LMFDB - Embedded newform 2058.2.e.i.361.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2058,2,Mod(361,2058)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2058, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 4]))

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

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

chi := DirichletCharacter("2058.361");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 2058 = 2 \cdot 3 \cdot 7^{3} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2058.e (of order $3$, 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:	$16.4332127360$
Analytic rank:	$0$
Dimension:	$6$
Relative dimension:	$3$ over $\Q(\zeta_{3})$
Coefficient field:	6.0.64827.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - x^{5} + 3x^{4} + 5x^{2} - 2x + 1 $ x^6 - x^5 + 3x^4 + 5x^2 - 2*x + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			361.3
Root			$0.222521 - 0.385418i$ of defining polynomial
Character	$\chi$	$=$	2058.361
Dual form			2058.2.e.i.667.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.500000 + 0.866025i) q^{2} +(0.500000 - 0.866025i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-0.0990311 - 0.171527i) q^{5} +1.00000 q^{6} -1.00000 q^{8} +(-0.500000 - 0.866025i) q^{9} +(0.0990311 - 0.171527i) q^{10} +(0.777479 - 1.34663i) q^{11} +(0.500000 + 0.866025i) q^{12} -0.890084 q^{13} -0.198062 q^{15} +(-0.500000 - 0.866025i) q^{16} +(-3.42543 + 5.93301i) q^{17} +(0.500000 - 0.866025i) q^{18} +(1.33244 + 2.30785i) q^{19} +0.198062 q^{20} +1.55496 q^{22} +(3.76055 + 6.51347i) q^{23} +(-0.500000 + 0.866025i) q^{24} +(2.48039 - 4.29615i) q^{25} +(-0.445042 - 0.770835i) q^{26} -1.00000 q^{27} +6.59179 q^{29} +(-0.0990311 - 0.171527i) q^{30} +(-0.425428 + 0.736862i) q^{31} +(0.500000 - 0.866025i) q^{32} +(-0.777479 - 1.34663i) q^{33} -6.85086 q^{34} +1.00000 q^{36} +(4.14795 + 7.18446i) q^{37} +(-1.33244 + 2.30785i) q^{38} +(-0.445042 + 0.770835i) q^{39} +(0.0990311 + 0.171527i) q^{40} +7.87263 q^{41} +3.70171 q^{43} +(0.777479 + 1.34663i) q^{44} +(-0.0990311 + 0.171527i) q^{45} +(-3.76055 + 6.51347i) q^{46} +(-0.554958 - 0.961216i) q^{47} -1.00000 q^{48} +4.96077 q^{50} +(3.42543 + 5.93301i) q^{51} +(0.445042 - 0.770835i) q^{52} +(1.46681 - 2.54059i) q^{53} +(-0.500000 - 0.866025i) q^{54} -0.307979 q^{55} +2.66487 q^{57} +(3.29590 + 5.70866i) q^{58} +(3.15883 - 5.47126i) q^{59} +(0.0990311 - 0.171527i) q^{60} +(2.93900 + 5.09050i) q^{61} -0.850855 q^{62} +1.00000 q^{64} +(0.0881460 + 0.152673i) q^{65} +(0.777479 - 1.34663i) q^{66} +(5.00000 - 8.66025i) q^{67} +(-3.42543 - 5.93301i) q^{68} +7.52111 q^{69} -2.19806 q^{71} +(0.500000 + 0.866025i) q^{72} +(-0.0881460 + 0.152673i) q^{73} +(-4.14795 + 7.18446i) q^{74} +(-2.48039 - 4.29615i) q^{75} -2.66487 q^{76} -0.890084 q^{78} +(3.85086 + 6.66988i) q^{79} +(-0.0990311 + 0.171527i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(3.93631 + 6.81789i) q^{82} +3.50604 q^{83} +1.35690 q^{85} +(1.85086 + 3.20578i) q^{86} +(3.29590 - 5.70866i) q^{87} +(-0.777479 + 1.34663i) q^{88} +(-0.574572 - 0.995189i) q^{89} -0.198062 q^{90} -7.52111 q^{92} +(0.425428 + 0.736862i) q^{93} +(0.554958 - 0.961216i) q^{94} +(0.263906 - 0.457098i) q^{95} +(-0.500000 - 0.866025i) q^{96} -13.9758 q^{97} -1.55496 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q + 3 q^{2} + 3 q^{3} - 3 q^{4} - 5 q^{5} + 6 q^{6} - 6 q^{8} - 3 q^{9} + 5 q^{10} + 5 q^{11} + 3 q^{12} - 4 q^{13} - 10 q^{15} - 3 q^{16} - 7 q^{17} + 3 q^{18} + 9 q^{19} + 10 q^{20} + 10 q^{22} + 7 q^{23}+ \cdots - 10 q^{99}+O(q^{100}) $ 6 * q + 3 * q^2 + 3 * q^3 - 3 * q^4 - 5 * q^5 + 6 * q^6 - 6 * q^8 - 3 * q^9 + 5 * q^10 + 5 * q^11 + 3 * q^12 - 4 * q^13 - 10 * q^15 - 3 * q^16 - 7 * q^17 + 3 * q^18 + 9 * q^19 + 10 * q^20 + 10 * q^22 + 7 * q^23 - 3 * q^24 + 2 * q^25 - 2 * q^26 - 6 * q^27 - 16 * q^29 - 5 * q^30 + 11 * q^31 + 3 * q^32 - 5 * q^33 - 14 * q^34 + 6 * q^36 + 11 * q^37 - 9 * q^38 - 2 * q^39 + 5 * q^40 + 14 * q^41 - 32 * q^43 + 5 * q^44 - 5 * q^45 - 7 * q^46 - 4 * q^47 - 6 * q^48 + 4 * q^50 + 7 * q^51 + 2 * q^52 + 2 * q^53 - 3 * q^54 - 12 * q^55 + 18 * q^57 - 8 * q^58 + 2 * q^59 + 5 * q^60 - 2 * q^61 + 22 * q^62 + 6 * q^64 + 8 * q^65 + 5 * q^66 + 30 * q^67 - 7 * q^68 + 14 * q^69 - 22 * q^71 + 3 * q^72 - 8 * q^73 - 11 * q^74 - 2 * q^75 - 18 * q^76 - 4 * q^78 - 4 * q^79 - 5 * q^80 - 3 * q^81 + 7 * q^82 + 40 * q^83 - 16 * q^86 - 8 * q^87 - 5 * q^88 - 17 * q^89 - 10 * q^90 - 14 * q^92 - 11 * q^93 + 4 * q^94 + 8 * q^95 - 3 * q^96 - 8 * q^97 - 10 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/2058\mathbb{Z}\right)^\times$.

$n$	$1373$	$1375$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$

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 $

$2$	0.500000	+	0.866025i	0.353553	+	0.612372i
$2$	0.500000	+	0.866025i	0.353553	+	0.612372i
$3$	0.500000	−	0.866025i	0.288675	−	0.500000i
$3$	0.500000	−	0.866025i	0.288675	−	0.500000i
$4$	−0.500000	+	0.866025i	−0.250000	+	0.433013i
$5$	−0.0990311	−	0.171527i	−0.0442881	−	0.0767092i	0.843032	−	0.537864i	$-0.180769\pi$
$5$	−0.0990311	−	0.171527i	−0.0442881	−	0.0767092i	−0.887320	+	0.461155i	$0.847435\pi$
$6$	1.00000			0.408248
$7$		0			0
$7$		0			0
$8$	−1.00000			−0.353553
$9$	−0.500000	−	0.866025i	−0.166667	−	0.288675i
$10$	0.0990311	−	0.171527i	0.0313164	−	0.0542416i
$11$	0.777479	−	1.34663i	0.234419	−	0.406025i	−0.724685	−	0.689080i	$-0.758015\pi$
$11$	0.777479	−	1.34663i	0.234419	−	0.406025i	0.959104	+	0.283055i	$0.0913480\pi$
$12$	0.500000	+	0.866025i	0.144338	+	0.250000i
$13$	−0.890084			−0.246865			−0.123432	−	0.992353i	$-0.539390\pi$
$13$	−0.890084			−0.246865			−0.123432	+	0.992353i	$0.539390\pi$
$14$		0			0
$15$	−0.198062			−0.0511395
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	−3.42543	+	5.93301i	−0.830788	+	1.43897i	0.0666258	+	0.997778i	$0.478777\pi$
$17$	−3.42543	+	5.93301i	−0.830788	+	1.43897i	−0.897414	+	0.441189i	$0.854557\pi$
$18$	0.500000	−	0.866025i	0.117851	−	0.204124i
$19$	1.33244	+	2.30785i	0.305682	+	0.529457i	0.977413	−	0.211338i	$-0.0677822\pi$
$19$	1.33244	+	2.30785i	0.305682	+	0.529457i	−0.671731	+	0.740795i	$0.734449\pi$
$20$	0.198062			0.0442881
$21$		0			0
$22$	1.55496			0.331518
$23$	3.76055	+	6.51347i	0.784130	+	1.35815i	0.929518	+	0.368778i	$0.120224\pi$
$23$	3.76055	+	6.51347i	0.784130	+	1.35815i	−0.145388	+	0.989375i	$0.546443\pi$
$24$	−0.500000	+	0.866025i	−0.102062	+	0.176777i
$25$	2.48039	−	4.29615i	0.496077	−	0.859231i
$26$	−0.445042	−	0.770835i	−0.0872799	−	0.151173i
$27$	−1.00000			−0.192450
$28$		0			0
$29$	6.59179			1.22407			0.612033	−	0.790832i	$-0.290352\pi$
$29$	6.59179			1.22407			0.612033	+	0.790832i	$0.290352\pi$
$30$	−0.0990311	−	0.171527i	−0.0180805	−	0.0313164i
$31$	−0.425428	+	0.736862i	−0.0764090	+	0.132344i	−0.901698	−	0.432366i	$-0.857679\pi$
$31$	−0.425428	+	0.736862i	−0.0764090	+	0.132344i	0.825289	+	0.564710i	$0.191012\pi$
$32$	0.500000	−	0.866025i	0.0883883	−	0.153093i
$33$	−0.777479	−	1.34663i	−0.135342	−	0.234419i
$34$	−6.85086			−1.17491
$35$		0			0
$36$	1.00000			0.166667
$37$	4.14795	+	7.18446i	0.681919	+	1.18112i	0.974395	+	0.224845i	$0.0721875\pi$
$37$	4.14795	+	7.18446i	0.681919	+	1.18112i	−0.292476	+	0.956273i	$0.594479\pi$
$38$	−1.33244	+	2.30785i	−0.216150	+	0.374383i
$39$	−0.445042	+	0.770835i	−0.0712637	+	0.123432i
$40$	0.0990311	+	0.171527i	0.0156582	+	0.0271208i
$41$	7.87263			1.22950			0.614749	−	0.788723i	$-0.289257\pi$
$41$	7.87263			1.22950			0.614749	+	0.788723i	$0.289257\pi$
$42$		0			0
$43$	3.70171			0.564506			0.282253	−	0.959340i	$-0.408918\pi$
$43$	3.70171			0.564506			0.282253	+	0.959340i	$0.408918\pi$
$44$	0.777479	+	1.34663i	0.117209	+	0.203013i
$45$	−0.0990311	+	0.171527i	−0.0147627	+	0.0255697i
$46$	−3.76055	+	6.51347i	−0.554463	+	0.960359i
$47$	−0.554958	−	0.961216i	−0.0809490	−	0.140208i	0.822709	−	0.568463i	$-0.192462\pi$
$47$	−0.554958	−	0.961216i	−0.0809490	−	0.140208i	−0.903658	+	0.428255i	$0.859128\pi$
$48$	−1.00000			−0.144338
$49$		0			0
$50$	4.96077			0.701559
$51$	3.42543	+	5.93301i	0.479656	+	0.830788i
$52$	0.445042	−	0.770835i	0.0617162	−	0.106896i
