LMFDB - Embedded newform 288.3.u.a.163.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [288,3,Mod(19,288)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(288, base_ring=CyclotomicField(8))

chi = DirichletCharacter(H, H._module([4, 7, 0]))

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("288.19");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 288 = 2^{5} \cdot 3^{2} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	288.u (of order $8$, degree $4$, 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:	$7.84743161358$
Analytic rank:	$0$
Dimension:	$28$
Relative dimension:	$7$ over $\Q(\zeta_{8})$
Twist minimal:	no (minimal twist has level 32)
Sato-Tate group:	$\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label			163.5
Character	$\chi$	$=$	288.163
Dual form			288.3.u.a.235.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.44490 + 1.38284i) q^{2} +(0.175499 + 3.99615i) q^{4} +(3.18221 + 7.68254i) q^{5} +(3.67370 + 3.67370i) q^{7} +(-5.27246 + 6.01674i) q^{8} +O(q^{10})$	\(q+(1.44490 + 1.38284i) q^{2} +(0.175499 + 3.99615i) q^{4} +(3.18221 + 7.68254i) q^{5} +(3.67370 + 3.67370i) q^{7} +(-5.27246 + 6.01674i) q^{8} +(-6.02574 + 15.5010i) q^{10} +(-6.10089 - 14.7288i) q^{11} +(2.82075 - 6.80990i) q^{13} +(0.228001 + 10.3883i) q^{14} +(-15.9384 + 1.40264i) q^{16} +3.67152i q^{17} +(-1.65751 - 0.686564i) q^{19} +(-30.1421 + 14.0649i) q^{20} +(11.5525 - 29.7183i) q^{22} +(8.31529 - 8.31529i) q^{23} +(-31.2172 + 31.2172i) q^{25} +(13.4927 - 5.93900i) q^{26} +(-14.0359 + 15.3254i) q^{28} +(38.8592 + 16.0960i) q^{29} +4.11293i q^{31} +(-24.9691 - 20.0136i) q^{32} +(-5.07713 + 5.30499i) q^{34} +(-16.5328 + 39.9138i) q^{35} +(19.8759 + 47.9847i) q^{37} +(-1.44554 - 3.28410i) q^{38} +(-63.0019 - 21.3593i) q^{40} +(-21.1187 - 21.1187i) q^{41} +(-0.102495 - 0.247444i) q^{43} +(57.7879 - 26.9649i) q^{44} +(23.5135 - 0.516073i) q^{46} +39.3838 q^{47} -22.0079i q^{49} +(-88.2745 + 1.93744i) q^{50} +(27.7084 + 10.0770i) q^{52} +(-22.6154 + 9.36759i) q^{53} +(93.7406 - 93.7406i) q^{55} +(-41.4731 + 2.73426i) q^{56} +(33.8896 + 76.9933i) q^{58} +(101.380 - 41.9931i) q^{59} +(-14.0475 - 5.81867i) q^{61} +(-5.68753 + 5.94279i) q^{62} +(-8.40232 - 63.4460i) q^{64} +61.2936 q^{65} +(3.67448 - 8.87098i) q^{67} +(-14.6719 + 0.644346i) q^{68} +(-79.0828 + 34.8093i) q^{70} +(-75.7712 - 75.7712i) q^{71} +(-29.0378 - 29.0378i) q^{73} +(-37.6364 + 96.8185i) q^{74} +(2.45272 - 6.74415i) q^{76} +(31.6965 - 76.5221i) q^{77} +2.76556 q^{79} +(-61.4952 - 117.984i) q^{80} +(-1.31069 - 59.7184i) q^{82} +(79.1972 + 32.8045i) q^{83} +(-28.2066 + 11.6835i) q^{85} +(0.194081 - 0.499267i) q^{86} +(120.786 + 40.9498i) q^{88} +(-72.4200 + 72.4200i) q^{89} +(35.3801 - 14.6549i) q^{91} +(34.6885 + 31.7698i) q^{92} +(56.9058 + 54.4615i) q^{94} -14.9187i q^{95} +66.0511 q^{97} +(30.4335 - 31.7993i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 28 q + 4 q^{2} - 4 q^{4} + 4 q^{5} - 4 q^{7} + 4 q^{8}+O(q^{10}) $ 28 * q + 4 * q^2 - 4 * q^4 + 4 * q^5 - 4 * q^7 + 4 * q^8	$ 28 q + 4 q^{2} - 4 q^{4} + 4 q^{5} - 4 q^{7} + 4 q^{8} - 44 q^{10} + 4 q^{11} - 4 q^{13} + 20 q^{14} + 16 q^{16} - 4 q^{19} - 76 q^{20} + 144 q^{22} + 68 q^{23} - 4 q^{25} - 96 q^{26} + 56 q^{28} + 4 q^{29} + 24 q^{32} - 48 q^{34} - 92 q^{35} - 4 q^{37} + 396 q^{38} - 408 q^{40} + 4 q^{41} + 92 q^{43} + 188 q^{44} - 36 q^{46} + 8 q^{47} - 308 q^{50} + 420 q^{52} + 164 q^{53} + 252 q^{55} - 552 q^{56} + 528 q^{58} - 124 q^{59} - 68 q^{61} - 216 q^{62} - 232 q^{64} + 8 q^{65} - 164 q^{67} + 368 q^{68} - 664 q^{70} + 260 q^{71} - 4 q^{73} + 532 q^{74} - 516 q^{76} - 220 q^{77} - 520 q^{79} - 312 q^{80} + 636 q^{82} + 484 q^{83} + 96 q^{85} - 688 q^{86} + 672 q^{88} + 4 q^{89} - 196 q^{91} - 616 q^{92} + 40 q^{94} - 8 q^{97} + 328 q^{98}+O(q^{100}) $ 28 * q + 4 * q^2 - 4 * q^4 + 4 * q^5 - 4 * q^7 + 4 * q^8 - 44 * q^10 + 4 * q^11 - 4 * q^13 + 20 * q^14 + 16 * q^16 - 4 * q^19 - 76 * q^20 + 144 * q^22 + 68 * q^23 - 4 * q^25 - 96 * q^26 + 56 * q^28 + 4 * q^29 + 24 * q^32 - 48 * q^34 - 92 * q^35 - 4 * q^37 + 396 * q^38 - 408 * q^40 + 4 * q^41 + 92 * q^43 + 188 * q^44 - 36 * q^46 + 8 * q^47 - 308 * q^50 + 420 * q^52 + 164 * q^53 + 252 * q^55 - 552 * q^56 + 528 * q^58 - 124 * q^59 - 68 * q^61 - 216 * q^62 - 232 * q^64 + 8 * q^65 - 164 * q^67 + 368 * q^68 - 664 * q^70 + 260 * q^71 - 4 * q^73 + 532 * q^74 - 516 * q^76 - 220 * q^77 - 520 * q^79 - 312 * q^80 + 636 * q^82 + 484 * q^83 + 96 * q^85 - 688 * q^86 + 672 * q^88 + 4 * q^89 - 196 * q^91 - 616 * q^92 + 40 * q^94 - 8 * q^97 + 328 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/288\mathbb{Z}\right)^\times$.

$n$	$37$	$65$	$127$
$\chi(n)$	$e\left(\frac{3}{8}\right)$	$1$	$-1$

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 $

$2$	1.44490	+	1.38284i	0.722452	+	0.691421i
$2$	1.44490	+	1.38284i	0.722452	+	0.691421i
$3$		0			0
$3$		0			0
$4$	0.175499	+	3.99615i	0.0438747	+	0.999037i
$5$	3.18221	+	7.68254i	0.636442	+	1.53651i	0.831387	+	0.555693i	$0.187547\pi$
$5$	3.18221	+	7.68254i	0.636442	+	1.53651i	−0.194945	+	0.980814i	$0.562453\pi$
$6$		0			0
$7$	3.67370	+	3.67370i	0.524814	+	0.524814i	0.919021	−	0.394208i	$-0.128981\pi$
$7$	3.67370	+	3.67370i	0.524814	+	0.524814i	−0.394208	+	0.919021i	$0.628981\pi$
$8$	−5.27246	+	6.01674i	−0.659058	+	0.752092i
$9$		0			0
$10$	−6.02574	+	15.5010i	−0.602574	+	1.55010i
$11$	−6.10089	−	14.7288i	−0.554626	−	1.33899i	−0.913971	−	0.405781i	$-0.867000\pi$
$11$	−6.10089	−	14.7288i	−0.554626	−	1.33899i	0.359345	−	0.933205i	$-0.383000\pi$
$12$		0			0
$13$	2.82075	−	6.80990i	0.216981	−	0.523839i	−0.777484	−	0.628902i	$-0.783505\pi$
$13$	2.82075	−	6.80990i	0.216981	−	0.523839i	0.994466	+	0.105063i	$0.0335046\pi$
$14$	0.228001	+	10.3883i	0.0162858	+	0.742020i
$15$		0			0
$16$	−15.9384	+	1.40264i	−0.996150	+	0.0876648i
$17$			3.67152i			0.215972i	0.994152	+	0.107986i	$0.0344401\pi$
$17$			3.67152i			0.215972i	−0.994152	+	0.107986i	$0.965560\pi$
$18$		0			0
$19$	−1.65751	−	0.686564i	−0.0872375	−	0.0361349i	0.338638	−	0.940917i	$-0.390034\pi$
$19$	−1.65751	−	0.686564i	−0.0872375	−	0.0361349i	−0.425875	+	0.904782i	$0.640034\pi$
$20$	−30.1421	+	14.0649i	−1.50710	+	0.703243i
$21$		0			0
$22$	11.5525	−	29.7183i	0.525112	−	1.35083i
$23$	8.31529	−	8.31529i	0.361534	−	0.361534i	−0.502843	−	0.864378i	$-0.667713\pi$
$23$	8.31529	−	8.31529i	0.361534	−	0.361534i	0.864378	+	0.502843i	$0.167713\pi$
$24$		0			0
$25$	−31.2172	+	31.2172i	−1.24869	+	1.24869i
$26$	13.4927	−	5.93900i	0.518951	−	0.228423i
$27$		0			0
$28$	−14.0359	+	15.3254i	−0.501282	+	0.547334i
$29$	38.8592	+	16.0960i	1.33997	+	0.555035i	0.933483	−	0.358621i	$-0.116753\pi$
$29$	38.8592	+	16.0960i	1.33997	+	0.555035i	0.406489	+	0.913656i	$0.366753\pi$
$30$		0			0
$31$			4.11293i			0.132675i	0.997797	+	0.0663376i	$0.0211314\pi$
$31$			4.11293i			0.132675i	−0.997797	+	0.0663376i	$0.978869\pi$
$32$	−24.9691	−	20.0136i	−0.780284	−	0.625425i
$33$		0			0
$34$	−5.07713	+	5.30499i	−0.149327	+	0.156029i
$35$	−16.5328	+	39.9138i	−0.472367	+	1.14039i
$36$		0			0
$37$	19.8759	+	47.9847i	0.537186	+	1.29688i	0.926679	+	0.375853i	$0.122650\pi$
$37$	19.8759	+	47.9847i	0.537186	+	1.29688i	−0.389493	+	0.921030i	$0.627350\pi$
$38$	−1.44554	−	3.28410i	−0.0380405	−	0.0864236i
$39$		0			0
$40$	−63.0019	−	21.3593i	−1.57505	−	0.533984i
$41$	−21.1187	−	21.1187i	−0.515091	−	0.515091i	0.400991	−	0.916082i	$-0.368666\pi$
$41$	−21.1187	−	21.1187i	−0.515091	−	0.515091i	−0.916082	+	0.400991i	$0.868666\pi$
$42$		0			0
$43$	−0.102495	−	0.247444i	−0.00238360	−	0.00575451i	0.922683	−	0.385559i	$-0.125991\pi$
$43$	−0.102495	−	0.247444i	−0.00238360	−	0.00575451i	−0.925067	+	0.379804i	$0.875991\pi$
$44$	57.7879	−	26.9649i	1.31336	−	0.612839i
$45$		0			0
$46$	23.5135	−	0.516073i	0.511164	−	0.0112190i
$47$	39.3838			0.837952			0.418976	−	0.907997i	$-0.362389\pi$
$47$	39.3838			0.837952			0.418976	+	0.907997i	$0.362389\pi$
$48$		0			0
