LMFDB - Embedded newform 804.2.e.a.535.16

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [804,2,Mod(535,804)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(804, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 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("804.535");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 804 = 2^{2} \cdot 3 \cdot 67 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	804.e (of order $2$, degree $1$, 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:	$6.41997232251$
Analytic rank:	$0$
Dimension:	$34$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			535.16
Character	$\chi$	$=$	804.535
Dual form			804.2.e.a.535.15

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.271785 + 1.38785i) q^{2} -1.00000 q^{3} +(-1.85227 - 0.754394i) q^{4} -0.299779i q^{5} +(0.271785 - 1.38785i) q^{6} -1.88035 q^{7} +(1.55041 - 2.36564i) q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+(-0.271785 + 1.38785i) q^{2} -1.00000 q^{3} +(-1.85227 - 0.754394i) q^{4} -0.299779i q^{5} +(0.271785 - 1.38785i) q^{6} -1.88035 q^{7} +(1.55041 - 2.36564i) q^{8} +1.00000 q^{9} +(0.416048 + 0.0814753i) q^{10} -2.47030 q^{11} +(1.85227 + 0.754394i) q^{12} +1.99858i q^{13} +(0.511050 - 2.60964i) q^{14} +0.299779i q^{15} +(2.86178 + 2.79468i) q^{16} +0.452397 q^{17} +(-0.271785 + 1.38785i) q^{18} -5.21266i q^{19} +(-0.226151 + 0.555270i) q^{20} +1.88035 q^{21} +(0.671389 - 3.42841i) q^{22} -0.807898i q^{23} +(-1.55041 + 2.36564i) q^{24} +4.91013 q^{25} +(-2.77374 - 0.543184i) q^{26} -1.00000 q^{27} +(3.48290 + 1.41852i) q^{28} +9.00503 q^{29} +(-0.416048 - 0.0814753i) q^{30} +8.22773 q^{31} +(-4.65639 + 3.21217i) q^{32} +2.47030 q^{33} +(-0.122955 + 0.627860i) q^{34} +0.563688i q^{35} +(-1.85227 - 0.754394i) q^{36} +1.31776 q^{37} +(7.23440 + 1.41672i) q^{38} -1.99858i q^{39} +(-0.709168 - 0.464778i) q^{40} +6.67060i q^{41} +(-0.511050 + 2.60964i) q^{42} +4.44399 q^{43} +(4.57565 + 1.86358i) q^{44} -0.299779i q^{45} +(1.12124 + 0.219575i) q^{46} +2.51300i q^{47} +(-2.86178 - 2.79468i) q^{48} -3.46429 q^{49} +(-1.33450 + 6.81454i) q^{50} -0.452397 q^{51} +(1.50772 - 3.70191i) q^{52} +0.990958i q^{53} +(0.271785 - 1.38785i) q^{54} +0.740542i q^{55} +(-2.91530 + 4.44822i) q^{56} +5.21266i q^{57} +(-2.44743 + 12.4976i) q^{58} +7.56006i q^{59} +(0.226151 - 0.555270i) q^{60} -9.06097i q^{61} +(-2.23617 + 11.4189i) q^{62} -1.88035 q^{63} +(-3.19249 - 7.33540i) q^{64} +0.599132 q^{65} +(-0.671389 + 3.42841i) q^{66} +(2.90832 - 7.65125i) q^{67} +(-0.837960 - 0.341286i) q^{68} +0.807898i q^{69} +(-0.782315 - 0.153202i) q^{70} +0.0862739i q^{71} +(1.55041 - 2.36564i) q^{72} +1.91010 q^{73} +(-0.358147 + 1.82885i) q^{74} -4.91013 q^{75} +(-3.93240 + 9.65523i) q^{76} +4.64502 q^{77} +(2.77374 + 0.543184i) q^{78} +8.30576 q^{79} +(0.837784 - 0.857900i) q^{80} +1.00000 q^{81} +(-9.25781 - 1.81297i) q^{82} +0.827060i q^{83} +(-3.48290 - 1.41852i) q^{84} -0.135619i q^{85} +(-1.20781 + 6.16760i) q^{86} -9.00503 q^{87} +(-3.82996 + 5.84383i) q^{88} +14.5391 q^{89} +(0.416048 + 0.0814753i) q^{90} -3.75803i q^{91} +(-0.609474 + 1.49644i) q^{92} -8.22773 q^{93} +(-3.48767 - 0.682996i) q^{94} -1.56264 q^{95} +(4.65639 - 3.21217i) q^{96} -6.11092i q^{97} +(0.941543 - 4.80793i) q^{98} -2.47030 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 34 q - 34 q^{3} + 2 q^{4} - 4 q^{7} + 6 q^{8} + 34 q^{9}+O(q^{10}) $ 34 * q - 34 * q^3 + 2 * q^4 - 4 * q^7 + 6 * q^8 + 34 * q^9	$ 34 q - 34 q^{3} + 2 q^{4} - 4 q^{7} + 6 q^{8} + 34 q^{9} - 6 q^{10} - 2 q^{12} - 4 q^{14} + 2 q^{16} + 12 q^{20} + 4 q^{21} - 8 q^{22} - 6 q^{24} - 34 q^{25} + 10 q^{26} - 34 q^{27} + 8 q^{28} - 16 q^{29} + 6 q^{30} + 4 q^{31} + 2 q^{36} + 12 q^{37} - 26 q^{38} - 18 q^{40} + 4 q^{42} + 4 q^{43} - 26 q^{44} + 4 q^{46} - 2 q^{48} + 46 q^{49} + 18 q^{50} - 32 q^{52} + 14 q^{56} - 4 q^{58} - 12 q^{60} - 2 q^{62} - 4 q^{63} + 26 q^{64} + 8 q^{66} + 18 q^{67} - 34 q^{68} - 56 q^{70} + 6 q^{72} + 12 q^{73} - 22 q^{74} + 34 q^{75} - 32 q^{76} - 8 q^{77} - 10 q^{78} + 12 q^{79} + 2 q^{80} + 34 q^{81} + 26 q^{82} - 8 q^{84} + 6 q^{86} + 16 q^{87} - 28 q^{88} - 6 q^{90} - 46 q^{92} - 4 q^{93} - 32 q^{94} + 40 q^{95} + 40 q^{98}+O(q^{100}) $ 34 * q - 34 * q^3 + 2 * q^4 - 4 * q^7 + 6 * q^8 + 34 * q^9 - 6 * q^10 - 2 * q^12 - 4 * q^14 + 2 * q^16 + 12 * q^20 + 4 * q^21 - 8 * q^22 - 6 * q^24 - 34 * q^25 + 10 * q^26 - 34 * q^27 + 8 * q^28 - 16 * q^29 + 6 * q^30 + 4 * q^31 + 2 * q^36 + 12 * q^37 - 26 * q^38 - 18 * q^40 + 4 * q^42 + 4 * q^43 - 26 * q^44 + 4 * q^46 - 2 * q^48 + 46 * q^49 + 18 * q^50 - 32 * q^52 + 14 * q^56 - 4 * q^58 - 12 * q^60 - 2 * q^62 - 4 * q^63 + 26 * q^64 + 8 * q^66 + 18 * q^67 - 34 * q^68 - 56 * q^70 + 6 * q^72 + 12 * q^73 - 22 * q^74 + 34 * q^75 - 32 * q^76 - 8 * q^77 - 10 * q^78 + 12 * q^79 + 2 * q^80 + 34 * q^81 + 26 * q^82 - 8 * q^84 + 6 * q^86 + 16 * q^87 - 28 * q^88 - 6 * q^90 - 46 * q^92 - 4 * q^93 - 32 * q^94 + 40 * q^95 + 40 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/804\mathbb{Z}\right)^\times$.

$n$	$269$	$337$	$403$
$\chi(n)$	$1$	$-1$	$-1$

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 $

$2$	−0.271785	+	1.38785i	−0.192181	+	0.981360i
$2$	−0.271785	+	1.38785i	−0.192181	+	0.981360i
$3$	−1.00000			−0.577350
$3$	−1.00000			−0.577350
$4$	−1.85227	−	0.754394i	−0.926133	−	0.377197i
$5$		−	0.299779i		−	0.134065i	−0.997751	−	0.0670325i	$-0.978647\pi$
$5$		−	0.299779i		−	0.134065i	0.997751	−	0.0670325i	$-0.0213531\pi$
$6$	0.271785	−	1.38785i	0.110956	−	0.566588i
$7$	−1.88035			−0.710704			−0.355352	−	0.934732i	$-0.615639\pi$
$7$	−1.88035			−0.710704			−0.355352	+	0.934732i	$0.615639\pi$
$8$	1.55041	−	2.36564i	0.548151	−	0.836379i
$9$	1.00000			0.333333
$10$	0.416048	+	0.0814753i	0.131566	+	0.0257647i
$11$	−2.47030			−0.744822			−0.372411	−	0.928068i	$-0.621469\pi$
$11$	−2.47030			−0.744822			−0.372411	+	0.928068i	$0.621469\pi$
$12$	1.85227	+	0.754394i	0.534703	+	0.217775i
$13$			1.99858i			0.554307i	0.960826	+	0.277153i	$0.0893910\pi$
$13$			1.99858i			0.554307i	−0.960826	+	0.277153i	$0.910609\pi$
$14$	0.511050	−	2.60964i	0.136584	−	0.697457i
$15$			0.299779i			0.0774025i
$16$	2.86178	+	2.79468i	0.715445	+	0.698669i
$17$	0.452397			0.109722			0.0548612	−	0.998494i	$-0.482528\pi$
$17$	0.452397			0.109722			0.0548612	+	0.998494i	$0.482528\pi$
$18$	−0.271785	+	1.38785i	−0.0640603	+	0.327120i
$19$		−	5.21266i		−	1.19587i	−0.801546	−	0.597933i	$-0.795989\pi$
$19$		−	5.21266i		−	1.19587i	0.801546	−	0.597933i	$-0.204011\pi$
$20$	−0.226151	+	0.555270i	−0.0505689	+	0.124162i
$21$	1.88035			0.410325
$22$	0.671389	−	3.42841i	0.143141	−	0.730939i
$23$		−	0.807898i		−	0.168458i	−0.996446	−	0.0842292i	$-0.973157\pi$
$23$		−	0.807898i		−	0.168458i	0.996446	−	0.0842292i	$-0.0268428\pi$
$24$	−1.55041	+	2.36564i	−0.316475	+	0.482884i
$25$	4.91013			0.982027
$26$	−2.77374	−	0.543184i	−0.543974	−	0.106527i
$27$	−1.00000			−0.192450
$28$	3.48290	+	1.41852i	0.658207	+	0.268076i
$29$	9.00503			1.67219			0.836096	−	0.548584i	$-0.184833\pi$
$29$	9.00503			1.67219			0.836096	+	0.548584i	$0.184833\pi$
$30$	−0.416048	−	0.0814753i	−0.0759597	−	0.0148753i
$31$	8.22773			1.47774			0.738872	−	0.673846i	$-0.235359\pi$
$31$	8.22773			1.47774			0.738872	+	0.673846i	$0.235359\pi$
$32$	−4.65639	+	3.21217i	−0.823141	+	0.567837i
$33$	2.47030			0.430023
$34$	−0.122955	+	0.627860i	−0.0210866	+	0.107677i
$35$			0.563688i			0.0952806i
$36$	−1.85227	−	0.754394i	−0.308711	−	0.125732i
$37$	1.31776			0.216638			0.108319	−	0.994116i	$-0.465453\pi$
$37$	1.31776			0.216638			0.108319	+	0.994116i	$0.465453\pi$
$38$	7.23440	+	1.41672i	1.17357	+	0.229823i
$39$		−	1.99858i		−	0.320029i
$40$	−0.709168	−	0.464778i	−0.112129	−	0.0734879i
$41$			6.67060i			1.04177i	0.853626	+	0.520887i	$0.174399\pi$
$41$			6.67060i			1.04177i	−0.853626	+	0.520887i	$0.825601\pi$
$42$	−0.511050	+	2.60964i	−0.0788567	+	0.402677i
$43$	4.44399			0.677702			0.338851	−	0.940840i	$-0.389962\pi$
$43$	4.44399			0.677702			0.338851	+	0.940840i	$0.389962\pi$
$44$	4.57565	+	1.86358i	0.689805	+	0.280945i
$45$		−	0.299779i		−	0.0446883i
$46$	1.12124	+	0.219575i	0.165318	+	0.0323745i
$47$			2.51300i			0.366559i	0.983061	+	0.183279i	$0.0586713\pi$
