0.737763i	−0.929476	−	0.368881i	$-0.879741\pi$
$73$		−	6.30345i		−	0.737763i	0.929476	−	0.368881i	$-0.120259\pi$
$74$		−	7.41437i		−	0.861903i
$75$	−0.428552	−	0.428552i	−0.0494849	−	0.0494849i
$76$	16.1960	−	16.1960i	1.85781	−	1.85781i
$77$		−	3.99703i		−	0.455504i
$78$	3.30312			0.374004
$79$	−1.26491	−	1.26491i	−0.142313	−	0.142313i	0.632361	−	0.774674i	$-0.282086\pi$
$79$	−1.26491	−	1.26491i	−0.142313	−	0.142313i	−0.774674	+	0.632361i	$0.782086\pi$
$80$		−	10.6856i		−	1.19469i
$81$	−3.23315			−0.359238
$82$	−6.24650	−	14.4955i	−0.689811	−	1.60076i
$83$	−5.53161			−0.607173			−0.303587	−	0.952804i	$-0.598184\pi$
$83$	−5.53161			−0.607173			−0.303587	+	0.952804i	$0.598184\pi$
$84$		−	3.39682i		−	0.370623i
$85$	0.332527	+	0.332527i	0.0360676	+	0.0360676i
$86$	14.1351			1.52423
$87$		−	8.27762i		−	0.887454i
$88$	14.4673	−	14.4673i	1.54222	−	1.54222i
$89$	5.88812	+	5.88812i	0.624139	+	0.624139i	0.946587	−	0.322448i	$-0.104506\pi$
$89$	5.88812	+	5.88812i	0.624139	+	0.624139i	−0.322448	+	0.946587i	$0.604506\pi$
$90$			13.6020i			1.43377i
$91$			1.60810i			0.168575i
$92$	−22.2293			−2.31757
$93$	4.83864	+	4.83864i	0.501744	+	0.501744i
$94$	−8.38456	−	8.38456i	−0.864801	−	0.864801i
$95$	9.50808	+	9.50808i	0.975509	+	0.975509i
$96$	0.453113	−	0.453113i	0.0462456	−	0.0462456i
$97$	4.75113	−	4.75113i	0.482405	−	0.482405i	−0.423494	−	0.905899i	$-0.639197\pi$
$97$	4.75113	−	4.75113i	0.482405	−	0.482405i	0.905899	+	0.423494i	$0.139197\pi$
$98$	2.46506			0.249009
$99$	−6.51659	+	6.51659i	−0.654942	+	0.654942i
$100$	2.96501			0.296501
$101$	−2.36442	+	2.36442i	−0.235269	+	0.235269i	−0.814888	−	0.579619i	$-0.803201\pi$
$101$	−2.36442	+	2.36442i	−0.235269	+	0.235269i	0.579619	+	0.814888i	$0.303201\pi$
$102$			0.403622i			0.0399645i
$103$			7.07453i			0.697074i	0.937295	+	0.348537i	$0.113321\pi$
$103$			7.07453i			0.697074i	−0.937295	+	0.348537i	$0.886679\pi$
$104$	−5.82056	+	5.82056i	−0.570752	+	0.570752i
$105$	1.99415			0.194609
$106$	15.7086	−	15.7086i	1.52576	−	1.52576i
$107$	0.179872			0.0173889			0.00869444	−	0.999962i	$-0.497232\pi$
$107$	0.179872			0.0173889			0.00869444	+	0.999962i	$0.497232\pi$
$108$	−12.7438	+	12.7438i	−1.22627	+	1.22627i
$109$	−12.2701	+	12.2701i	−1.17527	+	1.17527i	−0.194331	+	0.980936i	$0.562254\pi$
$109$	−12.2701	+	12.2701i	−1.17527	+	1.17527i	−0.980936	+	0.194331i	$0.937746\pi$
$110$	16.6735	+	16.6735i	1.58976	+	1.58976i
$111$	1.77220	+	1.77220i	0.168210	+	0.168210i
$112$	3.15725	+	3.15725i	0.298332	+	0.298332i
$113$	−3.24750			−0.305499			−0.152749	−	0.988265i	$-0.548813\pi$
$113$	−3.24750			−0.305499			−0.152749	+	0.988265i	$0.548813\pi$
$114$			11.5409i			1.08091i
$115$		−	13.0501i		−	1.21692i
$116$	28.6351	+	28.6351i	2.65870	+	2.65870i
$117$	2.62178	−	2.62178i	0.242384	−	0.242384i
$118$		−	9.31159i		−	0.857202i
$119$	−0.196501			−0.0180132
$120$	7.21787	+	7.21787i	0.658898	+	0.658898i
$121$			4.97625i			0.452387i
$122$	−24.1075			−2.18259
$123$	4.95781	+	1.97169i	0.447030	+	0.177782i
$124$	−33.4770			−3.00633
$125$		−	10.2253i		−	0.914576i
$126$	−4.01893	−	4.01893i	−0.358035	−	0.358035i
$127$	3.76156			0.333784			0.166892	−	0.985975i	$-0.446627\pi$
$127$	3.76156			0.333784			0.166892	+	0.985975i	$0.446627\pi$
$128$		−	18.8782i		−	1.66861i
$129$	−3.37861	+	3.37861i	−0.297470	+	0.297470i
$130$	−6.70815	−	6.70815i	−0.588344	−	0.588344i
$131$			18.7346i			1.63685i	0.574616	+	0.818423i	$0.305151\pi$
$131$			18.7346i			1.63685i	−0.574616	+	0.818423i	$0.694849\pi$
$132$			13.5772i			1.18174i
$133$	−5.61864			−0.487198
$134$	11.9842	+	11.9842i	1.03528	+	1.03528i
$135$	−7.48142	−	7.48142i	−0.643898	−	0.643898i
$136$	−0.711239	−	0.711239i	−0.0609883	−	0.0609883i
$137$	−11.9544	+	11.9544i	−1.02133	+	1.02133i	−0.0215668	+	0.999767i	$0.506865\pi$
$137$	−11.9544	+	11.9544i	−1.02133	+	1.02133i	−0.999767	+	0.0215668i	$0.993135\pi$
$138$	7.92011	−	7.92011i	0.674204	−	0.674204i
$139$	18.3025			1.55240			0.776198	−	0.630489i	$-0.217145\pi$
$139$	18.3025			1.55240			0.776198	+	0.630489i	$0.217145\pi$
$140$	−6.89846	+	6.89846i	−0.583026	+	0.583026i
$141$	4.00820			0.337551
$142$	4.71222	−	4.71222i	0.395441	−	0.395441i
$143$		−	6.42764i		−	0.537506i
$144$		−	10.2949i		−	0.857907i
$145$	−16.8107	+	16.8107i	−1.39605	+	1.39605i
$146$	−15.5384			−1.28597
$147$	−0.589206	+	0.589206i	−0.0485969	+	0.0485969i
$148$	−12.2613			−1.00787
$149$	−15.4752	+	15.4752i	−1.26778	+	1.26778i	−0.320545	+	0.947233i	$0.603866\pi$
$149$	−15.4752	+	15.4752i	−1.26778	+	1.26778i	−0.947233	+	0.320545i	$0.896134\pi$
$150$	−1.05641	+	1.05641i	−0.0862552	+	0.0862552i
$151$	−0.393113	−	0.393113i	−0.0319911	−	0.0319911i	0.690930	−	0.722921i	$-0.257201\pi$
$151$	−0.393113	−	0.393113i	−0.0319911	−	0.0319911i	−0.722921	+	0.690930i	$0.757201\pi$
$152$	−20.3368	−	20.3368i	−1.64953	−	1.64953i
$153$	0.320367	+	0.320367i	0.0259001	+	0.0259001i
$154$	−9.85293			−0.793971
$155$		−	19.6532i		−	1.57858i
$156$		−	5.46244i		−	0.437345i
$157$	10.0637	+	10.0637i	0.803170	+	0.803170i	0.983590	−	0.180420i	$-0.0577457\pi$
$157$	10.0637	+	10.0637i	0.803170	+	0.803170i	−0.180420	+	0.983590i	$0.557746\pi$
$158$	−3.11808	+	3.11808i	−0.248061	+	0.248061i
$159$			7.50944i			0.595537i
$160$	−1.84041			−0.145498
$161$	3.85586	+	3.85586i	0.303884	+	0.303884i
$162$			7.96990i			0.626175i
$163$	20.1768			1.58037			0.790184	−	0.612870i	$-0.209985\pi$
$163$	20.1768			1.58037			0.790184	+	0.612870i	$0.209985\pi$
$164$	−23.9715	+	10.3300i	−1.87186	+	0.806636i
$165$	−7.97069			−0.620517
$166$			13.6358i			1.05834i
$167$	−2.89761	−	2.89761i	−0.224224	−	0.224224i	0.586051	−	0.810274i	$-0.300682\pi$
$167$	−2.89761	−	2.89761i	−0.224224	−	0.224224i	−0.810274	+	0.586051i	$0.800682\pi$
$168$	−4.26528			−0.329074
$169$		−	10.4140i		−	0.801077i
$170$	0.819699	−	0.819699i	0.0628680	−	0.0628680i
$171$	9.16040	+	9.16040i	0.700513	+	0.700513i
$172$		−	23.3755i		−	1.78237i
$173$			0.159545i			0.0121300i	0.999982	+	0.00606501i	$0.00193056\pi$
$173$			0.159545i			0.0121300i	−0.999982	+	0.00606501i	$0.998069\pi$
$174$	−20.4048			−1.54689
$175$	−0.514305	−	0.514305i	−0.0388778	−	0.0388778i
$176$	−12.6196	−	12.6196i	−0.951240	−	0.951240i
$177$	2.22568	+	2.22568i	0.167293	+	0.167293i
$178$	14.5146	−	14.5146i	1.08791	−	1.08791i
$179$	4.93432	−	4.93432i	0.368809	−	0.368809i	−0.498234	−	0.867043i	$-0.666018\pi$
$179$	4.93432	−	4.93432i	0.368809	−	0.368809i	0.867043	+	0.498234i	$0.166018\pi$
$180$	22.4939			1.67660
$181$	−14.4797	+	14.4797i	−1.07627	+	1.07627i	−0.0794304	+	0.996840i	$0.525310\pi$
$181$	−14.4797	+	14.4797i	−1.07627	+	1.07627i	−0.996840	+	0.0794304i	$0.974690\pi$
$182$	3.96407			0.293837
$183$	5.76224	−	5.76224i	0.425957	−	0.425957i
$184$			27.9127i			2.05775i
$185$		−	7.19818i		−	0.529221i
$186$	11.9276	−	11.9276i	0.874571	−	0.874571i
$187$	0.785421			0.0574357
$188$	−13.8657	+	13.8657i	−1.01126	+	1.01126i
$189$	4.42102			0.321582
$190$	23.4380	−	23.4380i	1.70037	−	1.70037i
$191$	−15.1382	+	15.1382i	−1.09536	+	1.09536i	−0.100416	+	0.994946i	$0.532017\pi$
$191$	−15.1382	+	15.1382i	−1.09536	+	1.09536i	−0.994946	+	0.100416i	$0.967983\pi$