$53$	1.46681	−	2.54059i	0.201482	−	0.348977i	−0.747524	−	0.664235i	$-0.768758\pi$
$53$	1.46681	−	2.54059i	0.201482	−	0.348977i	0.949006	+	0.315257i	$0.102091\pi$
$54$	−0.500000	−	0.866025i	−0.0680414	−	0.117851i
$55$	−0.307979			−0.0415278
$56$		0			0
$57$	2.66487			0.352971
$58$	3.29590	+	5.70866i	0.432772	+	0.749584i
$59$	3.15883	−	5.47126i	0.411245	−	0.712297i	−0.583781	−	0.811911i	$-0.698427\pi$
$59$	3.15883	−	5.47126i	0.411245	−	0.712297i	0.995026	+	0.0996137i	$0.0317607\pi$
$60$	0.0990311	−	0.171527i	0.0127849	−	0.0221440i
$61$	2.93900	+	5.09050i	0.376301	+	0.651772i	0.990521	−	0.137363i	$-0.0438627\pi$
$61$	2.93900	+	5.09050i	0.376301	+	0.651772i	−0.614220	+	0.789135i	$0.710529\pi$
$62$	−0.850855			−0.108059
$63$		0			0
$64$	1.00000			0.125000
$65$	0.0881460	+	0.152673i	0.0109332	+	0.0189368i
$66$	0.777479	−	1.34663i	0.0957011	−	0.165759i
$67$	5.00000	−	8.66025i	0.610847	−	1.05802i	−0.380251	−	0.924883i	$-0.624162\pi$
$67$	5.00000	−	8.66025i	0.610847	−	1.05802i	0.991098	−	0.133135i	$-0.0425044\pi$
$68$	−3.42543	−	5.93301i	−0.415394	−	0.719484i
$69$	7.52111			0.905435
$70$		0			0
$71$	−2.19806			−0.260862			−0.130431	−	0.991457i	$-0.541636\pi$
$71$	−2.19806			−0.260862			−0.130431	+	0.991457i	$0.541636\pi$
$72$	0.500000	+	0.866025i	0.0589256	+	0.102062i
$73$	−0.0881460	+	0.152673i	−0.0103167	+	0.0178691i	−0.871138	−	0.491039i	$-0.836617\pi$
$73$	−0.0881460	+	0.152673i	−0.0103167	+	0.0178691i	0.860821	+	0.508908i	$0.169951\pi$
$74$	−4.14795	+	7.18446i	−0.482189	+	0.835176i
$75$	−2.48039	−	4.29615i	−0.286410	−	0.496077i
$76$	−2.66487			−0.305682
$77$		0			0
$78$	−0.890084			−0.100782
$79$	3.85086	+	6.66988i	0.433255	+	0.750420i	0.997151	−	0.0754258i	$-0.0240316\pi$
$79$	3.85086	+	6.66988i	0.433255	+	0.750420i	−0.563896	+	0.825846i	$0.690698\pi$
$80$	−0.0990311	+	0.171527i	−0.0110720	+	0.0191773i
$81$	−0.500000	+	0.866025i	−0.0555556	+	0.0962250i
$82$	3.93631	+	6.81789i	0.434693	+	0.752910i
$83$	3.50604			0.384838			0.192419	−	0.981313i	$-0.438367\pi$
$83$	3.50604			0.384838			0.192419	+	0.981313i	$0.438367\pi$
$84$		0			0
$85$	1.35690			0.147176
$86$	1.85086	+	3.20578i	0.199583	+	0.345688i
$87$	3.29590	−	5.70866i	0.353357	−	0.612033i
$88$	−0.777479	+	1.34663i	−0.0828795	+	0.143552i
$89$	−0.574572	−	0.995189i	−0.0609046	−	0.105490i	0.833965	−	0.551817i	$-0.186065\pi$
$89$	−0.574572	−	0.995189i	−0.0609046	−	0.105490i	−0.894870	+	0.446327i	$0.852732\pi$
$90$	−0.198062			−0.0208776
$91$		0			0
$92$	−7.52111			−0.784130
$93$	0.425428	+	0.736862i	0.0441148	+	0.0764090i
$94$	0.554958	−	0.961216i	0.0572396	−	0.0991418i
$95$	0.263906	−	0.457098i	0.0270761	−	0.0468972i
$96$	−0.500000	−	0.866025i	−0.0510310	−	0.0883883i
$97$	−13.9758			−1.41903			−0.709516	−	0.704690i	$-0.751086\pi$
$97$	−13.9758			−1.41903			−0.709516	+	0.704690i	$0.751086\pi$
$98$		0			0
$99$	−1.55496			−0.156279
$100$	2.48039	+	4.29615i	0.248039	+	0.429615i
$101$	−7.35958	+	12.7472i	−0.732306	+	1.26839i	0.223589	+	0.974683i	$0.428223\pi$
$101$	−7.35958	+	12.7472i	−0.732306	+	1.26839i	−0.955895	+	0.293708i	$0.905111\pi$
$102$	−3.42543	+	5.93301i	−0.339168	+	0.587456i
$103$	−8.13587	−	14.0917i	−0.801651	−	1.38850i	−0.918529	−	0.395354i	$-0.870622\pi$
$103$	−8.13587	−	14.0917i	−0.801651	−	1.38850i	0.116878	−	0.993146i	$-0.462711\pi$
$104$	0.890084			0.0872799
$105$		0			0
$106$	2.93362			0.284939
$107$	3.85205	+	6.67195i	0.372392	+	0.645002i	0.989933	−	0.141537i	$-0.0452044\pi$
$107$	3.85205	+	6.67195i	0.372392	+	0.645002i	−0.617541	+	0.786539i	$0.711871\pi$
$108$	0.500000	−	0.866025i	0.0481125	−	0.0833333i
$109$	−6.23221	+	10.7945i	−0.596937	+	1.03393i	0.396333	+	0.918107i	$0.370283\pi$
$109$	−6.23221	+	10.7945i	−0.596937	+	1.03393i	−0.993270	+	0.115819i	$0.963051\pi$
$110$	−0.153989	−	0.266717i	−0.0146823	−	0.0254305i
$111$	8.29590			0.787412
$112$		0			0
$113$		0			0			−	1.00000i	$-0.5\pi$
$113$		0			0				1.00000i	$0.5\pi$
$114$	1.33244	+	2.30785i	0.124794	+	0.216150i
$115$	0.744824	−	1.29007i	0.0694552	−	0.120300i
$116$	−3.29590	+	5.70866i	−0.306016	+	0.530036i
$117$	0.445042	+	0.770835i	0.0411441	+	0.0712637i
$118$	6.31767			0.581588
$119$		0			0
$120$	0.198062			0.0180805
$121$	4.29105	+	7.43232i	0.390096	+	0.675666i
$122$	−2.93900	+	5.09050i	−0.266085	+	0.460872i
$123$	3.93631	−	6.81789i	0.354925	−	0.614749i
$124$	−0.425428	−	0.736862i	−0.0382045	−	0.0661722i
$125$	−1.97285			−0.176457
$126$		0			0
$127$	−4.17629			−0.370586			−0.185293	−	0.982683i	$-0.559323\pi$
$127$	−4.17629			−0.370586			−0.185293	+	0.982683i	$0.559323\pi$
$128$	0.500000	+	0.866025i	0.0441942	+	0.0765466i
$129$	1.85086	−	3.20578i	0.162959	−	0.282253i
$130$	−0.0881460	+	0.152673i	−0.00773092	+	0.0133903i
$131$	11.1957	+	19.3915i	0.978170	+	1.69424i	0.669050	+	0.743217i	$0.266701\pi$
$131$	11.1957	+	19.3915i	0.978170	+	1.69424i	0.309120	+	0.951023i	$0.399965\pi$
$132$	1.55496			0.135342
$133$		0			0
$134$	10.0000			0.863868
$135$	0.0990311	+	0.171527i	0.00852324	+	0.0147627i
$136$	3.42543	−	5.93301i	0.293728	−	0.508752i
$137$	5.18598	−	8.98238i	0.443068	−	0.767417i	−0.554847	−	0.831952i	$-0.687223\pi$
$137$	5.18598	−	8.98238i	0.443068	−	0.767417i	0.997915	+	0.0645356i	$0.0205566\pi$
$138$	3.76055	+	6.51347i	0.320120	+	0.554463i
$139$	−17.6256			−1.49499			−0.747494	−	0.664269i	$-0.768743\pi$
$139$	−17.6256			−1.49499			−0.747494	+	0.664269i	$0.768743\pi$
$140$		0			0
$141$	−1.10992			−0.0934718
$142$	−1.09903	−	1.90358i	−0.0922286	−	0.159745i
$143$	−0.692021	+	1.19862i	−0.0578697	+	0.100233i
$144$	−0.500000	+	0.866025i	−0.0416667	+	0.0721688i
$145$	−0.652793	−	1.13067i	−0.0542115	−	0.0938971i
$146$	−0.176292			−0.0145900
$147$		0			0
$148$	−8.29590			−0.681919
$149$	0.713792	+	1.23632i	0.0584761	+	0.101284i	0.893782	−	0.448503i	$-0.148043\pi$
$149$	0.713792	+	1.23632i	0.0584761	+	0.101284i	−0.835305	+	0.549786i	$0.814709\pi$
$150$	2.48039	−	4.29615i	0.202523	−	0.350780i
$151$	−0.472189	+	0.817855i	−0.0384262	+	0.0665561i	−0.884599	−	0.466353i	$-0.845568\pi$
$151$	−0.472189	+	0.817855i	−0.0384262	+	0.0665561i	0.846173	+	0.532909i	$0.178901\pi$
$152$	−1.33244	−	2.30785i	−0.108075	−	0.187191i
$153$	6.85086			0.553859
$154$		0			0
$155$	0.168522			0.0135360
$156$	−0.445042	−	0.770835i	−0.0356319	−	0.0617162i
$157$	12.1860	−	21.1067i	0.972547	−	1.68450i	0.284744	−	0.958604i	$-0.408091\pi$
$157$	12.1860	−	21.1067i	0.972547	−	1.68450i	0.687803	−	0.725898i	$-0.258575\pi$
$158$	−3.85086	+	6.66988i	−0.306358	+	0.530627i
$159$	−1.46681	−	2.54059i	−0.116326	−	0.201482i
$160$	−0.198062			−0.0156582
$161$		0			0
$162$	−1.00000			−0.0785674
$163$	0.0609989	+	0.105653i	0.00477780	+	0.00827540i	0.868404	−	0.495857i	$-0.165146\pi$
$163$	0.0609989	+	0.105653i	0.00477780	+	0.00827540i	−0.863627	+	0.504132i	$0.831813\pi$
$164$	−3.93631	+	6.81789i	−0.307374	+	0.532388i
$165$	−0.153989	+	0.266717i	−0.0119880	+	0.0207639i
$166$	1.75302	+	3.03632i	0.136061	+	0.235664i
$167$	13.7995			1.06784			0.533920	−	0.845535i	$-0.320718\pi$
$167$	13.7995			1.06784			0.533920	+	0.845535i	$0.320718\pi$
$168$		0			0
$169$	−12.2078			−0.939058
$170$	0.678448	+	1.17511i	0.0520346	+	0.0901265i
$171$	1.33244	−	2.30785i	0.101894	−	0.176486i
$172$	−1.85086	+	3.20578i	−0.141126	+	0.244438i
$173$	−0.780167	−	1.35129i	−0.0593150	−	0.102737i	0.834843	−	0.550488i	$-0.185558\pi$
$173$	−0.780167	−	1.35129i	−0.0593150	−	0.102737i	−0.894158	+	0.447751i	$0.852225\pi$
$174$	6.59179			0.499723
$175$		0			0
$176$	−1.55496			−0.117209
$177$	−3.15883	−	5.47126i	−0.237432	−	0.411245i
$178$	0.574572	−	0.995189i	0.0430660	−	0.0745925i
$179$	5.51357	−	9.54979i	0.412104	−	0.713785i	−0.583016	−	0.812461i	$-0.698127\pi$
$179$	5.51357	−	9.54979i	0.412104	−	0.713785i	0.995120	+	0.0986761i	$0.0314608\pi$
$180$	−0.0990311	−	0.171527i	−0.00738134	−	0.0127849i
$181$	−11.9215			−0.886121			−0.443061	−	0.896492i	$-0.646107\pi$
$181$	−11.9215			−0.886121			−0.443061	+	0.896492i	$0.646107\pi$
$182$		0			0
$183$	5.87800			0.434514
$184$	−3.76055	−	6.51347i	−0.277232	−	0.480179i
$185$	0.821552	−	1.42297i	0.0604017	−	0.104619i
$186$	−0.425428	+	0.736862i	−0.0311939	+	0.0540294i
$187$	5.32640	+	9.22559i	0.389505	+	0.674642i
$188$	1.10992			0.0809490
$189$		0			0
