LMFDB - Embedded newform 300.2.j.d.43.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [300,2,Mod(7,300)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(300, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 0, 1]))

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

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

chi := DirichletCharacter("300.7");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 300 = 2^{2} \cdot 3 \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	300.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:	$2.39551206064$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(i)$
Coefficient field:	12.0.426337261060096.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 4x^{9} - 3x^{8} + 4x^{7} + 8x^{6} + 8x^{5} - 12x^{4} - 32x^{3} + 64 $ x^12 - 4x^9 - 3x^8 + 4x^7 + 8x^6 + 8x^5 - 12x^4 - 32*x^3 + 64
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	no (minimal twist has level 60)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			43.5
Root			$1.19252 + 0.760198i$ of defining polynomial
Character	$\chi$	$=$	300.43
Dual form			300.2.j.d.7.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.19252 + 0.760198i) q^{2} +(-0.707107 + 0.707107i) q^{3} +(0.844199 + 1.81310i) q^{4} +(-1.38078 + 0.305697i) q^{6} +(0.611393 + 0.611393i) q^{7} +(-0.371591 + 2.80391i) q^{8} -1.00000i q^{9} +O(q^{10})$	\(q+(1.19252 + 0.760198i) q^{2} +(-0.707107 + 0.707107i) q^{3} +(0.844199 + 1.81310i) q^{4} +(-1.38078 + 0.305697i) q^{6} +(0.611393 + 0.611393i) q^{7} +(-0.371591 + 2.80391i) q^{8} -1.00000i q^{9} +5.12822i q^{11} +(-1.87899 - 0.685116i) q^{12} +(-1.76156 - 1.76156i) q^{13} +(0.264318 + 1.19388i) q^{14} +(-2.57466 + 3.06123i) q^{16} +(3.76156 - 3.76156i) q^{17} +(0.760198 - 1.19252i) q^{18} +1.22279 q^{19} -0.864641 q^{21} +(-3.89846 + 6.11549i) q^{22} +(-1.07700 + 1.07700i) q^{23} +(-1.71991 - 2.24542i) q^{24} +(-0.761557 - 3.43982i) q^{26} +(0.707107 + 0.707107i) q^{27} +(-0.592379 + 1.62465i) q^{28} +0.864641i q^{29} -7.81086i q^{31} +(-5.39747 + 1.69333i) q^{32} +(-3.62620 - 3.62620i) q^{33} +(7.34525 - 1.62620i) q^{34} +(1.81310 - 0.844199i) q^{36} +(1.76156 - 1.76156i) q^{37} +(1.45820 + 0.929560i) q^{38} +2.49122 q^{39} +5.52311 q^{41} +(-1.03110 - 0.657298i) q^{42} +(6.20522 - 6.20522i) q^{43} +(-9.29797 + 4.32924i) q^{44} +(-2.10308 + 0.465611i) q^{46} +(2.29979 + 2.29979i) q^{47} +(-0.344061 - 3.98518i) q^{48} -6.25240i q^{49} +5.31965i q^{51} +(1.70677 - 4.68098i) q^{52} +(2.62620 + 2.62620i) q^{53} +(0.305697 + 1.38078i) q^{54} +(-1.94148 + 1.48710i) q^{56} +(-0.864641 + 0.864641i) q^{57} +(-0.657298 + 1.03110i) q^{58} +0.528636 q^{59} +4.98168 q^{61} +(5.93780 - 9.31460i) q^{62} +(0.611393 - 0.611393i) q^{63} +(-7.72384 - 2.08382i) q^{64} +(-1.56768 - 7.08093i) q^{66} +(-6.20522 - 6.20522i) q^{67} +(9.99558 + 3.64457i) q^{68} -1.52311i q^{69} -8.10243i q^{71} +(2.80391 + 0.371591i) q^{72} +(2.25240 + 2.25240i) q^{73} +(3.43982 - 0.761557i) q^{74} +(1.03228 + 2.21703i) q^{76} +(-3.13536 + 3.13536i) q^{77} +(2.97082 + 1.89382i) q^{78} -15.9133 q^{79} -1.00000 q^{81} +(6.58641 + 4.19866i) q^{82} +(-7.95665 + 7.95665i) q^{83} +(-0.729929 - 1.56768i) q^{84} +(12.1170 - 2.68264i) q^{86} +(-0.611393 - 0.611393i) q^{87} +(-14.3791 - 1.90560i) q^{88} +7.25240i q^{89} -2.15401i q^{91} +(-2.86192 - 1.04351i) q^{92} +(5.52311 + 5.52311i) q^{93} +(0.994247 + 4.49084i) q^{94} +(2.61922 - 5.01395i) q^{96} +(-0.793833 + 0.793833i) q^{97} +(4.75306 - 7.45610i) q^{98} +5.12822 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 4 q^{6} + 12 q^{8}+O(q^{10}) $ 12 * q - 4 * q^6 + 12 * q^8	$ 12 q - 4 q^{6} + 12 q^{8} + 8 q^{12} + 4 q^{13} + 12 q^{16} + 20 q^{17} - 12 q^{22} + 16 q^{26} + 4 q^{28} - 20 q^{32} - 8 q^{33} + 4 q^{36} - 4 q^{37} - 16 q^{38} + 16 q^{41} - 20 q^{42} - 40 q^{46} - 16 q^{48} + 8 q^{52} - 4 q^{53} - 64 q^{56} + 20 q^{58} - 32 q^{61} + 56 q^{62} - 24 q^{66} + 16 q^{68} + 12 q^{72} - 44 q^{73} + 8 q^{76} - 48 q^{77} + 24 q^{78} - 12 q^{81} - 16 q^{82} + 64 q^{86} - 60 q^{88} - 56 q^{92} + 16 q^{93} + 44 q^{96} + 20 q^{97} - 24 q^{98}+O(q^{100}) $ 12 * q - 4 * q^6 + 12 * q^8 + 8 * q^12 + 4 * q^13 + 12 * q^16 + 20 * q^17 - 12 * q^22 + 16 * q^26 + 4 * q^28 - 20 * q^32 - 8 * q^33 + 4 * q^36 - 4 * q^37 - 16 * q^38 + 16 * q^41 - 20 * q^42 - 40 * q^46 - 16 * q^48 + 8 * q^52 - 4 * q^53 - 64 * q^56 + 20 * q^58 - 32 * q^61 + 56 * q^62 - 24 * q^66 + 16 * q^68 + 12 * q^72 - 44 * q^73 + 8 * q^76 - 48 * q^77 + 24 * q^78 - 12 * q^81 - 16 * q^82 + 64 * q^86 - 60 * q^88 - 56 * q^92 + 16 * q^93 + 44 * q^96 + 20 * q^97 - 24 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/300\mathbb{Z}\right)^\times$.

$n$	$101$	$151$	$277$
$\chi(n)$	$1$	$-1$	$e\left(\frac{3}{4}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	1.19252	+	0.760198i	0.843238	+	0.537541i
$2$	1.19252	+	0.760198i	0.843238	+	0.537541i
$3$	−0.707107	+	0.707107i	−0.408248	+	0.408248i
$3$	−0.707107	+	0.707107i	−0.408248	+	0.408248i
$4$	0.844199	+	1.81310i	0.422099	+	0.906550i
$5$		0			0
$5$		0			0
$6$	−1.38078	+	0.305697i	−0.563700	+	0.124800i
$7$	0.611393	+	0.611393i	0.231085	+	0.231085i	0.813145	−	0.582060i	$-0.197753\pi$
$7$	0.611393	+	0.611393i	0.231085	+	0.231085i	−0.582060	+	0.813145i	$0.697753\pi$
$8$	−0.371591	+	2.80391i	−0.131377	+	0.991332i
$9$		−	1.00000i		−	0.333333i
$10$		0			0
$11$			5.12822i			1.54622i	0.634274	+	0.773108i	$0.281299\pi$
$11$			5.12822i			1.54622i	−0.634274	+	0.773108i	$0.718701\pi$
$12$	−1.87899	−	0.685116i	−0.542419	−	0.197776i
$13$	−1.76156	−	1.76156i	−0.488568	−	0.488568i	0.419286	−	0.907854i	$-0.362280\pi$
$13$	−1.76156	−	1.76156i	−0.488568	−	0.488568i	−0.907854	+	0.419286i	$0.862280\pi$
$14$	0.264318	+	1.19388i	0.0706419	+	0.319077i
$15$		0			0
$16$	−2.57466	+	3.06123i	−0.643664	+	0.765308i
$17$	3.76156	−	3.76156i	0.912312	−	0.912312i	−0.0841421	−	0.996454i	$-0.526815\pi$
$17$	3.76156	−	3.76156i	0.912312	−	0.912312i	0.996454	+	0.0841421i	$0.0268150\pi$
$18$	0.760198	−	1.19252i	0.179180	−	0.281079i
$19$	1.22279			0.280527			0.140263	−	0.990114i	$-0.455205\pi$
$19$	1.22279			0.280527			0.140263	+	0.990114i	$0.455205\pi$
$20$		0			0
$21$	−0.864641			−0.188680
$22$	−3.89846	+	6.11549i	−0.831154	+	1.30383i
$23$	−1.07700	+	1.07700i	−0.224571	+	0.224571i	−0.810420	−	0.585849i	$-0.800761\pi$
$23$	−1.07700	+	1.07700i	−0.224571	+	0.224571i	0.585849	+	0.810420i	$0.300761\pi$
$24$	−1.71991	−	2.24542i	−0.351075	−	0.458344i
$25$		0			0
$26$	−0.761557	−	3.43982i	−0.149354	−	0.674604i
$27$	0.707107	+	0.707107i	0.136083	+	0.136083i
$28$	−0.592379	+	1.62465i	−0.111949	+	0.307031i
$29$			0.864641i			0.160560i	0.996772	+	0.0802799i	$0.0255814\pi$
$29$			0.864641i			0.160560i	−0.996772	+	0.0802799i	$0.974419\pi$
$30$		0			0
$31$		−	7.81086i		−	1.40287i	−0.712732	−	0.701436i	$-0.752543\pi$
$31$		−	7.81086i		−	1.40287i	0.712732	−	0.701436i	$-0.247457\pi$
$32$	−5.39747	+	1.69333i	−0.954146	+	0.299341i
$33$	−3.62620	−	3.62620i	−0.631240	−	0.631240i
$34$	7.34525	−	1.62620i	1.25970	−	0.278891i
$35$		0			0
$36$	1.81310	−	0.844199i	0.302183	−	0.140700i
$37$	1.76156	−	1.76156i	0.289598	−	0.289598i	−0.547323	−	0.836921i	$-0.684353\pi$
$37$	1.76156	−	1.76156i	0.289598	−	0.289598i	0.836921	+	0.547323i	$0.184353\pi$
$38$	1.45820	+	0.929560i	0.236551	+	0.150795i
$39$	2.49122			0.398914
$40$		0			0
$41$	5.52311			0.862566			0.431283	−	0.902217i	$-0.358061\pi$
$41$	5.52311			0.862566			0.431283	+	0.902217i	$0.358061\pi$
$42$	−1.03110	−	0.657298i	−0.159102	−	0.101423i
$43$	6.20522	−	6.20522i	0.946288	−	0.946288i	−0.0523416	−	0.998629i	$-0.516668\pi$
$43$	6.20522	−	6.20522i	0.946288	−	0.946288i	0.998629	+	0.0523416i	$0.0166685\pi$
$44$	−9.29797	+	4.32924i	−1.40172	+	0.652657i
$45$		0			0
$46$	−2.10308	+	0.465611i	−0.310083	+	0.0686506i
$47$	2.29979	+	2.29979i	0.335459	+	0.335459i	0.854655	−	0.519196i	$-0.173769\pi$
$47$	2.29979	+	2.29979i	0.335459	+	0.335459i	−0.519196	+	0.854655i	$0.673769\pi$
$48$	−0.344061	−	3.98518i	−0.0496610	−	0.575210i
$49$		−	6.25240i		−	0.893199i
$50$		0			0
$51$			5.31965i			0.744899i
$52$	1.70677	−	4.68098i	0.236687	−	0.649135i
$53$	2.62620	+	2.62620i	0.360736	+	0.360736i	0.864084	−	0.503348i	$-0.167899\pi$
