LMFDB - Embedded newform 124.5.o.a.17.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [124,5,Mod(13,124)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(124, base_ring=CyclotomicField(30))

chi = DirichletCharacter(H, H._module([0, 11]))

N = Newforms(chi, 5, names="a")

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

chi := DirichletCharacter("124.13");

S:= CuspForms(chi, 5);

N := Newforms(S);

Level:	$ N $	$=$	$ 124 = 2^{2} \cdot 31 $
Weight:	$ k $	$=$	$ 5 $
Character orbit:	$[\chi]$	$=$	124.o (of order $30$, degree $8$, 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:	$12.8178754224$
Analytic rank:	$0$
Dimension:	$88$
Relative dimension:	$11$ over $\Q(\zeta_{30})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{30}]$

Embedding invariants

Embedding label			17.7
Character	$\chi$	$=$	124.17
Dual form			124.5.o.a.73.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(3.32625 + 2.99497i) q^{3} +(10.0265 - 17.3665i) q^{5} +(0.840912 - 8.00074i) q^{7} +(-6.37270 - 60.6322i) q^{9} +O(q^{10})$	\(q+(3.32625 + 2.99497i) q^{3} +(10.0265 - 17.3665i) q^{5} +(0.840912 - 8.00074i) q^{7} +(-6.37270 - 60.6322i) q^{9} +(-53.5258 - 120.221i) q^{11} +(-40.7018 + 191.487i) q^{13} +(85.3630 - 27.7361i) q^{15} +(210.863 - 473.607i) q^{17} +(-7.71531 + 1.63994i) q^{19} +(26.7591 - 24.0940i) q^{21} +(-324.598 - 446.771i) q^{23} +(111.437 + 193.014i) q^{25} +(373.496 - 514.073i) q^{27} +(1246.36 + 404.968i) q^{29} +(197.070 - 940.577i) q^{31} +(182.018 - 560.193i) q^{33} +(-130.513 - 94.8235i) q^{35} +(-44.2770 + 25.5633i) q^{37} +(-708.882 + 515.033i) q^{39} +(-2120.74 - 2355.32i) q^{41} +(-261.555 - 1230.52i) q^{43} +(-1116.86 - 497.260i) q^{45} +(1174.85 + 3615.80i) q^{47} +(2285.23 + 485.740i) q^{49} +(2119.82 - 943.807i) q^{51} +(-176.408 + 18.5412i) q^{53} +(-2624.49 - 275.845i) q^{55} +(-30.5747 - 17.6523i) q^{57} +(-1152.75 + 1280.26i) q^{59} +1725.27i q^{61} -490.461 q^{63} +(2917.36 + 2626.80i) q^{65} +(-3502.26 + 6066.09i) q^{67} +(258.371 - 2458.24i) q^{69} +(-244.506 - 2326.32i) q^{71} +(4261.62 + 9571.75i) q^{73} +(-207.405 + 975.763i) q^{75} +(-1006.87 + 327.151i) q^{77} +(-662.553 + 1488.12i) q^{79} +(-2048.37 + 435.395i) q^{81} +(-9367.73 + 8434.74i) q^{83} +(-6110.66 - 8410.60i) q^{85} +(2932.86 + 5079.85i) q^{87} +(1115.83 - 1535.80i) q^{89} +(1497.81 + 486.668i) q^{91} +(3472.51 - 2538.38i) q^{93} +(-48.8779 + 150.431i) q^{95} +(-1202.13 - 873.399i) q^{97} +(-6948.15 + 4011.52i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 88 q - 9 q^{3} + 3 q^{5} - 215 q^{7} - 254 q^{9}+O(q^{10}) $ 88 * q - 9 * q^3 + 3 * q^5 - 215 * q^7 - 254 * q^9	$ 88 q - 9 q^{3} + 3 q^{5} - 215 q^{7} - 254 q^{9} - 42 q^{11} + 6 q^{13} + 665 q^{15} - 585 q^{17} - 153 q^{19} - 402 q^{21} - 1365 q^{23} - 5933 q^{25} - 9225 q^{27} - 1140 q^{29} + 117 q^{31} + 5151 q^{33} + 2898 q^{35} + 6594 q^{37} + 3173 q^{39} - 9393 q^{41} - 5322 q^{43} + 2010 q^{45} - 5112 q^{47} - 5210 q^{49} - 1829 q^{51} + 7395 q^{53} + 10585 q^{55} + 40485 q^{57} + 5625 q^{59} - 14954 q^{63} - 17094 q^{65} + 8909 q^{67} - 35370 q^{69} - 11811 q^{71} - 22105 q^{73} + 79377 q^{75} + 71490 q^{77} + 219 q^{79} - 5422 q^{81} + 10545 q^{83} - 53630 q^{85} + 13732 q^{87} - 40305 q^{89} + 42760 q^{91} - 1028 q^{93} + 62319 q^{95} + 35201 q^{97} + 16197 q^{99}+O(q^{100}) $ 88 * q - 9 * q^3 + 3 * q^5 - 215 * q^7 - 254 * q^9 - 42 * q^11 + 6 * q^13 + 665 * q^15 - 585 * q^17 - 153 * q^19 - 402 * q^21 - 1365 * q^23 - 5933 * q^25 - 9225 * q^27 - 1140 * q^29 + 117 * q^31 + 5151 * q^33 + 2898 * q^35 + 6594 * q^37 + 3173 * q^39 - 9393 * q^41 - 5322 * q^43 + 2010 * q^45 - 5112 * q^47 - 5210 * q^49 - 1829 * q^51 + 7395 * q^53 + 10585 * q^55 + 40485 * q^57 + 5625 * q^59 - 14954 * q^63 - 17094 * q^65 + 8909 * q^67 - 35370 * q^69 - 11811 * q^71 - 22105 * q^73 + 79377 * q^75 + 71490 * q^77 + 219 * q^79 - 5422 * q^81 + 10545 * q^83 - 53630 * q^85 + 13732 * q^87 - 40305 * q^89 + 42760 * q^91 - 1028 * q^93 + 62319 * q^95 + 35201 * q^97 + 16197 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/124\mathbb{Z}\right)^\times$.

$n$	$63$	$65$
$\chi(n)$	$1$	$e\left(\frac{7}{30}\right)$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	3.32625	+	2.99497i	0.369584	+	0.332775i	0.832905	−	0.553416i	$-0.186676\pi$
$3$	3.32625	+	2.99497i	0.369584	+	0.332775i	−0.463322	+	0.886190i	$0.653342\pi$
$4$		0			0
$5$	10.0265	−	17.3665i	0.401062	−	0.694660i	−0.592792	−	0.805355i	$-0.701975\pi$
$5$	10.0265	−	17.3665i	0.401062	−	0.694660i	0.993854	+	0.110696i	$0.0353079\pi$
$6$		0			0
$7$	0.840912	−	8.00074i	0.0171615	−	0.163280i	−0.982585	−	0.185816i	$-0.940507\pi$
$7$	0.840912	−	8.00074i	0.0171615	−	0.163280i	0.999746	+	0.0225355i	$0.00717387\pi$
$8$		0			0
$9$	−6.37270	−	60.6322i	−0.0786753	−	0.748546i
$10$		0			0
$11$	−53.5258	−	120.221i	−0.442362	−	0.993561i	−0.987845	−	0.155439i	$-0.950321\pi$
$11$	−53.5258	−	120.221i	−0.442362	−	0.993561i	0.545484	−	0.838121i	$-0.316346\pi$
$12$		0			0
$13$	−40.7018	+	191.487i	−0.240839	+	1.13306i	0.676962	+	0.736018i	$0.263296\pi$
$13$	−40.7018	+	191.487i	−0.240839	+	1.13306i	−0.917801	+	0.397040i	$0.870037\pi$
$14$		0			0
$15$	85.3630	−	27.7361i	0.379391	−	0.123272i
$16$		0			0
$17$	210.863	−	473.607i	0.729631	−	1.63878i	−0.0391236	−	0.999234i	$-0.512457\pi$
$17$	210.863	−	473.607i	0.729631	−	1.63878i	0.768755	−	0.639544i	$-0.220877\pi$
$18$		0			0
$19$	−7.71531	+	1.63994i	−0.0213720	+	0.00454277i	−0.218585	−	0.975818i	$-0.570144\pi$
$19$	−7.71531	+	1.63994i	−0.0213720	+	0.00454277i	0.197213	+	0.980361i	$0.436811\pi$
$20$		0			0
$21$	26.7591	−	24.0940i	0.0606782	−	0.0546349i
$22$		0			0
$23$	−324.598	−	446.771i	−0.613608	−	0.844558i	0.383261	−	0.923640i	$-0.374801\pi$
$23$	−324.598	−	446.771i	−0.613608	−	0.844558i	−0.996868	+	0.0790819i	$0.974801\pi$
$24$		0			0
$25$	111.437	+	193.014i	0.178299	+	0.308822i
$26$		0			0
$27$	373.496	−	514.073i	0.512340	−	0.705175i
$28$		0			0
$29$	1246.36	+	404.968i	1.48200	+	0.481532i	0.934711	−	0.355410i	$-0.115659\pi$
$29$	1246.36	+	404.968i	1.48200	+	0.481532i	0.547292	+	0.836942i	$0.315659\pi$
$30$		0			0
$31$	197.070	−	940.577i	0.205067	−	0.978748i
$31$	197.070	−	940.577i	0.205067	−	0.978748i
$32$		0			0
$33$	182.018	−	560.193i	0.167142	−	0.514411i
$34$		0			0
$35$	−130.513	−	94.8235i	−0.106542	−	0.0774069i
$36$		0			0
$37$	−44.2770	+	25.5633i	−0.0323426	+	0.0186730i	−0.516084	−	0.856538i	$-0.672611\pi$
$37$	−44.2770	+	25.5633i	−0.0323426	+	0.0186730i	0.483742	+	0.875211i	$0.339277\pi$
$38$		0			0
$39$	−708.882	+	515.033i	−0.466063	+	0.338615i
$40$		0			0
$41$	−2120.74	−	2355.32i	−1.26159	−	1.40114i	−0.878719	−	0.477340i	$-0.841601\pi$