$47$			2.51300i			0.366559i	−0.983061	+	0.183279i	$0.941329\pi$
$48$	−2.86178	−	2.79468i	−0.413062	−	0.403377i
$49$	−3.46429			−0.494899
$50$	−1.33450	+	6.81454i	−0.188727	+	0.963721i
$51$	−0.452397			−0.0633483
$52$	1.50772	−	3.70191i	0.209083	−	0.513362i
$53$			0.990958i			0.136118i	0.997681	+	0.0680592i	$0.0216807\pi$
$53$			0.990958i			0.136118i	−0.997681	+	0.0680592i	$0.978319\pi$
$54$	0.271785	−	1.38785i	0.0369852	−	0.188863i
$55$			0.740542i			0.0998547i
$56$	−2.91530	+	4.44822i	−0.389573	+	0.594419i
$57$			5.21266i			0.690434i
$58$	−2.44743	+	12.4976i	−0.321363	+	1.64102i
$59$			7.56006i			0.984236i	0.870529	+	0.492118i	$0.163777\pi$
$59$			7.56006i			0.984236i	−0.870529	+	0.492118i	$0.836223\pi$
$60$	0.226151	−	0.555270i	0.0291960	−	0.0716850i
$61$		−	9.06097i		−	1.16014i	−0.814567	−	0.580069i	$-0.803025\pi$
$61$		−	9.06097i		−	1.16014i	0.814567	−	0.580069i	$-0.196975\pi$
$62$	−2.23617	+	11.4189i	−0.283994	+	1.45020i
$63$	−1.88035			−0.236901
$64$	−3.19249	−	7.33540i	−0.399061	−	0.916924i
$65$	0.599132			0.0743132
$66$	−0.671389	+	3.42841i	−0.0826423	+	0.422008i
$67$	2.90832	−	7.65125i	0.355308	−	0.934749i
$67$	2.90832	−	7.65125i	0.355308	−	0.934749i
$68$	−0.837960	−	0.341286i	−0.101618	−	0.0413870i
$69$			0.807898i			0.0972595i
$70$	−0.782315	−	0.153202i	−0.0935045	−	0.0183111i
$71$			0.0862739i			0.0102388i	0.999987	+	0.00511941i	$0.00162957\pi$
$71$			0.0862739i			0.0102388i	−0.999987	+	0.00511941i	$0.998370\pi$
$72$	1.55041	−	2.36564i	0.182717	−	0.278793i
$73$	1.91010			0.223560			0.111780	−	0.993733i	$-0.464345\pi$
$73$	1.91010			0.223560			0.111780	+	0.993733i	$0.464345\pi$
$74$	−0.358147	+	1.82885i	−0.0416337	+	0.212600i
$75$	−4.91013			−0.566973
$76$	−3.93240	+	9.65523i	−0.451077	+	1.10753i
$77$	4.64502			0.529349
$78$	2.77374	+	0.543184i	0.314064	+	0.0615035i
$79$	8.30576			0.934471			0.467236	−	0.884133i	$-0.345250\pi$
$79$	8.30576			0.934471			0.467236	+	0.884133i	$0.345250\pi$
$80$	0.837784	−	0.857900i	0.0936671	−	0.0959161i
$81$	1.00000			0.111111
$82$	−9.25781	−	1.81297i	−1.02235	−	0.200209i
$83$			0.827060i			0.0907816i	0.998969	+	0.0453908i	$0.0144533\pi$
$83$			0.827060i			0.0907816i	−0.998969	+	0.0453908i	$0.985547\pi$
$84$	−3.48290	−	1.41852i	−0.380016	−	0.154774i
$85$		−	0.135619i		−	0.0147099i
$86$	−1.20781	+	6.16760i	−0.130241	+	0.665070i
$87$	−9.00503			−0.965440
$88$	−3.82996	+	5.84383i	−0.408275	+	0.622954i
$89$	14.5391			1.54114			0.770571	−	0.637354i	$-0.219971\pi$
$89$	14.5391			1.54114			0.770571	+	0.637354i	$0.219971\pi$
$90$	0.416048	+	0.0814753i	0.0438553	+	0.00858825i
$91$		−	3.75803i		−	0.393948i
$92$	−0.609474	+	1.49644i	−0.0635420	+	0.156015i
$93$	−8.22773			−0.853176
$94$	−3.48767	−	0.682996i	−0.359726	−	0.0704456i
$95$	−1.56264			−0.160324
$96$	4.65639	−	3.21217i	0.475240	−	0.327841i
$97$		−	6.11092i		−	0.620470i	−0.950660	−	0.310235i	$-0.899592\pi$
$97$		−	6.11092i		−	0.620470i	0.950660	−	0.310235i	$-0.100408\pi$
$98$	0.941543	−	4.80793i	0.0951102	−	0.485674i
$99$	−2.47030			−0.248274
$100$	−9.09487	−	3.70418i	−0.909487	−	0.370418i
$101$		−	16.5489i		−	1.64668i	−0.567548	−	0.823341i	$-0.692108\pi$
$101$		−	16.5489i		−	1.64668i	0.567548	−	0.823341i	$-0.307892\pi$
$102$	0.122955	−	0.627860i	0.0121743	−	0.0621674i
$103$		−	1.25864i		−	0.124017i	−0.998076	−	0.0620085i	$-0.980249\pi$
$103$		−	1.25864i		−	0.124017i	0.998076	−	0.0620085i	$-0.0197506\pi$
$104$	4.72792	+	3.09861i	0.463611	+	0.303844i
$105$		−	0.563688i		−	0.0550103i
$106$	−1.37530	−	0.269327i	−0.133581	−	0.0261594i
$107$			11.4199i			1.10400i	0.833844	+	0.552001i	$0.186135\pi$
$107$			11.4199i			1.10400i	−0.833844	+	0.552001i	$0.813865\pi$
$108$	1.85227	+	0.754394i	0.178234	+	0.0725916i
$109$		−	6.20771i		−	0.594591i	−0.954786	−	0.297295i	$-0.903915\pi$
$109$		−	6.20771i		−	0.594591i	0.954786	−	0.297295i	$-0.0960846\pi$
$110$	−1.02776	−	0.201268i	−0.0979933	−	0.0191902i
$111$	−1.31776			−0.125076
$112$	−5.38114	−	5.25496i	−0.508470	−	0.496547i
$113$			12.9323i			1.21656i	0.793721	+	0.608282i	$0.208141\pi$
$113$			12.9323i			1.21656i	−0.793721	+	0.608282i	$0.791859\pi$
$114$	−7.23440	−	1.41672i	−0.677564	−	0.132688i
$115$	−0.242191			−0.0225844
$116$	−16.6797	−	6.79334i	−1.54867	−	0.630746i
$117$			1.99858i			0.184769i
$118$	−10.4922	−	2.05471i	−0.965889	−	0.189151i
$119$	−0.850664			−0.0779802
$120$	0.709168	+	0.464778i	0.0647378	+	0.0424283i
$121$	−4.89763			−0.445239
$122$	12.5753	+	2.46264i	1.13851	+	0.222957i
$123$		−	6.67060i		−	0.601468i
$124$	−15.2399	−	6.20695i	−1.36859	−	0.557401i
$125$		−	2.97085i		−	0.265720i
$126$	0.511050	−	2.60964i	0.0455279	−	0.232486i
$127$			1.17875i			0.104597i	0.998631	+	0.0522986i	$0.0166548\pi$
$127$			1.17875i			0.104597i	−0.998631	+	0.0522986i	$0.983345\pi$
$128$	11.0481	−	2.43705i	0.976524	−	0.215407i
$129$	−4.44399			−0.391272
$130$	−0.162835	+	0.831507i	−0.0142816	+	0.0729279i
$131$			8.74378i			0.763948i	0.924173	+	0.381974i	$0.124756\pi$
$131$			8.74378i			0.763948i	−0.924173	+	0.381974i	$0.875244\pi$
$132$	−4.57565	−	1.86358i	−0.398259	−	0.162204i
$133$			9.80161i			0.849908i
$134$	9.82837	+	6.11581i	0.849042	+	0.528326i
$135$			0.299779i			0.0258008i
$136$	0.701399	−	1.07021i	0.0601445	−	0.0917696i
$137$		−	16.4759i		−	1.40763i	−0.710384	−	0.703814i	$-0.751479\pi$
$137$		−	16.4759i		−	1.40763i	0.710384	−	0.703814i	$-0.248521\pi$
$138$	−1.12124	−	0.219575i	−0.0954466	−	0.0186914i
$139$	13.7850			1.16923			0.584613	−	0.811312i	$-0.301246\pi$
$139$	13.7850			1.16923			0.584613	+	0.811312i	$0.301246\pi$
$140$	0.425243	−	1.04410i	0.0359396	−	0.0882425i
$141$		−	2.51300i		−	0.211633i
$142$	−0.119735	−	0.0234479i	−0.0100480	−	0.00196771i
$143$		−	4.93709i		−	0.412860i
$144$	2.86178	+	2.79468i	0.238482	+	0.232890i
$145$		−	2.69951i		−	0.224182i
$146$	−0.519135	+	2.65093i	−0.0429639	+	0.219393i
$147$	3.46429			0.285730
$148$	−2.44084	−	0.994109i	−0.200636	−	0.0817153i
$149$	4.35465			0.356747			0.178374	−	0.983963i	$-0.442916\pi$
$149$	4.35465			0.356747			0.178374	+	0.983963i	$0.442916\pi$
$150$	1.33450	−	6.81454i	0.108961	−	0.556405i
$151$		−	6.96999i		−	0.567210i	−0.958941	−	0.283605i	$-0.908470\pi$
$151$		−	6.96999i		−	0.567210i	0.958941	−	0.283605i	$-0.0915304\pi$
$152$	−12.3313	−	8.08174i	−1.00020	−	0.655515i
$153$	0.452397			0.0365741
$154$	−1.26244	+	6.44659i	−0.101731	+	0.519481i
$155$		−	2.46650i		−	0.198114i
$156$	−1.50772	+	3.70191i	−0.120714	+	0.296390i
$157$	−7.05972			−0.563427			−0.281713	−	0.959499i	$-0.590903\pi$
$157$	−7.05972			−0.563427			−0.281713	+	0.959499i	$0.590903\pi$
$158$	−2.25738	+	11.5272i	−0.179588	+	0.917052i
$159$		−	0.990958i		−	0.0785880i
$160$	0.962941	+	1.39588i	0.0761272	+	0.110354i
$161$			1.51913i			0.119724i
$162$	−0.271785	+	1.38785i	−0.0213534	+	0.109040i
$163$		−	19.2430i		−	1.50723i	−0.657317	−	0.753614i	$-0.728309\pi$
$163$		−	19.2430i		−	1.50723i	0.657317	−	0.753614i	$-0.271691\pi$
$164$	5.03226	−	12.3557i	0.392954	−	0.964821i
$165$		−	0.740542i		−	0.0576511i
$166$	−1.14784	−	0.224782i	−0.0890894	−	0.0174465i
$167$			13.2882i			1.02828i	0.857708	+	0.514138i	$0.171888\pi$
$167$			13.2882i			1.02828i	−0.857708	+	0.514138i	$0.828112\pi$
$168$	2.91530	−	4.44822i	0.224920	−	0.343188i
$169$	9.00567			0.692744
$170$	0.188219	+	0.0368592i	0.0144357	+	0.00282697i
$171$		−	5.21266i		−	0.398622i
$172$	−8.23145	−	3.35252i	−0.627642	−	0.255627i
$173$	−18.7393			−1.42472			−0.712360	−	0.701815i	$-0.752373\pi$
$173$	−18.7393			−1.42472			−0.712360	+	0.701815i	$0.752373\pi$
$174$	2.44743	−	12.4976i	0.185539	−	0.947444i
$175$	−9.23276			−0.697931
$176$	−7.06944	−	6.90368i	−0.532879	−	0.520385i
$177$		−	7.56006i		−	0.568249i
$178$	−3.95151	+	20.1781i	−0.296178	+	1.51241i
$179$	0.698346			0.0521969			0.0260984	−	0.999659i	$-0.491692\pi$
$179$	0.698346			0.0521969			0.0260984	+	0.999659i	$0.491692\pi$
$180$	−0.226151	+	0.555270i	−0.0168563	+	0.0413874i
$181$	1.39540			0.103719			0.0518597	−	0.998654i	$-0.483485\pi$
$181$	1.39540			0.103719			0.0518597	+	0.998654i	$0.483485\pi$
$182$	5.21559	+	1.02138i	0.386605	+	0.0757094i
$183$			9.06097i			0.669806i
$184$	−1.91120	−	1.25257i	−0.140895	−	0.0923407i
$185$		−	0.395036i		−	0.0290436i
$186$	2.23617	−	11.4189i	0.163964	−	0.837272i
$187$	−1.11756			−0.0817237
