LMFDB - Embedded newform 644.4.i.b.93.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [644,4,Mod(93,644)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(644, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 2, 0]))

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

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

chi := DirichletCharacter("644.93");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 644 = 2^{2} \cdot 7 \cdot 23 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	644.i (of order $3$, degree $2$, 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:	$37.9972300437$
Analytic rank:	$0$
Dimension:	$44$
Relative dimension:	$22$ over $\Q(\zeta_{3})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			93.8
Character	$\chi$	$=$	644.93
Dual form			644.4.i.b.277.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.77144 - 3.06822i) q^{3} +(-3.18380 + 5.51450i) q^{5} +(10.8024 - 15.0435i) q^{7} +(7.22402 - 12.5124i) q^{9} +O(q^{10})$	\(q+(-1.77144 - 3.06822i) q^{3} +(-3.18380 + 5.51450i) q^{5} +(10.8024 - 15.0435i) q^{7} +(7.22402 - 12.5124i) q^{9} +(-17.6630 - 30.5931i) q^{11} +21.5141 q^{13} +22.5596 q^{15} +(-9.63879 - 16.6949i) q^{17} +(-13.4375 + 23.2744i) q^{19} +(-65.2926 - 6.49550i) q^{21} +(11.5000 - 19.9186i) q^{23} +(42.2269 + 73.1391i) q^{25} -146.845 q^{27} +242.289 q^{29} +(27.3321 + 47.3406i) q^{31} +(-62.5776 + 108.388i) q^{33} +(48.5648 + 107.465i) q^{35} +(189.151 - 327.619i) q^{37} +(-38.1109 - 66.0101i) q^{39} -323.948 q^{41} -489.724 q^{43} +(45.9996 + 79.6737i) q^{45} +(106.883 - 185.126i) q^{47} +(-109.616 - 325.013i) q^{49} +(-34.1490 + 59.1478i) q^{51} +(155.408 + 269.174i) q^{53} +224.941 q^{55} +95.2146 q^{57} +(-166.432 - 288.269i) q^{59} +(276.922 - 479.642i) q^{61} +(-110.193 - 243.839i) q^{63} +(-68.4966 + 118.640i) q^{65} +(-98.5879 - 170.759i) q^{67} -81.4861 q^{69} -1093.69 q^{71} +(-163.470 - 283.139i) q^{73} +(149.605 - 259.123i) q^{75} +(-651.032 - 64.7665i) q^{77} +(-127.983 + 221.674i) q^{79} +(65.0783 + 112.719i) q^{81} -956.190 q^{83} +122.752 q^{85} +(-429.199 - 743.395i) q^{87} +(-486.922 + 843.374i) q^{89} +(232.405 - 323.649i) q^{91} +(96.8342 - 167.722i) q^{93} +(-85.5644 - 148.202i) q^{95} -582.580 q^{97} -510.391 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 44 q + 12 q^{3} + 10 q^{5} - 6 q^{7} - 238 q^{9}+O(q^{10}) $ 44 * q + 12 * q^3 + 10 * q^5 - 6 * q^7 - 238 * q^9	$ 44 q + 12 q^{3} + 10 q^{5} - 6 q^{7} - 238 q^{9} + 28 q^{11} - 152 q^{13} + 208 q^{15} - 52 q^{17} + 38 q^{19} - 10 q^{21} + 506 q^{23} - 516 q^{25} - 876 q^{27} - 100 q^{29} + 230 q^{31} + 424 q^{33} + 98 q^{35} + 18 q^{37} - 350 q^{39} + 784 q^{41} - 336 q^{43} + 1156 q^{45} + 452 q^{47} + 546 q^{49} - 498 q^{51} - 508 q^{53} - 3084 q^{55} - 1916 q^{57} + 508 q^{59} + 1386 q^{61} + 1290 q^{63} + 360 q^{65} - 1896 q^{67} + 552 q^{69} - 3352 q^{71} + 990 q^{73} + 3328 q^{75} + 1328 q^{77} + 524 q^{79} - 4486 q^{81} - 1120 q^{83} - 5296 q^{85} + 3700 q^{87} + 1216 q^{89} + 1438 q^{91} + 366 q^{93} + 90 q^{95} + 716 q^{97} + 5716 q^{99}+O(q^{100}) $ 44 * q + 12 * q^3 + 10 * q^5 - 6 * q^7 - 238 * q^9 + 28 * q^11 - 152 * q^13 + 208 * q^15 - 52 * q^17 + 38 * q^19 - 10 * q^21 + 506 * q^23 - 516 * q^25 - 876 * q^27 - 100 * q^29 + 230 * q^31 + 424 * q^33 + 98 * q^35 + 18 * q^37 - 350 * q^39 + 784 * q^41 - 336 * q^43 + 1156 * q^45 + 452 * q^47 + 546 * q^49 - 498 * q^51 - 508 * q^53 - 3084 * q^55 - 1916 * q^57 + 508 * q^59 + 1386 * q^61 + 1290 * q^63 + 360 * q^65 - 1896 * q^67 + 552 * q^69 - 3352 * q^71 + 990 * q^73 + 3328 * q^75 + 1328 * q^77 + 524 * q^79 - 4486 * q^81 - 1120 * q^83 - 5296 * q^85 + 3700 * q^87 + 1216 * q^89 + 1438 * q^91 + 366 * q^93 + 90 * q^95 + 716 * q^97 + 5716 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/644\mathbb{Z}\right)^\times$.

$n$	$185$	$281$	$323$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$1$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−1.77144	−	3.06822i	−0.340913	−	0.590479i	0.643689	−	0.765287i	$-0.277403\pi$
$3$	−1.77144	−	3.06822i	−0.340913	−	0.590479i	−0.984603	+	0.174808i	$0.944070\pi$
$4$		0			0
$5$	−3.18380	+	5.51450i	−0.284767	+	0.493232i	−0.972553	−	0.232683i	$-0.925250\pi$
$5$	−3.18380	+	5.51450i	−0.284767	+	0.493232i	0.687785	+	0.725914i	$0.258583\pi$
$6$		0			0
$7$	10.8024	−	15.0435i	0.583276	−	0.812274i
$7$	10.8024	−	15.0435i	0.583276	−	0.812274i
$8$		0			0
$9$	7.22402	−	12.5124i	0.267556	−	0.463421i
$10$		0			0
$11$	−17.6630	−	30.5931i	−0.484144	−	0.838562i	0.515690	−	0.856775i	$-0.327536\pi$
$11$	−17.6630	−	30.5931i	−0.484144	−	0.838562i	−0.999834	+	0.0182132i	$0.994202\pi$
$12$		0			0
$13$	21.5141			0.458996			0.229498	−	0.973309i	$-0.426292\pi$
$13$	21.5141			0.458996			0.229498	+	0.973309i	$0.426292\pi$
$14$		0			0
$15$	22.5596			0.388324
$16$		0			0
$17$	−9.63879	−	16.6949i	−0.137515	−	0.238183i	0.789041	−	0.614341i	$-0.210578\pi$
$17$	−9.63879	−	16.6949i	−0.137515	−	0.238183i	−0.926555	+	0.376159i	$0.877245\pi$
$18$		0			0
$19$	−13.4375	+	23.2744i	−0.162251	+	0.281027i	−0.935676	−	0.352861i	$-0.885209\pi$
$19$	−13.4375	+	23.2744i	−0.162251	+	0.281027i	0.773425	+	0.633888i	$0.218542\pi$
$20$		0			0
$21$	−65.2926	−	6.49550i	−0.678477	−	0.0674969i
$22$		0			0
$23$	11.5000	−	19.9186i	0.104257	−	0.180579i
$23$	11.5000	−	19.9186i	0.104257	−	0.180579i
$24$		0			0
$25$	42.2269	+	73.1391i	0.337815	+	0.585113i
$26$		0			0
$27$	−146.845			−1.04668
$28$		0			0
$29$	242.289			1.55145			0.775723	−	0.631074i	$-0.217386\pi$
$29$	242.289			1.55145			0.775723	+	0.631074i	$0.217386\pi$
$30$		0			0
$31$	27.3321	+	47.3406i	0.158355	+	0.274278i	0.934275	−	0.356552i	$-0.116048\pi$
$31$	27.3321	+	47.3406i	0.158355	+	0.274278i	−0.775921	+	0.630830i	$0.782714\pi$
$32$		0			0
$33$	−62.5776	+	108.388i	−0.330102	+	0.571754i
$34$		0			0
$35$	48.5648	+	107.465i	0.234541	+	0.518999i
$36$		0			0
$37$	189.151	−	327.619i	0.840438	−	1.45568i	−0.0490872	−	0.998794i	$-0.515631\pi$
$37$	189.151	−	327.619i	0.840438	−	1.45568i	0.889525	−	0.456886i	$-0.151035\pi$
$38$		0			0
$39$	−38.1109	−	66.0101i	−0.156478	−	0.271028i
$40$		0			0
$41$	−323.948			−1.23396			−0.616978	−	0.786980i	$-0.711643\pi$
$41$	−323.948			−1.23396			−0.616978	+	0.786980i	$0.711643\pi$
$42$		0			0
$43$	−489.724			−1.73680			−0.868398	−	0.495868i	$-0.834850\pi$
$43$	−489.724			−1.73680			−0.868398	+	0.495868i	$0.834850\pi$
$44$		0			0
$45$	45.9996	+	79.6737i	0.152383	+	0.263935i
$46$		0			0
$47$	106.883	−	185.126i	0.331711	−	0.574540i	−0.651136	−	0.758961i	$-0.725707\pi$
$47$	106.883	−	185.126i	0.331711	−	0.574540i	0.982847	+	0.184420i	$0.0590408\pi$
$48$		0			0
$49$	−109.616	−	325.013i	−0.319579	−	0.947560i
$50$		0			0
