LMFDB - Embedded newform 300.2.j.d.7.2

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			7.2
Root			$-0.760198 + 1.19252i$ of defining polynomial
Character	$\chi$	$=$	300.7
Dual form			300.2.j.d.43.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.760198 + 1.19252i) q^{2} +(0.707107 + 0.707107i) q^{3} +(-0.844199 - 1.81310i) q^{4} +(-1.38078 + 0.305697i) q^{6} +(-0.611393 + 0.611393i) q^{7} +(2.80391 + 0.371591i) q^{8} +1.00000i q^{9} +O(q^{10})$	\(q+(-0.760198 + 1.19252i) 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} +(2.80391 + 0.371591i) q^{8} +1.00000i q^{9} +5.12822i q^{11} +(0.685116 - 1.87899i) 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} +(-1.19252 - 0.760198i) q^{18} -1.22279 q^{19} -0.864641 q^{21} +(-6.11549 - 3.89846i) 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} +(1.62465 + 0.592379i) q^{28} -0.864641i q^{29} -7.81086i q^{31} +(-1.69333 - 5.39747i) 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} +(0.929560 - 1.45820i) q^{38} -2.49122 q^{39} +5.52311 q^{41} +(0.657298 - 1.03110i) 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} +(-3.98518 + 0.344061i) q^{48} +6.25240i q^{49} +5.31965i q^{51} +(4.68098 + 1.70677i) 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} +(1.03110 + 0.657298i) q^{58} -0.528636 q^{59} +4.98168 q^{61} +(9.31460 + 5.93780i) 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} +(3.64457 - 9.99558i) q^{68} +1.52311i q^{69} -8.10243i q^{71} +(-0.371591 + 2.80391i) 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} +(1.89382 - 2.97082i) q^{78} +15.9133 q^{79} -1.00000 q^{81} +(-4.19866 + 6.58641i) 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} +(-1.90560 + 14.3791i) q^{88} -7.25240i q^{89} -2.15401i q^{91} +(1.04351 - 2.86192i) 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} +(-7.45610 - 4.75306i) 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 $\left(\mathbb{Z}/300\mathbb{Z}\right)^\times$.

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

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 $

$2$	−0.760198	+	1.19252i	−0.537541	+	0.843238i
$2$	−0.760198	+	1.19252i	−0.537541	+	0.843238i
$3$	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	$-0.802247\pi$
$7$	−0.611393	+	0.611393i	−0.231085	+	0.231085i	0.582060	+	0.813145i	$0.302247\pi$
$8$	2.80391	+	0.371591i	0.991332	+	0.131377i
$9$			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	$0.718701\pi$
$12$	0.685116	−	1.87899i	0.197776	−	0.542419i
$13$	−1.76156	+	1.76156i	−0.488568	+	0.488568i	−0.907854	−	0.419286i	$-0.862280\pi$
$13$	−1.76156	+	1.76156i	−0.488568	+	0.488568i	0.419286	+	0.907854i	$0.362280\pi$
$14$	−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	0.996454	−	0.0841421i	$-0.0268150\pi$
$17$	3.76156	+	3.76156i	0.912312	+	0.912312i	−0.0841421	+	0.996454i	$0.526815\pi$
$18$	−1.19252	−	0.760198i	−0.281079	−	0.179180i
$19$	−1.22279			−0.280527			−0.140263	−	0.990114i	$-0.544795\pi$
$19$	−1.22279			−0.280527			−0.140263	+	0.990114i	$0.544795\pi$
$20$		0			0
$21$	−0.864641			−0.188680
$22$	−6.11549	−	3.89846i	−1.30383	−	0.831154i
$23$	1.07700	+	1.07700i	0.224571	+	0.224571i	0.810420	−	0.585849i	$-0.199239\pi$
$23$	1.07700	+	1.07700i	0.224571	+	0.224571i	−0.585849	+	0.810420i	$0.699239\pi$
$24$	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
$28$	1.62465	+	0.592379i	0.307031	+	0.111949i
$29$		−	0.864641i		−	0.160560i	−0.996772	−	0.0802799i	$-0.974419\pi$
$29$		−	0.864641i		−	0.160560i	0.996772	−	0.0802799i	$-0.0255814\pi$
$30$		0			0
$31$		−	7.81086i		−	1.40287i	−0.712732	−	0.701436i	$-0.752543\pi$
$31$		−	7.81086i		−	1.40287i	0.712732	−	0.701436i	$-0.247457\pi$
$32$	−1.69333	−	5.39747i	−0.299341	−	0.954146i
$33$	−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	0.836921	−	0.547323i	$-0.184353\pi$
$37$	1.76156	+	1.76156i	0.289598	+	0.289598i	−0.547323	+	0.836921i	$0.684353\pi$
$38$	0.929560	−	1.45820i	0.150795	−	0.236551i
$39$	−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	$0.358061\pi$
$42$	0.657298	−	1.03110i	0.101423	−	0.159102i
$43$	−6.20522	−	6.20522i	−0.946288	−	0.946288i	0.0523416	−	0.998629i	$-0.483332\pi$
$43$	−6.20522	−	6.20522i	−0.946288	−	0.946288i	−0.998629	+	0.0523416i	$0.983332\pi$
$44$	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	$-0.826231\pi$
$47$	−2.29979	+	2.29979i	−0.335459	+	0.335459i	0.519196	+	0.854655i	$0.326231\pi$
$48$	−3.98518	+	0.344061i	−0.575210	+	0.0496610i
$49$			6.25240i			0.893199i
$50$		0			0
$51$			5.31965i			0.744899i
$52$	4.68098	+	1.70677i	0.649135	+	0.236687i
$53$	2.62620	−	2.62620i	0.360736	−	0.360736i	−0.503348	−	0.864084i	$-0.667899\pi$
$53$	2.62620	−	2.62620i	0.360736	−	0.360736i	0.864084	+	0.503348i	$0.167899\pi$
$54$	−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
$58$	1.03110	+	0.657298i	0.135390	+	0.0863075i
$59$	−0.528636			−0.0688225			−0.0344113	−	0.999408i	$-0.510956\pi$
$59$	−0.528636			−0.0688225			−0.0344113	+	0.999408i	$0.510956\pi$
$60$		0			0
$61$	4.98168			0.637838			0.318919	−	0.947782i	$-0.396680\pi$
$61$	4.98168			0.637838			0.318919	+	0.947782i	$0.396680\pi$
$62$	9.31460	+	5.93780i	1.18295	+	0.754101i
$63$	−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	$-0.569916\pi$
$67$	6.20522	−	6.20522i	0.758089	−	0.758089i	0.975974	+	0.217886i	$0.0699160\pi$
$68$	3.64457	−	9.99558i	0.441969	−	1.21214i
$69$			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	$-0.159650\pi$
$72$	−0.371591	+	2.80391i	−0.0437924	+	0.330444i
$73$	2.25240	−	2.25240i	0.263623	−	0.263623i	−0.562901	−	0.826524i	$-0.690315\pi$