$188$	1.89579	−	4.65475i	0.138265	−	0.339482i
$189$	1.88035			0.136775
$190$	0.424703	−	2.16872i	0.0308112	−	0.157335i
$191$	−7.48899			−0.541884			−0.270942	−	0.962596i	$-0.587335\pi$
$191$	−7.48899			−0.541884			−0.270942	+	0.962596i	$0.587335\pi$
$192$	3.19249	+	7.33540i	0.230398	+	0.529387i
$193$	22.3190			1.60656			0.803279	−	0.595603i	$-0.203087\pi$
$193$	22.3190			1.60656			0.803279	+	0.595603i	$0.203087\pi$
$194$	8.48105	+	1.66085i	0.608904	+	0.119242i
$195$	−0.599132			−0.0429047
$196$	6.41679	+	2.61344i	0.458342	+	0.186675i
$197$		−	21.7278i		−	1.54804i	−0.633160	−	0.774021i	$-0.718242\pi$
$197$		−	21.7278i		−	1.54804i	0.633160	−	0.774021i	$-0.281758\pi$
$198$	0.671389	−	3.42841i	0.0477136	−	0.243646i
$199$		−	20.9659i		−	1.48624i	−0.669161	−	0.743118i	$-0.733346\pi$
$199$		−	20.9659i		−	1.48624i	0.669161	−	0.743118i	$-0.266654\pi$
$200$	7.61270	−	11.6156i	0.538299	−	0.821347i
$201$	−2.90832	+	7.65125i	−0.205137	+	0.539678i
$202$	22.9675	+	4.49775i	1.61599	+	0.316461i
$203$	−16.9326			−1.18843
$204$	0.837960	+	0.341286i	0.0586689	+	0.0238948i
$205$	1.99970			0.139665
$206$	1.74680	+	0.342078i	0.121705	+	0.0238337i
$207$		−	0.807898i		−	0.0561528i
$208$	−5.58539	+	5.71950i	−0.387277	+	0.396576i
$209$			12.8768i			0.890708i
$210$	0.782315	+	0.153202i	0.0539849	+	0.0105719i
$211$			6.97627i			0.480266i	0.970740	+	0.240133i	$0.0771911\pi$
$211$			6.97627i			0.480266i	−0.970740	+	0.240133i	$0.922809\pi$
$212$	0.747573	−	1.83552i	0.0513435	−	0.126064i
$213$		−	0.0862739i		−	0.00591139i
$214$	−15.8491	−	3.10375i	−1.08342	−	0.212168i
$215$		−	1.33221i		−	0.0908562i
$216$	−1.55041	+	2.36564i	−0.105492	+	0.160961i
$217$	−15.4710			−1.05024
$218$	8.61538	+	1.68716i	0.583507	+	0.114269i
$219$	−1.91010			−0.129072
$220$	0.558661	−	1.37168i	0.0376649	−	0.0924787i
$221$			0.904153i			0.0608199i
$222$	0.358147	−	1.82885i	0.0240372	−	0.122745i
$223$			27.0486i			1.81131i	0.424020	+	0.905653i	$0.360619\pi$
$223$			27.0486i			1.81131i	−0.424020	+	0.905653i	$0.639381\pi$
$224$	8.75562	−	6.04000i	0.585010	−	0.403565i
$225$	4.91013			0.327342
$226$	−17.9481	−	3.51479i	−1.19389	−	0.233800i
$227$		−	11.0542i		−	0.733693i	−0.930282	−	0.366846i	$-0.880437\pi$
$227$		−	11.0542i		−	0.733693i	0.930282	−	0.366846i	$-0.119563\pi$
$228$	3.93240	−	9.65523i	0.260430	−	0.639433i
$229$		−	11.8822i		−	0.785199i	−0.919710	−	0.392600i	$-0.871576\pi$
$229$		−	11.8822i		−	0.785199i	0.919710	−	0.392600i	$-0.128424\pi$
$230$	0.0658237	−	0.336125i	0.00434029	−	0.0221634i
$231$	−4.64502			−0.305620
$232$	13.9614	−	21.3026i	0.916614	−	1.39859i
$233$			5.38131i			0.352542i	0.984342	+	0.176271i	$0.0564034\pi$
$233$			5.38131i			0.352542i	−0.984342	+	0.176271i	$0.943597\pi$
$234$	−2.77374	−	0.543184i	−0.181325	−	0.0355091i
$235$	0.753344			0.0491427
$236$	5.70327	−	14.0032i	0.371251	−	0.911533i
$237$	−8.30576			−0.539517
$238$	0.231198	−	1.18060i	0.0149863	−	0.0765266i
$239$	14.4375			0.933883			0.466941	−	0.884288i	$-0.345356\pi$
$239$	14.4375			0.933883			0.466941	+	0.884288i	$0.345356\pi$
$240$	−0.837784	+	0.857900i	−0.0540788	+	0.0553772i
$241$	−7.02196			−0.452324			−0.226162	−	0.974090i	$-0.572618\pi$
$241$	−7.02196			−0.452324			−0.226162	+	0.974090i	$0.572618\pi$
$242$	1.33110	−	6.79719i	0.0855665	−	0.436940i
$243$	−1.00000			−0.0641500
$244$	−6.83555	+	16.7833i	−0.437601	+	1.07444i
$245$			1.03852i			0.0663487i
$246$	9.25781	+	1.81297i	0.590256	+	0.115591i
$247$	10.4179			0.662877
$248$	12.7563	−	19.4638i	0.810027	−	1.23595i
$249$		−	0.827060i		−	0.0524128i
$250$	4.12309	+	0.807431i	0.260767	+	0.0510664i
$251$	15.9704			1.00804			0.504021	−	0.863691i	$-0.331853\pi$
$251$	15.9704			1.00804			0.504021	+	0.863691i	$0.331853\pi$
$252$	3.48290	+	1.41852i	0.219402	+	0.0893586i
$253$			1.99575i			0.125472i
$254$	−1.63593	−	0.320366i	−0.102647	−	0.0201016i
$255$			0.135619i			0.00849279i
$256$	0.379553	+	15.9955i	0.0237221	+	0.999719i
$257$	−5.54733			−0.346033			−0.173016	−	0.984919i	$-0.555351\pi$
$257$	−5.54733			−0.346033			−0.173016	+	0.984919i	$0.555351\pi$
$258$	1.20781	−	6.16760i	0.0751949	−	0.383978i
$259$	−2.47784			−0.153966
$260$	−1.10975	−	0.451982i	−0.0688239	−	0.0280307i
$261$	9.00503			0.557397
$262$	−12.1351	−	2.37643i	−0.749707	−	0.146816i
$263$			19.4297i			1.19808i	0.800718	+	0.599042i	$0.204452\pi$
$263$			19.4297i			1.19808i	−0.800718	+	0.599042i	$0.795548\pi$
$264$	3.82996	−	5.84383i	0.235718	−	0.359663i
$265$	0.297068			0.0182487
$266$	−13.6032	−	2.66393i	−0.834065	−	0.163336i
$267$	−14.5391			−0.889779
$268$	−11.1590	+	11.9781i	−0.681647	+	0.731681i
$269$	5.13142			0.312868			0.156434	−	0.987688i	$-0.450000\pi$
$269$	5.13142			0.312868			0.156434	+	0.987688i	$0.450000\pi$
$270$	−0.416048	−	0.0814753i	−0.0253199	−	0.00495843i
$271$	4.15615			0.252468			0.126234	−	0.992000i	$-0.459711\pi$
$271$	4.15615			0.252468			0.126234	+	0.992000i	$0.459711\pi$
$272$	1.29466	+	1.26430i	0.0785003	+	0.0766597i
$273$			3.75803i			0.227446i
$274$	22.8661	+	4.47789i	1.38139	+	0.270519i
$275$	−12.1295			−0.731435
$276$	0.609474	−	1.49644i	0.0366860	−	0.0900753i
$277$	0.861448			0.0517594			0.0258797	−	0.999665i	$-0.491761\pi$
$277$	0.861448			0.0517594			0.0258797	+	0.999665i	$0.491761\pi$
$278$	−3.74655	+	19.1315i	−0.224703	+	1.14743i
$279$	8.22773			0.492581
$280$	1.33348	+	0.873945i	0.0796907	+	0.0522282i
$281$			12.5745i			0.750134i	0.926998	+	0.375067i	$0.122380\pi$
$281$			12.5745i			0.750134i	−0.926998	+	0.375067i	$0.877620\pi$
$282$	3.48767	+	0.682996i	0.207688	+	0.0406718i
$283$			11.4059i			0.678013i	0.940784	+	0.339006i	$0.110091\pi$
$283$			11.4059i			0.678013i	−0.940784	+	0.339006i	$0.889909\pi$
$284$	0.0650845	−	0.159802i	0.00386206	−	0.00948252i
$285$	1.56264			0.0925630
$286$	6.85195	+	1.34183i	0.405164	+	0.0793439i
$287$		−	12.5431i		−	0.740393i
$288$	−4.65639	+	3.21217i	−0.274380	+	0.189279i
$289$	−16.7953			−0.987961
$290$	3.74653	+	0.733687i	0.220004	+	0.0430836i
$291$			6.11092i			0.358228i
$292$	−3.53801	−	1.44097i	−0.207046	−	0.0843261i
$293$	−10.9531			−0.639890			−0.319945	−	0.947436i	$-0.603664\pi$
$293$	−10.9531			−0.639890			−0.319945	+	0.947436i	$0.603664\pi$
$294$	−0.941543	+	4.80793i	−0.0549119	+	0.280404i
$295$	2.26634			0.131952
$296$	2.04306	−	3.11734i	0.118750	−	0.181192i
$297$	2.47030			0.143341
$298$	−1.18353	+	6.04361i	−0.0685600	+	0.350097i
$299$	1.61465			0.0933777
$300$	9.09487	+	3.70418i	0.525093	+	0.213861i
$301$	−8.35625			−0.481646
$302$	9.67332	+	1.89434i	0.556637	+	0.109007i
$303$			16.5489i			0.950712i
$304$	14.5677	−	14.9175i	0.835515	−	0.855576i
$305$	−2.71629			−0.155534
$306$	−0.122955	+	0.627860i	−0.00702885	+	0.0358924i
$307$			5.44353i			0.310679i	0.987861	+	0.155339i	$0.0496471\pi$
$307$			5.44353i			0.310679i	−0.987861	+	0.155339i	$0.950353\pi$
$308$	−8.60380	−	3.50417i	−0.490247	−	0.199669i
$309$			1.25864i			0.0716013i
$310$	3.42313	+	0.670357i	0.194421	+	0.0380737i
$311$	−25.9978			−1.47420			−0.737099	−	0.675785i	$-0.763805\pi$
$311$	−25.9978			−1.47420			−0.737099	+	0.675785i	$0.763805\pi$
$312$	−4.72792	−	3.09861i	−0.267666	−	0.175424i
$313$		−	10.3628i		−	0.585740i	−0.956152	−	0.292870i	$-0.905390\pi$
$313$		−	10.3628i		−	0.585740i	0.956152	−	0.292870i	$-0.0946104\pi$
$314$	1.91872	−	9.79784i	0.108280	−	0.552924i
$315$			0.563688i			0.0317602i
$316$	−15.3845	−	6.26582i	−0.865445	−	0.352480i
$317$	−16.5470			−0.929375			−0.464687	−	0.885475i	$-0.653833\pi$
$317$	−16.5470			−0.929375			−0.464687	+	0.885475i	$0.653833\pi$
$318$	1.37530	+	0.269327i	0.0771231	+	0.0151031i
$319$	−22.2451			−1.24549
$320$	−2.19899	+	0.957039i	−0.122928	+	0.0535001i
$321$		−	11.4199i		−	0.637396i
$322$	−2.10833	−	0.412876i	−0.117492	−	0.0230087i
$323$		−	2.35819i		−	0.131213i
$324$	−1.85227	−	0.754394i	−0.102904	−	0.0419108i
$325$			9.81330i			0.544344i
$326$	26.7064	+	5.22995i	1.47913	+	0.289660i
$327$			6.20771i			0.343287i
$328$	15.7802	+	10.3421i	0.871318	+	0.571049i
$329$		−	4.72531i		−	0.260515i
$330$	1.02776	+	0.201268i	0.0565765	+	0.0110794i
$331$	5.88317			0.323368			0.161684	−	0.986843i	$-0.448307\pi$
$331$	5.88317			0.323368			0.161684	+	0.986843i	$0.448307\pi$
$332$	0.623929	−	1.53194i	0.0342426	−	0.0840759i
$333$	1.31776			0.0722127
$334$	−18.4421	−	3.61154i	−1.00911	−	0.197615i
