LMFDB - Embedded newform 288.3.u.a.235.5

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			235.5
Character	$\chi$	$=$	288.235
Dual form			288.3.u.a.163.5

$q$-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 $\left(\mathbb{Z}/288\mathbb{Z}\right)^\times$.

$n$	$37$	$65$	$127$
$\chi(n)$	$e\left(\frac{5}{8}\right)$	$1$	$-1$

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	−0.194945	−	0.980814i	$-0.562453\pi$
$5$	3.18221	−	7.68254i	0.636442	−	1.53651i	0.831387	−	0.555693i	$-0.187547\pi$
$6$		0			0
$7$	3.67370	−	3.67370i	0.524814	−	0.524814i	−0.394208	−	0.919021i	$-0.628981\pi$
$7$	3.67370	−	3.67370i	0.524814	−	0.524814i	0.919021	+	0.394208i	$0.128981\pi$
$8$	−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	0.359345	+	0.933205i	$0.383000\pi$
$11$	−6.10089	+	14.7288i	−0.554626	+	1.33899i	−0.913971	+	0.405781i	$0.867000\pi$
$12$		0			0
$13$	2.82075	+	6.80990i	0.216981	+	0.523839i	0.994466	−	0.105063i	$-0.0335046\pi$
$13$	2.82075	+	6.80990i	0.216981	+	0.523839i	−0.777484	+	0.628902i	$0.783505\pi$
$14$	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	$-0.965560\pi$
$17$		−	3.67152i		−	0.215972i	0.994152	−	0.107986i	$-0.0344401\pi$
$18$		0			0
$19$	−1.65751	+	0.686564i	−0.0872375	+	0.0361349i	−0.425875	−	0.904782i	$-0.640034\pi$
$19$	−1.65751	+	0.686564i	−0.0872375	+	0.0361349i	0.338638	+	0.940917i	$0.390034\pi$
$20$	−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	0.864378	−	0.502843i	$-0.167713\pi$
$23$	8.31529	+	8.31529i	0.361534	+	0.361534i	−0.502843	+	0.864378i	$0.667713\pi$
$24$		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	0.406489	−	0.913656i	$-0.366753\pi$
$29$	38.8592	−	16.0960i	1.33997	−	0.555035i	0.933483	+	0.358621i	$0.116753\pi$
$30$		0			0
$31$		−	4.11293i		−	0.132675i	−0.997797	−	0.0663376i	$-0.978869\pi$
$31$		−	4.11293i		−	0.132675i	0.997797	−	0.0663376i	$-0.0211314\pi$
$32$	−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	−0.389493	−	0.921030i	$-0.627350\pi$
$37$	19.8759	−	47.9847i	0.537186	−	1.29688i	0.926679	−	0.375853i	$-0.122650\pi$
$38$	−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	−0.916082	−	0.400991i	$-0.868666\pi$
$41$	−21.1187	+	21.1187i	−0.515091	+	0.515091i	0.400991	+	0.916082i	$0.368666\pi$
$42$		0			0
$43$	−0.102495	+	0.247444i	−0.00238360	+	0.00575451i	−0.925067	−	0.379804i	$-0.875991\pi$
$43$	−0.102495	+	0.247444i	−0.00238360	+	0.00575451i	0.922683	+	0.385559i	$0.125991\pi$
$44$	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	0.158987	−	0.987281i	$-0.449177\pi$
$53$	−22.6154	−	9.36759i	−0.426705	−	0.176747i	−0.585692	+	0.810534i	$0.699177\pi$
$54$		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	0.999869	+	0.0161592i	$0.00514387\pi$
$59$	101.380	+	41.9931i	1.71831	+	0.711747i	0.718441	+	0.695588i	$0.244856\pi$
$60$		0			0
$61$	−14.0475	+	5.81867i	−0.230287	+	0.0953880i	−0.494843	−	0.868982i	$-0.664775\pi$
$61$	−14.0475	+	5.81867i	−0.230287	+	0.0953880i	0.264556	+	0.964370i	$0.414775\pi$
$62$	−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	0.948926	−	0.315498i	$-0.102172\pi$
$67$	3.67448	+	8.87098i	0.0548430	+	0.132403i	−0.894083	+	0.447901i	$0.852172\pi$
$68$	−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	−0.0696271	+	0.997573i	$0.522181\pi$
$71$	−75.7712	+	75.7712i	−1.06720	+	1.06720i	−0.997573	+	0.0696271i	$0.977819\pi$
$72$		0			0