$73$	2.25240	−	2.25240i	0.263623	−	0.263623i	0.826524	+	0.562901i	$0.190315\pi$
$74$	−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
$78$	1.89382	−	2.97082i	0.214433	−	0.336379i
$79$	15.9133			1.79039			0.895193	−	0.445680i	$-0.147038\pi$
$79$	15.9133			1.79039			0.895193	+	0.445680i	$0.147038\pi$
$80$		0			0
$81$	−1.00000			−0.111111
$82$	−4.19866	+	6.58641i	−0.463664	+	0.727348i
$83$	7.95665	+	7.95665i	0.873355	+	0.873355i	0.992836	−	0.119481i	$-0.0381231\pi$
$83$	7.95665	+	7.95665i	0.873355	+	0.873355i	−0.119481	+	0.992836i	$0.538123\pi$
$84$	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
$88$	−1.90560	+	14.3791i	−0.203138	+	1.53281i
$89$		−	7.25240i		−	0.768752i	−0.923177	−	0.384376i	$-0.874417\pi$
$89$		−	7.25240i		−	0.768752i	0.923177	−	0.384376i	$-0.125583\pi$
$90$		0			0
$91$		−	2.15401i		−	0.225801i
$92$	1.04351	−	2.86192i	0.108793	−	0.298376i
$93$	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	0.665657	−	0.746258i	$-0.268152\pi$
$97$	−0.793833	−	0.793833i	−0.0806015	−	0.0806015i	−0.746258	+	0.665657i	$0.768152\pi$
$98$	−7.45610	−	4.75306i	−0.753179	−	0.480131i
$99$	−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	$0.667896\pi$
$102$	−6.34377	−	4.04398i	−0.628127	−	0.400414i
$103$	−3.82267	−	3.82267i	−0.376659	−	0.376659i	0.493236	−	0.869895i	$-0.335814\pi$
$103$	−3.82267	−	3.82267i	−0.376659	−	0.376659i	−0.869895	+	0.493236i	$0.835814\pi$
$104$	−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	$-0.872951\pi$
$107$	−5.51107	+	5.51107i	−0.532775	+	0.532775i	0.388622	+	0.921397i	$0.372951\pi$
$108$	1.87899	+	0.685116i	0.180806	+	0.0659253i
$109$		−	7.31695i		−	0.700836i	−0.936593	−	0.350418i	$-0.886039\pi$
$109$		−	7.31695i		−	0.700836i	0.936593	−	0.350418i	$-0.113961\pi$
$110$		0			0
$111$			2.49122i			0.236456i
$112$	−0.297490	−	3.44575i	−0.0281101	−	0.325592i
$113$	0.509161	−	0.509161i	0.0478978	−	0.0478978i	−0.682752	−	0.730650i	$-0.739217\pi$
$113$	0.509161	−	0.509161i	0.0478978	−	0.0478978i	0.730650	+	0.682752i	$0.239217\pi$
$114$	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
$118$	0.401868	−	0.630408i	0.0369949	−	0.0580337i
$119$	−4.59958			−0.421643
$120$		0			0
$121$	−15.2986			−1.39078
$122$	−3.78706	+	5.94074i	−0.342864	+	0.537849i
$123$	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	$-0.594243\pi$
$127$	7.49103	−	7.49103i	0.664722	−	0.664722i	0.956489	+	0.291767i	$0.0942433\pi$
$128$	−8.35664	+	7.62671i	−0.738629	+	0.674112i
$129$		−	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	$0.790593\pi$
$132$	9.63589	+	3.51342i	0.838696	+	0.305804i
$133$	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	0.340869	−	0.940111i	$-0.389279\pi$
$137$	−7.01395	−	7.01395i	−0.599242	−	0.599242i	−0.940111	+	0.340869i	$0.889279\pi$
$138$	−1.81634	−	1.15787i	−0.154617	−	0.0985643i
$139$	−2.28006			−0.193392			−0.0966960	−	0.995314i	$-0.530827\pi$
$139$	−2.28006			−0.193392			−0.0966960	+	0.995314i	$0.530827\pi$
$140$		0			0
$141$	−3.25240			−0.273901
$142$	9.66229	+	6.15945i	0.810842	+	0.516889i
$143$	−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
$148$	1.70677	−	4.68098i	0.140296	−	0.384774i
$149$			10.1170i			0.828820i	0.910090	+	0.414410i	$0.136012\pi$
$149$			10.1170i			0.828820i	−0.910090	+	0.414410i	$0.863988\pi$
$150$		0			0
$151$		−	7.93691i		−	0.645897i	−0.946417	−	0.322948i	$-0.895326\pi$
$151$		−	7.93691i		−	0.645897i	0.946417	−	0.322948i	$-0.104674\pi$
$152$	−3.42859	−	0.454377i	−0.278095	−	0.0368548i
$153$	−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	0.249089	−	0.968481i	$-0.419869\pi$
$157$	−9.01395	−	9.01395i	−0.719392	−	0.719392i	−0.968481	+	0.249089i	$0.919869\pi$
$158$	−12.0972	+	18.9769i	−0.962405	+	1.50972i
$159$	3.71400			0.294540
$160$		0			0
$161$	−1.31695			−0.103790
$162$	0.760198	−	1.19252i	0.0597268	−	0.0936931i
$163$	13.0849	+	13.0849i	1.02489	+	1.02489i	0.999682	+	0.0252033i	$0.00802331\pi$
$163$	13.0849	+	13.0849i	1.02489	+	1.02489i	0.0252033	+	0.999682i	$0.491977\pi$
$164$	−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	$-0.537076\pi$
$167$	11.3334	−	11.3334i	0.877008	−	0.877008i	0.993224	+	0.116216i	$0.0370765\pi$
$168$	−2.42438	−	0.321293i	−0.187045	−	0.0247883i
$169$			6.79383i			0.522603i
$170$		0			0
$171$		−	1.22279i		−	0.0935088i
$172$	−6.01224	+	16.4891i	−0.458429	+	1.25728i
$173$	−7.96772	+	7.96772i	−0.605775	+	0.605775i	−0.941839	−	0.336064i	$-0.890904\pi$
$173$	−7.96772	+	7.96772i	−0.605775	+	0.605775i	0.336064	+	0.941839i	$0.390904\pi$
$174$	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
$178$	8.64861	+	5.51325i	0.648241	+	0.413236i
$179$	−12.6475			−0.945320			−0.472660	−	0.881245i	$-0.656706\pi$
$179$	−12.6475			−0.945320			−0.472660	+	0.881245i	$0.656706\pi$
$180$		0			0
$181$	7.72928			0.574513			0.287256	−	0.957854i	$-0.407257\pi$
$181$	7.72928			0.574513			0.287256	+	0.957854i	$0.407257\pi$
$182$	2.56869	+	1.63747i	0.190404	+	0.121378i
$183$	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
$188$	6.11123	+	2.22827i	0.445707	+	0.162513i
$189$		−	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	$0.917962\pi$
$192$	3.98810	+	6.93506i	0.287816	+	0.500495i
$193$	11.5048	−	11.5048i	0.828133	−	0.828133i	−0.159125	−	0.987258i	$-0.550867\pi$
$193$	11.5048	−	11.5048i	0.828133	−	0.828133i	0.987258	+	0.159125i	$0.0508674\pi$
$194$	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	0.368358	−	0.929684i	$-0.379920\pi$
$197$	−7.87859	−	7.87859i	−0.561327	−	0.561327i	−0.929684	+	0.368358i	$0.879920\pi$
$198$	3.89846	−	6.11549i	0.277051	−	0.434609i
$199$	−11.4792			−0.813741			−0.406870	−	0.913486i	$-0.633380\pi$
