LMFDB - Embedded newform 600.2.b.h.251.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [600,2,Mod(251,600)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(600, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("600.251");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 600 = 2^{3} \cdot 3 \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	600.b (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:	$4.79102412128$
Analytic rank:	$0$
Dimension:	$12$
Coefficient field:	12.0.537291533250985984.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 5x^{10} + 14x^{8} - 30x^{6} + 56x^{4} - 80x^{2} + 64 $ x^12 - 5x^10 + 14x^8 - 30x^6 + 56x^4 - 80*x^2 + 64
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			251.11
Root			$-1.39298 + 0.244153i$ of defining polynomial
Character	$\chi$	$=$	600.251
Dual form			600.2.b.h.251.12

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.39298 - 0.244153i) q^{2} +(-1.31310 + 1.12950i) q^{3} +(1.88078 - 0.680200i) q^{4} +(-1.55335 + 1.89397i) q^{6} +4.34495i q^{7} +(2.45381 - 1.40670i) q^{8} +(0.448458 - 2.96629i) q^{9} +O(q^{10})$	\(q+(1.39298 - 0.244153i) q^{2} +(-1.31310 + 1.12950i) q^{3} +(1.88078 - 0.680200i) q^{4} +(-1.55335 + 1.89397i) q^{6} +4.34495i q^{7} +(2.45381 - 1.40670i) q^{8} +(0.448458 - 2.96629i) q^{9} +1.83679i q^{11} +(-1.70136 + 3.01751i) q^{12} -0.588129i q^{13} +(1.06083 + 6.05242i) q^{14} +(3.07466 - 2.55861i) q^{16} +5.37818i q^{17} +(-0.0995365 - 4.24147i) q^{18} -5.38776 q^{19} +(-4.90762 - 5.70535i) q^{21} +(0.448458 + 2.55861i) q^{22} +2.40885 q^{23} +(-1.63323 + 4.61872i) q^{24} +(-0.143593 - 0.819251i) q^{26} +(2.76156 + 4.40157i) q^{27} +(2.95543 + 8.17189i) q^{28} +7.98077 q^{29} +7.06575i q^{31} +(3.65824 - 4.31478i) q^{32} +(-2.07466 - 2.41189i) q^{33} +(1.31310 + 7.49169i) q^{34} +(-1.17422 - 5.88398i) q^{36} -2.72080i q^{37} +(-7.50503 + 1.31544i) q^{38} +(0.664291 + 0.772271i) q^{39} -3.42496i q^{41} +(-8.22919 - 6.74922i) q^{42} -2.96772 q^{43} +(1.24939 + 3.45460i) q^{44} +(3.35548 - 0.588129i) q^{46} +9.81525 q^{47} +(-1.14738 + 6.83253i) q^{48} -11.8786 q^{49} +(-6.07466 - 7.06208i) q^{51} +(-0.400045 - 1.10614i) q^{52} -6.65218 q^{53} +(4.92145 + 5.45705i) q^{54} +(6.11205 + 10.6617i) q^{56} +(7.07466 - 6.08547i) q^{57} +(11.1170 - 1.94853i) q^{58} -10.7564i q^{59} -9.27803i q^{61} +(1.72512 + 9.84244i) q^{62} +(12.8884 + 1.94853i) q^{63} +(4.04238 - 6.90356i) q^{64} +(-3.47882 - 2.85318i) q^{66} -4.13536 q^{67} +(3.65824 + 10.1152i) q^{68} +(-3.16306 + 2.72080i) q^{69} +12.2241 q^{71} +(-3.07226 - 7.90957i) q^{72} -4.42003 q^{73} +(-0.664291 - 3.79002i) q^{74} +(-10.1332 + 3.66475i) q^{76} -7.98077 q^{77} +(1.11390 + 0.913568i) q^{78} -12.5870i q^{79} +(-8.59777 - 2.66052i) q^{81} +(-0.836213 - 4.77089i) q^{82} -11.5594i q^{83} +(-13.1109 - 7.39234i) q^{84} +(-4.13398 + 0.724579i) q^{86} +(-10.4795 + 9.01428i) q^{87} +(2.58382 + 4.50714i) q^{88} +4.21222i q^{89} +2.55539 q^{91} +(4.53052 - 1.63850i) q^{92} +(-7.98077 - 9.27803i) q^{93} +(13.6724 - 2.39642i) q^{94} +(0.0699132 + 9.79771i) q^{96} -2.16763 q^{97} +(-16.5466 + 2.90019i) q^{98} +(5.44846 + 0.823724i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 2 q^{3} + 10 q^{4} + 7 q^{6} - 2 q^{9}+O(q^{10}) $ 12 * q + 2 * q^3 + 10 * q^4 + 7 * q^6 - 2 * q^9	$ 12 q + 2 q^{3} + 10 q^{4} + 7 q^{6} - 2 q^{9} - 3 q^{12} - 6 q^{16} - 5 q^{18} - 4 q^{19} - 2 q^{22} + 5 q^{24} + 8 q^{27} - 20 q^{28} + 18 q^{33} - 2 q^{34} + 19 q^{36} - 14 q^{42} - 40 q^{43} - 16 q^{46} - 27 q^{48} - 36 q^{49} - 30 q^{51} - 4 q^{52} - 30 q^{54} + 42 q^{57} + 52 q^{58} + 10 q^{64} + 7 q^{66} - 60 q^{67} - 39 q^{72} + 12 q^{73} - 38 q^{76} + 54 q^{78} - 10 q^{81} + 58 q^{82} - 34 q^{84} + 34 q^{88} - 24 q^{91} + 28 q^{94} - 31 q^{96} - 32 q^{97} + 58 q^{99}+O(q^{100}) $ 12 * q + 2 * q^3 + 10 * q^4 + 7 * q^6 - 2 * q^9 - 3 * q^12 - 6 * q^16 - 5 * q^18 - 4 * q^19 - 2 * q^22 + 5 * q^24 + 8 * q^27 - 20 * q^28 + 18 * q^33 - 2 * q^34 + 19 * q^36 - 14 * q^42 - 40 * q^43 - 16 * q^46 - 27 * q^48 - 36 * q^49 - 30 * q^51 - 4 * q^52 - 30 * q^54 + 42 * q^57 + 52 * q^58 + 10 * q^64 + 7 * q^66 - 60 * q^67 - 39 * q^72 + 12 * q^73 - 38 * q^76 + 54 * q^78 - 10 * q^81 + 58 * q^82 - 34 * q^84 + 34 * q^88 - 24 * q^91 + 28 * q^94 - 31 * q^96 - 32 * q^97 + 58 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/600\mathbb{Z}\right)^\times$.

$n$	$151$	$301$	$401$	$577$
$\chi(n)$	$-1$	$-1$	$-1$	$1$

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 $

$2$	1.39298	−	0.244153i	0.984985	−	0.172642i
$2$	1.39298	−	0.244153i	0.984985	−	0.172642i
$3$	−1.31310	+	1.12950i	−0.758118	+	0.652117i
$3$	−1.31310	+	1.12950i	−0.758118	+	0.652117i
$4$	1.88078	−	0.680200i	0.940389	−	0.340100i
$5$		0			0
$5$		0			0
$6$	−1.55335	+	1.89397i	−0.634152	+	0.773209i
$7$			4.34495i			1.64224i	0.570758	+	0.821118i	$0.306650\pi$
$7$			4.34495i			1.64224i	−0.570758	+	0.821118i	$0.693350\pi$
$8$	2.45381	−	1.40670i	0.867553	−	0.497344i
$9$	0.448458	−	2.96629i	0.149486	−	0.988764i
$10$		0			0
$11$			1.83679i			0.553813i	0.960897	+	0.276907i	$0.0893093\pi$
$11$			1.83679i			0.553813i	−0.960897	+	0.276907i	$0.910691\pi$
$12$	−1.70136	+	3.01751i	−0.491141	+	0.871080i
$13$		−	0.588129i		−	0.163118i	−0.996669	−	0.0815588i	$-0.974010\pi$
$13$		−	0.588129i		−	0.163118i	0.996669	−	0.0815588i	$-0.0259898\pi$
$14$	1.06083	+	6.05242i	0.283520	+	1.61758i
$15$		0			0
$16$	3.07466	−	2.55861i	0.768664	−	0.639653i
$17$			5.37818i			1.30440i	0.758047	+	0.652200i	$0.226154\pi$
$17$			5.37818i			1.30440i	−0.758047	+	0.652200i	$0.773846\pi$
$18$	−0.0995365	−	4.24147i	−0.0234610	−	0.999725i
$19$	−5.38776			−1.23604			−0.618018	−	0.786164i	$-0.712064\pi$
$19$	−5.38776			−1.23604			−0.618018	+	0.786164i	$0.712064\pi$
$20$		0			0
$21$	−4.90762	−	5.70535i	−1.07093	−	1.24501i
$22$	0.448458	+	2.55861i	0.0956116	+	0.545498i
$23$	2.40885			0.502280			0.251140	−	0.967951i	$-0.419194\pi$
$23$	2.40885			0.502280			0.251140	+	0.967951i	$0.419194\pi$
$24$	−1.63323	+	4.61872i	−0.333381	+	0.942792i
$25$		0			0
$26$	−0.143593	−	0.819251i	−0.0281610	−	0.160668i
$27$	2.76156	+	4.40157i	0.531462	+	0.847082i
$28$	2.95543	+	8.17189i	0.558525	+	1.54434i
$29$	7.98077			1.48199			0.740996	−	0.671510i	$-0.234354\pi$
$29$	7.98077			1.48199			0.740996	+	0.671510i	$0.234354\pi$
$30$		0			0
$31$			7.06575i			1.26905i	0.772904	+	0.634523i	$0.218803\pi$
$31$			7.06575i			1.26905i	−0.772904	+	0.634523i	$0.781197\pi$
$32$	3.65824	−	4.31478i	0.646691	−	0.762752i
$33$	−2.07466	−	2.41189i	−0.361151	−	0.419856i
$34$	1.31310	+	7.49169i	0.225195	+	1.28481i
$35$		0			0
$36$	−1.17422	−	5.88398i	−0.195703	−	0.980663i
$37$		−	2.72080i		−	0.447297i	−0.974670	−	0.223648i	$-0.928203\pi$
$37$		−	2.72080i		−	0.447297i	0.974670	−	0.223648i	$-0.0717967\pi$
$38$	−7.50503	+	1.31544i	−1.21748	+	0.213392i
$39$	0.664291	+	0.772271i	0.106372	+	0.123662i
$40$		0			0
$41$		−	3.42496i		−	0.534888i	−0.963573	−	0.267444i	$-0.913821\pi$
$41$		−	3.42496i		−	0.534888i	0.963573	−	0.267444i	$-0.0861791\pi$
$42$	−8.22919	−	6.74922i	−1.26979	−	1.04143i
$43$	−2.96772			−0.452574			−0.226287	−	0.974061i	$-0.572659\pi$
$43$	−2.96772			−0.452574			−0.226287	+	0.974061i	$0.572659\pi$
$44$	1.24939	+	3.45460i	0.188352	+	0.520800i
$45$		0			0
$46$	3.35548	−	0.588129i	0.494739	−	0.0867148i
$47$	9.81525			1.43170			0.715850	−	0.698254i	$-0.246039\pi$
$47$	9.81525			1.43170			0.715850	+	0.698254i	$0.246039\pi$
$48$	−1.14738	+	6.83253i	−0.165610	+	0.986191i
$49$	−11.8786			−1.69694
$50$		0			0
$51$	−6.07466	−	7.06208i	−0.850622	−	0.988889i
$52$	−0.400045	−	1.10614i	−0.0554763	−	0.153394i
$53$	−6.65218			−0.913748			−0.456874	−	0.889531i	$-0.651031\pi$
$53$	−6.65218			−0.913748			−0.456874	+	0.889531i	$0.651031\pi$
$54$	4.92145	+	5.45705i	0.669724	+	0.742610i
$55$		0			0
$56$	6.11205	+	10.6617i	0.816757	+	1.42473i
$57$	7.07466	−	6.08547i	0.937061	−	0.806040i