$73$	−29.0378	+	29.0378i	−0.397779	+	0.397779i	−0.877449	−	0.479670i	$-0.840756\pi$
$73$	−29.0378	+	29.0378i	−0.397779	+	0.397779i	0.479670	+	0.877449i	$0.340756\pi$
$74$	−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	0.149381	−	0.988780i	$-0.452272\pi$
$83$	79.1972	−	32.8045i	0.954183	−	0.395235i	0.804801	+	0.593544i	$0.202272\pi$
$84$		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	0.171480	−	0.985188i	$-0.445145\pi$
$89$	−72.4200	−	72.4200i	−0.813708	−	0.813708i	−0.985188	+	0.171480i	$0.945145\pi$
$90$		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	−0.882320	−	0.470650i	$-0.844019\pi$
$101$	7.51179	−	18.1351i	0.0743742	−	0.179555i	0.956694	+	0.291095i	$0.0940195\pi$
$102$		0			0
$103$	0.589180	−	0.589180i	0.00572020	−	0.00572020i	−0.704241	−	0.709961i	$-0.748712\pi$
$103$	0.589180	−	0.589180i	0.00572020	−	0.00572020i	0.709961	+	0.704241i	$0.248712\pi$
$104$	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	−0.420668	−	0.907215i	$-0.638204\pi$
$107$	55.4567	−	133.884i	0.518287	−	1.25126i	0.938955	−	0.344041i	$-0.111796\pi$
$108$		0			0
$109$	29.4015	+	70.9815i	0.269739	+	0.651207i	0.999471	−	0.0325264i	$-0.0103553\pi$
$109$	29.4015	+	70.9815i	0.269739	+	0.651207i	−0.729732	+	0.683733i	$0.760355\pi$
$110$	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	$-0.797496\pi$
$113$		−	134.274i		−	1.18826i	0.804368	−	0.594131i	$-0.202504\pi$
$114$		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	$0.122699\pi$
$127$			95.5030i			0.751992i	−0.926621	+	0.375996i	$0.877301\pi$
$128$	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	0.942508	+	0.334183i	$0.108460\pi$
$131$	67.1188	+	162.039i	0.512357	+	1.23694i	−0.430151	+	0.902757i	$0.641540\pi$
$132$		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	−0.952418	−	0.304794i	$-0.901412\pi$
$137$	−88.7244	+	88.7244i	−0.647624	+	0.647624i	0.304794	+	0.952418i	$0.401412\pi$
$138$		0			0
$139$	−27.6838	+	66.8346i	−0.199164	+	0.480824i	−0.991633	−	0.129087i	$-0.958795\pi$
$139$	−27.6838	+	66.8346i	−0.199164	+	0.480824i	0.792469	+	0.609912i	$0.208795\pi$
$140$	−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	0.693625	−	0.720336i	$-0.256013\pi$
$149$	100.536	+	41.6433i	0.674737	+	0.279485i	−0.0188878	+	0.999822i	$0.506013\pi$
$150$		0			0
$151$	−134.706	−	134.706i	−0.892096	−	0.892096i	0.102624	−	0.994720i	$-0.467276\pi$
$151$	−134.706	−	134.706i	−0.892096	−	0.892096i	−0.994720	+	0.102624i	$0.967276\pi$
$152$	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	−0.553976	−	0.832533i	$-0.686890\pi$
$157$	−56.0501	+	23.2167i	−0.357007	+	0.147877i	0.196969	+	0.980410i	$0.436890\pi$
$158$	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	0.934029	+	0.357198i	$0.116268\pi$
$163$	85.7621	+	207.048i	0.526148	+	1.27023i	−0.407881	+	0.913035i	$0.633732\pi$
$164$	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	−0.890314	−	0.455347i	$-0.849515\pi$
$167$	−72.6395	+	72.6395i	−0.434967	+	0.434967i	0.455347	+	0.890314i	$0.349515\pi$
$168$		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	0.935165	−	0.354212i	$-0.115251\pi$
$173$	4.05480	+	9.78916i	0.0234382	+	0.0565847i	−0.911727	+	0.410796i	$0.865251\pi$
$174$		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	−0.889817	−	0.456317i	$-0.849168\pi$
$179$	−214.146	+	88.7024i	−1.19635	+	0.495544i	−0.306531	+	0.951861i	$0.599168\pi$
$180$		0			0