$53$	2.62620	+	2.62620i	0.360736	+	0.360736i	−0.503348	+	0.864084i	$0.667899\pi$
$54$	0.305697	+	1.38078i	0.0416001	+	0.187900i
$55$		0			0
$56$	−1.94148	+	1.48710i	−0.259441	+	0.198723i
$57$	−0.864641	+	0.864641i	−0.114524	+	0.114524i
$58$	−0.657298	+	1.03110i	−0.0863075	+	0.135390i
$59$	0.528636			0.0688225			0.0344113	−	0.999408i	$-0.489044\pi$
$59$	0.528636			0.0688225			0.0344113	+	0.999408i	$0.489044\pi$
$60$		0			0
$61$	4.98168			0.637838			0.318919	−	0.947782i	$-0.396680\pi$
$61$	4.98168			0.637838			0.318919	+	0.947782i	$0.396680\pi$
$62$	5.93780	−	9.31460i	0.754101	−	1.18295i
$63$	0.611393	−	0.611393i	0.0770283	−	0.0770283i
$64$	−7.72384	−	2.08382i	−0.965480	−	0.260477i
$65$		0			0
$66$	−1.56768	−	7.08093i	−0.192968	−	0.871603i
$67$	−6.20522	−	6.20522i	−0.758089	−	0.758089i	0.217886	−	0.975974i	$-0.430084\pi$
$67$	−6.20522	−	6.20522i	−0.758089	−	0.758089i	−0.975974	+	0.217886i	$0.930084\pi$
$68$	9.99558	+	3.64457i	1.21214	+	0.441969i
$69$		−	1.52311i		−	0.183361i
$70$		0			0
$71$		−	8.10243i		−	0.961581i	−0.876835	−	0.480791i	$-0.840350\pi$
$71$		−	8.10243i		−	0.961581i	0.876835	−	0.480791i	$-0.159650\pi$
$72$	2.80391	+	0.371591i	0.330444	+	0.0437924i
$73$	2.25240	+	2.25240i	0.263623	+	0.263623i	0.826524	−	0.562901i	$-0.190315\pi$
$73$	2.25240	+	2.25240i	0.263623	+	0.263623i	−0.562901	+	0.826524i	$0.690315\pi$
$74$	3.43982	−	0.761557i	0.399871	−	0.0885292i
$75$		0			0
$76$	1.03228	+	2.21703i	0.118410	+	0.254311i
$77$	−3.13536	+	3.13536i	−0.357307	+	0.357307i
$78$	2.97082	+	1.89382i	0.336379	+	0.214433i
$79$	−15.9133			−1.79039			−0.895193	−	0.445680i	$-0.852962\pi$
$79$	−15.9133			−1.79039			−0.895193	+	0.445680i	$0.852962\pi$
$80$		0			0
$81$	−1.00000			−0.111111
$82$	6.58641	+	4.19866i	0.727348	+	0.463664i
$83$	−7.95665	+	7.95665i	−0.873355	+	0.873355i	−0.992836	−	0.119481i	$-0.961877\pi$
$83$	−7.95665	+	7.95665i	−0.873355	+	0.873355i	0.119481	+	0.992836i	$0.461877\pi$
$84$	−0.729929	−	1.56768i	−0.0796418	−	0.171048i
$85$		0			0
$86$	12.1170	−	2.68264i	1.30661	−	0.289277i
$87$	−0.611393	−	0.611393i	−0.0655483	−	0.0655483i
$88$	−14.3791	−	1.90560i	−1.53281	−	0.203138i
$89$			7.25240i			0.768752i	0.923177	+	0.384376i	$0.125583\pi$
$89$			7.25240i			0.768752i	−0.923177	+	0.384376i	$0.874417\pi$
$90$		0			0
$91$		−	2.15401i		−	0.225801i
$92$	−2.86192	−	1.04351i	−0.298376	−	0.108793i
$93$	5.52311	+	5.52311i	0.572720	+	0.572720i
$94$	0.994247	+	4.49084i	0.102549	+	0.463195i
$95$		0			0
$96$	2.61922	−	5.01395i	0.267323	−	0.511734i
$97$	−0.793833	+	0.793833i	−0.0806015	+	0.0806015i	−0.746258	−	0.665657i	$-0.768152\pi$
$97$	−0.793833	+	0.793833i	−0.0806015	+	0.0806015i	0.665657	+	0.746258i	$0.268152\pi$
$98$	4.75306	−	7.45610i	0.480131	−	0.753179i
$99$	5.12822			0.515405
$100$		0			0
$101$	−10.1170			−1.00668			−0.503341	−	0.864088i	$-0.667896\pi$
$101$	−10.1170			−1.00668			−0.503341	+	0.864088i	$0.667896\pi$
$102$	−4.04398	+	6.34377i	−0.400414	+	0.628127i
$103$	3.82267	−	3.82267i	0.376659	−	0.376659i	−0.493236	−	0.869895i	$-0.664186\pi$
$103$	3.82267	−	3.82267i	0.376659	−	0.376659i	0.869895	+	0.493236i	$0.164186\pi$
$104$	5.59383	−	4.28467i	0.548520	−	0.420147i
$105$		0			0
$106$	1.13536	+	5.12822i	0.110276	+	0.498097i
$107$	5.51107	+	5.51107i	0.532775	+	0.532775i	0.921397	−	0.388622i	$-0.127049\pi$
$107$	5.51107	+	5.51107i	0.532775	+	0.532775i	−0.388622	+	0.921397i	$0.627049\pi$
$108$	−0.685116	+	1.87899i	−0.0659253	+	0.180806i
$109$			7.31695i			0.700836i	0.936593	+	0.350418i	$0.113961\pi$
$109$			7.31695i			0.700836i	−0.936593	+	0.350418i	$0.886039\pi$
$110$		0			0
$111$			2.49122i			0.236456i
$112$	−3.44575	+	0.297490i	−0.325592	+	0.0281101i
$113$	0.509161	+	0.509161i	0.0478978	+	0.0478978i	0.730650	−	0.682752i	$-0.239217\pi$
$113$	0.509161	+	0.509161i	0.0478978	+	0.0478978i	−0.682752	+	0.730650i	$0.739217\pi$
$114$	−1.68840	+	0.373802i	−0.158133	+	0.0350098i
$115$		0			0
$116$	−1.56768	+	0.729929i	−0.145555	+	0.0677722i
$117$	−1.76156	+	1.76156i	−0.162856	+	0.162856i
$118$	0.630408	+	0.401868i	0.0580337	+	0.0369949i
$119$	4.59958			0.421643
$120$		0			0
$121$	−15.2986			−1.39078
$122$	5.94074	+	3.78706i	0.537849	+	0.342864i
$123$	−3.90543	+	3.90543i	−0.352141	+	0.352141i
$124$	14.1619	−	6.59392i	1.27177	−	0.592152i
$125$		0			0
$126$	1.19388	−	0.264318i	0.106359	−	0.0235473i
$127$	−7.49103	−	7.49103i	−0.664722	−	0.664722i	0.291767	−	0.956489i	$-0.405757\pi$
$127$	−7.49103	−	7.49103i	−0.664722	−	0.664722i	−0.956489	+	0.291767i	$0.905757\pi$
$128$	−7.62671	−	8.35664i	−0.674112	−	0.738629i
$129$			8.77551i			0.772641i
$130$		0			0
$131$			13.9964i			1.22287i	0.791296	+	0.611434i	$0.209407\pi$
$131$			13.9964i			1.22287i	−0.791296	+	0.611434i	$0.790593\pi$
$132$	3.51342	−	9.63589i	0.305804	−	0.838696i
$133$	0.747604	+	0.747604i	0.0648255	+	0.0648255i
$134$	−2.68264	−	12.1170i	−0.231745	−	1.04675i
$135$		0			0
$136$	9.14931	+	11.9448i	0.784547	+	1.02426i
$137$	−7.01395	+	7.01395i	−0.599242	+	0.599242i	−0.940111	−	0.340869i	$-0.889279\pi$
$137$	−7.01395	+	7.01395i	−0.599242	+	0.599242i	0.340869	+	0.940111i	$0.389279\pi$
$138$	1.15787	−	1.81634i	0.0985643	−	0.154617i
$139$	2.28006			0.193392			0.0966960	−	0.995314i	$-0.469173\pi$
$139$	2.28006			0.193392			0.0966960	+	0.995314i	$0.469173\pi$
$140$		0			0
$141$	−3.25240			−0.273901
$142$	6.15945	−	9.66229i	0.516889	−	0.810842i
$143$	9.03365	−	9.03365i	0.755432	−	0.755432i
$144$	3.06123	+	2.57466i	0.255103	+	0.214555i
$145$		0			0
$146$	0.973757	+	4.39829i	0.0805887	+	0.364005i
$147$	4.42111	+	4.42111i	0.364647	+	0.364647i
$148$	4.68098	+	1.70677i	0.384774	+	0.140296i
$149$		−	10.1170i		−	0.828820i	−0.910090	−	0.414410i	$-0.863988\pi$
$149$		−	10.1170i		−	0.828820i	0.910090	−	0.414410i	$-0.136012\pi$
$150$		0			0
$151$		−	7.93691i		−	0.645897i	−0.946417	−	0.322948i	$-0.895326\pi$
$151$		−	7.93691i		−	0.645897i	0.946417	−	0.322948i	$-0.104674\pi$
$152$	−0.454377	+	3.42859i	−0.0368548	+	0.278095i
$153$	−3.76156	−	3.76156i	−0.304104	−	0.304104i
$154$	−6.12247	+	1.35548i	−0.493362	+	0.109228i
$155$		0			0
$156$	2.10308	+	4.51683i	0.168381	+	0.361635i
$157$	−9.01395	+	9.01395i	−0.719392	+	0.719392i	−0.968481	−	0.249089i	$-0.919869\pi$
$157$	−9.01395	+	9.01395i	−0.719392	+	0.719392i	0.249089	+	0.968481i	$0.419869\pi$
$158$	−18.9769	−	12.0972i	−1.50972	−	0.962405i
$159$	−3.71400			−0.294540
$160$		0			0
$161$	−1.31695			−0.103790
$162$	−1.19252	−	0.760198i	−0.0936931	−	0.0597268i
$163$	−13.0849	+	13.0849i	−1.02489	+	1.02489i	−0.0252033	+	0.999682i	$0.508023\pi$
$163$	−13.0849	+	13.0849i	−1.02489	+	1.02489i	−0.999682	+	0.0252033i	$0.991977\pi$
$164$	4.66261	+	10.0140i	0.364088	+	0.781958i
$165$		0			0
$166$	−15.5371	+	3.43982i	−1.20591	+	0.266982i
$167$	−11.3334	−	11.3334i	−0.877008	−	0.877008i	0.116216	−	0.993224i	$-0.462924\pi$
$167$	−11.3334	−	11.3334i	−0.877008	−	0.877008i	−0.993224	+	0.116216i	$0.962924\pi$
$168$	0.321293	−	2.42438i	0.0247883	−	0.187045i
$169$		−	6.79383i		−	0.522603i
$170$		0			0
$171$		−	1.22279i		−	0.0935088i
$172$	16.4891	+	6.01224i	1.25728	+	0.458429i
$173$	−7.96772	−	7.96772i	−0.605775	−	0.605775i	0.336064	−	0.941839i	$-0.390904\pi$
$173$	−7.96772	−	7.96772i	−0.605775	−	0.605775i	−0.941839	+	0.336064i	$0.890904\pi$
$174$	−0.264318	−	1.19388i	−0.0200379	−	0.0905076i
$175$		0			0
$176$	−15.6987	−	13.2034i	−1.18333	−	0.995244i
$177$	−0.373802	+	0.373802i	−0.0280967	+	0.0280967i
$178$	−5.51325	+	8.64861i	−0.413236	+	0.648241i
$179$	12.6475			0.945320			0.472660	−	0.881245i	$-0.343294\pi$
$179$	12.6475			0.945320			0.472660	+	0.881245i	$0.343294\pi$
$180$		0			0
$181$	7.72928			0.574513			0.287256	−	0.957854i	$-0.407257\pi$
$181$	7.72928			0.574513			0.287256	+	0.957854i	$0.407257\pi$
$182$	1.63747	−	2.56869i	0.121378	−	0.190404i
$183$	−3.52258	+	3.52258i	−0.260396	+	0.260396i
$184$	−2.61962	−	3.42003i	−0.193121	−	0.252128i
$185$		0			0
$186$	2.38776	+	10.7851i	0.175079	+	0.790800i
$187$	19.2901	+	19.2901i	1.41063	+	1.41063i
$188$	−2.22827	+	6.11123i	−0.162513	+	0.445707i
$189$			0.864641i			0.0628934i
$190$		0			0
$191$			7.04516i			0.509770i	0.966971	+	0.254885i	$0.0820376\pi$
$191$			7.04516i			0.509770i	−0.966971	+	0.254885i	$0.917962\pi$
$192$	6.93506	−	3.98810i	0.500495	−	0.287816i