$49$		−	22.0079i		−	0.449141i
$50$	−88.2745	+	1.93744i	−1.76549	+	0.0387488i
$51$		0			0
$52$	27.7084	+	10.0770i	0.532854	+	0.193789i
$53$	−22.6154	+	9.36759i	−0.426705	+	0.176747i	−0.585692	−	0.810534i	$-0.699177\pi$
$53$	−22.6154	+	9.36759i	−0.426705	+	0.176747i	0.158987	+	0.987281i	$0.449177\pi$
$54$		0			0
$55$	93.7406	−	93.7406i	1.70437	−	1.70437i
$56$	−41.4731	+	2.73426i	−0.740591	+	0.0488260i
$57$		0			0
$58$	33.8896	+	76.9933i	0.584304	+	1.32747i
$59$	101.380	−	41.9931i	1.71831	−	0.711747i	0.718441	−	0.695588i	$-0.244856\pi$
$59$	101.380	−	41.9931i	1.71831	−	0.711747i	0.999869	−	0.0161592i	$-0.00514387\pi$
$60$		0			0
$61$	−14.0475	−	5.81867i	−0.230287	−	0.0953880i	0.264556	−	0.964370i	$-0.414775\pi$
$61$	−14.0475	−	5.81867i	−0.230287	−	0.0953880i	−0.494843	+	0.868982i	$0.664775\pi$
$62$	−5.68753	+	5.94279i	−0.0917344	+	0.0958515i
$63$		0			0
$64$	−8.40232	−	63.4460i	−0.131286	−	0.991345i
$65$	61.2936			0.942978
$66$		0			0
$67$	3.67448	−	8.87098i	0.0548430	−	0.132403i	−0.894083	−	0.447901i	$-0.852172\pi$
$67$	3.67448	−	8.87098i	0.0548430	−	0.132403i	0.948926	+	0.315498i	$0.102172\pi$
$68$	−14.6719	+	0.644346i	−0.215764	+	0.00947568i
$69$		0			0
$70$	−79.0828	+	34.8093i	−1.12975	+	0.497276i
$71$	−75.7712	−	75.7712i	−1.06720	−	1.06720i	−0.997573	−	0.0696271i	$-0.977819\pi$
$71$	−75.7712	−	75.7712i	−1.06720	−	1.06720i	−0.0696271	−	0.997573i	$-0.522181\pi$
$72$		0			0
$73$	−29.0378	−	29.0378i	−0.397779	−	0.397779i	0.479670	−	0.877449i	$-0.340756\pi$
$73$	−29.0378	−	29.0378i	−0.397779	−	0.397779i	−0.877449	+	0.479670i	$0.840756\pi$
$74$	−37.6364	+	96.8185i	−0.508600	+	1.30836i
$75$		0			0
$76$	2.45272	−	6.74415i	0.0322726	−	0.0887389i
$77$	31.6965	−	76.5221i	0.411643	−	0.993793i
$78$		0			0
$79$	2.76556			0.0350072			0.0175036	−	0.999847i	$-0.494428\pi$
$79$	2.76556			0.0350072			0.0175036	+	0.999847i	$0.494428\pi$
$80$	−61.4952	−	117.984i	−0.768690	−	1.47480i
$81$		0			0
$82$	−1.31069	−	59.7184i	−0.0159841	−	0.728273i
$83$	79.1972	+	32.8045i	0.954183	+	0.395235i	0.804801	−	0.593544i	$-0.202272\pi$
$83$	79.1972	+	32.8045i	0.954183	+	0.395235i	0.149381	+	0.988780i	$0.452272\pi$
$84$		0			0
$85$	−28.2066	+	11.6835i	−0.331842	+	0.137453i
$86$	0.194081	−	0.499267i	0.00225675	−	0.00580543i
$87$		0			0
$88$	120.786	+	40.9498i	1.37257	+	0.465339i
$89$	−72.4200	+	72.4200i	−0.813708	+	0.813708i	−0.985188	−	0.171480i	$-0.945145\pi$
$89$	−72.4200	+	72.4200i	−0.813708	+	0.813708i	0.171480	+	0.985188i	$0.445145\pi$
$90$		0			0
$91$	35.3801	−	14.6549i	0.388792	−	0.161043i
$92$	34.6885	+	31.7698i	0.377048	+	0.345324i
$93$		0			0
$94$	56.9058	+	54.4615i	0.605380	+	0.579378i
$95$		−	14.9187i		−	0.157039i
$96$		0			0
$97$	66.0511			0.680940			0.340470	−	0.940255i	$-0.389414\pi$
$97$	66.0511			0.680940			0.340470	+	0.940255i	$0.389414\pi$
$98$	30.4335	−	31.7993i	0.310545	−	0.324483i
$99$		0			0
$100$	−130.227	−	119.270i	−1.30227	−	1.19270i
$101$	7.51179	+	18.1351i	0.0743742	+	0.179555i	0.956694	−	0.291095i	$-0.0940195\pi$
$101$	7.51179	+	18.1351i	0.0743742	+	0.179555i	−0.882320	+	0.470650i	$0.844019\pi$
$102$		0			0
$103$	0.589180	+	0.589180i	0.00572020	+	0.00572020i	0.709961	−	0.704241i	$-0.248712\pi$
$103$	0.589180	+	0.589180i	0.00572020	+	0.00572020i	−0.704241	+	0.709961i	$0.748712\pi$
$104$	26.1011	+	52.8767i	0.250972	+	0.508430i
$105$		0			0
$106$	−45.6309	−	17.7382i	−0.430480	−	0.167341i
$107$	55.4567	+	133.884i	0.518287	+	1.25126i	0.938955	+	0.344041i	$0.111796\pi$
$107$	55.4567	+	133.884i	0.518287	+	1.25126i	−0.420668	+	0.907215i	$0.638204\pi$
$108$		0			0
$109$	29.4015	−	70.9815i	0.269739	−	0.651207i	−0.729732	−	0.683733i	$-0.760355\pi$
$109$	29.4015	−	70.9815i	0.269739	−	0.651207i	0.999471	+	0.0325264i	$0.0103553\pi$
$110$	265.075	−	5.81783i	2.40977	−	0.0528894i
$111$		0			0
$112$	−63.7057	−	53.4000i	−0.568801	−	0.476786i
$113$			134.274i			1.18826i	0.804368	+	0.594131i	$0.202504\pi$
$113$			134.274i			1.18826i	−0.804368	+	0.594131i	$0.797496\pi$
$114$		0			0
$115$	90.3436	+	37.4215i	0.785596	+	0.325405i
$116$	−57.5023	+	158.112i	−0.495709	+	1.36303i
$117$		0			0
$118$	204.555	+	79.5169i	1.73351	+	0.673872i
$119$	−13.4880	+	13.4880i	−0.113345	+	0.113345i
$120$		0			0
$121$	−94.1580	+	94.1580i	−0.778166	+	0.778166i
$122$	−12.2510	−	27.8329i	−0.100418	−	0.228138i
$123$		0			0
$124$	−16.4359	+	0.721814i	−0.132547	+	0.00582108i
$125$	−147.104	−	60.9325i	−1.17683	−	0.487460i
$126$		0			0
$127$		−	95.5030i		−	0.751992i	−0.926621	−	0.375996i	$-0.877301\pi$
$127$		−	95.5030i		−	0.751992i	0.926621	−	0.375996i	$-0.122699\pi$
$128$	75.5953	−	103.293i	0.590588	−	0.806973i
$129$		0			0
$130$	88.5634	+	84.7593i	0.681257	+	0.651995i
$131$	67.1188	−	162.039i	0.512357	−	1.23694i	−0.430151	−	0.902757i	$-0.641540\pi$
$131$	67.1188	−	162.039i	0.512357	−	1.23694i	0.942508	−	0.334183i	$-0.108460\pi$
$132$		0			0
$133$	−3.56697	−	8.61142i	−0.0268193	−	0.0647475i
$134$	17.5764	−	7.73649i	0.131167	−	0.0577350i
$135$		0			0
$136$	−22.0906	−	19.3579i	−0.162431	−	0.142338i
$137$	−88.7244	−	88.7244i	−0.647624	−	0.647624i	0.304794	−	0.952418i	$-0.401412\pi$
$137$	−88.7244	−	88.7244i	−0.647624	−	0.647624i	−0.952418	+	0.304794i	$0.901412\pi$
$138$		0			0
$139$	−27.6838	−	66.8346i	−0.199164	−	0.480824i	0.792469	−	0.609912i	$-0.208795\pi$
$139$	−27.6838	−	66.8346i	−0.199164	−	0.480824i	−0.991633	+	0.129087i	$0.958795\pi$
$140$	−162.403	−	59.0628i	−1.16002	−	0.421877i
$141$		0			0
$142$	−4.70260	−	214.262i	−0.0331169	−	1.50889i
$143$	−117.511			−0.821756
$144$		0			0
$145$			349.758i			2.41213i
$146$	−1.80218	−	82.1116i	−0.0123437	−	0.562409i
$147$		0			0
$148$	−188.266	+	87.8483i	−1.27207	+	0.593569i
$149$	100.536	−	41.6433i	0.674737	−	0.279485i	−0.0188878	−	0.999822i	$-0.506013\pi$
$149$	100.536	−	41.6433i	0.674737	−	0.279485i	0.693625	+	0.720336i	$0.256013\pi$
$150$		0			0
$151$	−134.706	+	134.706i	−0.892096	+	0.892096i	−0.994720	−	0.102624i	$-0.967276\pi$
$151$	−134.706	+	134.706i	−0.892096	+	0.892096i	0.102624	+	0.994720i	$0.467276\pi$
$152$	12.8700	−	6.35294i	0.0846713	−	0.0417956i
$153$		0			0
$154$	151.616	−	66.7359i	0.984522	−	0.433350i
$155$	−31.5977	+	13.0882i	−0.203856	+	0.0844401i
$156$		0			0
$157$	−56.0501	−	23.2167i	−0.357007	−	0.147877i	0.196969	−	0.980410i	$-0.436890\pi$
$157$	−56.0501	−	23.2167i	−0.357007	−	0.147877i	−0.553976	+	0.832533i	$0.686890\pi$
$158$	3.99598	+	3.82434i	0.0252910	+	0.0242047i
$159$		0			0
$160$	74.2983	−	255.514i	0.464365	−	1.59696i
$161$	61.0957			0.379476
$162$		0			0
$163$	85.7621	−	207.048i	0.526148	−	1.27023i	−0.407881	−	0.913035i	$-0.633732\pi$
$163$	85.7621	−	207.048i	0.526148	−	1.27023i	0.934029	−	0.357198i	$-0.116268\pi$
$164$	80.6872	−	88.0998i	0.491995	−	0.537194i
$165$		0			0
$166$	69.0689	+	156.917i	0.416077	+	0.945280i
$167$	−72.6395	−	72.6395i	−0.434967	−	0.434967i	0.455347	−	0.890314i	$-0.349515\pi$
$167$	−72.6395	−	72.6395i	−0.434967	−	0.434967i	−0.890314	+	0.455347i	$0.849515\pi$
$168$		0			0
$169$	81.0829	+	81.0829i	0.479781	+	0.479781i
$170$	−56.9123	−	22.1236i	−0.334778	−	0.130139i
$171$		0			0
$172$	0.970835	−	0.453010i	0.00564439	−	0.00263378i
$173$	4.05480	−	9.78916i	0.0234382	−	0.0565847i	−0.911727	−	0.410796i	$-0.865251\pi$
$173$	4.05480	−	9.78916i	0.0234382	−	0.0565847i	0.935165	+	0.354212i	$0.115251\pi$
$174$		0			0
$175$	−229.365			−1.31066
$176$	117.898	+	226.197i	0.669873	+	1.28521i
$177$		0			0
$178$	−204.785	+	4.49461i	−1.15048	+	0.0252506i
$179$	−214.146	−	88.7024i	−1.19635	−	0.495544i	−0.306531	−	0.951861i	$-0.599168\pi$
$179$	−214.146	−	88.7024i	−1.19635	−	0.495544i	−0.889817	+	0.456317i	$0.849168\pi$
$180$		0			0
$181$	−98.2125	+	40.6810i	−0.542611	+	0.224757i	−0.637116	−	0.770768i	$-0.719873\pi$
$181$	−98.2125	+	40.6810i	−0.542611	+	0.224757i	0.0945057	+	0.995524i	$0.469873\pi$
$182$	71.3863	+	27.7501i	0.392233	+	0.152473i
$183$		0			0
$184$	6.18890	+	93.8730i	0.0336353	+	0.510179i
$185$	−305.395	+	305.395i	−1.65078	+	1.65078i
$186$		0			0