$58$	11.1170	−	1.94853i	1.45974	−	0.255854i
$59$		−	10.7564i		−	1.40036i	−0.713967	−	0.700179i	$-0.753103\pi$
$59$		−	10.7564i		−	1.40036i	0.713967	−	0.700179i	$-0.246897\pi$
$60$		0			0
$61$		−	9.27803i		−	1.18793i	−0.804491	−	0.593965i	$-0.797562\pi$
$61$		−	9.27803i		−	1.18793i	0.804491	−	0.593965i	$-0.202438\pi$
$62$	1.72512	+	9.84244i	0.219091	+	1.24999i
$63$	12.8884	+	1.94853i	1.62378	+	0.245492i
$64$	4.04238	−	6.90356i	0.505298	−	0.862945i
$65$		0			0
$66$	−3.47882	−	2.85318i	−0.428213	−	0.351202i
$67$	−4.13536			−0.505215			−0.252607	−	0.967569i	$-0.581288\pi$
$67$	−4.13536			−0.505215			−0.252607	+	0.967569i	$0.581288\pi$
$68$	3.65824	+	10.1152i	0.443626	+	1.22664i
$69$	−3.16306	+	2.72080i	−0.380788	+	0.327546i
$70$		0			0
$71$	12.2241			1.45073			0.725367	−	0.688363i	$-0.241670\pi$
$71$	12.2241			1.45073			0.725367	+	0.688363i	$0.241670\pi$
$72$	−3.07226	−	7.90957i	−0.362069	−	0.932151i
$73$	−4.42003			−0.517325			−0.258663	−	0.965968i	$-0.583282\pi$
$73$	−4.42003			−0.517325			−0.258663	+	0.965968i	$0.583282\pi$
$74$	−0.664291	−	3.79002i	−0.0772223	−	0.440580i
$75$		0			0
$76$	−10.1332	+	3.66475i	−1.16235	+	0.420376i
$77$	−7.98077			−0.909493
$78$	1.11390	+	0.913568i	0.126124	+	0.103441i
$79$		−	12.5870i		−	1.41614i	−0.706141	−	0.708072i	$-0.749565\pi$
$79$		−	12.5870i		−	1.41614i	0.706141	−	0.708072i	$-0.250435\pi$
$80$		0			0
$81$	−8.59777	−	2.66052i	−0.955308	−	0.295613i
$82$	−0.836213	−	4.77089i	−0.0923443	−	0.526857i
$83$		−	11.5594i		−	1.26881i	−0.773002	−	0.634404i	$-0.781246\pi$
$83$		−	11.5594i		−	1.26881i	0.773002	−	0.634404i	$-0.218754\pi$
$84$	−13.1109	−	7.39234i	−1.43052	−	0.806570i
$85$		0			0
$86$	−4.13398	+	0.724579i	−0.445778	+	0.0781334i
$87$	−10.4795	+	9.01428i	−1.12352	+	0.966432i
$88$	2.58382	+	4.50714i	0.275436	+	0.480463i
$89$			4.21222i			0.446495i	0.974762	+	0.223247i	$0.0716658\pi$
$89$			4.21222i			0.446495i	−0.974762	+	0.223247i	$0.928334\pi$
$90$		0			0
$91$	2.55539			0.267878
$92$	4.53052	−	1.63850i	0.472339	−	0.170826i
$93$	−7.98077	−	9.27803i	−0.827567	−	0.962087i
$94$	13.6724	−	2.39642i	1.41020	−	0.247172i
$95$		0			0
$96$	0.0699132	+	9.79771i	0.00713549	+	0.999975i
$97$	−2.16763			−0.220090			−0.110045	−	0.993927i	$-0.535099\pi$
$97$	−2.16763			−0.220090			−0.110045	+	0.993927i	$0.535099\pi$
$98$	−16.5466	+	2.90019i	−1.67146	+	0.292964i
$99$	5.44846	+	0.823724i	0.547591	+	0.0827874i
$100$		0			0
$101$	3.16306			0.314736			0.157368	−	0.987540i	$-0.449699\pi$
$101$	3.16306			0.314736			0.157368	+	0.987540i	$0.449699\pi$
$102$	−10.1861	−	8.35418i	−1.00857	−	0.827188i
$103$			12.5870i			1.24023i	0.784511	+	0.620115i	$0.212914\pi$
$103$			12.5870i			1.24023i	−0.784511	+	0.620115i	$0.787086\pi$
$104$	−0.827322	−	1.44316i	−0.0811256	−	0.141513i
$105$		0			0
$106$	−9.26635	+	1.62415i	−0.900027	+	0.157751i
$107$			3.79002i			0.366395i	0.983076	+	0.183197i	$0.0586447\pi$
$107$			3.79002i			0.366395i	−0.983076	+	0.183197i	$0.941355\pi$
$108$	8.18782	+	6.39996i	0.787874	+	0.615837i
$109$			0.588129i			0.0563325i	0.999603	+	0.0281663i	$0.00896678\pi$
$109$			0.588129i			0.0563325i	−0.999603	+	0.0281663i	$0.991033\pi$
$110$		0			0
$111$	3.07314	+	3.57268i	0.291690	+	0.339104i
$112$	11.1170	+	13.3592i	1.05046	+	1.26233i
$113$		−	11.0621i		−	1.04064i	−0.853972	−	0.520319i	$-0.825813\pi$
$113$		−	11.0621i		−	1.04064i	0.853972	−	0.520319i	$-0.174187\pi$
$114$	8.36906	−	10.2042i	0.783834	−	0.955714i
$115$		0			0
$116$	15.0101	−	5.42852i	1.39365	−	0.504025i
$117$	−1.74456	−	0.263751i	−0.161285	−	0.0243838i
$118$	−2.62620	−	14.9834i	−0.241761	−	1.37933i
$119$	−23.3679			−2.14213
$120$		0			0
$121$	7.62620			0.693291
$122$	−2.26526	−	12.9241i	−0.205087	−	1.17009i
$123$	3.86849	+	4.49731i	0.348810	+	0.405508i
$124$	4.80612	+	13.2891i	0.431603	+	1.19340i
$125$		0			0
$126$	18.4290	−	0.432481i	1.64178	−	0.0385285i
$127$		−	12.9552i		−	1.14959i	−0.818297	−	0.574796i	$-0.805081\pi$
$127$		−	12.9552i		−	1.14959i	0.818297	−	0.574796i	$-0.194919\pi$
$128$	3.94542	−	10.6035i	0.348730	−	0.937223i
$129$	3.89692	−	3.35205i	0.343104	−	0.295131i
$130$		0			0
$131$			2.98699i			0.260974i	0.991450	+	0.130487i	$0.0416541\pi$
$131$			2.98699i			0.260974i	−0.991450	+	0.130487i	$0.958346\pi$
$132$	−5.54254	−	3.12505i	−0.482416	−	0.272000i
$133$		−	23.4095i		−	2.02986i
$134$	−5.76047	+	1.00966i	−0.497629	+	0.0872214i
$135$		0			0
$136$	7.56550	+	13.1970i	0.648736	+	1.13164i
$137$		−	5.66820i		−	0.484267i	−0.970243	−	0.242133i	$-0.922153\pi$
$137$		−	5.66820i		−	0.484267i	0.970243	−	0.242133i	$-0.0778471\pi$
$138$	−3.74179	+	4.56229i	−0.318522	+	0.388368i
$139$	−2.69075			−0.228226			−0.114113	−	0.993468i	$-0.536403\pi$
$139$	−2.69075			−0.228226			−0.114113	+	0.993468i	$0.536403\pi$
$140$		0			0
$141$	−12.8884	+	11.0863i	−1.08540	+	0.933637i
$142$	17.0279	−	2.98455i	1.42895	−	0.250458i
$143$	1.08027			0.0903367
$144$	−6.21073	−	10.2678i	−0.517561	−	0.855646i
$145$		0			0
$146$	−6.15701	+	1.07916i	−0.509558	+	0.0893122i
$147$	15.5978	−	13.4169i	1.28648	−	1.10661i
$148$	−1.85069	−	5.11722i	−0.152126	−	0.420633i
$149$	20.9591			1.71703			0.858517	−	0.512785i	$-0.171386\pi$
$149$	20.9591			1.71703			0.858517	+	0.512785i	$0.171386\pi$
$150$		0			0
$151$		−	3.16869i		−	0.257865i	−0.991653	−	0.128932i	$-0.958845\pi$
$151$		−	3.16869i		−	0.257865i	0.991653	−	0.128932i	$-0.0411550\pi$
$152$	−13.2205	+	7.57896i	−1.07233	+	0.614735i
$153$	15.9533	+	2.41189i	1.28974	+	0.194990i
$154$	−11.1170	+	1.94853i	−0.895836	+	0.157017i
$155$		0			0
$156$	1.77468	+	1.00062i	0.142088	+	0.0801137i
$157$		−	11.9988i		−	0.957611i	−0.877921	−	0.478805i	$-0.841070\pi$
$157$		−	11.9988i		−	0.957611i	0.877921	−	0.478805i	$-0.158930\pi$
$158$	−3.07314	−	17.5334i	−0.244486	−	1.39488i
$159$	8.73498	−	7.51364i	0.692729	−	0.595871i
$160$		0			0
$161$			10.4663i			0.824864i
$162$	−12.6261	−	1.60687i	−0.991999	−	0.126248i
$163$	−13.1816			−1.03246			−0.516231	−	0.856449i	$-0.672665\pi$
$163$	−13.1816			−1.03246			−0.516231	+	0.856449i	$0.672665\pi$
$164$	−2.32965	−	6.44158i	−0.181915	−	0.503003i
$165$		0			0
$166$	−2.82226	−	16.1020i	−0.219050	−	1.24976i
$167$	3.73744			0.289211			0.144606	−	0.989489i	$-0.453809\pi$
$167$	3.73744			0.289211			0.144606	+	0.989489i	$0.453809\pi$
$168$	−20.0681	−	7.09629i	−1.54829	−	0.547491i
$169$	12.6541			0.973393
$170$		0			0
$171$	−2.41618	+	15.9817i	−0.184770	+	1.22215i
$172$	−5.58163	+	2.01865i	−0.425596	+	0.153920i
$173$	−6.65218			−0.505756			−0.252878	−	0.967498i	$-0.581377\pi$
$173$	−6.65218			−0.505756			−0.252878	+	0.967498i	$0.581377\pi$
$174$	−12.3969	+	15.1153i	−0.939807	+	1.14589i
$175$		0			0
$176$	4.69963	+	5.64750i	0.354248	+	0.425696i
$177$	12.1493	+	14.1242i	0.913198	+	1.06164i
$178$	1.02843	+	5.86754i	0.0770839	+	0.439791i
$179$			18.4093i			1.37598i	0.725722	+	0.687988i	$0.241506\pi$
$179$			18.4093i			1.37598i	−0.725722	+	0.687988i	$0.758494\pi$
$180$		0			0
$181$			19.5125i			1.45035i	0.688564	+	0.725175i	$0.258241\pi$
$181$			19.5125i			1.45035i	−0.688564	+	0.725175i	$0.741759\pi$
$182$	3.55960	−	0.623906i	0.263855	−	0.0462470i
$183$	10.4795	+	12.1830i	0.774670	+	0.900591i
$184$	5.91087	−	3.38854i	0.435755	−	0.249806i
$185$		0			0
$186$	−13.3823	−	10.9756i	−0.981238	−	0.804768i
$187$	−9.87859			−0.722394
$188$	18.4603	−	6.67633i	1.34636	−	0.486921i
$189$	−19.1246	+	11.9988i	−1.39111	+	0.872786i
$190$		0			0
$191$	−8.73498			−0.632041			−0.316020	−	0.948752i	$-0.602347\pi$
$191$	−8.73498			−0.632041			−0.316020	+	0.948752i	$0.602347\pi$
$192$	2.48953	+	13.6309i	0.179666	+	0.983728i
$193$	1.47689			0.106309			0.0531543	−	0.998586i	$-0.483072\pi$
$193$	1.47689			0.106309			0.0531543	+	0.998586i	$0.483072\pi$
$194$	−3.01947	+	0.529235i	−0.216785	+	0.0379968i
$195$		0			0
$196$	−22.3410	+	8.07982i	−1.59579	+	0.577130i
$197$	−11.1438			−0.793965			−0.396982	−	0.917826i	$-0.629943\pi$