$335$	−2.29368	−	0.871852i	−0.125317	−	0.0476344i
$336$	5.38114	+	5.25496i	0.293565	+	0.286682i
$337$			23.4236i			1.27596i	0.770052	+	0.637981i	$0.220230\pi$
$337$			23.4236i			1.27596i	−0.770052	+	0.637981i	$0.779770\pi$
$338$	−2.44760	+	12.4985i	−0.133132	+	0.679831i
$339$		−	12.9323i		−	0.702384i
$340$	−0.102310	+	0.251202i	−0.00554855	+	0.0136234i
$341$	−20.3249			−1.10066
$342$	7.23440	+	1.41672i	0.391192	+	0.0766076i
$343$	19.6765			1.06243
$344$	6.88999	−	10.5129i	0.371483	−	0.566816i
$345$	0.242191			0.0130391
$346$	5.09305	−	26.0073i	0.273804	−	1.39816i
$347$	−14.2125			−0.762965			−0.381483	−	0.924376i	$-0.624586\pi$
$347$	−14.2125			−0.762965			−0.381483	+	0.924376i	$0.624586\pi$
$348$	16.6797	+	6.79334i	0.894126	+	0.364161i
$349$	−25.9097			−1.38691			−0.693457	−	0.720498i	$-0.743913\pi$
$349$	−25.9097			−1.38691			−0.693457	+	0.720498i	$0.743913\pi$
$350$	2.50932	−	12.8137i	0.134129	−	0.684921i
$351$		−	1.99858i		−	0.106676i
$352$	11.5027	−	7.93502i	0.613094	−	0.422938i
$353$			32.5138i			1.73054i	0.501309	+	0.865269i	$0.332852\pi$
$353$			32.5138i			1.73054i	−0.501309	+	0.865269i	$0.667148\pi$
$354$	10.4922	+	2.05471i	0.557656	+	0.109207i
$355$	0.0258631			0.00137267
$356$	−26.9303	−	10.9682i	−1.42730	−	0.581315i
$357$	0.850664			0.0450219
$358$	−0.189800	+	0.969201i	−0.0100312	+	0.0512239i
$359$		−	20.9244i		−	1.10435i	−0.833729	−	0.552175i	$-0.813798\pi$
$359$		−	20.9244i		−	1.10435i	0.833729	−	0.552175i	$-0.186202\pi$
$360$	−0.709168	−	0.464778i	−0.0373764	−	0.0244960i
$361$	−8.17183			−0.430096
$362$	−0.379249	+	1.93661i	−0.0199329	+	0.101786i
$363$	4.89763			0.257059
$364$	−2.83504	+	6.96087i	−0.148596	+	0.364849i
$365$		−	0.572606i		−	0.0299716i
$366$	−12.5753	−	2.46264i	−0.657321	−	0.128724i
$367$	31.9614			1.66837			0.834186	−	0.551484i	$-0.185938\pi$
$367$	31.9614			1.66837			0.834186	+	0.551484i	$0.185938\pi$
$368$	2.25782	−	2.31203i	0.117697	−	0.120523i
$369$			6.67060i			0.347258i
$370$	0.548251	+	0.107365i	0.0285022	+	0.00558162i
$371$		−	1.86334i		−	0.0967400i
$372$	15.2399	+	6.20695i	0.790154	+	0.321816i
$373$			4.12613i			0.213643i	0.994278	+	0.106822i	$0.0340674\pi$
$373$			4.12613i			0.213643i	−0.994278	+	0.106822i	$0.965933\pi$
$374$	0.303735	−	1.55100i	0.0157057	−	0.0802004i
$375$			2.97085i			0.153414i
$376$	5.94485	+	3.89617i	0.306582	+	0.200930i
$377$			17.9973i			0.926907i
$378$	−0.511050	+	2.60964i	−0.0262856	+	0.134226i
$379$	−8.75420			−0.449673			−0.224836	−	0.974397i	$-0.572185\pi$
$379$	−8.75420			−0.449673			−0.224836	+	0.974397i	$0.572185\pi$
$380$	2.89443	+	1.17885i	0.148481	+	0.0604737i
$381$		−	1.17875i		−	0.0603892i
$382$	2.03539	−	10.3936i	0.104140	−	0.531783i
$383$	7.08452			0.362002			0.181001	−	0.983483i	$-0.442066\pi$
$383$	7.08452			0.362002			0.181001	+	0.983483i	$0.442066\pi$
$384$	−11.0481	+	2.43705i	−0.563797	+	0.124365i
$385$		−	1.39248i		−	0.0709672i
$386$	−6.06597	+	30.9755i	−0.308750	+	1.57661i
$387$	4.44399			0.225901
$388$	−4.61004	+	11.3190i	−0.234039	+	0.574637i
$389$	−18.4108			−0.933466			−0.466733	−	0.884398i	$-0.654569\pi$
$389$	−18.4108			−0.933466			−0.466733	+	0.884398i	$0.654569\pi$
$390$	0.162835	−	0.831507i	0.00824547	−	0.0421050i
$391$		−	0.365491i		−	0.0184837i
$392$	−5.37106	+	8.19527i	−0.271279	+	0.413923i
$393$		−	8.74378i		−	0.441065i
$394$	30.1550	+	5.90529i	1.51919	+	0.297504i
$395$		−	2.48989i		−	0.125280i
$396$	4.57565	+	1.86358i	0.229935	+	0.0936483i
$397$	1.97019			0.0988812			0.0494406	−	0.998777i	$-0.484256\pi$
$397$	1.97019			0.0988812			0.0494406	+	0.998777i	$0.484256\pi$
$398$	29.0976	+	5.69822i	1.45853	+	0.285626i
$399$		−	9.80161i		−	0.490694i
$400$	14.0517	+	13.7222i	0.702586	+	0.686112i
$401$			15.8711i			0.792565i	0.918129	+	0.396282i	$0.129700\pi$
$401$			15.8711i			0.792565i	−0.918129	+	0.396282i	$0.870300\pi$
$402$	−9.82837	−	6.11581i	−0.490194	−	0.305029i
$403$			16.4438i			0.819124i
$404$	−12.4844	+	30.6530i	−0.621123	+	1.52505i
$405$		−	0.299779i		−	0.0148961i
$406$	4.60202	−	23.4999i	0.228394	−	1.16628i
$407$	−3.25525			−0.161357
$408$	−0.701399	+	1.07021i	−0.0347244	+	0.0529832i
$409$			21.7609i			1.07601i	0.842942	+	0.538004i	$0.180822\pi$
$409$			21.7609i			1.07601i	−0.842942	+	0.538004i	$0.819178\pi$
$410$	−0.543489	+	2.77529i	−0.0268410	+	0.137062i
$411$			16.4759i			0.812695i
$412$	−0.949508	+	2.33133i	−0.0467789	+	0.114856i
$413$		−	14.2155i		−	0.699501i
$414$	1.12124	+	0.219575i	0.0551061	+	0.0107915i
$415$	0.247935			0.0121706
$416$	−6.41979	−	9.30617i	−0.314756	−	0.456273i
$417$	−13.7850			−0.675053
$418$	−17.8711	−	3.49972i	−0.874105	−	0.171177i
$419$		−	8.01500i		−	0.391558i	−0.980648	−	0.195779i	$-0.937276\pi$
$419$		−	8.01500i		−	0.391558i	0.980648	−	0.195779i	$-0.0627236\pi$
$420$	−0.425243	+	1.04410i	−0.0207497	+	0.0509468i
$421$	13.0724			0.637108			0.318554	−	0.947905i	$-0.396803\pi$
$421$	13.0724			0.637108			0.318554	+	0.947905i	$0.396803\pi$
$422$	−9.68203	−	1.89604i	−0.471314	−	0.0922980i
$423$			2.51300i			0.122186i
$424$	2.34425	+	1.53639i	0.113847	+	0.0746135i
$425$	2.22133			0.107750
$426$	0.119735	+	0.0234479i	0.00580120	+	0.00113606i
$427$			17.0378i			0.824516i
$428$	8.61509	−	21.1527i	0.416426	−	1.02245i
$429$			4.93709i			0.238365i
$430$	1.84891	+	0.362075i	0.0891626	+	0.0174608i
$431$		−	11.2297i		−	0.540915i	−0.962732	−	0.270457i	$-0.912825\pi$
$431$		−	11.2297i		−	0.540915i	0.962732	−	0.270457i	$-0.0871749\pi$
$432$	−2.86178	−	2.79468i	−0.137687	−	0.134459i
$433$			37.9064i			1.82167i	0.412775	+	0.910833i	$0.364560\pi$
$433$			37.9064i			1.82167i	−0.412775	+	0.910833i	$0.635440\pi$
$434$	4.20478	−	21.4714i	0.201836	−	1.03066i
$435$			2.69951i			0.129432i
$436$	−4.68306	+	11.4983i	−0.224278	+	0.550670i
$437$	−4.21130			−0.201454
$438$	0.519135	−	2.65093i	0.0248052	−	0.126666i
$439$			16.5889i			0.791747i	0.918305	+	0.395873i	$0.129558\pi$
$439$			16.5889i			0.791747i	−0.918305	+	0.395873i	$0.870442\pi$
$440$	1.75185	+	1.14814i	0.0835164	+	0.0547354i
$441$	−3.46429			−0.164966
$442$	−1.25483	−	0.245735i	−0.0596862	−	0.0116884i
$443$	20.1784			0.958707			0.479353	−	0.877622i	$-0.340871\pi$
$443$	20.1784			0.958707			0.479353	+	0.877622i	$0.340871\pi$
$444$	2.44084	+	0.994109i	0.115837	+	0.0471783i
$445$		−	4.35851i		−	0.206613i
$446$	−37.5394	−	7.35139i	−1.77754	−	0.348098i
$447$	−4.35465			−0.205968
$448$	6.00298	+	13.7931i	0.283614	+	0.651662i
$449$	17.0132			0.802902			0.401451	−	0.915881i	$-0.368506\pi$
$449$	17.0132			0.802902			0.401451	+	0.915881i	$0.368506\pi$
$450$	−1.33450	+	6.81454i	−0.0629089	+	0.321240i
$451$		−	16.4784i		−	0.775936i
$452$	9.75602	−	23.9540i	0.458885	−	1.12670i
$453$			6.96999i			0.327479i
$454$	15.3416	+	3.00436i	0.720016	+	0.141002i
$455$	−1.12658			−0.0528147
$456$	12.3313	+	8.08174i	0.577464	+	0.378462i
$457$	−10.6168			−0.496631			−0.248316	−	0.968679i	$-0.579877\pi$
$457$	−10.6168			−0.496631			−0.248316	+	0.968679i	$0.579877\pi$
$458$	16.4908	+	3.22941i	0.770563	+	0.150900i
$459$	−0.452397			−0.0211161
$460$	0.448601	+	0.182707i	0.0209161	+	0.00851877i
$461$	26.5139			1.23488			0.617438	−	0.786619i	$-0.288171\pi$
$461$	26.5139			1.23488			0.617438	+	0.786619i	$0.288171\pi$
$462$	1.26244	−	6.44659i	0.0587343	−	0.299923i
$463$	6.87423			0.319472			0.159736	−	0.987160i	$-0.448936\pi$
$463$	6.87423			0.319472			0.159736	+	0.987160i	$0.448936\pi$
$464$	25.7704	+	25.1661i	1.19636	+	1.16831i
$465$			2.46650i			0.114381i
$466$	−7.46846	−	1.46256i	−0.345970	−	0.0677517i
$467$			26.5463i			1.22842i	0.789144	+	0.614208i	$0.210524\pi$
$467$			26.5463i			1.22842i	−0.789144	+	0.614208i	$0.789476\pi$
$468$	1.50772	−	3.70191i	0.0696943	−	0.171121i
$469$	−5.46865	+	14.3870i	−0.252519	+	0.664331i
$470$	−0.204747	+	1.04553i	−0.00944429	+	0.0482267i
$471$	7.05972			0.325295
$472$	17.8844	+	11.7212i	0.823195	+	0.539510i
$473$	−10.9780			−0.504768
$474$	2.25738	−	11.5272i	0.103685	−	0.529460i
$475$		−	25.5949i		−	1.17437i
$476$	1.57566	+	0.641736i	0.0722201	+	0.0294139i
$477$			0.990958i			0.0453728i
$478$	−3.92389	+	20.0371i	−0.179474	+	0.916475i
$479$			21.1438i			0.966085i	0.875597	+	0.483043i	$0.160468\pi$
$479$			21.1438i			0.966085i	−0.875597	+	0.483043i	$0.839532\pi$
$480$	−0.962941	−	1.39588i	−0.0439520	−	0.0637131i
