LMFDB - Embedded newform 300.2.j.d.43.2

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			43.2
Root			$-0.760198 - 1.19252i$ of defining polynomial
Character	$\chi$	$=$	300.43
Dual form			300.2.j.d.7.2

$q$-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 $\left(\mathbb{Z}/300\mathbb{Z}\right)^\times$.

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

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 $

$2$	−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	0.582060	−	0.813145i	$-0.302247\pi$
$7$	−0.611393	−	0.611393i	−0.231085	−	0.231085i	−0.813145	+	0.582060i	$0.802247\pi$
$8$	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	$-0.718701\pi$
$11$		−	5.12822i		−	1.54622i	0.634274	−	0.773108i	$-0.281299\pi$
$12$	0.685116	+	1.87899i	0.197776	+	0.542419i
$13$	−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	$0.0268150\pi$
$18$	−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	−0.585849	−	0.810420i	$-0.699239\pi$
$23$	1.07700	−	1.07700i	0.224571	−	0.224571i	0.810420	+	0.585849i	$0.199239\pi$
$24$	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	$0.0255814\pi$
$29$			0.864641i			0.160560i	−0.996772	+	0.0802799i	$0.974419\pi$
$30$		0			0
$31$			7.81086i			1.40287i	0.712732	+	0.701436i	$0.247457\pi$
$31$			7.81086i			1.40287i	−0.712732	+	0.701436i	$0.752543\pi$
$32$	−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	−0.547323	−	0.836921i	$-0.684353\pi$
$37$	1.76156	−	1.76156i	0.289598	−	0.289598i	0.836921	+	0.547323i	$0.184353\pi$
$38$	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	−0.998629	−	0.0523416i	$-0.983332\pi$
$43$	−6.20522	+	6.20522i	−0.946288	+	0.946288i	0.0523416	+	0.998629i	$0.483332\pi$
$44$	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	0.519196	−	0.854655i	$-0.326231\pi$
$47$	−2.29979	−	2.29979i	−0.335459	−	0.335459i	−0.854655	+	0.519196i	$0.826231\pi$
$48$	−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	0.864084	−	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
$58$	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	0.975974	−	0.217886i	$-0.0699160\pi$
$67$	6.20522	+	6.20522i	0.758089	+	0.758089i	−0.217886	+	0.975974i	$0.569916\pi$
$68$	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	$0.159650\pi$
$71$			8.10243i			0.961581i	−0.876835	+	0.480791i	$0.840350\pi$
$72$	−0.371591	−	2.80391i	−0.0437924	−	0.330444i
$73$	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
$78$	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	−0.119481	−	0.992836i	$-0.538123\pi$
$83$	7.95665	−	7.95665i	0.873355	−	0.873355i	0.992836	+	0.119481i	$0.0381231\pi$
$84$	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	$0.125583\pi$
$89$			7.25240i			0.768752i	−0.923177	+	0.384376i	$0.874417\pi$
$90$		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	−0.746258	−	0.665657i	$-0.768152\pi$
$97$	−0.793833	+	0.793833i	−0.0806015	+	0.0806015i	0.665657	+	0.746258i	$0.268152\pi$
$98$	−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	−0.869895	−	0.493236i	$-0.835814\pi$
$103$	−3.82267	+	3.82267i	−0.376659	+	0.376659i	0.493236	+	0.869895i	$0.335814\pi$
$104$	−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	0.388622	−	0.921397i	$-0.372951\pi$
$107$	−5.51107	−	5.51107i	−0.532775	−	0.532775i	−0.921397	+	0.388622i	$0.872951\pi$
$108$	1.87899	−	0.685116i	0.180806	−	0.0659253i
$109$			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
$112$	−0.297490	+	3.44575i	−0.0281101	+	0.325592i
$113$	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
$118$	0.401868	+	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	0.956489	−	0.291767i	$-0.0942433\pi$
$127$	7.49103	+	7.49103i	0.664722	+	0.664722i	−0.291767	+	0.956489i	$0.594243\pi$
$128$	−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	$-0.790593\pi$
$131$		−	13.9964i		−	1.22287i	0.791296	−	0.611434i	$-0.209407\pi$
$132$	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	−0.940111	−	0.340869i	$-0.889279\pi$
$137$	−7.01395	+	7.01395i	−0.599242	+	0.599242i	0.340869	+	0.940111i	$0.389279\pi$
$138$	−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	$-0.863988\pi$