$190$	0.527811			0.0382914
$191$	12.5722	+	21.7757i	0.909691	+	1.57563i	0.814494	+	0.580173i	$0.197015\pi$
$191$	12.5722	+	21.7757i	0.909691	+	1.57563i	0.0951974	+	0.995458i	$0.469652\pi$
$192$	0.500000	−	0.866025i	0.0360844	−	0.0625000i
$193$	9.17510	−	15.8917i	0.660438	−	1.14391i	−0.320063	−	0.947396i	$-0.603704\pi$
$193$	9.17510	−	15.8917i	0.660438	−	1.14391i	0.980501	−	0.196516i	$-0.0629626\pi$
$194$	−6.98792	−	12.1034i	−0.501703	−	0.868976i
$195$	0.176292			0.0126245
$196$		0			0
$197$	−22.2392			−1.58448			−0.792239	−	0.610211i	$-0.791085\pi$
$197$	−22.2392			−1.58448			−0.792239	+	0.610211i	$0.791085\pi$
$198$	−0.777479	−	1.34663i	−0.0552530	−	0.0957011i
$199$	3.12618	−	5.41470i	0.221609	−	0.383838i	−0.733688	−	0.679487i	$-0.762203\pi$
$199$	3.12618	−	5.41470i	0.221609	−	0.383838i	0.955297	+	0.295649i	$0.0955358\pi$
$200$	−2.48039	+	4.29615i	−0.175390	+	0.303784i
$201$	−5.00000	−	8.66025i	−0.352673	−	0.610847i
$202$	−14.7192			−1.03564
$203$		0			0
$204$	−6.85086			−0.479656
$205$	−0.779635	−	1.35037i	−0.0544521	−	0.0943138i
$206$	8.13587	−	14.0917i	0.566853	−	0.981818i
$207$	3.76055	−	6.51347i	0.261377	−	0.452717i
$208$	0.445042	+	0.770835i	0.0308581	+	0.0534478i
$209$	4.14377			0.286630
$210$		0			0
$211$		0			0			−	1.00000i	$-0.5\pi$
$211$		0			0				1.00000i	$0.5\pi$
$212$	1.46681	+	2.54059i	0.100741	+	0.174489i
$213$	−1.09903	+	1.90358i	−0.0753044	+	0.130431i
$214$	−3.85205	+	6.67195i	−0.263321	+	0.456085i
$215$	−0.366585	−	0.634943i	−0.0250009	−	0.0433028i
$216$	1.00000			0.0680414
$217$		0			0
$218$	−12.4644			−0.844197
$219$	0.0881460	+	0.152673i	0.00595635	+	0.0103167i
$220$	0.153989	−	0.266717i	0.0103820	−	0.0179821i
$221$	3.04892	−	5.28088i	0.205092	−	0.355230i
$222$	4.14795	+	7.18446i	0.278392	+	0.482189i
$223$	−13.7942			−0.923726			−0.461863	−	0.886951i	$-0.652819\pi$
$223$	−13.7942			−0.923726			−0.461863	+	0.886951i	$0.652819\pi$
$224$		0			0
$225$	−4.96077			−0.330718
$226$		0			0
$227$	−7.44265	+	12.8910i	−0.493986	+	0.855609i	−0.999976	−	0.00693055i	$-0.997794\pi$
$227$	−7.44265	+	12.8910i	−0.493986	+	0.855609i	0.505990	+	0.862539i	$0.331127\pi$
$228$	−1.33244	+	2.30785i	−0.0882428	+	0.152841i
$229$	1.88471	+	3.26441i	0.124545	+	0.215718i	0.921555	−	0.388248i	$-0.126920\pi$
$229$	1.88471	+	3.26441i	0.124545	+	0.215718i	−0.797010	+	0.603966i	$0.793586\pi$
$230$	1.48965			0.0982244
$231$		0			0
$232$	−6.59179			−0.432772
$233$	−3.54288	−	6.13644i	−0.232102	−	0.402012i	0.726325	−	0.687352i	$-0.241227\pi$
$233$	−3.54288	−	6.13644i	−0.232102	−	0.402012i	−0.958426	+	0.285340i	$0.907894\pi$
$234$	−0.445042	+	0.770835i	−0.0290933	+	0.0503911i
$235$	−0.109916	+	0.190381i	−0.00717015	+	0.0124191i
$236$	3.15883	+	5.47126i	0.205623	+	0.356149i
$237$	7.70171			0.500280
$238$		0			0
$239$	3.06100			0.198000			0.0989998	−	0.995087i	$-0.468436\pi$
$239$	3.06100			0.198000			0.0989998	+	0.995087i	$0.468436\pi$
$240$	0.0990311	+	0.171527i	0.00639243	+	0.0110720i
$241$	−9.34481	+	16.1857i	−0.601952	+	1.04261i	0.390573	+	0.920572i	$0.372277\pi$
$241$	−9.34481	+	16.1857i	−0.601952	+	1.04261i	−0.992525	+	0.122040i	$0.961056\pi$
$242$	−4.29105	+	7.43232i	−0.275839	+	0.477768i
$243$	0.500000	+	0.866025i	0.0320750	+	0.0555556i
$244$	−5.87800			−0.376301
$245$		0			0
$246$	7.87263			0.501940
$247$	−1.18598	−	2.05418i	−0.0754621	−	0.130704i
$248$	0.425428	−	0.736862i	0.0270147	−	0.0467908i
$249$	1.75302	−	3.03632i	0.111093	−	0.192419i
$250$	−0.986426	−	1.70854i	−0.0623871	−	0.108058i
$251$	13.4276			0.847542			0.423771	−	0.905769i	$-0.360706\pi$
$251$	13.4276			0.847542			0.423771	+	0.905769i	$0.360706\pi$
$252$		0			0
$253$	11.6950			0.735259
$254$	−2.08815	−	3.61677i	−0.131022	−	0.226937i
$255$	0.678448	−	1.17511i	0.0424861	−	0.0735880i
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	8.13587	+	14.0917i	0.507501	+	0.879018i	0.999962	+	0.00868368i	$0.00276413\pi$
$257$	8.13587	+	14.0917i	0.507501	+	0.879018i	−0.492461	+	0.870335i	$0.663903\pi$
$258$	3.70171			0.230458
$259$		0			0
$260$	−0.176292			−0.0109332
$261$	−3.29590	−	5.70866i	−0.204011	−	0.353357i
$262$	−11.1957	+	19.3915i	−0.691671	+	1.19801i
$263$	1.51693	−	2.62739i	0.0935377	−	0.162012i	−0.815460	−	0.578814i	$-0.803516\pi$
$263$	1.51693	−	2.62739i	0.0935377	−	0.162012i	0.908997	+	0.416802i	$0.136849\pi$
$264$	0.777479	+	1.34663i	0.0478505	+	0.0828795i
$265$	−0.581040			−0.0356930
$266$		0			0
$267$	−1.14914			−0.0703265
$268$	5.00000	+	8.66025i	0.305424	+	0.529009i
$269$	3.18329	−	5.51362i	0.194089	−	0.336172i	−0.752513	−	0.658578i	$-0.771158\pi$
$269$	3.18329	−	5.51362i	0.194089	−	0.336172i	0.946601	+	0.322406i	$0.104492\pi$
$270$	−0.0990311	+	0.171527i	−0.00602684	+	0.0104388i
$271$	−8.62983	−	14.9473i	−0.524225	−	0.907984i	−0.999602	−	0.0282018i	$-0.991022\pi$
$271$	−8.62983	−	14.9473i	−0.524225	−	0.907984i	0.475378	−	0.879782i	$-0.342311\pi$
$272$	6.85086			0.415394
$273$		0			0
$274$	10.3720			0.626593
$275$	−3.85690	−	6.68034i	−0.232580	−	0.402840i
$276$	−3.76055	+	6.51347i	−0.226359	+	0.392065i
$277$	5.94116	−	10.2904i	0.356970	−	0.618289i	−0.630483	−	0.776203i	$-0.717143\pi$
$277$	5.94116	−	10.2904i	0.356970	−	0.618289i	0.987453	+	0.157913i	$0.0504767\pi$
$278$	−8.81282	−	15.2643i	−0.528558	−	0.915489i
$279$	0.850855			0.0509394
$280$		0			0
$281$	14.1414			0.843604			0.421802	−	0.906688i	$-0.361398\pi$
$281$	14.1414			0.843604			0.421802	+	0.906688i	$0.361398\pi$
$282$	−0.554958	−	0.961216i	−0.0330473	−	0.0572396i
$283$	0.628867	−	1.08923i	0.0373822	−	0.0647479i	−0.846729	−	0.532024i	$-0.821431\pi$
$283$	0.628867	−	1.08923i	0.0373822	−	0.0647479i	0.884111	+	0.467277i	$0.154765\pi$
$284$	1.09903	−	1.90358i	0.0652155	−	0.112957i
$285$	−0.263906	−	0.457098i	−0.0156324	−	0.0270761i
$286$	−1.38404			−0.0818402
$287$		0			0
$288$	−1.00000			−0.0589256
$289$	−14.9671	−	25.9238i	−0.880418	−	1.52493i
$290$	0.652793	−	1.13067i	0.0383333	−	0.0663952i
$291$	−6.98792	+	12.1034i	−0.409639	+	0.709516i
$292$	−0.0881460	−	0.152673i	−0.00515835	−	0.00893453i
$293$	−21.3163			−1.24531			−0.622657	−	0.782495i	$-0.713947\pi$
$293$	−21.3163			−1.24531			−0.622657	+	0.782495i	$0.713947\pi$
$294$		0			0
$295$	−1.25129			−0.0728530
$296$	−4.14795	−	7.18446i	−0.241095	−	0.417588i
$297$	−0.777479	+	1.34663i	−0.0451139	+	0.0781396i
$298$	−0.713792	+	1.23632i	−0.0413488	+	0.0716183i
$299$	−3.34721	−	5.79753i	−0.193574	−	0.335280i
$300$	4.96077			0.286410
$301$		0			0
$302$	−0.944378			−0.0543428
$303$	7.35958	+	12.7472i	0.422797	+	0.732306i
$304$	1.33244	−	2.30785i	0.0764205	−	0.132364i
$305$	0.582105	−	1.00824i	0.0333312	−	0.0577314i
$306$	3.42543	+	5.93301i	0.195819	+	0.339168i
$307$	−14.6853			−0.838135			−0.419068	−	0.907955i	$-0.637643\pi$
$307$	−14.6853			−0.838135			−0.419068	+	0.907955i	$0.637643\pi$
$308$		0			0
$309$	−16.2717			−0.925667
$310$	0.0842611	+	0.145945i	0.00478571	+	0.00828910i
$311$	−5.95108	+	10.3076i	−0.337455	+	0.584489i	−0.983953	−	0.178426i	$-0.942899\pi$
$311$	−5.95108	+	10.3076i	−0.337455	+	0.584489i	0.646498	+	0.762915i	$0.276233\pi$
$312$	0.445042	−	0.770835i	0.0251955	−	0.0436399i
$313$	−13.4601	−	23.3136i	−0.760810	−	1.31776i	−0.942433	−	0.334394i	$-0.891468\pi$
$313$	−13.4601	−	23.3136i	−0.760810	−	1.31776i	0.181623	−	0.983368i	$-0.441865\pi$
$314$	24.3720			1.37539
$315$		0			0
$316$	−7.70171			−0.433255
$317$	−16.1250	−	27.9293i	−0.905669	−	1.56867i	−0.820016	−	0.572340i	$-0.806036\pi$
$317$	−16.1250	−	27.9293i	−0.905669	−	1.56867i	−0.0856528	−	0.996325i	$-0.527298\pi$
$318$	1.46681	−	2.54059i	0.0822547	−	0.142469i
$319$	5.12498	−	8.87673i	0.286944	−	0.497001i
$320$	−0.0990311	−	0.171527i	−0.00553601	−	0.00958865i
$321$	7.70410			0.430001
$322$		0			0
$323$	−18.2567			−1.01583
$324$	−0.500000	−	0.866025i	−0.0277778	−	0.0481125i
$325$	−2.20775	+	3.82394i	−0.122464	+	0.212114i
$326$	−0.0609989	+	0.105653i	−0.00337842	+	0.00585159i
$327$	6.23221	+	10.7945i	0.344642	+	0.596937i
$328$	−7.87263			−0.434693
$329$		0			0
$330$	−0.307979			−0.0169537
$331$	8.59179	+	14.8814i	0.472248	+	0.817957i	0.999496	−	0.0317544i	$-0.0101095\pi$
$331$	8.59179	+	14.8814i	0.472248	+	0.817957i	−0.527248	+	0.849711i	$0.676776\pi$