$181$	−98.2125	−	40.6810i	−0.542611	−	0.224757i	0.0945057	−	0.995524i	$-0.469873\pi$
$181$	−98.2125	−	40.6810i	−0.542611	−	0.224757i	−0.637116	+	0.770768i	$0.719873\pi$
$182$	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	$0.157923\pi$
$191$			181.842i			0.952052i	−0.879431	+	0.476026i	$0.842077\pi$
$192$		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	−0.879847	−	0.475256i	$-0.842355\pi$
$197$	15.4361	−	37.2660i	0.0783556	−	0.189167i	0.958203	+	0.286089i	$0.0923553\pi$
$198$		0			0
$199$	−135.618	+	135.618i	−0.681498	+	0.681498i	−0.960338	−	0.278840i	$-0.910050\pi$
$199$	−135.618	+	135.618i	−0.681498	+	0.681498i	0.278840	+	0.960338i	$0.410050\pi$
$200$	−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	−0.0308532	−	0.999524i	$-0.509822\pi$
$211$	138.015	−	57.1678i	0.654100	−	0.270937i	0.684954	+	0.728587i	$0.259822\pi$
$212$	−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	$0.0218727\pi$
$223$			30.6228i			0.137322i	−0.997640	+	0.0686609i	$0.978127\pi$
$224$	−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	0.904268	−	0.426965i	$-0.140417\pi$
$227$	−8.41171	−	20.3077i	−0.0370560	−	0.0894611i	−0.941324	+	0.337504i	$0.890417\pi$
$228$		0			0
$229$	76.6532	−	185.057i	0.334730	−	0.808110i	−0.663474	−	0.748199i	$-0.730919\pi$
$229$	76.6532	−	185.057i	0.334730	−	0.808110i	0.998204	−	0.0599101i	$-0.0190814\pi$
$230$	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	−0.378245	−	0.925706i	$-0.623472\pi$
$233$	127.558	−	127.558i	0.547461	−	0.547461i	0.925706	+	0.378245i	$0.123472\pi$
$234$		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	$0.312928\pi$
$241$			401.128i			1.66443i	−0.554451	+	0.832216i	$0.687072\pi$
$242$	−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	−0.101829	−	0.994802i	$-0.532469\pi$
$251$	−220.193	−	91.2070i	−0.877264	−	0.363375i	−0.775435	+	0.631427i	$0.782469\pi$
$252$		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	0.272219	−	0.962235i	$-0.412242\pi$
$263$	324.662	−	324.662i	1.23445	−	1.23445i	0.962235	−	0.272219i	$-0.0877576\pi$
$264$		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	0.994193	+	0.107612i	$0.0343205\pi$
$269$	98.7998	+	238.524i	0.367286	+	0.886706i	−0.626907	+	0.779094i	$0.715680\pi$
$270$		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	0.458556	−	0.888666i	$-0.348367\pi$
$277$	42.7749	+	17.7179i	0.154422	+	0.0639636i	−0.304134	+	0.952629i	$0.598367\pi$
$278$	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	0.939196	−	0.343382i	$-0.111573\pi$
$281$	167.424	+	167.424i	0.595813	+	0.595813i	−0.343382	+	0.939196i	$0.611573\pi$
$282$		0			0
$283$	−494.380	−	204.779i	−1.74693	−	0.723601i	−0.998151	−	0.0607762i	$-0.980642\pi$
$283$	−494.380	−	204.779i	−1.74693	−	0.723601i	−0.748775	−	0.662824i	$-0.769358\pi$
$284$	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	0.448075	+	0.893996i	$0.352110\pi$
$293$	−146.767	+	354.328i	−0.500913	+	1.20931i	−0.948987	+	0.315314i	$0.897890\pi$
$294$		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	−0.468003	−	0.883727i	$-0.655026\pi$
$307$	−53.4306	+	22.1317i	−0.174041	+	0.0720902i	0.293962	+	0.955817i	$0.405026\pi$
$308$	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	0.111122	−	0.993807i	$-0.464556\pi$
$311$	−274.515	−	274.515i	−0.882685	−	0.882685i	−0.993807	+	0.111122i	$0.964556\pi$
$312$		0			0
$313$	−78.4013	−	78.4013i	−0.250483	−	0.250483i	0.570685	−	0.821169i	$-0.306678\pi$