$51$	−34.1490	+	59.1478i	−0.0937612	+	0.162399i
$52$		0			0
$53$	155.408	+	269.174i	0.402772	+	0.697622i	0.994059	−	0.108839i	$-0.0347134\pi$
$53$	155.408	+	269.174i	0.402772	+	0.697622i	−0.591287	+	0.806461i	$0.701380\pi$
$54$		0			0
$55$	224.941			0.551474
$56$		0			0
$57$	95.2146			0.221254
$58$		0			0
$59$	−166.432	−	288.269i	−0.367248	−	0.636092i	0.621886	−	0.783108i	$-0.286367\pi$
$59$	−166.432	−	288.269i	−0.367248	−	0.636092i	−0.989134	+	0.147015i	$0.953033\pi$
$60$		0			0
$61$	276.922	−	479.642i	0.581249	−	1.00675i	−0.414083	−	0.910239i	$-0.635898\pi$
$61$	276.922	−	479.642i	0.581249	−	1.00675i	0.995332	−	0.0965131i	$-0.0307690\pi$
$62$		0			0
$63$	−110.193	−	243.839i	−0.220366	−	0.487632i
$64$		0			0
$65$	−68.4966	+	118.640i	−0.130707	+	0.226391i
$66$		0			0
$67$	−98.5879	−	170.759i	−0.179768	−	0.311367i	0.762033	−	0.647538i	$-0.224201\pi$
$67$	−98.5879	−	170.759i	−0.179768	−	0.311367i	−0.941801	+	0.336171i	$0.890868\pi$
$68$		0			0
$69$	−81.4861			−0.142171
$70$		0			0
$71$	−1093.69			−1.82812			−0.914061	−	0.405577i	$-0.867071\pi$
$71$	−1093.69			−1.82812			−0.914061	+	0.405577i	$0.867071\pi$
$72$		0			0
$73$	−163.470	−	283.139i	−0.262092	−	0.453957i	0.704706	−	0.709500i	$-0.251079\pi$
$73$	−163.470	−	283.139i	−0.262092	−	0.453957i	−0.966798	+	0.255543i	$0.917746\pi$
$74$		0			0
$75$	149.605	−	259.123i	0.230331	−	0.398945i
$76$		0			0
$77$	−651.032	−	64.7665i	−0.963532	−	0.0958550i
$78$		0			0
$79$	−127.983	+	221.674i	−0.182269	+	0.315699i	−0.942653	−	0.333775i	$-0.891678\pi$
$79$	−127.983	+	221.674i	−0.182269	+	0.315699i	0.760384	+	0.649474i	$0.225011\pi$
$80$		0			0
$81$	65.0783	+	112.719i	0.0892707	+	0.154621i
$82$		0			0
$83$	−956.190			−1.26452			−0.632262	−	0.774755i	$-0.717873\pi$
$83$	−956.190			−1.26452			−0.632262	+	0.774755i	$0.717873\pi$
$84$		0			0
$85$	122.752			0.156639
$86$		0			0
$87$	−429.199	−	743.395i	−0.528908	−	0.916096i
$88$		0			0
$89$	−486.922	+	843.374i	−0.579929	+	1.00447i	0.415558	+	0.909567i	$0.363586\pi$
$89$	−486.922	+	843.374i	−0.579929	+	1.00447i	−0.995487	+	0.0948997i	$0.969747\pi$
$90$		0			0
$91$	232.405	−	323.649i	0.267721	−	0.372831i
$92$		0			0
$93$	96.8342	−	167.722i	0.107970	−	0.187010i
$94$		0			0
$95$	−85.5644	−	148.202i	−0.0924076	−	0.160055i
$96$		0			0
$97$	−582.580			−0.609815			−0.304907	−	0.952382i	$-0.598626\pi$
$97$	−582.580			−0.609815			−0.304907	+	0.952382i	$0.598626\pi$
$98$		0			0
$99$	−510.391			−0.518143
$100$		0			0
$101$	−258.008	−	446.883i	−0.254186	−	0.440263i	0.710488	−	0.703709i	$-0.248474\pi$
$101$	−258.008	−	446.883i	−0.254186	−	0.440263i	−0.964674	+	0.263446i	$0.915141\pi$
$102$		0			0
$103$	−912.943	+	1581.26i	−0.873349	+	1.51268i	−0.0148377	+	0.999890i	$0.504723\pi$
$103$	−912.943	+	1581.26i	−0.873349	+	1.51268i	−0.858511	+	0.512795i	$0.828610\pi$
$104$		0			0
$105$	243.698	−	339.376i	0.226500	−	0.315425i
$106$		0			0
$107$	135.255	−	234.269i	0.122202	−	0.211660i	−0.798434	−	0.602083i	$-0.794338\pi$
$107$	135.255	−	234.269i	0.122202	−	0.211660i	0.920636	+	0.390423i	$0.127671\pi$
$108$		0			0
$109$	40.7056	+	70.5041i	0.0357696	+	0.0619548i	0.883356	−	0.468703i	$-0.155278\pi$
$109$	40.7056	+	70.5041i	0.0357696	+	0.0619548i	−0.847586	+	0.530657i	$0.821945\pi$
$110$		0			0
$111$	−1340.27			−1.14607
$112$		0			0
$113$	253.302			0.210873			0.105437	−	0.994426i	$-0.466376\pi$
$113$	253.302			0.210873			0.105437	+	0.994426i	$0.466376\pi$
$114$		0			0
$115$	73.2273	+	126.833i	0.0593781	+	0.102846i
$116$		0			0
$117$	155.419	−	269.193i	0.122807	−	0.212709i
$118$		0			0
$119$	−355.272	−	35.3435i	−0.273679	−	0.0272263i
$120$		0			0
$121$	41.5395	−	71.9486i	0.0312093	−	0.0540561i
$122$		0			0
$123$	573.854	+	993.944i	0.420672	+	0.728625i
$124$		0			0
$125$	−1333.72			−0.954330
$126$		0			0
$127$	321.448			0.224598			0.112299	−	0.993674i	$-0.464179\pi$
$127$	321.448			0.224598			0.112299	+	0.993674i	$0.464179\pi$
$128$		0			0
$129$	867.515	+	1502.58i	0.592097	+	1.02554i
$130$		0			0
$131$	−80.0673	+	138.681i	−0.0534009	+	0.0924930i	−0.891490	−	0.453040i	$-0.850339\pi$
$131$	−80.0673	+	138.681i	−0.0534009	+	0.0924930i	0.838089	+	0.545533i	$0.183673\pi$
$132$		0			0
$133$	204.972	+	453.567i	0.133634	+	0.295709i
$134$		0			0
$135$	467.525	−	809.777i	0.298060	−	0.516256i
$136$		0			0
$137$	−817.421	−	1415.82i	−0.509759	−	0.882929i	−0.999936	−	0.0113058i	$-0.996401\pi$
$137$	−817.421	−	1415.82i	−0.509759	−	0.882929i	0.490177	−	0.871623i	$-0.336932\pi$
$138$		0			0
$139$	2491.87			1.52056			0.760278	−	0.649597i	$-0.225063\pi$
$139$	2491.87			1.52056			0.760278	+	0.649597i	$0.225063\pi$
$140$		0			0
$141$	−757.343			−0.452339
$142$		0			0
$143$	−380.004	−	658.185i	−0.222220	−	0.384897i
$144$		0			0
$145$	−771.398	+	1336.10i	−0.441801	+	0.765222i
$146$		0			0
$147$	−803.033	+	912.065i	−0.450565	+	0.511740i
$148$		0			0
$149$	345.299	−	598.076i	0.189853	−	0.328834i	−0.755348	−	0.655323i	$-0.772532\pi$
$149$	345.299	−	598.076i	0.189853	−	0.328834i	0.945201	+	0.326489i	$0.105866\pi$
$150$		0			0
$151$	−1212.94	−	2100.88i	−0.653696	−	1.13223i	−0.982219	−	0.187738i	$-0.939884\pi$
$151$	−1212.94	−	2100.88i	−0.653696	−	1.13223i	0.328524	−	0.944496i	$-0.393449\pi$
$152$		0			0
$153$	−278.523			−0.147172
$154$		0			0
$155$	−348.080			−0.180377
$156$		0			0
$157$	873.387	+	1512.75i	0.443974	+	0.768985i	0.997980	−	0.0635272i	$-0.0202350\pi$
$157$	873.387	+	1512.75i	0.443974	+	0.768985i	−0.554006	+	0.832513i	$0.686902\pi$
$158$		0			0
$159$	550.591	−	953.651i	0.274621	−	0.475657i
$160$		0			0
$161$	−175.418	−	388.169i	−0.0858688	−	0.190013i
$162$		0			0
$163$	1878.07	−	3252.92i	0.902466	−	1.56312i	0.0781832	−	0.996939i	$-0.475088\pi$
$163$	1878.07	−	3252.92i	0.902466	−	1.56312i	0.824283	−	0.566178i	$-0.191579\pi$
$164$		0			0
$165$	−398.469	−	690.168i	−0.188005	−	0.325634i
$166$		0			0
$167$	−3138.03			−1.45406			−0.727030	−	0.686606i	$-0.759100\pi$
$167$	−3138.03			−1.45406			−0.727030	+	0.686606i	$0.759100\pi$
$168$		0			0
$169$	−1734.14			−0.789323
$170$		0			0
$171$	194.145	+	336.270i	0.0868226	+	0.150381i
$172$		0			0
$173$	608.732	−	1054.35i	0.267520	−	0.463359i	−0.700700	−	0.713456i	$-0.747129\pi$
$173$	608.732	−	1054.35i	0.267520	−	0.463359i	0.968221	+	0.250097i	$0.0804624\pi$
$174$		0			0
$175$	1556.42	+	154.838i	0.672312	+	0.0668835i
$176$		0			0
$177$	−589.649	+	1021.30i	−0.250399	+	0.433705i
$178$		0			0
$179$	−262.606	−	454.846i	−0.109654	−	0.189926i	0.805976	−	0.591948i	$-0.201641\pi$
$179$	−262.606	−	454.846i	−0.109654	−	0.189926i	−0.915630	+	0.402022i	$0.868308\pi$
$180$		0			0
$181$	3848.54			1.58044			0.790220	−	0.612823i	$-0.209966\pi$
$181$	3848.54			1.58044			0.790220	+	0.612823i	$0.209966\pi$
$182$		0			0
$183$	−1962.20			−0.792621
$184$		0			0
