LMFDB - Embedded newform 475.2.j.b.49.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [475,2,Mod(49,475)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(475, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 4]))

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

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

chi := DirichletCharacter("475.49");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 475 = 5^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	475.j (of order $6$, degree $2$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$3.79289409601$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(\zeta_{6})$
Coefficient field:	12.0.50712647503417344.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 13x^{10} + 119x^{8} - 552x^{6} + 1863x^{4} - 2450x^{2} + 2401 $ x^12 - 13x^10 + 119x^8 - 552x^6 + 1863x^4 - 2450*x^2 + 2401
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 95)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			49.2
Root			$-1.97899 - 1.14257i$ of defining polynomial
Character	$\chi$	$=$	475.49
Dual form			475.2.j.b.349.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.97899 - 1.14257i) q^{2} +(-2.17114 - 1.25351i) q^{3} +(1.61094 + 2.79023i) q^{4} +(2.86445 + 4.96137i) q^{6} +3.50702i q^{7} -2.79216i q^{8} +(1.64257 + 2.84502i) q^{9} +O(q^{10})$	\(q+(-1.97899 - 1.14257i) q^{2} +(-2.17114 - 1.25351i) q^{3} +(1.61094 + 2.79023i) q^{4} +(2.86445 + 4.96137i) q^{6} +3.50702i q^{7} -2.79216i q^{8} +(1.64257 + 2.84502i) q^{9} -4.50702 q^{11} -8.07730i q^{12} +(4.33013 - 2.50000i) q^{13} +(4.00702 - 6.94036i) q^{14} +(0.0316332 - 0.0547902i) q^{16} +(-0.137360 - 0.0793049i) q^{17} -7.50702i q^{18} +(4.26053 - 0.920816i) q^{19} +(4.39608 - 7.61423i) q^{21} +(8.91935 + 5.14959i) q^{22} +(-1.00339 + 0.579305i) q^{23} +(-3.50000 + 6.06218i) q^{24} -11.4257 q^{26} -0.714858i q^{27} +(-9.78538 + 5.64959i) q^{28} +(-1.75351 - 3.03717i) q^{29} -2.28514 q^{31} +(-4.96137 + 2.86445i) q^{32} +(9.78538 + 5.64959i) q^{33} +(0.181223 + 0.313888i) q^{34} +(-5.29216 + 9.16629i) q^{36} -10.9648i q^{37} +(-9.48365 - 3.04567i) q^{38} -12.5351 q^{39} +(-3.03865 + 5.26310i) q^{41} +(-17.3996 + 10.0457i) q^{42} +(-2.89981 - 1.67420i) q^{43} +(-7.26053 - 12.5756i) q^{44} +2.64759 q^{46} +(2.65287 - 1.53163i) q^{47} +(-0.137360 + 0.0793049i) q^{48} -5.29918 q^{49} +(0.198819 + 0.344364i) q^{51} +(13.9511 + 8.05469i) q^{52} +(4.97353 - 2.87147i) q^{53} +(-0.816776 + 1.41470i) q^{54} +9.79216 q^{56} +(-10.4045 - 3.34139i) q^{57} +8.01404i q^{58} +(1.53163 - 2.65287i) q^{59} +(0.436734 + 0.756445i) q^{61} +(4.52228 + 2.61094i) q^{62} +(-9.97753 + 5.76053i) q^{63} +12.9648 q^{64} +(-12.9101 - 22.3610i) q^{66} +(-7.31250 + 4.22188i) q^{67} -0.511021i q^{68} +2.90466 q^{69} +(8.11796 - 14.0607i) q^{71} +(7.94375 - 4.58632i) q^{72} +(-6.19954 - 3.57930i) q^{73} +(-12.5281 + 21.6993i) q^{74} +(9.43273 + 10.4045i) q^{76} -15.8062i q^{77} +(24.8068 + 14.3222i) q^{78} +(-5.06327 + 8.76983i) q^{79} +(4.03163 - 6.98299i) q^{81} +(12.0269 - 6.94375i) q^{82} -4.85543i q^{83} +28.3273 q^{84} +(3.82580 + 6.62647i) q^{86} +8.79216i q^{87} +12.5843i q^{88} +(-0.556248 - 0.963449i) q^{89} +(8.76755 + 15.1858i) q^{91} +(-3.23278 - 1.86645i) q^{92} +(4.96137 + 2.86445i) q^{93} -7.00000 q^{94} +14.3624 q^{96} +(-1.40254 - 0.809757i) q^{97} +(10.4870 + 6.05469i) q^{98} +(-7.40310 - 12.8225i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 14 q^{4} + 12 q^{6} + 8 q^{9}+O(q^{10}) $ 12 * q + 14 * q^4 + 12 * q^6 + 8 * q^9	$ 12 q + 14 q^{4} + 12 q^{6} + 8 q^{9} - 20 q^{11} + 14 q^{14} - 6 q^{16} + 24 q^{21} - 42 q^{24} - 20 q^{26} - 4 q^{29} - 4 q^{31} - 50 q^{34} - 6 q^{36} + 20 q^{39} + 4 q^{41} - 36 q^{44} - 96 q^{46} + 28 q^{49} + 12 q^{51} + 20 q^{54} + 60 q^{56} + 12 q^{59} + 18 q^{61} + 32 q^{64} - 58 q^{66} + 20 q^{69} + 58 q^{71} - 14 q^{74} - 38 q^{76} - 48 q^{79} + 42 q^{81} + 112 q^{84} + 64 q^{86} - 28 q^{89} + 20 q^{91} - 84 q^{94} + 68 q^{96} - 26 q^{99}+O(q^{100}) $ 12 * q + 14 * q^4 + 12 * q^6 + 8 * q^9 - 20 * q^11 + 14 * q^14 - 6 * q^16 + 24 * q^21 - 42 * q^24 - 20 * q^26 - 4 * q^29 - 4 * q^31 - 50 * q^34 - 6 * q^36 + 20 * q^39 + 4 * q^41 - 36 * q^44 - 96 * q^46 + 28 * q^49 + 12 * q^51 + 20 * q^54 + 60 * q^56 + 12 * q^59 + 18 * q^61 + 32 * q^64 - 58 * q^66 + 20 * q^69 + 58 * q^71 - 14 * q^74 - 38 * q^76 - 48 * q^79 + 42 * q^81 + 112 * q^84 + 64 * q^86 - 28 * q^89 + 20 * q^91 - 84 * q^94 + 68 * q^96 - 26 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/475\mathbb{Z}\right)^\times$.

$n$	$77$	$401$
$\chi(n)$	$-1$	$e\left(\frac{2}{3}\right)$

Coefficient data

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

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

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

$2$	−1.97899	−	1.14257i	−1.39936	−	0.807920i	−0.405033	−	0.914302i	$-0.632740\pi$
$2$	−1.97899	−	1.14257i	−1.39936	−	0.807920i	−0.994325	+	0.106382i	$0.966073\pi$
$3$	−2.17114	−	1.25351i	−1.25351	−	0.723714i	−0.281705	−	0.959501i	$-0.590900\pi$
$3$	−2.17114	−	1.25351i	−1.25351	−	0.723714i	−0.971805	+	0.235787i	$0.924233\pi$
$4$	1.61094	+	2.79023i	0.805469	+	1.39511i
$5$		0			0
$5$		0			0
$6$	2.86445	+	4.96137i	1.16941	+	2.02547i
$7$			3.50702i			1.32553i	0.748828	+	0.662764i	$0.230617\pi$
$7$			3.50702i			1.32553i	−0.748828	+	0.662764i	$0.769383\pi$
$8$		−	2.79216i		−	0.987178i
$9$	1.64257	+	2.84502i	0.547524	+	0.948339i
$10$		0			0
$11$	−4.50702			−1.35892			−0.679459	−	0.733714i	$-0.737785\pi$
$11$	−4.50702			−1.35892			−0.679459	+	0.733714i	$0.737785\pi$
$12$		−	8.07730i		−	2.33172i
$13$	4.33013	−	2.50000i	1.20096	−	0.693375i	0.240192	−	0.970725i	$-0.422790\pi$
$13$	4.33013	−	2.50000i	1.20096	−	0.693375i	0.960769	+	0.277350i	$0.0894562\pi$
$14$	4.00702	−	6.94036i	1.07092	−	1.85489i
$15$		0			0
$16$	0.0316332	−	0.0547902i	0.00790829	−	0.0136976i
$17$	−0.137360	−	0.0793049i	−0.0333147	−	0.0192343i	0.483250	−	0.875482i	$-0.339456\pi$
$17$	−0.137360	−	0.0793049i	−0.0333147	−	0.0192343i	−0.516565	+	0.856248i	$0.672790\pi$
$18$		−	7.50702i		−	1.76942i
$19$	4.26053	−	0.920816i	0.977432	−	0.211250i
$19$	4.26053	−	0.920816i	0.977432	−	0.211250i
$20$		0			0
$21$	4.39608	−	7.61423i	0.959303	−	1.66156i
$22$	8.91935	+	5.14959i	1.90161	+	1.09790i
$23$	−1.00339	+	0.579305i	−0.209220	+	0.120793i	−0.600949	−	0.799287i	$-0.705211\pi$
$23$	−1.00339	+	0.579305i	−0.209220	+	0.120793i	0.391729	+	0.920081i	$0.371877\pi$
$24$	−3.50000	+	6.06218i	−0.714435	+	1.23744i
$25$		0			0
$26$	−11.4257			−2.24077
$27$		−	0.714858i		−	0.137574i
$28$	−9.78538	+	5.64959i	−1.84926	+	1.06767i
$29$	−1.75351	−	3.03717i	−0.325619	−	0.563988i	0.656019	−	0.754745i	$-0.272239\pi$
$29$	−1.75351	−	3.03717i	−0.325619	−	0.563988i	−0.981637	+	0.190757i	$0.938906\pi$
$30$		0			0
$31$	−2.28514			−0.410424			−0.205212	−	0.978718i	$-0.565788\pi$
$31$	−2.28514			−0.410424			−0.205212	+	0.978718i	$0.565788\pi$
$32$	−4.96137	+	2.86445i	−0.877054	+	0.506368i
$33$	9.78538	+	5.64959i	1.70342	+	0.983467i
$34$	0.181223	+	0.313888i	0.0310795	+	0.0538313i
$35$		0			0
$36$	−5.29216	+	9.16629i	−0.882027	+	1.52772i
$37$		−	10.9648i		−	1.80260i	−0.433192	−	0.901302i	$-0.642613\pi$
$37$		−	10.9648i		−	1.80260i	0.433192	−	0.901302i	$-0.357387\pi$
$38$	−9.48365	−	3.04567i	−1.53845	−	0.494073i
$39$	−12.5351			−2.00722
$40$		0			0
$41$	−3.03865	+	5.26310i	−0.474558	+	0.821958i	−0.999576	−	0.0291332i	$-0.990725\pi$
$41$	−3.03865	+	5.26310i	−0.474558	+	0.821958i	0.525018	+	0.851091i	$0.324059\pi$
$42$	−17.3996	+	10.0457i	−2.68482	+	1.55008i
$43$	−2.89981	−	1.67420i	−0.442216	−	0.255314i	0.262321	−	0.964981i	$-0.415512\pi$
$43$	−2.89981	−	1.67420i	−0.442216	−	0.255314i	−0.704537	+	0.709667i	$0.748845\pi$
$44$	−7.26053	−	12.5756i	−1.09457	−	1.89584i
$45$		0			0
$46$	2.64759			0.390366
$47$	2.65287	−	1.53163i	0.386960	−	0.223412i	−0.293882	−	0.955842i	$-0.594947\pi$
$47$	2.65287	−	1.53163i	0.386960	−	0.223412i	0.680842	+	0.732430i	$0.261614\pi$
$48$	−0.137360	+	0.0793049i	−0.0198262	+	0.0114467i
$49$	−5.29918			−0.757026
