LMFDB - Embedded newform 351.4.l.a.127.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [351,4,Mod(127,351)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(351, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([4, 5]))

N = Newforms(chi, 4, names="a")

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

chi := DirichletCharacter("351.127");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 351 = 3^{3} \cdot 13 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	351.l (of order $6$, degree $2$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$20.7096704120$
Analytic rank:	$0$
Dimension:	$80$
Relative dimension:	$40$ over $\Q(\zeta_{6})$
Twist minimal:	no (minimal twist has level 117)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			127.10
Character	$\chi$	$=$	351.127
Dual form			351.4.l.a.199.31

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-3.67076i q^{2} -5.47446 q^{4} +(-15.6805 + 9.05312i) q^{5} +(27.0172 - 15.5984i) q^{7} -9.27065i q^{8} +O(q^{10})$	\(q-3.67076i q^{2} -5.47446 q^{4} +(-15.6805 + 9.05312i) q^{5} +(27.0172 - 15.5984i) q^{7} -9.27065i q^{8} +(33.2318 + 57.5592i) q^{10} +5.30011i q^{11} +(-3.93395 - 46.7068i) q^{13} +(-57.2580 - 99.1737i) q^{14} -77.8260 q^{16} +(1.95690 - 3.38945i) q^{17} +(19.5736 + 11.3008i) q^{19} +(85.8420 - 49.5609i) q^{20} +19.4554 q^{22} +(27.9664 - 48.4393i) q^{23} +(101.418 - 175.661i) q^{25} +(-171.449 + 14.4406i) q^{26} +(-147.905 + 85.3928i) q^{28} -294.507 q^{29} +(-150.573 + 86.9333i) q^{31} +211.515i q^{32} +(-12.4419 - 7.18331i) q^{34} +(-282.428 + 489.180i) q^{35} +(-328.880 + 189.879i) q^{37} +(41.4826 - 71.8500i) q^{38} +(83.9283 + 145.368i) q^{40} +(-114.876 - 66.3235i) q^{41} +(30.3001 + 52.4813i) q^{43} -29.0152i q^{44} +(-177.809 - 102.658i) q^{46} +(-229.733 - 132.636i) q^{47} +(315.121 - 545.805i) q^{49} +(-644.809 - 372.281i) q^{50} +(21.5362 + 255.694i) q^{52} +446.339 q^{53} +(-47.9825 - 83.1082i) q^{55} +(-144.607 - 250.467i) q^{56} +1081.06i q^{58} -253.923i q^{59} +(-176.091 - 304.998i) q^{61} +(319.111 + 552.716i) q^{62} +153.812 q^{64} +(484.528 + 696.770i) q^{65} +(-387.416 - 223.675i) q^{67} +(-10.7130 + 18.5554i) q^{68} +(1795.66 + 1036.73i) q^{70} +(260.787 + 150.566i) q^{71} -86.9083i q^{73} +(697.000 + 1207.24i) q^{74} +(-107.155 - 61.8659i) q^{76} +(82.6732 + 143.194i) q^{77} +(-243.931 + 422.500i) q^{79} +(1220.35 - 704.568i) q^{80} +(-243.457 + 421.681i) q^{82} +(-842.406 - 486.363i) q^{83} +70.8642i q^{85} +(192.646 - 111.224i) q^{86} +49.1355 q^{88} +(789.927 - 456.065i) q^{89} +(-834.836 - 1200.52i) q^{91} +(-153.101 + 265.179i) q^{92} +(-486.875 + 843.293i) q^{94} -409.231 q^{95} +(-11.9039 + 6.87274i) q^{97} +(-2003.52 - 1156.73i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 80 q - 306 q^{4} - 3 q^{7}+O(q^{10}) $ 80 * q - 306 * q^4 - 3 * q^7	$ 80 q - 306 q^{4} - 3 q^{7} - 10 q^{10} - 13 q^{13} - 126 q^{14} + 1102 q^{16} + 138 q^{17} - 96 q^{19} + 387 q^{20} + 62 q^{22} + 327 q^{23} + 798 q^{25} - 510 q^{26} + 18 q^{28} + 402 q^{29} + 180 q^{31} + 24 q^{34} - 297 q^{35} + 246 q^{37} + 768 q^{38} + 328 q^{40} - 381 q^{41} - 83 q^{43} - 6 q^{46} - 372 q^{47} + 1613 q^{49} + 708 q^{50} + 402 q^{52} + 2568 q^{53} - 127 q^{55} + 2298 q^{56} - 419 q^{61} - 135 q^{62} - 3178 q^{64} - 363 q^{65} + 879 q^{67} - 1950 q^{68} - 1005 q^{70} + 2598 q^{71} - 471 q^{74} + 1485 q^{76} + 1584 q^{77} - 260 q^{79} + 1332 q^{80} - 1273 q^{82} - 1194 q^{83} + 2910 q^{86} - 1562 q^{88} + 1056 q^{89} + 537 q^{91} - 1056 q^{92} + 539 q^{94} - 10584 q^{95} + 789 q^{97} + 6339 q^{98}+O(q^{100}) $ 80 * q - 306 * q^4 - 3 * q^7 - 10 * q^10 - 13 * q^13 - 126 * q^14 + 1102 * q^16 + 138 * q^17 - 96 * q^19 + 387 * q^20 + 62 * q^22 + 327 * q^23 + 798 * q^25 - 510 * q^26 + 18 * q^28 + 402 * q^29 + 180 * q^31 + 24 * q^34 - 297 * q^35 + 246 * q^37 + 768 * q^38 + 328 * q^40 - 381 * q^41 - 83 * q^43 - 6 * q^46 - 372 * q^47 + 1613 * q^49 + 708 * q^50 + 402 * q^52 + 2568 * q^53 - 127 * q^55 + 2298 * q^56 - 419 * q^61 - 135 * q^62 - 3178 * q^64 - 363 * q^65 + 879 * q^67 - 1950 * q^68 - 1005 * q^70 + 2598 * q^71 - 471 * q^74 + 1485 * q^76 + 1584 * q^77 - 260 * q^79 + 1332 * q^80 - 1273 * q^82 - 1194 * q^83 + 2910 * q^86 - 1562 * q^88 + 1056 * q^89 + 537 * q^91 - 1056 * q^92 + 539 * q^94 - 10584 * q^95 + 789 * q^97 + 6339 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/351\mathbb{Z}\right)^\times$.

$n$	$28$	$326$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{2}{3}\right)$

Coefficient data

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

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

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

$2$		−	3.67076i		−	1.29781i	−0.760870	−	0.648904i	$-0.775228\pi$
$2$		−	3.67076i		−	1.29781i	0.760870	−	0.648904i	$-0.224772\pi$
$3$		0			0
$3$		0			0
$4$	−5.47446			−0.684307
$5$	−15.6805	+	9.05312i	−1.40250	+	0.809736i	−0.994649	−	0.103311i	$-0.967056\pi$
$5$	−15.6805	+	9.05312i	−1.40250	+	0.809736i	−0.407854	+	0.913047i	$0.633723\pi$
$6$		0			0
$7$	27.0172	−	15.5984i	1.45879	−	0.842235i	0.459841	−	0.888001i	$-0.347906\pi$
$7$	27.0172	−	15.5984i	1.45879	−	0.842235i	0.998952	+	0.0457664i	$0.0145730\pi$
$8$		−	9.27065i		−	0.409709i
$9$		0			0
$10$	33.2318	+	57.5592i	1.05088	+	1.82018i
$11$			5.30011i			0.145277i	0.997358	+	0.0726383i	$0.0231419\pi$
$11$			5.30011i			0.145277i	−0.997358	+	0.0726383i	$0.976858\pi$
$12$		0			0
$13$	−3.93395	−	46.7068i	−0.0839293	−	0.996472i
$13$	−3.93395	−	46.7068i	−0.0839293	−	0.996472i
$14$	−57.2580	−	99.1737i	−1.09306	−	1.89323i
$15$		0			0
$16$	−77.8260			−1.21603
$17$	1.95690	−	3.38945i	0.0279187	−	0.0483566i	−0.851728	−	0.523983i	$-0.824445\pi$
$17$	1.95690	−	3.38945i	0.0279187	−	0.0483566i	0.879647	+	0.475627i	$0.157779\pi$
$18$		0			0
$19$	19.5736	+	11.3008i	0.236342	+	0.136452i	0.613494	−	0.789699i	$-0.289763\pi$
$19$	19.5736	+	11.3008i	0.236342	+	0.136452i	−0.377152	+	0.926151i	$0.623097\pi$
$20$	85.8420	−	49.5609i	0.959743	−	0.554108i
$21$		0			0
$22$	19.4554			0.188541
$23$	27.9664	−	48.4393i	0.253539	−	0.439143i	−0.710958	−	0.703234i	$-0.751739\pi$
$23$	27.9664	−	48.4393i	0.253539	−	0.439143i	0.964498	+	0.264091i	$0.0850719\pi$
$24$		0			0
$25$	101.418	−	175.661i	0.811344	−	1.40529i
$26$	−171.449	+	14.4406i	−1.29323	+	0.108924i
$27$		0			0
$28$	−147.905	+	85.3928i	−0.998263	+	0.576347i
$29$	−294.507			−1.88581			−0.942905	−	0.333060i	$-0.891919\pi$
$29$	−294.507			−1.88581			−0.942905	+	0.333060i	$0.891919\pi$
$30$		0			0
$31$	−150.573	+	86.9333i	−0.872377	+	0.503667i	−0.868137	−	0.496324i	$-0.834683\pi$
$31$	−150.573	+	86.9333i	−0.872377	+	0.503667i	−0.00423943	+	0.999991i	$0.501349\pi$
$32$			211.515i			1.16847i
$33$		0			0
$34$	−12.4419	−	7.18331i	−0.0627577	−	0.0362332i
$35$	−282.428	+	489.180i	−1.36398	+	2.36247i
$36$		0			0
$37$	−328.880	+	189.879i	−1.46129	+	0.843674i	−0.999071	−	0.0430940i	$-0.986279\pi$
$37$	−328.880	+	189.879i	−1.46129	+	0.843674i	−0.462215	+	0.886768i	$0.652945\pi$
$38$	41.4826	−	71.8500i	0.177089	−	0.306726i
$39$		0			0
$40$	83.9283	+	145.368i	0.331756	+	0.574618i
$41$	−114.876	−	66.3235i	−0.437575	−	0.252634i	0.264994	−	0.964250i	$-0.414630\pi$
$41$	−114.876	−	66.3235i	−0.437575	−	0.252634i	−0.702568	+	0.711616i	$0.747963\pi$
$42$		0			0
$43$	30.3001	+	52.4813i	0.107459	+	0.186124i	0.914740	−	0.404043i	$-0.132395\pi$
$43$	30.3001	+	52.4813i	0.107459	+	0.186124i	−0.807281	+	0.590167i	$0.799062\pi$
$44$		−	29.0152i		−	0.0994138i
$45$		0			0
$46$	−177.809	−	102.658i	−0.569924	−	0.329046i