$193$	11.5048	+	11.5048i	0.828133	+	0.828133i	0.987258	−	0.159125i	$-0.0508674\pi$
$193$	11.5048	+	11.5048i	0.828133	+	0.828133i	−0.159125	+	0.987258i	$0.550867\pi$
$194$	−1.55013	+	0.343190i	−0.111293	+	0.0246396i
$195$		0			0
$196$	11.3362	−	5.27827i	0.809730	−	0.377019i
$197$	−7.87859	+	7.87859i	−0.561327	+	0.561327i	−0.929684	−	0.368358i	$-0.879920\pi$
$197$	−7.87859	+	7.87859i	−0.561327	+	0.561327i	0.368358	+	0.929684i	$0.379920\pi$
$198$	6.11549	+	3.89846i	0.434609	+	0.277051i
$199$	11.4792			0.813741			0.406870	−	0.913486i	$-0.366620\pi$
$199$	11.4792			0.813741			0.406870	+	0.913486i	$0.366620\pi$
$200$		0			0
$201$	8.77551			0.618977
$202$	−12.0648	−	7.69095i	−0.848873	−	0.541133i
$203$	−0.528636	+	0.528636i	−0.0371030	+	0.0371030i
$204$	−9.64504	+	4.49084i	−0.675288	+	0.314422i
$205$		0			0
$206$	7.46460	−	1.65262i	0.520083	−	0.115143i
$207$	1.07700	+	1.07700i	0.0748570	+	0.0748570i
$208$	9.92794	−	0.857132i	0.688379	−	0.0594314i
$209$			6.27072i			0.433755i
$210$		0			0
$211$			5.49134i			0.378039i	0.981973	+	0.189020i	$0.0605310\pi$
$211$			5.49134i			0.378039i	−0.981973	+	0.189020i	$0.939469\pi$
$212$	−2.54452	+	6.97859i	−0.174759	+	0.479292i
$213$	5.72928	+	5.72928i	0.392564	+	0.392564i
$214$	2.38255	+	10.7616i	0.162868	+	0.735645i
$215$		0			0
$216$	−2.24542	+	1.71991i	−0.152781	+	0.117025i
$217$	4.77551	−	4.77551i	0.324183	−	0.324183i
$218$	−5.56233	+	8.72559i	−0.376728	+	0.590972i
$219$	−3.18537			−0.215247
$220$		0			0
$221$	−13.2524			−0.891453
$222$	−1.89382	+	2.97082i	−0.127105	+	0.199389i
$223$	10.8678	−	10.8678i	0.727764	−	0.727764i	−0.242410	−	0.970174i	$-0.577938\pi$
$223$	10.8678	−	10.8678i	0.727764	−	0.727764i	0.970174	+	0.242410i	$0.0779380\pi$
$224$	−4.33526	−	2.26469i	−0.289662	−	0.151316i
$225$		0			0
$226$	0.220121	+	0.994247i	0.0146422	+	0.0661363i
$227$	−4.98244	−	4.98244i	−0.330696	−	0.330696i	0.522155	−	0.852851i	$-0.325128\pi$
$227$	−4.98244	−	4.98244i	−0.330696	−	0.330696i	−0.852851	+	0.522155i	$0.825128\pi$
$228$	−2.29761	−	0.837751i	−0.152163	−	0.0554814i
$229$			25.7572i			1.70208i	0.525098	+	0.851041i	$0.324028\pi$
$229$			25.7572i			1.70208i	−0.525098	+	0.851041i	$0.675972\pi$
$230$		0			0
$231$		−	4.43407i		−	0.291740i
$232$	−2.42438	−	0.321293i	−0.159168	−	0.0210939i
$233$	0.715328	+	0.715328i	0.0468627	+	0.0468627i	0.730150	−	0.683287i	$-0.239450\pi$
$233$	0.715328	+	0.715328i	0.0468627	+	0.0468627i	−0.683287	+	0.730150i	$0.739450\pi$
$234$	−3.43982	+	0.761557i	−0.224868	+	0.0497846i
$235$		0			0
$236$	0.446274	+	0.958469i	0.0290499	+	0.0623910i
$237$	11.2524	−	11.2524i	0.730922	−	0.730922i
$238$	5.48509	+	3.49659i	0.355545	+	0.226650i
$239$	−26.9354			−1.74231			−0.871154	−	0.491009i	$-0.836628\pi$
$239$	−26.9354			−1.74231			−0.871154	+	0.491009i	$0.836628\pi$
$240$		0			0
$241$	14.0925			0.907775			0.453887	−	0.891059i	$-0.350037\pi$
$241$	14.0925			0.907775			0.453887	+	0.891059i	$0.350037\pi$
$242$	−18.2439	−	11.6300i	−1.17276	−	0.747603i
$243$	0.707107	−	0.707107i	0.0453609	−	0.0453609i
$244$	4.20553	+	9.03228i	0.269231	+	0.578232i
$245$		0			0
$246$	−7.62620	+	1.68840i	−0.486229	+	0.107648i
$247$	−2.15401	−	2.15401i	−0.137056	−	0.137056i
$248$	21.9010	+	2.90245i	1.39071	+	0.184306i
$249$		−	11.2524i		−	0.713092i
$250$		0			0
$251$		−	17.2471i		−	1.08863i	−0.838882	−	0.544314i	$-0.816790\pi$
$251$		−	17.2471i		−	1.08863i	0.838882	−	0.544314i	$-0.183210\pi$
$252$	1.62465	+	0.592379i	0.102344	+	0.0373164i
$253$	−5.52311	−	5.52311i	−0.347235	−	0.347235i
$254$	−3.23853	−	14.6279i	−0.203203	−	0.917834i
$255$		0			0
$256$	−2.74229	−	15.7632i	−0.171393	−	0.985203i
$257$	15.0140	−	15.0140i	0.936545	−	0.936545i	−0.0615588	−	0.998103i	$-0.519607\pi$
$257$	15.0140	−	15.0140i	0.936545	−	0.936545i	0.998103	+	0.0615588i	$0.0196072\pi$
$258$	−6.67112	+	10.4650i	−0.415326	+	0.651520i
$259$	2.15401			0.133844
$260$		0			0
$261$	0.864641			0.0535199
$262$	−10.6400	+	16.6909i	−0.657341	+	1.03117i
$263$	6.73386	−	6.73386i	0.415228	−	0.415228i	−0.468327	−	0.883555i	$-0.655143\pi$
$263$	6.73386	−	6.73386i	0.415228	−	0.415228i	0.883555	+	0.468327i	$0.155143\pi$
$264$	11.5150	−	8.82008i	0.708699	−	0.542838i
$265$		0			0
$266$	0.323204	+	1.45986i	0.0198169	+	0.0895096i
$267$	−5.12822	−	5.12822i	−0.313842	−	0.313842i
$268$	6.01224	−	16.4891i	0.367256	−	1.00723i
$269$		−	25.7047i		−	1.56724i	−0.621238	−	0.783622i	$-0.713370\pi$
$269$		−	25.7047i		−	1.56724i	0.621238	−	0.783622i	$-0.286630\pi$
$270$		0			0
$271$			0.931222i			0.0565677i	0.999600	+	0.0282839i	$0.00900423\pi$
$271$			0.931222i			0.0565677i	−0.999600	+	0.0282839i	$0.990996\pi$
$272$	1.83029	+	21.1997i	0.110977	+	1.28542i
$273$	1.52311	+	1.52311i	0.0921831	+	0.0921831i
$274$	−13.6963	+	3.03228i	−0.827421	+	0.183186i
$275$		0			0
$276$	2.76156	−	1.28581i	0.166226	−	0.0773968i
$277$	22.0602	−	22.0602i	1.32547	−	1.32547i	0.416190	−	0.909277i	$-0.363365\pi$
$277$	22.0602	−	22.0602i	1.32547	−	1.32547i	0.909277	−	0.416190i	$-0.136635\pi$
$278$	2.71901	+	1.73330i	0.163075	+	0.103956i
$279$	−7.81086			−0.467624
$280$		0			0
$281$	8.56934			0.511204			0.255602	−	0.966782i	$-0.417726\pi$
$281$	8.56934			0.511204			0.255602	+	0.966782i	$0.417726\pi$
$282$	−3.87854	−	2.47246i	−0.230964	−	0.147233i
$283$	−11.5705	+	11.5705i	−0.687796	+	0.687796i	−0.961744	−	0.273949i	$-0.911670\pi$
$283$	−11.5705	+	11.5705i	−0.687796	+	0.687796i	0.273949	+	0.961744i	$0.411670\pi$
$284$	14.6905	−	6.84006i	0.871721	−	0.405883i
$285$		0			0
$286$	17.6402	−	3.90543i	1.04308	−	0.230933i
$287$	3.37680	+	3.37680i	0.199326	+	0.199326i
$288$	1.69333	+	5.39747i	0.0997803	+	0.318049i
$289$		−	11.2986i		−	0.664625i
$290$		0			0
$291$		−	1.12265i		−	0.0658108i
$292$	−2.18235	+	5.98529i	−0.127712	+	0.350262i
$293$	−12.8969	−	12.8969i	−0.753446	−	0.753446i	0.221675	−	0.975121i	$-0.428848\pi$
$293$	−12.8969	−	12.8969i	−0.753446	−	0.753446i	−0.975121	+	0.221675i	$0.928848\pi$
$294$	1.91134	+	8.63317i	0.111471	+	0.503497i
$295$		0			0
$296$	4.28467	+	5.59383i	0.249041	+	0.325135i
$297$	−3.62620	+	3.62620i	−0.210413	+	0.210413i
$298$	7.69095	−	12.0648i	0.445525	−	0.698892i
$299$	3.79441			0.219436
$300$		0			0
$301$	7.58767			0.437346
$302$	6.03362	−	9.46491i	0.347196	−	0.544644i
$303$	7.15383	−	7.15383i	0.410977	−	0.410977i
$304$	−3.14826	+	3.74324i	−0.180565	+	0.214689i
$305$		0			0
$306$	−1.62620	−	7.34525i	−0.0929636	−	0.419900i
$307$	−1.60564	−	1.60564i	−0.0916387	−	0.0916387i	0.659801	−	0.751440i	$-0.270640\pi$
$307$	−1.60564	−	1.60564i	−0.0916387	−	0.0916387i	−0.751440	+	0.659801i	$0.770640\pi$
$308$	−8.33158	−	3.03785i	−0.474736	−	0.173098i
$309$			5.40608i			0.307541i
$310$		0			0
$311$		−	19.4161i		−	1.10099i	−0.834839	−	0.550494i	$-0.814439\pi$
$311$		−	19.4161i		−	1.10099i	0.834839	−	0.550494i	$-0.185561\pi$
$312$	−0.925715	+	6.98516i	−0.0524083	+	0.395457i
$313$	−17.7110	−	17.7110i	−1.00108	−	1.00108i	−0.999999	−	0.00108322i	$-0.999655\pi$
$313$	−17.7110	−	17.7110i	−1.00108	−	1.00108i	−0.00108322	−	0.999999i	$-0.500345\pi$
$314$	−17.6017	+	3.89692i	−0.993321	+	0.219916i
$315$		0			0
$316$	−13.4340	−	28.8524i	−0.755721	−	1.62307i
$317$	7.78946	−	7.78946i	0.437500	−	0.437500i	−0.453670	−	0.891170i	$-0.649885\pi$
$317$	7.78946	−	7.78946i	0.437500	−	0.437500i	0.891170	+	0.453670i	$0.149885\pi$
$318$	−4.42902	−	2.82338i	−0.248367	−	0.158327i
$319$	−4.43407			−0.248260
$320$		0			0
$321$	−7.79383			−0.435009
$322$	−1.57048	−	1.00114i	−0.0875196	−	0.0557914i
$323$	4.59958	−	4.59958i	0.255928	−	0.255928i
$324$	−0.844199	−	1.81310i	−0.0468999	−	0.100728i
$325$		0			0
$326$	−25.5510	+	5.65685i	−1.41514	+	0.313304i
$327$	−5.17386	−	5.17386i	−0.286115	−	0.286115i
$328$	−2.05234	+	15.4863i	−0.113322	+	0.855089i
$329$			2.81215i			0.155039i
$330$		0			0
$331$			31.7005i			1.74242i	0.490912	+	0.871209i	$0.336664\pi$
$331$			31.7005i			1.74242i	−0.490912	+	0.871209i	$0.663336\pi$
$332$	−21.1432	−	7.70919i	−1.16038	−	0.423097i
$333$	−1.76156	−	1.76156i	−0.0965327	−	0.0965327i
$334$	−4.89968	−	22.1310i	−0.268098	−	1.21095i
$335$		0			0
$336$	2.22615	−	2.64687i	0.121447	−	0.144398i
$337$	−18.9634	+	18.9634i	−1.03300	+	1.03300i	−0.0335632	+	0.999437i	$0.510686\pi$