$41$	−2120.74	−	2355.32i	−1.26159	−	1.40114i	−0.382874	−	0.923801i	$-0.625066\pi$
$42$		0			0
$43$	−261.555	−	1230.52i	−0.141457	−	0.665505i	−0.990538	−	0.137241i	$-0.956176\pi$
$43$	−261.555	−	1230.52i	−0.141457	−	0.665505i	0.849080	−	0.528264i	$-0.177157\pi$
$44$		0			0
$45$	−1116.86	−	497.260i	−0.551538	−	0.245561i
$46$		0			0
$47$	1174.85	+	3615.80i	0.531845	+	1.63685i	0.750369	+	0.661019i	$0.229876\pi$
$47$	1174.85	+	3615.80i	0.531845	+	1.63685i	−0.218524	+	0.975832i	$0.570124\pi$
$48$		0			0
$49$	2285.23	+	485.740i	0.951782	+	0.202307i
$50$		0			0
$51$	2119.82	−	943.807i	0.815004	−	0.362863i
$52$		0			0
$53$	−176.408	+	18.5412i	−0.0628011	+	0.00660066i	−0.135877	−	0.990726i	$-0.543385\pi$
$53$	−176.408	+	18.5412i	−0.0628011	+	0.00660066i	0.0730758	+	0.997326i	$0.476718\pi$
$54$		0			0
$55$	−2624.49	−	275.845i	−0.867601	−	0.0911886i
$56$		0			0
$57$	−30.5747	−	17.6523i	−0.00941048	−	0.00543314i
$58$		0			0
$59$	−1152.75	+	1280.26i	−0.331156	+	0.367786i	−0.885611	−	0.464428i	$-0.846260\pi$
$59$	−1152.75	+	1280.26i	−0.331156	+	0.367786i	0.554455	+	0.832214i	$0.312927\pi$
$60$		0			0
$61$			1725.27i			0.463657i	0.972757	+	0.231829i	$0.0744709\pi$
$61$			1725.27i			0.463657i	−0.972757	+	0.231829i	$0.925529\pi$
$62$		0			0
$63$	−490.461			−0.123573
$64$		0			0
$65$	2917.36	+	2626.80i	0.690498	+	0.621728i
$66$		0			0
$67$	−3502.26	+	6066.09i	−0.780187	+	1.35132i	0.151645	+	0.988435i	$0.451543\pi$
$67$	−3502.26	+	6066.09i	−0.780187	+	1.35132i	−0.931832	+	0.362889i	$0.881790\pi$
$68$		0			0
$69$	258.371	−	2458.24i	0.0542683	−	0.516328i
$70$		0			0
$71$	−244.506	−	2326.32i	−0.0485035	−	0.461480i	−0.991636	−	0.129064i	$-0.958803\pi$
$71$	−244.506	−	2326.32i	−0.0485035	−	0.461480i	0.943133	−	0.332416i	$-0.107864\pi$
$72$		0			0
$73$	4261.62	+	9571.75i	0.799703	+	1.79616i	0.567228	+	0.823561i	$0.308016\pi$
$73$	4261.62	+	9571.75i	0.799703	+	1.79616i	0.232476	+	0.972602i	$0.425317\pi$
$74$		0			0
$75$	−207.405	+	975.763i	−0.0368720	+	0.173469i
$76$		0			0
$77$	−1006.87	+	327.151i	−0.169821	+	0.0551781i
$78$		0			0
$79$	−662.553	+	1488.12i	−0.106161	+	0.238442i	−0.958813	−	0.284037i	$-0.908326\pi$
$79$	−662.553	+	1488.12i	−0.106161	+	0.238442i	0.852652	+	0.522479i	$0.174993\pi$
$80$		0			0
$81$	−2048.37	+	435.395i	−0.312204	+	0.0663611i
$82$		0			0
$83$	−9367.73	+	8434.74i	−1.35981	+	1.22438i	−0.409793	+	0.912178i	$0.634399\pi$
$83$	−9367.73	+	8434.74i	−1.35981	+	1.22438i	−0.950016	+	0.312200i	$0.898934\pi$
$84$		0			0
$85$	−6110.66	−	8410.60i	−0.845766	−	1.16410i
$86$		0			0
$87$	2932.86	+	5079.85i	0.387483	+	0.671139i
$88$		0			0
$89$	1115.83	−	1535.80i	0.140869	−	0.193890i	−0.732753	−	0.680495i	$-0.761765\pi$
$89$	1115.83	−	1535.80i	0.140869	−	0.193890i	0.873622	+	0.486605i	$0.161765\pi$
$90$		0			0
$91$	1497.81	+	486.668i	0.180873	+	0.0587692i
$92$		0			0
$93$	3472.51	−	2538.38i	0.401492	−	0.293488i
$94$		0			0
$95$	−48.8779	+	150.431i	−0.00541584	+	0.0166682i
$96$		0			0
$97$	−1202.13	−	873.399i	−0.127764	−	0.0928259i	0.522068	−	0.852904i	$-0.325161\pi$
$97$	−1202.13	−	873.399i	−0.127764	−	0.0928259i	−0.649832	+	0.760078i	$0.725161\pi$
$98$		0			0
$99$	−6948.15	+	4011.52i	−0.708923	+	0.409297i
$100$		0			0
$101$	13290.8	−	9656.31i	1.30289	−	0.946604i	0.302910	−	0.953019i	$-0.402042\pi$
$101$	13290.8	−	9656.31i	1.30289	−	0.946604i	0.999979	+	0.00641493i	$0.00204195\pi$
$102$		0			0
$103$	1402.34	+	1557.45i	0.132184	+	0.146805i	0.805603	−	0.592456i	$-0.201842\pi$
$103$	1402.34	+	1557.45i	0.132184	+	0.146805i	−0.673419	+	0.739261i	$0.735175\pi$
$104$		0			0
$105$	−150.127	−	706.291i	−0.0136169	−	0.0640627i
$106$		0			0
$107$	1399.37	+	623.039i	0.122226	+	0.0544186i	0.466939	−	0.884290i	$-0.345357\pi$
$107$	1399.37	+	623.039i	0.122226	+	0.0544186i	−0.344712	+	0.938708i	$0.612024\pi$
$108$		0			0
$109$	−3400.84	−	10466.7i	−0.286242	−	0.880961i	−0.986024	−	0.166605i	$-0.946720\pi$
$109$	−3400.84	−	10466.7i	−0.286242	−	0.880961i	0.699782	−	0.714356i	$-0.253280\pi$
$110$		0			0
$111$	−223.838	−	47.5783i	−0.0181672	−	0.00386156i
$112$		0			0
$113$	11131.6	−	4956.12i	0.871770	−	0.388137i	0.0784327	−	0.996919i	$-0.475008\pi$
$113$	11131.6	−	4956.12i	0.871770	−	0.388137i	0.793337	+	0.608782i	$0.208342\pi$
$114$		0			0
$115$	−11013.5	+	1157.56i	−0.832775	+	0.0875282i
$116$		0			0
$117$	11869.6	+	1247.55i	0.867094	+	0.0911352i
$118$		0			0
$119$	−3611.89	−	2085.32i	−0.255059	−	0.147258i
$120$		0			0
$121$	−1791.31	+	1989.45i	−0.122349	+	0.135882i
$122$		0			0
$123$		−	14185.9i		−	0.937665i
$124$		0			0
$125$	17002.5			1.08816
$126$		0			0
$127$	−19100.8	−	17198.4i	−1.18425	−	1.06631i	−0.996458	−	0.0840977i	$-0.973199\pi$
$127$	−19100.8	−	17198.4i	−1.18425	−	1.06631i	−0.187795	−	0.982208i	$-0.560134\pi$
$128$		0			0
$129$	2815.37	−	4876.37i	0.169183	−	0.293033i
$130$		0			0
$131$	−1833.51	+	17444.7i	−0.106842	+	1.01653i	0.801413	+	0.598111i	$0.204082\pi$
$131$	−1833.51	+	17444.7i	−0.106842	+	1.01653i	−0.908255	+	0.418418i	$0.862585\pi$
$132$		0			0
$133$	6.63284	+	63.1072i	0.000374970	+	0.00356760i
$134$		0			0
$135$	−5182.77	−	11640.7i	−0.284377	−	0.638721i
$136$		0			0
$137$	978.743	−	4604.62i	0.0521468	−	0.245331i	−0.944352	−	0.328936i	$-0.893310\pi$
$137$	978.743	−	4604.62i	0.0521468	−	0.245331i	0.996499	+	0.0836047i	$0.0266433\pi$
$138$		0			0
$139$	407.974	−	132.559i	0.0211156	−	0.00686087i	−0.298440	−	0.954428i	$-0.596466\pi$
$139$	407.974	−	132.559i	0.0211156	−	0.00686087i	0.319556	+	0.947567i	$0.396466\pi$
$140$		0			0
$141$	−6921.40	+	15545.7i	−0.348141	+	0.781938i
$142$		0			0
$143$	25199.3	−	5356.28i	1.23230	−	0.261933i
$144$		0			0
$145$	19529.6	−	17584.5i	0.928876	−	0.836363i
$146$		0			0
$147$	6146.47	+	8459.89i	0.284440	+	0.391498i
$148$		0			0
$149$	6515.03	+	11284.4i	0.293457	+	0.508282i	0.974625	−	0.223845i	$-0.0718610\pi$
$149$	6515.03	+	11284.4i	0.293457	+	0.508282i	−0.681168	+	0.732127i	$0.738528\pi$
$150$		0			0
$151$	−606.944	+	835.387i	−0.0266192	+	0.0366382i	−0.822119	−	0.569315i	$-0.807208\pi$
$151$	−606.944	+	835.387i	−0.0266192	+	0.0366382i	0.795500	+	0.605954i	$0.207208\pi$
$152$		0			0
$153$	−30059.6	−	9766.95i	−1.28410	−	0.417231i
$154$		0			0
$155$	−14358.6	−	12853.1i	−0.597652	−	0.534991i
$156$		0			0
$157$	9367.39	−	28829.9i	0.380031	−	1.16962i	−0.559990	−	0.828500i	$-0.689195\pi$
$157$	9367.39	−	28829.9i	0.380031	−	1.16962i	0.940021	−	0.341117i	$-0.110805\pi$
$158$		0			0
$159$	−642.309	−	466.665i	−0.0254068	−	0.0184591i
$160$		0			0
$161$	−3847.46	+	2221.33i	−0.148430	+	0.0856963i
$162$		0			0
$163$	17704.7	−	12863.2i	0.666368	−	0.484145i	−0.202439	−	0.979295i	$-0.564887\pi$
$163$	17704.7	−	12863.2i	0.666368	−	0.484145i	0.868807	+	0.495150i	$0.164887\pi$