$149$		−	10.1170i		−	0.828820i	0.910090	−	0.414410i	$-0.136012\pi$
$150$		0			0
$151$			7.93691i			0.645897i	0.946417	+	0.322948i	$0.104674\pi$
$151$			7.93691i			0.645897i	−0.946417	+	0.322948i	$0.895326\pi$
$152$	−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	−0.968481	−	0.249089i	$-0.919869\pi$
$157$	−9.01395	+	9.01395i	−0.719392	+	0.719392i	0.249089	+	0.968481i	$0.419869\pi$
$158$	−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	0.0252033	−	0.999682i	$-0.491977\pi$
$163$	13.0849	−	13.0849i	1.02489	−	1.02489i	0.999682	−	0.0252033i	$-0.00802331\pi$
$164$	−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	0.993224	−	0.116216i	$-0.0370765\pi$
$167$	11.3334	+	11.3334i	0.877008	+	0.877008i	−0.116216	+	0.993224i	$0.537076\pi$
$168$	−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	0.336064	−	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
$178$	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	$-0.917962\pi$
$191$		−	7.04516i		−	0.509770i	0.966971	−	0.254885i	$-0.0820376\pi$
$192$	3.98810	−	6.93506i	0.287816	−	0.500495i
$193$	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	$0.379920\pi$
$198$	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	$-0.939469\pi$
$211$		−	5.49134i		−	0.378039i	0.981973	−	0.189020i	$-0.0605310\pi$
$212$	−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	−0.970174	−	0.242410i	$-0.922062\pi$
$223$	−10.8678	+	10.8678i	−0.727764	+	0.727764i	0.242410	+	0.970174i	$0.422062\pi$
$224$	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	0.852851	−	0.522155i	$-0.174872\pi$
$227$	4.98244	+	4.98244i	0.330696	+	0.330696i	−0.522155	+	0.852851i	$0.674872\pi$
$228$	−0.837751	−	2.29761i	−0.0554814	−	0.152163i
$229$			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
$232$	0.321293	+	2.42438i	0.0210939	+	0.159168i
$233$	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
$238$	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	$0.183210\pi$
$251$			17.2471i			1.08863i	−0.838882	+	0.544314i	$0.816790\pi$
$252$	−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	−0.0615588	−	0.998103i	$-0.519607\pi$
$257$	15.0140	−	15.0140i	0.936545	−	0.936545i	0.998103	+	0.0615588i	$0.0196072\pi$
$258$	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	−0.883555	−	0.468327i	$-0.844857\pi$
$263$	−6.73386	+	6.73386i	−0.415228	+	0.415228i	0.468327	+	0.883555i	$0.344857\pi$
$264$	−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	$-0.713370\pi$
$269$		−	25.7047i		−	1.56724i	0.621238	−	0.783622i	$-0.286630\pi$
$270$		0			0
$271$		−	0.931222i		−	0.0565677i	−0.999600	−	0.0282839i	$-0.990996\pi$
$271$		−	0.931222i		−	0.0565677i	0.999600	−	0.0282839i	$-0.00900423\pi$
$272$	−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	0.416190	−	0.909277i	$-0.363365\pi$
$277$	22.0602	−	22.0602i	1.32547	−	1.32547i	0.909277	−	0.416190i	$-0.136635\pi$
$278$	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	−0.273949	−	0.961744i	$-0.588330\pi$
$283$	11.5705	−	11.5705i	0.687796	−	0.687796i	0.961744	+	0.273949i	$0.0883299\pi$
$284$	−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	0.221675	−	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
$298$	−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	0.751440	−	0.659801i	$-0.229360\pi$
$307$	1.60564	+	1.60564i	0.0916387	+	0.0916387i	−0.659801	+	0.751440i	$0.729360\pi$
$308$	−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	$0.185561\pi$
$311$			19.4161i			1.10099i	−0.834839	+	0.550494i	$0.814439\pi$
$312$	−6.98516	+	0.925715i	−0.395457	+	0.0524083i
$313$	−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	$0.149885\pi$
$318$	−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	$-0.663336\pi$
$331$		−	31.7005i		−	1.74242i	0.490912	−	0.871209i	$-0.336664\pi$
$332$	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	−0.0335632	+	0.999437i	$0.510686\pi$
$337$	−18.9634	+	18.9634i	−1.03300	+	1.03300i	−0.999437	+	0.0335632i	$0.989314\pi$
$338$	−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	0.468863	−	0.883271i	$-0.344664\pi$
