LMFDB - Embedded newform 400.2.j.c.307.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [400,2,Mod(43,400)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(400, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 1, 3]))

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

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

chi := DirichletCharacter("400.43");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 400 = 2^{4} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	400.j (of order $4$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$3.19401608085$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 2x^{14} + 6x^{12} - 12x^{10} + 36x^{8} - 48x^{6} + 96x^{4} - 128x^{2} + 256 $ x^16 - 2x^14 + 6x^12 - 12x^10 + 36x^8 - 48x^6 + 96x^4 - 128*x^2 + 256
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{6} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			307.3
Root			$0.859408 - 1.12313i$ of defining polynomial
Character	$\chi$	$=$	400.307
Dual form			400.2.j.c.43.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.859408 - 1.12313i) q^{2} +1.54564i q^{3} +(-0.522835 + 1.93045i) q^{4} +(1.73595 - 1.32833i) q^{6} +(-1.17442 - 1.17442i) q^{7} +(2.61747 - 1.07183i) q^{8} +0.611000 q^{9} +O(q^{10})$	\(q+(-0.859408 - 1.12313i) q^{2} +1.54564i q^{3} +(-0.522835 + 1.93045i) q^{4} +(1.73595 - 1.32833i) q^{6} +(-1.17442 - 1.17442i) q^{7} +(2.61747 - 1.07183i) q^{8} +0.611000 q^{9} +(2.04567 + 2.04567i) q^{11} +(-2.98378 - 0.808115i) q^{12} -2.14367 q^{13} +(-0.309719 + 2.32833i) q^{14} +(-3.45329 - 2.01862i) q^{16} +(2.07308 + 2.07308i) q^{17} +(-0.525098 - 0.686231i) q^{18} +(4.47190 + 4.47190i) q^{19} +(1.81523 - 1.81523i) q^{21} +(0.539485 - 4.05562i) q^{22} +(-4.86373 + 4.86373i) q^{23} +(1.65667 + 4.04567i) q^{24} +(1.84229 + 2.40762i) q^{26} +5.58130i q^{27} +(2.88119 - 1.65314i) q^{28} +(-5.51757 + 5.51757i) q^{29} +5.72181i q^{31} +(0.700618 + 5.61330i) q^{32} +(-3.16187 + 3.16187i) q^{33} +(0.546713 - 4.10996i) q^{34} +(-0.319452 + 1.17951i) q^{36} +11.0214 q^{37} +(1.17933 - 8.86571i) q^{38} -3.31334i q^{39} -11.4241i q^{41} +(-3.59877 - 0.478714i) q^{42} -0.251676 q^{43} +(-5.01862 + 2.87952i) q^{44} +(9.64252 + 1.28266i) q^{46} +(0.119541 - 0.119541i) q^{47} +(3.12005 - 5.33754i) q^{48} -4.24147i q^{49} +(-3.20423 + 3.20423i) q^{51} +(1.12079 - 4.13825i) q^{52} -2.69520i q^{53} +(6.26852 - 4.79662i) q^{54} +(-4.33281 - 1.81523i) q^{56} +(-6.91195 + 6.91195i) q^{57} +(10.9388 + 1.45510i) q^{58} +(1.24990 - 1.24990i) q^{59} +(-2.48034 - 2.48034i) q^{61} +(6.42632 - 4.91737i) q^{62} +(-0.717571 - 0.717571i) q^{63} +(5.70234 - 5.61100i) q^{64} +(6.26852 + 0.833849i) q^{66} +9.23670 q^{67} +(-5.08586 + 2.91810i) q^{68} +(-7.51757 - 7.51757i) q^{69} -8.85246 q^{71} +(1.59928 - 0.654891i) q^{72} +(7.85956 + 7.85956i) q^{73} +(-9.47190 - 12.3785i) q^{74} +(-10.9709 + 6.29472i) q^{76} -4.80496i q^{77} +(-3.72131 + 2.84751i) q^{78} +4.86934 q^{79} -6.79368 q^{81} +(-12.8308 + 9.81801i) q^{82} -4.94936i q^{83} +(2.55515 + 4.45329i) q^{84} +(0.216293 + 0.282665i) q^{86} +(-8.52818 - 8.52818i) q^{87} +(7.54711 + 3.16187i) q^{88} -3.63047 q^{89} +(2.51757 + 2.51757i) q^{91} +(-6.84627 - 11.9321i) q^{92} -8.84385 q^{93} +(-0.236994 - 0.0315254i) q^{94} +(-8.67614 + 1.08290i) q^{96} +(-9.89595 - 9.89595i) q^{97} +(-4.76371 + 3.64515i) q^{98} +(1.24990 + 1.24990i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 4 q^{4} - 12 q^{6} - 16 q^{9}+O(q^{10}) $ 16 * q + 4 * q^4 - 12 * q^6 - 16 * q^9	$ 16 q + 4 q^{4} - 12 q^{6} - 16 q^{9} + 8 q^{11} - 20 q^{14} - 16 q^{16} - 8 q^{19} - 24 q^{24} + 16 q^{26} + 16 q^{29} + 48 q^{34} - 4 q^{36} - 40 q^{44} + 36 q^{46} - 48 q^{51} + 32 q^{54} + 64 q^{56} - 8 q^{59} - 16 q^{61} + 16 q^{64} + 32 q^{66} - 16 q^{69} - 32 q^{71} - 72 q^{74} - 32 q^{76} + 80 q^{79} + 16 q^{81} + 136 q^{84} - 60 q^{86} - 64 q^{91} - 28 q^{94} - 56 q^{96} - 8 q^{99}+O(q^{100}) $ 16 * q + 4 * q^4 - 12 * q^6 - 16 * q^9 + 8 * q^11 - 20 * q^14 - 16 * q^16 - 8 * q^19 - 24 * q^24 + 16 * q^26 + 16 * q^29 + 48 * q^34 - 4 * q^36 - 40 * q^44 + 36 * q^46 - 48 * q^51 + 32 * q^54 + 64 * q^56 - 8 * q^59 - 16 * q^61 + 16 * q^64 + 32 * q^66 - 16 * q^69 - 32 * q^71 - 72 * q^74 - 32 * q^76 + 80 * q^79 + 16 * q^81 + 136 * q^84 - 60 * q^86 - 64 * q^91 - 28 * q^94 - 56 * q^96 - 8 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/400\mathbb{Z}\right)^\times$.

$n$	$101$	$177$	$351$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$e\left(\frac{1}{4}\right)$	$-1$

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 $

$2$	−0.859408	−	1.12313i	−0.607693	−	0.794172i
$2$	−0.859408	−	1.12313i	−0.607693	−	0.794172i
$3$			1.54564i			0.892375i	0.894939	+	0.446188i	$0.147219\pi$
$3$			1.54564i			0.892375i	−0.894939	+	0.446188i	$0.852781\pi$
$4$	−0.522835	+	1.93045i	−0.261418	+	0.965226i
$5$		0			0
$5$		0			0
$6$	1.73595	−	1.32833i	0.708699	−	0.542290i
$7$	−1.17442	−	1.17442i	−0.443890	−	0.443890i	0.449427	−	0.893317i	$-0.351628\pi$
$7$	−1.17442	−	1.17442i	−0.443890	−	0.443890i	−0.893317	+	0.449427i	$0.851628\pi$
$8$	2.61747	−	1.07183i	0.925417	−	0.378951i
$9$	0.611000			0.203667
$10$		0			0
$11$	2.04567	+	2.04567i	0.616793	+	0.616793i	0.944707	−	0.327915i	$-0.106346\pi$
$11$	2.04567	+	2.04567i	0.616793	+	0.616793i	−0.327915	+	0.944707i	$0.606346\pi$
$12$	−2.98378	−	0.808115i	−0.861344	−	0.233283i
$13$	−2.14367			−0.594547			−0.297273	−	0.954792i	$-0.596077\pi$
$13$	−2.14367			−0.594547			−0.297273	+	0.954792i	$0.596077\pi$
$14$	−0.309719	+	2.32833i	−0.0827759	+	0.622274i
$15$		0			0
$16$	−3.45329	−	2.01862i	−0.863322	−	0.504654i
$17$	2.07308	+	2.07308i	0.502796	+	0.502796i	0.912306	−	0.409510i	$-0.134300\pi$
$17$	2.07308	+	2.07308i	0.502796	+	0.502796i	−0.409510	+	0.912306i	$0.634300\pi$
$18$	−0.525098	−	0.686231i	−0.123767	−	0.161746i
$19$	4.47190	+	4.47190i	1.02592	+	1.02592i	0.999655	+	0.0262700i	$0.00836295\pi$
$19$	4.47190	+	4.47190i	1.02592	+	1.02592i	0.0262700	+	0.999655i	$0.491637\pi$
$20$		0			0
$21$	1.81523	−	1.81523i	0.396116	−	0.396116i
$22$	0.539485	−	4.05562i	0.115019	−	0.864660i
$23$	−4.86373	+	4.86373i	−1.01416	+	1.01416i	−0.0142597	+	0.999898i	$0.504539\pi$
$23$	−4.86373	+	4.86373i	−1.01416	+	1.01416i	−0.999898	+	0.0142597i	$0.995461\pi$
$24$	1.65667	+	4.04567i	0.338166	+	0.825819i
$25$		0			0
$26$	1.84229	+	2.40762i	0.361302	+	0.472172i
$27$			5.58130i			1.07412i
$28$	2.88119	−	1.65314i	0.544495	−	0.312413i
$29$	−5.51757	+	5.51757i	−1.02459	+	1.02459i	−0.0248976	+	0.999690i	$0.507926\pi$
$29$	−5.51757	+	5.51757i	−1.02459	+	1.02459i	−0.999690	+	0.0248976i	$0.992074\pi$
$30$		0			0
$31$			5.72181i			1.02767i	0.857890	+	0.513833i	$0.171775\pi$
$31$			5.72181i			1.02767i	−0.857890	+	0.513833i	$0.828225\pi$
$32$	0.700618	+	5.61330i	0.123853	+	0.992301i
$33$	−3.16187	+	3.16187i	−0.550411	+	0.550411i
$34$	0.546713	−	4.10996i	0.0937605	−	0.704852i
$35$		0			0
$36$	−0.319452	+	1.17951i	−0.0532420	+	0.196584i
$37$	11.0214			1.81191			0.905956	−	0.423373i	$-0.139154\pi$
$37$	11.0214			1.81191			0.905956	+	0.423373i	$0.139154\pi$
$38$	1.17933	−	8.86571i	0.191313	−	1.43821i
$39$		−	3.31334i		−	0.530559i
$40$		0			0
$41$		−	11.4241i		−	1.78415i	−0.451885	−	0.892076i	$-0.649248\pi$
$41$		−	11.4241i		−	1.78415i	0.451885	−	0.892076i	$-0.350752\pi$
$42$	−3.59877	−	0.478714i	−0.555302	−	0.0738671i
$43$	−0.251676			−0.0383802			−0.0191901	−	0.999816i	$-0.506109\pi$
$43$	−0.251676			−0.0383802			−0.0191901	+	0.999816i	$0.506109\pi$
$44$	−5.01862	+	2.87952i	−0.756585	+	0.434104i
$45$		0			0
$46$	9.64252	+	1.28266i	1.42171	+	0.189119i
$47$	0.119541	−	0.119541i	0.0174368	−	0.0174368i	−0.698335	−	0.715771i	$-0.746075\pi$
$47$	0.119541	−	0.119541i	0.0174368	−	0.0174368i	0.715771	+	0.698335i	$0.246075\pi$
$48$	3.12005	−	5.33754i	0.450341	−	0.770407i
$49$		−	4.24147i		−	0.605924i
$50$		0			0
$51$	−3.20423	+	3.20423i	−0.448682	+	0.448682i
$52$	1.12079	−	4.13825i	0.155425	−	0.573872i
$53$		−	2.69520i		−	0.370214i	−0.982718	−	0.185107i	$-0.940737\pi$
$53$		−	2.69520i		−	0.370214i	0.982718	−	0.185107i	$-0.0592632\pi$
$54$	6.26852	−	4.79662i	0.853037	−	0.652737i