$164$		0			0
$165$	−7903.58	−	8777.82i	−0.290306	−	0.322418i
$166$		0			0
$167$	7408.58	+	34854.6i	0.265645	+	1.24976i	0.885349	+	0.464926i	$0.153919\pi$
$167$	7408.58	+	34854.6i	0.265645	+	1.24976i	−0.619704	+	0.784835i	$0.712747\pi$
$168$		0			0
$169$	−8918.79	−	3970.90i	−0.312272	−	0.139032i
$170$		0			0
$171$	148.600	+	457.345i	0.00508192	+	0.0156405i
$172$		0			0
$173$	−5177.25	−	1100.46i	−0.172984	−	0.0367690i	0.120605	−	0.992701i	$-0.461517\pi$
$173$	−5177.25	−	1100.46i	−0.172984	−	0.0367690i	−0.293589	+	0.955932i	$0.594850\pi$
$174$		0			0
$175$	1637.96	−	729.268i	0.0534845	−	0.0238128i
$176$		0			0
$177$	−7668.70	+	806.013i	−0.244780	+	0.0257274i
$178$		0			0
$179$	42333.2	+	4449.40i	1.32122	+	0.138866i	0.738746	−	0.673984i	$-0.235418\pi$
$179$	42333.2	+	4449.40i	1.32122	+	0.138866i	0.582474	+	0.812849i	$0.302085\pi$
$180$		0			0
$181$	27631.5	+	15953.1i	0.843427	+	0.486953i	0.858428	−	0.512935i	$-0.171442\pi$
$181$	27631.5	+	15953.1i	0.843427	+	0.486953i	−0.0150005	+	0.999887i	$0.504775\pi$
$182$		0			0
$183$	−5167.14	+	5738.68i	−0.154294	+	0.171360i
$184$		0			0
$185$			1025.25i			0.0299561i
$186$		0			0
$187$	−68224.1			−1.95099
$188$		0			0
$189$	−3798.89	−	3420.53i	−0.106349	−	0.0957569i
$190$		0			0
$191$	16126.5	−	27931.8i	0.442051	−	0.765654i	−0.555791	−	0.831322i	$-0.687584\pi$
$191$	16126.5	−	27931.8i	0.442051	−	0.765654i	0.997842	+	0.0656679i	$0.0209178\pi$
$192$		0			0
$193$	−3623.52	+	34475.5i	−0.0972784	+	0.925542i	0.831654	+	0.555294i	$0.187394\pi$
$193$	−3623.52	+	34475.5i	−0.0972784	+	0.925542i	−0.928933	+	0.370248i	$0.879273\pi$
$194$		0			0
$195$	1836.68	+	17474.8i	0.0483018	+	0.459561i
$196$		0			0
$197$	5644.89	+	12678.6i	0.145453	+	0.326693i	0.971550	−	0.236835i	$-0.0761102\pi$
$197$	5644.89	+	12678.6i	0.145453	+	0.326693i	−0.826097	+	0.563528i	$0.809444\pi$
$198$		0			0
$199$	−13472.2	+	63381.8i	−0.340199	+	1.60051i	0.392364	+	0.919810i	$0.371657\pi$
$199$	−13472.2	+	63381.8i	−0.340199	+	1.60051i	−0.732563	+	0.680700i	$0.761676\pi$
$200$		0			0
$201$	−29817.2	+	9688.19i	−0.738031	+	0.239801i
$202$		0			0
$203$	4288.13	−	9631.30i	0.104058	−	0.233718i
$204$		0			0
$205$	−62167.3	+	13214.1i	−1.47929	+	0.314433i
$206$		0			0
$207$	−25020.2	+	22528.3i	−0.583915	+	0.525759i
$208$		0			0
$209$	610.123	+	839.762i	0.0139677	+	0.0192249i
$210$		0			0
$211$	−26361.5	−	45659.5i	−0.592115	−	1.02557i	−0.993947	−	0.109860i	$-0.964960\pi$
$211$	−26361.5	−	45659.5i	−0.592115	−	1.02557i	0.401832	−	0.915713i	$-0.368374\pi$
$212$		0			0
$213$	6153.98	−	8470.23i	0.135643	−	0.186696i
$214$		0			0
$215$	−23992.3	−	7795.57i	−0.519033	−	0.168644i
$216$		0			0
$217$	−7359.59	−	2367.65i	−0.156291	−	0.0502802i
$218$		0			0
$219$	−14491.9	+	44601.5i	−0.302160	+	0.929954i
$220$		0			0
$221$	82107.0	+	59654.2i	1.68111	+	1.22140i
$222$		0			0
$223$	62808.7	−	36262.6i	1.26302	−	0.729204i	0.289361	−	0.957220i	$-0.406557\pi$
$223$	62808.7	−	36262.6i	1.26302	−	0.729204i	0.973657	+	0.228016i	$0.0732237\pi$
$224$		0			0
$225$	10992.7	−	7986.67i	0.217140	−	0.157761i
$226$		0			0
$227$	33374.5	+	37066.1i	0.647684	+	0.719326i	0.974155	−	0.225882i	$-0.0725263\pi$
$227$	33374.5	+	37066.1i	0.647684	+	0.719326i	−0.326471	+	0.945207i	$0.605860\pi$
$228$		0			0
$229$	14572.1	+	68556.4i	0.277876	+	1.30731i	0.866613	+	0.498981i	$0.166292\pi$
$229$	14572.1	+	68556.4i	0.277876	+	1.30731i	−0.588737	+	0.808325i	$0.700375\pi$
$230$		0			0
$231$	−4328.90	−	1927.35i	−0.0811248	−	0.0361191i
$232$		0			0
$233$	14883.1	+	45805.6i	0.274147	+	0.843736i	0.989444	+	0.144916i	$0.0462912\pi$
$233$	14883.1	+	45805.6i	0.274147	+	0.843736i	−0.715297	+	0.698820i	$0.753709\pi$
$234$		0			0
$235$	74573.5	+	15851.1i	1.35036	+	0.287027i
$236$		0			0
$237$	−6660.70	+	2965.53i	−0.118583	+	0.0527966i
$238$		0			0
$239$	31166.7	−	3275.75i	0.545626	−	0.0573476i	0.172294	−	0.985046i	$-0.444882\pi$
$239$	31166.7	−	3275.75i	0.545626	−	0.0573476i	0.373332	+	0.927698i	$0.378215\pi$
$240$		0			0
$241$	−93583.6	−	9836.03i	−1.61126	−	0.169350i	−0.744341	−	0.667800i	$-0.767236\pi$
$241$	−93583.6	−	9836.03i	−1.61126	−	0.169350i	−0.866919	+	0.498449i	$0.833903\pi$
$242$		0			0
$243$	−52691.5	−	30421.4i	−0.892335	−	0.515190i
$244$		0			0
$245$	31348.6	−	34816.1i	0.522258	−	0.580027i
$246$		0			0
$247$		−	1544.13i		−	0.0253098i
$248$		0			0
$249$	−56421.3			−0.910006
$250$		0			0
$251$	−42172.3	−	37972.1i	−0.669391	−	0.602723i	0.262730	−	0.964869i	$-0.415377\pi$
$251$	−42172.3	−	37972.1i	−0.669391	−	0.602723i	−0.932121	+	0.362147i	$0.882044\pi$
$252$		0			0
$253$	−36336.9	+	62937.3i	−0.567684	+	0.983257i
$254$		0			0
$255$	4863.91	−	46277.0i	0.0748007	−	0.711681i
$256$		0			0
$257$	−1176.55	−	11194.1i	−0.0178133	−	0.169482i	0.981998	−	0.188889i	$-0.0604887\pi$
$257$	−1176.55	−	11194.1i	−0.0178133	−	0.169482i	−0.999812	+	0.0194074i	$0.993822\pi$
$258$		0			0
$259$	167.293	+	375.745i	0.00249389	+	0.00560137i
$260$		0			0
$261$	16611.4	−	78150.5i	0.243852	−	1.14723i
$262$		0			0
$263$	27686.3	−	8995.83i	0.400271	−	0.130056i	−0.101962	−	0.994788i	$-0.532512\pi$
$263$	27686.3	−	8995.83i	0.400271	−	0.130056i	0.502233	+	0.864732i	$0.332512\pi$
$264$		0			0
$265$	−1446.77	+	3249.50i	−0.0206019	+	0.0462726i
$266$		0			0
$267$	8311.21	−	1766.60i	0.116585	−	0.0247809i
$268$		0			0
$269$	14470.7	−	13029.5i	0.199979	−	0.180062i	−0.563056	−	0.826418i	$-0.690375\pi$
$269$	14470.7	−	13029.5i	0.199979	−	0.180062i	0.763036	+	0.646356i	$0.223708\pi$
$270$		0			0
$271$	−34478.4	−	47455.4i	−0.469470	−	0.646171i	0.506969	−	0.861965i	$-0.330766\pi$
$271$	−34478.4	−	47455.4i	−0.469470	−	0.646171i	−0.976439	+	0.215794i	$0.930766\pi$
$272$		0			0
$273$	3524.54	+	6104.68i	0.0472908	+	0.0819101i
$274$		0			0
$275$	17239.6	−	23728.2i	0.227961	−	0.313762i
$276$		0			0
$277$	69337.3	+	22529.1i	0.903665	+	0.293618i	0.723749	−	0.690063i	$-0.242417\pi$
$277$	69337.3	+	22529.1i	0.903665	+	0.293618i	0.179916	+	0.983682i	$0.442417\pi$
$278$		0			0
$279$	−58285.1	−	5954.75i	−0.748771	−	0.0764989i
$280$		0			0
$281$	22177.0	−	68253.8i	0.280860	−	0.864399i	−0.706749	−	0.707465i	$-0.749839\pi$
$281$	22177.0	−	68253.8i	0.280860	−	0.864399i	0.987609	−	0.156935i	$-0.0501612\pi$
$282$		0			0
$283$	61095.7	+	44388.6i	0.762848	+	0.554242i	0.899783	−	0.436339i	$-0.143725\pi$
$283$	61095.7	+	44388.6i	0.762848	+	0.554242i	−0.136935	+	0.990580i	$0.543725\pi$
$284$		0			0
$285$	−613.117	+	353.983i	−0.00754837	+	0.00435805i
$286$		0			0
$287$	−20627.6	+	14986.9i	−0.250430	+	0.181948i
$288$		0			0
$289$	−123954.	−	137664.i	−1.48410	−	1.64826i
$290$		0			0
$291$	−1382.79	−	6505.49i	−0.0163293	−	0.0768235i
$292$		0			0
