LMFDB - Embedded newform 600.2.b.f.251.6

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:	$8$
Coefficient field:	8.0.1649659456.5
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{7} - 2x^{5} + 4x^{4} - 4x^{3} - 8x + 16 $ x^8 - x^7 - 2x^5 + 4x^4 - 4x^3 - 8x + 16
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	no (minimal twist has level 120)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			251.6
Root			$0.814732 + 1.15595i$ of defining polynomial
Character	$\chi$	$=$	600.251
Dual form			600.2.b.f.251.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.814732 + 1.15595i) q^{2} +(-1.48716 - 0.887900i) q^{3} +(-0.672424 + 1.88357i) q^{4} +(-0.185268 - 2.44247i) q^{6} -0.797253i q^{7} +(-2.72515 + 0.757320i) q^{8} +(1.42327 + 2.64089i) q^{9} +O(q^{10})$	\(q+(0.814732 + 1.15595i) q^{2} +(-1.48716 - 0.887900i) q^{3} +(-0.672424 + 1.88357i) q^{4} +(-0.185268 - 2.44247i) q^{6} -0.797253i q^{7} +(-2.72515 + 0.757320i) q^{8} +(1.42327 + 2.64089i) q^{9} +0.320548i q^{11} +(2.67242 - 2.20412i) q^{12} +4.30324i q^{13} +(0.921582 - 0.649548i) q^{14} +(-3.09569 - 2.53312i) q^{16} +2.57305i q^{17} +(-1.89315 + 3.79684i) q^{18} -6.10546 q^{19} +(-0.707881 + 1.18564i) q^{21} +(-0.370537 + 0.261161i) q^{22} -3.13115 q^{23} +(4.72515 + 1.29341i) q^{24} +(-4.97431 + 3.50598i) q^{26} +(0.228229 - 5.19114i) q^{27} +(1.50168 + 0.536093i) q^{28} -8.79516 q^{29} +9.90557i q^{31} +(0.405993 - 5.64227i) q^{32} +(0.284615 - 0.476705i) q^{33} +(-2.97431 + 2.09635i) q^{34} +(-5.93135 + 0.905026i) q^{36} +8.49593i q^{37} +(-4.97431 - 7.05758i) q^{38} +(3.82085 - 6.39959i) q^{39} -5.28178i q^{41} +(-1.94727 + 0.147706i) q^{42} +2.97431 q^{43} +(-0.603776 - 0.215544i) q^{44} +(-2.55105 - 3.61944i) q^{46} +6.56192 q^{47} +(2.35462 + 6.51581i) q^{48} +6.36439 q^{49} +(2.28461 - 3.82653i) q^{51} +(-8.10546 - 2.89360i) q^{52} -3.94862 q^{53} +(6.18662 - 3.96556i) q^{54} +(0.603776 + 2.17264i) q^{56} +(9.07977 + 5.42104i) q^{57} +(-7.16569 - 10.1667i) q^{58} -12.4786i q^{59} +8.83339i q^{61} +(-11.4503 + 8.07038i) q^{62} +(2.10546 - 1.13470i) q^{63} +(6.85293 - 4.12763i) q^{64} +(0.782930 - 0.0593874i) q^{66} -4.66738 q^{67} +(-4.84653 - 1.73018i) q^{68} +(4.65651 + 2.78015i) q^{69} +3.43077 q^{71} +(-5.87862 - 6.11897i) q^{72} +1.43077 q^{73} +(-9.82085 + 6.92191i) q^{74} +(4.10546 - 11.5001i) q^{76} +0.255558 q^{77} +(10.5105 - 0.797253i) q^{78} -2.89360i q^{79} +(-4.94862 + 7.51739i) q^{81} +(6.10546 - 4.30324i) q^{82} +3.37031i q^{83} +(-1.75724 - 2.13060i) q^{84} +(2.42327 + 3.43815i) q^{86} +(13.0798 + 7.80922i) q^{87} +(-0.242757 - 0.873543i) q^{88} +13.7526i q^{89} +3.43077 q^{91} +(2.10546 - 5.89774i) q^{92} +(8.79516 - 14.7311i) q^{93} +(5.34620 + 7.58523i) q^{94} +(-5.61354 + 8.03045i) q^{96} +4.26230 q^{97} +(5.18527 + 7.35689i) q^{98} +(-0.846533 + 0.456225i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + q^{2} + q^{4} - 7 q^{6} + 7 q^{8}+O(q^{10}) $ 8 * q + q^2 + q^4 - 7 * q^6 + 7 * q^8	$ 8 q + q^{2} + q^{4} - 7 q^{6} + 7 q^{8} + 15 q^{12} + 6 q^{14} - 7 q^{16} - 11 q^{18} - 4 q^{19} + 4 q^{21} - 14 q^{22} - 4 q^{23} + 9 q^{24} - 16 q^{26} + 12 q^{27} + 2 q^{28} + 11 q^{32} + 4 q^{33} - 19 q^{36} - 16 q^{38} - 16 q^{39} - 38 q^{42} + 30 q^{44} - 8 q^{46} + 28 q^{47} - 21 q^{48} - 16 q^{49} + 20 q^{51} - 20 q^{52} + 16 q^{53} - 15 q^{54} - 30 q^{56} + 4 q^{57} + 2 q^{58} - 34 q^{62} - 28 q^{63} + 25 q^{64} + 18 q^{66} + 32 q^{67} - 16 q^{68} - 20 q^{69} + 24 q^{71} - 41 q^{72} + 8 q^{73} - 32 q^{74} - 12 q^{76} + 12 q^{78} + 8 q^{81} + 4 q^{82} - 2 q^{84} + 8 q^{86} + 36 q^{87} - 14 q^{88} + 24 q^{91} - 28 q^{92} - 40 q^{94} + 17 q^{96} - 8 q^{97} + 47 q^{98} + 16 q^{99}+O(q^{100}) $ 8 * q + q^2 + q^4 - 7 * q^6 + 7 * q^8 + 15 * q^12 + 6 * q^14 - 7 * q^16 - 11 * q^18 - 4 * q^19 + 4 * q^21 - 14 * q^22 - 4 * q^23 + 9 * q^24 - 16 * q^26 + 12 * q^27 + 2 * q^28 + 11 * q^32 + 4 * q^33 - 19 * q^36 - 16 * q^38 - 16 * q^39 - 38 * q^42 + 30 * q^44 - 8 * q^46 + 28 * q^47 - 21 * q^48 - 16 * q^49 + 20 * q^51 - 20 * q^52 + 16 * q^53 - 15 * q^54 - 30 * q^56 + 4 * q^57 + 2 * q^58 - 34 * q^62 - 28 * q^63 + 25 * q^64 + 18 * q^66 + 32 * q^67 - 16 * q^68 - 20 * q^69 + 24 * q^71 - 41 * q^72 + 8 * q^73 - 32 * q^74 - 12 * q^76 + 12 * q^78 + 8 * q^81 + 4 * q^82 - 2 * q^84 + 8 * q^86 + 36 * q^87 - 14 * q^88 + 24 * q^91 - 28 * q^92 - 40 * q^94 + 17 * q^96 - 8 * q^97 + 47 * q^98 + 16 * 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 $

$2$	0.814732	+	1.15595i	0.576102	+	0.817378i
$2$	0.814732	+	1.15595i	0.576102	+	0.817378i
$3$	−1.48716	−	0.887900i	−0.858610	−	0.512629i
$3$	−1.48716	−	0.887900i	−0.858610	−	0.512629i
$4$	−0.672424	+	1.88357i	−0.336212	+	0.941786i
$5$		0			0
$5$		0			0
$6$	−0.185268	−	2.44247i	−0.0756354	−	0.997136i
$7$		−	0.797253i		−	0.301333i	−0.988585	−	0.150667i	$-0.951858\pi$
$7$		−	0.797253i		−	0.301333i	0.988585	−	0.150667i	$-0.0481420\pi$
$8$	−2.72515	+	0.757320i	−0.963488	+	0.267753i
$9$	1.42327	+	2.64089i	0.474422	+	0.880297i
$10$		0			0
$11$			0.320548i			0.0966489i	0.998832	+	0.0483245i	$0.0153881\pi$
$11$			0.320548i			0.0966489i	−0.998832	+	0.0483245i	$0.984612\pi$
$12$	2.67242	−	2.20412i	0.771462	−	0.636275i
$13$			4.30324i			1.19350i	0.802426	+	0.596752i	$0.203542\pi$
$13$			4.30324i			1.19350i	−0.802426	+	0.596752i	$0.796458\pi$
$14$	0.921582	−	0.649548i	0.246303	−	0.173599i
$15$		0			0
$16$	−3.09569	−	2.53312i	−0.773923	−	0.633280i
$17$			2.57305i			0.624057i	0.950073	+	0.312029i	$0.101008\pi$
$17$			2.57305i			0.624057i	−0.950073	+	0.312029i	$0.898992\pi$
$18$	−1.89315	+	3.79684i	−0.446220	+	0.894923i
$19$	−6.10546			−1.40069			−0.700344	−	0.713805i	$-0.746970\pi$
$19$	−6.10546			−1.40069			−0.700344	+	0.713805i	$0.746970\pi$
$20$		0			0
$21$	−0.707881	+	1.18564i	−0.154472	+	0.258728i
$22$	−0.370537	+	0.261161i	−0.0789986	+	0.0556797i
$23$	−3.13115			−0.652889			−0.326445	−	0.945216i	$-0.605851\pi$
$23$	−3.13115			−0.652889			−0.326445	+	0.945216i	$0.605851\pi$
$24$	4.72515	+	1.29341i	0.964518	+	0.264017i
$25$		0			0
$26$	−4.97431	+	3.50598i	−0.975543	+	0.687580i
$27$	0.228229	−	5.19114i	0.0439227	−	0.999035i
$28$	1.50168	+	0.536093i	0.283792	+	0.101312i
$29$	−8.79516			−1.63322			−0.816610	−	0.577190i	$-0.804149\pi$
$29$	−8.79516			−1.63322			−0.816610	+	0.577190i	$0.804149\pi$
$30$		0			0
$31$			9.90557i			1.77909i	0.456845	+	0.889546i	$0.348980\pi$
$31$			9.90557i			1.77909i	−0.456845	+	0.889546i	$0.651020\pi$
$32$	0.405993	−	5.64227i	0.0717702	−	0.997421i
$33$	0.284615	−	0.476705i	0.0495451	−	0.0829837i
$34$	−2.97431	+	2.09635i	−0.510090	+	0.359521i
$35$		0			0
$36$	−5.93135	+	0.905026i	−0.988559	+	0.150838i
$37$			8.49593i			1.39672i	0.715745	+	0.698362i	$0.246087\pi$
$37$			8.49593i			1.39672i	−0.715745	+	0.698362i	$0.753913\pi$
$38$	−4.97431	−	7.05758i	−0.806940	−	1.14489i
$39$	3.82085	−	6.39959i	0.611825	−	1.02475i
$40$		0			0
$41$		−	5.28178i		−	0.824876i	−0.910986	−	0.412438i	$-0.864677\pi$
$41$		−	5.28178i		−	0.824876i	0.910986	−	0.412438i	$-0.135323\pi$
$42$	−1.94727	+	0.147706i	−0.300470	+	0.0227915i
$43$	2.97431			0.453578			0.226789	−	0.973944i	$-0.427177\pi$
$43$	2.97431			0.453578			0.226789	+	0.973944i	$0.427177\pi$
$44$	−0.603776	−	0.215544i	−0.0910226	−	0.0324945i
$45$		0			0
$46$	−2.55105	−	3.61944i	−0.376131	−	0.533657i
$47$	6.56192			0.957154			0.478577	−	0.878046i	$-0.341153\pi$
$47$	6.56192			0.957154			0.478577	+	0.878046i	$0.341153\pi$
$48$	2.35462	+	6.51581i	0.339860	+	0.940476i
$49$	6.36439			0.909198
$50$		0			0
$51$	2.28461	−	3.82653i	0.319910	−	0.535822i
$52$	−8.10546	−	2.89360i	−1.12403	−	0.401270i
$53$	−3.94862			−0.542385			−0.271193	−	0.962525i	$-0.587418\pi$
$53$	−3.94862			−0.542385			−0.271193	+	0.962525i	$0.587418\pi$
$54$	6.18662	−	3.96556i	0.841893	−	0.539645i
$55$		0			0
$56$	0.603776	+	2.17264i	0.0806829	+	0.290331i
$57$	9.07977	+	5.42104i	1.20265	+	0.718034i
$58$	−7.16569	−	10.1667i	−0.940902	−	1.33496i
