LMFDB - Embedded newform 804.2.e.a.535.27

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			535.27
Character	$\chi$	$=$	804.535
Dual form			804.2.e.a.535.28

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.16630 - 0.799841i) q^{2} -1.00000 q^{3} +(0.720507 - 1.86571i) q^{4} -0.864540i q^{5} +(-1.16630 + 0.799841i) q^{6} +1.73467 q^{7} +(-0.651944 - 2.75227i) q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+(1.16630 - 0.799841i) q^{2} -1.00000 q^{3} +(0.720507 - 1.86571i) q^{4} -0.864540i q^{5} +(-1.16630 + 0.799841i) q^{6} +1.73467 q^{7} +(-0.651944 - 2.75227i) q^{8} +1.00000 q^{9} +(-0.691495 - 1.00831i) q^{10} +5.29746 q^{11} +(-0.720507 + 1.86571i) q^{12} +1.41228i q^{13} +(2.02315 - 1.38746i) q^{14} +0.864540i q^{15} +(-2.96174 - 2.68851i) q^{16} -4.82537 q^{17} +(1.16630 - 0.799841i) q^{18} -4.26064i q^{19} +(-1.61298 - 0.622907i) q^{20} -1.73467 q^{21} +(6.17843 - 4.23713i) q^{22} -1.92153i q^{23} +(0.651944 + 2.75227i) q^{24} +4.25257 q^{25} +(1.12960 + 1.64714i) q^{26} -1.00000 q^{27} +(1.24984 - 3.23639i) q^{28} -2.13848 q^{29} +(0.691495 + 1.00831i) q^{30} +5.52447 q^{31} +(-5.60466 - 0.766689i) q^{32} -5.29746 q^{33} +(-5.62783 + 3.85953i) q^{34} -1.49969i q^{35} +(0.720507 - 1.86571i) q^{36} -7.24325 q^{37} +(-3.40783 - 4.96918i) q^{38} -1.41228i q^{39} +(-2.37944 + 0.563632i) q^{40} -0.306352i q^{41} +(-2.02315 + 1.38746i) q^{42} -1.13429 q^{43} +(3.81686 - 9.88352i) q^{44} -0.864540i q^{45} +(-1.53692 - 2.24107i) q^{46} -11.9232i q^{47} +(2.96174 + 2.68851i) q^{48} -3.99091 q^{49} +(4.95977 - 3.40138i) q^{50} +4.82537 q^{51} +(2.63490 + 1.01756i) q^{52} -8.91687i q^{53} +(-1.16630 + 0.799841i) q^{54} -4.57987i q^{55} +(-1.13091 - 4.77428i) q^{56} +4.26064i q^{57} +(-2.49411 + 1.71044i) q^{58} +14.4219i q^{59} +(1.61298 + 0.622907i) q^{60} +12.4421i q^{61} +(6.44318 - 4.41870i) q^{62} +1.73467 q^{63} +(-7.14994 + 3.58865i) q^{64} +1.22097 q^{65} +(-6.17843 + 4.23713i) q^{66} +(7.97425 - 1.84697i) q^{67} +(-3.47672 + 9.00274i) q^{68} +1.92153i q^{69} +(-1.19952 - 1.74909i) q^{70} +8.13841i q^{71} +(-0.651944 - 2.75227i) q^{72} +12.8776 q^{73} +(-8.44779 + 5.79345i) q^{74} -4.25257 q^{75} +(-7.94910 - 3.06982i) q^{76} +9.18937 q^{77} +(-1.12960 - 1.64714i) q^{78} +8.20011 q^{79} +(-2.32433 + 2.56054i) q^{80} +1.00000 q^{81} +(-0.245033 - 0.357299i) q^{82} -0.390864i q^{83} +(-1.24984 + 3.23639i) q^{84} +4.17173i q^{85} +(-1.32292 + 0.907249i) q^{86} +2.13848 q^{87} +(-3.45365 - 14.5800i) q^{88} -5.73285 q^{89} +(-0.691495 - 1.00831i) q^{90} +2.44984i q^{91} +(-3.58501 - 1.38447i) q^{92} -5.52447 q^{93} +(-9.53668 - 13.9060i) q^{94} -3.68349 q^{95} +(5.60466 + 0.766689i) q^{96} +14.5334i q^{97} +(-4.65459 + 3.19209i) q^{98} +5.29746 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 $

$2$	1.16630	−	0.799841i	0.824698	−	0.565573i
$2$	1.16630	−	0.799841i	0.824698	−	0.565573i
$3$	−1.00000			−0.577350
$3$	−1.00000			−0.577350
$4$	0.720507	−	1.86571i	0.360254	−	0.932854i
$5$		−	0.864540i		−	0.386634i	−0.981136	−	0.193317i	$-0.938075\pi$
$5$		−	0.864540i		−	0.386634i	0.981136	−	0.193317i	$-0.0619246\pi$
$6$	−1.16630	+	0.799841i	−0.476140	+	0.326534i
$7$	1.73467			0.655645			0.327822	−	0.944739i	$-0.393685\pi$
$7$	1.73467			0.655645			0.327822	+	0.944739i	$0.393685\pi$
$8$	−0.651944	−	2.75227i	−0.230497	−	0.973073i
$9$	1.00000			0.333333
$10$	−0.691495	−	1.00831i	−0.218670	−	0.318856i
$11$	5.29746			1.59725			0.798623	−	0.601832i	$-0.205562\pi$
$11$	5.29746			1.59725			0.798623	+	0.601832i	$0.205562\pi$
$12$	−0.720507	+	1.86571i	−0.207993	+	0.538584i
$13$			1.41228i			0.391696i	0.980634	+	0.195848i	$0.0627459\pi$
$13$			1.41228i			0.391696i	−0.980634	+	0.195848i	$0.937254\pi$
$14$	2.02315	−	1.38746i	0.540709	−	0.370815i
$15$			0.864540i			0.223223i
$16$	−2.96174	−	2.68851i	−0.740435	−	0.672128i
$17$	−4.82537			−1.17033			−0.585163	−	0.810916i	$-0.698969\pi$
$17$	−4.82537			−1.17033			−0.585163	+	0.810916i	$0.698969\pi$
$18$	1.16630	−	0.799841i	0.274899	−	0.188524i
$19$		−	4.26064i		−	0.977457i	−0.872436	−	0.488728i	$-0.837461\pi$
$19$		−	4.26064i		−	0.977457i	0.872436	−	0.488728i	$-0.162539\pi$
$20$	−1.61298	−	0.622907i	−0.360673	−	0.139286i
$21$	−1.73467			−0.378537
$22$	6.17843	−	4.23713i	1.31724	−	0.903359i
$23$		−	1.92153i		−	0.400666i	−0.979728	−	0.200333i	$-0.935798\pi$
$23$		−	1.92153i		−	0.400666i	0.979728	−	0.200333i	$-0.0642024\pi$
$24$	0.651944	+	2.75227i	0.133078	+	0.561804i
$25$	4.25257			0.850514
$26$	1.12960	+	1.64714i	0.221533	+	0.323031i
$27$	−1.00000			−0.192450
$28$	1.24984	−	3.23639i	0.236198	−	0.611621i
$29$	−2.13848			−0.397106			−0.198553	−	0.980090i	$-0.563624\pi$
$29$	−2.13848			−0.397106			−0.198553	+	0.980090i	$0.563624\pi$
$30$	0.691495	+	1.00831i	0.126249	+	0.184092i
$31$	5.52447			0.992223			0.496112	−	0.868259i	$-0.334761\pi$
$31$	5.52447			0.992223			0.496112	+	0.868259i	$0.334761\pi$
$32$	−5.60466	−	0.766689i	−0.990773	−	0.135533i
$33$	−5.29746			−0.922170
$34$	−5.62783	+	3.85953i	−0.965165	+	0.661905i
$35$		−	1.49969i		−	0.253495i
$36$	0.720507	−	1.86571i	0.120085	−	0.310951i
$37$	−7.24325			−1.19078			−0.595391	−	0.803436i	$-0.703003\pi$
$37$	−7.24325			−1.19078			−0.595391	+	0.803436i	$0.703003\pi$
$38$	−3.40783	−	4.96918i	−0.552823	−	0.806107i
$39$		−	1.41228i		−	0.226146i
$40$	−2.37944	+	0.563632i	−0.376223	+	0.0891181i
$41$		−	0.306352i		−	0.0478442i	−0.999714	−	0.0239221i	$-0.992385\pi$
$41$		−	0.306352i		−	0.0478442i	0.999714	−	0.0239221i	$-0.00761537\pi$
$42$	−2.02315	+	1.38746i	−0.312178	+	0.214090i
$43$	−1.13429			−0.172977			−0.0864885	−	0.996253i	$-0.527565\pi$
$43$	−1.13429			−0.172977			−0.0864885	+	0.996253i	$0.527565\pi$
$44$	3.81686	−	9.88352i	0.575413	−	1.49000i
$45$		−	0.864540i		−	0.128878i
$46$	−1.53692	−	2.24107i	−0.226606	−	0.330428i
$47$		−	11.9232i		−	1.73918i	−0.493775	−	0.869590i	$-0.664383\pi$
$47$		−	11.9232i		−	1.73918i	0.493775	−	0.869590i	$-0.335617\pi$
$48$	2.96174	+	2.68851i	0.427490	+	0.388053i
$49$	−3.99091			−0.570130
$50$	4.95977	−	3.40138i	0.701417	−	0.481028i
$51$	4.82537			0.675687
$52$	2.63490	+	1.01756i	0.365395	+	0.141110i
$53$		−	8.91687i		−	1.22483i	−0.790538	−	0.612413i	$-0.790199\pi$
$53$		−	8.91687i		−	1.22483i	0.790538	−	0.612413i	$-0.209801\pi$
$54$	−1.16630	+	0.799841i	−0.158713	+	0.108845i
$55$		−	4.57987i		−	0.617550i
$56$	−1.13091	−	4.77428i	−0.151124	−	0.637990i
$57$			4.26064i			0.564335i
$58$	−2.49411	+	1.71044i	−0.327492	+	0.224592i
$59$			14.4219i			1.87757i	0.344508	+	0.938784i	$0.388046\pi$
$59$			14.4219i			1.87757i	−0.344508	+	0.938784i	$0.611954\pi$
$60$	1.61298	+	0.622907i	0.208235	+	0.0804170i
$61$			12.4421i			1.59305i	0.604606	+	0.796525i	$0.293331\pi$
$61$			12.4421i			1.59305i	−0.604606	+	0.796525i	$0.706669\pi$
$62$	6.44318	−	4.41870i	0.818285	−	0.561175i
$63$	1.73467			0.218548
$64$	−7.14994	+	3.58865i	−0.893742	+	0.448581i
$65$	1.22097			0.151443
$66$	−6.17843	+	4.23713i	−0.760512	+	0.521555i
$67$	7.97425	−	1.84697i	0.974210	−	0.225644i
$67$	7.97425	−	1.84697i	0.974210	−	0.225644i
$68$	−3.47672	+	9.00274i	−0.421614	+	1.09174i
$69$			1.92153i			0.231324i
$70$	−1.19952	−	1.74909i	−0.143370	−	0.209057i
$71$			8.13841i			0.965852i	0.875661	+	0.482926i	$0.160426\pi$
$71$			8.13841i			0.965852i	−0.875661	+	0.482926i	$0.839574\pi$
$72$	−0.651944	−	2.75227i	−0.0768324	−	0.324358i
$73$	12.8776			1.50720			0.753602	−	0.657331i	$-0.228315\pi$
$73$	12.8776			1.50720			0.753602	+	0.657331i	$0.228315\pi$
$74$	−8.44779	+	5.79345i	−0.982036	+	0.673475i
$75$	−4.25257			−0.491045
$76$	−7.94910	−	3.06982i	−0.911825	−	0.352132i
$77$	9.18937			1.04723
$78$	−1.12960	−	1.64714i	−0.127902	−	0.186502i