$313$	−78.4013	−	78.4013i	−0.250483	−	0.250483i	−0.821169	+	0.570685i	$0.806678\pi$
$314$	−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	−0.156814	−	0.987628i	$-0.550122\pi$
$317$	136.520	−	56.5483i	0.430661	−	0.178386i	0.587475	+	0.809243i	$0.300122\pi$
$318$		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	−0.543841	−	0.839189i	$-0.683030\pi$
$331$	143.690	−	346.898i	0.434109	−	1.04803i	0.977949	−	0.208843i	$-0.0669696\pi$
$332$	−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	$0.251705\pi$
$337$			479.136i			1.42177i	−0.703310	+	0.710884i	$0.748295\pi$
$338$	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	0.120585	−	0.992703i	$-0.461523\pi$
$347$	−172.145	−	71.3048i	−0.496095	−	0.205489i	−0.616680	+	0.787214i	$0.711523\pi$
$348$		0			0
$349$	388.120	−	160.765i	1.11209	−	0.460644i	0.250434	−	0.968134i	$-0.419427\pi$
$349$	388.120	−	160.765i	1.11209	−	0.460644i	0.861658	+	0.507490i	$0.169427\pi$
$350$	−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	−0.833610	−	0.552353i	$-0.813730\pi$
$359$	−100.971	+	100.971i	−0.281257	+	0.281257i	0.552353	+	0.833610i	$0.313730\pi$
$360$		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	0.994593	−	0.103845i	$-0.0331146\pi$
$373$	605.919	+	250.980i	1.62445	+	0.672868i	0.629854	+	0.776713i	$0.283115\pi$
$374$	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	−0.268011	−	0.963416i	$-0.586366\pi$
$379$	−431.591	−	178.771i	−1.13876	−	0.471691i	−0.870750	+	0.491725i	$0.836366\pi$
$380$	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	$0.275972\pi$
$383$			583.987i			1.52477i	−0.647124	+	0.762385i	$0.724028\pi$
$384$		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	−0.831806	−	0.555067i	$-0.812693\pi$
$389$	57.9070	−	139.800i	0.148861	−	0.359383i	0.980667	+	0.195684i	$0.0626927\pi$
$390$		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	0.920944	+	0.389696i	$0.127420\pi$
$397$	216.482	+	522.634i	0.545295	+	1.31646i	−0.375649	+	0.926762i	$0.622580\pi$
$398$	−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	$-0.889902\pi$
$401$		−	271.900i		−	0.678055i	0.940776	−	0.339028i	$-0.110098\pi$
$402$		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	0.449147	−	0.893458i	$-0.351728\pi$
$409$	−181.723	−	181.723i	−0.444310	−	0.444310i	−0.893458	+	0.449147i	$0.851728\pi$
$410$	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	0.992084	−	0.125575i	$-0.0400775\pi$
$419$	84.5458	+	204.112i	0.201780	+	0.487140i	−0.790304	+	0.612715i	$0.790077\pi$
$420$		0			0
$421$	13.1417	−	31.7269i	0.0312155	−	0.0753608i	−0.907503	−	0.420045i	$-0.862014\pi$
$421$	13.1417	−	31.7269i	0.0312155	−	0.0753608i	0.938719	+	0.344685i	$0.112014\pi$
$422$	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	$-0.859361\pi$
$433$		−	370.297i		−	0.855190i	0.903970	−	0.427595i	$-0.140639\pi$
$434$	−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	0.705429	−	0.708780i	$-0.250754\pi$
$439$	−1.47108	−	1.47108i	−0.00335099	−	0.00335099i	−0.708780	+	0.705429i	$0.750754\pi$
$440$	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	0.365124	−	0.930959i	$-0.381027\pi$
$443$	−15.4970	−	6.41908i	−0.0349820	−	0.0144900i	−0.400106	+	0.916469i	$0.631027\pi$
$444$		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	−0.499767	−	0.866160i	$-0.666581\pi$
$457$	167.442	−	167.442i	0.366393	−	0.366393i	0.866160	+	0.499767i	$0.166581\pi$