$59$		−	12.4786i		−	1.62458i	−0.583255	−	0.812289i	$-0.698221\pi$
$59$		−	12.4786i		−	1.62458i	0.583255	−	0.812289i	$-0.301779\pi$
$60$		0			0
$61$			8.83339i			1.13100i	0.824749	+	0.565500i	$0.191317\pi$
$61$			8.83339i			1.13100i	−0.824749	+	0.565500i	$0.808683\pi$
$62$	−11.4503	+	8.07038i	−1.45419	+	1.02494i
$63$	2.10546	−	1.13470i	0.265263	−	0.142959i
$64$	6.85293	−	4.12763i	0.856617	−	0.515953i
$65$		0			0
$66$	0.782930	−	0.0593874i	0.0963721	−	0.00731008i
$67$	−4.66738			−0.570211			−0.285106	−	0.958496i	$-0.592029\pi$
$67$	−4.66738			−0.570211			−0.285106	+	0.958496i	$0.592029\pi$
$68$	−4.84653	−	1.73018i	−0.587728	−	0.209816i
$69$	4.65651	+	2.78015i	0.560577	+	0.334690i
$70$		0			0
$71$	3.43077			0.407158			0.203579	−	0.979059i	$-0.434743\pi$
$71$	3.43077			0.407158			0.203579	+	0.979059i	$0.434743\pi$
$72$	−5.87862	−	6.11897i	−0.692802	−	0.721128i
$73$	1.43077			0.167459			0.0837295	−	0.996489i	$-0.473317\pi$
$73$	1.43077			0.167459			0.0837295	+	0.996489i	$0.473317\pi$
$74$	−9.82085	+	6.92191i	−1.14165	+	0.804655i
$75$		0			0
$76$	4.10546	−	11.5001i	0.470929	−	1.31915i
$77$	0.255558			0.0291235
$78$	10.5105	−	0.797253i	1.19008	−	0.0902712i
$79$		−	2.89360i		−	0.325556i	−0.986663	−	0.162778i	$-0.947955\pi$
$79$		−	2.89360i		−	0.325556i	0.986663	−	0.162778i	$-0.0520454\pi$
$80$		0			0
$81$	−4.94862	+	7.51739i	−0.549847	+	0.835265i
$82$	6.10546	−	4.30324i	0.674235	−	0.475213i
$83$			3.37031i			0.369939i	0.982744	+	0.184970i	$0.0592187\pi$
$83$			3.37031i			0.369939i	−0.982744	+	0.184970i	$0.940781\pi$
$84$	−1.75724	−	2.13060i	−0.191731	−	0.232467i
$85$		0			0
$86$	2.42327	+	3.43815i	0.261308	+	0.370745i
$87$	13.0798	+	7.80922i	1.40230	+	0.837236i
$88$	−0.242757	−	0.873543i	−0.0258780	−	0.0931200i
$89$			13.7526i			1.45777i	0.684636	+	0.728885i	$0.259961\pi$
$89$			13.7526i			1.45777i	−0.684636	+	0.728885i	$0.740039\pi$
$90$		0			0
$91$	3.43077			0.359642
$92$	2.10546	−	5.89774i	0.219509	−	0.614882i
$93$	8.79516	−	14.7311i	0.912015	−	1.52755i
$94$	5.34620	+	7.58523i	0.551419	+	0.782356i
$95$		0			0
$96$	−5.61354	+	8.03045i	−0.572930	+	0.819604i
$97$	4.26230			0.432771			0.216385	−	0.976308i	$-0.430573\pi$
$97$	4.26230			0.432771			0.216385	+	0.976308i	$0.430573\pi$
$98$	5.18527	+	7.35689i	0.523791	+	0.743158i
$99$	−0.846533	+	0.456225i	−0.0850798	+	0.0458524i
$100$		0			0
$101$	15.3130			1.52370			0.761851	−	0.647753i	$-0.224291\pi$
$101$	15.3130			1.52370			0.761851	+	0.647753i	$0.224291\pi$
$102$	6.28461	−	0.476705i	0.622270	−	0.0472008i
$103$			7.25936i			0.715286i	0.933858	+	0.357643i	$0.116419\pi$
$103$			7.25936i			0.715286i	−0.933858	+	0.357643i	$0.883581\pi$
$104$	−3.25893	−	11.7270i	−0.319564	−	1.14993i
$105$		0			0
$106$	−3.21707	−	4.56440i	−0.312469	−	0.443334i
$107$		−	13.2928i		−	1.28506i	−0.766260	−	0.642531i	$-0.777884\pi$
$107$		−	13.2928i		−	1.28506i	0.766260	−	0.642531i	$-0.222116\pi$
$108$	9.62442	+	3.92053i	0.926110	+	0.377254i
$109$			3.41592i			0.327186i	0.986528	+	0.163593i	$0.0523084\pi$
$109$			3.41592i			0.327186i	−0.986528	+	0.163593i	$0.947692\pi$
$110$		0			0
$111$	7.54354	−	12.6348i	0.716001	−	1.19924i
$112$	−2.01954	+	2.46805i	−0.190828	+	0.233209i
$113$		−	10.2261i		−	0.961992i	−0.876723	−	0.480996i	$-0.840275\pi$
$113$		−	10.2261i		−	0.961992i	0.876723	−	0.480996i	$-0.159725\pi$
$114$	1.13115	+	14.9124i	0.105942	+	1.39668i
$115$		0			0
$116$	5.91408	−	16.5663i	0.549108	−	1.53814i
$117$	−11.3644	+	6.12465i	−1.05064	+	0.566224i
$118$	14.4246	−	10.1667i	1.32789	−	0.935923i
$119$	2.05138			0.188049
$120$		0			0
$121$	10.8972			0.990659
$122$	−10.2109	+	7.19684i	−0.924453	+	0.651571i
$123$	−4.68970	+	7.85484i	−0.422856	+	0.708247i
$124$	−18.6579	−	6.66075i	−1.67553	−	0.598153i
$125$		0			0
$126$	3.02704	+	1.50932i	0.269670	+	0.134461i
$127$		−	4.98995i		−	0.442786i	−0.975185	−	0.221393i	$-0.928940\pi$
$127$		−	4.98995i		−	0.442786i	0.975185	−	0.221393i	$-0.0710604\pi$
$128$	10.3546	+	4.55872i	0.915228	+	0.402937i
$129$	−4.42327	−	2.64089i	−0.389447	−	0.232518i
$130$		0			0
$131$			8.92702i			0.779958i	0.920824	+	0.389979i	$0.127518\pi$
$131$			8.92702i			0.779958i	−0.920824	+	0.389979i	$0.872482\pi$
$132$	0.706527	+	0.856641i	0.0614953	+	0.0745610i
$133$			4.86760i			0.422074i
$134$	−3.80266	−	5.39524i	−0.328500	−	0.466078i
$135$		0			0
$136$	−1.94862	−	7.01197i	−0.167093	−	0.601271i
$137$		−	1.61964i		−	0.138375i	−0.997604	−	0.0691877i	$-0.977959\pi$
$137$		−	1.61964i		−	0.138375i	0.997604	−	0.0691877i	$-0.0220407\pi$
$138$	0.580102	+	7.64775i	0.0493816	+	0.651019i
$139$	3.58761			0.304297			0.152148	−	0.988358i	$-0.451381\pi$
$139$	3.58761			0.304297			0.152148	+	0.988358i	$0.451381\pi$
$140$		0			0
$141$	−9.75860	−	5.82633i	−0.821822	−	0.490665i
$142$	2.79516	+	3.96579i	0.234564	+	0.332801i
$143$	−1.37939			−0.115351
$144$	2.28370	−	11.7807i	0.190309	−	0.981724i
$145$		0			0
$146$	1.16569	+	1.65389i	0.0964735	+	0.136877i
$147$	−9.46484	−	5.65094i	−0.780647	−	0.466082i
$148$	−16.0027	−	5.71287i	−1.31541	−	0.469595i
$149$	−2.31367			−0.189543			−0.0947717	−	0.995499i	$-0.530212\pi$
$149$	−2.31367			−0.189543			−0.0947717	+	0.995499i	$0.530212\pi$
$150$		0			0
$151$		−	3.44347i		−	0.280225i	−0.990136	−	0.140113i	$-0.955254\pi$
$151$		−	3.44347i		−	0.280225i	0.990136	−	0.140113i	$-0.0447465\pi$
$152$	16.6383	−	4.62379i	1.34955	−	0.375039i
$153$	−6.79516	+	3.66214i	−0.549356	+	0.296067i
$154$	0.208211	+	0.295411i	0.0167781	+	0.0238049i
$155$		0			0
$156$	9.48486	+	11.5001i	0.759396	+	0.920743i
$157$		−	9.17084i		−	0.731912i	−0.930632	−	0.365956i	$-0.880742\pi$
$157$		−	9.17084i		−	0.731912i	0.930632	−	0.365956i	$-0.119258\pi$
$158$	3.34485	−	2.35751i	0.266102	−	0.187553i
$159$	5.87222	+	3.50598i	0.465697	+	0.278043i
$160$		0			0
$161$			2.49632i			0.196737i
$162$	−12.7215	+	0.404309i	−0.999495	+	0.0317656i
$163$	10.6160			0.831510			0.415755	−	0.909477i	$-0.363517\pi$
$163$	10.6160			0.831510			0.415755	+	0.909477i	$0.363517\pi$
$164$	9.94862	+	3.55160i	0.776857	+	0.277333i
$165$		0			0
$166$	−3.89589	+	2.74590i	−0.302380	+	0.213123i
$167$	−13.3353			−1.03192			−0.515959	−	0.856613i	$-0.672564\pi$
$167$	−13.3353			−1.03192			−0.515959	+	0.856613i	$0.672564\pi$
$168$	1.03118	−	3.76715i	0.0795571	−	0.290642i
$169$	−5.51785			−0.424450
$170$		0			0
$171$	−8.68970	−	16.1239i	−0.664518	−	1.23302i
$172$	−2.00000	+	5.60233i	−0.152499	+	0.427174i
$173$	13.8972			1.05659			0.528294	−	0.849061i	$-0.322832\pi$
$173$	13.8972			1.05659			0.528294	+	0.849061i	$0.322832\pi$
$174$	1.62946	+	21.4819i	0.123529	+	1.62854i
$175$		0			0
$176$	0.811987	−	0.992318i	0.0612058	−	0.0747988i
$177$	−11.0798	+	18.5577i	−0.832807	+	1.39488i
$178$	−15.8972	+	11.2047i	−1.19155	+	0.839825i
$179$			5.18815i			0.387780i	0.981023	+	0.193890i	$0.0621105\pi$
$179$			5.18815i			0.387780i	−0.981023	+	0.193890i	$0.937889\pi$
$180$		0			0
$181$		−	2.59819i		−	0.193122i	−0.995327	−	0.0965610i	$-0.969216\pi$
$181$		−	2.59819i		−	0.193122i	0.995327	−	0.0965610i	$-0.0307843\pi$
$182$	2.79516	+	3.96579i	0.207191	+	0.293964i
$183$	7.84316	−	13.1366i	0.579783	−	0.971087i
$184$	8.53286	−	2.37128i	0.629051	−	0.174813i
$185$		0			0
$186$	24.1941	−	1.83519i	1.77400	−	0.134562i
$187$	−0.824788			−0.0603144
$188$	−4.41239	+	12.3598i	−0.321807	+	0.901435i
$189$	−4.13865	−	0.181956i	−0.301043	−	0.0132354i
$190$		0			0
$191$	−12.2556			−0.886781			−0.443391	−	0.896329i	$-0.646225\pi$
$191$	−12.2556			−0.886781			−0.443391	+	0.896329i	$0.646225\pi$
$192$	−13.8563	+	0.0537046i	−0.999992	+	0.00387579i
$193$	−8.26230			−0.594733			−0.297367	−	0.954763i	$-0.596108\pi$
$193$	−8.26230			−0.594733			−0.297367	+	0.954763i	$0.596108\pi$
$194$	3.47263	+	4.92699i	0.249320	+	0.353737i
$195$		0			0
$196$	−4.27957	+	11.9878i	−0.305683	+	0.856270i
$197$	−10.8102			−0.770192			−0.385096	−	0.922876i	$-0.625832\pi$
$197$	−10.8102			−0.770192			−0.385096	+	0.922876i	$0.625832\pi$
$198$	−1.21707	−	0.606846i	−0.0864934	−	0.0431266i