$47$	−229.733	−	132.636i	−0.712978	−	0.411638i	0.0991849	−	0.995069i	$-0.468376\pi$
$47$	−229.733	−	132.636i	−0.712978	−	0.411638i	−0.812163	+	0.583431i	$0.801710\pi$
$48$		0			0
$49$	315.121	−	545.805i	0.918719	−	1.59127i
$50$	−644.809	−	372.281i	−1.82380	−	1.05297i
$51$		0			0
$52$	21.5362	+	255.694i	0.0574334	+	0.681893i
$53$	446.339			1.15678			0.578390	−	0.815761i	$-0.303681\pi$
$53$	446.339			1.15678			0.578390	+	0.815761i	$0.303681\pi$
$54$		0			0
$55$	−47.9825	−	83.1082i	−0.117636	−	0.203751i
$56$	−144.607	−	250.467i	−0.345071	−	0.597681i
$57$		0			0
$58$			1081.06i			2.44742i
$59$		−	253.923i		−	0.560304i	−0.959956	−	0.280152i	$-0.909615\pi$
$59$		−	253.923i		−	0.560304i	0.959956	−	0.280152i	$-0.0903849\pi$
$60$		0			0
$61$	−176.091	−	304.998i	−0.369608	−	0.640180i	0.619896	−	0.784684i	$-0.287175\pi$
$61$	−176.091	−	304.998i	−0.369608	−	0.640180i	−0.989504	+	0.144504i	$0.953841\pi$
$62$	319.111	+	552.716i	0.653663	+	1.13218i
$63$		0			0
$64$	153.812			0.300415
$65$	484.528	+	696.770i	0.924590	+	1.32959i
$66$		0			0
$67$	−387.416	−	223.675i	−0.706424	−	0.407854i	0.103312	−	0.994649i	$-0.467056\pi$
$67$	−387.416	−	223.675i	−0.706424	−	0.407854i	−0.809735	+	0.586795i	$0.800389\pi$
$68$	−10.7130	+	18.5554i	−0.0191050	+	0.0330908i
$69$		0			0
$70$	1795.66	+	1036.73i	3.06604	+	1.77018i
$71$	260.787	+	150.566i	0.435912	+	0.251674i	0.701862	−	0.712313i	$-0.252352\pi$
$71$	260.787	+	150.566i	0.435912	+	0.251674i	−0.265950	+	0.963987i	$0.585686\pi$
$72$		0			0
$73$		−	86.9083i		−	0.139340i	−0.997570	−	0.0696702i	$-0.977805\pi$
$73$		−	86.9083i		−	0.139340i	0.997570	−	0.0696702i	$-0.0221947\pi$
$74$	697.000	+	1207.24i	1.09493	+	1.89647i
$75$		0			0
$76$	−107.155	−	61.8659i	−0.161730	−	0.0933751i
$77$	82.6732	+	143.194i	0.122357	+	0.211929i
$78$		0			0
$79$	−243.931	+	422.500i	−0.347397	+	0.601709i	−0.985786	−	0.168005i	$-0.946268\pi$
$79$	−243.931	+	422.500i	−0.347397	+	0.601709i	0.638389	+	0.769714i	$0.279601\pi$
$80$	1220.35	−	704.568i	1.70549	−	0.984664i
$81$		0			0
$82$	−243.457	+	421.681i	−0.327870	+	0.567888i
$83$	−842.406	−	486.363i	−1.11405	−	0.643196i	−0.174174	−	0.984715i	$-0.555725\pi$
$83$	−842.406	−	486.363i	−1.11405	−	0.643196i	−0.939875	+	0.341519i	$0.889059\pi$
$84$		0			0
$85$			70.8642i			0.0904271i
$86$	192.646	−	111.224i	0.241553	−	0.139461i
$87$		0			0
$88$	49.1355			0.0595211
$89$	789.927	−	456.065i	0.940810	−	0.543177i	0.0505959	−	0.998719i	$-0.483888\pi$
$89$	789.927	−	456.065i	0.940810	−	0.543177i	0.890214	+	0.455542i	$0.150555\pi$
$90$		0			0
$91$	−834.836	−	1200.52i	−0.961699	−	1.38296i
$92$	−153.101	+	265.179i	−0.173499	+	0.300509i
$93$		0			0
$94$	−486.875	+	843.293i	−0.534227	+	0.925309i
$95$	−409.231			−0.441960
$96$		0			0
$97$	−11.9039	+	6.87274i	−0.0124604	+	0.00719403i	−0.506217	−	0.862406i	$-0.668957\pi$
$97$	−11.9039	+	6.87274i	−0.0124604	+	0.00719403i	0.493757	+	0.869600i	$0.335623\pi$
$98$	−2003.52	−	1156.73i	−2.06516	−	1.19232i
$99$		0			0
$100$	−555.208	+	961.649i	−0.555208	+	0.961649i
$101$	−905.068			−0.891660			−0.445830	−	0.895118i	$-0.647091\pi$
$101$	−905.068			−0.891660			−0.445830	+	0.895118i	$0.647091\pi$
$102$		0			0
$103$	784.818	+	1359.35i	0.750781	+	1.30039i	0.947445	+	0.319920i	$0.103656\pi$
$103$	784.818	+	1359.35i	0.750781	+	1.30039i	−0.196664	+	0.980471i	$0.563011\pi$
$104$	−433.002	+	36.4703i	−0.408263	+	0.0343866i
$105$		0			0
$106$		−	1638.40i		−	1.50128i
$107$	−436.686	−	756.363i	−0.394542	−	0.683368i	0.598500	−	0.801123i	$-0.295764\pi$
$107$	−436.686	−	756.363i	−0.394542	−	0.683368i	−0.993043	+	0.117755i	$0.962430\pi$
$108$		0			0
$109$		−	1947.88i		−	1.71168i	−0.517240	−	0.855841i	$-0.673040\pi$
$109$		−	1947.88i		−	1.71168i	0.517240	−	0.855841i	$-0.326960\pi$
$110$	−305.070	+	176.132i	−0.264430	+	0.152669i
$111$		0			0
$112$	−2102.64	+	1213.96i	−1.77394	+	1.02418i
$113$	1325.76			1.10369			0.551846	−	0.833946i	$-0.313924\pi$
$113$	1325.76			1.10369			0.551846	+	0.833946i	$0.313924\pi$
$114$		0			0
$115$			1012.73i			0.821200i
$116$	1612.26			1.29047
$117$		0			0
$118$	−932.089			−0.727167
$119$		−	122.098i		−	0.0940565i
$120$		0			0
$121$	1302.91			0.978895
$122$	−1119.57	+	646.386i	−0.830831	+	0.479681i
$123$		0			0
$124$	824.305	−	475.912i	0.596974	−	0.344663i
$125$			1409.32i			1.00842i
$126$		0			0
$127$	881.977	+	1527.63i	0.616243	+	1.06736i	0.990165	+	0.139904i	$0.0446794\pi$
$127$	881.977	+	1527.63i	0.616243	+	1.06736i	−0.373922	+	0.927460i	$0.621987\pi$
$128$			1127.51i			0.778585i
$129$		0			0
$130$	2557.67	−	1778.59i	1.72556	−	1.19994i
$131$	−464.088	−	803.823i	−0.309523	−	0.536110i	0.668735	−	0.743501i	$-0.266836\pi$
$131$	−464.088	−	803.823i	−0.309523	−	0.536110i	−0.978258	+	0.207391i	$0.933503\pi$
$132$		0			0
$133$	705.100			0.459699
$134$	−821.055	+	1422.11i	−0.529316	+	0.916803i
$135$		0			0
$136$	−31.4224	−	18.1418i	−0.0198121	−	0.0114385i
$137$	790.102	−	456.166i	0.492722	−	0.284473i	−0.232981	−	0.972481i	$-0.574848\pi$
$137$	790.102	−	456.166i	0.492722	−	0.284473i	0.725703	+	0.688008i	$0.241515\pi$
$138$		0			0
$139$	−2425.50			−1.48006			−0.740030	−	0.672574i	$-0.765189\pi$
$139$	−2425.50			−1.48006			−0.740030	+	0.672574i	$0.765189\pi$
$140$	1546.14	−	2678.00i	0.933378	−	1.61666i
$141$		0			0
$142$	552.689	−	957.286i	0.326624	−	0.565730i
$143$	247.551	−	20.8504i	0.144764	−	0.0121930i
$144$		0			0
$145$	4618.00	−	2666.20i	2.64486	−	1.52701i
$146$	−319.019			−0.180837
$147$		0			0
$148$	1800.44	−	1039.49i	0.999969	−	0.577332i
$149$			593.988i			0.326587i	0.986578	+	0.163293i	$0.0522117\pi$
$149$			593.988i			0.326587i	−0.986578	+	0.163293i	$0.947788\pi$
$150$		0			0
$151$	−1410.87	−	814.564i	−0.760362	−	0.438995i	0.0690639	−	0.997612i	$-0.477999\pi$
$151$	−1410.87	−	814.564i	−0.760362	−	0.438995i	−0.829426	+	0.558617i	$0.811332\pi$
$152$	104.766	−	181.460i	0.0559056	−	0.0968313i
$153$		0			0
$154$	525.631	−	303.473i	0.275043	−	0.158796i
$155$	1574.03	−	2726.31i	0.815674	−	1.41279i
$156$		0			0
$157$	−1393.74	−	2414.03i	−0.708489	−	1.22714i	−0.965417	−	0.260709i	$-0.916044\pi$
$157$	−1393.74	−	2414.03i	−0.708489	−	1.22714i	0.256928	−	0.966430i	$-0.417290\pi$
$158$	1550.90	+	895.410i	0.780903	+	0.450854i
$159$		0			0
$160$	−1914.87	−	3316.65i	−0.946149	−	1.63878i
$161$		−	1744.93i		−	0.854159i
$162$		0			0
$163$	−658.915	−	380.425i	−0.316627	−	0.182805i	0.333261	−	0.942835i	$-0.391851\pi$
$163$	−658.915	−	380.425i	−0.316627	−	0.182805i	−0.649888	+	0.760030i	$0.725184\pi$
$164$	628.882	+	363.085i	0.299436	+	0.172879i
$165$		0			0
$166$	−1785.32	+	3092.27i	−0.834746	+	1.44582i
$167$	−877.056	−	506.369i	−0.406399	−	0.234635i	0.282842	−	0.959166i	$-0.408723\pi$
$167$	−877.056	−	506.369i	−0.406399	−	0.234635i	−0.689241	+	0.724532i	$0.742056\pi$
$168$		0			0
$169$	−2166.05	+	367.484i	−0.985912	+	0.167266i
$170$	260.125			0.117357
$171$		0			0
$172$	−165.876	−	287.307i	−0.0735347	−	0.127366i
$173$	880.012	+	1524.23i	0.386740	+	0.669854i	0.992009	−	0.126167i	$-0.0402676\pi$
$173$	880.012	+	1524.23i	0.386740	+	0.669854i	−0.605269	+	0.796021i	$0.706934\pi$
$174$		0			0
$175$		−	6327.83i		−	2.73337i
$176$		−	412.486i		−	0.176661i
$177$		0			0
$178$	−1674.10	−	2899.63i	−0.704940	−	1.22099i
$179$	1156.00	+	2002.26i	0.482702	+	0.836065i	0.999803	−	0.0198600i	$-0.00632204\pi$
$179$	1156.00	+	2002.26i	0.482702	+	0.836065i	−0.517101	+	0.855925i	$0.672989\pi$
$180$		0			0
$181$	−590.593			−0.242533			−0.121266	−	0.992620i	$-0.538696\pi$
$181$	−590.593			−0.242533			−0.121266	+	0.992620i	$0.538696\pi$