$458$	−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	−0.812107	−	0.583508i	$-0.801680\pi$
$461$	−299.864	−	723.935i	−0.650463	−	1.57036i	0.161644	−	0.986849i	$-0.448320\pi$
$462$		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	−0.284416	−	0.958701i	$-0.591800\pi$
$467$	89.8391	−	37.2126i	0.192375	−	0.0796843i	0.476791	+	0.879017i	$0.341800\pi$
$468$		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	$-0.610800\pi$
$479$		−	900.546i		−	1.88005i	0.341101	−	0.940027i	$-0.389200\pi$
$480$		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	−0.863924	−	0.503623i	$-0.832000\pi$
$487$	−175.466	+	175.466i	−0.360301	+	0.360301i	0.503623	+	0.863924i	$0.332000\pi$
$488$	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	−0.767858	−	0.640620i	$-0.778678\pi$
$491$	111.990	−	270.368i	0.228086	−	0.550648i	0.995944	+	0.0899713i	$0.0286775\pi$
$492$		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	−0.283980	−	0.958830i	$-0.591655\pi$
$499$	96.4128	−	39.9355i	0.193212	−	0.0800310i	0.477192	+	0.878799i	$0.341655\pi$
$500$	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	0.0232864	−	0.999729i	$-0.492587\pi$
$503$	−491.151	−	491.151i	−0.976442	−	0.976442i	−0.999729	+	0.0232864i	$0.992587\pi$
$504$		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	−0.753457	+	0.657498i	$0.771615\pi$
$509$	−891.336	+	369.204i	−1.75115	+	0.725351i	−0.997695	+	0.0678534i	$0.978385\pi$
$510$		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	−0.925982	−	0.377569i	$-0.876760\pi$
$521$	−285.723	+	285.723i	−0.548413	+	0.548413i	0.377569	+	0.925982i	$0.376760\pi$
$522$		0			0
$523$	260.696	−	629.375i	0.498462	−	1.20339i	−0.451849	−	0.892094i	$-0.649236\pi$
$523$	260.696	−	629.375i	0.498462	−	1.20339i	0.950312	−	0.311300i	$-0.100764\pi$
$524$	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	−0.0295603	−	0.999563i	$-0.509411\pi$
$541$	355.077	−	147.078i	0.656335	−	0.271863i	0.685895	+	0.727700i	$0.259411\pi$
$542$	−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	0.605010	+	0.796218i	$0.293169\pi$
$547$	404.897	+	977.508i	0.740214	+	1.78704i	0.135204	+	0.990818i	$0.456831\pi$
$548$	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	0.929441	+	0.368970i	$0.120289\pi$
$557$	296.952	+	716.907i	0.533128	+	1.28709i	−0.396313	+	0.918115i	$0.629711\pi$
$558$		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	−0.342644	−	0.939465i	$-0.611322\pi$
$563$	44.6869	−	18.5099i	0.0793728	−	0.0328773i	0.422017	+	0.906588i	$0.361322\pi$
$564$		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	0.134818	−	0.990870i	$-0.456955\pi$
$569$	−487.094	−	487.094i	−0.856053	−	0.856053i	−0.990870	+	0.134818i	$0.956955\pi$
$570$		0			0
$571$	−252.561	−	104.614i	−0.442313	−	0.183212i	0.150401	−	0.988625i	$-0.451944\pi$
$571$	−252.561	−	104.614i	−0.442313	−	0.183212i	−0.592714	+	0.805413i	$0.701944\pi$
$572$	−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	−0.971319	−	0.237780i	$-0.923580\pi$
$587$	−68.3015	+	164.895i	−0.116357	+	0.280911i	0.854962	+	0.518690i	$0.173580\pi$
$588$		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	$0.0451182\pi$
$593$			167.545i			0.282538i	−0.989971	+	0.141269i	$0.954882\pi$
$594$		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	0.920338	−	0.391125i	$-0.127914\pi$
$599$	316.998	+	316.998i	0.529213	+	0.529213i	−0.391125	+	0.920338i	$0.627914\pi$