$192$	4.14469	+	4.14469i	0.299117	+	0.299117i
$193$	−14.0406	−	14.0406i	−1.01066	−	1.01066i	−0.999943	−	0.0107194i	$-0.996588\pi$
$193$	−14.0406	−	14.0406i	−1.01066	−	1.01066i	−0.0107194	−	0.999943i	$-0.503412\pi$
$194$	−11.7118	−	11.7118i	−0.840861	−	0.840861i
$195$	3.20680			0.229644
$196$		−	4.07653i		−	0.291181i
$197$			1.09409i			0.0779503i	0.999240	+	0.0389752i	$0.0124093\pi$
$197$			1.09409i			0.0779503i	−0.999240	+	0.0389752i	$0.987591\pi$
$198$	16.0638	+	16.0638i	1.14160	+	1.14160i
$199$	5.11248	−	5.11248i	0.362414	−	0.362414i	−0.502287	−	0.864701i	$-0.667508\pi$
$199$	5.11248	−	5.11248i	0.362414	−	0.362414i	0.864701	+	0.502287i	$0.167508\pi$
$200$		−	3.72307i		−	0.263261i
$201$	−5.72901			−0.404093
$202$	5.82845	+	5.82845i	0.410088	+	0.410088i
$203$		−	9.93399i		−	0.697229i
$204$	0.667479			0.0467329
$205$	−6.06437	−	14.0728i	−0.423554	−	0.982888i
$206$	17.4391			1.21504
$207$		−	12.5729i		−	0.873874i
$208$	5.07718	+	5.07718i	0.352039	+	0.352039i
$209$	22.4579			1.55345
$210$		−	4.91571i		−	0.339216i
$211$	4.87250	−	4.87250i	0.335437	−	0.335437i	−0.519210	−	0.854647i	$-0.673774\pi$
$211$	4.87250	−	4.87250i	0.335437	−	0.335437i	0.854647	+	0.519210i	$0.173774\pi$
$212$	−25.9777	−	25.9777i	−1.78416	−	1.78416i
$213$			2.25266i			0.154350i
$214$		−	0.443396i		−	0.0303099i
$215$	13.7229			0.935897
$216$	16.0020	+	16.0020i	1.08880	+	1.08880i
$217$	5.80686	+	5.80686i	0.394196	+	0.394196i
$218$	30.2467	+	30.2467i	2.04856	+	2.04856i
$219$	3.71403	−	3.71403i	0.250971	−	0.250971i
$220$	27.5733	−	27.5733i	1.85899	−	1.85899i
$221$	−0.315994			−0.0212561
$222$	4.36859	−	4.36859i	0.293201	−	0.293201i
$223$	−22.6309			−1.51547			−0.757737	−	0.652560i	$-0.773695\pi$
$223$	−22.6309			−1.51547			−0.757737	+	0.652560i	$0.773695\pi$
$224$	0.543781	−	0.543781i	0.0363329	−	0.0363329i
$225$			1.67700i			0.111800i
$226$			8.00528i			0.532503i
$227$	14.3373	−	14.3373i	0.951599	−	0.951599i	−0.0472825	−	0.998882i	$-0.515056\pi$
$227$	14.3373	−	14.3373i	0.951599	−	0.951599i	0.998882	+	0.0472825i	$0.0150561\pi$
$228$	19.0855			1.26397
$229$	−8.55212	+	8.55212i	−0.565140	+	0.565140i	−0.930763	−	0.365623i	$-0.880856\pi$
$229$	−8.55212	+	8.55212i	−0.565140	+	0.565140i	0.365623	+	0.930763i	$0.380856\pi$
$230$	−32.1692			−2.12117
$231$	2.35507	−	2.35507i	0.154952	−	0.154952i
$232$	35.9562	−	35.9562i	2.36064	−	2.36064i
$233$	−10.9606	−	10.9606i	−0.718054	−	0.718054i	0.250153	−	0.968206i	$-0.419519\pi$
$233$	−10.9606	−	10.9606i	−0.718054	−	0.718054i	−0.968206	+	0.250153i	$0.919519\pi$
$234$	−6.46285	−	6.46285i	−0.422490	−	0.422490i
$235$	−8.14008	−	8.14008i	−0.531000	−	0.531000i
$236$	−15.3988			−1.00238
$237$		−	1.49058i		−	0.0968238i
$238$			0.484387i			0.0313982i
$239$	−10.9676	−	10.9676i	−0.709434	−	0.709434i	0.256982	−	0.966416i	$-0.417272\pi$
$239$	−10.9676	−	10.9676i	−0.709434	−	0.709434i	−0.966416	+	0.256982i	$0.917272\pi$
$240$	6.29604	−	6.29604i	0.406408	−	0.406408i
$241$		−	15.8406i		−	1.02038i	−0.860061	−	0.510191i	$-0.829575\pi$
$241$		−	15.8406i		−	1.02038i	0.860061	−	0.510191i	$-0.170425\pi$
$242$	12.2668			0.788538
$243$	−11.2834	−	11.2834i	−0.723830	−	0.723830i
$244$			39.8671i			2.55223i
$245$	2.39319			0.152895
$246$	4.86035	−	12.2213i	0.309884	−	0.779201i
$247$	−9.03536			−0.574906
$248$			42.0361i			2.66929i
$249$	−3.25926	−	3.25926i	−0.206547	−	0.206547i
$250$	−25.2059			−1.59416
$251$			20.1801i			1.27376i	0.770965	+	0.636878i	$0.219774\pi$
$251$			20.1801i			1.27376i	−0.770965	+	0.636878i	$0.780226\pi$
$252$	−6.64620	+	6.64620i	−0.418671	+	0.418671i
$253$	−15.4120	−	15.4120i	−0.968943	−	0.968943i
$254$		−	9.27247i		−	0.581807i
$255$			0.391853i			0.0245388i
$256$	−32.4672			−2.02920
$257$	17.9972	+	17.9972i	1.12264	+	1.12264i	0.991344	+	0.131293i	$0.0419127\pi$
$257$	17.9972	+	17.9972i	1.12264	+	1.12264i	0.131293	+	0.991344i	$0.458087\pi$
$258$	8.32848	+	8.32848i	0.518508	+	0.518508i
$259$	2.12682	+	2.12682i	0.132154	+	0.132154i
$260$	−11.0934	+	11.0934i	−0.687985	+	0.687985i
$261$	−16.1959	+	16.1959i	−1.00250	+	1.00250i
$262$	46.1818			2.85312
$263$	6.36987	−	6.36987i	0.392783	−	0.392783i	−0.482895	−	0.875678i	$-0.660415\pi$
$263$	6.36987	−	6.36987i	0.392783	−	0.392783i	0.875678	+	0.482895i	$0.160415\pi$
$264$	17.0485			1.04926
$265$	15.2506	−	15.2506i	0.936837	−	0.936837i
$266$			13.8503i			0.849217i
$267$			6.93863i			0.424637i
$268$	19.8186	−	19.8186i	1.21061	−	1.21061i
$269$	−14.6325			−0.892161			−0.446080	−	0.894993i	$-0.647180\pi$
$269$	−14.6325			−0.892161			−0.446080	+	0.894993i	$0.647180\pi$
$270$	−18.4422	+	18.4422i	−1.12235	+	1.12235i
$271$	1.64720			0.100060			0.0500300	−	0.998748i	$-0.484068\pi$
$271$	1.64720			0.100060			0.0500300	+	0.998748i	$0.484068\pi$
$272$	−0.620403	+	0.620403i	−0.0376175	+	0.0376175i
$273$	−0.947504	+	0.947504i	−0.0573455	+	0.0573455i
$274$	29.4684	+	29.4684i	1.78025	+	1.78025i
$275$	2.05569	+	2.05569i	0.123963	+	0.123963i
$276$	−13.0977	−	13.0977i	−0.788386	−	0.788386i
$277$	−18.1865			−1.09272			−0.546362	−	0.837549i	$-0.683988\pi$
$277$	−18.1865			−1.09272			−0.546362	+	0.837549i	$0.683988\pi$
$278$		−	45.1168i		−	2.70592i
$279$		−	18.9345i		−	1.13358i
$280$	8.66218	+	8.66218i	0.517664	+	0.517664i
$281$	11.9938	−	11.9938i	0.715490	−	0.715490i	−0.252188	−	0.967678i	$-0.581150\pi$
$281$	11.9938	−	11.9938i	0.715490	−	0.715490i	0.967678	+	0.252188i	$0.0811502\pi$
$282$		−	9.88046i		−	0.588373i
$283$	−29.9618			−1.78104			−0.890521	−	0.454942i	$-0.849660\pi$
$283$	−29.9618			−1.78104			−0.890521	+	0.454942i	$0.849660\pi$
$284$	−7.79271	−	7.79271i	−0.462412	−	0.462412i
$285$			11.2044i			0.663694i
$286$	−15.8445			−0.936906
$287$	5.94987	+	2.36623i	0.351210	+	0.139674i
$288$	−1.77312			−0.104482
$289$			16.9614i			0.997729i
$290$	41.4393	+	41.4393i	2.43340	+	2.43340i
$291$	5.59879			0.328207
$292$			25.6962i			1.50376i
$293$	8.43995	−	8.43995i	0.493067	−	0.493067i	−0.416204	−	0.909271i	$-0.636640\pi$
$293$	8.43995	−	8.43995i	0.493067	−	0.493067i	0.909271	+	0.416204i	$0.136640\pi$
$294$	1.45243	+	1.45243i	0.0847074	+	0.0847074i
$295$		−	9.04009i		−	0.526334i
$296$			15.3962i			0.894883i
$297$	−17.6710			−1.02537
$298$	38.1473	+	38.1473i	2.20982	+	2.20982i
$299$	6.20062	+	6.20062i	0.358591	+	0.358591i
$300$	1.74700	+	1.74700i	0.100863	+	0.100863i
$301$	−4.05467	+	4.05467i	−0.233707	+	0.233707i
$302$	−0.969047	+	0.969047i	−0.0557624	+	0.0557624i
$303$	−2.78626			−0.160067
$304$	−17.7395	+	17.7395i	−1.01743	+	1.01743i
$305$	−23.4046			−1.34014
$306$	0.789725	−	0.789725i	0.0451455	−	0.0451455i
$307$		−	22.8994i		−	1.30694i	−0.756952	−	0.653470i	$-0.773313\pi$
$307$		−	22.8994i		−	1.30694i	0.756952	−	0.653470i	$-0.226687\pi$
$308$			16.2940i			0.928437i
$309$	−4.16835	+	4.16835i	−0.237129	+	0.237129i
$310$	−48.4463			−2.75157
$311$	2.56035	−	2.56035i	0.145184	−	0.145184i	−0.630779	−	0.775963i	$-0.717264\pi$
$311$	2.56035	−	2.56035i	0.145184	−	0.145184i	0.775963	+	0.630779i	$0.217264\pi$
$312$	−6.85901			−0.388315
$313$	14.0459	−	14.0459i	0.793921	−	0.793921i	−0.188208	−	0.982129i	$-0.560268\pi$
$313$	14.0459	−	14.0459i	0.793921	−	0.793921i	0.982129	+	0.188208i	$0.0602679\pi$