$197$	−11.1438			−0.793965			−0.396982	+	0.917826i	$0.629943\pi$
$198$	7.79070	−	0.182828i	0.553661	−	0.0129930i
$199$			2.80041i			0.198516i	0.995062	+	0.0992578i	$0.0316469\pi$
$199$			2.80041i			0.198516i	−0.995062	+	0.0992578i	$0.968353\pi$
$200$		0			0
$201$	5.43014	−	4.67089i	0.383012	−	0.329459i
$202$	4.40608	−	0.772271i	0.310011	−	0.0543368i
$203$			34.6760i			2.43378i
$204$	−16.2287	−	9.15023i	−1.13624	−	0.640645i
$205$		0			0
$206$	3.07314	+	17.5334i	0.214116	+	1.22161i
$207$	1.08027	−	7.14536i	0.0750839	−	0.496637i
$208$	−1.50479	−	1.80829i	−0.104339	−	0.125383i
$209$		−	9.89618i		−	0.684533i
$210$		0			0
$211$	9.86464			0.679110			0.339555	−	0.940586i	$-0.389724\pi$
$211$	9.86464			0.679110			0.339555	+	0.940586i	$0.389724\pi$
$212$	−12.5113	+	4.52481i	−0.859279	+	0.310766i
$213$	−16.0515	+	13.8071i	−1.09983	+	0.946048i
$214$	0.925344	+	5.27941i	0.0632552	+	0.360893i
$215$		0			0
$216$	12.9680	+	6.91593i	0.882363	+	0.470569i
$217$	−30.7003			−2.08407
$218$	0.143593	+	0.819251i	0.00972537	+	0.0554867i
$219$	5.80394	−	4.99243i	0.392194	−	0.337357i
$220$		0			0
$221$	3.16306			0.212771
$222$	5.15310	+	4.22635i	0.345854	+	0.283654i
$223$			1.62415i			0.108761i	0.998520	+	0.0543806i	$0.0173184\pi$
$223$			1.62415i			0.108761i	−0.998520	+	0.0543806i	$0.982682\pi$
$224$	18.7475	+	15.8949i	1.25262	+	1.06202i
$225$		0			0
$226$	−2.70085	−	15.4093i	−0.179658	−	1.02501i
$227$			4.94021i			0.327893i	0.986469	+	0.163947i	$0.0524225\pi$
$227$			4.94021i			0.327893i	−0.986469	+	0.163947i	$0.947578\pi$
$228$	9.16653	−	16.2576i	0.607068	−	1.07669i
$229$			15.2471i			1.00756i	0.863832	+	0.503779i	$0.168058\pi$
$229$			15.2471i			1.00756i	−0.863832	+	0.503779i	$0.831942\pi$
$230$		0			0
$231$	10.4795	−	9.01428i	0.689503	−	0.593096i
$232$	19.5833	−	11.2266i	1.28571	−	0.737060i
$233$			22.3000i			1.46092i	0.682955	+	0.730460i	$0.260694\pi$
$233$			22.3000i			1.46092i	−0.682955	+	0.730460i	$0.739306\pi$
$234$	−2.49453	+	0.0585403i	−0.163073	+	0.00382690i
$235$		0			0
$236$	−7.31648	−	20.2303i	−0.476262	−	1.31688i
$237$	14.2170	+	16.5279i	0.923492	+	1.07360i
$238$	−32.5510	+	5.70535i	−2.10997	+	0.369823i
$239$	−14.8813			−0.962589			−0.481294	−	0.876559i	$-0.659833\pi$
$239$	−14.8813			−0.962589			−0.481294	+	0.876559i	$0.659833\pi$
$240$		0			0
$241$	−0.523114			−0.0336968			−0.0168484	−	0.999858i	$-0.505363\pi$
$241$	−0.523114			−0.0336968			−0.0168484	+	0.999858i	$0.505363\pi$
$242$	10.6231	−	1.86196i	0.682881	−	0.119691i
$243$	14.2948	−	6.21766i	0.917010	−	0.398863i
$244$	−6.31091	−	17.4499i	−0.404015	−	1.11712i
$245$		0			0
$246$	6.48675	+	5.32015i	0.413580	+	0.339200i
$247$			3.16869i			0.201619i
$248$	9.93940	+	17.3380i	0.631153	+	1.10097i
$249$	13.0563	+	15.1786i	0.827412	+	0.961906i
$250$		0			0
$251$		−	4.82378i		−	0.304474i	−0.988344	−	0.152237i	$-0.951352\pi$
$251$		−	4.82378i		−	0.304474i	0.988344	−	0.152237i	$-0.0486477\pi$
$252$	25.5656	−	5.10193i	1.61048	−	0.321391i
$253$			4.42456i			0.278170i
$254$	−3.16306	−	18.0464i	−0.198468	−	1.13233i
$255$		0			0
$256$	2.90702	−	15.7337i	0.181689	−	0.983356i
$257$		−	22.8859i		−	1.42758i	−0.700358	−	0.713792i	$-0.746976\pi$
$257$		−	22.8859i		−	1.42758i	0.700358	−	0.713792i	$-0.253024\pi$
$258$	4.60991	−	5.62077i	0.287000	−	0.349934i
$259$	11.8217			0.734567
$260$		0			0
$261$	3.57904	−	23.6733i	0.221537	−	1.46534i
$262$	0.729282	+	4.16081i	0.0450552	+	0.257056i
$263$	−13.5527			−0.835694			−0.417847	−	0.908517i	$-0.637215\pi$
$263$	−13.5527			−0.835694			−0.417847	+	0.908517i	$0.637215\pi$
$264$	−8.48362	−	2.99990i	−0.522131	−	0.184631i
$265$		0			0
$266$	−5.71551	−	32.6090i	−0.350440	−	1.99938i
$267$	−4.75771	−	5.53107i	−0.291167	−	0.338496i
$268$	−7.77769	+	2.81287i	−0.475098	+	0.171823i
$269$	12.9783			0.791301			0.395651	−	0.918401i	$-0.370519\pi$
$269$	12.9783			0.791301			0.395651	+	0.918401i	$0.370519\pi$
$270$		0			0
$271$		0			0		1.00000			$0$
$271$		0			0		−1.00000			$\pi$
$272$	13.7607	+	16.5361i	0.834363	+	1.00265i
$273$	−3.35548	+	2.88631i	−0.203083	+	0.174688i
$274$	−1.38391	−	7.89568i	−0.0836049	−	0.476995i
$275$		0			0
$276$	−4.09833	+	7.26874i	−0.246691	+	0.437526i
$277$			16.7917i			1.00891i	0.863437	+	0.504457i	$0.168307\pi$
$277$			16.7917i			1.00891i	−0.863437	+	0.504457i	$0.831693\pi$
$278$	−3.74816	+	0.656955i	−0.224799	+	0.0394015i
$279$	20.9591	+	3.16869i	1.25479	+	0.189705i
$280$		0			0
$281$			11.0464i			0.658972i	0.944161	+	0.329486i	$0.106875\pi$
$281$			11.0464i			0.658972i	−0.944161	+	0.329486i	$0.893125\pi$
$282$	−15.2465	+	18.5897i	−0.907915	+	1.10700i
$283$	18.7047			1.11188			0.555940	−	0.831223i	$-0.312359\pi$
$283$	18.7047			1.11188			0.555940	+	0.831223i	$0.312359\pi$
$284$	22.9908	−	8.31483i	1.36425	−	0.493394i
$285$		0			0
$286$	1.50479	−	0.263751i	0.0889802	−	0.0155959i
$287$	14.8813			0.878413
$288$	−11.1583	−	12.7864i	−0.657510	−	0.753446i
$289$	−11.9248			−0.701460
$290$		0			0
$291$	2.84632	−	2.44834i	0.166854	−	0.143524i
$292$	−8.31310	+	3.00650i	−0.486487	+	0.175942i
$293$	29.4457			1.72024			0.860119	−	0.510093i	$-0.170389\pi$
$293$	29.4457			1.72024			0.860119	+	0.510093i	$0.170389\pi$
$294$	18.4516	−	22.4977i	1.07612	−	1.31209i
$295$		0			0
$296$	−3.82735	−	6.67633i	−0.222460	−	0.388054i
$297$	−8.08476	+	5.07240i	−0.469125	+	0.294331i
$298$	29.1955	−	5.11722i	1.69125	−	0.296433i
$299$		−	1.41672i		−	0.0819308i
$300$		0			0
$301$		−	12.8946i		−	0.743233i
$302$	−0.773646	−	4.41392i	−0.0445183	−	0.253993i
$303$	−4.15341	+	3.57268i	−0.238607	+	0.205245i
$304$	−16.5655	+	13.7852i	−0.950096	+	0.790634i
$305$		0			0
$306$	22.8114	−	0.535325i	1.30404	−	0.0306025i
$307$	−33.2095			−1.89537			−0.947683	−	0.319213i	$-0.896581\pi$
$307$	−33.2095			−1.89537			−0.947683	+	0.319213i	$0.896581\pi$
$308$	−15.0101	+	5.42852i	−0.855277	+	0.309318i
$309$	−14.2170	−	16.5279i	−0.808775	−	0.940241i
$310$		0			0
$311$	−25.7768			−1.46167			−0.730834	−	0.682556i	$-0.760868\pi$
$311$	−25.7768			−1.46167			−0.730834	+	0.682556i	$0.760868\pi$
$312$	2.71640	+	0.960548i	0.153786	+	0.0543803i
$313$	9.65410			0.545682			0.272841	−	0.962059i	$-0.412037\pi$
$313$	9.65410			0.545682			0.272841	+	0.962059i	$0.412037\pi$
$314$	−2.92955	−	16.7141i	−0.165324	−	0.943232i
$315$		0			0
$316$	−8.56165	−	23.6733i	−0.481630	−	1.33173i
$317$	4.81770			0.270589			0.135295	−	0.990805i	$-0.456802\pi$
$317$	4.81770			0.270589			0.135295	+	0.990805i	$0.456802\pi$
$318$	10.3332	−	12.5990i	0.579455	−	0.706518i
$319$			14.6590i			0.820747i
$320$		0			0
$321$	−4.28082	−	4.97667i	−0.238932	−	0.277770i
$322$	2.55539	+	14.5794i	0.142406	+	0.812478i
$323$		−	28.9763i		−	1.61229i
$324$	−17.9802	+	0.844363i	−0.998899	+	0.0469090i
$325$		0			0
$326$	−18.3617	+	3.21832i	−1.01696	+	0.178247i
$327$	−0.664291	−	0.772271i	−0.0367354	−	0.0427067i
$328$	−4.81789	−	8.40420i	−0.266024	−	0.464044i
$329$			42.6468i			2.35119i
$330$		0			0
$331$	−1.37380			−0.0755110			−0.0377555	−	0.999287i	$-0.512021\pi$
$331$	−1.37380			−0.0755110			−0.0377555	+	0.999287i	$0.512021\pi$
$332$	−7.86270	−	21.7407i	−0.431521	−	1.19317i
$333$	−8.07068	−	1.22016i	−0.442271	−	0.0668646i
$334$	5.20617	−	0.912506i	0.284869	−	0.0499301i
$335$		0			0
$336$	−29.6870	−	4.98529i	−1.61956	−	0.271970i
$337$	13.0925			0.713192			0.356596	−	0.934259i	$-0.383937\pi$
$337$	13.0925			0.713192			0.356596	+	0.934259i	$0.383937\pi$
$338$	17.6269	−	3.08954i	0.958777	−	0.168049i
$339$	12.4947	+	14.5257i	0.678618	+	0.788927i
$340$		0			0
$341$	−12.9783			−0.702815
$342$	0.536278	+	22.8520i	0.0289986	+	1.23570i
$343$		−	21.1972i		−	1.14454i
$344$	−7.28224	+	4.17470i	−0.392632	+	0.225085i
$345$		0			0
$346$	−9.26635	+	1.62415i	−0.498162	+	0.0873149i
$347$			3.97936i			0.213623i	0.994279	+	0.106812i	$0.0340642\pi$
$347$			3.97936i			0.213623i	−0.994279	+	0.106812i	$0.965936\pi$
$348$	−13.5782	+	24.0820i	−0.727867	+	1.29093i
$349$		−	12.5870i		−	0.673764i	−0.941547	−	0.336882i	$-0.890628\pi$