$481$			2.63365i			0.120084i
$482$	1.90846	−	9.74544i	0.0869281	−	0.443893i
$483$		−	1.51913i		−	0.0691228i
$484$	9.07172	+	3.69475i	0.412351	+	0.167943i
$485$	−1.83192			−0.0831833
$486$	0.271785	−	1.38785i	0.0123284	−	0.0629542i
$487$	−6.38117			−0.289159			−0.144579	−	0.989493i	$-0.546183\pi$
$487$	−6.38117			−0.289159			−0.144579	+	0.989493i	$0.546183\pi$
$488$	−21.4350	−	14.0482i	−0.970316	−	0.635931i
$489$			19.2430i			0.870198i
$490$	−1.44131	−	0.282254i	−0.0651119	−	0.0127509i
$491$		−	29.2851i		−	1.32162i	−0.750554	−	0.660810i	$-0.770213\pi$
$491$		−	29.2851i		−	1.32162i	0.750554	−	0.660810i	$-0.229787\pi$
$492$	−5.03226	+	12.3557i	−0.226872	+	0.557039i
$493$	4.07385			0.183477
$494$	−2.83144	+	14.4585i	−0.127392	+	0.650521i
$495$			0.740542i			0.0332849i
$496$	23.5459	+	22.9939i	1.05724	+	1.03245i
$497$		−	0.162225i		−	0.00727678i
$498$	1.14784	+	0.224782i	0.0514358	+	0.0100727i
$499$	40.2222			1.80059			0.900295	−	0.435280i	$-0.143350\pi$
$499$	40.2222			1.80059			0.900295	+	0.435280i	$0.143350\pi$
$500$	−2.24119	+	5.50280i	−0.100229	+	0.246092i
$501$		−	13.2882i		−	0.593675i
$502$	−4.34051	+	22.1645i	−0.193727	+	0.989252i
$503$	32.3036			1.44035			0.720173	−	0.693794i	$-0.244062\pi$
$503$	32.3036			1.44035			0.720173	+	0.693794i	$0.244062\pi$
$504$	−2.91530	+	4.44822i	−0.129858	+	0.198140i
$505$	−4.96102			−0.220762
$506$	−2.76980	−	0.542414i	−0.123133	−	0.0241133i
$507$	−9.00567			−0.399956
$508$	0.889242	−	2.18336i	0.0394537	−	0.0968709i
$509$	−5.29721			−0.234795			−0.117397	−	0.993085i	$-0.537455\pi$
$509$	−5.29721			−0.234795			−0.117397	+	0.993085i	$0.537455\pi$
$510$	−0.188219	−	0.0368592i	−0.00833448	−	0.00163215i
$511$	−3.59164			−0.158885
$512$	−22.3025	−	3.82057i	−0.985642	−	0.168847i
$513$			5.21266i			0.230145i
$514$	1.50768	−	7.69887i	0.0665009	−	0.339582i
$515$	−0.377312			−0.0166264
$516$	8.23145	+	3.35252i	0.362370	+	0.147587i
$517$		−	6.20786i		−	0.273021i
$518$	0.673440	−	3.43888i	0.0295893	−	0.151096i
$519$	18.7393			0.822562
$520$	0.928897	−	1.41733i	0.0407348	−	0.0621540i
$521$		−	21.2420i		−	0.930628i	−0.885146	−	0.465314i	$-0.845941\pi$
$521$		−	21.2420i		−	0.930628i	0.885146	−	0.465314i	$-0.154059\pi$
$522$	−2.44743	+	12.4976i	−0.107121	+	0.547007i
$523$		−	32.5083i		−	1.42149i	−0.703450	−	0.710745i	$-0.748358\pi$
$523$		−	32.5083i		−	1.42149i	0.703450	−	0.710745i	$-0.251642\pi$
$524$	6.59626	−	16.1958i	0.288159	−	0.707517i
$525$	9.23276			0.402950
$526$	−26.9655	−	5.28069i	−1.17575	−	0.230249i
$527$	3.72220			0.162142
$528$	7.06944	+	6.90368i	0.307658	+	0.300444i
$529$	22.3473			0.971622
$530$	−0.0807385	+	0.412286i	−0.00350706	+	0.0179086i
$531$			7.56006i			0.328079i
$532$	7.39428	−	18.1552i	0.320583	−	0.787127i
$533$	−13.3317			−0.577462
$534$	3.95151	−	20.1781i	0.170999	−	0.873193i
$535$	3.42343			0.148008
$536$	−13.5910	−	18.7426i	−0.587043	−	0.809556i
$537$	−0.698346			−0.0301359
$538$	−1.39464	+	7.12165i	−0.0601273	+	0.307036i
$539$	8.55783			0.368612
$540$	0.226151	−	0.555270i	0.00973200	−	0.0238950i
$541$		−	32.7893i		−	1.40972i	−0.709346	−	0.704860i	$-0.751010\pi$
$541$		−	32.7893i		−	1.40972i	0.709346	−	0.704860i	$-0.248990\pi$
$542$	−1.12958	+	5.76812i	−0.0485195	+	0.247762i
$543$	−1.39540			−0.0598824
$544$	−2.10654	+	1.45318i	−0.0903170	+	0.0623045i
$545$	−1.86094			−0.0797138
$546$	−5.21559	−	1.02138i	−0.223207	−	0.0437108i
$547$	4.08784			0.174784			0.0873918	−	0.996174i	$-0.472147\pi$
$547$	4.08784			0.174784			0.0873918	+	0.996174i	$0.472147\pi$
$548$	−12.4293	+	30.5177i	−0.530954	+	1.30365i
$549$		−	9.06097i		−	0.386713i
$550$	3.29661	−	16.8339i	0.140568	−	0.717801i
$551$		−	46.9401i		−	1.99972i
$552$	1.91120	+	1.25257i	0.0813459	+	0.0533129i
$553$	−15.6177			−0.664133
$554$	−0.234129	+	1.19556i	−0.00994717	+	0.0507946i
$555$			0.395036i			0.0167683i
$556$	−25.5334	−	10.3993i	−1.08286	−	0.441029i
$557$	−1.60738			−0.0681067			−0.0340534	−	0.999420i	$-0.510842\pi$
$557$	−1.60738			−0.0681067			−0.0340534	+	0.999420i	$0.510842\pi$
$558$	−2.23617	+	11.4189i	−0.0946647	+	0.483399i
$559$			8.88168i			0.375655i
$560$	−1.57533	+	1.61315i	−0.0665697	+	0.0681680i
$561$	1.11756			0.0471832
$562$	−17.4516	−	3.41757i	−0.736151	−	0.144161i
$563$	−4.68199			−0.197322			−0.0986612	−	0.995121i	$-0.531456\pi$
$563$	−4.68199			−0.197322			−0.0986612	+	0.995121i	$0.531456\pi$
$564$	−1.89579	+	4.65475i	−0.0798273	+	0.196000i
$565$	3.87681			0.163099
$566$	−15.8298	−	3.09996i	−0.665374	−	0.130301i
$567$	−1.88035			−0.0789672
$568$	0.204093	+	0.133760i	0.00856354	+	0.00561243i
$569$	19.5493			0.819549			0.409775	−	0.912187i	$-0.365607\pi$
$569$	19.5493			0.819549			0.409775	+	0.912187i	$0.365607\pi$
$570$	−0.424703	+	2.16872i	−0.0177888	+	0.0908376i
$571$			6.62279i			0.277155i	0.990352	+	0.138578i	$0.0442531\pi$
$571$			6.62279i			0.277155i	−0.990352	+	0.138578i	$0.955747\pi$
$572$	−3.72451	+	9.14480i	−0.155730	+	0.382364i
$573$	7.48899			0.312857
$574$	17.4079	+	3.40901i	0.726592	+	0.142289i
$575$		−	3.96689i		−	0.165431i
$576$	−3.19249	−	7.33540i	−0.133020	−	0.305641i
$577$		−	26.8816i		−	1.11910i	−0.828798	−	0.559548i	$-0.810975\pi$
$577$		−	26.8816i		−	1.11910i	0.828798	−	0.559548i	$-0.189025\pi$
$578$	4.56472	−	23.3094i	0.189867	−	0.969545i
$579$	−22.3190			−0.927546
$580$	−2.03650	+	5.00022i	−0.0845610	+	0.207623i
$581$		−	1.55516i		−	0.0645189i
$582$	−8.48105	−	1.66085i	−0.351551	−	0.0688446i
$583$		−	2.44796i		−	0.101384i
$584$	2.96142	−	4.51860i	0.122545	−	0.186981i
$585$	0.599132			0.0247711
$586$	2.97690	−	15.2013i	0.122975	−	0.627962i
$587$	−22.3682			−0.923233			−0.461616	−	0.887080i	$-0.652730\pi$
$587$	−22.3682			−0.923233			−0.461616	+	0.887080i	$0.652730\pi$
$588$	−6.41679	−	2.61344i	−0.264624	−	0.107777i
$589$		−	42.8884i		−	1.76718i
$590$	−0.615958	+	3.14535i	−0.0253586	+	0.129492i
$591$			21.7278i			0.893763i
$592$	3.77113	+	3.68271i	0.154993	+	0.151358i
$593$			25.0785i			1.02985i	0.857235	+	0.514925i	$0.172180\pi$
$593$			25.0785i			1.02985i	−0.857235	+	0.514925i	$0.827820\pi$
$594$	−0.671389	+	3.42841i	−0.0275474	+	0.140669i
$595$			0.255011i			0.0104544i
$596$	−8.06598	−	3.28513i	−0.330395	−	0.134564i
$597$			20.9659i			0.858078i
$598$	−0.438838	+	2.24090i	−0.0179454	+	0.0916371i
$599$	−14.4555			−0.590637			−0.295319	−	0.955399i	$-0.595426\pi$
$599$	−14.4555			−0.590637			−0.295319	+	0.955399i	$0.595426\pi$
$600$	−7.61270	+	11.6156i	−0.310787	+	0.474205i
$601$	18.7178			0.763516			0.381758	−	0.924262i	$-0.375319\pi$
$601$	18.7178			0.763516			0.381758	+	0.924262i	$0.375319\pi$
$602$	2.27110	−	11.5972i	0.0925632	−	0.472668i
$603$	2.90832	−	7.65125i	0.118436	−	0.311583i
$604$	−5.25812	+	12.9103i	−0.213950	+	0.525312i
$605$			1.46821i			0.0596910i
$606$	−22.9675	−	4.49775i	−0.932990	−	0.182709i
$607$			35.3581i			1.43514i	0.696486	+	0.717570i	$0.254746\pi$
$607$			35.3581i			1.43514i	−0.696486	+	0.717570i	$0.745254\pi$
$608$	16.7440	+	24.2722i	0.679058	+	0.984366i
$609$	16.9326			0.686143
$610$	0.738245	−	3.76980i	0.0298907	−	0.152635i
$611$	−5.02244			−0.203186
$612$	−0.837960	−	0.341286i	−0.0338725	−	0.0137957i
$613$	8.76727			0.354107			0.177053	−	0.984201i	$-0.443343\pi$
$613$	8.76727			0.354107			0.177053	+	0.984201i	$0.443343\pi$
$614$	−7.55482	−	1.47947i	−0.304888	−	0.0597065i
$615$	−1.99970			−0.0806358
$616$	7.20166	−	10.9884i	0.290163	−	0.442736i
$617$	7.12749			0.286942			0.143471	−	0.989655i	$-0.454174\pi$
$617$	7.12749			0.286942			0.143471	+	0.989655i	$0.454174\pi$
$618$	−1.74680	−	0.342078i	−0.0702666	−	0.0137604i
$619$		−	14.9731i		−	0.601820i	−0.953653	−	0.300910i	$-0.902710\pi$
$619$		−	14.9731i		−	0.601820i	0.953653	−	0.300910i	$-0.0972904\pi$
$620$	−1.86071	+	4.56861i	−0.0747280	+	0.183480i
$621$			0.807898i			0.0324198i
$622$	7.06580	−	36.0810i	0.283313	−	1.44672i
$623$	−27.3386			−1.09530
$624$	5.58539	−	5.71950i	0.223595	−	0.228963i
$625$	23.6601			0.946403
$626$	14.3820	+	2.81645i	0.574822	+	0.112568i
$627$		−	12.8768i		−	0.514251i
$628$	13.0765	+	5.32581i	0.521808	+	0.212523i
$629$	0.596150			0.0237701
$630$	−0.782315	−	0.153202i	−0.0311682	−	0.00610371i
$631$	−19.6966			−0.784109			−0.392055	−	0.919942i	$-0.628236\pi$
$631$	−19.6966			−0.784109			−0.392055	+	0.919942i	$0.628236\pi$