$182$	−4406.83	+	3064.48i	−1.79481	+	1.24810i
$183$		0			0
$184$	−449.064	−	259.267i	−0.179921	−	0.103877i
$185$	3438.00	−	5954.79i	1.36631	−	2.36651i
$186$		0			0
$187$	17.9645	+	10.3718i	0.00702509	+	0.00405594i
$188$	1257.66	+	726.111i	0.487896	+	0.281687i
$189$		0			0
$190$			1502.19i			0.573580i
$191$	1408.36	+	2439.36i	0.533537	+	0.924114i	0.999233	+	0.0391685i	$0.0124709\pi$
$191$	1408.36	+	2439.36i	0.533537	+	0.924114i	−0.465695	+	0.884945i	$0.654196\pi$
$192$		0			0
$193$	3108.07	+	1794.44i	1.15919	+	0.669259i	0.951110	−	0.308853i	$-0.0999452\pi$
$193$	3108.07	+	1794.44i	1.15919	+	0.669259i	0.208080	+	0.978112i	$0.433279\pi$
$194$	25.2282	+	43.6965i	0.00933648	+	0.0161713i
$195$		0			0
$196$	−1725.11	+	2987.99i	−0.628686	+	1.08892i
$197$	3226.92	−	1863.06i	1.16705	−	0.673795i	0.214064	−	0.976820i	$-0.431330\pi$
$197$	3226.92	−	1863.06i	1.16705	−	0.673795i	0.952983	+	0.303025i	$0.0979965\pi$
$198$		0			0
$199$	818.404	−	1417.52i	0.291533	−	0.504950i	−0.682639	−	0.730755i	$-0.739168\pi$
$199$	818.404	−	1417.52i	0.291533	−	0.504950i	0.974172	+	0.225805i	$0.0725013\pi$
$200$	−1628.49	−	940.211i	−0.575759	−	0.332415i
$201$		0			0
$202$			3322.29i			1.15720i
$203$	−7956.76	+	4593.83i	−2.75101	+	1.58830i
$204$		0			0
$205$	2401.74			0.818267
$206$	4989.83	−	2880.88i	1.68766	−	0.974370i
$207$		0			0
$208$	306.163	+	3635.00i	0.102061	+	1.21174i
$209$	−59.8956	+	103.742i	−0.0198233	+	0.0343349i
$210$		0			0
$211$	1865.72	−	3231.53i	0.608728	−	1.05435i	−0.382722	−	0.923863i	$-0.625013\pi$
$211$	1865.72	−	3231.53i	0.608728	−	1.05435i	0.991450	−	0.130485i	$-0.0416533\pi$
$212$	−2443.46			−0.791593
$213$		0			0
$214$	−2776.42	+	1602.97i	−0.886880	+	0.512041i
$215$	−950.239	−	548.620i	−0.301422	−	0.174026i
$216$		0			0
$217$	−2712.04	+	4697.39i	−0.848412	+	1.46949i
$218$	−7150.20			−2.22143
$219$		0			0
$220$	262.678	+	454.972i	0.0804989	+	0.139428i
$221$	−166.009	−	78.0666i	−0.0505292	−	0.0237617i
$222$		0			0
$223$		−	2239.68i		−	0.672556i	−0.941763	−	0.336278i	$-0.890832\pi$
$223$		−	2239.68i		−	0.672556i	0.941763	−	0.336278i	$-0.109168\pi$
$224$	3299.30	+	5714.55i	0.984123	+	1.70455i
$225$		0			0
$226$		−	4866.55i		−	1.43238i
$227$	1311.34	−	757.100i	0.383420	−	0.221368i	−0.295885	−	0.955224i	$-0.595615\pi$
$227$	1311.34	−	757.100i	0.383420	−	0.221368i	0.679305	+	0.733856i	$0.262281\pi$
$228$		0			0
$229$	2765.65	−	1596.75i	0.798077	−	0.460770i	−0.0447214	−	0.998999i	$-0.514240\pi$
$229$	2765.65	−	1596.75i	0.798077	−	0.460770i	0.842798	+	0.538230i	$0.180907\pi$
$230$	3717.50			1.06576
$231$		0			0
$232$			2730.27i			0.772633i
$233$	−4521.57			−1.27132			−0.635661	−	0.771968i	$-0.719272\pi$
$233$	−4521.57			−1.27132			−0.635661	+	0.771968i	$0.719272\pi$
$234$		0			0
$235$	4803.09			1.33327
$236$			1390.09i			0.383420i
$237$		0			0
$238$	−448.193			−0.122067
$239$	616.585	−	355.985i	0.166877	−	0.0963464i	−0.414236	−	0.910170i	$-0.635951\pi$
$239$	616.585	−	355.985i	0.166877	−	0.0963464i	0.581112	+	0.813823i	$0.302618\pi$
$240$		0			0
$241$	−575.708	+	332.385i	−0.153878	+	0.0888416i	−0.574962	−	0.818180i	$-0.694983\pi$
$241$	−575.708	+	332.385i	−0.153878	+	0.0888416i	0.421084	+	0.907022i	$0.361650\pi$
$242$		−	4782.66i		−	1.27042i
$243$		0			0
$244$	964.001	+	1669.70i	0.252926	+	0.438080i
$245$			11411.3i			2.97568i
$246$		0			0
$247$	450.824	−	958.678i	0.116135	−	0.246960i
$248$	805.928	+	1395.91i	0.206357	+	0.357420i
$249$		0			0
$250$	5173.26			1.30874
$251$	3552.61	−	6153.31i	0.893383	−	1.54738i	0.0575887	−	0.998340i	$-0.481659\pi$
$251$	3552.61	−	6153.31i	0.893383	−	1.54738i	0.835794	−	0.549044i	$-0.185008\pi$
$252$		0			0
$253$	256.734	+	148.225i	0.0637972	+	0.0368334i
$254$	5607.56	−	3237.53i	1.38523	−	0.799765i
$255$		0			0
$256$	5369.32			1.31087
$257$	3557.55	−	6161.86i	0.863478	−	1.49559i	−0.00507226	−	0.999987i	$-0.501615\pi$
$257$	3557.55	−	6161.86i	0.863478	−	1.49559i	0.868550	−	0.495601i	$-0.165052\pi$
$258$		0			0
$259$	−5923.62	+	10260.0i	−1.42114	+	2.46149i
$260$	−2652.53	−	3814.44i	−0.632703	−	0.909851i
$261$		0			0
$262$	−2950.64	+	1703.55i	−0.695768	+	0.401702i
$263$	5431.87			1.27355			0.636774	−	0.771050i	$-0.280268\pi$
$263$	5431.87			1.27355			0.636774	+	0.771050i	$0.280268\pi$
$264$		0			0
$265$	−6998.80	+	4040.76i	−1.62239	+	0.936686i
$266$		−	2588.25i		−	0.596601i
$267$		0			0
$268$	2120.89	+	1224.50i	0.483411	+	0.279097i
$269$	−2049.04	+	3549.04i	−0.464431	+	0.804419i	−0.999176	−	0.0405953i	$-0.987075\pi$
$269$	−2049.04	+	3549.04i	−0.464431	+	0.804419i	0.534744	+	0.845014i	$0.320408\pi$
$270$		0			0
$271$	−2034.93	+	1174.87i	−0.456138	+	0.263351i	−0.710419	−	0.703779i	$-0.751494\pi$
$271$	−2034.93	+	1174.87i	−0.456138	+	0.263351i	0.254281	+	0.967130i	$0.418161\pi$
$272$	−152.298	+	263.787i	−0.0339500	+	0.0588032i
$273$		0			0
$274$	−1674.47	−	2900.27i	−0.369192	−	0.639459i
$275$	931.023	+	537.526i	0.204156	+	0.117869i
$276$		0			0
$277$	1615.56	+	2798.24i	0.350432	+	0.606967i	0.986325	−	0.164811i	$-0.0527013\pi$
$277$	1615.56	+	2798.24i	0.350432	+	0.606967i	−0.635893	+	0.771777i	$0.719368\pi$
$278$			8903.42i			1.92083i
$279$		0			0
$280$	4535.02	+	2618.30i	0.967927	+	0.558833i
$281$	−660.709	−	381.461i	−0.140265	−	0.0809823i	0.428225	−	0.903672i	$-0.359139\pi$
$281$	−660.709	−	381.461i	−0.140265	−	0.0809823i	−0.568491	+	0.822690i	$0.692472\pi$
$282$		0			0
$283$	−2153.83	+	3730.54i	−0.452409	+	0.783596i	−0.998535	−	0.0541071i	$-0.982769\pi$
$283$	−2153.83	+	3730.54i	−0.452409	+	0.783596i	0.546126	+	0.837703i	$0.316102\pi$
$284$	−1427.67	−	824.265i	−0.298298	−	0.172222i
$285$		0			0
$286$	−76.5366	−	908.700i	−0.0158241	−	0.187876i
$287$	−4138.16			−0.851108
$288$		0			0
$289$	2448.84	+	4241.52i	0.498441	+	0.863325i
$290$	−9786.99	−	16951.6i	−1.98176	−	3.43252i
$291$		0			0
$292$			475.776i			0.0953517i
$293$		−	1952.55i		−	0.389314i	−0.980871	−	0.194657i	$-0.937641\pi$
$293$		−	1952.55i		−	0.389314i	0.980871	−	0.194657i	$-0.0623594\pi$
$294$		0			0
$295$	2298.79	+	3981.63i	0.453698	+	0.785828i
$296$	1760.30	+	3048.93i	0.345661	+	0.598702i
$297$		0			0
$298$	2180.39			0.423847
$299$	−2372.46	−	1115.67i	−0.458873	−	0.215788i
$300$		0			0
$301$	1637.25	+	945.266i	0.313520	+	0.181011i
$302$	−2990.07	+	5178.95i	−0.569732	+	0.986804i
$303$		0			0
$304$	−1523.34	−	879.498i	−0.287399	−	0.165930i
$305$	5522.37	+	3188.34i	1.03675	+	0.598570i
$306$		0			0
$307$			4583.08i			0.852021i	0.904718	+	0.426011i	$0.140081\pi$
$307$			4583.08i			0.852021i	−0.904718	+	0.426011i	$0.859919\pi$
$308$	−452.591	−	783.911i	−0.0837298	−	0.145024i
$309$		0			0
$310$	−10007.6	−	5777.90i	−1.83353	−	1.05859i
$311$	2718.46	+	4708.51i	0.495658	+	0.858504i	0.999987	−	0.00500685i	$-0.00159374\pi$
$311$	2718.46	+	4708.51i	0.495658	+	0.858504i	−0.504330	+	0.863511i	$0.668260\pi$
$312$		0			0
$313$	−1428.47	+	2474.18i	−0.257961	+	0.446802i	−0.965696	−	0.259677i	$-0.916384\pi$
$313$	−1428.47	+	2474.18i	−0.257961	+	0.446802i	0.707734	+	0.706479i	$0.249717\pi$
$314$	−8861.33	+	5116.09i	−1.59259	+	0.919483i
$315$		0			0
$316$	1335.39	−	2312.96i	0.237726	−	0.411754i
$317$	−211.113	−	121.886i	−0.0374046	−	0.0215956i	0.481181	−	0.876621i	$-0.340208\pi$
$317$	−211.113	−	121.886i	−0.0374046	−	0.0215956i	−0.518586	+	0.855026i	$0.673541\pi$
$318$		0			0
$319$		−	1560.92i		−	0.273964i
$320$	−2411.85	+	1392.48i	−0.421333	+	0.243257i
$321$		0			0
$322$	−6405.21			−1.10853
$323$	76.6073	−	44.2292i	0.0131967	−	0.00761913i
$324$		0			0
$325$	−8603.54	−	4045.87i	−1.46843	−	0.690536i
$326$	−1396.45	+	2418.72i	−0.237245	+	0.410921i
$327$		0			0
