LMFDB - Embedded newform 177.6.d.b.176.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [177,6,Mod(176,177)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(177, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 1]))

N = Newforms(chi, 6, names="a")

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

chi := DirichletCharacter("177.176");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 177 = 3 \cdot 59 $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	177.d (of order $2$, degree $1$, 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:	$28.3879361069$
Analytic rank:	$0$
Dimension:	$92$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			176.10
Character	$\chi$	$=$	177.176
Dual form			177.6.d.b.176.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-9.63720 q^{2} +(15.3454 + 2.74211i) q^{3} +60.8757 q^{4} +48.0995i q^{5} +(-147.887 - 26.4263i) q^{6} +55.2643 q^{7} -278.281 q^{8} +(227.962 + 84.1575i) q^{9} +O(q^{10})$	\(q-9.63720 q^{2} +(15.3454 + 2.74211i) q^{3} +60.8757 q^{4} +48.0995i q^{5} +(-147.887 - 26.4263i) q^{6} +55.2643 q^{7} -278.281 q^{8} +(227.962 + 84.1575i) q^{9} -463.545i q^{10} -33.0223 q^{11} +(934.161 + 166.928i) q^{12} +847.868i q^{13} -532.594 q^{14} +(-131.894 + 738.106i) q^{15} +733.828 q^{16} +1128.87i q^{17} +(-2196.91 - 811.043i) q^{18} -1381.08 q^{19} +2928.09i q^{20} +(848.052 + 151.541i) q^{21} +318.243 q^{22} +468.321 q^{23} +(-4270.33 - 763.077i) q^{24} +811.434 q^{25} -8171.08i q^{26} +(3267.39 + 1916.53i) q^{27} +3364.25 q^{28} -408.390i q^{29} +(1271.09 - 7113.28i) q^{30} -5084.86i q^{31} +1832.94 q^{32} +(-506.740 - 90.5508i) q^{33} -10879.1i q^{34} +2658.19i q^{35} +(13877.3 + 5123.15i) q^{36} +1578.30i q^{37} +13309.8 q^{38} +(-2324.95 + 13010.9i) q^{39} -13385.2i q^{40} -16986.4i q^{41} +(-8172.85 - 1460.43i) q^{42} +11165.2i q^{43} -2010.26 q^{44} +(-4047.94 + 10964.9i) q^{45} -4513.30 q^{46} -12073.6 q^{47} +(11260.9 + 2012.24i) q^{48} -13752.9 q^{49} -7819.96 q^{50} +(-3095.48 + 17322.9i) q^{51} +51614.6i q^{52} -9984.02i q^{53} +(-31488.5 - 18469.9i) q^{54} -1588.36i q^{55} -15379.0 q^{56} +(-21193.2 - 3787.08i) q^{57} +3935.73i q^{58} +(19800.7 + 17968.2i) q^{59} +(-8029.16 + 44932.7i) q^{60} +50439.9i q^{61} +49003.8i q^{62} +(12598.1 + 4650.91i) q^{63} -41146.9 q^{64} -40782.1 q^{65} +(4883.55 + 872.656i) q^{66} +34064.3i q^{67} +68720.5i q^{68} +(7186.57 + 1284.19i) q^{69} -25617.5i q^{70} +18917.3i q^{71} +(-63437.4 - 23419.4i) q^{72} -23663.0i q^{73} -15210.4i q^{74} +(12451.8 + 2225.04i) q^{75} -84074.3 q^{76} -1824.95 q^{77} +(22406.0 - 125388. i) q^{78} -61929.7 q^{79} +35296.8i q^{80} +(44884.0 + 38369.4i) q^{81} +163701. i q^{82} -31566.8 q^{83} +(51625.8 + 9225.16i) q^{84} -54297.9 q^{85} -107601. i q^{86} +(1119.85 - 6266.90i) q^{87} +9189.48 q^{88} +52358.2 q^{89} +(39010.8 - 105671. i) q^{90} +46856.9i q^{91} +28509.4 q^{92} +(13943.2 - 78029.1i) q^{93} +116356. q^{94} -66429.4i q^{95} +(28127.2 + 5026.12i) q^{96} -25026.4i q^{97} +132539. q^{98} +(-7527.82 - 2779.07i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 92 q + 22 q^{3} + 1724 q^{4} - 80 q^{7} + 2 q^{9}+O(q^{10}) $ 92 * q + 22 * q^3 + 1724 * q^4 - 80 * q^7 + 2 * q^9	$ 92 q + 22 q^{3} + 1724 q^{4} - 80 q^{7} + 2 q^{9} - 1244 q^{12} + 1116 q^{15} + 14724 q^{16} + 1784 q^{19} + 6388 q^{21} - 8140 q^{22} - 48208 q^{25} - 6458 q^{27} - 19092 q^{28} - 20832 q^{36} - 134984 q^{45} + 51180 q^{46} + 61720 q^{48} + 174556 q^{49} + 8332 q^{51} + 236784 q^{57} + 375208 q^{60} - 429890 q^{63} + 561472 q^{64} - 11596 q^{66} + 169948 q^{75} + 111488 q^{76} + 356264 q^{78} + 180260 q^{79} + 79554 q^{81} + 269308 q^{84} + 111028 q^{85} - 318764 q^{87} - 1242976 q^{88} - 513608 q^{94}+O(q^{100}) $ 92 * q + 22 * q^3 + 1724 * q^4 - 80 * q^7 + 2 * q^9 - 1244 * q^12 + 1116 * q^15 + 14724 * q^16 + 1784 * q^19 + 6388 * q^21 - 8140 * q^22 - 48208 * q^25 - 6458 * q^27 - 19092 * q^28 - 20832 * q^36 - 134984 * q^45 + 51180 * q^46 + 61720 * q^48 + 174556 * q^49 + 8332 * q^51 + 236784 * q^57 + 375208 * q^60 - 429890 * q^63 + 561472 * q^64 - 11596 * q^66 + 169948 * q^75 + 111488 * q^76 + 356264 * q^78 + 180260 * q^79 + 79554 * q^81 + 269308 * q^84 + 111028 * q^85 - 318764 * q^87 - 1242976 * q^88 - 513608 * q^94

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/177\mathbb{Z}\right)^\times$.

$n$	$61$	$119$
$\chi(n)$	$-1$	$-1$

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 $

$2$	−9.63720			−1.70363			−0.851817	−	0.523840i	$-0.824499\pi$
$2$	−9.63720			−1.70363			−0.851817	+	0.523840i	$0.824499\pi$
$3$	15.3454	+	2.74211i	0.984407	+	0.175907i
$3$	15.3454	+	2.74211i	0.984407	+	0.175907i
$4$	60.8757			1.90237
$5$			48.0995i			0.860431i	0.902726	+	0.430215i	$0.141562\pi$
$5$			48.0995i			0.860431i	−0.902726	+	0.430215i	$0.858438\pi$
$6$	−147.887	−	26.4263i	−1.67707	−	0.299680i
$7$	55.2643			0.426285			0.213142	−	0.977021i	$-0.431630\pi$
$7$	55.2643			0.426285			0.213142	+	0.977021i	$0.431630\pi$
$8$	−278.281			−1.53730
$9$	227.962	+	84.1575i	0.938114	+	0.346327i
$10$		−	463.545i		−	1.46586i
$11$	−33.0223			−0.0822859			−0.0411430	−	0.999153i	$-0.513100\pi$
$11$	−33.0223			−0.0822859			−0.0411430	+	0.999153i	$0.513100\pi$
$12$	934.161	+	166.928i	1.87270	+	0.334638i
$13$			847.868i			1.39146i	0.718305	+	0.695729i	$0.244918\pi$
$13$			847.868i			1.39146i	−0.718305	+	0.695729i	$0.755082\pi$
$14$	−532.594			−0.726233
$15$	−131.894	+	738.106i	−0.151355	+	0.847014i
$16$	733.828			0.716629
$17$			1128.87i			0.947371i	0.880694	+	0.473686i	$0.157077\pi$
$17$			1128.87i			0.947371i	−0.880694	+	0.473686i	$0.842923\pi$
$18$	−2196.91	−	811.043i	−1.59820	−	0.590014i
$19$	−1381.08			−0.877678			−0.438839	−	0.898566i	$-0.644610\pi$
$19$	−1381.08			−0.877678			−0.438839	+	0.898566i	$0.644610\pi$
$20$			2928.09i			1.63685i
$21$	848.052	+	151.541i	0.419638	+	0.0749863i
$22$	318.243			0.140185
$23$	468.321			0.184597			0.0922984	−	0.995731i	$-0.470579\pi$
$23$	468.321			0.184597			0.0922984	+	0.995731i	$0.470579\pi$
$24$	−4270.33	−	763.077i	−1.51333	−	0.270421i
$25$	811.434			0.259659
$26$		−	8171.08i		−	2.37053i
$27$	3267.39	+	1916.53i	0.862564	+	0.505947i
$28$	3364.25			0.810949
$29$		−	408.390i		−	0.0901737i	−0.998983	−	0.0450868i	$-0.985644\pi$
$29$		−	408.390i		−	0.0901737i	0.998983	−	0.0450868i	$-0.0143565\pi$
$30$	1271.09	−	7113.28i	0.257854	−	1.44300i
$31$		−	5084.86i		−	0.950330i	−0.879897	−	0.475165i	$-0.842388\pi$
$31$		−	5084.86i		−	0.950330i	0.879897	−	0.475165i	$-0.157612\pi$
$32$	1832.94			0.316427
$33$	−506.740	−	90.5508i	−0.0810028	−	0.0144746i
$34$		−	10879.1i		−	1.61397i
$35$			2658.19i			0.366789i
$36$	13877.3	+	5123.15i	1.78464	+	0.658841i
$37$			1578.30i			0.189533i	0.995500	+	0.0947666i	$0.0302105\pi$
$37$			1578.30i			0.189533i	−0.995500	+	0.0947666i	$0.969790\pi$
$38$	13309.8			1.49524
$39$	−2324.95	+	13010.9i	−0.244766	+	1.36976i
$40$		−	13385.2i		−	1.32274i
$41$		−	16986.4i		−	1.57813i	−0.614312	−	0.789063i	$-0.710566\pi$
$41$		−	16986.4i		−	1.57813i	0.614312	−	0.789063i	$-0.289434\pi$
$42$	−8172.85	−	1460.43i	−0.714909	−	0.127749i
$43$			11165.2i			0.920863i	0.887695	+	0.460431i	$0.152305\pi$
$43$			11165.2i			0.920863i	−0.887695	+	0.460431i	$0.847695\pi$
$44$	−2010.26			−0.156538
$45$	−4047.94	+	10964.9i	−0.297991	+	0.807182i
$46$	−4513.30			−0.314485
$47$	−12073.6			−0.797249			−0.398624	−	0.917114i	$-0.630512\pi$
$47$	−12073.6			−0.797249			−0.398624	+	0.917114i	$0.630512\pi$
$48$	11260.9	+	2012.24i	0.705455	+	0.126060i
$49$	−13752.9			−0.818281
$50$	−7819.96			−0.442364
$51$	−3095.48	+	17322.9i	−0.166649	+	0.932599i
$52$			51614.6i			2.64706i
$53$		−	9984.02i		−	0.488220i	−0.969748	−	0.244110i	$-0.921504\pi$
$53$		−	9984.02i		−	0.488220i	0.969748	−	0.244110i	$-0.0784958\pi$
$54$	−31488.5	−	18469.9i	−1.46949	−	0.861948i