$50$		0			0
$51$	0.198819	+	0.344364i	0.0278402	+	0.0482207i
$52$	13.9511	+	8.05469i	1.93467	+	1.11698i
$53$	4.97353	−	2.87147i	0.683166	−	0.394426i	−0.117881	−	0.993028i	$-0.537610\pi$
$53$	4.97353	−	2.87147i	0.683166	−	0.394426i	0.801047	+	0.598602i	$0.204277\pi$
$54$	−0.816776	+	1.41470i	−0.111149	+	0.192516i
$55$		0			0
$56$	9.79216			1.30853
$57$	−10.4045	−	3.34139i	−1.37810	−	0.442578i
$58$			8.01404i			1.05229i
$59$	1.53163	−	2.65287i	0.199402	−	0.345374i	−0.748933	−	0.662646i	$-0.769433\pi$
$59$	1.53163	−	2.65287i	0.199402	−	0.345374i	0.948335	+	0.317272i	$0.102767\pi$
$60$		0			0
$61$	0.436734	+	0.756445i	0.0559180	+	0.0968528i	0.892629	−	0.450791i	$-0.148858\pi$
$61$	0.436734	+	0.756445i	0.0559180	+	0.0968528i	−0.836711	+	0.547644i	$0.815525\pi$
$62$	4.52228	+	2.61094i	0.574330	+	0.331589i
$63$	−9.97753	+	5.76053i	−1.25705	+	0.725758i
$64$	12.9648			1.62060
$65$		0			0
$66$	−12.9101	−	22.3610i	−1.58913	−	2.75245i
$67$	−7.31250	+	4.22188i	−0.893365	+	0.515784i	−0.875042	−	0.484048i	$-0.839166\pi$
$67$	−7.31250	+	4.22188i	−0.893365	+	0.515784i	−0.0183230	+	0.999832i	$0.505833\pi$
$68$		−	0.511021i		−	0.0619704i
$69$	2.90466			0.349680
$70$		0			0
$71$	8.11796	−	14.0607i	0.963424	−	1.66870i	0.249634	−	0.968340i	$-0.419690\pi$
$71$	8.11796	−	14.0607i	0.963424	−	1.66870i	0.713790	−	0.700359i	$-0.246977\pi$
$72$	7.94375	−	4.58632i	0.936179	−	0.540503i
$73$	−6.19954	−	3.57930i	−0.725601	−	0.418926i	0.0912097	−	0.995832i	$-0.470927\pi$
$73$	−6.19954	−	3.57930i	−0.725601	−	0.418926i	−0.816811	+	0.576906i	$0.804260\pi$
$74$	−12.5281	+	21.6993i	−1.45636	+	2.52249i
$75$		0			0
$76$	9.43273	+	10.4045i	1.08201	+	1.19347i
$77$		−	15.8062i		−	1.80128i
$78$	24.8068	+	14.3222i	2.80882	+	1.62167i
$79$	−5.06327	+	8.76983i	−0.569662	+	0.986683i	0.426937	+	0.904281i	$0.359593\pi$
$79$	−5.06327	+	8.76983i	−0.569662	+	0.986683i	−0.996599	+	0.0824022i	$0.973741\pi$
$80$		0			0
$81$	4.03163	−	6.98299i	0.447959	−	0.775888i
$82$	12.0269	−	6.94375i	1.32815	−	0.766809i
$83$		−	4.85543i		−	0.532952i	−0.963841	−	0.266476i	$-0.914141\pi$
$83$		−	4.85543i		−	0.532952i	0.963841	−	0.266476i	$-0.0858594\pi$
$84$	28.3273			3.09076
$85$		0			0
$86$	3.82580	+	6.62647i	0.412546	+	0.714551i
$87$			8.79216i			0.942619i
$88$			12.5843i			1.34149i
$89$	−0.556248	−	0.963449i	−0.0589621	−	0.102125i	0.835038	−	0.550193i	$-0.185446\pi$
$89$	−0.556248	−	0.963449i	−0.0589621	−	0.102125i	−0.894000	+	0.448067i	$0.852112\pi$
$90$		0			0
$91$	8.76755	+	15.1858i	0.919089	+	1.59191i
$92$	−3.23278	−	1.86645i	−0.337041	−	0.194591i
$93$	4.96137	+	2.86445i	0.514470	+	0.297029i
$94$	−7.00000			−0.721995
$95$		0			0
$96$	14.3624			1.46586
$97$	−1.40254	−	0.809757i	−0.142406	−	0.0822184i	0.427104	−	0.904203i	$-0.359534\pi$
$97$	−1.40254	−	0.809757i	−0.142406	−	0.0822184i	−0.569510	+	0.821984i	$0.692867\pi$
$98$	10.4870	+	6.05469i	1.05935	+	0.611616i
$99$	−7.40310	−	12.8225i	−0.744039	−	1.28871i
$100$		0			0
$101$	−6.15661	−	10.6636i	−0.612605	−	1.06106i	−0.990800	−	0.135337i	$-0.956788\pi$
$101$	−6.15661	−	10.6636i	−0.612605	−	1.06106i	0.378194	−	0.925726i	$-0.376545\pi$
$102$		−	0.908659i		−	0.0899707i
$103$		−	10.6164i		−	1.04606i	−0.852313	−	0.523032i	$-0.824801\pi$
$103$		−	10.6164i		−	1.04606i	0.852313	−	0.523032i	$-0.175199\pi$
$104$	−6.98040	−	12.0904i	−0.684485	−	1.18556i
$105$		0			0
$106$	−13.1234			−1.27466
$107$		−	2.17265i		−	0.210038i	−0.994470	−	0.105019i	$-0.966510\pi$
$107$		−	2.17265i		−	0.210038i	0.994470	−	0.105019i	$-0.0334903\pi$
$108$	1.99461	−	1.15159i	0.191932	−	0.110812i
$109$	7.91012	−	13.7007i	0.757652	−	1.31229i	−0.186393	−	0.982475i	$-0.559680\pi$
$109$	7.91012	−	13.7007i	0.757652	−	1.31229i	0.944045	−	0.329816i	$-0.106987\pi$
$110$		0			0
$111$	−13.7445	+	23.8062i	−1.30457	+	2.25958i
$112$	0.192150	+	0.110938i	0.0181565	+	0.0104827i
$113$		−	9.83828i		−	0.925507i	−0.886487	−	0.462754i	$-0.846861\pi$
$113$		−	9.83828i		−	0.925507i	0.886487	−	0.462754i	$-0.153139\pi$
$114$	16.7726	+	18.5004i	1.57089	+	1.73272i
$115$		0			0
$116$	5.64959	−	9.78538i	0.524551	−	0.908549i
$117$	14.2251	+	8.21286i	1.31511	+	0.759279i
$118$	−6.06218	+	3.50000i	−0.558069	+	0.322201i
$119$	0.278124	−	0.481725i	0.0254956	−	0.0441596i
$120$		0			0
$121$	9.31322			0.846656
$122$		−	1.99600i		−	0.180709i
$123$	13.1947	−	7.61796i	1.18972	−	0.686888i
$124$	−3.68122	−	6.37607i	−0.330584	−	0.572588i
$125$		0			0
$126$	26.3273			2.34542
$127$	13.6060	−	7.85543i	1.20734	−	0.697056i	0.245160	−	0.969483i	$-0.421159\pi$
$127$	13.6060	−	7.85543i	1.20734	−	0.697056i	0.962177	+	0.272426i	$0.0878260\pi$
$128$	−15.7345	−	9.08432i	−1.39075	−	0.802948i
$129$	4.19726	+	7.26987i	0.369548	+	0.640076i
$130$		0			0
$131$	5.76755	−	9.98968i	0.503913	−	0.872803i	−0.496077	−	0.868279i	$-0.665227\pi$
$131$	5.76755	−	9.98968i	0.503913	−	0.872803i	0.999990	−	0.00452412i	$-0.00144008\pi$
$132$			36.4046i			3.16861i
$133$	3.22932	+	14.9418i	0.280017	+	1.29561i
$134$	19.2952			1.66685
$135$		0			0
$136$	−0.221432	+	0.383532i	−0.0189876	+	0.0328876i
$137$	0.0947266	−	0.0546904i	0.00809304	−	0.00467252i	−0.495948	−	0.868352i	$-0.665179\pi$
$137$	0.0947266	−	0.0546904i	0.00809304	−	0.00467252i	0.504041	+	0.863680i	$0.331846\pi$
$138$	−5.74829	−	3.31878i	−0.489327	−	0.282513i
$139$	0.721876	+	1.25033i	0.0612287	+	0.106051i	0.895015	−	0.446036i	$-0.147165\pi$
$139$	0.721876	+	1.25033i	0.0612287	+	0.106051i	−0.833786	+	0.552088i	$0.813831\pi$
$140$		0			0
$141$	−7.67967			−0.646745
$142$	−32.1307	+	18.5507i	−2.69635	+	1.55674i
$143$	−19.5160	+	11.2675i	−1.63201	+	0.942240i
$144$	0.207839			0.0173199
$145$		0			0
$146$	8.17922	+	14.1668i	0.676917	+	1.17245i
$147$	11.5053	+	6.64257i	0.948939	+	0.547870i
$148$	30.5943	−	17.6636i	2.51484	−	1.45194i
$149$	0.864447	−	1.49727i	0.0708183	−	0.122661i	−0.828442	−	0.560075i	$-0.810772\pi$
$149$	0.864447	−	1.49727i	0.0708183	−	0.122661i	0.899260	+	0.437414i	$0.144106\pi$
$150$		0			0
$151$	−20.1406			−1.63902			−0.819508	−	0.573068i	$-0.805753\pi$
$151$	−20.1406			−1.63902			−0.819508	+	0.573068i	$0.805753\pi$
$152$	−2.57107	−	11.8961i	−0.208541	−	0.964900i
$153$		−	0.521056i		−	0.0421249i
$154$	−18.0597	+	31.2803i	−1.45529	+	2.52064i
$155$		0			0
$156$	−20.1933	−	34.9758i	−1.61675	−	2.80030i
$157$	−3.27195	−	1.88906i	−0.261130	−	0.150764i	0.363720	−	0.931508i	$-0.381507\pi$
$157$	−3.27195	−	1.88906i	−0.261130	−	0.150764i	−0.624850	+	0.780745i	$0.714840\pi$
$158$	20.0403	−	11.5703i	1.59432	−	0.920482i
$159$	−14.3976			−1.14181
$160$		0			0
$161$	−2.03163	−	3.51889i	−0.160115	−	0.277328i
$162$	−15.9571	+	9.21286i	−1.25371	+	0.723830i
$163$			1.61640i			0.126606i	0.997994	+	0.0633031i	$0.0201635\pi$
$163$			1.61640i			0.126606i	−0.997994	+	0.0633031i	$0.979837\pi$
$164$	−19.5803			−1.52897
$165$		0			0
$166$	−5.54767	+	9.60885i	−0.430583	+	0.745791i
$167$	5.62309	−	3.24649i	0.435128	−	0.251221i	−0.266401	−	0.963862i	$-0.585835\pi$
$167$	5.62309	−	3.24649i	0.435128	−	0.251221i	0.701529	+	0.712641i	$0.252501\pi$
$168$	−21.2602	−	12.2746i	−1.64026	−	0.947003i
$169$	6.00000	−	10.3923i	0.461538	−	0.799408i
$170$		0			0
$171$	9.61796	+	10.6088i	0.735504	+	0.811273i
$172$		−	10.7882i		−	0.822589i
$173$	7.37945	+	4.26053i	0.561049	+	0.323922i	0.753567	−	0.657372i	$-0.228332\pi$
$173$	7.37945	+	4.26053i	0.561049	+	0.323922i	−0.192517	+	0.981294i	$0.561665\pi$
$174$	10.0457	−	17.3996i	0.761560	−	1.31906i
$175$		0			0
$176$	−0.142571	+	0.246941i	−0.0107467	+	0.0186139i
$177$	−6.65079	+	3.83983i	−0.499904	+	0.288620i
$178$			2.54221i			0.190547i
$179$	10.2711			0.767698			0.383849	−	0.923396i	$-0.374598\pi$
$179$	10.2711			0.767698			0.383849	+	0.923396i	$0.374598\pi$
$180$		0			0
$181$	−6.13355	−	10.6236i	−0.455903	−	0.789648i	0.542836	−	0.839838i	$-0.317350\pi$
$181$	−6.13355	−	10.6236i	−0.455903	−	0.789648i	−0.998740	+	0.0501908i	$0.984017\pi$
$182$		−	40.0702i		−	2.97020i
$183$		−	2.18980i		−	0.161875i
$184$	1.61751	+	2.80161i	0.119245	+	0.206538i
$185$		0			0
$186$	−6.54567	−	11.3374i	−0.479952	−	0.831301i
$187$	0.619085	+	0.357429i	0.0452720	+	0.0261378i