$337$	−18.9634	+	18.9634i	−1.03300	+	1.03300i	−0.999437	+	0.0335632i	$0.989314\pi$
$338$	5.16466	−	8.10177i	0.280920	−	0.440678i
$339$	−0.720062			−0.0391084
$340$		0			0
$341$	40.0558			2.16914
$342$	0.929560	−	1.45820i	0.0502648	−	0.0788502i
$343$	8.10243	−	8.10243i	0.437490	−	0.437490i
$344$	15.0931	+	19.7047i	0.813765	+	1.06241i
$345$		0			0
$346$	−3.44461	−	15.5587i	−0.185183	−	0.836441i
$347$	7.71957	+	7.71957i	0.414408	+	0.414408i	0.883271	−	0.468863i	$-0.155336\pi$
$347$	7.71957	+	7.71957i	0.414408	+	0.414408i	−0.468863	+	0.883271i	$0.655336\pi$
$348$	0.592379	−	1.62465i	0.0317549	−	0.0870906i
$349$		−	27.0741i		−	1.44925i	−0.689146	−	0.724623i	$-0.742014\pi$
$349$		−	27.0741i		−	1.44925i	0.689146	−	0.724623i	$-0.257986\pi$
$350$		0			0
$351$		−	2.49122i		−	0.132971i
$352$	−8.68375	−	27.6794i	−0.462846	−	1.47532i
$353$	9.96772	+	9.96772i	0.530528	+	0.530528i	0.920730	−	0.390201i	$-0.127595\pi$
$353$	9.96772	+	9.96772i	0.530528	+	0.530528i	−0.390201	+	0.920730i	$0.627595\pi$
$354$	−0.729929	+	0.161602i	−0.0387953	+	0.00858906i
$355$		0			0
$356$	−13.1493	+	6.12247i	−0.696912	+	0.324490i
$357$	−3.25240	+	3.25240i	−0.172135	+	0.172135i
$358$	15.0824	+	9.61461i	0.797129	+	0.508148i
$359$	14.2334			0.751211			0.375606	−	0.926780i	$-0.377435\pi$
$359$	14.2334			0.751211			0.375606	+	0.926780i	$0.377435\pi$
$360$		0			0
$361$	−17.5048			−0.921305
$362$	9.21731	+	5.87578i	0.484451	+	0.308824i
$363$	10.8178	−	10.8178i	0.567785	−	0.567785i
$364$	3.90543	−	1.81841i	0.204700	−	0.0953107i
$365$		0			0
$366$	−6.87859	+	1.52288i	−0.359550	+	0.0796023i
$367$	−2.89145	−	2.89145i	−0.150933	−	0.150933i	0.627602	−	0.778534i	$-0.284037\pi$
$367$	−2.89145	−	2.89145i	−0.150933	−	0.150933i	−0.778534	+	0.627602i	$0.784037\pi$
$368$	−0.524045	−	6.06988i	−0.0273177	−	0.316414i
$369$		−	5.52311i		−	0.287522i
$370$		0			0
$371$			3.21128i			0.166721i
$372$	−5.35135	+	14.6766i	−0.277454	+	0.760944i
$373$	11.2847	+	11.2847i	0.584298	+	0.584298i	0.936081	−	0.351783i	$-0.114425\pi$
$373$	11.2847	+	11.2847i	0.584298	+	0.584298i	−0.351783	+	0.936081i	$0.614425\pi$
$374$	8.33950	+	37.6681i	0.431225	+	1.94777i
$375$		0			0
$376$	−7.30299	+	5.59383i	−0.376623	+	0.288480i
$377$	1.52311	−	1.52311i	0.0784444	−	0.0784444i
$378$	−0.657298	+	1.03110i	−0.0338078	+	0.0530341i
$379$	15.4562			0.793932			0.396966	−	0.917833i	$-0.370063\pi$
$379$	15.4562			0.793932			0.396966	+	0.917833i	$0.370063\pi$
$380$		0			0
$381$	10.5939			0.542743
$382$	−5.35571	+	8.40148i	−0.274022	+	0.429857i
$383$	−12.5562	+	12.5562i	−0.641593	+	0.641593i	−0.950947	−	0.309354i	$-0.899887\pi$
$383$	−12.5562	+	12.5562i	−0.641593	+	0.641593i	0.309354	+	0.950947i	$0.399887\pi$
$384$	11.3019	+	0.516138i	0.576749	+	0.0263390i
$385$		0			0
$386$	4.97376	+	22.4656i	0.253158	+	1.14347i
$387$	−6.20522	−	6.20522i	−0.315429	−	0.315429i
$388$	−2.10945	−	0.769144i	−0.107091	−	0.0390474i
$389$			5.16327i			0.261788i	0.991396	+	0.130894i	$0.0417848\pi$
$389$			5.16327i			0.261788i	−0.991396	+	0.130894i	$0.958215\pi$
$390$		0			0
$391$			8.10243i			0.409757i
$392$	17.5312	+	2.32333i	0.885458	+	0.117346i
$393$	−9.89692	−	9.89692i	−0.499233	−	0.499233i
$394$	−15.3847	+	3.40608i	−0.775068	+	0.171596i
$395$		0			0
$396$	4.32924	+	9.29797i	0.217552	+	0.467240i
$397$	3.46293	−	3.46293i	0.173800	−	0.173800i	−0.614847	−	0.788646i	$-0.710782\pi$
$397$	3.46293	−	3.46293i	0.173800	−	0.173800i	0.788646	+	0.614847i	$0.210782\pi$
$398$	13.6892	+	8.72648i	0.686177	+	0.437419i
$399$	−1.05727			−0.0529298
$400$		0			0
$401$	3.49521			0.174542			0.0872712	−	0.996185i	$-0.472185\pi$
$401$	3.49521			0.174542			0.0872712	+	0.996185i	$0.472185\pi$
$402$	10.4650	+	6.67112i	0.521945	+	0.332725i
$403$	−13.7593	+	13.7593i	−0.685399	+	0.685399i
$404$	−8.54079	−	18.3432i	−0.424920	−	0.912608i
$405$		0			0
$406$	−1.03228	+	0.228540i	−0.0512310	+	0.0113423i
$407$	9.03365	+	9.03365i	0.447781	+	0.447781i
$408$	−14.9158	−	1.97673i	−0.738443	−	0.0978629i
$409$			14.8034i			0.731982i	0.930618	+	0.365991i	$0.119270\pi$
$409$			14.8034i			0.731982i	−0.930618	+	0.365991i	$0.880730\pi$
$410$		0			0
$411$		−	9.91923i		−	0.489279i
$412$	10.1580	+	3.70379i	0.500448	+	0.182473i
$413$	0.323204	+	0.323204i	0.0159039	+	0.0159039i
$414$	0.465611	+	2.10308i	0.0228835	+	0.103361i
$415$		0			0
$416$	12.4908	+	6.52505i	0.612414	+	0.319917i
$417$	−1.61224	+	1.61224i	−0.0789520	+	0.0789520i
$418$	−4.76699	+	7.47795i	−0.233161	+	0.365758i
$419$	−19.0701			−0.931634			−0.465817	−	0.884881i	$-0.654240\pi$
$419$	−19.0701			−0.931634			−0.465817	+	0.884881i	$0.654240\pi$
$420$		0			0
$421$	−20.8034			−1.01390			−0.506948	−	0.861976i	$-0.669226\pi$
$421$	−20.8034			−1.01390			−0.506948	+	0.861976i	$0.669226\pi$
$422$	−4.17450	+	6.54852i	−0.203212	+	0.318777i
$423$	2.29979	−	2.29979i	0.111820	−	0.111820i
$424$	−8.33950	+	6.38776i	−0.405002	+	0.310217i
$425$		0			0
$426$	2.47689	+	11.1877i	0.120006	+	0.542044i
$427$	3.04577	+	3.04577i	0.147395	+	0.147395i
$428$	−5.33968	+	14.6446i	−0.258103	+	0.707872i
$429$			12.7755i			0.616807i
$430$		0			0
$431$		−	15.3302i		−	0.738428i	−0.929344	−	0.369214i	$-0.879627\pi$
$431$		−	15.3302i		−	0.738428i	0.929344	−	0.369214i	$-0.120373\pi$
$432$	−3.98518	+	0.344061i	−0.191737	+	0.0165537i
$433$	−16.2803	−	16.2803i	−0.782381	−	0.782381i	0.197851	−	0.980232i	$-0.436604\pi$
$433$	−16.2803	−	16.2803i	−0.782381	−	0.782381i	−0.980232	+	0.197851i	$0.936604\pi$
$434$	9.32521	−	2.06455i	0.447625	−	0.0991016i
$435$		0			0
$436$	−13.2663	+	6.17696i	−0.635343	+	0.295823i
$437$	−1.31695	+	1.31695i	−0.0629981	+	0.0629981i
$438$	−3.79861	−	2.42151i	−0.181505	−	0.115704i
$439$	24.6554			1.17674			0.588368	−	0.808593i	$-0.299770\pi$
$439$	24.6554			1.17674			0.588368	+	0.808593i	$0.299770\pi$
$440$		0			0
$441$	−6.25240			−0.297733
$442$	−15.8037	−	10.0744i	−0.751706	−	0.479192i
$443$	−1.77116	+	1.77116i	−0.0841501	+	0.0841501i	−0.747929	−	0.663779i	$-0.768952\pi$
$443$	−1.77116	+	1.77116i	−0.0841501	+	0.0841501i	0.663779	+	0.747929i	$0.268952\pi$
$444$	−4.51683	+	2.10308i	−0.214359	+	0.0998079i
$445$		0			0
$446$	21.2218	−	4.69839i	1.00488	−	0.222475i
$447$	7.15383	+	7.15383i	0.338364	+	0.338364i
$448$	−3.44827	−	5.99634i	−0.162916	−	0.283300i
$449$			33.1512i			1.56450i	0.622963	+	0.782251i	$0.285929\pi$
$449$			33.1512i			1.56450i	−0.622963	+	0.782251i	$0.714071\pi$
$450$		0			0
$451$			28.3237i			1.33371i
$452$	−0.493326	+	1.35299i	−0.0232041	+	0.0636394i
$453$	5.61224	+	5.61224i	0.263686	+	0.263686i
$454$	−2.15401	−	9.72928i	−0.101093	−	0.456618i
$455$		0			0
$456$	−2.10308	−	2.74567i	−0.0984859	−	0.128578i
$457$	7.50479	−	7.50479i	0.351059	−	0.351059i	−0.509444	−	0.860504i	$-0.670149\pi$
$457$	7.50479	−	7.50479i	0.351059	−	0.351059i	0.860504	+	0.509444i	$0.170149\pi$
$458$	−19.5806	+	30.7159i	−0.914939	+	1.43526i
$459$	5.31965			0.248300
$460$		0			0
$461$	−27.0216			−1.25852			−0.629262	−	0.777193i	$-0.716643\pi$
$461$	−27.0216			−1.25852			−0.629262	+	0.777193i	$0.716643\pi$
$462$	3.37077	−	5.28771i	0.156822	−	0.246006i
$463$	−27.7123	+	27.7123i	−1.28790	+	1.28790i	−0.351843	+	0.936059i	$0.614445\pi$
$463$	−27.7123	+	27.7123i	−1.28790	+	1.28790i	−0.936059	+	0.351843i	$0.885555\pi$
$464$	−2.64687	−	2.22615i	−0.122878	−	0.103347i
$465$		0			0
$466$	0.309251	+	1.39683i	0.0143258	+	0.0647070i
$467$	2.00823	+	2.00823i	0.0929296	+	0.0929296i	0.752043	−	0.659114i	$-0.229068\pi$
$467$	2.00823	+	2.00823i	0.0929296	+	0.0929296i	−0.659114	+	0.752043i	$0.729068\pi$
$468$	−4.68098	−	1.70677i	−0.216378	−	0.0788956i
$469$		−	7.58767i		−	0.350366i
$470$		0			0
$471$		−	12.7477i		−	0.587381i
$472$	−0.196436	+	1.48225i	−0.00904172	+	0.0682260i
$473$	31.8217	+	31.8217i	1.46317	+	1.46317i
$474$	21.9727	−	4.86464i	1.00924	−	0.223440i
$475$		0			0
$476$	3.88296	+	8.33950i	0.177975	+	0.382240i
$477$	2.62620	−	2.62620i	0.120245	−	0.120245i
$478$	−32.1210	−	20.4763i	−1.46918	−	0.936562i
$479$	−13.7593			−0.628678			−0.314339	−	0.949311i	$-0.601783\pi$
$479$	−13.7593			−0.628678			−0.314339	+	0.949311i	$0.601783\pi$
$480$		0			0
$481$	−6.20617			−0.282977
$482$	16.8055	+	10.7131i	0.765470	+	0.487966i
$483$	0.931222	−	0.931222i	0.0423721	−	0.0423721i
$484$	−12.9151	−	27.7379i	−0.587049	−	1.26081i
$485$		0			0