$187$	54.0772	−	22.3995i	0.289183	−	0.119783i
$188$	6.91180	+	157.383i	0.0367649	+	0.837145i
$189$		0			0
$190$	20.6302	−	21.5561i	0.108580	−	0.113453i
$191$		−	181.842i		−	0.952052i	−0.879431	−	0.476026i	$-0.842077\pi$
$191$		−	181.842i		−	0.952052i	0.879431	−	0.476026i	$-0.157923\pi$
$192$		0			0
$193$	−221.267			−1.14646			−0.573230	−	0.819394i	$-0.694310\pi$
$193$	−221.267			−1.14646			−0.573230	+	0.819394i	$0.694310\pi$
$194$	95.4376	+	91.3383i	0.491946	+	0.470816i
$195$		0			0
$196$	87.9469	−	3.86236i	0.448709	−	0.0197059i
$197$	15.4361	+	37.2660i	0.0783556	+	0.189167i	0.958203	−	0.286089i	$-0.0923553\pi$
$197$	15.4361	+	37.2660i	0.0783556	+	0.189167i	−0.879847	+	0.475256i	$0.842355\pi$
$198$		0			0
$199$	−135.618	−	135.618i	−0.681498	−	0.681498i	0.278840	−	0.960338i	$-0.410050\pi$
$199$	−135.618	−	135.618i	−0.681498	−	0.681498i	−0.960338	+	0.278840i	$0.910050\pi$
$200$	−23.2343	−	352.418i	−0.116172	−	1.76209i
$201$		0			0
$202$	−14.2241	+	36.5911i	−0.0704164	+	0.181144i
$203$	83.6250	+	201.889i	0.411946	+	0.994526i
$204$		0			0
$205$	95.0411	−	229.450i	0.463615	−	1.11927i
$206$	0.0365664	+	1.66605i	0.000177507	+	0.00808763i
$207$		0			0
$208$	−35.4065	+	112.495i	−0.170223	+	0.540844i
$209$			28.6019i			0.136851i
$210$		0			0
$211$	138.015	+	57.1678i	0.654100	+	0.270937i	0.684954	−	0.728587i	$-0.259822\pi$
$211$	138.015	+	57.1678i	0.654100	+	0.270937i	−0.0308532	+	0.999524i	$0.509822\pi$
$212$	−41.4032	−	88.7303i	−0.195298	−	0.418539i
$213$		0			0
$214$	−105.011	+	270.138i	−0.490706	+	1.26233i
$215$	1.57484	−	1.57484i	0.00732483	−	0.00732483i
$216$		0			0
$217$	−15.1097	+	15.1097i	−0.0696298	+	0.0696298i
$218$	140.639	−	61.9039i	0.645131	−	0.283963i
$219$		0			0
$220$	391.053	+	358.150i	1.77751	+	1.62795i
$221$	25.0027	+	10.3564i	0.113134	+	0.0468618i
$222$		0			0
$223$		−	30.6228i		−	0.137322i	−0.997640	−	0.0686609i	$-0.978127\pi$
$223$		−	30.6228i		−	0.137322i	0.997640	−	0.0686609i	$-0.0218727\pi$
$224$	−18.2050	−	165.253i	−0.0812721	−	0.737736i
$225$		0			0
$226$	−185.679	+	194.013i	−0.821589	+	0.858463i
$227$	−8.41171	+	20.3077i	−0.0370560	+	0.0894611i	−0.941324	−	0.337504i	$-0.890417\pi$
$227$	−8.41171	+	20.3077i	−0.0370560	+	0.0894611i	0.904268	+	0.426965i	$0.140417\pi$
$228$		0			0
$229$	76.6532	+	185.057i	0.334730	+	0.808110i	0.998204	+	0.0599101i	$0.0190814\pi$
$229$	76.6532	+	185.057i	0.334730	+	0.808110i	−0.663474	+	0.748199i	$0.730919\pi$
$230$	78.7898	+	179.001i	0.342564	+	0.778267i
$231$		0			0
$232$	−301.729	+	148.940i	−1.30056	+	0.641983i
$233$	127.558	+	127.558i	0.547461	+	0.547461i	0.925706	−	0.378245i	$-0.123472\pi$
$233$	127.558	+	127.558i	0.547461	+	0.547461i	−0.378245	+	0.925706i	$0.623472\pi$
$234$		0			0
$235$	125.327	+	302.567i	0.533308	+	1.28752i
$236$	185.603	+	397.761i	0.786452	+	1.68543i
$237$		0			0
$238$	−38.1408	+	0.837110i	−0.160255	+	0.00351727i
$239$	−397.241			−1.66210			−0.831048	−	0.556200i	$-0.812259\pi$
$239$	−397.241			−1.66210			−0.831048	+	0.556200i	$0.812259\pi$
$240$		0			0
$241$		−	401.128i		−	1.66443i	−0.554451	−	0.832216i	$-0.687072\pi$
$241$		−	401.128i		−	1.66443i	0.554451	−	0.832216i	$-0.312928\pi$
$242$	−266.255	+	5.84374i	−1.10023	+	0.0241477i
$243$		0			0
$244$	20.7869	−	57.1571i	0.0851924	−	0.234250i
$245$	169.077	−	70.0338i	0.690109	−	0.285852i
$246$		0			0
$247$	−9.35087	+	9.35087i	−0.0378578	+	0.0378578i
$248$	−24.7464	−	21.6853i	−0.0997840	−	0.0874406i
$249$		0			0
$250$	−128.291	−	291.463i	−0.513166	−	1.16585i
$251$	−220.193	+	91.2070i	−0.877264	+	0.363375i	−0.775435	−	0.631427i	$-0.782469\pi$
$251$	−220.193	+	91.2070i	−0.877264	+	0.363375i	−0.101829	+	0.994802i	$0.532469\pi$
$252$		0			0
$253$	−173.205	−	71.7440i	−0.684606	−	0.283573i
$254$	132.066	−	137.993i	0.519943	−	0.543279i
$255$		0			0
$256$	252.065	−	44.7116i	0.984630	−	0.174655i
$257$	−436.624			−1.69893			−0.849463	−	0.527648i	$-0.823074\pi$
$257$	−436.624			−1.69893			−0.849463	+	0.527648i	$0.823074\pi$
$258$		0			0
$259$	−103.263	+	249.299i	−0.398699	+	0.962545i
$260$	10.7569	+	244.938i	0.0413729	+	0.942070i
$261$		0			0
$262$	321.055	−	141.316i	1.22540	−	0.539376i
$263$	324.662	+	324.662i	1.23445	+	1.23445i	0.962235	+	0.272219i	$0.0877576\pi$
$263$	324.662	+	324.662i	1.23445	+	1.23445i	0.272219	+	0.962235i	$0.412242\pi$
$264$		0			0
$265$	−143.934	−	143.934i	−0.543146	−	0.543146i
$266$	6.75430	−	17.3752i	0.0253921	−	0.0653204i
$267$		0			0
$268$	36.0946	+	13.1269i	0.134681	+	0.0489810i
$269$	98.7998	−	238.524i	0.367286	−	0.886706i	−0.626907	−	0.779094i	$-0.715680\pi$
$269$	98.7998	−	238.524i	0.367286	−	0.886706i	0.994193	−	0.107612i	$-0.0343205\pi$
$270$		0			0
$271$	−91.7678			−0.338627			−0.169313	−	0.985562i	$-0.554155\pi$
$271$	−91.7678			−0.338627			−0.169313	+	0.985562i	$0.554155\pi$
$272$	−5.14981	−	58.5181i	−0.0189331	−	0.215140i
$273$		0			0
$274$	−5.50651	−	250.890i	−0.0200968	−	0.915658i
$275$	650.247	+	269.341i	2.36453	+	0.979422i
$276$		0			0
$277$	42.7749	−	17.7179i	0.154422	−	0.0639636i	−0.304134	−	0.952629i	$-0.598367\pi$
$277$	42.7749	−	17.7179i	0.154422	−	0.0639636i	0.458556	+	0.888666i	$0.348367\pi$
$278$	52.4212	−	134.852i	0.188566	−	0.485079i
$279$		0			0
$280$	−152.982	−	309.918i	−0.546365	−	1.10685i
$281$	167.424	−	167.424i	0.595813	−	0.595813i	−0.343382	−	0.939196i	$-0.611573\pi$
$281$	167.424	−	167.424i	0.595813	−	0.595813i	0.939196	+	0.343382i	$0.111573\pi$
$282$		0			0
$283$	−494.380	+	204.779i	−1.74693	+	0.723601i	−0.748775	+	0.662824i	$0.769358\pi$
$283$	−494.380	+	204.779i	−1.74693	+	0.723601i	−0.998151	+	0.0607762i	$0.980642\pi$
$284$	289.495	−	316.091i	1.01935	−	1.11300i
$285$		0			0
$286$	−169.792	−	162.499i	−0.593679	−	0.568179i
$287$		−	155.168i		−	0.540653i
$288$		0			0
$289$	275.520			0.953356
$290$	−483.660	+	505.367i	−1.66779	+	1.74265i
$291$		0			0
$292$	110.943	−	121.136i	0.379943	−	0.414848i
$293$	−146.767	−	354.328i	−0.500913	−	1.20931i	−0.948987	−	0.315314i	$-0.897890\pi$
$293$	−146.767	−	354.328i	−0.500913	−	1.20931i	0.448075	−	0.893996i	$-0.352110\pi$
$294$		0			0
$295$	645.227	+	645.227i	2.18721	+	2.18721i
$296$	−393.506	−	133.409i	−1.32941	−	0.450707i
$297$		0			0
$298$	202.851	+	78.8545i	0.680707	+	0.264613i
$299$	−33.1709	−	80.0817i	−0.110940	−	0.267832i
$300$		0			0
$301$	0.532500	−	1.28557i	0.00176910	−	0.00427099i
$302$	−380.916	+	8.36030i	−1.26131	+	0.0276831i
$303$		0			0
$304$	27.3811	+	8.61784i	0.0900694	+	0.0283482i
$305$		−	126.437i		−	0.414547i
$306$		0			0
$307$	−53.4306	−	22.1317i	−0.174041	−	0.0720902i	0.293962	−	0.955817i	$-0.405026\pi$
$307$	−53.4306	−	22.1317i	−0.174041	−	0.0720902i	−0.468003	+	0.883727i	$0.655026\pi$
$308$	311.356	+	113.234i	1.01090	+	0.367644i
$309$		0			0
$310$	−63.7547	−	24.7835i	−0.205660	−	0.0799466i
$311$	−274.515	+	274.515i	−0.882685	+	0.882685i	−0.993807	−	0.111122i	$-0.964556\pi$
$311$	−274.515	+	274.515i	−0.882685	+	0.882685i	0.111122	+	0.993807i	$0.464556\pi$
$312$		0			0
$313$	−78.4013	+	78.4013i	−0.250483	+	0.250483i	−0.821169	−	0.570685i	$-0.806678\pi$
$313$	−78.4013	+	78.4013i	−0.250483	+	0.250483i	0.570685	+	0.821169i	$0.306678\pi$
$314$	−48.8820	−	111.054i	−0.155675	−	0.353676i
$315$		0			0
$316$	0.485353	+	11.0516i	0.00153593	+	0.0349734i
$317$	136.520	+	56.5483i	0.430661	+	0.178386i	0.587475	−	0.809243i	$-0.300122\pi$
$317$	136.520	+	56.5483i	0.430661	+	0.178386i	−0.156814	+	0.987628i	$0.550122\pi$
$318$		0			0
$319$		−	670.551i		−	2.10204i
$320$	460.689	−	266.450i	1.43965	−	0.832656i
$321$		0			0
$322$	88.2775	+	84.4857i	0.274154	+	0.262378i
$323$	2.52073	−	6.08558i	0.00780412	−	0.0188408i
$324$		0			0
$325$	124.530	+	300.643i	0.383170	+	0.925054i
$326$	410.232	−	180.569i	1.25838	−	0.553893i
$327$		0			0
$328$	238.413	−	15.7182i	0.726870	−	0.0479214i
$329$	144.684	+	144.684i	0.439769	+	0.439769i
$330$		0			0
$331$	143.690	+	346.898i	0.434109	+	1.04803i	0.977949	+	0.208843i	$0.0669696\pi$
$331$	143.690	+	346.898i	0.434109	+	1.04803i	−0.543841	+	0.839189i	$0.683030\pi$