$199$			5.71287i			0.404975i	0.979285	+	0.202487i	$0.0649025\pi$
$199$			5.71287i			0.404975i	−0.979285	+	0.202487i	$0.935097\pi$
$200$		0			0
$201$	6.94112	+	4.14417i	0.489589	+	0.292307i
$202$	12.4760	+	17.7010i	0.877808	+	1.24544i
$203$			7.01197i			0.492144i
$204$	5.67132	+	6.87629i	0.397072	+	0.481437i
$205$		0			0
$206$	−8.39143	+	5.91443i	−0.584659	+	0.412078i
$207$	−4.45646	−	8.26902i	−0.309745	−	0.574737i
$208$	10.9006	−	13.3215i	0.755822	−	0.923679i
$209$		−	1.95709i		−	0.135375i
$210$		0			0
$211$	−8.15684			−0.561540			−0.280770	−	0.959775i	$-0.590590\pi$
$211$	−8.15684			−0.561540			−0.280770	+	0.959775i	$0.590590\pi$
$212$	2.65515	−	7.43752i	0.182357	−	0.510811i
$213$	−5.10209	−	3.04618i	−0.349590	−	0.208721i
$214$	15.3657	−	10.8300i	1.05038	−	0.740327i
$215$		0			0
$216$	3.30939	+	14.3195i	0.225176	+	0.974318i
$217$	7.89725			0.536100
$218$	−3.94862	+	2.78306i	−0.267435	+	0.188493i
$219$	−2.12778	−	1.27038i	−0.143782	−	0.0858444i
$220$		0			0
$221$	−11.0725			−0.744814
$222$	20.7511	−	1.57403i	1.39272	−	0.105642i
$223$			20.6084i			1.38004i	0.723790	+	0.690020i	$0.242398\pi$
$223$			20.6084i			1.38004i	−0.723790	+	0.690020i	$0.757602\pi$
$224$	−4.49832	−	0.323680i	−0.300556	−	0.0216268i
$225$		0			0
$226$	11.8208	−	8.33154i	0.786311	−	0.554206i
$227$			27.0044i			1.79235i	0.443706	+	0.896173i	$0.353664\pi$
$227$			27.0044i			1.79235i	−0.443706	+	0.896173i	$0.646336\pi$
$228$	−16.3164	+	13.4572i	−1.08058	+	0.891223i
$229$		−	9.65112i		−	0.637764i	−0.947794	−	0.318882i	$-0.896693\pi$
$229$		−	9.65112i		−	0.637764i	0.947794	−	0.318882i	$-0.103307\pi$
$230$		0			0
$231$	−0.380055	−	0.226910i	−0.0250058	−	0.0149296i
$232$	23.9682	−	6.66075i	1.57359	−	0.437299i
$233$		−	1.29086i		−	0.0845671i	−0.999106	−	0.0422836i	$-0.986537\pi$
$233$		−	1.29086i		−	0.0845671i	0.999106	−	0.0422836i	$-0.0134633\pi$
$234$	−16.3387	−	8.14667i	−1.06809	−	0.532565i
$235$		0			0
$236$	23.5044	+	8.39093i	1.53001	+	0.546203i
$237$	−2.56923	+	4.30324i	−0.166889	+	0.279525i
$238$	1.67132	+	2.37128i	0.108336	+	0.153707i
$239$	4.21092			0.272382			0.136191	−	0.990683i	$-0.456514\pi$
$239$	4.21092			0.272382			0.136191	+	0.990683i	$0.456514\pi$
$240$		0			0
$241$	−19.5686			−1.26052			−0.630261	−	0.776383i	$-0.717052\pi$
$241$	−19.5686			−1.26052			−0.630261	+	0.776383i	$0.717052\pi$
$242$	8.87833	+	12.5966i	0.570721	+	0.809742i
$243$	14.0341	−	6.78564i	0.900286	−	0.435299i
$244$	−16.6383	−	5.93978i	−1.06516	−	0.380256i
$245$		0			0
$246$	−12.9006	+	0.978547i	−0.822513	+	0.0623899i
$247$		−	26.2732i		−	1.67173i
$248$	−7.50168	−	26.9942i	−0.476357	−	1.71413i
$249$	2.99250	−	5.01217i	0.189642	−	0.317634i
$250$		0			0
$251$			17.5335i			1.10670i	0.832947	+	0.553352i	$0.186652\pi$
$251$			17.5335i			1.10670i	−0.832947	+	0.553352i	$0.813348\pi$
$252$	0.721535	+	4.72879i	0.0454524	+	0.297886i
$253$		−	1.00368i		−	0.0631011i
$254$	5.76812	−	4.06547i	0.361924	−	0.255090i
$255$		0			0
$256$	3.16660	+	15.6835i	0.197913	+	0.980220i
$257$		−	1.16582i		−	0.0727221i	−0.999339	−	0.0363610i	$-0.988423\pi$
$257$		−	1.16582i		−	0.0727221i	0.999339	−	0.0363610i	$-0.0115766\pi$
$258$	−0.551046	−	7.26468i	−0.0343066	−	0.452279i
$259$	6.77341			0.420879
$260$		0			0
$261$	−12.5179	−	23.2271i	−0.774836	−	1.43772i
$262$	−10.3192	+	7.27313i	−0.637520	+	0.449335i
$263$	−15.3867			−0.948785			−0.474392	−	0.880313i	$-0.657332\pi$
$263$	−15.3867			−0.948785			−0.474392	+	0.880313i	$0.657332\pi$
$264$	−0.414601	+	1.51464i	−0.0255169	+	0.0932196i
$265$		0			0
$266$	−5.62668	+	3.96579i	−0.344994	+	0.243158i
$267$	12.2109	−	20.4522i	0.747296	−	1.25166i
$268$	3.13846	−	8.79135i	0.191712	−	0.537017i
$269$	−2.82479			−0.172230			−0.0861152	−	0.996285i	$-0.527445\pi$
$269$	−2.82479			−0.172230			−0.0861152	+	0.996285i	$0.527445\pi$
$270$		0			0
$271$		−	3.89729i		−	0.236743i	−0.992969	−	0.118372i	$-0.962233\pi$
$271$		−	3.89729i		−	0.236743i	0.992969	−	0.118372i	$-0.0377674\pi$
$272$	6.51785	−	7.96538i	0.395203	−	0.482972i
$273$	−5.10209	−	3.04618i	−0.308793	−	0.184363i
$274$	1.87222	−	1.31957i	0.113105	−	0.0797184i
$275$		0			0
$276$	−8.36776	+	6.90143i	−0.503680	+	0.415417i
$277$		−	21.8450i		−	1.31254i	−0.754527	−	0.656269i	$-0.772134\pi$
$277$		−	21.8450i		−	1.31254i	0.754527	−	0.656269i	$-0.227866\pi$
$278$	2.92294	+	4.14708i	0.175306	+	0.248725i
$279$	−26.1595	+	14.0983i	−1.56613	+	0.844041i
$280$		0			0
$281$		−	20.7201i		−	1.23606i	−0.786155	−	0.618029i	$-0.787931\pi$
$281$		−	20.7201i		−	1.23606i	0.786155	−	0.618029i	$-0.212069\pi$
$282$	−1.21572	−	16.0273i	−0.0723948	−	0.954412i
$283$	−1.23661			−0.0735087			−0.0367544	−	0.999324i	$-0.511702\pi$
$283$	−1.23661			−0.0735087			−0.0367544	+	0.999324i	$0.511702\pi$
$284$	−2.30693	+	6.46211i	−0.136891	+	0.383455i
$285$		0			0
$286$	−1.12384	−	1.59451i	−0.0664539	−	0.0942852i
$287$	−4.21092			−0.248563
$288$	15.4785	−	6.95826i	0.912077	−	0.410020i
$289$	10.3794			0.610553
$290$		0			0
$291$	−6.33870	−	3.78449i	−0.371581	−	0.221851i
$292$	−0.962085	+	2.69496i	−0.0563018	+	0.157711i
$293$	−6.00000			−0.350524			−0.175262	−	0.984522i	$-0.556077\pi$
$293$	−6.00000			−0.350524			−0.175262	+	0.984522i	$0.556077\pi$
$294$	−1.17912	−	15.5448i	−0.0687676	−	0.906594i
$295$		0			0
$296$	−6.43414	−	23.1527i	−0.373977	−	1.34573i
$297$	1.66401	+	0.0731584i	0.0965556	+	0.00424508i
$298$	−1.88502	−	2.67448i	−0.109196	−	0.154928i
$299$		−	13.4741i		−	0.779226i
$300$		0			0
$301$		−	2.37128i		−	0.136678i
$302$	3.98046	−	2.80550i	0.229050	−	0.161438i
$303$	−22.7728	−	13.5964i	−1.30827	−	0.781094i
$304$	18.9006	+	15.4659i	1.08402	+	0.887028i
$305$		0			0
$306$	−9.76947	−	4.87118i	−0.558483	−	0.278467i
$307$	−6.71875			−0.383460			−0.191730	−	0.981448i	$-0.561410\pi$
$307$	−6.71875			−0.383460			−0.191730	+	0.981448i	$0.561410\pi$
$308$	−0.171843	+	0.481362i	−0.00979169	+	0.0274282i
$309$	6.44559	−	10.7958i	0.366677	−	0.614152i
$310$		0			0
$311$	−22.0568			−1.25073			−0.625363	−	0.780334i	$-0.715049\pi$
$311$	−22.0568			−1.25073			−0.625363	+	0.780334i	$0.715049\pi$
$312$	−5.56586	+	20.3335i	−0.315105	+	1.15116i
$313$	11.0357			0.623775			0.311888	−	0.950119i	$-0.399039\pi$
$313$	11.0357			0.623775			0.311888	+	0.950119i	$0.399039\pi$
$314$	10.6010	−	7.47177i	0.598249	−	0.421656i
$315$		0			0
$316$	5.45031	+	1.94573i	0.306604	+	0.109456i
$317$	24.3705			1.36878			0.684391	−	0.729115i	$-0.260068\pi$
$317$	24.3705			1.36878			0.684391	+	0.729115i	$0.260068\pi$
$318$	0.731555	+	9.64441i	0.0410236	+	0.540832i
$319$		−	2.81927i		−	0.157849i
$320$		0			0
$321$	−11.8027	+	19.7684i	−0.658760	+	1.10337i
$322$	−2.88561	+	2.03383i	−0.160809	+	0.113341i
$323$		−	15.7097i		−	0.874110i
$324$	−10.8320	−	14.3760i	−0.601776	−	0.798665i
$325$		0			0
$326$	8.64919	+	12.2715i	0.479035	+	0.679657i
$327$	3.03300	−	5.08001i	0.167725	−	0.280925i
$328$	4.00000	+	14.3937i	0.220863	+	0.794758i
$329$		−	5.23151i		−	0.288423i
$330$		0			0
$331$	13.1925			0.725128			0.362564	−	0.931959i	$-0.381901\pi$
$331$	13.1925			0.725128			0.362564	+	0.931959i	$0.381901\pi$
$332$	−6.34822	−	2.26628i	−0.348404	−	0.124378i
$333$	−22.4368	+	12.0920i	−1.22953	+	0.662636i
$334$	−10.8647	−	15.4149i	−0.594491	−	0.843467i
$335$		0			0
$336$	5.19475	−	1.87723i	0.283397	−	0.102411i
$337$	−27.4876			−1.49734			−0.748672	−	0.662941i	$-0.769308\pi$
$337$	−27.4876			−1.49734			−0.748672	+	0.662941i	$0.769308\pi$
$338$	−4.49557	−	6.37834i	−0.244527	−	0.346936i
$339$	−9.07977	+	15.2078i	−0.493146	+	0.825976i
$340$		0			0
$341$	−3.17521			−0.171947
$342$	11.5585	−	23.1814i	0.625015	−	1.25351i
$343$		−	10.6548i		−	0.575305i
$344$	−8.10546	+	2.25251i	−0.437017	+	0.121447i
$345$		0			0
$346$	11.3225	+	16.0645i	0.608703	+	0.863632i
$347$			10.9731i			0.589067i	0.955641	+	0.294533i	$0.0951642\pi$
$347$			10.9731i			0.589067i	−0.955641	+	0.294533i	$0.904836\pi$
$348$	−23.5044	+	19.3856i	−1.25997	+	1.03918i
$349$			31.6066i			1.69186i	0.533291	+	0.845932i	$0.320955\pi$