$55$		0			0
$56$	−4.33281	−	1.81523i	−0.578996	−	0.242571i
$57$	−6.91195	+	6.91195i	−0.915510	+	0.915510i
$58$	10.9388	+	1.45510i	1.43633	+	0.191063i
$59$	1.24990	−	1.24990i	0.162724	−	0.162724i	−0.621049	−	0.783772i	$-0.713293\pi$
$59$	1.24990	−	1.24990i	0.162724	−	0.162724i	0.783772	+	0.621049i	$0.213293\pi$
$60$		0			0
$61$	−2.48034	−	2.48034i	−0.317575	−	0.317575i	0.530260	−	0.847835i	$-0.322094\pi$
$61$	−2.48034	−	2.48034i	−0.317575	−	0.317575i	−0.847835	+	0.530260i	$0.822094\pi$
$62$	6.42632	−	4.91737i	0.816144	−	0.624506i
$63$	−0.717571	−	0.717571i	−0.0904055	−	0.0904055i
$64$	5.70234	−	5.61100i	0.712793	−	0.701375i
$65$		0			0
$66$	6.26852	+	0.833849i	0.771601	+	0.102640i
$67$	9.23670			1.12844			0.564221	−	0.825623i	$-0.309176\pi$
$67$	9.23670			1.12844			0.564221	+	0.825623i	$0.309176\pi$
$68$	−5.08586	+	2.91810i	−0.616751	+	0.353872i
$69$	−7.51757	−	7.51757i	−0.905009	−	0.905009i
$70$		0			0
$71$	−8.85246			−1.05059			−0.525297	−	0.850919i	$-0.676046\pi$
$71$	−8.85246			−1.05059			−0.525297	+	0.850919i	$0.676046\pi$
$72$	1.59928	−	0.654891i	0.188476	−	0.0771796i
$73$	7.85956	+	7.85956i	0.919892	+	0.919892i	0.997021	−	0.0771295i	$-0.0245755\pi$
$73$	7.85956	+	7.85956i	0.919892	+	0.919892i	−0.0771295	+	0.997021i	$0.524576\pi$
$74$	−9.47190	−	12.3785i	−1.10109	−	1.43897i
$75$		0			0
$76$	−10.9709	+	6.29472i	−1.25844	+	0.722054i
$77$		−	4.80496i		−	0.547576i
$78$	−3.72131	+	2.84751i	−0.421355	+	0.322417i
$79$	4.86934			0.547844			0.273922	−	0.961752i	$-0.411679\pi$
$79$	4.86934			0.547844			0.273922	+	0.961752i	$0.411679\pi$
$80$		0			0
$81$	−6.79368			−0.754853
$82$	−12.8308	+	9.81801i	−1.41692	+	1.08422i
$83$		−	4.94936i		−	0.543263i	−0.962401	−	0.271632i	$-0.912437\pi$
$83$		−	4.94936i		−	0.543263i	0.962401	−	0.271632i	$-0.0875632\pi$
$84$	2.55515	+	4.45329i	0.278790	+	0.485893i
$85$		0			0
$86$	0.216293	+	0.282665i	0.0233234	+	0.0304805i
$87$	−8.52818	−	8.52818i	−0.914317	−	0.914317i
$88$	7.54711	+	3.16187i	0.804525	+	0.337056i
$89$	−3.63047			−0.384829			−0.192414	−	0.981314i	$-0.561632\pi$
$89$	−3.63047			−0.384829			−0.192414	+	0.981314i	$0.561632\pi$
$90$		0			0
$91$	2.51757	+	2.51757i	0.263913	+	0.263913i
$92$	−6.84627	−	11.9321i	−0.713773	−	1.24401i
$93$	−8.84385			−0.917064
$94$	−0.236994	−	0.0315254i	−0.0244441	−	0.00325159i
$95$		0			0
$96$	−8.67614	+	1.08290i	−0.885504	+	0.110523i
$97$	−9.89595	−	9.89595i	−1.00478	−	1.00478i	−0.999989	−	0.00479337i	$-0.998474\pi$
$97$	−9.89595	−	9.89595i	−1.00478	−	1.00478i	−0.00479337	−	0.999989i	$-0.501526\pi$
$98$	−4.76371	+	3.64515i	−0.481207	+	0.368216i
$99$	1.24990	+	1.24990i	0.125620	+	0.125620i
$100$		0			0
$101$	6.29557	−	6.29557i	0.626433	−	0.626433i	−0.320736	−	0.947169i	$-0.603930\pi$
$101$	6.29557	−	6.29557i	0.626433	−	0.626433i	0.947169	+	0.320736i	$0.103930\pi$
$102$	6.35251	+	0.845021i	0.628992	+	0.0836696i
$103$	−3.06642	+	3.06642i	−0.302143	+	0.302143i	−0.841852	−	0.539709i	$-0.818534\pi$
$103$	−3.06642	+	3.06642i	−0.302143	+	0.302143i	0.539709	+	0.841852i	$0.318534\pi$
$104$	−5.61100	+	2.29766i	−0.550204	+	0.225304i
$105$		0			0
$106$	−3.02705	+	2.31628i	−0.294014	+	0.224977i
$107$			13.1186i			1.26822i	0.773242	+	0.634111i	$0.218634\pi$
$107$			13.1186i			1.26822i	−0.773242	+	0.634111i	$0.781366\pi$
$108$	−10.7744	−	2.91810i	−1.03677	−	0.280794i
$109$	2.00000	−	2.00000i	0.191565	−	0.191565i	−0.604807	−	0.796372i	$-0.706750\pi$
$109$	2.00000	−	2.00000i	0.191565	−	0.191565i	0.796372	+	0.604807i	$0.206750\pi$
$110$		0			0
$111$			17.0351i			1.61690i
$112$	1.68491	+	6.42632i	0.159209	+	0.607231i
$113$	−0.551529	+	0.551529i	−0.0518835	+	0.0518835i	−0.732572	−	0.680689i	$-0.761681\pi$
$113$	−0.551529	+	0.551529i	−0.0518835	+	0.0518835i	0.680689	+	0.732572i	$0.261681\pi$
$114$	13.7032	+	1.82282i	1.28342	+	0.170723i
$115$		0			0
$116$	−7.76663	−	13.5362i	−0.721113	−	1.25680i
$117$	−1.30978			−0.121089
$118$	−2.47798	−	0.329625i	−0.228117	−	0.0303444i
$119$		−	4.86934i		−	0.446372i
$120$		0			0
$121$		−	2.63047i		−	0.239133i
$122$	−0.654116	+	4.91737i	−0.0592209	+	0.445198i
$123$	17.6576			1.59213
$124$	−11.0457	−	2.99156i	−0.991930	−	0.268650i
$125$		0			0
$126$	−0.189238	+	1.42261i	−0.0168587	+	0.126736i
$127$	9.39015	−	9.39015i	0.833241	−	0.833241i	−0.154717	−	0.987959i	$-0.549447\pi$
$127$	9.39015	−	9.39015i	0.833241	−	0.833241i	0.987959	+	0.154717i	$0.0494467\pi$
$128$	−11.2025	−	1.58232i	−0.990171	−	0.139859i
$129$		−	0.389000i		−	0.0342496i
$130$		0			0
$131$	−0.471903	+	0.471903i	−0.0412303	+	0.0412303i	−0.727421	−	0.686191i	$-0.759281\pi$
$131$	−0.471903	+	0.471903i	−0.0412303	+	0.0412303i	0.686191	+	0.727421i	$0.259281\pi$
$132$	−4.45070	−	7.75697i	−0.387384	−	0.675158i
$133$		−	10.5038i		−	0.910795i
$134$	−7.93810	−	10.3740i	−0.685747	−	0.896178i
$135$		0			0
$136$	7.64823	+	3.20423i	0.655830	+	0.274761i
$137$	−16.2564	+	16.2564i	−1.38888	+	1.38888i	−0.561186	+	0.827690i	$0.689655\pi$
$137$	−16.2564	+	16.2564i	−1.38888	+	1.38888i	−0.827690	+	0.561186i	$0.810345\pi$
$138$	−1.98254	+	14.9039i	−0.168765	+	1.26870i
$139$	5.26767	−	5.26767i	0.446798	−	0.446798i	−0.447491	−	0.894289i	$-0.647682\pi$
$139$	5.26767	−	5.26767i	0.446798	−	0.446798i	0.894289	+	0.447491i	$0.147682\pi$
$140$		0			0
$141$	0.184767	+	0.184767i	0.0155602	+	0.0155602i
$142$	7.60788	+	9.94246i	0.638439	+	0.834352i
$143$	−4.38524	−	4.38524i	−0.366712	−	0.366712i
$144$	−2.10996	−	1.23337i	−0.175830	−	0.102781i
$145$		0			0
$146$	2.07272	−	15.5819i	0.171540	−	1.28956i
$147$	6.55577			0.540711
$148$	−5.76239	+	21.2763i	−0.473665	+	1.74890i
$149$	3.70234	+	3.70234i	0.303308	+	0.303308i	0.842306	−	0.538999i	$-0.181197\pi$
$149$	3.70234	+	3.70234i	0.303308	+	0.303308i	−0.538999	+	0.842306i	$0.681197\pi$
$150$		0			0
$151$	11.3133			0.920667			0.460333	−	0.887746i	$-0.347730\pi$
$151$	11.3133			0.920667			0.460333	+	0.887746i	$0.347730\pi$
$152$	16.4982	+	6.91195i	1.33818	+	0.560633i
$153$	1.26665	+	1.26665i	0.102403	+	0.102403i
$154$	−5.39659	+	4.12942i	−0.434870	+	0.332758i
$155$		0			0
$156$	6.39624	+	1.73233i	0.512109	+	0.138697i
$157$		−	18.7622i		−	1.49739i	−0.662916	−	0.748694i	$-0.730681\pi$
$157$		−	18.7622i		−	1.49739i	0.662916	−	0.748694i	$-0.269319\pi$
$158$	−4.18475	−	5.46890i	−0.332921	−	0.435082i
$159$	4.16580			0.330370
$160$		0			0
$161$	11.4241			0.900349
$162$	5.83854	+	7.63018i	0.458719	+	0.599483i
$163$		−	17.9093i		−	1.40276i	−0.712786	−	0.701382i	$-0.752567\pi$
$163$		−	17.9093i		−	1.40276i	0.712786	−	0.701382i	$-0.247433\pi$
$164$	22.0538	+	5.97295i	1.72211	+	0.466409i
$165$		0			0
$166$	−5.55877	+	4.25352i	−0.431444	+	0.330138i
$167$	−12.7939	−	12.7939i	−0.990020	−	0.990020i	0.00993072	−	0.999951i	$-0.496839\pi$
$167$	−12.7939	−	12.7939i	−0.990020	−	0.990020i	−0.999951	+	0.00993072i	$0.996839\pi$
$168$	2.80570	−	6.69695i	0.216464	−	0.516681i
$169$	−8.40468			−0.646514
$170$		0			0
$171$	2.73233	+	2.73233i	0.208947	+	0.208947i
$172$	0.131585	−	0.485849i	0.0100333	−	0.0370456i
$173$	17.2040			1.30799			0.653997	−	0.756497i	$-0.273091\pi$
$173$	17.2040			1.30799			0.653997	+	0.756497i	$0.273091\pi$
$174$	−2.24905	+	16.9074i	−0.170500	+	1.28175i
$175$		0			0
$176$	−2.93486	−	11.1937i	−0.221224	−	0.843758i
$177$	1.93190	+	1.93190i	0.145210	+	0.145210i
$178$	3.12005	+	4.07748i	0.233858	+	0.305620i
$179$	−3.76748	−	3.76748i	−0.281594	−	0.281594i	0.552150	−	0.833745i	$-0.313807\pi$
$179$	−3.76748	−	3.76748i	−0.281594	−	0.281594i	−0.833745	+	0.552150i	$0.813807\pi$
$180$		0			0
$181$	−4.29557	+	4.29557i	−0.319288	+	0.319288i	−0.848493	−	0.529206i	$-0.822490\pi$
$181$	−4.29557	+	4.29557i	−0.319288	+	0.319288i	0.529206	+	0.848493i	$0.322490\pi$
$182$	0.663935	−	4.99118i	0.0492141	−	0.369971i
$183$	3.83371	−	3.83371i	0.283396	−	0.283396i
$184$	−7.51757	+	17.9438i	−0.554203	+	1.32283i
$185$		0			0
$186$	7.60048	+	9.93278i	0.557294	+	0.728307i
$187$			8.48168i			0.620242i
$188$	0.168268	+	0.293268i	0.0122722	+	0.0213888i
$189$	6.55481	−	6.55481i	0.476792	−	0.476792i
$190$		0			0
$191$		−	25.8876i		−	1.87316i	−0.350451	−	0.936581i	$-0.613972\pi$
$191$		−	25.8876i		−	1.87316i	0.350451	−	0.936581i	$-0.386028\pi$