$347$	−7.71957	−	7.71957i	−0.414408	−	0.414408i	−0.883271	+	0.468863i	$0.844664\pi$
$348$	−1.62465	+	0.592379i	−0.0870906	+	0.0317549i
$349$		−	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
$352$	27.6794	+	8.68375i	1.47532	+	0.462846i
$353$	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
$358$	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	0.778534	−	0.627602i	$-0.215963\pi$
$367$	2.89145	+	2.89145i	0.150933	+	0.150933i	−0.627602	+	0.778534i	$0.715963\pi$
$368$	−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	0.936081	−	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
$378$	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	−0.309354	−	0.950947i	$-0.600113\pi$
$383$	12.5562	−	12.5562i	0.641593	−	0.641593i	0.950947	+	0.309354i	$0.100113\pi$
$384$	−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	$0.0417848\pi$
$389$			5.16327i			0.261788i	−0.991396	+	0.130894i	$0.958215\pi$
$390$		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	−0.614847	−	0.788646i	$-0.710782\pi$
$397$	3.46293	−	3.46293i	0.173800	−	0.173800i	0.788646	+	0.614847i	$0.210782\pi$
$398$	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	$0.119270\pi$
$409$			14.8034i			0.731982i	−0.930618	+	0.365991i	$0.880730\pi$
$410$		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	$0.120373\pi$
$431$			15.3302i			0.738428i	−0.929344	+	0.369214i	$0.879627\pi$
$432$	−0.344061	+	3.98518i	−0.0165537	+	0.191737i
$433$	−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
$438$	−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	−0.663779	−	0.747929i	$-0.731048\pi$
$443$	1.77116	−	1.77116i	0.0841501	−	0.0841501i	0.747929	+	0.663779i	$0.231048\pi$
$444$	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	$0.285929\pi$
$449$			33.1512i			1.56450i	−0.622963	+	0.782251i	$0.714071\pi$
$450$		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	−0.509444	−	0.860504i	$-0.670149\pi$
$457$	7.50479	−	7.50479i	0.351059	−	0.351059i	0.860504	+	0.509444i	$0.170149\pi$
$458$	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	0.351843	−	0.936059i	$-0.385555\pi$
$463$	27.7123	−	27.7123i	1.28790	−	1.28790i	0.936059	−	0.351843i	$-0.114445\pi$
$464$	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	0.659114	−	0.752043i	$-0.270932\pi$
$467$	−2.00823	−	2.00823i	−0.0929296	−	0.0929296i	−0.752043	+	0.659114i	$0.770932\pi$
$468$	−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	−0.994078	−	0.108671i	$-0.965340\pi$
$487$	−24.3355	−	24.3355i	−1.10275	−	1.10275i	−0.108671	−	0.994078i	$-0.534660\pi$
$488$	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	$-0.773957\pi$
$491$		−	28.8918i		−	1.30387i	0.758275	−	0.651935i	$-0.226043\pi$
$492$	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	−0.878906	−	0.476995i	$-0.841726\pi$
$503$	−9.01392	+	9.01392i	−0.401911	+	0.401911i	0.476995	+	0.878906i	$0.341726\pi$
$504$	−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	$0.166534\pi$
$509$			22.5448i			0.999279i	−0.866233	+	0.499640i	$0.833466\pi$
$510$		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	−0.999006	−	0.0445800i	$-0.985805\pi$
$523$	−21.8269	+	21.8269i	−0.954426	+	0.954426i	0.0445800	+	0.999006i	$0.485805\pi$
$524$	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	0.976597	−	0.215076i	$-0.0689998\pi$
$547$	17.8105	+	17.8105i	0.761522	+	0.761522i	−0.215076	+	0.976597i	$0.569000\pi$
$548$	−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	−0.999938	−	0.0111112i	$-0.996463\pi$
$557$	−23.3372	+	23.3372i	−0.988827	+	0.988827i	0.0111112	+	0.999938i	$0.496463\pi$
$558$	−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	−0.809455	−	0.587182i	$-0.800237\pi$
$563$	−5.27400	+	5.27400i	−0.222273	+	0.222273i	0.587182	+	0.809455i	$0.300237\pi$
$564$	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	$-0.795699\pi$
$569$		−	28.5606i		−	1.19732i	0.801002	−	0.598661i	$-0.204301\pi$
$570$		0			0
$571$			32.2837i			1.35103i	0.737347	+	0.675515i	$0.236078\pi$
$571$			32.2837i			1.35103i	−0.737347	+	0.675515i	$0.763922\pi$