$332$	−117.193	+	322.241i	−0.352990	+	0.970605i
$333$		0			0
$334$	−4.50823	−	205.406i	−0.0134977	−	0.614988i
$335$	79.8446			0.238342
$336$		0			0
$337$		−	479.136i		−	1.42177i	−0.703310	−	0.710884i	$-0.748295\pi$
$337$		−	479.136i		−	1.42177i	0.703310	−	0.710884i	$-0.251705\pi$
$338$	5.03226	+	229.282i	0.0148883	+	0.678349i
$339$		0			0
$340$	−51.6394	−	110.667i	−0.151881	−	0.325492i
$341$	60.5787	−	25.0925i	0.177650	−	0.0735851i
$342$		0			0
$343$	260.861	−	260.861i	0.760529	−	0.760529i
$344$	2.02920	+	0.687955i	0.00589885	+	0.00199987i
$345$		0			0
$346$	19.3957	−	8.53725i	0.0560568	−	0.0246741i
$347$	−172.145	+	71.3048i	−0.496095	+	0.205489i	−0.616680	−	0.787214i	$-0.711523\pi$
$347$	−172.145	+	71.3048i	−0.496095	+	0.205489i	0.120585	+	0.992703i	$0.461523\pi$
$348$		0			0
$349$	388.120	+	160.765i	1.11209	+	0.460644i	0.861658	−	0.507490i	$-0.169427\pi$
$349$	388.120	+	160.765i	1.11209	+	0.460644i	0.250434	+	0.968134i	$0.419427\pi$
$350$	−331.411	−	317.176i	−0.946889	−	0.906217i
$351$		0			0
$352$	−142.444	+	489.867i	−0.404669	+	1.39167i
$353$	165.952			0.470120			0.235060	−	0.971981i	$-0.424471\pi$
$353$	165.952			0.470120			0.235060	+	0.971981i	$0.424471\pi$
$354$		0			0
$355$	340.995	−	823.235i	0.960550	−	2.31897i
$356$	−302.111	−	276.691i	−0.848626	−	0.777223i
$357$		0			0
$358$	−186.760	−	424.297i	−0.521676	−	1.18519i
$359$	−100.971	−	100.971i	−0.281257	−	0.281257i	0.552353	−	0.833610i	$-0.313730\pi$
$359$	−100.971	−	100.971i	−0.281257	−	0.281257i	−0.833610	+	0.552353i	$0.813730\pi$
$360$		0			0
$361$	−252.990	−	252.990i	−0.700802	−	0.700802i
$362$	−198.163	−	77.0322i	−0.547412	−	0.212796i
$363$		0			0
$364$	64.7724	+	138.812i	0.177946	+	0.381352i
$365$	130.680	−	315.489i	0.358027	−	0.864353i
$366$		0			0
$367$	−651.959			−1.77645			−0.888227	−	0.459405i	$-0.848063\pi$
$367$	−651.959			−1.77645			−0.888227	+	0.459405i	$0.848063\pi$
$368$	−120.869	+	144.196i	−0.328449	+	0.391836i
$369$		0			0
$370$	−863.579	+	18.9537i	−2.33400	+	0.0512263i
$371$	−117.496	−	48.6683i	−0.316700	−	0.131181i
$372$		0			0
$373$	605.919	−	250.980i	1.62445	−	0.672868i	0.629854	−	0.776713i	$-0.283115\pi$
$373$	605.919	−	250.980i	1.62445	−	0.672868i	0.994593	+	0.103845i	$0.0331146\pi$
$374$	109.111	+	42.4150i	0.291742	+	0.113409i
$375$		0			0
$376$	−207.649	+	236.962i	−0.552259	+	0.630218i
$377$	219.224	−	219.224i	0.581497	−	0.581497i
$378$		0			0
$379$	−431.591	+	178.771i	−1.13876	+	0.471691i	−0.870750	−	0.491725i	$-0.836366\pi$
$379$	−431.591	+	178.771i	−1.13876	+	0.471691i	−0.268011	+	0.963416i	$0.586366\pi$
$380$	59.6173	−	2.61821i	0.156888	−	0.00689003i
$381$		0			0
$382$	251.459	−	262.744i	0.658269	−	0.687812i
$383$		−	583.987i		−	1.52477i	−0.647124	−	0.762385i	$-0.724028\pi$
$383$		−	583.987i		−	1.52477i	0.647124	−	0.762385i	$-0.275972\pi$
$384$		0			0
$385$	688.749			1.78896
$386$	−319.710	−	305.977i	−0.828263	−	0.792687i
$387$		0			0
$388$	11.5919	+	263.950i	0.0298760	+	0.680284i
$389$	57.9070	+	139.800i	0.148861	+	0.359383i	0.980667	−	0.195684i	$-0.0626927\pi$
$389$	57.9070	+	139.800i	0.148861	+	0.359383i	−0.831806	+	0.555067i	$0.812693\pi$
$390$		0			0
$391$	30.5297	+	30.5297i	0.0780812	+	0.0780812i
$392$	132.416	+	116.036i	0.337796	+	0.296010i
$393$		0			0
$394$	−29.2293	+	75.1914i	−0.0741860	+	0.190841i
$395$	8.80061	+	21.2466i	0.0222800	+	0.0537888i
$396$		0			0
$397$	216.482	−	522.634i	0.545295	−	1.31646i	−0.375649	−	0.926762i	$-0.622580\pi$
$397$	216.482	−	522.634i	0.545295	−	1.31646i	0.920944	−	0.389696i	$-0.127420\pi$
$398$	−8.41688	−	383.493i	−0.0211479	−	0.963551i
$399$		0			0
$400$	453.767	−	541.340i	1.13442	−	1.35335i
$401$			271.900i			0.678055i	0.940776	+	0.339028i	$0.110098\pi$
$401$			271.900i			0.678055i	−0.940776	+	0.339028i	$0.889902\pi$
$402$		0			0
$403$	28.0087	+	11.6016i	0.0695004	+	0.0287880i
$404$	−71.1521	+	33.2009i	−0.176119	+	0.0821805i
$405$		0			0
$406$	−158.350	+	407.350i	−0.390024	+	1.00333i
$407$	585.498	−	585.498i	1.43857	−	1.43857i
$408$		0			0
$409$	−181.723	+	181.723i	−0.444310	+	0.444310i	−0.893458	−	0.449147i	$-0.851728\pi$
$409$	−181.723	+	181.723i	−0.444310	+	0.444310i	0.449147	+	0.893458i	$0.351728\pi$
$410$	454.618	−	200.106i	1.10882	−	0.488063i
$411$		0			0
$412$	−2.25105	+	2.45785i	−0.00546372	+	0.00596566i
$413$	526.710	+	218.171i	1.27533	+	0.528258i
$414$		0			0
$415$			712.826i			1.71765i
$416$	−206.722	+	113.584i	−0.496929	+	0.273038i
$417$		0			0
$418$	−39.5519	+	41.3270i	−0.0946217	+	0.0988684i
$419$	84.5458	−	204.112i	0.201780	−	0.487140i	−0.790304	−	0.612715i	$-0.790077\pi$
$419$	84.5458	−	204.112i	0.201780	−	0.487140i	0.992084	+	0.125575i	$0.0400775\pi$
$420$		0			0
$421$	13.1417	+	31.7269i	0.0312155	+	0.0753608i	0.938719	−	0.344685i	$-0.112014\pi$
$421$	13.1417	+	31.7269i	0.0312155	+	0.0753608i	−0.907503	+	0.420045i	$0.862014\pi$
$422$	120.365	+	273.455i	0.285225	+	0.647998i
$423$		0			0
$424$	62.8762	−	185.461i	0.148293	−	0.437408i
$425$	−114.615	−	114.615i	−0.269682	−	0.269682i
$426$		0			0
$427$	−30.2302	−	72.9823i	−0.0707968	−	0.170919i
$428$	−525.289	+	245.110i	−1.22731	+	0.572686i
$429$		0			0
$430$	4.45324	−	0.0977393i	0.0103564	−	0.000227301i
$431$	−18.4839			−0.0428861			−0.0214431	−	0.999770i	$-0.506826\pi$
$431$	−18.4839			−0.0428861			−0.0214431	+	0.999770i	$0.506826\pi$
$432$		0			0
$433$			370.297i			0.855190i	0.903970	+	0.427595i	$0.140639\pi$
$433$			370.297i			0.855190i	−0.903970	+	0.427595i	$0.859361\pi$
$434$	−42.7263	+	0.937752i	−0.0984476	+	0.00216072i
$435$		0			0
$436$	288.813	+	105.036i	0.662414	+	0.240907i
$437$	−19.4917	+	8.07372i	−0.0446034	+	0.0184753i
$438$		0			0
$439$	−1.47108	+	1.47108i	−0.00335099	+	0.00335099i	−0.708780	−	0.705429i	$-0.750754\pi$
$439$	−1.47108	+	1.47108i	−0.00335099	+	0.00335099i	0.705429	+	0.708780i	$0.250754\pi$
$440$	69.7691	+	1058.26i	0.158566	+	2.40513i
$441$		0			0
$442$	21.8052	+	49.5388i	0.0493329	+	0.112079i
$443$	−15.4970	+	6.41908i	−0.0349820	+	0.0144900i	−0.400106	−	0.916469i	$-0.631027\pi$
$443$	−15.4970	+	6.41908i	−0.0349820	+	0.0144900i	0.365124	+	0.930959i	$0.381027\pi$
$444$		0			0
$445$	−786.825	−	325.914i	−1.76815	−	0.732390i
$446$	42.3464	−	44.2470i	0.0949472	−	0.0992085i
$447$		0			0
$448$	202.214	−	263.949i	0.451370	−	0.589172i
$449$	349.645			0.778719			0.389359	−	0.921086i	$-0.372696\pi$
$449$	349.645			0.778719			0.389359	+	0.921086i	$0.372696\pi$
$450$		0			0
$451$	−182.211	+	439.897i	−0.404016	+	0.975382i
$452$	−536.577	+	23.5648i	−1.18712	+	0.0521346i
$453$		0			0
$454$	−40.2364	+	17.7106i	−0.0886264	+	0.0390101i
$455$	225.174	+	225.174i	0.494888	+	0.494888i
$456$		0			0
$457$	167.442	+	167.442i	0.366393	+	0.366393i	0.866160	−	0.499767i	$-0.166581\pi$
$457$	167.442	+	167.442i	0.366393	+	0.366393i	−0.499767	+	0.866160i	$0.666581\pi$
$458$	−145.148	+	373.389i	−0.316917	+	0.815260i
$459$		0			0
$460$	−133.687	+	367.594i	−0.290623	+	0.799117i
$461$	−299.864	+	723.935i	−0.650463	+	1.57036i	0.161644	+	0.986849i	$0.448320\pi$
$461$	−299.864	+	723.935i	−0.650463	+	1.57036i	−0.812107	+	0.583508i	$0.801680\pi$
$462$		0			0
$463$	−70.4485			−0.152157			−0.0760783	−	0.997102i	$-0.524240\pi$
$463$	−70.4485			−0.152157			−0.0760783	+	0.997102i	$0.524240\pi$
$464$	−641.930	−	202.039i	−1.38347	−	0.435429i
$465$		0			0
$466$	7.91667	+	360.703i	0.0169886	+	0.774040i
$467$	89.8391	+	37.2126i	0.192375	+	0.0796843i	0.476791	−	0.879017i	$-0.341800\pi$
$467$	89.8391	+	37.2126i	0.192375	+	0.0796843i	−0.284416	+	0.958701i	$0.591800\pi$
$468$		0			0
$469$	46.0882	−	19.0904i	0.0982691	−	0.0407044i
$470$	−237.316	+	610.489i	−0.504928	+	1.29891i
$471$		0			0
$472$	−281.862	+	831.386i	−0.597166	+	1.76141i
$473$	−3.01925	+	3.01925i	−0.00638320	+	0.00638320i
$474$		0			0
$475$	73.1756	−	30.3103i	0.154054	−	0.0638112i
$476$	−56.2673	−	51.5331i	−0.118209	−	0.108263i
$477$		0			0
$478$	−573.975	−	549.321i	−1.20079	−	1.14921i
$479$			900.546i			1.88005i	0.341101	+	0.940027i	$0.389200\pi$