$192$	8.67258	+	8.81376i	0.625890	+	0.636078i
$193$	10.1105	−	10.1105i	0.727770	−	0.727770i	−0.242405	−	0.970175i	$-0.577936\pi$
$193$	10.1105	−	10.1105i	0.727770	−	0.727770i	0.970175	+	0.242405i	$0.0779364\pi$
$194$	−2.60976	+	19.6191i	−0.187370	+	1.40857i
$195$		0			0
$196$	8.18794	+	2.21759i	0.584853	+	0.158399i
$197$	15.6118			1.11230			0.556149	−	0.831083i	$-0.312278\pi$
$197$	15.6118			1.11230			0.556149	+	0.831083i	$0.312278\pi$
$198$	0.329625	−	2.47798i	0.0234254	−	0.176102i
$199$			25.2178i			1.78764i	0.448422	+	0.893822i	$0.351986\pi$
$199$			25.2178i			1.78764i	−0.448422	+	0.893822i	$0.648014\pi$
$200$		0			0
$201$			14.2766i			1.00699i
$202$	−12.4812	−	1.66027i	−0.878175	−	0.116816i
$203$	12.9599			0.909608
$204$	−4.51033	−	7.86090i	−0.315786	−	0.550373i
$205$		0			0
$206$	6.07928	+	0.808676i	0.423564	+	0.0563431i
$207$	−2.97174	+	2.97174i	−0.206550	+	0.206550i
$208$	7.40271	+	4.32725i	0.513285	+	0.300041i
$209$			18.2961i			1.26557i
$210$		0			0
$211$	−6.84144	+	6.84144i	−0.470984	+	0.470984i	−0.902233	−	0.431249i	$-0.858073\pi$
$211$	−6.84144	+	6.84144i	−0.470984	+	0.470984i	0.431249	+	0.902233i	$0.358073\pi$
$212$	5.20295	+	1.40914i	0.357340	+	0.0967805i
$213$		−	13.6827i		−	0.937524i
$214$	14.7339	−	11.2742i	1.00719	−	0.770690i
$215$		0			0
$216$	5.98223	+	14.6089i	0.407039	+	0.994011i
$217$	6.71982	−	6.71982i	0.456171	−	0.456171i
$218$	−3.96507	−	0.527441i	−0.268549	−	0.0357228i
$219$	−12.1480	+	12.1480i	−0.820888	+	0.820888i
$220$		0			0
$221$	−4.44400	−	4.44400i	−0.298936	−	0.298936i
$222$	19.1327	−	14.6401i	1.28410	−	0.982582i
$223$	−1.31883	−	1.31883i	−0.0883151	−	0.0883151i	0.661569	−	0.749884i	$-0.269891\pi$
$223$	−1.31883	−	1.31883i	−0.0883151	−	0.0883151i	−0.749884	+	0.661569i	$0.769891\pi$
$224$	5.76956	−	7.41520i	0.385495	−	0.495449i
$225$		0			0
$226$	1.09343	+	0.145449i	0.0727336	+	0.00967515i
$227$	−4.63692			−0.307763			−0.153882	−	0.988089i	$-0.549177\pi$
$227$	−4.63692			−0.307763			−0.153882	+	0.988089i	$0.549177\pi$
$228$	−9.72937	−	16.9570i	−0.644343	−	1.12300i
$229$	12.7396	+	12.7396i	0.841855	+	0.841855i	0.989100	−	0.147245i	$-0.0470407\pi$
$229$	12.7396	+	12.7396i	0.841855	+	0.841855i	−0.147245	+	0.989100i	$0.547041\pi$
$230$		0			0
$231$	7.42674			0.488643
$232$	−8.52818	+	20.3560i	−0.559902	+	1.33644i
$233$	12.0057	+	12.0057i	0.786521	+	0.786521i	0.980922	−	0.194401i	$-0.0622764\pi$
$233$	12.0057	+	12.0057i	0.786521	+	0.786521i	−0.194401	+	0.980922i	$0.562276\pi$
$234$	1.12564	+	1.47105i	0.0735852	+	0.0961657i
$235$		0			0
$236$	1.75938	+	3.06637i	0.114526	+	0.199604i
$237$			7.52625i			0.488882i
$238$	−5.46890	+	4.18475i	−0.354496	+	0.271257i
$239$	−2.64356			−0.170997			−0.0854987	−	0.996338i	$-0.527248\pi$
$239$	−2.64356			−0.170997			−0.0854987	+	0.996338i	$0.527248\pi$
$240$		0			0
$241$	7.01568			0.451920			0.225960	−	0.974137i	$-0.427448\pi$
$241$	7.01568			0.451920			0.225960	+	0.974137i	$0.427448\pi$
$242$	−2.95435	+	2.26064i	−0.189913	+	0.145320i
$243$			6.24333i			0.400510i
$244$	6.08499	−	3.49137i	0.389551	−	0.223512i
$245$		0			0
$246$	−15.1751	−	19.8318i	−0.967529	−	1.26443i
$247$	−9.58628	−	9.58628i	−0.609961	−	0.609961i
$248$	6.13283	+	14.9767i	0.389435	+	0.951020i
$249$	7.64993			0.484795
$250$		0			0
$251$	−15.7675	−	15.7675i	−0.995234	−	0.995234i	0.00475439	−	0.999989i	$-0.498487\pi$
$251$	−15.7675	−	15.7675i	−0.995234	−	0.995234i	−0.999989	+	0.00475439i	$0.998487\pi$
$252$	1.76041	−	1.01007i	0.110895	−	0.0636281i
$253$	−19.8992			−1.25105
$254$	−18.6163	−	2.47637i	−1.16809	−	0.155382i
$255$		0			0
$256$	7.85038	+	13.9417i	0.490649	+	0.871357i
$257$	−7.27135	−	7.27135i	−0.453574	−	0.453574i	0.442965	−	0.896539i	$-0.353927\pi$
$257$	−7.27135	−	7.27135i	−0.453574	−	0.453574i	−0.896539	+	0.442965i	$0.853927\pi$
$258$	−0.436897	+	0.334310i	−0.0272000	+	0.0208132i
$259$	−12.9438	−	12.9438i	−0.804289	−	0.804289i
$260$		0			0
$261$	−3.37123	+	3.37123i	−0.208674	+	0.208674i
$262$	0.935565	+	0.124450i	0.0577994	+	0.00768857i
$263$	−5.32058	+	5.32058i	−0.328081	+	0.328081i	−0.851856	−	0.523775i	$-0.824523\pi$
$263$	−5.32058	+	5.32058i	−0.328081	+	0.328081i	0.523775	+	0.851856i	$0.324523\pi$
$264$	−4.88711	+	11.6651i	−0.300781	+	0.717938i
$265$		0			0
$266$	−11.7971	+	9.02705i	−0.723328	+	0.553484i
$267$		−	5.61139i		−	0.343411i
$268$	−4.82927	+	17.8310i	−0.294995	+	1.08920i
$269$	−2.29766	+	2.29766i	−0.140091	+	0.140091i	−0.773674	−	0.633584i	$-0.781583\pi$
$269$	−2.29766	+	2.29766i	−0.140091	+	0.140091i	0.633584	+	0.773674i	$0.281583\pi$
$270$		0			0
$271$		−	14.9396i		−	0.907518i	−0.891124	−	0.453759i	$-0.850083\pi$
$271$		−	14.9396i		−	0.907518i	0.891124	−	0.453759i	$-0.149917\pi$
$272$	−2.97419	−	11.3437i	−0.180337	−	0.687812i
$273$	−3.89126	+	3.89126i	−0.235510	+	0.235510i
$274$	32.2289	+	4.28714i	1.94702	+	0.258995i
$275$		0			0
$276$	18.4428	−	10.5819i	1.11012	−	0.636953i
$277$	11.2360			0.675104			0.337552	−	0.941307i	$-0.390401\pi$
$277$	11.2360			0.675104			0.337552	+	0.941307i	$0.390401\pi$
$278$	−10.4433	−	1.38919i	−0.626350	−	0.0833182i
$279$			3.49602i			0.209301i
$280$		0			0
$281$			15.0546i			0.898083i	0.893511	+	0.449041i	$0.148234\pi$
$281$			15.0546i			0.898083i	−0.893511	+	0.449041i	$0.851766\pi$
$282$	0.0487268	−	0.366308i	0.00290164	−	0.0218133i
$283$	−18.8230			−1.11891			−0.559455	−	0.828861i	$-0.688990\pi$
$283$	−18.8230			−1.11891			−0.559455	+	0.828861i	$0.688990\pi$
$284$	4.62838	−	17.0893i	0.274644	−	1.01406i
$285$		0			0
$286$	−1.15648	+	8.69390i	−0.0683839	+	0.514081i
$287$	−13.4168	+	13.4168i	−0.791967	+	0.791967i
$288$	0.428077	+	3.42972i	0.0252247	+	0.202098i
$289$		−	8.40468i		−	0.494393i
$290$		0			0
$291$	15.2956	−	15.2956i	0.896642	−	0.896642i
$292$	−19.2817	+	11.0632i	−1.12838	+	0.647427i
$293$		−	6.18256i		−	0.361189i	−0.983558	−	0.180594i	$-0.942198\pi$
$293$		−	6.18256i		−	0.361189i	0.983558	−	0.180594i	$-0.0578021\pi$
$294$	−5.63409	−	7.36298i	−0.328587	−	0.429418i
$295$		0			0
$296$	28.8483	−	11.8131i	1.67677	−	0.686625i
$297$	−11.4175	+	11.4175i	−0.662511	+	0.662511i
$298$	0.976382	−	7.34003i	0.0565603	−	0.425196i
$299$	10.4262	−	10.4262i	0.602965	−	0.602965i
$300$		0			0
$301$	0.295574	+	0.295574i	0.0170366	+	0.0170366i
$302$	−9.72278	−	12.7063i	−0.559483	−	0.731167i
$303$	9.73069	+	9.73069i	0.559013	+	0.559013i
$304$	−6.41571	−	24.4698i	−0.367966	−	1.40344i
$305$		0			0
$306$	0.334042	−	2.51118i	0.0190959	−	0.143555i
$307$	−4.85636			−0.277167			−0.138584	−	0.990351i	$-0.544255\pi$
$307$	−4.85636			−0.277167			−0.138584	+	0.990351i	$0.544255\pi$
$308$	9.27574	+	2.51220i	0.528535	+	0.143146i
$309$	−4.73957	−	4.73957i	−0.269625	−	0.269625i
$310$		0			0
$311$	2.09551			0.118826			0.0594128	−	0.998233i	$-0.481077\pi$
$311$	2.09551			0.118826			0.0594128	+	0.998233i	$0.481077\pi$
$312$	−3.55135	−	8.67258i	−0.201056	−	0.490988i
$313$	−13.6684	−	13.6684i	−0.772586	−	0.772586i	0.205972	−	0.978558i	$-0.433965\pi$
$313$	−13.6684	−	13.6684i	−0.772586	−	0.772586i	−0.978558	+	0.205972i	$0.933965\pi$
$314$	−21.0724	+	16.1244i	−1.18918	+	0.909953i
$315$		0			0
$316$	−2.54586	+	9.40003i	−0.143216	+	0.528793i
$317$		−	6.21646i		−	0.349151i	−0.984644	−	0.174576i	$-0.944145\pi$
$317$		−	6.21646i		−	0.349151i	0.984644	−	0.174576i	$-0.0558554\pi$
$318$	−3.58013	−	4.67873i	−0.200764	−	0.262370i
$319$	−22.5743			−1.26392
$320$		0			0
$321$	−20.2766			−1.13173
$322$	−9.81801	−	12.8308i	−0.547136	−	0.715032i
$323$			18.5412i			1.03166i
$324$	3.55198	−	13.1149i	0.197332	−	0.728604i
$325$		0			0
$326$	−20.1144	+	15.3914i	−1.11404	+	0.852450i
$327$	3.09128	+	3.09128i	0.170948	+	0.170948i
$328$	−12.2448	−	29.9024i	−0.676106	−	1.65108i
$329$	−0.280783			−0.0154801
$330$		0			0
$331$	8.28922	+	8.28922i	0.455617	+	0.455617i	0.897214	−	0.441597i	$-0.145588\pi$
$331$	8.28922	+	8.28922i	0.455617	+	0.455617i	−0.441597	+	0.897214i	$0.645588\pi$
$332$	9.55451	+	2.58770i	0.524372	+	0.142019i
$333$	6.73409			0.369026
$334$	−3.37401	+	25.3643i	−0.184617	+	1.38787i
$335$		0			0
$336$	−9.93278	+	2.60426i	−0.541877	+	0.142074i
$337$	11.4175	+	11.4175i	0.621951	+	0.621951i	0.946030	−	0.324079i	$-0.105054\pi$