$328$	−614.862	+	1064.97i	−0.103506	+	0.179278i
$329$	−8275.65			−1.38678
$330$		0			0
$331$	7686.80	−	4437.97i	1.27645	−	0.736958i	0.300255	−	0.953859i	$-0.402928\pi$
$331$	7686.80	−	4437.97i	1.27645	−	0.736958i	0.976194	+	0.216901i	$0.0695949\pi$
$332$	4611.71	+	2662.57i	0.762351	+	0.440144i
$333$		0			0
$334$	−1858.76	+	3219.46i	−0.304511	+	0.527428i
$335$	8099.81			1.32102
$336$		0			0
$337$	−2517.56	−	4360.54i	−0.406944	−	0.704848i	0.587601	−	0.809151i	$-0.300072\pi$
$337$	−2517.56	−	4360.54i	−0.406944	−	0.704848i	−0.994546	+	0.104302i	$0.966739\pi$
$338$	1348.95	+	7951.04i	0.217080	+	1.27952i
$339$		0			0
$340$		−	387.943i		−	0.0618799i
$341$	−460.756	−	798.052i	−0.0731710	−	0.126736i
$342$		0			0
$343$		−	8961.01i		−	1.41064i
$344$	486.536	−	280.902i	0.0762565	−	0.0440267i
$345$		0			0
$346$	5595.06	−	3230.31i	0.869342	−	0.501915i
$347$	1047.29			0.162022			0.0810110	−	0.996713i	$-0.474185\pi$
$347$	1047.29			0.162022			0.0810110	+	0.996713i	$0.474185\pi$
$348$		0			0
$349$		−	3715.05i		−	0.569805i	−0.958557	−	0.284902i	$-0.908039\pi$
$349$		−	3715.05i		−	0.569805i	0.958557	−	0.284902i	$-0.0919612\pi$
$350$	−23227.9			−3.54739
$351$		0			0
$352$	−1121.05			−0.169751
$353$		−	3215.70i		−	0.484856i	−0.970169	−	0.242428i	$-0.922056\pi$
$353$		−	3215.70i		−	0.484856i	0.970169	−	0.242428i	$-0.0779439\pi$
$354$		0			0
$355$	−5452.35			−0.815157
$356$	−4324.42	+	2496.71i	−0.643803	+	0.371700i
$357$		0			0
$358$	7349.79	−	4243.40i	1.08505	−	0.626455i
$359$		−	2456.41i		−	0.361126i	−0.983563	−	0.180563i	$-0.942208\pi$
$359$		−	2456.41i		−	0.361126i	0.983563	−	0.180563i	$-0.0577920\pi$
$360$		0			0
$361$	−3174.08	−	5497.67i	−0.462762	−	0.801527i
$362$			2167.92i			0.314761i
$363$		0			0
$364$	4570.27	+	6572.22i	0.658097	+	0.946368i
$365$	786.792	+	1362.76i	0.112829	+	0.195425i
$366$		0			0
$367$	7207.65			1.02517			0.512583	−	0.858638i	$-0.328689\pi$
$367$	7207.65			1.02517			0.512583	+	0.858638i	$0.328689\pi$
$368$	−2176.52	+	3769.84i	−0.308312	+	0.534012i
$369$		0			0
$370$	−21858.6	−	12620.1i	−3.07128	−	1.77320i
$371$	12058.8	−	6962.17i	1.68750	−	0.974280i
$372$		0			0
$373$	3618.03			0.502237			0.251118	−	0.967956i	$-0.419202\pi$
$373$	3618.03			0.502237			0.251118	+	0.967956i	$0.419202\pi$
$374$	38.0723	−	65.9432i	0.00526383	−	0.00911722i
$375$		0			0
$376$	−1229.62	+	2129.77i	−0.168652	+	0.292113i
$377$	1158.57	+	13755.5i	0.158275	+	1.87916i
$378$		0			0
$379$	3693.56	−	2132.48i	0.500594	−	0.289018i	−0.228365	−	0.973576i	$-0.573338\pi$
$379$	3693.56	−	2132.48i	0.500594	−	0.289018i	0.728959	+	0.684557i	$0.240005\pi$
$380$	2240.32			0.302437
$381$		0			0
$382$	8954.29	−	5169.76i	1.19932	−	0.692429i
$383$		−	2198.87i		−	0.293360i	−0.989184	−	0.146680i	$-0.953141\pi$
$383$		−	2198.87i		−	0.293360i	0.989184	−	0.146680i	$-0.0468588\pi$
$384$		0			0
$385$	−2592.71	−	1496.90i	−0.343212	−	0.198154i
$386$	6586.97	−	11409.0i	0.868570	−	1.50441i
$387$		0			0
$388$	65.1676	−	37.6245i	0.00852676	−	0.00492293i
$389$	−4728.07	+	8189.26i	−0.616254	+	1.06738i	0.373910	+	0.927465i	$0.378017\pi$
$389$	−4728.07	+	8189.26i	−0.616254	+	1.06738i	−0.990163	+	0.139917i	$0.955316\pi$
$390$		0			0
$391$	−109.455	−	189.582i	−0.0141570	−	0.0245206i
$392$	−5059.97	−	2921.37i	−0.651956	−	0.376407i
$393$		0			0
$394$	−6838.84	−	11845.2i	−0.874457	−	1.51460i
$395$		−	8833.33i		−	1.12520i
$396$		0			0
$397$	353.202	+	203.921i	0.0446516	+	0.0257796i	0.522160	−	0.852848i	$-0.325127\pi$
$397$	353.202	+	203.921i	0.0446516	+	0.0257796i	−0.477508	+	0.878627i	$0.658460\pi$
$398$	−5203.36	−	3004.16i	−0.655329	−	0.378354i
$399$		0			0
$400$	−7892.95	+	13671.0i	−0.986619	+	1.70887i
$401$	−9601.64	−	5543.51i	−1.19572	−	0.690348i	−0.236121	−	0.971724i	$-0.575876\pi$
$401$	−9601.64	−	5543.51i	−1.19572	−	0.690348i	−0.959598	+	0.281375i	$0.909209\pi$
$402$		0			0
$403$	4652.72	+	6690.78i	0.575108	+	0.827026i
$404$	4954.76			0.610169
$405$		0			0
$406$	16862.9	+	29207.3i	2.06130	+	3.57028i
$407$	−1006.38	−	1743.10i	−0.122566	−	0.212291i
$408$		0			0
$409$		−	4555.43i		−	0.550738i	−0.961339	−	0.275369i	$-0.911200\pi$
$409$		−	4555.43i		−	0.550738i	0.961339	−	0.275369i	$-0.0887999\pi$
$410$		−	8816.20i		−	1.06195i
$411$		0			0
$412$	−4296.45	−	7441.68i	−0.513765	−	0.889867i
$413$	−3960.79	−	6860.29i	−0.471907	−	0.817368i
$414$		0			0
$415$	17612.4			2.08328
$416$	9879.19	−	832.089i	1.16434	−	0.0980686i
$417$		0			0
$418$	380.813	+	219.862i	0.0445602	+	0.0257268i
$419$	−2619.83	+	4537.68i	−0.305458	+	0.529070i	−0.977363	−	0.211568i	$-0.932143\pi$
$419$	−2619.83	+	4537.68i	−0.305458	+	0.529070i	0.671905	+	0.740637i	$0.265476\pi$
$420$		0			0
$421$	−2347.39	−	1355.27i	−0.271746	−	0.156892i	0.357935	−	0.933746i	$-0.383481\pi$
$421$	−2347.39	−	1355.27i	−0.271746	−	0.156892i	−0.629681	+	0.776854i	$0.716814\pi$
$422$	−11862.1	−	6848.61i	−1.36834	−	0.790013i
$423$		0			0
$424$		−	4137.85i		−	0.473943i
$425$	−396.930	−	687.503i	−0.0453034	−	0.0784677i
$426$		0			0
$427$	−9514.96	−	5493.47i	−1.07836	−	0.622594i
$428$	2390.62	+	4140.67i	0.269988	+	0.467633i
$429$		0			0
$430$	−2013.85	+	3488.09i	−0.225853	+	0.391188i
$431$	6956.90	−	4016.57i	0.777499	−	0.448889i	−0.0580440	−	0.998314i	$-0.518486\pi$
$431$	6956.90	−	4016.57i	0.777499	−	0.448889i	0.835543	+	0.549425i	$0.185153\pi$
$432$		0			0
$433$	−6078.19	+	10527.7i	−0.674594	+	1.16843i	0.301993	+	0.953310i	$0.402348\pi$
$433$	−6078.19	+	10527.7i	−0.674594	+	1.16843i	−0.976587	+	0.215122i	$0.930985\pi$
$434$	17243.0	+	9955.24i	1.90712	+	1.10108i
$435$		0			0
$436$			10663.6i			1.17132i
$437$	1094.81	−	632.088i	0.119844	−	0.0691919i
$438$		0			0
$439$	9173.30			0.997307			0.498654	−	0.866801i	$-0.333828\pi$
$439$	9173.30			0.997307			0.498654	+	0.866801i	$0.333828\pi$
$440$	−770.467	+	444.829i	−0.0834786	+	0.0481964i
$441$		0			0
$442$	−286.564	+	609.378i	−0.0308381	+	0.0655773i
$443$	−2512.51	+	4351.80i	−0.269465	+	0.466727i	−0.968724	−	0.248141i	$-0.920180\pi$
$443$	−2512.51	+	4351.80i	−0.269465	+	0.466727i	0.699259	+	0.714869i	$0.253514\pi$
$444$		0			0
$445$	−8257.61	+	14302.6i	−0.879660	+	1.52361i
$446$	−8221.31			−0.872848
$447$		0			0
$448$	4155.59	−	2399.23i	0.438243	−	0.253020i
$449$	−1955.56	−	1129.04i	−0.205542	−	0.118670i	0.393696	−	0.919241i	$-0.371196\pi$
$449$	−1955.56	−	1129.04i	−0.205542	−	0.118670i	−0.599238	+	0.800571i	$0.704530\pi$
$450$		0			0
$451$	351.522	−	608.853i	0.0367018	−	0.0635694i
$452$	−7257.82			−0.755264
$453$		0			0
$454$	−2779.13	−	4813.60i	−0.287293	−	0.497606i
$455$	23959.1	+	11266.9i	2.46862	+	1.16088i
$456$		0			0
$457$		−	14006.0i		−	1.43364i	−0.697257	−	0.716821i	$-0.745596\pi$
$457$		−	14006.0i		−	1.43364i	0.697257	−	0.716821i	$-0.254404\pi$
$458$	−5861.29	−	10152.0i	−0.597991	−	1.03575i
$459$		0			0
$460$		−	5544.17i		−	0.561953i
$461$	−6714.29	+	3876.50i	−0.678342	+	0.391641i	−0.799230	−	0.601025i	$-0.794759\pi$
$461$	−6714.29	+	3876.50i	−0.678342	+	0.391641i	0.120888	+	0.992666i	$0.461426\pi$
$462$		0			0
$463$	6468.88	−	3734.81i	0.649319	−	0.374884i	−0.138876	−	0.990310i	$-0.544349\pi$
$463$	6468.88	−	3734.81i	0.649319	−	0.374884i	0.788195	+	0.615425i	$0.211016\pi$
$464$	22920.3			2.29320
$465$		0			0
$466$			16597.6i			1.64993i
$467$	17196.4			1.70398			0.851988	−	0.523562i	$-0.175397\pi$
$467$	17196.4			1.70398			0.851988	+	0.523562i	$0.175397\pi$
$468$		0			0
$469$	−13955.9			−1.37403
$470$		−	17631.0i		−	1.73033i
$471$		0			0
$472$	−2354.03			−0.229561
$473$	−278.156	+	160.594i	−0.0270394	+	0.0156112i
$474$		0			0
$475$	3970.23	−	2292.21i	0.383509	−	0.221419i