$79$	8.20011			0.922584			0.461292	−	0.887248i	$-0.347386\pi$
$79$	8.20011			0.922584			0.461292	+	0.887248i	$0.347386\pi$
$80$	−2.32433	+	2.56054i	−0.259868	+	0.286277i
$81$	1.00000			0.111111
$82$	−0.245033	−	0.357299i	−0.0270594	−	0.0394570i
$83$		−	0.390864i		−	0.0429029i	−0.999770	−	0.0214514i	$-0.993171\pi$
$83$		−	0.390864i		−	0.0429029i	0.999770	−	0.0214514i	$-0.00682873\pi$
$84$	−1.24984	+	3.23639i	−0.136369	+	0.353120i
$85$			4.17173i			0.452488i
$86$	−1.32292	+	0.907249i	−0.142654	+	0.0978312i
$87$	2.13848			0.229269
$88$	−3.45365	−	14.5800i	−0.368160	−	1.55424i
$89$	−5.73285			−0.607681			−0.303840	−	0.952723i	$-0.598269\pi$
$89$	−5.73285			−0.607681			−0.303840	+	0.952723i	$0.598269\pi$
$90$	−0.691495	−	1.00831i	−0.0728900	−	0.106285i
$91$			2.44984i			0.256813i
$92$	−3.58501	−	1.38447i	−0.373763	−	0.144341i
$93$	−5.52447			−0.572860
$94$	−9.53668	−	13.9060i	−0.983634	−	1.43430i
$95$	−3.68349			−0.377918
$96$	5.60466	+	0.766689i	0.572023	+	0.0782499i
$97$			14.5334i			1.47564i	0.674998	+	0.737820i	$0.264144\pi$
$97$			14.5334i			1.47564i	−0.674998	+	0.737820i	$0.735856\pi$
$98$	−4.65459	+	3.19209i	−0.470185	+	0.322450i
$99$	5.29746			0.532415
$100$	3.06401	−	7.93406i	0.306401	−	0.793406i
$101$			13.9988i			1.39293i	0.717591	+	0.696465i	$0.245245\pi$
$101$			13.9988i			1.39293i	−0.717591	+	0.696465i	$0.754755\pi$
$102$	5.62783	−	3.85953i	0.557238	−	0.382151i
$103$			13.2752i			1.30805i	0.756474	+	0.654024i	$0.226920\pi$
$103$			13.2752i			1.30805i	−0.756474	+	0.654024i	$0.773080\pi$
$104$	3.88697	−	0.920728i	0.381149	−	0.0902848i
$105$			1.49969i			0.146355i
$106$	−7.13209	−	10.3997i	−0.692729	−	1.01011i
$107$		−	18.1278i		−	1.75248i	−0.481871	−	0.876242i	$-0.660043\pi$
$107$		−	18.1278i		−	1.75248i	0.481871	−	0.876242i	$-0.339957\pi$
$108$	−0.720507	+	1.86571i	−0.0693308	+	0.179528i
$109$		−	0.269146i		−	0.0257795i	−0.999917	−	0.0128897i	$-0.995897\pi$
$109$		−	0.269146i		−	0.0257795i	0.999917	−	0.0128897i	$-0.00410304\pi$
$110$	−3.66317	−	5.34150i	−0.349270	−	0.509292i
$111$	7.24325			0.687499
$112$	−5.13765	−	4.66369i	−0.485462	−	0.440677i
$113$			8.30424i			0.781198i	0.920561	+	0.390599i	$0.127732\pi$
$113$			8.30424i			0.781198i	−0.920561	+	0.390599i	$0.872268\pi$
$114$	3.40783	+	4.96918i	0.319173	+	0.465406i
$115$	−1.66124			−0.154911
$116$	−1.54079	+	3.98978i	−0.143059	+	0.370442i
$117$			1.41228i			0.130565i
$118$	11.5352	+	16.8202i	1.06190	+	1.54843i
$119$	−8.37045			−0.767317
$120$	2.37944	−	0.563632i	0.217213	−	0.0514523i
$121$	17.0631			1.55119
$122$	9.95172	+	14.5112i	0.900986	+	1.31378i
$123$			0.306352i			0.0276229i
$124$	3.98042	−	10.3070i	0.357452	−	0.925600i
$125$		−	7.99922i		−	0.715472i
$126$	2.02315	−	1.38746i	0.180236	−	0.123605i
$127$			5.90821i			0.524269i	0.965031	+	0.262135i	$0.0844265\pi$
$127$			5.90821i			0.524269i	−0.965031	+	0.262135i	$0.915574\pi$
$128$	−5.46862	+	9.90425i	−0.483362	+	0.875421i
$129$	1.13429			0.0998683
$130$	1.42402	−	0.976585i	0.124895	−	0.0856522i
$131$			6.08889i			0.531989i	0.963975	+	0.265994i	$0.0857003\pi$
$131$			6.08889i			0.531989i	−0.963975	+	0.265994i	$0.914300\pi$
$132$	−3.81686	+	9.88352i	−0.332215	+	0.860250i
$133$		−	7.39081i		−	0.640864i
$134$	7.82308	−	8.53226i	0.675811	−	0.737075i
$135$			0.864540i			0.0744078i
$136$	3.14587	+	13.2807i	0.269757	+	1.13881i
$137$		−	15.3658i		−	1.31279i	−0.754418	−	0.656394i	$-0.772081\pi$
$137$		−	15.3658i		−	1.31279i	0.754418	−	0.656394i	$-0.227919\pi$
$138$	1.53692	+	2.24107i	0.130831	+	0.190773i
$139$	−5.86116			−0.497137			−0.248569	−	0.968614i	$-0.579960\pi$
$139$	−5.86116			−0.497137			−0.248569	+	0.968614i	$0.579960\pi$
$140$	−2.79799	−	1.08054i	−0.236474	−	0.0913224i
$141$			11.9232i			1.00412i
$142$	6.50944	+	9.49182i	0.546260	+	0.796536i
$143$			7.48150i			0.625635i
$144$	−2.96174	−	2.68851i	−0.246812	−	0.224043i
$145$			1.84880i			0.153535i
$146$	15.0191	−	10.3000i	1.24299	−	0.852434i
$147$	3.99091			0.329165
$148$	−5.21881	+	13.5138i	−0.428984	+	1.11083i
$149$	−6.79582			−0.556735			−0.278368	−	0.960475i	$-0.589793\pi$
$149$	−6.79582			−0.556735			−0.278368	+	0.960475i	$0.589793\pi$
$150$	−4.95977	+	3.40138i	−0.404963	+	0.277722i
$151$			7.39573i			0.601856i	0.953647	+	0.300928i	$0.0972964\pi$
$151$			7.39573i			0.601856i	−0.953647	+	0.300928i	$0.902704\pi$
$152$	−11.7264	+	2.77770i	−0.951137	+	0.225301i
$153$	−4.82537			−0.390108
$154$	10.7175	−	7.35004i	0.863645	−	0.592283i
$155$		−	4.77612i		−	0.383627i
$156$	−2.63490	−	1.01756i	−0.210961	−	0.0814699i
$157$	−0.0538536			−0.00429799			−0.00214899	−	0.999998i	$-0.500684\pi$
$157$	−0.0538536			−0.00429799			−0.00214899	+	0.999998i	$0.500684\pi$
$158$	9.56378	−	6.55879i	0.760853	−	0.521789i
$159$			8.91687i			0.707154i
$160$	−0.662834	+	4.84545i	−0.0524016	+	0.383067i
$161$		−	3.33322i		−	0.262694i
$162$	1.16630	−	0.799841i	0.0916331	−	0.0628415i
$163$			12.2858i			0.962295i	0.876640	+	0.481148i	$0.159780\pi$
$163$			12.2858i			0.962295i	−0.876640	+	0.481148i	$0.840220\pi$
$164$	−0.571564	−	0.220729i	−0.0446317	−	0.0172361i
$165$			4.57987i			0.356542i
$166$	−0.312629	−	0.455864i	−0.0242647	−	0.0353819i
$167$			4.12074i			0.318873i	0.987208	+	0.159436i	$0.0509677\pi$
$167$			4.12074i			0.318873i	−0.987208	+	0.159436i	$0.949032\pi$
$168$	1.13091	+	4.77428i	0.0872516	+	0.368344i
$169$	11.0055			0.846574
$170$	3.33672	+	4.86548i	0.255915	+	0.373166i
$171$		−	4.26064i		−	0.325819i
$172$	−0.817261	+	2.11625i	−0.0623156	+	0.161362i
$173$	−7.30908			−0.555699			−0.277850	−	0.960625i	$-0.589622\pi$
$173$	−7.30908			−0.555699			−0.277850	+	0.960625i	$0.589622\pi$
$174$	2.49411	−	1.71044i	0.189078	−	0.129668i
$175$	7.37682			0.557635
$176$	−15.6897	−	14.2423i	−1.18266	−	1.07355i
$177$		−	14.4219i		−	1.08401i
$178$	−6.68621	+	4.58537i	−0.501153	+	0.343688i
$179$	−0.730284			−0.0545840			−0.0272920	−	0.999628i	$-0.508688\pi$
$179$	−0.730284			−0.0545840			−0.0272920	+	0.999628i	$0.508688\pi$
$180$	−1.61298	−	0.622907i	−0.120224	−	0.0464288i
$181$	−12.7461			−0.947412			−0.473706	−	0.880683i	$-0.657084\pi$
$181$	−12.7461			−0.947412			−0.473706	+	0.880683i	$0.657084\pi$
$182$	1.95949	+	2.85725i	0.145247	+	0.211794i
$183$		−	12.4421i		−	0.919747i
$184$	−5.28855	+	1.25273i	−0.389877	+	0.0923523i
$185$			6.26208i			0.460397i
$186$	−6.44318	+	4.41870i	−0.472437	+	0.323995i
$187$	−25.5622			−1.86930
$188$	−22.2452	−	8.59076i	−1.62240	−	0.626546i
$189$	−1.73467			−0.126179
$190$	−4.29605	+	2.94621i	−0.311668	+	0.213740i
$191$	22.8704			1.65484			0.827420	−	0.561583i	$-0.189808\pi$
$191$	22.8704			1.65484			0.827420	+	0.561583i	$0.189808\pi$
$192$	7.14994	−	3.58865i	0.516002	−	0.258988i
$193$	17.6675			1.27173			0.635866	−	0.771800i	$-0.280643\pi$
$193$	17.6675			1.27173			0.635866	+	0.771800i	$0.280643\pi$
$194$	11.6244	+	16.9502i	0.834582	+	1.21696i
$195$	−1.22097			−0.0874357
$196$	−2.87548	+	7.44587i	−0.205391	+	0.531848i
$197$		−	8.79635i		−	0.626714i	−0.949635	−	0.313357i	$-0.898546\pi$
$197$		−	8.79635i		−	0.626714i	0.949635	−	0.313357i	$-0.101454\pi$
$198$	6.17843	−	4.23713i	0.439082	−	0.301120i
$199$			12.5962i			0.892921i	0.894803	+	0.446461i	$0.147316\pi$
$199$			12.5962i			0.892921i	−0.894803	+	0.446461i	$0.852684\pi$
$200$	−2.77244	−	11.7042i	−0.196041	−	0.827612i
$201$	−7.97425	+	1.84697i	−0.562460	+	0.130275i
$202$	11.1968	+	16.3268i	0.787804	+	1.14875i
$203$	−3.70956			−0.260360
$204$	3.47672	−	9.00274i	0.243419	−	0.630318i
$205$	−0.264854			−0.0184982
$206$	10.6181	+	15.4829i	0.739797	+	1.07874i
$207$		−	1.92153i		−	0.133555i
$208$	3.79693	−	4.18280i	0.263270	−	0.290025i
$209$		−	22.5706i		−	1.56124i
$210$	1.19952	+	1.74909i	0.0827746	+	0.120699i