$293$	31166.0	+	13876.0i	0.363033	+	0.161633i	0.580143	−	0.814514i	$-0.302997\pi$
$293$	31166.0	+	13876.0i	0.363033	+	0.161633i	−0.217110	+	0.976147i	$0.569663\pi$
$294$		0			0
$295$	10675.5	+	32855.9i	0.122672	+	0.377545i
$296$		0			0
$297$	−81793.9	−	17385.8i	−0.927274	−	0.197098i
$298$		0			0
$299$	98762.6	−	43971.9i	1.10471	−	0.491850i
$300$		0			0
$301$	−10065.0	+	1057.88i	−0.111092	+	0.0116762i
$302$		0			0
$303$	73128.9	+	7686.15i	0.796533	+	0.0837190i
$304$		0			0
$305$	29961.9	+	17298.5i	0.322084	+	0.185955i
$306$		0			0
$307$	57292.3	−	63629.5i	0.607882	−	0.675122i	−0.358114	−	0.933678i	$-0.616580\pi$
$307$	57292.3	−	63629.5i	0.607882	−	0.675122i	0.965996	+	0.258556i	$0.0832468\pi$
$308$		0			0
$309$			9380.44i			0.0982441i
$310$		0			0
$311$	94656.1			0.978651			0.489326	−	0.872101i	$-0.337243\pi$
$311$	94656.1			0.978651			0.489326	+	0.872101i	$0.337243\pi$
$312$		0			0
$313$	−17941.4	−	16154.5i	−0.183134	−	0.164894i	0.572465	−	0.819929i	$-0.305987\pi$
$313$	−17941.4	−	16154.5i	−0.183134	−	0.164894i	−0.755599	+	0.655035i	$0.772654\pi$
$314$		0			0
$315$	−4917.63	+	8517.59i	−0.0495604	+	0.0858412i
$316$		0			0
$317$	4062.21	−	38649.4i	0.0404244	−	0.384613i	−0.955540	−	0.294862i	$-0.904726\pi$
$317$	4062.21	−	38649.4i	0.0404244	−	0.384613i	0.995964	−	0.0897507i	$-0.0286070\pi$
$318$		0			0
$319$	−18027.0	−	171515.i	−0.177150	−	1.68547i
$320$		0			0
$321$	2788.67	+	6263.45i	0.0270637	+	0.0607860i
$322$		0			0
$323$	−850.189	+	3999.83i	−0.00814912	+	0.0383386i
$324$		0			0
$325$	−41495.3	+	13482.6i	−0.392855	+	0.127646i
$326$		0			0
$327$	20035.4	−	45000.3i	0.187371	−	0.420843i
$328$		0			0
$329$	29917.0	−	6359.06i	0.276393	−	0.0587491i
$330$		0			0
$331$	10225.4	−	9207.00i	0.0933308	−	0.0840354i	−0.621145	−	0.783696i	$-0.713332\pi$
$331$	10225.4	−	9207.00i	0.0933308	−	0.0840354i	0.714475	+	0.699661i	$0.246665\pi$
$332$		0			0
$333$	1832.13	+	2521.70i	0.0165222	+	0.0227408i
$334$		0			0
$335$	70231.2	+	121644.i	0.625807	+	1.08393i
$336$		0			0
$337$	−46755.8	+	64353.8i	−0.411695	+	0.566650i	−0.963631	−	0.267237i	$-0.913889\pi$
$337$	−46755.8	+	64353.8i	−0.411695	+	0.566650i	0.551936	+	0.833887i	$0.313889\pi$
$338$		0			0
$339$	51870.1	+	16853.6i	0.451354	+	0.146654i
$340$		0			0
$341$	−123625.	+	26653.2i	−1.06316	+	0.229214i
$342$		0			0
$343$	11776.8	−	36245.3i	0.100101	−	0.308080i
$344$		0			0
$345$	−40100.4	−	29134.7i	−0.336907	−	0.244778i
$346$		0			0
$347$	−67304.3	+	38858.2i	−0.558964	+	0.322718i	−0.752730	−	0.658330i	$-0.771263\pi$
$347$	−67304.3	+	38858.2i	−0.558964	+	0.322718i	0.193766	+	0.981048i	$0.437930\pi$
$348$		0			0
$349$	60952.6	−	44284.7i	0.500428	−	0.363582i	−0.308752	−	0.951142i	$-0.599911\pi$
$349$	60952.6	−	44284.7i	0.500428	−	0.363582i	0.809180	+	0.587560i	$0.199911\pi$
$350$		0			0
$351$	83236.2	+	92443.2i	0.675613	+	0.750344i
$352$		0			0
$353$	2075.42	+	9764.09i	0.0166555	+	0.0783579i	0.985690	−	0.168566i	$-0.0539136\pi$
$353$	2075.42	+	9764.09i	0.0166555	+	0.0783579i	−0.969035	+	0.246924i	$0.920580\pi$
$354$		0			0
$355$	−42851.6	−	19078.8i	−0.340025	−	0.151389i
$356$		0			0
$357$	−5768.57	−	17753.8i	−0.0452618	−	0.139301i
$358$		0			0
$359$	−22806.0	−	4847.56i	−0.176954	−	0.0376127i	0.118583	−	0.992944i	$-0.462165\pi$
$359$	−22806.0	−	4847.56i	−0.176954	−	0.0376127i	−0.295536	+	0.955332i	$0.595498\pi$
$360$		0			0
$361$	−118997.	+	52981.0i	−0.913109	+	0.406542i
$362$		0			0
$363$	−11916.7	+	1252.49i	−0.0904361	+	0.00950522i
$364$		0			0
$365$	208957.	+	21962.3i	1.56845	+	0.164851i
$366$		0			0
$367$	−88826.5	−	51284.0i	−0.659493	−	0.380759i	0.132591	−	0.991171i	$-0.457670\pi$
$367$	−88826.5	−	51284.0i	−0.659493	−	0.380759i	−0.792084	+	0.610412i	$0.791004\pi$
$368$		0			0
$369$	−129293.	+	143595.i	−0.949561	+	1.05459i
$370$		0			0
$371$			1426.99i			0.0103675i
$372$		0			0
$373$	242532.			1.74322			0.871608	−	0.490203i	$-0.163077\pi$
$373$	242532.			1.74322			0.871608	+	0.490203i	$0.163077\pi$
$374$		0			0
$375$	56554.6	+	50922.0i	0.402166	+	0.362112i
$376$		0			0
$377$	−128275.	+	222179.i	−0.902528	+	1.56322i
$378$		0			0
$379$	12453.2	−	118485.i	0.0866970	−	0.824867i	−0.861622	−	0.507550i	$-0.830551\pi$
$379$	12453.2	−	118485.i	0.0866970	−	0.824867i	0.948319	−	0.317317i	$-0.102782\pi$
$380$		0			0
$381$	−12025.3	−	114413.i	−0.0828409	−	0.788179i
$382$		0			0
$383$	−97965.6	−	220034.i	−0.667845	−	1.50001i	−0.855518	−	0.517774i	$-0.826761\pi$
$383$	−97965.6	−	220034.i	−0.667845	−	1.50001i	0.187672	−	0.982232i	$-0.439906\pi$
$384$		0			0
$385$	−4413.93	+	20765.9i	−0.0297786	+	0.140097i
$386$		0			0
$387$	−72942.3	+	23700.4i	−0.487032	+	0.158246i
$388$		0			0
$389$	−42933.9	+	96431.1i	−0.283727	+	0.637262i	−0.998041	−	0.0625638i	$-0.980072\pi$
$389$	−42933.9	+	96431.1i	−0.283727	+	0.637262i	0.714314	+	0.699826i	$0.246739\pi$
$390$		0			0
$391$	−280040.	+	59524.3i	−1.83175	+	0.389351i
$392$		0			0
$393$	−58345.0	+	52534.1i	−0.377762	+	0.340139i
$394$		0			0
$395$	19200.3	+	26426.9i	0.123059	+	0.169376i
$396$		0			0
$397$	−32826.6	−	56857.3i	−0.208279	−	0.360749i	0.742894	−	0.669409i	$-0.233453\pi$
$397$	−32826.6	−	56857.3i	−0.208279	−	0.360749i	−0.951172	+	0.308660i	$0.900119\pi$
$398$		0			0
$399$	−166.942	+	229.776i	−0.00104862	+	0.00144331i
$400$		0			0
$401$	119671.	+	38883.5i	0.744219	+	0.241811i	0.656492	−	0.754333i	$-0.272040\pi$
$401$	119671.	+	38883.5i	0.744219	+	0.241811i	0.0877271	+	0.996145i	$0.472040\pi$
$402$		0			0
$403$	172087.	+	76019.4i	1.05959	+	0.468074i
$404$		0			0
$405$	−12976.8	+	39938.5i	−0.0791149	+	0.243491i
$406$		0			0
$407$	5443.21	+	3954.72i	0.0328599	+	0.0238741i
$408$		0			0
$409$	−129215.	+	74602.3i	−0.772442	+	0.445970i	−0.833745	−	0.552149i	$-0.813808\pi$
$409$	−129215.	+	74602.3i	−0.772442	+	0.445970i	0.0613029	+	0.998119i	$0.480474\pi$
$410$		0			0
$411$	17046.3	−	12384.8i	0.100913	−	0.0733173i
$412$		0			0
$413$	9273.68	+	10299.5i	0.0543691	+	0.0603830i
$414$		0			0
$415$	52555.9	+	247256.i	0.305158	+	1.43566i
$416$		0			0
$417$	1754.04	+	780.947i	0.0100871	+	0.00449107i
$418$		0			0
$419$	−31651.2	−	97412.4i	−0.180286	−	0.554863i	0.819549	−	0.573009i	$-0.194224\pi$
$419$	−31651.2	−	97412.4i	−0.180286	−	0.554863i	−0.999835	+	0.0181453i	$0.994224\pi$
$420$		0			0
$421$	−3192.41	−	678.568i	−0.0180117	−	0.00382851i	0.198897	−	0.980020i	$-0.436264\pi$
$421$	−3192.41	−	678.568i	−0.0180117	−	0.00382851i	−0.216909	+	0.976192i	$0.569597\pi$
$422$		0			0
$423$	211747.	−	94275.9i	1.18341	−	0.526890i
$424$		0			0
$425$	114911.	−	12077.6i	0.636183	−	0.0668656i
$426$		0			0
$427$	13803.4	+	1450.80i	0.0757062	+	0.00795704i
$428$		0			0
$429$	99861.2	+	57654.9i	0.542603	+	0.313272i
$430$		0			0