$349$		−	12.5870i		−	0.673764i	0.941547	−	0.336882i	$-0.109372\pi$
$350$		0			0
$351$	2.58869	−	1.62415i	0.138174	−	0.0866908i
$352$	7.92534	+	6.71942i	0.422422	+	0.358146i
$353$		−	0.787269i		−	0.0419021i	−0.999781	−	0.0209510i	$-0.993331\pi$
$353$		−	0.787269i		−	0.0419021i	0.999781	−	0.0209510i	$-0.00666941\pi$
$354$	20.3722	+	16.7084i	1.08277	+	0.888040i
$355$		0			0
$356$	2.86515	+	7.92226i	0.151853	+	0.419879i
$357$	30.6844	−	26.3941i	1.62399	−	1.39692i
$358$	4.49469	+	25.6438i	0.237552	+	1.35531i
$359$	1.08027			0.0570144			0.0285072	−	0.999594i	$-0.490925\pi$
$359$	1.08027			0.0570144			0.0285072	+	0.999594i	$0.490925\pi$
$360$		0			0
$361$	10.0279			0.527785
$362$	4.76403	+	27.1805i	0.250392	+	1.42857i
$363$	−10.0140	+	8.61379i	−0.525596	+	0.452107i
$364$	4.80612	−	1.73818i	0.251909	−	0.0911052i
$365$		0			0
$366$	17.5723	+	14.4120i	0.918518	+	0.753328i
$367$			14.5794i			0.761038i	0.924773	+	0.380519i	$0.124255\pi$
$367$			14.5794i			0.761038i	−0.924773	+	0.380519i	$0.875745\pi$
$368$	7.40639	−	6.16332i	0.386085	−	0.321285i
$369$	−10.1594	−	1.53595i	−0.528878	−	0.0799583i
$370$		0			0
$371$		−	28.9034i		−	1.50059i
$372$	−21.3210	−	12.0214i	−1.10544	−	0.623281i
$373$			31.5719i			1.63473i	0.576118	+	0.817366i	$0.304567\pi$
$373$			31.5719i			1.63473i	−0.576118	+	0.817366i	$0.695433\pi$
$374$	−13.7607	+	2.41189i	−0.711547	+	0.124716i
$375$		0			0
$376$	24.0848	−	13.8071i	1.24208	−	0.712048i
$377$		−	4.69372i		−	0.241739i
$378$	−23.7106	+	21.3834i	−1.21954	+	1.09985i
$379$	4.61224			0.236915			0.118458	−	0.992959i	$-0.462205\pi$
$379$	4.61224			0.236915			0.118458	+	0.992959i	$0.462205\pi$
$380$		0			0
$381$	14.6330	+	17.0115i	0.749669	+	0.871526i
$382$	−12.1676	+	2.13267i	−0.622550	+	0.109117i
$383$	−14.6330			−0.747709			−0.373854	−	0.927487i	$-0.621964\pi$
$383$	−14.6330			−0.747709			−0.373854	+	0.927487i	$0.621964\pi$
$384$	6.79589	+	18.3798i	0.346801	+	0.937939i
$385$		0			0
$386$	2.05727	−	0.360586i	0.104712	−	0.0183533i
$387$	−1.33090	+	8.80314i	−0.0676535	+	0.447489i
$388$	−4.07684	+	1.47442i	−0.206970	+	0.0748526i
$389$	−15.1388			−0.767570			−0.383785	−	0.923422i	$-0.625380\pi$
$389$	−15.1388			−0.767570			−0.383785	+	0.923422i	$0.625380\pi$
$390$		0			0
$391$			12.9552i			0.655175i
$392$	−29.1478	+	16.7096i	−1.47219	+	0.843964i
$393$	−3.37380	−	3.92221i	−0.170186	−	0.197849i
$394$	−15.5231	+	2.72080i	−0.782043	+	0.137072i
$395$		0			0
$396$	10.8076	−	2.15680i	0.543104	−	0.108383i
$397$		−	18.3362i		−	0.920268i	−0.887849	−	0.460134i	$-0.847801\pi$
$397$		−	18.3362i		−	0.920268i	0.887849	−	0.460134i	$-0.152199\pi$
$398$	0.683728	+	3.90091i	0.0342722	+	0.195535i
$399$	26.4411	+	30.7390i	1.32371	+	1.53888i
$400$		0			0
$401$		−	34.2381i		−	1.70977i	−0.518820	−	0.854884i	$-0.673628\pi$
$401$		−	34.2381i		−	1.70977i	0.518820	−	0.854884i	$-0.326372\pi$
$402$	6.42365	−	7.83223i	0.320383	−	0.390636i
$403$	4.15557			0.207004
$404$	5.94902	−	2.15151i	0.295975	−	0.107042i
$405$		0			0
$406$	8.46626	+	48.3030i	0.420173	+	2.39724i
$407$	4.99754			0.247719
$408$	−24.8403	−	8.78379i	−1.22978	−	0.434862i
$409$	18.6926			0.924291			0.462146	−	0.886804i	$-0.347080\pi$
$409$	18.6926			0.924291			0.462146	+	0.886804i	$0.347080\pi$
$410$		0			0
$411$	6.40223	+	7.44290i	0.315799	+	0.367131i
$412$	8.56165	+	23.6733i	0.421802	+	1.16630i
$413$	46.7359			2.29972
$414$	−0.239769	−	10.2171i	−0.0117840	−	0.502142i
$415$		0			0
$416$	−2.53764	−	2.15151i	−0.124418	−	0.105487i
$417$	3.53322	−	3.03920i	0.173023	−	0.148830i
$418$	−2.41618	−	13.7852i	−0.118179	−	0.674255i
$419$		−	5.24599i		−	0.256283i	−0.991756	−	0.128142i	$-0.959099\pi$
$419$		−	5.24599i		−	0.256283i	0.991756	−	0.128142i	$-0.0409012\pi$
$420$		0			0
$421$			4.42456i			0.215640i	0.994170	+	0.107820i	$0.0343870\pi$
$421$			4.42456i			0.215640i	−0.994170	+	0.107820i	$0.965613\pi$
$422$	13.7412	−	2.40848i	0.668913	−	0.117243i
$423$	4.40173	−	29.1149i	0.214019	−	1.41561i
$424$	−16.3232	+	9.35764i	−0.792725	+	0.454447i
$425$		0			0
$426$	−18.9883	+	23.1520i	−0.919985	+	1.12172i
$427$	40.3126			1.95086
$428$	2.57797	+	7.12818i	0.124611	+	0.344554i
$429$	−1.41850	+	1.22016i	−0.0684859	+	0.0589101i
$430$		0			0
$431$	−5.89797			−0.284095			−0.142048	−	0.989860i	$-0.545369\pi$
$431$	−5.89797			−0.284095			−0.142048	+	0.989860i	$0.545369\pi$
$432$	19.7527	+	6.46756i	0.950354	+	0.311171i
$433$	−32.2158			−1.54819			−0.774095	−	0.633069i	$-0.781795\pi$
$433$	−32.2158			−1.54819			−0.774095	+	0.633069i	$0.781795\pi$
$434$	−42.7649	+	7.49558i	−2.05278	+	0.359799i
$435$		0			0
$436$	0.400045	+	1.10614i	0.0191587	+	0.0529745i
$437$	−12.9783			−0.620837
$438$	6.86585	−	8.37139i	0.328063	−	0.400001i
$439$			2.27291i			0.108480i	0.998528	+	0.0542399i	$0.0172736\pi$
$439$			2.27291i			0.108480i	−0.998528	+	0.0542399i	$0.982726\pi$
$440$		0			0
$441$	−5.32705	+	35.2354i	−0.253669	+	1.67787i
$442$	4.40608	−	0.772271i	0.209576	−	0.0367332i
$443$		−	4.59091i		−	0.218121i	−0.994035	−	0.109060i	$-0.965216\pi$
$443$		−	4.59091i		−	0.218121i	0.994035	−	0.109060i	$-0.0347842\pi$
$444$	8.21004	+	4.62907i	0.389631	+	0.219686i
$445$		0			0
$446$	0.396541	+	2.26241i	0.0187768	+	0.107128i
$447$	−27.5213	+	23.6733i	−1.30171	+	1.11971i
$448$	29.9956	+	17.5639i	1.41716	+	0.829818i
$449$		−	39.0461i		−	1.84270i	−0.388736	−	0.921349i	$-0.627088\pi$
$449$		−	39.0461i		−	1.84270i	0.388736	−	0.921349i	$-0.372912\pi$
$450$		0			0
$451$	6.29093			0.296228
$452$	−7.52446	−	20.8054i	−0.353921	−	0.978605i
$453$	3.57904	+	4.16081i	0.168158	+	0.195492i
$454$	1.20617	+	6.88161i	0.0566082	+	0.322970i
$455$		0			0
$456$	8.79943	−	24.8845i	0.412071	−	1.16532i
$457$	4.96147			0.232088			0.116044	−	0.993244i	$-0.462979\pi$
$457$	4.96147			0.232088			0.116044	+	0.993244i	$0.462979\pi$
$458$	3.72263	+	21.2389i	0.173947	+	0.992430i
$459$	−23.6724	+	14.8522i	−1.10493	+	0.693239i
$460$		0			0
$461$	14.1271			0.657963			0.328981	−	0.944336i	$-0.393295\pi$
$461$	14.1271			0.657963			0.328981	+	0.944336i	$0.393295\pi$
$462$	12.3969	−	15.1153i	0.576756	−	0.703228i
$463$		−	14.2907i		−	0.664146i	−0.943254	−	0.332073i	$-0.892252\pi$
$463$		−	14.2907i		−	0.664146i	0.943254	−	0.332073i	$-0.107748\pi$
$464$	24.5381	−	20.4197i	1.13915	−	0.947960i
$465$		0			0
$466$	5.44461	+	31.0634i	0.252217	+	1.43898i
$467$		−	31.8469i		−	1.47370i	−0.676058	−	0.736849i	$-0.736313\pi$
$467$		−	31.8469i		−	1.47370i	0.676058	−	0.736849i	$-0.263687\pi$
$468$	−3.46054	+	0.690593i	−0.159963	+	0.0319227i
$469$		−	17.9679i		−	0.829682i
$470$		0			0
$471$	13.5527	+	15.7557i	0.624475	+	0.725982i
$472$	−15.1310	−	26.3941i	−0.696460	−	1.21489i
$473$		−	5.45109i		−	0.250641i
$474$	23.8393	+	19.5519i	1.09497	+	0.898050i
$475$		0			0
$476$	−43.9499	+	15.8949i	−2.01444	+	0.728540i
$477$	−2.98323	+	19.7323i	−0.136593	+	0.903481i
$478$	−20.7293	+	3.63331i	−0.948135	+	0.166184i
$479$	−25.9566			−1.18599			−0.592994	−	0.805207i	$-0.702054\pi$
$479$	−25.9566			−1.18599			−0.592994	+	0.805207i	$0.702054\pi$
$480$		0			0
$481$	−1.60018			−0.0729619
$482$	−0.728687	+	0.127720i	−0.0331908	+	0.00581748i
$483$	−11.8217	−	13.7433i	−0.537908	−	0.625344i
$484$	14.3432	−	5.18734i	0.651963	−	0.235788i
$485$		0			0
$486$	18.3943	−	12.1512i	0.834380	−	0.551189i
$487$		−	24.4456i		−	1.10773i	−0.832605	−	0.553867i	$-0.813152\pi$
$487$		−	24.4456i		−	1.10773i	0.832605	−	0.553867i	$-0.186848\pi$
$488$	−13.0514	−	22.7665i	−0.590810	−	1.03059i
$489$	17.3087	−	14.8886i	0.782728	−	0.673286i
$490$		0			0
$491$			37.6630i			1.69971i	0.527018	+	0.849854i	$0.323310\pi$
$491$			37.6630i			1.69971i	−0.527018	+	0.849854i	$0.676690\pi$
$492$	10.3348	+	5.82709i	0.465930	+	0.262706i
$493$			42.9220i			1.93311i
$494$	0.773646	+	4.41392i	0.0348080	+	0.198592i
$495$		0			0
$496$	18.0785	+	21.7248i	0.811749	+	0.975470i
$497$			53.1131i			2.38245i
$498$	21.8931	+	17.9558i	0.981053	+	0.804617i