$211$			22.3042i			1.53549i	0.640757	+	0.767744i	$0.278621\pi$
$211$			22.3042i			1.53549i	−0.640757	+	0.767744i	$0.721379\pi$
$212$	−16.6363	−	6.42467i	−1.14259	−	0.441248i
$213$		−	8.13841i		−	0.557635i
$214$	−14.4994	−	21.1425i	−0.991158	−	1.44527i
$215$			0.980636i			0.0668788i
$216$	0.651944	+	2.75227i	0.0443592	+	0.187268i
$217$	9.58314			0.650546
$218$	−0.215274	−	0.313904i	−0.0145802	−	0.0212603i
$219$	−12.8776			−0.870184
$220$	−8.54470	−	3.29983i	−0.576084	−	0.222474i
$221$		−	6.81478i		−	0.458412i
$222$	8.44779	−	5.79345i	0.566979	−	0.388831i
$223$			7.97926i			0.534331i	0.963651	+	0.267165i	$0.0860870\pi$
$223$			7.97926i			0.534331i	−0.963651	+	0.267165i	$0.913913\pi$
$224$	−9.72225	−	1.32996i	−0.649595	−	0.0888614i
$225$	4.25257			0.283505
$226$	6.64208	+	9.68523i	0.441825	+	0.644252i
$227$		−	2.50636i		−	0.166353i	−0.996535	−	0.0831765i	$-0.973493\pi$
$227$		−	2.50636i		−	0.166353i	0.996535	−	0.0831765i	$-0.0265065\pi$
$228$	7.94910	+	3.06982i	0.526442	+	0.203304i
$229$		−	14.1223i		−	0.933226i	−0.884462	−	0.466613i	$-0.845474\pi$
$229$		−	14.1223i		−	0.933226i	0.884462	−	0.466613i	$-0.154526\pi$
$230$	−1.93750	+	1.32873i	−0.127755	+	0.0876136i
$231$	−9.18937			−0.604616
$232$	1.39417	+	5.88567i	0.0915317	+	0.386413i
$233$			19.5570i			1.28122i	0.767866	+	0.640610i	$0.221318\pi$
$233$			19.5570i			1.28122i	−0.767866	+	0.640610i	$0.778682\pi$
$234$	1.12960	+	1.64714i	0.0738443	+	0.107677i
$235$	−10.3081			−0.672426
$236$	26.9070	+	10.3911i	1.75150	+	0.676400i
$237$	−8.20011			−0.532654
$238$	−9.76244	+	6.69503i	−0.632805	+	0.433974i
$239$	2.10620			0.136239			0.0681193	−	0.997677i	$-0.478300\pi$
$239$	2.10620			0.136239			0.0681193	+	0.997677i	$0.478300\pi$
$240$	2.32433	−	2.56054i	0.150035	−	0.165282i
$241$	6.84337			0.440821			0.220410	−	0.975407i	$-0.429260\pi$
$241$	6.84337			0.440821			0.220410	+	0.975407i	$0.429260\pi$
$242$	19.9007	−	13.6478i	1.27927	−	0.877313i
$243$	−1.00000			−0.0641500
$244$	23.2134	+	8.96463i	1.48608	+	0.573902i
$245$			3.45030i			0.220432i
$246$	0.245033	+	0.357299i	0.0156228	+	0.0227805i
$247$	6.01721			0.382866
$248$	−3.60164	−	15.2048i	−0.228705	−	0.965506i
$249$			0.390864i			0.0247700i
$250$	−6.39811	−	9.32948i	−0.404652	−	0.590048i
$251$	−23.8453			−1.50510			−0.752551	−	0.658534i	$-0.771177\pi$
$251$	−23.8453			−1.50510			−0.752551	+	0.658534i	$0.771177\pi$
$252$	1.24984	−	3.23639i	0.0787328	−	0.203874i
$253$		−	10.1792i		−	0.639961i
$254$	4.72564	+	6.89075i	0.296513	+	0.432364i
$255$		−	4.17173i		−	0.261244i
$256$	1.54379	+	15.9253i	0.0964870	+	0.995334i
$257$	9.09968			0.567623			0.283811	−	0.958880i	$-0.408401\pi$
$257$	9.09968			0.567623			0.283811	+	0.958880i	$0.408401\pi$
$258$	1.32292	−	0.907249i	0.0823612	−	0.0564829i
$259$	−12.5647			−0.780731
$260$	0.879720	−	2.27798i	0.0545579	−	0.141274i
$261$	−2.13848			−0.132369
$262$	4.87015	+	7.10147i	0.300879	+	0.438730i
$263$		−	27.3721i		−	1.68783i	−0.536474	−	0.843917i	$-0.680244\pi$
$263$		−	27.3721i		−	1.68783i	0.536474	−	0.843917i	$-0.319756\pi$
$264$	3.45365	+	14.5800i	0.212558	+	0.897339i
$265$	−7.70900			−0.473560
$266$	−5.91148	−	8.61989i	−0.362456	−	0.528520i
$267$	5.73285			0.350845
$268$	2.29959	−	16.2084i	0.140470	−	0.990085i
$269$	6.06672			0.369894			0.184947	−	0.982748i	$-0.440789\pi$
$269$	6.06672			0.369894			0.184947	+	0.982748i	$0.440789\pi$
$270$	0.691495	+	1.00831i	0.0420831	+	0.0613639i
$271$	0.0167864			0.00101970			0.000509850	−	1.00000i	$-0.499838\pi$
$271$	0.0167864			0.00101970			0.000509850		1.00000i	$0.499838\pi$
$272$	14.2915	+	12.9731i	0.866549	+	0.786609i
$273$		−	2.44984i		−	0.148271i
$274$	−12.2902	−	17.9211i	−0.742478	−	1.08265i
$275$	22.5278			1.35848
$276$	3.58501	+	1.38447i	0.215792	+	0.0833355i
$277$	2.17332			0.130582			0.0652911	−	0.997866i	$-0.479202\pi$
$277$	2.17332			0.130582			0.0652911	+	0.997866i	$0.479202\pi$
$278$	−6.83587	+	4.68800i	−0.409988	+	0.281168i
$279$	5.52447			0.330741
$280$	−4.12756	+	0.977717i	−0.246669	+	0.0584298i
$281$		−	12.9816i		−	0.774419i	−0.921992	−	0.387210i	$-0.873439\pi$
$281$		−	12.9816i		−	0.774419i	0.921992	−	0.387210i	$-0.126561\pi$
$282$	9.53668	+	13.9060i	0.567901	+	0.828092i
$283$		−	21.6115i		−	1.28467i	−0.766423	−	0.642336i	$-0.777965\pi$
$283$		−	21.6115i		−	1.28467i	0.766423	−	0.642336i	$-0.222035\pi$
$284$	15.1839	+	5.86378i	0.900999	+	0.347952i
$285$	3.68349			0.218191
$286$	5.98402	+	8.72567i	0.353842	+	0.515960i
$287$		−	0.531421i		−	0.0313688i
$288$	−5.60466	−	0.766689i	−0.330258	−	0.0451776i
$289$	6.28423			0.369661
$290$	1.47875	+	2.15626i	0.0868351	+	0.126620i
$291$		−	14.5334i		−	0.851961i
$292$	9.27837	−	24.0258i	0.542976	−	1.40600i
$293$	−20.3556			−1.18919			−0.594594	−	0.804026i	$-0.702687\pi$
$293$	−20.3556			−1.18919			−0.594594	+	0.804026i	$0.702687\pi$
$294$	4.65459	−	3.19209i	0.271461	−	0.186167i
$295$	12.4683			0.725932
$296$	4.72219	+	19.9353i	0.274472	+	1.15872i
$297$	−5.29746			−0.307390
$298$	−7.92596	+	5.43558i	−0.459139	+	0.314875i
$299$	2.71373			0.156939
$300$	−3.06401	+	7.93406i	−0.176901	+	0.458073i
$301$	−1.96762			−0.113411
$302$	5.91541	+	8.62564i	0.340394	+	0.496350i
$303$		−	13.9988i		−	0.804209i
$304$	−11.4548	+	12.6189i	−0.656976	+	0.723743i
$305$	10.7567			0.615927
$306$	−5.62783	+	3.85953i	−0.321722	+	0.220635i
$307$		−	19.9608i		−	1.13922i	−0.821914	−	0.569612i	$-0.807093\pi$
$307$		−	19.9608i		−	1.13922i	0.821914	−	0.569612i	$-0.192907\pi$
$308$	6.62101	−	17.1447i	0.377267	−	0.976909i
$309$		−	13.2752i		−	0.755202i
$310$	−3.82014	−	5.57039i	−0.216969	−	0.316377i
$311$	−5.81890			−0.329960			−0.164980	−	0.986297i	$-0.552756\pi$
$311$	−5.81890			−0.329960			−0.164980	+	0.986297i	$0.552756\pi$
$312$	−3.88697	+	0.920728i	−0.220056	+	0.0521260i
$313$			6.55868i			0.370719i	0.982671	+	0.185359i	$0.0593449\pi$
$313$			6.55868i			0.370719i	−0.982671	+	0.185359i	$0.940655\pi$
$314$	−0.0628094	+	0.0430744i	−0.00354454	+	0.00243083i
$315$		−	1.49969i		−	0.0844982i
$316$	5.90824	−	15.2990i	0.332364	−	0.860637i
$317$	−31.6370			−1.77691			−0.888455	−	0.458963i	$-0.848221\pi$
$317$	−31.6370			−1.77691			−0.888455	+	0.458963i	$0.848221\pi$
$318$	7.13209	+	10.3997i	0.399948	+	0.583189i
$319$	−11.3285			−0.634275
$320$	3.10253	+	6.18141i	0.173437	+	0.345551i
$321$			18.1278i			1.01180i
$322$	−2.66605	−	3.88753i	−0.148573	−	0.216644i
$323$			20.5592i			1.14394i
$324$	0.720507	−	1.86571i	0.0400282	−	0.103650i
$325$			6.00582i			0.333143i
$326$	9.82666	+	14.3289i	0.544248	+	0.793603i
$327$			0.269146i			0.0148838i
$328$	−0.843163	+	0.199725i	−0.0465559	+	0.0110280i
$329$		−	20.6829i		−	1.14028i
$330$	3.66317	+	5.34150i	0.201651	+	0.294040i
$331$	−10.0039			−0.549863			−0.274932	−	0.961464i	$-0.588655\pi$
$331$	−10.0039			−0.549863			−0.274932	+	0.961464i	$0.588655\pi$
$332$	−0.729238	−	0.281620i	−0.0400221	−	0.0154559i
$333$	−7.24325			−0.396928
$334$	3.29594	+	4.80602i	0.180346	+	0.262974i
$335$	−1.59678	−	6.89406i	−0.0872415	−	0.376663i
$336$	5.13765	+	4.66369i	0.280282	+	0.254425i
$337$		−	6.57449i		−	0.358135i	−0.983837	−	0.179068i	$-0.942692\pi$
$337$		−	6.57449i		−	0.358135i	0.983837	−	0.179068i	$-0.0573081\pi$
$338$	12.8357	−	8.80263i	0.698168	−	0.478800i
$339$		−	8.30424i		−	0.451025i
$340$	7.78323	+	3.00576i	0.422105	+	0.163010i
$341$	29.2657			1.58482
$342$	−3.40783	−	4.96918i	−0.184274	−	0.268702i
$343$	−19.0656			−1.02945
$344$	0.739491	+	3.12186i	0.0398707	+	0.168319i
$345$	1.66124			0.0894379
$346$	−8.52458	+	5.84611i	−0.458284	+	0.314289i
$347$	−16.0583			−0.862053			−0.431026	−	0.902339i	$-0.641848\pi$
$347$	−16.0583			−0.862053			−0.431026	+	0.902339i	$0.641848\pi$
$348$	1.54079	−	3.98978i	0.0825950	−	0.213875i