$185$	1204.43	+	2086.14i	0.478658	+	0.829061i
$186$		0			0
$187$	−340.499	+	589.762i	−0.133154	+	0.230629i
$188$		0			0
$189$	−1586.28	+	2209.07i	−0.610503	+	0.850192i
$190$		0			0
$191$	1980.20	−	3429.81i	0.750168	−	1.29933i	−0.197572	−	0.980288i	$-0.563306\pi$
$191$	1980.20	−	3429.81i	0.750168	−	1.29933i	0.947741	−	0.319041i	$-0.103361\pi$
$192$		0			0
$193$	321.479	+	556.818i	0.119899	+	0.207672i	0.919728	−	0.392557i	$-0.128409\pi$
$193$	321.479	+	556.818i	0.119899	+	0.207672i	−0.799828	+	0.600229i	$0.795076\pi$
$194$		0			0
$195$	485.350			0.178239
$196$		0			0
$197$	835.378			0.302123			0.151061	−	0.988524i	$-0.451731\pi$
$197$	835.378			0.302123			0.151061	+	0.988524i	$0.451731\pi$
$198$		0			0
$199$	−2142.84	−	3711.50i	−0.763325	−	1.32212i	−0.941127	−	0.338052i	$-0.890232\pi$
$199$	−2142.84	−	3711.50i	−0.763325	−	1.32212i	0.177802	−	0.984066i	$-0.443101\pi$
$200$		0			0
$201$	−349.285	+	604.979i	−0.122570	+	0.212298i
$202$		0			0
$203$	2617.30	−	3644.88i	0.904920	−	1.26020i
$204$		0			0
$205$	1031.39	−	1786.41i	0.351391	−	0.608626i
$206$		0			0
$207$	−166.153	−	287.785i	−0.0557894	−	0.0966300i
$208$		0			0
$209$	949.383			0.314211
$210$		0			0
$211$	−1525.83			−0.497832			−0.248916	−	0.968525i	$-0.580074\pi$
$211$	−1525.83			−0.497832			−0.248916	+	0.968525i	$0.580074\pi$
$212$		0			0
$213$	1937.40	+	3355.67i	0.623231	+	1.07947i
$214$		0			0
$215$	1559.18	−	2700.58i	0.494583	−	0.856642i
$216$		0			0
$217$	1007.42	+	100.221i	0.315154	+	0.0313524i
$218$		0			0
$219$	−579.154	+	1003.12i	−0.178701	+	0.309520i
$220$		0			0
$221$	−207.370	−	359.176i	−0.0631187	−	0.109325i
$222$		0			0
$223$	4040.11			1.21321			0.606605	−	0.795003i	$-0.292531\pi$
$223$	4040.11			1.21321			0.606605	+	0.795003i	$0.292531\pi$
$224$		0			0
$225$	1220.19			0.361538
$226$		0			0
$227$	545.744	+	945.257i	0.159570	+	0.276383i	0.934714	−	0.355402i	$-0.115656\pi$
$227$	545.744	+	945.257i	0.159570	+	0.276383i	−0.775144	+	0.631785i	$0.782323\pi$
$228$		0			0
$229$	−929.484	+	1609.91i	−0.268219	+	0.464568i	−0.968402	−	0.249395i	$-0.919768\pi$
$229$	−929.484	+	1609.91i	−0.268219	+	0.464568i	0.700183	+	0.713963i	$0.253102\pi$
$230$		0			0
$231$	954.543	+	2112.24i	0.271880	+	0.601623i
$232$		0			0
$233$	−2182.90	+	3780.90i	−0.613762	+	1.06307i	0.376838	+	0.926279i	$0.377011\pi$
$233$	−2182.90	+	3780.90i	−0.613762	+	1.06307i	−0.990600	+	0.136788i	$0.956322\pi$
$234$		0			0
$235$	680.584	+	1178.81i	0.188921	+	0.327221i
$236$		0			0
$237$	906.858			0.248552
$238$		0			0
$239$	3154.27			0.853693			0.426846	−	0.904324i	$-0.359624\pi$
$239$	3154.27			0.853693			0.426846	+	0.904324i	$0.359624\pi$
$240$		0			0
$241$	1338.99	+	2319.20i	0.357893	+	0.619888i	0.987609	−	0.156937i	$-0.0501620\pi$
$241$	1338.99	+	2319.20i	0.357893	+	0.619888i	−0.629716	+	0.776826i	$0.716829\pi$
$242$		0			0
$243$	−1751.85	+	3034.29i	−0.462473	+	0.801027i
$244$		0			0
$245$	2141.28	+	430.300i	0.558372	+	0.112207i
$246$		0			0
$247$	−289.096	+	500.729i	−0.0744726	+	0.128990i
$248$		0			0
$249$	1693.83	+	2933.80i	0.431093	+	0.746674i
$250$		0			0
$251$	−1505.12			−0.378496			−0.189248	−	0.981929i	$-0.560605\pi$
$251$	−1505.12			−0.378496			−0.189248	+	0.981929i	$0.560605\pi$
$252$		0			0
$253$	−812.496			−0.201902
$254$		0			0
$255$	−217.447	−	376.629i	−0.0534002	−	0.0924919i
$256$		0			0
$257$	1042.67	−	1805.96i	0.253074	−	0.438337i	−0.711296	−	0.702892i	$-0.751892\pi$
$257$	1042.67	−	1805.96i	0.253074	−	0.438337i	0.964371	+	0.264555i	$0.0852250\pi$
$258$		0			0
$259$	−2885.26	−	6384.57i	−0.692205	−	1.53173i
$260$		0			0
$261$	1750.30	−	3031.61i	0.415099	−	0.718973i
$262$		0			0
$263$	2146.62	+	3718.05i	0.503293	+	0.871728i	0.999993	+	0.00380620i	$0.00121155\pi$
$263$	2146.62	+	3718.05i	0.503293	+	0.871728i	−0.496700	+	0.867922i	$0.665455\pi$
$264$		0			0
$265$	−1979.15			−0.458785
$266$		0			0
$267$	3450.21			0.790822
$268$		0			0
$269$	970.919	+	1681.68i	0.220067	+	0.381167i	0.954828	−	0.297159i	$-0.0960391\pi$
$269$	970.919	+	1681.68i	0.220067	+	0.381167i	−0.734761	+	0.678326i	$0.762706\pi$
$270$		0			0
$271$	−156.748	+	271.495i	−0.0351356	+	0.0608567i	−0.883058	−	0.469263i	$-0.844520\pi$
$271$	−156.748	+	271.495i	−0.0351356	+	0.0608567i	0.847923	+	0.530120i	$0.177853\pi$
$272$		0			0
$273$	−1404.72	−	139.745i	−0.311418	−	0.0309808i
$274$		0			0
$275$	1491.70	−	2583.71i	0.327102	−	0.566558i
$276$		0			0
$277$	2716.28	+	4704.74i	0.589190	+	1.02051i	0.994339	+	0.106256i	$0.0338862\pi$
$277$	2716.28	+	4704.74i	0.589190	+	1.02051i	−0.405149	+	0.914251i	$0.632780\pi$
$278$		0			0
$279$	789.791			0.169475
$280$		0			0
$281$	−8731.61			−1.85368			−0.926840	−	0.375455i	$-0.877486\pi$
$281$	−8731.61			−1.85368			−0.926840	+	0.375455i	$0.877486\pi$
$282$		0			0
$283$	4561.65	+	7901.01i	0.958170	+	1.65960i	0.726942	+	0.686699i	$0.240941\pi$
$283$	4561.65	+	7901.01i	0.958170	+	1.65960i	0.231227	+	0.972900i	$0.425726\pi$
$284$		0			0
$285$	−303.144	+	525.061i	−0.0630059	+	0.109129i
$286$		0			0
$287$	−3499.42	+	4873.33i	−0.719737	+	1.00231i
$288$		0			0
$289$	2270.69	−	3932.95i	0.462179	−	0.800518i
$290$		0			0
$291$	1032.00	+	1787.48i	0.207894	+	0.360083i
$292$		0			0
$293$	−8099.68			−1.61498			−0.807489	−	0.589882i	$-0.799174\pi$
$293$	−8099.68			−1.61498			−0.807489	+	0.589882i	$0.799174\pi$
$294$		0			0
$295$	2119.55			0.418321
$296$		0			0
$297$	2593.72	+	4492.46i	0.506744	+	0.877706i
$298$		0			0
$299$	247.413	−	428.531i	0.0478537	−	0.0828850i
$300$		0			0
$301$	−5290.20	+	7367.18i	−1.01303	+	1.41075i
$302$		0			0
$303$	−914.090	+	1583.25i	−0.173311	+	0.300183i
$304$		0			0
$305$	1763.32	+	3054.17i	0.331041	+	0.573380i
$306$		0			0
$307$	3329.19			0.618915			0.309457	−	0.950913i	$-0.399853\pi$
$307$	3329.19			0.618915			0.309457	+	0.950913i	$0.399853\pi$
$308$		0			0
$309$	6468.88			1.19094
$310$		0			0
$311$	5176.82	+	8966.51i	0.943892	+	1.63487i	0.757955	+	0.652307i	$0.226199\pi$
$311$	5176.82	+	8966.51i	0.943892	+	1.63487i	0.185937	+	0.982562i	$0.440468\pi$
$312$		0			0
$313$	1885.99	−	3266.64i	0.340583	−	0.589908i	−0.643958	−	0.765061i	$-0.722709\pi$
$313$	1885.99	−	3266.64i	0.340583	−	0.589908i	0.984541	+	0.175153i	$0.0560421\pi$
$314$		0			0
$315$	1695.48	+	168.671i	0.303268	+	0.0301700i
$316$		0			0
$317$	716.204	−	1240.50i	0.126896	−	0.219790i	−0.795577	−	0.605853i	$-0.792832\pi$
$317$	716.204	−	1240.50i	0.126896	−	0.219790i	0.922472	+	0.386063i	$0.126165\pi$
$318$		0			0
$319$	−4279.54	−	7412.38i	−0.751123	−	1.30098i
$320$		0			0
$321$	−958.383			−0.166641
$322$		0			0
$323$	518.084			0.0892476
$324$		0			0
$325$	908.475	+	1573.53i	0.155056	+	0.268565i
$326$		0			0
$327$	144.215	−	249.787i	0.0243887	−	0.0422424i
$328$		0			0
$329$	−1630.36	−	3607.70i	−0.273205	−	0.604556i