$314$	24.8076	−	24.8076i	1.39997	−	1.39997i
$315$	−3.90175	−	3.90175i	−0.219839	−	0.219839i
$316$	5.15644	+	5.15644i	0.290072	+	0.290072i
$317$	−11.5267	−	11.5267i	−0.647404	−	0.647404i	0.304961	−	0.952365i	$-0.401357\pi$
$317$	−11.5267	−	11.5267i	−0.647404	−	0.647404i	−0.952365	+	0.304961i	$0.901357\pi$
$318$	18.5112			1.03806
$319$			39.7064i			2.22313i
$320$		−	16.8345i		−	0.941079i
$321$	0.105982	+	0.105982i	0.00591532	+	0.00591532i
$322$	9.50493	−	9.50493i	0.529689	−	0.529689i
$323$		−	1.10407i		−	0.0614321i
$324$	13.1800			0.732223
$325$	−0.827056	−	0.827056i	−0.0458768	−	0.0458768i
$326$		−	49.7370i		−	2.75468i
$327$	−14.4593			−0.799600
$328$	12.9710	+	30.1003i	0.716206	+	1.66201i
$329$	4.81025			0.265197
$330$			19.6482i			1.08160i
$331$	18.7730	+	18.7730i	1.03186	+	1.03186i	0.999476	+	0.0323808i	$0.0103089\pi$
$331$	18.7730	+	18.7730i	1.03186	+	1.03186i	0.0323808	+	0.999476i	$0.489691\pi$
$332$	22.5498			1.23758
$333$		−	6.93497i		−	0.380034i
$334$	−7.14278	+	7.14278i	−0.390836	+	0.390836i
$335$	11.6348	+	11.6348i	0.635677	+	0.635677i
$336$			3.72054i			0.202972i
$337$			12.9816i			0.707155i	0.935405	+	0.353577i	$0.115035\pi$
$337$			12.9816i			0.707155i	−0.935405	+	0.353577i	$0.884965\pi$
$338$	−25.6712			−1.39633
$339$	−1.91344	−	1.91344i	−0.103924	−	0.103924i
$340$	−1.35555	−	1.35555i	−0.0735153	−	0.0735153i
$341$	−23.2102	−	23.2102i	−1.25690	−	1.25690i
$342$	22.5809	−	22.5809i	1.22104	−	1.22104i
$343$	−0.707107	+	0.707107i	−0.0381802	+	0.0381802i
$344$	−29.3519			−1.58255
$345$	7.68917	−	7.68917i	0.413971	−	0.413971i
$346$	0.393289			0.0211434
$347$	1.18385	−	1.18385i	0.0635525	−	0.0635525i	−0.674616	−	0.738169i	$-0.735691\pi$
$347$	1.18385	−	1.18385i	0.0635525	−	0.0635525i	0.738169	+	0.674616i	$0.235691\pi$
$348$			33.7440i			1.80887i
$349$			29.3728i			1.57229i	0.618041	+	0.786146i	$0.287927\pi$
$349$			29.3728i			1.57229i	−0.618041	+	0.786146i	$0.712073\pi$
$350$	−1.26779	+	1.26779i	−0.0677665	+	0.0677665i
$351$	7.10946			0.379475
$352$	−2.17351	+	2.17351i	−0.115849	+	0.115849i
$353$	23.8039			1.26695			0.633476	−	0.773762i	$-0.281628\pi$
$353$	23.8039			1.26695			0.633476	+	0.773762i	$0.281628\pi$
$354$	5.48645	−	5.48645i	0.291601	−	0.291601i
$355$	4.57483	−	4.57483i	0.242807	−	0.242807i
$356$	−24.0031	−	24.0031i	−1.27216	−	1.27216i
$357$	−0.115780	−	0.115780i	−0.00612771	−	0.00612771i
$358$	−12.1634	−	12.1634i	−0.642856	−	0.642856i
$359$	31.2029			1.64683			0.823413	−	0.567442i	$-0.192067\pi$
$359$	31.2029			1.64683			0.823413	+	0.567442i	$0.192067\pi$
$360$		−	28.2449i		−	1.48864i
$361$		−	12.5692i		−	0.661535i
$362$	35.6935	+	35.6935i	1.87601	+	1.87601i
$363$	−2.93204	+	2.93204i	−0.153892	+	0.153892i
$364$		−	6.55548i		−	0.343600i
$365$	−15.0853			−0.789602
$366$	−14.2043	−	14.2043i	−0.742469	−	0.742469i
$367$			28.8040i			1.50356i	0.659414	+	0.751780i	$0.270804\pi$
$367$			28.8040i			1.50356i	−0.659414	+	0.751780i	$0.729196\pi$
$368$	24.3478			1.26922
$369$	−5.84261	−	13.5582i	−0.304154	−	0.705812i
$370$	−17.7440			−0.922465
$371$			9.01209i			0.467884i
$372$	−19.7249	−	19.7249i	−1.02269	−	1.02269i
$373$	20.5469			1.06388			0.531939	−	0.846783i	$-0.321464\pi$
$373$	20.5469			1.06388			0.531939	+	0.846783i	$0.321464\pi$
$374$		−	1.93611i		−	0.100114i
$375$	6.02479	−	6.02479i	0.311119	−	0.311119i
$376$	17.4108	+	17.4108i	0.897892	+	0.897892i
$377$		−	15.9749i		−	0.822748i
$378$		−	10.8981i		−	0.560537i
$379$	24.9256			1.28034			0.640170	−	0.768233i	$-0.278864\pi$
$379$	24.9256			1.28034			0.640170	+	0.768233i	$0.278864\pi$
$380$	−38.7600	−	38.7600i	−1.98834	−	1.98834i
$381$	2.21633	+	2.21633i	0.113546	+	0.113546i
$382$	37.3166	+	37.3166i	1.90928	+	1.90928i
$383$	−15.2366	+	15.2366i	−0.778554	+	0.778554i	−0.979585	−	0.201031i	$-0.935571\pi$
$383$	−15.2366	+	15.2366i	−0.778554	+	0.778554i	0.201031	+	0.979585i	$0.435571\pi$
$384$	11.1231	−	11.1231i	0.567625	−	0.567625i
$385$	−9.56564			−0.487510
$386$	−34.6109	+	34.6109i	−1.76165	+	1.76165i
$387$	13.2211			0.672068
$388$	−19.3681	+	19.3681i	−0.983268	+	0.983268i
$389$			18.1344i			0.919450i	0.888061	+	0.459725i	$0.152052\pi$
$389$			18.1344i			0.919450i	−0.888061	+	0.459725i	$0.847948\pi$
$390$		−	7.90497i		−	0.400284i
$391$	−0.757681	+	0.757681i	−0.0383176	+	0.0383176i
$392$	−5.11877			−0.258537
$393$	−11.0385	+	11.0385i	−0.556819	+	0.556819i
$394$	2.69699			0.135872
$395$	−3.02716	+	3.02716i	−0.152313	+	0.152313i
$396$	26.5650	−	26.5650i	1.33494	−	1.33494i
$397$	2.83377	+	2.83377i	0.142223	+	0.142223i	0.774633	−	0.632411i	$-0.217934\pi$
$397$	2.83377	+	2.83377i	0.142223	+	0.142223i	−0.632411	+	0.774633i	$0.717934\pi$
$398$	−12.6026	−	12.6026i	−0.631710	−	0.631710i
$399$	−3.31054	−	3.31054i	−0.165734	−	0.165734i
$400$	−3.24758			−0.162379
$401$		−	30.0879i		−	1.50252i	−0.660008	−	0.751258i	$-0.729447\pi$
$401$		−	30.0879i		−	1.50252i	0.660008	−	0.751258i	$-0.270553\pi$
$402$			14.1224i			0.704359i
$403$	9.33803	+	9.33803i	0.465161	+	0.465161i
$404$	9.63864	−	9.63864i	0.479540	−	0.479540i
$405$			7.73752i			0.384480i
$406$	−24.4879			−1.21531
$407$	−8.50098	−	8.50098i	−0.421378	−	0.421378i
$408$		−	0.838133i		−	0.0414938i
$409$	−6.06483			−0.299887			−0.149943	−	0.988695i	$-0.547909\pi$
$409$	−6.06483			−0.299887			−0.149943	+	0.988695i	$0.547909\pi$
$410$	−34.6904	+	14.9490i	−1.71324	+	0.738280i
$411$	−14.0872			−0.694871
$412$		−	28.8395i		−	1.42082i
$413$	2.67105	+	2.67105i	0.131434	+	0.131434i
$414$	−30.9929			−1.52322
$415$			13.2382i			0.649836i
$416$	0.874456	−	0.874456i	0.0428738	−	0.0428738i
$417$	10.7839	+	10.7839i	0.528092	+	0.528092i
$418$		−	55.3601i		−	2.70775i
$419$		−	34.0152i		−	1.66175i	−0.556458	−	0.830875i	$-0.687840\pi$
$419$		−	34.0152i		−	1.66175i	0.556458	−	0.830875i	$-0.312160\pi$
$420$	−8.12922			−0.396665
$421$	4.62197	+	4.62197i	0.225261	+	0.225261i	0.810709	−	0.585449i	$-0.199082\pi$
$421$	4.62197	+	4.62197i	0.225261	+	0.225261i	−0.585449	+	0.810709i	$0.699082\pi$
$422$	−12.0110	−	12.0110i	−0.584687	−	0.584687i
$423$	−7.84242	−	7.84242i	−0.381311	−	0.381311i
$424$	−32.6194	+	32.6194i	−1.58414	+	1.58414i
$425$	0.101062	−	0.101062i	0.00490221	−	0.00490221i
$426$	5.55294			0.269041
$427$	6.91527	−	6.91527i	0.334653	−	0.334653i
$428$	−0.733253			−0.0354431
$429$	3.78720	−	3.78720i	0.182848	−	0.182848i
$430$		−	33.8279i		−	1.63133i
$431$		−	8.13138i		−	0.391675i	−0.980636	−	0.195837i	$-0.937258\pi$
$431$		−	8.13138i		−	0.391675i	0.980636	−	0.195837i	$-0.0627425\pi$
$432$	13.9583	−	13.9583i	0.671567	−	0.671567i
$433$	−4.16838			−0.200320			−0.100160	−	0.994971i	$-0.531935\pi$
$433$	−4.16838			−0.200320			−0.100160	+	0.994971i	$0.531935\pi$
$434$	14.3143	−	14.3143i	0.687107	−	0.687107i
$435$	−19.8099			−0.949811
$436$	50.0196	−	50.0196i	2.39550	−	2.39550i
$437$	−21.6647	+	21.6647i	−1.03636	+	1.03636i
$438$	−9.15531	−	9.15531i	−0.437458	−	0.437458i
$439$	−1.22381	−	1.22381i	−0.0584093	−	0.0584093i	0.677299	−	0.735708i	$-0.263150\pi$
$439$	−1.22381	−	1.22381i	−0.0584093	−	0.0584093i	−0.735708	+	0.677299i	$0.763150\pi$