$337$	11.4175	+	11.4175i	0.621951	+	0.621951i	−0.324079	+	0.946030i	$0.605054\pi$
$338$	7.22305	+	9.43954i	0.392882	+	0.513443i
$339$	−0.852465	−	0.852465i	−0.0462995	−	0.0462995i
$340$		0			0
$341$	−11.7049	+	11.7049i	−0.633857	+	0.633857i
$342$	0.720571	−	5.41695i	0.0389640	−	0.292915i
$343$	−13.2022	+	13.2022i	−0.712853	+	0.712853i
$344$	−0.658756	+	0.269755i	−0.0355177	+	0.0145442i
$345$		0			0
$346$	−14.7852	−	19.3223i	−0.794860	−	1.03877i
$347$			1.73654i			0.0932226i	0.998913	+	0.0466113i	$0.0148422\pi$
$347$			1.73654i			0.0932226i	−0.998913	+	0.0466113i	$0.985158\pi$
$348$	20.9221	−	12.0044i	1.12154	−	0.643504i
$349$	20.1087	−	20.1087i	1.07640	−	1.07640i	0.0795655	−	0.996830i	$-0.474647\pi$
$349$	20.1087	−	20.1087i	1.07640	−	1.07640i	0.996830	−	0.0795655i	$-0.0253533\pi$
$350$		0			0
$351$		−	11.9645i		−	0.638616i
$352$	−10.0497	+	12.9162i	−0.535652	+	0.688435i
$353$	−14.7572	+	14.7572i	−0.785448	+	0.785448i	−0.980744	−	0.195296i	$-0.937433\pi$
$353$	−14.7572	+	14.7572i	−0.785448	+	0.785448i	0.195296	+	0.980744i	$0.437433\pi$
$354$	0.509481	−	3.83006i	0.0270786	−	0.203566i
$355$		0			0
$356$	1.89814	−	7.00844i	0.100601	−	0.371446i
$357$	7.52625			0.398331
$358$	−0.993560	+	7.46916i	−0.0525113	+	0.394757i
$359$		−	25.3481i		−	1.33782i	−0.743343	−	0.668911i	$-0.766761\pi$
$359$		−	25.3481i		−	1.33782i	0.743343	−	0.668911i	$-0.233239\pi$
$360$		0			0
$361$			20.9958i			1.10504i
$362$	8.51613	+	1.13283i	0.447598	+	0.0595402i
$363$	4.06575			0.213397
$364$	−6.17633	+	3.54378i	−0.323728	+	0.185744i
$365$		0			0
$366$	−7.60048	−	1.01103i	−0.397283	−	0.0528473i
$367$	19.4798	−	19.4798i	1.01684	−	1.01684i	0.0169808	−	0.999856i	$-0.494595\pi$
$367$	19.4798	−	19.4798i	1.01684	−	1.01684i	0.999856	−	0.0169808i	$-0.00540540\pi$
$368$	26.6139	−	6.97785i	1.38734	−	0.363746i
$369$		−	6.98015i		−	0.363372i
$370$		0			0
$371$	−3.16530	+	3.16530i	−0.164334	+	0.164334i
$372$	4.62387	−	17.0726i	0.239737	−	0.885174i
$373$			25.4963i			1.32015i	0.751200	+	0.660074i	$0.229475\pi$
$373$			25.4963i			1.32015i	−0.751200	+	0.660074i	$0.770525\pi$
$374$	9.52601	−	7.28922i	0.492578	−	0.376917i
$375$		0			0
$376$	0.184767	−	0.441023i	0.00952864	−	0.0227440i
$377$	11.8279	−	11.8279i	0.609165	−	0.609165i
$378$	−12.9951	−	1.72864i	−0.668398	−	0.0889114i
$379$	−6.82367	+	6.82367i	−0.350508	+	0.350508i	−0.860299	−	0.509790i	$-0.829723\pi$
$379$	−6.82367	+	6.82367i	−0.350508	+	0.350508i	0.509790	+	0.860299i	$0.329723\pi$
$380$		0			0
$381$	14.5138	+	14.5138i	0.743564	+	0.743564i
$382$	−29.0751	+	22.2480i	−1.48761	+	1.13831i
$383$	−2.08490	−	2.08490i	−0.106533	−	0.106533i	0.651831	−	0.758364i	$-0.274001\pi$
$383$	−2.08490	−	2.08490i	−0.106533	−	0.106533i	−0.758364	+	0.651831i	$0.774001\pi$
$384$	2.44570	−	17.3150i	0.124807	−	0.883604i
$385$		0			0
$386$	−20.0444	−	2.66634i	−1.02023	−	0.135713i
$387$	−0.153774			−0.00781677
$388$	24.2776	−	13.9297i	1.23251	−	0.707174i
$389$	7.92395	+	7.92395i	0.401760	+	0.401760i	0.878853	−	0.477093i	$-0.158309\pi$
$389$	7.92395	+	7.92395i	0.401760	+	0.401760i	−0.477093	+	0.878853i	$0.658309\pi$
$390$		0			0
$391$	−20.1658			−1.01983
$392$	−4.54615	−	11.1019i	−0.229615	−	0.560732i
$393$	−0.729391	−	0.729391i	−0.0367929	−	0.0367929i
$394$	−13.4169	−	17.5341i	−0.675936	−	0.883355i
$395$		0			0
$396$	−3.06637	+	1.75938i	−0.154091	+	0.0884124i
$397$			24.1865i			1.21389i	0.794745	+	0.606943i	$0.207605\pi$
$397$			24.1865i			1.21389i	−0.794745	+	0.606943i	$0.792395\pi$
$398$	28.3229	−	21.6724i	1.41970	−	1.08634i
$399$	16.2351			0.812771
$400$		0			0
$401$	13.9958			0.698918			0.349459	−	0.936952i	$-0.386365\pi$
$401$	13.9958			0.698918			0.349459	+	0.936952i	$0.386365\pi$
$402$	16.0345	−	12.2694i	0.799727	−	0.611944i
$403$		−	12.2657i		−	0.610996i
$404$	8.86175	+	15.4448i	0.440889	+	0.768410i
$405$		0			0
$406$	−11.1379	−	14.5557i	−0.552763	−	0.722385i
$407$	22.5462	+	22.5462i	1.11757	+	1.11757i
$408$	−4.95259	+	11.8214i	−0.245190	+	0.585247i
$409$	11.4241			0.564888			0.282444	−	0.959284i	$-0.408855\pi$
$409$	11.4241			0.564888			0.282444	+	0.959284i	$0.408855\pi$
$410$		0			0
$411$	−25.1265	−	25.1265i	−1.23940	−	1.23940i
$412$	−4.31634	−	7.52280i	−0.212651	−	0.370622i
$413$	−2.93583			−0.144463
$414$	5.89158	+	0.783707i	0.289555	+	0.0385171i
$415$		0			0
$416$	−1.50189	−	12.0331i	−0.0736364	−	0.589969i
$417$	8.14192	+	8.14192i	0.398711	+	0.398711i
$418$	20.5488	−	15.7238i	1.00508	−	0.769076i
$419$	−16.5455	−	16.5455i	−0.808299	−	0.808299i	0.176077	−	0.984376i	$-0.443659\pi$
$419$	−16.5455	−	16.5455i	−0.808299	−	0.808299i	−0.984376	+	0.176077i	$0.943659\pi$
$420$		0			0
$421$	−15.5900	+	15.5900i	−0.759808	+	0.759808i	−0.976287	−	0.216479i	$-0.930543\pi$
$421$	−15.5900	+	15.5900i	−0.759808	+	0.759808i	0.216479	+	0.976287i	$0.430543\pi$
$422$	13.5634	+	1.80423i	0.660256	+	0.0878283i
$423$	0.0730395	−	0.0730395i	0.00355130	−	0.00355130i
$424$	−2.88881	−	7.05461i	−0.140293	−	0.342602i
$425$		0			0
$426$	−15.3674	+	11.7590i	−0.744555	+	0.569727i
$427$			5.82594i			0.281937i
$428$	−25.3248	−	6.85886i	−1.22412	−	0.331536i
$429$	6.77800	−	6.77800i	0.327245	−	0.327245i
$430$		0			0
$431$			18.4609i			0.889229i	0.895722	+	0.444615i	$0.146659\pi$
$431$			18.4609i			0.889229i	−0.895722	+	0.444615i	$0.853341\pi$
$432$	11.2665	−	19.2738i	0.542060	−	0.927313i
$433$	13.7872	−	13.7872i	0.662571	−	0.662571i	−0.293414	−	0.955985i	$-0.594792\pi$
$433$	13.7872	−	13.7872i	0.662571	−	0.662571i	0.955985	+	0.293414i	$0.0947915\pi$
$434$	−13.3223	−	1.77215i	−0.639490	−	0.0850660i
$435$		0			0
$436$	2.81523	+	4.90657i	0.134825	+	0.234982i
$437$	−43.5003			−2.08090
$438$	24.0839	+	3.20368i	1.15077	+	0.153078i
$439$		−	16.9049i		−	0.806826i	−0.915018	−	0.403413i	$-0.867824\pi$
$439$		−	16.9049i		−	0.806826i	0.915018	−	0.403413i	$-0.132176\pi$
$440$		0			0
$441$		−	2.59153i		−	0.123406i
$442$	−1.17197	+	8.81039i	−0.0557450	+	0.419067i
$443$	−12.2979			−0.584291			−0.292145	−	0.956374i	$-0.594369\pi$
$443$	−12.2979			−0.584291			−0.292145	+	0.956374i	$0.594369\pi$
$444$	−32.8855	−	8.90657i	−1.56068	−	0.422687i
$445$		0			0
$446$	−0.347801	+	2.61462i	−0.0164689	+	0.123806i
$447$	−5.72248	+	5.72248i	−0.270664	+	0.270664i
$448$	−13.2866	−	0.107273i	−0.627735	−	0.00506815i
$449$			9.34968i			0.441239i	0.975360	+	0.220619i	$0.0708079\pi$
$449$			9.34968i			0.441239i	−0.975360	+	0.220619i	$0.929192\pi$
$450$		0			0
$451$	23.3700	−	23.3700i	1.10045	−	1.10045i
$452$	−0.776341	−	1.35306i	−0.0365160	−	0.0636425i
$453$			17.4863i			0.821580i
$454$	3.98500	+	5.20785i	0.187026	+	0.244417i
$455$		0			0
$456$	−10.6834	+	25.5003i	−0.500295	+	1.19416i
$457$	14.9127	−	14.9127i	0.697586	−	0.697586i	−0.266303	−	0.963889i	$-0.585802\pi$
$457$	14.9127	−	14.9127i	0.697586	−	0.697586i	0.963889	+	0.266303i	$0.0858023\pi$
$458$	3.35968	−	25.2567i	0.156988	−	1.18017i
$459$	−11.5705	+	11.5705i	−0.540064	+	0.540064i
$460$		0			0
$461$	18.0005	+	18.0005i	0.838367	+	0.838367i	0.988644	−	0.150277i	$-0.0480165\pi$
$461$	18.0005	+	18.0005i	0.838367	+	0.838367i	−0.150277	+	0.988644i	$0.548017\pi$
$462$	−6.38260	−	8.34118i	−0.296945	−	0.388067i
$463$	−6.25392	−	6.25392i	−0.290644	−	0.290644i	0.546690	−	0.837335i	$-0.315887\pi$
$463$	−6.25392	−	6.25392i	−0.290644	−	0.290644i	−0.837335	+	0.546690i	$0.815887\pi$
$464$	30.1916	−	7.91590i	1.40161	−	0.367486i
$465$		0			0
$466$	3.16615	−	23.8018i	0.146669	−	1.10260i
$467$	23.9988			1.11053			0.555267	−	0.831672i	$-0.312616\pi$
$467$	23.9988			1.11053			0.555267	+	0.831672i	$0.312616\pi$
$468$	0.684800	−	2.52847i	0.0316549	−	0.116879i
$469$	−10.8478	−	10.8478i	−0.500904	−	0.500904i
$470$		0			0
$471$	28.9996			1.33623
$472$	1.93190	−	4.61128i	0.0889229	−	0.212251i
$473$	−0.514846	−	0.514846i	−0.0236727	−	0.0236727i
$474$	8.45294	−	6.46812i	0.388256	−	0.297090i
$475$		0			0
$476$	9.40003	+	2.54586i	0.430850	+	0.116689i
$477$		−	1.64677i		−	0.0754002i
$478$	2.27189	+	2.96905i	0.103914	+	0.135801i
$479$	−23.6618			−1.08114			−0.540568	−	0.841300i	$-0.681791\pi$
$479$	−23.6618			−1.08114			−0.540568	+	0.841300i	$0.681791\pi$
$480$		0			0
$481$	−23.6263			−1.07727