$499$	−36.7249			−1.64403			−0.822016	−	0.569464i	$-0.807151\pi$
$499$	−36.7249			−1.64403			−0.822016	+	0.569464i	$0.807151\pi$
$500$		0			0
$501$	−4.90762	+	4.22143i	−0.219256	+	0.188600i
$502$	−1.17774	−	6.71942i	−0.0525651	−	0.299902i
$503$	−29.5142			−1.31597			−0.657987	−	0.753029i	$-0.728592\pi$
$503$	−29.5142			−1.31597			−0.657987	+	0.753029i	$0.728592\pi$
$504$	34.3667	−	13.3488i	1.53081	−	0.594603i
$505$		0			0
$506$	1.08027	+	6.16332i	0.0480238	+	0.273993i
$507$	−16.6161	+	14.2928i	−0.737947	+	0.634766i
$508$	−8.81215	−	24.3659i	−0.390976	−	1.08106i
$509$	−2.16054			−0.0957642			−0.0478821	−	0.998853i	$-0.515247\pi$
$509$	−2.16054			−0.0957642			−0.0478821	+	0.998853i	$0.515247\pi$
$510$		0			0
$511$		−	19.2048i		−	0.849571i
$512$	0.207989	−	22.6265i	0.00919190	−	0.999958i
$513$	−14.8786	−	23.7146i	−0.656906	−	1.04702i
$514$	−5.58767	−	31.8796i	−0.246461	−	1.40615i
$515$		0			0
$516$	5.04918	−	8.95514i	0.222278	−	0.394228i
$517$			18.0286i			0.792895i
$518$	16.4674	−	2.88631i	0.723537	−	0.126817i
$519$	8.73498	−	7.51364i	0.383423	−	0.329812i
$520$		0			0
$521$			9.39893i			0.411775i	0.978576	+	0.205887i	$0.0660080\pi$
$521$			9.39893i			0.411775i	−0.978576	+	0.205887i	$0.933992\pi$
$522$	−0.794377	−	33.8502i	−0.0347690	−	1.48158i
$523$	−9.68638			−0.423556			−0.211778	−	0.977318i	$-0.567925\pi$
$523$	−9.68638			−0.423556			−0.211778	+	0.977318i	$0.567925\pi$
$524$	2.03175	+	5.61786i	0.0887573	+	0.245417i
$525$		0			0
$526$	−18.8786	+	3.30893i	−0.823146	+	0.144276i
$527$	−38.0009			−1.65534
$528$	−12.5499	−	2.10749i	−0.546166	−	0.0917168i
$529$	−17.1974			−0.747714
$530$		0			0
$531$	−31.9065	−	4.82378i	−1.38462	−	0.209334i
$532$	−15.9232	−	44.0281i	−0.690357	−	1.90886i
$533$	−2.01431			−0.0872497
$534$	−7.97781	−	6.54305i	−0.345234	−	0.283145i
$535$		0			0
$536$	−10.1474	+	5.81722i	−0.438301	+	0.251265i
$537$	−20.7933	−	24.1732i	−0.897298	−	1.04315i
$538$	18.0785	−	3.16869i	0.779420	−	0.136612i
$539$		−	21.8185i		−	0.939789i
$540$		0			0
$541$		−	13.1751i		−	0.566441i	−0.959055	−	0.283221i	$-0.908597\pi$
$541$		−	13.1751i		−	0.566441i	0.959055	−	0.283221i	$-0.0914029\pi$
$542$		0			0
$543$	−22.0393	−	25.6218i	−0.945799	−	1.09954i
$544$	23.2056	+	19.6747i	0.994934	+	0.843544i
$545$		0			0
$546$	−3.96941	+	4.83982i	−0.169875	+	0.207125i
$547$	28.4113			1.21478			0.607390	−	0.794404i	$-0.292217\pi$
$547$	28.4113			1.21478			0.607390	+	0.794404i	$0.292217\pi$
$548$	−3.85551	−	10.6606i	−0.164699	−	0.455399i
$549$	−27.5213	−	4.16081i	−1.17458	−	0.177579i
$550$		0			0
$551$	−42.9984			−1.83179
$552$	−3.93420	+	11.1258i	−0.167451	+	0.473546i
$553$	54.6897			2.32564
$554$	4.09974	+	23.3904i	0.174181	+	0.993765i
$555$		0			0
$556$	−5.06070	+	1.83025i	−0.214622	+	0.0776198i
$557$	−32.1029			−1.36024			−0.680122	−	0.733099i	$-0.738073\pi$
$557$	−32.1029			−1.36024			−0.680122	+	0.733099i	$0.738073\pi$
$558$	29.9692	−	0.703300i	1.26870	−	0.0297731i
$559$			1.74540i			0.0738227i
$560$		0			0
$561$	12.9716	−	11.1579i	0.547660	−	0.471086i
$562$	2.69701	+	15.3874i	0.113766	+	0.649077i
$563$			14.2406i			0.600170i	0.953913	+	0.300085i	$0.0970150\pi$
$563$			14.2406i			0.600170i	−0.953913	+	0.300085i	$0.902985\pi$
$564$	−16.6993	+	29.6176i	−0.703167	+	1.24713i
$565$		0			0
$566$	26.0552	−	4.56681i	1.09518	−	0.191957i
$567$	11.5598	−	37.3569i	0.485466	−	1.56884i
$568$	29.9956	−	17.1957i	1.25859	−	0.721514i
$569$		−	9.08328i		−	0.380791i	−0.981707	−	0.190396i	$-0.939023\pi$
$569$		−	9.08328i		−	0.380791i	0.981707	−	0.190396i	$-0.0609770\pi$
$570$		0			0
$571$	−15.7432			−0.658834			−0.329417	−	0.944185i	$-0.606852\pi$
$571$	−15.7432			−0.658834			−0.329417	+	0.944185i	$0.606852\pi$
$572$	2.03175	−	0.734799i	0.0849516	−	0.0307235i
$573$	11.4699	−	9.86616i	0.479161	−	0.412165i
$574$	20.7293	−	3.63331i	0.865224	−	0.151651i
$575$		0			0
$576$	−18.6651	−	15.0868i	−0.777714	−	0.628618i
$577$	33.1974			1.38203			0.691014	−	0.722842i	$-0.257164\pi$
$577$	33.1974			1.38203			0.691014	+	0.722842i	$0.257164\pi$
$578$	−16.6110	+	2.91148i	−0.690927	+	0.121102i
$579$	−1.93930	+	1.66814i	−0.0805944	+	0.0693256i
$580$		0			0
$581$	50.2250			2.08368
$582$	3.36709	−	4.10543i	0.139570	−	0.170175i
$583$		−	12.2187i		−	0.506046i
$584$	−10.8459	+	6.21766i	−0.448807	+	0.257289i
$585$		0			0
$586$	41.0173	−	7.18927i	1.69441	−	0.296986i
$587$			0.613686i			0.0253295i	0.999920	+	0.0126648i	$0.00403143\pi$
$587$			0.613686i			0.0253295i	−0.999920	+	0.0126648i	$0.995969\pi$
$588$	20.2098	−	35.8438i	0.833438	−	1.47817i
$589$		−	38.0685i		−	1.56859i
$590$		0			0
$591$	14.6330	−	12.5870i	0.601919	−	0.517758i
$592$	−6.96147	−	8.36552i	−0.286115	−	0.343821i
$593$			15.5545i			0.638747i	0.947629	+	0.319374i	$0.103472\pi$
$593$			15.5545i			0.638747i	−0.947629	+	0.319374i	$0.896528\pi$
$594$	−10.0235	+	9.03967i	−0.411267	+	0.370902i
$595$		0			0
$596$	39.4194	−	14.2564i	1.61468	−	0.583963i
$597$	−3.16306	−	3.67721i	−0.129456	−	0.150498i
$598$	−0.345895	−	1.97345i	−0.0141447	−	0.0807005i
$599$	39.0811			1.59681			0.798406	−	0.602119i	$-0.205677\pi$
$599$	39.0811			1.59681			0.798406	+	0.602119i	$0.205677\pi$
$600$		0			0
$601$	−20.5231			−0.837155			−0.418578	−	0.908181i	$-0.637471\pi$
$601$	−20.5231			−0.837155			−0.418578	+	0.908181i	$0.637471\pi$
$602$	−3.14826	−	17.9619i	−0.128313	−	0.732073i
$603$	−1.85454	+	12.2667i	−0.0755225	+	0.499538i
$604$	−2.15534	−	5.95961i	−0.0876997	−	0.242493i
$605$		0			0
$606$	−4.91334	+	5.99073i	−0.199591	+	0.243357i
$607$			10.8832i			0.441735i	0.975304	+	0.220868i	$0.0708889\pi$
$607$			10.8832i			0.441735i	−0.975304	+	0.220868i	$0.929111\pi$
$608$	−19.7097	+	23.2470i	−0.799333	+	0.942789i
$609$	−39.1666	−	45.5331i	−1.58711	−	1.84509i
$610$		0			0
$611$		−	5.77263i		−	0.233535i
$612$	31.6451	−	6.31517i	1.27918	−	0.255276i
$613$		−	30.3350i		−	1.22522i	−0.790385	−	0.612610i	$-0.790119\pi$
$613$		−	30.3350i		−	1.22522i	0.790385	−	0.612610i	$-0.209881\pi$
$614$	−46.2601	+	8.10820i	−1.86691	+	0.327220i
$615$		0			0
$616$	−19.5833	+	11.2266i	−0.789033	+	0.452331i
$617$		−	8.71447i		−	0.350831i	−0.984494	−	0.175416i	$-0.943873\pi$
$617$		−	8.71447i		−	0.350831i	0.984494	−	0.175416i	$-0.0561269\pi$
$618$	−23.8393	−	19.5519i	−0.958956	−	0.786494i
$619$	13.0323			0.523811			0.261906	−	0.965093i	$-0.415649\pi$
$619$	13.0323			0.523811			0.261906	+	0.965093i	$0.415649\pi$
$620$		0			0
$621$	6.65218	+	10.6027i	0.266943	+	0.425473i
$622$	−35.9065	+	6.29348i	−1.43972	+	0.252346i
$623$	−18.3019			−0.733250
$624$	4.01841	+	0.674805i	0.160865	+	0.0270138i
$625$		0			0
$626$	13.4480	−	2.35708i	0.537489	−	0.0942078i
$627$	11.1777	+	12.9947i	0.446396	+	0.518957i
$628$	−8.16160	−	22.5671i	−0.325683	−	0.900527i
$629$	14.6330			0.583454
$630$		0			0
$631$		−	14.8599i		−	0.591562i	−0.955256	−	0.295781i	$-0.904420\pi$
$631$		−	14.8599i		−	0.591562i	0.955256	−	0.295781i	$-0.0955798\pi$
$632$	−17.7061	−	30.8860i	−0.704311	−	1.22858i
$633$	−12.9533	+	11.1421i	−0.514845	+	0.442859i
$634$	6.71096	−	1.17626i	0.266526	−	0.0467151i
$635$		0			0
$636$	11.3178	−	20.0730i	0.448779	−	0.795947i
$637$			6.98614i			0.276801i
$638$	3.57904	+	20.4197i	0.141696	+	0.808423i
$639$	5.48200	−	36.2602i	0.216864	−	1.43443i
$640$		0			0
$641$		−	5.97397i		−	0.235958i	−0.993016	−	0.117979i	$-0.962358\pi$
$641$		−	5.97397i		−	0.235958i	0.993016	−	0.117979i	$-0.0376415\pi$
$642$	−7.17816	−	5.88721i	−0.283300	−	0.232350i
$643$	15.7938			0.622848			0.311424	−	0.950271i	$-0.399194\pi$
$643$	15.7938			0.622848			0.311424	+	0.950271i	$0.399194\pi$
$644$	7.11921	+	19.6849i	0.280536	+	0.775693i
$645$		0			0
$646$	−7.07466	−	40.3634i	−0.278349	−	1.58808i
$647$	14.8128			0.582351			0.291175	−	0.956670i	$-0.405954\pi$
$647$	14.8128			0.582351			0.291175	+	0.956670i	$0.405954\pi$
$648$	−24.8399	+	5.56610i	−0.975802	+	0.218657i
$649$	19.7572			0.775537
$650$		0			0