$188$	8.54721	+	4.93473i	0.623369	+	0.359902i
$189$	2.50702			0.182359
$190$		0			0
$191$	5.71085			0.413223			0.206611	−	0.978423i	$-0.433756\pi$
$191$	5.71085			0.413223			0.206611	+	0.978423i	$0.433756\pi$
$192$	−28.1484	−	16.2515i	−2.03144	−	1.17285i
$193$	−8.79761	−	5.07930i	−0.633266	−	0.365616i	0.148750	−	0.988875i	$-0.452475\pi$
$193$	−8.79761	−	5.07930i	−0.633266	−	0.365616i	−0.782016	+	0.623259i	$0.785808\pi$
$194$	1.85041	+	3.20500i	0.132852	+	0.230106i
$195$		0			0
$196$	−8.53665	−	14.7859i	−0.609761	−	1.05614i
$197$			16.2038i			1.15448i	0.816576	+	0.577238i	$0.195869\pi$
$197$			16.2038i			1.15448i	−0.816576	+	0.577238i	$0.804131\pi$
$198$			33.8343i			2.40450i
$199$	0.167186	+	0.289574i	0.0118515	+	0.0205274i	0.871890	−	0.489701i	$-0.162894\pi$
$199$	0.167186	+	0.289574i	0.0118515	+	0.0205274i	−0.860039	+	0.510229i	$0.829561\pi$
$200$		0			0
$201$	21.1686			1.49312
$202$			28.1375i			1.97974i
$203$	10.6514	−	6.14959i	0.747582	−	0.431617i
$204$	−0.640570	+	1.10950i	−0.0448489	+	0.0776805i
$205$		0			0
$206$	−12.1300	+	21.0098i	−0.845137	+	1.46382i
$207$	−3.29626	−	1.90310i	−0.229106	−	0.132275i
$208$		−	0.316332i		−	0.0219336i
$209$	−19.2023	+	4.15013i	−1.32825	+	0.287071i
$210$		0			0
$211$	−1.01404	+	1.75636i	−0.0698092	+	0.120913i	−0.898817	−	0.438324i	$-0.855572\pi$
$211$	−1.01404	+	1.75636i	−0.0698092	+	0.120913i	0.829008	+	0.559237i	$0.188906\pi$
$212$	16.0241	+	9.25151i	1.10054	+	0.635396i
$213$	−35.2505	+	20.3519i	−2.41532	+	1.39449i
$214$	−2.48240	+	4.29965i	−0.169694	+	0.293918i
$215$		0			0
$216$	−1.99600			−0.135810
$217$		−	8.01404i		−	0.544028i
$218$	−31.3081	+	18.0757i	−2.12045	+	1.22424i
$219$	8.97338	+	15.5424i	0.606365	+	1.05026i
$220$		0			0
$221$	−0.793049			−0.0533463
$222$	54.4005	−	31.4081i	3.65112	−	2.10797i
$223$	−16.6553	−	9.61596i	−1.11532	−	0.643932i	−0.175120	−	0.984547i	$-0.556031\pi$
$223$	−16.6553	−	9.61596i	−1.11532	−	0.643932i	−0.940203	+	0.340615i	$0.889365\pi$
$224$	−10.0457	−	17.3996i	−0.671205	−	1.16256i
$225$		0			0
$226$	−11.2409	+	19.4699i	−0.747736	+	1.29512i
$227$			4.00000i			0.265489i	0.991150	+	0.132745i	$0.0423790\pi$
$227$			4.00000i			0.265489i	−0.991150	+	0.132745i	$0.957621\pi$
$228$	−7.43771	−	34.4136i	−0.492574	−	2.27909i
$229$	12.9788			0.857666			0.428833	−	0.903384i	$-0.358925\pi$
$229$	12.9788			0.857666			0.428833	+	0.903384i	$0.358925\pi$
$230$		0			0
$231$	−19.8132	+	34.3175i	−1.30361	+	2.25793i
$232$	−8.48026	+	4.89608i	−0.556756	+	0.321443i
$233$	23.4462	+	13.5367i	1.53601	+	0.886815i	0.999067	+	0.0431968i	$0.0137543\pi$
$233$	23.4462	+	13.5367i	1.53601	+	0.886815i	0.536943	+	0.843619i	$0.319579\pi$
$234$	−18.7675	−	32.5063i	−1.22687	−	2.12501i
$235$		0			0
$236$	9.86946			0.642447
$237$	21.9861	−	12.6937i	1.42815	−	0.824545i
$238$	−1.10081	+	0.635553i	−0.0713549	+	0.0411968i
$239$	−20.0602			−1.29758			−0.648792	−	0.760966i	$-0.724725\pi$
$239$	−20.0602			−1.29758			−0.648792	+	0.760966i	$0.724725\pi$
$240$		0			0
$241$	10.7922	+	18.6926i	0.695184	+	1.20409i	0.970119	+	0.242631i	$0.0780105\pi$
$241$	10.7922	+	18.6926i	0.695184	+	1.20409i	−0.274934	+	0.961463i	$0.588656\pi$
$242$	−18.4308	−	10.6410i	−1.18478	−	0.684030i
$243$	−19.3637	+	11.1797i	−1.24219	+	0.717176i
$244$	−1.40710	+	2.43717i	−0.0900805	+	0.156024i
$245$		0			0
$246$	−34.8162			−2.21980
$247$	16.1466	−	14.6386i	1.02738	−	0.931430i
$248$			6.38049i			0.405161i
$249$	−6.08632	+	10.5418i	−0.385705	+	0.668061i
$250$		0			0
$251$	3.63400	+	6.29426i	0.229376	+	0.397290i	0.957623	−	0.288024i	$-0.0929982\pi$
$251$	3.63400	+	6.29426i	0.229376	+	0.397290i	−0.728248	+	0.685314i	$0.759665\pi$
$252$	−32.1464	−	18.5597i	−2.02503	−	1.16915i
$253$	4.52228	−	2.61094i	0.284313	−	0.164148i
$254$	−35.9015			−2.25266
$255$		0			0
$256$	7.79416	+	13.4999i	0.487135	+	0.843743i
$257$	13.0573	−	7.53865i	0.814494	−	0.470248i	−0.0340202	−	0.999421i	$-0.510831\pi$
$257$	13.0573	−	7.53865i	0.814494	−	0.470248i	0.848514	+	0.529173i	$0.177498\pi$
$258$		−	19.1827i		−	1.19426i
$259$	38.4538			2.38940
$260$		0			0
$261$	5.76053	−	9.97753i	0.356568	−	0.617593i
$262$	−22.8279	+	13.1797i	−1.41031	+	0.814242i
$263$	17.4544	+	10.0773i	1.07628	+	0.621393i	0.929892	−	0.367833i	$-0.119900\pi$
$263$	17.4544	+	10.0773i	1.07628	+	0.621393i	0.146393	+	0.989227i	$0.453234\pi$
$264$	15.7746	−	27.3223i	0.970857	−	1.68157i
$265$		0			0
$266$	10.6812	−	33.2593i	0.654908	−	2.03926i
$267$			2.78905i			0.170687i
$268$	−23.5600	−	13.6024i	−1.43915	−	0.830897i
$269$	−3.86245	+	6.68995i	−0.235497	+	0.407894i	−0.959417	−	0.281991i	$-0.909005\pi$
$269$	−3.86245	+	6.68995i	−0.235497	+	0.407894i	0.723920	+	0.689884i	$0.242339\pi$
$270$		0			0
$271$	2.64257	−	4.57707i	0.160525	−	0.278037i	−0.774532	−	0.632534i	$-0.782015\pi$
$271$	2.64257	−	4.57707i	0.160525	−	0.278037i	0.935057	+	0.354497i	$0.115348\pi$
$272$	−0.00869027	+	0.00501733i	−0.000526925	+	0.000304220i
$273$		−	43.9608i		−	2.66063i
$274$	−0.249951			−0.0151001
$275$		0			0
$276$	4.67922	+	8.10465i	0.281656	+	0.487843i
$277$			30.6264i			1.84016i	0.391726	+	0.920082i	$0.371878\pi$
$277$			30.6264i			1.84016i	−0.391726	+	0.920082i	$0.628122\pi$
$278$		−	3.29918i		−	0.197872i
$279$	−3.75351	−	6.50127i	−0.224717	−	0.389221i
$280$		0			0
$281$	−6.68122	−	11.5722i	−0.398568	−	0.690341i	0.594981	−	0.803740i	$-0.297159\pi$
$281$	−6.68122	−	11.5722i	−0.398568	−	0.690341i	−0.993550	+	0.113399i	$0.963826\pi$
$282$	15.1980	+	8.77457i	0.905027	+	0.522518i
$283$	3.54667	+	2.04767i	0.210828	+	0.121721i	0.601696	−	0.798725i	$-0.294492\pi$
$283$	3.54667	+	2.04767i	0.210828	+	0.121721i	−0.390868	+	0.920447i	$0.627825\pi$
$284$	52.3101			3.10403
$285$		0			0
$286$	51.4959			3.04502
$287$	−18.4578	−	10.6566i	−1.08953	−	0.629040i
$288$	−16.2988	−	9.41012i	−0.960416	−	0.554497i
$289$	−8.48742	−	14.7006i	−0.499260	−	0.864744i
$290$		0			0
$291$	2.03008	+	3.51619i	0.119005	+	0.206123i
$292$		−	23.0642i		−	1.34973i
$293$		−	12.1726i		−	0.711134i	−0.934651	−	0.355567i	$-0.884288\pi$
$293$		−	12.1726i		−	0.711134i	0.934651	−	0.355567i	$-0.115712\pi$
$294$	−15.1792	−	26.2912i	−0.885270	−	1.53333i
$295$		0			0
$296$	−30.6155			−1.77949
$297$			3.22188i			0.186952i
$298$	−3.42147	+	1.97539i	−0.198200	+	0.114431i
$299$	−2.89652	+	5.01693i	−0.167510	+	0.290136i
$300$		0			0
$301$	5.87147	−	10.1697i	0.338426	−	0.586170i
$302$	39.8580	+	23.0120i	2.29357	+	1.32419i
$303$			30.8695i			1.77340i
$304$	0.0843223	−	0.262564i	0.00483621	−	0.0150591i
$305$		0			0
$306$	−0.595344	+	1.03117i	−0.0340335	+	0.0589478i
$307$	−21.2480	−	12.2675i	−1.21269	−	0.700146i	−0.249344	−	0.968415i	$-0.580215\pi$
$307$	−21.2480	−	12.2675i	−1.21269	−	0.700146i	−0.963344	+	0.268269i	$0.913548\pi$
$308$	44.1029	−	25.4628i	2.51299	−	1.45088i
$309$	−13.3078	+	23.0497i	−0.757052	+	1.31125i
$310$		0			0
$311$	−10.2038			−0.578606			−0.289303	−	0.957238i	$-0.593424\pi$
$311$	−10.2038			−0.578606			−0.289303	+	0.957238i	$0.593424\pi$
$312$			35.0000i			1.98148i
$313$	27.6972	−	15.9910i	1.56554	−	0.903864i	0.568859	−	0.822435i	$-0.307385\pi$
$313$	27.6972	−	15.9910i	1.56554	−	0.903864i	0.996679	−	0.0814282i	$-0.0259481\pi$
$314$	4.31678	+	7.47687i	0.243610	+	0.421944i
$315$		0			0
$316$	−32.6264			−1.83538
$317$	1.93636	−	1.11796i	0.108757	−	0.0627907i	−0.444635	−	0.895712i	$-0.646667\pi$
$317$	1.93636	−	1.11796i	0.108757	−	0.0627907i	0.553392	+	0.832921i	$0.313333\pi$
$318$	28.4928	+	16.4503i	1.59780	+	0.922489i
$319$	7.90310	+	13.6886i	0.442489	+	0.766413i
$320$		0			0
$321$	−2.72343	+	4.71713i	−0.152007	+	0.263284i
$322$			9.28514i			0.517441i
$323$	−0.658252	−	0.211397i	−0.0366261	−	0.0117625i
$324$	25.9788			1.44327
$325$		0			0
$326$	1.84685	−	3.19884i	0.102288	−	0.177167i
$327$	−34.3480	+	19.8308i	−1.89945	+	1.09665i
$328$	14.6954	+	8.48441i	0.811419	+	0.468473i
$329$	5.37147	+	9.30365i	0.296139	+	0.512927i
$330$		0			0
$331$	−10.0913			−0.554670			−0.277335	−	0.960773i	$-0.589451\pi$
$331$	−10.0913			−0.554670			−0.277335	+	0.960773i	$0.589451\pi$
$332$	13.5477	−	7.82179i	0.743529	−	0.429277i