$349$	−7.85175			−0.420294			−0.210147	−	0.977670i	$-0.567394\pi$
$349$	−7.85175			−0.420294			−0.210147	+	0.977670i	$0.567394\pi$
$350$	8.60358	−	5.90029i	0.459881	−	0.315384i
$351$		−	1.41228i		−	0.0753819i
$352$	−29.6905	−	4.06151i	−1.58251	−	0.216479i
$353$			8.89900i			0.473646i	0.971553	+	0.236823i	$0.0761061\pi$
$353$			8.89900i			0.473646i	−0.971553	+	0.236823i	$0.923894\pi$
$354$	−11.5352	−	16.8202i	−0.613089	−	0.893984i
$355$	7.03598			0.373431
$356$	−4.13056	+	10.6958i	−0.218919	+	0.566877i
$357$	8.37045			0.443011
$358$	−0.851729	+	0.584111i	−0.0450153	+	0.0308712i
$359$		−	14.9369i		−	0.788339i	−0.919038	−	0.394169i	$-0.871032\pi$
$359$		−	14.9369i		−	0.788339i	0.919038	−	0.394169i	$-0.128968\pi$
$360$	−2.37944	+	0.563632i	−0.125408	+	0.0297060i
$361$	0.846986			0.0445782
$362$	−14.8658	+	10.1949i	−0.781329	+	0.535831i
$363$	−17.0631			−0.895581
$364$	4.57070	+	1.76513i	0.239570	+	0.0925180i
$365$		−	11.1332i		−	0.582736i
$366$	−9.95172	−	14.5112i	−0.520185	−	0.758514i
$367$	−26.5010			−1.38334			−0.691672	−	0.722212i	$-0.743125\pi$
$367$	−26.5010			−1.38334			−0.691672	+	0.722212i	$0.743125\pi$
$368$	−5.16605	+	5.69106i	−0.269299	+	0.296667i
$369$		−	0.306352i		−	0.0159481i
$370$	5.00867	+	7.30346i	0.260388	+	0.379689i
$371$		−	15.4679i		−	0.803051i
$372$	−3.98042	+	10.3070i	−0.206375	+	0.534395i
$373$			20.8471i			1.07942i	0.841850	+	0.539711i	$0.181467\pi$
$373$			20.8471i			1.07942i	−0.841850	+	0.539711i	$0.818533\pi$
$374$	−29.8132	+	20.4457i	−1.54160	+	1.05722i
$375$			7.99922i			0.413078i
$376$	−32.8159	+	7.77327i	−1.69235	+	0.400876i
$377$		−	3.02013i		−	0.155545i
$378$	−2.02315	+	1.38746i	−0.104059	+	0.0713634i
$379$	26.9070			1.38212			0.691059	−	0.722799i	$-0.257145\pi$
$379$	26.9070			1.38212			0.691059	+	0.722799i	$0.257145\pi$
$380$	−2.65398	+	6.87232i	−0.136146	+	0.352543i
$381$		−	5.90821i		−	0.302687i
$382$	26.6737	−	18.2927i	1.36474	−	0.935934i
$383$	10.2607			0.524299			0.262149	−	0.965027i	$-0.415569\pi$
$383$	10.2607			0.524299			0.262149	+	0.965027i	$0.415569\pi$
$384$	5.46862	−	9.90425i	0.279069	−	0.505424i
$385$		−	7.94458i		−	0.404893i
$386$	20.6055	−	14.1312i	1.04879	−	0.719258i
$387$	−1.13429			−0.0576590
$388$	27.1150	+	10.4714i	1.37656	+	0.531604i
$389$	6.96170			0.352972			0.176486	−	0.984303i	$-0.443527\pi$
$389$	6.96170			0.352972			0.176486	+	0.984303i	$0.443527\pi$
$390$	−1.42402	+	0.976585i	−0.0721080	+	0.0494513i
$391$			9.27208i			0.468909i
$392$	2.60185	+	10.9840i	0.131413	+	0.554778i
$393$		−	6.08889i		−	0.307144i
$394$	−7.03568	−	10.2592i	−0.354453	−	0.516850i
$395$		−	7.08932i		−	0.356703i
$396$	3.81686	−	9.88352i	0.191804	−	0.496666i
$397$	6.12220			0.307265			0.153632	−	0.988128i	$-0.450903\pi$
$397$	6.12220			0.307265			0.153632	+	0.988128i	$0.450903\pi$
$398$	10.0750	+	14.6909i	0.505013	+	0.736391i
$399$			7.39081i			0.370003i
$400$	−12.5950	−	11.4331i	−0.629750	−	0.571655i
$401$			27.0636i			1.35149i	0.737134	+	0.675747i	$0.236179\pi$
$401$			27.0636i			1.35149i	−0.737134	+	0.675747i	$0.763821\pi$
$402$	−7.82308	+	8.53226i	−0.390180	+	0.425550i
$403$			7.80209i			0.388650i
$404$	26.1176	+	10.0862i	1.29940	+	0.501808i
$405$		−	0.864540i		−	0.0429593i
$406$	−4.32646	+	2.96706i	−0.214719	+	0.147253i
$407$	−38.3708			−1.90197
$408$	−3.14587	−	13.2807i	−0.155744	−	0.657493i
$409$		−	20.7912i		−	1.02806i	−0.857773	−	0.514028i	$-0.828153\pi$
$409$		−	20.7912i		−	1.02806i	0.857773	−	0.514028i	$-0.171847\pi$
$410$	−0.308899	+	0.211841i	−0.0152554	+	0.0104621i
$411$			15.3658i			0.757939i
$412$	24.7677	+	9.56490i	1.22022	+	0.471229i
$413$			25.0172i			1.23102i
$414$	−1.53692	−	2.24107i	−0.0755353	−	0.110143i
$415$	−0.337917			−0.0165877
$416$	1.08278	−	7.91535i	0.0530877	−	0.388082i
$417$	5.86116			0.287022
$418$	−18.0529	−	26.3240i	−0.882995	−	1.28755i
$419$		−	14.1385i		−	0.690710i	−0.938472	−	0.345355i	$-0.887759\pi$
$419$		−	14.1385i		−	0.690710i	0.938472	−	0.345355i	$-0.112241\pi$
$420$	2.79799	+	1.08054i	0.136528	+	0.0527250i
$421$	−17.8438			−0.869652			−0.434826	−	0.900515i	$-0.643190\pi$
$421$	−17.8438			−0.869652			−0.434826	+	0.900515i	$0.643190\pi$
$422$	17.8399	+	26.0134i	0.868431	+	1.26631i
$423$		−	11.9232i		−	0.579726i
$424$	−24.5416	+	5.81331i	−1.19185	+	0.282319i
$425$	−20.5202			−0.995378
$426$	−6.50944	−	9.49182i	−0.315383	−	0.459880i
$427$			21.5830i			1.04447i
$428$	−33.8213	−	13.0612i	−1.63481	−	0.631339i
$429$		−	7.48150i		−	0.361210i
$430$	0.784353	+	1.14371i	0.0378249	+	0.0551548i
$431$		−	8.97477i		−	0.432300i	−0.976360	−	0.216150i	$-0.930650\pi$
$431$		−	8.97477i		−	0.432300i	0.976360	−	0.216150i	$-0.0693500\pi$
$432$	2.96174	+	2.68851i	0.142497	+	0.129351i
$433$			33.9473i			1.63140i	0.578473	+	0.815701i	$0.303649\pi$
$433$			33.9473i			1.63140i	−0.578473	+	0.815701i	$0.696351\pi$
$434$	11.1768	−	7.66499i	0.536504	−	0.367931i
$435$		−	1.84880i		−	0.0886433i
$436$	−0.502147	−	0.193921i	−0.0240485	−	0.00928715i
$437$	−8.18692			−0.391633
$438$	−15.0191	+	10.3000i	−0.717639	+	0.492153i
$439$		−	5.66649i		−	0.270447i	−0.990815	−	0.135223i	$-0.956825\pi$
$439$		−	5.66649i		−	0.270447i	0.990815	−	0.135223i	$-0.0431752\pi$
$440$	−12.6050	+	2.98582i	−0.600921	+	0.142343i
$441$	−3.99091			−0.190043
$442$	−5.45074	−	7.94807i	−0.259265	−	0.378051i
$443$	1.87188			0.0889358			0.0444679	−	0.999011i	$-0.485841\pi$
$443$	1.87188			0.0889358			0.0444679	+	0.999011i	$0.485841\pi$
$444$	5.21881	−	13.5138i	0.247674	−	0.641336i
$445$			4.95628i			0.234950i
$446$	6.38215	+	9.30621i	0.302203	+	0.440662i
$447$	6.79582			0.321431
$448$	−12.4028	+	6.22513i	−0.585977	+	0.294110i
$449$	4.44786			0.209907			0.104954	−	0.994477i	$-0.466531\pi$
$449$	4.44786			0.209907			0.104954	+	0.994477i	$0.466531\pi$
$450$	4.95977	−	3.40138i	0.233806	−	0.160343i
$451$		−	1.62289i		−	0.0764189i
$452$	15.4933	+	5.98327i	0.728744	+	0.281429i
$453$		−	7.39573i		−	0.347482i
$454$	−2.00469	−	2.92317i	−0.0940848	−	0.137191i
$455$	2.11799			0.0992929
$456$	11.7264	−	2.77770i	0.549139	−	0.130078i
$457$	−2.77148			−0.129644			−0.0648221	−	0.997897i	$-0.520648\pi$
$457$	−2.77148			−0.129644			−0.0648221	+	0.997897i	$0.520648\pi$
$458$	−11.2956	−	16.4708i	−0.527808	−	0.769629i
$459$	4.82537			0.225229
$460$	−1.19693	+	3.09938i	−0.0558073	+	0.144509i
$461$	−13.1624			−0.613033			−0.306517	−	0.951865i	$-0.599163\pi$
$461$	−13.1624			−0.613033			−0.306517	+	0.951865i	$0.599163\pi$
$462$	−10.7175	+	7.35004i	−0.498626	+	0.341955i
$463$	−39.7716			−1.84834			−0.924170	−	0.381980i	$-0.875242\pi$
$463$	−39.7716			−1.84834			−0.924170	+	0.381980i	$0.875242\pi$
$464$	6.33362	+	5.74933i	0.294031	+	0.266906i
$465$			4.77612i			0.221487i
$466$	15.6425	+	22.8093i	0.724624	+	1.05662i
$467$			7.56735i			0.350175i	0.984553	+	0.175088i	$0.0560209\pi$
$467$			7.56735i			0.350175i	−0.984553	+	0.175088i	$0.943979\pi$
$468$	2.63490	+	1.01756i	0.121798	+	0.0470366i
$469$	13.8327	−	3.20389i	0.638736	−	0.147942i
$470$	−12.0223	+	8.24484i	−0.554549	+	0.380306i
$471$	0.0538536			0.00248144
$472$	39.6928	−	9.40225i	1.82701	−	0.432774i
$473$	−6.00884			−0.276287
$474$	−9.56378	+	6.55879i	−0.439279	+	0.301255i
$475$		−	18.1187i		−	0.831341i
$476$	−6.03097	+	15.6168i	−0.276429	+	0.715795i
$477$		−	8.91687i		−	0.408276i
$478$	2.45646	−	1.68462i	0.112356	−	0.0770529i
$479$			2.91534i			0.133205i	0.997780	+	0.0666027i	$0.0212160\pi$
$479$			2.91534i			0.133205i	−0.997780	+	0.0666027i	$0.978784\pi$
$480$	0.662834	−	4.84545i	0.0302541	−	0.221164i
$481$		−	10.2295i		−	0.466425i
$482$	7.98142	−	5.47361i	0.363544	−	0.249316i
$483$			3.33322i			0.151667i
$484$	12.2941	−	31.8348i	0.558823	−	1.44704i
$485$	12.5647			0.570532
$486$	−1.16630	+	0.799841i	−0.0529044	+	0.0362815i