$482$	−6.02933	−	7.87951i	−0.274629	−	0.358902i
$483$			17.6576i			0.803449i
$484$	5.07799	+	1.37530i	0.230818	+	0.0625136i
$485$		0			0
$486$	7.01206	−	5.36557i	0.318073	−	0.243387i
$487$	21.1809	+	21.1809i	0.959797	+	0.959797i	0.999223	−	0.0394255i	$-0.0125528\pi$
$487$	21.1809	+	21.1809i	0.959797	+	0.959797i	−0.0394255	+	0.999223i	$0.512553\pi$
$488$	−9.15074	−	3.83371i	−0.414235	−	0.173544i
$489$	27.6813			1.25179
$490$		0			0
$491$	13.2854	+	13.2854i	0.599563	+	0.599563i	0.940196	−	0.340633i	$-0.110641\pi$
$491$	13.2854	+	13.2854i	0.599563	+	0.599563i	−0.340633	+	0.940196i	$0.610641\pi$
$492$	−9.23202	+	34.0872i	−0.416212	+	1.53677i
$493$	−22.8767			−1.03032
$494$	−2.52810	+	19.0052i	−0.113744	+	0.855082i
$495$		0			0
$496$	11.5501	−	19.7590i	0.518616	−	0.887207i
$497$	10.3965	+	10.3965i	0.466348	+	0.466348i
$498$	−6.57441	−	8.59186i	−0.294607	−	0.385010i
$499$	24.8026	+	24.8026i	1.11032	+	1.11032i	0.993107	+	0.117211i	$0.0373953\pi$
$499$	24.8026	+	24.8026i	1.11032	+	1.11032i	0.117211	+	0.993107i	$0.462605\pi$
$500$		0			0
$501$	19.7747	−	19.7747i	0.883469	−	0.883469i
$502$	−4.15820	+	31.2596i	−0.185590	+	1.39518i
$503$	23.2205	−	23.2205i	1.03535	−	1.03535i	0.0359989	−	0.999352i	$-0.488539\pi$
$503$	23.2205	−	23.2205i	1.03535	−	1.03535i	0.999352	−	0.0359989i	$-0.0114613\pi$
$504$	−2.64734	−	1.10911i	−0.117922	−	0.0494035i
$505$		0			0
$506$	17.1015	+	22.3493i	0.760255	+	0.993549i
$507$		−	12.9906i		−	0.576933i
$508$	13.2177	+	23.0367i	0.586442	+	1.02209i
$509$	−30.5917	+	30.5917i	−1.35595	+	1.35595i	−0.477105	+	0.878847i	$0.658314\pi$
$509$	−30.5917	+	30.5917i	−1.35595	+	1.35595i	−0.878847	+	0.477105i	$0.841686\pi$
$510$		0			0
$511$		−	18.4609i		−	0.816661i
$512$	8.91166	−	20.7986i	0.393844	−	0.919177i
$513$	−24.9590	+	24.9590i	−1.10197	+	1.10197i
$514$	−1.91760	+	14.4157i	−0.0845818	+	0.635850i
$515$		0			0
$516$	0.750947	+	0.203383i	0.0330586	+	0.00895344i
$517$	0.489083			0.0215098
$518$	−3.41354	+	25.6616i	−0.149983	+	1.12750i
$519$			26.5911i			1.16722i
$520$		0			0
$521$		−	13.1096i		−	0.574342i	−0.957879	−	0.287171i	$-0.907285\pi$
$521$		−	13.1096i		−	0.574342i	0.957879	−	0.287171i	$-0.0927149\pi$
$522$	6.68360	+	0.889063i	0.292533	+	0.0389132i
$523$	−31.0886			−1.35941			−0.679706	−	0.733485i	$-0.737893\pi$
$523$	−31.0886			−1.35941			−0.679706	+	0.733485i	$0.737893\pi$
$524$	−0.664258	−	1.15771i	−0.0290182	−	0.0505749i
$525$		0			0
$526$	10.5482	+	1.40315i	0.459925	+	0.0611800i
$527$	−11.8618	+	11.8618i	−0.516706	+	0.516706i
$528$	17.3014	−	4.53624i	0.752948	−	0.197415i
$529$		−	24.3118i		−	1.05703i
$530$		0			0
$531$	0.763691	−	0.763691i	0.0331413	−	0.0331413i
$532$	20.2771	+	5.49176i	0.879123	+	0.238098i
$533$			24.4896i			1.06076i
$534$	−6.30231	+	4.82247i	−0.272728	+	0.208689i
$535$		0			0
$536$	24.1768	−	9.90022i	1.04428	−	0.427624i
$537$	5.82316	−	5.82316i	0.251288	−	0.251288i
$538$	4.55519	+	0.605940i	0.196388	+	0.0261239i
$539$	8.67664	−	8.67664i	0.373729	−	0.373729i
$540$		0			0
$541$	−0.926425	−	0.926425i	−0.0398301	−	0.0398301i	0.686911	−	0.726741i	$-0.258966\pi$
$541$	−0.926425	−	0.926425i	−0.0398301	−	0.0398301i	−0.726741	+	0.686911i	$0.758966\pi$
$542$	−16.7791	+	12.8392i	−0.720725	+	0.551493i
$543$	−6.63941	−	6.63941i	−0.284924	−	0.284924i
$544$	−10.1844	+	13.0893i	−0.436652	+	0.561197i
$545$		0			0
$546$	7.71456	+	1.02620i	0.330153	+	0.0439175i
$547$	−17.1171			−0.731875			−0.365938	−	0.930639i	$-0.619252\pi$
$547$	−17.1171			−0.731875			−0.365938	+	0.930639i	$0.619252\pi$
$548$	−22.8827	−	39.8815i	−0.977502	−	1.70366i
$549$	−1.51549	−	1.51549i	−0.0646794	−	0.0646794i
$550$		0			0
$551$	−49.3481			−2.10230
$552$	−27.7346	−	11.6195i	−1.18047	−	0.494557i
$553$	−5.71866	−	5.71866i	−0.243182	−	0.243182i
$554$	−9.65628	−	12.6194i	−0.410256	−	0.536149i
$555$		0			0
$556$	7.41486	+	12.9231i	0.314460	+	0.548062i
$557$			12.5797i			0.533017i	0.963833	+	0.266509i	$0.0858701\pi$
$557$			12.5797i			0.533017i	−0.963833	+	0.266509i	$0.914130\pi$
$558$	3.92648	−	3.00451i	0.166221	−	0.127191i
$559$	0.539510			0.0228189
$560$		0			0
$561$	−13.1096			−0.553488
$562$	16.9083	−	12.9381i	0.713232	−	0.545759i
$563$			19.4227i			0.818569i	0.912407	+	0.409284i	$0.134222\pi$
$563$			19.4227i			0.818569i	−0.912407	+	0.409284i	$0.865778\pi$
$564$	−0.453287	+	0.260081i	−0.0190868	+	0.0109514i
$565$		0			0
$566$	16.1766	+	21.1406i	0.679954	+	0.888607i
$567$	7.97865	+	7.97865i	0.335072	+	0.335072i
$568$	−23.1711	+	9.48838i	−0.972238	+	0.398124i
$569$	−5.57547			−0.233736			−0.116868	−	0.993147i	$-0.537285\pi$
$569$	−5.57547			−0.233736			−0.116868	+	0.993147i	$0.537285\pi$
$570$		0			0
$571$	5.58062	+	5.58062i	0.233542	+	0.233542i	0.814169	−	0.580627i	$-0.197193\pi$
$571$	5.58062	+	5.58062i	0.233542	+	0.233542i	−0.580627	+	0.814169i	$0.697193\pi$
$572$	10.7583	−	6.17274i	0.449825	−	0.258095i
$573$	40.0129			1.67156
$574$	26.5992	+	3.53827i	1.11023	+	0.147685i
$575$		0			0
$576$	3.48413	−	3.42832i	0.145172	−	0.142847i
$577$	−27.7472	−	27.7472i	−1.15513	−	1.15513i	−0.985509	−	0.169624i	$-0.945745\pi$
$577$	−27.7472	−	27.7472i	−1.15513	−	1.15513i	−0.169624	−	0.985509i	$-0.554255\pi$
$578$	−9.43954	+	7.22305i	−0.392633	+	0.300439i
$579$	15.6272	+	15.6272i	0.649444	+	0.649444i
$580$		0			0
$581$	−5.81264	+	5.81264i	−0.241149	+	0.241149i
$582$	−30.3240	−	4.03375i	−1.25697	−	0.167204i
$583$	5.51349	−	5.51349i	0.228345	−	0.228345i
$584$	28.9963	+	12.1480i	1.19988	+	0.502689i
$585$		0			0
$586$	−6.94381	+	5.31334i	−0.286846	+	0.219492i
$587$		−	30.8977i		−	1.27529i	−0.770332	−	0.637643i	$-0.779909\pi$
$587$		−	30.8977i		−	1.27529i	0.770332	−	0.637643i	$-0.220091\pi$
$588$	−3.42759	+	12.6556i	−0.141351	+	0.521908i
$589$	−25.5874	+	25.5874i	−1.05431	+	1.05431i
$590$		0			0
$591$			24.1303i			0.992587i
$592$	−38.0601	−	22.2480i	−1.56426	−	0.914388i
$593$	7.82287	−	7.82287i	0.321247	−	0.321247i	−0.527998	−	0.849245i	$-0.677057\pi$
$593$	7.82287	−	7.82287i	0.321247	−	0.321247i	0.849245	+	0.527998i	$0.177057\pi$
$594$	22.6356	+	3.01103i	0.928751	+	0.123544i
$595$		0			0
$596$	−9.08290	+	5.21147i	−0.372050	+	0.213470i
$597$	−38.9777			−1.59525
$598$	−20.6704	−	2.74961i	−0.845275	−	0.112440i
$599$		−	24.3316i		−	0.994163i	−0.867704	−	0.497081i	$-0.834405\pi$
$599$		−	24.3316i		−	0.994163i	0.867704	−	0.497081i	$-0.165595\pi$
$600$		0			0
$601$		−	30.6420i		−	1.24991i	−0.780660	−	0.624956i	$-0.785117\pi$
$601$		−	30.6420i		−	1.24991i	0.780660	−	0.624956i	$-0.214883\pi$
$602$	0.0779489	−	0.585986i	0.00317696	−	0.0238830i
$603$	5.64362			0.229826
$604$	−5.91501	+	21.8399i	−0.240678	+	0.888651i
$605$		0			0
$606$	2.56618	−	19.2914i	0.104244	−	0.783661i
$607$	10.0615	−	10.0615i	0.408386	−	0.408386i	−0.472790	−	0.881175i	$-0.656753\pi$
$607$	10.0615	−	10.0615i	0.408386	−	0.408386i	0.881175	+	0.472790i	$0.156753\pi$
$608$	−21.9690	+	28.2352i	−0.890962	+	1.14509i
$609$			20.0314i			0.811712i
$610$		0			0
$611$	−0.256256	+	0.256256i	−0.0103670	+	0.0103670i
$612$	−3.10746	+	1.78296i	−0.125612	+	0.0720718i
$613$		−	9.66991i		−	0.390564i	−0.980747	−	0.195282i	$-0.937438\pi$
$613$		−	9.66991i		−	0.390564i	0.980747	−	0.195282i	$-0.0625622\pi$
$614$	4.17360	+	5.45432i	0.168433	+	0.220118i
$615$		0			0
$616$	−5.15012	−	12.5769i	−0.207504	−	0.506736i
$617$	4.46520	−	4.46520i	0.179762	−	0.179762i	−0.611490	−	0.791252i	$-0.709430\pi$
$617$	4.46520	−	4.46520i	0.179762	−	0.179762i	0.791252	+	0.611490i	$0.209430\pi$
$618$	−1.24992	+	9.39638i	−0.0502792	+	0.377978i
$619$	−5.32437	+	5.32437i	−0.214004	+	0.214004i	−0.805966	−	0.591962i	$-0.798354\pi$
$619$	−5.32437	+	5.32437i	−0.214004	+	0.214004i	0.591962	+	0.805966i	$0.298354\pi$
$620$		0			0
$621$	−27.1460	−	27.1460i	−1.08933	−	1.08933i
$622$	−1.80090	−	2.35353i	−0.0722095	−	0.0943679i
$623$	4.26370	+	4.26370i	0.170822	+	0.170822i
$624$	−6.68836	+	11.4419i	−0.267749	+	0.458043i
$625$		0			0
$626$	−3.60465	+	27.0982i	−0.144071	+	1.08306i
$627$	−28.2791			−1.12936
$628$	36.2195	+	9.80955i	1.44532	+	0.391443i
$629$	22.8483	+	22.8483i	0.911021	+	0.911021i
$630$		0			0
$631$	24.1303			0.960611			0.480306	−	0.877101i	$-0.340526\pi$