$486$	1.38078	−	0.305697i	0.0626334	−	0.0138667i
$487$	24.3355	+	24.3355i	1.10275	+	1.10275i	0.994078	+	0.108671i	$0.0346596\pi$
$487$	24.3355	+	24.3355i	1.10275	+	1.10275i	0.108671	+	0.994078i	$0.465340\pi$
$488$	−1.85115	+	13.9682i	−0.0837975	+	0.632310i
$489$		−	18.5048i		−	0.836816i
$490$		0			0
$491$			28.8918i			1.30387i	0.758275	+	0.651935i	$0.226043\pi$
$491$			28.8918i			1.30387i	−0.758275	+	0.651935i	$0.773957\pi$
$492$	−10.3779	−	3.78397i	−0.467872	−	0.170595i
$493$	3.25240	+	3.25240i	0.146481	+	0.146481i
$494$	−0.931222	−	4.20617i	−0.0418977	−	0.189244i
$495$		0			0
$496$	23.9109	+	20.1103i	1.07363	+	0.902979i
$497$	4.95377	−	4.95377i	0.222207	−	0.222207i
$498$	8.55405	−	13.4187i	0.383316	−	0.601306i
$499$	−12.5365			−0.561211			−0.280605	−	0.959823i	$-0.590535\pi$
$499$	−12.5365			−0.561211			−0.280605	+	0.959823i	$0.590535\pi$
$500$		0			0
$501$	16.0279			0.716074
$502$	13.1112	−	20.5675i	0.585182	−	0.917972i
$503$	9.01392	−	9.01392i	0.401911	−	0.401911i	−0.476995	−	0.878906i	$-0.658274\pi$
$503$	9.01392	−	9.01392i	0.401911	−	0.401911i	0.878906	+	0.476995i	$0.158274\pi$
$504$	1.48710	+	1.94148i	0.0662409	+	0.0864805i
$505$		0			0
$506$	−2.38776	−	10.7851i	−0.106149	−	0.479455i
$507$	4.80397	+	4.80397i	0.213352	+	0.213352i
$508$	7.25806	−	19.9059i	0.322025	−	0.883182i
$509$			22.5448i			0.999279i	0.866233	+	0.499640i	$0.166534\pi$
$509$			22.5448i			0.999279i	−0.866233	+	0.499640i	$0.833466\pi$
$510$		0			0
$511$			2.75420i			0.121839i
$512$	8.71295	−	20.8826i	0.385062	−	0.922891i
$513$	0.864641	+	0.864641i	0.0381748	+	0.0381748i
$514$	29.3180	−	6.49084i	1.29316	−	0.286299i
$515$		0			0
$516$	−15.9109	+	7.40828i	−0.700437	+	0.326131i
$517$	−11.7938	+	11.7938i	−0.518692	+	0.518692i
$518$	2.56869	+	1.63747i	0.112862	+	0.0719464i
$519$	11.2681			0.494613
$520$		0			0
$521$	−18.9046			−0.828226			−0.414113	−	0.910225i	$-0.635908\pi$
$521$	−18.9046			−0.828226			−0.414113	+	0.910225i	$0.635908\pi$
$522$	1.03110	+	0.657298i	0.0451300	+	0.0287692i
$523$	21.8269	−	21.8269i	0.954426	−	0.954426i	−0.0445800	−	0.999006i	$-0.514195\pi$
$523$	21.8269	−	21.8269i	0.954426	−	0.954426i	0.999006	+	0.0445800i	$0.0141949\pi$
$524$	−25.3768	+	11.8157i	−1.10859	+	0.516172i
$525$		0			0
$526$	13.1493	−	2.91118i	0.573337	−	0.126934i
$527$	−29.3810	−	29.3810i	−1.27986	−	1.27986i
$528$	20.4368	−	1.76442i	0.889400	−	0.0767866i
$529$			20.6801i			0.899136i
$530$		0			0
$531$		−	0.528636i		−	0.0229408i
$532$	−0.724353	+	1.98661i	−0.0314047	+	0.0861303i
$533$	−9.72928	−	9.72928i	−0.421422	−	0.421422i
$534$	−2.21703	−	10.0140i	−0.0959404	−	0.433346i
$535$		0			0
$536$	19.7047	−	15.0931i	0.851114	−	0.651922i
$537$	−8.94315	+	8.94315i	−0.385925	+	0.385925i
$538$	19.5407	−	30.6533i	0.842457	−	1.32156i
$539$	32.0637			1.38108
$540$		0			0
$541$	7.85838			0.337858			0.168929	−	0.985628i	$-0.445969\pi$
$541$	7.85838			0.337858			0.168929	+	0.985628i	$0.445969\pi$
$542$	−0.707913	+	1.11050i	−0.0304075	+	0.0477000i
$543$	−5.46543	+	5.46543i	−0.234544	+	0.234544i
$544$	−13.9333	+	26.6724i	−0.597387	+	1.14357i
$545$		0			0
$546$	0.658473	+	2.97421i	0.0281801	+	0.127284i
$547$	−17.8105	−	17.8105i	−0.761522	−	0.761522i	0.215076	−	0.976597i	$-0.431000\pi$
$547$	−17.8105	−	17.8105i	−0.761522	−	0.761522i	−0.976597	+	0.215076i	$0.931000\pi$
$548$	−18.6382	−	6.79582i	−0.796183	−	0.290303i
$549$		−	4.98168i		−	0.212613i
$550$		0			0
$551$			1.05727i			0.0450413i
$552$	4.27068	+	0.565976i	0.181772	+	0.0240895i
$553$	−9.72928	−	9.72928i	−0.413731	−	0.413731i
$554$	43.0773	−	9.53707i	1.83018	−	0.405191i
$555$		0			0
$556$	1.92482	+	4.13397i	0.0816307	+	0.175319i
$557$	−23.3372	+	23.3372i	−0.988827	+	0.988827i	−0.999938	−	0.0111112i	$-0.996463\pi$
$557$	−23.3372	+	23.3372i	−0.988827	+	0.988827i	0.0111112	+	0.999938i	$0.496463\pi$
$558$	−9.31460	−	5.93780i	−0.394318	−	0.251367i
$559$	−21.8617			−0.924652
$560$		0			0
$561$	−27.2803			−1.15178
$562$	10.2191	+	6.51439i	0.431067	+	0.274793i
$563$	5.27400	−	5.27400i	0.222273	−	0.222273i	−0.587182	−	0.809455i	$-0.699763\pi$
$563$	5.27400	−	5.27400i	0.222273	−	0.222273i	0.809455	+	0.587182i	$0.199763\pi$
$564$	−2.74567	−	5.89692i	−0.115614	−	0.248305i
$565$		0			0
$566$	−22.5939	+	5.00217i	−0.949693	+	0.210257i
$567$	−0.611393	−	0.611393i	−0.0256761	−	0.0256761i
$568$	22.7185	+	3.01079i	0.953247	+	0.126330i
$569$		−	28.5606i		−	1.19732i	−0.801002	−	0.598661i	$-0.795699\pi$
$569$		−	28.5606i		−	1.19732i	0.801002	−	0.598661i	$-0.204301\pi$
$570$		0			0
$571$		−	32.2837i		−	1.35103i	−0.737347	−	0.675515i	$-0.763922\pi$
$571$		−	32.2837i		−	1.35103i	0.737347	−	0.675515i	$-0.236078\pi$
$572$	24.0051	+	8.75270i	1.00370	+	0.365969i
$573$	−4.98168	−	4.98168i	−0.208113	−	0.208113i
$574$	1.45986	+	6.59392i	0.0609333	+	0.275225i
$575$		0			0
$576$	−2.08382	+	7.72384i	−0.0868257	+	0.321827i
$577$	−27.0279	+	27.0279i	−1.12519	+	1.12519i	−0.134237	+	0.990949i	$0.542858\pi$
$577$	−27.0279	+	27.0279i	−1.12519	+	1.12519i	−0.990949	+	0.134237i	$0.957142\pi$
$578$	8.58919	−	13.4738i	0.357263	−	0.560437i
$579$	−16.2702			−0.676168
$580$		0			0
$581$	−9.72928			−0.403639
$582$	0.853435	−	1.33878i	0.0353760	−	0.0554942i
$583$	−13.4677	+	13.4677i	−0.557776	+	0.557776i
$584$	−7.15249	+	5.47855i	−0.295972	+	0.226704i
$585$		0			0
$586$	−5.57560	−	25.1840i	−0.230326	−	1.04034i
$587$	−17.1558	−	17.1558i	−0.708096	−	0.708096i	0.258039	−	0.966135i	$-0.416924\pi$
$587$	−17.1558	−	17.1558i	−0.708096	−	0.708096i	−0.966135	+	0.258039i	$0.916924\pi$
$588$	−4.28362	+	11.7482i	−0.176653	+	0.484488i
$589$		−	9.55102i		−	0.393543i
$590$		0			0
$591$		−	11.1420i		−	0.458321i
$592$	0.857132	+	9.92794i	0.0352279	+	0.408036i
$593$	21.5833	+	21.5833i	0.886320	+	0.886320i	0.994167	−	0.107848i	$-0.0343959\pi$
$593$	21.5833	+	21.5833i	0.886320	+	0.886320i	−0.107848	+	0.994167i	$0.534396\pi$
$594$	−7.08093	+	1.56768i	−0.290534	+	0.0643227i
$595$		0			0
$596$	18.3432	−	8.54079i	0.751366	−	0.349844i
$597$	−8.11704	+	8.11704i	−0.332208	+	0.332208i
$598$	4.52490	+	2.88450i	0.185037	+	0.117956i
$599$	−23.7636			−0.970955			−0.485478	−	0.874249i	$-0.661354\pi$
$599$	−23.7636			−0.970955			−0.485478	+	0.874249i	$0.661354\pi$
$600$		0			0
$601$	22.1695			0.904314			0.452157	−	0.891938i	$-0.350655\pi$
$601$	22.1695			0.904314			0.452157	+	0.891938i	$0.350655\pi$
$602$	9.04843	+	5.76813i	0.368786	+	0.235091i
$603$	−6.20522	+	6.20522i	−0.252696	+	0.252696i
$604$	14.3904	−	6.70033i	0.585537	−	0.272633i
$605$		0			0
$606$	13.9694	−	3.09275i	0.567468	−	0.125634i
$607$	−9.35348	−	9.35348i	−0.379646	−	0.379646i	0.491328	−	0.870974i	$-0.336511\pi$
$607$	−9.35348	−	9.35348i	−0.379646	−	0.379646i	−0.870974	+	0.491328i	$0.836511\pi$
$608$	−6.59995	+	2.07058i	−0.267663	+	0.0839731i
$609$		−	0.747604i		−	0.0302944i
$610$		0			0
$611$		−	8.10243i		−	0.327789i
$612$	3.64457	−	9.99558i	0.147323	−	0.404047i
$613$	24.1247	+	24.1247i	0.974389	+	0.974389i	0.999680	−	0.0252913i	$-0.00805134\pi$
$613$	24.1247	+	24.1247i	0.974389	+	0.974389i	−0.0252913	+	0.999680i	$0.508051\pi$
$614$	−0.694151	−	3.13536i	−0.0280137	−	0.126533i
$615$		0			0
$616$	−7.62620	−	9.95634i	−0.307268	−	0.401152i
$617$	−3.82611	+	3.82611i	−0.154033	+	0.154033i	−0.779917	−	0.625883i	$-0.784739\pi$
$617$	−3.82611	+	3.82611i	−0.154033	+	0.154033i	0.625883	+	0.779917i	$0.284739\pi$
$618$	−4.10969	+	6.44685i	−0.165316	+	0.259330i
$619$	30.1297			1.21101			0.605507	−	0.795840i	$-0.292971\pi$
$619$	30.1297			1.21101			0.605507	+	0.795840i	$0.292971\pi$
$620$		0			0
$621$	−1.52311			−0.0611205
$622$	14.7601	−	23.1541i	0.591826	−	0.928395i
$623$	−4.43407	+	4.43407i	−0.177647	+	0.177647i
$624$	−6.41403	+	7.62620i	−0.256767	+	0.305292i
$625$		0			0
$626$	−7.65681	−	34.5845i	−0.306028	−	1.38227i
$627$	−4.43407	−	4.43407i	−0.177080	−	0.177080i
$628$	−23.9528	−	8.73362i	−0.955819	−	0.348509i
$629$		−	13.2524i		−	0.528408i
$630$		0			0
$631$		−	21.5701i		−	0.858694i	−0.903140	−	0.429347i	$-0.858744\pi$
$631$		−	21.5701i		−	0.858694i	0.903140	−	0.429347i	$-0.141256\pi$
$632$	5.91324	−	44.6195i	0.235216	−	1.77487i
$633$	−3.88296	−	3.88296i	−0.154334	−	0.154334i
$634$	15.2106	−	3.36754i	0.604090	−	0.133742i
$635$		0			0
$636$	−3.13536	−	6.73386i	−0.124325	−	0.267015i