$199$	−11.4792			−0.813741			−0.406870	+	0.913486i	$0.633380\pi$
$200$		0			0
$201$	8.77551			0.618977
$202$	7.69095	−	12.0648i	0.541133	−	0.848873i
$203$	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
$208$	−0.857132	−	9.92794i	−0.0594314	−	0.688379i
$209$		−	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	$0.939469\pi$
$212$	−6.97859	−	2.54452i	−0.479292	−	0.174759i
$213$	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
$218$	8.72559	+	5.56233i	0.590972	+	0.376728i
$219$	3.18537			0.215247
$220$		0			0
$221$	−13.2524			−0.891453
$222$	−2.97082	−	1.89382i	−0.199389	−	0.127105i
$223$	−10.8678	−	10.8678i	−0.727764	−	0.727764i	0.242410	−	0.970174i	$-0.422062\pi$
$223$	−10.8678	−	10.8678i	−0.727764	−	0.727764i	−0.970174	+	0.242410i	$0.922062\pi$
$224$	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	$-0.674872\pi$
$227$	4.98244	−	4.98244i	0.330696	−	0.330696i	0.852851	+	0.522155i	$0.174872\pi$
$228$	−0.837751	+	2.29761i	−0.0554814	+	0.152163i
$229$		−	25.7572i		−	1.70208i	−0.525098	−	0.851041i	$-0.675972\pi$
$229$		−	25.7572i		−	1.70208i	0.525098	−	0.851041i	$-0.324028\pi$
$230$		0			0
$231$		−	4.43407i		−	0.291740i
$232$	0.321293	−	2.42438i	0.0210939	−	0.159168i
$233$	0.715328	−	0.715328i	0.0468627	−	0.0468627i	−0.683287	−	0.730150i	$-0.739450\pi$
$233$	0.715328	−	0.715328i	0.0468627	−	0.0468627i	0.730150	+	0.683287i	$0.239450\pi$
$234$	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
$238$	3.49659	−	5.48509i	0.226650	−	0.355545i
$239$	26.9354			1.74231			0.871154	−	0.491009i	$-0.163372\pi$
$239$	26.9354			1.74231			0.871154	+	0.491009i	$0.163372\pi$
$240$		0			0
$241$	14.0925			0.907775			0.453887	−	0.891059i	$-0.350037\pi$
$241$	14.0925			0.907775			0.453887	+	0.891059i	$0.350037\pi$
$242$	11.6300	−	18.2439i	0.747603	−	1.17276i
$243$	−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
$248$	2.90245	−	21.9010i	0.184306	−	1.39071i
$249$			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	$-0.183210\pi$
$252$	−0.592379	+	1.62465i	−0.0373164	+	0.102344i
$253$	−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	0.998103	−	0.0615588i	$-0.0196072\pi$
$257$	15.0140	+	15.0140i	0.936545	+	0.936545i	−0.0615588	+	0.998103i	$0.519607\pi$
$258$	10.4650	+	6.67112i	0.651520	+	0.415326i
$259$	−2.15401			−0.133844
$260$		0			0
$261$	0.864641			0.0535199
$262$	−16.6909	−	10.6400i	−1.03117	−	0.657341i
$263$	−6.73386	−	6.73386i	−0.415228	−	0.415228i	0.468327	−	0.883555i	$-0.344857\pi$
$263$	−6.73386	−	6.73386i	−0.415228	−	0.415228i	−0.883555	+	0.468327i	$0.844857\pi$
$264$	−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
$268$	−16.4891	−	6.01224i	−1.00723	−	0.367256i
$269$			25.7047i			1.56724i	0.621238	+	0.783622i	$0.286630\pi$
$269$			25.7047i			1.56724i	−0.621238	+	0.783622i	$0.713370\pi$
$270$		0			0
$271$			0.931222i			0.0565677i	0.999600	+	0.0282839i	$0.00900423\pi$
$271$			0.931222i			0.0565677i	−0.999600	+	0.0282839i	$0.990996\pi$
$272$	−21.1997	+	1.83029i	−1.28542	+	0.110977i
$273$	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	0.909277	+	0.416190i	$0.136635\pi$
$277$	22.0602	+	22.0602i	1.32547	+	1.32547i	0.416190	+	0.909277i	$0.363365\pi$
$278$	1.73330	−	2.71901i	0.103956	−	0.163075i
$279$	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	$0.417726\pi$
$282$	2.47246	−	3.87854i	0.147233	−	0.230964i
$283$	11.5705	+	11.5705i	0.687796	+	0.687796i	0.961744	−	0.273949i	$-0.0883299\pi$
$283$	11.5705	+	11.5705i	0.687796	+	0.687796i	−0.273949	+	0.961744i	$0.588330\pi$
$284$	−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
$288$	5.39747	−	1.69333i	0.318049	−	0.0997803i
$289$			11.2986i			0.664625i
$290$		0			0
$291$		−	1.12265i		−	0.0658108i
$292$	−5.98529	−	2.18235i	−0.350262	−	0.127712i
$293$	−12.8969	+	12.8969i	−0.753446	+	0.753446i	−0.975121	−	0.221675i	$-0.928848\pi$
$293$	−12.8969	+	12.8969i	−0.753446	+	0.753446i	0.221675	+	0.975121i	$0.428848\pi$
$294$	−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
$298$	−12.0648	−	7.69095i	−0.698892	−	0.445525i
$299$	−3.79441			−0.219436
$300$		0			0
$301$	7.58767			0.437346
$302$	9.46491	+	6.03362i	0.544644	+	0.347196i
$303$	−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	$-0.729360\pi$
$307$	1.60564	−	1.60564i	0.0916387	−	0.0916387i	0.751440	+	0.659801i	$0.229360\pi$
$308$	−3.03785	+	8.33158i	−0.173098	+	0.474736i
$309$		−	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	$-0.185561\pi$
$312$	−6.98516	−	0.925715i	−0.395457	−	0.0524083i
$313$	−17.7110	+	17.7110i	−1.00108	+	1.00108i	−0.00108322	+	0.999999i	$0.500345\pi$
$313$	−17.7110	+	17.7110i	−1.00108	+	1.00108i	−0.999999	+	0.00108322i	$0.999655\pi$
$314$	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	0.891170	−	0.453670i	$-0.149885\pi$
$317$	7.78946	+	7.78946i	0.437500	+	0.437500i	−0.453670	+	0.891170i	$0.649885\pi$
$318$	−2.82338	+	4.42902i	−0.158327	+	0.248367i
$319$	4.43407			0.248260
$320$		0			0
$321$	−7.79383			−0.435009
$322$	1.00114	−	1.57048i	0.0557914	−	0.0875196i
$323$	−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
$328$	15.4863	+	2.05234i	0.855089	+	0.113322i
$329$		−	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	$0.663336\pi$
$332$	7.70919	−	21.1432i	0.423097	−	1.16038i
$333$	−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	−0.999437	−	0.0335632i	$-0.989314\pi$
$337$	−18.9634	−	18.9634i	−1.03300	−	1.03300i	−0.0335632	−	0.999437i	$-0.510686\pi$
$338$	−8.10177	−	5.16466i	−0.440678	−	0.280920i
$339$	0.720062			0.0391084
$340$		0			0
$341$	40.0558			2.16914
$342$	1.45820	+	0.929560i	0.0788502	+	0.0502648i