$431$	−239748.	+	266267.i	−1.29062	+	1.43338i	−0.448798	+	0.893633i	$0.648148\pi$
$431$	−239748.	+	266267.i	−1.29062	+	1.43338i	−0.841826	+	0.539750i	$0.818519\pi$
$432$		0			0
$433$		−	65102.9i		−	0.347236i	−0.984813	−	0.173618i	$-0.944454\pi$
$433$		−	65102.9i		−	0.347236i	0.984813	−	0.173618i	$-0.0555458\pi$
$434$		0			0
$435$	117626.			0.621618
$436$		0			0
$437$	3237.06	+	2914.66i	0.0169507	+	0.0152625i
$438$		0			0
$439$	−107114.	+	185527.i	−0.555798	+	0.962670i	0.442043	+	0.896994i	$0.354254\pi$
$439$	−107114.	+	185527.i	−0.555798	+	0.962670i	−0.997841	+	0.0656764i	$0.979080\pi$
$440$		0			0
$441$	14888.4	−	141654.i	0.0765546	−	0.728369i
$442$		0			0
$443$	3022.93	+	28761.3i	0.0154036	+	0.146555i	0.999520	−	0.0309668i	$-0.00985862\pi$
$443$	3022.93	+	28761.3i	0.0154036	+	0.146555i	−0.984117	+	0.177522i	$0.943192\pi$
$444$		0			0
$445$	−15483.6	−	34776.8i	−0.0781903	−	0.175618i
$446$		0			0
$447$	−12125.7	+	57047.0i	−0.0606865	+	0.285508i
$448$		0			0
$449$	−11134.3	+	3617.74i	−0.0552292	+	0.0179450i	−0.336501	−	0.941683i	$-0.609244\pi$
$449$	−11134.3	+	3617.74i	−0.0552292	+	0.0179450i	0.281272	+	0.959628i	$0.409244\pi$
$450$		0			0
$451$	−169644.	+	381027.i	−0.834038	+	1.87328i
$452$		0			0
$453$	−4520.81	+	960.928i	−0.0220303	+	0.00468268i
$454$		0			0
$455$	23469.6	−	21132.1i	0.113366	−	0.102075i
$456$		0			0
$457$	79267.1	+	109102.i	0.379543	+	0.522396i	0.955463	−	0.295110i	$-0.0953563\pi$
$457$	79267.1	+	109102.i	0.379543	+	0.522396i	−0.575921	+	0.817506i	$0.695356\pi$
$458$		0			0
$459$	−164712.	−	285289.i	−0.781807	−	1.35413i
$460$		0			0
$461$	2010.36	−	2767.03i	0.00945961	−	0.0130200i	−0.804261	−	0.594276i	$-0.797439\pi$
$461$	2010.36	−	2767.03i	0.00945961	−	0.0130200i	0.813721	+	0.581256i	$0.197439\pi$
$462$		0			0
$463$	−264255.	−	85861.5i	−1.23271	−	0.400531i	−0.381014	−	0.924569i	$-0.624425\pi$
$463$	−264255.	−	85861.5i	−1.23271	−	0.400531i	−0.851695	+	0.524038i	$0.824425\pi$
$464$		0			0
$465$	−9265.50	−	85756.4i	−0.0428512	−	0.396607i
$466$		0			0
$467$	58804.8	−	180983.i	0.269637	−	0.829856i	−0.720952	−	0.692985i	$-0.756295\pi$
$467$	58804.8	−	180983.i	0.269637	−	0.829856i	0.990589	−	0.136871i	$-0.0437047\pi$
$468$		0			0
$469$	45588.1	+	33121.7i	0.207256	+	0.150580i
$470$		0			0
$471$	117503.	−	67840.4i	0.529672	−	0.305806i
$472$		0			0
$473$	−133934.	+	97308.8i	−0.598645	+	0.434941i
$474$		0			0
$475$	−1176.30	−	1306.41i	−0.00521351	−	0.00579019i
$476$		0			0
$477$	2248.39	+	10577.9i	0.00988179	+	0.0464902i
$478$		0			0
$479$	280475.	+	124876.i	1.22243	+	0.544260i	0.913505	−	0.406827i	$-0.133365\pi$
$479$	280475.	+	124876.i	1.22243	+	0.544260i	0.308923	+	0.951087i	$0.400031\pi$
$480$		0			0
$481$	−3092.89	−	9518.94i	−0.0133682	−	0.0411432i
$482$		0			0
$483$	−19450.5	−	4134.32i	−0.0833750	−	0.0177219i
$484$		0			0
$485$	−27221.1	+	12119.6i	−0.115724	+	0.0515235i
$486$		0			0
$487$	−119904.	+	12602.4i	−0.505563	+	0.0531368i	−0.353877	−	0.935292i	$-0.615137\pi$
$487$	−119904.	+	12602.4i	−0.505563	+	0.0531368i	−0.151686	+	0.988429i	$0.548470\pi$
$488$		0			0
$489$	97415.5	+	10238.8i	0.407390	+	0.0428184i
$490$		0			0
$491$	−347817.	−	200812.i	−1.44274	−	0.832965i	−0.444707	−	0.895676i	$-0.646692\pi$
$491$	−347817.	−	200812.i	−1.44274	−	0.832965i	−0.998032	+	0.0627109i	$0.980025\pi$
$492$		0			0
$493$	454608.	−	504894.i	1.87044	−	2.07733i
$494$		0			0
$495$			160887.i			0.656613i
$496$		0			0
$497$	−18817.9			−0.0761831
$498$		0			0
$499$	271610.	+	244559.i	1.09080	+	0.982161i	0.999906	−	0.0136999i	$-0.00436095\pi$
$499$	271610.	+	244559.i	1.09080	+	0.982161i	0.0908938	+	0.995861i	$0.471028\pi$
$500$		0			0
$501$	−79745.8	+	138124.i	−0.317711	+	0.550292i
$502$		0			0
$503$	4986.57	−	47444.0i	0.0197090	−	0.187519i	−0.980238	−	0.197822i	$-0.936613\pi$
$503$	4986.57	−	47444.0i	0.0197090	−	0.187519i	0.999947	+	0.0103034i	$0.00327973\pi$
$504$		0			0
$505$	−34435.7	−	327634.i	−0.135029	−	1.28471i
$506$		0			0
$507$	−17773.4	−	39919.8i	−0.0691441	−	0.155300i
$508$		0			0
$509$	−78074.8	+	367313.i	−0.301353	+	1.41775i	0.523317	+	0.852138i	$0.324694\pi$
$509$	−78074.8	+	367313.i	−0.301353	+	1.41775i	−0.824670	+	0.565615i	$0.808639\pi$
$510$		0			0
$511$	80164.8	−	26047.1i	0.307002	−	0.0997511i
$512$		0			0
$513$	−2038.59	+	4578.74i	−0.00774630	+	0.0173985i
$514$		0			0
$515$	41108.1	−	8737.79i	0.154993	−	0.0329448i
$516$		0			0
$517$	371810.	−	334780.i	1.39104	−	1.25250i
$518$		0			0
$519$	−13925.0	−	19166.1i	−0.0516964	−	0.0711541i
$520$		0			0
$521$	−224099.	−	388152.i	−0.825592	−	1.42997i	−0.901466	−	0.432850i	$-0.857508\pi$
$521$	−224099.	−	388152.i	−0.825592	−	1.42997i	0.0758742	−	0.997117i	$-0.475825\pi$
$522$		0			0
$523$	222170.	−	305791.i	0.812237	−	1.11795i	−0.178738	−	0.983897i	$-0.557201\pi$
$523$	222170.	−	305791.i	0.812237	−	1.11795i	0.990974	−	0.134051i	$-0.0427986\pi$
$524$		0			0
$525$	7632.42	+	2479.92i	0.0276913	+	0.00899745i
$526$		0			0
$527$	−403909.	−	291667.i	−1.45433	−	1.05018i
$528$		0			0
$529$	−7764.93	+	23898.0i	−0.0277476	+	0.0853984i
$530$		0			0
$531$	84971.2	+	61735.2i	0.301358	+	0.218949i
$532$		0			0
$533$	537330.	−	310228.i	1.89141	−	1.09201i
$534$		0			0
$535$	24850.8	−	18055.2i	0.0868227	−	0.0630804i
$536$		0			0
$537$	127485.	+	141587.i	0.442091	+	0.490991i
$538$		0			0
$539$	−63922.5	−	300732.i	−0.220027	−	1.03515i
$540$		0			0
$541$	−17047.7	−	7590.13i	−0.0582467	−	0.0259331i	0.377407	−	0.926048i	$-0.376816\pi$
$541$	−17047.7	−	7590.13i	−0.0582467	−	0.0259331i	−0.435653	+	0.900115i	$0.643483\pi$
$542$		0			0
$543$	44130.5	+	135820.i	0.149671	+	0.460641i
$544$		0			0
$545$	−215868.	−	45884.3i	−0.726769	−	0.154479i
$546$		0			0
$547$	−246626.	+	109805.i	−0.824260	+	0.366984i	−0.775125	−	0.631808i	$-0.782313\pi$
$547$	−246626.	+	109805.i	−0.824260	+	0.366984i	−0.0491353	+	0.998792i	$0.515647\pi$
$548$		0			0
$549$	104607.	−	10994.6i	0.347069	−	0.0364784i
$550$		0			0
$551$	−10280.2	−	1080.49i	−0.0338609	−	0.00355893i
$552$		0			0
$553$	11348.9	+	6552.29i	0.0371111	+	0.0214261i
$554$		0			0
$555$	−3070.59	+	3410.24i	−0.00996864	+	0.0110713i
$556$		0			0
$557$		−	7446.73i		−	0.0240024i	−0.999928	−	0.0120012i	$-0.996180\pi$
$557$		−	7446.73i		−	0.0240024i	0.999928	−	0.0120012i	$-0.00382020\pi$
$558$		0			0
$559$	246274.			0.788124
$560$		0			0
$561$	−226931.	−	204329.i	−0.721053	−	0.649239i
$562$		0			0
$563$	−167460.	+	290049.i	−0.528316	+	0.915070i	0.471139	+	0.882059i	$0.343843\pi$
$563$	−167460.	+	290049.i	−0.528316	+	0.915070i	−0.999455	+	0.0330110i	$0.989490\pi$
$564$		0			0
$565$	25541.4	−	243010.i	0.0800106	−	0.761250i
$566$		0			0
$567$	1760.98	+	16754.6i	0.00547758	+	0.0521157i
$568$		0			0