$330$		0			0
$331$	1182.83	−	2048.73i	0.196418	−	0.340207i	−0.750946	−	0.660363i	$-0.770402\pi$
$331$	1182.83	−	2048.73i	0.196418	−	0.340207i	0.947365	+	0.320157i	$0.103736\pi$
$332$		0			0
$333$	−2732.86	−	4733.45i	−0.449729	−	0.778954i
$334$		0			0
$335$	1255.54			0.204768
$336$		0			0
$337$	5009.55			0.809756			0.404878	−	0.914371i	$-0.367314\pi$
$337$	5009.55			0.809756			0.404878	+	0.914371i	$0.367314\pi$
$338$		0			0
$339$	−448.709	−	777.186i	−0.0718894	−	0.124516i
$340$		0			0
$341$	965.532	−	1672.35i	0.153333	−	0.265580i
$342$		0			0
$343$	−6073.46	−	1861.92i	−0.956081	−	0.293102i
$344$		0			0
$345$	259.435	−	449.355i	0.0404856	−	0.0701230i
$346$		0			0
$347$	−6263.00	−	10847.8i	−0.968921	−	1.67822i	−0.698689	−	0.715426i	$-0.746233\pi$
$347$	−6263.00	−	10847.8i	−0.968921	−	1.67822i	−0.270232	−	0.962795i	$-0.587101\pi$
$348$		0			0
$349$	−1681.83			−0.257955			−0.128978	−	0.991648i	$-0.541170\pi$
$349$	−1681.83			−0.257955			−0.128978	+	0.991648i	$0.541170\pi$
$350$		0			0
$351$	−3159.25			−0.480422
$352$		0			0
$353$	4164.56	+	7213.23i	0.627924	+	1.08760i	0.987968	+	0.154661i	$0.0494286\pi$
$353$	4164.56	+	7213.23i	0.627924	+	1.08760i	−0.360043	+	0.932936i	$0.617238\pi$
$354$		0			0
$355$	3482.07	−	6031.13i	0.520589	−	0.901687i
$356$		0			0
$357$	520.901	+	1152.66i	0.0772240	+	0.170883i
$358$		0			0
$359$	2345.53	−	4062.58i	0.344825	−	0.597255i	−0.640497	−	0.767961i	$-0.721271\pi$
$359$	2345.53	−	4062.58i	0.344825	−	0.597255i	0.985322	+	0.170706i	$0.0546048\pi$
$360$		0			0
$361$	3068.37	+	5314.57i	0.447349	+	0.774832i
$362$		0			0
$363$	−294.339			−0.0425586
$364$		0			0
$365$	2081.82			0.298541
$366$		0			0
$367$	−367.038	−	635.728i	−0.0522050	−	0.0904217i	0.838742	−	0.544529i	$-0.183292\pi$
$367$	−367.038	−	635.728i	−0.0522050	−	0.0904217i	−0.890947	+	0.454107i	$0.849958\pi$
$368$		0			0
$369$	−2340.21	+	4053.36i	−0.330153	+	0.571842i
$370$		0			0
$371$	5728.12	+	569.850i	0.801587	+	0.0797443i
$372$		0			0
$373$	607.420	−	1052.08i	0.0843191	−	0.146045i	−0.820782	−	0.571242i	$-0.806462\pi$
$373$	607.420	−	1052.08i	0.0843191	−	0.146045i	0.905101	+	0.425197i	$0.139795\pi$
$374$		0			0
$375$	2362.59	+	4092.13i	0.325344	+	0.563511i
$376$		0			0
$377$	5212.64			0.712107
$378$		0			0
$379$	9535.08			1.29231			0.646153	−	0.763208i	$-0.276377\pi$
$379$	9535.08			1.29231			0.646153	+	0.763208i	$0.276377\pi$
$380$		0			0
$381$	−569.426	−	986.274i	−0.0765684	−	0.132620i
$382$		0			0
$383$	1635.58	−	2832.90i	0.218209	−	0.377949i	−0.736051	−	0.676926i	$-0.763312\pi$
$383$	1635.58	−	2832.90i	0.218209	−	0.377949i	0.954261	+	0.298976i	$0.0966452\pi$
$384$		0			0
$385$	2429.91	−	3383.91i	0.321661	−	0.447948i
$386$		0			0
$387$	−3537.78	+	6127.61i	−0.464691	+	0.804868i
$388$		0			0
$389$	3349.82	+	5802.06i	0.436614	+	0.756237i	0.997426	−	0.0717060i	$-0.0228443\pi$
$389$	3349.82	+	5802.06i	0.436614	+	0.756237i	−0.560812	+	0.827943i	$0.689511\pi$
$390$		0			0
$391$	−443.384			−0.0573476
$392$		0			0
$393$	567.337			0.0728202
$394$		0			0
$395$	−814.946	−	1411.53i	−0.103809	−	0.179802i
$396$		0			0
$397$	3881.59	−	6723.11i	0.490709	−	0.849933i	−0.509234	−	0.860628i	$-0.670071\pi$
$397$	3881.59	−	6723.11i	0.490709	−	0.849933i	0.999943	+	0.0106954i	$0.00340452\pi$
$398$		0			0
$399$	1028.55	−	1432.36i	0.129052	−	0.179719i
$400$		0			0
$401$	−7265.16	+	12583.6i	−0.904750	+	1.56707i	−0.0834965	+	0.996508i	$0.526609\pi$
$401$	−7265.16	+	12583.6i	−0.904750	+	1.56707i	−0.821253	+	0.570564i	$0.806725\pi$
$402$		0			0
$403$	588.027	+	1018.49i	0.0726842	+	0.125893i
$404$		0			0
$405$	−828.785			−0.101686
$406$		0			0
$407$	−13363.9			−1.62757
$408$		0			0
$409$	−3542.04	−	6134.99i	−0.428222	−	0.741701i	0.568494	−	0.822688i	$-0.307526\pi$
$409$	−3542.04	−	6134.99i	−0.428222	−	0.741701i	−0.996715	+	0.0809862i	$0.974193\pi$
$410$		0			0
$411$	−2896.02	+	5016.05i	−0.347567	+	0.602004i
$412$		0			0
$413$	−6134.46	−	610.274i	−0.730888	−	0.0727109i
$414$		0			0
$415$	3044.31	−	5272.90i	0.360095	−	0.623703i
$416$		0			0
$417$	−4414.18	−	7645.59i	−0.518378	−	0.897857i
$418$		0			0
$419$	5289.95			0.616780			0.308390	−	0.951260i	$-0.400210\pi$
$419$	5289.95			0.616780			0.308390	+	0.951260i	$0.400210\pi$
$420$		0			0
$421$	10861.8			1.25742			0.628709	−	0.777640i	$-0.283584\pi$
$421$	10861.8			1.25742			0.628709	+	0.777640i	$0.283584\pi$
$422$		0			0
$423$	−1544.24	−	2674.71i	−0.177503	−	0.307444i
$424$		0			0
$425$	814.032	−	1409.95i	0.0929091	−	0.160923i
$426$		0			0
$427$	−4224.09	−	9347.17i	−0.478731	−	1.05935i
$428$		0			0
$429$	−1346.30	+	2331.87i	−0.151516	+	0.262433i
$430$		0			0
$431$	−4458.91	−	7723.06i	−0.498325	−	0.863125i	0.501673	−	0.865058i	$-0.332718\pi$
$431$	−4458.91	−	7723.06i	−0.498325	−	0.863125i	−0.999998	+	0.00193248i	$0.999385\pi$
$432$		0			0
$433$	−16578.7			−1.84001			−0.920003	−	0.391911i	$-0.871814\pi$
$433$	−16578.7			−1.84001			−0.920003	+	0.391911i	$0.871814\pi$
$434$		0			0
$435$	5465.93			0.602463
$436$		0			0
$437$	309.062	+	535.311i	0.0338317	+	0.0585982i
$438$		0			0
$439$	−7627.69	+	13211.6i	−0.829271	+	1.43634i	0.0693401	+	0.997593i	$0.477911\pi$
$439$	−7627.69	+	13211.6i	−0.829271	+	1.43634i	−0.898611	+	0.438746i	$0.855423\pi$
$440$		0			0
$441$	−4858.55	−	976.349i	−0.524625	−	0.105426i
$442$		0			0
$443$	1817.96	−	3148.79i	0.194975	−	0.337706i	−0.751918	−	0.659257i	$-0.770871\pi$
$443$	1817.96	−	3148.79i	0.194975	−	0.337706i	0.946892	+	0.321551i	$0.104204\pi$
$444$		0			0
$445$	−3100.52	−	5370.26i	−0.330290	−	0.572078i
$446$		0			0
$447$	−2446.70			−0.258893
$448$		0			0
$449$	12816.7			1.34712			0.673558	−	0.739134i	$-0.264765\pi$
$449$	12816.7			1.34712			0.673558	+	0.739134i	$0.264765\pi$
$450$		0			0
$451$	5721.89	+	9910.60i	0.597413	+	1.03475i
$452$		0			0
$453$	−4297.31	+	7443.16i	−0.445707	+	0.771987i
$454$		0			0
$455$	1044.83	+	2312.03i	0.107654	+	0.238219i
$456$		0			0
$457$	3379.55	−	5853.55i	0.345927	−	0.599163i	−0.639595	−	0.768712i	$-0.720898\pi$
$457$	3379.55	−	5853.55i	0.345927	−	0.599163i	0.985522	+	0.169549i	$0.0542311\pi$
$458$		0			0
$459$	1415.41	+	2451.56i	0.143934	+	0.249301i
$460$		0			0
$461$	14845.6			1.49984			0.749922	−	0.661527i	$-0.230091\pi$
$461$	14845.6			1.49984			0.749922	+	0.661527i	$0.230091\pi$
$462$		0			0
$463$	−4548.71			−0.456580			−0.228290	−	0.973593i	$-0.573313\pi$
$463$	−4548.71			−0.456580			−0.228290	+	0.973593i	$0.573313\pi$
$464$		0			0
$465$	616.601	+	1067.98i	0.0614929	+	0.106509i
$466$		0			0
$467$	3001.90	−	5199.44i	0.297454	−	0.515206i	−0.678098	−	0.734971i	$-0.737196\pi$
$467$	3001.90	−	5199.44i	0.297454	−	0.515206i	0.975553	+	0.219765i	$0.0705290\pi$
$468$		0			0
$469$	−3633.81	−	361.502i	−0.357769	−	0.0355919i
$470$		0			0