$55$		−	1588.36i		−	0.0708013i
$56$	−15379.0			−0.655327
$57$	−21193.2	−	3787.08i	−0.863992	−	0.154389i
$58$			3935.73i			0.153623i
$59$	19800.7	+	17968.2i	0.740543	+	0.672009i
$59$	19800.7	+	17968.2i	0.740543	+	0.672009i
$60$	−8029.16	+	44932.7i	−0.287933	+	1.61133i
$61$			50439.9i			1.73560i	0.496914	+	0.867800i	$0.334466\pi$
$61$			50439.9i			1.73560i	−0.496914	+	0.867800i	$0.665534\pi$
$62$			49003.8i			1.61901i
$63$	12598.1	+	4650.91i	0.399904	+	0.147634i
$64$	−41146.9			−1.25570
$65$	−40782.1			−1.19725
$66$	4883.55	+	872.656i	0.137999	+	0.0246595i
$67$			34064.3i			0.927070i	0.886079	+	0.463535i	$0.153419\pi$
$67$			34064.3i			0.927070i	−0.886079	+	0.463535i	$0.846581\pi$
$68$			68720.5i			1.80225i
$69$	7186.57	+	1284.19i	0.181718	+	0.0324718i
$70$		−	25617.5i		−	0.624873i
$71$			18917.3i			0.445363i	0.974891	+	0.222682i	$0.0714810\pi$
$71$			18917.3i			0.445363i	−0.974891	+	0.222682i	$0.928519\pi$
$72$	−63437.4	−	23419.4i	−1.44216	−	0.532409i
$73$		−	23663.0i		−	0.519711i	−0.965647	−	0.259856i	$-0.916325\pi$
$73$		−	23663.0i		−	0.519711i	0.965647	−	0.259856i	$-0.0836750\pi$
$74$		−	15210.4i		−	0.322895i
$75$	12451.8	+	2225.04i	0.255610	+	0.0456757i
$76$	−84074.3			−1.66966
$77$	−1824.95			−0.0350772
$78$	22406.0	−	125388.i	0.416992	−	2.33357i
$79$	−61929.7			−1.11643			−0.558214	−	0.829697i	$-0.688513\pi$
$79$	−61929.7			−1.11643			−0.558214	+	0.829697i	$0.688513\pi$
$80$			35296.8i			0.616610i
$81$	44884.0	+	38369.4i	0.760115	+	0.649789i
$82$			163701.i			2.68855i
$83$	−31566.8			−0.502962			−0.251481	−	0.967862i	$-0.580918\pi$
$83$	−31566.8			−0.502962			−0.251481	+	0.967862i	$0.580918\pi$
$84$	51625.8	+	9225.16i	0.798304	+	0.142651i
$85$	−54297.9			−0.815147
$86$		−	107601.i		−	1.56881i
$87$	1119.85	−	6266.90i	0.0158621	−	0.0887676i
$88$	9189.48			0.126498
$89$	52358.2			0.700664			0.350332	−	0.936626i	$-0.386069\pi$
$89$	52358.2			0.700664			0.350332	+	0.936626i	$0.386069\pi$
$90$	39010.8	−	105671.i	0.507667	−	1.37514i
$91$			46856.9i			0.593157i
$92$	28509.4			0.351170
$93$	13943.2	−	78029.1i	0.167169	−	0.935512i
$94$	116356.			1.35822
$95$		−	66429.4i		−	0.755181i
$96$	28127.2	+	5026.12i	0.311493	+	0.0556615i
$97$		−	25026.4i		−	0.270066i	−0.990841	−	0.135033i	$-0.956886\pi$
$97$		−	25026.4i		−	0.270066i	0.990841	−	0.135033i	$-0.0431140\pi$
$98$	132539.			1.39405
$99$	−7527.82	−	2779.07i	−0.0771936	−	0.0284978i
$100$	49396.6			0.493966
$101$	−43891.2			−0.428128			−0.214064	−	0.976820i	$-0.568670\pi$
$101$	−43891.2			−0.428128			−0.214064	+	0.976820i	$0.568670\pi$
$102$	29831.7	−	166944.i	0.283908	−	1.58881i
$103$		−	13348.4i		−	0.123976i	−0.998077	−	0.0619880i	$-0.980256\pi$
$103$		−	13348.4i		−	0.123976i	0.998077	−	0.0619880i	$-0.0197440\pi$
$104$		−	235946.i		−	2.13909i
$105$	−7289.05	+	40790.9i	−0.0645205	+	0.361069i
$106$			96218.0i			0.831748i
$107$			202715.i			1.71170i	0.517226	+	0.855849i	$0.326965\pi$
$107$			202715.i			1.71170i	−0.517226	+	0.855849i	$0.673035\pi$
$108$	198905.	+	116670.i	1.64091	+	0.962496i
$109$		−	25308.3i		−	0.204031i	−0.994783	−	0.102016i	$-0.967471\pi$
$109$		−	25308.3i		−	0.204031i	0.994783	−	0.102016i	$-0.0325292\pi$
$110$			15307.3i			0.120619i
$111$	−4327.87	+	24219.6i	−0.0333401	+	0.186578i
$112$	40554.5			0.305488
$113$	−158888.			−1.17056			−0.585281	−	0.810831i	$-0.699016\pi$
$113$	−158888.			−1.17056			−0.585281	+	0.810831i	$0.699016\pi$
$114$	204243.	+	36496.8i	1.47193	+	0.263023i
$115$			22526.0i			0.158833i
$116$		−	24861.0i		−	0.171543i
$117$	−71354.5	+	193281.i	−0.481899	+	1.30535i
$118$	−190823.	−	173163.i	−1.26161	−	1.14486i
$119$			62386.0i			0.403850i
$120$	36703.7	−	205401.i	0.232679	−	1.30211i
$121$	−159961.			−0.993229
$122$		−	486099.i		−	2.95682i
$123$	46578.6	−	260663.i	0.277603	−	1.55352i
$124$		−	309544.i		−	1.80788i
$125$			189341.i			1.08385i
$126$	−121411.	−	44821.7i	−0.681289	−	0.251514i
$127$	22410.3			0.123293			0.0616464	−	0.998098i	$-0.480365\pi$
$127$	22410.3			0.123293			0.0616464	+	0.998098i	$0.480365\pi$
$128$	337887.			1.82283
$129$	−30616.2	+	171334.i	−0.161986	+	0.906504i
$130$	393025.			2.03968
$131$	21644.2			0.110195			0.0550976	−	0.998481i	$-0.482453\pi$
$131$	21644.2			0.110195			0.0550976	+	0.998481i	$0.482453\pi$
$132$	−30848.1	−	5512.34i	−0.154097	−	0.0275360i
$133$	−76324.5			−0.374141
$134$		−	328285.i		−	1.57939i
$135$	−92184.0	+	157160.i	−0.435333	+	0.742177i
$136$		−	314142.i		−	1.45639i
$137$		−	79532.7i		−	0.362030i	−0.983480	−	0.181015i	$-0.942062\pi$
$137$		−	79532.7i		−	0.362030i	0.983480	−	0.181015i	$-0.0579382\pi$
$138$	−69258.4	−	12376.0i	−0.309581	−	0.0553200i
$139$	102245.			0.448852			0.224426	−	0.974491i	$-0.427949\pi$
$139$	102245.			0.448852			0.224426	+	0.974491i	$0.427949\pi$
$140$			161819.i			0.697766i
$141$	−185275.	−	33107.3i	−0.784817	−	0.140241i
$142$		−	182310.i		−	0.758735i
$143$		−	27998.5i		−	0.114497i
$144$	167285.	+	61757.1i	0.672280	+	0.248188i
$145$	19643.4			0.0775882
$146$			228045.i			0.885398i
$147$	−211043.	−	37711.9i	−0.805522	−	0.143941i
$148$			96080.1i			0.360561i
$149$	73849.9			0.272511			0.136256	−	0.990674i	$-0.456493\pi$
$149$	73849.9			0.272511			0.136256	+	0.990674i	$0.456493\pi$
$150$	−120000.	−	21443.2i	−0.435466	−	0.0778146i
$151$			396440.i			1.41493i	0.706748	+	0.707465i	$0.250161\pi$
$151$			396440.i			1.41493i	−0.706748	+	0.707465i	$0.749839\pi$
$152$	384329.			1.34925
$153$	−95002.5	+	257338.i	−0.328100	+	0.888742i
$154$	17587.5			0.0597587
$155$	244579.			0.817694
$156$	−141533.	+	792045.i	−0.465635	+	2.60578i
$157$		−	318654.i		−	1.03174i	−0.856667	−	0.515870i	$-0.827469\pi$
$157$		−	318654.i		−	1.03174i	0.856667	−	0.515870i	$-0.172531\pi$
$158$	596829.			1.90198
$159$	27377.3	−	153209.i	0.0858811	−	0.480607i
$160$			88163.5i			0.272263i
$161$	25881.4			0.0786908
$162$	−432557.	−	369773.i	−1.29496	−	1.10700i
$163$	−44552.9			−0.131343			−0.0656715	−	0.997841i	$-0.520919\pi$
$163$	−44552.9			−0.131343			−0.0656715	+	0.997841i	$0.520919\pi$
$164$		−	1.03406e6i		−	3.00217i
$165$	4355.45	−	24373.9i	0.0124544	−	0.0696973i
$166$	304216.			0.856863
$167$		−	217795.i		−	0.604305i	−0.953260	−	0.302152i	$-0.902295\pi$
$167$		−	217795.i		−	0.604305i	0.953260	−	0.302152i	$-0.0977052\pi$
$168$	−235997.	−	42171.0i	−0.645109	−	0.115276i
$169$	−347587.			−0.936153
$170$	523280.			1.38871
$171$	−314834.	−	116228.i	−0.823362	−	0.303964i
$172$			679689.i			1.75182i
$173$	320693.			0.814657			0.407328	−	0.913282i	$-0.366460\pi$
$173$	320693.			0.814657			0.407328	+	0.913282i	$0.366460\pi$
$174$	−10792.2	+	60395.4i	−0.0270233	+	0.151227i
$175$	44843.4			0.110689
$176$	−24232.7			−0.0589685
$177$	254579.	+	330025.i	0.610785	+	0.791796i
$178$	−504587.			−1.19367
$179$	309289.			0.721492			0.360746	−	0.932664i	$-0.382522\pi$
$179$	309289.			0.721492			0.360746	+	0.932664i	$0.382522\pi$
$180$	−246421.	+	667493.i	−0.566887	+	1.53556i
$181$	−519260.			−1.17812			−0.589058	−	0.808090i	$-0.700501\pi$
$181$	−519260.			−1.17812			−0.589058	+	0.808090i	$0.700501\pi$
$182$		−	451569.i		−	1.01052i
$183$	−138312.	+	774019.i	−0.305303	+	1.70854i
$184$	−130325.			−0.283781
$185$	−75915.5			−0.163080
$186$	−134374.	+	751982.i	−0.284795	+	1.59377i
$187$		−	37277.7i		−	0.0779553i
$188$	−734992.			−1.51666
$189$	180570.	+	105915.i	0.367698	+	0.215678i
$190$			640193.i			1.28655i
$191$	−381662.			−0.757000			−0.378500	−	0.925601i	$-0.623560\pi$
$191$	−381662.			−0.757000			−0.378500	+	0.925601i	$0.623560\pi$
$192$	−631415.	−	112829.i	−1.23612	−	0.220887i
$193$	383123.			0.740364			0.370182	−	0.928959i	$-0.379295\pi$
$193$	383123.			0.740364			0.370182	+	0.928959i	$0.379295\pi$
$194$			241185.i			0.460093i
$195$	−625816.	−	111829.i	−1.17858	−	0.210605i
$196$	−837215.			−1.55667