$476$			668.421i			0.0643635i
$477$		0			0
$478$	−1306.74	−	2263.33i	−0.125039	−	0.216574i
$479$			985.534i			0.0940087i	0.998895	+	0.0470044i	$0.0149675\pi$
$479$			985.534i			0.0940087i	−0.998895	+	0.0470044i	$0.985033\pi$
$480$		0			0
$481$	10162.4	+	14614.0i	0.963342	+	1.38532i
$482$	1220.11	+	2113.29i	0.115299	+	0.199704i
$483$		0			0
$484$	−7132.72			−0.669865
$485$	124.440	−	215.536i	0.0116505	−	0.0201793i
$486$		0			0
$487$	−9271.86	−	5353.11i	−0.862727	−	0.498096i	0.00219755	−	0.999998i	$-0.499300\pi$
$487$	−9271.86	−	5353.11i	−0.862727	−	0.498096i	−0.864925	+	0.501902i	$0.832634\pi$
$488$	−2827.53	+	1632.48i	−0.262287	+	0.151432i
$489$		0			0
$490$	41888.1			3.86186
$491$	−705.204	+	1221.45i	−0.0648176	+	0.112267i	−0.896613	−	0.442815i	$-0.853980\pi$
$491$	−705.204	+	1221.45i	−0.0648176	+	0.112267i	0.831795	+	0.555082i	$0.187313\pi$
$492$		0			0
$493$	−576.320	+	998.216i	−0.0526494	+	0.0911915i
$494$	−3519.07	−	1654.87i	−0.320507	−	0.150720i
$495$		0			0
$496$	11718.5	−	6765.67i	1.06084	−	0.612475i
$497$	9394.33			0.847874
$498$		0			0
$499$	−4911.34	+	2835.56i	−0.440605	+	0.254383i	−0.703854	−	0.710345i	$-0.748539\pi$
$499$	−4911.34	+	2835.56i	−0.440605	+	0.254383i	0.263249	+	0.964728i	$0.415206\pi$
$500$		−	7715.24i		−	0.690072i
$501$		0			0
$502$	−22587.3	−	13040.8i	−2.00821	−	1.15944i
$503$	−1271.73	+	2202.70i	−0.112731	+	0.195255i	−0.916870	−	0.399185i	$-0.869293\pi$
$503$	−1271.73	+	2202.70i	−0.112731	+	0.195255i	0.804140	+	0.594441i	$0.202626\pi$
$504$		0			0
$505$	14191.9	−	8193.69i	1.25056	−	0.722009i
$506$	544.099	−	942.407i	0.0478026	−	0.0827966i
$507$		0			0
$508$	−4828.35	−	8362.94i	−0.421699	−	0.730405i
$509$	−3751.14	−	2165.72i	−0.326653	−	0.188593i	0.327701	−	0.944781i	$-0.393726\pi$
$509$	−3751.14	−	2165.72i	−0.326653	−	0.188593i	−0.654354	+	0.756188i	$0.727059\pi$
$510$		0			0
$511$	−1355.63	−	2348.02i	−0.117357	−	0.203269i
$512$		−	10689.4i		−	0.922673i
$513$		0			0
$514$	−22618.7	−	13058.9i	−1.94099	−	1.12063i
$515$	−24612.6	−	14210.1i	−2.10595	−	1.21587i
$516$		0			0
$517$	702.986	−	1217.61i	0.0598014	−	0.103579i
$518$	37662.0	+	21744.2i	3.19455	+	1.84437i
$519$		0			0
$520$	6459.51	−	4491.89i	0.544747	−	0.378813i
$521$	−8320.00			−0.699627			−0.349814	−	0.936819i	$-0.613755\pi$
$521$	−8320.00			−0.699627			−0.349814	+	0.936819i	$0.613755\pi$
$522$		0			0
$523$	−994.860	−	1723.15i	−0.0831781	−	0.144069i	0.821435	−	0.570302i	$-0.193174\pi$
$523$	−994.860	−	1723.15i	−0.0831781	−	0.144069i	−0.904613	+	0.426233i	$0.859840\pi$
$524$	2540.63	+	4400.50i	0.211809	+	0.366864i
$525$		0			0
$526$		−	19939.1i		−	1.65282i
$527$			680.479i			0.0562469i
$528$		0			0
$529$	4519.26	+	7827.58i	0.371435	+	0.643345i
$530$	14832.6	+	25690.9i	1.21564	+	2.10555i
$531$		0			0
$532$	−3860.04			−0.314575
$533$	−2645.84	+	5626.39i	−0.215017	+	0.457234i
$534$		0			0
$535$	13694.9	+	7906.74i	1.10669	+	0.638950i
$536$	−2073.61	+	3591.60i	−0.167101	+	0.289428i
$537$		0			0
$538$	13027.7	+	7521.52i	1.04398	+	0.602743i
$539$	2892.82	+	1670.17i	0.231174	+	0.133468i
$540$		0			0
$541$		−	5180.38i		−	0.411686i	−0.978585	−	0.205843i	$-0.934006\pi$
$541$		−	5180.38i		−	0.411686i	0.978585	−	0.205843i	$-0.0659936\pi$
$542$	4312.66	+	7469.74i	0.341780	+	0.591980i
$543$		0			0
$544$	716.920	+	413.914i	0.0565031	+	0.0326221i
$545$	17634.4	+	30543.7i	1.38601	+	2.40064i
$546$		0			0
$547$	3793.38	−	6570.33i	0.296514	−	0.513577i	−0.678822	−	0.734303i	$-0.737509\pi$
$547$	3793.38	−	6570.33i	0.296514	−	0.513577i	0.975336	+	0.220725i	$0.0708425\pi$
$548$	−4325.38	+	2497.26i	−0.337173	+	0.194667i
$549$		0			0
$550$	1973.13	−	3417.56i	0.152972	−	0.264955i
$551$	−5764.56	−	3328.17i	−0.445696	−	0.257323i
$552$		0			0
$553$			15219.7i			1.17036i
$554$	10271.7	−	5930.34i	0.787727	−	0.454794i
$555$		0			0
$556$	13278.3			1.01282
$557$	−11208.0	+	6470.93i	−0.852599	+	0.492248i	−0.861527	−	0.507712i	$-0.830491\pi$
$557$	−11208.0	+	6470.93i	−0.852599	+	0.492248i	0.00892808	+	0.999960i	$0.497158\pi$
$558$		0			0
$559$	2332.03	−	1621.68i	0.176448	−	0.122701i
$560$	21980.3	−	38070.9i	1.65864	−	2.87284i
$561$		0			0
$562$	−1400.25	+	2425.30i	−0.105100	+	0.182038i
$563$	−860.355			−0.0644043			−0.0322022	−	0.999481i	$-0.510252\pi$
$563$	−860.355			−0.0644043			−0.0322022	+	0.999481i	$0.510252\pi$
$564$		0			0
$565$	−20788.6	+	12002.3i	−1.54793	+	0.893698i
$566$	13693.9	+	7906.18i	1.01696	+	0.587141i
$567$		0			0
$568$	1395.84	−	2417.67i	0.103113	−	0.178597i
$569$	−175.472			−0.0129283			−0.00646413	−	0.999979i	$-0.502058\pi$
$569$	−175.472			−0.0129283			−0.00646413	+	0.999979i	$0.502058\pi$
$570$		0			0
$571$	−5355.41	−	9275.84i	−0.392499	−	0.679828i	0.600280	−	0.799790i	$-0.295056\pi$
$571$	−5355.41	−	9275.84i	−0.392499	−	0.679828i	−0.992778	+	0.119962i	$0.961723\pi$
$572$	−1355.21	+	114.144i	−0.0990631	+	0.00834374i
$573$		0			0
$574$			15190.2i			1.10458i
$575$	−5672.60	−	9825.23i	−0.411415	−	0.712592i
$576$		0			0
$577$		−	4210.54i		−	0.303790i	−0.988397	−	0.151895i	$-0.951462\pi$
$577$		−	4210.54i		−	0.303790i	0.988397	−	0.151895i	$-0.0485376\pi$
$578$	15569.6	−	8989.10i	1.12043	−	0.646881i
$579$		0			0
$580$	−25281.1	+	14596.0i	−1.80989	+	1.04494i
$581$	−30346.0			−2.16689
$582$		0			0
$583$			2365.64i			0.168053i
$584$	−805.697			−0.0570890
$585$		0			0
$586$	−7167.33			−0.505255
$587$			26112.5i			1.83608i	0.396488	+	0.918040i	$0.370229\pi$
$587$			26112.5i			1.83608i	−0.396488	+	0.918040i	$0.629771\pi$
$588$		0			0
$589$	−3929.67			−0.274906
$590$	14615.6	−	8438.31i	1.01985	−	0.588813i
$591$		0			0
$592$	25595.4	−	14777.5i	1.77697	−	1.02593i
$593$		−	18330.1i		−	1.26935i	−0.772779	−	0.634676i	$-0.781134\pi$
$593$		−	18330.1i		−	1.26935i	0.772779	−	0.634676i	$-0.218866\pi$
$594$		0			0
$595$	1105.37	+	1914.56i	0.0761609	+	0.131914i
$596$		−	3251.76i		−	0.223486i
$597$		0			0
$598$	−4095.34	+	8708.74i	−0.280051	+	0.595530i
$599$	−3567.25	−	6178.66i	−0.243329	−	0.421458i	0.718332	−	0.695701i	$-0.244906\pi$
$599$	−3567.25	−	6178.66i	−0.243329	−	0.421458i	−0.961660	+	0.274243i	$0.911573\pi$
$600$		0			0
$601$	−8910.23			−0.604752			−0.302376	−	0.953189i	$-0.597780\pi$
$601$	−8910.23			−0.604752			−0.302376	+	0.953189i	$0.597780\pi$
$602$	3469.84	−	6009.94i	0.234917	−	0.406889i
$603$		0			0
$604$	7723.72	+	4459.29i	0.520321	+	0.300407i
$605$	−20430.2	+	11795.4i	−1.37290	+	0.792646i
$606$		0			0
$607$	−24487.8			−1.63744			−0.818722	−	0.574191i	$-0.805317\pi$
$607$	−24487.8			−1.63744			−0.818722	+	0.574191i	$0.805317\pi$
$608$	−2390.30	+	4140.11i	−0.159440	+	0.276158i
$609$		0			0
$610$	11703.6	−	20271.3i	0.776829	−	1.34551i
$611$	−5291.25	+	11251.9i	−0.350346	+	0.745011i
$612$		0			0
$613$	−1218.37	+	703.428i	−0.0802767	+	0.0463478i	−0.539601	−	0.841921i	$-0.681425\pi$
$613$	−1218.37	+	703.428i	−0.0802767	+	0.0463478i	0.459324	+	0.888269i	$0.348092\pi$
$614$	16823.4			1.10576
$615$		0			0
$616$	1327.50	−	766.435i	0.0868290	−	0.0501308i
$617$		−	10833.8i		−	0.706889i	−0.935455	−	0.353445i	$-0.885010\pi$
$617$		−	10833.8i		−	0.706889i	0.935455	−	0.353445i	$-0.114990\pi$
$618$		0			0
$619$	−18673.7	−	10781.3i	−1.21254	−	0.700059i	−0.249226	−	0.968445i	$-0.580176\pi$
$619$	−18673.7	−	10781.3i	−1.21254	−	0.700059i	−0.963311	+	0.268386i	$0.913510\pi$
$620$	−8616.99	+	14925.1i	−0.558172	+	0.966782i
$621$		0			0
$622$	17283.8	−	9978.79i	1.11417	−	0.643269i
$623$	14227.8	−	24643.2i	0.914965	−	1.58477i
$624$		0			0
$625$	−81.4616	−	141.096i	−0.00521354	−	0.00903012i
$626$	9082.12	+	5243.57i	0.579864	+	0.334784i
$627$		0			0