$349$			31.6066i			1.69186i	−0.533291	+	0.845932i	$0.679045\pi$
$350$		0			0
$351$	22.3387	+	0.982124i	1.19235	+	0.0524219i
$352$	1.80862	+	0.130140i	0.0963997	+	0.00693651i
$353$			21.4646i			1.14244i	0.820795	+	0.571222i	$0.193531\pi$
$353$			21.4646i			1.14244i	−0.820795	+	0.571222i	$0.806469\pi$
$354$	−30.4787	+	2.31189i	−1.61992	+	0.122876i
$355$		0			0
$356$	−25.9040	−	9.24757i	−1.37291	−	0.490120i
$357$	−3.05072	−	1.82142i	−0.161461	−	0.0963996i
$358$	−5.99722	+	4.22695i	−0.316963	+	0.223401i
$359$	34.3124			1.81094			0.905468	−	0.424414i	$-0.139520\pi$
$359$	34.3124			1.81094			0.905468	+	0.424414i	$0.139520\pi$
$360$		0			0
$361$	18.2766			0.961929
$362$	3.00337	−	2.11683i	0.157854	−	0.111258i
$363$	−16.2059	−	9.67567i	−0.850590	−	0.507841i
$364$	−2.30693	+	6.46211i	−0.120916	+	0.338706i
$365$		0			0
$366$	21.5753	−	1.63655i	1.12776	−	0.0855436i
$367$			27.9901i			1.46107i	0.682874	+	0.730536i	$0.260730\pi$
$367$			27.9901i			1.46107i	−0.682874	+	0.730536i	$0.739270\pi$
$368$	9.69307	+	7.93157i	0.505286	+	0.413462i
$369$	13.9486	−	7.51739i	0.726136	−	0.391340i
$370$		0			0
$371$			3.14805i			0.163439i
$372$	21.8331	+	26.4719i	1.13199	+	1.37250i
$373$			13.9134i			0.720408i	0.932873	+	0.360204i	$0.117293\pi$
$373$			13.9134i			0.720408i	−0.932873	+	0.360204i	$0.882707\pi$
$374$	−0.671981	−	0.953410i	−0.0347473	−	0.0492997i
$375$		0			0
$376$	−17.8822	+	4.96947i	−0.922206	+	0.256281i
$377$		−	37.8477i		−	1.94925i
$378$	−3.16156	−	4.93231i	−0.162613	−	0.253690i
$379$	7.79853			0.400583			0.200292	−	0.979736i	$-0.435811\pi$
$379$	7.79853			0.400583			0.200292	+	0.979736i	$0.435811\pi$
$380$		0			0
$381$	−4.43058	+	7.42084i	−0.226985	+	0.380181i
$382$	−9.98499	−	14.1668i	−0.510877	−	0.724835i
$383$	27.8386			1.42248			0.711242	−	0.702947i	$-0.248133\pi$
$383$	27.8386			1.42248			0.711242	+	0.702947i	$0.248133\pi$
$384$	−11.3512	−	15.9734i	−0.579266	−	0.815139i
$385$		0			0
$386$	−6.73155	−	9.55077i	−0.342627	−	0.486121i
$387$	4.23324	+	7.85484i	0.215188	+	0.399284i
$388$	−2.86607	+	8.02834i	−0.145503	+	0.407577i
$389$	18.5246			0.939234			0.469617	−	0.882870i	$-0.344392\pi$
$389$	18.5246			0.939234			0.469617	+	0.882870i	$0.344392\pi$
$390$		0			0
$391$		−	8.05661i		−	0.407440i
$392$	−17.3439	+	4.81988i	−0.876001	+	0.243441i
$393$	7.92631	−	13.2759i	0.399829	−	0.669679i
$394$	−8.80738	−	12.4960i	−0.443710	−	0.629538i
$395$		0			0
$396$	−0.290104	−	1.90128i	−0.0145783	−	0.0955431i
$397$			4.97814i			0.249846i	0.992166	+	0.124923i	$0.0398683\pi$
$397$			4.97814i			0.249846i	−0.992166	+	0.124923i	$0.960132\pi$
$398$	−6.60378	+	4.65446i	−0.331017	+	0.233307i
$399$	4.32194	−	7.23888i	0.216368	−	0.362397i
$400$		0			0
$401$		−	16.8094i		−	0.839422i	−0.907658	−	0.419711i	$-0.862132\pi$
$401$		−	16.8094i		−	0.839422i	0.907658	−	0.419711i	$-0.137868\pi$
$402$	0.864717	+	11.3999i	0.0431282	+	0.568578i
$403$	−42.6260			−2.12335
$404$	−10.2968	+	28.8432i	−0.512287	+	1.43500i
$405$		0			0
$406$	−8.10546	+	5.71287i	−0.402267	+	0.283525i
$407$	−2.72336			−0.134992
$408$	−3.32802	+	12.1581i	−0.164762	+	0.601914i
$409$	−17.6053			−0.870527			−0.435264	−	0.900303i	$-0.643345\pi$
$409$	−17.6053			−0.870527			−0.435264	+	0.900303i	$0.643345\pi$
$410$		0			0
$411$	−1.43808	+	2.40866i	−0.0709353	+	0.118811i
$412$	−13.6735	−	4.88137i	−0.673646	−	0.240488i
$413$	−9.94862			−0.489540
$414$	5.92773	−	11.8885i	0.291332	−	0.584286i
$415$		0			0
$416$	24.2800	+	1.74709i	1.19043	+	0.0856580i
$417$	−5.33533	−	3.18544i	−0.261272	−	0.155991i
$418$	2.26230	−	1.59451i	0.110653	−	0.0779899i
$419$			13.3408i			0.651741i	0.945414	+	0.325870i	$0.105657\pi$
$419$			13.3408i			0.651741i	−0.945414	+	0.325870i	$0.894343\pi$
$420$		0			0
$421$			16.7650i			0.817074i	0.912742	+	0.408537i	$0.133961\pi$
$421$			16.7650i			0.817074i	−0.912742	+	0.408537i	$0.866039\pi$
$422$	−6.64563	−	9.42887i	−0.323504	−	0.458990i
$423$	9.33936	+	17.3293i	0.454095	+	0.842580i
$424$	10.7606	−	2.99037i	0.522581	−	0.145225i
$425$		0			0
$426$	−0.635613	−	8.37957i	−0.0307955	−	0.405991i
$427$	7.04245			0.340808
$428$	25.0379	+	8.93839i	1.21025	+	0.432053i
$429$	2.05138	+	1.22476i	0.0990413	+	0.0591322i
$430$		0			0
$431$	−28.9911			−1.39645			−0.698225	−	0.715878i	$-0.746027\pi$
$431$	−28.9911			−1.39645			−0.698225	+	0.715878i	$0.746027\pi$
$432$	−13.8563	+	15.4920i	−0.666662	+	0.745360i
$433$	23.6484			1.13647			0.568235	−	0.822866i	$-0.307626\pi$
$433$	23.6484			1.13647			0.568235	+	0.822866i	$0.307626\pi$
$434$	6.43414	+	9.12880i	0.308849	+	0.438196i
$435$		0			0
$436$	−6.43414	−	2.29695i	−0.308139	−	0.110004i
$437$	19.1171			0.914495
$438$	−0.265076	−	3.49462i	−0.0126658	−	0.166979i
$439$		−	7.85724i		−	0.375006i	−0.982264	−	0.187503i	$-0.939961\pi$
$439$		−	7.85724i		−	0.375006i	0.982264	−	0.187503i	$-0.0600394\pi$
$440$		0			0
$441$	9.05822	+	16.8077i	0.431344	+	0.800365i
$442$	−9.02109	−	12.7992i	−0.429089	−	0.608795i
$443$			12.9805i			0.616721i	0.951270	+	0.308360i	$0.0997802\pi$
$443$			12.9805i			0.616721i	−0.951270	+	0.308360i	$0.900220\pi$
$444$	18.7261	+	22.7047i	0.888700	+	1.07752i
$445$		0			0
$446$	−23.8222	+	16.7903i	−1.12801	+	0.795044i
$447$	3.44079	+	2.05431i	0.162744	+	0.0971655i
$448$	−3.29076	−	5.46352i	−0.155474	−	0.258127i
$449$			13.4847i			0.636383i	0.948026	+	0.318191i	$0.103075\pi$
$449$			13.4847i			0.636383i	−0.948026	+	0.318191i	$0.896925\pi$
$450$		0			0
$451$	1.69307			0.0797234
$452$	19.2616	+	6.87629i	0.905991	+	0.323434i
$453$	−3.05745	+	5.12097i	−0.143652	+	0.240604i
$454$	−31.2156	+	22.0013i	−1.46502	+	1.03257i
$455$		0			0
$456$	−28.8492	−	7.89688i	−1.35099	−	0.369805i
$457$	28.1014			1.31453			0.657265	−	0.753660i	$-0.271713\pi$
$457$	28.1014			1.31453			0.657265	+	0.753660i	$0.271713\pi$
$458$	11.1562	−	7.86307i	0.521294	−	0.367417i
$459$	13.3571	+	0.587246i	0.623455	+	0.0274103i
$460$		0			0
$461$	29.2170			1.36077			0.680386	−	0.732854i	$-0.261812\pi$
$461$	29.2170			1.36077			0.680386	+	0.732854i	$0.261812\pi$
$462$	−0.0473468	−	0.624194i	−0.00220277	−	0.0290401i
$463$		−	14.1463i		−	0.657434i	−0.944429	−	0.328717i	$-0.893384\pi$
$463$		−	14.1463i		−	0.657434i	0.944429	−	0.328717i	$-0.106616\pi$
$464$	27.2271	+	22.2792i	1.26399	+	1.03429i
$465$		0			0
$466$	1.49217	−	1.05171i	0.0691233	−	0.0487193i
$467$			28.9687i			1.34051i	0.742131	+	0.670255i	$0.233815\pi$
$467$			28.9687i			1.34051i	−0.742131	+	0.670255i	$0.766185\pi$
$468$	−3.89454	−	25.5240i	−0.180025	−	1.17985i
$469$			3.72108i			0.171824i
$470$		0			0
$471$	−8.14279	+	13.6385i	−0.375200	+	0.628427i
$472$	9.45031	+	34.0062i	0.434986	+	1.56526i
$473$			0.953410i			0.0438379i
$474$	−7.06755	+	0.536093i	−0.324623	+	0.0246235i
$475$		0			0
$476$	−1.37939	+	3.86391i	−0.0632245	+	0.177102i
$477$	−5.61995	−	10.4279i	−0.257320	−	0.477460i
$478$	3.43077	+	4.86760i	0.156920	+	0.222639i
$479$	−37.9040			−1.73188			−0.865939	−	0.500150i	$-0.833278\pi$
$479$	−37.9040			−1.73188			−0.865939	+	0.500150i	$0.833278\pi$
$480$		0			0
$481$	−36.5600			−1.66699
$482$	−15.9431	−	22.6202i	−0.726190	−	1.03032i
$483$	2.21648	−	3.71241i	0.100853	−	0.168921i
$484$	−7.32758	+	20.5258i	−0.333072	+	0.932989i
$485$		0			0
$486$	19.2778	+	10.6941i	0.874461	+	0.485096i
$487$			41.9180i			1.89949i	0.313031	+	0.949743i	$0.398656\pi$
$487$			41.9180i			1.89949i	−0.313031	+	0.949743i	$0.601344\pi$
$488$	−6.68970	−	24.0723i	−0.302828	−	1.08970i
$489$	−15.7877	−	9.42595i	−0.713942	−	0.426256i
$490$		0			0
$491$		−	5.09691i		−	0.230020i	−0.993364	−	0.115010i	$-0.963310\pi$
$491$		−	5.09691i		−	0.230020i	0.993364	−	0.115010i	$-0.0366901\pi$
$492$	−11.6417	−	14.1152i	−0.524848	−	0.636361i
$493$		−	22.6304i		−	1.01922i
$494$	30.3705	−	21.4056i	1.36643	−	0.963086i
$495$		0			0
$496$	25.0920	−	30.6646i	1.12666	−	1.37688i
$497$		−	2.73519i		−	0.122690i
$498$	8.23188	−	0.624411i	0.368880	−	0.0279805i
$499$	−27.3821			−1.22579			−0.612896	−	0.790164i	$-0.709995\pi$