$197$			536432.i			0.984802i	0.870368	+	0.492401i	$0.163881\pi$
$197$			536432.i			0.984802i	−0.870368	+	0.492401i	$0.836119\pi$
$198$	72547.1	+	26782.5i	0.131509	+	0.0485499i
$199$	694003.			1.24231			0.621153	−	0.783689i	$-0.286665\pi$
$199$	694003.			1.24231			0.621153	+	0.783689i	$0.286665\pi$
$200$	−225807.			−0.399174
$201$	−93408.1	+	522730.i	−0.163078	+	0.912614i
$202$	422988.			0.729373
$203$		−	22569.4i		−	0.0384397i
$204$	−188439.	+	1.05454e6i	−0.317027	+	1.77414i
$205$	817038.			1.35787
$206$			128642.i			0.211210i
$207$	106759.	+	39412.7i	0.173173	+	0.0639309i
$208$			622189.i			0.997159i
$209$	45606.5			0.0722205
$210$	70246.1	−	393111.i	0.109919	−	0.615129i
$211$		−	328315.i		−	0.507673i	−0.967247	−	0.253836i	$-0.918307\pi$
$211$		−	328315.i		−	0.507673i	0.967247	−	0.253836i	$-0.0816925\pi$
$212$		−	607784.i		−	0.928773i
$213$	−51873.5	+	290294.i	−0.0783423	+	0.438419i
$214$		−	1.95361e6i		−	2.91611i
$215$	−537040.			−0.792339
$216$	−909252.	−	533333.i	−1.32602	−	0.777792i
$217$		−	281011.i		−	0.405111i
$218$			243901.i			0.347594i
$219$	64886.5	−	363118.i	0.0914206	−	0.511608i
$220$		−	96692.3i		−	0.134690i
$221$	−957129.			−1.31823
$222$	41708.6	−	233409.i	0.0567993	−	0.317860i
$223$	1.15178e6			1.55098			0.775492	−	0.631358i	$-0.217502\pi$
$223$	1.15178e6			1.55098			0.775492	+	0.631358i	$0.217502\pi$
$224$	101296.			0.134888
$225$	184976.	+	68288.3i	0.243590	+	0.0899269i
$226$	1.53123e6			1.99421
$227$	1.07066e6			1.37907			0.689535	−	0.724252i	$-0.257815\pi$
$227$	1.07066e6			1.37907			0.689535	+	0.724252i	$0.257815\pi$
$228$	−1.29015e6	−	230541.i	−1.64363	−	0.293705i
$229$		−	1.32871e6i		−	1.67433i	−0.546950	−	0.837165i	$-0.684211\pi$
$229$		−	1.32871e6i		−	1.67433i	0.546950	−	0.837165i	$-0.315789\pi$
$230$		−	217088.i		−	0.270593i
$231$	−28004.6	−	5004.23i	−0.0345303	−	0.00617031i
$232$			113647.i			0.138624i
$233$	−1.58830e6			−1.91664			−0.958322	−	0.285690i	$-0.907777\pi$
$233$	−1.58830e6			−1.91664			−0.958322	+	0.285690i	$0.907777\pi$
$234$	687657.	−	1.86269e6i	0.820980	−	2.22383i
$235$		−	580737.i		−	0.685977i
$236$	1.20538e6	+	1.09383e6i	1.40878	+	1.27841i
$237$	−950334.	−	169818.i	−1.09902	−	0.196387i
$238$		−	601227.i		−	0.688012i
$239$		−	820213.i		−	0.928821i	−0.885620	−	0.464410i	$-0.846266\pi$
$239$		−	820213.i		−	0.928821i	0.885620	−	0.464410i	$-0.153734\pi$
$240$	−96787.7	+	541643.i	−0.108466	+	0.606995i
$241$	1.58114e6			1.75359			0.876794	−	0.480867i	$-0.159678\pi$
$241$	1.58114e6			1.75359			0.876794	+	0.480867i	$0.159678\pi$
$242$	1.54157e6			1.69210
$243$	583550.	+	711870.i	0.633960	+	0.773366i
$244$			3.07056e6i			3.30174i
$245$		−	661506.i		−	0.704074i
$246$	−448888.	+	2.51206e6i	−0.472933	+	2.64663i
$247$		−	1.17097e6i		−	1.22125i
$248$			1.41502e6i			1.46094i
$249$	−484405.	−	86559.7i	−0.495120	−	0.0884743i
$250$		−	1.82471e6i		−	1.84648i
$251$			1.28330e6i			1.28572i	0.765985	+	0.642858i	$0.222252\pi$
$251$			1.28330e6i			1.28572i	−0.765985	+	0.642858i	$0.777748\pi$
$252$	766921.	+	283127.i	0.760763	+	0.280854i
$253$	−15465.0			−0.0151897
$254$	−215972.			−0.210046
$255$	−833223.	−	148891.i	−0.802436	−	0.143390i
$256$	−1.93959e6			−1.84973
$257$			369551.i			0.349013i	0.984656	+	0.174507i	$0.0558330\pi$
$257$			369551.i			0.349013i	−0.984656	+	0.174507i	$0.944167\pi$
$258$	295054.	−	1.65118e6i	0.275964	−	1.54435i
$259$			87223.7i			0.0807951i
$260$	−2.48264e6			−2.27761
$261$	34369.1	−	93097.2i	0.0312296	−	0.0845932i
$262$	−208589.			−0.187732
$263$		−	408145.i		−	0.363852i	−0.983312	−	0.181926i	$-0.941767\pi$
$263$		−	408145.i		−	0.363852i	0.983312	−	0.181926i	$-0.0582332\pi$
$264$	141016.	+	25198.6i	0.124526	+	0.0222518i
$265$	480227.			0.420080
$266$	735555.			0.637399
$267$	803457.	+	143572.i	0.689738	+	0.123251i
$268$			2.07369e6i			1.76363i
$269$	−1.05990e6			−0.893070			−0.446535	−	0.894766i	$-0.647342\pi$
$269$	−1.05990e6			−0.893070			−0.446535	+	0.894766i	$0.647342\pi$
$270$	888396.	−	1.51458e6i	0.741647	−	1.26440i
$271$	477246.			0.394747			0.197373	−	0.980328i	$-0.436759\pi$
$271$	477246.			0.394747			0.197373	+	0.980328i	$0.436759\pi$
$272$			828394.i			0.678914i
$273$	−128487.	+	719037.i	−0.104340	+	0.583908i
$274$			766472.i			0.616766i
$275$	−26795.4			−0.0213663
$276$	437487.	+	78175.9i	0.345695	+	0.0617732i
$277$	924308.			0.723798			0.361899	−	0.932217i	$-0.382129\pi$
$277$	924308.			0.723798			0.361899	+	0.932217i	$0.382129\pi$
$278$	−985352.			−0.764679
$279$	427929.	−	1.15915e6i	0.329125	−	0.891518i
$280$		−	739723.i		−	0.563864i
$281$			621749.i			0.469731i	0.972028	+	0.234865i	$0.0754649\pi$
$281$			621749.i			0.469731i	−0.972028	+	0.234865i	$0.924535\pi$
$282$	1.78553e6	+	319062.i	1.33704	+	0.238920i
$283$		−	325081.i		−	0.241282i	−0.992696	−	0.120641i	$-0.961505\pi$
$283$		−	325081.i		−	0.241282i	0.992696	−	0.120641i	$-0.0384950\pi$
$284$			1.15161e6i			0.847244i
$285$	182157.	−	1.01938e6i	0.132841	−	0.743406i
$286$			269828.i			0.195061i
$287$		−	938742.i		−	0.672731i
$288$	417840.	+	154256.i	0.296844	+	0.109587i
$289$	145519.			0.102488
$290$	−189307.			−0.132182
$291$	68625.2	−	384040.i	0.0475063	−	0.265854i
$292$		−	1.44050e6i		−	0.988681i
$293$			2.07939e6i			1.41503i	0.706697	+	0.707517i	$0.250185\pi$
$293$			2.07939e6i			1.41503i	−0.706697	+	0.707517i	$0.749815\pi$
$294$	2.03386e6	+	363437.i	1.37231	+	0.245223i
$295$	−864263.	+	952405.i	−0.578217	+	0.637186i
$296$		−	439211.i		−	0.291369i
$297$	−107897.	−	63288.1i	−0.0709769	−	0.0416323i
$298$	−711707.			−0.464259
$299$			397074.i			0.256858i
$300$	758010.	+	135451.i	0.486264	+	0.0868919i
$301$			617037.i			0.392550i
$302$		−	3.82057e6i		−	2.41052i
$303$	−673527.	−	120354.i	−0.421452	−	0.0753105i
$304$	−1.01348e6			−0.628970
$305$	−2.42614e6			−1.49336
$306$	915559.	−	2.48002e6i	0.558963	−	1.51409i
$307$	−394536.			−0.238913			−0.119457	−	0.992839i	$-0.538115\pi$
$307$	−394536.			−0.238913			−0.119457	+	0.992839i	$0.538115\pi$
$308$	−111095.			−0.0667297
$309$	36602.9	−	204837.i	0.0218082	−	0.122043i
$310$	−2.35706e6			−1.39305
$311$			1.25601e6i			0.736362i	0.929754	+	0.368181i	$0.120019\pi$
$311$			1.25601e6i			0.736362i	−0.929754	+	0.368181i	$0.879981\pi$
$312$	646989.	−	3.62068e6i	0.376279	−	2.10573i
$313$		−	2.31075e6i		−	1.33319i	−0.745421	−	0.666594i	$-0.767752\pi$
$313$		−	2.31075e6i		−	1.33319i	0.745421	−	0.666594i	$-0.232248\pi$
$314$			3.07093e6i			1.75771i
$315$	−223707.	+	605965.i	−0.127029	+	0.344089i
$316$	−3.77001e6			−2.12386
$317$		−	1.10004e6i		−	0.614839i	−0.951574	−	0.307419i	$-0.900535\pi$
$317$		−	1.10004e6i		−	0.614839i	0.951574	−	0.307419i	$-0.0994654\pi$
$318$	−263840.	+	1.47650e6i	−0.146310	+	0.818778i
$319$			13486.0i			0.00742002i
$320$		−	1.97915e6i		−	1.08045i
$321$	−555868.	+	3.11074e6i	−0.301099	+	1.68501i
$322$	−249425.			−0.134060
$323$		−	1.55906e6i		−	0.831487i
$324$	2.73235e6	+	2.33576e6i	1.44602	+	1.23614i
$325$			687989.i			0.361304i
$326$	429365.			0.223760
$327$	69398.2	−	388366.i	0.0358904	−	0.200850i
$328$			4.72699e6i			2.42605i
$329$	−667242.			−0.339855
$330$	−41974.4	+	234897.i	−0.0212178	+	0.118739i
$331$	1.71679e6			0.861288			0.430644	−	0.902522i	$-0.358287\pi$
$331$	1.71679e6			0.861288			0.430644	+	0.902522i	$0.358287\pi$
$332$	−1.92165e6			−0.956818
$333$	−132826.	+	359792.i	−0.0656405	+	0.177804i
$334$			2.09893e6i			1.02951i
$335$	−1.63848e6			−0.797680
$336$	622325.	+	111205.i	0.300725	+	0.0537373i
$337$			2.23142e6i			1.07030i	0.844757	+	0.535151i	$0.179745\pi$
$337$			2.23142e6i			1.07030i	−0.844757	+	0.535151i	$0.820255\pi$
$338$	3.34977e6			1.59486
$339$	−2.43819e6	−	435688.i	−1.15231	−	0.205909i
$340$	−3.30542e6			−1.55071
$341$			167914.i			0.0781988i
$342$	3.03412e6	+	1.12012e6i	1.40271	+	0.517843i
$343$	−1.68887e6			−0.775106
$344$		−	3.10706e6i		−	1.41564i