$332$	−1.75302	+	3.03632i	−0.0962095	+	0.166640i
$333$	4.14795	−	7.18446i	0.227306	−	0.393706i
$334$	6.89977	+	11.9508i	0.377539	+	0.653916i
$335$	−1.98062			−0.108213
$336$		0			0
$337$	−21.2556			−1.15787			−0.578933	−	0.815375i	$-0.696531\pi$
$337$	−21.2556			−1.15787			−0.578933	+	0.815375i	$0.696531\pi$
$338$	−6.10388	−	10.5722i	−0.332007	−	0.575053i
$339$		0			0
$340$	−0.678448	+	1.17511i	−0.0367940	+	0.0637291i
$341$	0.661522	+	1.14579i	0.0358234	+	0.0620480i
$342$	2.66487			0.144100
$343$		0			0
$344$	−3.70171			−0.199583
$345$	−0.744824	−	1.29007i	−0.0401000	−	0.0694552i
$346$	0.780167	−	1.35129i	0.0419421	−	0.0726458i
$347$	−3.69753	+	6.40431i	−0.198494	+	0.343801i	−0.948040	−	0.318150i	$-0.896938\pi$
$347$	−3.69753	+	6.40431i	−0.198494	+	0.343801i	0.749546	+	0.661952i	$0.230272\pi$
$348$	3.29590	+	5.70866i	0.176679	+	0.306016i
$349$	10.9772			0.587594			0.293797	−	0.955868i	$-0.405081\pi$
$349$	10.9772			0.587594			0.293797	+	0.955868i	$0.405081\pi$
$350$		0			0
$351$	0.890084			0.0475092
$352$	−0.777479	−	1.34663i	−0.0414398	−	0.0717758i
$353$	2.82371	−	4.89081i	0.150291	−	0.260311i	−0.781044	−	0.624477i	$-0.785312\pi$
$353$	2.82371	−	4.89081i	0.150291	−	0.260311i	0.931334	+	0.364165i	$0.118646\pi$
$354$	3.15883	−	5.47126i	0.167890	−	0.290794i
$355$	0.217677	+	0.377027i	0.0115531	+	0.0200105i
$356$	1.14914			0.0609046
$357$		0			0
$358$	11.0271			0.582803
$359$	−8.32855	−	14.4255i	−0.439564	−	0.761347i	0.558092	−	0.829779i	$-0.311534\pi$
$359$	−8.32855	−	14.4255i	−0.439564	−	0.761347i	−0.997656	+	0.0684318i	$0.978200\pi$
$360$	0.0990311	−	0.171527i	0.00521940	−	0.00904026i
$361$	5.94922	−	10.3044i	0.313117	−	0.542334i
$362$	−5.96077	−	10.3244i	−0.313291	−	0.542636i
$363$	8.58211			0.450444
$364$		0			0
$365$	0.0349168			0.00182763
$366$	2.93900	+	5.09050i	0.153624	+	0.266085i
$367$	9.09999	−	15.7616i	0.475016	−	0.822751i	−0.524575	−	0.851364i	$-0.675776\pi$
$367$	9.09999	−	15.7616i	0.475016	−	0.822751i	0.999591	+	0.0286131i	$0.00910906\pi$
$368$	3.76055	−	6.51347i	0.196032	−	0.339538i
$369$	−3.93631	−	6.81789i	−0.204916	−	0.354925i
$370$	1.64310			0.0854209
$371$		0			0
$372$	−0.850855			−0.0441148
$373$	−10.9291	−	18.9297i	−0.565886	−	0.980143i	−0.996967	−	0.0778300i	$-0.975201\pi$
$373$	−10.9291	−	18.9297i	−0.565886	−	0.980143i	0.431081	−	0.902313i	$-0.358132\pi$
$374$	−5.32640	+	9.22559i	−0.275421	+	0.477044i
$375$	−0.986426	+	1.70854i	−0.0509388	+	0.0882287i
$376$	0.554958	+	0.961216i	0.0286198	+	0.0495709i
$377$	−5.86725			−0.302179
$378$		0			0
$379$	−29.5555			−1.51817			−0.759083	−	0.650994i	$-0.774352\pi$
$379$	−29.5555			−1.51817			−0.759083	+	0.650994i	$0.774352\pi$
$380$	0.263906	+	0.457098i	0.0135381	+	0.0234486i
$381$	−2.08815	+	3.61677i	−0.106979	+	0.185293i
$382$	−12.5722	+	21.7757i	−0.643249	+	1.11414i
$383$	15.2838	+	26.4723i	0.780966	+	1.35267i	0.931379	+	0.364050i	$0.118606\pi$
$383$	15.2838	+	26.4723i	0.780966	+	1.35267i	−0.150413	+	0.988623i	$0.548060\pi$
$384$	1.00000			0.0510310
$385$		0			0
$386$	18.3502			0.934000
$387$	−1.85086	−	3.20578i	−0.0940843	−	0.162959i
$388$	6.98792	−	12.1034i	0.354758	−	0.614459i
$389$	−2.12200	+	3.67541i	−0.107590	+	0.186351i	−0.914793	−	0.403922i	$-0.867647\pi$
$389$	−2.12200	+	3.67541i	−0.107590	+	0.186351i	0.807204	+	0.590273i	$0.200980\pi$
$390$	0.0881460	+	0.152673i	0.00446345	+	0.00773092i
$391$	−51.5260			−2.60578
$392$		0			0
$393$	22.3913			1.12949
$394$	−11.1196	−	19.2597i	−0.560198	−	0.970291i
$395$	0.762709	−	1.32105i	0.0383761	−	0.0664693i
$396$	0.777479	−	1.34663i	0.0390698	−	0.0676709i
$397$	−1.39612	−	2.41816i	−0.0700695	−	0.121364i	0.828862	−	0.559453i	$-0.188989\pi$
$397$	−1.39612	−	2.41816i	−0.0700695	−	0.121364i	−0.898932	+	0.438089i	$0.855655\pi$
$398$	6.25236			0.313402
$399$		0			0
$400$	−4.96077			−0.248039
$401$	−16.9269	−	29.3183i	−0.845290	−	1.46409i	−0.885369	−	0.464889i	$-0.846094\pi$
$401$	−16.9269	−	29.3183i	−0.845290	−	1.46409i	0.0400791	−	0.999197i	$-0.487239\pi$
$402$	5.00000	−	8.66025i	0.249377	−	0.431934i
$403$	0.378666	−	0.655869i	0.0188627	−	0.0326712i
$404$	−7.35958	−	12.7472i	−0.366153	−	0.634196i
$405$	0.198062			0.00984179
$406$		0			0
$407$	12.8998			0.639418
$408$	−3.42543	−	5.93301i	−0.169584	−	0.293728i
$409$	−14.6963	+	25.4548i	−0.726687	+	1.25866i	0.231589	+	0.972814i	$0.425608\pi$
$409$	−14.6963	+	25.4548i	−0.726687	+	1.25866i	−0.958276	+	0.285845i	$0.907726\pi$
$410$	0.779635	−	1.35037i	0.0385034	−	0.0666899i
$411$	−5.18598	−	8.98238i	−0.255806	−	0.443068i
$412$	16.2717			0.801651
$413$		0			0
$414$	7.52111			0.369642
$415$	−0.347207	−	0.601380i	−0.0170437	−	0.0295206i
$416$	−0.445042	+	0.770835i	−0.0218200	+	0.0377933i
$417$	−8.81282	+	15.2643i	−0.431566	+	0.747494i
$418$	2.07188	+	3.58861i	0.101339	+	0.175525i
$419$	22.8853			1.11802			0.559010	−	0.829161i	$-0.311181\pi$
$419$	22.8853			1.11802			0.559010	+	0.829161i	$0.311181\pi$
$420$		0			0
$421$	37.3545			1.82055			0.910274	−	0.414007i	$-0.135871\pi$
$421$	37.3545			1.82055			0.910274	+	0.414007i	$0.135871\pi$
$422$		0			0
$423$	−0.554958	+	0.961216i	−0.0269830	+	0.0467359i
$424$	−1.46681	+	2.54059i	−0.0712347	+	0.123382i
$425$	16.9928	+	29.4323i	0.824270	+	1.42768i
$426$	−2.19806			−0.106496
$427$		0			0
$428$	−7.70410			−0.372392
$429$	0.692021	+	1.19862i	0.0334111	+	0.0578697i
$430$	0.366585	−	0.634943i	0.0176783	−	0.0306197i
$431$	−1.98092	+	3.43105i	−0.0954175	+	0.165268i	−0.909783	−	0.415085i	$-0.863752\pi$
$431$	−1.98092	+	3.43105i	−0.0954175	+	0.165268i	0.814365	+	0.580353i	$0.197085\pi$
$432$	0.500000	+	0.866025i	0.0240563	+	0.0416667i
$433$	−32.6896			−1.57096			−0.785482	−	0.618885i	$-0.787585\pi$
$433$	−32.6896			−1.57096			−0.785482	+	0.618885i	$0.787585\pi$
$434$		0			0
$435$	−1.30559			−0.0625980
$436$	−6.23221	−	10.7945i	−0.298469	−	0.516963i
$437$	−10.0214	+	17.3576i	−0.479389	+	0.830326i
$438$	−0.0881460	+	0.152673i	−0.00421178	+	0.00729501i
$439$	−15.7141	−	27.2176i	−0.749992	−	1.29903i	−0.947826	−	0.318789i	$-0.896724\pi$
$439$	−15.7141	−	27.2176i	−0.749992	−	1.29903i	0.197833	−	0.980236i	$-0.436610\pi$
$440$	0.307979			0.0146823
$441$		0			0
$442$	6.09783			0.290044
$443$	4.77748	+	8.27484i	0.226985	+	0.393149i	0.956913	−	0.290374i	$-0.0937799\pi$
$443$	4.77748	+	8.27484i	0.226985	+	0.393149i	−0.729928	+	0.683524i	$0.760447\pi$
$444$	−4.14795	+	7.18446i	−0.196853	+	0.340959i
$445$	−0.113801	+	0.197109i	−0.00539469	+	0.00934388i
$446$	−6.89708	−	11.9461i	−0.326586	−	0.565664i
$447$	1.42758			0.0675224
$448$		0			0
$449$	19.7366			0.931429			0.465715	−	0.884935i	$-0.345797\pi$
$449$	19.7366			0.931429			0.465715	+	0.884935i	$0.345797\pi$
$450$	−2.48039	−	4.29615i	−0.116927	−	0.202523i
$451$	6.12080	−	10.6015i	0.288217	−	0.499207i
$452$		0			0
$453$	0.472189	+	0.817855i	0.0221854	+	0.0384262i
$454$	−14.8853			−0.698602
$455$		0			0
$456$	−2.66487			−0.124794
$457$	−14.0027	−	24.2534i	−0.655018	−	1.13452i	−0.981889	−	0.189456i	$-0.939328\pi$
$457$	−14.0027	−	24.2534i	−0.655018	−	1.13452i	0.326871	−	0.945069i	$-0.394006\pi$
$458$	−1.88471	+	3.26441i	−0.0880666	+	0.152536i
$459$	3.42543	−	5.93301i	0.159885	−	0.276929i
$460$	0.744824	+	1.29007i	0.0347276	+	0.0601499i
$461$	30.7482			1.43209			0.716044	−	0.698055i	$-0.245951\pi$
$461$	30.7482			1.43209			0.716044	+	0.698055i	$0.245951\pi$
$462$		0			0
$463$	33.0944			1.53803			0.769013	−	0.639233i	$-0.220748\pi$
$463$	33.0944			1.53803			0.769013	+	0.639233i	$0.220748\pi$
$464$	−3.29590	−	5.70866i	−0.153008	−	0.265018i
$465$	0.0842611	−	0.145945i	0.00390752	−	0.00676802i
$466$	3.54288	−	6.13644i	0.164121	−	0.284265i
$467$	−8.41119	−	14.5686i	−0.389223	−	0.674155i	0.603122	−	0.797649i	$-0.293923\pi$
$467$	−8.41119	−	14.5686i	−0.389223	−	0.674155i	−0.992345	+	0.123494i	$0.960590\pi$
$468$	−0.890084			−0.0411441
$469$		0			0
$470$	−0.219833			−0.0101401
$471$	−12.1860	−	21.1067i	−0.561500	−	0.972547i
$472$	−3.15883	+	5.47126i	−0.145397	+	0.251835i
$473$	2.87800	−	4.98485i	0.132331	−	0.229203i
$474$	3.85086	+	6.66988i	0.176876	+	0.306358i
$475$	13.2198			0.606568
$476$		0			0
$477$	−2.93362			−0.134321
$478$	1.53050	+	2.65090i	0.0700034	+	0.121249i