$569$	−223197.	−	501309.i	−0.689389	−	1.54839i	−0.829654	−	0.558278i	$-0.811462\pi$
$569$	−223197.	−	501309.i	−0.689389	−	1.54839i	0.140265	−	0.990114i	$-0.455204\pi$
$570$		0			0
$571$	−106488.	+	500986.i	−0.326608	+	1.53657i	0.442096	+	0.896968i	$0.354235\pi$
$571$	−106488.	+	500986.i	−0.326608	+	1.53657i	−0.768704	+	0.639604i	$0.779098\pi$
$572$		0			0
$573$	137296.	−	44610.1i	0.418165	−	0.135870i
$574$		0			0
$575$	50060.9	−	112439.i	0.151413	−	0.340079i
$576$		0			0
$577$	−288162.	+	61250.6i	−0.865535	+	0.183975i	−0.619223	−	0.785215i	$-0.712552\pi$
$577$	−288162.	+	61250.6i	−0.865535	+	0.183975i	−0.246312	+	0.969191i	$0.579219\pi$
$578$		0			0
$579$	−115306.	+	103822.i	−0.343949	+	0.309693i
$580$		0			0
$581$	59606.7	+	82041.6i	0.176581	+	0.243042i
$582$		0			0
$583$	11671.4	+	20215.5i	0.0343389	+	0.0594768i
$584$		0			0
$585$	140677.	−	193625.i	0.411066	−	0.565784i
$586$		0			0
$587$	397146.	+	129041.i	1.15259	+	0.374498i	0.822117	−	0.569318i	$-0.192793\pi$
$587$	397146.	+	129041.i	1.15259	+	0.374498i	0.330470	+	0.943816i	$0.392793\pi$
$588$		0			0
$589$	22.0357	+	7580.02i	6.35181e−5	+	0.0218494i
$590$		0			0
$591$	−19195.8	+	59078.6i	−0.0549581	+	0.169144i
$592$		0			0
$593$	458641.	+	333222.i	1.30426	+	0.947599i	0.999988	−	0.00498699i	$-0.00158742\pi$
$593$	458641.	+	333222.i	1.30426	+	0.947599i	0.304270	+	0.952586i	$0.401587\pi$
$594$		0			0
$595$	−72429.6	+	41817.2i	−0.204589	+	0.118119i
$596$		0			0
$597$	−234639.	+	170475.i	−0.658341	+	0.478313i
$598$		0			0
$599$	−400072.	−	444325.i	−1.11502	−	1.23836i	−0.968463	−	0.249158i	$-0.919846\pi$
$599$	−400072.	−	444325.i	−1.11502	−	1.23836i	−0.146561	−	0.989202i	$-0.546820\pi$
$600$		0			0
$601$	77879.4	+	366394.i	0.215612	+	1.01438i	0.944187	+	0.329410i	$0.106850\pi$
$601$	77879.4	+	366394.i	0.215612	+	1.01438i	−0.728575	+	0.684966i	$0.759817\pi$
$602$		0			0
$603$	390119.	+	173692.i	1.07291	+	0.477690i
$604$		0			0
$605$	16589.1	+	51056.0i	0.0453223	+	0.139488i
$606$		0			0
$607$	246886.	+	52477.3i	0.670069	+	0.142428i	0.530370	−	0.847766i	$-0.322053\pi$
$607$	246886.	+	52477.3i	0.670069	+	0.142428i	0.139699	+	0.990194i	$0.455386\pi$
$608$		0			0
$609$	43108.9	−	19193.3i	0.116234	−	0.0517506i
$610$		0			0
$611$	−740197.	+	77797.8i	−1.98274	+	0.208394i
$612$		0			0
$613$	545110.	+	57293.4i	1.45065	+	0.152470i	0.796842	−	0.604188i	$-0.206502\pi$
$613$	545110.	+	57293.4i	1.45065	+	0.152470i	0.653811	+	0.756658i	$0.273169\pi$
$614$		0			0
$615$	−246360.	−	142236.i	−0.651358	−	0.376062i
$616$		0			0
$617$	135971.	−	151011.i	0.357170	−	0.396678i	−0.537603	−	0.843198i	$-0.680670\pi$
$617$	135971.	−	151011.i	0.357170	−	0.396678i	0.894774	+	0.446520i	$0.147337\pi$
$618$		0			0
$619$			98640.2i			0.257438i	0.991681	+	0.128719i	$0.0410865\pi$
$619$			98640.2i			0.257438i	−0.991681	+	0.128719i	$0.958913\pi$
$620$		0			0
$621$	−350909.			−0.909937
$622$		0			0
$623$	−11349.3	−	10218.9i	−0.0292409	−	0.0263287i
$624$		0			0
$625$	100828.	−	174640.i	0.258121	−	0.447078i
$626$		0			0
$627$	−485.641	+	4620.56i	−0.00123532	+	0.0117533i
$628$		0			0
$629$	2770.58	+	26360.3i	0.00700275	+	0.0666267i
$630$		0			0
$631$	21555.3	+	48413.9i	0.0541371	+	0.121594i	0.938589	−	0.345038i	$-0.112134\pi$
$631$	21555.3	+	48413.9i	0.0541371	+	0.121594i	−0.884452	+	0.466632i	$0.845467\pi$
$632$		0			0
$633$	49063.9	−	230827.i	0.122449	−	0.576076i
$634$		0			0
$635$	−490192.	+	159273.i	−1.21568	+	0.394998i
$636$		0			0
$637$	−186026.	+	417820.i	−0.458452	+	1.02970i
$638$		0			0
$639$	−139492.	+	29649.9i	−0.341623	+	0.0726142i
$640$		0			0
$641$	−441756.	+	397759.i	−1.07514	+	0.968063i	−0.999577	−	0.0290781i	$-0.990743\pi$
$641$	−441756.	+	397759.i	−1.07514	+	0.968063i	−0.0755654	+	0.997141i	$0.524076\pi$
$642$		0			0
$643$	417848.	+	575118.i	1.01064	+	1.39103i	0.918563	+	0.395274i	$0.129350\pi$
$643$	417848.	+	575118.i	1.01064	+	1.39103i	0.0920759	+	0.995752i	$0.470650\pi$
$644$		0			0
$645$	−56457.0	−	97786.3i	−0.135706	−	0.235049i
$646$		0			0
$647$	163441.	−	224958.i	0.390439	−	0.537394i	−0.567873	−	0.823116i	$-0.692234\pi$
$647$	163441.	−	224958.i	0.390439	−	0.537394i	0.958312	+	0.285722i	$0.0922335\pi$
$648$		0			0
$649$	215616.	+	70057.9i	0.511908	+	0.166329i
$650$		0			0
$651$	−17388.8	−	29917.2i	−0.0410307	−	0.0705925i
$652$		0			0
$653$	−111293.	+	342525.i	−0.261001	+	0.803278i	0.731587	+	0.681748i	$0.238780\pi$
$653$	−111293.	+	342525.i	−0.261001	+	0.803278i	−0.992588	+	0.121530i	$0.961220\pi$
$654$		0			0
$655$	284569.	+	206751.i	0.663292	+	0.481910i
$656$		0			0
$657$	553198.	−	319389.i	1.28159	−	0.739928i
$658$		0			0
$659$	−339977.	+	247008.i	−0.782851	+	0.568775i	−0.905833	−	0.423634i	$-0.860754\pi$
$659$	−339977.	+	247008.i	−0.782851	+	0.568775i	0.122982	+	0.992409i	$0.460754\pi$
$660$		0			0
$661$	230258.	+	255727.i	0.527002	+	0.585294i	0.946598	−	0.322416i	$-0.104495\pi$
$661$	230258.	+	255727.i	0.527002	+	0.585294i	−0.419596	+	0.907711i	$0.637828\pi$
$662$		0			0
$663$	94445.9	+	444333.i	0.214860	+	1.01084i
$664$		0			0
$665$	1162.46	+	517.559i	0.00262865	+	0.00117035i
$666$		0			0
$667$	−223640.	−	688292.i	−0.502686	−	1.54711i
$668$		0			0
$669$	317523.	+	67491.6i	0.709452	+	0.150799i
$670$		0			0
$671$	207413.	−	92346.4i	0.460672	−	0.205104i
$672$		0			0
$673$	−460551.	+	48405.8i	−1.01683	+	0.106873i	−0.598251	−	0.801309i	$-0.704138\pi$
$673$	−460551.	+	48405.8i	−1.01683	+	0.106873i	−0.418577	+	0.908182i	$0.637471\pi$
$674$		0			0
$675$	140844.	+	14803.3i	0.309123	+	0.0324902i
$676$		0			0
$677$	−83406.9	−	48155.0i	−0.181980	−	0.105066i	0.406242	−	0.913765i	$-0.366839\pi$
$677$	−83406.9	−	48155.0i	−0.181980	−	0.105066i	−0.588223	+	0.808699i	$0.700172\pi$
$678$		0			0
$679$	−7998.72	+	8883.48i	−0.0173493	+	0.0192683i
$680$		0			0
$681$			223247.i			0.481384i
$682$		0			0
$683$	246359.			0.528114			0.264057	−	0.964507i	$-0.414939\pi$
$683$	246359.			0.528114			0.264057	+	0.964507i	$0.414939\pi$
$684$		0			0
$685$	−70152.7	−	63165.8i	−0.149508	−	0.134617i
$686$		0			0
$687$	−156854.	+	271679.i	−0.332340	+	0.575629i
$688$		0			0
$689$	3629.72	−	34534.5i	0.00764601	−	0.0727469i
$690$		0			0
$691$	−90216.3	−	858351.i	−0.188942	−	1.79767i	−0.520116	−	0.854096i	$-0.674111\pi$
$691$	−90216.3	−	858351.i	−0.188942	−	1.79767i	0.331174	−	0.943570i	$-0.392555\pi$
$692$		0			0
$693$	26252.3	+	58963.7i	0.0546640	+	0.122777i
$694$		0			0
$695$	1788.49	−	8414.19i	0.00370269	−	0.0174198i
$696$		0			0
$697$	−1.56268e6	+	507746.i	−3.21666	+	1.04515i
$698$		0			0
$699$	−87681.4	+	196936.i	−0.179454	+	0.403060i
$700$		0			0
$701$	−162527.	+	34546.1i	−0.330741	+	0.0703012i	−0.370289	−	0.928916i	$-0.620741\pi$