$628$	7629.99	+	13215.5i	0.484824	+	0.839740i
$629$			1486.30i			0.0942172i
$630$		0			0
$631$	12316.3	+	7110.82i	0.777027	+	0.448617i	0.835376	−	0.549680i	$-0.185250\pi$
$631$	12316.3	+	7110.82i	0.777027	+	0.448617i	−0.0583487	+	0.998296i	$0.518584\pi$
$632$	3916.85	+	2261.40i	0.246525	+	0.142332i
$633$		0			0
$634$	−447.414	+	774.943i	−0.0280269	+	0.0485441i
$635$	−27659.6	−	15969.3i	−1.72857	−	0.997988i
$636$		0			0
$637$	−26732.5	−	12571.1i	−1.66276	−	0.781923i
$638$	−5729.75			−0.355553
$639$		0			0
$640$	−10207.5	−	17679.9i	−0.630448	−	1.09197i
$641$	−14814.9	−	25660.2i	−0.912877	−	1.58115i	−0.809980	−	0.586457i	$-0.800522\pi$
$641$	−14814.9	−	25660.2i	−0.912877	−	1.58115i	−0.102897	−	0.994692i	$-0.532811\pi$
$642$		0			0
$643$		−	21519.2i		−	1.31980i	−0.751352	−	0.659902i	$-0.770598\pi$
$643$		−	21519.2i		−	1.31980i	0.751352	−	0.659902i	$-0.229402\pi$
$644$			9552.53i			0.584507i
$645$		0			0
$646$	−162.355	−	281.207i	−0.00988817	−	0.0171268i
$647$	−15501.1	−	26848.6i	−0.941901	−	1.63142i	−0.761840	−	0.647765i	$-0.775704\pi$
$647$	−15501.1	−	26848.6i	−0.941901	−	1.63142i	−0.180061	−	0.983655i	$-0.557629\pi$
$648$		0			0
$649$	1345.82			0.0813991
$650$	−14851.4	+	31581.5i	−0.896184	+	1.90574i
$651$		0			0
$652$	3607.20	+	2082.62i	0.216670	+	0.125095i
$653$	−2890.04	+	5005.69i	−0.173194	+	0.299982i	−0.939535	−	0.342453i	$-0.888742\pi$
$653$	−2890.04	+	5005.69i	−0.173194	+	0.299982i	0.766341	+	0.642435i	$0.222076\pi$
$654$		0			0
$655$	14554.2	+	8402.88i	0.868214	+	0.501264i
$656$	8940.31	+	5161.69i	0.532104	+	0.307211i
$657$		0			0
$658$			30377.9i			1.79978i
$659$	9660.89	+	16733.2i	0.571070	+	0.989122i	0.996456	+	0.0841102i	$0.0268048\pi$
$659$	9660.89	+	16733.2i	0.571070	+	0.989122i	−0.425387	+	0.905012i	$0.639862\pi$
$660$		0			0
$661$	10613.2	+	6127.56i	0.624519	+	0.360566i	0.778626	−	0.627488i	$-0.215917\pi$
$661$	10613.2	+	6127.56i	0.624519	+	0.360566i	−0.154107	+	0.988054i	$0.549250\pi$
$662$	−16290.7	−	28216.4i	−0.956430	−	1.65659i
$663$		0			0
$664$	−4508.90	+	7809.65i	−0.263523	+	0.456436i
$665$	−11056.3	+	6383.35i	−0.644729	+	0.372234i
$666$		0			0
$667$	−8236.31	+	14265.7i	−0.478127	+	0.828141i
$668$	4801.41	+	2772.09i	0.278102	+	0.160562i
$669$		0			0
$670$		−	29732.4i		−	1.71442i
$671$	1616.52	−	933.300i	0.0930032	−	0.0536954i
$672$		0			0
$673$	24278.7			1.39060			0.695301	−	0.718719i	$-0.255271\pi$
$673$	24278.7			1.39060			0.695301	+	0.718719i	$0.255271\pi$
$674$	−16006.5	+	9241.35i	−0.914758	+	0.528136i
$675$		0			0
$676$	11857.9	−	2011.78i	0.674666	−	0.114462i
$677$	−1040.37	+	1801.98i	−0.0590618	+	0.102298i	−0.894044	−	0.447978i	$-0.852144\pi$
$677$	−1040.37	+	1801.98i	−0.0590618	+	0.102298i	0.834983	+	0.550276i	$0.185478\pi$
$678$		0			0
$679$	−214.408	+	371.365i	−0.0121181	+	0.0209892i
$680$	656.958			0.0370488
$681$		0			0
$682$	−2929.46	+	1691.32i	−0.164479	+	0.0949620i
$683$	−1724.70	−	995.758i	−0.0966236	−	0.0557857i	0.450910	−	0.892570i	$-0.351100\pi$
$683$	−1724.70	−	995.758i	−0.0966236	−	0.0557857i	−0.547533	+	0.836784i	$0.684433\pi$
$684$		0			0
$685$	−8259.44	+	14305.8i	−0.460696	+	0.797950i
$686$	−32893.7			−1.83074
$687$		0			0
$688$	−2358.13	−	4084.41i	−0.130673	−	0.226332i
$689$	−1755.87	−	20847.0i	−0.0970877	−	1.15270i
$690$		0			0
$691$			6214.52i			0.342129i	0.985260	+	0.171065i	$0.0547207\pi$
$691$			6214.52i			0.342129i	−0.985260	+	0.171065i	$0.945279\pi$
$692$	−4817.59	−	8344.31i	−0.264649	−	0.458386i
$693$		0			0
$694$		−	3844.36i		−	0.210274i
$695$	38033.0	−	21958.4i	2.07579	−	1.19846i
$696$		0			0
$697$	−449.601	+	259.577i	−0.0244331	+	0.0141064i
$698$	−13637.0			−0.739497
$699$		0			0
$700$			34641.5i			1.87046i
$701$	28692.5			1.54594			0.772969	−	0.634444i	$-0.218771\pi$
$701$	28692.5			1.54594			0.772969	+	0.634444i	$0.218771\pi$
$702$		0			0
$703$	−8583.17			−0.460484
$704$			815.223i			0.0436433i
$705$		0			0
$706$	−11804.0			−0.629251
$707$	−24452.4	+	14117.6i	−1.30075	+	0.750987i
$708$		0			0
$709$	−12389.9	+	7153.33i	−0.656295	+	0.378912i	−0.790864	−	0.611992i	$-0.790368\pi$
$709$	−12389.9	+	7153.33i	−0.656295	+	0.378912i	0.134569	+	0.990904i	$0.457035\pi$
$710$			20014.3i			1.05792i
$711$		0			0
$712$	−4228.02	−	7323.14i	−0.222544	−	0.385458i
$713$			9724.86i			0.510798i
$714$		0			0
$715$	−3692.95	+	2568.05i	−0.193159	+	0.134321i
$716$	−6328.49	−	10961.3i	−0.330317	−	0.572125i
$717$		0			0
$718$	−9016.89			−0.468673
$719$	−7489.59	+	12972.3i	−0.388476	+	0.672861i	−0.992245	−	0.124299i	$-0.960332\pi$
$719$	−7489.59	+	12972.3i	−0.388476	+	0.672861i	0.603768	+	0.797160i	$0.293665\pi$
$720$		0			0
$721$	42407.2	+	24483.8i	2.19047	+	1.26467i
$722$	−20180.6	+	11651.3i	−1.04023	+	0.600576i
$723$		0			0
$724$	3233.18			0.165967
$725$	−29868.3	+	51733.4i	−1.53004	+	2.65011i
$726$		0			0
$727$	−14255.9	+	24691.9i	−0.727264	+	1.25966i	0.230771	+	0.973008i	$0.425875\pi$
$727$	−14255.9	+	24691.9i	−0.727264	+	1.25966i	−0.958035	+	0.286651i	$0.907458\pi$
$728$	−11129.6	+	7739.47i	−0.566610	+	0.394016i
$729$		0			0
$730$	5002.37	−	2888.12i	0.253625	−	0.146430i
$731$	237.177			0.0120004
$732$		0			0
$733$	−1279.08	+	738.479i	−0.0644530	+	0.0372119i	−0.531880	−	0.846820i	$-0.678514\pi$
$733$	−1279.08	+	738.479i	−0.0644530	+	0.0372119i	0.467427	+	0.884032i	$0.345181\pi$
$734$		−	26457.5i		−	1.33047i
$735$		0			0
$736$	10245.6	+	5915.32i	0.513124	+	0.296252i
$737$	1185.50	−	2053.35i	0.0592516	−	0.102627i
$738$		0			0
$739$	5378.35	−	3105.19i	0.267721	−	0.154569i	−0.360131	−	0.932902i	$-0.617268\pi$
$739$	5378.35	−	3105.19i	0.267721	−	0.154569i	0.627851	+	0.778333i	$0.283935\pi$
$740$	−18821.2	+	32599.2i	−0.934973	+	1.61942i
$741$		0			0
$742$	−25556.4	−	44265.0i	−1.26443	−	2.19006i
$743$	−21362.4	−	12333.6i	−1.05479	−	0.608986i	−0.130807	−	0.991408i	$-0.541757\pi$
$743$	−21362.4	−	12333.6i	−1.05479	−	0.608986i	−0.923988	+	0.382422i	$0.875090\pi$
$744$		0			0
$745$	−5377.45	−	9314.01i	−0.264449	−	0.458039i
$746$		−	13280.9i		−	0.651807i
$747$		0			0
$748$	−98.3457	−	56.7799i	−0.00480732	−	0.00277551i
$749$	−23596.1	−	13623.2i	−1.15111	−	0.664595i
$750$		0			0
$751$	7372.23	−	12769.1i	0.358211	−	0.620440i	−0.629451	−	0.777040i	$-0.716720\pi$
$751$	7372.23	−	12769.1i	0.358211	−	0.620440i	0.987662	+	0.156601i	$0.0500535\pi$
$752$	17879.2	+	10322.5i	0.867003	+	0.500564i
$753$		0			0
$754$	50493.0	−	4252.84i	2.43879	−	0.205410i
$755$	29497.4			1.42188
$756$		0			0
$757$	−14902.9	−	25812.6i	−0.715530	−	1.23933i	−0.962755	−	0.270376i	$-0.912852\pi$
$757$	−14902.9	−	25812.6i	−0.715530	−	1.23933i	0.247224	−	0.968958i	$-0.420482\pi$
$758$	−7827.80	−	13558.1i	−0.375090	−	0.649675i
$759$		0			0
$760$			3793.84i			0.181075i
$761$		−	23987.0i		−	1.14261i	−0.820737	−	0.571306i	$-0.806437\pi$
$761$		−	23987.0i		−	1.14261i	0.820737	−	0.571306i	$-0.193563\pi$
$762$		0			0
$763$	−30383.9	−	52626.4i	−1.44164	−	2.49699i
$764$	−7710.03	−	13354.2i	−0.365103	−	0.632378i
$765$		0			0
$766$	−8071.52			−0.380726
$767$	−11859.9	+	998.919i	−0.558327	+	0.0470259i
$768$		0			0
$769$	8670.15	+	5005.71i	0.406572	+	0.234734i	0.689316	−	0.724461i	$-0.257911\pi$
$769$	8670.15	+	5005.71i	0.406572	+	0.234734i	−0.282744	+	0.959195i	$0.591245\pi$
$770$	−5494.76	+	9517.21i	−0.257166	+	0.445424i
$771$		0			0
$772$	−17015.0	−	9823.61i	−0.793242	−	0.457978i
$773$	−26216.7	−	15136.2i	−1.21986	−	0.704285i	−0.254970	−	0.966949i	$-0.582066\pi$
$773$	−26216.7	−	15136.2i	−1.21986	−	0.704285i	−0.964887	+	0.262664i	$0.915399\pi$
$774$		0			0
$775$			35266.4i			1.63459i
$776$	63.7148	+	110.357i	0.00294746	+	0.00510515i