$479$	10.0925	−	17.4806i	0.461136	−	0.798711i	−0.537882	−	0.843020i	$-0.680775\pi$
$479$	10.0925	−	17.4806i	0.461136	−	0.798711i	0.999018	+	0.0443091i	$0.0141086\pi$
$480$	−0.0990311	+	0.171527i	−0.00452013	+	0.00782910i
$481$	−3.69202	−	6.39477i	−0.168342	−	0.291576i
$482$	−18.6896			−0.851289
$483$		0			0
$484$	−8.58211			−0.390096
$485$	1.38404	+	2.39723i	0.0628462	+	0.108853i
$486$	−0.500000	+	0.866025i	−0.0226805	+	0.0392837i
$487$	−4.81163	+	8.33398i	−0.218036	+	0.377649i	−0.954207	−	0.299146i	$-0.903298\pi$
$487$	−4.81163	+	8.33398i	−0.218036	+	0.377649i	0.736172	+	0.676795i	$0.236632\pi$
$488$	−2.93900	−	5.09050i	−0.133042	−	0.230436i
$489$	0.121998			0.00551693
$490$		0			0
$491$	−1.13169			−0.0510723			−0.0255361	−	0.999674i	$-0.508129\pi$
$491$	−1.13169			−0.0510723			−0.0255361	+	0.999674i	$0.508129\pi$
$492$	3.93631	+	6.81789i	0.177463	+	0.307374i
$493$	−22.5797	+	39.1092i	−1.01694	+	1.76139i
$494$	1.18598	−	2.05418i	0.0533598	−	0.0924219i
$495$	0.153989	+	0.266717i	0.00692130	+	0.0119880i
$496$	0.850855			0.0382045
$497$		0			0
$498$	3.50604			0.157109
$499$	1.48188	+	2.56669i	0.0663380	+	0.114901i	0.897287	−	0.441448i	$-0.145535\pi$
$499$	1.48188	+	2.56669i	0.0663380	+	0.114901i	−0.830949	+	0.556349i	$0.812202\pi$
$500$	0.986426	−	1.70854i	0.0441143	−	0.0764083i
$501$	6.89977	−	11.9508i	0.308259	−	0.533920i
$502$	6.71379	+	11.6286i	0.299651	+	0.519011i
$503$	38.9396			1.73623			0.868115	−	0.496363i	$-0.165331\pi$
$503$	38.9396			1.73623			0.868115	+	0.496363i	$0.165331\pi$
$504$		0			0
$505$	2.91531			0.129730
$506$	5.84750	+	10.1282i	0.259953	+	0.450252i
$507$	−6.10388	+	10.5722i	−0.271083	+	0.469529i
$508$	2.08815	−	3.61677i	0.0926465	−	0.160468i
$509$	17.2741	+	29.9197i	0.765662	+	1.32617i	0.939896	+	0.341461i	$0.110922\pi$
$509$	17.2741	+	29.9197i	0.765662	+	1.32617i	−0.174234	+	0.984704i	$0.555745\pi$
$510$	1.35690			0.0600844
$511$		0			0
$512$	−1.00000			−0.0441942
$513$	−1.33244	−	2.30785i	−0.0588285	−	0.101894i
$514$	−8.13587	+	14.0917i	−0.358858	+	0.621560i
$515$	−1.61141	+	2.79104i	−0.0710071	+	0.122988i
$516$	1.85086	+	3.20578i	0.0814794	+	0.141126i
$517$	−1.72587			−0.0759038
$518$		0			0
$519$	−1.56033			−0.0684911
$520$	−0.0881460	−	0.152673i	−0.00386546	−	0.00669517i
$521$	15.7708	−	27.3158i	0.690930	−	1.19673i	−0.280603	−	0.959824i	$-0.590535\pi$
$521$	15.7708	−	27.3158i	0.690930	−	1.19673i	0.971533	−	0.236902i	$-0.0761321\pi$
$522$	3.29590	−	5.70866i	0.144257	−	0.249861i
$523$	16.6139	+	28.7760i	0.726473	+	1.25829i	0.958365	+	0.285547i	$0.0921753\pi$
$523$	16.6139	+	28.7760i	0.726473	+	1.25829i	−0.231891	+	0.972742i	$0.574491\pi$
$524$	−22.3913			−0.978170
$525$		0			0
$526$	3.03385			0.132282
$527$	−2.91454	−	5.04814i	−0.126959	−	0.219900i
$528$	−0.777479	+	1.34663i	−0.0338354	+	0.0586047i
$529$	−16.7835	+	29.0699i	−0.729718	+	1.26391i
$530$	−0.290520	−	0.503196i	−0.0126194	−	0.0218574i
$531$	−6.31767			−0.274163
$532$		0			0
$533$	−7.00730			−0.303520
$534$	−0.574572	−	0.995189i	−0.0248642	−	0.0430660i
$535$	0.762946	−	1.32146i	0.0329850	−	0.0571318i
$536$	−5.00000	+	8.66025i	−0.215967	+	0.374066i
$537$	−5.51357	−	9.54979i	−0.237928	−	0.412104i
$538$	6.36658			0.274483
$539$		0			0
$540$	−0.198062			−0.00852324
$541$	−14.5179	−	25.1457i	−0.624173	−	1.08110i	−0.988700	−	0.149906i	$-0.952103\pi$
$541$	−14.5179	−	25.1457i	−0.624173	−	1.08110i	0.364528	−	0.931193i	$-0.381230\pi$
$542$	8.62983	−	14.9473i	0.370683	−	0.642041i
$543$	−5.96077	+	10.3244i	−0.255801	+	0.443061i
$544$	3.42543	+	5.93301i	0.146864	+	0.254376i
$545$	2.46873			0.105749
$546$		0			0
$547$	−1.78017			−0.0761145			−0.0380572	−	0.999276i	$-0.512117\pi$
$547$	−1.78017			−0.0761145			−0.0380572	+	0.999276i	$0.512117\pi$
$548$	5.18598	+	8.98238i	0.221534	+	0.383708i
$549$	2.93900	−	5.09050i	0.125434	−	0.217257i
$550$	3.85690	−	6.68034i	0.164459	−	0.284851i
$551$	8.78315	+	15.2129i	0.374175	+	0.648090i
$552$	−7.52111			−0.320120
$553$		0			0
$554$	11.8823			0.504831
$555$	−0.821552	−	1.42297i	−0.0348729	−	0.0604017i
$556$	8.81282	−	15.2643i	0.373747	−	0.647349i
$557$	−15.4373	+	26.7381i	−0.654098	+	1.13293i	0.328021	+	0.944670i	$0.393618\pi$
$557$	−15.4373	+	26.7381i	−0.654098	+	1.13293i	−0.982119	+	0.188261i	$0.939715\pi$
$558$	0.425428	+	0.736862i	0.0180098	+	0.0311939i
$559$	−3.29483			−0.139357
$560$		0			0
$561$	10.6528			0.449761
$562$	7.07069	+	12.2468i	0.298259	+	0.516600i
$563$	22.4862	−	38.9472i	0.947680	−	1.64143i	0.197385	−	0.980326i	$-0.436755\pi$
$563$	22.4862	−	38.9472i	0.947680	−	1.64143i	0.750294	−	0.661104i	$-0.229912\pi$
$564$	0.554958	−	0.961216i	0.0233680	−	0.0404745i
$565$		0			0
$566$	1.25773			0.0528665
$567$		0			0
$568$	2.19806			0.0922286
$569$	−3.26875	−	5.66164i	−0.137033	−	0.237348i	0.789339	−	0.613957i	$-0.210423\pi$
$569$	−3.26875	−	5.66164i	−0.137033	−	0.237348i	−0.926372	+	0.376609i	$0.877090\pi$
$570$	0.263906	−	0.457098i	0.0110538	−	0.0191457i
$571$	−18.8931	+	32.7238i	−0.790650	+	1.36945i	0.134915	+	0.990857i	$0.456924\pi$
$571$	−18.8931	+	32.7238i	−0.790650	+	1.36945i	−0.925565	+	0.378589i	$0.876409\pi$
$572$	−0.692021	−	1.19862i	−0.0289349	−	0.0501167i
$573$	25.1444			1.05042
$574$		0			0
$575$	37.3105			1.55595
$576$	−0.500000	−	0.866025i	−0.0208333	−	0.0360844i
$577$	8.10321	−	14.0352i	0.337341	−	0.584292i	−0.646591	−	0.762837i	$-0.723806\pi$
$577$	8.10321	−	14.0352i	0.337341	−	0.584292i	0.983932	+	0.178545i	$0.0571391\pi$
$578$	14.9671	−	25.9238i	0.622550	−	1.07829i
$579$	−9.17510	−	15.8917i	−0.381304	−	0.660438i
$580$	1.30559			0.0542115
$581$		0			0
$582$	−13.9758			−0.579317
$583$	−2.28083	−	3.95052i	−0.0944624	−	0.163614i
$584$	0.0881460	−	0.152673i	0.00364751	−	0.00631767i
$585$	0.0881460	−	0.152673i	0.00364439	−	0.00631227i
$586$	−10.6582	−	18.4605i	−0.440285	−	0.762596i
$587$	−23.3163			−0.962368			−0.481184	−	0.876620i	$-0.659793\pi$
$587$	−23.3163			−0.962368			−0.481184	+	0.876620i	$0.659793\pi$
$588$		0			0
$589$	−2.26742			−0.0934275
$590$	−0.625646	−	1.08365i	−0.0257574	−	0.0446132i
$591$	−11.1196	+	19.2597i	−0.457399	+	0.792239i
$592$	4.14795	−	7.18446i	0.170480	−	0.295279i
$593$	−17.2216	−	29.8287i	−0.707207	−	1.22492i	−0.965889	−	0.258956i	$-0.916621\pi$
$593$	−17.2216	−	29.8287i	−0.707207	−	1.22492i	0.258682	−	0.965963i	$-0.416712\pi$
$594$	−1.55496			−0.0638007
$595$		0			0
$596$	−1.42758			−0.0584761
$597$	−3.12618	−	5.41470i	−0.127946	−	0.221609i
$598$	3.34721	−	5.79753i	0.136877	−	0.237079i
$599$	2.53750	−	4.39508i	0.103679	−	0.179578i	−0.809518	−	0.587094i	$-0.800272\pi$
$599$	2.53750	−	4.39508i	0.103679	−	0.179578i	0.913198	+	0.407516i	$0.133605\pi$
$600$	2.48039	+	4.29615i	0.101261	+	0.175390i
$601$	46.5870			1.90032			0.950162	−	0.311757i	$-0.100918\pi$
$601$	46.5870			1.90032			0.950162	+	0.311757i	$0.100918\pi$
$602$		0			0
$603$	−10.0000			−0.407231
$604$	−0.472189	−	0.817855i	−0.0192131	−	0.0332781i
$605$	0.849896	−	1.47206i	0.0345532	−	0.0598478i
$606$	−7.35958	+	12.7472i	−0.298963	+	0.517819i
$607$	6.75422	+	11.6986i	0.274145	+	0.474833i	0.969919	−	0.243427i	$-0.0782718\pi$
$607$	6.75422	+	11.6986i	0.274145	+	0.474833i	−0.695774	+	0.718261i	$0.744938\pi$
$608$	2.66487			0.108075
$609$		0			0
$610$	1.16421			0.0471375
$611$	0.493959	+	0.855562i	0.0199835	+	0.0346124i
$612$	−3.42543	+	5.93301i	−0.138465	+	0.239828i
$613$	14.9025	−	25.8118i	0.601905	−	1.04253i	−0.390628	−	0.920549i	$-0.627742\pi$
$613$	14.9025	−	25.8118i	0.601905	−	1.04253i	0.992532	−	0.121981i	$-0.0389246\pi$
$614$	−7.34266	−	12.7179i	−0.296326	−	0.513251i
$615$	−1.55927			−0.0628758
$616$		0			0
$617$	−20.3129			−0.817766			−0.408883	−	0.912587i	$-0.634082\pi$
$617$	−20.3129			−0.817766			−0.408883	+	0.912587i	$0.634082\pi$
$618$	−8.13587	−	14.0917i	−0.327273	−	0.566853i
$619$	1.03952	−	1.80051i	0.0417820	−	0.0723686i	−0.844378	−	0.535748i	$-0.820030\pi$
$619$	1.03952	−	1.80051i	0.0417820	−	0.0723686i	0.886160	+	0.463379i	$0.153363\pi$
$620$	−0.0842611	+	0.145945i	−0.00338401	+	0.00586128i
$621$	−3.76055	−	6.51347i	−0.150906	−	0.261377i
$622$	−11.9022			−0.477233
$623$		0			0
$624$	0.890084			0.0356319
$625$	−12.2066	−	21.1424i	−0.488262	−	0.845695i
$626$	13.4601	−	23.3136i	0.537974	−	0.931798i