$479$			900.546i			1.88005i	−0.341101	+	0.940027i	$0.610800\pi$
$480$		0			0
$481$	382.836			0.795917
$482$	554.697	−	579.592i	1.15082	−	1.20247i
$483$		0			0
$484$	−392.794	−	359.745i	−0.811558	−	0.743274i
$485$	210.189	+	507.440i	0.433379	+	1.04627i
$486$		0			0
$487$	−175.466	−	175.466i	−0.360301	−	0.360301i	0.503623	−	0.863924i	$-0.332000\pi$
$487$	−175.466	−	175.466i	−0.360301	−	0.360301i	−0.863924	+	0.503623i	$0.832000\pi$
$488$	109.074	−	53.8415i	0.223513	−	0.110331i
$489$		0			0
$490$	341.145	+	132.614i	0.696215	+	0.270641i
$491$	111.990	+	270.368i	0.228086	+	0.550648i	0.995944	−	0.0899713i	$-0.0286775\pi$
$491$	111.990	+	270.368i	0.228086	+	0.550648i	−0.767858	+	0.640620i	$0.778678\pi$
$492$		0			0
$493$	−59.0968	+	142.672i	−0.119872	+	0.289396i
$494$	−26.4419	+	0.580344i	−0.0535261	+	0.00117478i
$495$		0			0
$496$	−5.76895	−	65.5535i	−0.0116309	−	0.132164i
$497$		−	556.721i		−	1.12016i
$498$		0			0
$499$	96.4128	+	39.9355i	0.193212	+	0.0800310i	0.477192	−	0.878799i	$-0.341655\pi$
$499$	96.4128	+	39.9355i	0.193212	+	0.0800310i	−0.283980	+	0.958830i	$0.591655\pi$
$500$	217.679	−	598.544i	0.435358	−	1.19709i
$501$		0			0
$502$	−444.283	−	172.707i	−0.885026	−	0.344038i
$503$	−491.151	+	491.151i	−0.976442	+	0.976442i	−0.999729	−	0.0232864i	$-0.992587\pi$
$503$	−491.151	+	491.151i	−0.976442	+	0.976442i	0.0232864	+	0.999729i	$0.492587\pi$
$504$		0			0
$505$	−115.419	+	115.419i	−0.228553	+	0.228553i
$506$	−151.055	−	343.179i	−0.298527	−	0.678219i
$507$		0			0
$508$	381.644	−	16.7607i	0.751268	−	0.0329934i
$509$	−891.336	−	369.204i	−1.75115	−	0.725351i	−0.997695	−	0.0678534i	$-0.978385\pi$
$509$	−891.336	−	369.204i	−1.75115	−	0.725351i	−0.753457	−	0.657498i	$-0.771615\pi$
$510$		0			0
$511$		−	213.352i		−	0.417519i
$512$	426.039	+	283.962i	0.832108	+	0.554614i
$513$		0			0
$514$	−630.880	−	603.782i	−1.22739	−	1.17467i
$515$	−2.65150	+	6.40130i	−0.00514855	+	0.0124297i
$516$		0			0
$517$	−240.276	−	580.077i	−0.464750	−	1.12201i
$518$	−493.946	+	217.417i	−0.953564	+	0.419724i
$519$		0			0
$520$	−323.168	+	368.787i	−0.621477	+	0.709207i
$521$	−285.723	−	285.723i	−0.548413	−	0.548413i	0.377569	−	0.925982i	$-0.376760\pi$
$521$	−285.723	−	285.723i	−0.548413	−	0.548413i	−0.925982	+	0.377569i	$0.876760\pi$
$522$		0			0
$523$	260.696	+	629.375i	0.498462	+	1.20339i	0.950312	+	0.311300i	$0.100764\pi$
$523$	260.696	+	629.375i	0.498462	+	1.20339i	−0.451849	+	0.892094i	$0.649236\pi$
$524$	659.312	+	239.779i	1.25823	+	0.457594i
$525$		0			0
$526$	20.1495	+	918.060i	0.0383070	+	1.74536i
$527$	−15.1007			−0.0286541
$528$		0			0
$529$			390.712i			0.738586i
$530$	−8.93297	−	407.008i	−0.0168547	−	0.767939i
$531$		0			0
$532$	33.7865	−	15.7654i	0.0635085	−	0.0296343i
$533$	−203.387	+	84.2457i	−0.381589	+	0.158059i
$534$		0			0
$535$	−852.096	+	852.096i	−1.59270	+	1.59270i
$536$	34.0008	+	68.8802i	0.0634343	+	0.128508i
$537$		0			0
$538$	472.597	−	208.020i	0.878433	−	0.386654i
$539$	−324.151	+	134.268i	−0.601393	+	0.249105i
$540$		0			0
$541$	355.077	+	147.078i	0.656335	+	0.271863i	0.685895	−	0.727700i	$-0.259411\pi$
$541$	355.077	+	147.078i	0.656335	+	0.271863i	−0.0295603	+	0.999563i	$0.509411\pi$
$542$	−132.596	−	126.900i	−0.244642	−	0.234134i
$543$		0			0
$544$	73.4803	−	91.6745i	0.135074	−	0.168519i
$545$	638.880			1.17226
$546$		0			0
$547$	404.897	−	977.508i	0.740214	−	1.78704i	0.135204	−	0.990818i	$-0.456831\pi$
$547$	404.897	−	977.508i	0.740214	−	1.78704i	0.605010	−	0.796218i	$-0.293169\pi$
$548$	338.985	−	370.127i	0.618586	−	0.675414i
$549$		0			0
$550$	567.089	+	1288.36i	1.03107	+	2.34247i
$551$	−53.3586	−	53.3586i	−0.0968396	−	0.0968396i
$552$		0			0
$553$	10.1598	+	10.1598i	0.0183722	+	0.0183722i
$554$	86.3067	+	33.5501i	0.155788	+	0.0605598i
$555$		0			0
$556$	262.222	−	122.358i	0.471623	−	0.220068i
$557$	296.952	−	716.907i	0.533128	−	1.28709i	−0.396313	−	0.918115i	$-0.629711\pi$
$557$	296.952	−	716.907i	0.533128	−	1.28709i	0.929441	−	0.368970i	$-0.120289\pi$
$558$		0			0
$559$	−1.97418			−0.00353163
$560$	207.522	−	659.352i	0.370576	−	1.17741i
$561$		0			0
$562$	473.431	−	10.3908i	0.842405	−	0.0184890i
$563$	44.6869	+	18.5099i	0.0793728	+	0.0328773i	0.422017	−	0.906588i	$-0.361322\pi$
$563$	44.6869	+	18.5099i	0.0793728	+	0.0328773i	−0.342644	+	0.939465i	$0.611322\pi$
$564$		0			0
$565$	−1031.56	+	427.287i	−1.82577	+	0.756260i
$566$	−997.509	−	387.763i	−1.76238	−	0.685094i
$567$		0			0
$568$	855.396	−	56.3949i	1.50598	−	0.0992868i
$569$	−487.094	+	487.094i	−0.856053	+	0.856053i	−0.990870	−	0.134818i	$-0.956955\pi$
$569$	−487.094	+	487.094i	−0.856053	+	0.856053i	0.134818	+	0.990870i	$0.456955\pi$
$570$		0			0
$571$	−252.561	+	104.614i	−0.442313	+	0.183212i	−0.592714	−	0.805413i	$-0.701944\pi$
$571$	−252.561	+	104.614i	−0.442313	+	0.183212i	0.150401	+	0.988625i	$0.451944\pi$
$572$	−20.6230	−	469.592i	−0.0360543	−	0.820964i
$573$		0			0
$574$	214.572	−	224.202i	0.373819	−	0.390596i
$575$			519.161i			0.902889i
$576$		0			0
$577$	460.004			0.797234			0.398617	−	0.917118i	$-0.369490\pi$
$577$	460.004			0.797234			0.398617	+	0.917118i	$0.369490\pi$
$578$	398.100	+	381.000i	0.688754	+	0.659170i
$579$		0			0
$580$	−1397.69	+	61.3821i	−2.40980	+	0.105831i
$581$	170.432	+	411.460i	0.293343	+	0.708193i
$582$		0			0
$583$	275.947	+	275.947i	0.473323	+	0.473323i
$584$	327.814	−	21.6123i	0.561325	−	0.0370073i
$585$		0			0
$586$	277.914	−	714.926i	0.474257	−	1.22001i
$587$	−68.3015	−	164.895i	−0.116357	−	0.280911i	0.854962	−	0.518690i	$-0.173580\pi$
$587$	−68.3015	−	164.895i	−0.116357	−	0.280911i	−0.971319	+	0.237780i	$0.923580\pi$
$588$		0			0
$589$	2.82379	−	6.81723i	0.00479421	−	0.0115742i
$590$	40.0448	+	1824.54i	0.0678725	+	3.09244i
$591$		0			0
$592$	−384.095	−	736.920i	−0.648809	−	1.24480i
$593$		−	167.545i		−	0.282538i	−0.989971	−	0.141269i	$-0.954882\pi$
$593$		−	167.545i		−	0.282538i	0.989971	−	0.141269i	$-0.0451182\pi$
$594$		0			0
$595$	−146.544	−	60.7006i	−0.246293	−	0.102018i
$596$	184.057	+	394.448i	0.308820	+	0.661825i
$597$		0			0
$598$	62.8115	−	161.581i	0.105036	−	0.270202i
$599$	316.998	−	316.998i	0.529213	−	0.529213i	−0.391125	−	0.920338i	$-0.627914\pi$
$599$	316.998	−	316.998i	0.529213	−	0.529213i	0.920338	+	0.391125i	$0.127914\pi$
$600$		0			0
$601$	−224.198	+	224.198i	−0.373042	+	0.373042i	−0.868584	−	0.495542i	$-0.834970\pi$
$601$	−224.198	+	224.198i	−0.373042	+	0.373042i	0.495542	+	0.868584i	$0.334970\pi$
$602$	2.54715	−	1.12116i	0.00423114	−	0.00186239i
$603$		0			0
$604$	−561.948	−	514.666i	−0.930377	−	0.852096i
$605$	−1023.00	−	423.742i	−1.69091	−	0.700400i
$606$		0			0
$607$		−	89.2468i		−	0.147029i	−0.997294	−	0.0735146i	$-0.976578\pi$
$607$		−	89.2468i		−	0.147029i	0.997294	−	0.0735146i	$-0.0234216\pi$
$608$	27.6459	+	50.3157i	0.0454703	+	0.0827560i
$609$		0			0
$610$	174.842	−	182.689i	0.286626	−	0.299490i
$611$	111.092	−	268.200i	0.181820	−	0.438952i
$612$		0			0
$613$	202.134	+	487.995i	0.329746	+	0.796076i	0.998611	+	0.0526926i	$0.0167803\pi$
$613$	202.134	+	487.995i	0.329746	+	0.796076i	−0.668865	+	0.743384i	$0.733220\pi$
$614$	−46.5975	−	105.864i	−0.0758918	−	0.172417i
$615$		0			0
$616$	293.295	+	594.169i	0.476128	+	0.964560i
$617$	−380.984	−	380.984i	−0.617479	−	0.617479i	0.327405	−	0.944884i	$-0.393826\pi$
$617$	−380.984	−	380.984i	−0.617479	−	0.617479i	−0.944884	+	0.327405i	$0.893826\pi$
$618$		0			0
$619$	−371.320	−	896.447i	−0.599871	−	1.44822i	−0.873712	−	0.486443i	$-0.838294\pi$
$619$	−371.320	−	896.447i	−0.599871	−	1.44822i	0.273841	−	0.961775i	$-0.411706\pi$
$620$	−57.8478	−	123.972i	−0.0933029	−	0.199955i
$621$		0			0
$622$	−776.259	+	17.0373i	−1.24800	+	0.0273911i
$623$	−532.098			−0.854090
$624$		0			0
$625$		−	220.337i		−	0.352539i
$626$	−221.699	+	4.86583i	−0.354152	+	0.00777289i
$627$		0			0
$628$	82.9407	−	228.059i	0.132071	−	0.363151i
$629$	−176.177	+	72.9747i	−0.280090	+	0.116017i
$630$		0			0
$631$	384.726	−	384.726i	0.609708	−	0.609708i	−0.333162	−	0.942870i	$-0.608115\pi$