$637$	−11.0140	+	11.0140i	−0.436389	+	0.436389i
$638$	−5.28771	−	3.37077i	−0.209342	−	0.133450i
$639$	−8.10243			−0.320527
$640$		0			0
$641$	48.3911			1.91133			0.955666	−	0.294452i	$-0.0951370\pi$
$641$	48.3911			1.91133			0.955666	+	0.294452i	$0.0951370\pi$
$642$	−9.29429	−	5.92485i	−0.366816	−	0.233835i
$643$	23.3413	−	23.3413i	0.920491	−	0.920491i	−0.0765729	−	0.997064i	$-0.524398\pi$
$643$	23.3413	−	23.3413i	0.920491	−	0.920491i	0.997064	+	0.0765729i	$0.0243978\pi$
$644$	−1.11177	−	2.38776i	−0.0438097	−	0.0940907i
$645$		0			0
$646$	8.98168	−	1.98849i	0.353379	−	0.0782362i
$647$	32.4465	+	32.4465i	1.27560	+	1.27560i	0.943103	+	0.332501i	$0.107892\pi$
$647$	32.4465	+	32.4465i	1.27560	+	1.27560i	0.332501	+	0.943103i	$0.392108\pi$
$648$	0.371591	−	2.80391i	0.0145975	−	0.110148i
$649$			2.71096i			0.106414i
$650$		0			0
$651$			6.75359i			0.264694i
$652$	−34.7704	−	12.6779i	−1.36171	−	0.496506i
$653$	−18.4725	−	18.4725i	−0.722885	−	0.722885i	0.246307	−	0.969192i	$-0.420783\pi$
$653$	−18.4725	−	18.4725i	−0.722885	−	0.722885i	−0.969192	+	0.246307i	$0.920783\pi$
$654$	−2.23677	−	10.1031i	−0.0874645	−	0.395062i
$655$		0			0
$656$	−14.2201	+	16.9075i	−0.555202	+	0.660128i
$657$	2.25240	−	2.25240i	0.0878743	−	0.0878743i
$658$	−2.13779	+	3.35355i	−0.0833399	+	0.130735i
$659$	−47.5028			−1.85045			−0.925223	−	0.379423i	$-0.876122\pi$
$659$	−47.5028			−1.85045			−0.925223	+	0.379423i	$0.876122\pi$
$660$		0			0
$661$	−46.1204			−1.79387			−0.896937	−	0.442158i	$-0.854213\pi$
$661$	−46.1204			−1.79387			−0.896937	+	0.442158i	$0.854213\pi$
$662$	−24.0987	+	37.8035i	−0.936621	+	1.46927i
$663$	9.37086	−	9.37086i	0.363934	−	0.363934i
$664$	−19.3531	−	25.2663i	−0.751046	−	0.980525i
$665$		0			0
$666$	−0.761557	−	3.43982i	−0.0295097	−	0.133290i
$667$	−0.931222	−	0.931222i	−0.0360571	−	0.0360571i
$668$	10.9810	−	30.1163i	0.424867	−	1.16524i
$669$			15.3694i			0.594217i
$670$		0			0
$671$			25.5471i			0.986236i
$672$	4.66687	−	1.46412i	0.180028	−	0.0564797i
$673$	−3.60599	−	3.60599i	−0.139001	−	0.139001i	0.634183	−	0.773183i	$-0.281337\pi$
$673$	−3.60599	−	3.60599i	−0.139001	−	0.139001i	−0.773183	+	0.634183i	$0.781337\pi$
$674$	−37.0300	+	8.19825i	−1.42634	+	0.315785i
$675$		0			0
$676$	12.3179	−	5.73535i	0.473765	−	0.220590i
$677$	8.26635	−	8.26635i	0.317702	−	0.317702i	−0.530182	−	0.847884i	$-0.677876\pi$
$677$	8.26635	−	8.26635i	0.317702	−	0.317702i	0.847884	+	0.530182i	$0.177876\pi$
$678$	−0.858688	−	0.547390i	−0.0329777	−	0.0210224i
$679$	−0.970688			−0.0372516
$680$		0			0
$681$	7.04623			0.270012
$682$	47.7673	+	30.4503i	1.82910	+	1.16600i
$683$	8.43079	−	8.43079i	0.322595	−	0.322595i	−0.527167	−	0.849762i	$-0.676746\pi$
$683$	8.43079	−	8.43079i	0.322595	−	0.322595i	0.849762	+	0.527167i	$0.176746\pi$
$684$	2.21703	−	1.03228i	0.0847704	−	0.0394700i
$685$		0			0
$686$	15.8217	−	3.50285i	0.604077	−	0.133739i
$687$	−18.2131	−	18.2131i	−0.694872	−	0.694872i
$688$	3.01932	+	34.9719i	0.115110	+	1.33329i
$689$		−	9.25240i		−	0.352488i
$690$		0			0
$691$		−	21.9182i		−	0.833809i	−0.908950	−	0.416905i	$-0.863115\pi$
$691$		−	21.9182i		−	0.833809i	0.908950	−	0.416905i	$-0.136885\pi$
$692$	7.71993	−	21.1726i	0.293468	−	0.804862i
$693$	3.13536	+	3.13536i	0.119102	+	0.119102i
$694$	3.33733	+	15.0741i	0.126683	+	0.572206i
$695$		0			0
$696$	1.94148	−	1.48710i	0.0735917	−	0.0563686i
$697$	20.7755	−	20.7755i	0.786929	−	0.786929i
$698$	20.5817	−	32.2864i	0.779029	−	1.22206i
$699$	−1.01163			−0.0382633
$700$		0			0
$701$	−21.8184			−0.824070			−0.412035	−	0.911168i	$-0.635182\pi$
$701$	−21.8184			−0.824070			−0.412035	+	0.911168i	$0.635182\pi$
$702$	1.89382	−	2.97082i	0.0714776	−	0.112126i
$703$	2.15401	−	2.15401i	0.0812400	−	0.0812400i
$704$	10.6863	−	39.6095i	0.402754	−	1.49284i
$705$		0			0
$706$	4.30925	+	19.4641i	0.162181	+	0.732542i
$707$	−6.18549	−	6.18549i	−0.232629	−	0.232629i
$708$	−0.993303	−	0.362177i	−0.0373306	−	0.0136114i
$709$			31.7938i			1.19404i	0.802225	+	0.597021i	$0.203649\pi$
$709$			31.7938i			1.19404i	−0.802225	+	0.597021i	$0.796351\pi$
$710$		0			0
$711$			15.9133i			0.596795i
$712$	−20.3351	−	2.69493i	−0.762089	−	0.100997i
$713$	8.41233	+	8.41233i	0.315044	+	0.315044i
$714$	−6.35101	+	1.40608i	−0.237680	+	0.0526211i
$715$		0			0
$716$	10.6770	+	22.9312i	0.399019	+	0.856979i
$717$	19.0462	−	19.0462i	0.711294	−	0.711294i
$718$	16.9736	+	10.8202i	0.633450	+	0.403807i
$719$	52.0874			1.94253			0.971265	−	0.237999i	$-0.0764916\pi$
$719$	52.0874			1.94253			0.971265	+	0.237999i	$0.0764916\pi$
$720$		0			0
$721$	4.67432			0.174081
$722$	−20.8748	−	13.3071i	−0.776879	−	0.495239i
$723$	−9.96487	+	9.96487i	−0.370598	+	0.370598i
$724$	6.52505	+	14.0140i	0.242502	+	0.520824i
$725$		0			0
$726$	21.1240	−	4.67674i	0.783986	−	0.173570i
$727$	8.13069	+	8.13069i	0.301551	+	0.301551i	0.841620	−	0.540070i	$-0.181602\pi$
$727$	8.13069	+	8.13069i	0.301551	+	0.301551i	−0.540070	+	0.841620i	$0.681602\pi$
$728$	6.03965	+	0.800411i	0.223844	+	0.0296652i
$729$			1.00000i			0.0370370i
$730$		0			0
$731$		−	46.6826i		−	1.72662i
$732$	−9.36054	−	3.41303i	−0.345976	−	0.126149i
$733$	29.9956	+	29.9956i	1.10791	+	1.10791i	0.993424	+	0.114489i	$0.0365232\pi$
$733$	29.9956	+	29.9956i	1.10791	+	1.10791i	0.114489	+	0.993424i	$0.463477\pi$
$734$	−1.25003	−	5.64618i	−0.0461396	−	0.208404i
$735$		0			0
$736$	3.98937	−	7.63682i	0.147050	−	0.281497i
$737$	31.8217	−	31.8217i	1.17217	−	1.17217i
$738$	4.19866	−	6.58641i	0.154555	−	0.242449i
$739$	−39.4719			−1.45200			−0.725999	−	0.687696i	$-0.758622\pi$
$739$	−39.4719			−1.45200			−0.725999	+	0.687696i	$0.758622\pi$
$740$		0			0
$741$	3.04623			0.111906
$742$	−2.44121	+	3.82951i	−0.0896196	+	0.140586i
$743$	−12.2252	+	12.2252i	−0.448499	+	0.448499i	−0.894855	−	0.446356i	$-0.852721\pi$
$743$	−12.2252	+	12.2252i	−0.448499	+	0.448499i	0.446356	+	0.894855i	$0.352721\pi$
$744$	−17.5387	+	13.4340i	−0.642999	+	0.492514i
$745$		0			0
$746$	4.87859	+	22.0358i	0.178618	+	0.806786i
$747$	7.95665	+	7.95665i	0.291118	+	0.291118i
$748$	−18.6902	+	51.2595i	−0.683380	+	1.87423i
$749$			6.73887i			0.246233i
$750$		0			0
$751$			28.9069i			1.05483i	0.849609	+	0.527413i	$0.176838\pi$
$751$			28.9069i			1.05483i	−0.849609	+	0.527413i	$0.823162\pi$
$752$	−12.9614	+	1.11902i	−0.472652	+	0.0408066i
$753$	12.1955	+	12.1955i	0.444430	+	0.444430i
$754$	2.97421	−	0.658473i	0.108314	−	0.0239802i
$755$		0			0
$756$	−1.56768	+	0.729929i	−0.0570160	+	0.0265473i
$757$	16.2018	−	16.2018i	0.588864	−	0.588864i	−0.348459	−	0.937324i	$-0.613295\pi$
$757$	16.2018	−	16.2018i	0.588864	−	0.588864i	0.937324	+	0.348459i	$0.113295\pi$
$758$	18.4318	+	11.7498i	0.669474	+	0.426771i
$759$	7.81086			0.283516
$760$		0			0
$761$	−6.64641			−0.240932			−0.120466	−	0.992717i	$-0.538439\pi$
$761$	−6.64641			−0.240932			−0.120466	+	0.992717i	$0.538439\pi$
$762$	12.6334	+	8.05348i	0.457661	+	0.291747i
$763$	−4.47353	+	4.47353i	−0.161953	+	0.161953i
$764$	−12.7736	+	5.94751i	−0.462131	+	0.215173i
$765$		0			0
$766$	−24.5187	+	5.42831i	−0.885898	+	0.196133i
$767$	−0.931222	−	0.931222i	−0.0336245	−	0.0336245i
$768$	13.0854	+	9.20720i	0.472178	+	0.332236i
$769$		−	29.3449i		−	1.05820i	−0.848559	−	0.529101i	$-0.822529\pi$
$769$		−	29.3449i		−	1.05820i	0.848559	−	0.529101i	$-0.177471\pi$
$770$		0			0
$771$			21.2329i			0.764686i
$772$	−11.1470	+	30.5717i	−0.401189	+	1.10030i
$773$	−37.5833	−	37.5833i	−1.35178	−	1.35178i	−0.883674	−	0.468104i	$-0.844937\pi$
$773$	−37.5833	−	37.5833i	−1.35178	−	1.35178i	−0.468104	−	0.883674i	$-0.655063\pi$
$774$	−2.68264	−	12.1170i	−0.0964257	−	0.435538i
$775$		0			0
$776$	−1.93086	−	2.52082i	−0.0693137	−	0.0904921i
$777$	−1.52311	+	1.52311i	−0.0546414	+	0.0546414i
$778$	−3.92510	+	6.15729i	−0.140722	+	0.220749i
$779$	6.75359			0.241973
$780$		0			0
$781$	41.5510			1.48681
$782$	−6.15945	+	9.66229i	−0.220261	+	0.345523i
$783$	−0.611393	+	0.611393i	−0.0218494	+	0.0218494i
$784$	19.1400	+	16.0978i	0.683573	+	0.574920i
$785$		0			0
$786$	−4.27864	−	19.3259i	−0.152614	−	0.689331i
$787$	7.59353	+	7.59353i	0.270680	+	0.270680i	0.829374	−	0.558694i	$-0.188697\pi$
$787$	7.59353	+	7.59353i	0.270680	+	0.270680i	−0.558694	+	0.829374i	$0.688697\pi$