$333$	31.1951	−	18.0105i	1.70948	−	0.986968i
$334$	−14.8374			−0.811866
$335$		0			0
$336$	−0.278124	−	0.481725i	−0.0151729	−	0.0262802i
$337$	−4.86048	−	2.80620i	−0.264767	−	0.152863i	0.361740	−	0.932279i	$-0.382183\pi$
$337$	−4.86048	−	2.80620i	−0.264767	−	0.152863i	−0.626507	+	0.779416i	$0.715516\pi$
$338$	−23.7479	+	13.7109i	−1.29172	+	0.745772i
$339$	−12.3324	+	21.3603i	−0.669802	+	1.16013i
$340$		0			0
$341$	10.2992			0.557732
$342$	−6.91258	−	31.9839i	−0.373790	−	1.72949i
$343$			5.96481i			0.322069i
$344$	−4.67465	+	8.09673i	−0.252040	+	0.436546i
$345$		0			0
$346$	−9.73591	−	16.8631i	−0.523406	−	0.906566i
$347$	−4.74144	−	2.73747i	−0.254534	−	0.146955i	0.367305	−	0.930101i	$-0.380281\pi$
$347$	−4.74144	−	2.73747i	−0.254534	−	0.146955i	−0.621838	+	0.783146i	$0.713614\pi$
$348$	−24.5321	+	14.1636i	−1.31506	+	0.759250i
$349$	18.8202			1.00742			0.503712	−	0.863872i	$-0.331967\pi$
$349$	18.8202			1.00742			0.503712	+	0.863872i	$0.331967\pi$
$350$		0			0
$351$	−1.78714	−	3.09542i	−0.0953907	−	0.165222i
$352$	22.3610	−	12.9101i	1.19184	−	0.688112i
$353$			12.7008i			0.675996i	0.941147	+	0.337998i	$0.109750\pi$
$353$			12.7008i			0.675996i	−0.941147	+	0.337998i	$0.890250\pi$
$354$	17.5491			0.932726
$355$		0			0
$356$	1.79216	−	3.10411i	0.0949843	−	0.164518i
$357$	−1.20769	+	0.697262i	−0.0639179	+	0.0369030i
$358$	−20.3264	−	11.7355i	−1.07429	−	0.620239i
$359$	−5.54021	+	9.59592i	−0.292401	+	0.506453i	−0.974377	−	0.224921i	$-0.927788\pi$
$359$	−5.54021	+	9.59592i	−0.292401	+	0.506453i	0.681976	+	0.731375i	$0.261121\pi$
$360$		0			0
$361$	17.3042	−	7.84632i	0.910747	−	0.412964i
$362$			28.0321i			1.47333i
$363$	−20.2203	−	11.6742i	−1.06129	−	0.612737i
$364$	−28.2479	+	48.9269i	−1.48059	+	2.56447i
$365$		0			0
$366$	−2.50200	+	4.33359i	−0.130782	+	0.226521i
$367$	−17.8752	+	10.3202i	−0.933076	+	0.538712i	−0.887783	−	0.460262i	$-0.847756\pi$
$367$	−17.8752	+	10.3202i	−0.933076	+	0.538712i	−0.0452932	+	0.998974i	$0.514422\pi$
$368$			0.0733010i			0.00382108i
$369$	−19.9648			−1.03933
$370$		0			0
$371$	10.0703	+	17.4422i	0.522823	+	0.905556i
$372$			18.4578i			0.956992i
$373$		−	4.55313i		−	0.235752i	−0.993028	−	0.117876i	$-0.962391\pi$
$373$		−	4.55313i		−	0.235752i	0.993028	−	0.117876i	$-0.0376086\pi$
$374$	−0.816776	−	1.41470i	−0.0422345	−	0.0731522i
$375$		0			0
$376$	−4.27657	−	7.40723i	−0.220547	−	0.381999i
$377$	−15.1858	−	8.76755i	−0.782110	−	0.451552i
$378$	−4.96137	−	2.86445i	−0.255185	−	0.147331i
$379$	19.9187			1.02315			0.511577	−	0.859237i	$-0.329061\pi$
$379$	19.9187			1.02315			0.511577	+	0.859237i	$0.329061\pi$
$380$		0			0
$381$	−39.3874			−2.01788
$382$	−11.3017	−	6.52506i	−0.578247	−	0.333851i
$383$	−17.2987	−	9.98742i	−0.883923	−	0.510333i	−0.0119734	−	0.999928i	$-0.503811\pi$
$383$	−17.2987	−	9.98742i	−0.883923	−	0.510333i	−0.871950	+	0.489595i	$0.837145\pi$
$384$	22.7746	+	39.4467i	1.16221	+	2.01301i
$385$		0			0
$386$	11.6069	+	20.1038i	0.590777	+	1.02326i
$387$		−	11.0000i		−	0.559161i
$388$		−	5.21787i		−	0.264897i
$389$	6.90110	+	11.9531i	0.349900	+	0.606044i	0.986231	−	0.165372i	$-0.0528824\pi$
$389$	6.90110	+	11.9531i	0.349900	+	0.606044i	−0.636332	+	0.771416i	$0.719549\pi$
$390$		0			0
$391$	0.183767			0.00929349
$392$			14.7962i			0.747319i
$393$	−25.0443	+	14.4593i	−1.26332	+	0.729378i
$394$	18.5140	−	32.0673i	0.932724	−	1.61552i
$395$		0			0
$396$	23.8519	−	41.3126i	1.19860	−	2.07604i
$397$	14.3320	+	8.27457i	0.719301	+	0.415289i	0.814495	−	0.580170i	$-0.197014\pi$
$397$	14.3320	+	8.27457i	0.719301	+	0.415289i	−0.0951945	+	0.995459i	$0.530347\pi$
$398$		−	0.764087i		−	0.0383002i
$399$	11.7183	−	36.4886i	0.586650	−	1.82672i
$400$		0			0
$401$	−4.26253	+	7.38292i	−0.212861	+	0.368685i	−0.952609	−	0.304199i	$-0.901611\pi$
$401$	−4.26253	+	7.38292i	−0.212861	+	0.368685i	0.739748	+	0.672884i	$0.234945\pi$
$402$	−41.8926	−	24.1867i	−2.08941	−	1.20632i
$403$	−9.89496	+	5.71286i	−0.492903	+	0.284578i
$404$	19.8358	−	34.3567i	0.986869	−	1.70931i
$405$		0			0
$406$	−28.1054			−1.39485
$407$			49.4186i			2.44959i
$408$	0.961521	−	0.555134i	0.0476024	−	0.0274833i
$409$	−5.78314	−	10.0167i	−0.285958	−	0.495294i	0.686883	−	0.726768i	$-0.258978\pi$
$409$	−5.78314	−	10.0167i	−0.285958	−	0.495294i	−0.972841	+	0.231474i	$0.925645\pi$
$410$		0			0
$411$	−0.274220			−0.0135263
$412$	29.6222	−	17.1024i	1.45938	−	0.842573i
$413$	9.30365	+	5.37147i	0.457803	+	0.264313i
$414$	4.34885	+	7.53243i	0.213734	+	0.370199i
$415$		0			0
$416$	−14.3222	+	24.8068i	−0.702205	+	1.21626i
$417$		−	3.61951i		−	0.177248i
$418$	42.7430	+	13.7269i	2.09063	+	0.671404i
$419$	21.7149			1.06084			0.530420	−	0.847735i	$-0.322034\pi$
$419$	21.7149			1.06084			0.530420	+	0.847735i	$0.322034\pi$
$420$		0			0
$421$	3.46135	−	5.99523i	0.168696	−	0.292190i	−0.769266	−	0.638929i	$-0.779378\pi$
$421$	3.46135	−	5.99523i	0.168696	−	0.292190i	0.937962	+	0.346739i	$0.112711\pi$
$422$	4.01354	−	2.31722i	0.195376	−	0.112800i
$423$	8.71504	+	5.03163i	0.423740	+	0.244646i
$424$	−8.01760	−	13.8869i	−0.389369	−	0.674407i
$425$		0			0
$426$	93.0138			4.50654
$427$	−2.65287	+	1.53163i	−0.128381	+	0.0741209i
$428$	6.06218	−	3.50000i	0.293026	−	0.169179i
$429$	56.4959			2.72765
$430$		0			0
$431$	13.9894	+	24.2304i	0.673847	+	1.16714i	0.976805	+	0.214133i	$0.0686926\pi$
$431$	13.9894	+	24.2304i	0.673847	+	1.16714i	−0.302958	+	0.953004i	$0.597974\pi$
$432$	−0.0391672	−	0.0226132i	−0.00188443	−	0.00108798i
$433$	−5.41608	+	3.12698i	−0.260280	+	0.150273i	−0.624462	−	0.781055i	$-0.714682\pi$
$433$	−5.41608	+	3.12698i	−0.260280	+	0.150273i	0.364182	+	0.931328i	$0.381349\pi$
$434$	−9.15661	+	15.8597i	−0.439531	+	0.761290i
$435$		0			0
$436$	50.9708			2.44106
$437$	−3.74152	+	3.39208i	−0.178981	+	0.162265i
$438$		−	41.0109i		−	1.95958i
$439$	15.5988	−	27.0179i	0.744490	−	1.28949i	−0.205942	−	0.978564i	$-0.566026\pi$
$439$	15.5988	−	27.0179i	0.744490	−	1.28949i	0.950433	−	0.310931i	$-0.100641\pi$
$440$		0			0
$441$	−8.70428	−	15.0763i	−0.414490	−	0.717917i
$442$	1.56944	+	0.906115i	0.0746505	+	0.0430995i
$443$	28.3223	−	16.3519i	1.34563	−	0.776901i	0.358004	−	0.933720i	$-0.383457\pi$
$443$	28.3223	−	16.3519i	1.34563	−	0.776901i	0.987627	+	0.156819i	$0.0501240\pi$
$444$	−88.5661			−4.20316
$445$		0			0
$446$	21.9738	+	38.0598i	1.04049	+	1.80218i
$447$	−3.75368	+	2.16719i	−0.177543	+	0.102504i
$448$			45.4678i			2.14815i
$449$	−25.6304			−1.20958			−0.604788	−	0.796387i	$-0.706742\pi$
$449$	−25.6304			−1.20958			−0.604788	+	0.796387i	$0.706742\pi$
$450$		0			0
$451$	13.6953	−	23.7209i	0.644885	−	1.11697i
$452$	27.4510	−	15.8489i	1.29119	−	0.745467i
$453$	43.7280	+	25.2464i	2.05452	+	1.18618i
$454$	4.57028	−	7.91597i	0.214494	−	0.371515i
$455$		0			0
$456$	−9.32970	+	29.0509i	−0.436903	+	1.36043i
$457$			33.1646i			1.55138i	0.631116	+	0.775688i	$0.282597\pi$
$457$			33.1646i			1.55138i	−0.631116	+	0.775688i	$0.717403\pi$
$458$	−25.6850	−	14.8293i	−1.20018	−	0.692926i
$459$	−0.0566917	+	0.0981929i	−0.00264614	+	0.00458325i
$460$		0			0
$461$	−1.08788	+	1.88426i	−0.0506677	+	0.0877590i	−0.890247	−	0.455478i	$-0.849468\pi$
$461$	−1.08788	+	1.88426i	−0.0506677	+	0.0877590i	0.839579	+	0.543237i	$0.182802\pi$
$462$	78.4204	−	45.2760i	3.64845	−	2.10643i
$463$			6.20072i			0.288172i	0.989565	+	0.144086i	$0.0460242\pi$
$463$			6.20072i			0.288172i	−0.989565	+	0.144086i	$0.953976\pi$
$464$	−0.221876			−0.0103003
$465$		0			0
$466$	−30.9332	−	53.5778i	−1.43295	−	2.48195i
$467$		−	17.1546i		−	0.793821i	−0.917857	−	0.396910i	$-0.870082\pi$
$467$		−	17.1546i		−	0.793821i	0.917857	−	0.396910i	$-0.129918\pi$
$468$			52.9216i			2.44630i
$469$	−14.8062	−	25.6451i	−0.683687	−	1.18418i
$470$		0			0
$471$	4.73591	+	8.20284i	0.218219	+	0.377967i
$472$	−7.40723	−	4.27657i	−0.340945	−	0.196845i
$473$	13.0695	+	7.54567i	0.600936	+	0.346950i
$474$	−58.0138			−2.66466
$475$		0			0
$476$	1.79216			0.0821436
$477$	16.3387	+	9.43318i	0.748099	+	0.431915i
$478$	39.6989	+	22.9202i	1.81578	+	1.04834i
$479$	−17.8891	−	30.9848i	−0.817372	−	1.41573i	−0.907612	−	0.419810i	$-0.862097\pi$