$572$	−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	−0.134237	+	0.990949i	$0.542858\pi$
$577$	−27.0279	+	27.0279i	−1.12519	+	1.12519i	−0.990949	+	0.134237i	$0.957142\pi$
$578$	−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	0.966135	−	0.258039i	$-0.0830761\pi$
$587$	17.1558	+	17.1558i	0.708096	+	0.708096i	−0.258039	+	0.966135i	$0.583076\pi$
$588$	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	0.994167	−	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
$598$	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	0.870974	−	0.491328i	$-0.163489\pi$
$607$	9.35348	+	9.35348i	0.379646	+	0.379646i	−0.491328	+	0.870974i	$0.663489\pi$
$608$	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	0.999680	−	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	$0.284739\pi$
$618$	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	$0.141256\pi$
$631$			21.5701i			0.858694i	−0.903140	+	0.429347i	$0.858744\pi$
$632$	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	−0.997064	−	0.0765729i	$-0.975602\pi$
$643$	−23.3413	+	23.3413i	−0.920491	+	0.920491i	0.0765729	+	0.997064i	$0.475602\pi$
$644$	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	$-0.892108\pi$
$647$	−32.4465	−	32.4465i	−1.27560	−	1.27560i	−0.332501	−	0.943103i	$-0.607892\pi$
$648$	−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	0.246307	−	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
$658$	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	0.634183	−	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	$0.177876\pi$
$678$	−0.547390	−	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	−0.849762	−	0.527167i	$-0.823254\pi$
$683$	−8.43079	+	8.43079i	−0.322595	+	0.322595i	0.527167	+	0.849762i	$0.323254\pi$
$684$	−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	$0.136885\pi$
$691$			21.9182i			0.833809i	−0.908950	+	0.416905i	$0.863115\pi$
$692$	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	$0.203649\pi$
$709$			31.7938i			1.19404i	−0.802225	+	0.597021i	$0.796351\pi$
$710$		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	0.540070	−	0.841620i	$-0.318398\pi$
$727$	−8.13069	−	8.13069i	−0.301551	−	0.301551i	−0.841620	+	0.540070i	$0.818398\pi$
$728$	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	0.993424	+	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
$738$	−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	−0.446356	−	0.894855i	$-0.647279\pi$
$743$	12.2252	−	12.2252i	0.448499	−	0.448499i	0.894855	+	0.446356i	$0.147279\pi$
$744$	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	$-0.823162\pi$
$751$		−	28.9069i		−	1.05483i	0.849609	−	0.527413i	$-0.176838\pi$
$752$	−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	−0.348459	−	0.937324i	$-0.613295\pi$
$757$	16.2018	−	16.2018i	0.588864	−	0.588864i	0.937324	+	0.348459i	$0.113295\pi$
$758$	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	$-0.822529\pi$
$769$		−	29.3449i		−	1.05820i	0.848559	−	0.529101i	$-0.177471\pi$
$770$		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	−0.883674	−	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
$778$	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	0.558694	−	0.829374i	$-0.311303\pi$
$787$	−7.59353	−	7.59353i	−0.270680	−	0.270680i	−0.829374	+	0.558694i	$0.811303\pi$
$788$	−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	−0.999665	−	0.0258893i	$-0.991758\pi$
$797$	−27.4908	+	27.4908i	−0.973775	+	0.973775i	0.0258893	+	0.999665i	$0.491758\pi$
$798$	−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	$0.316791\pi$
$809$			47.7205i			1.67776i	−0.544313	+	0.838882i	$0.683209\pi$
$810$		0			0
$811$			37.3179i			1.31041i	0.755451	+	0.655205i	$0.227418\pi$
$811$			37.3179i			1.31041i	−0.755451	+	0.655205i	$0.772582\pi$
$812$	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	−0.998811	−	0.0487521i	$-0.984476\pi$
$823$	−27.2553	+	27.2553i	−0.950059	+	0.950059i	0.0487521	+	0.998811i	$0.484476\pi$
$824$	−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	$-0.968678\pi$
$827$	−31.4437	−	31.4437i	−1.09341	−	1.09341i	−0.0982432	−	0.995162i	$-0.531322\pi$