$631$	24.1303			0.960611			0.480306	+	0.877101i	$0.340526\pi$
$632$	12.7454	−	5.21913i	0.506984	−	0.207606i
$633$	−10.5744	−	10.5744i	−0.420294	−	0.420294i
$634$	−6.98189	+	5.34248i	−0.277286	+	0.212177i
$635$		0			0
$636$	−2.17803	+	8.04188i	−0.0863645	+	0.318881i
$637$			9.09230i			0.360250i
$638$	19.4005	+	25.3538i	0.768074	+	1.00377i
$639$	−5.40885			−0.213971
$640$		0			0
$641$	40.1642			1.58639			0.793196	−	0.608967i	$-0.208416\pi$
$641$	40.1642			1.58639			0.793196	+	0.608967i	$0.208416\pi$
$642$	17.4259	+	22.7732i	0.687745	+	0.898788i
$643$		−	38.2226i		−	1.50735i	−0.657245	−	0.753677i	$-0.728278\pi$
$643$		−	38.2226i		−	1.50735i	0.657245	−	0.753677i	$-0.271722\pi$
$644$	−5.97295	+	22.0538i	−0.235367	+	0.869040i
$645$		0			0
$646$	20.8242	−	15.9345i	0.819316	−	0.626934i
$647$	4.07480	+	4.07480i	0.160197	+	0.160197i	0.782654	−	0.622457i	$-0.213866\pi$
$647$	4.07480	+	4.07480i	0.160197	+	0.160197i	−0.622457	+	0.782654i	$0.713866\pi$
$648$	−17.7823	+	7.28170i	−0.698554	+	0.286052i
$649$	5.11378			0.200733
$650$		0			0
$651$	10.3864	+	10.3864i	0.407076	+	0.407076i
$652$	34.5730	+	9.36360i	1.35398	+	0.366707i
$653$	18.5270			0.725016			0.362508	−	0.931981i	$-0.381921\pi$
$653$	18.5270			0.725016			0.362508	+	0.931981i	$0.381921\pi$
$654$	0.815233	−	6.12857i	0.0318781	−	0.239646i
$655$		0			0
$656$	−23.0610	+	39.4509i	−0.900379	+	1.54030i
$657$	4.80219	+	4.80219i	0.187351	+	0.187351i
$658$	0.241307	+	0.315355i	0.00940713	+	0.0122938i
$659$	11.4021	+	11.4021i	0.444163	+	0.444163i	0.893409	−	0.449245i	$-0.148307\pi$
$659$	11.4021	+	11.4021i	0.444163	+	0.444163i	−0.449245	+	0.893409i	$0.648307\pi$
$660$		0			0
$661$	6.03893	−	6.03893i	0.234887	−	0.234887i	−0.579842	−	0.814729i	$-0.696886\pi$
$661$	6.03893	−	6.03893i	0.234887	−	0.234887i	0.814729	+	0.579842i	$0.196886\pi$
$662$	2.18604	−	16.4337i	0.0849627	−	0.638713i
$663$	6.86882	−	6.86882i	0.266763	−	0.266763i
$664$	−5.30490	−	12.9548i	−0.205870	−	0.502745i
$665$		0			0
$666$	−5.78733	−	7.56324i	−0.224254	−	0.293070i
$667$		−	53.6720i		−	2.07819i
$668$	31.3871	−	18.0089i	1.21440	−	0.696784i
$669$	2.03843	−	2.03843i	0.0788102	−	0.0788102i
$670$		0			0
$671$		−	10.1479i		−	0.391756i
$672$	11.4612	+	8.91766i	0.442127	+	0.344006i
$673$	20.5070	−	20.5070i	0.790488	−	0.790488i	−0.191085	−	0.981573i	$-0.561201\pi$
$673$	20.5070	−	20.5070i	0.790488	−	0.790488i	0.981573	+	0.191085i	$0.0612008\pi$
$674$	3.01103	−	22.6356i	0.115980	−	0.871892i
$675$		0			0
$676$	4.39426	−	16.2248i	0.169010	−	0.624032i
$677$	−15.8942			−0.610864			−0.305432	−	0.952214i	$-0.598801\pi$
$677$	−15.8942			−0.610864			−0.305432	+	0.952214i	$0.598801\pi$
$678$	−0.224812	+	1.69004i	−0.00863386	+	0.0649057i
$679$			23.2441i			0.892025i
$680$		0			0
$681$		−	7.16700i		−	0.274640i
$682$	23.2055	+	3.08683i	0.888583	+	0.118201i
$683$	7.34149			0.280914			0.140457	−	0.990087i	$-0.455143\pi$
$683$	7.34149			0.280914			0.140457	+	0.990087i	$0.455143\pi$
$684$	−6.70319	+	3.84607i	−0.256303	+	0.147058i
$685$		0			0
$686$	26.1739	+	3.48169i	0.999324	+	0.132932i
$687$	−19.6908	+	19.6908i	−0.751250	+	0.751250i
$688$	0.869110	+	0.508037i	0.0331345	+	0.0193687i
$689$			5.77762i			0.220110i
$690$		0			0
$691$	−28.5464	+	28.5464i	−1.08595	+	1.08595i	−0.0900145	+	0.995940i	$0.528691\pi$
$691$	−28.5464	+	28.5464i	−1.08595	+	1.08595i	−0.995940	+	0.0900145i	$0.971309\pi$
$692$	−8.99485	+	33.2115i	−0.341933	+	1.26251i
$693$		−	2.93583i		−	0.111523i
$694$	1.95036	−	1.49240i	0.0740347	−	0.0566507i
$695$		0			0
$696$	−31.4631	−	13.1815i	−1.19260	−	0.499643i
$697$	23.6832	−	23.6832i	0.897064	−	0.897064i
$698$	−39.8663	−	5.30308i	−1.50896	−	0.200724i
$699$	−18.5565	+	18.5565i	−0.701871	+	0.701871i
$700$		0			0
$701$	17.7049	+	17.7049i	0.668706	+	0.668706i	0.957416	−	0.288710i	$-0.0932265\pi$
$701$	17.7049	+	17.7049i	0.668706	+	0.668706i	−0.288710	+	0.957416i	$0.593227\pi$
$702$	−13.4376	+	10.2824i	−0.507171	+	0.388083i
$703$	49.2867	+	49.2867i	1.85888	+	1.85888i
$704$	23.1434	+	0.186853i	0.872248	+	0.00704228i
$705$		0			0
$706$	29.2568	+	3.89178i	1.10109	+	0.146469i
$707$	−14.7873			−0.556135
$708$	−4.73950	+	2.71937i	−0.178121	+	0.102200i
$709$	−31.2225	−	31.2225i	−1.17259	−	1.17259i	−0.981591	−	0.190995i	$-0.938829\pi$
$709$	−31.2225	−	31.2225i	−1.17259	−	1.17259i	−0.190995	−	0.981591i	$-0.561171\pi$
$710$		0			0
$711$	2.97517			0.111577
$712$	−9.50265	+	3.89126i	−0.356127	+	0.145831i
$713$	−27.8293	−	27.8293i	−1.04222	−	1.04222i
$714$	−6.46812	−	8.45294i	−0.242063	−	0.316343i
$715$		0			0
$716$	9.24270	−	5.30316i	0.345416	−	0.198188i
$717$		−	4.08598i		−	0.152594i
$718$	−28.4692	+	21.7844i	−1.06246	+	0.812985i
$719$	30.7570			1.14704			0.573520	−	0.819191i	$-0.305577\pi$
$719$	30.7570			1.14704			0.573520	+	0.819191i	$0.305577\pi$
$720$		0			0
$721$	7.20253			0.268236
$722$	23.5810	−	18.0440i	0.877594	−	0.671528i
$723$			10.8437i			0.403282i
$724$	−6.04652	−	10.5383i	−0.224717	−	0.391652i
$725$		0			0
$726$	−3.49414	−	4.56636i	−0.129680	−	0.169474i
$727$	20.0526	+	20.0526i	0.743711	+	0.743711i	0.973290	−	0.229579i	$-0.0737350\pi$
$727$	20.0526	+	20.0526i	0.743711	+	0.743711i	−0.229579	+	0.973290i	$0.573735\pi$
$728$	9.28810	+	3.89126i	0.344240	+	0.144220i
$729$	−30.0310			−1.11226
$730$		0			0
$731$	−0.521745	−	0.521745i	−0.0192974	−	0.0192974i
$732$	5.39640	+	9.40520i	0.199457	+	0.347626i
$733$	−4.69214			−0.173308			−0.0866540	−	0.996238i	$-0.527617\pi$
$733$	−4.69214			−0.173308			−0.0866540	+	0.996238i	$0.527617\pi$
$734$	−38.6194	−	5.13722i	−1.42547	−	0.189618i
$735$		0			0
$736$	−30.7092	−	23.8940i	−1.13196	−	0.880743i
$737$	18.8953	+	18.8953i	0.696016	+	0.696016i
$738$	−7.83960	+	5.99880i	−0.288580	+	0.220819i
$739$	5.45035	+	5.45035i	0.200494	+	0.200494i	0.800212	−	0.599717i	$-0.204720\pi$
$739$	5.45035	+	5.45035i	0.200494	+	0.200494i	−0.599717	+	0.800212i	$0.704720\pi$
$740$		0			0
$741$	14.8169	−	14.8169i	0.544314	−	0.544314i
$742$	6.27533	+	0.834754i	0.230374	+	0.0306448i
$743$	28.8916	−	28.8916i	1.05993	−	1.05993i	0.0618433	−	0.998086i	$-0.480302\pi$
$743$	28.8916	−	28.8916i	1.05993	−	1.05993i	0.998086	−	0.0618433i	$-0.0196979\pi$
$744$	−23.1485	+	9.47914i	−0.848667	+	0.347522i
$745$		0			0
$746$	28.6356	−	21.9117i	1.04842	−	0.802245i
$747$		−	3.02406i		−	0.110645i
$748$	−16.3735	−	4.43452i	−0.598673	−	0.162142i
$749$	15.4068	−	15.4068i	0.562951	−	0.562951i
$750$		0			0
$751$			34.7738i			1.26892i	0.772958	+	0.634458i	$0.218776\pi$
$751$			34.7738i			1.26892i	−0.772958	+	0.634458i	$0.781224\pi$
$752$	−0.654116	+	0.171502i	−0.0238532	+	0.00625403i
$753$	24.3708	−	24.3708i	0.888122	−	0.888122i
$754$	−23.4492	−	3.11925i	−0.853968	−	0.113596i
$755$		0			0
$756$	9.22665	+	16.0808i	0.335570	+	0.584854i
$757$	13.0634			0.474796			0.237398	−	0.971412i	$-0.423705\pi$
$757$	13.0634			0.474796			0.237398	+	0.971412i	$0.423705\pi$
$758$	13.5282	+	1.79954i	0.491366	+	0.0653623i
$759$		−	30.7570i		−	1.11641i
$760$		0			0
$761$			7.48332i			0.271270i	0.990759	+	0.135635i	$0.0433074\pi$
$761$			7.48332i			0.271270i	−0.990759	+	0.135635i	$0.956693\pi$
$762$	3.82758	−	28.7741i	0.138659	−	1.04238i
$763$	−4.69769			−0.170068
$764$	49.9748	+	13.5350i	1.80802	+	0.489677i
$765$		0			0
$766$	−0.549830	+	4.13339i	−0.0198662	+	0.149345i
$767$	−2.67938	+	2.67938i	−0.0967468	+	0.0967468i
$768$	−21.5489	+	12.1339i	−0.777578	+	0.437843i
$769$		−	21.5518i		−	0.777179i	−0.921411	−	0.388589i	$-0.872962\pi$
$769$		−	21.5518i		−	0.777179i	0.921411	−	0.388589i	$-0.127038\pi$
$770$		0			0
$771$	11.2389	−	11.2389i	0.404758	−	0.404758i
$772$	14.2317	+	24.8040i	0.512210	+	0.892714i
$773$		−	28.6752i		−	1.03138i	−0.856777	−	0.515688i	$-0.827536\pi$
$773$		−	28.6752i		−	1.03138i	0.856777	−	0.515688i	$-0.172464\pi$
$774$	0.132155	+	0.172708i	0.00475020	+	0.00620786i
$775$		0			0
$776$	−36.5092	−	15.2956i	−1.31060	−	0.549079i
$777$	20.0065	−	20.0065i	0.717727	−	0.717727i
$778$	2.08971	−	15.7095i	0.0749196	−	0.563214i
$779$	51.0877	−	51.0877i	1.83041	−	1.83041i
$780$		0			0
$781$	−18.1092	−	18.1092i	−0.647999	−	0.647999i
$782$	17.3307	+	22.6488i	0.619743	+	0.809919i
$783$	−30.7952	−	30.7952i	−1.10053	−	1.10053i