$471$	3094.30	−	5359.49i	0.302713	−	0.524314i
$472$		0			0
$473$	8649.98	+	14982.2i	0.840859	+	1.45641i
$474$		0			0
$475$	−2269.69			−0.219243
$476$		0			0
$477$	4490.68			0.431057
$478$		0			0
$479$	4351.79	+	7537.53i	0.415112	+	0.718995i	0.995440	−	0.0953878i	$-0.0304091\pi$
$479$	4351.79	+	7537.53i	0.415112	+	0.718995i	−0.580328	+	0.814383i	$0.697076\pi$
$480$		0			0
$481$	4069.42	−	7048.44i	0.385758	−	0.668152i
$482$		0			0
$483$	−880.247	+	1225.84i	−0.0829246	+	0.115482i
$484$		0			0
$485$	1854.82	−	3212.64i	0.173655	−	0.300780i
$486$		0			0
$487$	−4998.98	−	8658.49i	−0.465145	−	0.805654i	0.534063	−	0.845444i	$-0.320664\pi$
$487$	−4998.98	−	8658.49i	−0.465145	−	0.805654i	−0.999208	+	0.0397902i	$0.987331\pi$
$488$		0			0
$489$	−13307.5			−1.23065
$490$		0			0
$491$	−5782.17			−0.531458			−0.265729	−	0.964048i	$-0.585613\pi$
$491$	−5782.17			−0.531458			−0.265729	+	0.964048i	$0.585613\pi$
$492$		0			0
$493$	−2335.37	−	4044.98i	−0.213347	−	0.369527i
$494$		0			0
$495$	1624.98	−	2814.55i	0.147550	−	0.255565i
$496$		0			0
$497$	−11814.4	+	16452.9i	−1.06630	+	1.48494i
$498$		0			0
$499$	6455.50	−	11181.3i	0.579134	−	1.00309i	−0.416444	−	0.909161i	$-0.636724\pi$
$499$	6455.50	−	11181.3i	0.579134	−	1.00309i	0.995579	−	0.0939291i	$-0.0299427\pi$
$500$		0			0
$501$	5558.82	+	9628.16i	0.495708	+	0.858592i
$502$		0			0
$503$	1147.80			0.101746			0.0508728	−	0.998705i	$-0.483800\pi$
$503$	1147.80			0.101746			0.0508728	+	0.998705i	$0.483800\pi$
$504$		0			0
$505$	3285.78			0.289535
$506$		0			0
$507$	3071.92	+	5320.73i	0.269090	+	0.466078i
$508$		0			0
$509$	−5618.93	+	9732.26i	−0.489302	+	0.847495i	−0.999924	−	0.0123098i	$-0.996082\pi$
$509$	−5618.93	+	9732.26i	−0.489302	+	0.847495i	0.510623	+	0.859805i	$0.329415\pi$
$510$		0			0
$511$	−6025.28	−	599.412i	−0.521610	−	0.0518913i
$512$		0			0
$513$	1973.23	−	3417.73i	0.169825	−	0.294146i
$514$		0			0
$515$	−5813.25	−	10068.8i	−0.497402	−	0.861526i
$516$		0			0
$517$	−7551.45			−0.642384
$518$		0			0
$519$	−4313.32			−0.364805
$520$		0			0
$521$	−4311.37	−	7467.52i	−0.362543	−	0.627942i	0.625836	−	0.779955i	$-0.284758\pi$
$521$	−4311.37	−	7467.52i	−0.362543	−	0.627942i	−0.988379	+	0.152013i	$0.951425\pi$
$522$		0			0
$523$	10392.6	−	18000.5i	0.868903	−	1.50498i	0.00578441	−	0.999983i	$-0.498159\pi$
$523$	10392.6	−	18000.5i	0.868903	−	1.50498i	0.863119	−	0.505001i	$-0.168508\pi$
$524$		0			0
$525$	−2282.03	−	5049.73i	−0.189707	−	0.419787i
$526$		0			0
$527$	526.897	−	912.613i	0.0435522	−	0.0754346i
$528$		0			0
$529$	−264.500	−	458.127i	−0.0217391	−	0.0376533i
$530$		0			0
$531$	−4809.24			−0.393038
$532$		0			0
$533$	−6969.47			−0.566381
$534$		0			0
$535$	861.249	+	1491.73i	0.0695982	+	0.120548i
$536$		0			0
$537$	−930.379	+	1611.46i	−0.0747650	+	0.129497i
$538$		0			0
$539$	−8007.03	+	9094.18i	−0.639865	+	0.726742i
$540$		0			0
$541$	−3186.03	+	5518.36i	−0.253194	+	0.438545i	−0.964403	−	0.264435i	$-0.914815\pi$
$541$	−3186.03	+	5518.36i	−0.253194	+	0.438545i	0.711209	+	0.702980i	$0.248148\pi$
$542$		0			0
$543$	−6817.45	−	11808.2i	−0.538793	−	0.933217i
$544$		0			0
$545$	−518.393			−0.0407441
$546$		0			0
$547$	3993.87			0.312186			0.156093	−	0.987742i	$-0.450110\pi$
$547$	3993.87			0.312186			0.156093	+	0.987742i	$0.450110\pi$
$548$		0			0
$549$	−4000.97	−	6929.89i	−0.311034	−	0.538726i
$550$		0			0
$551$	−3255.75	+	5639.13i	−0.251724	+	0.435998i
$552$		0			0
$553$	1952.23	+	4319.93i	0.150121	+	0.332192i
$554$		0			0
$555$	4267.16	−	7390.94i	0.326362	−	0.565276i
$556$		0			0
$557$	−9132.51	−	15818.0i	−0.694716	−	1.20328i	−0.970276	−	0.242000i	$-0.922197\pi$
$557$	−9132.51	−	15818.0i	−0.694716	−	1.20328i	0.275560	−	0.961284i	$-0.411137\pi$
$558$		0			0
$559$	−10536.0			−0.797183
$560$		0			0
$561$	2412.69			0.181576
$562$		0			0
$563$	−6066.79	−	10508.0i	−0.454147	−	0.786605i	0.544492	−	0.838766i	$-0.316722\pi$
$563$	−6066.79	−	10508.0i	−0.454147	−	0.786605i	−0.998639	+	0.0521608i	$0.983389\pi$
$564$		0			0
$565$	−806.462	+	1396.83i	−0.0600498	+	0.104009i
$566$		0			0
$567$	2398.69	+	238.629i	0.177664	+	0.0176746i
$568$		0			0
$569$	3237.52	−	5607.54i	0.238530	−	0.413147i	−0.721762	−	0.692141i	$-0.756668\pi$
$569$	3237.52	−	5607.54i	0.238530	−	0.413147i	0.960293	+	0.278994i	$0.0900010\pi$
$570$		0			0
$571$	−2946.71	−	5103.85i	−0.215965	−	0.374062i	0.737606	−	0.675232i	$-0.235956\pi$
$571$	−2946.71	−	5103.85i	−0.215965	−	0.374062i	−0.953571	+	0.301170i	$0.902623\pi$
$572$		0			0
$573$	−14031.2			−1.02297
$574$		0			0
$575$	1942.44			0.140879
$576$		0			0
$577$	12902.2	+	22347.2i	0.930890	+	1.61235i	0.781804	+	0.623525i	$0.214300\pi$
$577$	12902.2	+	22347.2i	0.930890	+	1.61235i	0.149086	+	0.988824i	$0.452367\pi$
$578$		0			0
$579$	1138.96	−	1972.74i	0.0817506	−	0.141596i
$580$		0			0
$581$	−10329.2	+	14384.5i	−0.737566	+	1.02714i
$582$		0			0
$583$	5489.93	−	9508.84i	0.389999	−	0.675499i
$584$		0			0
$585$	989.643	+	1714.11i	0.0699431	+	0.121145i
$586$		0			0
$587$	−24326.2			−1.71048			−0.855238	−	0.518236i	$-0.826589\pi$
$587$	−24326.2			−1.71048			−0.855238	+	0.518236i	$0.826589\pi$
$588$		0			0
$589$	−1469.10			−0.102773
$590$		0			0
$591$	−1479.82	−	2563.12i	−0.102998	−	0.178397i
$592$		0			0
$593$	2567.04	−	4446.24i	0.177767	−	0.307901i	−0.763349	−	0.645987i	$-0.776446\pi$
$593$	2567.04	−	4446.24i	0.177767	−	0.307901i	0.941115	+	0.338086i	$0.109779\pi$
$594$		0			0
$595$	1326.02	−	1846.62i	0.0913636	−	0.127234i
$596$		0			0
$597$	−7591.80	+	13149.4i	−0.520455	+	0.901455i
$598$		0			0
$599$	−5220.01	−	9041.32i	−0.356066	−	0.616725i	0.631234	−	0.775593i	$-0.282549\pi$
$599$	−5220.01	−	9041.32i	−0.356066	−	0.616725i	−0.987300	+	0.158868i	$0.949216\pi$
$600$		0			0
$601$	19196.8			1.30292			0.651459	−	0.758684i	$-0.274157\pi$
$601$	19196.8			1.30292			0.651459	+	0.758684i	$0.274157\pi$
$602$		0			0
$603$	−2848.81			−0.192392
$604$		0			0
$605$	264.507	+	458.139i	0.0177748	+	0.0307868i
$606$		0			0
$607$	11763.4	−	20374.9i	0.786596	−	1.36242i	−0.141446	−	0.989946i	$-0.545175\pi$
$607$	11763.4	−	20374.9i	0.786596	−	1.36242i	0.928041	−	0.372477i	$-0.121492\pi$
$608$		0			0
$609$	−15819.7	−	1573.79i	−1.05262	−	0.104718i
$610$		0			0
$611$	2299.49	−	3982.83i	0.152254	−	0.263712i
$612$		0			0
$613$	−11835.0	−	20498.8i	−0.779788	−	1.35063i	−0.932064	−	0.362295i	$-0.881993\pi$
$613$	−11835.0	−	20498.8i	−0.779788	−	1.35063i	0.152276	−	0.988338i	$-0.451340\pi$
$614$		0			0
$615$	−7308.13			−0.479175
$616$		0			0
$617$	−17077.7			−1.11430			−0.557149	−	0.830413i	$-0.688105\pi$
$617$	−17077.7			−1.11430			−0.557149	+	0.830413i	$0.688105\pi$
$618$		0			0
$619$	2361.44	+	4090.14i	0.153335	+	0.265584i	0.932452	−	0.361295i	$-0.117665\pi$