$499$	−27.3821			−1.22579			−0.612896	+	0.790164i	$0.709995\pi$
$500$		0			0
$501$	19.8317	+	11.8404i	0.886016	+	0.528992i
$502$	−20.2678	+	14.2851i	−0.904596	+	0.637575i
$503$	21.7572			0.970104			0.485052	−	0.874485i	$-0.338801\pi$
$503$	21.7572			0.970104			0.485052	+	0.874485i	$0.338801\pi$
$504$	−4.87837	+	4.68675i	−0.217300	+	0.208764i
$505$		0			0
$506$	1.16020	−	0.817733i	0.0515774	−	0.0363527i
$507$	8.20591	+	4.89930i	0.364437	+	0.217586i
$508$	9.39893	+	3.35536i	0.417010	+	0.148870i
$509$	25.0061			1.10837			0.554187	−	0.832392i	$-0.313029\pi$
$509$	25.0061			1.10837			0.554187	+	0.832392i	$0.313029\pi$
$510$		0			0
$511$		−	1.14069i		−	0.0504610i
$512$	−15.5494	+	16.4383i	−0.687192	+	0.726476i
$513$	−1.39344	+	31.6943i	−0.0615220	+	1.39934i
$514$	1.34763	−	0.949833i	0.0594414	−	0.0418953i
$515$		0			0
$516$	7.94862	−	6.55574i	0.349919	−	0.288600i
$517$			2.10341i			0.0925079i
$518$	5.51851	+	7.82970i	0.242470	+	0.344017i
$519$	−20.6674	−	12.3394i	−0.907197	−	0.541638i
$520$		0			0
$521$		−	26.3235i		−	1.15325i	−0.817007	−	0.576627i	$-0.804369\pi$
$521$		−	26.3235i		−	1.15325i	0.817007	−	0.576627i	$-0.195631\pi$
$522$	16.6505	−	33.3938i	0.728775	−	1.46161i
$523$	23.5435			1.02949			0.514744	−	0.857344i	$-0.327887\pi$
$523$	23.5435			1.02949			0.514744	+	0.857344i	$0.327887\pi$
$524$	−16.8147	−	6.00275i	−0.734553	−	0.262231i
$525$		0			0
$526$	−12.5360	−	17.7862i	−0.546597	−	0.775516i
$527$	−25.4876			−1.11026
$528$	−2.08863	+	0.754768i	−0.0908960	+	0.0328471i
$529$	−13.1959			−0.573735
$530$		0			0
$531$	32.9547	−	17.7604i	1.43011	−	0.770736i
$532$	−9.16847	−	3.27309i	−0.397504	−	0.141907i
$533$	22.7288			0.984492
$534$	33.5903	−	2.54792i	1.45360	−	0.110259i
$535$		0			0
$536$	12.7193	−	3.53470i	0.549391	−	0.152676i
$537$	4.60656	−	7.71558i	0.198788	−	0.332952i
$538$	−2.30144	−	3.26530i	−0.0992223	−	0.140777i
$539$			2.04009i			0.0878730i
$540$		0			0
$541$		−	18.2576i		−	0.784955i	−0.919762	−	0.392478i	$-0.871618\pi$
$541$		−	18.2576i		−	0.784955i	0.919762	−	0.392478i	$-0.128382\pi$
$542$	4.50505	−	3.17524i	0.193509	−	0.136388i
$543$	−2.30693	+	3.86391i	−0.0990000	+	0.165816i
$544$	14.5179	+	1.04464i	0.622448	+	0.0447887i
$545$		0			0
$546$	−0.635613	−	8.37957i	−0.0272017	−	0.358612i
$547$	6.40508			0.273862			0.136931	−	0.990581i	$-0.456276\pi$
$547$	6.40508			0.273862			0.136931	+	0.990581i	$0.456276\pi$
$548$	3.05072	+	1.08909i	0.130320	+	0.0465235i
$549$	−23.3280	+	12.5723i	−0.995616	+	0.536571i
$550$		0			0
$551$	53.6985			2.28763
$552$	−14.7952	−	4.04987i	−0.629724	−	0.172374i
$553$	−2.30693			−0.0981008
$554$	25.2516	−	17.7978i	1.07284	−	0.756156i
$555$		0			0
$556$	−2.41239	+	6.75752i	−0.102308	+	0.286583i
$557$	7.79582			0.330319			0.165160	−	0.986267i	$-0.447186\pi$
$557$	7.79582			0.330319			0.165160	+	0.986267i	$0.447186\pi$
$558$	−37.6099	−	18.7527i	−1.59215	−	0.793866i
$559$			12.7992i			0.541347i
$560$		0			0
$561$	1.22659	+	0.732329i	0.0517866	+	0.0309190i
$562$	23.9513	−	16.8813i	1.01033	−	0.712096i
$563$			4.37399i			0.184342i	0.995743	+	0.0921709i	$0.0293806\pi$
$563$			4.37399i			0.184342i	−0.995743	+	0.0921709i	$0.970619\pi$
$564$	17.5362	−	14.4633i	0.738409	−	0.609013i
$565$		0			0
$566$	−1.00750	−	1.42945i	−0.0423485	−	0.0600844i
$567$	5.99326	+	3.94531i	0.251693	+	0.165687i
$568$	−9.34938	+	2.59819i	−0.392291	+	0.109018i
$569$		−	21.8198i		−	0.914735i	−0.889278	−	0.457368i	$-0.848792\pi$
$569$		−	21.8198i		−	0.914735i	0.889278	−	0.457368i	$-0.151208\pi$
$570$		0			0
$571$	1.42806			0.0597625			0.0298813	−	0.999553i	$-0.490487\pi$
$571$	1.42806			0.0597625			0.0298813	+	0.999553i	$0.490487\pi$
$572$	0.927539	−	2.59819i	0.0387823	−	0.108636i
$573$	18.2259	+	10.8817i	0.761399	+	0.454590i
$574$	−3.43077	−	4.86760i	−0.143198	−	0.203170i
$575$		0			0
$576$	20.6542	+	12.2231i	0.860590	+	0.509298i
$577$	−43.3548			−1.80488			−0.902442	−	0.430812i	$-0.858227\pi$
$577$	−43.3548			−1.80488			−0.902442	+	0.430812i	$0.858227\pi$
$578$	8.45642	+	11.9980i	0.351741	+	0.499052i
$579$	12.2873	+	7.33609i	0.510644	+	0.304878i
$580$		0			0
$581$	2.68699			0.111475
$582$	−0.789668	−	10.4105i	−0.0327328	−	0.431531i
$583$		−	1.26572i		−	0.0524209i
$584$	−3.89907	+	1.08355i	−0.161345	+	0.0448377i
$585$		0			0
$586$	−4.88839	−	6.93568i	−0.201938	−	0.286510i
$587$			6.88810i			0.284302i	0.989845	+	0.142151i	$0.0454019\pi$
$587$			6.88810i			0.284302i	−0.989845	+	0.142151i	$0.954598\pi$
$588$	17.0083	−	14.0279i	0.701412	−	0.578500i
$589$		−	60.4781i		−	2.49196i
$590$		0			0
$591$	16.0764	+	9.59835i	0.661295	+	0.394823i
$592$	21.5212	−	26.3008i	0.884517	−	1.08096i
$593$			0.894469i			0.0367314i	0.999831	+	0.0183657i	$0.00584632\pi$
$593$			0.894469i			0.0367314i	−0.999831	+	0.0183657i	$0.994154\pi$
$594$	1.27115	+	1.98311i	0.0521561	+	0.0813680i
$595$		0			0
$596$	1.55577	−	4.35797i	0.0637268	−	0.178509i
$597$	5.07246	−	8.49593i	0.207602	−	0.347715i
$598$	15.5753	−	10.9778i	0.636922	−	0.448914i
$599$	−11.5836			−0.473292			−0.236646	−	0.971596i	$-0.576048\pi$
$599$	−11.5836			−0.473292			−0.236646	+	0.971596i	$0.576048\pi$
$600$		0			0
$601$	24.9480			1.01765			0.508824	−	0.860870i	$-0.330080\pi$
$601$	24.9480			1.01765			0.508824	+	0.860870i	$0.330080\pi$
$602$	2.74107	−	1.93196i	0.111718	−	0.0787407i
$603$	−6.64292	−	12.3260i	−0.270521	−	0.501955i
$604$	6.48602	+	2.31547i	0.263912	+	0.0942151i
$605$		0			0
$606$	−2.83701	−	37.4016i	−0.115246	−	1.51934i
$607$		−	21.8741i		−	0.887843i	−0.896066	−	0.443922i	$-0.853587\pi$
$607$		−	21.8741i		−	0.887843i	0.896066	−	0.443922i	$-0.146413\pi$
$608$	−2.47878	+	34.4486i	−0.100528	+	1.39708i
$609$	6.22593	−	10.4279i	0.252287	−	0.422560i
$610$		0			0
$611$			28.2375i			1.14237i
$612$	−2.32868	−	15.2617i	−0.0941313	−	0.616917i
$613$		−	25.8339i		−	1.04342i	−0.853122	−	0.521711i	$-0.825294\pi$
$613$		−	25.8339i		−	1.04342i	0.853122	−	0.521711i	$-0.174706\pi$
$614$	−5.47398	−	7.76652i	−0.220912	−	0.313431i
$615$		0			0
$616$	−0.696435	+	0.193539i	−0.0280602	+	0.00779792i
$617$		−	27.5641i		−	1.10969i	−0.831954	−	0.554845i	$-0.812778\pi$
$617$		−	27.5641i		−	1.10969i	0.831954	−	0.554845i	$-0.187222\pi$
$618$	17.7308	−	1.34493i	0.713237	−	0.0541010i
$619$	22.2136			0.892841			0.446421	−	0.894823i	$-0.352699\pi$
$619$	22.2136			0.892841			0.446421	+	0.894823i	$0.352699\pi$
$620$		0			0
$621$	−0.714619	+	16.2542i	−0.0286767	+	0.652259i
$622$	−17.9704	−	25.4965i	−0.720546	−	1.02232i
$623$	10.9643			0.439275
$624$	−28.0391	+	10.1325i	−1.12246	+	0.405624i
$625$		0			0
$626$	8.99114	+	12.7567i	0.359358	+	0.509860i
$627$	−1.73770	+	2.91050i	−0.0693972	+	0.116234i
$628$	17.2739	+	6.16669i	0.689305	+	0.246078i
$629$	−21.8605			−0.871635
$630$		0			0
$631$			26.2225i			1.04390i	0.852975	+	0.521951i	$0.174796\pi$
$631$			26.2225i			1.04390i	−0.852975	+	0.521951i	$0.825204\pi$
$632$	2.19138	+	7.88551i	0.0871685	+	0.313669i
$633$	12.1305	+	7.24246i	0.482144	+	0.287862i
$634$	19.8554	+	28.1710i	0.788558	+	1.11881i
$635$		0			0
$636$	−10.5524	+	8.70324i	−0.418430	+	0.345106i
$637$			27.3875i			1.08513i
$638$	3.25893	−	2.29695i	0.129022	−	0.0909371i
$639$	4.88290	+	9.06030i	0.193165	+	0.358420i
$640$		0			0
$641$			47.0436i			1.85811i	0.369940	+	0.929056i	$0.379378\pi$
$641$			47.0436i			1.85811i	−0.369940	+	0.929056i	$0.620622\pi$
$642$	−32.4673	+	2.46273i	−1.28138	+	0.0971962i
$643$	18.1696			0.716538			0.358269	−	0.933618i	$-0.383367\pi$
$643$	18.1696			0.716538			0.358269	+	0.933618i	$0.383367\pi$
$644$	−4.70200	−	1.67859i	−0.185285	−	0.0661455i
$645$		0			0
$646$	18.1595	−	12.7992i	0.714478	−	0.503577i
$647$	−36.9324			−1.45196			−0.725981	−	0.687715i	$-0.758614\pi$
$647$	−36.9324			−1.45196			−0.725981	+	0.687715i	$0.758614\pi$
$648$	7.79270	−	24.2337i	0.306126	−	0.951991i
$649$	4.00000			0.157014
$650$		0			0
$651$	−11.7444	−	7.01197i	−0.460301	−	0.274821i
$652$	−7.13846	+	19.9960i	−0.279564	+	0.783104i
$653$	−1.11710			−0.0437155			−0.0218577	−	0.999761i	$-0.506958\pi$