$777$		0			0
$778$	30060.8	+	17355.6i	1.38526	+	0.799779i
$779$	−1499.02	−	2596.38i	−0.0689448	−	0.119416i
$780$		0			0
$781$	−798.014	+	1382.20i	−0.0365623	+	0.0633278i
$782$	−695.909	+	401.783i	−0.0318231	+	0.0183731i
$783$		0			0
$784$	−24524.6	+	42477.8i	−1.11719	+	1.93503i
$785$	43709.1	+	25235.4i	1.98732	+	1.14738i
$786$		0			0
$787$		−	19094.1i		−	0.864842i	−0.901672	−	0.432421i	$-0.857659\pi$
$787$		−	19094.1i		−	0.864842i	0.901672	−	0.432421i	$-0.142341\pi$
$788$	−17665.6	+	10199.2i	−0.798619	+	0.461083i
$789$		0			0
$790$	−32425.0			−1.46029
$791$	35818.4	−	20679.8i	1.61006	−	0.929567i
$792$		0			0
$793$	−13552.7	+	9424.48i	−0.606900	+	0.422034i
$794$	748.545	−	1296.52i	0.0334570	−	0.0579492i
$795$		0			0
$796$	−4480.32	+	7760.13i	−0.199498	+	0.345541i
$797$	23412.4			1.04054			0.520269	−	0.854002i	$-0.325832\pi$
$797$	23412.4			1.04054			0.520269	+	0.854002i	$0.325832\pi$
$798$		0			0
$799$	−899.128	+	519.112i	−0.0398108	+	0.0229848i
$800$	37155.0	+	21451.4i	1.64203	+	0.948028i
$801$		0			0
$802$	−20348.9	+	35245.3i	−0.895940	+	1.55181i
$803$	460.624			0.0202429
$804$		0			0
$805$	15797.0	+	27361.3i	0.691643	+	1.19796i
$806$	24560.2	−	17079.0i	1.07332	−	0.746380i
$807$		0			0
$808$			8390.57i			0.365321i
$809$	125.058	+	216.607i	0.00543486	+	0.00941345i	0.868730	−	0.495286i	$-0.164937\pi$
$809$	125.058	+	216.607i	0.00543486	+	0.00941345i	−0.863295	+	0.504699i	$0.831603\pi$
$810$		0			0
$811$		−	2544.87i		−	0.110188i	−0.998481	−	0.0550941i	$-0.982454\pi$
$811$		−	2544.87i		−	0.110188i	0.998481	−	0.0550941i	$-0.0175459\pi$
$812$	43558.9	−	25148.8i	1.88253	−	1.08688i
$813$		0			0
$814$	−6398.50	+	3694.18i	−0.275513	+	0.159067i
$815$	13776.1			0.592094
$816$		0			0
$817$			1369.66i			0.0586518i
$818$	−16721.9			−0.714752
$819$		0			0
$820$	−13148.2			−0.559946
$821$			17444.1i			0.741538i	0.928725	+	0.370769i	$0.120906\pi$
$821$			17444.1i			0.741538i	−0.928725	+	0.370769i	$0.879094\pi$
$822$		0			0
$823$	−21736.6			−0.920645			−0.460322	−	0.887752i	$-0.652266\pi$
$823$	−21736.6			−0.920645			−0.460322	+	0.887752i	$0.652266\pi$
$824$	12602.0	−	7275.78i	0.532782	−	0.307602i
$825$		0			0
$826$	−25182.5	+	14539.1i	−1.06079	+	0.612446i
$827$			31700.0i			1.33291i	0.745544	+	0.666456i	$0.232190\pi$
$827$			31700.0i			1.33291i	−0.745544	+	0.666456i	$0.767810\pi$
$828$		0			0
$829$	17175.2	+	29748.3i	0.719565	+	1.24632i	0.961172	+	0.275949i	$0.0889920\pi$
$829$	17175.2	+	29748.3i	0.719565	+	1.24632i	−0.241608	+	0.970374i	$0.577675\pi$
$830$		−	64650.9i		−	2.70369i
$831$		0			0
$832$	−605.090	−	7184.09i	−0.0252136	−	0.299355i
$833$	−1233.32	−	2136.17i	−0.0512989	−	0.0888523i
$834$		0			0
$835$	18336.9			0.759968
$836$	327.896	−	567.933i	0.0135652	−	0.0234956i
$837$		0			0
$838$	16656.7	+	9616.76i	0.686631	+	0.396427i
$839$	−34912.6	+	20156.8i	−1.43661	+	0.829427i	−0.997612	−	0.0690608i	$-0.978000\pi$
$839$	−34912.6	+	20156.8i	−1.43661	+	0.829427i	−0.438998	+	0.898488i	$0.644666\pi$
$840$		0			0
$841$	62345.2			2.55628
$842$	−4974.86	+	8616.71i	−0.203616	+	0.352674i
$843$		0			0
$844$	−10213.8	+	17690.9i	−0.416557	+	0.721498i
$845$	30637.8	−	25371.8i	1.24730	−	1.03292i
$846$		0			0
$847$	35201.0	−	20323.3i	1.42801	−	0.824459i
$848$	−34736.7			−1.40668
$849$		0			0
$850$	−2523.66	+	1457.03i	−0.101836	+	0.0587951i
$851$			21241.0i			0.855618i
$852$		0			0
$853$	9517.24	+	5494.78i	0.382021	+	0.220560i	0.678697	−	0.734418i	$-0.262545\pi$
$853$	9517.24	+	5494.78i	0.382021	+	0.220560i	−0.296676	+	0.954978i	$0.595878\pi$
$854$	−20165.2	+	34927.1i	−0.808007	+	1.39951i
$855$		0			0
$856$	−7011.97	+	4048.37i	−0.279982	+	0.161648i
$857$	4133.04	−	7158.63i	0.164740	−	0.285338i	−0.771823	−	0.635837i	$-0.780655\pi$
$857$	4133.04	−	7158.63i	0.164740	−	0.285338i	0.936563	+	0.350500i	$0.113988\pi$
$858$		0			0
$859$	16811.7	+	29118.8i	0.667764	+	1.15660i	0.978528	+	0.206113i	$0.0660816\pi$
$859$	16811.7	+	29118.8i	0.667764	+	1.15660i	−0.310765	+	0.950487i	$0.600585\pi$
$860$	5202.04	+	3003.40i	0.206265	+	0.119087i
$861$		0			0
$862$	−14743.9	−	25537.1i	−0.582573	−	1.00905i
$863$			23570.2i			0.929709i	0.885387	+	0.464855i	$0.153893\pi$
$863$			23570.2i			0.929709i	−0.885387	+	0.464855i	$0.846107\pi$
$864$		0			0
$865$	−27598.0	−	15933.7i	−1.08481	−	0.626315i
$866$	38644.8	+	22311.6i	1.51640	+	0.875495i
$867$		0			0
$868$	14847.0	−	25715.7i	0.580574	−	1.00558i
$869$	−2239.30	−	1292.86i	−0.0874142	−	0.0504686i
$870$		0			0
$871$	−8923.05	+	18974.9i	−0.347125	+	0.738162i
$872$	−18058.1			−0.701291
$873$		0			0
$874$	−2320.24	−	4018.78i	−0.0897979	−	0.155535i
$875$	21983.1	+	38075.8i	0.849330	+	1.47108i
$876$		0			0
$877$		−	39291.0i		−	1.51284i	−0.654085	−	0.756421i	$-0.726946\pi$
$877$		−	39291.0i		−	1.51284i	0.654085	−	0.756421i	$-0.273054\pi$
$878$		−	33673.0i		−	1.29431i
$879$		0			0
$880$	3734.29	+	6467.97i	0.143049	+	0.247767i
$881$	−8048.55	−	13940.5i	−0.307789	−	0.533107i	0.670089	−	0.742281i	$-0.266256\pi$
$881$	−8048.55	−	13940.5i	−0.307789	−	0.533107i	−0.977878	+	0.209174i	$0.932923\pi$
$882$		0			0
$883$	50307.6			1.91731			0.958656	−	0.284567i	$-0.0918500\pi$
$883$	50307.6			1.91731			0.958656	+	0.284567i	$0.0918500\pi$
$884$	908.808	+	427.372i	0.0345775	+	0.0162603i
$885$		0			0
$886$	15974.4	+	9222.82i	0.605723	+	0.349714i
$887$	−10617.0	+	18389.2i	−0.401899	+	0.696109i	−0.993955	−	0.109788i	$-0.964983\pi$
$887$	−10617.0	+	18389.2i	−0.401899	+	0.696109i	0.592056	+	0.805897i	$0.298316\pi$
$888$		0			0
$889$	47657.2	+	27514.9i	1.79794	+	1.03804i
$890$	52501.4	+	30311.7i	1.97736	+	1.14163i
$891$		0			0
$892$			12261.0i			0.460235i
$893$	−2997.80	−	5192.34i	−0.112338	−	0.194574i
$894$		0			0
$895$	−36253.3	−	20930.9i	−1.35398	−	0.781722i
$896$	17587.4	+	30462.3i	0.655752	+	1.13580i
$897$		0			0
$898$	−4144.43	+	7178.37i	−0.154011	+	0.266754i
$899$	44344.7	−	25602.4i	1.64514	−	0.949821i
$900$		0			0
$901$	873.440	−	1512.84i	0.0322958	−	0.0559380i
$902$	−2234.95	−	1290.35i	−0.0825009	−	0.0476319i
$903$		0			0
$904$		−	12290.7i		−	0.452192i
$905$	9260.77	−	5346.71i	0.340153	−	0.196387i
$906$		0			0
$907$	−18513.6			−0.677768			−0.338884	−	0.940828i	$-0.610049\pi$
$907$	−18513.6			−0.677768			−0.338884	+	0.940828i	$0.610049\pi$
$908$	−7178.85	+	4144.71i	−0.262377	+	0.151484i
$909$		0			0
$910$	41358.1	−	87948.1i	1.50660	−	3.20379i
$911$	−1537.30	+	2662.68i	−0.0559088	+	0.0968369i	−0.892625	−	0.450799i	$-0.851139\pi$
$911$	−1537.30	+	2662.68i	−0.0559088	+	0.0968369i	0.836716	+	0.547636i	$0.184472\pi$
$912$		0			0
$913$	2577.78	−	4464.84i	0.0934414	−	0.161845i
$914$	−51412.7			−1.86059
$915$		0			0
$916$	−15140.5	+	8741.35i	−0.546130	+	0.315308i
$917$	−25076.7	−	14478.1i	−0.903060	−	0.521382i
$918$		0			0
$919$	1520.38	−	2633.38i	0.0545733	−	0.0945237i	−0.837448	−	0.546517i	$-0.815953\pi$
$919$	1520.38	−	2633.38i	0.0545733	−	0.0945237i	0.892021	+	0.451993i	$0.149287\pi$
$920$	9388.71			0.336453
$921$		0			0
$922$	14229.7	+	24646.5i	0.508275	+	0.880359i
$923$	6006.51	−	12772.8i	0.214200	−	0.455497i
$924$		0			0
$925$			77028.6i			2.73804i
$926$	−13709.6	−	23745.7i	−0.486528	−	0.842691i
$927$		0			0
$928$		−	62292.6i		−	2.20351i
$929$	−29546.3	+	17058.6i	−1.04347	+	0.602447i	−0.920814	−	0.390002i	$-0.872474\pi$
$929$	−29546.3	+	17058.6i	−1.04347	+	0.602447i	−0.122655	+	0.992449i	$0.539141\pi$
$930$		0			0
$931$	12336.1	−	7122.25i	0.434263	−	0.250722i
$932$	24753.2			0.869975
$933$		0			0
$934$		−	63124.0i		−	2.21143i
$935$	−375.588			−0.0131369
$936$		0			0
$937$	−5165.26			−0.180087			−0.0900436	−	0.995938i	$-0.528701\pi$