$479$	−17.8891	−	30.9848i	−0.817372	−	1.41573i	0.0902399	−	0.995920i	$-0.471237\pi$
$480$		0			0
$481$	−27.4120	−	47.4790i	−1.24988	−	2.16486i
$482$		−	49.3233i		−	2.24661i
$483$			10.1867i			0.463510i
$484$	15.0030	+	25.9860i	0.681955	+	1.18118i
$485$		0			0
$486$	51.0943			2.31768
$487$		−	23.7149i		−	1.07462i	−0.843384	−	0.537311i	$-0.819440\pi$
$487$		−	23.7149i		−	1.07462i	0.843384	−	0.537311i	$-0.180560\pi$
$488$	2.11212	−	1.21943i	0.0956110	−	0.0552010i
$489$	2.02617	−	3.50943i	0.0916267	−	0.158702i
$490$		0			0
$491$	19.5933	−	33.9367i	0.884235	−	1.53154i	0.0376474	−	0.999291i	$-0.488014\pi$
$491$	19.5933	−	33.9367i	0.884235	−	1.53154i	0.846588	−	0.532249i	$-0.178653\pi$
$492$	42.5117	+	24.5441i	1.91657	+	1.10653i
$493$			0.556248i			0.0250521i
$494$	−48.6796	+	10.5210i	−2.19020	+	0.473361i
$495$		0			0
$496$	−0.0722863	+	0.125204i	−0.00324575	+	0.00562180i
$497$	49.3112	+	28.4698i	2.21191	+	1.27705i
$498$	24.0896	−	13.9081i	1.07948	−	0.623238i
$499$	−4.68824	+	8.12027i	−0.209875	+	0.363513i	−0.951675	−	0.307107i	$-0.900639\pi$
$499$	−4.68824	+	8.12027i	−0.209875	+	0.363513i	0.741800	+	0.670621i	$0.233972\pi$
$500$		0			0
$501$	−16.2780			−0.727249
$502$		−	16.6084i		−	0.741269i
$503$	−11.6853	+	6.74649i	−0.521020	+	0.300811i	−0.737352	−	0.675509i	$-0.763924\pi$
$503$	−11.6853	+	6.74649i	−0.521020	+	0.300811i	0.216332	+	0.976320i	$0.430591\pi$
$504$	16.0843	+	27.8589i	0.716453	+	1.24093i
$505$		0			0
$506$	−11.9327			−0.530475
$507$	−26.0537	+	15.0421i	−1.15709	+	0.668044i
$508$	43.8368	+	25.3092i	1.94495	+	1.12291i
$509$	12.8534	+	22.2628i	0.569718	+	0.986781i	0.996594	+	0.0824703i	$0.0262809\pi$
$509$	12.8534	+	22.2628i	0.569718	+	0.986781i	−0.426875	+	0.904310i	$0.640386\pi$
$510$		0			0
$511$	12.5527	−	21.7419i	0.555298	−	0.961805i
$512$			0.715746i			0.0316318i
$513$	−0.658252	−	3.04567i	−0.0290625	−	0.134470i
$514$	−34.4538			−1.51969
$515$		0			0
$516$	−13.5231	+	23.4226i	−0.595319	+	1.03112i
$517$	−11.9565	+	6.90310i	−0.525847	+	0.303598i
$518$	−76.0997	−	43.9362i	−3.34363	−	1.93045i
$519$	−10.6812	−	18.5004i	−0.468854	−	0.812078i
$520$		0			0
$521$	−37.7358			−1.65324			−0.826618	−	0.562763i	$-0.809738\pi$
$521$	−37.7358			−1.65324			−0.826618	+	0.562763i	$0.809738\pi$
$522$	−22.8001	+	13.1636i	−0.997932	+	0.576156i
$523$	−33.2559	+	19.2003i	−1.45418	+	0.839570i	−0.998715	−	0.0506855i	$-0.983859\pi$
$523$	−33.2559	+	19.2003i	−1.45418	+	0.839570i	−0.455462	+	0.890255i	$0.650526\pi$
$524$	37.1646			1.62354
$525$		0			0
$526$	−23.0281	−	39.8858i	−1.00407	−	1.73910i
$527$	0.313888	+	0.181223i	0.0136732	+	0.00789420i
$528$	0.619085	−	0.357429i	0.0269422	−	0.0155551i
$529$	−10.8288	+	18.7561i	−0.470818	+	0.815481i
$530$		0			0
$531$	10.0633			0.436709
$532$	−36.4886	+	33.0808i	−1.58198	+	1.43423i
$533$			30.3865i			1.31619i
$534$	3.18668	−	5.51950i	0.137901	−	0.238852i
$535$		0			0
$536$	11.7882	+	20.4177i	0.509171	+	0.881910i
$537$	−22.3000	−	12.8749i	−0.962317	−	0.555594i
$538$	15.2875	−	8.82624i	0.659091	−	0.380526i
$539$	23.8835			1.02874
$540$		0			0
$541$	6.40310	+	11.0905i	0.275291	+	0.476818i	0.970208	−	0.242272i	$-0.0778926\pi$
$541$	6.40310	+	11.0905i	0.275291	+	0.476818i	−0.694918	+	0.719089i	$0.744559\pi$
$542$	−10.4593	+	6.03865i	−0.449263	+	0.259382i
$543$			30.7539i			1.31977i
$544$	0.908659			0.0389584
$545$		0			0
$546$	−50.2284	+	86.9981i	−2.14958	+	3.72317i
$547$	−15.8111	+	9.12853i	−0.676033	+	0.390308i	−0.798359	−	0.602182i	$-0.794298\pi$
$547$	−15.8111	+	9.12853i	−0.676033	+	0.390308i	0.122326	+	0.992490i	$0.460965\pi$
$548$	0.305197	+	0.176206i	0.0130374	+	0.00752714i
$549$	−1.43473	+	2.48503i	−0.0612329	+	0.106058i
$550$		0			0
$551$	−10.2675	−	11.3253i	−0.437412	−	0.482473i
$552$		−	8.11027i		−	0.345196i
$553$	−30.7560	−	17.7570i	−1.30788	−	0.755103i
$554$	34.9929	−	60.6095i	1.48671	−	2.57505i
$555$		0			0
$556$	−2.32580	+	4.02840i	−0.0986357	+	0.170842i
$557$	12.9078	−	7.45233i	0.546922	−	0.315765i	−0.200958	−	0.979600i	$-0.564405\pi$
$557$	12.9078	−	7.45233i	0.546922	−	0.315765i	0.747879	+	0.663835i	$0.231072\pi$
$558$			17.1546i			0.726212i
$559$	−16.7420			−0.708113
$560$		0			0
$561$	−0.896081	−	1.55206i	−0.0378326	−	0.0655279i
$562$			30.5351i			1.28805i
$563$		−	45.7810i		−	1.92944i	−0.263276	−	0.964720i	$-0.584803\pi$
$563$		−	45.7810i		−	1.92944i	0.263276	−	0.964720i	$-0.415197\pi$
$564$	−12.3715	−	21.4280i	−0.520933	−	0.902282i
$565$		0			0
$566$	−4.67922	−	8.10465i	−0.196682	−	0.340664i
$567$	24.4895	+	14.1390i	1.02846	+	0.593783i
$568$	−39.2598	−	22.6666i	−1.64730	−	0.951071i
$569$	−0.379598			−0.0159136			−0.00795679	−	0.999968i	$-0.502533\pi$
$569$	−0.379598			−0.0159136			−0.00795679	+	0.999968i	$0.502533\pi$
$570$		0			0
$571$	−15.8514			−0.663361			−0.331681	−	0.943392i	$-0.607616\pi$
$571$	−15.8514			−0.663361			−0.331681	+	0.943392i	$0.607616\pi$
$572$	−62.8780	−	36.3026i	−2.62906	−	1.51789i
$573$	−12.3991	−	7.15861i	−0.517979	−	0.299055i
$574$	24.3519	+	42.1787i	1.01643	+	1.76050i
$575$		0			0
$576$	21.2956	+	36.8851i	0.887318	+	1.53688i
$577$		−	19.2350i		−	0.800765i	−0.916348	−	0.400382i	$-0.868877\pi$
$577$		−	19.2350i		−	0.800765i	0.916348	−	0.400382i	$-0.131123\pi$
$578$			38.7899i			1.61345i
$579$	12.7339	+	22.0558i	0.529203	+	0.916607i
$580$		0			0
$581$	17.0281			0.706444
$582$		−	9.27803i		−	0.384587i
$583$	−22.4158	+	12.9418i	−0.928366	+	0.535993i
$584$	−9.99400	+	17.3101i	−0.413554	+	0.716297i
$585$		0			0
$586$	−13.9081	+	24.0896i	−0.574539	+	0.995131i
$587$	−35.3757	−	20.4242i	−1.46011	−	0.842995i	−0.461095	−	0.887351i	$-0.652543\pi$
$587$	−35.3757	−	20.4242i	−1.46011	−	0.842995i	−0.999016	+	0.0443559i	$0.985876\pi$
$588$			42.8031i			1.76517i
$589$	−9.73591	+	2.10419i	−0.401161	+	0.0867018i
$590$		0			0
$591$	20.3117	−	35.1808i	0.835510	−	1.44715i
$592$	−0.600764	−	0.346852i	−0.0246913	−	0.0142555i
$593$	12.3381	−	7.12342i	0.506666	−	0.292524i	−0.224796	−	0.974406i	$-0.572172\pi$
$593$	12.3381	−	7.12342i	0.506666	−	0.292524i	0.731462	+	0.681882i	$0.238838\pi$
$594$	3.68122	−	6.37607i	0.151042	−	0.261613i
$595$		0			0
$596$	5.57028			0.228168
$597$		−	0.838276i		−	0.0343083i
$598$	11.4644	−	6.61897i	0.468814	−	0.270670i
$599$	−7.92571	−	13.7277i	−0.323836	−	0.560900i	0.657440	−	0.753507i	$-0.271639\pi$
$599$	−7.92571	−	13.7277i	−0.323836	−	0.560900i	−0.981276	+	0.192607i	$0.938306\pi$
$600$		0			0
$601$	16.4718			0.671900			0.335950	−	0.941880i	$-0.390943\pi$
$601$	16.4718			0.671900			0.335950	+	0.941880i	$0.390943\pi$
$602$	−23.2392	+	13.4171i	−0.947158	+	0.546842i
$603$	−24.0226	−	13.8695i	−0.978277	−	0.564808i
$604$	−32.4452	−	56.1968i	−1.32018	−	2.28661i
$605$		0			0
$606$	35.2706	−	61.0904i	1.43277	−	2.48163i
$607$		−	10.3914i		−	0.421774i	−0.977510	−	0.210887i	$-0.932365\pi$
$607$		−	10.3914i		−	0.421774i	0.977510	−	0.210887i	$-0.0676353\pi$
$608$	−18.5004	+	16.7726i	−0.750291	+	0.680217i
$609$	−30.8343			−1.24947
$610$		0			0
$611$	7.65817	−	13.2643i	0.309816	−	0.536617i
$612$	1.45386	−	0.839389i	0.0587690	−	0.0339303i
$613$	−18.8664	−	10.8925i	−0.762007	−	0.439945i	0.0680090	−	0.997685i	$-0.478335\pi$
$613$	−18.8664	−	10.8925i	−0.762007	−	0.439945i	−0.830016	+	0.557740i	$0.811669\pi$
$614$	28.0331	+	48.5547i	1.13132	+	1.95951i
$615$		0			0
$616$	−44.1335			−1.77819
$617$	−37.0408	+	21.3855i	−1.49121	+	0.860948i	−0.999949	−	0.0100671i	$-0.996795\pi$
$617$	−37.0408	+	21.3855i	−1.49121	+	0.860948i	−0.491256	+	0.871015i	$0.663462\pi$
$618$	52.6719	−	30.4101i	2.11877	−	1.22327i
$619$	−28.7882			−1.15709			−0.578547	−	0.815649i	$-0.696380\pi$
$619$	−28.7882			−1.15709			−0.578547	+	0.815649i	$0.696380\pi$
$620$		0			0
$621$	0.414120	+	0.717278i	0.0166181	+	0.0287834i
$622$	20.1933	+	11.6586i	0.809678	+	0.467468i
$623$	3.37883	−	1.95077i	0.135370	−	0.0781560i
$624$	−0.396525	+	0.686801i	−0.0158737	+	0.0274940i
$625$		0			0
$626$	−73.0833			−2.92100
$627$	46.8931	+	15.0597i	1.87273	+	0.601427i
$628$		−	12.1726i		−	0.485742i
$629$	−0.869563	+	1.50613i	−0.0346718	+	0.0600532i
$630$		0			0
$631$	9.69370	+	16.7900i	0.385900	+	0.668399i	0.991894	−	0.127071i	$-0.0405576\pi$