$653$	−1.11710			−0.0437155			−0.0218577	+	0.999761i	$0.506958\pi$
$654$	8.34330	−	0.632862i	0.326249	−	0.0247469i
$655$		0			0
$656$	−13.3794	+	16.3508i	−0.522378	+	0.638390i
$657$	2.03637	+	3.77851i	0.0794463	+	0.147414i
$658$	6.04735	−	4.26228i	0.235750	−	0.166161i
$659$			30.7865i			1.19927i	0.800273	+	0.599636i	$0.204688\pi$
$659$			30.7865i			1.19927i	−0.800273	+	0.599636i	$0.795312\pi$
$660$		0			0
$661$		−	11.5686i		−	0.449966i	−0.974363	−	0.224983i	$-0.927767\pi$
$661$		−	11.5686i		−	0.449966i	0.974363	−	0.224983i	$-0.0722326\pi$
$662$	10.7484	+	15.2499i	0.417748	+	0.592703i
$663$	16.4665	+	9.83124i	0.639505	+	0.381814i
$664$	−2.55240	−	9.18461i	−0.0990523	−	0.356432i
$665$		0			0
$666$	−32.2577	−	16.0841i	−1.24996	−	0.623245i
$667$	27.5389			1.06631
$668$	8.96700	−	25.1181i	0.346944	−	0.971847i
$669$	18.2982	−	30.6479i	0.707449	−	1.18492i
$670$		0			0
$671$	−2.83153			−0.109310
$672$	6.40230	+	4.47542i	0.246974	+	0.172643i
$673$	−30.4072			−1.17211			−0.586056	−	0.810271i	$-0.699320\pi$
$673$	−30.4072			−1.17211			−0.586056	+	0.810271i	$0.699320\pi$
$674$	−22.3950	−	31.7742i	−0.862623	−	1.22389i
$675$		0			0
$676$	3.71034	−	10.3933i	0.142705	−	0.399741i
$677$	29.9608			1.15149			0.575743	−	0.817631i	$-0.304713\pi$
$677$	29.9608			1.15149			0.575743	+	0.817631i	$0.304713\pi$
$678$	−24.9770	+	1.89458i	−0.959237	+	0.0727607i
$679$		−	3.39813i		−	0.130408i
$680$		0			0
$681$	23.9772	−	40.1598i	0.918809	−	1.53893i
$682$	−2.58695	−	3.67038i	−0.0990593	−	0.140546i
$683$		−	30.8345i		−	1.17985i	−0.807458	−	0.589925i	$-0.799157\pi$
$683$		−	30.8345i		−	1.17985i	0.807458	−	0.589925i	$-0.200843\pi$
$684$	36.2136	−	5.52560i	1.38466	−	0.211276i
$685$		0			0
$686$	12.3164	−	8.68081i	0.470242	−	0.331435i
$687$	−8.56923	+	14.3527i	−0.326936	+	0.547590i
$688$	−9.20755	−	7.53429i	−0.351035	−	0.287242i
$689$		−	16.9919i		−	0.647339i
$690$		0			0
$691$	−19.2293			−0.731517			−0.365758	−	0.930710i	$-0.619190\pi$
$691$	−19.2293			−0.731517			−0.365758	+	0.930710i	$0.619190\pi$
$692$	−9.34485	+	26.1765i	−0.355238	+	0.995080i
$693$	0.363727	+	0.674901i	0.0138169	+	0.0256374i
$694$	−12.6843	+	8.94013i	−0.481490	+	0.339363i
$695$		0			0
$696$	−41.5585	−	11.3758i	−1.57527	−	0.431197i
$697$	13.5903			0.514770
$698$	−36.5356	+	25.7509i	−1.38289	+	0.974687i
$699$	−1.14616	+	1.91971i	−0.0433516	+	0.0726102i
$700$		0			0
$701$	25.8972			0.978126			0.489063	−	0.872249i	$-0.337339\pi$
$701$	25.8972			0.978126			0.489063	+	0.872249i	$0.337339\pi$
$702$	17.0648	+	26.6225i	0.644068	+	1.00480i
$703$		−	51.8716i		−	1.95637i
$704$	1.32310	+	2.19670i	0.0498663	+	0.0827911i
$705$		0			0
$706$	−24.8119	+	17.4879i	−0.933809	+	0.658165i
$707$		−	12.2083i		−	0.459142i
$708$	−27.5044	−	33.3482i	−1.03368	−	1.25330i
$709$		−	6.00828i		−	0.225646i	−0.993615	−	0.112823i	$-0.964011\pi$
$709$		−	6.00828i		−	0.225646i	0.993615	−	0.112823i	$-0.0359893\pi$
$710$		0			0
$711$	7.64169	−	4.11837i	0.286586	−	0.154451i
$712$	−10.4151	−	37.4779i	−0.390322	−	1.40454i
$713$		−	31.0158i		−	1.16155i
$714$	−0.380055	−	5.01043i	−0.0142232	−	0.187511i
$715$		0			0
$716$	−9.77225	−	3.48864i	−0.365206	−	0.130376i
$717$	−6.26230	−	3.73888i	−0.233870	−	0.139631i
$718$	27.9554	+	39.6632i	1.04328	+	1.48022i
$719$	3.34264			0.124659			0.0623297	−	0.998056i	$-0.480147\pi$
$719$	3.34264			0.124659			0.0623297	+	0.998056i	$0.480147\pi$
$720$		0			0
$721$	5.78755			0.215540
$722$	14.8906	+	21.1268i	0.554169	+	0.786259i
$723$	29.1015	+	17.3749i	1.08230	+	0.646181i
$724$	4.89388	+	1.74709i	0.181880	+	0.0649300i
$725$		0			0
$726$	−2.01891	−	26.6162i	−0.0749289	−	0.987821i
$727$			15.4120i			0.571600i	0.958289	+	0.285800i	$0.0922593\pi$
$727$			15.4120i			0.571600i	−0.958289	+	0.285800i	$0.907741\pi$
$728$	−9.34938	+	2.59819i	−0.346511	+	0.0962953i
$729$	−26.8958	−	2.36954i	−0.996142	−	0.0877607i
$730$		0			0
$731$			7.65306i			0.283059i
$732$	19.4698	+	23.6066i	0.719626	+	0.872523i
$733$			42.7008i			1.57719i	0.614914	+	0.788594i	$0.289191\pi$
$733$			42.7008i			1.57719i	−0.614914	+	0.788594i	$0.710809\pi$
$734$	−32.3551	+	22.8044i	−1.19425	+	0.841727i
$735$		0			0
$736$	−1.27123	+	17.6668i	−0.0468580	+	0.651206i
$737$		−	1.49612i		−	0.0551103i
$738$	20.0541	+	9.99921i	0.738201	+	0.368076i
$739$	30.4546			1.12029			0.560145	−	0.828395i	$-0.310746\pi$
$739$	30.4546			1.12029			0.560145	+	0.828395i	$0.310746\pi$
$740$		0			0
$741$	−23.3280	+	39.0724i	−0.856976	+	1.43536i
$742$	−3.63898	+	2.56482i	−0.133591	+	0.0941575i
$743$	−49.8954			−1.83048			−0.915242	−	0.402906i	$-0.868000\pi$
$743$	−49.8954			−1.83048			−0.915242	+	0.402906i	$0.868000\pi$
$744$	−12.8120	+	46.8054i	−0.469710	+	1.71597i
$745$		0			0
$746$	−16.0831	+	11.3357i	−0.588846	+	0.415029i
$747$	−8.90062	+	4.79685i	−0.325657	+	0.175507i
$748$	0.554607	−	1.55355i	0.0202785	−	0.0568033i
$749$	−10.5977			−0.387232
$750$		0			0
$751$			3.81321i			0.139146i	0.997577	+	0.0695730i	$0.0221637\pi$
$751$			3.81321i			0.139146i	−0.997577	+	0.0695730i	$0.977836\pi$
$752$	−20.3137	−	16.6221i	−0.740763	−	0.606147i
$753$	15.5680	−	26.0750i	0.567329	−	0.950228i
$754$	43.7499	−	30.8357i	1.59328	−	1.12297i
$755$		0			0
$756$	3.12566	−	7.67310i	0.113679	−	0.279068i
$757$			38.1793i			1.38765i	0.720144	+	0.693825i	$0.244076\pi$
$757$			38.1793i			1.38765i	−0.720144	+	0.693825i	$0.755924\pi$
$758$	6.35371	+	9.01468i	0.230777	+	0.327428i
$759$	−0.891171	+	1.49263i	−0.0323475	+	0.0541792i
$760$		0			0
$761$		−	10.7460i		−	0.389543i	−0.980849	−	0.194772i	$-0.937603\pi$
$761$		−	10.7460i		−	0.389543i	0.980849	−	0.194772i	$-0.0623966\pi$
$762$	−12.1878	+	0.924479i	−0.441518	+	0.0334904i
$763$	2.72336			0.0985921
$764$	8.24094	−	23.0842i	0.298147	−	0.835158i
$765$		0			0
$766$	22.6810	+	32.1799i	0.819496	+	1.16271i
$767$	53.6985			1.93894
$768$	9.21616	−	26.1355i	0.332559	−	0.943082i
$769$	1.13172			0.0408109			0.0204055	−	0.999792i	$-0.493504\pi$
$769$	1.13172			0.0408109			0.0204055	+	0.999792i	$0.493504\pi$
$770$		0			0
$771$	−1.03513	+	1.73376i	−0.0372795	+	0.0624399i
$772$	5.55577	−	15.5626i	0.199957	−	0.560111i
$773$	−13.7144			−0.493274			−0.246637	−	0.969108i	$-0.579325\pi$
$773$	−13.7144			−0.493274			−0.246637	+	0.969108i	$0.579325\pi$
$774$	−5.63082	+	11.2930i	−0.202396	+	0.405918i
$775$		0			0
$776$	−11.6154	+	3.22792i	−0.416969	+	0.115876i
$777$	−10.0731	−	6.01411i	−0.361371	−	0.215755i
$778$	15.0926	+	21.4134i	0.541095	+	0.767709i
$779$			32.2477i			1.15539i
$780$		0			0
$781$			1.09973i			0.0393513i
$782$	9.31301	−	6.56398i	0.333033	−	0.234727i
$783$	−2.00731	+	45.6569i	−0.0717354	+	1.63164i
$784$	−19.7022	−	16.1218i	−0.703649	−	0.575777i
$785$		0			0
$786$	21.8040	−	1.65389i	0.777723	−	0.0589924i
$787$	32.6374			1.16340			0.581698	−	0.813405i	$-0.302388\pi$
$787$	32.6374			1.16340			0.581698	+	0.813405i	$0.302388\pi$
$788$	7.26902	−	20.3617i	0.258948	−	0.725357i
$789$	22.8824	+	13.6619i	0.814636	+	0.486375i
$790$		0			0
$791$	−8.15281			−0.289880
$792$	1.96143	−	1.88438i	0.0696962	−	0.0669586i
$793$	−38.0122			−1.34985
$794$	−5.75446	+	4.05585i	−0.204218	+	0.143937i
$795$		0			0
$796$	−10.7606	−	3.84148i	−0.381400	−	0.136157i
$797$	−39.1293			−1.38603			−0.693015	−	0.720923i	$-0.743718\pi$
$797$	−39.1293			−1.38603			−0.693015	+	0.720923i	$0.743718\pi$
$798$	11.8890	−	0.901811i	0.420865	−	0.0319238i
$799$			16.8842i			0.597319i
$800$		0			0
$801$	−36.3191	+	19.5736i	−1.28327	+	0.691599i
$802$	19.4308	−	13.6952i	0.686124	−	0.483593i
$803$			0.458631i			0.0161847i
$804$	−12.4732	+	10.2875i	−0.439896	+	0.362811i
$805$		0			0
$806$	−34.7288	−	49.2734i	−1.22327	−	1.73558i
$807$	4.20090	+	2.50813i	0.147879	+	0.0882903i
$808$	−41.7303	+	11.5968i	−1.46807	+	0.407976i
$809$			25.5481i			0.898222i	0.893476	+	0.449111i	$0.148259\pi$
$809$			25.5481i			0.898222i	−0.893476	+	0.449111i	$0.851741\pi$
$810$		0			0
$811$	5.63898			0.198011			0.0990057	−	0.995087i	$-0.468434\pi$