$600$		0			0
$601$	−224.198	−	224.198i	−0.373042	−	0.373042i	0.495542	−	0.868584i	$-0.334970\pi$
$601$	−224.198	−	224.198i	−0.373042	−	0.373042i	−0.868584	+	0.495542i	$0.834970\pi$
$602$	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	$0.0234216\pi$
$607$			89.2468i			0.147029i	−0.997294	+	0.0735146i	$0.976578\pi$
$608$	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	−0.668865	−	0.743384i	$-0.733220\pi$
$613$	202.134	−	487.995i	0.329746	−	0.796076i	0.998611	−	0.0526926i	$-0.0167803\pi$
$614$	−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	−0.944884	−	0.327405i	$-0.893826\pi$
$617$	−380.984	+	380.984i	−0.617479	+	0.617479i	0.327405	+	0.944884i	$0.393826\pi$
$618$		0			0
$619$	−371.320	+	896.447i	−0.599871	+	1.44822i	0.273841	+	0.961775i	$0.411706\pi$
$619$	−371.320	+	896.447i	−0.599871	+	1.44822i	−0.873712	+	0.486443i	$0.838294\pi$
$620$	−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	0.942870	−	0.333162i	$-0.108115\pi$
$631$	384.726	+	384.726i	0.609708	+	0.609708i	−0.333162	+	0.942870i	$0.608115\pi$
$632$	−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	−0.951313	−	0.308226i	$-0.900265\pi$
$643$	−319.302	−	770.863i	−0.496582	−	1.19885i	0.454732	−	0.890629i	$-0.349735\pi$
$644$	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	−0.668505	−	0.743708i	$-0.733065\pi$
$647$	48.6565	−	48.6565i	0.0752033	−	0.0752033i	0.743708	+	0.668505i	$0.233065\pi$
$648$		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	0.974436	+	0.224663i	$0.0721282\pi$
$653$	290.106	+	700.378i	0.444267	+	1.07255i	−0.530170	+	0.847892i	$0.677872\pi$
$654$		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	−0.904134	−	0.427248i	$-0.859483\pi$
$659$	−818.045	+	338.845i	−1.24134	+	0.514181i	−0.337209	+	0.941430i	$0.609483\pi$
$660$		0			0
$661$	−35.2123	−	14.5854i	−0.0532712	−	0.0220657i	0.355889	−	0.934528i	$-0.384178\pi$
$661$	−35.2123	−	14.5854i	−0.0532712	−	0.0220657i	−0.409160	+	0.912463i	$0.634178\pi$
$662$	−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	−0.685310	−	0.728252i	$-0.740333\pi$
$677$	212.733	−	513.583i	0.314229	−	0.758617i	0.999539	−	0.0303647i	$-0.00966689\pi$
$678$		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	0.397959	+	0.917403i	$0.369719\pi$
$683$	−363.453	+	877.454i	−0.532142	+	1.28471i	−0.930102	+	0.367302i	$0.880281\pi$
$684$		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	−0.817168	−	0.576399i	$-0.804457\pi$
$691$	−682.306	+	282.620i	−0.987418	+	0.409002i	−0.170249	+	0.985401i	$0.554457\pi$
$692$	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	0.0591703	−	0.998248i	$-0.481154\pi$
$701$	565.621	−	234.288i	0.806878	−	0.334220i	0.747708	+	0.664028i	$0.231154\pi$
$702$		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	−0.206360	−	0.978476i	$-0.566162\pi$
$709$	447.695	−	1080.83i	0.631446	−	1.52444i	0.837806	−	0.545968i	$-0.183838\pi$
$710$	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	0.941038	−	0.338301i	$-0.109852\pi$
$727$	438.189	+	438.189i	0.602736	+	0.602736i	−0.338301	+	0.941038i	$0.609852\pi$
$728$	−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	−0.768099	−	0.640331i	$-0.778797\pi$
$733$	−629.241	+	260.640i	−0.858446	+	0.355580i	−0.0903463	+	0.995910i	$0.528797\pi$
$734$	−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	0.957018	−	0.290028i	$-0.0936646\pi$