$701$	−162527.	+	34546.1i	−0.330741	+	0.0703012i	0.0395482	+	0.999218i	$0.487408\pi$
$702$		0			0
$703$	299.688	−	269.841i	0.000606400	−	0.000546005i
$704$		0			0
$705$	200577.	+	276070.i	0.403555	+	0.555445i
$706$		0			0
$707$	−66081.3	−	114456.i	−0.132202	−	0.228981i
$708$		0			0
$709$	−163615.	+	225197.i	−0.325485	+	0.447992i	−0.940132	−	0.340811i	$-0.889299\pi$
$709$	−163615.	+	225197.i	−0.325485	+	0.447992i	0.614647	+	0.788802i	$0.289299\pi$
$710$		0			0
$711$	94450.2	+	30688.7i	0.186837	+	0.0607071i
$712$		0			0
$713$	−484191.	+	217265.i	−0.952441	+	0.427376i
$714$		0			0
$715$	159642.	−	491329.i	0.312274	−	0.961081i
$716$		0			0
$717$	113479.	+	82447.4i	0.220738	+	0.160376i
$718$		0			0
$719$	−519200.	+	299760.i	−1.00433	+	0.579850i	−0.909527	−	0.415646i	$-0.863556\pi$
$719$	−519200.	+	299760.i	−1.00433	+	0.579850i	−0.0948036	+	0.995496i	$0.530222\pi$
$720$		0			0
$721$	13640.0	−	9910.05i	0.0262388	−	0.0190636i
$722$		0			0
$723$	−281824.	−	312997.i	−0.539140	−	0.598776i
$724$		0			0
$725$	60726.1	+	285694.i	0.115531	+	0.543532i
$726$		0			0
$727$	−51889.4	−	23102.7i	−0.0981771	−	0.0437113i	0.357060	−	0.934081i	$-0.383779\pi$
$727$	−51889.4	−	23102.7i	−0.0981771	−	0.0437113i	−0.455238	+	0.890370i	$0.650446\pi$
$728$		0			0
$729$	−31736.9	−	97676.3i	−0.0597186	−	0.183795i
$730$		0			0
$731$	−637935.	−	135597.i	−1.19383	−	0.253756i
$732$		0			0
$733$	727986.	−	324120.i	1.35492	−	0.603251i	0.404595	−	0.914496i	$-0.367413\pi$
$733$	727986.	−	324120.i	1.35492	−	0.603251i	0.950330	+	0.311245i	$0.100746\pi$
$734$		0			0
$735$	208546.	−	21919.1i	0.386036	−	0.0405741i
$736$		0			0
$737$	916732.	+	96352.4i	1.68775	+	0.177389i
$738$		0			0
$739$	876155.	+	505848.i	1.60432	+	0.926257i	0.990609	+	0.136729i	$0.0436589\pi$
$739$	876155.	+	505848.i	1.60432	+	0.926257i	0.613715	+	0.789528i	$0.289674\pi$
$740$		0			0
$741$	4624.62	−	5136.16i	0.00842248	−	0.00935411i
$742$		0			0
$743$			69208.2i			0.125366i	0.998033	+	0.0626831i	$0.0199657\pi$
$743$			69208.2i			0.125366i	−0.998033	+	0.0626831i	$0.980034\pi$
$744$		0			0
$745$	261293.			0.470777
$746$		0			0
$747$	571115.	+	514234.i	1.02349	+	0.921551i
$748$		0			0
$749$	6161.51	−	10672.1i	0.0109831	−	0.0190232i
$750$		0			0
$751$	71199.0	−	677414.i	0.126239	−	1.20109i	−0.729611	−	0.683862i	$-0.760299\pi$
$751$	71199.0	−	677414.i	0.126239	−	1.20109i	0.855850	−	0.517224i	$-0.173034\pi$
$752$		0			0
$753$	−26550.4	−	252610.i	−0.0468253	−	0.445513i
$754$		0			0
$755$	8422.19	+	18916.5i	0.0147751	+	0.0331855i
$756$		0			0
$757$	140757.	−	662212.i	0.245629	−	1.15559i	−0.666440	−	0.745558i	$-0.732183\pi$
$757$	140757.	−	662212.i	0.245629	−	1.15559i	0.912070	−	0.410036i	$-0.134484\pi$
$758$		0			0
$759$	−309361.	+	100518.i	−0.537010	+	0.174485i
$760$		0			0
$761$	−213272.	+	479018.i	−0.368269	+	0.827146i	0.630434	+	0.776243i	$0.282877\pi$
$761$	−213272.	+	479018.i	−0.368269	+	0.827146i	−0.998704	+	0.0509036i	$0.983790\pi$
$762$		0			0
$763$	−86601.1	+	18407.6i	−0.148756	+	0.0316191i
$764$		0			0
$765$	−471012.	+	424101.i	−0.804839	+	0.724680i
$766$		0			0
$767$	−198234.	−	272846.i	−0.336967	−	0.463796i
$768$		0			0
$769$	−376436.	−	652006.i	−0.636559	−	1.10255i	−0.986183	−	0.165662i	$-0.947024\pi$
$769$	−376436.	−	652006.i	−0.636559	−	1.10255i	0.349624	−	0.936890i	$-0.386309\pi$
$770$		0			0
$771$	29612.5	−	40758.2i	0.0498158	−	0.0685655i
$772$		0			0
$773$	611476.	+	198681.i	1.02334	+	0.332504i	0.772154	−	0.635435i	$-0.219179\pi$
$773$	611476.	+	198681.i	1.02334	+	0.332504i	0.251187	+	0.967939i	$0.419179\pi$
$774$		0			0
$775$	203505.	−	66777.5i	0.338822	−	0.111180i
$776$		0			0
$777$	−568.889	+	1750.86i	−0.000942293	+	0.00290008i
$778$		0			0
$779$	20224.7	+	14694.1i	0.0333279	+	0.0242141i
$780$		0			0
$781$	−266585.	+	153913.i	−0.437053	+	0.252332i
$782$		0			0
$783$	673695.	−	489468.i	1.09885	−	0.798364i
$784$		0			0
$785$	−406751.	−	451743.i	−0.660069	−	0.733081i
$786$		0			0
$787$	5517.19	+	25956.3i	0.00890775	+	0.0419077i	0.982377	−	0.186910i	$-0.0598473\pi$
$787$	5517.19	+	25956.3i	0.00890775	+	0.0419077i	−0.973469	+	0.228818i	$0.926514\pi$
$788$		0			0
$789$	119034.	+	52997.4i	0.191213	+	0.0851335i
$790$		0			0
$791$	−30291.9	−	93229.0i	−0.0484143	−	0.149004i
$792$		0			0
$793$	−330366.	−	70221.5i	−0.525351	−	0.111667i
$794$		0			0
$795$	−14544.5	+	6475.62i	−0.0230125	+	0.0102458i
$796$		0			0
$797$	−736535.	+	77413.0i	−1.15952	+	0.121870i	−0.664688	−	0.747121i	$-0.731436\pi$
$797$	−736535.	+	77413.0i	−1.15952	+	0.121870i	−0.494828	+	0.868991i	$0.664769\pi$
$798$		0			0
$799$	1.96020e6	+	206025.i	3.07049	+	0.322721i
$800$		0			0
$801$	−100230.	−	57867.8i	−0.156219	−	0.0901928i
$802$		0			0
$803$	922618.	−	1.02467e6i	1.43084	−	1.58911i
$804$		0			0
$805$			89089.2i			0.137478i
$806$		0			0
$807$	87156.2			0.133829
$808$		0			0
$809$	−227697.	−	205020.i	−0.347905	−	0.313255i	0.476588	−	0.879127i	$-0.341873\pi$
$809$	−227697.	−	205020.i	−0.347905	−	0.313255i	−0.824494	+	0.565871i	$0.808540\pi$
$810$		0			0
$811$	−298648.	+	517273.i	−0.454064	+	0.786463i	−0.998634	−	0.0522532i	$-0.983360\pi$
$811$	−298648.	+	517273.i	−0.454064	+	0.786463i	0.544569	+	0.838716i	$0.316693\pi$
$812$		0			0
$813$	27443.8	−	261111.i	0.0415206	−	0.395042i
$814$		0			0
$815$	−45872.0	−	436443.i	−0.0690609	−	0.657071i
$816$		0			0
$817$	4035.95	+	9064.90i	0.00604647	+	0.0135806i
$818$		0			0
$819$	19962.6	−	93916.9i	0.0297612	−	0.140015i
$820$		0			0
$821$	−579704.	+	188357.i	−0.860043	+	0.279445i	−0.705646	−	0.708564i	$-0.749343\pi$
$821$	−579704.	+	188357.i	−0.860043	+	0.279445i	−0.154396	+	0.988009i	$0.549343\pi$
$822$		0			0
$823$	−320878.	+	720704.i	−0.473740	+	1.06404i	0.505775	+	0.862666i	$0.331207\pi$
$823$	−320878.	+	720704.i	−0.473740	+	1.06404i	−0.979515	+	0.201372i	$0.935460\pi$
$824$		0			0
$825$	128409.	−	27294.1i	0.188663	−	0.0401015i
$826$		0			0
$827$	−166289.	+	149727.i	−0.243138	+	0.218922i	−0.781685	−	0.623673i	$-0.785640\pi$
$827$	−166289.	+	149727.i	−0.243138	+	0.218922i	0.538548	+	0.842595i	$0.318973\pi$
$828$		0			0
$829$	−502939.	−	692236.i	−0.731823	−	1.00727i	−0.999048	−	0.0436338i	$-0.986107\pi$
$829$	−502939.	−	692236.i	−0.731823	−	1.00727i	0.267225	−	0.963634i	$-0.413893\pi$
$830$		0			0
$831$	163160.	+	282601.i	0.236271	+	0.409233i
$832$		0			0
$833$	711921.	−	979875.i	1.02599	−	1.41215i
$834$		0			0
$835$	679585.	+	220810.i	0.974699	+	0.316699i
$836$		0			0
$837$	−409920.	−	452609.i	−0.585125	−	0.646060i
$838$		0			0
$839$	287653.	−	885304.i	0.408643	−	1.25768i	−0.509171	−	0.860665i	$-0.670048\pi$
$839$	287653.	−	885304.i	0.408643	−	1.25768i	0.917814	−	0.397010i	$-0.129952\pi$
$840$		0			0
$841$	817222.	+	593747.i	1.15544	+	0.839478i