$631$	384.726	−	384.726i	0.609708	−	0.609708i	0.942870	+	0.333162i	$0.108115\pi$
$632$	−14.5813	+	16.6397i	−0.0230717	+	0.0263286i
$633$		0			0
$634$	119.061	+	270.492i	0.187793	+	0.426643i
$635$	733.706	−	303.911i	1.15544	−	0.478600i
$636$		0			0
$637$	−149.872	−	62.0789i	−0.235277	−	0.0974551i
$638$	927.266	−	968.882i	1.45339	−	1.51862i
$639$		0			0
$640$	1034.11	+	252.065i	1.61580	+	0.393851i
$641$	407.931			0.636398			0.318199	−	0.948024i	$-0.396922\pi$
$641$	407.931			0.636398			0.318199	+	0.948024i	$0.396922\pi$
$642$		0			0
$643$	−319.302	+	770.863i	−0.496582	+	1.19885i	0.454732	+	0.890629i	$0.349735\pi$
$643$	−319.302	+	770.863i	−0.496582	+	1.19885i	−0.951313	+	0.308226i	$0.900265\pi$
$644$	10.7222	+	244.148i	0.0166494	+	0.379111i
$645$		0			0
$646$	12.0576	−	5.30732i	0.0186650	−	0.00821566i
$647$	48.6565	+	48.6565i	0.0752033	+	0.0752033i	0.743708	−	0.668505i	$-0.233065\pi$
$647$	48.6565	+	48.6565i	0.0752033	+	0.0752033i	−0.668505	+	0.743708i	$0.733065\pi$
$648$		0			0
$649$	−1237.02	−	1237.02i	−1.90604	−	1.90604i
$650$	−235.807	+	606.606i	−0.362780	+	0.933239i
$651$		0			0
$652$	842.445	+	306.381i	1.29209	+	0.469910i
$653$	290.106	−	700.378i	0.444267	−	1.07255i	−0.530170	−	0.847892i	$-0.677872\pi$
$653$	290.106	−	700.378i	0.444267	−	1.07255i	0.974436	−	0.224663i	$-0.0721282\pi$
$654$		0			0
$655$	1458.46			2.22665
$656$	366.220	+	306.977i	0.558263	+	0.467952i
$657$		0			0
$658$	8.97953	+	409.129i	0.0136467	+	0.621777i
$659$	−818.045	−	338.845i	−1.24134	−	0.514181i	−0.337209	−	0.941430i	$-0.609483\pi$
$659$	−818.045	−	338.845i	−1.24134	−	0.514181i	−0.904134	+	0.427248i	$0.859483\pi$
$660$		0			0
$661$	−35.2123	+	14.5854i	−0.0532712	+	0.0220657i	−0.409160	−	0.912463i	$-0.634178\pi$
$661$	−35.2123	+	14.5854i	−0.0532712	+	0.0220657i	0.355889	+	0.934528i	$0.384178\pi$
$662$	−272.087	+	699.936i	−0.411008	+	1.05730i
$663$		0			0
$664$	−614.940	+	303.548i	−0.926115	+	0.457151i
$665$	54.8067	−	54.8067i	0.0824161	−	0.0824161i
$666$		0			0
$667$	456.969	−	189.283i	0.685110	−	0.283782i
$668$	277.530	−	303.026i	0.415464	−	0.453632i
$669$		0			0
$670$	115.368	+	110.412i	0.172191	+	0.164795i
$671$			242.402i			0.361256i
$672$		0			0
$673$	114.199			0.169687			0.0848434	−	0.996394i	$-0.472961\pi$
$673$	114.199			0.169687			0.0848434	+	0.996394i	$0.472961\pi$
$674$	662.569	−	692.305i	0.983039	−	1.02716i
$675$		0			0
$676$	−309.789	+	338.249i	−0.458268	+	0.500369i
$677$	212.733	+	513.583i	0.314229	+	0.758617i	0.999539	+	0.0303647i	$0.00966689\pi$
$677$	212.733	+	513.583i	0.314229	+	0.758617i	−0.685310	+	0.728252i	$0.740333\pi$
$678$		0			0
$679$	242.652	+	242.652i	0.357366	+	0.357366i
$680$	78.4212	−	231.313i	0.115325	−	0.340166i
$681$		0			0
$682$	122.229	+	47.5144i	0.179222	+	0.0696693i
$683$	−363.453	−	877.454i	−0.532142	−	1.28471i	−0.930102	−	0.367302i	$-0.880281\pi$
$683$	−363.453	−	877.454i	−0.532142	−	1.28471i	0.397959	−	0.917403i	$-0.369719\pi$
$684$		0			0
$685$	399.289	−	963.969i	0.582904	−	1.40725i
$686$	737.650	−	16.1899i	1.07529	−	0.0236004i
$687$		0			0
$688$	1.98067	+	3.80010i	0.00287889	+	0.00552340i
$689$			180.432i			0.261875i
$690$		0			0
$691$	−682.306	−	282.620i	−0.987418	−	0.409002i	−0.170249	−	0.985401i	$-0.554457\pi$
$691$	−682.306	−	282.620i	−0.987418	−	0.409002i	−0.817168	+	0.576399i	$0.804457\pi$
$692$	39.8306	+	14.4856i	0.0575586	+	0.0209330i
$693$		0			0
$694$	−347.336	−	135.021i	−0.500485	−	0.194554i
$695$	425.364	−	425.364i	0.612034	−	0.612034i
$696$		0			0
$697$	77.5377	−	77.5377i	0.111245	−	0.111245i
$698$	338.485	+	768.998i	0.484935	+	1.10172i
$699$		0			0
$700$	−40.2533	−	916.578i	−0.0575047	−	1.30940i
$701$	565.621	+	234.288i	0.806878	+	0.334220i	0.747708	−	0.664028i	$-0.231154\pi$
$701$	565.621	+	234.288i	0.806878	+	0.334220i	0.0591703	+	0.998248i	$0.481154\pi$
$702$		0			0
$703$		−	93.1812i		−	0.132548i
$704$	−883.225	+	510.833i	−1.25458	+	0.725616i
$705$		0			0
$706$	239.785	+	229.486i	0.339639	+	0.325051i
$707$	−39.0267	+	94.2188i	−0.0552004	+	0.133266i
$708$		0			0
$709$	447.695	+	1080.83i	0.631446	+	1.52444i	0.837806	+	0.545968i	$0.183838\pi$
$709$	447.695	+	1080.83i	0.631446	+	1.52444i	−0.206360	+	0.978476i	$0.566162\pi$
$710$	1631.11	−	717.954i	2.29734	−	1.01120i
$711$		0			0
$712$	−53.9007	−	817.564i	−0.0757032	−	1.14826i
$713$	34.2002	+	34.2002i	0.0479666	+	0.0479666i
$714$		0			0
$715$	−373.945	−	902.783i	−0.523000	−	1.26263i
$716$	316.885	−	871.328i	0.442577	−	1.21694i
$717$		0			0
$718$	−6.26658	−	285.521i	−0.00872783	−	0.397661i
$719$	−122.001			−0.169681			−0.0848406	−	0.996395i	$-0.527038\pi$
$719$	−122.001			−0.169681			−0.0848406	+	0.996395i	$0.527038\pi$
$720$		0			0
$721$			4.32894i			0.00600408i
$722$	−15.7013	−	715.390i	−0.0217470	−	0.990845i
$723$		0			0
$724$	−179.803	−	385.332i	−0.248347	−	0.532227i
$725$	−1715.55	+	710.604i	−2.36628	+	0.980144i
$726$		0			0
$727$	438.189	−	438.189i	0.602736	−	0.602736i	−0.338301	−	0.941038i	$-0.609852\pi$
$727$	438.189	−	438.189i	0.602736	−	0.602736i	0.941038	+	0.338301i	$0.109852\pi$
$728$	−98.3654	+	290.140i	−0.135117	+	0.398545i
$729$		0			0
$730$	625.091	−	275.142i	0.856289	−	0.376907i
$731$	0.908495	−	0.376311i	0.00124281	−	0.000514789i
$732$		0			0
$733$	−629.241	−	260.640i	−0.858446	−	0.355580i	−0.0903463	−	0.995910i	$-0.528797\pi$
$733$	−629.241	−	260.640i	−0.858446	−	0.355580i	−0.768099	+	0.640331i	$0.778797\pi$
$734$	−942.018	−	901.555i	−1.28340	−	1.22828i
$735$		0			0
$736$	−374.044	+	41.2063i	−0.508212	+	0.0559869i
$737$	−153.077			−0.207703
$738$		0			0
$739$	55.5902	−	134.207i	0.0752235	−	0.181606i	−0.881795	−	0.471633i	$-0.843665\pi$
$739$	55.5902	−	134.207i	0.0752235	−	0.181606i	0.957018	+	0.290028i	$0.0936646\pi$
$740$	−1274.00	−	1166.81i	−1.72162	−	1.57676i
$741$		0			0
$742$	−102.469	−	232.799i	−0.138099	−	0.313745i
$743$	180.295	+	180.295i	0.242658	+	0.242658i	0.817949	−	0.575291i	$-0.195111\pi$
$743$	180.295	+	180.295i	0.242658	+	0.242658i	−0.575291	+	0.817949i	$0.695111\pi$
$744$		0			0
$745$	639.853	+	639.853i	0.858863	+	0.858863i
$746$	1222.56	+	475.248i	1.63882	+	0.637062i
$747$		0			0
$748$	99.0022	+	212.169i	0.132356	+	0.283649i
$749$	−288.119	+	695.581i	−0.384672	+	0.928680i
$750$		0			0
$751$	−264.213			−0.351815			−0.175908	−	0.984407i	$-0.556286\pi$
$751$	−264.213			−0.351815			−0.175908	+	0.984407i	$0.556286\pi$
$752$	−627.714	+	55.2411i	−0.834726	+	0.0734589i
$753$		0			0
$754$	619.911	−	13.6057i	0.822163	−	0.0180448i
$755$	−1463.55	−	606.223i	−1.93848	−	0.802945i
$756$		0			0
$757$	−691.098	+	286.262i	−0.912944	+	0.378154i	−0.789183	−	0.614158i	$-0.789496\pi$
$757$	−691.098	+	286.262i	−0.912944	+	0.378154i	−0.123761	+	0.992312i	$0.539496\pi$
$758$	−870.819	−	338.515i	−1.14884	−	0.446590i
$759$		0			0
$760$	89.7619	+	78.6582i	0.118108	+	0.103498i
$761$	−287.342	+	287.342i	−0.377585	+	0.377585i	−0.870230	−	0.492645i	$-0.836030\pi$
$761$	−287.342	+	287.342i	−0.377585	+	0.377585i	0.492645	+	0.870230i	$0.336030\pi$
$762$		0			0
$763$	368.777	−	152.752i	0.483325	−	0.200200i
$764$	726.667	−	31.9130i	0.951135	−	0.0417710i
$765$		0			0
$766$	807.561	−	843.805i	1.05426	−	1.10157i
$767$		−	808.842i		−	1.05455i
$768$		0			0
$769$	−1240.31			−1.61289			−0.806446	−	0.591308i	$-0.798612\pi$
$769$	−1240.31			−1.61289			−0.806446	+	0.591308i	$0.798612\pi$
$770$	995.176	+	952.430i	1.29244	+	1.23692i
$771$		0			0
$772$	−38.8321	−	884.215i	−0.0503006	−	1.14536i
$773$	318.633	+	769.248i	0.412203	+	0.995146i	0.984545	+	0.175131i	$0.0560350\pi$
$773$	318.633	+	769.248i	0.412203	+	0.995146i	−0.572342	+	0.820015i	$0.693965\pi$
$774$		0			0
$775$	−128.394	−	128.394i	−0.165670	−	0.165670i
$776$	−348.252	+	397.413i	−0.448778	+	0.512130i
$777$		0			0
$778$	−109.651	+	282.074i	−0.140940	+	0.362563i
$779$	20.5052	+	49.5039i	0.0263224	+	0.0635480i
$780$		0			0
$781$	−653.751	+	1578.29i	−0.837069	+	2.02086i
$782$	1.89477	+	86.3304i	0.00242298	+	0.110397i
$783$		0			0