$345$	−61768.9	+	345671.i	−0.0279397	+	0.156356i
$346$	−3.09059e6			−1.38788
$347$	4.17683e6			1.86219			0.931093	−	0.364781i	$-0.118856\pi$
$347$	4.17683e6			1.86219			0.931093	+	0.364781i	$0.118856\pi$
$348$	68171.6	−	381502.i	0.0301756	−	0.168868i
$349$			3.68822e6i			1.62089i	0.585816	+	0.810444i	$0.300774\pi$
$349$			3.68822e6i			1.62089i	−0.585816	+	0.810444i	$0.699226\pi$
$350$	−432165.			−0.188573
$351$	−1.62496e6	+	2.77032e6i	−0.704004	+	1.20022i
$352$	−60527.9			−0.0260375
$353$	4.38448e6			1.87276			0.936378	−	0.350993i	$-0.114156\pi$
$353$	4.38448e6			1.87276			0.936378	+	0.350993i	$0.114156\pi$
$354$	−2.45343e6	−	3.18052e6i	−1.04055	−	1.34893i
$355$	−909916.			−0.383204
$356$	3.18734e6			1.33292
$357$	−171069.	+	957338.i	−0.0710398	+	0.397553i
$358$	−2.98068e6			−1.22916
$359$			4.69179e6i			1.92133i	0.277704	+	0.960667i	$0.410427\pi$
$359$			4.69179e6i			1.92133i	−0.277704	+	0.960667i	$0.589573\pi$
$360$	1.12646e6	−	3.05131e6i	0.458101	−	1.24088i
$361$	−568714.			−0.229681
$362$	5.00421e6			2.00708
$363$	−2.45466e6	−	438630.i	−0.977741	−	0.174715i
$364$			2.85244e6i			1.12840i
$365$	1.13818e6			0.447176
$366$	1.33294e6	−	7.45938e6i	0.520125	−	2.91072i
$367$		−	2.42409e6i		−	0.939471i	−0.882807	−	0.469736i	$-0.844349\pi$
$367$		−	2.42409e6i		−	0.939471i	0.882807	−	0.469736i	$-0.155651\pi$
$368$	343667.			0.132287
$369$	1.42953e6	−	3.87225e6i	0.546548	−	1.48046i
$370$	731613.			0.277829
$371$		−	551760.i		−	0.208121i
$372$	848805.	−	4.75008e6i	0.318017	−	1.77969i
$373$	−182981.			−0.0680978			−0.0340489	−	0.999420i	$-0.510840\pi$
$373$	−182981.			−0.0680978			−0.0340489	+	0.999420i	$0.510840\pi$
$374$			359253.i			0.132807i
$375$	−519193.	+	2.90551e6i	−0.190656	+	1.06695i
$376$	3.35987e6			1.22561
$377$	346261.			0.125473
$378$	−1.74019e6	−	1.02073e6i	−0.626423	−	0.367435i
$379$	2.41234e6			0.862661			0.431330	−	0.902194i	$-0.358044\pi$
$379$	2.41234e6			0.862661			0.431330	+	0.902194i	$0.358044\pi$
$380$		−	4.04393e6i		−	1.43663i
$381$	343894.	+	61451.4i	0.121370	+	0.0216880i
$382$	3.67816e6			1.28965
$383$		−	2.53581e6i		−	0.883324i	−0.897181	−	0.441662i	$-0.854389\pi$
$383$		−	2.53581e6i		−	0.883324i	0.897181	−	0.441662i	$-0.145611\pi$
$384$	5.18501e6	+	926524.i	1.79441	+	0.320648i
$385$		−	87779.5i		−	0.0301815i
$386$	−3.69224e6			−1.26131
$387$	−939634.	+	2.54523e6i	−0.318920	+	0.863874i
$388$		−	1.52350e6i		−	0.513764i
$389$		−	4.74262e6i		−	1.58908i	−0.607214	−	0.794538i	$-0.707713\pi$
$389$		−	4.74262e6i		−	1.58908i	0.607214	−	0.794538i	$-0.292287\pi$
$390$	6.03112e6	+	1.07772e6i	2.00787	+	0.358793i
$391$			528672.i			0.174882i
$392$	3.82716e6			1.25794
$393$	332138.	+	59350.7i	0.108477	+	0.0193840i
$394$		−	5.16970e6i		−	1.67774i
$395$		−	2.97879e6i		−	0.960610i
$396$	−458261.	−	169178.i	−0.146850	−	0.0542133i
$397$		−	5.12390e6i		−	1.63164i	−0.578306	−	0.815820i	$-0.696286\pi$
$397$		−	5.12390e6i		−	1.63164i	0.578306	−	0.815820i	$-0.303714\pi$
$398$	−6.68825e6			−2.11643
$399$	−1.17123e6	−	209290.i	−0.368307	−	0.0658138i
$400$	595453.			0.186079
$401$	4.04090e6			1.25492			0.627461	−	0.778648i	$-0.284094\pi$
$401$	4.04090e6			1.25492			0.627461	+	0.778648i	$0.284094\pi$
$402$	900193.	−	5.03765e6i	0.277824	−	1.55476i
$403$	4.31129e6			1.32234
$404$	−2.67190e6			−0.814456
$405$	−1.84555e6	+	2.15890e6i	−0.559098	+	0.654026i
$406$			217506.i			0.0654871i
$407$		−	52119.1i		−	0.0155959i
$408$	861412.	−	4.82063e6i	0.256189	−	1.43368i
$409$			3.45461e6i			1.02115i	0.859832	+	0.510577i	$0.170568\pi$
$409$			3.45461e6i			1.02115i	−0.859832	+	0.510577i	$0.829432\pi$
$410$	−7.87397e6			−2.31331
$411$	218087.	−	1.22046e6i	0.0636834	−	0.356384i
$412$		−	812596.i		−	0.235848i
$413$	1.09427e6	+	993001.i	0.315682	+	0.286467i
$414$	−1.02886e6	−	379828.i	−0.295023	−	0.108915i
$415$		−	1.51835e6i		−	0.432764i
$416$			1.55409e6i			0.440294i
$417$	1.56898e6	+	280366.i	0.441853	+	0.0789560i
$418$	−439519.			−0.123037
$419$	905432.			0.251954			0.125977	−	0.992033i	$-0.459793\pi$
$419$	905432.			0.251954			0.125977	+	0.992033i	$0.459793\pi$
$420$	−443726.	+	2.48318e6i	−0.122742	+	0.686885i
$421$		−	6.97621e6i		−	1.91829i	−0.282914	−	0.959145i	$-0.591301\pi$
$421$		−	6.97621e6i		−	1.91829i	0.282914	−	0.959145i	$-0.408699\pi$
$422$			3.16403e6i			0.864888i
$423$	−2.75233e6	−	1.01609e6i	−0.747910	−	0.276109i
$424$			2.77836e6i			0.750541i
$425$			916000.i			0.245993i
$426$	499915.	−	2.79762e6i	0.133467	−	0.746904i
$427$			2.78753e6i			0.739860i
$428$			1.23404e7i			3.25628i
$429$	76775.1	−	429648.i	0.0201408	−	0.112712i
$430$	5.17557e6			1.34985
$431$	−5.22450e6			−1.35473			−0.677363	−	0.735649i	$-0.736877\pi$
$431$	−5.22450e6			−1.35473			−0.677363	+	0.735649i	$0.736877\pi$
$432$	2.39770e6	+	1.40640e6i	0.618139	+	0.362576i
$433$	530639.			0.136013			0.0680064	−	0.997685i	$-0.478336\pi$
$433$	530639.			0.136013			0.0680064	+	0.997685i	$0.478336\pi$
$434$			2.70816e6i			0.690161i
$435$	301435.	+	53864.3i	0.0763784	+	0.0136483i
$436$		−	1.54066e6i		−	0.388142i
$437$	−646789.			−0.162017
$438$	−625325.	+	3.49944e6i	−0.155747	+	0.871591i
$439$	−2.98179e6			−0.738441			−0.369221	−	0.929342i	$-0.620375\pi$
$439$	−2.98179e6			−0.738441			−0.369221	+	0.929342i	$0.620375\pi$
$440$			442010.i			0.108843i
$441$	−3.13512e6	−	1.15741e6i	−0.767641	−	0.283393i
$442$	9.22405e6			2.24577
$443$	6.64975e6			1.60989			0.804944	−	0.593350i	$-0.202195\pi$
$443$	6.64975e6			1.60989			0.804944	+	0.593350i	$0.202195\pi$
$444$	−263462.	+	1.47439e6i	−0.0634251	+	0.354939i
$445$			2.51840e6i			0.602873i
$446$	−1.10999e7			−2.64231
$447$	1.13326e6	+	202505.i	0.268262	+	0.0479365i
$448$	−2.27396e6			−0.535288
$449$		−	8.28821e6i		−	1.94019i	−0.242722	−	0.970096i	$-0.578040\pi$
$449$		−	8.28821e6i		−	1.94019i	0.242722	−	0.970096i	$-0.421960\pi$
$450$	−1.78265e6	−	658108.i	−0.414987	−	0.153203i
$451$			560930.i			0.129858i
$452$	−9.67240e6			−2.22684
$453$	−1.08708e6	+	6.08352e6i	−0.248895	+	1.39287i
$454$	−1.03182e7			−2.34943
$455$	−2.25379e6			−0.510371
$456$	5.89767e6	+	1.05387e6i	1.32822	+	0.237343i
$457$		−	3.74700e6i		−	0.839253i	−0.907697	−	0.419626i	$-0.862161\pi$
$457$		−	3.74700e6i		−	0.839253i	0.907697	−	0.419626i	$-0.137839\pi$
$458$			1.28050e7i			2.85245i
$459$	−2.16350e6	+	3.68845e6i	−0.479320	+	0.817169i
$460$			1.37129e6i			0.302158i
$461$			3.49127e6i			0.765122i	0.923930	+	0.382561i	$0.124958\pi$
$461$			3.49127e6i			0.765122i	−0.923930	+	0.382561i	$0.875042\pi$
$462$	269886.	+	48226.8i	0.0588269	+	0.0105120i
$463$			2.88066e6i			0.624511i	0.949998	+	0.312255i	$0.101084\pi$
$463$			2.88066e6i			0.624511i	−0.949998	+	0.312255i	$0.898916\pi$
$464$		−	299688.i		−	0.0646211i
$465$	3.75316e6	+	670664.i	0.804943	+	0.143838i
$466$	1.53067e7			3.26526
$467$	−1.99736e6			−0.423803			−0.211901	−	0.977291i	$-0.567966\pi$
$467$	−1.99736e6			−0.423803			−0.211901	+	0.977291i	$0.567966\pi$
$468$	−4.34375e6	+	1.17661e7i	−0.916749	+	2.48324i
$469$			1.88254e6i			0.395196i
$470$			5.59668e6i			1.16865i
$471$	873785.	−	4.88987e6i	0.181490	−	1.01565i
$472$	−5.51016e6	−	5.00021e6i	−1.13844	−	1.03308i
$473$		−	368700.i		−	0.0757740i
$474$	9.15857e6	+	1.63657e6i	1.87233	+	0.334572i
$475$	−1.12066e6			−0.227897
$476$			3.79779e6i			0.768270i
$477$	840230.	−	2.27597e6i	0.169084	−	0.458006i
$478$			7.90456e6i			1.58237i
$479$		−	2.25462e6i		−	0.448988i	−0.974475	−	0.224494i	$-0.927927\pi$
$479$		−	2.25462e6i		−	0.448988i	0.974475	−	0.224494i	$-0.0720729\pi$
$480$	−241754.	+	1.35290e6i	−0.0478929	+	0.268018i
$481$	−1.33819e6			−0.263727
$482$	−1.52378e7			−2.98747
$483$	397161.	+	70969.8i	0.0774637	+	0.0138422i
$484$	−9.73771e6			−1.88948
$485$	1.20376e6			0.232373
$486$	−5.62379e6	−	6.86043e6i	−1.08004	−	1.31753i
$487$	7.50521e6			1.43397			0.716985	−	0.697088i	$-0.245522\pi$