$440$	−34.6230	−	34.6230i	−1.65059	−	1.65059i
$441$	2.30567			0.109794
$442$			0.778945i			0.0370506i
$443$			4.19753i			0.199430i	0.995016	+	0.0997152i	$0.0317932\pi$
$443$			4.19753i			0.199430i	−0.995016	+	0.0997152i	$0.968207\pi$
$444$	−7.22444	−	7.22444i	−0.342857	−	0.342857i
$445$	14.0914	−	14.0914i	0.667994	−	0.667994i
$446$			55.7865i			2.64156i
$447$	−18.2362			−0.862541
$448$	4.97404	+	4.97404i	0.235002	+	0.235002i
$449$		−	17.4079i		−	0.821527i	−0.911742	−	0.410764i	$-0.865262\pi$
$449$		−	17.4079i		−	0.821527i	0.911742	−	0.410764i	$-0.134738\pi$
$450$	4.13391			0.194875
$451$	−23.7818	−	9.45790i	−1.11984	−	0.445355i
$452$	13.2385			0.622687
$453$		−	0.463249i		−	0.0217653i
$454$	−35.3423	−	35.3423i	−1.65870	−	1.65870i
$455$	3.84849			0.180420
$456$		−	23.9651i		−	1.12227i
$457$	−12.2173	+	12.2173i	−0.571500	+	0.571500i	−0.932547	−	0.361048i	$-0.882419\pi$
$457$	−12.2173	+	12.2173i	−0.571500	+	0.571500i	0.361048	+	0.932547i	$0.382419\pi$
$458$	21.0815	+	21.0815i	0.985074	+	0.985074i
$459$			0.868736i			0.0405491i
$460$			53.1989i			2.48041i
$461$	9.77057			0.455061			0.227530	−	0.973771i	$-0.426935\pi$
$461$	9.77057			0.455061			0.227530	+	0.973771i	$0.426935\pi$
$462$	−5.80540	−	5.80540i	−0.270092	−	0.270092i
$463$	−10.2924	−	10.2924i	−0.478329	−	0.478329i	0.426268	−	0.904597i	$-0.359828\pi$
$463$	−10.2924	−	10.2924i	−0.478329	−	0.478329i	−0.904597	+	0.426268i	$0.859828\pi$
$464$	−31.3641	−	31.3641i	−1.45604	−	1.45604i
$465$	11.5798	−	11.5798i	0.536999	−	0.536999i
$466$	−27.0186	+	27.0186i	−1.25161	+	1.25161i
$467$	2.80733			0.129908			0.0649539	−	0.997888i	$-0.479310\pi$
$467$	2.80733			0.129908			0.0649539	+	0.997888i	$0.479310\pi$
$468$	−10.6878	+	10.6878i	−0.494042	+	0.494042i
$469$	−6.87539			−0.317476
$470$	−20.0658	+	20.0658i	−0.925566	+	0.925566i
$471$			11.8592i			0.546442i
$472$			19.3358i			0.890002i
$473$	16.2067	−	16.2067i	0.745183	−	0.745183i
$474$	−3.67438			−0.168770
$475$	2.88970	−	2.88970i	0.132588	−	0.132588i
$476$	0.801043			0.0367157
$477$	14.6929	−	14.6929i	0.672743	−	0.672743i
$478$	−27.0358	+	27.0358i	−1.23659	+	1.23659i
$479$	−12.0272	−	12.0272i	−0.549538	−	0.549538i	0.376769	−	0.926307i	$-0.377035\pi$
$479$	−12.0272	−	12.0272i	−0.549538	−	0.549538i	−0.926307	+	0.376769i	$0.877035\pi$
$480$	−1.08438	−	1.08438i	−0.0494951	−	0.0494951i
$481$	3.42015	+	3.42015i	0.155946	+	0.155946i
$482$	−39.0480			−1.77859
$483$			4.54379i			0.206750i
$484$		−	20.2858i		−	0.922084i
$485$	−11.3703	−	11.3703i	−0.516301	−	0.516301i
$486$	−27.8142	+	27.8142i	−1.26168	+	1.26168i
$487$			18.6924i			0.847033i	0.905888	+	0.423517i	$0.139204\pi$
$487$			18.6924i			0.847033i	−0.905888	+	0.423517i	$0.860796\pi$
$488$	50.0599			2.26610
$489$	11.8883	+	11.8883i	0.537607	+	0.537607i
$490$		−	5.89935i		−	0.266505i
$491$	−31.9922			−1.44379			−0.721894	−	0.692004i	$-0.756728\pi$
$491$	−31.9922			−1.44379			−0.721894	+	0.692004i	$0.756728\pi$
$492$	−20.2106	−	8.03766i	−0.911166	−	0.362366i
$493$	1.95204			0.0879155
$494$			22.2727i			1.00210i
$495$	15.5954	+	15.5954i	0.700961	+	0.700961i
$496$	36.6674			1.64642
$497$			2.70342i			0.121265i
$498$	−8.03427	+	8.03427i	−0.360024	+	0.360024i
$499$	15.2569	+	15.2569i	0.682994	+	0.682994i	0.960674	−	0.277680i	$-0.0895655\pi$
$499$	15.2569	+	15.2569i	0.682994	+	0.682994i	−0.277680	+	0.960674i	$0.589566\pi$
$500$			41.6836i			1.86415i
$501$		−	3.41458i		−	0.152552i
$502$	49.7451			2.22023
$503$	20.5231	+	20.5231i	0.915078	+	0.915078i	0.996666	−	0.0815879i	$-0.0259991\pi$
$503$	20.5231	+	20.5231i	0.915078	+	0.915078i	−0.0815879	+	0.996666i	$0.525999\pi$
$504$	8.34542	+	8.34542i	0.371735	+	0.371735i
$505$	5.65850	+	5.65850i	0.251800	+	0.251800i
$506$	−37.9915	+	37.9915i	−1.68893	+	1.68893i
$507$	6.13599	−	6.13599i	0.272509	−	0.272509i
$508$	−15.3341			−0.680341
$509$	14.4621	−	14.4621i	0.641020	−	0.641020i	−0.309786	−	0.950806i	$-0.600257\pi$
$509$	14.4621	−	14.4621i	0.641020	−	0.641020i	0.950806	+	0.309786i	$0.100257\pi$
$510$	0.965943			0.0427727
$511$	4.45721	−	4.45721i	0.197175	−	0.197175i
$512$			42.2772i			1.86840i
$513$			24.8401i			1.09672i
$514$	44.3643	−	44.3643i	1.95682	−	1.95682i
$515$	16.9307			0.746054
$516$	13.7730	−	13.7730i	0.606322	−	0.606322i
$517$	−19.2267			−0.845589
$518$	5.24275	−	5.24275i	0.230353	−	0.230353i
$519$	−0.0940051	+	0.0940051i	−0.00412636	+	0.00412636i
$520$	13.9297	+	13.9297i	0.610856	+	0.610856i
$521$	29.6468	+	29.6468i	1.29885	+	1.29885i	0.929153	+	0.369696i	$0.120538\pi$
$521$	29.6468	+	29.6468i	1.29885	+	1.29885i	0.369696	+	0.929153i	$0.379462\pi$
$522$	39.9240	+	39.9240i	1.74743	+	1.74743i
$523$	35.5044			1.55250			0.776249	−	0.630427i	$-0.217120\pi$
$523$	35.5044			1.55250			0.776249	+	0.630427i	$0.217120\pi$
$524$		−	76.3720i		−	3.33632i
$525$		−	0.606063i		−	0.0264508i
$526$	−15.7021	−	15.7021i	−0.684645	−	0.684645i
$527$	−1.14106	+	1.14106i	−0.0497052	+	0.0497052i
$528$		−	14.8711i		−	0.647182i
$529$	6.73530			0.292839
$530$	−37.5937	−	37.5937i	−1.63296	−	1.63296i
$531$		−	8.70951i		−	0.377961i
$532$	22.9046			0.993039
$533$	9.56800	+	3.80515i	0.414436	+	0.164819i
$534$	17.1041			0.740169
$535$		−	0.430467i		−	0.0186107i
$536$	−24.8856	−	24.8856i	−1.07489	−	1.07489i
$537$	5.81467			0.250921
$538$			36.0701i			1.55509i
$539$	2.82633	−	2.82633i	0.121739	−	0.121739i
$540$	30.4982	+	30.4982i	1.31243	+	1.31243i
$541$			16.8530i			0.724565i	0.932068	+	0.362283i	$0.118002\pi$
$541$			16.8530i			0.724565i	−0.932068	+	0.362283i	$0.881998\pi$
$542$		−	4.06044i		−	0.174411i
$543$	−17.0631			−0.732248
$544$	0.106854	+	0.106854i	0.00458131	+	0.00458131i
$545$	29.3647	+	29.3647i	1.25785	+	1.25785i
$546$	2.33566	+	2.33566i	0.0999568	+	0.0999568i
$547$	−21.1042	+	21.1042i	−0.902351	+	0.902351i	−0.995639	−	0.0932879i	$-0.970262\pi$
$547$	−21.1042	+	21.1042i	−0.902351	+	0.902351i	0.0932879	+	0.995639i	$0.470262\pi$
$548$	48.7325	−	48.7325i	2.08175	−	2.08175i
$549$	−22.5487			−0.962356
$550$	5.06741	−	5.06741i	0.216075	−	0.216075i
$551$	55.8155			2.37782
$552$	−16.4463	+	16.4463i	−0.700002	+	0.700002i
$553$		−	1.78885i		−	0.0760697i
$554$			44.8310i			1.90469i
$555$	4.24121	−	4.24121i	0.180029	−	0.180029i
$556$	−74.6106			−3.16419
$557$	19.7810	−	19.7810i	0.838149	−	0.838149i	−0.150466	−	0.988615i	$-0.548077\pi$
$557$	19.7810	−	19.7810i	0.838149	−	0.838149i	0.988615	+	0.150466i	$0.0480774\pi$
$558$	−46.6748			−1.97590
$559$	−6.52033	+	6.52033i	−0.275781	+	0.275781i
$560$	7.55588	−	7.55588i	0.319294	−	0.319294i
$561$	0.462775	+	0.462775i	0.0195384	+	0.0195384i
$562$	−29.5655	−	29.5655i	−1.24714	−	1.24714i
$563$	−23.5929	−	23.5929i	−0.994323	−	0.994323i	0.00566089	−	0.999984i	$-0.498198\pi$
$563$	−23.5929	−	23.5929i	−0.994323	−	0.994323i	−0.999984	+	0.00566089i	$0.998198\pi$
$564$	−16.3395			−0.688019
$565$			7.77186i			0.326965i
$566$			73.8576i			3.10447i
$567$	−2.28618	−	2.28618i	−0.0960105	−	0.0960105i
$568$	−9.78507	+	9.78507i	−0.410572	+	0.410572i
$569$			15.9039i			0.666725i	0.942799	+	0.333363i	$0.108183\pi$
$569$			15.9039i			0.666725i	−0.942799	+	0.333363i	$0.891817\pi$
$570$	27.6196			1.15686