$784$	−8.56189	+	14.6470i	−0.305782	+	0.523107i
$785$		0			0
$786$	−0.192355	+	1.44605i	−0.00686109	+	0.0515787i
$787$	−35.9487			−1.28143			−0.640716	−	0.767778i	$-0.721363\pi$
$787$	−35.9487			−1.28143			−0.640716	+	0.767778i	$0.721363\pi$
$788$	−8.16242	+	30.1379i	−0.290774	+	1.07362i
$789$	−8.22370	−	8.22370i	−0.292771	−	0.292771i
$790$		0			0
$791$	1.29546			0.0460611
$792$	4.61128	+	1.93190i	0.163855	+	0.0686471i
$793$	5.31703	+	5.31703i	0.188813	+	0.188813i
$794$	27.1646	−	20.7861i	0.964034	−	0.737671i
$795$		0			0
$796$	−48.6818	−	13.1848i	−1.72548	−	0.467322i
$797$			10.7052i			0.379196i	0.981862	+	0.189598i	$0.0607185\pi$
$797$			10.7052i			0.379196i	−0.981862	+	0.189598i	$0.939282\pi$
$798$	−13.9526	−	18.2341i	−0.493916	−	0.645480i
$799$	0.495636			0.0175343
$800$		0			0
$801$	−2.21821			−0.0783767
$802$	−12.0281	−	15.7191i	−0.424728	−	0.555061i
$803$			32.1561i			1.13476i
$804$	−27.5603	−	7.46431i	−0.971977	−	0.263246i
$805$		0			0
$806$	−13.7759	+	10.5412i	−0.485236	+	0.371298i
$807$	−3.55135	−	3.55135i	−0.125014	−	0.125014i
$808$	9.73069	−	23.2263i	0.342324	−	0.817099i
$809$	−10.3002			−0.362137			−0.181069	−	0.983470i	$-0.557956\pi$
$809$	−10.3002			−0.362137			−0.181069	+	0.983470i	$0.557956\pi$
$810$		0			0
$811$	27.0808	+	27.0808i	0.950936	+	0.950936i	0.998851	−	0.0479153i	$-0.0152578\pi$
$811$	27.0808	+	27.0808i	0.950936	+	0.950936i	−0.0479153	+	0.998851i	$0.515258\pi$
$812$	−6.77590	+	25.0185i	−0.237788	+	0.877977i
$813$	23.0913			0.809847
$814$	5.94589	−	44.6987i	0.208403	−	1.56669i
$815$		0			0
$816$	17.5333	−	4.59702i	0.613787	−	0.160928i
$817$	−1.12547	−	1.12547i	−0.0393752	−	0.0393752i
$818$	−9.81801	−	12.8308i	−0.343278	−	0.448618i
$819$	1.53824	+	1.53824i	0.0537503	+	0.0537503i
$820$		0			0
$821$	6.00000	−	6.00000i	0.209401	−	0.209401i	−0.594612	−	0.804013i	$-0.702694\pi$
$821$	6.00000	−	6.00000i	0.209401	−	0.209401i	0.804013	+	0.594612i	$0.202694\pi$
$822$	−6.62636	+	49.8142i	−0.231121	+	1.73747i
$823$	17.4197	−	17.4197i	0.607214	−	0.607214i	−0.335003	−	0.942217i	$-0.608737\pi$
$823$	17.4197	−	17.4197i	0.607214	−	0.607214i	0.942217	+	0.335003i	$0.108737\pi$
$824$	−4.73957	+	11.3130i	−0.165111	+	0.394105i
$825$		0			0
$826$	2.52308	+	3.29731i	0.0877890	+	0.114728i
$827$			3.05415i			0.106203i	0.998589	+	0.0531016i	$0.0169107\pi$
$827$			3.05415i			0.106203i	−0.998589	+	0.0531016i	$0.983089\pi$
$828$	−4.18307	−	7.29052i	−0.145372	−	0.253363i
$829$	2.18527	−	2.18527i	0.0758976	−	0.0758976i	−0.668139	−	0.744037i	$-0.732909\pi$
$829$	2.18527	−	2.18527i	0.0758976	−	0.0758976i	0.744037	+	0.668139i	$0.232909\pi$
$830$		0			0
$831$			17.3668i			0.602446i
$832$	−12.2239	+	12.0281i	−0.423789	+	0.417000i
$833$	8.79290	−	8.79290i	0.304656	−	0.304656i
$834$	2.14719	−	16.1416i	0.0743511	−	0.558940i
$835$		0			0
$836$	−35.3197	−	9.56583i	−1.22156	−	0.330841i
$837$	−31.9351			−1.10384
$838$	−4.36338	+	32.8020i	−0.150730	+	1.13313i
$839$		−	1.68627i		−	0.0582167i	−0.999576	−	0.0291083i	$-0.990733\pi$
$839$		−	1.68627i		−	0.0582167i	0.999576	−	0.0291083i	$-0.00926678\pi$
$840$		0			0
$841$		−	31.8872i		−	1.09956i
$842$	30.9076	+	4.11139i	1.06515	+	0.141688i
$843$	−23.2690			−0.801427
$844$	−9.63012	−	16.7840i	−0.331482	−	0.577729i
$845$		0			0
$846$	−0.144803	−	0.0192620i	−0.00497844	−	0.000662241i
$847$	−3.08928	+	3.08928i	−0.106149	+	0.106149i
$848$	−5.44057	+	9.30729i	−0.186830	+	0.319614i
$849$		−	29.0935i		−	0.998488i
$850$		0			0
$851$	−53.6052	+	53.6052i	−1.83756	+	1.83756i
$852$	26.4138	+	7.15381i	0.904923	+	0.245085i
$853$			38.0838i			1.30396i	0.758235	+	0.651982i	$0.226062\pi$
$853$			38.0838i			1.30396i	−0.758235	+	0.651982i	$0.773938\pi$
$854$	6.54327	−	5.00686i	0.223906	−	0.171331i
$855$		0			0
$856$	14.0610	+	34.3376i	0.480594	+	1.17363i
$857$	27.9027	−	27.9027i	0.953138	−	0.953138i	−0.0458123	−	0.998950i	$-0.514588\pi$
$857$	27.9027	−	27.9027i	0.953138	−	0.953138i	0.998950	+	0.0458123i	$0.0145876\pi$
$858$	−13.4376	−	1.78750i	−0.458753	−	0.0610241i
$859$	−7.51122	+	7.51122i	−0.256280	+	0.256280i	−0.823539	−	0.567260i	$-0.808004\pi$
$859$	−7.51122	+	7.51122i	−0.256280	+	0.256280i	0.567260	+	0.823539i	$0.308004\pi$
$860$		0			0
$861$	−20.7375	−	20.7375i	−0.706732	−	0.706732i
$862$	20.7339	−	15.8654i	0.706201	−	0.540379i
$863$	−35.6257	−	35.6257i	−1.21271	−	1.21271i	−0.970131	−	0.242580i	$-0.922006\pi$
$863$	−35.6257	−	35.6257i	−1.21271	−	1.21271i	−0.242580	−	0.970131i	$-0.577994\pi$
$864$	−31.3295	+	3.91036i	−1.06585	+	0.133033i
$865$		0			0
$866$	−27.3337	−	3.63597i	−0.928835	−	0.123555i
$867$	12.9906			0.441184
$868$	9.45892	+	16.4856i	0.321057	+	0.559559i
$869$	9.96107	+	9.96107i	0.337906	+	0.337906i
$870$		0			0
$871$	−19.8004			−0.670912
$872$	3.09128	−	7.37862i	0.104684	−	0.249872i
$873$	−6.04642	−	6.04642i	−0.204640	−	0.204640i
$874$	37.3845	+	48.8564i	1.26455	+	1.65259i
$875$		0			0
$876$	−17.0998	−	29.8026i	−0.577748	−	1.00694i
$877$			30.6461i			1.03484i	0.855730	+	0.517422i	$0.173108\pi$
$877$			30.6461i			1.03484i	−0.855730	+	0.517422i	$0.826892\pi$
$878$	−18.9863	+	14.5282i	−0.640758	+	0.490303i
$879$	9.55600			0.322316
$880$		0			0
$881$	−20.5286			−0.691625			−0.345813	−	0.938304i	$-0.612397\pi$
$881$	−20.5286			−0.691625			−0.345813	+	0.938304i	$0.612397\pi$
$882$	−2.91062	+	2.22718i	−0.0980058	+	0.0749932i
$883$		−	20.5650i		−	0.692068i	−0.938222	−	0.346034i	$-0.887528\pi$
$883$		−	20.5650i		−	0.692068i	0.938222	−	0.346034i	$-0.112472\pi$
$884$	10.9024	−	6.25544i	0.366687	−	0.210393i
$885$		0			0
$886$	10.5689	+	13.8121i	0.355070	+	0.464027i
$887$	−23.6473	−	23.6473i	−0.793997	−	0.793997i	0.188144	−	0.982141i	$-0.439753\pi$
$887$	−23.6473	−	23.6473i	−0.793997	−	0.793997i	−0.982141	+	0.188144i	$0.939753\pi$
$888$	18.2589	+	44.5891i	0.612727	+	1.49631i
$889$	−22.0560			−0.739735
$890$		0			0
$891$	−13.8976	−	13.8976i	−0.465588	−	0.465588i
$892$	3.23546	−	1.85640i	0.108331	−	0.0621569i
$893$	1.06915			0.0357778
$894$	11.3450	+	1.50913i	0.379435	+	0.0504730i
$895$		0			0
$896$	11.2982	+	15.0148i	0.377445	+	0.501609i
$897$	16.1152	+	16.1152i	0.538071	+	0.538071i
$898$	10.5009	−	8.03519i	0.350419	−	0.268138i
$899$	−31.5705	−	31.5705i	−1.05293	−	1.05293i
$900$		0			0
$901$	5.58736	−	5.58736i	0.186142	−	0.186142i
$902$	−46.3320	−	6.16315i	−1.54269	−	0.205211i
$903$	−0.456851	+	0.456851i	−0.0152030	+	0.0152030i
$904$	−0.852465	+	2.03476i	−0.0283526	+	0.0676751i
$905$		0			0
$906$	19.6394	−	15.0279i	0.652476	−	0.499269i
$907$		−	3.63021i		−	0.120539i	−0.998182	−	0.0602696i	$-0.980804\pi$
$907$		−	3.63021i		−	0.120539i	0.998182	−	0.0602696i	$-0.0191961\pi$
$908$	2.42434	−	8.95134i	0.0804547	−	0.297061i
$909$	3.84659	−	3.84659i	0.127583	−	0.127583i
$910$		0			0
$911$			44.3485i			1.46933i	0.678430	+	0.734665i	$0.262661\pi$
$911$			44.3485i			1.46933i	−0.678430	+	0.734665i	$0.737339\pi$
$912$	37.8215	−	9.91637i	1.25240	−	0.328364i
$913$	10.1248	−	10.1248i	0.335081	−	0.335081i
$914$	−29.5649	−	3.93278i	−0.977921	−	0.130085i
$915$		0			0
$916$	−31.2538	+	17.9324i	−1.03266	+	0.592504i
$917$	1.10843			0.0366035
$918$	22.9389	+	3.05137i	0.757097	+	0.100710i
$919$			13.3312i			0.439756i	0.975527	+	0.219878i	$0.0705660\pi$
$919$			13.3312i			0.439756i	−0.975527	+	0.219878i	$0.929434\pi$
$920$		0			0
$921$		−	7.50618i		−	0.247337i
$922$	4.74710	−	35.6867i	0.156337	−	1.17528i
$923$	18.9768			0.624628
$924$	−3.88296	+	14.3370i	−0.127740	+	0.471651i
$925$		0			0
$926$	−1.64929	+	12.3986i	−0.0541989	+	0.407444i
$927$	−1.87358	+	1.87358i	−0.0615364	+	0.0615364i
$928$	−34.8375	−	27.1061i	−1.14360	−	0.889801i
$929$			13.5713i			0.445260i	0.974903	+	0.222630i	$0.0714641\pi$
$929$			13.5713i			0.445260i	−0.974903	+	0.222630i	$0.928536\pi$
$930$		0			0
$931$	18.9674	−	18.9674i	0.621632	−	0.621632i
$932$	−29.4535	+	16.8994i	−0.964780	+	0.553560i
$933$			3.23891i			0.106037i
$934$	−20.6248	−	26.9538i	−0.674864	−	0.881955i
$935$		0			0
$936$	−3.42832	+	1.40387i	−0.112058	+	0.0458869i
$937$	−10.5066	+	10.5066i	−0.343235	+	0.343235i	−0.857582	−	0.514347i	$-0.828034\pi$
$937$	−10.5066	+	10.5066i	−0.343235	+	0.343235i	0.514347	+	0.857582i	$0.328034\pi$