$811$	5.63898			0.198011			0.0990057	+	0.995087i	$0.468434\pi$
$812$	−13.2076	−	4.71502i	−0.463494	−	0.165465i
$813$	−3.46040	+	5.79587i	−0.121362	+	0.203270i
$814$	−2.21880	−	3.14805i	−0.0777691	−	0.110339i
$815$		0			0
$816$	−16.7655	+	6.05856i	−0.586911	+	0.212092i
$817$	−18.1595			−0.635322
$818$	−14.3436	−	20.3508i	−0.501513	−	0.711549i
$819$	4.88290	+	9.06030i	0.170622	+	0.316592i
$820$		0			0
$821$	−26.8248			−0.936192			−0.468096	−	0.883678i	$-0.655060\pi$
$821$	−26.8248			−0.936192			−0.468096	+	0.883678i	$0.655060\pi$
$822$	−3.95594	+	0.300068i	−0.137979	+	0.0104661i
$823$			8.35909i			0.291379i	0.989330	+	0.145690i	$0.0465401\pi$
$823$			8.35909i			0.291379i	−0.989330	+	0.145690i	$0.953460\pi$
$824$	−5.49766	−	19.7829i	−0.191520	−	0.689169i
$825$		0			0
$826$	−8.10546	−	11.5001i	−0.282025	−	0.400139i
$827$			6.27366i			0.218156i	0.994033	+	0.109078i	$0.0347899\pi$
$827$			6.27366i			0.218156i	−0.994033	+	0.109078i	$0.965210\pi$
$828$	18.5719	−	2.83377i	0.645419	−	0.0984803i
$829$		−	8.61230i		−	0.299118i	−0.988753	−	0.149559i	$-0.952215\pi$
$829$		−	8.61230i		−	0.299118i	0.988753	−	0.149559i	$-0.0477853\pi$
$830$		0			0
$831$	−19.3962	+	32.4869i	−0.672845	+	1.12696i
$832$	17.7622	+	29.4898i	0.615792	+	1.02237i
$833$			16.3759i			0.567392i
$834$	−0.664670	−	8.76263i	−0.0230156	−	0.303425i
$835$		0			0
$836$	3.68633	+	1.31600i	0.127494	+	0.0455147i
$837$	51.4212	+	2.26074i	1.77738	+	0.0781426i
$838$	−15.4213	+	10.8692i	−0.532718	+	0.375469i
$839$	−2.93969			−0.101490			−0.0507448	−	0.998712i	$-0.516160\pi$
$839$	−2.93969			−0.101490			−0.0507448	+	0.998712i	$0.516160\pi$
$840$		0			0
$841$	48.3548			1.66741
$842$	−19.3794	+	13.6589i	−0.667858	+	0.470718i
$843$	−18.3974	+	30.8140i	−0.633640	+	1.06129i
$844$	5.48486	−	15.3640i	0.188796	−	0.528850i
$845$		0			0
$846$	−12.4227	+	24.9145i	−0.427101	+	0.856580i
$847$		−	8.68787i		−	0.298519i
$848$	12.2237	+	10.0023i	0.419764	+	0.343482i
$849$	1.83903	+	1.09798i	0.0631153	+	0.0376827i
$850$		0			0
$851$		−	26.6020i		−	0.911906i
$852$	9.16847	−	7.56183i	0.314107	−	0.259064i
$853$		−	34.2193i		−	1.17165i	−0.810439	−	0.585824i	$-0.800771\pi$
$853$		−	34.2193i		−	1.17165i	0.810439	−	0.585824i	$-0.199229\pi$
$854$	5.73770	+	8.14069i	0.196340	+	0.278569i
$855$		0			0
$856$	10.0669	+	36.2249i	0.344079	+	1.23814i
$857$		−	0.519916i		−	0.0177600i	−0.999961	−	0.00888000i	$-0.997173\pi$
$857$		−	0.519916i		−	0.0177600i	0.999961	−	0.00888000i	$-0.00282663\pi$
$858$	0.255558	+	3.36914i	0.00872461	+	0.115020i
$859$	−32.9724			−1.12500			−0.562502	−	0.826796i	$-0.690161\pi$
$859$	−32.9724			−1.12500			−0.562502	+	0.826796i	$0.690161\pi$
$860$		0			0
$861$	6.26230	+	3.73888i	0.213418	+	0.127421i
$862$	−23.6199	−	33.5121i	−0.804499	−	1.14143i
$863$	−21.8453			−0.743623			−0.371811	−	0.928308i	$-0.621263\pi$
$863$	−21.8453			−0.743623			−0.371811	+	0.928308i	$0.621263\pi$
$864$	−29.1971	−	3.39530i	−0.993306	−	0.115510i
$865$		0			0
$866$	19.2671	+	27.3363i	0.654724	+	0.928926i
$867$	−15.4358	−	9.21587i	−0.524227	−	0.312987i
$868$	−5.31030	+	14.8750i	−0.180243	+	0.504892i
$869$	0.927539			0.0314646
$870$		0			0
$871$		−	20.0848i		−	0.680549i
$872$	−2.58695	−	9.30892i	−0.0876051	−	0.315240i
$873$	6.06638	+	11.2563i	0.205316	+	0.380967i
$874$	15.5753	+	22.0983i	0.526843	+	0.747488i
$875$		0			0
$876$	3.82363	−	3.15359i	0.129188	−	0.106550i
$877$		−	37.2187i		−	1.25679i	−0.777896	−	0.628393i	$-0.783713\pi$
$877$		−	37.2187i		−	1.25679i	0.777896	−	0.628393i	$-0.216287\pi$
$878$	9.08255	−	6.40155i	0.306521	−	0.216042i
$879$	8.92294	+	5.32740i	0.300963	+	0.179689i
$880$		0			0
$881$		−	17.2984i		−	0.582796i	−0.956602	−	0.291398i	$-0.905880\pi$
$881$		−	17.2984i		−	0.582796i	0.956602	−	0.291398i	$-0.0941205\pi$
$882$	−12.0487	+	24.1646i	−0.405702	+	0.813663i
$883$	−51.3234			−1.72717			−0.863585	−	0.504203i	$-0.831786\pi$
$883$	−51.3234			−1.72717			−0.863585	+	0.504203i	$0.831786\pi$
$884$	7.44539	−	20.8558i	0.250416	−	0.701456i
$885$		0			0
$886$	−15.0047	+	10.5756i	−0.504094	+	0.355294i
$887$	15.3867			0.516635			0.258318	−	0.966060i	$-0.416832\pi$
$887$	15.3867			0.516635			0.258318	+	0.966060i	$0.416832\pi$
$888$	−10.9887	+	40.1446i	−0.368758	+	1.34716i
$889$	−3.97825			−0.133426
$890$		0			0
$891$	−2.40968	−	1.58627i	−0.0807275	−	0.0531421i
$892$	−38.8174	−	13.8576i	−1.29970	−	0.463986i
$893$	−40.0635			−1.34067
$894$	0.428650	+	5.65108i	0.0143362	+	0.189000i
$895$		0			0
$896$	3.63445	−	8.25525i	0.121418	−	0.275789i
$897$	−11.9636	+	20.0381i	−0.399454	+	0.669051i
$898$	−15.5876	+	10.9864i	−0.520165	+	0.366622i
$899$		−	87.1211i		−	2.90565i
$900$		0			0
$901$		−	10.1600i		−	0.338479i
$902$	1.37939	+	1.95709i	0.0459288	+	0.0651641i
$903$	−2.10546	+	3.52646i	−0.0700653	+	0.117353i
$904$	7.74444	+	27.8678i	0.257576	+	0.926868i
$905$		0			0
$906$	−8.41057	+	0.637965i	−0.279423	+	0.0211950i
$907$	−34.3304			−1.13992			−0.569962	−	0.821671i	$-0.693042\pi$
$907$	−34.3304			−1.13992			−0.569962	+	0.821671i	$0.693042\pi$
$908$	−50.8648	−	18.1584i	−1.68801	−	0.602608i
$909$	21.7945	+	40.4400i	0.722878	+	1.34131i
$910$		0			0
$911$	20.7856			0.688657			0.344328	−	0.938849i	$-0.388107\pi$
$911$	20.7856			0.688657			0.344328	+	0.938849i	$0.388107\pi$
$912$	−14.3760	−	39.7820i	−0.476038	−	1.31731i
$913$	−1.08035			−0.0357542
$914$	22.8951	+	32.4837i	0.757304	+	1.07447i
$915$		0			0
$916$	18.1786	+	6.48965i	0.600637	+	0.214424i
$917$	7.11710			0.235027
$918$	10.2036	+	15.9185i	0.336769	+	0.525389i
$919$			35.6290i			1.17529i	0.809119	+	0.587645i	$0.199945\pi$
$919$			35.6290i			1.17529i	−0.809119	+	0.587645i	$0.800055\pi$
$920$		0			0
$921$	9.99184	+	5.96558i	0.329242	+	0.196573i
$922$	23.8040	+	33.7733i	0.783944	+	1.11226i
$923$			14.7634i			0.485944i
$924$	0.682960	−	0.563281i	0.0224677	−	0.0185306i
$925$		0			0
$926$	16.3524	−	11.5254i	0.537372	−	0.378749i
$927$	−19.1712	+	10.3320i	−0.629664	+	0.339347i
$928$	−3.57078	+	49.6246i	−0.117216	+	1.62901i
$929$		−	44.9041i		−	1.47325i	−0.676299	−	0.736627i	$-0.736417\pi$
$929$		−	44.9041i		−	1.47325i	0.676299	−	0.736627i	$-0.263583\pi$
$930$		0			0
$931$	−38.8575			−1.27350
$932$	2.43143	+	0.868006i	0.0796441	+	0.0284325i
$933$	32.8019	+	19.5842i	1.07389	+	0.641159i
$934$	−33.4862	+	23.6017i	−1.09570	+	0.772271i
$935$		0			0
$936$	26.3314	−	25.2971i	0.860668	−	0.826862i
$937$	56.5086			1.84606			0.923029	−	0.384731i	$-0.125706\pi$
$937$	56.5086			1.84606			0.923029	+	0.384731i	$0.125706\pi$
$938$	−4.30137	+	3.03168i	−0.140445	+	0.0989880i
$939$	−16.4118	−	9.79861i	−0.535580	−	0.319765i
$940$		0			0
$941$	−29.6334			−0.966022			−0.483011	−	0.875614i	$-0.660457\pi$
$941$	−29.6334			−0.966022			−0.483011	+	0.875614i	$0.660457\pi$
$942$	−22.3995	+	1.69906i	−0.729816	+	0.0553585i
$943$			16.5380i			0.538553i
$944$	−31.6099	+	38.6300i	−1.02881	+	1.25730i
$945$		0			0
$946$	−1.10209	+	0.776774i	−0.0358321	+	0.0252551i
$947$		−	29.2810i		−	0.951504i	−0.879580	−	0.475752i	$-0.842176\pi$
$947$		−	29.2810i		−	0.951504i	0.879580	−	0.475752i	$-0.157824\pi$
$948$	−6.37785	−	7.73293i	−0.207143	−	0.251154i
$949$			6.15695i			0.199863i
$950$		0			0
$951$	−36.2427	−	21.6385i	−1.17525	−	0.701678i
$952$	−5.59032	+	1.55355i	−0.181183	+	0.0503508i
$953$			40.2311i			1.30321i	0.758557	+	0.651606i	$0.225905\pi$
$953$			40.2311i			1.30321i	−0.758557	+	0.651606i	$0.774095\pi$
$954$	7.47534	−	14.9923i	0.242023	−	0.485393i
$955$		0			0
$956$	−2.83153	+	7.93157i	−0.0915781	+	0.256525i
$957$	−2.50323	+	4.19270i	−0.0809180	+	0.135531i
$958$	−30.8816	−	43.8150i	−0.997739	−	1.41560i
$959$	−1.29127			−0.0416972
$960$		0			0
$961$	−67.1203			−2.16517
$962$	−29.7866	−	42.2614i	−0.960359	−	1.36256i
$963$	35.1048	−	18.9192i	1.13124	−	0.609662i
$964$	13.1584	−	36.8588i	0.423803	−	1.18714i
$965$		0			0
$966$	6.09719	−	0.462488i	0.196174	−	0.0148803i
$967$		−	34.4522i		−	1.10791i	−0.832547	−	0.553954i	$-0.813118\pi$
$967$		−	34.4522i		−	1.10791i	0.832547	−	0.553954i	$-0.186882\pi$