$651$	40.3126	−	34.6760i	1.57997	−	1.35906i
$652$	−24.7916	+	8.96611i	−0.970916	+	0.351140i
$653$	3.48912			0.136540			0.0682699	−	0.997667i	$-0.478252\pi$
$653$	3.48912			0.136540			0.0682699	+	0.997667i	$0.478252\pi$
$654$	−1.11390	−	0.913568i	−0.0435568	−	0.0357234i
$655$		0			0
$656$	−8.76313	−	10.5306i	−0.342143	−	0.411149i
$657$	−1.98220	+	13.1111i	−0.0773329	+	0.511513i
$658$	10.4123	+	59.4060i	0.405915	+	2.31589i
$659$		−	36.5563i		−	1.42403i	−0.702163	−	0.712017i	$-0.747782\pi$
$659$		−	36.5563i		−	1.42403i	0.702163	−	0.712017i	$-0.252218\pi$
$660$		0			0
$661$			42.9220i			1.66947i	0.550650	+	0.834736i	$0.314380\pi$
$661$			42.9220i			1.66947i	−0.550650	+	0.834736i	$0.685620\pi$
$662$	−1.91368	+	0.335418i	−0.0743772	+	0.0130364i
$663$	−4.15341	+	3.57268i	−0.161305	+	0.138751i
$664$	−16.2606	−	28.3646i	−0.631034	−	1.10076i
$665$		0			0
$666$	−11.5402	+	0.270819i	−0.447174	+	0.0104940i
$667$	19.2245			0.744375
$668$	7.02929	−	2.54220i	0.271971	−	0.0983608i
$669$	−1.83448	−	2.13267i	−0.0709251	−	0.0824538i
$670$		0			0
$671$	17.0418			0.657892
$672$	−42.5706	+	0.303769i	−1.64220	+	0.0117182i
$673$	−46.2899			−1.78434			−0.892172	−	0.451696i	$-0.850819\pi$
$673$	−46.2899			−1.78434			−0.892172	+	0.451696i	$0.850819\pi$
$674$	18.2375	−	3.19656i	0.702483	−	0.123127i
$675$		0			0
$676$	23.7996	−	8.60732i	0.915368	−	0.331051i
$677$	27.7911			1.06810			0.534049	−	0.845453i	$-0.320670\pi$
$677$	27.7911			1.06810			0.534049	+	0.845453i	$0.320670\pi$
$678$	20.9513	+	17.1833i	0.804631	+	0.659922i
$679$		−	9.41826i		−	0.361440i
$680$		0			0
$681$	−5.57997	−	6.48699i	−0.213825	−	0.248582i
$682$	−18.0785	+	3.16869i	−0.692262	+	0.121336i
$683$		−	33.6521i		−	1.28766i	−0.765167	−	0.643832i	$-0.777344\pi$
$683$		−	33.6521i		−	1.28766i	0.765167	−	0.643832i	$-0.222656\pi$
$684$	6.32641	+	31.7014i	0.241896	+	1.21213i
$685$		0			0
$686$	−5.17537	−	29.5273i	−0.197597	−	1.12736i
$687$	−17.2216	−	20.0210i	−0.657047	−	0.763849i
$688$	−9.12473	+	7.59325i	−0.347877	+	0.289490i
$689$			3.91234i			0.149048i
$690$		0			0
$691$	−22.6820			−0.862864			−0.431432	−	0.902145i	$-0.641992\pi$
$691$	−22.6820			−0.862864			−0.431432	+	0.902145i	$0.641992\pi$
$692$	−12.5113	+	4.52481i	−0.475608	+	0.172008i
$693$	−3.57904	+	23.6733i	−0.135956	+	0.899274i
$694$	0.971573	+	5.54316i	0.0368804	+	0.210416i
$695$		0			0
$696$	−13.0344	+	36.8609i	−0.494068	+	1.39721i
$697$	18.4200			0.697708
$698$	−3.07314	−	17.5334i	−0.116320	−	0.663648i
$699$	−25.1878	−	29.2821i	−0.952692	−	1.10755i
$700$		0			0
$701$	−10.6379			−0.401789			−0.200895	−	0.979613i	$-0.564385\pi$
$701$	−10.6379			−0.401789			−0.200895	+	0.979613i	$0.564385\pi$
$702$	3.20945	−	2.89444i	0.121133	−	0.109244i
$703$			14.6590i			0.552875i
$704$	12.6804	+	7.42501i	0.477911	+	0.279841i
$705$		0			0
$706$	−0.192214	−	1.09665i	−0.00723407	−	0.0412729i
$707$			13.7433i			0.516872i
$708$	32.4574	+	18.3005i	1.21982	+	0.687774i
$709$			20.5295i			0.771002i	0.922707	+	0.385501i	$0.125971\pi$
$709$			20.5295i			0.771002i	−0.922707	+	0.385501i	$0.874029\pi$
$710$		0			0
$711$	−37.3366	−	5.64472i	−1.40023	−	0.211694i
$712$	5.92534	+	10.3360i	0.222062	+	0.387358i
$713$			17.0203i			0.637417i
$714$	36.2985	−	44.2581i	1.35844	−	1.65632i
$715$		0			0
$716$	12.5220	+	34.6238i	0.467969	+	1.29395i
$717$	19.5406	−	16.8084i	0.729756	−	0.627721i
$718$	1.50479	−	0.263751i	0.0561583	−	0.00984310i
$719$	14.8813			0.554977			0.277489	−	0.960729i	$-0.410498\pi$
$719$	14.8813			0.554977			0.277489	+	0.960729i	$0.410498\pi$
$720$		0			0
$721$	−54.6897			−2.03675
$722$	13.9687	−	2.44834i	0.519860	−	0.0911179i
$723$	0.686901	−	0.590858i	0.0255461	−	0.0219742i
$724$	13.2724	+	36.6986i	0.493264	+	1.36389i
$725$		0			0
$726$	−11.8461	+	14.4438i	−0.439651	+	0.536058i
$727$		−	16.1239i		−	0.598004i	−0.954253	−	0.299002i	$-0.903346\pi$
$727$		−	16.1239i		−	0.598004i	0.954253	−	0.299002i	$-0.0966537\pi$
$728$	6.27044	−	3.59467i	0.232398	−	0.133227i
$729$	−11.7476	+	24.3104i	−0.435096	+	0.900384i
$730$		0			0
$731$		−	15.9610i		−	0.590337i
$732$	27.9965	+	15.7853i	1.03478	+	0.583441i
$733$		−	16.7310i		−	0.617975i	−0.951066	−	0.308988i	$-0.900010\pi$
$733$		−	16.7310i		−	0.617975i	0.951066	−	0.308988i	$-0.0999902\pi$
$734$	3.55960	+	20.3088i	0.131387	+	0.749611i
$735$		0			0
$736$	8.81215	−	10.3937i	0.324820	−	0.383115i
$737$		−	7.59579i		−	0.279795i
$738$	−14.5269	+	0.340908i	−0.534741	+	0.0125490i
$739$	12.5693			0.462371			0.231185	−	0.972910i	$-0.425740\pi$
$739$	12.5693			0.462371			0.231185	+	0.972910i	$0.425740\pi$
$740$		0			0
$741$	−3.57904	−	4.16081i	−0.131479	−	0.152851i
$742$	−7.05685	−	40.2618i	−0.259065	−	1.47806i
$743$	22.2877			0.817655			0.408827	−	0.912612i	$-0.365938\pi$
$743$	22.2877			0.817655			0.408827	+	0.912612i	$0.365938\pi$
$744$	−32.6347	−	11.5400i	−1.19645	−	0.423076i
$745$		0			0
$746$	7.70838	+	43.9790i	0.282224	+	1.61019i
$747$	−34.2885	−	5.18390i	−1.25455	−	0.189669i
$748$	−18.5794	+	6.71942i	−0.679332	+	0.245686i
$749$	−16.4674			−0.601707
$750$		0			0
$751$		−	35.1279i		−	1.28183i	−0.767610	−	0.640917i	$-0.778554\pi$
$751$		−	35.1279i		−	1.28183i	0.767610	−	0.640917i	$-0.221446\pi$
$752$	30.1785	−	25.1134i	1.10050	−	0.915791i
$753$	5.44846	+	6.33410i	0.198553	+	0.230827i
$754$	−1.14599	−	6.53825i	−0.0417343	−	0.238109i
$755$		0			0
$756$	−27.8075	+	35.5757i	−1.01135	+	1.29388i
$757$			20.6887i			0.751945i	0.926631	+	0.375972i	$0.122691\pi$
$757$			20.6887i			0.751945i	−0.926631	+	0.375972i	$0.877309\pi$
$758$	6.42476	−	1.12609i	0.233358	−	0.0409016i
$759$	−4.99754	−	5.80988i	−0.181399	−	0.210885i
$760$		0			0
$761$			22.8130i			0.826971i	0.910511	+	0.413485i	$0.135689\pi$
$761$			22.8130i			0.826971i	−0.910511	+	0.413485i	$0.864311\pi$
$762$	24.5368	+	20.1240i	0.888874	+	0.729016i
$763$	−2.55539			−0.0925113
$764$	−16.4286	+	5.94153i	−0.594364	+	0.214957i
$765$		0			0
$766$	−20.3834	+	3.57268i	−0.736482	+	0.129086i
$767$	−6.32612			−0.228423
$768$	13.9540	+	23.9434i	0.503522	+	0.863982i
$769$	−46.3082			−1.66992			−0.834958	−	0.550313i	$-0.814508\pi$
$769$	−46.3082			−1.66992			−0.834958	+	0.550313i	$0.814508\pi$
$770$		0			0
$771$	25.8496	+	30.0515i	0.930952	+	1.08228i
$772$	2.77769	−	1.00458i	0.0999714	−	0.0361555i
$773$	30.2684			1.08868			0.544340	−	0.838865i	$-0.316780\pi$
$773$	30.2684			1.08868			0.544340	+	0.838865i	$0.316780\pi$
$774$	0.295397	+	12.5875i	0.0106178	+	0.452449i
$775$		0			0
$776$	−5.31897	+	3.04922i	−0.190940	+	0.109460i
$777$	−15.5231	+	13.3527i	−0.556889	+	0.479024i
$778$	−21.0881	+	3.69620i	−0.756045	+	0.132515i
$779$			18.4528i			0.661141i
$780$		0			0
$781$			22.4531i			0.803436i
$782$	3.16306	+	18.0464i	0.113111	+	0.645337i
$783$	22.0393	+	35.1279i	0.787622	+	1.25537i
$784$	−36.5226	+	30.3927i	−1.30438	+	1.08545i
$785$		0			0
$786$	−5.65725	−	4.63983i	−0.201788	−	0.165497i
$787$	−19.4080			−0.691819			−0.345910	−	0.938268i	$-0.612430\pi$
$787$	−19.4080			−0.691819			−0.345910	+	0.938268i	$0.612430\pi$
$788$	−20.9591	+	7.58003i	−0.746636	+	0.270027i
$789$	17.7960	−	15.3078i	0.633555	−	0.544971i
$790$		0			0
$791$	48.0644			1.70897
$792$	14.5282	−	5.64309i	0.516238	−	0.200519i
$793$	−5.45667			−0.193772
$794$	−4.47684	−	25.5420i	−0.158877	−	0.906450i
$795$		0			0
$796$	1.90484	+	5.26695i	0.0675152	+	0.186682i
$797$	30.7743			1.09008			0.545041	−	0.838409i	$-0.316514\pi$
$797$	30.7743			1.09008			0.545041	+	0.838409i	$0.316514\pi$
$798$	44.3369	+	36.3631i	1.56951	+	1.28724i
$799$			52.7882i			1.86751i
$800$		0			0
$801$	12.4947	+	1.88901i	0.441478	+	0.0667448i
$802$	−8.35933	−	47.6929i	−0.295178	−	1.68409i
$803$		−	8.11867i		−	0.286502i
$804$	7.03575	−	12.4785i	0.248132	−	0.440082i
$805$		0			0
$806$	5.78862	−	1.01460i	0.203895	−	0.0357376i
$807$	−17.0418	+	14.6590i	−0.599900	+	0.516021i
$808$	7.76156	−	4.44948i	0.273051	−	0.156532i
$809$			37.5744i			1.32104i	0.750807	+	0.660522i	$0.229665\pi$