$788$	−20.9358	−	7.63357i	−0.745806	−	0.271935i
$789$			9.52311i			0.339032i
$790$		0			0
$791$			0.622595i			0.0221369i
$792$	−1.90560	+	14.3791i	−0.0677126	+	0.510938i
$793$	−8.77551	−	8.77551i	−0.311628	−	0.311628i
$794$	6.76212	−	1.49710i	0.239979	−	0.0531300i
$795$		0			0
$796$	9.69075	+	20.8130i	0.343479	+	0.737696i
$797$	−27.4908	+	27.4908i	−0.973775	+	0.973775i	−0.999665	−	0.0258893i	$-0.991758\pi$
$797$	−27.4908	+	27.4908i	−0.973775	+	0.973775i	0.0258893	+	0.999665i	$0.491758\pi$
$798$	−1.26082	−	0.803735i	−0.0446324	−	0.0284519i
$799$	17.3016			0.612086
$800$		0			0
$801$	7.25240			0.256251
$802$	4.16810	+	2.65705i	0.147181	+	0.0938237i
$803$	−11.5508	+	11.5508i	−0.407618	+	0.407618i
$804$	7.40828	+	15.9109i	0.261270	+	0.561133i
$805$		0			0
$806$	−26.8680	+	5.94842i	−0.946384	+	0.209524i
$807$	18.1760	+	18.1760i	0.639824	+	0.639824i
$808$	3.75940	−	28.3673i	0.132255	−	0.997957i
$809$			47.7205i			1.67776i	0.544313	+	0.838882i	$0.316791\pi$
$809$			47.7205i			1.67776i	−0.544313	+	0.838882i	$0.683209\pi$
$810$		0			0
$811$		−	37.3179i		−	1.31041i	−0.755451	−	0.655205i	$-0.772582\pi$
$811$		−	37.3179i		−	1.31041i	0.755451	−	0.655205i	$-0.227418\pi$
$812$	−1.40474	−	0.512195i	−0.0492968	−	0.0179745i
$813$	−0.658473	−	0.658473i	−0.0230937	−	0.0230937i
$814$	3.90543	+	17.6402i	0.136885	+	0.618287i
$815$		0			0
$816$	−16.2847	−	13.6963i	−0.570078	−	0.479465i
$817$	7.58767	−	7.58767i	0.265459	−	0.265459i
$818$	−11.2535	+	17.6533i	−0.393470	+	0.617235i
$819$	−2.15401			−0.0752672
$820$		0			0
$821$	−0.686380			−0.0239548			−0.0119774	−	0.999928i	$-0.503813\pi$
$821$	−0.686380			−0.0239548			−0.0119774	+	0.999928i	$0.503813\pi$
$822$	7.54057	−	11.8289i	0.263008	−	0.412579i
$823$	27.2553	−	27.2553i	0.950059	−	0.950059i	−0.0487521	−	0.998811i	$-0.515524\pi$
$823$	27.2553	−	27.2553i	0.950059	−	0.950059i	0.998811	+	0.0487521i	$0.0155244\pi$
$824$	9.29797	+	12.1389i	0.323910	+	0.422879i
$825$		0			0
$826$	0.139728	+	0.631126i	0.00486175	+	0.0219597i
$827$	31.4437	+	31.4437i	1.09341	+	1.09341i	0.995162	+	0.0982432i	$0.0313223\pi$
$827$	31.4437	+	31.4437i	1.09341	+	1.09341i	0.0982432	+	0.995162i	$0.468678\pi$
$828$	−1.04351	+	2.86192i	−0.0362645	+	0.0994587i
$829$			0.270718i			0.00940243i	0.999989	+	0.00470122i	$0.00149645\pi$
$829$			0.270718i			0.00940243i	−0.999989	+	0.00470122i	$0.998504\pi$
$830$		0			0
$831$			31.1978i			1.08224i
$832$	9.93522	+	17.2767i	0.344442	+	0.598964i
$833$	−23.5187	−	23.5187i	−0.814876	−	0.814876i
$834$	−3.14826	+	0.697006i	−0.109015	+	0.0241354i
$835$		0			0
$836$	−11.3694	+	5.29373i	−0.393220	+	0.183088i
$837$	5.52311	−	5.52311i	0.190907	−	0.190907i
$838$	−22.7414	−	14.4970i	−0.785589	−	0.500792i
$839$	31.0214			1.07098			0.535489	−	0.844542i	$-0.320127\pi$
$839$	31.0214			1.07098			0.535489	+	0.844542i	$0.320127\pi$
$840$		0			0
$841$	28.2524			0.974221
$842$	−24.8085	−	15.8147i	−0.854956	−	0.545011i
$843$	−6.05944	+	6.05944i	−0.208698	+	0.208698i
$844$	−9.95634	+	4.63578i	−0.342711	+	0.159570i
$845$		0			0
$846$	4.49084	−	0.994247i	0.154398	−	0.0341829i
$847$	−9.35348	−	9.35348i	−0.321389	−	0.321389i
$848$	−14.8010	+	1.27785i	−0.508267	+	0.0438814i
$849$		−	16.3632i		−	0.561583i
$850$		0			0
$851$			3.79441i			0.130071i
$852$	−5.55110	+	15.2244i	−0.190178	+	0.521580i
$853$	−3.82611	−	3.82611i	−0.131003	−	0.131003i	0.638565	−	0.769568i	$-0.279528\pi$
$853$	−3.82611	−	3.82611i	−0.131003	−	0.131003i	−0.769568	+	0.638565i	$0.779528\pi$
$854$	1.31675	+	5.94751i	0.0450581	+	0.203520i
$855$		0			0
$856$	−17.5004	+	13.4047i	−0.598152	+	0.458163i
$857$	−20.7711	+	20.7711i	−0.709529	+	0.709529i	−0.966436	−	0.256907i	$-0.917296\pi$
$857$	−20.7711	+	20.7711i	−0.709529	+	0.709529i	0.256907	+	0.966436i	$0.417296\pi$
$858$	−9.71191	+	15.2350i	−0.331559	+	0.520115i
$859$	1.69693			0.0578985			0.0289492	−	0.999581i	$-0.490784\pi$
$859$	1.69693			0.0578985			0.0289492	+	0.999581i	$0.490784\pi$
$860$		0			0
$861$	−4.77551			−0.162749
$862$	11.6540	−	18.2815i	0.396935	−	0.622670i
$863$	−5.92869	+	5.92869i	−0.201815	+	0.201815i	−0.800777	−	0.598962i	$-0.795580\pi$
$863$	−5.92869	+	5.92869i	−0.201815	+	0.201815i	0.598962	+	0.800777i	$0.295580\pi$
$864$	−5.01395	−	2.61922i	−0.170578	−	0.0891077i
$865$		0			0
$866$	−7.03831	−	31.7908i	−0.239171	−	1.08030i
$867$	7.98933	+	7.98933i	0.271332	+	0.271332i
$868$	12.6900	+	4.62699i	0.430725	+	0.157050i
$869$		−	81.6068i		−	2.76832i
$870$		0			0
$871$			21.8617i			0.740756i
$872$	−20.5161	−	2.71891i	−0.694762	−	0.0920740i
$873$	0.793833	+	0.793833i	0.0268672	+	0.0268672i
$874$	−2.57162	+	0.569343i	−0.0869865	+	0.0192583i
$875$		0			0
$876$	−2.68909	−	5.77539i	−0.0908558	−	0.195132i
$877$	10.0323	−	10.0323i	0.338766	−	0.338766i	−0.517137	−	0.855903i	$-0.673002\pi$
$877$	10.0323	−	10.0323i	0.338766	−	0.338766i	0.855903	+	0.517137i	$0.173002\pi$
$878$	29.4020	+	18.7430i	0.992269	+	0.632544i
$879$	18.2390			0.615186
$880$		0			0
$881$	−29.8130			−1.00443			−0.502213	−	0.864744i	$-0.667481\pi$
$881$	−29.8130			−1.00443			−0.502213	+	0.864744i	$0.667481\pi$
$882$	−7.45610	−	4.75306i	−0.251060	−	0.160044i
$883$	5.56557	−	5.56557i	0.187296	−	0.187296i	−0.607230	−	0.794526i	$-0.707719\pi$
$883$	5.56557	−	5.56557i	0.187296	−	0.187296i	0.794526	+	0.607230i	$0.207719\pi$
$884$	−11.1877	−	24.0279i	−0.376282	−	0.808146i
$885$		0			0
$886$	−3.45856	+	0.765707i	−0.116193	+	0.0257244i
$887$	−8.59630	−	8.59630i	−0.288636	−	0.288636i	0.547905	−	0.836541i	$-0.315426\pi$
$887$	−8.59630	−	8.59630i	−0.288636	−	0.288636i	−0.836541	+	0.547905i	$0.815426\pi$
$888$	−6.98516	−	0.925715i	−0.234406	−	0.0310649i
$889$		−	9.15994i		−	0.307214i
$890$		0			0
$891$		−	5.12822i		−	0.171802i
$892$	28.8791	+	10.5298i	0.966943	+	0.352565i
$893$	2.81215	+	2.81215i	0.0941052	+	0.0941052i
$894$	3.09275	+	13.9694i	0.103437	+	0.467206i
$895$		0			0
$896$	0.446274	−	9.77211i	0.0149090	−	0.326463i
$897$	−2.68305	+	2.68305i	−0.0895845	+	0.0895845i
$898$	−25.2015	+	39.5334i	−0.840984	+	1.31925i
$899$	6.75359			0.225245
$900$		0			0
$901$	19.7572			0.658207
$902$	−21.5316	+	33.7766i	−0.716925	+	1.12464i
$903$	−5.36529	+	5.36529i	−0.178546	+	0.178546i
$904$	−1.61684	+	1.23844i	−0.0537754	+	0.0411900i
$905$		0			0
$906$	2.42629	+	10.9591i	0.0806080	+	0.364092i
$907$	−31.6263	−	31.6263i	−1.05013	−	1.05013i	−0.998675	−	0.0514592i	$-0.983613\pi$
$907$	−31.6263	−	31.6263i	−1.05013	−	1.05013i	−0.0514592	−	0.998675i	$-0.516387\pi$
$908$	4.82748	−	13.2398i	0.160206	−	0.439379i
$909$			10.1170i			0.335561i
$910$		0			0
$911$			42.2656i			1.40032i	0.713985	+	0.700161i	$0.246888\pi$
$911$			42.2656i			1.40032i	−0.713985	+	0.700161i	$0.753112\pi$
$912$	−0.420714	−	4.87302i	−0.0139312	−	0.161362i
$913$	−40.8034	−	40.8034i	−1.35040	−	1.35040i
$914$	14.6547	−	3.24448i	0.484735	−	0.107318i
$915$		0			0
$916$	−46.7003	+	21.7442i	−1.54302	+	0.718448i
$917$	−8.55728	+	8.55728i	−0.282586	+	0.282586i
$918$	6.34377	+	4.04398i	0.209376	+	0.133471i
$919$	−31.2829			−1.03193			−0.515964	−	0.856610i	$-0.672566\pi$
$919$	−31.2829			−1.03193			−0.515964	+	0.856610i	$0.672566\pi$
$920$		0			0
$921$	2.27072			0.0748227
$922$	−32.2238	−	20.5418i	−1.06123	−	0.676508i
$923$	−14.2729	+	14.2729i	−0.469798	+	0.469798i
$924$	8.03940	−	3.74324i	0.264477	−	0.123143i
$925$		0			0
$926$	−54.1143	+	11.9806i	−1.77831	+	0.393707i
$927$	−3.82267	−	3.82267i	−0.125553	−	0.125553i
$928$	−1.46412	−	4.66687i	−0.0480621	−	0.153198i
$929$		−	22.1050i		−	0.725241i	−0.931937	−	0.362620i	$-0.881882\pi$
$929$		−	22.1050i		−	0.725241i	0.931937	−	0.362620i	$-0.118118\pi$
$930$		0			0
$931$		−	7.64535i		−	0.250566i
$932$	−0.693082	+	1.90084i	−0.0227026	+	0.0622641i
$933$	13.7293	+	13.7293i	0.449477	+	0.449477i
$934$	0.868197	+	3.92150i	0.0284083	+	0.128315i
$935$		0			0
$936$	−4.28467	−	5.59383i	−0.140049	−	0.182840i
$937$	15.2986	−	15.2986i	0.499784	−	0.499784i	−0.411586	−	0.911371i	$-0.635025\pi$
$937$	15.2986	−	15.2986i	0.499784	−	0.499784i	0.911371	+	0.411586i	$0.135025\pi$
$938$	5.76813	−	9.04843i	0.188336	−	0.295442i
$939$	25.0471			0.817381
$940$		0			0
$941$	25.5264			0.832138			0.416069	−	0.909333i	$-0.363407\pi$
$941$	25.5264			0.832138			0.416069	+	0.909333i	$0.363407\pi$
$942$	9.69074	−	15.2018i	0.315741	−	0.495302i