$937$	−5165.26			−0.180087			−0.0900436	+	0.995938i	$0.528701\pi$
$938$			51228.6i			1.78323i
$939$		0			0
$940$	−26294.3			−0.912367
$941$	22962.4	−	13257.3i	0.795485	−	0.459274i	−0.0464048	−	0.998923i	$-0.514776\pi$
$941$	22962.4	−	13257.3i	0.795485	−	0.459274i	0.841890	+	0.539649i	$0.181443\pi$
$942$		0			0
$943$	−6425.33	+	3709.66i	−0.221885	+	0.128105i
$944$			19761.8i			0.681347i
$945$		0			0
$946$	589.500	+	1021.04i	0.0202604	+	0.0350920i
$947$		−	17080.6i		−	0.586107i	−0.956096	−	0.293054i	$-0.905329\pi$
$947$		−	17080.6i		−	0.586107i	0.956096	−	0.293054i	$-0.0946715\pi$
$948$		0			0
$949$	−4059.21	+	341.893i	−0.138849	+	0.0116947i
$950$	−8414.16	−	14573.8i	−0.287359	−	0.497721i
$951$		0			0
$952$	−1131.93			−0.0385358
$953$	−2582.09	+	4472.31i	−0.0877671	+	0.152017i	−0.906567	−	0.422062i	$-0.861306\pi$
$953$	−2582.09	+	4472.31i	−0.0877671	+	0.152017i	0.818800	+	0.574079i	$0.194640\pi$
$954$		0			0
$955$	−44167.6	−	25500.2i	−1.49658	−	0.864048i
$956$	−3375.47	+	1948.83i	−0.114195	+	0.0659305i
$957$		0			0
$958$	3617.65			0.122005
$959$	14230.9	−	24648.7i	0.479187	−	0.829976i
$960$		0			0
$961$	219.286	−	379.815i	0.00736082	−	0.0127493i
$962$	53644.3	−	37303.9i	1.79788	−	1.25023i
$963$		0			0
$964$	3151.69	−	1819.63i	0.105300	−	0.0607950i
$965$	−64981.3			−2.16769
$966$		0			0
$967$	−20692.4	+	11946.7i	−0.688129	+	0.397292i	−0.802911	−	0.596099i	$-0.796717\pi$
$967$	−20692.4	+	11946.7i	−0.688129	+	0.397292i	0.114781	+	0.993391i	$0.463383\pi$
$968$		−	12078.8i		−	0.401062i
$969$		0			0
$970$	−791.179	−	456.787i	−0.0261889	−	0.0151202i
$971$	−1767.00	+	3060.54i	−0.0583994	+	0.101151i	−0.893747	−	0.448571i	$-0.851933\pi$
$971$	−1767.00	+	3060.54i	−0.0583994	+	0.101151i	0.835348	+	0.549722i	$0.185266\pi$
$972$		0			0
$973$	−65530.3	+	37833.9i	−2.15910	+	1.24656i
$974$	−19650.0	+	34034.7i	−0.646433	+	1.11965i
$975$		0			0
$976$	13704.4	+	23736.8i	0.449455	+	0.778479i
$977$	21527.2	+	12428.7i	0.704929	+	0.406991i	0.809181	−	0.587560i	$-0.199911\pi$
$977$	21527.2	+	12428.7i	0.704929	+	0.406991i	−0.104252	+	0.994551i	$0.533245\pi$
$978$		0			0
$979$	2417.19	+	4186.70i	0.0789109	+	0.136678i
$980$		−	62470.7i		−	2.03628i
$981$		0			0
$982$	4483.64	+	2588.63i	0.145701	+	0.0841208i
$983$	16346.0	+	9437.38i	0.530373	+	0.306211i	0.741168	−	0.671319i	$-0.234272\pi$
$983$	16346.0	+	9437.38i	0.530373	+	0.306211i	−0.210795	+	0.977530i	$0.567605\pi$
$984$		0			0
$985$	−33733.0	+	58427.3i	−1.09119	+	1.89000i
$986$	3664.21	+	2115.53i	0.118349	+	0.0683289i
$987$		0			0
$988$	−2468.02	+	5248.24i	−0.0794717	+	0.168997i
$989$	3389.54			0.108980
$990$		0			0
$991$	−6486.71	−	11235.3i	−0.207928	−	0.360143i	0.743133	−	0.669143i	$-0.233339\pi$
$991$	−6486.71	−	11235.3i	−0.207928	−	0.360143i	−0.951062	+	0.309001i	$0.900005\pi$
$992$	−18387.7	−	31848.4i	−0.588518	−	1.01934i
$993$		0			0
$994$		−	34484.3i		−	1.10038i
$995$			29636.4i			0.944259i
$996$		0			0
$997$	−30380.5	−	52620.6i	−0.965056	−	1.67153i	−0.709465	−	0.704741i	$-0.751063\pi$
$997$	−30380.5	−	52620.6i	−0.965056	−	1.67153i	−0.255591	−	0.966785i	$-0.582270\pi$
$998$	10408.7	+	18028.3i	0.330141	+	0.571821i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	351.4.l.a.127.10		80
3.2	odd	2		117.4.l.a.88.31	yes	80
9.4	even	3		351.4.r.a.10.31		80
9.5	odd	6		117.4.r.a.49.10	yes	80
13.4	even	6		351.4.r.a.316.31		80
39.17	odd	6		117.4.r.a.43.10	yes	80
117.4	even	6	inner	351.4.l.a.199.31		80
117.95	odd	6		117.4.l.a.4.10	✓	80

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
117.4.l.a.4.10	✓	80	117.95	odd	6
117.4.l.a.88.31	yes	80	3.2	odd	2
117.4.r.a.43.10	yes	80	39.17	odd	6
117.4.r.a.49.10	yes	80	9.5	odd	6
351.4.l.a.127.10		80	1.1	even	1	trivial
351.4.l.a.199.31		80	117.4	even	6	inner
351.4.r.a.10.31		80	9.4	even	3
351.4.r.a.316.31		80	13.4	even	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 351 = 3^{3} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	351.l (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q-3.67076i q^{2} -5.47446 q^{4} +(-15.6805 + 9.05312i) q^{5} +(27.0172 - 15.5984i) q^{7} -9.27065i q^{8} +O(q^{10})\)	\(q-3.67076i q^{2} -5.47446 q^{4} +(-15.6805 + 9.05312i) q^{5} +(27.0172 - 15.5984i) q^{7} -9.27065i q^{8} +(33.2318 + 57.5592i) q^{10} +5.30011i q^{11} +(-3.93395 - 46.7068i) q^{13} +(-57.2580 - 99.1737i) q^{14} -77.8260 q^{16} +(1.95690 - 3.38945i) q^{17} +(19.5736 + 11.3008i) q^{19} +(85.8420 - 49.5609i) q^{20} +19.4554 q^{22} +(27.9664 - 48.4393i) q^{23} +(101.418 - 175.661i) q^{25} +(-171.449 + 14.4406i) q^{26} +(-147.905 + 85.3928i) q^{28} -294.507 q^{29} +(-150.573 + 86.9333i) q^{31} +211.515i q^{32} +(-12.4419 - 7.18331i) q^{34} +(-282.428 + 489.180i) q^{35} +(-328.880 + 189.879i) q^{37} +(41.4826 - 71.8500i) q^{38} +(83.9283 + 145.368i) q^{40} +(-114.876 - 66.3235i) q^{41} +(30.3001 + 52.4813i) q^{43} -29.0152i q^{44} +(-177.809 - 102.658i) q^{46} +(-229.733 - 132.636i) q^{47} +(315.121 - 545.805i) q^{49} +(-644.809 - 372.281i) q^{50} +(21.5362 + 255.694i) q^{52} +446.339 q^{53} +(-47.9825 - 83.1082i) q^{55} +(-144.607 - 250.467i) q^{56} +1081.06i q^{58} -253.923i q^{59} +(-176.091 - 304.998i) q^{61} +(319.111 + 552.716i) q^{62} +153.812 q^{64} +(484.528 + 696.770i) q^{65} +(-387.416 - 223.675i) q^{67} +(-10.7130 + 18.5554i) q^{68} +(1795.66 + 1036.73i) q^{70} +(260.787 + 150.566i) q^{71} -86.9083i q^{73} +(697.000 + 1207.24i) q^{74} +(-107.155 - 61.8659i) q^{76} +(82.6732 + 143.194i) q^{77} +(-243.931 + 422.500i) q^{79} +(1220.35 - 704.568i) q^{80} +(-243.457 + 421.681i) q^{82} +(-842.406 - 486.363i) q^{83} +70.8642i q^{85} +(192.646 - 111.224i) q^{86} +49.1355 q^{88} +(789.927 - 456.065i) q^{89} +(-834.836 - 1200.52i) q^{91} +(-153.101 + 265.179i) q^{92} +(-486.875 + 843.293i) q^{94} -409.231 q^{95} +(-11.9039 + 6.87274i) q^{97} +(-2003.52 - 1156.73i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 80 q - 306 q^{4} - 3 q^{7}+O(q^{10}) \) 80 * q - 306 * q^4 - 3 * q^7	\( 80 q - 306 q^{4} - 3 q^{7} - 10 q^{10} - 13 q^{13} - 126 q^{14} + 1102 q^{16} + 138 q^{17} - 96 q^{19} + 387 q^{20} + 62 q^{22} + 327 q^{23} + 798 q^{25} - 510 q^{26} + 18 q^{28} + 402 q^{29} + 180 q^{31} + 24 q^{34} - 297 q^{35} + 246 q^{37} + 768 q^{38} + 328 q^{40} - 381 q^{41} - 83 q^{43} - 6 q^{46} - 372 q^{47} + 1613 q^{49} + 708 q^{50} + 402 q^{52} + 2568 q^{53} - 127 q^{55} + 2298 q^{56} - 419 q^{61} - 135 q^{62} - 3178 q^{64} - 363 q^{65} + 879 q^{67} - 1950 q^{68} - 1005 q^{70} + 2598 q^{71} - 471 q^{74} + 1485 q^{76} + 1584 q^{77} - 260 q^{79} + 1332 q^{80} - 1273 q^{82} - 1194 q^{83} + 2910 q^{86} - 1562 q^{88} + 1056 q^{89} + 537 q^{91} - 1056 q^{92} + 539 q^{94} - 10584 q^{95} + 789 q^{97} + 6339 q^{98}+O(q^{100}) \) 80 * q - 306 * q^4 - 3 * q^7 - 10 * q^10 - 13 * q^13 - 126 * q^14 + 1102 * q^16 + 138 * q^17 - 96 * q^19 + 387 * q^20 + 62 * q^22 + 327 * q^23 + 798 * q^25 - 510 * q^26 + 18 * q^28 + 402 * q^29 + 180 * q^31 + 24 * q^34 - 297 * q^35 + 246 * q^37 + 768 * q^38 + 328 * q^40 - 381 * q^41 - 83 * q^43 - 6 * q^46 - 372 * q^47 + 1613 * q^49 + 708 * q^50 + 402 * q^52 + 2568 * q^53 - 127 * q^55 + 2298 * q^56 - 419 * q^61 - 135 * q^62 - 3178 * q^64 - 363 * q^65 + 879 * q^67 - 1950 * q^68 - 1005 * q^70 + 2598 * q^71 - 471 * q^74 + 1485 * q^76 + 1584 * q^77 - 260 * q^79 + 1332 * q^80 - 1273 * q^82 - 1194 * q^83 + 2910 * q^86 - 1562 * q^88 + 1056 * q^89 + 537 * q^91 - 1056 * q^92 + 539 * q^94 - 10584 * q^95 + 789 * q^97 + 6339 * q^98

Introduction

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