$619$	2361.44	+	4090.14i	0.153335	+	0.265584i	−0.779117	+	0.626879i	$0.784332\pi$
$620$		0			0
$621$	−1688.72	+	2924.95i	−0.109124	+	0.189008i
$622$		0			0
$623$	7427.39	+	16435.5i	0.477644	+	1.05694i
$624$		0			0
$625$	−1032.08	+	1787.62i	−0.0660532	+	0.114408i
$626$		0			0
$627$	−1681.77	−	2912.91i	−0.107119	−	0.185535i
$628$		0			0
$629$	−7292.74			−0.462290
$630$		0			0
$631$	25351.7			1.59942			0.799710	−	0.600387i	$-0.204987\pi$
$631$	25351.7			1.59942			0.799710	+	0.600387i	$0.204987\pi$
$632$		0			0
$633$	2702.91	+	4681.58i	0.169717	+	0.293959i
$634$		0			0
$635$	−1023.43	+	1772.63i	−0.0639582	+	0.110779i
$636$		0			0
$637$	−2358.29	−	6992.38i	−0.146686	−	0.434926i
$638$		0			0
$639$	−7900.81	+	13684.6i	−0.489126	+	0.847191i
$640$		0			0
$641$	−7789.06	−	13491.0i	−0.479952	−	0.831301i	0.519784	−	0.854298i	$-0.326013\pi$
$641$	−7789.06	−	13491.0i	−0.479952	−	0.831301i	−0.999736	+	0.0229967i	$0.992679\pi$
$642$		0			0
$643$	−22594.6			−1.38576			−0.692880	−	0.721053i	$-0.743658\pi$
$643$	−22594.6			−1.38576			−0.692880	+	0.721053i	$0.743658\pi$
$644$		0			0
$645$	−11048.0			−0.674439
$646$		0			0
$647$	10693.4	+	18521.6i	0.649771	+	1.12544i	0.983177	+	0.182653i	$0.0584685\pi$
$647$	10693.4	+	18521.6i	0.649771	+	1.12544i	−0.333406	+	0.942783i	$0.608198\pi$
$648$		0			0
$649$	−5879.37	+	10183.4i	−0.355602	+	0.615921i
$650$		0			0
$651$	−1477.08	−	3268.53i	−0.0889271	−	0.196780i
$652$		0			0
$653$	11067.2	−	19169.0i	0.663239	−	1.14876i	−0.316521	−	0.948586i	$-0.602515\pi$
$653$	11067.2	−	19169.0i	0.663239	−	1.14876i	0.979760	−	0.200178i	$-0.0641519\pi$
$654$		0			0
$655$	−509.836	−	883.062i	−0.0304136	−	0.0526780i
$656$		0			0
$657$	−4723.65			−0.280498
$658$		0			0
$659$	−4411.52			−0.260771			−0.130386	−	0.991463i	$-0.541622\pi$
$659$	−4411.52			−0.260771			−0.130386	+	0.991463i	$0.541622\pi$
$660$		0			0
$661$	1424.82	+	2467.87i	0.0838415	+	0.145218i	0.904897	−	0.425631i	$-0.139948\pi$
$661$	1424.82	+	2467.87i	0.0838415	+	0.145218i	−0.821055	+	0.570848i	$0.806614\pi$
$662$		0			0
$663$	−734.687	+	1272.52i	−0.0430360	+	0.0745406i
$664$		0			0
$665$	−3153.78	−	313.748i	−0.183907	−	0.0182957i
$666$		0			0
$667$	2786.32	−	4826.05i	0.161749	−	0.280158i
$668$		0			0
$669$	−7156.80	−	12395.9i	−0.413599	−	0.716375i
$670$		0			0
$671$	−19565.0			−1.12563
$672$		0			0
$673$	5819.27			0.333308			0.166654	−	0.986015i	$-0.446704\pi$
$673$	5819.27			0.333308			0.166654	+	0.986015i	$0.446704\pi$
$674$		0			0
$675$	−6200.82	−	10740.1i	−0.353584	−	0.612426i
$676$		0			0
$677$	−4078.84	+	7064.76i	−0.231555	+	0.401065i	−0.958266	−	0.285879i	$-0.907715\pi$
$677$	−4078.84	+	7064.76i	−0.231555	+	0.401065i	0.726711	+	0.686943i	$0.241048\pi$
$678$		0			0
$679$	−6293.27	+	8764.06i	−0.355690	+	0.495337i
$680$		0			0
$681$	1933.50	−	3348.92i	0.108799	−	0.188445i
$682$		0			0
$683$	−1027.37	−	1779.45i	−0.0575566	−	0.0996909i	0.835811	−	0.549017i	$-0.184998\pi$
$683$	−1027.37	−	1779.45i	−0.0575566	−	0.0996909i	−0.893368	+	0.449326i	$0.851664\pi$
$684$		0			0
$685$	10410.0			0.580651
$686$		0			0
$687$	6586.09			0.365757
$688$		0			0
$689$	3343.47	+	5791.06i	0.184871	+	0.320206i
$690$		0			0
$691$	−11594.5	+	20082.2i	−0.638314	+	1.10559i	0.347488	+	0.937684i	$0.387035\pi$
$691$	−11594.5	+	20082.2i	−0.638314	+	1.10559i	−0.985803	+	0.167908i	$0.946299\pi$
$692$		0			0
$693$	−5513.45	+	7678.08i	−0.302220	+	0.420875i
$694$		0			0
$695$	−7933.60	+	13741.4i	−0.433005	+	0.749987i
$696$		0			0
$697$	3122.47	+	5408.28i	0.169687	+	0.293907i
$698$		0			0
$699$	15467.5			0.836959
$700$		0			0
$701$	22918.1			1.23482			0.617408	−	0.786643i	$-0.288183\pi$
$701$	22918.1			1.23482			0.617408	+	0.786643i	$0.288183\pi$
$702$		0			0
$703$	5083.42	+	8804.74i	0.272724	+	0.472372i
$704$		0			0
$705$	2411.22	−	4176.36i	0.128811	−	0.223108i
$706$		0			0
$707$	−9509.81	−	946.064i	−0.505874	−	0.0503259i
$708$		0			0
$709$	12100.7	−	20959.1i	0.640977	−	1.11020i	−0.344238	−	0.938882i	$-0.611863\pi$
$709$	12100.7	−	20959.1i	0.640977	−	1.11020i	0.985215	−	0.171322i	$-0.0548039\pi$
$710$		0			0
$711$	1849.11	+	3202.75i	0.0975345	+	0.168935i
$712$		0			0
$713$	1257.28			0.0660384
$714$		0			0
$715$	4839.41			0.253124
$716$		0			0
$717$	−5587.59	−	9677.98i	−0.291035	−	0.504088i
$718$		0			0
$719$	12153.9	−	21051.3i	0.630411	−	1.09190i	−0.357056	−	0.934083i	$-0.616220\pi$
$719$	12153.9	−	21051.3i	0.630411	−	1.09190i	0.987468	−	0.157821i	$-0.0504470\pi$
$720$		0			0
$721$	13925.8	+	30815.3i	0.719312	+	1.59171i
$722$		0			0
$723$	4743.88	−	8216.65i	0.244021	−	0.422656i
$724$		0			0
$725$	10231.1	+	17720.8i	0.524102	+	0.907771i
$726$		0			0
$727$	−75.3326			−0.00384310			−0.00192155	−	0.999998i	$-0.500612\pi$
$727$	−75.3326			−0.00384310			−0.00192155	+	0.999998i	$0.500612\pi$
$728$		0			0
$729$	15927.4			0.809194
$730$		0			0
$731$	4720.35	+	8175.88i	0.238835	+	0.413674i
$732$		0			0
$733$	9054.14	−	15682.2i	0.456238	−	0.790227i	−0.542521	−	0.840042i	$-0.682530\pi$
$733$	9054.14	−	15682.2i	0.456238	−	0.790227i	0.998758	+	0.0498156i	$0.0158634\pi$
$734$		0			0
$735$	−2472.88	−	7332.15i	−0.124100	−	0.367960i
$736$		0			0
$737$	−3482.71	+	6032.23i	−0.174067	+	0.301493i
$738$		0			0
$739$	4206.91	+	7286.59i	0.209410	+	0.362708i	0.951529	−	0.307560i	$-0.0995124\pi$
$739$	4206.91	+	7286.59i	0.209410	+	0.362708i	−0.742119	+	0.670268i	$0.766179\pi$
$740$		0			0
$741$	2048.46			0.101555
$742$		0			0
$743$	1274.28			0.0629189			0.0314594	−	0.999505i	$-0.489984\pi$
$743$	1274.28			0.0629189			0.0314594	+	0.999505i	$0.489984\pi$
$744$		0			0
$745$	2198.73	+	3808.30i	0.108128	+	0.187282i
$746$		0			0
$747$	−6907.54	+	11964.2i	−0.338331	+	0.586007i
$748$		0			0
$749$	−2063.15	−	4565.38i	−0.100649	−	0.222718i
$750$		0			0
$751$	138.410	−	239.734i	0.00672525	−	0.0116485i	−0.862643	−	0.505813i	$-0.831193\pi$
$751$	138.410	−	239.734i	0.00672525	−	0.0116485i	0.869368	+	0.494164i	$0.164526\pi$
$752$		0			0
$753$	2666.23	+	4618.04i	0.129034	+	0.223494i
$754$		0			0
$755$	15447.1			0.744605
$756$		0			0
$757$	−6041.57			−0.290072			−0.145036	−	0.989426i	$-0.546330\pi$
$757$	−6041.57			−0.290072			−0.145036	+	0.989426i	$0.546330\pi$
$758$		0			0
$759$	1439.29	+	2492.92i	0.0688310	+	0.119219i
$760$		0			0
$761$	7106.26	−	12308.4i	0.338504	−	0.586307i	−0.645647	−	0.763636i	$-0.723412\pi$
$761$	7106.26	−	12308.4i	0.338504	−	0.586307i	0.984152	+	0.177329i	$0.0567457\pi$
$762$		0			0
$763$	1500.35	+	149.259i	0.0711878	+	0.00708197i
$764$		0			0
$765$	886.762	−	1535.92i	0.0419097	−	0.0725898i
$766$		0			0
$767$	−3580.65	−	6201.87i	−0.168565	−	0.291964i
$768$		0			0
$769$	−2400.24			−0.112555			−0.0562777	−	0.998415i	$-0.517923\pi$
$769$	−2400.24			−0.112555			−0.0562777	+	0.998415i	$0.517923\pi$
$770$		0			0
$771$	−7388.11			−0.345105