$343$	−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	$-0.844664\pi$
$347$	−7.71957	+	7.71957i	−0.414408	+	0.414408i	0.468863	+	0.883271i	$0.344664\pi$
$348$	−1.62465	−	0.592379i	−0.0870906	−	0.0317549i
$349$			27.0741i			1.44925i	0.689146	+	0.724623i	$0.257986\pi$
$349$			27.0741i			1.44925i	−0.689146	+	0.724623i	$0.742014\pi$
$350$		0			0
$351$		−	2.49122i		−	0.132971i
$352$	27.6794	−	8.68375i	1.47532	−	0.462846i
$353$	9.96772	−	9.96772i	0.530528	−	0.530528i	−0.390201	−	0.920730i	$-0.627595\pi$
$353$	9.96772	−	9.96772i	0.530528	−	0.530528i	0.920730	+	0.390201i	$0.127595\pi$
$354$	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
$358$	9.61461	−	15.0824i	0.508148	−	0.797129i
$359$	−14.2334			−0.751211			−0.375606	−	0.926780i	$-0.622565\pi$
$359$	−14.2334			−0.751211			−0.375606	+	0.926780i	$0.622565\pi$
$360$		0			0
$361$	−17.5048			−0.921305
$362$	−5.87578	+	9.21731i	−0.308824	+	0.484451i
$363$	−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	$-0.715963\pi$
$367$	2.89145	−	2.89145i	0.150933	−	0.150933i	0.778534	+	0.627602i	$0.215963\pi$
$368$	−6.06988	+	0.524045i	−0.316414	+	0.0273177i
$369$			5.52311i			0.287522i
$370$		0			0
$371$			3.21128i			0.166721i
$372$	−14.6766	−	5.35135i	−0.760944	−	0.277454i
$373$	11.2847	−	11.2847i	0.584298	−	0.584298i	−0.351783	−	0.936081i	$-0.614425\pi$
$373$	11.2847	−	11.2847i	0.584298	−	0.584298i	0.936081	+	0.351783i	$0.114425\pi$
$374$	−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
$378$	1.03110	+	0.657298i	0.0530341	+	0.0338078i
$379$	−15.4562			−0.793932			−0.396966	−	0.917833i	$-0.629937\pi$
$379$	−15.4562			−0.793932			−0.396966	+	0.917833i	$0.629937\pi$
$380$		0			0
$381$	10.5939			0.542743
$382$	−8.40148	−	5.35571i	−0.429857	−	0.274022i
$383$	12.5562	+	12.5562i	0.641593	+	0.641593i	0.950947	−	0.309354i	$-0.100113\pi$
$383$	12.5562	+	12.5562i	0.641593	+	0.641593i	−0.309354	+	0.950947i	$0.600113\pi$
$384$	−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
$388$	−0.769144	+	2.10945i	−0.0390474	+	0.107091i
$389$		−	5.16327i		−	0.261788i	−0.991396	−	0.130894i	$-0.958215\pi$
$389$		−	5.16327i		−	0.261788i	0.991396	−	0.130894i	$-0.0417848\pi$
$390$		0			0
$391$			8.10243i			0.409757i
$392$	−2.32333	+	17.5312i	−0.117346	+	0.885458i
$393$	−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	0.788646	−	0.614847i	$-0.210782\pi$
$397$	3.46293	+	3.46293i	0.173800	+	0.173800i	−0.614847	+	0.788646i	$0.710782\pi$
$398$	8.72648	−	13.6892i	0.437419	−	0.686177i
$399$	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	$0.472185\pi$
$402$	−6.67112	+	10.4650i	−0.332725	+	0.521945i
$403$	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
$408$	−1.97673	+	14.9158i	−0.0978629	+	0.738443i
$409$		−	14.8034i		−	0.731982i	−0.930618	−	0.365991i	$-0.880730\pi$
$409$		−	14.8034i		−	0.731982i	0.930618	−	0.365991i	$-0.119270\pi$
$410$		0			0
$411$		−	9.91923i		−	0.489279i
$412$	−3.70379	+	10.1580i	−0.182473	+	0.500448i
$413$	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
$418$	7.47795	+	4.76699i	0.365758	+	0.233161i
$419$	19.0701			0.931634			0.465817	−	0.884881i	$-0.345760\pi$
$419$	19.0701			0.931634			0.465817	+	0.884881i	$0.345760\pi$
$420$		0			0
$421$	−20.8034			−1.01390			−0.506948	−	0.861976i	$-0.669226\pi$
$421$	−20.8034			−1.01390			−0.506948	+	0.861976i	$0.669226\pi$
$422$	−6.54852	−	4.17450i	−0.318777	−	0.203212i
$423$	−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
$428$	14.6446	+	5.33968i	0.707872	+	0.258103i
$429$		−	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	$-0.120373\pi$
$432$	−0.344061	−	3.98518i	−0.0165537	−	0.191737i
$433$	−16.2803	+	16.2803i	−0.782381	+	0.782381i	−0.980232	−	0.197851i	$-0.936604\pi$
$433$	−16.2803	+	16.2803i	−0.782381	+	0.782381i	0.197851	+	0.980232i	$0.436604\pi$
$434$	−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
$438$	−2.42151	+	3.79861i	−0.115704	+	0.181505i
$439$	−24.6554			−1.17674			−0.588368	−	0.808593i	$-0.700230\pi$
$439$	−24.6554			−1.17674			−0.588368	+	0.808593i	$0.700230\pi$
$440$		0			0
$441$	−6.25240			−0.297733
$442$	10.0744	−	15.8037i	0.479192	−	0.751706i
$443$	1.77116	+	1.77116i	0.0841501	+	0.0841501i	0.747929	−	0.663779i	$-0.231048\pi$
$443$	1.77116	+	1.77116i	0.0841501	+	0.0841501i	−0.663779	+	0.747929i	$0.731048\pi$
$444$	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
$448$	−5.99634	+	3.44827i	−0.283300	+	0.162916i
$449$		−	33.1512i		−	1.56450i	−0.622963	−	0.782251i	$-0.714071\pi$
$449$		−	33.1512i		−	1.56450i	0.622963	−	0.782251i	$-0.285929\pi$
$450$		0			0
$451$			28.3237i			1.33371i
$452$	−1.35299	−	0.493326i	−0.0636394	−	0.0232041i
$453$	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	0.860504	−	0.509444i	$-0.170149\pi$
$457$	7.50479	+	7.50479i	0.351059	+	0.351059i	−0.509444	+	0.860504i	$0.670149\pi$
$458$	30.7159	+	19.5806i	1.43526	+	0.914939i
$459$	−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	$0.716643\pi$
$462$	5.28771	+	3.37077i	0.246006	+	0.156822i
$463$	27.7123	+	27.7123i	1.28790	+	1.28790i	0.936059	+	0.351843i	$0.114445\pi$
$463$	27.7123	+	27.7123i	1.28790	+	1.28790i	0.351843	+	0.936059i	$0.385555\pi$
$464$	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	$-0.770932\pi$
$467$	−2.00823	+	2.00823i	−0.0929296	+	0.0929296i	0.659114	+	0.752043i	$0.270932\pi$
$468$	−1.70677	+	4.68098i	−0.0788956	+	0.216378i
$469$			7.58767i			0.350366i
$470$		0			0
$471$		−	12.7477i		−	0.587381i
$472$	−1.48225	−	0.196436i	−0.0682260	−	0.00904172i
$473$	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
$478$	−20.4763	+	32.1210i	−0.936562	+	1.46918i
$479$	13.7593			0.628678			0.314339	−	0.949311i	$-0.398217\pi$