$631$	9.69370	+	16.7900i	0.385900	+	0.668399i	−0.605993	+	0.795470i	$0.707224\pi$
$632$	24.4868	+	14.1375i	0.974032	+	0.562358i
$633$	4.40324	−	2.54221i	0.175013	−	0.101044i
$634$	−5.10938			−0.202919
$635$		0			0
$636$	−23.1937	−	40.1727i	−0.919690	−	1.59295i
$637$	−22.9461	+	13.2479i	−0.909158	+	0.524903i
$638$		−	36.1194i		−	1.42998i
$639$	53.3373			2.10999
$640$		0			0
$641$	−20.3433	+	35.2356i	−0.803512	+	1.39172i	0.113779	+	0.993506i	$0.463704\pi$
$641$	−20.3433	+	35.2356i	−0.803512	+	1.39172i	−0.917291	+	0.398217i	$0.869629\pi$
$642$	10.7793	−	6.22343i	0.425425	−	0.245619i
$643$	−29.5361	−	17.0527i	−1.16479	−	0.672492i	−0.212344	−	0.977195i	$-0.568110\pi$
$643$	−29.5361	−	17.0527i	−1.16479	−	0.672492i	−0.952448	+	0.304703i	$0.901443\pi$
$644$	6.54567	−	11.3374i	0.257936	−	0.446757i
$645$		0			0
$646$	1.06114	+	1.17045i	0.0417499	+	0.0460509i
$647$		−	48.0029i		−	1.88719i	−0.331103	−	0.943595i	$-0.607421\pi$
$647$		−	48.0029i		−	1.88719i	0.331103	−	0.943595i	$-0.392579\pi$
$648$	−19.4976	−	11.2570i	−0.765940	−	0.442216i
$649$	−6.90310	+	11.9565i	−0.270970	+	0.469334i
$650$		0			0
$651$	−10.0457	+	17.3996i	−0.393721	+	0.681945i
$652$	−4.51012	+	2.60392i	−0.176630	+	0.101977i
$653$		−	3.90866i		−	0.152958i	−0.997071	−	0.0764788i	$-0.975632\pi$
$653$		−	3.90866i		−	0.152958i	0.997071	−	0.0764788i	$-0.0243678\pi$
$654$	90.6325			3.54401
$655$		0			0
$656$	0.192244	+	0.332977i	0.00750588	+	0.0130006i
$657$		−	23.5171i		−	0.917488i
$658$		−	24.5491i		−	0.957025i
$659$	6.54411	+	11.3347i	0.254922	+	0.441539i	0.964874	−	0.262711i	$-0.0846167\pi$
$659$	6.54411	+	11.3347i	0.254922	+	0.441539i	−0.709952	+	0.704250i	$0.751283\pi$
$660$		0			0
$661$	11.9714	+	20.7350i	0.465633	+	0.806500i	0.999230	−	0.0392391i	$-0.0124934\pi$
$661$	11.9714	+	20.7350i	0.465633	+	0.806500i	−0.533597	+	0.845739i	$0.679160\pi$
$662$	19.9707	+	11.5301i	0.776182	+	0.448129i
$663$	1.72182	+	0.994095i	0.0668700	+	0.0386074i
$664$	−13.5571			−0.526119
$665$		0			0
$666$	−82.3130			−3.18956
$667$	3.51889	+	2.03163i	0.136252	+	0.0786652i
$668$	18.1169	+	10.4598i	0.700963	+	0.404701i
$669$	24.1074	+	41.7552i	0.932045	+	1.61435i
$670$		0			0
$671$	−1.96837	−	3.40931i	−0.0759880	−	0.131615i
$672$			50.3694i			1.94304i
$673$			11.3304i			0.436754i	0.975865	+	0.218377i	$0.0700762\pi$
$673$			11.3304i			0.436754i	−0.975865	+	0.218377i	$0.929924\pi$
$674$	6.41256	+	11.1069i	0.247003	+	0.427821i
$675$		0			0
$676$	38.6625			1.48702
$677$			8.90466i			0.342234i	0.985251	+	0.171117i	$0.0547376\pi$
$677$			8.90466i			0.342234i	−0.985251	+	0.171117i	$0.945262\pi$
$678$	48.8113	−	28.1812i	1.87459	−	1.08229i
$679$	2.83983	−	4.91873i	0.108983	−	0.188764i
$680$		0			0
$681$	5.01404	−	8.68457i	0.192138	−	0.332793i
$682$	−20.3820	−	11.7675i	−0.780467	−	0.450603i
$683$			26.6977i			1.02156i	0.859712	+	0.510780i	$0.170643\pi$
$683$			26.6977i			1.02156i	−0.859712	+	0.510780i	$0.829357\pi$
$684$	−14.1069	+	43.9263i	−0.539392	+	1.67957i
$685$		0			0
$686$	6.81522	−	11.8043i	0.260206	−	0.450690i
$687$	−28.1789	−	16.2691i	−1.07509	−	0.620705i
$688$	−0.183460	+	0.105921i	−0.00699435	+	0.00403819i
$689$	14.3573	−	24.8676i	0.546971	−	0.947381i
$690$		0			0
$691$	35.9708			1.36840			0.684198	−	0.729297i	$-0.260153\pi$
$691$	35.9708			1.36840			0.684198	+	0.729297i	$0.260153\pi$
$692$			27.4538i			1.04364i
$693$	44.9689	−	25.9628i	1.70823	−	0.986245i
$694$	6.25551	+	10.8349i	0.237456	+	0.411286i
$695$		0			0
$696$	24.5491			0.930532
$697$	0.834779	−	0.481960i	0.0316195	−	0.0182555i
$698$	−37.2451	−	21.5035i	−1.40975	−	0.813918i
$699$	−33.9366	−	58.7800i	−1.28360	−	2.22326i
$700$		0			0
$701$	−1.22543	+	2.12252i	−0.0462840	+	0.0801663i	−0.888239	−	0.459381i	$-0.848071\pi$
$701$	−1.22543	+	2.12252i	−0.0462840	+	0.0801663i	0.841955	+	0.539547i	$0.181405\pi$
$702$			8.16776i			0.308272i
$703$	−10.0966	−	46.7159i	−0.380799	−	1.76192i
$704$	−58.4326			−2.20226
$705$		0			0
$706$	14.5116	−	25.1348i	0.546151	−	0.945961i
$707$	37.3973	−	21.5913i	1.40647	−	0.812026i
$708$	−21.4280	−	12.3715i	−0.805314	−	0.464948i
$709$	−25.1440	−	43.5507i	−0.944304	−	1.63558i	−0.757139	−	0.653254i	$-0.773403\pi$
$709$	−25.1440	−	43.5507i	−0.944304	−	1.63558i	−0.187165	−	0.982329i	$-0.559930\pi$
$710$		0			0
$711$	−33.2671			−1.24761
$712$	−2.69011	+	1.55313i	−0.100816	+	0.0582061i
$713$	2.29288	−	1.32379i	0.0858690	−	0.0495765i
$714$	3.18668			0.119259
$715$		0			0
$716$	16.5461	+	28.6587i	0.618357	+	1.07103i
$717$	43.5534	+	25.1456i	1.62653	+	0.939079i
$718$	21.9281	−	12.6602i	0.818348	−	0.472473i
$719$	−24.0491	+	41.6543i	−0.896881	+	1.55344i	−0.0654223	+	0.997858i	$0.520839\pi$
$719$	−24.0491	+	41.6543i	−0.896881	+	1.55344i	−0.831459	+	0.555586i	$0.812494\pi$
$720$		0			0
$721$	37.2319			1.38659
$722$	−43.2098	−	4.24347i	−1.60810	−	0.157926i
$723$		−	54.1123i		−	2.01246i
$724$	19.7615	−	34.2280i	0.734432	−	1.27207i
$725$		0			0
$726$	26.6772	+	46.2063i	0.990085	+	1.71488i
$727$	14.4450	+	8.33983i	0.535736	+	0.309307i	0.743349	−	0.668904i	$-0.233236\pi$
$727$	14.4450	+	8.33983i	0.535736	+	0.309307i	−0.207613	+	0.978211i	$0.566570\pi$
$728$	42.4013	−	24.4804i	1.57150	−	0.907304i
$729$	31.8655			1.18020
$730$		0			0
$731$	0.265545	+	0.459938i	0.00982155	+	0.0170114i
$732$	6.11004	−	3.52763i	0.225833	−	0.130385i
$733$			4.13365i			0.152680i	0.997082	+	0.0763399i	$0.0243234\pi$
$733$			4.13365i			0.152680i	−0.997082	+	0.0763399i	$0.975677\pi$
$734$	47.1664			1.74094
$735$		0			0
$736$	3.31878	−	5.74829i	0.122332	−	0.211885i
$737$	32.9576	−	19.0281i	1.21401	−	0.700908i
$738$	39.5102	+	22.8112i	1.45439	+	0.839692i
$739$	23.4870	−	40.6806i	0.863982	−	1.49646i	−0.00407159	−	0.999992i	$-0.501296\pi$
$739$	23.4870	−	40.6806i	0.863982	−	1.49646i	0.868054	−	0.496470i	$-0.165371\pi$
$740$		0			0
$741$	−53.4061	+	11.5425i	−1.96192	+	0.424025i
$742$		−	46.0241i		−	1.68960i
$743$	35.6923	+	20.6069i	1.30942	+	0.755995i	0.982000	−	0.188883i	$-0.0604867\pi$
$743$	35.6923	+	20.6069i	1.30942	+	0.755995i	0.327422	+	0.944878i	$0.393820\pi$
$744$	7.99800	−	13.8529i	0.293221	−	0.507873i
$745$		0			0
$746$	−5.20228	+	9.01061i	−0.190469	+	0.329902i
$747$	13.8138	−	7.97539i	0.505420	−	0.291804i
$748$			2.30318i			0.0842127i
$749$	7.61951			0.278411
$750$		0			0
$751$	−2.98942	−	5.17783i	−0.109086	−	0.188942i	0.806314	−	0.591487i	$-0.201459\pi$
$751$	−2.98942	−	5.17783i	−0.109086	−	0.188942i	−0.915400	+	0.402545i	$0.868126\pi$
$752$		−	0.193802i		−	0.00706722i
$753$		−	18.2210i		−	0.664010i
$754$	20.0351	+	34.7018i	0.729635	+	1.26376i
$755$		0			0
$756$	4.03865	+	6.99515i	0.146884	+	0.254411i
$757$	−31.5178	−	18.1968i	−1.14553	−	0.661375i	−0.197739	−	0.980255i	$-0.563360\pi$
$757$	−31.5178	−	18.1968i	−1.14553	−	0.661375i	−0.947795	+	0.318880i	$0.896693\pi$
$758$	−39.4189	−	22.7585i	−1.43176	−	0.826627i
$759$	−13.0913			−0.475186
$760$		0			0
$761$	−2.71397			−0.0983813			−0.0491907	−	0.998789i	$-0.515664\pi$
$761$	−2.71397			−0.0983813			−0.0491907	+	0.998789i	$0.515664\pi$
$762$	77.9473	+	45.0029i	2.82373	+	1.63028i
$763$	48.0487	+	27.7409i	1.73948	+	1.00429i
$764$	9.19983	+	15.9346i	0.332838	+	0.576493i
$765$		0			0
$766$	22.8227	+	39.5300i	0.824617	+	1.42828i
$767$		−	15.3163i		−	0.553041i
$768$		−	39.0802i		−	1.41019i
$769$	19.8995	+	34.4670i	0.717596	+	1.24291i	0.961950	+	0.273226i	$0.0880908\pi$
$769$	19.8995	+	34.4670i	0.717596	+	1.24291i	−0.244354	+	0.969686i	$0.578576\pi$
$770$		0			0
$771$	−37.7991			−1.36130
$772$		−	32.7298i		−	1.17797i
$773$	−38.9494	+	22.4874i	−1.40091	+	0.808816i	−0.994486	−	0.104868i	$-0.966558\pi$
$773$	−38.9494	+	22.4874i	−1.40091	+	0.808816i	−0.406425	+	0.913684i	$0.633225\pi$
$774$	−12.5683	+	21.7689i	−0.451758	+	0.782467i
$775$		0			0
$776$	−2.26097	+	3.91612i	−0.0811642	+	0.140580i
$777$	−83.4886	−	48.2022i	−2.99514	−	1.72924i
$778$		−	31.5400i		−	1.13076i
$779$	−8.09992	+	25.2216i	−0.290210	+	0.903658i
$780$		0			0
$781$	−36.5878	+	63.3719i	−1.30921	+	2.26762i
$782$	−0.363673	−	0.209967i	−0.0130049	−	0.00750840i
$783$	−2.17114	+	1.25351i	−0.0775903	+	0.0447968i