$784$	30.8691	+	350.771i	0.0393739	+	0.447412i
$785$		−	504.487i		−	0.642659i
$786$		0			0
$787$	584.664	+	242.176i	0.742902	+	0.307720i	0.721842	−	0.692058i	$-0.243296\pi$
$787$	584.664	+	242.176i	0.742902	+	0.307720i	0.0210600	+	0.999778i	$0.493296\pi$
$788$	−146.211	+	68.2249i	−0.185547	+	0.0865798i
$789$		0			0
$790$	−16.6646	+	42.8691i	−0.0210944	+	0.0542647i
$791$	−493.280	+	493.280i	−0.623616	+	0.623616i
$792$		0			0
$793$	−79.2491	+	79.2491i	−0.0999358	+	0.0999358i
$794$	1035.52	−	455.796i	1.30418	−	0.574050i
$795$		0			0
$796$	518.149	−	565.751i	0.650941	−	0.710742i
$797$	651.965	+	270.053i	0.818024	+	0.338837i	0.752150	−	0.658991i	$-0.229017\pi$
$797$	651.965	+	270.053i	0.818024	+	0.338837i	0.0658733	+	0.997828i	$0.479017\pi$
$798$		0			0
$799$			144.598i			0.180974i
$800$	1404.24	−	154.697i	1.75530	−	0.193371i
$801$		0			0
$802$	−375.995	+	392.870i	−0.468822	+	0.489863i
$803$	−250.537	+	604.850i	−0.312002	+	0.753238i
$804$		0			0
$805$	194.419	+	469.370i	0.241515	+	0.583068i
$806$	24.4267	+	55.4947i	0.0303061	+	0.0688520i
$807$		0			0
$808$	−148.720	−	50.4200i	−0.184059	−	0.0624009i
$809$	734.385	+	734.385i	0.907769	+	0.907769i	0.996092	−	0.0883227i	$-0.0281507\pi$
$809$	734.385	+	734.385i	0.907769	+	0.907769i	−0.0883227	+	0.996092i	$0.528151\pi$
$810$		0			0
$811$	430.173	+	1038.53i	0.530423	+	1.28055i	0.931243	+	0.364398i	$0.118725\pi$
$811$	430.173	+	1038.53i	0.530423	+	1.28055i	−0.400820	+	0.916157i	$0.631275\pi$
$812$	−792.101	+	369.609i	−0.975494	+	0.455184i
$813$		0			0
$814$	1655.64	−	36.3378i	2.03395	−	0.0446410i
$815$	1863.57			2.28658
$816$		0			0
$817$			0.480510i			0.000588140i
$818$	−513.866	+	11.2783i	−0.628199	+	0.0137876i
$819$		0			0
$820$	933.594	+	339.530i	1.13853	+	0.414061i
$821$	−30.8969	+	12.7979i	−0.0376333	+	0.0155882i	−0.401421	−	0.915894i	$-0.631483\pi$
$821$	−30.8969	+	12.7979i	−0.0376333	+	0.0155882i	0.363787	+	0.931482i	$0.381483\pi$
$822$		0			0
$823$	581.324	−	581.324i	0.706348	−	0.706348i	−0.259417	−	0.965765i	$-0.583530\pi$
$823$	581.324	−	581.324i	0.706348	−	0.706348i	0.965765	+	0.259417i	$0.0835305\pi$
$824$	−6.65138	+	0.438515i	−0.00807206	+	0.000532178i
$825$		0			0
$826$	459.351	+	1043.59i	0.556115	+	1.26343i
$827$	−625.862	+	259.241i	−0.756786	+	0.313471i	−0.727507	−	0.686100i	$-0.759321\pi$
$827$	−625.862	+	259.241i	−0.756786	+	0.313471i	−0.0292791	+	0.999571i	$0.509321\pi$
$828$		0			0
$829$	1209.84	+	501.131i	1.45939	+	0.604500i	0.964412	−	0.264403i	$-0.0851750\pi$
$829$	1209.84	+	501.131i	1.45939	+	0.604500i	0.494981	+	0.868904i	$0.335175\pi$
$830$	−985.726	+	1029.97i	−1.18762	+	1.24092i
$831$		0			0
$832$	−455.762	−	121.747i	−0.547791	−	0.146330i
$833$	80.8024			0.0970017
$834$		0			0
$835$	326.901	−	789.210i	0.391499	−	0.945162i
$836$	−114.297	+	5.01959i	−0.136719	+	0.00600430i
$837$		0			0
$838$	404.415	−	178.008i	0.482595	−	0.212421i
$839$	92.2651	+	92.2651i	0.109970	+	0.109970i	0.759951	−	0.649981i	$-0.225223\pi$
$839$	92.2651	+	92.2651i	0.109970	+	0.109970i	−0.649981	+	0.759951i	$0.725223\pi$
$840$		0			0
$841$	656.279	+	656.279i	0.780355	+	0.780355i
$842$	−24.8848	+	64.0152i	−0.0295543	+	0.0760276i
$843$		0			0
$844$	−204.229	+	561.562i	−0.241978	+	0.665358i
$845$	−364.900	+	880.946i	−0.431834	+	1.04254i
$846$		0			0
$847$	−691.816			−0.816784
$848$	347.313	−	181.025i	0.409567	−	0.213473i
$849$		0			0
$850$	−7.11334	−	324.101i	−0.00836864	−	0.381296i
$851$	564.280	+	233.733i	0.663079	+	0.274656i
$852$		0			0
$853$	404.566	−	167.577i	0.474286	−	0.196456i	−0.132719	−	0.991154i	$-0.542371\pi$
$853$	404.566	−	167.577i	0.474286	−	0.196456i	0.607005	+	0.794698i	$0.292371\pi$
$854$	57.2431	−	147.256i	0.0670294	−	0.172431i
$855$		0			0
$856$	−1097.94	−	372.231i	−1.28264	−	0.434850i
$857$	870.817	−	870.817i	1.01612	−	1.01612i	0.0162551	−	0.999868i	$-0.494826\pi$
$857$	870.817	−	870.817i	1.01612	−	1.01612i	0.999868	−	0.0162551i	$-0.00517439\pi$
$858$		0			0
$859$	−1000.98	+	414.619i	−1.16528	+	0.482677i	−0.879631	−	0.475657i	$-0.842211\pi$
$859$	−1000.98	+	414.619i	−1.16528	+	0.482677i	−0.285653	+	0.958333i	$0.592211\pi$
$860$	6.56967	+	6.01690i	0.00763915	+	0.00699640i
$861$		0			0
$862$	−26.7075	−	25.5603i	−0.0309832	−	0.0296524i
$863$			130.559i			0.151285i	0.997135	+	0.0756423i	$0.0241007\pi$
$863$			130.559i			0.151285i	−0.997135	+	0.0756423i	$0.975899\pi$
$864$		0			0
$865$	88.1088			0.101860
$866$	−512.062	+	535.044i	−0.591296	+	0.617834i
$867$		0			0
$868$	−63.0322	−	57.7287i	−0.0726177	−	0.0665077i
$869$	−16.8724	−	40.7336i	−0.0194159	−	0.0468741i
$870$		0			0
$871$	−50.0457	−	50.0457i	−0.0574577	−	0.0574577i
$872$	272.059	+	551.149i	0.311994	+	0.632051i
$873$		0			0
$874$	−39.3283	−	15.2881i	−0.0449980	−	0.0174922i
$875$	−316.568	−	764.264i	−0.361792	−	0.873444i
$876$		0			0
$877$	−251.771	+	607.829i	−0.287082	+	0.693077i	−0.999966	−	0.00820433i	$-0.997388\pi$
$877$	−251.771	+	607.829i	−0.287082	+	0.693077i	0.712884	+	0.701282i	$0.247388\pi$
$878$	−4.15985	+	0.0912999i	−0.00473787	+	0.000103986i
$879$		0			0
$880$	−1362.59	+	1625.56i	−1.54840	+	1.84723i
$881$		−	349.331i		−	0.396516i	−0.980150	−	0.198258i	$-0.936472\pi$
$881$		−	349.331i		−	0.396516i	0.980150	−	0.198258i	$-0.0635284\pi$
$882$		0			0
$883$	−1394.24	−	577.514i	−1.57898	−	0.654036i	−0.590731	−	0.806869i	$-0.701161\pi$
$883$	−1394.24	−	577.514i	−1.57898	−	0.654036i	−0.988252	+	0.152832i	$0.951161\pi$
$884$	−36.9980	+	101.732i	−0.0418529	+	0.115081i
$885$		0			0
$886$	−31.2683	−	12.1550i	−0.0352916	−	0.0137189i
$887$	980.070	−	980.070i	1.10493	−	1.10493i	0.111120	−	0.993807i	$-0.464556\pi$
$887$	980.070	−	980.070i	1.10493	−	1.10493i	0.993807	−	0.111120i	$-0.0354439\pi$
$888$		0			0
$889$	350.849	−	350.849i	0.394656	−	0.394656i
$890$	−686.200	−	1558.97i	−0.771012	−	1.75165i
$891$		0			0
$892$	122.373	−	5.37426i	0.137190	−	0.00602495i
$893$	−65.2790	−	27.0395i	−0.0731008	−	0.0302793i
$894$		0			0
$895$		−	1927.46i		−	2.15358i
$896$	657.180	−	101.751i	0.733459	−	0.113562i
$897$		0			0
$898$	505.203	+	483.503i	0.562587	+	0.538422i
$899$	−66.2018	+	159.825i	−0.0736393	+	0.177781i
$900$		0			0
$901$	−34.3933	−	83.0327i	−0.0381723	−	0.0921561i
$902$	−871.586	+	383.640i	−0.966282	+	0.425321i
$903$		0			0
$904$	−807.889	−	707.952i	−0.893683	−	0.783133i
$905$	−625.066	−	625.066i	−0.690681	−	0.690681i
$906$		0			0
$907$	64.9162	+	156.722i	0.0715725	+	0.172791i	0.955617	−	0.294611i	$-0.0951900\pi$
$907$	64.9162	+	156.722i	0.0715725	+	0.172791i	−0.884045	+	0.467402i	$0.845190\pi$
$908$	−82.6287	−	30.0505i	−0.0910007	−	0.0330952i
$909$		0			0
$910$	13.9750	+	636.735i	0.0153571	+	0.699709i
$911$	989.468			1.08613			0.543067	−	0.839689i	$-0.317263\pi$
$911$	989.468			1.08613			0.543067	+	0.839689i	$0.317263\pi$
$912$		0			0
$913$		−	1366.62i		−	1.49684i
$914$	10.3919	+	473.482i	0.0113697	+	0.518033i
$915$		0			0
$916$	−726.063	+	338.795i	−0.792645	+	0.369863i
$917$	841.857	−	348.708i	0.918055	−	0.380271i
$918$		0			0
$919$	594.043	−	594.043i	0.646402	−	0.646402i	−0.305720	−	0.952122i	$-0.598897\pi$
$919$	594.043	−	594.043i	0.646402	−	0.646402i	0.952122	+	0.305720i	$0.0988970\pi$
$920$	−701.488	+	346.270i	−0.762487	+	0.376381i
$921$		0			0
$922$	−1434.36	+	631.353i	−1.55571	+	0.684764i
$923$	−729.727	+	302.263i	−0.790603	+	0.327478i
$924$		0			0
$925$	−2118.42	−	877.478i	−2.29018	−	0.948625i
$926$	−101.791	−	97.4191i	−0.109926	−	0.105204i
$927$		0			0
$928$	−648.140	−	1179.62i	−0.698427	−	1.27114i
$929$	−1637.29			−1.76242			−0.881209	−	0.472726i	$-0.843270\pi$
$929$	−1637.29			−1.76242			−0.881209	+	0.472726i	$0.843270\pi$
$930$		0			0
$931$	−15.1098	+	36.4784i	−0.0162297	+	0.0391819i
$932$	−487.356	+	532.129i	−0.522914	+	0.570954i
$933$		0			0
$934$	78.3498	+	178.002i	0.0838863	+	0.190580i
$935$	344.170	+	344.170i	0.368096	+	0.368096i
$936$		0			0
$937$	−407.126	−	407.126i	−0.434500	−	0.434500i	0.455656	−	0.890156i	$-0.349405\pi$
$937$	−407.126	−	407.126i	−0.434500	−	0.434500i	−0.890156	+	0.455656i	$0.849405\pi$