$632$	12.8773	−	19.6484i	0.512232	−	0.781573i
$633$		−	6.97627i		−	0.277282i
$634$	4.49724	−	22.9649i	0.178608	−	0.912051i
$635$	0.353364			0.0140228
$636$	−0.747573	+	1.83552i	−0.0296432	+	0.0727830i
$637$		−	6.92368i		−	0.274326i
$638$	6.04588	−	30.8729i	0.239359	−	1.22227i
$639$			0.0862739i			0.00341294i
$640$	−0.730575	−	3.31199i	−0.0288785	−	0.130918i
$641$		−	37.1892i		−	1.46889i	−0.678670	−	0.734443i	$-0.737443\pi$
$641$		−	37.1892i		−	1.46889i	0.678670	−	0.734443i	$-0.262557\pi$
$642$	15.8491	+	3.10375i	0.625514	+	0.122495i
$643$		−	19.1573i		−	0.755490i	−0.925910	−	0.377745i	$-0.876700\pi$
$643$		−	19.1573i		−	0.755490i	0.925910	−	0.377745i	$-0.123300\pi$
$644$	1.14602	−	2.81383i	0.0451596	−	0.110881i
$645$			1.33221i			0.0524558i
$646$	3.27282	+	0.640921i	0.128767	+	0.0252167i
$647$	−35.0807			−1.37916			−0.689582	−	0.724208i	$-0.742206\pi$
$647$	−35.0807			−1.37916			−0.689582	+	0.724208i	$0.742206\pi$
$648$	1.55041	−	2.36564i	0.0609057	−	0.0929310i
$649$		−	18.6756i		−	0.733081i
$650$	−13.6194	−	2.66711i	−0.534197	−	0.104613i
$651$	15.4710			0.606356
$652$	−14.5168	+	35.6431i	−0.568522	+	1.39589i
$653$			5.38448i			0.210711i	0.994435	+	0.105356i	$0.0335981\pi$
$653$			5.38448i			0.210711i	−0.994435	+	0.105356i	$0.966402\pi$
$654$	−8.61538	−	1.68716i	−0.336888	−	0.0659732i
$655$	2.62120			0.102419
$656$	−18.6422	+	19.0898i	−0.727855	+	0.745331i
$657$	1.91010			0.0745200
$658$	6.55804	+	1.28427i	0.255659	+	0.0500660i
$659$			31.2248i			1.21635i	0.793804	+	0.608174i	$0.208098\pi$
$659$			31.2248i			1.21635i	−0.793804	+	0.608174i	$0.791902\pi$
$660$	−0.558661	+	1.37168i	−0.0217458	+	0.0533926i
$661$		−	50.2687i		−	1.95523i	−0.210412	−	0.977613i	$-0.567481\pi$
$661$		−	50.2687i		−	1.95523i	0.210412	−	0.977613i	$-0.432519\pi$
$662$	−1.59896	+	8.16496i	−0.0621452	+	0.317340i
$663$		−	0.904153i		−	0.0351144i
$664$	1.95652	+	1.28228i	0.0759279	+	0.0497621i
$665$	2.93831			0.113943
$666$	−0.358147	+	1.82885i	−0.0138779	+	0.0708666i
$667$		−	7.27515i		−	0.281695i
$668$	10.0246	−	24.6134i	0.387863	−	0.952320i
$669$		−	27.0486i		−	1.04576i
$670$	1.83339	−	2.94633i	0.0708300	−	0.113827i
$671$			22.3833i			0.864097i
$672$	−8.75562	+	6.04000i	−0.337756	+	0.232998i
$673$			43.7398i			1.68604i	0.537879	+	0.843022i	$0.319226\pi$
$673$			43.7398i			1.68604i	−0.537879	+	0.843022i	$0.680774\pi$
$674$	−32.5084	−	6.36617i	−1.25218	−	0.245216i
$675$	−4.91013			−0.188991
$676$	−16.6809	−	6.79383i	−0.641573	−	0.261301i
$677$			20.5319i			0.789106i	0.918873	+	0.394553i	$0.129100\pi$
$677$			20.5319i			0.789106i	−0.918873	+	0.394553i	$0.870900\pi$
$678$	17.9481	+	3.51479i	0.689291	+	0.134985i
$679$			11.4906i			0.440970i
$680$	−0.320825	−	0.210264i	−0.0123031	−	0.00806327i
$681$			11.0542i			0.423598i
$682$	5.52401	−	28.2080i	0.211525	−	1.08014i
$683$	25.7395			0.984894			0.492447	−	0.870342i	$-0.336103\pi$
$683$	25.7395			0.984894			0.492447	+	0.870342i	$0.336103\pi$
$684$	−3.93240	+	9.65523i	−0.150359	+	0.369177i
$685$	−4.93911			−0.188714
$686$	−5.34778	+	27.3081i	−0.204179	+	1.04263i
$687$			11.8822i			0.453335i
$688$	12.7177	+	12.4195i	0.484858	+	0.473490i
$689$	−1.98051			−0.0754514
$690$	−0.0658237	+	0.336125i	−0.00250587	+	0.0127960i
$691$			7.42817i			0.282581i	0.989968	+	0.141291i	$0.0451252\pi$
$691$			7.42817i			0.282581i	−0.989968	+	0.141291i	$0.954875\pi$
$692$	34.7101	+	14.1368i	1.31948	+	0.537400i
$693$	4.64502			0.176450
$694$	3.86273	−	19.7248i	0.146627	−	0.748743i
$695$		−	4.13244i		−	0.156752i
$696$	−13.9614	+	21.3026i	−0.529207	+	0.807474i
$697$			3.01776i			0.114306i
$698$	7.04187	−	35.9588i	0.266539	−	1.36106i
$699$		−	5.38131i		−	0.203540i
$700$	17.1015	+	6.96514i	0.646377	+	0.263257i
$701$		−	16.4094i		−	0.619776i	−0.950773	−	0.309888i	$-0.899709\pi$
$701$		−	16.4094i		−	0.619776i	0.950773	−	0.309888i	$-0.100291\pi$
$702$	2.77374	+	0.543184i	0.104688	+	0.0205012i
$703$		−	6.86902i		−	0.259070i
$704$	7.88639	+	18.1206i	0.297229	+	0.682946i
$705$	−0.753344			−0.0283726
$706$	−45.1244	−	8.83677i	−1.69828	−	0.332576i
$707$			31.1178i			1.17030i
$708$	−5.70327	+	14.0032i	−0.214342	+	0.526274i
$709$	25.0894			0.942250			0.471125	−	0.882066i	$-0.343848\pi$
$709$	25.0894			0.942250			0.471125	+	0.882066i	$0.343848\pi$
$710$	−0.00702919	+	0.0358941i	−0.000263801	+	0.00134708i
$711$	8.30576			0.311490
$712$	22.5415	−	34.3943i	0.844779	−	1.28898i
$713$		−	6.64717i		−	0.248939i
$714$	−0.231198	+	1.18060i	−0.00865235	+	0.0441827i
$715$	−1.48003			−0.0553501
$716$	−1.29352	−	0.526828i	−0.0483412	−	0.0196885i
$717$	−14.4375			−0.539177
$718$	29.0400	+	5.68694i	1.08376	+	0.212235i
$719$		−	27.9871i		−	1.04374i	−0.853024	−	0.521872i	$-0.825234\pi$
$719$		−	27.9871i		−	1.04374i	0.853024	−	0.521872i	$-0.174766\pi$
$720$	0.837784	−	0.857900i	0.0312224	−	0.0319720i
$721$			2.36667i			0.0881395i
$722$	2.22098	−	11.3413i	0.0826563	−	0.422079i
$723$	7.02196			0.261150
$724$	−2.58465	−	1.05268i	−0.0960579	−	0.0391226i
$725$	44.2159			1.64214
$726$	−1.33110	+	6.79719i	−0.0494019	+	0.252267i
$727$	−36.2677			−1.34509			−0.672547	−	0.740054i	$-0.734800\pi$
$727$	−36.2677			−1.34509			−0.672547	+	0.740054i	$0.734800\pi$
$728$	−8.89013	−	5.82647i	−0.329490	−	0.215943i
$729$	1.00000			0.0370370
$730$	0.794692	+	0.155626i	0.0294129	+	0.00575996i
$731$	2.01045			0.0743591
$732$	6.83555	−	16.7833i	0.252649	−	0.620330i
$733$		−	33.3050i		−	1.23015i	−0.788469	−	0.615075i	$-0.789126\pi$
$733$		−	33.3050i		−	1.23015i	0.788469	−	0.615075i	$-0.210874\pi$
$734$	−8.68662	+	44.3577i	−0.320629	+	1.63727i
$735$		−	1.03852i		−	0.0383064i
$736$	2.59511	+	3.76189i	0.0956570	+	0.138665i
$737$	−7.18441	+	18.9009i	−0.264641	+	0.696222i
$738$	−9.25781	−	1.81297i	−0.340785	−	0.0667363i
$739$	−51.5367			−1.89581			−0.947905	−	0.318554i	$-0.896803\pi$
$739$	−51.5367			−1.89581			−0.947905	+	0.318554i	$0.896803\pi$
$740$	−0.298013	+	0.731711i	−0.0109552	+	0.0268982i
$741$	−10.4179			−0.382712
$742$	2.58605	+	0.506429i	0.0949367	+	0.0185916i
$743$		−	31.2773i		−	1.14745i	−0.819047	−	0.573726i	$-0.805497\pi$
$743$		−	31.2773i		−	1.14745i	0.819047	−	0.573726i	$-0.194503\pi$
$744$	−12.7563	+	19.4638i	−0.467669	+	0.713579i
$745$		−	1.30543i		−	0.0478273i
$746$	−5.72646	−	1.12142i	−0.209661	−	0.0410581i
$747$			0.827060i			0.0302605i
$748$	2.07001	+	0.843077i	0.0756871	+	0.0308260i
$749$		−	21.4733i		−	0.784619i
$750$	−4.12309	−	0.807431i	−0.150554	−	0.0294832i
$751$			2.19849i			0.0802239i	0.999195	+	0.0401119i	$0.0127715\pi$
$751$			2.19849i			0.0802239i	−0.999195	+	0.0401119i	$0.987229\pi$
$752$	−7.02303	+	7.19165i	−0.256103	+	0.262253i
$753$	−15.9704			−0.581994
$754$	−24.9776	−	4.89139i	−0.909629	−	0.178134i
$755$	−2.08945			−0.0760430
$756$	−3.48290	−	1.41852i	−0.126672	−	0.0515912i
$757$			22.9756i			0.835062i	0.908663	+	0.417531i	$0.137105\pi$
$757$			22.9756i			0.835062i	−0.908663	+	0.417531i	$0.862895\pi$
$758$	2.37926	−	12.1495i	0.0864186	−	0.441291i
$759$		−	1.99575i		−	0.0724411i
$760$	−2.42273	+	3.69665i	−0.0878817	+	0.134092i
$761$	−23.3543			−0.846592			−0.423296	−	0.905992i	$-0.639127\pi$
$761$	−23.3543			−0.846592			−0.423296	+	0.905992i	$0.639127\pi$
$762$	1.63593	+	0.320366i	0.0592635	+	0.0116057i
$763$			11.6727i			0.422578i
$764$	13.8716	+	5.64965i	0.501857	+	0.204397i
$765$		−	0.135619i		−	0.00490331i
$766$	−1.92547	+	9.83227i	−0.0695699	+	0.355254i
$767$	−15.1094			−0.545569
$768$	−0.379553	−	15.9955i	−0.0136959	−	0.577188i
$769$			31.8435i			1.14830i	0.818749	+	0.574152i	$0.194668\pi$
$769$			31.8435i			1.14830i	−0.818749	+	0.574152i	$0.805332\pi$
$770$	1.93255	+	0.378454i	0.0696443	+	0.0136385i
$771$	5.54733			0.199782
$772$	−41.3407	−	16.8373i	−1.48789	−	0.605989i
$773$	−8.96827			−0.322566			−0.161283	−	0.986908i	$-0.551563\pi$
$773$	−8.96827			−0.322566			−0.161283	+	0.986908i	$0.551563\pi$
$774$	−1.20781	+	6.16760i	−0.0434138	+	0.221690i
$775$	40.3993			1.45118
$776$	−14.4562	−	9.47440i	−0.518948	−	0.340111i
$777$	2.47784			0.0888921
$778$	5.00378	−	25.5515i	0.179394	−	0.916065i
$779$	34.7716			1.24582
$780$	1.10975	+	0.451982i	0.0397355	+	0.0161835i
$781$		−	0.213122i		−	0.00762611i
$782$	0.507247	+	0.0993349i	0.0181391	+	0.00355221i
$783$	−9.00503			−0.321813
$784$	−9.91404	−	9.68158i	−0.354073	−	0.345771i