$739$	55.5902	+	134.207i	0.0752235	+	0.181606i	−0.881795	+	0.471633i	$0.843665\pi$
$740$	−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	−0.575291	−	0.817949i	$-0.695111\pi$
$743$	180.295	−	180.295i	0.242658	−	0.242658i	0.817949	+	0.575291i	$0.195111\pi$
$744$		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	−0.123761	−	0.992312i	$-0.539496\pi$
$757$	−691.098	−	286.262i	−0.912944	−	0.378154i	−0.789183	+	0.614158i	$0.789496\pi$
$758$	−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	0.492645	−	0.870230i	$-0.336030\pi$
$761$	−287.342	−	287.342i	−0.377585	−	0.377585i	−0.870230	+	0.492645i	$0.836030\pi$
$762$		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	−0.572342	−	0.820015i	$-0.693965\pi$
$773$	318.633	−	769.248i	0.412203	−	0.995146i	0.984545	−	0.175131i	$-0.0560350\pi$
$774$		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	0.0210600	−	0.999778i	$-0.493296\pi$
$787$	584.664	−	242.176i	0.742902	−	0.307720i	0.721842	+	0.692058i	$0.243296\pi$
$788$	−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	0.0658733	−	0.997828i	$-0.479017\pi$
$797$	651.965	−	270.053i	0.818024	−	0.338837i	0.752150	+	0.658991i	$0.229017\pi$
$798$		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	−0.0883227	−	0.996092i	$-0.528151\pi$
$809$	734.385	−	734.385i	0.907769	−	0.907769i	0.996092	+	0.0883227i	$0.0281507\pi$
$810$		0			0
$811$	430.173	−	1038.53i	0.530423	−	1.28055i	−0.400820	−	0.916157i	$-0.631275\pi$
$811$	430.173	−	1038.53i	0.530423	−	1.28055i	0.931243	−	0.364398i	$-0.118725\pi$
$812$	−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	0.363787	−	0.931482i	$-0.381483\pi$
$821$	−30.8969	−	12.7979i	−0.0376333	−	0.0155882i	−0.401421	+	0.915894i	$0.631483\pi$
$822$		0			0
$823$	581.324	+	581.324i	0.706348	+	0.706348i	0.965765	−	0.259417i	$-0.0835305\pi$
$823$	581.324	+	581.324i	0.706348	+	0.706348i	−0.259417	+	0.965765i	$0.583530\pi$
$824$	−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	−0.0292791	−	0.999571i	$-0.509321\pi$
$827$	−625.862	−	259.241i	−0.756786	−	0.313471i	−0.727507	+	0.686100i	$0.759321\pi$
$828$		0			0
$829$	1209.84	−	501.131i	1.45939	−	0.604500i	0.494981	−	0.868904i	$-0.335175\pi$
$829$	1209.84	−	501.131i	1.45939	−	0.604500i	0.964412	+	0.264403i	$0.0851750\pi$
$830$	−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	−0.649981	−	0.759951i	$-0.725223\pi$
$839$	92.2651	−	92.2651i	0.109970	−	0.109970i	0.759951	+	0.649981i	$0.225223\pi$
$840$		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	0.607005	−	0.794698i	$-0.292371\pi$
$853$	404.566	+	167.577i	0.474286	+	0.196456i	−0.132719	+	0.991154i	$0.542371\pi$
$854$	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	0.999868	+	0.0162551i	$0.00517439\pi$
$857$	870.817	+	870.817i	1.01612	+	1.01612i	0.0162551	+	0.999868i	$0.494826\pi$
$858$		0			0
$859$	−1000.98	−	414.619i	−1.16528	−	0.482677i	−0.285653	−	0.958333i	$-0.592211\pi$
$859$	−1000.98	−	414.619i	−1.16528	−	0.482677i	−0.879631	+	0.475657i	$0.842211\pi$
$860$	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	$-0.975899\pi$
$863$		−	130.559i		−	0.151285i	0.997135	−	0.0756423i	$-0.0241007\pi$
$864$		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	0.712884	−	0.701282i	$-0.247388\pi$
$877$	−251.771	−	607.829i	−0.287082	−	0.693077i	−0.999966	+	0.00820433i	$0.997388\pi$
$878$	−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	$0.0635284\pi$