$487$	7.50521e6			1.43397			0.716985	+	0.697088i	$0.245522\pi$
$488$		−	1.40365e7i		−	2.66814i
$489$	−683681.	−	122169.i	−0.129295	−	0.0231041i
$490$			6.37507e6i			1.19948i
$491$		−	5.42009e6i		−	1.01462i	−0.861764	−	0.507309i	$-0.830640\pi$
$491$		−	5.42009e6i		−	1.01462i	0.861764	−	0.507309i	$-0.169360\pi$
$492$	2.83551e6	−	1.58680e7i	0.528102	−	2.95536i
$493$	461017.			0.0854279
$494$			1.12849e7i			2.08056i
$495$	133672.	−	362084.i	0.0245204	−	0.0664197i
$496$		−	3.73141e6i		−	0.681034i
$497$			1.04545e6i			0.189852i
$498$	4.66831e6	+	834193.i	0.843502	+	0.150728i
$499$	−7.03295e6			−1.26441			−0.632203	−	0.774803i	$-0.717849\pi$
$499$	−7.03295e6			−1.26441			−0.632203	+	0.774803i	$0.717849\pi$
$500$			1.15262e7i			2.06188i
$501$	597217.	−	3.34214e6i	0.106301	−	0.594882i
$502$		−	1.23675e7i		−	2.19039i
$503$	−3.22241e6			−0.567885			−0.283942	−	0.958841i	$-0.591642\pi$
$503$	−3.22241e6			−0.567885			−0.283942	+	0.958841i	$0.591642\pi$
$504$	−3.50583e6	−	1.29426e6i	−0.614772	−	0.226958i
$505$		−	2.11114e6i		−	0.368374i
$506$	149040.			0.0258777
$507$	−5.33386e6	−	953123.i	−0.921556	−	0.164675i
$508$	1.36424e6			0.234548
$509$	7.78339e6			1.33160			0.665800	−	0.746130i	$-0.268090\pi$
$509$	7.78339e6			1.33160			0.665800	+	0.746130i	$0.268090\pi$
$510$	8.02994e6	+	1.43489e6i	1.36706	+	0.244283i
$511$		−	1.30772e6i		−	0.221545i
$512$	7.87980e6			1.32843
$513$	−4.51253e6	−	2.64688e6i	−0.757054	−	0.444059i
$514$		−	3.56144e6i		−	0.594590i
$515$	642054.			0.106673
$516$	−1.86378e6	+	1.04301e7i	−0.308156	+	1.72450i
$517$	398699.			0.0656023
$518$		−	840593.i		−	0.137645i
$519$	4.92116e6	+	879377.i	0.801954	+	0.143303i
$520$	1.13489e7			1.84054
$521$			3.75797e6i			0.606539i	0.952905	+	0.303270i	$0.0980783\pi$
$521$			3.75797e6i			0.606539i	−0.952905	+	0.303270i	$0.901922\pi$
$522$	−331222.	+	897197.i	−0.0532038	+	0.144116i
$523$	−1.66971e6			−0.266923			−0.133462	−	0.991054i	$-0.542609\pi$
$523$	−1.66971e6			−0.266923			−0.133462	+	0.991054i	$0.542609\pi$
$524$	1.31760e6			0.209631
$525$	688139.	+	122965.i	0.108963	+	0.0194709i
$526$			3.93338e6i			0.619871i
$527$	5.74012e6			0.900316
$528$	−371860.	−	66448.7i	−0.0580490	−	0.0103729i
$529$	−6.21702e6			−0.965924
$530$	−4.62804e6			−0.715661
$531$	3.00164e6	+	5.76244e6i	0.461979	+	0.886891i
$532$	−4.64631e6			−0.711753
$533$	1.44022e7			2.19590
$534$	−7.74307e6	−	1.38363e6i	−1.17506	−	0.209975i
$535$	−9.75051e6			−1.47280
$536$		−	9.47945e6i		−	1.42518i
$537$	4.74615e6	+	848104.i	0.710241	+	0.126915i
$538$	1.02145e7			1.52146
$539$	454151.			0.0673330
$540$	−5.61176e6	+	9.56722e6i	−0.828162	+	1.41189i
$541$			9.67521e6i			1.42124i	0.703576	+	0.710620i	$0.251585\pi$
$541$			9.67521e6i			1.42124i	−0.703576	+	0.710620i	$0.748415\pi$
$542$	−4.59931e6			−0.672504
$543$	−7.96824e6	−	1.42387e6i	−1.15975	−	0.207238i
$544$			2.06914e6i			0.299774i
$545$	1.21732e6			0.175555
$546$	1.23825e6	−	6.92950e6i	0.177757	−	0.994765i
$547$	5.44757e6			0.778456			0.389228	−	0.921141i	$-0.372742\pi$
$547$	5.44757e6			0.778456			0.389228	+	0.921141i	$0.372742\pi$
$548$		−	4.84161e6i		−	0.688713i
$549$	−4.24490e6	+	1.14984e7i	−0.601085	+	1.62819i
$550$	258233.			0.0364003
$551$			564019.i			0.0791435i
$552$	−1.99988e6	−	357365.i	−0.279355	−	0.0499188i
$553$	−3.42250e6			−0.475917
$554$	−8.90775e6			−1.23309
$555$	−1.16495e6	−	208169.i	−0.160537	−	0.0286869i
$556$	6.22421e6			0.853881
$557$			1.58568e6i			0.216560i	0.994120	+	0.108280i	$0.0345343\pi$
$557$			1.58568e6i			0.216560i	−0.994120	+	0.108280i	$0.965466\pi$
$558$	−4.12404e6	+	1.11710e7i	−0.560709	+	1.51882i
$559$	−9.46661e6			−1.28134
$560$			1.95065e6i			0.262851i
$561$	102220.	−	572041.i	0.0137128	−	0.0767397i
$562$		−	5.99192e6i		−	0.800249i
$563$	−9.24513e6			−1.22925			−0.614627	−	0.788818i	$-0.710694\pi$
$563$	−9.24513e6			−1.22925			−0.614627	+	0.788818i	$0.710694\pi$
$564$	−1.12787e7	−	2.01543e6i	−1.49301	−	0.266790i
$565$		−	7.64242e6i		−	1.00719i
$566$			3.13287e6i			0.411057i
$567$	2.48049e6	+	2.12046e6i	0.324025	+	0.276995i
$568$		−	5.26434e6i		−	0.684657i
$569$	5.61709e6			0.727328			0.363664	−	0.931530i	$-0.381526\pi$
$569$	5.61709e6			0.727328			0.363664	+	0.931530i	$0.381526\pi$
$570$	−1.75548e6	+	9.82401e6i	−0.226313	+	1.26649i
$571$		−	4.82900e6i		−	0.619822i	−0.950766	−	0.309911i	$-0.899701\pi$
$571$		−	4.82900e6i		−	0.619822i	0.950766	−	0.309911i	$-0.100299\pi$
$572$		−	1.70443e6i		−	0.217816i
$573$	−5.85676e6	−	1.04656e6i	−0.745196	−	0.133161i
$574$			9.04685e6i			1.14609i
$575$	380012.			0.0479322
$576$	−9.37992e6	−	3.46282e6i	−1.17799	−	0.434884i
$577$	3.89350e6			0.486856			0.243428	−	0.969919i	$-0.421728\pi$
$577$	3.89350e6			0.486856			0.243428	+	0.969919i	$0.421728\pi$
$578$	−1.40239e6			−0.174602
$579$	5.87917e6	+	1.05057e6i	0.728819	+	0.130235i
$580$	1.19580e6			0.147601
$581$	−1.74452e6			−0.214405
$582$	−661355.	+	3.70107e6i	−0.0809333	+	0.452918i
$583$			329695.i			0.0401736i
$584$			6.58496e6i			0.798952i
$585$	−9.29675e6	−	3.43212e6i	−1.12316	−	0.414641i
$586$		−	2.00395e7i		−	2.41070i
$587$	−4.16847e6			−0.499323			−0.249661	−	0.968333i	$-0.580319\pi$
$587$	−4.16847e6			−0.499323			−0.249661	+	0.968333i	$0.580319\pi$
$588$	−1.28474e7	−	2.29574e6i	−1.53240	−	0.273828i
$589$			7.02260e6i			0.834084i
$590$	8.32907e6	−	9.17852e6i	0.985069	−	1.08553i
$591$	−1.47096e6	+	8.23175e6i	−0.173233	+	0.969446i
$592$			1.15820e6i			0.135825i
$593$		−	4.87840e6i		−	0.569692i	−0.958573	−	0.284846i	$-0.908057\pi$
$593$		−	4.87840e6i		−	0.569692i	0.958573	−	0.284846i	$-0.0919425\pi$
$594$	1.03982e6	+	609920.i	0.120919	+	0.0709262i
$595$	−3.00074e6			−0.347485
$596$	4.49566e6			0.518416
$597$	1.06497e7	+	1.90303e6i	1.22293	+	0.218530i
$598$		−	3.82669e6i		−	0.437593i
$599$			1.20293e7i			1.36985i	0.728613	+	0.684925i	$0.240165\pi$
$599$			1.20293e7i			1.36985i	−0.728613	+	0.684925i	$0.759835\pi$
$600$	−3.46509e6	−	619187.i	−0.392949	−	0.0702172i
$601$		−	1.12790e6i		−	0.127375i	−0.997970	−	0.0636874i	$-0.979714\pi$
$601$		−	1.12790e6i		−	0.127375i	0.997970	−	0.0636874i	$-0.0202861\pi$
$602$		−	5.94651e6i		−	0.668761i
$603$	−2.86677e6	+	7.76536e6i	−0.321070	+	0.869697i
$604$			2.41336e7i			2.69171i
$605$		−	7.69403e6i		−	0.854605i
$606$	6.49091e6	+	1.15988e6i	0.718000	+	0.128301i
$607$	1.48593e7			1.63691			0.818457	−	0.574568i	$-0.194830\pi$
$607$	1.48593e7			1.63691			0.818457	+	0.574568i	$0.194830\pi$
$608$	−2.53144e6			−0.277721
$609$	61887.8	−	346336.i	0.00676179	−	0.0378403i
$610$	2.33812e7			2.54414
$611$		−	1.02369e7i		−	1.10934i
$612$	−5.78335e6	+	1.56656e7i	−0.624167	+	1.69071i
$613$		−	8.32649e6i		−	0.894975i	−0.894290	−	0.447488i	$-0.852319\pi$
$613$		−	8.32649e6i		−	0.894975i	0.894290	−	0.447488i	$-0.147681\pi$
$614$	3.80222e6			0.407021
$615$	1.25378e7	+	2.24041e6i	1.33670	+	0.238858i
$616$	507850.			0.0539242
$617$		−	1.68119e7i		−	1.77789i	−0.458016	−	0.888944i	$-0.651440\pi$
$617$		−	1.68119e7i		−	1.77789i	0.458016	−	0.888944i	$-0.348560\pi$
$618$	−352750.	+	1.97406e6i	−0.0371531	+	0.207916i
$619$	1.19071e7			1.24905			0.624525	−	0.781005i	$-0.285293\pi$
$619$	1.19071e7			1.24905			0.624525	+	0.781005i	$0.285293\pi$
$620$	1.48889e7			1.55555
$621$	1.53019e6	+	897549.i	0.159227	+	0.0933962i
$622$		−	1.21044e7i		−	1.25449i
$623$	2.89354e6			0.298682
$624$	−1.70611e6	+	9.54774e6i	−0.175407	+	0.981610i
$625$	−6.57147e6			−0.672918
$626$			2.22691e7i			2.27126i
$627$	699849.	+	125058.i	0.0710944	+	0.0127041i
$628$		−	1.93983e7i		−	1.96275i
$629$	−1.78169e6			−0.179558
$630$	2.15591e6	−	5.83981e6i	0.216411	−	0.586202i
$631$	−3.12556e6			−0.312503			−0.156251	−	0.987717i	$-0.549941\pi$
$631$	−3.12556e6			−0.312503			−0.156251	+	0.987717i	$0.549941\pi$
$632$	1.72338e7			1.71629
$633$	900275.	−	5.03811e6i	0.0893030	−	0.499757i
$634$			1.06013e7i			1.04746i