$809$			37.5744i			1.32104i	−0.750807	+	0.660522i	$0.770335\pi$
$810$		0			0
$811$	−30.3492			−1.06571			−0.532853	−	0.846208i	$-0.678880\pi$
$811$	−30.3492			−1.06571			−0.532853	+	0.846208i	$0.678880\pi$
$812$	23.5866	+	65.2179i	0.827729	+	2.28870i
$813$		0			0
$814$	6.96147	−	1.22016i	0.243999	−	0.0427668i
$815$		0			0
$816$	−36.7466	−	6.17080i	−1.28639	−	0.216021i
$817$	15.9894			0.559397
$818$	26.0384	−	4.56386i	0.910413	−	0.159572i
$819$	1.14599	−	7.58003i	0.0400440	−	0.264868i
$820$		0			0
$821$	−6.97824			−0.243542			−0.121771	−	0.992558i	$-0.538857\pi$
$821$	−6.97824			−0.243542			−0.121771	+	0.992558i	$0.538857\pi$
$822$	10.7354	+	8.80468i	0.374439	+	0.307099i
$823$			0.569147i			0.0198392i	0.999951	+	0.00991960i	$0.00315756\pi$
$823$			0.569147i			0.0198392i	−0.999951	+	0.00991960i	$0.996842\pi$
$824$	17.7061	+	30.8860i	0.616821	+	1.07597i
$825$		0			0
$826$	65.1020	−	11.4107i	2.26519	−	0.397029i
$827$			23.0851i			0.802748i	0.915914	+	0.401374i	$0.131467\pi$
$827$			23.0851i			0.802748i	−0.915914	+	0.401374i	$0.868533\pi$
$828$	−2.82852	−	14.1736i	−0.0982980	−	0.492568i
$829$			48.3636i			1.67974i	0.542790	+	0.839869i	$0.317368\pi$
$829$			48.3636i			1.67974i	−0.542790	+	0.839869i	$0.682632\pi$
$830$		0			0
$831$	−18.9662	−	22.0491i	−0.657930	−	0.764876i
$832$	−4.06018	−	2.37744i	−0.140761	−	0.0824229i
$833$		−	63.8852i		−	2.21349i
$834$	4.17967	−	5.09619i	0.144730	−	0.176467i
$835$		0			0
$836$	−6.73138	−	18.6125i	−0.232810	−	0.643728i
$837$	−31.1004	+	19.5125i	−1.07499	+	0.674450i
$838$	−1.28082	−	7.30755i	−0.0442453	−	0.252435i
$839$	−22.0393			−0.760883			−0.380441	−	0.924805i	$-0.624228\pi$
$839$	−22.0393			−0.760883			−0.380441	+	0.924805i	$0.624228\pi$
$840$		0			0
$841$	34.6926			1.19630
$842$	1.08027	+	6.16332i	0.0372285	+	0.212402i
$843$	−12.4769	−	14.5050i	−0.429727	−	0.499578i
$844$	18.5532	−	6.70993i	0.638628	−	0.230965i
$845$		0			0
$846$	−0.976975	−	41.6311i	−0.0335891	−	1.43131i
$847$			33.1355i			1.13855i
$848$	−20.4532	+	17.0203i	−0.702365	+	0.584481i
$849$	−24.5611	+	21.1270i	−0.842936	+	0.725076i
$850$		0			0
$851$		−	6.55400i		−	0.224668i
$852$	−20.7976	+	36.8863i	−0.712515	+	1.26371i
$853$		−	6.39801i		−	0.219064i	−0.993983	−	0.109532i	$-0.965065\pi$
$853$		−	6.39801i		−	0.219064i	0.993983	−	0.109532i	$-0.0349352\pi$
$854$	56.1546	−	9.84244i	1.92157	−	0.336801i
$855$		0			0
$856$	5.33142	+	9.29998i	0.182224	+	0.317867i
$857$		−	27.2124i		−	0.929559i	−0.885426	−	0.464780i	$-0.846134\pi$
$857$		−	27.2124i		−	0.929559i	0.885426	−	0.464780i	$-0.153866\pi$
$858$	−1.67803	+	2.04599i	−0.0572871	+	0.0698491i
$859$	23.4663			0.800658			0.400329	−	0.916371i	$-0.368896\pi$
$859$	23.4663			0.800658			0.400329	+	0.916371i	$0.368896\pi$
$860$		0			0
$861$	−19.5406	+	16.8084i	−0.665941	+	0.572828i
$862$	−8.21575	+	1.44001i	−0.279830	+	0.0490469i
$863$	−12.4724			−0.424566			−0.212283	−	0.977208i	$-0.568090\pi$
$863$	−12.4724			−0.424566			−0.212283	+	0.977208i	$0.568090\pi$
$864$	29.0942	+	4.18648i	0.989805	+	0.142427i
$865$		0			0
$866$	−44.8759	+	7.86557i	−1.52494	+	0.267283i
$867$	15.6585	−	13.4691i	0.531790	−	0.457434i
$868$	−57.7405	+	20.8824i	−1.95984	+	0.708794i
$869$	23.1196			0.784279
$870$		0			0
$871$			2.43212i			0.0824093i
$872$	0.827322	+	1.44316i	0.0280166	+	0.0488715i
$873$	−0.972093	+	6.42984i	−0.0329004	+	0.217617i
$874$	−18.0785	+	3.16869i	−0.611515	+	0.107183i
$875$		0			0
$876$	7.52007	−	13.3375i	0.254080	−	0.450632i
$877$			48.9517i			1.65298i	0.562950	+	0.826491i	$0.309667\pi$
$877$			48.9517i			1.65298i	−0.562950	+	0.826491i	$0.690333\pi$
$878$	0.554937	+	3.16611i	0.0187282	+	0.106851i
$879$	−38.6652	+	33.2590i	−1.30414	+	1.12180i
$880$		0			0
$881$		−	9.76612i		−	0.329029i	−0.986375	−	0.164514i	$-0.947394\pi$
$881$		−	9.76612i		−	0.329029i	0.986375	−	0.164514i	$-0.0526057\pi$
$882$	1.18235	+	50.3827i	0.0398119	+	1.69647i
$883$	−37.1170			−1.24909			−0.624544	−	0.780990i	$-0.714715\pi$
$883$	−37.1170			−1.24909			−0.624544	+	0.780990i	$0.714715\pi$
$884$	5.94902	−	2.15151i	0.200087	−	0.0723633i
$885$		0			0
$886$	−1.12088	−	6.39504i	−0.0376569	−	0.214846i
$887$	20.7792			0.697699			0.348849	−	0.937179i	$-0.386573\pi$
$887$	20.7792			0.697699			0.348849	+	0.937179i	$0.386573\pi$
$888$	12.5666	+	4.44368i	0.421708	+	0.149120i
$889$	56.2899			1.88790
$890$		0			0
$891$	4.88681	−	15.7923i	0.163714	−	0.529062i
$892$	1.10475	+	3.05467i	0.0369897	+	0.102278i
$893$	−52.8821			−1.76963
$894$	−32.5567	+	39.6958i	−1.08886	+	1.32763i
$895$		0			0
$896$	46.0716	+	17.1427i	1.53914	+	0.572697i
$897$	1.60018	+	1.86029i	0.0534285	+	0.0621132i
$898$	−9.53322	−	54.3904i	−0.318128	−	1.81503i
$899$			56.3901i			1.88072i
$900$		0			0
$901$		−	35.7766i		−	1.19189i
$902$	8.76313	−	1.53595i	0.291780	−	0.0511415i
$903$	14.5645	+	16.9319i	0.484675	+	0.563459i
$904$	−15.5611	−	27.1444i	−0.517555	−	0.902809i
$905$		0			0
$906$	6.00140	+	4.92208i	0.199383	+	0.163525i
$907$	25.5231			0.847481			0.423741	−	0.905784i	$-0.360717\pi$
$907$	25.5231			0.847481			0.423741	+	0.905784i	$0.360717\pi$
$908$	3.36033	+	9.29144i	0.111516	+	0.308347i
$909$	1.41850	−	9.38256i	0.0470487	−	0.311200i
$910$		0			0
$911$	−18.6187			−0.616865			−0.308433	−	0.951246i	$-0.599804\pi$
$911$	−18.6187			−0.616865			−0.308433	+	0.951246i	$0.599804\pi$
$912$	6.18178	−	36.8120i	0.204699	−	1.21897i
$913$	21.2322			0.702683
$914$	6.91122	−	1.21136i	0.228603	−	0.0400681i
$915$		0			0
$916$	10.3711	+	28.6765i	0.342671	+	0.947497i
$917$	−12.9783			−0.428581
$918$	−29.3490	+	26.4684i	−0.968661	+	0.873588i
$919$		−	27.9743i		−	0.922788i	−0.887195	−	0.461394i	$-0.847350\pi$
$919$		−	27.9743i		−	0.922788i	0.887195	−	0.461394i	$-0.152650\pi$
$920$		0			0
$921$	43.6074	−	37.5101i	1.43691	−	1.23600i
$922$	19.6787	−	3.44916i	0.648083	−	0.113592i
$923$		−	7.18934i		−	0.236640i
$924$	13.5782	−	24.0820i	0.446689	−	0.792241i
$925$		0			0
$926$	−3.48912	−	19.9067i	−0.114660	−	0.654174i
$927$	37.3366	+	5.64472i	1.22629	+	0.185397i
$928$	29.1955	−	34.4352i	0.958391	−	1.13039i
$929$		−	46.7604i		−	1.53416i	−0.641551	−	0.767080i	$-0.721709\pi$
$929$		−	46.7604i		−	1.53416i	0.641551	−	0.767080i	$-0.278291\pi$
$930$		0			0
$931$	63.9990			2.09748
$932$	15.1685	+	41.9413i	0.496859	+	1.37383i
$933$	33.8475	−	29.1149i	1.10812	−	0.953178i
$934$	−7.77551	−	44.3620i	−0.254422	−	1.45157i
$935$		0			0
$936$	−4.65184	+	1.80688i	−0.152050	+	0.0590598i
$937$	−41.2253			−1.34677			−0.673387	−	0.739291i	$-0.735161\pi$
$937$	−41.2253			−1.34677			−0.673387	+	0.739291i	$0.735161\pi$
$938$	−4.38692	−	25.0289i	−0.143238	−	0.817224i
$939$	−12.6768	+	10.9043i	−0.413692	+	0.355849i
$940$		0			0
$941$	0.179836			0.00586248			0.00293124	−	0.999996i	$-0.499067\pi$
$941$	0.179836			0.00586248			0.00293124	+	0.999996i	$0.499067\pi$
$942$	22.7254	+	18.6384i	0.740433	+	0.607270i
$943$		−	8.25021i		−	0.268664i
$944$	−27.5213	−	33.0721i	−0.895743	−	1.07641i
$945$		0			0
$946$	−1.33090	−	7.59325i	−0.0432713	−	0.246878i
$947$			21.3864i			0.694965i	0.937686	+	0.347483i	$0.112963\pi$
$947$			21.3864i			0.694965i	−0.937686	+	0.347483i	$0.887037\pi$
$948$	37.9813	+	21.4150i	1.23357	+	0.695526i
$949$			2.59955i			0.0843849i
$950$		0			0
$951$	−6.32612	+	5.44160i	−0.205139	+	0.176456i
$952$	−57.3405	+	32.8717i	−1.85842	+	1.06538i
$953$			11.0306i			0.357317i	0.983911	+	0.178658i	$0.0571757\pi$
$953$			11.0306i			0.357317i	−0.983911	+	0.178658i	$0.942824\pi$
$954$	0.662135	+	28.2151i	0.0214374	+	0.913496i
$955$		0			0
$956$	−27.9884	+	10.1222i	−0.905208	+	0.327376i
$957$	−16.5573	−	19.2487i	−0.535223	−	0.622223i
$958$	−36.1570	+	6.33739i	−1.16818	+	0.204752i
$959$	24.6280			0.795281
$960$		0			0
$961$	−18.9248			−0.610478
$962$	−2.22902	+	0.390689i	−0.0718664	+	0.0125963i
$963$	11.2423	+	1.69966i	0.362278	+	0.0547709i
$964$	−0.983862	+	0.355822i	−0.0316881	+	0.0114603i
$965$		0			0