$772$		0			0
$773$	−17456.6	−	30235.8i	−0.812253	−	1.40686i	−0.911284	−	0.411779i	$-0.864908\pi$
$773$	−17456.6	−	30235.8i	−0.812253	−	1.40686i	0.0990309	−	0.995084i	$-0.468426\pi$
$774$		0			0
$775$	−2308.30	+	3998.09i	−0.106989	+	0.185311i
$776$		0			0
$777$	−14478.2	+	20162.5i	−0.668472	+	0.930919i
$778$		0			0
$779$	4353.05	−	7539.70i	0.200211	−	0.346775i
$780$		0			0
$781$	19317.7	+	33459.3i	0.885074	+	1.53299i
$782$		0			0
$783$	−35579.0			−1.62387
$784$		0			0
$785$	−11122.7			−0.505717
$786$		0			0
$787$	−1570.90	−	2720.89i	−0.0711521	−	0.123239i	0.828254	−	0.560352i	$-0.189334\pi$
$787$	−1570.90	−	2720.89i	−0.0711521	−	0.123239i	−0.899406	+	0.437113i	$0.856001\pi$
$788$		0			0
$789$	7605.19	−	13172.6i	0.343158	−	0.594367i
$790$		0			0
$791$	2736.28	−	3810.56i	0.122997	−	0.171287i
$792$		0			0
$793$	5957.73	−	10319.1i	0.266791	−	0.462095i
$794$		0			0
$795$	3505.94	+	6072.46i	0.156406	+	0.270903i
$796$		0			0
$797$	−15436.7			−0.686069			−0.343035	−	0.939323i	$-0.611455\pi$
$797$	−15436.7			−0.686069			−0.343035	+	0.939323i	$0.611455\pi$
$798$		0			0
$799$	−4120.87			−0.182461
$800$		0			0
$801$	7035.08	+	12185.1i	0.310327	+	0.537503i
$802$		0			0
$803$	−5774.73	+	10002.1i	−0.253781	+	0.439561i
$804$		0			0
$805$	2699.05	+	268.510i	0.118173	+	0.0117562i
$806$		0			0
$807$	3439.84	−	5957.99i	0.150047	−	0.259890i
$808$		0			0
$809$	13591.0	+	23540.3i	0.590648	+	1.02303i	0.994145	+	0.108052i	$0.0344613\pi$
$809$	13591.0	+	23540.3i	0.590648	+	1.02303i	−0.403497	+	0.914981i	$0.632205\pi$
$810$		0			0
$811$	21323.3			0.923257			0.461629	−	0.887073i	$-0.347265\pi$
$811$	21323.3			0.923257			0.461629	+	0.887073i	$0.347265\pi$
$812$		0			0
$813$	1110.68			0.0479128
$814$		0			0
$815$	11958.8	+	20713.2i	0.513986	+	0.890249i
$816$		0			0
$817$	6580.66	−	11398.0i	0.281797	−	0.488087i
$818$		0			0
$819$	−2370.72	−	5245.98i	−0.101147	−	0.223821i
$820$		0			0
$821$	−1734.89	+	3004.92i	−0.0737492	+	0.127737i	−0.900542	−	0.434770i	$-0.856830\pi$
$821$	−1734.89	+	3004.92i	−0.0737492	+	0.127737i	0.826792	+	0.562507i	$0.190163\pi$
$822$		0			0
$823$	−7461.20	−	12923.2i	−0.316016	−	0.547356i	0.663637	−	0.748055i	$-0.269012\pi$
$823$	−7461.20	−	12923.2i	−0.316016	−	0.547356i	−0.979653	+	0.200699i	$0.935679\pi$
$824$		0			0
$825$	−10569.8			−0.446054
$826$		0			0
$827$	42439.5			1.78448			0.892241	−	0.451560i	$-0.149132\pi$
$827$	42439.5			1.78448			0.892241	+	0.451560i	$0.149132\pi$
$828$		0			0
$829$	−5760.91	−	9978.19i	−0.241357	−	0.418042i	0.719744	−	0.694239i	$-0.244259\pi$
$829$	−5760.91	−	9978.19i	−0.241357	−	0.418042i	−0.961101	+	0.276197i	$0.910926\pi$
$830$		0			0
$831$	9623.44	−	16668.3i	0.401725	−	0.695808i
$832$		0			0
$833$	−4369.49	+	4962.75i	−0.181745	+	0.206422i
$834$		0			0
$835$	9990.85	−	17304.7i	0.414069	−	0.717188i
$836$		0			0
$837$	−4013.59	−	6951.74i	−0.165747	−	0.287082i
$838$		0			0
$839$	−37734.2			−1.55272			−0.776359	−	0.630291i	$-0.782936\pi$
$839$	−37734.2			−1.55272			−0.776359	+	0.630291i	$0.782936\pi$
$840$		0			0
$841$	34314.9			1.40698
$842$		0			0
$843$	15467.5	+	26790.5i	0.631944	+	1.09456i
$844$		0			0
$845$	5521.15	−	9562.92i	0.224773	−	0.389319i
$846$		0			0
$847$	−633.634	−	1402.12i	−0.0257047	−	0.0568801i
$848$		0			0
$849$	16161.4	−	27992.3i	0.653305	−	1.13156i
$850$		0			0
$851$	−4350.47	−	7535.23i	−0.175243	−	0.303530i
$852$		0			0
$853$	23793.8			0.955079			0.477540	−	0.878610i	$-0.341529\pi$
$853$	23793.8			0.955079			0.477540	+	0.878610i	$0.341529\pi$
$854$		0			0
$855$	−2472.48			−0.0988970
$856$		0			0
$857$	3002.83	+	5201.06i	0.119691	+	0.207310i	0.919645	−	0.392751i	$-0.128476\pi$
$857$	3002.83	+	5201.06i	0.119691	+	0.207310i	−0.799955	+	0.600061i	$0.795143\pi$
$858$		0			0
$859$	18375.4	−	31827.1i	0.729873	−	1.26418i	−0.227063	−	0.973880i	$-0.572912\pi$
$859$	18375.4	−	31827.1i	0.729873	−	1.26418i	0.956937	−	0.290297i	$-0.0937542\pi$
$860$		0			0
$861$	21151.4	+	2104.21i	0.837211	+	0.0832883i
$862$		0			0
$863$	−7298.93	+	12642.1i	−0.287901	+	0.498659i	−0.973309	−	0.229501i	$-0.926291\pi$
$863$	−7298.93	+	12642.1i	−0.287901	+	0.498659i	0.685408	+	0.728160i	$0.259624\pi$
$864$		0			0
$865$	3876.16	+	6713.70i	0.152362	+	0.263899i
$866$		0			0
$867$	−16089.5			−0.630252
$868$		0			0
$869$	9042.27			0.352978
$870$		0			0
$871$	−2121.04	−	3673.74i	−0.0825127	−	0.142916i
$872$		0			0
$873$	−4208.57	+	7289.46i	−0.163160	+	0.282601i
$874$		0			0
$875$	−14407.4	+	20063.8i	−0.556637	+	0.775177i
$876$		0			0
$877$	−7071.46	+	12248.1i	−0.272276	+	0.471596i	−0.969444	−	0.245312i	$-0.921110\pi$
$877$	−7071.46	+	12248.1i	−0.272276	+	0.471596i	0.697168	+	0.716908i	$0.254443\pi$
$878$		0			0
$879$	14348.1	+	24851.6i	0.550567	+	0.953611i
$880$		0			0
$881$	6495.29			0.248390			0.124195	−	0.992258i	$-0.460365\pi$
$881$	6495.29			0.248390			0.124195	+	0.992258i	$0.460365\pi$
$882$		0			0
$883$	30186.2			1.15045			0.575224	−	0.817996i	$-0.304915\pi$
$883$	30186.2			1.15045			0.575224	+	0.817996i	$0.304915\pi$
$884$		0			0
$885$	−3754.64	−	6503.23i	−0.142611	−	0.247010i
$886$		0			0
$887$	1840.98	−	3188.68i	0.0696891	−	0.120705i	−0.829075	−	0.559137i	$-0.811133\pi$
$887$	1840.98	−	3188.68i	0.0696891	−	0.120705i	0.898764	+	0.438432i	$0.144466\pi$
$888$		0			0
$889$	3472.42	−	4835.72i	0.131003	−	0.182435i
$890$		0			0
$891$	2298.95	−	3981.90i	0.0864397	−	0.149718i
$892$		0			0
$893$	2872.46	+	4975.25i	0.107641	+	0.186440i
$894$		0			0
$895$	3344.33			0.124904
$896$		0			0
$897$	−1753.10			−0.0652558
$898$		0			0
$899$	6622.27	+	11470.1i	0.245679	+	0.425528i
$900$		0			0
$901$	2995.89	−	5189.03i	0.110774	−	0.191867i
$902$		0			0
$903$	31975.4	+	3181.00i	1.17838	+	0.117228i
$904$		0			0
$905$	−12253.0	+	21222.8i	−0.450058	+	0.779523i
$906$		0			0
$907$	−4972.40	−	8612.46i	−0.182035	−	0.315294i	0.760538	−	0.649293i	$-0.224935\pi$
$907$	−4972.40	−	8612.46i	−0.182035	−	0.315294i	−0.942573	+	0.333999i	$0.891602\pi$
$908$		0			0
$909$	−7455.43			−0.272036
$910$		0			0
$911$	−25287.7			−0.919669			−0.459835	−	0.888005i	$-0.652091\pi$
$911$	−25287.7			−0.919669			−0.459835	+	0.888005i	$0.652091\pi$
$912$		0			0
$913$	16889.1	+	29252.8i	0.612211	+	1.06038i
$914$		0			0
$915$	6247.23	−	10820.5i	0.225713	−	0.390946i
$916$		0			0
$917$	1221.33	+	2702.58i	0.0439823	+	0.0973251i
$918$		0			0
$919$	−9378.39	+	16243.9i	−0.336632	+	0.583063i	−0.983797	−	0.179287i	$-0.942621\pi$
$919$	−9378.39	+	16243.9i	−0.336632	+	0.583063i	0.647165	+	0.762350i	$0.275954\pi$
$920$		0			0
$921$	−5897.45	−	10214.7i	−0.210996	−	0.365456i
$922$		0			0
$923$	−23529.7			−0.839101
$924$		0			0
$925$	31949.0			1.13565
$926$		0			0
$927$	13190.2	+	22846.2i	0.467340	+	0.809457i
$928$		0			0