$479$	13.7593			0.628678			0.314339	+	0.949311i	$0.398217\pi$
$480$		0			0
$481$	−6.20617			−0.282977
$482$	−10.7131	+	16.8055i	−0.487966	+	0.765470i
$483$	−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	−0.108671	+	0.994078i	$0.534660\pi$
$487$	−24.3355	+	24.3355i	−1.10275	+	1.10275i	−0.994078	+	0.108671i	$0.965340\pi$
$488$	13.9682	+	1.85115i	0.632310	+	0.0837975i
$489$			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	$0.773957\pi$
$492$	3.78397	−	10.3779i	0.170595	−	0.467872i
$493$	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
$498$	−13.4187	−	8.55405i	−0.601306	−	0.383316i
$499$	12.5365			0.561211			0.280605	−	0.959823i	$-0.409465\pi$
$499$	12.5365			0.561211			0.280605	+	0.959823i	$0.409465\pi$
$500$		0			0
$501$	16.0279			0.716074
$502$	20.5675	+	13.1112i	0.917972	+	0.585182i
$503$	−9.01392	−	9.01392i	−0.401911	−	0.401911i	0.476995	−	0.878906i	$-0.341726\pi$
$503$	−9.01392	−	9.01392i	−0.401911	−	0.401911i	−0.878906	+	0.476995i	$0.841726\pi$
$504$	−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
$508$	−19.9059	−	7.25806i	−0.883182	−	0.322025i
$509$		−	22.5448i		−	0.999279i	−0.866233	−	0.499640i	$-0.833466\pi$
$509$		−	22.5448i		−	0.999279i	0.866233	−	0.499640i	$-0.166534\pi$
$510$		0			0
$511$			2.75420i			0.121839i
$512$	20.8826	+	8.71295i	0.922891	+	0.385062i
$513$	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
$518$	1.63747	−	2.56869i	0.0719464	−	0.112862i
$519$	−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	$0.635908\pi$
$522$	−0.657298	+	1.03110i	−0.0287692	+	0.0451300i
$523$	−21.8269	−	21.8269i	−0.954426	−	0.954426i	0.0445800	−	0.999006i	$-0.485805\pi$
$523$	−21.8269	−	21.8269i	−0.954426	−	0.954426i	−0.999006	+	0.0445800i	$0.985805\pi$
$524$	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
$528$	−1.76442	−	20.4368i	−0.0767866	−	0.889400i
$529$		−	20.6801i		−	0.899136i
$530$		0			0
$531$		−	0.528636i		−	0.0229408i
$532$	−1.98661	−	0.724353i	−0.0861303	−	0.0314047i
$533$	−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
$538$	−30.6533	−	19.5407i	−1.32156	−	0.842457i
$539$	−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	$0.445969\pi$
$542$	−1.11050	−	0.707913i	−0.0477000	−	0.0304075i
$543$	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	$-0.569000\pi$
$547$	17.8105	−	17.8105i	0.761522	−	0.761522i	0.976597	+	0.215076i	$0.0689998\pi$
$548$	−6.79582	+	18.6382i	−0.290303	+	0.796183i
$549$			4.98168i			0.212613i
$550$		0			0
$551$			1.05727i			0.0450413i
$552$	−0.565976	+	4.27068i	−0.0240895	+	0.181772i
$553$	−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	0.0111112	−	0.999938i	$-0.496463\pi$
$557$	−23.3372	−	23.3372i	−0.988827	−	0.988827i	−0.999938	+	0.0111112i	$0.996463\pi$
$558$	−5.93780	+	9.31460i	−0.251367	+	0.394318i
$559$	21.8617			0.924652
$560$		0			0
$561$	−27.2803			−1.15178
$562$	−6.51439	+	10.2191i	−0.274793	+	0.431067i
$563$	−5.27400	−	5.27400i	−0.222273	−	0.222273i	0.587182	−	0.809455i	$-0.300237\pi$
$563$	−5.27400	−	5.27400i	−0.222273	−	0.222273i	−0.809455	+	0.587182i	$0.800237\pi$
$564$	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
$568$	3.01079	−	22.7185i	0.126330	−	0.953247i
$569$			28.5606i			1.19732i	0.801002	+	0.598661i	$0.204301\pi$
$569$			28.5606i			1.19732i	−0.801002	+	0.598661i	$0.795699\pi$
$570$		0			0
$571$		−	32.2837i		−	1.35103i	−0.737347	−	0.675515i	$-0.763922\pi$
$571$		−	32.2837i		−	1.35103i	0.737347	−	0.675515i	$-0.236078\pi$
$572$	−8.75270	+	24.0051i	−0.365969	+	1.00370i
$573$	−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	−0.990949	−	0.134237i	$-0.957142\pi$
$577$	−27.0279	−	27.0279i	−1.12519	−	1.12519i	−0.134237	−	0.990949i	$-0.542858\pi$
$578$	−13.4738	−	8.58919i	−0.560437	−	0.357263i
$579$	16.2702			0.676168
$580$		0			0
$581$	−9.72928			−0.403639
$582$	1.33878	+	0.853435i	0.0554942	+	0.0353760i
$583$	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	$-0.583076\pi$
$587$	17.1558	−	17.1558i	0.708096	−	0.708096i	0.966135	+	0.258039i	$0.0830761\pi$
$588$	11.7482	+	4.28362i	0.484488	+	0.176653i
$589$			9.55102i			0.393543i
$590$		0			0
$591$		−	11.1420i		−	0.458321i
$592$	−9.92794	+	0.857132i	−0.408036	+	0.0352279i
$593$	21.5833	−	21.5833i	0.886320	−	0.886320i	−0.107848	−	0.994167i	$-0.534396\pi$
$593$	21.5833	−	21.5833i	0.886320	−	0.886320i	0.994167	+	0.107848i	$0.0343959\pi$
$594$	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
$598$	2.88450	−	4.52490i	0.117956	−	0.185037i
$599$	23.7636			0.970955			0.485478	−	0.874249i	$-0.338646\pi$
$599$	23.7636			0.970955			0.485478	+	0.874249i	$0.338646\pi$
$600$		0			0
$601$	22.1695			0.904314			0.452157	−	0.891938i	$-0.350655\pi$
$601$	22.1695			0.904314			0.452157	+	0.891938i	$0.350655\pi$
$602$	−5.76813	+	9.04843i	−0.235091	+	0.368786i
$603$	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	$-0.663489\pi$
$607$	9.35348	−	9.35348i	0.379646	−	0.379646i	0.870974	+	0.491328i	$0.163489\pi$
$608$	2.07058	+	6.59995i	0.0839731	+	0.267663i
$609$			0.747604i			0.0302944i
$610$		0			0
$611$		−	8.10243i		−	0.327789i
$612$	9.99558	+	3.64457i	0.404047	+	0.147323i
$613$	24.1247	−	24.1247i	0.974389	−	0.974389i	−0.0252913	−	0.999680i	$-0.508051\pi$
$613$	24.1247	−	24.1247i	0.974389	−	0.974389i	0.999680	+	0.0252913i	$0.00805134\pi$
$614$	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	0.625883	−	0.779917i	$-0.284739\pi$
$617$	−3.82611	−	3.82611i	−0.154033	−	0.154033i	−0.779917	+	0.625883i	$0.784739\pi$
$618$	6.44685	+	4.10969i	0.259330	+	0.165316i
$619$	−30.1297			−1.21101			−0.605507	−	0.795840i	$-0.707029\pi$