$635$			1.07792e6i			0.106085i
$636$	1.66661e6	−	9.32668e6i	0.163377	−	0.914291i
$637$		−	1.16606e7i		−	1.13860i
$638$		−	129967.i		−	0.0126410i
$639$	−1.59204e6	+	4.31243e6i	−0.154241	+	0.417801i
$640$			1.62522e7i			1.56842i
$641$		−	9.31161e6i		−	0.895116i	−0.894255	−	0.447558i	$-0.852294\pi$
$641$		−	9.31161e6i		−	0.895116i	0.894255	−	0.447558i	$-0.147706\pi$
$642$	5.35701e6	−	2.99789e7i	0.512962	−	2.87063i
$643$	1.32930e7			1.26793			0.633965	−	0.773362i	$-0.281426\pi$
$643$	1.32930e7			1.26793			0.633965	+	0.773362i	$0.281426\pi$
$644$	1.57555e6			0.149699
$645$	−8.24109e6	−	1.47262e6i	−0.779984	−	0.139378i
$646$			1.50249e7i			1.41655i
$647$			9.08894e6i			0.853597i	0.904347	+	0.426798i	$0.140359\pi$
$647$			9.08894e6i			0.853597i	−0.904347	+	0.426798i	$0.859641\pi$
$648$	−1.24904e7	−	1.06775e7i	−1.16852	−	0.998920i
$649$	−653865.	−	593351.i	−0.0609363	−	0.0552968i
$650$		−	6.63029e6i		−	0.615530i
$651$	770564.	−	4.31223e6i	0.0712617	−	0.398794i
$652$	−2.71219e6			−0.249862
$653$		−	1.83478e7i		−	1.68384i	−0.539605	−	0.841919i	$-0.681426\pi$
$653$		−	1.83478e7i		−	1.68384i	0.539605	−	0.841919i	$-0.318574\pi$
$654$	−668804.	+	3.74276e6i	−0.0611441	+	0.342174i
$655$			1.04107e6i			0.0948153i
$656$		−	1.24651e7i		−	1.13093i
$657$	1.99142e6	−	5.39425e6i	0.179990	−	0.487548i
$658$	6.43035e6			0.578988
$659$	−5.04508e6			−0.452537			−0.226269	−	0.974065i	$-0.572653\pi$
$659$	−5.04508e6			−0.452537			−0.226269	+	0.974065i	$0.572653\pi$
$660$	265141.	−	1.48378e6i	0.0236929	−	0.132590i
$661$	−1.92331e7			−1.71216			−0.856081	−	0.516842i	$-0.827108\pi$
$661$	−1.92331e7			−1.71216			−0.856081	+	0.516842i	$0.827108\pi$
$662$	−1.65451e7			−1.46732
$663$	−1.46875e7	−	2.62456e6i	−1.29767	−	0.231885i
$664$	8.78444e6			0.773204
$665$		−	3.67117e6i		−	0.321922i
$666$	1.28007e6	−	3.46739e6i	0.111827	−	0.302912i
$667$		−	191257.i		−	0.0166458i
$668$		−	1.32584e7i		−	1.14961i
$669$	1.76745e7	+	3.15831e6i	1.52680	+	0.272828i
$670$	1.57903e7			1.35895
$671$		−	1.66564e6i		−	0.142815i
$672$	1.55443e6	+	277765.i	0.132785	+	0.0237277i
$673$		−	3.51575e6i		−	0.299213i	−0.988746	−	0.149607i	$-0.952199\pi$
$673$		−	3.51575e6i		−	0.299213i	0.988746	−	0.149607i	$-0.0478007\pi$
$674$		−	2.15046e7i		−	1.82340i
$675$	2.65127e6	+	1.55513e6i	0.223973	+	0.131374i
$676$	−2.11596e7			−1.78091
$677$			4.86746e6i			0.408160i	0.978954	+	0.204080i	$0.0654203\pi$
$677$			4.86746e6i			0.408160i	−0.978954	+	0.204080i	$0.934580\pi$
$678$	2.34974e7	+	4.19881e6i	1.96311	+	0.350794i
$679$		−	1.38307e6i		−	0.115125i
$680$	1.51101e7			1.25313
$681$	1.64297e7	+	2.93587e6i	1.35757	+	0.242587i
$682$		−	1.61822e6i		−	0.133222i
$683$	1.34481e7			1.10308			0.551541	−	0.834148i	$-0.314040\pi$
$683$	1.34481e7			1.10308			0.551541	+	0.834148i	$0.314040\pi$
$684$	−1.91657e7	−	7.07548e6i	−1.56634	−	0.578250i
$685$	3.82548e6			0.311501
$686$	1.62760e7			1.32050
$687$	3.64347e6	−	2.03896e7i	0.294526	−	1.64822i
$688$			8.19333e6i			0.659917i
$689$	8.46513e6			0.679337
$690$	595279.	−	3.33130e6i	0.0475990	−	0.266373i
$691$			2.19353e7i			1.74763i	0.486262	+	0.873813i	$0.338360\pi$
$691$			2.19353e7i			1.74763i	−0.486262	+	0.873813i	$0.661640\pi$
$692$	1.95224e7			1.54978
$693$	−416020.	−	153584.i	−0.0329064	−	0.0121482i
$694$	−4.02530e7			−3.17248
$695$			4.91792e6i			0.386206i
$696$	−311633.	+	1.74396e6i	−0.0243849	+	0.136462i
$697$	1.91754e7			1.49507
$698$		−	3.55441e7i		−	2.76140i
$699$	−2.43730e7	−	4.35528e6i	−1.88676	−	0.337150i
$700$	2.72987e6			0.210570
$701$	2.35117e7			1.80713			0.903565	−	0.428452i	$-0.140941\pi$
$701$	2.35117e7			1.80713			0.903565	+	0.428452i	$0.140941\pi$
$702$	1.56601e7	−	2.66981e7i	1.19936	−	2.04474i
$703$		−	2.17976e6i		−	0.166349i
$704$	1.35877e6			0.103327
$705$	1.59245e6	−	8.91163e6i	0.120668	−	0.675281i
$706$	−4.22541e7			−3.19049
$707$	−2.42562e6			−0.182504
$708$	1.54976e7	+	2.00905e7i	1.16194	+	1.50629i
$709$	−1.29200e7			−0.965263			−0.482632	−	0.875823i	$-0.660319\pi$
$709$	−1.29200e7			−0.965263			−0.482632	+	0.875823i	$0.660319\pi$
$710$	8.76904e6			0.652839
$711$	−1.41176e7	−	5.21185e6i	−1.04734	−	0.386650i
$712$	−1.45703e7			−1.07713
$713$		−	2.38135e6i		−	0.175428i
$714$	1.64863e6	−	9.22606e6i	0.121026	−	0.677284i
$715$	1.34672e6			0.0985170
$716$	1.88282e7			1.37254
$717$	2.24912e6	−	1.25865e7i	0.163386	−	0.914338i
$718$		−	4.52158e7i		−	3.27325i
$719$	3.00043e6			0.216452			0.108226	−	0.994126i	$-0.465483\pi$
$719$	3.00043e6			0.216452			0.108226	+	0.994126i	$0.465483\pi$
$720$	−2.97049e6	+	8.04632e6i	−0.213549	+	0.578450i
$721$		−	737693.i		−	0.0528491i
$722$	5.48081e6			0.391293
$723$	2.42632e7	+	4.33566e6i	1.72624	+	0.308467i
$724$	−3.16103e7			−2.24121
$725$		−	331381.i		−	0.0234144i
$726$	2.36560e7	+	4.22716e6i	1.66571	+	0.297651i
$727$	1.45696e7			1.02238			0.511191	−	0.859467i	$-0.329205\pi$
$727$	1.45696e7			1.02238			0.511191	+	0.859467i	$0.329205\pi$
$728$		−	1.30394e7i		−	0.911860i
$729$	7.00277e6	+	1.25241e7i	0.488035	+	0.872824i
$730$	−1.09689e7			−0.761823
$731$	−1.26040e7			−0.872399
$732$	−8.41983e6	+	4.71190e7i	−0.580798	+	3.25026i
$733$	3.65619e6			0.251344			0.125672	−	0.992072i	$-0.459891\pi$
$733$	3.65619e6			0.251344			0.125672	+	0.992072i	$0.459891\pi$
$734$			2.33614e7i			1.60051i
$735$	1.81392e6	−	1.01511e7i	0.123851	−	0.693096i
$736$	858404.			0.0584113
$737$		−	1.12488e6i		−	0.0762848i
$738$	−1.37767e7	+	3.73177e7i	−0.931118	+	2.52216i
$739$			1.91970e7i			1.29307i	0.762885	+	0.646535i	$0.223782\pi$
$739$			1.91970e7i			1.29307i	−0.762885	+	0.646535i	$0.776218\pi$
$740$	−4.62141e6			−0.310238
$741$	3.21094e6	−	1.79691e7i	0.214826	−	1.20221i
$742$			5.31742e6i			0.354561i
$743$			2.03356e7i			1.35140i	0.737175	+	0.675702i	$0.236159\pi$
$743$			2.03356e7i			1.35140i	−0.737175	+	0.675702i	$0.763841\pi$
$744$	−3.88014e6	+	2.17140e7i	−0.256989	+	1.43816i
$745$			3.55215e6i			0.234477i
$746$	1.76342e6			0.116014
$747$	−7.19602e6	−	2.65658e6i	−0.471836	−	0.174190i
$748$		−	2.26931e6i		−	0.148299i
$749$			1.12029e7i			0.729671i
$750$	5.00357e6	−	2.80009e7i	0.324808	−	1.81769i
$751$			1.95164e7i			1.26270i	0.775500	+	0.631348i	$0.217498\pi$
$751$			1.95164e7i			1.26270i	−0.775500	+	0.631348i	$0.782502\pi$
$752$	−8.85998e6			−0.571332
$753$	−3.51896e6	+	1.96928e7i	−0.226166	+	1.26567i
$754$	−3.33698e6			−0.213760
$755$	−1.90686e7			−1.21745
$756$	1.09923e7	+	6.44768e6i	0.699496	+	0.410298i
$757$	1.06126e7			0.673103			0.336551	−	0.941665i	$-0.390739\pi$
$757$	1.06126e7			0.673103			0.336551	+	0.941665i	$0.390739\pi$
$758$	−2.32482e7			−1.46966
$759$	−237317.	−	42406.8i	−0.0149529	−	0.00267197i
$760$			1.84860e7i			1.16094i
$761$		−	2.01406e7i		−	1.26070i	−0.776313	−	0.630348i	$-0.782912\pi$
$761$		−	2.01406e7i		−	1.26070i	0.776313	−	0.630348i	$-0.217088\pi$
$762$	−3.31418e6	−	592220.i	−0.206770	−	0.0369484i
$763$		−	1.39865e6i		−	0.0869754i
$764$	−2.32340e7			−1.44009
$765$	−1.23778e7	−	4.56958e6i	−0.764701	−	0.282308i
$766$			2.44381e7i			1.50486i
$767$	−1.52347e7	+	1.67884e7i	−0.935071	+	1.03043i
$768$	−2.97637e7	−	5.31856e6i	−1.82089	−	0.325380i
$769$		−	1.52355e7i		−	0.929053i	−0.885559	−	0.464526i	$-0.846225\pi$
$769$		−	1.52355e7i		−	0.929053i	0.885559	−	0.464526i	$-0.153775\pi$
$770$			845949.i			0.0514182i
$771$	−1.01335e6	+	5.67090e6i	−0.0613937	+	0.343571i
$772$	2.33229e7			1.40844
$773$	8.57975e6			0.516447			0.258224	−	0.966085i	$-0.416863\pi$
$773$	8.57975e6			0.516447			0.258224	+	0.966085i	$0.416863\pi$
$774$	9.05545e6	−	2.45289e7i	0.543322	−	1.47172i
$775$		−	4.12603e6i		−	0.246762i
$776$			6.96438e6i			0.415172i
$777$	−239177.	+	1.33848e6i	−0.0142124	+	0.0795353i
$778$			4.57056e7i			2.70720i
$779$			2.34596e7i			1.38509i
$780$	−3.80970e7	−	6.80767e6i	−2.24210	−	0.400647i
$781$		−	624694.i		−	0.0366471i