$627$	2.07188	−	3.58861i	0.0827431	−	0.143315i
$628$	12.1860	+	21.1067i	0.486274	+	0.842251i
$629$	−56.8340			−2.26612
$630$		0			0
$631$	46.2344			1.84056			0.920282	−	0.391256i	$-0.127959\pi$
$631$	46.2344			1.84056			0.920282	+	0.391256i	$0.127959\pi$
$632$	−3.85086	−	6.66988i	−0.153179	−	0.265313i
$633$		0			0
$634$	16.1250	−	27.9293i	0.640405	−	1.10921i
$635$	0.413583	+	0.716347i	0.0164125	+	0.0284273i
$636$	2.93362			0.116326
$637$		0			0
$638$	10.2500			0.405800
$639$	1.09903	+	1.90358i	0.0434770	+	0.0753044i
$640$	0.0990311	−	0.171527i	0.00391455	−	0.00678020i
$641$	−13.1860	+	22.8388i	−0.520815	+	0.902078i	0.478892	+	0.877874i	$0.341039\pi$
$641$	−13.1860	+	22.8388i	−0.520815	+	0.902078i	−0.999707	+	0.0242041i	$0.992295\pi$
$642$	3.85205	+	6.67195i	0.152028	+	0.263321i
$643$	−15.5120			−0.611734			−0.305867	−	0.952074i	$-0.598946\pi$
$643$	−15.5120			−0.611734			−0.305867	+	0.952074i	$0.598946\pi$
$644$		0			0
$645$	−0.733169			−0.0288685
$646$	−9.12833	−	15.8107i	−0.359150	−	0.622065i
$647$	13.5133	−	23.4058i	0.531264	−	0.920176i	−0.468070	−	0.883691i	$-0.655051\pi$
$647$	13.5133	−	23.4058i	0.531264	−	0.920176i	0.999334	−	0.0364851i	$-0.0116161\pi$
$648$	0.500000	−	0.866025i	0.0196419	−	0.0340207i
$649$	−4.91185	−	8.50758i	−0.192807	−	0.333952i
$650$	−4.41550			−0.173190
$651$		0			0
$652$	−0.121998			−0.00477780
$653$	7.64310	+	13.2382i	0.299098	+	0.518053i	0.975930	−	0.218085i	$-0.0699810\pi$
$653$	7.64310	+	13.2382i	0.299098	+	0.518053i	−0.676832	+	0.736138i	$0.736648\pi$
$654$	−6.23221	+	10.7945i	−0.243699	+	0.422098i
$655$	2.21744	−	3.84072i	0.0866425	−	0.150069i
$656$	−3.93631	−	6.81789i	−0.153687	−	0.266194i
$657$	0.176292			0.00687781
$658$		0			0
$659$	−4.43967			−0.172945			−0.0864724	−	0.996254i	$-0.527559\pi$
$659$	−4.43967			−0.172945			−0.0864724	+	0.996254i	$0.527559\pi$
$660$	−0.153989	−	0.266717i	−0.00599402	−	0.0103820i
$661$	15.2446	−	26.4044i	0.592946	−	1.02701i	−0.400888	−	0.916127i	$-0.631298\pi$
$661$	15.2446	−	26.4044i	0.592946	−	1.02701i	0.993833	−	0.110885i	$-0.0353685\pi$
$662$	−8.59179	+	14.8814i	−0.333930	+	0.578383i
$663$	−3.04892	−	5.28088i	−0.118410	−	0.205092i
$664$	−3.50604			−0.136061
$665$		0			0
$666$	8.29590			0.321459
$667$	24.7888	+	42.9354i	0.959826	+	1.66247i
$668$	−6.89977	+	11.9508i	−0.266960	+	0.462389i
$669$	−6.89708	+	11.9461i	−0.266657	+	0.461863i
$670$	−0.990311	−	1.71527i	−0.0382591	−	0.0662666i
$671$	9.14005			0.352848
$672$		0			0
$673$	−41.0901			−1.58391			−0.791953	−	0.610582i	$-0.790935\pi$
$673$	−41.0901			−1.58391			−0.791953	+	0.610582i	$0.790935\pi$
$674$	−10.6278	−	18.4079i	−0.409368	−	0.709046i
$675$	−2.48039	+	4.29615i	−0.0954701	+	0.165359i
$676$	6.10388	−	10.5722i	0.234764	−	0.406624i
$677$	15.6719	+	27.1445i	0.602319	+	1.04325i	0.992469	+	0.122496i	$0.0390898\pi$
$677$	15.6719	+	27.1445i	0.602319	+	1.04325i	−0.390150	+	0.920751i	$0.627577\pi$
$678$		0			0
$679$		0			0
$680$	−1.35690			−0.0520346
$681$	7.44265	+	12.8910i	0.285203	+	0.493986i
$682$	−0.661522	+	1.14579i	−0.0253310	+	0.0438746i
$683$	20.4415	−	35.4056i	0.782170	−	1.35476i	−0.148504	−	0.988912i	$-0.547446\pi$
$683$	20.4415	−	35.4056i	0.782170	−	1.35476i	0.930675	−	0.365847i	$-0.119221\pi$
$684$	1.33244	+	2.30785i	0.0509470	+	0.0882428i
$685$	−2.05429			−0.0784905
$686$		0			0
$687$	3.76941			0.143812
$688$	−1.85086	−	3.20578i	−0.0705632	−	0.122219i
$689$	−1.30559	+	2.26134i	−0.0497389	+	0.0861502i
$690$	0.744824	−	1.29007i	0.0283550	−	0.0491122i
$691$	−8.84385	−	15.3180i	−0.336436	−	0.582724i	0.647324	−	0.762215i	$-0.275888\pi$
$691$	−8.84385	−	15.3180i	−0.336436	−	0.582724i	−0.983760	+	0.179491i	$0.942555\pi$
$692$	1.56033			0.0593150
$693$		0			0
$694$	−7.39506			−0.280713
$695$	1.74549	+	3.02327i	0.0662101	+	0.114679i
$696$	−3.29590	+	5.70866i	−0.124931	+	0.216386i
$697$	−26.9671	+	46.7084i	−1.02145	+	1.76921i
$698$	5.48858	+	9.50650i	0.207746	+	0.359826i
$699$	−7.08575			−0.268008
$700$		0			0
$701$	4.28754			0.161938			0.0809690	−	0.996717i	$-0.474199\pi$
$701$	4.28754			0.161938			0.0809690	+	0.996717i	$0.474199\pi$
$702$	0.445042	+	0.770835i	0.0167970	+	0.0290933i
$703$	−11.0538	+	19.1457i	−0.416901	+	0.722093i
$704$	0.777479	−	1.34663i	0.0293023	−	0.0507532i
$705$	0.109916	+	0.190381i	0.00413969	+	0.00717015i
$706$	5.64742			0.212543
$707$		0			0
$708$	6.31767			0.237432
$709$	−5.67778	−	9.83421i	−0.213234	−	0.369332i	0.739491	−	0.673166i	$-0.235066\pi$
$709$	−5.67778	−	9.83421i	−0.213234	−	0.369332i	−0.952725	+	0.303835i	$0.901733\pi$
$710$	−0.217677	+	0.377027i	−0.00816926	+	0.0141496i
$711$	3.85086	−	6.66988i	0.144418	−	0.250140i
$712$	0.574572	+	0.995189i	0.0215330	+	0.0372963i
$713$	−6.39937			−0.239658
$714$		0			0
$715$	0.274127			0.0102518
$716$	5.51357	+	9.54979i	0.206052	+	0.356892i
$717$	1.53050	−	2.65090i	0.0571575	−	0.0989998i
$718$	8.32855	−	14.4255i	0.310819	−	0.538354i
$719$	0.697398	+	1.20793i	0.0260086	+	0.0450482i	0.878737	−	0.477307i	$-0.158387\pi$
$719$	0.697398	+	1.20793i	0.0260086	+	0.0450482i	−0.852728	+	0.522355i	$0.825054\pi$
$720$	0.198062			0.00738134
$721$		0			0
$722$	11.8984			0.442814
$723$	9.34481	+	16.1857i	0.347537	+	0.601952i
$724$	5.96077	−	10.3244i	0.221530	−	0.383702i
$725$	16.3502	−	28.3194i	0.607231	−	1.05175i
$726$	4.29105	+	7.43232i	0.159256	+	0.275839i
$727$	31.4795			1.16751			0.583755	−	0.811930i	$-0.301583\pi$
$727$	31.4795			1.16751			0.583755	+	0.811930i	$0.301583\pi$
$728$		0			0
$729$	1.00000			0.0370370
$730$	0.0174584	+	0.0302388i	0.000646164	+	0.00111919i
$731$	−12.6799	+	21.9623i	−0.468985	+	0.812305i
$732$	−2.93900	+	5.09050i	−0.108629	+	0.188150i
$733$	2.33513	+	4.04456i	0.0862498	+	0.149389i	0.905923	−	0.423442i	$-0.139178\pi$
$733$	2.33513	+	4.04456i	0.0862498	+	0.149389i	−0.819673	+	0.572831i	$0.805845\pi$
$734$	18.2000			0.671774
$735$		0			0
$736$	7.52111			0.277232
$737$	−7.77479	−	13.4663i	−0.286388	−	0.496039i
$738$	3.93631	−	6.81789i	0.144898	−	0.250970i
$739$	17.7530	−	30.7491i	0.653055	−	1.13113i	−0.329322	−	0.944218i	$-0.606820\pi$
$739$	17.7530	−	30.7491i	0.653055	−	1.13113i	0.982378	−	0.186908i	$-0.0598465\pi$
$740$	0.821552	+	1.42297i	0.0302009	+	0.0523094i
$741$	−2.37196			−0.0871362
$742$		0			0
$743$	−10.6987			−0.392498			−0.196249	−	0.980554i	$-0.562876\pi$
$743$	−10.6987			−0.392498			−0.196249	+	0.980554i	$0.562876\pi$
$744$	−0.425428	−	0.736862i	−0.0155969	−	0.0270147i
$745$	0.141375	−	0.244869i	0.00517959	−	0.00897131i
$746$	10.9291	−	18.9297i	0.400142	−	0.693066i
$747$	−1.75302	−	3.03632i	−0.0641397	−	0.111093i
$748$	−10.6528			−0.389505
$749$		0			0
$750$	−1.97285			−0.0720384
$751$	22.1323	+	38.3342i	0.807618	+	1.39884i	0.914509	+	0.404565i	$0.132577\pi$
$751$	22.1323	+	38.3342i	0.807618	+	1.39884i	−0.106891	+	0.994271i	$0.534090\pi$
$752$	−0.554958	+	0.961216i	−0.0202372	+	0.0350519i
$753$	6.71379	−	11.6286i	0.244664	−	0.423771i
$754$	−2.93362	−	5.08119i	−0.106836	−	0.185046i
$755$	0.187046			0.00680729
$756$		0			0
$757$	−18.9390			−0.688350			−0.344175	−	0.938906i	$-0.611841\pi$
$757$	−18.9390			−0.688350			−0.344175	+	0.938906i	$0.611841\pi$
$758$	−14.7778	−	25.5959i	−0.536753	−	0.929683i
$759$	5.84750	−	10.1282i	0.212251	−	0.367629i
$760$	−0.263906	+	0.457098i	−0.00957286	+	0.0165807i
$761$	−15.0221	−	26.0190i	−0.544549	−	0.943187i	−0.998635	−	0.0522293i	$-0.983367\pi$
$761$	−15.0221	−	26.0190i	−0.544549	−	0.943187i	0.454086	−	0.890958i	$-0.349966\pi$
$762$	−4.17629			−0.151291
$763$		0			0
$764$	−25.1444			−0.909691
$765$	−0.678448	−	1.17511i	−0.0245293	−	0.0424861i
$766$	−15.2838	+	26.4723i	−0.552227	+	0.956485i
$767$	−2.81163	+	4.86988i	−0.101522	+	0.175841i
$768$	0.500000	+	0.866025i	0.0180422	+	0.0312500i
$769$	−19.6233			−0.707633			−0.353816	−	0.935315i	$-0.615116\pi$
$769$	−19.6233			−0.707633			−0.353816	+	0.935315i	$0.615116\pi$
$770$		0			0
$771$	16.2717			0.586012
$772$	9.17510	+	15.8917i	0.330219	+	0.571956i
$773$	3.54610	−	6.14202i	0.127544	−	0.220913i	−0.795180	−	0.606373i	$-0.792624\pi$
$773$	3.54610	−	6.14202i	0.127544	−	0.220913i	0.922725	+	0.385460i	$0.125957\pi$
$774$	1.85086	−	3.20578i	0.0665276	−	0.115229i