$785$			2.11635i			0.0755358i
$786$	12.1351	+	2.37643i	0.432844	+	0.0847643i
$787$	−38.5330			−1.37355			−0.686777	−	0.726868i	$-0.740975\pi$
$787$	−38.5330			−1.37355			−0.686777	+	0.726868i	$0.740975\pi$
$788$	−16.3913	+	40.2457i	−0.583917	+	1.43369i
$789$		−	19.4297i		−	0.691714i
$790$	3.45560	+	0.676714i	0.122945	+	0.0240764i
$791$		−	24.3171i		−	0.864618i
$792$	−3.82996	+	5.84383i	−0.136092	+	0.207651i
$793$	18.1091			0.643073
$794$	−0.535469	+	2.73434i	−0.0190031	+	0.0970380i
$795$	−0.297068			−0.0105359
$796$	−15.8166	+	38.8345i	−0.560604	+	1.37645i
$797$	−20.0925			−0.711712			−0.355856	−	0.934541i	$-0.615811\pi$
$797$	−20.0925			−0.711712			−0.355856	+	0.934541i	$0.615811\pi$
$798$	13.6032	+	2.66393i	0.481548	+	0.0943021i
$799$			1.13687i			0.0402197i
$800$	−22.8635	+	15.7722i	−0.808346	+	0.557631i
$801$	14.5391			0.513714
$802$	−22.0267	−	4.31352i	−0.777791	−	0.152316i
$803$	−4.71850			−0.166512
$804$	11.1590	−	11.9781i	0.393549	−	0.422436i
$805$	0.455402			0.0160508
$806$	−22.8216	−	4.46917i	−0.803855	−	0.157420i
$807$	−5.13142			−0.180635
$808$	−39.1488	−	25.6576i	−1.37725	−	0.902630i
$809$		−	20.3847i		−	0.716689i	−0.933589	−	0.358345i	$-0.883341\pi$
$809$		−	20.3847i		−	0.716689i	0.933589	−	0.358345i	$-0.116659\pi$
$810$	0.416048	+	0.0814753i	0.0146184	+	0.00286275i
$811$	−42.9116			−1.50683			−0.753415	−	0.657546i	$-0.771595\pi$
$811$	−42.9116			−1.50683			−0.753415	+	0.657546i	$0.771595\pi$
$812$	31.3636	+	12.7738i	1.10065	+	0.448274i
$813$	−4.15615			−0.145762
$814$	0.884728	−	4.51781i	0.0310097	−	0.158349i
$815$	−5.76864			−0.202067
$816$	−1.29466	−	1.26430i	−0.0453222	−	0.0442595i
$817$		−	23.1650i		−	0.810441i
$818$	−30.2009	−	5.91429i	−1.05595	−	0.206788i
$819$		−	3.75803i		−	0.131316i
$820$	−3.70398	−	1.50856i	−0.129349	−	0.0526814i
$821$	34.9629			1.22021			0.610107	−	0.792319i	$-0.291127\pi$
$821$	34.9629			1.22021			0.610107	+	0.792319i	$0.291127\pi$
$822$	−22.8661	−	4.47789i	−0.797546	−	0.156184i
$823$			28.3173i			0.987078i	0.869724	+	0.493539i	$0.164297\pi$
$823$			28.3173i			0.987078i	−0.869724	+	0.493539i	$0.835703\pi$
$824$	−2.97748	−	1.95140i	−0.103725	−	0.0679801i
$825$	12.1295			0.422294
$826$	19.7291	+	3.86357i	0.686462	+	0.134431i
$827$			8.59099i			0.298738i	0.988782	+	0.149369i	$0.0477242\pi$
$827$			8.59099i			0.298738i	−0.988782	+	0.149369i	$0.952276\pi$
$828$	−0.609474	+	1.49644i	−0.0211807	+	0.0520050i
$829$	−0.421427			−0.0146368			−0.00731839	−	0.999973i	$-0.502330\pi$
$829$	−0.421427			−0.0146368			−0.00731839	+	0.999973i	$0.502330\pi$
$830$	−0.0673849	+	0.344097i	−0.00233897	+	0.0119438i
$831$	−0.861448			−0.0298833
$832$	14.6604	−	6.38045i	0.508258	−	0.221202i
$833$	−1.56724			−0.0543015
$834$	3.74655	−	19.1315i	0.129732	−	0.662470i
$835$	3.98353			0.137856
$836$	9.71420	−	23.8513i	0.335973	−	0.824914i
$837$	−8.22773			−0.284392
$838$	11.1236	+	2.17836i	0.384260	+	0.0752500i
$839$		−	32.5697i		−	1.12443i	−0.826991	−	0.562215i	$-0.809949\pi$
$839$		−	32.5697i		−	1.12443i	0.826991	−	0.562215i	$-0.190051\pi$
$840$	−1.33348	−	0.873945i	−0.0460095	−	0.0301540i
$841$	52.0905			1.79622
$842$	−3.55287	+	18.1425i	−0.122440	+	0.625232i
$843$		−	12.5745i		−	0.433090i
$844$	5.26286	−	12.9219i	0.181155	−	0.444790i
$845$		−	2.69971i		−	0.0928727i
$846$	−3.48767	−	0.682996i	−0.119909	−	0.0234819i
$847$	9.20925			0.316434
$848$	−2.76941	+	2.83590i	−0.0951018	+	0.0973852i
$849$		−	11.4059i		−	0.391451i
$850$	−0.603724	+	3.08288i	−0.0207076	+	0.105742i
$851$		−	1.06461i		−	0.0364945i
$852$	−0.0650845	+	0.159802i	−0.00222976	+	0.00547473i
$853$	−29.1301			−0.997395			−0.498697	−	0.866776i	$-0.666188\pi$
$853$	−29.1301			−0.997395			−0.498697	+	0.866776i	$0.666188\pi$
$854$	−23.6459	−	4.63061i	−0.809147	−	0.158456i
$855$	−1.56264			−0.0534413
$856$	27.0153	+	17.7054i	0.923364	+	0.605160i
$857$		−	4.30550i		−	0.147073i	−0.997293	−	0.0735365i	$-0.976571\pi$
$857$		−	4.30550i		−	0.147073i	0.997293	−	0.0735365i	$-0.0234285\pi$
$858$	−6.85195	−	1.34183i	−0.233922	−	0.0458092i
$859$			20.2428i			0.690674i	0.938479	+	0.345337i	$0.112235\pi$
$859$			20.2428i			0.690674i	−0.938479	+	0.345337i	$0.887765\pi$
$860$	−1.00501	+	2.46761i	−0.0342707	+	0.0841449i
$861$			12.5431i			0.427466i
$862$	15.5851	+	3.05206i	0.530832	+	0.103953i
$863$			10.5530i			0.359229i	0.983737	+	0.179615i	$0.0574851\pi$
$863$			10.5530i			0.359229i	−0.983737	+	0.179615i	$0.942515\pi$
$864$	4.65639	−	3.21217i	0.158413	−	0.109280i
$865$			5.61763i			0.191005i
$866$	−52.6085	−	10.3024i	−1.78771	−	0.350089i
$867$	16.7953			0.570400
$868$	28.6564	+	11.6712i	0.972661	+	0.396147i
$869$	−20.5177			−0.696015
$870$	−3.74653	−	0.733687i	−0.127019	−	0.0248743i
$871$	15.2917	+	5.81252i	0.518138	+	0.196950i
$872$	−14.6852	−	9.62447i	−0.497303	−	0.325926i
$873$		−	6.11092i		−	0.206823i
$874$	1.14457	−	5.84466i	0.0387156	−	0.197699i
$875$			5.58622i			0.188849i
$876$	3.53801	+	1.44097i	0.119538	+	0.0486857i
$877$	−9.53396			−0.321939			−0.160969	−	0.986959i	$-0.551462\pi$
$877$	−9.53396			−0.321939			−0.160969	+	0.986959i	$0.551462\pi$
$878$	−23.0230	−	4.50862i	−0.776988	−	0.152159i
$879$	10.9531			0.369440
$880$	−2.06958	+	2.11927i	−0.0697654	+	0.0714405i
$881$	−10.0837			−0.339728			−0.169864	−	0.985467i	$-0.554333\pi$
$881$	−10.0837			−0.339728			−0.169864	+	0.985467i	$0.554333\pi$
$882$	0.941543	−	4.80793i	0.0317034	−	0.161891i
$883$	23.6688			0.796520			0.398260	−	0.917273i	$-0.369614\pi$
$883$	23.6688			0.796520			0.398260	+	0.917273i	$0.369614\pi$
$884$	0.682088	−	1.67473i	0.0229411	−	0.0563273i
$885$	−2.26634			−0.0761823
$886$	−5.48419	+	28.0047i	−0.184245	+	0.940836i
$887$		−	54.6211i		−	1.83400i	−0.398890	−	0.916999i	$-0.630605\pi$
$887$		−	54.6211i		−	1.83400i	0.398890	−	0.916999i	$-0.369395\pi$
$888$	−2.04306	+	3.11734i	−0.0685606	+	0.104611i
$889$		−	2.21646i		−	0.0743377i
$890$	6.04897	+	1.18458i	0.202762	+	0.0397071i
$891$	−2.47030			−0.0827581
$892$	20.4053	−	50.1011i	0.683219	−	1.67751i
$893$	13.0994			0.438355
$894$	1.18353	−	6.04361i	0.0395831	−	0.202129i
$895$		−	0.209349i		−	0.00699777i
$896$	−20.7743	+	4.58250i	−0.694020	+	0.153091i
$897$	−1.61465			−0.0539116
$898$	−4.62392	+	23.6118i	−0.154302	+	0.787935i
$899$	74.0909			2.47107
$900$	−9.09487	−	3.70418i	−0.303162	−	0.123473i
$901$			0.448306i			0.0149353i
$902$	22.8695	+	4.47857i	0.761472	+	0.149120i
$903$	8.35625			0.278078
$904$	30.5930	+	20.0502i	1.01751	+	0.666861i
$905$		−	0.418311i		−	0.0139051i
$906$	−9.67332	−	1.89434i	−0.321374	−	0.0629352i
$907$			19.8827i			0.660195i	0.943947	+	0.330097i	$0.107082\pi$
$907$			19.8827i			0.660195i	−0.943947	+	0.330097i	$0.892918\pi$
$908$	−8.33922	+	20.4753i	−0.276747	+	0.679497i
$909$		−	16.5489i		−	0.548894i
$910$	0.306186	−	1.56352i	0.0101500	−	0.0518302i
$911$		−	28.2974i		−	0.937534i	−0.883322	−	0.468767i	$-0.844698\pi$
$911$		−	28.2974i		−	0.937534i	0.883322	−	0.468767i	$-0.155302\pi$
$912$	−14.5677	+	14.9175i	−0.482385	+	0.493967i
$913$		−	2.04308i		−	0.0676162i
$914$	2.88548	−	14.7345i	0.0954431	−	0.487374i
$915$	2.71629			0.0897976
$916$	−8.96388	+	22.0090i	−0.296175	+	0.727199i
$917$		−	16.4413i		−	0.542941i
$918$	0.122955	−	0.627860i	0.00405811	−	0.0207225i
$919$	−48.3093			−1.59358			−0.796788	−	0.604259i	$-0.793469\pi$
$919$	−48.3093			−1.59358			−0.796788	+	0.604259i	$0.793469\pi$
$920$	−0.375494	+	0.572935i	−0.0123797	+	0.0188891i
$921$		−	5.44353i		−	0.179371i
$922$	−7.20608	+	36.7974i	−0.237320	+	1.21186i
$923$	−0.172425			−0.00567545
$924$	8.60380	+	3.50417i	0.283044	+	0.115279i
$925$	6.47037			0.212744
$926$	−1.86831	+	9.54041i	−0.0613965	+	0.313517i
$927$		−	1.25864i		−	0.0413390i
$928$	−41.9309	+	28.9257i	−1.37645	+	0.949533i
$929$		−	12.6757i		−	0.415875i	−0.978142	−	0.207937i	$-0.933325\pi$
$929$		−	12.6757i		−	0.415875i	0.978142	−	0.207937i	$-0.0666750\pi$
$930$	−3.42313	−	0.670357i	−0.112249	−	0.0219819i
$931$			18.0582i			0.591833i
$932$	4.05963	−	9.96762i	0.132978	−	0.326500i
$933$	25.9978			0.851128
$934$	−36.8423	−	7.21488i	−1.20552	−	0.236078i
$935$			0.335019i			0.0109563i
$936$	4.72792	+	3.09861i	0.154537	+	0.101281i
$937$			32.8569i			1.07339i	0.843777	+	0.536694i	$0.180327\pi$
$937$			32.8569i			1.07339i	−0.843777	+	0.536694i	$0.819673\pi$