$571$	7.00511	+	7.00511i	0.293155	+	0.293155i	0.838325	−	0.545170i	$-0.183535\pi$
$571$	7.00511	+	7.00511i	0.293155	+	0.293155i	−0.545170	+	0.838325i	$0.683535\pi$
$572$			26.2024i			1.09558i
$573$	−17.8390			−0.745236
$574$	5.83291	−	14.6668i	0.243461	−	0.612180i
$575$	−3.96618			−0.165401
$576$		−	16.2189i		−	0.675789i
$577$	8.75770	+	8.75770i	0.364588	+	0.364588i	0.865499	−	0.500911i	$-0.167002\pi$
$577$	8.75770	+	8.75770i	0.364588	+	0.364588i	−0.500911	+	0.865499i	$0.667002\pi$
$578$	41.8109			1.73910
$579$		−	16.5456i		−	0.687610i
$580$	68.5292	−	68.5292i	2.84552	−	2.84552i
$581$	−3.91144	−	3.91144i	−0.162274	−	0.162274i
$582$		−	13.8014i		−	0.572085i
$583$		−	36.0216i		−	1.49186i
$584$	32.2659			1.33517
$585$	−6.27441	−	6.27441i	−0.259415	−	0.259415i
$586$	−20.8050	−	20.8050i	−0.859446	−	0.859446i
$587$	1.71714	+	1.71714i	0.0708741	+	0.0708741i	0.741655	−	0.670781i	$-0.234041\pi$
$587$	1.71714	+	1.71714i	0.0708741	+	0.0708741i	−0.670781	+	0.741655i	$0.734041\pi$
$588$	2.40191	−	2.40191i	0.0990533	−	0.0990533i
$589$	−32.6267	+	32.6267i	−1.34436	+	1.34436i
$590$	−22.2844			−0.917433
$591$	−0.644641	+	0.644641i	−0.0265170	+	0.0265170i
$592$	13.4298			0.551963
$593$	−1.55287	+	1.55287i	−0.0637688	+	0.0637688i	−0.738272	−	0.674503i	$-0.764358\pi$
$593$	−1.55287	+	1.55287i	−0.0637688	+	0.0637688i	0.674503	+	0.738272i	$0.264358\pi$
$594$			43.5600i			1.78729i
$595$			0.470264i			0.0192789i
$596$	63.0851	−	63.0851i	2.58407	−	2.58407i
$597$	6.02460			0.246570
$598$	15.2849	−	15.2849i	0.625046	−	0.625046i
$599$	−41.6504			−1.70179			−0.850894	−	0.525337i	$-0.823939\pi$
$599$	−41.6504			−1.70179			−0.850894	+	0.525337i	$0.823939\pi$
$600$	2.19366	−	2.19366i	0.0895557	−	0.0895557i
$601$	−6.20391	+	6.20391i	−0.253063	+	0.253063i	−0.822225	−	0.569162i	$-0.807268\pi$
$601$	−6.20391	+	6.20391i	−0.253063	+	0.253063i	0.569162	+	0.822225i	$0.307268\pi$
$602$	9.99502	+	9.99502i	0.407366	+	0.407366i
$603$	11.2093	+	11.2093i	0.456480	+	0.456480i
$604$	1.60254	+	1.60254i	0.0652062	+	0.0652062i
$605$	11.9091			0.484174
$606$			6.86831i			0.279006i
$607$			37.7538i			1.53238i	0.642614	+	0.766190i	$0.277850\pi$
$607$			37.7538i			1.53238i	−0.642614	+	0.766190i	$0.722150\pi$
$608$	3.05531	+	3.05531i	0.123909	+	0.123909i
$609$	5.85316	−	5.85316i	0.237182	−	0.237182i
$610$			57.6937i			2.33595i
$611$	7.73537			0.312940
$612$	−1.30599	−	1.30599i	−0.0527913	−	0.0527913i
$613$		−	29.4344i		−	1.18884i	−0.804153	−	0.594422i	$-0.797381\pi$
$613$		−	29.4344i		−	1.18884i	0.804153	−	0.594422i	$-0.202619\pi$
$614$	−56.4485			−2.27808
$615$	4.71863	−	11.8649i	0.190273	−	0.478441i
$616$	20.4599			0.824352
$617$		−	6.64540i		−	0.267534i	−0.991013	−	0.133767i	$-0.957293\pi$
$617$		−	6.64540i		−	0.267534i	0.991013	−	0.133767i	$-0.0427073\pi$
$618$	10.2752	+	10.2752i	0.413331	+	0.413331i
$619$	7.46564			0.300070			0.150035	−	0.988681i	$-0.452061\pi$
$619$	7.46564			0.300070			0.150035	+	0.988681i	$0.452061\pi$
$620$			80.1168i			3.21757i
$621$	17.0468	−	17.0468i	0.684066	−	0.684066i
$622$	−6.31141	−	6.31141i	−0.253065	−	0.253065i
$623$			8.32705i			0.333616i
$624$			5.98301i			0.239512i
$625$	−28.1077			−1.12431
$626$	−34.6240	−	34.6240i	−1.38385	−	1.38385i
$627$	13.2323	+	13.2323i	0.528448	+	0.528448i
$628$	−41.0249	−	41.0249i	−1.63707	−	1.63707i
$629$	−0.417923	+	0.417923i	−0.0166637	+	0.0166637i
$630$	−9.61805	+	9.61805i	−0.383192	+	0.383192i
$631$	26.1233			1.03995			0.519976	−	0.854181i	$-0.325941\pi$
$631$	26.1233			1.03995			0.519976	+	0.854181i	$0.325941\pi$
$632$	6.47478	−	6.47478i	0.257553	−	0.257553i
$633$	5.74181			0.228216
$634$	−28.4140	+	28.4140i	−1.12847	+	1.12847i
$635$		−	9.00211i		−	0.357238i
$636$		−	30.6124i		−	1.21386i
$637$	−1.13710	+	1.13710i	−0.0450536	+	0.0450536i
$638$	97.8788			3.87506
$639$	4.40754	−	4.40754i	0.174359	−	0.174359i
$640$	−45.1790			−1.78586
$641$	−9.24526	+	9.24526i	−0.365166	+	0.365166i	−0.865711	−	0.500545i	$-0.833133\pi$
$641$	−9.24526	+	9.24526i	−0.365166	+	0.365166i	0.500545	+	0.865711i	$0.333133\pi$
$642$	0.261251	−	0.261251i	0.0103108	−	0.0103108i
$643$	16.3126	+	16.3126i	0.643307	+	0.643307i	0.951367	−	0.308060i	$-0.0996798\pi$
$643$	16.3126	+	16.3126i	0.643307	+	0.643307i	−0.308060	+	0.951367i	$0.599680\pi$
$644$	−15.7185	−	15.7185i	−0.619396	−	0.619396i
$645$	8.08564	+	8.08564i	0.318372	+	0.318372i
$646$	−2.72160			−0.107080
$647$			37.1541i			1.46068i	0.683084	+	0.730340i	$0.260638\pi$
$647$			37.1541i			1.46068i	−0.683084	+	0.730340i	$0.739362\pi$
$648$		−	16.5497i		−	0.650135i
$649$	−10.6763	−	10.6763i	−0.419079	−	0.419079i
$650$	−2.03874	+	2.03874i	−0.0799661	+	0.0799661i
$651$			6.84288i			0.268193i
$652$	−82.2512			−3.22121
$653$	−9.38226	−	9.38226i	−0.367156	−	0.367156i	0.499283	−	0.866439i	$-0.333597\pi$
$653$	−9.38226	−	9.38226i	−0.367156	−	0.367156i	−0.866439	+	0.499283i	$0.833597\pi$
$654$			35.6430i			1.39375i
$655$	44.8353			1.75186
$656$	26.2560	−	11.3144i	1.02512	−	0.441755i
$657$	−14.5337			−0.567013
$658$		−	11.8576i		−	0.462256i
$659$	−17.1042	−	17.1042i	−0.666285	−	0.666285i	0.290569	−	0.956854i	$-0.406155\pi$
$659$	−17.1042	−	17.1042i	−0.666285	−	0.666285i	−0.956854	+	0.290569i	$0.906155\pi$
$660$	32.4927			1.26478
$661$		−	9.10680i		−	0.354213i	−0.984192	−	0.177107i	$-0.943326\pi$
$661$		−	9.10680i		−	0.354213i	0.984192	−	0.177107i	$-0.0566738\pi$
$662$	46.2766	−	46.2766i	1.79859	−	1.79859i
$663$	−0.186186	−	0.186186i	−0.00723085	−	0.00723085i
$664$		−	28.3150i		−	1.09884i
$665$			13.4465i			0.521431i
$666$	−17.0951			−0.662422
$667$	−38.3040	−	38.3040i	−1.48314	−	1.48314i
$668$	11.8122	+	11.8122i	0.457027	+	0.457027i
$669$	−13.3342	−	13.3342i	−0.515531	−	0.515531i
$670$	28.6805	−	28.6805i	1.10802	−	1.10802i
$671$	−27.6405	+	27.6405i	−1.06705	+	1.06705i
$672$	0.640798			0.0247193
$673$	19.9814	−	19.9814i	0.770227	−	0.770227i	−0.207919	−	0.978146i	$-0.566669\pi$
$673$	19.9814	−	19.9814i	0.770227	−	0.770227i	0.978146	+	0.207919i	$0.0666689\pi$
$674$	32.0005			1.23261
$675$	−2.27375	+	2.27375i	−0.0875169	+	0.0875169i
$676$			42.4530i			1.63281i
$677$			24.9427i			0.958628i	0.877644	+	0.479314i	$0.159114\pi$
$677$			24.9427i			0.958628i	−0.877644	+	0.479314i	$0.840886\pi$
$678$	−4.71676	+	4.71676i	−0.181146	+	0.181146i
$679$	6.71912			0.257856
$680$	−1.70213	+	1.70213i	−0.0652736	+	0.0652736i
$681$	16.8952			0.647426
$682$	−57.2146	+	57.2146i	−2.19086	+	2.19086i
$683$	9.48475	−	9.48475i	0.362924	−	0.362924i	−0.501964	−	0.864888i	$-0.667389\pi$
$683$	9.48475	−	9.48475i	0.362924	−	0.362924i	0.864888	+	0.501964i	$0.167389\pi$
$684$	−37.3426	−	37.3426i	−1.42783	−	1.42783i
$685$	28.6091	+	28.6091i	1.09310	+	1.09310i
$686$	1.74306	+	1.74306i	0.0665504	+	0.0665504i
$687$	−10.0779			−0.384497
$688$			25.6032i			0.976114i
$689$			14.4924i			0.552115i
$690$	−18.9543	−	18.9543i	−0.721577	−	0.721577i
$691$	9.69983	−	9.69983i	0.368999	−	0.368999i	−0.498113	−	0.867112i	$-0.665974\pi$
$691$	9.69983	−	9.69983i	0.368999	−	0.368999i	0.867112	+	0.498113i	$0.165974\pi$
$692$		−	0.650391i		−	0.0247242i
$693$	−9.21585			−0.350081
$694$	−2.91827	−	2.91827i	−0.110776	−	0.110776i