$619$	−30.1297			−1.21101			−0.605507	+	0.795840i	$0.707029\pi$
$620$		0			0
$621$	−1.52311			−0.0611205
$622$	23.1541	+	14.7601i	0.928395	+	0.591826i
$623$	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
$628$	−8.73362	+	23.9528i	−0.348509	+	0.955819i
$629$			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	$-0.141256\pi$
$632$	44.6195	+	5.91324i	1.77487	+	0.235216i
$633$	−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
$638$	−3.37077	+	5.28771i	−0.133450	+	0.209342i
$639$	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	$0.0951370\pi$
$642$	5.92485	−	9.29429i	0.233835	−	0.366816i
$643$	−23.3413	−	23.3413i	−0.920491	−	0.920491i	0.0765729	−	0.997064i	$-0.475602\pi$
$643$	−23.3413	−	23.3413i	−0.920491	−	0.920491i	−0.997064	+	0.0765729i	$0.975602\pi$
$644$	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	−0.332501	+	0.943103i	$0.607892\pi$
$647$	−32.4465	+	32.4465i	−1.27560	+	1.27560i	−0.943103	+	0.332501i	$0.892108\pi$
$648$	−2.80391	−	0.371591i	−0.110148	−	0.0145975i
$649$		−	2.71096i		−	0.106414i
$650$		0			0
$651$			6.75359i			0.264694i
$652$	12.6779	−	34.7704i	0.496506	−	1.36171i
$653$	−18.4725	+	18.4725i	−0.722885	+	0.722885i	−0.969192	−	0.246307i	$-0.920783\pi$
$653$	−18.4725	+	18.4725i	−0.722885	+	0.722885i	0.246307	+	0.969192i	$0.420783\pi$
$654$	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
$658$	3.35355	+	2.13779i	0.130735	+	0.0833399i
$659$	47.5028			1.85045			0.925223	−	0.379423i	$-0.123878\pi$
$659$	47.5028			1.85045			0.925223	+	0.379423i	$0.123878\pi$
$660$		0			0
$661$	−46.1204			−1.79387			−0.896937	−	0.442158i	$-0.854213\pi$
$661$	−46.1204			−1.79387			−0.896937	+	0.442158i	$0.854213\pi$
$662$	−37.8035	−	24.0987i	−1.46927	−	0.936621i
$663$	−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
$668$	−30.1163	−	10.9810i	−1.16524	−	0.424867i
$669$		−	15.3694i		−	0.594217i
$670$		0			0
$671$			25.5471i			0.986236i
$672$	1.46412	+	4.66687i	0.0564797	+	0.180028i
$673$	−3.60599	+	3.60599i	−0.139001	+	0.139001i	−0.773183	−	0.634183i	$-0.781337\pi$
$673$	−3.60599	+	3.60599i	−0.139001	+	0.139001i	0.634183	+	0.773183i	$0.281337\pi$
$674$	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	0.847884	−	0.530182i	$-0.177876\pi$
$677$	8.26635	+	8.26635i	0.317702	+	0.317702i	−0.530182	+	0.847884i	$0.677876\pi$
$678$	−0.547390	+	0.858688i	−0.0210224	+	0.0329777i
$679$	0.970688			0.0372516
$680$		0			0
$681$	7.04623			0.270012
$682$	−30.4503	+	47.7673i	−1.16600	+	1.82910i
$683$	−8.43079	−	8.43079i	−0.322595	−	0.322595i	0.527167	−	0.849762i	$-0.323254\pi$
$683$	−8.43079	−	8.43079i	−0.322595	−	0.322595i	−0.849762	+	0.527167i	$0.823254\pi$
$684$	−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
$688$	34.9719	−	3.01932i	1.33329	−	0.115110i
$689$			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	$-0.136885\pi$
$692$	21.1726	+	7.71993i	0.804862	+	0.293468i
$693$	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
$698$	−32.2864	−	20.5817i	−1.22206	−	0.779029i
$699$	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	$0.635182\pi$
$702$	2.97082	+	1.89382i	0.112126	+	0.0714776i
$703$	−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
$708$	−0.362177	+	0.993303i	−0.0136114	+	0.0373306i
$709$		−	31.7938i		−	1.19404i	−0.802225	−	0.597021i	$-0.796351\pi$
$709$		−	31.7938i		−	1.19404i	0.802225	−	0.597021i	$-0.203649\pi$
$710$		0			0
$711$			15.9133i			0.596795i
$712$	2.69493	−	20.3351i	0.100997	−	0.762089i
$713$	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
$718$	10.8202	−	16.9736i	0.403807	−	0.633450i
$719$	−52.0874			−1.94253			−0.971265	−	0.237999i	$-0.923508\pi$
$719$	−52.0874			−1.94253			−0.971265	+	0.237999i	$0.923508\pi$
$720$		0			0
$721$	4.67432			0.174081
$722$	13.3071	−	20.8748i	0.495239	−	0.776879i
$723$	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	$-0.818398\pi$
$727$	−8.13069	+	8.13069i	−0.301551	+	0.301551i	0.540070	+	0.841620i	$0.318398\pi$
$728$	0.800411	−	6.03965i	0.0296652	−	0.223844i
$729$		−	1.00000i		−	0.0370370i
$730$		0			0
$731$		−	46.6826i		−	1.72662i
$732$	3.41303	−	9.36054i	0.126149	−	0.345976i
$733$	29.9956	−	29.9956i	1.10791	−	1.10791i	0.114489	−	0.993424i	$-0.463477\pi$
$733$	29.9956	−	29.9956i	1.10791	−	1.10791i	0.993424	−	0.114489i	$-0.0365232\pi$
$734$	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
$738$	−6.58641	−	4.19866i	−0.242449	−	0.154555i
$739$	39.4719			1.45200			0.725999	−	0.687696i	$-0.241378\pi$
$739$	39.4719			1.45200			0.725999	+	0.687696i	$0.241378\pi$
$740$		0			0
$741$	3.04623			0.111906
$742$	−3.82951	−	2.44121i	−0.140586	−	0.0896196i
$743$	12.2252	+	12.2252i	0.448499	+	0.448499i	0.894855	−	0.446356i	$-0.147279\pi$
$743$	12.2252	+	12.2252i	0.448499	+	0.448499i	−0.446356	+	0.894855i	$0.647279\pi$
$744$	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
$748$	51.2595	+	18.6902i	1.87423	+	0.683380i
$749$		−	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	$0.823162\pi$
$752$	−1.11902	−	12.9614i	−0.0408066	−	0.472652i
$753$	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	0.937324	−	0.348459i	$-0.113295\pi$
$757$	16.2018	+	16.2018i	0.588864	+	0.588864i	−0.348459	+	0.937324i	$0.613295\pi$
$758$	11.7498	−	18.4318i	0.426771	−	0.669474i
$759$	−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	$0.538439\pi$
$762$	−8.05348	+	12.6334i	−0.291747	+	0.457661i
$763$	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
$768$	9.20720	−	13.0854i	0.332236	−	0.472178i
$769$			29.3449i			1.05820i	0.848559	+	0.529101i	$0.177471\pi$
$769$			29.3449i			1.05820i	−0.848559	+	0.529101i	$0.822529\pi$
$770$		0			0