$775$	2.11045	+	3.65540i	0.0758096	+	0.131306i
$776$	13.9758			0.501703
$777$		0			0
$778$	−4.24400			−0.152155
$779$	10.4898	+	18.1688i	0.375835	+	0.650966i
$780$	−0.0881460	+	0.152673i	−0.00315613	+	0.00546658i
$781$	−1.70895	+	2.95998i	−0.0611509	+	0.105917i
$782$	−25.7630	−	44.6228i	−0.921283	−	1.59571i
$783$	−6.59179			−0.235571
$784$		0			0
$785$	−4.82717			−0.172289
$786$	11.1957	+	19.3915i	0.399336	+	0.691671i
$787$	−19.2647	+	33.3675i	−0.686714	+	1.18942i	0.286181	+	0.958175i	$0.407614\pi$
$787$	−19.2647	+	33.3675i	−0.686714	+	1.18942i	−0.972895	+	0.231247i	$0.925719\pi$
$788$	11.1196	−	19.2597i	0.396120	−	0.686099i
$789$	−1.51693	−	2.62739i	−0.0540040	−	0.0935377i
$790$	1.52542			0.0542719
$791$		0			0
$792$	1.55496			0.0552530
$793$	−2.61596	−	4.53097i	−0.0928954	−	0.160899i
$794$	1.39612	−	2.41816i	0.0495466	−	0.0858172i
$795$	−0.290520	+	0.503196i	−0.0103037	+	0.0178465i
$796$	3.12618	+	5.41470i	0.110804	+	0.191919i
$797$	−1.19375			−0.0422848			−0.0211424	−	0.999776i	$-0.506730\pi$
$797$	−1.19375			−0.0422848			−0.0211424	+	0.999776i	$0.506730\pi$
$798$		0			0
$799$	7.60388			0.269006
$800$	−2.48039	−	4.29615i	−0.0876949	−	0.151892i
$801$	−0.574572	+	0.995189i	−0.0203015	+	0.0351633i
$802$	16.9269	−	29.3183i	0.597710	−	1.03526i
$803$	0.137063	+	0.237401i	0.00483686	+	0.00837769i
$804$	10.0000			0.352673
$805$		0			0
$806$	0.757332			0.0266759
$807$	−3.18329	−	5.51362i	−0.112057	−	0.194089i
$808$	7.35958	−	12.7472i	0.258909	−	0.448444i
$809$	−18.4795	+	32.0074i	−0.649704	+	1.12532i	0.333489	+	0.942754i	$0.391774\pi$
$809$	−18.4795	+	32.0074i	−0.649704	+	1.12532i	−0.983193	+	0.182567i	$0.941559\pi$
$810$	0.0990311	+	0.171527i	0.00347960	+	0.00602684i
$811$	50.0103			1.75610			0.878049	−	0.478570i	$-0.158845\pi$
$811$	50.0103			1.75610			0.878049	+	0.478570i	$0.158845\pi$
$812$		0			0
$813$	−17.2597			−0.605322
$814$	6.44989	+	11.1715i	0.226068	+	0.391562i
$815$	0.0120816	−	0.0209259i	0.000423199	−	0.000733003i
$816$	3.42543	−	5.93301i	0.119914	−	0.207697i
$817$	4.93230	+	8.54299i	0.172559	+	0.298881i
$818$	−29.3927			−1.02769
$819$		0			0
$820$	1.55927			0.0544521
$821$	−23.7235	−	41.0903i	−0.827955	−	1.43406i	−0.899640	−	0.436633i	$-0.856171\pi$
$821$	−23.7235	−	41.0903i	−0.827955	−	1.43406i	0.0716845	−	0.997427i	$-0.477163\pi$
$822$	5.18598	−	8.98238i	0.180882	−	0.313297i
$823$	−12.7778	+	22.1318i	−0.445405	+	0.771464i	−0.998080	−	0.0619323i	$-0.980274\pi$
$823$	−12.7778	+	22.1318i	−0.445405	+	0.771464i	0.552675	+	0.833397i	$0.313607\pi$
$824$	8.13587	+	14.0917i	0.283426	+	0.490909i
$825$	−7.71379			−0.268560
$826$		0			0
$827$	−37.2922			−1.29678			−0.648388	−	0.761310i	$-0.724557\pi$
$827$	−37.2922			−1.29678			−0.648388	+	0.761310i	$0.724557\pi$
$828$	3.76055	+	6.51347i	0.130688	+	0.226359i
$829$	10.4276	−	18.0611i	0.362165	−	0.627288i	−0.626152	−	0.779701i	$-0.715371\pi$
$829$	10.4276	−	18.0611i	0.362165	−	0.627288i	0.988317	+	0.152413i	$0.0487044\pi$
$830$	0.347207	−	0.601380i	0.0120517	−	0.0208742i
$831$	−5.94116	−	10.2904i	−0.206096	−	0.356970i
$832$	−0.890084			−0.0308581
$833$		0			0
$834$	−17.6256			−0.610326
$835$	−1.36658	−	2.36699i	−0.0472926	−	0.0819132i
$836$	−2.07188	+	3.58861i	−0.0716576	+	0.124115i
$837$	0.425428	−	0.736862i	0.0147049	−	0.0254697i
$838$	11.4426	+	19.8192i	0.395280	+	0.684645i
$839$	25.7453			0.888825			0.444412	−	0.895822i	$-0.353413\pi$
$839$	25.7453			0.888825			0.444412	+	0.895822i	$0.353413\pi$
$840$		0			0
$841$	14.4517			0.498336
$842$	18.6773	+	32.3499i	0.643661	+	1.11485i
$843$	7.07069	−	12.2468i	0.243527	−	0.421802i
$844$		0			0
$845$	1.20895	+	2.09396i	0.0415891	+	0.0720344i
$846$	−1.10992			−0.0381597
$847$		0			0
$848$	−2.93362			−0.100741
$849$	−0.628867	−	1.08923i	−0.0215826	−	0.0373822i
$850$	−16.9928	+	29.4323i	−0.582847	+	1.00952i
$851$	−31.1972	+	54.0351i	−1.06942	+	1.85230i
$852$	−1.09903	−	1.90358i	−0.0376522	−	0.0652155i
$853$	32.9444			1.12799			0.563997	−	0.825777i	$-0.309263\pi$
$853$	32.9444			1.12799			0.563997	+	0.825777i	$0.309263\pi$
$854$		0			0
$855$	−0.527811			−0.0180508
$856$	−3.85205	−	6.67195i	−0.131660	−	0.228043i
$857$	9.12379	−	15.8029i	0.311663	−	0.539815i	−0.667060	−	0.745004i	$-0.732447\pi$
$857$	9.12379	−	15.8029i	0.311663	−	0.539815i	0.978722	+	0.205189i	$0.0657808\pi$
$858$	−0.692021	+	1.19862i	−0.0236252	+	0.0409201i
$859$	−27.7146	−	48.0031i	−0.945611	−	1.63785i	−0.754524	−	0.656272i	$-0.772132\pi$
$859$	−27.7146	−	48.0031i	−0.945611	−	1.63785i	−0.191087	−	0.981573i	$-0.561201\pi$
$860$	0.733169			0.0250009
$861$		0			0
$862$	−3.96184			−0.134941
$863$	18.5432	+	32.1177i	0.631217	+	1.09330i	0.987303	+	0.158847i	$0.0507776\pi$
$863$	18.5432	+	32.1177i	0.631217	+	1.09330i	−0.356086	+	0.934453i	$0.615889\pi$
$864$	−0.500000	+	0.866025i	−0.0170103	+	0.0294628i
$865$	−0.154522	+	0.267639i	−0.00525390	+	0.00910002i
$866$	−16.3448	−	28.3100i	−0.555419	−	0.962015i
$867$	−29.9342			−1.01662
$868$		0			0
$869$	11.9758			0.406252
$870$	−0.652793	−	1.13067i	−0.0221317	−	0.0383333i
$871$	−4.45042	+	7.70835i	−0.150797	+	0.261188i
$872$	6.23221	−	10.7945i	0.211049	−	0.365548i
$873$	6.98792	+	12.1034i	0.236505	+	0.409639i
$874$	−20.0428			−0.677958
$875$		0			0
$876$	−0.176292			−0.00595635
$877$	−10.1020	−	17.4972i	−0.341121	−	0.590839i	0.643520	−	0.765429i	$-0.277473\pi$
$877$	−10.1020	−	17.4972i	−0.341121	−	0.590839i	−0.984641	+	0.174590i	$0.944140\pi$
$878$	15.7141	−	27.2176i	0.530325	−	0.918549i
$879$	−10.6582	+	18.4605i	−0.359491	+	0.622657i
$880$	0.153989	+	0.266717i	0.00519098	+	0.00899104i
$881$	−28.7549			−0.968779			−0.484389	−	0.874853i	$-0.660958\pi$
$881$	−28.7549			−0.968779			−0.484389	+	0.874853i	$0.660958\pi$
$882$		0			0
$883$	−38.1473			−1.28376			−0.641880	−	0.766805i	$-0.721845\pi$
$883$	−38.1473			−1.28376			−0.641880	+	0.766805i	$0.721845\pi$
$884$	3.04892	+	5.28088i	0.102546	+	0.177615i
$885$	−0.625646	+	1.08365i	−0.0210309	+	0.0364265i
$886$	−4.77748	+	8.27484i	−0.160503	+	0.277999i
$887$	23.1933	+	40.1719i	0.778754	+	1.34884i	0.932660	+	0.360756i	$0.117481\pi$
$887$	23.1933	+	40.1719i	0.778754	+	1.34884i	−0.153906	+	0.988085i	$0.549185\pi$
$888$	−8.29590			−0.278392
$889$		0			0
$890$	−0.227602			−0.00762924
$891$	0.777479	+	1.34663i	0.0260465	+	0.0451139i
$892$	6.89708	−	11.9461i	0.230931	−	0.399985i
$893$	1.47889	−	2.56152i	0.0494893	−	0.0857180i
$894$	0.713792	+	1.23632i	0.0238728	+	0.0413488i
$895$	−2.18406			−0.0730051
$896$		0			0
$897$	−6.69441			−0.223520
$898$	9.86831	+	17.0924i	0.329310	+	0.570381i
$899$	−2.80433	+	4.85724i	−0.0935297	+	0.161998i
$900$	2.48039	−	4.29615i	0.0826795	−	0.143205i
$901$	10.0489	+	17.4052i	0.334778	+	0.579852i
$902$	12.2416			0.407601
$903$		0			0
$904$		0			0
$905$	1.18060	+	2.04487i	0.0392446	+	0.0679736i
$906$	−0.472189	+	0.817855i	−0.0156874	+	0.0271714i
$907$	−9.31527	+	16.1345i	−0.309309	+	0.535738i	−0.978211	−	0.207612i	$-0.933431\pi$
$907$	−9.31527	+	16.1345i	−0.309309	+	0.535738i	0.668903	+	0.743350i	$0.266764\pi$
$908$	−7.44265	−	12.8910i	−0.246993	−	0.427804i
$909$	14.7192			0.488204
$910$		0			0
$911$	7.96077			0.263752			0.131876	−	0.991266i	$-0.457900\pi$
$911$	7.96077			0.263752			0.131876	+	0.991266i	$0.457900\pi$
$912$	−1.33244	−	2.30785i	−0.0441214	−	0.0764205i
$913$	2.72587	−	4.72135i	0.0902132	−	0.156254i
$914$	14.0027	−	24.2534i	0.463168	−	0.802230i
$915$	−0.582105	−	1.00824i	−0.0192438	−	0.0333312i
$916$	−3.76941			−0.124545
$917$		0			0
$918$	6.85086			0.226112
$919$	24.3884	+	42.2419i	0.804498	+	1.39343i	0.916630	+	0.399737i	$0.130899\pi$
$919$	24.3884	+	42.2419i	0.804498	+	1.39343i	−0.112132	+	0.993693i	$0.535768\pi$
$920$	−0.744824	+	1.29007i	−0.0245561	+	0.0425324i
$921$	−7.34266	+	12.7179i	−0.241949	+	0.419068i
$922$	15.3741	+	26.6288i	0.506320	+	0.876971i
$923$	1.95646			0.0643976
$924$		0			0
$925$	41.1540			1.35314
$926$	16.5472	+	28.6606i	0.543774	+	0.941845i
$927$	−8.13587	+	14.0917i	−0.267217	+	0.462833i
$928$	3.29590	−	5.70866i	0.108193	−	0.187396i
$929$	4.77599	+	8.27225i	0.156695	+	0.271404i	0.933675	−	0.358122i	$-0.116583\pi$
$929$	4.77599	+	8.27225i	0.156695	+	0.271404i	−0.776980	+	0.629525i	$0.783249\pi$