$966$	−19.8229	−	16.2579i	−0.637792	−	0.523089i
$967$			10.8832i			0.349980i	0.984570	+	0.174990i	$0.0559893\pi$
$967$			10.8832i			0.349980i	−0.984570	+	0.174990i	$0.944011\pi$
$968$	18.7133	−	10.7278i	0.601467	−	0.344804i
$969$	32.7288	+	38.0488i	1.05140	+	1.22230i
$970$		0			0
$971$		−	2.40482i		−	0.0771744i	−0.999255	−	0.0385872i	$-0.987714\pi$
$971$		−	2.40482i		−	0.0771744i	0.999255	−	0.0385872i	$-0.0122857\pi$
$972$	22.6561	−	21.4174i	0.726693	−	0.686962i
$973$		−	11.6912i		−	0.374802i
$974$	−5.96846	−	34.0521i	−0.191242	−	1.09110i
$975$		0			0
$976$	−23.7389	−	28.5268i	−0.759863	−	0.913119i
$977$			41.7609i			1.33605i	0.744138	+	0.668026i	$0.232860\pi$
$977$			41.7609i			1.33605i	−0.744138	+	0.668026i	$0.767140\pi$
$978$	20.4756	−	24.9655i	0.654737	−	0.798308i
$979$	−7.73698			−0.247275
$980$		0			0
$981$	1.74456	+	0.263751i	0.0556995	+	0.00842092i
$982$	9.19554	+	52.4638i	0.293442	+	1.67419i
$983$	33.2516			1.06056			0.530281	−	0.847822i	$-0.322086\pi$
$983$	33.2516			1.06056			0.530281	+	0.847822i	$0.322086\pi$
$984$	15.8189	+	5.59373i	0.504288	+	0.178322i
$985$		0			0
$986$	10.4795	+	59.7894i	0.333736	+	1.90408i
$987$	−48.1695	−	55.9994i	−1.53325	−	1.78248i
$988$	2.15534	+	5.95961i	0.0685707	+	0.189600i
$989$	−7.14881			−0.227319
$990$		0			0
$991$			33.9434i			1.07825i	0.842226	+	0.539124i	$0.181245\pi$
$991$			33.9434i			1.07825i	−0.842226	+	0.539124i	$0.818755\pi$
$992$	30.4871	+	25.8482i	0.967967	+	0.820681i
$993$	1.80394	−	1.55171i	0.0572462	−	0.0492420i
$994$	12.9677	+	73.9854i	0.411311	+	2.34667i
$995$		0			0
$996$	34.8806	+	19.6667i	1.10523	+	0.623164i
$997$		−	45.6428i		−	1.44552i	−0.691098	−	0.722761i	$-0.742873\pi$
$997$		−	45.6428i		−	1.44552i	0.691098	−	0.722761i	$-0.257127\pi$
$998$	−51.1570	+	8.96650i	−1.61935	+	0.283830i
$999$	11.9758	−	7.51364i	0.378897	−	0.237721i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	600.2.b.h.251.11	yes	12
3.2	odd	2	inner	600.2.b.h.251.2	yes	12
4.3	odd	2		2400.2.b.g.2351.9		12
5.2	odd	4		600.2.m.e.299.16		24
5.3	odd	4		600.2.m.e.299.9		24
5.4	even	2		600.2.b.g.251.2	yes	12
8.3	odd	2	inner	600.2.b.h.251.1	yes	12
8.5	even	2		2400.2.b.g.2351.10		12
12.11	even	2		2400.2.b.g.2351.11		12
15.2	even	4		600.2.m.e.299.10		24
15.8	even	4		600.2.m.e.299.15		24
15.14	odd	2		600.2.b.g.251.11	yes	12
20.3	even	4		2400.2.m.e.1199.19		24
20.7	even	4		2400.2.m.e.1199.6		24
20.19	odd	2		2400.2.b.h.2351.4		12
24.5	odd	2		2400.2.b.g.2351.12		12
24.11	even	2	inner	600.2.b.h.251.12	yes	12
40.3	even	4		600.2.m.e.299.11		24
40.13	odd	4		2400.2.m.e.1199.20		24
40.19	odd	2		600.2.b.g.251.12	yes	12
40.27	even	4		600.2.m.e.299.14		24
40.29	even	2		2400.2.b.h.2351.3		12
40.37	odd	4		2400.2.m.e.1199.5		24
60.23	odd	4		2400.2.m.e.1199.7		24
60.47	odd	4		2400.2.m.e.1199.18		24
60.59	even	2		2400.2.b.h.2351.2		12
120.29	odd	2		2400.2.b.h.2351.1		12
120.53	even	4		2400.2.m.e.1199.8		24
120.59	even	2		600.2.b.g.251.1	✓	12
120.77	even	4		2400.2.m.e.1199.17		24
120.83	odd	4		600.2.m.e.299.13		24
120.107	odd	4		600.2.m.e.299.12		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
600.2.b.g.251.1	✓	12	120.59	even	2
600.2.b.g.251.2	yes	12	5.4	even	2
600.2.b.g.251.11	yes	12	15.14	odd	2
600.2.b.g.251.12	yes	12	40.19	odd	2
600.2.b.h.251.1	yes	12	8.3	odd	2	inner
600.2.b.h.251.2	yes	12	3.2	odd	2	inner
600.2.b.h.251.11	yes	12	1.1	even	1	trivial
600.2.b.h.251.12	yes	12	24.11	even	2	inner
600.2.m.e.299.9		24	5.3	odd	4
600.2.m.e.299.10		24	15.2	even	4
600.2.m.e.299.11		24	40.3	even	4
600.2.m.e.299.12		24	120.107	odd	4
600.2.m.e.299.13		24	120.83	odd	4
600.2.m.e.299.14		24	40.27	even	4
600.2.m.e.299.15		24	15.8	even	4
600.2.m.e.299.16		24	5.2	odd	4
2400.2.b.g.2351.9		12	4.3	odd	2
2400.2.b.g.2351.10		12	8.5	even	2
2400.2.b.g.2351.11		12	12.11	even	2
2400.2.b.g.2351.12		12	24.5	odd	2
2400.2.b.h.2351.1		12	120.29	odd	2
2400.2.b.h.2351.2		12	60.59	even	2
2400.2.b.h.2351.3		12	40.29	even	2
2400.2.b.h.2351.4		12	20.19	odd	2
2400.2.m.e.1199.5		24	40.37	odd	4
2400.2.m.e.1199.6		24	20.7	even	4
2400.2.m.e.1199.7		24	60.23	odd	4
2400.2.m.e.1199.8		24	120.53	even	4
2400.2.m.e.1199.17		24	120.77	even	4
2400.2.m.e.1199.18		24	60.47	odd	4
2400.2.m.e.1199.19		24	20.3	even	4
2400.2.m.e.1199.20		24	40.13	odd	4

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:	\( N \)	\(=\)	\( 600 = 2^{3} \cdot 3 \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	600.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(1.39298 - 0.244153i) q^{2} +(-1.31310 + 1.12950i) q^{3} +(1.88078 - 0.680200i) q^{4} +(-1.55335 + 1.89397i) q^{6} +4.34495i q^{7} +(2.45381 - 1.40670i) q^{8} +(0.448458 - 2.96629i) q^{9} +O(q^{10})\)	\(q+(1.39298 - 0.244153i) q^{2} +(-1.31310 + 1.12950i) q^{3} +(1.88078 - 0.680200i) q^{4} +(-1.55335 + 1.89397i) q^{6} +4.34495i q^{7} +(2.45381 - 1.40670i) q^{8} +(0.448458 - 2.96629i) q^{9} +1.83679i q^{11} +(-1.70136 + 3.01751i) q^{12} -0.588129i q^{13} +(1.06083 + 6.05242i) q^{14} +(3.07466 - 2.55861i) q^{16} +5.37818i q^{17} +(-0.0995365 - 4.24147i) q^{18} -5.38776 q^{19} +(-4.90762 - 5.70535i) q^{21} +(0.448458 + 2.55861i) q^{22} +2.40885 q^{23} +(-1.63323 + 4.61872i) q^{24} +(-0.143593 - 0.819251i) q^{26} +(2.76156 + 4.40157i) q^{27} +(2.95543 + 8.17189i) q^{28} +7.98077 q^{29} +7.06575i q^{31} +(3.65824 - 4.31478i) q^{32} +(-2.07466 - 2.41189i) q^{33} +(1.31310 + 7.49169i) q^{34} +(-1.17422 - 5.88398i) q^{36} -2.72080i q^{37} +(-7.50503 + 1.31544i) q^{38} +(0.664291 + 0.772271i) q^{39} -3.42496i q^{41} +(-8.22919 - 6.74922i) q^{42} -2.96772 q^{43} +(1.24939 + 3.45460i) q^{44} +(3.35548 - 0.588129i) q^{46} +9.81525 q^{47} +(-1.14738 + 6.83253i) q^{48} -11.8786 q^{49} +(-6.07466 - 7.06208i) q^{51} +(-0.400045 - 1.10614i) q^{52} -6.65218 q^{53} +(4.92145 + 5.45705i) q^{54} +(6.11205 + 10.6617i) q^{56} +(7.07466 - 6.08547i) q^{57} +(11.1170 - 1.94853i) q^{58} -10.7564i q^{59} -9.27803i q^{61} +(1.72512 + 9.84244i) q^{62} +(12.8884 + 1.94853i) q^{63} +(4.04238 - 6.90356i) q^{64} +(-3.47882 - 2.85318i) q^{66} -4.13536 q^{67} +(3.65824 + 10.1152i) q^{68} +(-3.16306 + 2.72080i) q^{69} +12.2241 q^{71} +(-3.07226 - 7.90957i) q^{72} -4.42003 q^{73} +(-0.664291 - 3.79002i) q^{74} +(-10.1332 + 3.66475i) q^{76} -7.98077 q^{77} +(1.11390 + 0.913568i) q^{78} -12.5870i q^{79} +(-8.59777 - 2.66052i) q^{81} +(-0.836213 - 4.77089i) q^{82} -11.5594i q^{83} +(-13.1109 - 7.39234i) q^{84} +(-4.13398 + 0.724579i) q^{86} +(-10.4795 + 9.01428i) q^{87} +(2.58382 + 4.50714i) q^{88} +4.21222i q^{89} +2.55539 q^{91} +(4.53052 - 1.63850i) q^{92} +(-7.98077 - 9.27803i) q^{93} +(13.6724 - 2.39642i) q^{94} +(0.0699132 + 9.79771i) q^{96} -2.16763 q^{97} +(-16.5466 + 2.90019i) q^{98} +(5.44846 + 0.823724i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 2 q^{3} + 10 q^{4} + 7 q^{6} - 2 q^{9}+O(q^{10}) \) 12 * q + 2 * q^3 + 10 * q^4 + 7 * q^6 - 2 * q^9	\( 12 q + 2 q^{3} + 10 q^{4} + 7 q^{6} - 2 q^{9} - 3 q^{12} - 6 q^{16} - 5 q^{18} - 4 q^{19} - 2 q^{22} + 5 q^{24} + 8 q^{27} - 20 q^{28} + 18 q^{33} - 2 q^{34} + 19 q^{36} - 14 q^{42} - 40 q^{43} - 16 q^{46} - 27 q^{48} - 36 q^{49} - 30 q^{51} - 4 q^{52} - 30 q^{54} + 42 q^{57} + 52 q^{58} + 10 q^{64} + 7 q^{66} - 60 q^{67} - 39 q^{72} + 12 q^{73} - 38 q^{76} + 54 q^{78} - 10 q^{81} + 58 q^{82} - 34 q^{84} + 34 q^{88} - 24 q^{91} + 28 q^{94} - 31 q^{96} - 32 q^{97} + 58 q^{99}+O(q^{100}) \) 12 * q + 2 * q^3 + 10 * q^4 + 7 * q^6 - 2 * q^9 - 3 * q^12 - 6 * q^16 - 5 * q^18 - 4 * q^19 - 2 * q^22 + 5 * q^24 + 8 * q^27 - 20 * q^28 + 18 * q^33 - 2 * q^34 + 19 * q^36 - 14 * q^42 - 40 * q^43 - 16 * q^46 - 27 * q^48 - 36 * q^49 - 30 * q^51 - 4 * q^52 - 30 * q^54 + 42 * q^57 + 52 * q^58 + 10 * q^64 + 7 * q^66 - 60 * q^67 - 39 * q^72 + 12 * q^73 - 38 * q^76 + 54 * q^78 - 10 * q^81 + 58 * q^82 - 34 * q^84 + 34 * q^88 - 24 * q^91 + 28 * q^94 - 31 * q^96 - 32 * q^97 + 58 * q^99

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