$771$			21.2329i			0.764686i
$772$	−30.5717	−	11.1470i	−1.10030	−	0.401189i
$773$	−37.5833	+	37.5833i	−1.35178	+	1.35178i	−0.468104	+	0.883674i	$0.655063\pi$
$773$	−37.5833	+	37.5833i	−1.35178	+	1.35178i	−0.883674	+	0.468104i	$0.844937\pi$
$774$	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
$778$	6.15729	+	3.92510i	0.220749	+	0.140722i
$779$	−6.75359			−0.241973
$780$		0			0
$781$	41.5510			1.48681
$782$	−9.66229	−	6.15945i	−0.345523	−	0.220261i
$783$	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	$-0.811303\pi$
$787$	−7.59353	+	7.59353i	−0.270680	+	0.270680i	0.558694	+	0.829374i	$0.311303\pi$
$788$	−7.63357	+	20.9358i	−0.271935	+	0.745806i
$789$		−	9.52311i		−	0.339032i
$790$		0			0
$791$			0.622595i			0.0221369i
$792$	−14.3791	−	1.90560i	−0.510938	−	0.0677126i
$793$	−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	0.0258893	−	0.999665i	$-0.491758\pi$
$797$	−27.4908	−	27.4908i	−0.973775	−	0.973775i	−0.999665	+	0.0258893i	$0.991758\pi$
$798$	−0.803735	+	1.26082i	−0.0284519	+	0.0446324i
$799$	−17.3016			−0.612086
$800$		0			0
$801$	7.25240			0.256251
$802$	−2.65705	+	4.16810i	−0.0938237	+	0.147181i
$803$	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
$808$	−28.3673	−	3.75940i	−0.997957	−	0.132255i
$809$		−	47.7205i		−	1.67776i	−0.544313	−	0.838882i	$-0.683209\pi$
$809$		−	47.7205i		−	1.67776i	0.544313	−	0.838882i	$-0.316791\pi$
$810$		0			0
$811$		−	37.3179i		−	1.31041i	−0.755451	−	0.655205i	$-0.772582\pi$
$811$		−	37.3179i		−	1.31041i	0.755451	−	0.655205i	$-0.227418\pi$
$812$	0.512195	−	1.40474i	0.0179745	−	0.0492968i
$813$	−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
$818$	17.6533	+	11.2535i	0.617235	+	0.393470i
$819$	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	$0.503813\pi$
$822$	11.8289	+	7.54057i	0.412579	+	0.263008i
$823$	−27.2553	−	27.2553i	−0.950059	−	0.950059i	0.0487521	−	0.998811i	$-0.484476\pi$
$823$	−27.2553	−	27.2553i	−0.950059	−	0.950059i	−0.998811	+	0.0487521i	$0.984476\pi$
$824$	−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	−0.0982432	+	0.995162i	$0.531322\pi$
$827$	−31.4437	+	31.4437i	−1.09341	+	1.09341i	−0.995162	+	0.0982432i	$0.968678\pi$
$828$	2.86192	+	1.04351i	0.0994587	+	0.0362645i
$829$		−	0.270718i		−	0.00940243i	−0.999989	−	0.00470122i	$-0.998504\pi$
$829$		−	0.270718i		−	0.00940243i	0.999989	−	0.00470122i	$-0.00149645\pi$
$830$		0			0
$831$			31.1978i			1.08224i
$832$	−17.2767	+	9.93522i	−0.598964	+	0.344442i
$833$	−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
$838$	−14.4970	+	22.7414i	−0.500792	+	0.785589i
$839$	−31.0214			−1.07098			−0.535489	−	0.844542i	$-0.679873\pi$
$839$	−31.0214			−1.07098			−0.535489	+	0.844542i	$0.679873\pi$
$840$		0			0
$841$	28.2524			0.974221
$842$	15.8147	−	24.8085i	0.545011	−	0.854956i
$843$	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
$848$	1.27785	+	14.8010i	0.0438814	+	0.508267i
$849$			16.3632i			0.561583i
$850$		0			0
$851$			3.79441i			0.130071i
$852$	−15.2244	−	5.55110i	−0.521580	−	0.190178i
$853$	−3.82611	+	3.82611i	−0.131003	+	0.131003i	−0.769568	−	0.638565i	$-0.779528\pi$
$853$	−3.82611	+	3.82611i	−0.131003	+	0.131003i	0.638565	+	0.769568i	$0.279528\pi$
$854$	−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	0.256907	−	0.966436i	$-0.417296\pi$
$857$	−20.7711	−	20.7711i	−0.709529	−	0.709529i	−0.966436	+	0.256907i	$0.917296\pi$
$858$	15.2350	+	9.71191i	0.520115	+	0.331559i
$859$	−1.69693			−0.0578985			−0.0289492	−	0.999581i	$-0.509216\pi$
$859$	−1.69693			−0.0578985			−0.0289492	+	0.999581i	$0.509216\pi$
$860$		0			0
$861$	−4.77551			−0.162749
$862$	18.2815	+	11.6540i	0.622670	+	0.396935i
$863$	5.92869	+	5.92869i	0.201815	+	0.201815i	0.800777	−	0.598962i	$-0.204420\pi$
$863$	5.92869	+	5.92869i	0.201815	+	0.201815i	−0.598962	+	0.800777i	$0.704420\pi$
$864$	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
$868$	4.62699	−	12.6900i	0.157050	−	0.430725i
$869$			81.6068i			2.76832i
$870$		0			0
$871$			21.8617i			0.740756i
$872$	2.71891	−	20.5161i	0.0920740	−	0.694762i
$873$	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	0.855903	−	0.517137i	$-0.173002\pi$
$877$	10.0323	+	10.0323i	0.338766	+	0.338766i	−0.517137	+	0.855903i	$0.673002\pi$
$878$	18.7430	−	29.4020i	0.632544	−	0.992269i
$879$	−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	$0.667481\pi$
$882$	4.75306	−	7.45610i	0.160044	−	0.251060i
$883$	−5.56557	−	5.56557i	−0.187296	−	0.187296i	0.607230	−	0.794526i	$-0.292281\pi$
$883$	−5.56557	−	5.56557i	−0.187296	−	0.187296i	−0.794526	+	0.607230i	$0.792281\pi$
$884$	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	$-0.684574\pi$
$887$	8.59630	−	8.59630i	0.288636	−	0.288636i	0.836541	+	0.547905i	$0.184574\pi$
$888$	−0.925715	+	6.98516i	−0.0310649	+	0.234406i
$889$			9.15994i			0.307214i
$890$		0			0
$891$		−	5.12822i		−	0.171802i
$892$	−10.5298	+	28.8791i	−0.352565	+	0.966943i
$893$	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
$898$	39.5334	+	25.2015i	1.31925	+	0.840984i
$899$	−6.75359			−0.225245
$900$		0			0
$901$	19.7572			0.658207
$902$	−33.7766	−	21.5316i	−1.12464	−	0.716925i
$903$	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	0.0514592	−	0.998675i	$-0.483613\pi$
$907$	31.6263	−	31.6263i	1.05013	−	1.05013i	0.998675	−	0.0514592i	$-0.0163872\pi$
$908$	−13.2398	−	4.82748i	−0.439379	−	0.160206i
$909$		−	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	$0.753112\pi$
$912$	4.87302	−	0.420714i	0.161362	−	0.0139312i
$913$	−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
$918$	4.04398	−	6.34377i	0.133471	−	0.209376i