$487$	39.0862			1.77116			0.885582	−	0.464483i	$-0.153760\pi$
$487$	39.0862			1.77116			0.885582	+	0.464483i	$0.153760\pi$
$488$	34.2440	−	8.11156i	1.55015	−	0.367193i
$489$		−	12.2858i		−	0.555581i
$490$	2.75969	+	4.02408i	0.124670	+	0.181790i
$491$			9.17446i			0.414037i	0.978337	+	0.207019i	$0.0663761\pi$
$491$			9.17446i			0.414037i	−0.978337	+	0.207019i	$0.933624\pi$
$492$	0.571564	+	0.220729i	0.0257681	+	0.00995124i
$493$	10.3190			0.464743
$494$	7.01787	−	4.81281i	0.315749	−	0.216539i
$495$		−	4.57987i		−	0.205850i
$496$	−16.3620	−	14.8526i	−0.734677	−	0.666901i
$497$			14.1175i			0.633256i
$498$	0.312629	+	0.455864i	0.0140092	+	0.0204278i
$499$	22.8786			1.02419			0.512093	−	0.858930i	$-0.328870\pi$
$499$	22.8786			1.02419			0.512093	+	0.858930i	$0.328870\pi$
$500$	−14.9242	−	5.76350i	−0.667431	−	0.257751i
$501$		−	4.12074i		−	0.184101i
$502$	−27.8108	+	19.0725i	−1.24126	+	0.851246i
$503$	1.07299			0.0478422			0.0239211	−	0.999714i	$-0.492385\pi$
$503$	1.07299			0.0478422			0.0239211	+	0.999714i	$0.492385\pi$
$504$	−1.13091	−	4.77428i	−0.0503747	−	0.212663i
$505$	12.1025			0.538554
$506$	−8.14175	−	11.8720i	−0.361945	−	0.527775i
$507$	−11.0055			−0.488770
$508$	11.0230	+	4.25691i	0.489067	+	0.188870i
$509$	−40.6639			−1.80239			−0.901197	−	0.433410i	$-0.857310\pi$
$509$	−40.6639			−1.80239			−0.901197	+	0.433410i	$0.857310\pi$
$510$	−3.33672	−	4.86548i	−0.147753	−	0.215447i
$511$	22.3383			0.988190
$512$	14.5383	+	17.3389i	0.642507	+	0.766280i
$513$			4.26064i			0.188112i
$514$	10.6130	−	7.27830i	0.468117	−	0.321032i
$515$	11.4770			0.505736
$516$	0.817261	−	2.11625i	0.0359779	−	0.0931626i
$517$		−	63.1628i		−	2.77790i
$518$	−14.6542	+	10.0497i	−0.643867	+	0.441560i
$519$	7.30908			0.320833
$520$	−0.796006	−	3.36044i	−0.0349072	−	0.147365i
$521$		−	3.99748i		−	0.175133i	−0.996159	−	0.0875663i	$-0.972091\pi$
$521$		−	3.99748i		−	0.175133i	0.996159	−	0.0875663i	$-0.0279090\pi$
$522$	−2.49411	+	1.71044i	−0.109164	+	0.0748641i
$523$		−	0.0484445i		−	0.00211833i	−0.999999	−	0.00105916i	$-0.999663\pi$
$523$		−	0.0484445i		−	0.00211833i	0.999999	−	0.00105916i	$-0.000337143\pi$
$524$	11.3601	+	4.38709i	0.496268	+	0.191651i
$525$	−7.37682			−0.321951
$526$	−21.8933	−	31.9240i	−0.954594	−	1.39195i
$527$	−26.6576			−1.16122
$528$	15.6897	+	14.2423i	0.682807	+	0.619817i
$529$	19.3077			0.839467
$530$	−8.99100	+	6.16598i	−0.390544	+	0.267833i
$531$			14.4219i			0.625856i
$532$	−13.7891	−	5.32513i	−0.597833	−	0.230874i
$533$	0.432656			0.0187404
$534$	6.68621	−	4.58537i	0.289341	−	0.198428i
$535$	−15.6722			−0.677570
$536$	−10.2821	−	20.7431i	−0.444120	−	0.895967i
$537$	0.730284			0.0315141
$538$	7.07561	−	4.85241i	0.305051	−	0.209202i
$539$	−21.1417			−0.910637
$540$	1.61298	+	0.622907i	0.0694116	+	0.0268057i
$541$		−	1.19504i		−	0.0513788i	−0.999670	−	0.0256894i	$-0.991822\pi$
$541$		−	1.19504i		−	0.0513788i	0.999670	−	0.0256894i	$-0.00817809\pi$
$542$	0.0195779	−	0.0134264i	0.000840945	−	0.000576715i
$543$	12.7461			0.546988
$544$	27.0446	+	3.69956i	1.15953	+	0.158617i
$545$	−0.232687			−0.00996722
$546$	−1.95949	−	2.85725i	−0.0838583	−	0.122279i
$547$	−8.81373			−0.376848			−0.188424	−	0.982088i	$-0.560338\pi$
$547$	−8.81373			−0.376848			−0.188424	+	0.982088i	$0.560338\pi$
$548$	−28.6681	−	11.0712i	−1.22464	−	0.472937i
$549$			12.4421i			0.531016i
$550$	26.2742	−	18.0187i	1.12034	−	0.768320i
$551$			9.11128i			0.388154i
$552$	5.28855	−	1.25273i	0.225096	−	0.0533196i
$553$	14.2245			0.604888
$554$	2.53474	−	1.73831i	0.107691	−	0.0738538i
$555$		−	6.26208i		−	0.265810i
$556$	−4.22301	+	10.9352i	−0.179096	+	0.463757i
$557$	−10.9826			−0.465349			−0.232675	−	0.972555i	$-0.574748\pi$
$557$	−10.9826			−0.465349			−0.232675	+	0.972555i	$0.574748\pi$
$558$	6.44318	−	4.41870i	0.272762	−	0.187058i
$559$		−	1.60193i		−	0.0677544i
$560$	−4.03195	+	4.44170i	−0.170381	+	0.187696i
$561$	25.5622			1.07924
$562$	−10.3833	−	15.1405i	−0.437991	−	0.638662i
$563$	38.0350			1.60298			0.801491	−	0.598006i	$-0.204040\pi$
$563$	38.0350			1.60298			0.801491	+	0.598006i	$0.204040\pi$
$564$	22.2452	+	8.59076i	0.936694	+	0.361736i
$565$	7.17935			0.302038
$566$	−17.2858	−	25.2055i	−0.726576	−	1.05947i
$567$	1.73467			0.0728494
$568$	22.3991	−	5.30579i	0.939844	−	0.222626i
$569$	25.6937			1.07714			0.538569	−	0.842582i	$-0.318965\pi$
$569$	25.6937			1.07714			0.538569	+	0.842582i	$0.318965\pi$
$570$	4.29605	−	2.94621i	0.179942	−	0.123403i
$571$			0.476282i			0.0199318i	0.999950	+	0.00996588i	$0.00317229\pi$
$571$			0.476282i			0.0199318i	−0.999950	+	0.00996588i	$0.996828\pi$
$572$	13.9583	+	5.39048i	0.583626	+	0.225387i
$573$	−22.8704			−0.955423
$574$	−0.425053	−	0.619796i	−0.0177414	−	0.0258698i
$575$		−	8.17142i		−	0.340772i
$576$	−7.14994	+	3.58865i	−0.297914	+	0.149527i
$577$		−	33.5594i		−	1.39710i	−0.715563	−	0.698549i	$-0.753830\pi$
$577$		−	33.5594i		−	1.39710i	0.715563	−	0.698549i	$-0.246170\pi$
$578$	7.32929	−	5.02639i	0.304858	−	0.209070i
$579$	−17.6675			−0.734235
$580$	3.44933	+	1.33208i	0.143225	+	0.0553114i
$581$		−	0.678021i		−	0.0281290i
$582$	−11.6244	−	16.9502i	−0.481846	−	0.702610i
$583$		−	47.2368i		−	1.95635i
$584$	−8.39545	−	35.4425i	−0.347406	−	1.46662i
$585$	1.22097			0.0504810
$586$	−23.7407	+	16.2813i	−0.980721	+	0.672573i
$587$	30.0349			1.23967			0.619837	−	0.784731i	$-0.287199\pi$
$587$	30.0349			1.23967			0.619837	+	0.784731i	$0.287199\pi$
$588$	2.87548	−	7.44587i	0.118583	−	0.307063i
$589$		−	23.5377i		−	0.969855i
$590$	14.5417	−	9.97265i	0.598674	−	0.410568i
$591$			8.79635i			0.361833i
$592$	21.4526	+	19.4736i	0.881697	+	0.800359i
$593$			24.2923i			0.997565i	0.866727	+	0.498783i	$0.166219\pi$
$593$			24.2923i			0.997565i	−0.866727	+	0.498783i	$0.833781\pi$
$594$	−6.17843	+	4.23713i	−0.253504	+	0.173852i
$595$			7.23659i			0.296671i
$596$	−4.89644	+	12.6790i	−0.200566	+	0.519353i
$597$		−	12.5962i		−	0.515528i
$598$	3.16502	−	2.17056i	0.129427	−	0.0887606i
$599$	−19.6921			−0.804599			−0.402300	−	0.915508i	$-0.631789\pi$
$599$	−19.6921			−0.804599			−0.402300	+	0.915508i	$0.631789\pi$
$600$	2.77244	+	11.7042i	0.113184	+	0.477822i
$601$	−38.9082			−1.58710			−0.793549	−	0.608506i	$-0.791769\pi$
$601$	−38.9082			−1.58710			−0.793549	+	0.608506i	$0.791769\pi$
$602$	−2.29483	+	1.57378i	−0.0935302	+	0.0641425i
$603$	7.97425	−	1.84697i	0.324737	−	0.0752145i
$604$	13.7983	+	5.32868i	0.561444	+	0.216821i
$605$		−	14.7517i		−	0.599744i
$606$	−11.1968	−	16.3268i	−0.454839	−	0.663229i
$607$		−	40.9177i		−	1.66080i	−0.557169	−	0.830399i	$-0.688112\pi$
$607$		−	40.9177i		−	1.66080i	0.557169	−	0.830399i	$-0.311888\pi$
$608$	−3.26658	+	23.8794i	−0.132477	+	0.968438i
$609$	3.70956			0.150319
$610$	12.5455	−	8.60366i	0.507954	−	0.348352i
$611$	16.8389			0.681230
$612$	−3.47672	+	9.00274i	−0.140538	+	0.363914i
$613$	−16.6415			−0.672143			−0.336072	−	0.941836i	$-0.609098\pi$
$613$	−16.6415			−0.672143			−0.336072	+	0.941836i	$0.609098\pi$
$614$	−15.9655	−	23.2803i	−0.644315	−	0.939516i
$615$	0.264854			0.0106799
$616$	−5.99096	−	25.2916i	−0.241382	−	1.01903i
$617$	22.4008			0.901823			0.450911	−	0.892569i	$-0.351099\pi$
$617$	22.4008			0.901823			0.450911	+	0.892569i	$0.351099\pi$
$618$	−10.6181	−	15.4829i	−0.427122	−	0.622813i
$619$			12.4972i			0.502307i	0.967947	+	0.251153i	$0.0808098\pi$
$619$			12.4972i			0.502307i	−0.967947	+	0.251153i	$0.919190\pi$
$620$	−8.91085	−	3.44123i	−0.357869	−	0.138203i
$621$			1.92153i			0.0771082i
$622$	−6.78658	+	4.65420i	−0.272117	+	0.186616i
$623$	−9.94462			−0.398423
$624$	−3.79693	+	4.18280i	−0.151999	+	0.167446i
$625$	14.3472			0.573888
$626$	5.24590	+	7.64938i	0.209668	+	0.305731i