$695$		−	43.8013i		−	1.66148i
$696$	42.3712			1.60608
$697$	−0.464967	+	1.16916i	−0.0176119	+	0.0442850i
$698$	72.4058			2.74060
$699$		−	12.9161i		−	0.488532i
$700$	2.09658	+	2.09658i	0.0792433	+	0.0792433i
$701$	−21.0046			−0.793335			−0.396667	−	0.917962i	$-0.629833\pi$
$701$	−21.0046			−0.793335			−0.396667	+	0.917962i	$0.629833\pi$
$702$		−	17.5252i		−	0.661448i
$703$	−11.9499	+	11.9499i	−0.450698	+	0.450698i
$704$	−19.8814	−	19.8814i	−0.749309	−	0.749309i
$705$		−	9.59237i		−	0.361269i
$706$		−	58.6780i		−	2.20837i
$707$	−3.34380			−0.125757
$708$	−9.07306	−	9.07306i	−0.340986	−	0.340986i
$709$	−11.9081	−	11.9081i	−0.447216	−	0.447216i	0.447212	−	0.894428i	$-0.352417\pi$
$709$	−11.9081	−	11.9081i	−0.447216	−	0.447216i	−0.894428	+	0.447212i	$0.852417\pi$
$710$	−11.2772	−	11.2772i	−0.423227	−	0.423227i
$711$	−2.91647	+	2.91647i	−0.109376	+	0.109376i
$712$	−30.1399	+	30.1399i	−1.12954	+	1.12954i
$713$	44.7809			1.67706
$714$	−0.285404	+	0.285404i	−0.0106810	+	0.0106810i
$715$	−15.3825			−0.575274
$716$	−20.1149	+	20.1149i	−0.751730	+	0.751730i
$717$		−	12.9243i		−	0.482668i
$718$		−	76.9171i		−	2.87052i
$719$	2.09004	−	2.09004i	0.0779454	−	0.0779454i	−0.667059	−	0.745005i	$-0.732447\pi$
$719$	2.09004	−	2.09004i	0.0779454	−	0.0779454i	0.745005	+	0.667059i	$0.232447\pi$
$720$	−24.6376			−0.918188
$721$	−5.00244	+	5.00244i	−0.186301	+	0.186301i
$722$	−30.9838			−1.15310
$723$	9.33337	−	9.33337i	0.347112	−	0.347112i
$724$	59.0271	−	59.0271i	2.19372	−	2.19372i
$725$	5.10910	+	5.10910i	0.189747	+	0.189747i
$726$	7.22766	+	7.22766i	0.268243	+	0.268243i
$727$	7.87857	+	7.87857i	0.292200	+	0.292200i	0.837949	−	0.545749i	$-0.183755\pi$
$727$	7.87857	+	7.87857i	0.292200	+	0.292200i	−0.545749	+	0.837949i	$0.683755\pi$
$728$	−8.23151			−0.305080
$729$		−	3.59704i		−	0.133224i
$730$			37.1862i			1.37632i
$731$	−0.796748	−	0.796748i	−0.0294688	−	0.0294688i
$732$	−23.4899	+	23.4899i	−0.868213	+	0.868213i
$733$		−	35.0385i		−	1.29418i	−0.762415	−	0.647088i	$-0.775987\pi$
$733$		−	35.0385i		−	1.29418i	0.762415	−	0.647088i	$-0.224013\pi$
$734$	71.0038			2.62080
$735$	1.41008	+	1.41008i	0.0520115	+	0.0520115i
$736$		−	4.19349i		−	0.154574i
$737$	27.4811			1.01228
$738$	−33.4218	+	14.4024i	−1.23027	+	0.530159i
$739$	−25.1949			−0.926809			−0.463404	−	0.886147i	$-0.653372\pi$
$739$	−25.1949			−0.926809			−0.463404	+	0.886147i	$0.653372\pi$
$740$			29.3436i			1.07869i
$741$	−5.32369	−	5.32369i	−0.195571	−	0.195571i
$742$	22.2154			0.815551
$743$			16.3208i			0.598751i	0.954135	+	0.299376i	$0.0967784\pi$
$743$			16.3208i			0.598751i	−0.954135	+	0.299376i	$0.903222\pi$
$744$	−24.7679	+	24.7679i	−0.908035	+	0.908035i
$745$	37.0350	+	37.0350i	1.35686	+	1.35686i
$746$		−	50.6494i		−	1.85440i
$747$			12.7541i			0.466648i
$748$	−3.20179			−0.117069
$749$	0.127189	+	0.127189i	0.00464738	+	0.00464738i
$750$	−14.8515	−	14.8515i	−0.542299	−	0.542299i
$751$	14.5094	+	14.5094i	0.529455	+	0.529455i	0.920410	−	0.390955i	$-0.127855\pi$
$751$	14.5094	+	14.5094i	0.529455	+	0.529455i	−0.390955	+	0.920410i	$0.627855\pi$
$752$	15.1871	−	15.1871i	0.553818	−	0.553818i
$753$	−11.8902	+	11.8902i	−0.433304	+	0.433304i
$754$	−39.3790			−1.43410
$755$	−0.940792	+	0.940792i	−0.0342389	+	0.0342389i
$756$	−18.0224			−0.655469
$757$	33.2317	−	33.2317i	1.20783	−	1.20783i	0.236096	−	0.971730i	$-0.424132\pi$
$757$	33.2317	−	33.2317i	1.20783	−	1.20783i	0.971730	−	0.236096i	$-0.0758679\pi$
$758$		−	61.4431i		−	2.23171i
$759$		−	18.1617i		−	0.659227i
$760$	−48.6697	+	48.6697i	−1.76543	+	1.76543i
$761$	48.7077			1.76565			0.882827	−	0.469698i	$-0.155637\pi$
$761$	48.7077			1.76565			0.882827	+	0.469698i	$0.155637\pi$
$762$	5.46340	−	5.46340i	0.197918	−	0.197918i
$763$	−17.3526			−0.628207
$764$	61.7113	−	61.7113i	2.23264	−	2.23264i
$765$	0.766698	−	0.766698i	0.0277200	−	0.0277200i
$766$	37.5591	+	37.5591i	1.35707	+	1.35707i
$767$	4.29532	+	4.29532i	0.155095	+	0.155095i
$768$	−19.1298	−	19.1298i	−0.690288	−	0.690288i
$769$	−17.1925			−0.619977			−0.309989	−	0.950740i	$-0.600325\pi$
$769$	−17.1925			−0.619977			−0.309989	+	0.950740i	$0.600325\pi$
$770$			23.5799i			0.849760i
$771$			21.2081i			0.763793i
$772$	57.2368	+	57.2368i	2.06000	+	2.06000i
$773$	−21.6492	+	21.6492i	−0.778666	+	0.778666i	−0.979604	−	0.200938i	$-0.935601\pi$
$773$	−21.6492	+	21.6492i	−0.778666	+	0.778666i	0.200938	+	0.979604i	$0.435601\pi$
$774$		−	32.5909i		−	1.17146i
$775$	−5.97300			−0.214557
$776$	24.3200	+	24.3200i	0.873036	+	0.873036i
$777$			2.50627i			0.0899121i
$778$	44.7024			1.60266
$779$	−13.2950	+	33.4302i	−0.476343	+	1.19776i
$780$	−13.0726			−0.468075
$781$		−	10.8056i		−	0.386656i
$782$	1.86773	+	1.86773i	0.0667899	+	0.0667899i
$783$	−43.9184			−1.56951
$784$			4.46503i			0.159465i
$785$	24.0843	−	24.0843i	0.859605	−	0.859605i
$786$	27.2106	+	27.2106i	0.970570	+	0.970570i
$787$			36.9755i			1.31803i	0.752128	+	0.659017i	$0.229028\pi$
$787$			36.9755i			1.31803i	−0.752128	+	0.659017i	$0.770972\pi$
$788$		−	4.46007i		−	0.158883i
$789$	7.50632			0.267232
$790$	7.46214	+	7.46214i	0.265491	+	0.265491i
$791$	−2.29633	−	2.29633i	−0.0816479	−	0.0816479i
$792$	−33.3569	−	33.3569i	−1.18529	−	1.18529i
$793$	11.1205	−	11.1205i	0.394899	−	0.394899i
$794$	6.98541	−	6.98541i	0.247903	−	0.247903i
$795$	17.9715			0.637383
$796$	−20.8411	+	20.8411i	−0.738695	+	0.738695i
$797$	−2.81904			−0.0998555			−0.0499278	−	0.998753i	$-0.515899\pi$
$797$	−2.81904			−0.0998555			−0.0499278	+	0.998753i	$0.515899\pi$
$798$	−8.16068	+	8.16068i	−0.288885	+	0.288885i
$799$			0.945219i			0.0334394i
$800$			0.559339i			0.0197756i
$801$	13.5761	−	13.5761i	0.479687	−	0.479687i
$802$	−74.1684			−2.61898
$803$	−17.8156	+	17.8156i	−0.628699	+	0.628699i
$804$	23.3545			0.823648
$805$	9.22779	−	9.22779i	0.325237	−	0.325237i
$806$	23.0188	−	23.0188i	0.810804	−	0.810804i
$807$	−8.62157	−	8.62157i	−0.303494	−	0.303494i
$808$	−12.1029	−	12.1029i	−0.425780	−	0.425780i
$809$	−24.5461	−	24.5461i	−0.862994	−	0.862994i	0.128691	−	0.991685i	$-0.458923\pi$
$809$	−24.5461	−	24.5461i	−0.862994	−	0.862994i	−0.991685	+	0.128691i	$0.958923\pi$
$810$	19.0735			0.670173
$811$		−	1.83014i		−	0.0642649i	−0.999484	−	0.0321324i	$-0.989770\pi$
$811$		−	1.83014i		−	0.0642649i	0.999484	−	0.0321324i	$-0.0102298\pi$
$812$			40.4962i			1.42114i
$813$	0.970538	+	0.970538i	0.0340382	+	0.0340382i
$814$	−20.9554	+	20.9554i	−0.734488	+	0.734488i
$815$		−	48.2868i		−	1.69141i
$816$	−0.731091			−0.0255933
$817$	−22.7818	−	22.7818i	−0.797033	−	0.797033i
$818$			14.9502i			0.522721i
$819$	3.70776			0.129560
$820$	24.7216	+	57.3683i	0.863314	+	2.00339i
$821$	−20.9323			−0.730542			−0.365271	−	0.930901i	$-0.619024\pi$
$821$	−20.9323			−0.730542			−0.365271	+	0.930901i	$0.619024\pi$
$822$			34.7259i			1.21120i
$823$	−35.2431	−	35.2431i	−1.22850	−	1.22850i	−0.964532	−	0.263966i	$-0.914969\pi$
$823$	−35.2431	−	35.2431i	−1.22850	−	1.22850i	−0.263966	−	0.964532i	$-0.585031\pi$
$824$	−36.2129			−1.26153
$825$			2.42245i			0.0843390i
$826$	6.58429	−	6.58429i	0.229097	−	0.229097i