$919$	31.2829			1.03193			0.515964	−	0.856610i	$-0.327434\pi$
$919$	31.2829			1.03193			0.515964	+	0.856610i	$0.327434\pi$
$920$		0			0
$921$	2.27072			0.0748227
$922$	20.5418	−	32.2238i	0.676508	−	1.06123i
$923$	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
$928$	−4.66687	+	1.46412i	−0.153198	+	0.0480621i
$929$			22.1050i			0.725241i	0.931937	+	0.362620i	$0.118118\pi$
$929$			22.1050i			0.725241i	−0.931937	+	0.362620i	$0.881882\pi$
$930$		0			0
$931$		−	7.64535i		−	0.250566i
$932$	−1.90084	−	0.693082i	−0.0622641	−	0.0227026i
$933$	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	0.911371	−	0.411586i	$-0.135025\pi$
$937$	15.2986	+	15.2986i	0.499784	+	0.499784i	−0.411586	+	0.911371i	$0.635025\pi$
$938$	−9.04843	−	5.76813i	−0.295442	−	0.188336i
$939$	−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	$0.363407\pi$
$942$	15.2018	+	9.69074i	0.495302	+	0.315741i
$943$	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	$-0.661169\pi$
$947$	11.9881	−	11.9881i	0.389562	−	0.389562i	0.874531	+	0.484969i	$0.161169\pi$
$948$	10.9024	−	29.9010i	0.354095	−	0.971138i
$949$			7.93545i			0.257596i
$950$		0			0
$951$			11.0160i			0.357217i
$952$	−12.8968	−	1.70916i	−0.417988	−	0.0553943i
$953$	−5.99563	+	5.99563i	−0.194218	+	0.194218i	−0.797516	−	0.603298i	$-0.793853\pi$
$953$	−5.99563	+	5.99563i	−0.194218	+	0.194218i	0.603298	+	0.797516i	$0.293853\pi$
$954$	−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
$958$	−10.4598	+	16.4082i	−0.337940	+	0.530125i
$959$	8.57657			0.276952
$960$		0			0
$961$	−30.0096			−0.968051
$962$	4.71791	−	7.40097i	0.152112	−	0.238617i
$963$	−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	$-0.762081\pi$
$967$	−1.66866	+	1.66866i	−0.0536606	+	0.0536606i	0.679767	+	0.733428i	$0.262081\pi$
$968$	−42.8960	−	5.68483i	−1.37873	−	0.182717i
$969$		−	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	$-0.0245260\pi$
$972$	−0.685116	+	1.87899i	−0.0219751	+	0.0602687i
$973$	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	0.983137	−	0.182870i	$-0.0585387\pi$
$977$	25.0140	+	25.0140i	0.800267	+	0.800267i	−0.182870	+	0.983137i	$0.558539\pi$
$978$	−22.0673	−	14.0673i	−0.705634	−	0.449823i
$979$	37.1919			1.18866
$980$		0			0
$981$	7.31695			0.233612
$982$	−34.4540	−	21.9635i	−1.09947	−	0.700884i
$983$	−30.9151	−	30.9151i	−0.986038	−	0.986038i	0.0138655	−	0.999904i	$-0.495586\pi$
$983$	−30.9151	−	30.9151i	−0.986038	−	0.986038i	−0.999904	+	0.0138655i	$0.995586\pi$
$984$	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
$988$	−5.72384	−	2.08702i	−0.182100	−	0.0663969i
$989$		−	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	$0.861227\pi$
$992$	−42.1589	+	13.2264i	−1.33855	+	0.419937i
$993$	−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	0.745175	−	0.666869i	$-0.232366\pi$
$997$	2.47252	+	2.47252i	0.0783054	+	0.0783054i	−0.666869	+	0.745175i	$0.732366\pi$
$998$	−9.53021	+	14.9500i	−0.301674	+	0.473234i
$999$	−2.49122			−0.0788187

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
60.2.j.a.7.2	✓	12	20.19	odd	2
60.2.j.a.7.5	yes	12	5.4	even	2
60.2.j.a.43.2	yes	12	5.2	odd	4
60.2.j.a.43.5	yes	12	20.7	even	4
180.2.k.e.127.2		12	15.14	odd	2
180.2.k.e.127.5		12	60.59	even	2
180.2.k.e.163.2		12	60.47	odd	4
180.2.k.e.163.5		12	15.2	even	4
300.2.j.d.7.2		12	1.1	even	1	trivial
300.2.j.d.7.5		12	4.3	odd	2	inner
300.2.j.d.43.2		12	20.3	even	4	inner
300.2.j.d.43.5		12	5.3	odd	4	inner
900.2.k.n.307.2		12	12.11	even	2
900.2.k.n.307.5		12	3.2	odd	2
900.2.k.n.343.2		12	15.8	even	4
900.2.k.n.343.5		12	60.23	odd	4
960.2.w.g.127.2		12	40.19	odd	2
960.2.w.g.127.5		12	40.29	even	2
960.2.w.g.703.2		12	40.37	odd	4
960.2.w.g.703.5		12	40.27	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:	\( N \)	\(=\)	\( 300 = 2^{2} \cdot 3 \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	300.j (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.760198 + 1.19252i) q^{2} +(0.707107 + 0.707107i) q^{3} +(-0.844199 - 1.81310i) q^{4} +(-1.38078 + 0.305697i) q^{6} +(-0.611393 + 0.611393i) q^{7} +(2.80391 + 0.371591i) q^{8} +1.00000i q^{9} +O(q^{10})\)	\(q+(-0.760198 + 1.19252i) 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} +(2.80391 + 0.371591i) q^{8} +1.00000i q^{9} +5.12822i q^{11} +(0.685116 - 1.87899i) 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} +(-1.19252 - 0.760198i) q^{18} -1.22279 q^{19} -0.864641 q^{21} +(-6.11549 - 3.89846i) 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} +(1.62465 + 0.592379i) q^{28} -0.864641i q^{29} -7.81086i q^{31} +(-1.69333 - 5.39747i) 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} +(0.929560 - 1.45820i) q^{38} -2.49122 q^{39} +5.52311 q^{41} +(0.657298 - 1.03110i) 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} +(-3.98518 + 0.344061i) q^{48} +6.25240i q^{49} +5.31965i q^{51} +(4.68098 + 1.70677i) 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} +(1.03110 + 0.657298i) q^{58} -0.528636 q^{59} +4.98168 q^{61} +(9.31460 + 5.93780i) 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} +(3.64457 - 9.99558i) q^{68} +1.52311i q^{69} -8.10243i q^{71} +(-0.371591 + 2.80391i) 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} +(1.89382 - 2.97082i) q^{78} +15.9133 q^{79} -1.00000 q^{81} +(-4.19866 + 6.58641i) 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} +(-1.90560 + 14.3791i) q^{88} -7.25240i q^{89} -2.15401i q^{91} +(1.04351 - 2.86192i) 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} +(-7.45610 - 4.75306i) 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

Introduction

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