$627$			22.5706i			0.901381i
$628$	−0.0388019	+	0.100475i	−0.00154837	+	0.00400940i
$629$	34.9514			1.39360
$630$	−1.19952	−	1.74909i	−0.0477899	−	0.0696855i
$631$	−24.8311			−0.988509			−0.494255	−	0.869317i	$-0.664559\pi$
$631$	−24.8311			−0.988509			−0.494255	+	0.869317i	$0.664559\pi$
$632$	−5.34601	−	22.5689i	−0.212653	−	0.897742i
$633$		−	22.3042i		−	0.886514i
$634$	−36.8982	+	25.3046i	−1.46541	+	1.00497i
$635$	5.10789			0.202700
$636$	16.6363	+	6.42467i	0.659672	+	0.254755i
$637$		−	5.63628i		−	0.223318i
$638$	−13.2124	+	9.06102i	−0.523085	+	0.358729i
$639$			8.13841i			0.321951i
$640$	8.56263	+	4.72784i	0.338468	+	0.186884i
$641$			41.9807i			1.65814i	0.559146	+	0.829069i	$0.311129\pi$
$641$			41.9807i			1.65814i	−0.559146	+	0.829069i	$0.688871\pi$
$642$	14.4994	+	21.1425i	0.572246	+	0.834427i
$643$		−	29.9711i		−	1.18194i	−0.806692	−	0.590972i	$-0.798744\pi$
$643$		−	29.9711i		−	1.18194i	0.806692	−	0.590972i	$-0.201256\pi$
$644$	−6.21881	−	2.40161i	−0.245056	−	0.0946366i
$645$		−	0.980636i		−	0.0386125i
$646$	16.4441	+	23.9781i	0.646983	+	0.943407i
$647$	−1.75809			−0.0691176			−0.0345588	−	0.999403i	$-0.511003\pi$
$647$	−1.75809			−0.0691176			−0.0345588	+	0.999403i	$0.511003\pi$
$648$	−0.651944	−	2.75227i	−0.0256108	−	0.108119i
$649$			76.3993i			2.99893i
$650$	4.80370	+	7.00458i	0.188417	+	0.274742i
$651$	−9.58314			−0.375593
$652$	22.9217	+	8.85198i	0.897681	+	0.346670i
$653$			44.5874i			1.74484i	0.488756	+	0.872420i	$0.337451\pi$
$653$			44.5874i			1.74484i	−0.488756	+	0.872420i	$0.662549\pi$
$654$	0.215274	+	0.313904i	0.00841787	+	0.0122746i
$655$	5.26409			0.205685
$656$	−0.823633	+	0.907336i	−0.0321575	+	0.0354255i
$657$	12.8776			0.502401
$658$	−16.5430	−	24.1224i	−0.644914	−	0.940390i
$659$			18.8246i			0.733301i	0.930359	+	0.366650i	$0.119495\pi$
$659$			18.8246i			0.733301i	−0.930359	+	0.366650i	$0.880505\pi$
$660$	8.54470	+	3.29983i	0.332602	+	0.128446i
$661$		−	12.7361i		−	0.495376i	−0.968840	−	0.247688i	$-0.920329\pi$
$661$		−	12.7361i		−	0.495376i	0.968840	−	0.247688i	$-0.0796708\pi$
$662$	−11.6675	+	8.00152i	−0.453471	+	0.310988i
$663$			6.81478i			0.264664i
$664$	−1.07576	+	0.254821i	−0.0417476	+	0.00988899i
$665$	−6.38965			−0.247780
$666$	−8.44779	+	5.79345i	−0.327345	+	0.224492i
$667$			4.10914i			0.159107i
$668$	7.68811	+	2.96903i	0.297462	+	0.114875i
$669$		−	7.97926i		−	0.308496i
$670$	−7.37648	−	6.76337i	−0.284978	−	0.261292i
$671$			65.9116i			2.54449i
$672$	9.72225	+	1.32996i	0.375044	+	0.0513041i
$673$		−	47.3870i		−	1.82664i	−0.407247	−	0.913318i	$-0.633511\pi$
$673$		−	47.3870i		−	1.82664i	0.407247	−	0.913318i	$-0.366489\pi$
$674$	−5.25855	−	7.66782i	−0.202552	−	0.295354i
$675$	−4.25257			−0.163682
$676$	7.92952	−	20.5330i	0.304981	−	0.789730i
$677$			46.0441i			1.76962i	0.465954	+	0.884809i	$0.345711\pi$
$677$			46.0441i			1.76962i	−0.465954	+	0.884809i	$0.654289\pi$
$678$	−6.64208	−	9.68523i	−0.255088	−	0.371959i
$679$			25.2106i			0.967495i
$680$	11.4817	−	2.71974i	0.440303	−	0.104297i
$681$			2.50636i			0.0960440i
$682$	34.1325	−	23.4079i	1.30700	−	0.896334i
$683$	38.9088			1.48880			0.744402	−	0.667732i	$-0.232735\pi$
$683$	38.9088			1.48880			0.744402	+	0.667732i	$0.232735\pi$
$684$	−7.94910	−	3.06982i	−0.303942	−	0.117377i
$685$	−13.2844			−0.507569
$686$	−22.2362	+	15.2495i	−0.848983	+	0.582228i
$687$			14.1223i			0.538798i
$688$	3.35946	+	3.04954i	0.128078	+	0.116263i
$689$	12.5931			0.479760
$690$	1.93750	−	1.32873i	0.0737593	−	0.0505837i
$691$		−	25.1098i		−	0.955222i	−0.878571	−	0.477611i	$-0.841503\pi$
$691$		−	25.1098i		−	0.955222i	0.878571	−	0.477611i	$-0.158497\pi$
$692$	−5.26625	+	13.6366i	−0.200193	+	0.518386i
$693$	9.18937			0.349075
$694$	−18.7287	+	12.8441i	−0.710933	+	0.487554i
$695$			5.06721i			0.192210i
$696$	−1.39417	−	5.88567i	−0.0528459	−	0.223096i
$697$			1.47827i			0.0559933i
$698$	−9.15749	+	6.28015i	−0.346616	+	0.237707i
$699$		−	19.5570i		−	0.739713i
$700$	5.31505	−	13.7630i	0.200890	−	0.520192i
$701$		−	6.51175i		−	0.245945i	−0.992410	−	0.122973i	$-0.960757\pi$
$701$		−	6.51175i		−	0.245945i	0.992410	−	0.122973i	$-0.0392427\pi$
$702$	−1.12960	−	1.64714i	−0.0426340	−	0.0621673i
$703$			30.8608i			1.16394i
$704$	−37.8765	+	19.0107i	−1.42753	+	0.716494i
$705$	10.3081			0.388225
$706$	7.11779	+	10.3789i	0.267882	+	0.390615i
$707$			24.2833i			0.913267i
$708$	−26.9070	−	10.3911i	−1.01123	−	0.390520i
$709$	−18.8407			−0.707579			−0.353790	−	0.935325i	$-0.615107\pi$
$709$	−18.8407			−0.707579			−0.353790	+	0.935325i	$0.615107\pi$
$710$	8.20606	−	5.62767i	0.307968	−	0.211203i
$711$	8.20011			0.307528
$712$	3.73750	+	15.7783i	0.140069	+	0.591318i
$713$		−	10.6154i		−	0.397550i
$714$	9.76244	−	6.69503i	0.365350	−	0.250555i
$715$	6.46806			0.241892
$716$	−0.526175	+	1.36250i	−0.0196641	+	0.0509189i
$717$	−2.10620			−0.0786574
$718$	−11.9471	−	17.4209i	−0.445863	−	0.650141i
$719$			38.2761i			1.42746i	0.700423	+	0.713728i	$0.252995\pi$
$719$			38.2761i			1.42746i	−0.700423	+	0.713728i	$0.747005\pi$
$720$	−2.32433	+	2.56054i	−0.0866226	+	0.0954258i
$721$			23.0282i			0.857615i
$722$	0.987839	−	0.677454i	0.0367636	−	0.0252122i
$723$	−6.84337			−0.254508
$724$	−9.18367	+	23.7806i	−0.341309	+	0.883797i
$725$	−9.09404			−0.337744
$726$	−19.9007	+	13.6478i	−0.738584	+	0.506517i
$727$	19.4592			0.721703			0.360851	−	0.932623i	$-0.382486\pi$
$727$	19.4592			0.721703			0.360851	+	0.932623i	$0.382486\pi$
$728$	6.74262	−	1.59716i	0.249898	−	0.0591948i
$729$	1.00000			0.0370370
$730$	−8.90477	−	12.9846i	−0.329580	−	0.480582i
$731$	5.47335			0.202439
$732$	−23.2134	−	8.96463i	−0.857990	−	0.331342i
$733$		−	21.9331i		−	0.810118i	−0.914291	−	0.405059i	$-0.867251\pi$
$733$		−	21.9331i		−	0.810118i	0.914291	−	0.405059i	$-0.132749\pi$
$734$	−30.9082	+	21.1966i	−1.14084	+	0.782382i
$735$		−	3.45030i		−	0.127266i
$736$	−1.47321	+	10.7695i	−0.0543034	+	0.396969i
$737$	42.2433	−	9.78427i	1.55605	−	0.360408i
$738$	−0.245033	−	0.357299i	−0.00901980	−	0.0131523i
$739$	9.41137			0.346203			0.173101	−	0.984904i	$-0.444621\pi$
$739$	9.41137			0.346203			0.173101	+	0.984904i	$0.444621\pi$
$740$	11.6832	+	4.51187i	0.429484	+	0.165860i
$741$	−6.01721			−0.221048
$742$	−12.3718	−	18.0402i	−0.454184	−	0.662275i
$743$		−	8.39736i		−	0.308069i	−0.988065	−	0.154035i	$-0.950773\pi$
$743$		−	8.39736i		−	0.308069i	0.988065	−	0.154035i	$-0.0492268\pi$
$744$	3.60164	+	15.2048i	0.132043	+	0.557435i
$745$			5.87526i			0.215253i
$746$	16.6744	+	24.3140i	0.610492	+	0.890197i
$747$		−	0.390864i		−	0.0143010i
$748$	−18.4178	+	47.6917i	−0.673421	+	1.74378i
$749$		−	31.4459i		−	1.14901i
$750$	6.39811	+	9.32948i	0.233626	+	0.340665i
$751$		−	29.6677i		−	1.08259i	−0.840833	−	0.541295i	$-0.817934\pi$
$751$		−	29.6677i		−	1.08259i	0.840833	−	0.541295i	$-0.182066\pi$
$752$	−32.0557	+	35.3134i	−1.16895	+	1.28775i
$753$	23.8453			0.868971
$754$	−2.41563	−	3.52238i	−0.0879720	−	0.128277i
$755$	6.39391			0.232698
$756$	−1.24984	+	3.23639i	−0.0454564	+	0.117707i
$757$			29.9328i			1.08793i	0.839109	+	0.543963i	$0.183077\pi$
$757$			29.9328i			1.08793i	−0.839109	+	0.543963i	$0.816923\pi$
$758$	31.3816	−	21.5213i	1.13983	−	0.781689i
$759$			10.1792i			0.369482i
$760$	2.40143	+	10.1379i	0.0871090	+	0.367742i
$761$	7.91305			0.286848			0.143424	−	0.989661i	$-0.454189\pi$
$761$	7.91305			0.286848			0.143424	+	0.989661i	$0.454189\pi$
$762$	−4.72564	−	6.89075i	−0.171192	−	0.249625i
$763$		−	0.466880i		−	0.0169022i
$764$	16.4783	−	42.6694i	0.596162	−	1.54373i
$765$			4.17173i			0.150829i
$766$	11.9671	−	8.20695i	0.432388	−	0.296529i
$767$	−20.3677			−0.735436
$768$	−1.54379	−	15.9253i	−0.0557068	−	0.574656i
$769$		−	12.1581i		−	0.438433i	−0.975676	−	0.219216i	$-0.929650\pi$