$782$		−	5.09492e6i		−	0.297934i
$783$	782689.	−	1.33437e6i	0.0456231	−	0.0777806i
$784$	−1.00922e7			−0.586404
$785$	1.53271e7			0.887741
$786$	−3.20088e6	−	571975.i	−0.184805	−	0.0330233i
$787$	−3.09986e6			−0.178404			−0.0892022	−	0.996014i	$-0.528432\pi$
$787$	−3.09986e6			−0.178404			−0.0892022	+	0.996014i	$0.528432\pi$
$788$			3.26557e7i			1.87345i
$789$	1.11918e6	−	6.26314e6i	0.0640040	−	0.358179i
$790$			2.87072e7i			1.63653i
$791$	−8.78082e6			−0.498992
$792$	2.09485e6	+	773363.i	0.118670	+	0.0438097i
$793$	−4.27664e7			−2.41501
$794$			4.93801e7i			2.77972i
$795$	7.36926e6	+	1.31683e6i	0.413529	+	0.0738947i
$796$	4.22479e7			2.36332
$797$	−2.92005e7			−1.62834			−0.814169	−	0.580628i	$-0.802807\pi$
$797$	−2.92005e7			−1.62834			−0.814169	+	0.580628i	$0.802807\pi$
$798$	1.12874e7	+	2.01697e6i	0.627460	+	0.112123i
$799$		−	1.36295e7i		−	0.755290i
$800$	1.48731e6			0.0821630
$801$	1.19357e7	+	4.40633e6i	0.657302	+	0.242659i
$802$	−3.89429e7			−2.13793
$803$			781406.i			0.0427649i
$804$	−5.68628e6	+	3.18215e7i	−0.310233	+	1.73613i
$805$			1.24489e6i			0.0677080i
$806$	−4.15488e7			−2.25279
$807$	−1.62646e7	−	2.90637e6i	−0.879144	−	0.157097i
$808$	1.22141e7			0.658161
$809$	2.32021e6			0.124640			0.0623199	−	0.998056i	$-0.480150\pi$
$809$	2.32021e6			0.124640			0.0623199	+	0.998056i	$0.480150\pi$
$810$	1.77859e7	−	2.08058e7i	0.952498	−	1.11422i
$811$			2.10962e7i			1.12630i	0.826356	+	0.563148i	$0.190410\pi$
$811$			2.10962e7i			1.12630i	−0.826356	+	0.563148i	$0.809590\pi$
$812$		−	1.37393e6i		−	0.0731263i
$813$	7.32352e6	+	1.30866e6i	0.388592	+	0.0694386i
$814$			502282.i			0.0265697i
$815$		−	2.14297e6i		−	0.113012i
$816$	−2.27155e6	+	1.27120e7i	−0.119425	+	0.668327i
$817$		−	1.54200e7i		−	0.808221i
$818$		−	3.32928e7i		−	1.73967i
$819$	−3.94336e6	+	1.06816e7i	−0.205426	+	0.556449i
$820$	4.97378e7			2.58316
$821$	2.51023e7			1.29974			0.649869	−	0.760047i	$-0.274824\pi$
$821$	2.51023e7			1.29974			0.649869	+	0.760047i	$0.274824\pi$
$822$	−2.10175e6	+	1.17618e7i	−0.108493	+	0.607148i
$823$		−	132060.i		−	0.00679630i	−0.999994	−	0.00339815i	$-0.998918\pi$
$823$		−	132060.i		−	0.00679630i	0.999994	−	0.00339815i	$-0.00108167\pi$
$824$			3.71462e6i			0.190588i
$825$	−411186.	−	73476.0i	−0.0210331	−	0.00375847i
$826$	−1.05457e7	−	9.56975e6i	−0.537807	−	0.488035i
$827$		−	1.75072e7i		−	0.890129i	−0.895498	−	0.445065i	$-0.853181\pi$
$827$		−	1.75072e7i		−	0.890129i	0.895498	−	0.445065i	$-0.146819\pi$
$828$	6.49904e6	+	2.39928e6i	0.329438	+	0.121620i
$829$	−2.42099e7			−1.22351			−0.611753	−	0.791049i	$-0.709535\pi$
$829$	−2.42099e7			−1.22351			−0.611753	+	0.791049i	$0.709535\pi$
$830$			1.46326e7i			0.737271i
$831$	1.41839e7	+	2.53456e6i	0.712512	+	0.127321i
$832$		−	3.48872e7i		−	1.74726i
$833$		−	1.55251e7i		−	0.775216i
$834$	−1.51206e7	−	2.70194e6i	−0.752756	−	0.134512i
$835$	1.04758e7			0.519962
$836$	2.77633e6			0.137390
$837$	9.74526e6	−	1.66142e7i	0.480817	−	0.819721i
$838$	−8.72584e6			−0.429237
$839$	−3.71411e7			−1.82159			−0.910793	−	0.412862i	$-0.864529\pi$
$839$	−3.71411e7			−1.82159			−0.910793	+	0.412862i	$0.864529\pi$
$840$	2.02840e6	−	1.13513e7i	0.0991873	−	0.555072i
$841$	2.03444e7			0.991869
$842$			6.72312e7i			3.26806i
$843$	−1.70490e6	+	9.54097e6i	−0.0826287	+	0.462406i
$844$		−	1.99864e7i		−	0.965779i
$845$		−	1.67188e7i		−	0.805495i
$846$	2.65247e7	+	9.79225e6i	1.27416	+	0.470388i
$847$	−8.84011e6			−0.423398
$848$		−	7.32655e6i		−	0.349873i
$849$	891408.	−	4.98849e6i	0.0424431	−	0.237520i
$850$		−	8.82768e6i		−	0.419082i
$851$			739151.i			0.0349872i
$852$	−3.15783e6	+	1.76718e7i	−0.149036	+	0.834032i
$853$	−5.95680e6			−0.280311			−0.140156	−	0.990129i	$-0.544760\pi$
$853$	−5.95680e6			−0.280311			−0.140156	+	0.990129i	$0.544760\pi$
$854$		−	2.68640e7i		−	1.26045i
$855$	5.59053e6	−	1.51434e7i	0.261540	−	0.708446i
$856$		−	5.64118e7i		−	2.63139i
$857$	−1.24953e7			−0.581161			−0.290580	−	0.956851i	$-0.593848\pi$
$857$	−1.24953e7			−0.581161			−0.290580	+	0.956851i	$0.593848\pi$
$858$	−739898.	+	4.14061e6i	−0.0343126	+	0.192020i
$859$			2.29853e7i			1.06284i	0.847109	+	0.531419i	$0.178341\pi$
$859$			2.29853e7i			1.06284i	−0.847109	+	0.531419i	$0.821659\pi$
$860$	−3.26927e7			−1.50732
$861$	2.57414e6	−	1.44054e7i	0.118338	−	0.662241i
$862$	5.03496e7			2.30796
$863$	2.58072e7			1.17955			0.589773	−	0.807569i	$-0.299217\pi$
$863$	2.58072e7			1.17955			0.589773	+	0.807569i	$0.299217\pi$
$864$	5.98893e6	+	3.51288e6i	0.272938	+	0.160095i
$865$			1.54252e7i			0.700956i
$866$	−5.11388e6			−0.231716
$867$	2.23304e6	+	399028.i	0.100890	+	0.0180283i
$868$		−	1.71068e7i		−	0.770670i
$869$	2.04506e6			0.0918664
$870$	−2.90499e6	−	519101.i	−0.130121	−	0.0232516i
$871$	−2.88820e7			−1.28998
$872$			7.04282e6i			0.313657i
$873$	2.10616e6	−	5.70506e6i	0.0935311	−	0.253352i
$874$	6.23324e6			0.276017
$875$			1.04638e7i			0.462028i
$876$	3.95001e6	−	2.21050e7i	0.173915	−	0.973265i
$877$	−3.38946e7			−1.48810			−0.744049	−	0.668126i	$-0.767097\pi$
$877$	−3.38946e7			−1.48810			−0.744049	+	0.668126i	$0.767097\pi$
$878$	2.87361e7			1.25803
$879$	−5.70192e6	+	3.19090e7i	−0.248914	+	1.39297i
$880$		−	1.16558e6i		−	0.0507383i
$881$	2.03567e7			0.883623			0.441811	−	0.897108i	$-0.354336\pi$
$881$	2.03567e7			0.883623			0.441811	+	0.897108i	$0.354336\pi$
$882$	3.02138e7	+	1.11542e7i	1.30778	+	0.482798i
$883$	−2.28940e7			−0.988143			−0.494071	−	0.869421i	$-0.664492\pi$
$883$	−2.28940e7			−0.988143			−0.494071	+	0.869421i	$0.664492\pi$
$884$	−5.82659e7			−2.50775
$885$	−1.58740e7	+	1.22451e7i	−0.681286	+	0.525539i
$886$	−6.40850e7			−2.74266
$887$	1.50112e6			0.0640629			0.0320315	−	0.999487i	$-0.489802\pi$
$887$	1.50112e6			0.0640629			0.0320315	+	0.999487i	$0.489802\pi$
$888$	1.20437e6	−	6.73986e6i	0.0512538	−	0.286826i
$889$	1.23849e6			0.0525578
$890$		−	2.42704e7i		−	1.02707i
$891$	−1.48217e6	−	1.26704e6i	−0.0625468	−	0.0534684i
$892$	7.01154e7			2.95054
$893$	1.66747e7			0.699728
$894$	−1.09214e7	−	1.95158e6i	−0.457020	−	0.0816662i
$895$			1.48766e7i			0.620794i
$896$	1.86731e7			0.777046
$897$	−1.08882e6	+	6.09326e6i	−0.0451831	+	0.252853i
$898$			7.98751e7i			3.30537i
$899$	−2.07660e6			−0.0856948
$900$	1.12605e7	+	4.15710e6i	0.463397	+	0.171074i
$901$	1.12706e7			0.462526
$902$		−	5.40580e6i		−	0.221230i
$903$	−1.69198e6	+	9.46867e6i	−0.0690521	+	0.386429i
$904$	4.42154e7			1.79950
$905$		−	2.49762e7i		−	1.01369i
$906$	1.04764e7	−	5.86281e7i	0.424026	−	2.37293i
$907$	1.01396e7			0.409263			0.204632	−	0.978839i	$-0.434400\pi$
$907$	1.01396e7			0.409263			0.204632	+	0.978839i	$0.434400\pi$
$908$	6.51771e7			2.62350
$909$	−1.00055e7	−	3.69377e6i	−0.401633	−	0.148272i
$910$	2.17203e7			0.869484
$911$			5.21083e6i			0.208023i	0.994576	+	0.104011i	$0.0331678\pi$
$911$			5.21083e6i			0.208023i	−0.994576	+	0.104011i	$0.966832\pi$
$912$	−1.55522e7	−	2.77906e6i	−0.619162	−	0.110640i
$913$	1.04241e6			0.0413867
$914$			3.61106e7i			1.42978i
$915$	−3.72300e7	−	6.65273e6i	−1.47008	−	0.262692i
$916$		−	8.08861e7i		−	3.18519i
$917$	1.19615e6			0.0469745
$918$	2.08501e7	−	3.55463e7i	0.816585	−	1.39216i
$919$			1.47154e7i			0.574757i	0.957817	+	0.287378i	$0.0927837\pi$
$919$			1.47154e7i			0.574757i	−0.957817	+	0.287378i	$0.907216\pi$
$920$		−	6.26856e6i		−	0.244173i
$921$	−6.05430e6	−	1.08186e6i	−0.235188	−	0.0420264i
$922$		−	3.36460e7i		−	1.30349i
$923$	−1.60394e7			−0.619704
$924$	−1.70480e6	−	304636.i	−0.0656892	−	0.0117382i
$925$			1.28069e6i			0.0492140i
$926$		−	2.77615e7i		−	1.06394i
$927$	1.12337e6	−	3.04293e6i	0.0429362	−	0.116304i
$928$		−	748554.i		−	0.0285334i
$929$	5.17459e7			1.96715			0.983573	−	0.180512i	$-0.0577755\pi$
$929$	5.17459e7			1.96715			0.983573	+	0.180512i	$0.0577755\pi$
$930$	−3.61700e7	−	6.46332e6i	−1.37133	−	0.245047i