$930$	0.168522			0.00552606
$931$		0			0
$932$	7.08575			0.232102
$933$	5.95108	+	10.3076i	0.194830	+	0.337455i
$934$	8.41119	−	14.5686i	0.275223	−	0.476699i
$935$	1.05496	−	1.82724i	0.0345008	−	0.0597572i
$936$	−0.445042	−	0.770835i	−0.0145466	−	0.0251955i
$937$	58.4892			1.91076			0.955379	−	0.295383i	$-0.0954472\pi$
$937$	58.4892			1.91076			0.955379	+	0.295383i	$0.0954472\pi$
$938$		0			0
$939$	−26.9202			−0.878508
$940$	−0.109916	−	0.190381i	−0.00358507	−	0.00620953i
$941$	3.34399	−	5.79195i	0.109011	−	0.188812i	−0.806359	−	0.591426i	$-0.798565\pi$
$941$	3.34399	−	5.79195i	0.109011	−	0.188812i	0.915370	+	0.402614i	$0.131898\pi$
$942$	12.1860	−	21.1067i	0.397041	−	0.687695i
$943$	29.6054	+	51.2781i	0.964085	+	1.66984i
$944$	−6.31767			−0.205623
$945$		0			0
$946$	5.75600			0.187144
$947$	10.3324	+	17.8963i	0.335759	+	0.581552i	0.983630	−	0.180198i	$-0.0576739\pi$
$947$	10.3324	+	17.8963i	0.335759	+	0.581552i	−0.647871	+	0.761750i	$0.724341\pi$
$948$	−3.85086	+	6.66988i	−0.125070	+	0.216628i
$949$	0.0784573	−	0.135892i	0.00254683	−	0.00441124i
$950$	6.60992	+	11.4487i	0.214454	+	0.371445i
$951$	−32.2500			−1.04578
$952$		0			0
$953$	13.6668			0.442711			0.221355	−	0.975193i	$-0.428952\pi$
$953$	13.6668			0.442711			0.221355	+	0.975193i	$0.428952\pi$
$954$	−1.46681	−	2.54059i	−0.0474898	−	0.0822547i
$955$	2.49007	−	4.31294i	0.0805769	−	0.139563i
$956$	−1.53050	+	2.65090i	−0.0494999	+	0.0857363i
$957$	−5.12498	−	8.87673i	−0.165667	−	0.286944i
$958$	20.1849			0.652145
$959$		0			0
$960$	−0.198062			−0.00639243
$961$	15.1380	+	26.2198i	0.488323	+	0.845801i
$962$	3.69202	−	6.39477i	0.119036	−	0.206176i
$963$	3.85205	−	6.67195i	0.124131	−	0.215001i
$964$	−9.34481	−	16.1857i	−0.300976	−	0.521306i
$965$	−3.63448			−0.116998
$966$		0			0
$967$	−56.3188			−1.81109			−0.905546	−	0.424248i	$-0.860538\pi$
$967$	−56.3188			−1.81109			−0.905546	+	0.424248i	$0.860538\pi$
$968$	−4.29105	−	7.43232i	−0.137920	−	0.238884i
$969$	−9.12833	+	15.8107i	−0.293244	+	0.507914i
$970$	−1.38404	+	2.39723i	−0.0444389	+	0.0769705i
$971$	−21.9487	−	38.0162i	−0.704367	−	1.22000i	−0.966920	−	0.255082i	$-0.917898\pi$
$971$	−21.9487	−	38.0162i	−0.704367	−	1.22000i	0.262553	−	0.964918i	$-0.415436\pi$
$972$	−1.00000			−0.0320750
$973$		0			0
$974$	−9.62325			−0.308349
$975$	2.20775	+	3.82394i	0.0707046	+	0.122464i
$976$	2.93900	−	5.09050i	0.0940751	−	0.162943i
$977$	13.3666	−	23.1516i	0.427635	−	0.740685i	−0.569028	−	0.822318i	$-0.692680\pi$
$977$	13.3666	−	23.1516i	0.427635	−	0.740685i	0.996662	+	0.0816331i	$0.0260136\pi$
$978$	0.0609989	+	0.105653i	0.00195053	+	0.00337842i
$979$	−1.78687			−0.0571087
$980$		0			0
$981$	12.4644			0.397958
$982$	−0.565843	−	0.980069i	−0.0180568	−	0.0312753i
$983$	−23.9705	+	41.5181i	−0.764539	+	1.32422i	0.175951	+	0.984399i	$0.443700\pi$
$983$	−23.9705	+	41.5181i	−0.764539	+	1.32422i	−0.940490	+	0.339821i	$0.889633\pi$
$984$	−3.93631	+	6.81789i	−0.125485	+	0.217347i
$985$	2.20237	+	3.81462i	0.0701735	+	0.121544i
$986$	−45.1594			−1.43817
$987$		0			0
$988$	2.37196			0.0754621
$989$	13.9205	+	24.1110i	0.442645	+	0.766684i
$990$	−0.153989	+	0.266717i	−0.00489410	+	0.00847683i
$991$	−11.5211	+	19.9551i	−0.365980	+	0.633896i	−0.988933	−	0.148363i	$-0.952599\pi$
$991$	−11.5211	+	19.9551i	−0.365980	+	0.633896i	0.622953	+	0.782259i	$0.285933\pi$
$992$	0.425428	+	0.736862i	0.0135073	+	0.0233954i
$993$	17.1836			0.545305
$994$		0			0
$995$	−1.23836			−0.0392585
$996$	1.75302	+	3.03632i	0.0555466	+	0.0962095i
$997$	4.71140	−	8.16038i	0.149211	−	0.258442i	−0.781725	−	0.623624i	$-0.785660\pi$
$997$	4.71140	−	8.16038i	0.149211	−	0.258442i	0.930936	+	0.365182i	$0.118993\pi$
$998$	−1.48188	+	2.56669i	−0.0469080	+	0.0812471i
$999$	−4.14795	−	7.18446i	−0.131235	−	0.227306i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2058.2.e.i.361.3		6
7.2	even	3	inner	2058.2.e.i.667.3		6
7.3	odd	6		2058.2.a.e.1.3	yes	3
7.4	even	3		2058.2.a.d.1.1	✓	3
7.5	odd	6		2058.2.e.h.667.1		6
7.6	odd	2		2058.2.e.h.361.1		6
21.11	odd	6		6174.2.a.g.1.3		3
21.17	even	6		6174.2.a.p.1.1		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2058.2.a.d.1.1	✓	3	7.4	even	3
2058.2.a.e.1.3	yes	3	7.3	odd	6
2058.2.e.h.361.1		6	7.6	odd	2
2058.2.e.h.667.1		6	7.5	odd	6
2058.2.e.i.361.3		6	1.1	even	1	trivial
2058.2.e.i.667.3		6	7.2	even	3	inner
6174.2.a.g.1.3		3	21.11	odd	6
6174.2.a.p.1.1		3	21.17	even	6

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:	\( N \)	\(=\)	\( 2058 = 2 \cdot 3 \cdot 7^{3} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2058.e (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.500000 + 0.866025i) q^{2} +(0.500000 - 0.866025i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-0.0990311 - 0.171527i) q^{5} +1.00000 q^{6} -1.00000 q^{8} +(-0.500000 - 0.866025i) q^{9} +(0.0990311 - 0.171527i) q^{10} +(0.777479 - 1.34663i) q^{11} +(0.500000 + 0.866025i) q^{12} -0.890084 q^{13} -0.198062 q^{15} +(-0.500000 - 0.866025i) q^{16} +(-3.42543 + 5.93301i) q^{17} +(0.500000 - 0.866025i) q^{18} +(1.33244 + 2.30785i) q^{19} +0.198062 q^{20} +1.55496 q^{22} +(3.76055 + 6.51347i) q^{23} +(-0.500000 + 0.866025i) q^{24} +(2.48039 - 4.29615i) q^{25} +(-0.445042 - 0.770835i) q^{26} -1.00000 q^{27} +6.59179 q^{29} +(-0.0990311 - 0.171527i) q^{30} +(-0.425428 + 0.736862i) q^{31} +(0.500000 - 0.866025i) q^{32} +(-0.777479 - 1.34663i) q^{33} -6.85086 q^{34} +1.00000 q^{36} +(4.14795 + 7.18446i) q^{37} +(-1.33244 + 2.30785i) q^{38} +(-0.445042 + 0.770835i) q^{39} +(0.0990311 + 0.171527i) q^{40} +7.87263 q^{41} +3.70171 q^{43} +(0.777479 + 1.34663i) q^{44} +(-0.0990311 + 0.171527i) q^{45} +(-3.76055 + 6.51347i) q^{46} +(-0.554958 - 0.961216i) q^{47} -1.00000 q^{48} +4.96077 q^{50} +(3.42543 + 5.93301i) q^{51} +(0.445042 - 0.770835i) q^{52} +(1.46681 - 2.54059i) q^{53} +(-0.500000 - 0.866025i) q^{54} -0.307979 q^{55} +2.66487 q^{57} +(3.29590 + 5.70866i) q^{58} +(3.15883 - 5.47126i) q^{59} +(0.0990311 - 0.171527i) q^{60} +(2.93900 + 5.09050i) q^{61} -0.850855 q^{62} +1.00000 q^{64} +(0.0881460 + 0.152673i) q^{65} +(0.777479 - 1.34663i) q^{66} +(5.00000 - 8.66025i) q^{67} +(-3.42543 - 5.93301i) q^{68} +7.52111 q^{69} -2.19806 q^{71} +(0.500000 + 0.866025i) q^{72} +(-0.0881460 + 0.152673i) q^{73} +(-4.14795 + 7.18446i) q^{74} +(-2.48039 - 4.29615i) q^{75} -2.66487 q^{76} -0.890084 q^{78} +(3.85086 + 6.66988i) q^{79} +(-0.0990311 + 0.171527i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(3.93631 + 6.81789i) q^{82} +3.50604 q^{83} +1.35690 q^{85} +(1.85086 + 3.20578i) q^{86} +(3.29590 - 5.70866i) q^{87} +(-0.777479 + 1.34663i) q^{88} +(-0.574572 - 0.995189i) q^{89} -0.198062 q^{90} -7.52111 q^{92} +(0.425428 + 0.736862i) q^{93} +(0.554958 - 0.961216i) q^{94} +(0.263906 - 0.457098i) q^{95} +(-0.500000 - 0.866025i) q^{96} -13.9758 q^{97} -1.55496 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + 3 q^{2} + 3 q^{3} - 3 q^{4} - 5 q^{5} + 6 q^{6} - 6 q^{8} - 3 q^{9} + 5 q^{10} + 5 q^{11} + 3 q^{12} - 4 q^{13} - 10 q^{15} - 3 q^{16} - 7 q^{17} + 3 q^{18} + 9 q^{19} + 10 q^{20} + 10 q^{22} + 7 q^{23}+ \cdots - 10 q^{99}+O(q^{100}) \) 6 * q + 3 * q^2 + 3 * q^3 - 3 * q^4 - 5 * q^5 + 6 * q^6 - 6 * q^8 - 3 * q^9 + 5 * q^10 + 5 * q^11 + 3 * q^12 - 4 * q^13 - 10 * q^15 - 3 * q^16 - 7 * q^17 + 3 * q^18 + 9 * q^19 + 10 * q^20 + 10 * q^22 + 7 * q^23 - 3 * q^24 + 2 * q^25 - 2 * q^26 - 6 * q^27 - 16 * q^29 - 5 * q^30 + 11 * q^31 + 3 * q^32 - 5 * q^33 - 14 * q^34 + 6 * q^36 + 11 * q^37 - 9 * q^38 - 2 * q^39 + 5 * q^40 + 14 * q^41 - 32 * q^43 + 5 * q^44 - 5 * q^45 - 7 * q^46 - 4 * q^47 - 6 * q^48 + 4 * q^50 + 7 * q^51 + 2 * q^52 + 2 * q^53 - 3 * q^54 - 12 * q^55 + 18 * q^57 - 8 * q^58 + 2 * q^59 + 5 * q^60 - 2 * q^61 + 22 * q^62 + 6 * q^64 + 8 * q^65 + 5 * q^66 + 30 * q^67 - 7 * q^68 + 14 * q^69 - 22 * q^71 + 3 * q^72 - 8 * q^73 - 11 * q^74 - 2 * q^75 - 18 * q^76 - 4 * q^78 - 4 * q^79 - 5 * q^80 - 3 * q^81 + 7 * q^82 + 40 * q^83 - 16 * q^86 - 8 * q^87 - 5 * q^88 - 17 * q^89 - 10 * q^90 - 14 * q^92 - 11 * q^93 + 4 * q^94 + 8 * q^95 - 3 * q^96 - 8 * q^97 - 10 * q^99

Introduction

L-functions

Modular forms

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