$827$	−11.6293	−	11.6293i	−0.404390	−	0.404390i	0.475387	−	0.879777i	$-0.342308\pi$
$827$	−11.6293	−	11.6293i	−0.404390	−	0.404390i	−0.879777	+	0.475387i	$0.842308\pi$
$828$			51.2536i			1.78119i
$829$		−	49.3704i		−	1.71471i	−0.514729	−	0.857353i	$-0.672108\pi$
$829$		−	49.3704i		−	1.71471i	0.514729	−	0.857353i	$-0.327892\pi$
$830$	32.6329			1.13270
$831$	−10.7156	−	10.7156i	−0.371721	−	0.371721i
$832$	7.99878	+	7.99878i	0.277308	+	0.277308i
$833$	−0.138947	−	0.138947i	−0.00481424	−	0.00481424i
$834$	26.5831	−	26.5831i	0.920496	−	0.920496i
$835$	−6.93452	+	6.93452i	−0.239979	+	0.239979i
$836$	−91.5502			−3.16633
$837$	25.6723	−	25.6723i	0.887363	−	0.887363i
$838$	−83.8495			−2.89653
$839$	−18.1766	+	18.1766i	−0.627527	+	0.627527i	−0.947445	−	0.319918i	$-0.896345\pi$
$839$	−18.1766	+	18.1766i	−0.627527	+	0.627527i	0.319918	+	0.947445i	$0.396345\pi$
$840$			10.2076i			0.352196i
$841$			69.6841i			2.40290i
$842$	11.3934	−	11.3934i	0.392644	−	0.392644i
$843$	14.1336			0.486788
$844$	−19.8629	+	19.8629i	−0.683709	+	0.683709i
$845$	−24.9226			−0.857365
$846$	−19.3320	+	19.3320i	−0.664649	+	0.664649i
$847$	−3.51874	+	3.51874i	−0.120905	+	0.120905i
$848$	28.4534	+	28.4534i	0.977094	+	0.977094i
$849$	−17.6536	−	17.6536i	−0.605872	−	0.605872i
$850$	−0.249123	−	0.249123i	−0.00854485	−	0.00854485i
$851$	16.4015			0.562235
$852$		−	9.18302i		−	0.314605i
$853$		−	40.0261i		−	1.37047i	−0.728324	−	0.685233i	$-0.759700\pi$
$853$		−	40.0261i		−	1.37047i	0.728324	−	0.685233i	$-0.240300\pi$
$854$	−17.0466	−	17.0466i	−0.583321	−	0.583321i
$855$	21.9225	−	21.9225i	0.749735	−	0.749735i
$856$			0.920724i			0.0314697i
$857$	40.1406			1.37118			0.685588	−	0.727990i	$-0.259545\pi$
$857$	40.1406			1.37118			0.685588	+	0.727990i	$0.259545\pi$
$858$	−9.33568	−	9.33568i	−0.318715	−	0.318715i
$859$			38.6144i			1.31751i	0.752359	+	0.658754i	$0.228916\pi$
$859$			38.6144i			1.31751i	−0.752359	+	0.658754i	$0.771084\pi$
$860$	−55.9420			−1.90760
$861$	2.11150	+	4.89990i	0.0719597	+	0.166988i
$862$	−20.0444			−0.682713
$863$		−	31.4431i		−	1.07033i	−0.844746	−	0.535167i	$-0.820249\pi$
$863$		−	31.4431i		−	1.07033i	0.844746	−	0.535167i	$-0.179751\pi$
$864$	−2.40407	−	2.40407i	−0.0817881	−	0.0817881i
$865$	0.381822			0.0129823
$866$			10.2753i			0.349170i
$867$	−9.99375	+	9.99375i	−0.339406	+	0.339406i
$868$	−23.6718	−	23.6718i	−0.803475	−	0.803475i
$869$			7.15009i			0.242550i
$870$			48.8326i			1.65558i
$871$	−11.0563			−0.374630
$872$	−62.8081	−	62.8081i	−2.12695	−	2.12695i
$873$	−10.9546	−	10.9546i	−0.370756	−	0.370756i
$874$	53.4048	+	53.4048i	1.80645	+	1.80645i
$875$	7.23036	−	7.23036i	0.244431	−	0.244431i
$876$	−15.1403	+	15.1403i	−0.511545	+	0.511545i
$877$	0.684661			0.0231193			0.0115597	−	0.999933i	$-0.496320\pi$
$877$	0.684661			0.0231193			0.0115597	+	0.999933i	$0.496320\pi$
$878$	−3.01677	+	3.01677i	−0.101811	+	0.101811i
$879$	9.94573			0.335461
$880$	−30.2011	+	30.2011i	−1.01808	+	1.01808i
$881$			23.9631i			0.807336i	0.914905	+	0.403668i	$0.132265\pi$
$881$			23.9631i			0.807336i	−0.914905	+	0.403668i	$0.867735\pi$
$882$		−	5.68363i		−	0.191378i
$883$	−25.9430	+	25.9430i	−0.873052	+	0.873052i	−0.992804	−	0.119752i	$-0.961790\pi$
$883$	−25.9430	+	25.9430i	−0.873052	+	0.873052i	0.119752	+	0.992804i	$0.461790\pi$
$884$	1.28816			0.0433255
$885$	5.32647	−	5.32647i	0.179047	−	0.179047i
$886$	10.3472			0.347620
$887$	6.51115	−	6.51115i	0.218623	−	0.218623i	−0.589295	−	0.807918i	$-0.700594\pi$
$887$	6.51115	−	6.51115i	0.218623	−	0.218623i	0.807918	+	0.589295i	$0.200594\pi$
$888$	−9.07150	+	9.07150i	−0.304420	+	0.304420i
$889$	2.65982	+	2.65982i	0.0892076	+	0.0892076i
$890$	−34.7361	−	34.7361i	−1.16436	−	1.16436i
$891$	9.13793	+	9.13793i	0.306132	+	0.306132i
$892$	92.2553			3.08894
$893$			27.0271i			0.904426i
$894$			44.9533i			1.50346i
$895$	−11.8088	−	11.8088i	−0.394723	−	0.394723i
$896$	13.3489	−	13.3489i	0.445955	−	0.445955i
$897$			7.30688i			0.243970i
$898$	−42.9114			−1.43197
$899$	−57.6853	−	57.6853i	−1.92391	−	1.92391i
$900$		−	6.83635i		−	0.227878i
$901$	−1.77089			−0.0589968
$902$	−23.3143	+	58.6236i	−0.776282	+	1.95195i
$903$	−4.77807			−0.159004
$904$		−	16.6232i		−	0.552879i
$905$	34.6527	+	34.6527i	1.15190	+	1.15190i
$906$	−1.14194			−0.0379383
$907$			0.286333i			0.00950754i	0.999989	+	0.00475377i	$0.00151318\pi$
$907$			0.286333i			0.00950754i	−0.999989	+	0.00475377i	$0.998487\pi$
$908$	−58.4464	+	58.4464i	−1.93961	+	1.93961i
$909$	5.45159	+	5.45159i	0.180818	+	0.180818i
$910$		−	9.48676i		−	0.314483i
$911$		−	34.5921i		−	1.14609i	−0.819525	−	0.573043i	$-0.805763\pi$
$911$		−	34.5921i		−	1.14609i	0.819525	−	0.573043i	$-0.194237\pi$
$912$	−20.9044			−0.692214
$913$	15.6341	+	15.6341i	0.517415	+	0.517415i
$914$	30.1163	+	30.1163i	0.996159	+	0.996159i
$915$	−13.7901	−	13.7901i	−0.455887	−	0.455887i
$916$	34.8630	−	34.8630i	1.15190	−	1.15190i
$917$	−13.2473	+	13.2473i	−0.437466	+	0.437466i
$918$	2.14149			0.0706796
$919$	15.6828	−	15.6828i	0.517327	−	0.517327i	−0.399435	−	0.916762i	$-0.630794\pi$
$919$	15.6828	−	15.6828i	0.517327	−	0.517327i	0.916762	+	0.399435i	$0.130794\pi$
$920$	66.8003			2.20234
$921$	13.4925	−	13.4925i	0.444592	−	0.444592i
$922$		−	24.0851i		−	0.793199i
$923$			4.34737i			0.143096i
$924$	−9.60053	+	9.60053i	−0.315834	+	0.315834i
$925$	−2.18767			−0.0719303
$926$	−25.3714	+	25.3714i	−0.833757	+	0.833757i
$927$	16.3115			0.535741
$928$	−5.40192	+	5.40192i	−0.177327	+	0.177327i
$929$	18.5076	−	18.5076i	0.607214	−	0.607214i	−0.335003	−	0.942217i	$-0.608737\pi$
$929$	18.5076	−	18.5076i	0.607214	−	0.607214i	0.942217	+	0.335003i	$0.108737\pi$
$930$	−28.5449	−	28.5449i	−0.936023	−	0.936023i
$931$	−3.97298	−	3.97298i	−0.130209	−	0.130209i
$932$	44.6813	+	44.6813i	1.46358	+	1.46358i
$933$	3.01714			0.0987768
$934$		−	6.92024i		−	0.226437i
$935$		−	1.87966i		−	0.0614714i
$936$	13.4203	+	13.4203i	0.438656	+	0.438656i
$937$	−2.51490	+	2.51490i	−0.0821583	+	0.0821583i	−0.746992	−	0.664833i	$-0.768503\pi$
$937$	−2.51490	+	2.51490i	−0.0821583	+	0.0821583i	0.664833	+	0.746992i	$0.268503\pi$
$938$			16.9483i			0.553380i
$939$	16.5519			0.540149
$940$	33.1833	+	33.1833i	1.08232	+	1.08232i
$941$		−	22.2074i		−	0.723941i	−0.932190	−	0.361970i	$-0.882104\pi$
$941$		−	22.2074i		−	0.723941i	0.932190	−	0.361970i	$-0.117896\pi$
$942$	29.2336			0.952481
$943$	32.0657	−	13.8180i	1.04420	−	0.449976i
$944$	16.8663			0.548952
$945$		−	10.5803i		−	0.344178i
$946$	−39.9504	−	39.9504i	−1.29890	−	1.29890i
$947$	−54.4942			−1.77082			−0.885412	−	0.464806i	$-0.846124\pi$
$947$	−54.4942			−1.77082			−0.885412	+	0.464806i	$0.846124\pi$
$948$			6.07641i			0.197352i
$949$	7.16765	−	7.16765i	0.232672	−	0.232672i
$950$	−7.12329	−	7.12329i	−0.231110	−	0.231110i
$951$		−	13.5832i		−	0.440465i
$952$		−	1.00584i		−	0.0325996i
$953$	−23.0677			−0.747235			−0.373618	−	0.927583i	$-0.621883\pi$
$953$	−23.0677			−0.747235			−0.373618	+	0.927583i	$0.621883\pi$
$954$	−36.2190	−	36.2190i	−1.17263	−	1.17263i
$955$	36.2285	+	36.2285i	1.17233	+	1.17233i
$956$	44.7097	+	44.7097i	1.44601	+	1.44601i
$957$	−23.3953	+	23.3953i	−0.756262	+	0.756262i