$931$	1.89938e7			0.718188
$932$	−9.66886e7			−3.64616
$933$	−3.44411e6	+	1.92739e7i	−0.129531	+	0.724880i
$934$	1.92489e7			0.722004
$935$	1.79304e6			0.0670751
$936$	1.98566e7	−	5.37865e7i	0.740824	−	2.00671i
$937$			3.59782e7i			1.33872i	0.742938	+	0.669361i	$0.233432\pi$
$937$			3.59782e7i			1.33872i	−0.742938	+	0.669361i	$0.766568\pi$
$938$		−	1.81424e7i		−	0.673269i
$939$	6.33632e6	−	3.54593e7i	0.234516	−	1.31240i
$940$		−	3.53528e7i		−	1.30498i
$941$	9.25929e6			0.340882			0.170441	−	0.985368i	$-0.445481\pi$
$941$	9.25929e6			0.340882			0.170441	+	0.985368i	$0.445481\pi$
$942$	−8.42084e6	+	4.71247e7i	−0.309192	+	1.73030i
$943$		−	7.95509e6i		−	0.291317i
$944$	1.45303e7	+	1.31856e7i	0.530695	+	0.481581i
$945$	−5.09449e6	+	8.68534e6i	−0.185576	+	0.316379i
$946$			3.55324e6i			0.129091i
$947$			2.87335e7i			1.04115i	0.853816	+	0.520575i	$0.174283\pi$
$947$			2.87335e7i			1.04115i	−0.853816	+	0.520575i	$0.825717\pi$
$948$	−5.78523e7	−	1.03378e7i	−2.09074	−	0.373600i
$949$	2.00631e7			0.723156
$950$	1.08000e7			0.388253
$951$	3.01644e6	−	1.68806e7i	0.108154	−	0.605251i
$952$		−	1.73608e7i		−	0.620838i
$953$		−	2.87660e7i		−	1.02600i	−0.858388	−	0.513001i	$-0.828534\pi$
$953$		−	2.87660e7i		−	1.02600i	0.858388	−	0.513001i	$-0.171466\pi$
$954$	−8.09747e6	+	2.19340e7i	−0.288057	+	0.780274i
$955$		−	1.83578e7i		−	0.651346i
$956$		−	4.99310e7i		−	1.76696i
$957$	−36980.0	+	206947.i	−0.00130523	+	0.00730432i
$958$			2.17282e7i			0.764911i
$959$		−	4.39532e6i		−	0.154328i
$960$	5.42704e6	−	3.03708e7i	0.190058	−	1.06360i
$961$	2.77336e6			0.0968720
$962$	1.28964e7			0.449295
$963$	−1.70600e7	+	4.62113e7i	−0.592808	+	1.60577i
$964$	9.62529e7			3.33596
$965$			1.84280e7i			0.637032i
$966$	−3.82752e6	−	683950.i	−0.131970	−	0.0235821i
$967$		−	3.90085e7i		−	1.34151i	−0.741680	−	0.670754i	$-0.765971\pi$
$967$		−	3.90085e7i		−	1.34151i	0.741680	−	0.670754i	$-0.234029\pi$
$968$	4.45140e7			1.52689
$969$	4.27510e6	−	2.39243e7i	0.146264	−	0.818521i
$970$	−1.16009e7			−0.395878
$971$			4.42731e7i			1.50692i	0.657491	+	0.753462i	$0.271618\pi$
$971$			4.42731e7i			1.50692i	−0.657491	+	0.753462i	$0.728382\pi$
$972$	3.55240e7	+	4.33356e7i	1.20602	+	1.47122i
$973$	5.65048e6			0.191339
$974$	−7.23292e7			−2.44296
$975$	−1.88654e6	+	1.05575e7i	−0.0635558	+	0.355670i
$976$			3.70142e7i			1.24378i
$977$	352721.			0.0118221			0.00591105	−	0.999983i	$-0.498118\pi$
$977$	352721.			0.0118221			0.00591105	+	0.999983i	$0.498118\pi$
$978$	6.58877e6	+	1.17737e6i	0.220271	+	0.0393609i
$979$	−1.72899e6			−0.0576547
$980$		−	4.02696e7i		−	1.33941i
$981$	2.12988e6	−	5.76932e6i	0.0706616	−	0.191405i
$982$			5.22345e7i			1.72854i
$983$	−3.99184e7			−1.31762			−0.658809	−	0.752311i	$-0.728939\pi$
$983$	−3.99184e7			−1.31762			−0.658809	+	0.752311i	$0.728939\pi$
$984$	−1.29619e7	+	7.25375e7i	−0.426759	+	2.38822i
$985$	−2.58021e7			−0.847354
$986$	−4.44292e6			−0.145538
$987$	−1.02391e7	−	1.82965e6i	−0.334556	−	0.0597827i
$988$		−	7.12839e7i		−	2.32327i
$989$			5.22889e6i			0.169988i
$990$	−1.28823e6	+	3.48948e6i	−0.0417738	+	0.113155i
$991$			7.82069e6i			0.252965i	0.991969	+	0.126483i	$0.0403688\pi$
$991$			7.82069e6i			0.252965i	−0.991969	+	0.126483i	$0.959631\pi$
$992$		−	9.32024e6i		−	0.300710i
$993$	2.63449e7	+	4.70764e6i	0.847858	+	0.151506i
$994$		−	1.00753e7i		−	0.323437i
$995$			3.33812e7i			1.06892i
$996$	−2.94885e7	−	5.26938e6i	−0.941898	−	0.168311i
$997$	3.34225e7			1.06488			0.532441	−	0.846467i	$-0.321275\pi$
$997$	3.34225e7			1.06488			0.532441	+	0.846467i	$0.321275\pi$
$998$	6.77780e7			2.15408
$999$	−3.02485e6	+	5.15692e6i	−0.0958938	+	0.163485i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	177.6.d.b.176.10	yes	92
3.2	odd	2	inner	177.6.d.b.176.83	yes	92
59.58	odd	2	inner	177.6.d.b.176.84	yes	92
177.176	even	2	inner	177.6.d.b.176.9	✓	92

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
177.6.d.b.176.9	✓	92	177.176	even	2	inner
177.6.d.b.176.10	yes	92	1.1	even	1	trivial
177.6.d.b.176.83	yes	92	3.2	odd	2	inner
177.6.d.b.176.84	yes	92	59.58	odd	2	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 177 = 3 \cdot 59 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	177.d (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-9.63720 q^{2} +(15.3454 + 2.74211i) q^{3} +60.8757 q^{4} +48.0995i q^{5} +(-147.887 - 26.4263i) q^{6} +55.2643 q^{7} -278.281 q^{8} +(227.962 + 84.1575i) q^{9} +O(q^{10})\)	\(q-9.63720 q^{2} +(15.3454 + 2.74211i) q^{3} +60.8757 q^{4} +48.0995i q^{5} +(-147.887 - 26.4263i) q^{6} +55.2643 q^{7} -278.281 q^{8} +(227.962 + 84.1575i) q^{9} -463.545i q^{10} -33.0223 q^{11} +(934.161 + 166.928i) q^{12} +847.868i q^{13} -532.594 q^{14} +(-131.894 + 738.106i) q^{15} +733.828 q^{16} +1128.87i q^{17} +(-2196.91 - 811.043i) q^{18} -1381.08 q^{19} +2928.09i q^{20} +(848.052 + 151.541i) q^{21} +318.243 q^{22} +468.321 q^{23} +(-4270.33 - 763.077i) q^{24} +811.434 q^{25} -8171.08i q^{26} +(3267.39 + 1916.53i) q^{27} +3364.25 q^{28} -408.390i q^{29} +(1271.09 - 7113.28i) q^{30} -5084.86i q^{31} +1832.94 q^{32} +(-506.740 - 90.5508i) q^{33} -10879.1i q^{34} +2658.19i q^{35} +(13877.3 + 5123.15i) q^{36} +1578.30i q^{37} +13309.8 q^{38} +(-2324.95 + 13010.9i) q^{39} -13385.2i q^{40} -16986.4i q^{41} +(-8172.85 - 1460.43i) q^{42} +11165.2i q^{43} -2010.26 q^{44} +(-4047.94 + 10964.9i) q^{45} -4513.30 q^{46} -12073.6 q^{47} +(11260.9 + 2012.24i) q^{48} -13752.9 q^{49} -7819.96 q^{50} +(-3095.48 + 17322.9i) q^{51} +51614.6i q^{52} -9984.02i q^{53} +(-31488.5 - 18469.9i) q^{54} -1588.36i q^{55} -15379.0 q^{56} +(-21193.2 - 3787.08i) q^{57} +3935.73i q^{58} +(19800.7 + 17968.2i) q^{59} +(-8029.16 + 44932.7i) q^{60} +50439.9i q^{61} +49003.8i q^{62} +(12598.1 + 4650.91i) q^{63} -41146.9 q^{64} -40782.1 q^{65} +(4883.55 + 872.656i) q^{66} +34064.3i q^{67} +68720.5i q^{68} +(7186.57 + 1284.19i) q^{69} -25617.5i q^{70} +18917.3i q^{71} +(-63437.4 - 23419.4i) q^{72} -23663.0i q^{73} -15210.4i q^{74} +(12451.8 + 2225.04i) q^{75} -84074.3 q^{76} -1824.95 q^{77} +(22406.0 - 125388. i) q^{78} -61929.7 q^{79} +35296.8i q^{80} +(44884.0 + 38369.4i) q^{81} +163701. i q^{82} -31566.8 q^{83} +(51625.8 + 9225.16i) q^{84} -54297.9 q^{85} -107601. i q^{86} +(1119.85 - 6266.90i) q^{87} +9189.48 q^{88} +52358.2 q^{89} +(39010.8 - 105671. i) q^{90} +46856.9i q^{91} +28509.4 q^{92} +(13943.2 - 78029.1i) q^{93} +116356. q^{94} -66429.4i q^{95} +(28127.2 + 5026.12i) q^{96} -25026.4i q^{97} +132539. q^{98} +(-7527.82 - 2779.07i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 92 q + 22 q^{3} + 1724 q^{4} - 80 q^{7} + 2 q^{9}+O(q^{10}) \) 92 * q + 22 * q^3 + 1724 * q^4 - 80 * q^7 + 2 * q^9	\( 92 q + 22 q^{3} + 1724 q^{4} - 80 q^{7} + 2 q^{9} - 1244 q^{12} + 1116 q^{15} + 14724 q^{16} + 1784 q^{19} + 6388 q^{21} - 8140 q^{22} - 48208 q^{25} - 6458 q^{27} - 19092 q^{28} - 20832 q^{36} - 134984 q^{45} + 51180 q^{46} + 61720 q^{48} + 174556 q^{49} + 8332 q^{51} + 236784 q^{57} + 375208 q^{60} - 429890 q^{63} + 561472 q^{64} - 11596 q^{66} + 169948 q^{75} + 111488 q^{76} + 356264 q^{78} + 180260 q^{79} + 79554 q^{81} + 269308 q^{84} + 111028 q^{85} - 318764 q^{87} - 1242976 q^{88} - 513608 q^{94}+O(q^{100}) \) 92 * q + 22 * q^3 + 1724 * q^4 - 80 * q^7 + 2 * q^9 - 1244 * q^12 + 1116 * q^15 + 14724 * q^16 + 1784 * q^19 + 6388 * q^21 - 8140 * q^22 - 48208 * q^25 - 6458 * q^27 - 19092 * q^28 - 20832 * q^36 - 134984 * q^45 + 51180 * q^46 + 61720 * q^48 + 174556 * q^49 + 8332 * q^51 + 236784 * q^57 + 375208 * q^60 - 429890 * q^63 + 561472 * q^64 - 11596 * q^66 + 169948 * q^75 + 111488 * q^76 + 356264 * q^78 + 180260 * q^79 + 79554 * q^81 + 269308 * q^84 + 111028 * q^85 - 318764 * q^87 - 1242976 * q^88 - 513608 * q^94

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more