$943$	−5.94842	+	5.94842i	−0.193707	+	0.193707i
$944$	−1.36106	+	1.61828i	−0.0442986	+	0.0526704i
$945$		0			0
$946$	13.7572	+	62.1388i	0.447285	+	2.02031i
$947$	−11.9881	−	11.9881i	−0.389562	−	0.389562i	0.484969	−	0.874531i	$-0.338831\pi$
$947$	−11.9881	−	11.9881i	−0.389562	−	0.389562i	−0.874531	+	0.484969i	$0.838831\pi$
$948$	29.9010	+	10.9024i	0.971138	+	0.354095i
$949$		−	7.93545i		−	0.257596i
$950$		0			0
$951$			11.0160i			0.357217i
$952$	−1.70916	+	12.8968i	−0.0553943	+	0.417988i
$953$	−5.99563	−	5.99563i	−0.194218	−	0.194218i	0.603298	−	0.797516i	$-0.293853\pi$
$953$	−5.99563	−	5.99563i	−0.194218	−	0.194218i	−0.797516	+	0.603298i	$0.793853\pi$
$954$	5.12822	−	1.13536i	0.166032	−	0.0367586i
$955$		0			0
$956$	−22.7389	−	48.8366i	−0.735427	−	1.57949i
$957$	3.13536	−	3.13536i	0.101352	−	0.101352i
$958$	−16.4082	−	10.4598i	−0.530125	−	0.337940i
$959$	−8.57657			−0.276952
$960$		0			0
$961$	−30.0096			−0.968051
$962$	−7.40097	−	4.71791i	−0.238617	−	0.152112i
$963$	5.51107	−	5.51107i	0.177592	−	0.177592i
$964$	11.8968	+	25.5510i	0.383171	+	0.822943i
$965$		0			0
$966$	1.81841	−	0.402586i	0.0585065	−	0.0129530i
$967$	1.66866	+	1.66866i	0.0536606	+	0.0536606i	0.733428	−	0.679767i	$-0.237919\pi$
$967$	1.66866	+	1.66866i	0.0536606	+	0.0536606i	−0.679767	+	0.733428i	$0.737919\pi$
$968$	5.68483	−	42.8960i	0.182717	−	1.37873i
$969$			6.50479i			0.208964i
$970$		0			0
$971$		−	4.79719i		−	0.153949i	−0.997033	−	0.0769745i	$-0.975474\pi$
$971$		−	4.79719i		−	0.153949i	0.997033	−	0.0769745i	$-0.0245260\pi$
$972$	1.87899	+	0.685116i	0.0602687	+	0.0219751i
$973$	1.39401	+	1.39401i	0.0446900	+	0.0446900i
$974$	10.5208	+	47.5204i	0.337107	+	1.52265i
$975$		0			0
$976$	−12.8261	+	15.2501i	−0.410554	+	0.488143i
$977$	25.0140	−	25.0140i	0.800267	−	0.800267i	−0.182870	−	0.983137i	$-0.558539\pi$
$977$	25.0140	−	25.0140i	0.800267	−	0.800267i	0.983137	+	0.182870i	$0.0585387\pi$
$978$	14.0673	−	22.0673i	0.449823	−	0.705634i
$979$	−37.1919			−1.18866
$980$		0			0
$981$	7.31695			0.233612
$982$	−21.9635	+	34.4540i	−0.700884	+	1.09947i
$983$	30.9151	−	30.9151i	0.986038	−	0.986038i	−0.0138655	−	0.999904i	$-0.504414\pi$
$983$	30.9151	−	30.9151i	0.986038	−	0.986038i	0.999904	+	0.0138655i	$0.00441368\pi$
$984$	−9.49926	−	12.4017i	−0.302825	−	0.395352i
$985$		0			0
$986$	1.40608	+	6.35101i	0.0447786	+	0.202257i
$987$	−1.98849	−	1.98849i	−0.0632945	−	0.0632945i
$988$	2.08702	−	5.72384i	0.0663969	−	0.182100i
$989$			13.3661i			0.425017i
$990$		0			0
$991$			26.5873i			0.844575i	0.906462	+	0.422287i	$0.138773\pi$
$991$			26.5873i			0.844575i	−0.906462	+	0.422287i	$0.861227\pi$
$992$	13.2264	+	42.1589i	0.419937	+	1.33855i
$993$	−22.4157	−	22.4157i	−0.711340	−	0.711340i
$994$	9.67331	−	2.14162i	0.306819	−	0.0679280i
$995$		0			0
$996$	20.4017	−	9.49926i	0.646453	−	0.300996i
$997$	2.47252	−	2.47252i	0.0783054	−	0.0783054i	−0.666869	−	0.745175i	$-0.732366\pi$
$997$	2.47252	−	2.47252i	0.0783054	−	0.0783054i	0.745175	+	0.666869i	$0.232366\pi$
$998$	−14.9500	−	9.53021i	−0.473234	−	0.301674i
$999$	2.49122			0.0788187

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	300.2.j.d.43.5		12
3.2	odd	2		900.2.k.n.343.2		12
4.3	odd	2	inner	300.2.j.d.43.2		12
5.2	odd	4	inner	300.2.j.d.7.2		12
5.3	odd	4		60.2.j.a.7.5	yes	12
5.4	even	2		60.2.j.a.43.2	yes	12
12.11	even	2		900.2.k.n.343.5		12
15.2	even	4		900.2.k.n.307.5		12
15.8	even	4		180.2.k.e.127.2		12
15.14	odd	2		180.2.k.e.163.5		12
20.3	even	4		60.2.j.a.7.2	✓	12
20.7	even	4	inner	300.2.j.d.7.5		12
20.19	odd	2		60.2.j.a.43.5	yes	12
40.3	even	4		960.2.w.g.127.2		12
40.13	odd	4		960.2.w.g.127.5		12
40.19	odd	2		960.2.w.g.703.5		12
40.29	even	2		960.2.w.g.703.2		12
60.23	odd	4		180.2.k.e.127.5		12
60.47	odd	4		900.2.k.n.307.2		12
60.59	even	2		180.2.k.e.163.2		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
60.2.j.a.7.2	✓	12	20.3	even	4
60.2.j.a.7.5	yes	12	5.3	odd	4
60.2.j.a.43.2	yes	12	5.4	even	2
60.2.j.a.43.5	yes	12	20.19	odd	2
180.2.k.e.127.2		12	15.8	even	4
180.2.k.e.127.5		12	60.23	odd	4
180.2.k.e.163.2		12	60.59	even	2
180.2.k.e.163.5		12	15.14	odd	2
300.2.j.d.7.2		12	5.2	odd	4	inner
300.2.j.d.7.5		12	20.7	even	4	inner
300.2.j.d.43.2		12	4.3	odd	2	inner
300.2.j.d.43.5		12	1.1	even	1	trivial
900.2.k.n.307.2		12	60.47	odd	4
900.2.k.n.307.5		12	15.2	even	4
900.2.k.n.343.2		12	3.2	odd	2
900.2.k.n.343.5		12	12.11	even	2
960.2.w.g.127.2		12	40.3	even	4
960.2.w.g.127.5		12	40.13	odd	4
960.2.w.g.703.2		12	40.29	even	2
960.2.w.g.703.5		12	40.19	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 300 = 2^{2} \cdot 3 \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	300.j (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.19252 + 0.760198i) q^{2} +(-0.707107 + 0.707107i) q^{3} +(0.844199 + 1.81310i) q^{4} +(-1.38078 + 0.305697i) q^{6} +(0.611393 + 0.611393i) q^{7} +(-0.371591 + 2.80391i) q^{8} -1.00000i q^{9} +O(q^{10})\)	\(q+(1.19252 + 0.760198i) q^{2} +(-0.707107 + 0.707107i) q^{3} +(0.844199 + 1.81310i) q^{4} +(-1.38078 + 0.305697i) q^{6} +(0.611393 + 0.611393i) q^{7} +(-0.371591 + 2.80391i) q^{8} -1.00000i q^{9} +5.12822i q^{11} +(-1.87899 - 0.685116i) q^{12} +(-1.76156 - 1.76156i) q^{13} +(0.264318 + 1.19388i) q^{14} +(-2.57466 + 3.06123i) q^{16} +(3.76156 - 3.76156i) q^{17} +(0.760198 - 1.19252i) q^{18} +1.22279 q^{19} -0.864641 q^{21} +(-3.89846 + 6.11549i) q^{22} +(-1.07700 + 1.07700i) q^{23} +(-1.71991 - 2.24542i) q^{24} +(-0.761557 - 3.43982i) q^{26} +(0.707107 + 0.707107i) q^{27} +(-0.592379 + 1.62465i) q^{28} +0.864641i q^{29} -7.81086i q^{31} +(-5.39747 + 1.69333i) q^{32} +(-3.62620 - 3.62620i) q^{33} +(7.34525 - 1.62620i) q^{34} +(1.81310 - 0.844199i) q^{36} +(1.76156 - 1.76156i) q^{37} +(1.45820 + 0.929560i) q^{38} +2.49122 q^{39} +5.52311 q^{41} +(-1.03110 - 0.657298i) q^{42} +(6.20522 - 6.20522i) q^{43} +(-9.29797 + 4.32924i) q^{44} +(-2.10308 + 0.465611i) q^{46} +(2.29979 + 2.29979i) q^{47} +(-0.344061 - 3.98518i) q^{48} -6.25240i q^{49} +5.31965i q^{51} +(1.70677 - 4.68098i) q^{52} +(2.62620 + 2.62620i) q^{53} +(0.305697 + 1.38078i) q^{54} +(-1.94148 + 1.48710i) q^{56} +(-0.864641 + 0.864641i) q^{57} +(-0.657298 + 1.03110i) q^{58} +0.528636 q^{59} +4.98168 q^{61} +(5.93780 - 9.31460i) q^{62} +(0.611393 - 0.611393i) q^{63} +(-7.72384 - 2.08382i) q^{64} +(-1.56768 - 7.08093i) q^{66} +(-6.20522 - 6.20522i) q^{67} +(9.99558 + 3.64457i) q^{68} -1.52311i q^{69} -8.10243i q^{71} +(2.80391 + 0.371591i) q^{72} +(2.25240 + 2.25240i) q^{73} +(3.43982 - 0.761557i) q^{74} +(1.03228 + 2.21703i) q^{76} +(-3.13536 + 3.13536i) q^{77} +(2.97082 + 1.89382i) q^{78} -15.9133 q^{79} -1.00000 q^{81} +(6.58641 + 4.19866i) q^{82} +(-7.95665 + 7.95665i) q^{83} +(-0.729929 - 1.56768i) q^{84} +(12.1170 - 2.68264i) q^{86} +(-0.611393 - 0.611393i) q^{87} +(-14.3791 - 1.90560i) q^{88} +7.25240i q^{89} -2.15401i q^{91} +(-2.86192 - 1.04351i) q^{92} +(5.52311 + 5.52311i) q^{93} +(0.994247 + 4.49084i) q^{94} +(2.61922 - 5.01395i) q^{96} +(-0.793833 + 0.793833i) q^{97} +(4.75306 - 7.45610i) q^{98} +5.12822 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 4 q^{6} + 12 q^{8}+O(q^{10}) \) 12 * q - 4 * q^6 + 12 * q^8	\( 12 q - 4 q^{6} + 12 q^{8} + 8 q^{12} + 4 q^{13} + 12 q^{16} + 20 q^{17} - 12 q^{22} + 16 q^{26} + 4 q^{28} - 20 q^{32} - 8 q^{33} + 4 q^{36} - 4 q^{37} - 16 q^{38} + 16 q^{41} - 20 q^{42} - 40 q^{46} - 16 q^{48} + 8 q^{52} - 4 q^{53} - 64 q^{56} + 20 q^{58} - 32 q^{61} + 56 q^{62} - 24 q^{66} + 16 q^{68} + 12 q^{72} - 44 q^{73} + 8 q^{76} - 48 q^{77} + 24 q^{78} - 12 q^{81} - 16 q^{82} + 64 q^{86} - 60 q^{88} - 56 q^{92} + 16 q^{93} + 44 q^{96} + 20 q^{97} - 24 q^{98}+O(q^{100}) \) 12 * q - 4 * q^6 + 12 * q^8 + 8 * q^12 + 4 * q^13 + 12 * q^16 + 20 * q^17 - 12 * q^22 + 16 * q^26 + 4 * q^28 - 20 * q^32 - 8 * q^33 + 4 * q^36 - 4 * q^37 - 16 * q^38 + 16 * q^41 - 20 * q^42 - 40 * q^46 - 16 * q^48 + 8 * q^52 - 4 * q^53 - 64 * q^56 + 20 * q^58 - 32 * q^61 + 56 * q^62 - 24 * q^66 + 16 * q^68 + 12 * q^72 - 44 * q^73 + 8 * q^76 - 48 * q^77 + 24 * q^78 - 12 * q^81 - 16 * q^82 + 64 * q^86 - 60 * q^88 - 56 * q^92 + 16 * q^93 + 44 * q^96 + 20 * q^97 - 24 * q^98

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