$769$		−	12.1581i		−	0.438433i	0.975676	−	0.219216i	$-0.0703500\pi$
$770$	−6.35440	−	9.26575i	−0.228997	−	0.333915i
$771$	−9.09968			−0.327717
$772$	12.7295	−	32.9623i	0.458146	−	1.18634i
$773$	−26.3151			−0.946490			−0.473245	−	0.880931i	$-0.656917\pi$
$773$	−26.3151			−0.946490			−0.473245	+	0.880931i	$0.656917\pi$
$774$	−1.32292	+	0.907249i	−0.0475513	+	0.0326104i
$775$	23.4932			0.843900
$776$	39.9997	−	9.47494i	1.43590	−	0.340131i
$777$	12.5647			0.450755
$778$	8.11943	−	5.56826i	0.291096	−	0.199632i
$779$	−1.30526			−0.0467657
$780$	−0.879720	+	2.27798i	−0.0314990	+	0.0815648i
$781$			43.1129i			1.54270i
$782$	7.41619	+	10.8140i	0.265202	+	0.386708i
$783$	2.13848			0.0764230
$784$	11.8200	+	10.7296i	0.422144	+	0.383200i
$785$			0.0465586i			0.00166175i
$786$	−4.87015	−	7.10147i	−0.173712	−	0.253301i
$787$	−44.6798			−1.59266			−0.796332	−	0.604860i	$-0.793229\pi$
$787$	−44.6798			−1.59266			−0.796332	+	0.604860i	$0.793229\pi$
$788$	−16.4114	−	6.33783i	−0.584633	−	0.225776i
$789$			27.3721i			0.974471i
$790$	−5.67034	−	8.26827i	−0.201741	−	0.294172i
$791$			14.4051i			0.512188i
$792$	−3.45365	−	14.5800i	−0.122720	−	0.518079i
$793$	−17.5717			−0.623991
$794$	7.14032	−	4.89679i	0.253400	−	0.173781i
$795$	7.70900			0.273410
$796$	23.5009	+	9.07566i	0.832966	+	0.321678i
$797$	−37.3794			−1.32405			−0.662023	−	0.749484i	$-0.730302\pi$
$797$	−37.3794			−1.32405			−0.662023	+	0.749484i	$0.730302\pi$
$798$	5.91148	+	8.61989i	0.209264	+	0.305141i
$799$			57.5340i			2.03541i
$800$	−23.8342	−	3.26040i	−0.842666	−	0.115273i
$801$	−5.73285			−0.202560
$802$	21.6466	+	31.5643i	0.764369	+	1.11457i
$803$	68.2184			2.40737
$804$	−2.29959	+	16.2084i	−0.0811004	+	0.571626i
$805$	−2.88170			−0.101567
$806$	6.24044	+	9.09957i	0.219810	+	0.320519i
$807$	−6.06672			−0.213559
$808$	38.5284	−	9.12642i	1.35542	−	0.321066i
$809$		−	9.07289i		−	0.318986i	−0.987199	−	0.159493i	$-0.949014\pi$
$809$		−	9.07289i		−	0.318986i	0.987199	−	0.159493i	$-0.0509859\pi$
$810$	−0.691495	−	1.00831i	−0.0242967	−	0.0354285i
$811$	32.7514			1.15006			0.575028	−	0.818134i	$-0.304991\pi$
$811$	32.7514			1.15006			0.575028	+	0.818134i	$0.304991\pi$
$812$	−2.67277	+	6.92096i	−0.0937957	+	0.242878i
$813$	−0.0167864			−0.000588724
$814$	−44.7519	+	30.6906i	−1.56855	+	1.07570i
$815$	10.6215			0.372056
$816$	−14.2915	−	12.9731i	−0.500302	−	0.454149i
$817$			4.83278i			0.169078i
$818$	−16.6296	−	24.2487i	−0.581441	−	0.847836i
$819$			2.44984i			0.0856045i
$820$	−0.190829	+	0.494140i	−0.00666405	+	0.0172561i
$821$	−41.3209			−1.44211			−0.721054	−	0.692879i	$-0.756342\pi$
$821$	−41.3209			−1.44211			−0.721054	+	0.692879i	$0.756342\pi$
$822$	12.2902	+	17.9211i	0.428670	+	0.625071i
$823$		−	22.8183i		−	0.795397i	−0.917516	−	0.397698i	$-0.869809\pi$
$823$		−	22.8183i		−	0.795397i	0.917516	−	0.397698i	$-0.130191\pi$
$824$	36.5370	−	8.65471i	1.27283	−	0.301501i
$825$	−22.5278			−0.784318
$826$	20.0098	+	29.1776i	0.696230	+	1.01522i
$827$			1.08638i			0.0377773i	0.999822	+	0.0188886i	$0.00601280\pi$
$827$			1.08638i			0.0377773i	−0.999822	+	0.0188886i	$0.993987\pi$
$828$	−3.58501	−	1.38447i	−0.124588	−	0.0481138i
$829$	−17.9169			−0.622281			−0.311141	−	0.950364i	$-0.600711\pi$
$829$	−17.9169			−0.622281			−0.311141	+	0.950364i	$0.600711\pi$
$830$	−0.394113	+	0.270280i	−0.0136799	+	0.00938157i
$831$	−2.17332			−0.0753916
$832$	−5.06818	−	10.0977i	−0.175707	−	0.350075i
$833$	19.2576			0.667237
$834$	6.83587	−	4.68800i	0.236707	−	0.162332i
$835$	3.56255			0.123287
$836$	−42.1101	−	16.2623i	−1.45641	−	0.562442i
$837$	−5.52447			−0.190953
$838$	−11.3085	−	16.4897i	−0.390647	−	0.569627i
$839$		−	35.0959i		−	1.21164i	−0.795600	−	0.605822i	$-0.792844\pi$
$839$		−	35.0959i		−	1.21164i	0.795600	−	0.605822i	$-0.207156\pi$
$840$	4.12756	−	0.977717i	0.142414	−	0.0337345i
$841$	−24.4269			−0.842307
$842$	−20.8112	+	14.2722i	−0.717200	+	0.491852i
$843$			12.9816i			0.447111i
$844$	41.6132	+	16.0704i	1.43239	+	0.553165i
$845$		−	9.51467i		−	0.327314i
$846$	−9.53668	−	13.9060i	−0.327878	−	0.478099i
$847$	29.5989			1.01703
$848$	−23.9731	+	26.4095i	−0.823241	+	0.906904i
$849$			21.6115i			0.741705i
$850$	−23.9327	+	16.4129i	−0.820886	+	0.562959i
$851$			13.9181i			0.477106i
$852$	−15.1839	−	5.86378i	−0.520192	−	0.200890i
$853$	37.4575			1.28252			0.641261	−	0.767323i	$-0.278412\pi$
$853$	37.4575			1.28252			0.641261	+	0.767323i	$0.278412\pi$
$854$	17.2630	+	25.1722i	0.590727	+	0.861376i
$855$	−3.68349			−0.125973
$856$	−49.8926	+	11.8183i	−1.70530	+	0.403943i
$857$			45.7452i			1.56263i	0.624140	+	0.781313i	$0.285450\pi$
$857$			45.7452i			1.56263i	−0.624140	+	0.781313i	$0.714550\pi$
$858$	−5.98402	−	8.72567i	−0.204291	−	0.297889i
$859$			9.87087i			0.336790i	0.985720	+	0.168395i	$0.0538584\pi$
$859$			9.87087i			0.336790i	−0.985720	+	0.168395i	$0.946142\pi$
$860$	1.82958	+	0.706555i	0.0623882	+	0.0240933i
$861$			0.531421i			0.0181108i
$862$	−7.17840	−	10.4673i	−0.244497	−	0.356517i
$863$		−	25.9231i		−	0.882434i	−0.897400	−	0.441217i	$-0.854547\pi$
$863$		−	25.9231i		−	0.882434i	0.897400	−	0.441217i	$-0.145453\pi$
$864$	5.60466	+	0.766689i	0.190674	+	0.0260833i
$865$			6.31900i			0.214852i
$866$	27.1525	+	39.5927i	0.922678	+	1.34541i
$867$	−6.28423			−0.213424
$868$	6.90472	−	17.8794i	0.234362	−	0.606865i
$869$	43.4398			1.47359
$870$	−1.47875	−	2.15626i	−0.0501343	−	0.0731039i
$871$	2.60844	+	11.2619i	0.0883837	+	0.381594i
$872$	−0.740760	+	0.175468i	−0.0250853	+	0.00594209i
$873$			14.5334i			0.491880i
$874$	−9.54840	+	6.54824i	−0.322979	+	0.221497i
$875$		−	13.8760i		−	0.469095i
$876$	−9.27837	+	24.0258i	−0.313487	+	0.811755i
$877$	−30.3090			−1.02346			−0.511732	−	0.859145i	$-0.670996\pi$
$877$	−30.3090			−1.02346			−0.511732	+	0.859145i	$0.670996\pi$
$878$	−4.53230	−	6.60883i	−0.152958	−	0.223037i
$879$	20.3556			0.686578
$880$	−12.3130	+	13.5644i	−0.415073	+	0.457255i
$881$	−7.31036			−0.246292			−0.123146	−	0.992389i	$-0.539298\pi$
$881$	−7.31036			−0.246292			−0.123146	+	0.992389i	$0.539298\pi$
$882$	−4.65459	+	3.19209i	−0.156728	+	0.107483i
$883$	−7.29604			−0.245531			−0.122766	−	0.992436i	$-0.539176\pi$
$883$	−7.29604			−0.245531			−0.122766	+	0.992436i	$0.539176\pi$
$884$	−12.7144	−	4.91010i	−0.427631	−	0.165144i
$885$	−12.4683			−0.419117
$886$	2.18317	−	1.49721i	0.0733452	−	0.0502997i
$887$			4.94332i			0.165980i	0.996550	+	0.0829902i	$0.0264470\pi$
$887$			4.94332i			0.165980i	−0.996550	+	0.0829902i	$0.973553\pi$
$888$	−4.72219	−	19.9353i	−0.158466	−	0.668986i
$889$			10.2488i			0.343734i
$890$	3.96424	+	5.78050i	0.132881	+	0.193763i
$891$	5.29746			0.177472
$892$	14.8870	+	5.74912i	0.498453	+	0.192495i
$893$	−50.8005			−1.69997
$894$	7.92596	−	5.43558i	0.265084	−	0.181793i
$895$			0.631360i			0.0211040i
$896$	−9.48626	+	17.1806i	−0.316914	+	0.573965i
$897$	−2.71373			−0.0906089
$898$	5.18753	−	3.55758i	0.173110	−	0.118718i
$899$	−11.8140			−0.394018
$900$	3.06401	−	7.93406i	0.102134	−	0.264469i
$901$			43.0273i			1.43345i
$902$	−1.29806	−	1.89278i	−0.0432205	−	0.0630226i
$903$	1.96762			0.0654781
$904$	22.8555	−	5.41391i	0.760162	−	0.180064i
$905$			11.0195i			0.366302i
$906$	−5.91541	−	8.62564i	−0.196526	−	0.286568i
$907$			19.2151i			0.638028i	0.947750	+	0.319014i	$0.103352\pi$
$907$			19.2151i			0.638028i	−0.947750	+	0.319014i	$0.896648\pi$
$908$	−4.67614	−	1.80585i	−0.155183	−	0.0599293i
$909$			13.9988i			0.464310i
$910$	2.47021	−	1.69406i	0.0818866	−	0.0561574i
$911$		−	60.0029i		−	1.98799i	−0.109444	−	0.993993i	$-0.534907\pi$
$911$		−	60.0029i		−	1.98799i	0.109444	−	0.993993i	$-0.465093\pi$
$912$	11.4548	−	12.6189i	0.379306	−	0.417853i