$881$			349.331i			0.396516i	−0.980150	+	0.198258i	$0.936472\pi$
$882$		0			0
$883$	−1394.24	+	577.514i	−1.57898	+	0.654036i	−0.988252	−	0.152832i	$-0.951161\pi$
$883$	−1394.24	+	577.514i	−1.57898	+	0.654036i	−0.590731	+	0.806869i	$0.701161\pi$
$884$	−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	0.993807	+	0.111120i	$0.0354439\pi$
$887$	980.070	+	980.070i	1.10493	+	1.10493i	0.111120	+	0.993807i	$0.464556\pi$
$888$		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	−0.884045	−	0.467402i	$-0.845190\pi$
$907$	64.9162	−	156.722i	0.0715725	−	0.172791i	0.955617	+	0.294611i	$0.0951900\pi$
$908$	−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	0.952122	−	0.305720i	$-0.0988970\pi$
$919$	594.043	+	594.043i	0.646402	+	0.646402i	−0.305720	+	0.952122i	$0.598897\pi$
$920$	−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	−0.890156	−	0.455656i	$-0.849405\pi$
$937$	−407.126	+	407.126i	−0.434500	+	0.434500i	0.455656	+	0.890156i	$0.349405\pi$
$938$	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	−0.922618	−	0.385715i	$-0.873955\pi$
$941$	−510.935	−	1233.51i	−0.542970	−	1.31085i	0.379648	−	0.925131i	$-0.376045\pi$
$942$		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	−0.0259471	−	0.999663i	$-0.508260\pi$
$947$	627.458	−	259.902i	0.662574	−	0.274447i	0.688521	+	0.725216i	$0.258260\pi$
$948$		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	0.956330	+	0.292290i	$0.0944171\pi$
$953$	1189.93	+	1189.93i	1.24862	+	1.24862i	0.292290	+	0.956330i	$0.405583\pi$
$954$		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	−0.298841	−	0.954303i	$-0.596600\pi$
$967$	633.832	−	633.832i	0.655462	−	0.655462i	0.954303	+	0.298841i	$0.0965999\pi$
$968$	−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	−0.573301	−	0.819345i	$-0.694337\pi$
$971$	399.517	−	964.518i	0.411449	−	0.993325i	0.984749	−	0.173980i	$-0.0556627\pi$
$972$		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	$-0.980104\pi$
$977$		−	122.057i		−	0.124931i	0.998047	−	0.0624653i	$-0.0198963\pi$
$978$		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	−0.940835	−	0.338864i	$-0.889957\pi$
$983$	−1257.94	−	1257.94i	−1.27970	−	1.27970i	−0.338864	−	0.940835i	$-0.610043\pi$
$984$		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	$-0.748105\pi$
$991$		−	1409.81i		−	1.42261i	0.702884	−	0.711304i	$-0.251895\pi$
$992$	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	−0.951508	−	0.307625i	$-0.900466\pi$
$997$	−60.9825	+	147.225i	−0.0611660	+	0.147668i	0.890341	+	0.455293i	$0.150466\pi$
$998$	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.235.5		28
3.2	odd	2		32.3.h.a.11.3	yes	28
12.11	even	2		128.3.h.a.79.2		28
24.5	odd	2		256.3.h.b.159.2		28
24.11	even	2		256.3.h.a.159.6		28
32.3	odd	8	inner	288.3.u.a.163.5		28
96.29	odd	8		128.3.h.a.47.2		28
96.35	even	8		32.3.h.a.3.3	✓	28
96.77	odd	8		256.3.h.a.95.6		28
96.83	even	8		256.3.h.b.95.2		28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
32.3.h.a.3.3	✓	28	96.35	even	8
32.3.h.a.11.3	yes	28	3.2	odd	2
128.3.h.a.47.2		28	96.29	odd	8
128.3.h.a.79.2		28	12.11	even	2
256.3.h.a.95.6		28	96.77	odd	8
256.3.h.a.159.6		28	24.11	even	2
256.3.h.b.95.2		28	96.83	even	8
256.3.h.b.159.2		28	24.5	odd	2
288.3.u.a.163.5		28	32.3	odd	8	inner
288.3.u.a.235.5		28	1.1	even	1	trivial

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