$958$	−29.6479	+	29.6479i	−0.957879	+	0.957879i
$959$	−16.9061			−0.545926
$960$	9.91901	−	9.91901i	0.320135	−	0.320135i
$961$	36.4393			1.17546
$962$	8.43089	−	8.43089i	0.271823	−	0.271823i
$963$		−	0.414726i		−	0.0133644i
$964$			64.5746i			2.07981i
$965$	−33.6017	+	33.6017i	−1.08168	+	1.08168i
$966$	11.2007			0.360377
$967$	1.51760	−	1.51760i	0.0488027	−	0.0488027i	−0.682284	−	0.731087i	$-0.739013\pi$
$967$	1.51760	−	1.51760i	0.0488027	−	0.0488027i	0.731087	+	0.682284i	$0.239013\pi$
$968$	−25.4723			−0.818711
$969$	0.650525	−	0.650525i	0.0208979	−	0.0208979i
$970$	−28.0286	+	28.0286i	−0.899944	+	0.899944i
$971$	3.06012	+	3.06012i	0.0982038	+	0.0982038i	0.754502	−	0.656298i	$-0.227879\pi$
$971$	3.06012	+	3.06012i	0.0982038	+	0.0982038i	−0.656298	+	0.754502i	$0.727879\pi$
$972$	45.9971	+	45.9971i	1.47536	+	1.47536i
$973$	12.9418	+	12.9418i	0.414896	+	0.414896i
$974$	46.0779			1.47643
$975$		−	0.974612i		−	0.0312126i
$976$		−	43.6665i		−	1.39773i
$977$	−26.3113	−	26.3113i	−0.841773	−	0.841773i	0.147317	−	0.989089i	$-0.452936\pi$
$977$	−26.3113	−	26.3113i	−0.841773	−	0.841773i	−0.989089	+	0.147317i	$0.952936\pi$
$978$	29.3053	−	29.3053i	0.937081	−	0.937081i
$979$		−	33.2835i		−	1.06375i
$980$	−9.75589			−0.311640
$981$	28.2910	+	28.2910i	0.903261	+	0.903261i
$982$			78.8628i			2.51661i
$983$	−60.4274			−1.92734			−0.963668	−	0.267103i	$-0.913934\pi$
$983$	−60.4274			−1.92734			−0.963668	+	0.267103i	$0.913934\pi$
$984$	−10.0926	+	25.3779i	−0.321742	+	0.809017i
$985$	2.61835			0.0834275
$986$		−	4.81190i		−	0.153242i
$987$	2.83423	+	2.83423i	0.0902144	+	0.0902144i
$988$	36.8329			1.17181
$989$			31.2685i			0.994280i
$990$	38.4436	−	38.4436i	1.22182	−	1.22182i
$991$	18.3215	+	18.3215i	0.582003	+	0.582003i	0.935453	−	0.353450i	$-0.114992\pi$
$991$	18.3215	+	18.3215i	0.582003	+	0.582003i	−0.353450	+	0.935453i	$0.614992\pi$
$992$		−	6.31533i		−	0.200512i
$993$			22.1223i			0.702030i
$994$	6.66409			0.211372
$995$	−12.2351	−	12.2351i	−0.387879	−	0.387879i
$996$	13.2865	+	13.2865i	0.420998	+	0.420998i
$997$	−33.1711	−	33.1711i	−1.05054	−	1.05054i	−0.998653	−	0.0518847i	$-0.983477\pi$
$997$	−33.1711	−	33.1711i	−1.05054	−	1.05054i	−0.0518847	−	0.998653i	$-0.516523\pi$
$998$	37.6092	−	37.6092i	1.19050	−	1.19050i
$999$	9.40273	−	9.40273i	0.297489	−	0.297489i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	287.2.f.a.50.1	✓	40
41.32	even	4	inner	287.2.f.a.155.20	yes	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
287.2.f.a.50.1	✓	40	1.1	even	1	trivial
287.2.f.a.155.20	yes	40	41.32	even	4	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:	\( N \)	\(=\)	\( 287 = 7 \cdot 41 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	287.f (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q-2.46506i q^{2} +(0.589206 + 0.589206i) q^{3} -4.07653 q^{4} -2.39319i q^{5} +(1.45243 - 1.45243i) q^{6} +(0.707107 + 0.707107i) q^{7} +5.11877i q^{8} -2.30567i q^{9} +O(q^{10})\)	\(q-2.46506i q^{2} +(0.589206 + 0.589206i) q^{3} -4.07653 q^{4} -2.39319i q^{5} +(1.45243 - 1.45243i) q^{6} +(0.707107 + 0.707107i) q^{7} +5.11877i q^{8} -2.30567i q^{9} -5.89935 q^{10} +(-2.82633 - 2.82633i) q^{11} +(-2.40191 - 2.40191i) q^{12} +(1.13710 + 1.13710i) q^{13} +(1.74306 - 1.74306i) q^{14} +(1.41008 - 1.41008i) q^{15} +4.46503 q^{16} +(-0.138947 + 0.138947i) q^{17} -5.68363 q^{18} +(-3.97298 + 3.97298i) q^{19} +9.75589i q^{20} +0.833263i q^{21} +(-6.96707 + 6.96707i) q^{22} +5.45301 q^{23} +(-3.01601 + 3.01601i) q^{24} -0.727338 q^{25} +(2.80302 - 2.80302i) q^{26} +(3.12613 - 3.12613i) q^{27} +(-2.88254 - 2.88254i) q^{28} +(-7.02439 - 7.02439i) q^{29} +(-3.47593 - 3.47593i) q^{30} +8.21214 q^{31} -0.769023i q^{32} -3.33058i q^{33} +(0.342514 + 0.342514i) q^{34} +(1.69224 - 1.69224i) q^{35} +9.39914i q^{36} +3.00778 q^{37} +(9.79364 + 9.79364i) q^{38} +1.33997i q^{39} +12.2502 q^{40} +(5.88037 - 2.53401i) q^{41} +2.05404 q^{42} +5.73417i q^{43} +(11.5216 + 11.5216i) q^{44} -5.51790 q^{45} -13.4420i q^{46} +(3.40136 - 3.40136i) q^{47} +(2.63082 + 2.63082i) q^{48} +1.00000i q^{49} +1.79293i q^{50} -0.163737 q^{51} +(-4.63542 - 4.63542i) q^{52} +(6.37251 + 6.37251i) q^{53} +(-7.70611 - 7.70611i) q^{54} +(-6.76393 + 6.76393i) q^{55} +(-3.61952 + 3.61952i) q^{56} -4.68181 q^{57} +(-17.3155 + 17.3155i) q^{58} +3.77743 q^{59} +(-5.74823 + 5.74823i) q^{60} -9.77967i q^{61} -20.2434i q^{62} +(1.63036 - 1.63036i) q^{63} +7.03436 q^{64} +(2.72129 - 2.72129i) q^{65} -8.21008 q^{66} +(-4.86163 + 4.86163i) q^{67} +(0.566423 - 0.566423i) q^{68} +(3.21294 + 3.21294i) q^{69} +(-4.17147 - 4.17147i) q^{70} +(1.91160 + 1.91160i) q^{71} +11.8022 q^{72} -6.30345i q^{73} -7.41437i q^{74} +(-0.428552 - 0.428552i) q^{75} +(16.1960 - 16.1960i) q^{76} -3.99703i q^{77} +3.30312 q^{78} +(-1.26491 - 1.26491i) q^{79} -10.6856i q^{80} -3.23315 q^{81} +(-6.24650 - 14.4955i) q^{82} -5.53161 q^{83} -3.39682i q^{84} +(0.332527 + 0.332527i) q^{85} +14.1351 q^{86} -8.27762i q^{87} +(14.4673 - 14.4673i) q^{88} +(5.88812 + 5.88812i) q^{89} +13.6020i q^{90} +1.60810i q^{91} -22.2293 q^{92} +(4.83864 + 4.83864i) q^{93} +(-8.38456 - 8.38456i) q^{94} +(9.50808 + 9.50808i) q^{95} +(0.453113 - 0.453113i) q^{96} +(4.75113 - 4.75113i) q^{97} +2.46506 q^{98} +(-6.51659 + 6.51659i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q + 4 q^{3} - 36 q^{4} + 8 q^{6}+O(q^{10}) \) 40 * q + 4 * q^3 - 36 * q^4 + 8 * q^6	\( 40 q + 4 q^{3} - 36 q^{4} + 8 q^{6} - 32 q^{10} - 8 q^{11} + 16 q^{12} + 16 q^{13} - 8 q^{15} + 28 q^{16} + 20 q^{17} - 12 q^{18} - 20 q^{19} + 4 q^{22} + 16 q^{23} - 12 q^{24} - 40 q^{25} - 20 q^{26} - 20 q^{27} - 12 q^{29} + 4 q^{30} + 32 q^{34} + 4 q^{35} - 16 q^{38} + 64 q^{40} + 16 q^{41} + 32 q^{42} + 8 q^{44} + 72 q^{45} - 24 q^{47} - 40 q^{48} - 64 q^{51} - 96 q^{52} + 8 q^{53} + 52 q^{54} - 8 q^{55} - 88 q^{57} - 36 q^{58} + 48 q^{59} + 52 q^{60} - 8 q^{63} - 84 q^{64} - 44 q^{65} + 56 q^{66} + 40 q^{67} - 60 q^{68} + 28 q^{69} - 8 q^{70} + 20 q^{71} + 80 q^{72} - 20 q^{75} - 4 q^{76} + 12 q^{78} - 12 q^{79} + 16 q^{81} - 52 q^{82} + 40 q^{83} + 8 q^{85} + 80 q^{86} + 96 q^{88} - 8 q^{89} - 20 q^{92} - 64 q^{93} + 52 q^{94} + 68 q^{96} - 60 q^{97} - 4 q^{98} - 36 q^{99}+O(q^{100}) \) 40 * q + 4 * q^3 - 36 * q^4 + 8 * q^6 - 32 * q^10 - 8 * q^11 + 16 * q^12 + 16 * q^13 - 8 * q^15 + 28 * q^16 + 20 * q^17 - 12 * q^18 - 20 * q^19 + 4 * q^22 + 16 * q^23 - 12 * q^24 - 40 * q^25 - 20 * q^26 - 20 * q^27 - 12 * q^29 + 4 * q^30 + 32 * q^34 + 4 * q^35 - 16 * q^38 + 64 * q^40 + 16 * q^41 + 32 * q^42 + 8 * q^44 + 72 * q^45 - 24 * q^47 - 40 * q^48 - 64 * q^51 - 96 * q^52 + 8 * q^53 + 52 * q^54 - 8 * q^55 - 88 * q^57 - 36 * q^58 + 48 * q^59 + 52 * q^60 - 8 * q^63 - 84 * q^64 - 44 * q^65 + 56 * q^66 + 40 * q^67 - 60 * q^68 + 28 * q^69 - 8 * q^70 + 20 * q^71 + 80 * q^72 - 20 * q^75 - 4 * q^76 + 12 * q^78 - 12 * q^79 + 16 * q^81 - 52 * q^82 + 40 * q^83 + 8 * q^85 + 80 * q^86 + 96 * q^88 - 8 * q^89 - 20 * q^92 - 64 * q^93 + 52 * q^94 + 68 * q^96 - 60 * q^97 - 4 * q^98 - 36 * q^99

Introduction

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