$929$	10987.9	−	19031.7i	0.388055	−	0.672130i	−0.604133	−	0.796883i	$-0.706481\pi$
$929$	10987.9	−	19031.7i	0.388055	−	0.672130i	0.992188	+	0.124753i	$0.0398139\pi$
$930$		0			0
$931$	9037.44	+	1816.12i	0.318142	+	0.0639321i
$932$		0			0
$933$	18340.8	−	31767.2i	0.643570	−	1.11470i
$934$		0			0
$935$	−2168.16	−	3755.36i	−0.0758357	−	0.131351i
$936$		0			0
$937$	27496.3			0.958660			0.479330	−	0.877635i	$-0.340880\pi$
$937$	27496.3			0.958660			0.479330	+	0.877635i	$0.340880\pi$
$938$		0			0
$939$	−13363.7			−0.464438
$940$		0			0
$941$	10003.2	+	17326.0i	0.346540	+	0.600224i	0.985632	−	0.168905i	$-0.0540233\pi$
$941$	10003.2	+	17326.0i	0.346540	+	0.600224i	−0.639093	+	0.769130i	$0.720690\pi$
$942$		0			0
$943$	−3725.40	+	6452.59i	−0.128649	+	0.222826i
$944$		0			0
$945$	−7131.51	−	15780.8i	−0.245490	−	0.543226i
$946$		0			0
$947$	7019.65	−	12158.4i	0.240874	−	0.417207i	−0.720089	−	0.693882i	$-0.755899\pi$
$947$	7019.65	−	12158.4i	0.240874	−	0.417207i	0.960964	+	0.276675i	$0.0892325\pi$
$948$		0			0
$949$	−3516.92	−	6091.48i	−0.120299	−	0.208364i
$950$		0			0
$951$	−5074.84			−0.173042
$952$		0			0
$953$	4210.26			0.143110			0.0715550	−	0.997437i	$-0.477204\pi$
$953$	4210.26			0.143110			0.0715550	+	0.997437i	$0.477204\pi$
$954$		0			0
$955$	12609.1	+	21839.6i	0.427247	+	0.740013i
$956$		0			0
$957$	−15161.9	+	26261.1i	−0.512135	+	0.887044i
$958$		0			0
$959$	−30129.0	−	2997.32i	−1.01451	−	0.100926i
$960$		0			0
$961$	13401.4	−	23211.9i	0.449848	−	0.779159i
$962$		0			0
$963$	−1954.17	−	3384.73i	−0.0653918	−	0.113262i
$964$		0			0
$965$	−4094.10			−0.136574
$966$		0			0
$967$	7644.44			0.254218			0.127109	−	0.991889i	$-0.459430\pi$
$967$	7644.44			0.254218			0.127109	+	0.991889i	$0.459430\pi$
$968$		0			0
$969$	−917.754	−	1589.60i	−0.0304257	−	0.0526989i
$970$		0			0
$971$	−15433.1	+	26731.0i	−0.510065	+	0.883458i	0.489867	+	0.871797i	$0.337045\pi$
$971$	−15433.1	+	26731.0i	−0.510065	+	0.883458i	−0.999932	+	0.0116611i	$0.996288\pi$
$972$		0			0
$973$	26918.2	−	37486.5i	0.886904	−	1.23511i
$974$		0			0
$975$	3218.61	−	5574.80i	0.105721	−	0.183114i
$976$		0			0
$977$	10257.3	+	17766.1i	0.335885	+	0.581770i	0.983654	−	0.180067i	$-0.0576313\pi$
$977$	10257.3	+	17766.1i	0.335885	+	0.581770i	−0.647769	+	0.761836i	$0.724298\pi$
$978$		0			0
$979$	34402.0			1.12308
$980$		0			0
$981$	1176.23			0.0382816
$982$		0			0
$983$	14211.6	+	24615.2i	0.461118	+	0.798680i	0.999017	−	0.0443292i	$-0.0141151\pi$
$983$	14211.6	+	24615.2i	0.461118	+	0.798680i	−0.537899	+	0.843009i	$0.680782\pi$
$984$		0			0
$985$	−2659.67	+	4606.69i	−0.0860348	+	0.149017i
$986$		0			0
$987$	−8181.13	+	11393.1i	−0.263838	+	0.367423i
$988$		0			0
$989$	−5631.83	+	9754.61i	−0.181073	+	0.313628i
$990$		0			0
$991$	29934.8	+	51848.6i	0.959545	+	1.66198i	0.723605	+	0.690214i	$0.242484\pi$
$991$	29934.8	+	51848.6i	0.959545	+	1.66198i	0.235940	+	0.971768i	$0.424183\pi$
$992$		0			0
$993$	−8381.27			−0.267846
$994$		0			0
$995$	27289.4			0.869481
$996$		0			0
$997$	−10414.6	−	18038.6i	−0.330825	−	0.573006i	0.651849	−	0.758349i	$-0.273994\pi$
$997$	−10414.6	−	18038.6i	−0.330825	−	0.573006i	−0.982674	+	0.185343i	$0.940660\pi$
$998$		0			0
$999$	−27775.9	+	48109.2i	−0.879670	+	1.52363i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	644.4.i.b.93.8	✓	44
7.4	even	3	inner	644.4.i.b.277.8	yes	44

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
644.4.i.b.93.8	✓	44	1.1	even	1	trivial
644.4.i.b.277.8	yes	44	7.4	even	3	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:	\( N \)	\(=\)	\( 644 = 2^{2} \cdot 7 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	644.i (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.77144 - 3.06822i) q^{3} +(-3.18380 + 5.51450i) q^{5} +(10.8024 - 15.0435i) q^{7} +(7.22402 - 12.5124i) q^{9} +O(q^{10})\)	\(q+(-1.77144 - 3.06822i) q^{3} +(-3.18380 + 5.51450i) q^{5} +(10.8024 - 15.0435i) q^{7} +(7.22402 - 12.5124i) q^{9} +(-17.6630 - 30.5931i) q^{11} +21.5141 q^{13} +22.5596 q^{15} +(-9.63879 - 16.6949i) q^{17} +(-13.4375 + 23.2744i) q^{19} +(-65.2926 - 6.49550i) q^{21} +(11.5000 - 19.9186i) q^{23} +(42.2269 + 73.1391i) q^{25} -146.845 q^{27} +242.289 q^{29} +(27.3321 + 47.3406i) q^{31} +(-62.5776 + 108.388i) q^{33} +(48.5648 + 107.465i) q^{35} +(189.151 - 327.619i) q^{37} +(-38.1109 - 66.0101i) q^{39} -323.948 q^{41} -489.724 q^{43} +(45.9996 + 79.6737i) q^{45} +(106.883 - 185.126i) q^{47} +(-109.616 - 325.013i) q^{49} +(-34.1490 + 59.1478i) q^{51} +(155.408 + 269.174i) q^{53} +224.941 q^{55} +95.2146 q^{57} +(-166.432 - 288.269i) q^{59} +(276.922 - 479.642i) q^{61} +(-110.193 - 243.839i) q^{63} +(-68.4966 + 118.640i) q^{65} +(-98.5879 - 170.759i) q^{67} -81.4861 q^{69} -1093.69 q^{71} +(-163.470 - 283.139i) q^{73} +(149.605 - 259.123i) q^{75} +(-651.032 - 64.7665i) q^{77} +(-127.983 + 221.674i) q^{79} +(65.0783 + 112.719i) q^{81} -956.190 q^{83} +122.752 q^{85} +(-429.199 - 743.395i) q^{87} +(-486.922 + 843.374i) q^{89} +(232.405 - 323.649i) q^{91} +(96.8342 - 167.722i) q^{93} +(-85.5644 - 148.202i) q^{95} -582.580 q^{97} -510.391 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 44 q + 12 q^{3} + 10 q^{5} - 6 q^{7} - 238 q^{9}+O(q^{10}) \) 44 * q + 12 * q^3 + 10 * q^5 - 6 * q^7 - 238 * q^9	\( 44 q + 12 q^{3} + 10 q^{5} - 6 q^{7} - 238 q^{9} + 28 q^{11} - 152 q^{13} + 208 q^{15} - 52 q^{17} + 38 q^{19} - 10 q^{21} + 506 q^{23} - 516 q^{25} - 876 q^{27} - 100 q^{29} + 230 q^{31} + 424 q^{33} + 98 q^{35} + 18 q^{37} - 350 q^{39} + 784 q^{41} - 336 q^{43} + 1156 q^{45} + 452 q^{47} + 546 q^{49} - 498 q^{51} - 508 q^{53} - 3084 q^{55} - 1916 q^{57} + 508 q^{59} + 1386 q^{61} + 1290 q^{63} + 360 q^{65} - 1896 q^{67} + 552 q^{69} - 3352 q^{71} + 990 q^{73} + 3328 q^{75} + 1328 q^{77} + 524 q^{79} - 4486 q^{81} - 1120 q^{83} - 5296 q^{85} + 3700 q^{87} + 1216 q^{89} + 1438 q^{91} + 366 q^{93} + 90 q^{95} + 716 q^{97} + 5716 q^{99}+O(q^{100}) \) 44 * q + 12 * q^3 + 10 * q^5 - 6 * q^7 - 238 * q^9 + 28 * q^11 - 152 * q^13 + 208 * q^15 - 52 * q^17 + 38 * q^19 - 10 * q^21 + 506 * q^23 - 516 * q^25 - 876 * q^27 - 100 * q^29 + 230 * q^31 + 424 * q^33 + 98 * q^35 + 18 * q^37 - 350 * q^39 + 784 * q^41 - 336 * q^43 + 1156 * q^45 + 452 * q^47 + 546 * q^49 - 498 * q^51 - 508 * q^53 - 3084 * q^55 - 1916 * q^57 + 508 * q^59 + 1386 * q^61 + 1290 * q^63 + 360 * q^65 - 1896 * q^67 + 552 * q^69 - 3352 * q^71 + 990 * q^73 + 3328 * q^75 + 1328 * q^77 + 524 * q^79 - 4486 * q^81 - 1120 * q^83 - 5296 * q^85 + 3700 * q^87 + 1216 * q^89 + 1438 * q^91 + 366 * q^93 + 90 * q^95 + 716 * q^97 + 5716 * q^99

Introduction

L-functions

Modular forms

Varieties

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Database

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