$938$	92.9920	+	36.1489i	0.0991386	+	0.0385383i
$939$		0			0
$940$	−1187.11	+	553.927i	−1.26288	+	0.589284i
$941$	−510.935	+	1233.51i	−0.542970	+	1.31085i	0.379648	+	0.925131i	$0.376045\pi$
$941$	−510.935	+	1233.51i	−0.542970	+	1.31085i	−0.922618	+	0.385715i	$0.873955\pi$
$942$		0			0
$943$	−351.217			−0.372446
$944$	−1556.94	+	811.503i	−1.64930	+	0.859643i
$945$		0			0
$946$	−8.53768	+	0.187384i	−0.00902503	+	0.000198081i
$947$	627.458	+	259.902i	0.662574	+	0.274447i	0.688521	−	0.725216i	$-0.258260\pi$
$947$	627.458	+	259.902i	0.662574	+	0.274447i	−0.0259471	+	0.999663i	$0.508260\pi$
$948$		0			0
$949$	−279.654	+	115.836i	−0.294682	+	0.122061i
$950$	147.646	+	57.3947i	0.155417	+	0.0604155i
$951$		0			0
$952$	−10.0389	−	152.269i	−0.0105450	−	0.159947i
$953$	1189.93	−	1189.93i	1.24862	−	1.24862i	0.292290	−	0.956330i	$-0.405583\pi$
$953$	1189.93	−	1189.93i	1.24862	−	1.24862i	0.956330	−	0.292290i	$-0.0944171\pi$
$954$		0			0
$955$	1397.01	−	578.660i	1.46284	−	0.605926i
$956$	−69.7153	−	1587.43i	−0.0729239	−	1.66050i
$957$		0			0
$958$	−1245.31	+	1301.20i	−1.29991	+	1.35825i
$959$		−	651.893i		−	0.679764i
$960$		0			0
$961$	944.084			0.982397
$962$	553.161	+	529.401i	0.575012	+	0.550313i
$963$		0			0
$964$	1602.97	−	70.3975i	1.66283	−	0.0730264i
$965$	−704.118	−	1699.89i	−0.729656	−	1.76155i
$966$		0			0
$967$	633.832	+	633.832i	0.655462	+	0.655462i	0.954303	−	0.298841i	$-0.0965999\pi$
$967$	633.832	+	633.832i	0.655462	+	0.655462i	−0.298841	+	0.954303i	$0.596600\pi$
$968$	−70.0798	−	1062.97i	−0.0723965	−	1.09811i
$969$		0			0
$970$	−398.007	+	1023.86i	−0.410317	+	1.05553i
$971$	399.517	+	964.518i	0.411449	+	0.993325i	0.984749	+	0.173980i	$0.0556627\pi$
$971$	399.517	+	964.518i	0.411449	+	0.993325i	−0.573301	+	0.819345i	$0.694337\pi$
$972$		0			0
$973$	143.828	−	347.232i	0.147819	−	0.356867i
$974$	−10.8900	−	496.174i	−0.0111807	−	0.509419i
$975$		0			0
$976$	232.056	+	73.0367i	0.237762	+	0.0748327i
$977$			122.057i			0.124931i	0.998047	+	0.0624653i	$0.0198963\pi$
$977$			122.057i			0.124931i	−0.998047	+	0.0624653i	$0.980104\pi$
$978$		0			0
$979$	1508.49	+	624.837i	1.54085	+	0.638240i
$980$	309.538	+	663.364i	0.315855	+	0.676902i
$981$		0			0
$982$	−212.061	+	545.521i	−0.215948	+	0.555521i
$983$	−1257.94	+	1257.94i	−1.27970	+	1.27970i	−0.338864	+	0.940835i	$0.610043\pi$
$983$	−1257.94	+	1257.94i	−1.27970	+	1.27970i	−0.940835	+	0.338864i	$0.889957\pi$
$984$		0			0
$985$	−237.176	+	237.176i	−0.240788	+	0.240788i
$986$	−282.682	+	124.426i	−0.286696	+	0.126193i
$987$		0			0
$988$	−39.0085	−	35.7264i	−0.0394823	−	0.0361603i
$989$	−2.90984	−	1.20530i	−0.00294220	−	0.00121870i
$990$		0			0
$991$			1409.81i			1.42261i	0.702884	+	0.711304i	$0.251895\pi$
$991$			1409.81i			1.42261i	−0.702884	+	0.711304i	$0.748105\pi$
$992$	82.3146	−	102.696i	0.0829784	−	0.103524i
$993$		0			0
$994$	769.857	−	804.409i	0.774504	−	0.809264i
$995$	610.326	−	1473.46i	0.613393	−	1.48086i
$996$		0			0
$997$	−60.9825	−	147.225i	−0.0611660	−	0.147668i	0.890341	−	0.455293i	$-0.150466\pi$
$997$	−60.9825	−	147.225i	−0.0611660	−	0.147668i	−0.951508	+	0.307625i	$0.900466\pi$
$998$	84.0828	+	191.027i	0.0842513	+	0.191409i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	288.3.u.a.163.5		28
3.2	odd	2		32.3.h.a.3.3	✓	28
12.11	even	2		128.3.h.a.47.2		28
24.5	odd	2		256.3.h.b.95.2		28
24.11	even	2		256.3.h.a.95.6		28
32.11	odd	8	inner	288.3.u.a.235.5		28
96.5	odd	8		256.3.h.a.159.6		28
96.11	even	8		32.3.h.a.11.3	yes	28
96.53	odd	8		128.3.h.a.79.2		28
96.59	even	8		256.3.h.b.159.2		28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
32.3.h.a.3.3	✓	28	3.2	odd	2
32.3.h.a.11.3	yes	28	96.11	even	8
128.3.h.a.47.2		28	12.11	even	2
128.3.h.a.79.2		28	96.53	odd	8
256.3.h.a.95.6		28	24.11	even	2
256.3.h.a.159.6		28	96.5	odd	8
256.3.h.b.95.2		28	24.5	odd	2
256.3.h.b.159.2		28	96.59	even	8
288.3.u.a.163.5		28	1.1	even	1	trivial
288.3.u.a.235.5		28	32.11	odd	8	inner

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:	\( N \)	\(=\)	\( 288 = 2^{5} \cdot 3^{2} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	288.u (of order \(8\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(1.44490 + 1.38284i) q^{2} +(0.175499 + 3.99615i) q^{4} +(3.18221 + 7.68254i) q^{5} +(3.67370 + 3.67370i) q^{7} +(-5.27246 + 6.01674i) q^{8} +O(q^{10})\)	\(q+(1.44490 + 1.38284i) q^{2} +(0.175499 + 3.99615i) q^{4} +(3.18221 + 7.68254i) q^{5} +(3.67370 + 3.67370i) q^{7} +(-5.27246 + 6.01674i) q^{8} +(-6.02574 + 15.5010i) q^{10} +(-6.10089 - 14.7288i) q^{11} +(2.82075 - 6.80990i) q^{13} +(0.228001 + 10.3883i) q^{14} +(-15.9384 + 1.40264i) q^{16} +3.67152i q^{17} +(-1.65751 - 0.686564i) q^{19} +(-30.1421 + 14.0649i) q^{20} +(11.5525 - 29.7183i) q^{22} +(8.31529 - 8.31529i) q^{23} +(-31.2172 + 31.2172i) q^{25} +(13.4927 - 5.93900i) q^{26} +(-14.0359 + 15.3254i) q^{28} +(38.8592 + 16.0960i) q^{29} +4.11293i q^{31} +(-24.9691 - 20.0136i) q^{32} +(-5.07713 + 5.30499i) q^{34} +(-16.5328 + 39.9138i) q^{35} +(19.8759 + 47.9847i) q^{37} +(-1.44554 - 3.28410i) q^{38} +(-63.0019 - 21.3593i) q^{40} +(-21.1187 - 21.1187i) q^{41} +(-0.102495 - 0.247444i) q^{43} +(57.7879 - 26.9649i) q^{44} +(23.5135 - 0.516073i) q^{46} +39.3838 q^{47} -22.0079i q^{49} +(-88.2745 + 1.93744i) q^{50} +(27.7084 + 10.0770i) q^{52} +(-22.6154 + 9.36759i) q^{53} +(93.7406 - 93.7406i) q^{55} +(-41.4731 + 2.73426i) q^{56} +(33.8896 + 76.9933i) q^{58} +(101.380 - 41.9931i) q^{59} +(-14.0475 - 5.81867i) q^{61} +(-5.68753 + 5.94279i) q^{62} +(-8.40232 - 63.4460i) q^{64} +61.2936 q^{65} +(3.67448 - 8.87098i) q^{67} +(-14.6719 + 0.644346i) q^{68} +(-79.0828 + 34.8093i) q^{70} +(-75.7712 - 75.7712i) q^{71} +(-29.0378 - 29.0378i) q^{73} +(-37.6364 + 96.8185i) q^{74} +(2.45272 - 6.74415i) q^{76} +(31.6965 - 76.5221i) q^{77} +2.76556 q^{79} +(-61.4952 - 117.984i) q^{80} +(-1.31069 - 59.7184i) q^{82} +(79.1972 + 32.8045i) q^{83} +(-28.2066 + 11.6835i) q^{85} +(0.194081 - 0.499267i) q^{86} +(120.786 + 40.9498i) q^{88} +(-72.4200 + 72.4200i) q^{89} +(35.3801 - 14.6549i) q^{91} +(34.6885 + 31.7698i) q^{92} +(56.9058 + 54.4615i) q^{94} -14.9187i q^{95} +66.0511 q^{97} +(30.4335 - 31.7993i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q + 4 q^{2} - 4 q^{4} + 4 q^{5} - 4 q^{7} + 4 q^{8}+O(q^{10}) \) 28 * q + 4 * q^2 - 4 * q^4 + 4 * q^5 - 4 * q^7 + 4 * q^8	\( 28 q + 4 q^{2} - 4 q^{4} + 4 q^{5} - 4 q^{7} + 4 q^{8} - 44 q^{10} + 4 q^{11} - 4 q^{13} + 20 q^{14} + 16 q^{16} - 4 q^{19} - 76 q^{20} + 144 q^{22} + 68 q^{23} - 4 q^{25} - 96 q^{26} + 56 q^{28} + 4 q^{29} + 24 q^{32} - 48 q^{34} - 92 q^{35} - 4 q^{37} + 396 q^{38} - 408 q^{40} + 4 q^{41} + 92 q^{43} + 188 q^{44} - 36 q^{46} + 8 q^{47} - 308 q^{50} + 420 q^{52} + 164 q^{53} + 252 q^{55} - 552 q^{56} + 528 q^{58} - 124 q^{59} - 68 q^{61} - 216 q^{62} - 232 q^{64} + 8 q^{65} - 164 q^{67} + 368 q^{68} - 664 q^{70} + 260 q^{71} - 4 q^{73} + 532 q^{74} - 516 q^{76} - 220 q^{77} - 520 q^{79} - 312 q^{80} + 636 q^{82} + 484 q^{83} + 96 q^{85} - 688 q^{86} + 672 q^{88} + 4 q^{89} - 196 q^{91} - 616 q^{92} + 40 q^{94} - 8 q^{97} + 328 q^{98}+O(q^{100}) \) 28 * q + 4 * q^2 - 4 * q^4 + 4 * q^5 - 4 * q^7 + 4 * q^8 - 44 * q^10 + 4 * q^11 - 4 * q^13 + 20 * q^14 + 16 * q^16 - 4 * q^19 - 76 * q^20 + 144 * q^22 + 68 * q^23 - 4 * q^25 - 96 * q^26 + 56 * q^28 + 4 * q^29 + 24 * q^32 - 48 * q^34 - 92 * q^35 - 4 * q^37 + 396 * q^38 - 408 * q^40 + 4 * q^41 + 92 * q^43 + 188 * q^44 - 36 * q^46 + 8 * q^47 - 308 * q^50 + 420 * q^52 + 164 * q^53 + 252 * q^55 - 552 * q^56 + 528 * q^58 - 124 * q^59 - 68 * q^61 - 216 * q^62 - 232 * q^64 + 8 * q^65 - 164 * q^67 + 368 * q^68 - 664 * q^70 + 260 * q^71 - 4 * q^73 + 532 * q^74 - 516 * q^76 - 220 * q^77 - 520 * q^79 - 312 * q^80 + 636 * q^82 + 484 * q^83 + 96 * q^85 - 688 * q^86 + 672 * q^88 + 4 * q^89 - 196 * q^91 - 616 * q^92 + 40 * q^94 - 8 * q^97 + 328 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more