$828$	2.86192	−	1.04351i	0.0994587	−	0.0362645i
$829$			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
$832$	−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	0.638565	−	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	$0.417296\pi$
$858$	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	−0.598962	−	0.800777i	$-0.704420\pi$
$863$	5.92869	−	5.92869i	0.201815	−	0.201815i	0.800777	+	0.598962i	$0.204420\pi$
$864$	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	−0.517137	−	0.855903i	$-0.673002\pi$
$877$	10.0323	−	10.0323i	0.338766	−	0.338766i	0.855903	+	0.517137i	$0.173002\pi$
$878$	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	−0.794526	−	0.607230i	$-0.792281\pi$
$883$	−5.56557	+	5.56557i	−0.187296	+	0.187296i	0.607230	+	0.794526i	$0.292281\pi$
$884$	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	0.836541	−	0.547905i	$-0.184574\pi$
$887$	8.59630	+	8.59630i	0.288636	+	0.288636i	−0.547905	+	0.836541i	$0.684574\pi$
$888$	−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	0.998675	+	0.0514592i	$0.0163872\pi$
$907$	31.6263	+	31.6263i	1.05013	+	1.05013i	0.0514592	+	0.998675i	$0.483613\pi$
$908$	−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	$-0.753112\pi$
$911$		−	42.2656i		−	1.40032i	0.713985	−	0.700161i	$-0.246888\pi$
$912$	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	$-0.881882\pi$
$929$		−	22.1050i		−	0.725241i	0.931937	−	0.362620i	$-0.118118\pi$
$930$		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	−0.411586	−	0.911371i	$-0.635025\pi$
$937$	15.2986	−	15.2986i	0.499784	−	0.499784i	0.911371	+	0.411586i	$0.135025\pi$
$938$	−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	0.874531	−	0.484969i	$-0.161169\pi$
$947$	11.9881	+	11.9881i	0.389562	+	0.389562i	−0.484969	+	0.874531i	$0.661169\pi$
$948$	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	0.603298	−	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
$958$	−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	0.679767	−	0.733428i	$-0.262081\pi$
$967$	−1.66866	−	1.66866i	−0.0536606	−	0.0536606i	−0.733428	+	0.679767i	$0.762081\pi$
$968$	−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	$0.0245260\pi$
$971$			4.79719i			0.153949i	−0.997033	+	0.0769745i	$0.975474\pi$
$972$	−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	−0.182870	−	0.983137i	$-0.558539\pi$
$977$	25.0140	−	25.0140i	0.800267	−	0.800267i	0.983137	+	0.182870i	$0.0585387\pi$
$978$	−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	−0.999904	−	0.0138655i	$-0.995586\pi$
$983$	−30.9151	+	30.9151i	−0.986038	+	0.986038i	0.0138655	+	0.999904i	$0.495586\pi$
$984$	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	$-0.861227\pi$
$991$		−	26.5873i		−	0.844575i	0.906462	−	0.422287i	$-0.138773\pi$
$992$	−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	−0.666869	−	0.745175i	$-0.732366\pi$
$997$	2.47252	−	2.47252i	0.0783054	−	0.0783054i	0.745175	+	0.666869i	$0.232366\pi$
$998$	−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.43.2		12
3.2	odd	2		900.2.k.n.343.5		12
4.3	odd	2	inner	300.2.j.d.43.5		12
5.2	odd	4	inner	300.2.j.d.7.5		12
5.3	odd	4		60.2.j.a.7.2	✓	12
5.4	even	2		60.2.j.a.43.5	yes	12
12.11	even	2		900.2.k.n.343.2		12
15.2	even	4		900.2.k.n.307.2		12
15.8	even	4		180.2.k.e.127.5		12
15.14	odd	2		180.2.k.e.163.2		12
20.3	even	4		60.2.j.a.7.5	yes	12
20.7	even	4	inner	300.2.j.d.7.2		12
20.19	odd	2		60.2.j.a.43.2	yes	12
40.3	even	4		960.2.w.g.127.5		12
40.13	odd	4		960.2.w.g.127.2		12
40.19	odd	2		960.2.w.g.703.2		12
40.29	even	2		960.2.w.g.703.5		12
60.23	odd	4		180.2.k.e.127.2		12
60.47	odd	4		900.2.k.n.307.5		12
60.59	even	2		180.2.k.e.163.5		12

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

\(f(q)\)	\(=\)	\(q+(-0.760198 - 1.19252i) q^{2} +(0.707107 - 0.707107i) q^{3} +(-0.844199 + 1.81310i) q^{4} +(-1.38078 - 0.305697i) q^{6} +(-0.611393 - 0.611393i) q^{7} +(2.80391 - 0.371591i) q^{8} -1.00000i q^{9} +O(q^{10})\)	\(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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