$968$	−29.6967	+	8.25270i	−0.954488	+	0.265252i
$969$	−13.9486	+	23.3627i	−0.448094	+	0.750519i
$970$		0			0
$971$		−	26.9133i		−	0.863688i	−0.901948	−	0.431844i	$-0.857863\pi$
$971$		−	26.9133i		−	0.863688i	0.901948	−	0.431844i	$-0.142137\pi$
$972$	3.34441	+	30.9970i	0.107272	+	0.994230i
$973$		−	2.86023i		−	0.0916948i
$974$	−48.4550	+	34.1519i	−1.55260	+	1.09430i
$975$		0			0
$976$	22.3760	−	27.3454i	0.716239	−	0.875306i
$977$			41.9916i			1.34343i	0.740810	+	0.671715i	$0.234442\pi$
$977$			41.9916i			1.34343i	−0.740810	+	0.671715i	$0.765558\pi$
$978$	−1.96681	−	25.9293i	−0.0628916	−	0.829128i
$979$	−4.40837			−0.140892
$980$		0			0
$981$	−9.02109	+	4.86177i	−0.288021	+	0.155224i
$982$	5.89176	−	4.15262i	0.188014	−	0.132515i
$983$	3.83856			0.122431			0.0612156	−	0.998125i	$-0.480502\pi$
$983$	3.83856			0.122431			0.0612156	+	0.998125i	$0.480502\pi$
$984$	6.83153	−	24.9572i	0.217781	−	0.795608i
$985$		0			0
$986$	26.1595	−	18.4377i	0.833090	−	0.587176i
$987$	−4.64506	+	7.78007i	−0.147854	+	0.247642i
$988$	49.4876	+	17.6668i	1.57441	+	0.562055i
$989$	−9.31301			−0.296137
$990$		0			0
$991$		−	48.3440i		−	1.53570i	−0.640630	−	0.767850i	$-0.721327\pi$
$991$		−	48.3440i		−	1.53570i	0.640630	−	0.767850i	$-0.278673\pi$
$992$	55.8899	+	4.02160i	1.77451	+	0.127686i
$993$	−19.6194	−	11.7137i	−0.622602	−	0.371722i
$994$	3.16174	−	2.22845i	0.100284	−	0.0706821i
$995$		0			0
$996$	7.42856	+	9.00689i	0.235383	+	0.285394i
$997$		−	23.5236i		−	0.744998i	−0.928032	−	0.372499i	$-0.878501\pi$
$997$		−	23.5236i		−	0.744998i	0.928032	−	0.372499i	$-0.121499\pi$
$998$	−22.3091	−	31.6522i	−0.706181	−	1.00193i
$999$	44.1036	+	1.93902i	1.39538	+	0.0613479i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	600.2.b.f.251.6		8
3.2	odd	2		600.2.b.e.251.3		8
4.3	odd	2		2400.2.b.f.2351.8		8
5.2	odd	4		600.2.m.c.299.4		16
5.3	odd	4		600.2.m.c.299.13		16
5.4	even	2		120.2.b.a.11.3	✓	8
8.3	odd	2		600.2.b.e.251.4		8
8.5	even	2		2400.2.b.e.2351.8		8
12.11	even	2		2400.2.b.e.2351.7		8
15.2	even	4		600.2.m.d.299.13		16
15.8	even	4		600.2.m.d.299.4		16
15.14	odd	2		120.2.b.b.11.6	yes	8
20.3	even	4		2400.2.m.d.1199.6		16
20.7	even	4		2400.2.m.d.1199.11		16
20.19	odd	2		480.2.b.b.431.1		8
24.5	odd	2		2400.2.b.f.2351.7		8
24.11	even	2	inner	600.2.b.f.251.5		8
40.3	even	4		600.2.m.d.299.14		16
40.13	odd	4		2400.2.m.c.1199.6		16
40.19	odd	2		120.2.b.b.11.5	yes	8
40.27	even	4		600.2.m.d.299.3		16
40.29	even	2		480.2.b.a.431.1		8
40.37	odd	4		2400.2.m.c.1199.11		16
60.23	odd	4		2400.2.m.c.1199.12		16
60.47	odd	4		2400.2.m.c.1199.5		16
60.59	even	2		480.2.b.a.431.2		8
120.29	odd	2		480.2.b.b.431.2		8
120.53	even	4		2400.2.m.d.1199.12		16
120.59	even	2		120.2.b.a.11.4	yes	8
120.77	even	4		2400.2.m.d.1199.5		16
120.83	odd	4		600.2.m.c.299.3		16
120.107	odd	4		600.2.m.c.299.14		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
120.2.b.a.11.3	✓	8	5.4	even	2
120.2.b.a.11.4	yes	8	120.59	even	2
120.2.b.b.11.5	yes	8	40.19	odd	2
120.2.b.b.11.6	yes	8	15.14	odd	2
480.2.b.a.431.1		8	40.29	even	2
480.2.b.a.431.2		8	60.59	even	2
480.2.b.b.431.1		8	20.19	odd	2
480.2.b.b.431.2		8	120.29	odd	2
600.2.b.e.251.3		8	3.2	odd	2
600.2.b.e.251.4		8	8.3	odd	2
600.2.b.f.251.5		8	24.11	even	2	inner
600.2.b.f.251.6		8	1.1	even	1	trivial
600.2.m.c.299.3		16	120.83	odd	4
600.2.m.c.299.4		16	5.2	odd	4
600.2.m.c.299.13		16	5.3	odd	4
600.2.m.c.299.14		16	120.107	odd	4
600.2.m.d.299.3		16	40.27	even	4
600.2.m.d.299.4		16	15.8	even	4
600.2.m.d.299.13		16	15.2	even	4
600.2.m.d.299.14		16	40.3	even	4
2400.2.b.e.2351.7		8	12.11	even	2
2400.2.b.e.2351.8		8	8.5	even	2
2400.2.b.f.2351.7		8	24.5	odd	2
2400.2.b.f.2351.8		8	4.3	odd	2
2400.2.m.c.1199.5		16	60.47	odd	4
2400.2.m.c.1199.6		16	40.13	odd	4
2400.2.m.c.1199.11		16	40.37	odd	4
2400.2.m.c.1199.12		16	60.23	odd	4
2400.2.m.d.1199.5		16	120.77	even	4
2400.2.m.d.1199.6		16	20.3	even	4
2400.2.m.d.1199.11		16	20.7	even	4
2400.2.m.d.1199.12		16	120.53	even	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)

\(f(q)\)	\(=\)	\(q+(0.814732 + 1.15595i) q^{2} +(-1.48716 - 0.887900i) q^{3} +(-0.672424 + 1.88357i) q^{4} +(-0.185268 - 2.44247i) q^{6} -0.797253i q^{7} +(-2.72515 + 0.757320i) q^{8} +(1.42327 + 2.64089i) q^{9} +O(q^{10})\)	\(q+(0.814732 + 1.15595i) q^{2} +(-1.48716 - 0.887900i) q^{3} +(-0.672424 + 1.88357i) q^{4} +(-0.185268 - 2.44247i) q^{6} -0.797253i q^{7} +(-2.72515 + 0.757320i) q^{8} +(1.42327 + 2.64089i) q^{9} +0.320548i q^{11} +(2.67242 - 2.20412i) q^{12} +4.30324i q^{13} +(0.921582 - 0.649548i) q^{14} +(-3.09569 - 2.53312i) q^{16} +2.57305i q^{17} +(-1.89315 + 3.79684i) q^{18} -6.10546 q^{19} +(-0.707881 + 1.18564i) q^{21} +(-0.370537 + 0.261161i) q^{22} -3.13115 q^{23} +(4.72515 + 1.29341i) q^{24} +(-4.97431 + 3.50598i) q^{26} +(0.228229 - 5.19114i) q^{27} +(1.50168 + 0.536093i) q^{28} -8.79516 q^{29} +9.90557i q^{31} +(0.405993 - 5.64227i) q^{32} +(0.284615 - 0.476705i) q^{33} +(-2.97431 + 2.09635i) q^{34} +(-5.93135 + 0.905026i) q^{36} +8.49593i q^{37} +(-4.97431 - 7.05758i) q^{38} +(3.82085 - 6.39959i) q^{39} -5.28178i q^{41} +(-1.94727 + 0.147706i) q^{42} +2.97431 q^{43} +(-0.603776 - 0.215544i) q^{44} +(-2.55105 - 3.61944i) q^{46} +6.56192 q^{47} +(2.35462 + 6.51581i) q^{48} +6.36439 q^{49} +(2.28461 - 3.82653i) q^{51} +(-8.10546 - 2.89360i) q^{52} -3.94862 q^{53} +(6.18662 - 3.96556i) q^{54} +(0.603776 + 2.17264i) q^{56} +(9.07977 + 5.42104i) q^{57} +(-7.16569 - 10.1667i) q^{58} -12.4786i q^{59} +8.83339i q^{61} +(-11.4503 + 8.07038i) q^{62} +(2.10546 - 1.13470i) q^{63} +(6.85293 - 4.12763i) q^{64} +(0.782930 - 0.0593874i) q^{66} -4.66738 q^{67} +(-4.84653 - 1.73018i) q^{68} +(4.65651 + 2.78015i) q^{69} +3.43077 q^{71} +(-5.87862 - 6.11897i) q^{72} +1.43077 q^{73} +(-9.82085 + 6.92191i) q^{74} +(4.10546 - 11.5001i) q^{76} +0.255558 q^{77} +(10.5105 - 0.797253i) q^{78} -2.89360i q^{79} +(-4.94862 + 7.51739i) q^{81} +(6.10546 - 4.30324i) q^{82} +3.37031i q^{83} +(-1.75724 - 2.13060i) q^{84} +(2.42327 + 3.43815i) q^{86} +(13.0798 + 7.80922i) q^{87} +(-0.242757 - 0.873543i) q^{88} +13.7526i q^{89} +3.43077 q^{91} +(2.10546 - 5.89774i) q^{92} +(8.79516 - 14.7311i) q^{93} +(5.34620 + 7.58523i) q^{94} +(-5.61354 + 8.03045i) q^{96} +4.26230 q^{97} +(5.18527 + 7.35689i) q^{98} +(-0.846533 + 0.456225i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + q^{2} + q^{4} - 7 q^{6} + 7 q^{8}+O(q^{10}) \) 8 * q + q^2 + q^4 - 7 * q^6 + 7 * q^8	\( 8 q + q^{2} + q^{4} - 7 q^{6} + 7 q^{8} + 15 q^{12} + 6 q^{14} - 7 q^{16} - 11 q^{18} - 4 q^{19} + 4 q^{21} - 14 q^{22} - 4 q^{23} + 9 q^{24} - 16 q^{26} + 12 q^{27} + 2 q^{28} + 11 q^{32} + 4 q^{33} - 19 q^{36} - 16 q^{38} - 16 q^{39} - 38 q^{42} + 30 q^{44} - 8 q^{46} + 28 q^{47} - 21 q^{48} - 16 q^{49} + 20 q^{51} - 20 q^{52} + 16 q^{53} - 15 q^{54} - 30 q^{56} + 4 q^{57} + 2 q^{58} - 34 q^{62} - 28 q^{63} + 25 q^{64} + 18 q^{66} + 32 q^{67} - 16 q^{68} - 20 q^{69} + 24 q^{71} - 41 q^{72} + 8 q^{73} - 32 q^{74} - 12 q^{76} + 12 q^{78} + 8 q^{81} + 4 q^{82} - 2 q^{84} + 8 q^{86} + 36 q^{87} - 14 q^{88} + 24 q^{91} - 28 q^{92} - 40 q^{94} + 17 q^{96} - 8 q^{97} + 47 q^{98} + 16 q^{99}+O(q^{100}) \) 8 * q + q^2 + q^4 - 7 * q^6 + 7 * q^8 + 15 * q^12 + 6 * q^14 - 7 * q^16 - 11 * q^18 - 4 * q^19 + 4 * q^21 - 14 * q^22 - 4 * q^23 + 9 * q^24 - 16 * q^26 + 12 * q^27 + 2 * q^28 + 11 * q^32 + 4 * q^33 - 19 * q^36 - 16 * q^38 - 16 * q^39 - 38 * q^42 + 30 * q^44 - 8 * q^46 + 28 * q^47 - 21 * q^48 - 16 * q^49 + 20 * q^51 - 20 * q^52 + 16 * q^53 - 15 * q^54 - 30 * q^56 + 4 * q^57 + 2 * q^58 - 34 * q^62 - 28 * q^63 + 25 * q^64 + 18 * q^66 + 32 * q^67 - 16 * q^68 - 20 * q^69 + 24 * q^71 - 41 * q^72 + 8 * q^73 - 32 * q^74 - 12 * q^76 + 12 * q^78 + 8 * q^81 + 4 * q^82 - 2 * q^84 + 8 * q^86 + 36 * q^87 - 14 * q^88 + 24 * q^91 - 28 * q^92 - 40 * q^94 + 17 * q^96 - 8 * q^97 + 47 * q^98 + 16 * q^99

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