$784$	−0.167630	+	0.290343i	−0.00598678	+	0.0103694i
$785$		0			0
$786$	66.0833			2.35711
$787$		−	17.7149i		−	0.631466i	−0.948848	−	0.315733i	$-0.897750\pi$
$787$		−	17.7149i		−	0.631466i	0.948848	−	0.315733i	$-0.102250\pi$
$788$	−45.2124	+	26.1034i	−1.61062	+	0.929894i
$789$	−25.2640	−	43.7585i	−0.899422	−	1.55784i
$790$		0			0
$791$	34.5030			1.22679
$792$	−35.8026	+	20.6706i	−1.27219	+	0.734499i
$793$	3.78222	+	2.18367i	0.134311	+	0.0775443i
$794$	−18.9086	−	32.7506i	−0.671040	−	1.16227i
$795$		0			0
$796$	−0.538652	+	0.932972i	−0.0190920	+	0.0330683i
$797$			25.4930i			0.903008i	0.892269	+	0.451504i	$0.149112\pi$
$797$			25.4930i			0.903008i	−0.892269	+	0.451504i	$0.850888\pi$
$798$	−64.8813	+	58.8217i	−2.29677	+	2.08227i
$799$	−0.485864			−0.0171886
$800$		0			0
$801$	1.82735	−	3.16507i	0.0645663	−	0.111832i
$802$	16.8710	−	9.74049i	0.595736	−	0.343949i
$803$	27.9414	+	16.1320i	0.986032	+	0.569286i
$804$	34.1014	+	59.0653i	1.20266	+	2.08307i
$805$		0			0
$806$	26.1094			0.919664
$807$	16.7718	−	9.68322i	0.590397	−	0.340866i
$808$	−29.7744	+	17.1902i	−1.04746	+	0.604751i
$809$	20.4678			0.719610			0.359805	−	0.933027i	$-0.382843\pi$
$809$	20.4678			0.719610			0.359805	+	0.933027i	$0.382843\pi$
$810$		0			0
$811$	11.4508	+	19.8333i	0.402091	+	0.696442i	0.993978	−	0.109579i	$-0.0349502\pi$
$811$	11.4508	+	19.8333i	0.402091	+	0.696442i	−0.591887	+	0.806021i	$0.701617\pi$
$812$	34.3175	+	19.8132i	1.20431	+	0.695308i
$813$	−11.4748	+	6.62498i	−0.402439	+	0.232348i
$814$	56.4643	−	97.7990i	1.97907	−	3.42785i
$815$		0			0
$816$	0.0251571			0.000880674
$817$	−13.8963	−	4.46281i	−0.486171	−	0.156134i
$818$			26.4306i			0.924124i
$819$	−28.8026	+	49.8876i	−1.00645	+	1.74322i
$820$		0			0
$821$	−15.3609	−	26.6058i	−0.536099	−	0.928550i	−0.999109	−	0.0421975i	$-0.986564\pi$
$821$	−15.3609	−	26.6058i	−0.536099	−	0.928550i	0.463011	−	0.886353i	$-0.346769\pi$
$822$	0.542679	+	0.313316i	0.0189281	+	0.0109281i
$823$	−3.63464	+	2.09846i	−0.126695	+	0.0731476i	−0.562008	−	0.827132i	$-0.689971\pi$
$823$	−3.63464	+	2.09846i	−0.126695	+	0.0731476i	0.435313	+	0.900279i	$0.356638\pi$
$824$	−29.6427			−1.03265
$825$		0			0
$826$	−12.2746	−	21.2602i	−0.427087	−	0.739736i
$827$	−18.4726	+	10.6652i	−0.642357	+	0.370865i	−0.785522	−	0.618834i	$-0.787605\pi$
$827$	−18.4726	+	10.6652i	−0.642357	+	0.370865i	0.143165	+	0.989699i	$0.454272\pi$
$828$		−	12.2631i		−	0.426172i
$829$	−34.0390			−1.18222			−0.591112	−	0.806590i	$-0.701311\pi$
$829$	−34.0390			−1.18222			−0.591112	+	0.806590i	$0.701311\pi$
$830$		0			0
$831$	38.3905	−	66.4943i	1.33175	−	2.30666i
$832$	56.1393	−	32.4120i	1.94628	−	1.12368i
$833$	0.727896	+	0.420251i	0.0252201	+	0.0145608i
$834$	−4.13555	+	7.16299i	−0.143202	+	0.248034i
$835$		0			0
$836$	−42.5135	−	46.8931i	−1.47036	−	1.62183i
$837$			1.63355i			0.0564638i
$838$	−42.9735	−	24.8108i	−1.48450	−	0.857074i
$839$	5.20584	−	9.01678i	0.179725	−	0.311294i	−0.762061	−	0.647505i	$-0.775812\pi$
$839$	5.20584	−	9.01678i	0.179725	−	0.311294i	0.941786	+	0.336212i	$0.109146\pi$
$840$		0			0
$841$	8.35041	−	14.4633i	0.287945	−	0.498736i
$842$	−13.7000	+	7.90967i	−0.472132	+	0.272585i
$843$			33.4999i			1.15380i
$844$	−6.53421			−0.224917
$845$		0			0
$846$	−11.4980	−	19.9151i	−0.395309	−	0.684696i
$847$			32.6616i			1.12227i
$848$		−	0.363334i		−	0.0124769i
$849$	−5.13355	−	8.89157i	−0.176183	−	0.305158i
$850$		0			0
$851$	6.35197	+	11.0019i	0.217743	+	0.377141i
$852$	−113.573	−	65.5712i	−3.89093	−	2.24643i
$853$	−11.3714	−	6.56527i	−0.389349	−	0.224790i	0.292529	−	0.956257i	$-0.405503\pi$
$853$	−11.3714	−	6.56527i	−0.389349	−	0.224790i	−0.681878	+	0.731466i	$0.738836\pi$
$854$	7.00000			0.239535
$855$		0			0
$856$	−6.06638			−0.207345
$857$	37.4521	+	21.6230i	1.27934	+	0.738627i	0.976727	−	0.214487i	$-0.0688080\pi$
$857$	37.4521	+	21.6230i	1.27934	+	0.738627i	0.302612	+	0.953114i	$0.402141\pi$
$858$	−111.805	−	64.5506i	−3.81696	−	2.20372i
$859$	15.7344	+	27.2527i	0.536849	+	0.929850i	0.999071	+	0.0430861i	$0.0137190\pi$
$859$	15.7344	+	27.2527i	0.536849	+	0.929850i	−0.462222	+	0.886764i	$0.652948\pi$
$860$		0			0
$861$	26.7163	+	46.2740i	0.910490	+	1.57701i
$862$		−	63.9356i		−	2.17766i
$863$			23.7842i			0.809622i	0.914400	+	0.404811i	$0.132663\pi$
$863$			23.7842i			0.809622i	−0.914400	+	0.404811i	$0.867337\pi$
$864$	2.04767	+	3.54667i	0.0696632	+	0.120660i
$865$		0			0
$866$	14.2912			0.485634
$867$			42.5562i			1.44529i
$868$	22.3610	−	12.9101i	0.758981	−	0.438198i
$869$	22.8202	−	39.5258i	0.774123	−	1.34082i
$870$		0			0
$871$	−21.1094	+	36.5625i	−0.715264	+	1.23887i
$872$	−38.2546	−	22.0863i	−1.29547	−	0.747937i
$873$		−	5.32033i		−	0.180066i
$874$	11.2801	−	2.43794i	0.381556	−	0.0824646i
$875$		0			0
$876$	−28.9111	+	50.0756i	−0.976817	+	1.69190i
$877$	33.0558	+	19.0848i	1.11621	+	0.644447i	0.940432	−	0.339982i	$-0.110421\pi$
$877$	33.0558	+	19.0848i	1.11621	+	0.644447i	0.175783	+	0.984429i	$0.443754\pi$
$878$	−61.7398	+	35.6455i	−2.08362	+	1.20298i
$879$	−15.2585	+	26.4285i	−0.514657	+	0.891413i
$880$		0			0
$881$	5.49209			0.185033			0.0925167	−	0.995711i	$-0.470509\pi$
$881$	5.49209			0.185033			0.0925167	+	0.995711i	$0.470509\pi$
$882$			39.7810i			1.33950i
$883$	29.7032	−	17.1491i	0.999592	−	0.577115i	0.0914644	−	0.995808i	$-0.470845\pi$
$883$	29.7032	−	17.1491i	0.999592	−	0.577115i	0.908128	+	0.418694i	$0.137512\pi$
$884$	−1.27755	−	2.21279i	−0.0429688	−	0.0744241i
$885$		0			0
$886$	−74.7327			−2.51069
$887$	−32.4907	+	18.7585i	−1.09093	+	0.629850i	−0.933824	−	0.357732i	$-0.883550\pi$
$887$	−32.4907	+	18.7585i	−1.09093	+	0.629850i	−0.157107	+	0.987582i	$0.550217\pi$
$888$	66.4706	+	38.3768i	2.23061	+	1.28784i
$889$	27.5491	+	47.7165i	0.923968	+	1.60036i
$890$		0			0
$891$	−18.1706	+	31.4725i	−0.608740	+	1.05437i
$892$		−	61.9628i		−	2.07467i
$893$	9.89226	−	8.96837i	0.331032	−	0.300115i
$894$	9.90466			0.331261
$895$		0			0
$896$	31.8589	−	55.1812i	1.06433	−	1.84347i
$897$	12.5775	−	7.26164i	0.419952	−	0.242459i
$898$	50.7224	+	29.2846i	1.69263	+	0.977240i
$899$	4.00702	+	6.94036i	0.133642	+	0.231474i
$900$		0			0
$901$	−0.910886			−0.0303460
$902$	−54.2056	+	31.2956i	−1.80485	+	1.04203i
$903$	−25.4956	+	14.7199i	−0.848439	+	0.489847i
$904$	−27.4701			−0.913640
$905$		0			0
$906$	−57.6916	−	99.9248i	−1.91668	−	3.31978i
$907$	19.2717	+	11.1265i	0.639907	+	0.369450i	0.784579	−	0.620029i	$-0.212879\pi$
$907$	19.2717	+	11.1265i	0.639907	+	0.369450i	−0.144672	+	0.989480i	$0.546213\pi$
$908$	−11.1609	+	6.44375i	−0.370388	+	0.213843i
$909$	20.2253	−	35.0313i	0.670832	−	1.16192i
$910$		0			0
$911$	10.0421			0.332710			0.166355	−	0.986066i	$-0.446800\pi$
$911$	10.0421			0.332710			0.166355	+	0.986066i	$0.446800\pi$
$912$	−0.512202	+	0.464364i	−0.0169607	+	0.0153766i
$913$			21.8835i			0.724238i
$914$	37.8930	−	65.6325i	1.25339	−	2.17093i
$915$		0			0
$916$	20.9081	+	36.2139i	0.690824	+	1.19654i
$917$	35.0340	+	20.2269i	1.15692	+	0.667951i
$918$	0.224385	−	0.129549i	0.00740580	−	0.00427574i
$919$	−6.06104			−0.199935			−0.0999676	−	0.994991i	$-0.531874\pi$
$919$	−6.06104			−0.199935			−0.0999676	+	0.994991i	$0.531874\pi$
$920$		0			0
$921$	30.7550	+	53.2692i	1.01341	+	1.75528i
$922$	4.30581	−	2.48596i	0.141804	−	0.0818708i
$923$		−	81.1796i		−	2.67206i
$924$	−127.671			−4.20008
$925$		0			0
$926$	7.08477	−	12.2712i	0.232820	−	0.403256i
$927$	30.2038	−	17.4382i	0.992024	−	0.572745i
$928$	17.3996	+	10.0457i	0.571170	+	0.329765i
$929$	−25.9382	+	44.9263i	−0.851004	+	1.47398i	0.0292983	+	0.999571i	$0.490673\pi$
$929$	−25.9382	+	44.9263i	−0.851004	+	1.47398i	−0.880303	+	0.474412i	$0.842661\pi$
$930$		0			0
$931$	−22.5773	+	4.87957i	−0.739941	+	0.159921i
$932$			87.2268i			2.85721i
$933$	22.1540	+	12.7906i	0.725289	+	0.418746i
$934$	−19.6004	+	33.9488i	−0.641343	+	1.11084i
$935$		0			0
$936$	22.9316	−	39.7187i	0.749543	−	1.29825i
$937$	21.8237	−	12.5999i	0.712949	−	0.411621i	−0.0992029	−	0.995067i	$-0.531629\pi$
$937$	21.8237	−	12.5999i	0.712949	−	0.411621i	0.812152	+	0.583446i	$0.198296\pi$