$913$		−	2.07059i		−	0.0685264i
$914$	−3.23237	+	2.21674i	−0.106917	+	0.0733233i
$915$	−10.7567			−0.355606
$916$	−26.3480	−	10.1752i	−0.870564	−	0.336198i
$917$			10.5622i			0.348796i
$918$	5.62783	−	3.85953i	0.185746	−	0.127384i
$919$	−8.51458			−0.280870			−0.140435	−	0.990090i	$-0.544850\pi$
$919$	−8.51458			−0.280870			−0.140435	+	0.990090i	$0.544850\pi$
$920$	1.08303	+	4.57216i	0.0357065	+	0.150740i
$921$			19.9608i			0.657731i
$922$	−15.3513	+	10.5278i	−0.505567	+	0.346715i
$923$	−11.4937			−0.378320
$924$	−6.62101	+	17.1447i	−0.217815	+	0.564019i
$925$	−30.8024			−1.01278
$926$	−46.3855	+	31.8109i	−1.52432	+	1.04537i
$927$			13.2752i			0.436016i
$928$	11.9854	+	1.63955i	0.393442	+	0.0538209i
$929$		−	22.5248i		−	0.739015i	−0.929228	−	0.369508i	$-0.879526\pi$
$929$		−	22.5248i		−	0.739015i	0.929228	−	0.369508i	$-0.120474\pi$
$930$	3.82014	+	5.57039i	0.125267	+	0.182660i
$931$			17.0038i			0.557277i
$932$	36.4876	+	14.0909i	1.19519	+	0.461564i
$933$	5.81890			0.190502
$934$	6.05268	+	8.82579i	0.198050	+	0.288789i
$935$			22.0996i			0.722734i
$936$	3.88697	−	0.920728i	0.127050	−	0.0300949i
$937$			27.8226i			0.908925i	0.890766	+	0.454462i	$0.150169\pi$
$937$			27.8226i			0.908925i	−0.890766	+	0.454462i	$0.849831\pi$
$938$	13.5705	−	14.8007i	0.443092	−	0.483259i
$939$		−	6.55868i		−	0.214034i
$940$	−7.42706	+	19.2319i	−0.242244	+	0.627276i
$941$		−	24.9112i		−	0.812083i	−0.913855	−	0.406041i	$-0.866909\pi$
$941$		−	24.9112i		−	0.812083i	0.913855	−	0.406041i	$-0.133091\pi$
$942$	0.0628094	−	0.0430744i	0.00204644	−	0.00140344i
$943$	−0.588664			−0.0191695
$944$	38.7734	−	42.7138i	1.26197	−	1.39022i
$945$			1.49969i			0.0487851i
$946$	−7.00810	+	4.80612i	−0.227853	+	0.156260i
$947$			11.5419i			0.375063i	0.982259	+	0.187531i	$0.0600486\pi$
$947$			11.5419i			0.375063i	−0.982259	+	0.187531i	$0.939951\pi$
$948$	−5.90824	+	15.2990i	−0.191891	+	0.496889i
$949$			18.1867i			0.590366i
$950$	−14.4920	−	21.1318i	−0.470184	−	0.685605i
$951$	31.6370			1.02590
$952$	5.45706	+	23.0377i	0.176864	+	0.746656i
$953$	43.5243			1.40989			0.704945	−	0.709262i	$-0.250972\pi$
$953$	43.5243			1.40989			0.704945	+	0.709262i	$0.250972\pi$
$954$	−7.13209	−	10.3997i	−0.230910	−	0.336704i
$955$		−	19.7723i		−	0.639818i
$956$	1.51753	−	3.92955i	0.0490805	−	0.127091i
$957$	11.3285			0.366199
$958$	2.33181	+	3.40016i	0.0753374	+	0.109854i
$959$		−	26.6546i		−	0.860723i
$960$	−3.10253	−	6.18141i	−0.100134	−	0.199504i
$961$	−0.480281			−0.0154929
$962$	−8.18198	−	11.9307i	−0.263797	−	0.384660i
$963$		−	18.1278i		−	0.584161i
$964$	4.93070	−	12.7677i	0.158807	−	0.411221i
$965$		−	15.2742i		−	0.491695i
$966$	2.66605	+	3.88753i	0.0857786	+	0.125079i
$967$		−	41.0188i		−	1.31908i	−0.751671	−	0.659538i	$-0.770752\pi$
$967$		−	41.0188i		−	1.31908i	0.751671	−	0.659538i	$-0.229248\pi$
$968$	−11.1242	−	46.9622i	−0.357545	−	1.50942i
$969$		−	20.5592i		−	0.660455i
$970$	14.6542	−	10.0497i	0.470517	−	0.322678i
$971$			55.4321i			1.77890i	0.457030	+	0.889451i	$0.348913\pi$
$971$			55.4321i			1.77890i	−0.457030	+	0.889451i	$0.651087\pi$
$972$	−0.720507	+	1.86571i	−0.0231103	+	0.0598426i
$973$	−10.1672			−0.325946
$974$	45.5862	−	31.2627i	1.46068	−	1.00172i
$975$		−	6.00582i		−	0.192340i
$976$	33.4508	−	36.8503i	1.07073	−	1.17955i
$977$	−0.869537			−0.0278189			−0.0139095	−	0.999903i	$-0.504428\pi$
$977$	−0.869537			−0.0278189			−0.0139095	+	0.999903i	$0.504428\pi$
$978$	−9.82666	−	14.3289i	−0.314222	−	0.458187i
$979$	−30.3695			−0.970615
$980$	6.43726	+	2.48597i	0.205631	+	0.0794113i
$981$		−	0.269146i		−	0.00859316i
$982$	7.33811	+	10.7002i	0.234168	+	0.341456i
$983$	−22.6312			−0.721824			−0.360912	−	0.932600i	$-0.617535\pi$
$983$	−22.6312			−0.721824			−0.360912	+	0.932600i	$0.617535\pi$
$984$	0.843163	−	0.199725i	0.0268791	−	0.00636699i
$985$	−7.60480			−0.242309
$986$	12.0350	−	8.25353i	0.383272	−	0.262846i
$987$			20.6829i			0.658343i
$988$	4.33544	−	11.2264i	0.137929	−	0.357158i
$989$			2.17956i			0.0693060i
$990$	−3.66317	−	5.34150i	−0.116423	−	0.169764i
$991$	51.1914			1.62615			0.813074	−	0.582160i	$-0.197792\pi$
$991$	51.1914			1.62615			0.813074	+	0.582160i	$0.197792\pi$
$992$	−30.9627	−	4.23555i	−0.983068	−	0.134479i
$993$	10.0039			0.317464
$994$	11.2917	+	16.4652i	0.358152	+	0.522245i
$995$	10.8899			0.345234
$996$	0.729238	+	0.281620i	0.0231068	+	0.00892347i
$997$	−27.9124			−0.883995			−0.441997	−	0.897016i	$-0.645730\pi$
$997$	−27.9124			−0.883995			−0.441997	+	0.897016i	$0.645730\pi$
$998$	26.6832	−	18.2992i	0.844643	−	0.579252i
$999$	7.24325			0.229166

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	804.2.e.a.535.27	✓	34
4.3	odd	2		804.2.e.b.535.7	yes	34
67.66	odd	2		804.2.e.b.535.8	yes	34
268.267	even	2	inner	804.2.e.a.535.28	yes	34

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
804.2.e.a.535.27	✓	34	1.1	even	1	trivial
804.2.e.a.535.28	yes	34	268.267	even	2	inner
804.2.e.b.535.7	yes	34	4.3	odd	2
804.2.e.b.535.8	yes	34	67.66	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)

\(f(q)\)	\(=\)	\(q+(1.16630 - 0.799841i) q^{2} -1.00000 q^{3} +(0.720507 - 1.86571i) q^{4} -0.864540i q^{5} +(-1.16630 + 0.799841i) q^{6} +1.73467 q^{7} +(-0.651944 - 2.75227i) q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+(1.16630 - 0.799841i) q^{2} -1.00000 q^{3} +(0.720507 - 1.86571i) q^{4} -0.864540i q^{5} +(-1.16630 + 0.799841i) q^{6} +1.73467 q^{7} +(-0.651944 - 2.75227i) q^{8} +1.00000 q^{9} +(-0.691495 - 1.00831i) q^{10} +5.29746 q^{11} +(-0.720507 + 1.86571i) q^{12} +1.41228i q^{13} +(2.02315 - 1.38746i) q^{14} +0.864540i q^{15} +(-2.96174 - 2.68851i) q^{16} -4.82537 q^{17} +(1.16630 - 0.799841i) q^{18} -4.26064i q^{19} +(-1.61298 - 0.622907i) q^{20} -1.73467 q^{21} +(6.17843 - 4.23713i) q^{22} -1.92153i q^{23} +(0.651944 + 2.75227i) q^{24} +4.25257 q^{25} +(1.12960 + 1.64714i) q^{26} -1.00000 q^{27} +(1.24984 - 3.23639i) q^{28} -2.13848 q^{29} +(0.691495 + 1.00831i) q^{30} +5.52447 q^{31} +(-5.60466 - 0.766689i) q^{32} -5.29746 q^{33} +(-5.62783 + 3.85953i) q^{34} -1.49969i q^{35} +(0.720507 - 1.86571i) q^{36} -7.24325 q^{37} +(-3.40783 - 4.96918i) q^{38} -1.41228i q^{39} +(-2.37944 + 0.563632i) q^{40} -0.306352i q^{41} +(-2.02315 + 1.38746i) q^{42} -1.13429 q^{43} +(3.81686 - 9.88352i) q^{44} -0.864540i q^{45} +(-1.53692 - 2.24107i) q^{46} -11.9232i q^{47} +(2.96174 + 2.68851i) q^{48} -3.99091 q^{49} +(4.95977 - 3.40138i) q^{50} +4.82537 q^{51} +(2.63490 + 1.01756i) q^{52} -8.91687i q^{53} +(-1.16630 + 0.799841i) q^{54} -4.57987i q^{55} +(-1.13091 - 4.77428i) q^{56} +4.26064i q^{57} +(-2.49411 + 1.71044i) q^{58} +14.4219i q^{59} +(1.61298 + 0.622907i) q^{60} +12.4421i q^{61} +(6.44318 - 4.41870i) q^{62} +1.73467 q^{63} +(-7.14994 + 3.58865i) q^{64} +1.22097 q^{65} +(-6.17843 + 4.23713i) q^{66} +(7.97425 - 1.84697i) q^{67} +(-3.47672 + 9.00274i) q^{68} +1.92153i q^{69} +(-1.19952 - 1.74909i) q^{70} +8.13841i q^{71} +(-0.651944 - 2.75227i) q^{72} +12.8776 q^{73} +(-8.44779 + 5.79345i) q^{74} -4.25257 q^{75} +(-7.94910 - 3.06982i) q^{76} +9.18937 q^{77} +(-1.12960 - 1.64714i) q^{78} +8.20011 q^{79} +(-2.32433 + 2.56054i) q^{80} +1.00000 q^{81} +(-0.245033 - 0.357299i) q^{82} -0.390864i q^{83} +(-1.24984 + 3.23639i) q^{84} +4.17173i q^{85} +(-1.32292 + 0.907249i) q^{86} +2.13848 q^{87} +(-3.45365 - 14.5800i) q^{88} -5.73285 q^{89} +(-0.691495 - 1.00831i) q^{90} +2.44984i q^{91} +(-3.58501 - 1.38447i) q^{92} -5.52447 q^{93} +(-9.53668 - 13.9060i) q^{94} -3.68349 q^{95} +(5.60466 + 0.766689i) q^{96} +14.5334i q^{97} +(-4.65459 + 3.19209i) q^{98} +5.29746 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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