$938$	−18.4807	−	11.4999i	−0.603418	−	0.375484i
$939$			10.3628i			0.338177i
$940$	−1.39539	−	0.568318i	−0.0455127	−	0.0185365i
$941$		−	36.8088i		−	1.19993i	−0.800025	−	0.599966i	$-0.795181\pi$
$941$		−	36.8088i		−	1.19993i	0.800025	−	0.599966i	$-0.204819\pi$
$942$	−1.91872	+	9.79784i	−0.0625154	+	0.319231i
$943$	5.38917			0.175495
$944$	−21.1279	+	21.6352i	−0.687656	+	0.704166i
$945$		−	0.563688i		−	0.0183368i
$946$	2.98365	−	15.2358i	0.0970068	−	0.495359i
$947$			40.6020i			1.31939i	0.751534	+	0.659695i	$0.229314\pi$
$947$			40.6020i			1.31939i	−0.751534	+	0.659695i	$0.770686\pi$
$948$	15.3845	+	6.26582i	0.499665	+	0.203504i
$949$			3.81748i			0.123921i
$950$	35.5219	+	6.95629i	1.15248	+	0.225692i
$951$	16.5470			0.536575
$952$	−1.31887	+	2.01236i	−0.0427449	+	0.0652211i
$953$	9.13641			0.295957			0.147979	−	0.988991i	$-0.452723\pi$
$953$	9.13641			0.295957			0.147979	+	0.988991i	$0.452723\pi$
$954$	−1.37530	−	0.269327i	−0.0445271	−	0.00871979i
$955$			2.24504i			0.0726477i
$956$	−26.7420	−	10.8915i	−0.864900	−	0.352258i
$957$	22.2451			0.719082
$958$	−29.3445	−	5.74657i	−0.948077	−	0.185663i
$959$			30.9804i			1.00041i
$960$	2.19899	−	0.957039i	0.0709722	−	0.0308883i
$961$	36.6956			1.18373
$962$	−3.65511	−	0.715785i	−0.117846	−	0.0230778i
$963$			11.4199i			0.368000i
$964$	13.0065	+	5.29733i	0.418912	+	0.170615i
$965$		−	6.69076i		−	0.215383i
$966$	2.10833	+	0.412876i	0.0678343	+	0.0132841i
$967$		−	47.9005i		−	1.54037i	−0.637818	−	0.770187i	$-0.720163\pi$
$967$		−	47.9005i		−	1.54037i	0.637818	−	0.770187i	$-0.279837\pi$
$968$	−7.59332	+	11.5860i	−0.244058	+	0.372389i
$969$			2.35819i			0.0757561i
$970$	0.497889	−	2.54244i	0.0159862	−	0.0816327i
$971$			11.1845i			0.358927i	0.983765	+	0.179463i	$0.0574361\pi$
$971$			11.1845i			0.358927i	−0.983765	+	0.179463i	$0.942564\pi$
$972$	1.85227	+	0.754394i	0.0594115	+	0.0241972i
$973$	−25.9205			−0.830975
$974$	1.73431	−	8.85613i	0.0555708	−	0.283769i
$975$		−	9.81330i		−	0.314277i
$976$	25.3225	−	25.9305i	0.810554	−	0.830015i
$977$	46.6725			1.49319			0.746593	−	0.665281i	$-0.231688\pi$
$977$	46.6725			1.49319			0.746593	+	0.665281i	$0.231688\pi$
$978$	−26.7064	−	5.22995i	−0.853977	−	0.167236i
$979$	−35.9159			−1.14788
$980$	0.783454	−	1.92362i	0.0250265	−	0.0614477i
$981$		−	6.20771i		−	0.198197i
$982$	40.6434	+	7.95925i	1.29698	+	0.253990i
$983$	−21.7762			−0.694552			−0.347276	−	0.937763i	$-0.612893\pi$
$983$	−21.7762			−0.694552			−0.347276	+	0.937763i	$0.612893\pi$
$984$	−15.7802	−	10.3421i	−0.503055	−	0.329695i
$985$	−6.51353			−0.207538
$986$	−1.10721	+	5.65390i	−0.0352608	+	0.180057i
$987$			4.72531i			0.150408i
$988$	−19.2968	−	7.85923i	−0.613912	−	0.250035i
$989$		−	3.59029i		−	0.114165i
$990$	−1.02776	−	0.201268i	−0.0326644	−	0.00639672i
$991$	−41.2891			−1.31159			−0.655796	−	0.754938i	$-0.727667\pi$
$991$	−41.2891			−1.31159			−0.655796	+	0.754938i	$0.727667\pi$
$992$	−38.3115	+	26.4289i	−1.21639	+	0.839119i
$993$	−5.88317			−0.186697
$994$	0.225144	+	0.0440903i	0.00714114	+	0.00139846i
$995$	−6.28514			−0.199252
$996$	−0.623929	+	1.53194i	−0.0197700	+	0.0485412i
$997$	−49.6290			−1.57177			−0.785884	−	0.618375i	$-0.787792\pi$
$997$	−49.6290			−1.57177			−0.785884	+	0.618375i	$0.787792\pi$
$998$	−10.9318	+	55.8224i	−0.346039	+	1.76703i
$999$	−1.31776			−0.0416920

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	804.2.e.a.535.16	yes	34
4.3	odd	2		804.2.e.b.535.20	yes	34
67.66	odd	2		804.2.e.b.535.19	yes	34
268.267	even	2	inner	804.2.e.a.535.15	✓	34

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
804.2.e.a.535.15	✓	34	268.267	even	2	inner
804.2.e.a.535.16	yes	34	1.1	even	1	trivial
804.2.e.b.535.19	yes	34	67.66	odd	2
804.2.e.b.535.20	yes	34	4.3	odd	2

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:	\( N \)	\(=\)	\( 804 = 2^{2} \cdot 3 \cdot 67 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	804.e (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.271785 + 1.38785i) q^{2} -1.00000 q^{3} +(-1.85227 - 0.754394i) q^{4} -0.299779i q^{5} +(0.271785 - 1.38785i) q^{6} -1.88035 q^{7} +(1.55041 - 2.36564i) q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+(-0.271785 + 1.38785i) q^{2} -1.00000 q^{3} +(-1.85227 - 0.754394i) q^{4} -0.299779i q^{5} +(0.271785 - 1.38785i) q^{6} -1.88035 q^{7} +(1.55041 - 2.36564i) q^{8} +1.00000 q^{9} +(0.416048 + 0.0814753i) q^{10} -2.47030 q^{11} +(1.85227 + 0.754394i) q^{12} +1.99858i q^{13} +(0.511050 - 2.60964i) q^{14} +0.299779i q^{15} +(2.86178 + 2.79468i) q^{16} +0.452397 q^{17} +(-0.271785 + 1.38785i) q^{18} -5.21266i q^{19} +(-0.226151 + 0.555270i) q^{20} +1.88035 q^{21} +(0.671389 - 3.42841i) q^{22} -0.807898i q^{23} +(-1.55041 + 2.36564i) q^{24} +4.91013 q^{25} +(-2.77374 - 0.543184i) q^{26} -1.00000 q^{27} +(3.48290 + 1.41852i) q^{28} +9.00503 q^{29} +(-0.416048 - 0.0814753i) q^{30} +8.22773 q^{31} +(-4.65639 + 3.21217i) q^{32} +2.47030 q^{33} +(-0.122955 + 0.627860i) q^{34} +0.563688i q^{35} +(-1.85227 - 0.754394i) q^{36} +1.31776 q^{37} +(7.23440 + 1.41672i) q^{38} -1.99858i q^{39} +(-0.709168 - 0.464778i) q^{40} +6.67060i q^{41} +(-0.511050 + 2.60964i) q^{42} +4.44399 q^{43} +(4.57565 + 1.86358i) q^{44} -0.299779i q^{45} +(1.12124 + 0.219575i) q^{46} +2.51300i q^{47} +(-2.86178 - 2.79468i) q^{48} -3.46429 q^{49} +(-1.33450 + 6.81454i) q^{50} -0.452397 q^{51} +(1.50772 - 3.70191i) q^{52} +0.990958i q^{53} +(0.271785 - 1.38785i) q^{54} +0.740542i q^{55} +(-2.91530 + 4.44822i) q^{56} +5.21266i q^{57} +(-2.44743 + 12.4976i) q^{58} +7.56006i q^{59} +(0.226151 - 0.555270i) q^{60} -9.06097i q^{61} +(-2.23617 + 11.4189i) q^{62} -1.88035 q^{63} +(-3.19249 - 7.33540i) q^{64} +0.599132 q^{65} +(-0.671389 + 3.42841i) q^{66} +(2.90832 - 7.65125i) q^{67} +(-0.837960 - 0.341286i) q^{68} +0.807898i q^{69} +(-0.782315 - 0.153202i) q^{70} +0.0862739i q^{71} +(1.55041 - 2.36564i) q^{72} +1.91010 q^{73} +(-0.358147 + 1.82885i) q^{74} -4.91013 q^{75} +(-3.93240 + 9.65523i) q^{76} +4.64502 q^{77} +(2.77374 + 0.543184i) q^{78} +8.30576 q^{79} +(0.837784 - 0.857900i) q^{80} +1.00000 q^{81} +(-9.25781 - 1.81297i) q^{82} +0.827060i q^{83} +(-3.48290 - 1.41852i) q^{84} -0.135619i q^{85} +(-1.20781 + 6.16760i) q^{86} -9.00503 q^{87} +(-3.82996 + 5.84383i) q^{88} +14.5391 q^{89} +(0.416048 + 0.0814753i) q^{90} -3.75803i q^{91} +(-0.609474 + 1.49644i) q^{92} -8.22773 q^{93} +(-3.48767 - 0.682996i) q^{94} -1.56264 q^{95} +(4.65639 - 3.21217i) q^{96} -6.11092i q^{97} +(0.941543 - 4.80793i) q^{98} -2.47030 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 34 q - 34 q^{3} + 2 q^{4} - 4 q^{7} + 6 q^{8} + 34 q^{9}+O(q^{10}) \) 34 * q - 34 * q^3 + 2 * q^4 - 4 * q^7 + 6 * q^8 + 34 * q^9	\( 34 q - 34 q^{3} + 2 q^{4} - 4 q^{7} + 6 q^{8} + 34 q^{9} - 6 q^{10} - 2 q^{12} - 4 q^{14} + 2 q^{16} + 12 q^{20} + 4 q^{21} - 8 q^{22} - 6 q^{24} - 34 q^{25} + 10 q^{26} - 34 q^{27} + 8 q^{28} - 16 q^{29} + 6 q^{30} + 4 q^{31} + 2 q^{36} + 12 q^{37} - 26 q^{38} - 18 q^{40} + 4 q^{42} + 4 q^{43} - 26 q^{44} + 4 q^{46} - 2 q^{48} + 46 q^{49} + 18 q^{50} - 32 q^{52} + 14 q^{56} - 4 q^{58} - 12 q^{60} - 2 q^{62} - 4 q^{63} + 26 q^{64} + 8 q^{66} + 18 q^{67} - 34 q^{68} - 56 q^{70} + 6 q^{72} + 12 q^{73} - 22 q^{74} + 34 q^{75} - 32 q^{76} - 8 q^{77} - 10 q^{78} + 12 q^{79} + 2 q^{80} + 34 q^{81} + 26 q^{82} - 8 q^{84} + 6 q^{86} + 16 q^{87} - 28 q^{88} - 6 q^{90} - 46 q^{92} - 4 q^{93} - 32 q^{94} + 40 q^{95} + 40 q^{98}+O(q^{100}) \) 34 * q - 34 * q^3 + 2 * q^4 - 4 * q^7 + 6 * q^8 + 34 * q^9 - 6 * q^10 - 2 * q^12 - 4 * q^14 + 2 * q^16 + 12 * q^20 + 4 * q^21 - 8 * q^22 - 6 * q^24 - 34 * q^25 + 10 * q^26 - 34 * q^27 + 8 * q^28 - 16 * q^29 + 6 * q^30 + 4 * q^31 + 2 * q^36 + 12 * q^37 - 26 * q^38 - 18 * q^40 + 4 * q^42 + 4 * q^43 - 26 * q^44 + 4 * q^46 - 2 * q^48 + 46 * q^49 + 18 * q^50 - 32 * q^52 + 14 * q^56 - 4 * q^58 - 12 * q^60 - 2 * q^62 - 4 * q^63 + 26 * q^64 + 8 * q^66 + 18 * q^67 - 34 * q^68 - 56 * q^70 + 6 * q^72 + 12 * q^73 - 22 * q^74 + 34 * q^75 - 32 * q^76 - 8 * q^77 - 10 * q^78 + 12 * q^79 + 2 * q^80 + 34 * q^81 + 26 * q^82 - 8 * q^84 + 6 * q^86 + 16 * q^87 - 28 * q^88 - 6 * q^90 - 46 * q^92 - 4 * q^93 - 32 * q^94 + 40 * q^95 + 40 * q^98

Introduction

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