$938$	−2.86078	+	21.5061i	−0.0934079	+	0.702200i
$939$	21.1265	−	21.1265i	0.689437	−	0.689437i
$940$		0			0
$941$	−4.25664	−	4.25664i	−0.138763	−	0.138763i	0.634313	−	0.773076i	$-0.281283\pi$
$941$	−4.25664	−	4.25664i	−0.138763	−	0.138763i	−0.773076	+	0.634313i	$0.781283\pi$
$942$	−24.9225	−	32.5703i	−0.812019	−	1.06120i
$943$	55.5640	+	55.5640i	1.80941	+	1.80941i
$944$	−6.83935	+	1.79320i	−0.222602	+	0.0583637i
$945$		0			0
$946$	−0.135775	+	1.02070i	−0.00441444	+	0.0331859i
$947$	−27.2068			−0.884101			−0.442050	−	0.896990i	$-0.645749\pi$
$947$	−27.2068			−0.884101			−0.442050	+	0.896990i	$0.645749\pi$
$948$	−14.5291	−	3.93499i	−0.471882	−	0.127802i
$949$	−16.8483	−	16.8483i	−0.546919	−	0.546919i
$950$		0			0
$951$	9.60841			0.311574
$952$	−5.21913	−	12.7454i	−0.169153	−	0.413080i
$953$	0.537259	+	0.537259i	0.0174035	+	0.0174035i	0.715755	−	0.698351i	$-0.246083\pi$
$953$	0.537259	+	0.537259i	0.0174035	+	0.0174035i	−0.698351	+	0.715755i	$0.746083\pi$
$954$	−1.84953	+	1.41524i	−0.0598807	+	0.0458202i
$955$		0			0
$956$	1.38214	−	5.10326i	0.0447017	−	0.165051i
$957$		−	34.8917i		−	1.12789i
$958$	20.3352	+	26.5753i	0.656999	+	0.858608i
$959$	38.1837			1.23302
$960$		0			0
$961$	−1.73907			−0.0560990
$962$	20.3046	+	26.5354i	0.654648	+	0.855534i
$963$			8.01545i			0.258294i
$964$	−3.66804	+	13.5434i	−0.118140	+	0.436205i
$965$		0			0
$966$	19.8318	−	15.1751i	0.638077	−	0.488251i
$967$	9.89350	+	9.89350i	0.318154	+	0.318154i	0.848058	−	0.529904i	$-0.177772\pi$
$967$	9.89350	+	9.89350i	0.318154	+	0.318154i	−0.529904	+	0.848058i	$0.677772\pi$
$968$	−2.81942	−	6.88518i	−0.0906197	−	0.221298i
$969$	−28.6580			−0.920629
$970$		0			0
$971$	14.8635	+	14.8635i	0.476992	+	0.476992i	0.904168	−	0.427176i	$-0.140492\pi$
$971$	14.8635	+	14.8635i	0.476992	+	0.476992i	−0.427176	+	0.904168i	$0.640492\pi$
$972$	−12.0524	−	3.26423i	−0.386582	−	0.104700i
$973$	−12.3729			−0.396658
$974$	5.58583	−	41.9919i	0.178981	−	1.34551i
$975$		0			0
$976$	3.55847	+	13.5722i	0.113904	+	0.434435i
$977$	−11.4685	−	11.4685i	−0.366908	−	0.366908i	0.499440	−	0.866348i	$-0.333539\pi$
$977$	−11.4685	−	11.4685i	−0.366908	−	0.366908i	−0.866348	+	0.499440i	$0.833539\pi$
$978$	−23.7895	−	31.0896i	−0.760705	−	0.994137i
$979$	−7.42674	−	7.42674i	−0.237360	−	0.237360i
$980$		0			0
$981$	1.22200	−	1.22200i	0.0390154	−	0.0390154i
$982$	3.50364	−	26.3389i	0.111806	−	0.840507i
$983$	−34.9827	+	34.9827i	−1.11577	+	1.11577i	−0.123420	+	0.992355i	$0.539386\pi$
$983$	−34.9827	+	34.9827i	−1.11577	+	1.11577i	−0.992355	+	0.123420i	$0.960614\pi$
$984$	46.2183	−	18.9260i	1.47339	−	0.603340i
$985$		0			0
$986$	19.6605	+	25.6935i	0.626116	+	0.818248i
$987$		−	0.433989i		−	0.0138140i
$988$	23.5179	−	13.4938i	0.748204	−	0.429295i
$989$	1.22408	−	1.22408i	0.0389236	−	0.0389236i
$990$		0			0
$991$		−	42.0365i		−	1.33533i	−0.744460	−	0.667667i	$-0.767293\pi$
$991$		−	42.0365i		−	1.33533i	0.744460	−	0.667667i	$-0.232707\pi$
$992$	−32.1182	+	4.00880i	−1.01975	+	0.127280i
$993$	−12.8121	+	12.8121i	−0.406581	+	0.406581i
$994$	2.74178	−	20.6115i	0.0869639	−	0.653757i
$995$		0			0
$996$	−3.99965	+	14.7678i	−0.126734	+	0.467936i
$997$	−31.7128			−1.00435			−0.502177	−	0.864765i	$-0.667467\pi$
$997$	−31.7128			−1.00435			−0.502177	+	0.864765i	$0.667467\pi$
$998$	6.54096	−	49.1721i	0.207050	−	1.55652i
$999$			61.5139i			1.94621i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	400.2.j.c.307.3	yes	16
4.3	odd	2		1600.2.j.c.1007.3		16
5.2	odd	4		400.2.s.c.243.7	yes	16
5.3	odd	4		400.2.s.c.243.2	yes	16
5.4	even	2	inner	400.2.j.c.307.6	yes	16
16.5	even	4		1600.2.s.c.207.6		16
16.11	odd	4		400.2.s.c.107.2	yes	16
20.3	even	4		1600.2.s.c.943.6		16
20.7	even	4		1600.2.s.c.943.3		16
20.19	odd	2		1600.2.j.c.1007.6		16
80.27	even	4	inner	400.2.j.c.43.6	yes	16
80.37	odd	4		1600.2.j.c.143.3		16
80.43	even	4	inner	400.2.j.c.43.3	✓	16
80.53	odd	4		1600.2.j.c.143.6		16
80.59	odd	4		400.2.s.c.107.7	yes	16
80.69	even	4		1600.2.s.c.207.3		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
400.2.j.c.43.3	✓	16	80.43	even	4	inner
400.2.j.c.43.6	yes	16	80.27	even	4	inner
400.2.j.c.307.3	yes	16	1.1	even	1	trivial
400.2.j.c.307.6	yes	16	5.4	even	2	inner
400.2.s.c.107.2	yes	16	16.11	odd	4
400.2.s.c.107.7	yes	16	80.59	odd	4
400.2.s.c.243.2	yes	16	5.3	odd	4
400.2.s.c.243.7	yes	16	5.2	odd	4
1600.2.j.c.143.3		16	80.37	odd	4
1600.2.j.c.143.6		16	80.53	odd	4
1600.2.j.c.1007.3		16	4.3	odd	2
1600.2.j.c.1007.6		16	20.19	odd	2
1600.2.s.c.207.3		16	80.69	even	4
1600.2.s.c.207.6		16	16.5	even	4
1600.2.s.c.943.3		16	20.7	even	4
1600.2.s.c.943.6		16	20.3	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:	\( N \)	\(=\)	\( 400 = 2^{4} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	400.j (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.859408 - 1.12313i) q^{2} +1.54564i q^{3} +(-0.522835 + 1.93045i) q^{4} +(1.73595 - 1.32833i) q^{6} +(-1.17442 - 1.17442i) q^{7} +(2.61747 - 1.07183i) q^{8} +0.611000 q^{9} +O(q^{10})\)	\(q+(-0.859408 - 1.12313i) q^{2} +1.54564i q^{3} +(-0.522835 + 1.93045i) q^{4} +(1.73595 - 1.32833i) q^{6} +(-1.17442 - 1.17442i) q^{7} +(2.61747 - 1.07183i) q^{8} +0.611000 q^{9} +(2.04567 + 2.04567i) q^{11} +(-2.98378 - 0.808115i) q^{12} -2.14367 q^{13} +(-0.309719 + 2.32833i) q^{14} +(-3.45329 - 2.01862i) q^{16} +(2.07308 + 2.07308i) q^{17} +(-0.525098 - 0.686231i) q^{18} +(4.47190 + 4.47190i) q^{19} +(1.81523 - 1.81523i) q^{21} +(0.539485 - 4.05562i) q^{22} +(-4.86373 + 4.86373i) q^{23} +(1.65667 + 4.04567i) q^{24} +(1.84229 + 2.40762i) q^{26} +5.58130i q^{27} +(2.88119 - 1.65314i) q^{28} +(-5.51757 + 5.51757i) q^{29} +5.72181i q^{31} +(0.700618 + 5.61330i) q^{32} +(-3.16187 + 3.16187i) q^{33} +(0.546713 - 4.10996i) q^{34} +(-0.319452 + 1.17951i) q^{36} +11.0214 q^{37} +(1.17933 - 8.86571i) q^{38} -3.31334i q^{39} -11.4241i q^{41} +(-3.59877 - 0.478714i) q^{42} -0.251676 q^{43} +(-5.01862 + 2.87952i) q^{44} +(9.64252 + 1.28266i) q^{46} +(0.119541 - 0.119541i) q^{47} +(3.12005 - 5.33754i) q^{48} -4.24147i q^{49} +(-3.20423 + 3.20423i) q^{51} +(1.12079 - 4.13825i) q^{52} -2.69520i q^{53} +(6.26852 - 4.79662i) q^{54} +(-4.33281 - 1.81523i) q^{56} +(-6.91195 + 6.91195i) q^{57} +(10.9388 + 1.45510i) q^{58} +(1.24990 - 1.24990i) q^{59} +(-2.48034 - 2.48034i) q^{61} +(6.42632 - 4.91737i) q^{62} +(-0.717571 - 0.717571i) q^{63} +(5.70234 - 5.61100i) q^{64} +(6.26852 + 0.833849i) q^{66} +9.23670 q^{67} +(-5.08586 + 2.91810i) q^{68} +(-7.51757 - 7.51757i) q^{69} -8.85246 q^{71} +(1.59928 - 0.654891i) q^{72} +(7.85956 + 7.85956i) q^{73} +(-9.47190 - 12.3785i) q^{74} +(-10.9709 + 6.29472i) q^{76} -4.80496i q^{77} +(-3.72131 + 2.84751i) q^{78} +4.86934 q^{79} -6.79368 q^{81} +(-12.8308 + 9.81801i) q^{82} -4.94936i q^{83} +(2.55515 + 4.45329i) q^{84} +(0.216293 + 0.282665i) q^{86} +(-8.52818 - 8.52818i) q^{87} +(7.54711 + 3.16187i) q^{88} -3.63047 q^{89} +(2.51757 + 2.51757i) q^{91} +(-6.84627 - 11.9321i) q^{92} -8.84385 q^{93} +(-0.236994 - 0.0315254i) q^{94} +(-8.67614 + 1.08290i) q^{96} +(-9.89595 - 9.89595i) q^{97} +(-4.76371 + 3.64515i) q^{98} +(1.24990 + 1.24990i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 4 q^{4} - 12 q^{6} - 16 q^{9}+O(q^{10}) \) 16 * q + 4 * q^4 - 12 * q^6 - 16 * q^9	\( 16 q + 4 q^{4} - 12 q^{6} - 16 q^{9} + 8 q^{11} - 20 q^{14} - 16 q^{16} - 8 q^{19} - 24 q^{24} + 16 q^{26} + 16 q^{29} + 48 q^{34} - 4 q^{36} - 40 q^{44} + 36 q^{46} - 48 q^{51} + 32 q^{54} + 64 q^{56} - 8 q^{59} - 16 q^{61} + 16 q^{64} + 32 q^{66} - 16 q^{69} - 32 q^{71} - 72 q^{74} - 32 q^{76} + 80 q^{79} + 16 q^{81} + 136 q^{84} - 60 q^{86} - 64 q^{91} - 28 q^{94} - 56 q^{96} - 8 q^{99}+O(q^{100}) \) 16 * q + 4 * q^4 - 12 * q^6 - 16 * q^9 + 8 * q^11 - 20 * q^14 - 16 * q^16 - 8 * q^19 - 24 * q^24 + 16 * q^26 + 16 * q^29 + 48 * q^34 - 4 * q^36 - 40 * q^44 + 36 * q^46 - 48 * q^51 + 32 * q^54 + 64 * q^56 - 8 * q^59 - 16 * q^61 + 16 * q^64 + 32 * q^66 - 16 * q^69 - 32 * q^71 - 72 * q^74 - 32 * q^76 + 80 * q^79 + 16 * q^81 + 136 * q^84 - 60 * q^86 - 64 * q^91 - 28 * q^94 - 56 * q^96 - 8 * q^99

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