$938$			67.6685i			2.20946i
$939$	−80.1794			−2.61655
$940$		0			0
$941$	0.967923	+	1.67649i	0.0315534	+	0.0546521i	0.881371	−	0.472425i	$-0.156621\pi$
$941$	0.967923	+	1.67649i	0.0315534	+	0.0546521i	−0.849817	+	0.527077i	$0.823288\pi$
$942$		−	21.6445i		−	0.705215i
$943$		−	7.04122i		−	0.229294i
$944$	−0.0969008	−	0.167837i	−0.00315385	−	0.00546263i
$945$		0			0
$946$	−17.2429	−	29.8656i	−0.560616	−	0.971016i
$947$	−27.1607	−	15.6812i	−0.882603	−	0.509571i	−0.0110875	−	0.999939i	$-0.503529\pi$
$947$	−27.1607	−	15.6812i	−0.882603	−	0.509571i	−0.871516	+	0.490367i	$0.836863\pi$
$948$	70.8366	+	40.8975i	2.30067	+	1.32829i
$949$	−35.7930			−1.16189
$950$		0			0
$951$	−5.60548			−0.181770
$952$	−1.34505	−	0.776567i	−0.0435934	−	0.0251687i
$953$	45.8201	+	26.4542i	1.48426	+	0.856937i	0.999840	−	0.0179001i	$-0.00569808\pi$
$953$	45.8201	+	26.4542i	1.48426	+	0.856937i	0.484418	+	0.874837i	$0.339031\pi$
$954$	−21.5561	−	37.3363i	−0.697906	−	1.20881i
$955$		0			0
$956$	−32.3157	−	55.9724i	−1.04516	−	1.81028i
$957$		−	39.6264i		−	1.28094i
$958$			81.7581i			2.64148i
$959$	0.191800	+	0.332208i	0.00619355	+	0.0107275i
$960$		0			0
$961$	−25.7781			−0.831552
$962$			125.281i			4.03921i
$963$	6.18122	−	3.56873i	0.199187	−	0.115001i
$964$	−34.7710	+	60.2252i	−1.11990	+	1.93972i
$965$		0			0
$966$	11.6390	−	20.1594i	0.374479	−	0.648617i
$967$	51.9858	+	30.0140i	1.67175	+	0.965186i	0.966657	+	0.256073i	$0.0824287\pi$
$967$	51.9858	+	30.0140i	1.67175	+	0.965186i	0.705094	+	0.709113i	$0.250905\pi$
$968$		−	26.0040i		−	0.835800i
$969$	1.16417	+	1.28410i	0.0373985	+	0.0412512i
$970$		0			0
$971$	−0.875025	+	1.51559i	−0.0280809	+	0.0486375i	−0.879724	−	0.475484i	$-0.842273\pi$
$971$	−0.875025	+	1.51559i	−0.0280809	+	0.0486375i	0.851643	+	0.524122i	$0.175606\pi$
$972$	−62.3876	−	36.0195i	−2.00108	−	1.15533i
$973$	−4.38492	+	2.53163i	−0.140574	+	0.0811604i
$974$	−27.0959	+	46.9315i	−0.868209	+	1.50378i
$975$		0			0
$976$	0.0552611			0.00176886
$977$			5.47583i			0.175187i	0.996156	+	0.0875937i	$0.0279177\pi$
$977$			5.47583i			0.175187i	−0.996156	+	0.0875937i	$0.972082\pi$
$978$	−8.01955	+	4.63009i	−0.256437	+	0.148054i
$979$	2.50702	+	4.34228i	0.0801247	+	0.138780i
$980$		0			0
$981$	51.9717			1.65933
$982$	−77.5501	+	44.7736i	−2.47472	+	1.42878i
$983$	4.38145	+	2.52963i	0.139747	+	0.0806827i	0.568243	−	0.822861i	$-0.307623\pi$
$983$	4.38145	+	2.52963i	0.139747	+	0.0806827i	−0.428497	+	0.903543i	$0.640957\pi$
$984$	−21.2706	−	36.8417i	−0.678081	−	1.17447i
$985$		0			0
$986$	0.635553	−	1.10081i	0.0202401	−	0.0350569i
$987$		−	26.9327i		−	0.857278i
$988$	66.8561	+	21.4708i	2.12698	+	0.683078i
$989$	3.87950			0.123361
$990$		0			0
$991$	−0.0492290	+	0.0852672i	−0.00156381	+	0.00270860i	−0.866806	−	0.498645i	$-0.833831\pi$
$991$	−0.0492290	+	0.0852672i	−0.00156381	+	0.00270860i	0.865242	+	0.501354i	$0.167164\pi$
$992$	11.3374	−	6.54567i	0.359964	−	0.207825i
$993$	21.9097	+	12.6496i	0.695284	+	0.401423i
$994$	−65.0576	−	112.683i	−2.06350	−	3.57409i
$995$		0			0
$996$	−39.2188			−1.24269
$997$	15.8996	−	9.17967i	0.503547	−	0.290723i	−0.226630	−	0.973981i	$-0.572771\pi$
$997$	15.8996	−	9.17967i	0.503547	−	0.290723i	0.730177	+	0.683258i	$0.239438\pi$
$998$	18.5560	−	10.7133i	0.587379	−	0.339124i
$999$	−7.83828			−0.247992

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	475.2.j.b.49.2		12
5.2	odd	4		475.2.e.d.201.3		6
5.3	odd	4		95.2.e.b.11.1	✓	6
5.4	even	2	inner	475.2.j.b.49.5		12
15.8	even	4		855.2.k.g.676.3		6
19.7	even	3	inner	475.2.j.b.349.5		12
20.3	even	4		1520.2.q.j.961.1		6
95.7	odd	12		475.2.e.d.26.3		6
95.8	even	12		1805.2.a.g.1.1		3
95.27	even	12		9025.2.a.ba.1.3		3
95.64	even	6	inner	475.2.j.b.349.2		12
95.68	odd	12		1805.2.a.h.1.3		3
95.83	odd	12		95.2.e.b.26.1	yes	6
95.87	odd	12		9025.2.a.z.1.1		3
285.83	even	12		855.2.k.g.406.3		6
380.83	even	12		1520.2.q.j.881.1		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
95.2.e.b.11.1	✓	6	5.3	odd	4
95.2.e.b.26.1	yes	6	95.83	odd	12
475.2.e.d.26.3		6	95.7	odd	12
475.2.e.d.201.3		6	5.2	odd	4
475.2.j.b.49.2		12	1.1	even	1	trivial
475.2.j.b.49.5		12	5.4	even	2	inner
475.2.j.b.349.2		12	95.64	even	6	inner
475.2.j.b.349.5		12	19.7	even	3	inner
855.2.k.g.406.3		6	285.83	even	12
855.2.k.g.676.3		6	15.8	even	4
1520.2.q.j.881.1		6	380.83	even	12
1520.2.q.j.961.1		6	20.3	even	4
1805.2.a.g.1.1		3	95.8	even	12
1805.2.a.h.1.3		3	95.68	odd	12
9025.2.a.z.1.1		3	95.87	odd	12
9025.2.a.ba.1.3		3	95.27	even	12

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:	\( N \)	\(=\)	\( 475 = 5^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	475.j (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.97899 - 1.14257i) q^{2} +(-2.17114 - 1.25351i) q^{3} +(1.61094 + 2.79023i) q^{4} +(2.86445 + 4.96137i) q^{6} +3.50702i q^{7} -2.79216i q^{8} +(1.64257 + 2.84502i) q^{9} +O(q^{10})\)	\(q+(-1.97899 - 1.14257i) q^{2} +(-2.17114 - 1.25351i) q^{3} +(1.61094 + 2.79023i) q^{4} +(2.86445 + 4.96137i) q^{6} +3.50702i q^{7} -2.79216i q^{8} +(1.64257 + 2.84502i) q^{9} -4.50702 q^{11} -8.07730i q^{12} +(4.33013 - 2.50000i) q^{13} +(4.00702 - 6.94036i) q^{14} +(0.0316332 - 0.0547902i) q^{16} +(-0.137360 - 0.0793049i) q^{17} -7.50702i q^{18} +(4.26053 - 0.920816i) q^{19} +(4.39608 - 7.61423i) q^{21} +(8.91935 + 5.14959i) q^{22} +(-1.00339 + 0.579305i) q^{23} +(-3.50000 + 6.06218i) q^{24} -11.4257 q^{26} -0.714858i q^{27} +(-9.78538 + 5.64959i) q^{28} +(-1.75351 - 3.03717i) q^{29} -2.28514 q^{31} +(-4.96137 + 2.86445i) q^{32} +(9.78538 + 5.64959i) q^{33} +(0.181223 + 0.313888i) q^{34} +(-5.29216 + 9.16629i) q^{36} -10.9648i q^{37} +(-9.48365 - 3.04567i) q^{38} -12.5351 q^{39} +(-3.03865 + 5.26310i) q^{41} +(-17.3996 + 10.0457i) q^{42} +(-2.89981 - 1.67420i) q^{43} +(-7.26053 - 12.5756i) q^{44} +2.64759 q^{46} +(2.65287 - 1.53163i) q^{47} +(-0.137360 + 0.0793049i) q^{48} -5.29918 q^{49} +(0.198819 + 0.344364i) q^{51} +(13.9511 + 8.05469i) q^{52} +(4.97353 - 2.87147i) q^{53} +(-0.816776 + 1.41470i) q^{54} +9.79216 q^{56} +(-10.4045 - 3.34139i) q^{57} +8.01404i q^{58} +(1.53163 - 2.65287i) q^{59} +(0.436734 + 0.756445i) q^{61} +(4.52228 + 2.61094i) q^{62} +(-9.97753 + 5.76053i) q^{63} +12.9648 q^{64} +(-12.9101 - 22.3610i) q^{66} +(-7.31250 + 4.22188i) q^{67} -0.511021i q^{68} +2.90466 q^{69} +(8.11796 - 14.0607i) q^{71} +(7.94375 - 4.58632i) q^{72} +(-6.19954 - 3.57930i) q^{73} +(-12.5281 + 21.6993i) q^{74} +(9.43273 + 10.4045i) q^{76} -15.8062i q^{77} +(24.8068 + 14.3222i) q^{78} +(-5.06327 + 8.76983i) q^{79} +(4.03163 - 6.98299i) q^{81} +(12.0269 - 6.94375i) q^{82} -4.85543i q^{83} +28.3273 q^{84} +(3.82580 + 6.62647i) q^{86} +8.79216i q^{87} +12.5843i q^{88} +(-0.556248 - 0.963449i) q^{89} +(8.76755 + 15.1858i) q^{91} +(-3.23278 - 1.86645i) q^{92} +(4.96137 + 2.86445i) q^{93} -7.00000 q^{94} +14.3624 q^{96} +(-1.40254 - 0.809757i) q^{97} +(10.4870 + 6.05469i) q^{98} +(-7.40310 - 12.8225i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 14 q^{4} + 12 q^{6} + 8 q^{9}+O(q^{10}) \) 12 * q + 14 * q^4 + 12 * q^6 + 8 * q^9	\( 12 q + 14 q^{4} + 12 q^{6} + 8 q^{9} - 20 q^{11} + 14 q^{14} - 6 q^{16} + 24 q^{21} - 42 q^{24} - 20 q^{26} - 4 q^{29} - 4 q^{31} - 50 q^{34} - 6 q^{36} + 20 q^{39} + 4 q^{41} - 36 q^{44} - 96 q^{46} + 28 q^{49} + 12 q^{51} + 20 q^{54} + 60 q^{56} + 12 q^{59} + 18 q^{61} + 32 q^{64} - 58 q^{66} + 20 q^{69} + 58 q^{71} - 14 q^{74} - 38 q^{76} - 48 q^{79} + 42 q^{81} + 112 q^{84} + 64 q^{86} - 28 q^{89} + 20 q^{91} - 84 q^{94} + 68 q^{96} - 26 q^{99}+O(q^{100}) \) 12 * q + 14 * q^4 + 12 * q^6 + 8 * q^9 - 20 * q^11 + 14 * q^14 - 6 * q^16 + 24 * q^21 - 42 * q^24 - 20 * q^26 - 4 * q^29 - 4 * q^31 - 50 * q^34 - 6 * q^36 + 20 * q^39 + 4 * q^41 - 36 * q^44 - 96 * q^46 + 28 * q^49 + 12 * q^51 + 20 * q^54 + 60 * q^56 + 12 * q^59 + 18 * q^61 + 32 * q^64 - 58 * q^66 + 20 * q^69 + 58 * q^71 - 14 * q^74 - 38 * q^76 - 48 * q^79 + 42 * q^81 + 112 * q^84 + 64 * q^86 - 28 * q^89 + 20 * q^91 - 84 * q^94 + 68 * q^96 - 26 * q^99

Introduction

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