$842$		0			0
$843$	278185.	−	160610.i	0.391452	−	0.226005i
$844$		0			0
$845$	−158385.	+	115074.i	−0.221820	+	0.161162i
$846$		0			0
$847$	14410.7	+	16004.7i	0.0200872	+	0.0223091i
$848$		0			0
$849$	70277.1	+	330628.i	0.0974987	+	0.458695i
$850$		0			0
$851$	25793.2	+	11483.9i	0.0356161	+	0.0158573i
$852$		0			0
$853$	−372125.	−	1.14528e6i	−0.511435	−	1.57404i	−0.789676	−	0.613524i	$-0.789751\pi$
$853$	−372125.	−	1.14528e6i	−0.511435	−	1.57404i	0.278241	−	0.960511i	$-0.410249\pi$
$854$		0			0
$855$	9432.43	+	2004.93i	0.0129030	+	0.00274262i
$856$		0			0
$857$	−546024.	+	243106.i	−0.743448	+	0.331004i	−0.743266	−	0.668996i	$-0.766724\pi$
$857$	−546024.	+	243106.i	−0.743448	+	0.331004i	−0.000181368		1.00000i	$0.500058\pi$
$858$		0			0
$859$	−1.14658e6	+	120511.i	−1.55388	+	0.163320i	−0.842195	−	0.539174i	$-0.818737\pi$
$859$	−1.14658e6	+	120511.i	−1.55388	+	0.163320i	−0.711690	+	0.702494i	$0.752070\pi$
$860$		0			0
$861$	−113498.	−	11929.1i	−0.153102	−	0.0160917i
$862$		0			0
$863$	−887679.	−	512502.i	−1.19188	−	0.688135i	−0.233151	−	0.972441i	$-0.574904\pi$
$863$	−887679.	−	512502.i	−1.19188	−	0.688135i	−0.958734	+	0.284306i	$0.908237\pi$
$864$		0			0
$865$	−71021.1	+	78876.9i	−0.0949194	+	0.105419i
$866$		0			0
$867$		−	829145.i		−	1.10304i
$868$		0			0
$869$	214367.			0.283869
$870$		0			0
$871$	−1.01903e6	−	917537.i	−1.34323	−	1.20945i
$872$		0			0
$873$	−45295.3	+	78453.7i	−0.0594325	+	0.102940i
$874$		0			0
$875$	14297.6	−	136032.i	0.0186744	−	0.177675i
$876$		0			0
$877$	105413.	+	1.00294e6i	0.137055	+	1.30400i	0.819509	+	0.573066i	$0.194246\pi$
$877$	105413.	+	1.00294e6i	0.137055	+	1.30400i	−0.682454	+	0.730929i	$0.739087\pi$
$878$		0			0
$879$	62107.8	+	139496.i	0.0803838	+	0.180545i
$880$		0			0
$881$	−163687.	+	770088.i	−0.210894	+	0.992176i	0.737565	+	0.675276i	$0.235975\pi$
$881$	−163687.	+	770088.i	−0.210894	+	0.992176i	−0.948459	+	0.316900i	$0.897358\pi$
$882$		0			0
$883$	893373.	−	290274.i	1.14581	−	0.372295i	0.326244	−	0.945286i	$-0.394217\pi$
$883$	893373.	−	290274.i	1.14581	−	0.372295i	0.819562	+	0.572991i	$0.194217\pi$
$884$		0			0
$885$	−62893.0	+	141260.i	−0.0803000	+	0.180357i
$886$		0			0
$887$	12849.4	−	2731.23i	0.0163319	−	0.00347145i	−0.199739	−	0.979849i	$-0.564009\pi$
$887$	12849.4	−	2731.23i	0.0163319	−	0.00347145i	0.216070	+	0.976378i	$0.430676\pi$
$888$		0			0
$889$	−153662.	+	138358.i	−0.194430	+	0.175066i
$890$		0			0
$891$	161984.	+	222952.i	0.204041	+	0.280838i
$892$		0			0
$893$	−14994.0	−	25970.4i	−0.0188024	−	0.0325668i
$894$		0			0
$895$	501727.	−	690567.i	0.626356	−	0.862105i
$896$		0			0
$897$	460204.	+	149529.i	0.571960	+	0.185841i
$898$		0			0
$899$	626524.	−	1.09249e6i	0.775209	−	1.35176i
$900$		0			0
$901$	−28416.8	+	87457.8i	−0.0350046	+	0.107733i
$902$		0			0
$903$	−36647.1	−	26625.7i	−0.0449432	−	0.0326531i
$904$		0			0
$905$	554098.	−	319908.i	0.676533	−	0.390597i
$906$		0			0
$907$	−983278.	+	714393.i	−1.19526	+	0.868406i	−0.993810	−	0.111094i	$-0.964565\pi$
$907$	−983278.	+	714393.i	−1.19526	+	0.868406i	−0.201448	+	0.979499i	$0.564565\pi$
$908$		0			0
$909$	−670181.	−	744312.i	−0.811082	−	0.900797i
$910$		0			0
$911$	166493.	+	783288.i	0.200613	+	0.943810i	0.957090	+	0.289790i	$0.0935854\pi$
$911$	166493.	+	783288.i	0.200613	+	0.943810i	−0.756477	+	0.654020i	$0.773081\pi$
$912$		0			0
$913$	1.51545e6	+	674720.i	1.81802	+	0.809436i
$914$		0			0
$915$	47852.3	+	147274.i	0.0571558	+	0.175908i
$916$		0			0
$917$	138028.	+	29338.8i	0.164146	+	0.0348903i
$918$		0			0
$919$	849316.	−	378140.i	1.00563	−	0.447735i	0.163230	−	0.986588i	$-0.447809\pi$
$919$	849316.	−	378140.i	1.00563	−	0.447735i	0.842400	+	0.538853i	$0.181142\pi$
$920$		0			0
$921$	381137.	−	40059.2i	0.449327	−	0.0472262i
$922$		0			0
$923$	455412.	+	47865.7i	0.534566	+	0.0561851i
$924$		0			0
$925$	−9868.16	−	5697.39i	−0.0115333	−	0.00665874i
$926$		0			0
$927$	85495.1	−	94951.9i	0.0994905	−	0.110495i
$928$		0			0
$929$			813379.i			0.942457i	0.882011	+	0.471228i	$0.156189\pi$
$929$			813379.i			0.942457i	−0.882011	+	0.471228i	$0.843811\pi$
$930$		0			0
$931$	−18427.8			−0.0212606
$932$		0			0
$933$	314850.	+	283493.i	0.361694	+	0.325670i
$934$		0			0
$935$	−684052.	+	1.18481e6i	−0.782467	+	1.35527i
$936$		0			0
$937$	43140.0	−	410450.i	0.0491361	−	0.467499i	−0.942094	−	0.335350i	$-0.891145\pi$
$937$	43140.0	−	410450.i	0.0491361	−	0.467499i	0.991230	−	0.132149i	$-0.0421878\pi$
$938$		0			0
$939$	−11295.4	−	107468.i	−0.0128106	−	0.121885i
$940$		0			0
$941$	−188088.	−	422453.i	−0.212413	−	0.477088i	0.775645	−	0.631170i	$-0.217425\pi$
$941$	−188088.	−	422453.i	−0.212413	−	0.477088i	−0.988058	+	0.154081i	$0.950758\pi$
$942$		0			0
$943$	−363900.	+	1.71202e6i	−0.409222	+	1.92524i
$944$		0			0
$945$	−97492.3	+	31677.2i	−0.109171	+	0.0354718i
$946$		0			0
$947$	−655986.	+	1.47337e6i	−0.731466	+	1.64290i	0.0339976	+	0.999422i	$0.489176\pi$
$947$	−655986.	+	1.47337e6i	−0.731466	+	1.64290i	−0.765464	+	0.643479i	$0.777491\pi$
$948$		0			0
$949$	−2.00632e6	+	426456.i	−2.22776	+	0.473524i
$950$		0			0
$951$	129266.	−	116391.i	0.142930	−	0.128694i
$952$		0			0
$953$	285233.	+	392589.i	0.314061	+	0.432268i	0.936642	−	0.350287i	$-0.113916\pi$
$953$	285233.	+	392589.i	0.314061	+	0.432268i	−0.622581	+	0.782555i	$0.713916\pi$
$954$		0			0
$955$	−323385.	−	560120.i	−0.354579	−	0.614150i
$956$		0			0
$957$	453721.	−	624494.i	0.495410	−	0.681874i
$958$		0			0
$959$	−36017.4	−	11702.7i	−0.0391629	−	0.0127248i
$960$		0			0
$961$	−845848.	−	370718.i	−0.915895	−	0.401418i
$962$		0			0
$963$	28858.4	−	88817.2i	0.0311186	−	0.0957733i
$964$		0			0
$965$	562387.	+	408598.i	0.603922	+	0.438775i
$966$		0			0
$967$	263286.	−	152008.i	0.281563	−	0.162560i	−0.352568	−	0.935786i	$-0.614691\pi$
$967$	263286.	−	152008.i	0.281563	−	0.162560i	0.634131	+	0.773226i	$0.281358\pi$
$968$		0			0
$969$	−14807.3	+	10758.1i	−0.0157699	+	0.0114575i
$970$		0			0
$971$	−598003.	−	664150.i	−0.634257	−	0.704413i	0.337253	−	0.941414i	$-0.390502\pi$
$971$	−598003.	−	664150.i	−0.634257	−	0.704413i	−0.971509	+	0.237001i	$0.923836\pi$
$972$		0			0
$973$	−717.499	−	3375.57i	−0.000757872	−	0.00356551i
$974$		0			0
$975$	−178404.	−	79430.6i	−0.187670	−	0.0835562i
$976$		0			0
$977$	140181.	+	431433.i	0.146859	+	0.451985i	0.997245	−	0.0741735i	$-0.0236319\pi$
$977$	140181.	+	431433.i	0.146859	+	0.451985i	−0.850387	+	0.526158i	$0.823632\pi$
$978$		0			0
$979$	−244361.	−	51940.6i	−0.254957	−	0.0541928i
$980$		0			0
$981$	−612946.	+	272901.i	−0.636919	+	0.283575i
$982$		0			0
$983$	−259957.	+	27322.6i	−0.269027	+	0.0282758i	−0.238081	−	0.971245i	$-0.576518\pi$
$983$	−259957.	+	27322.6i	−0.269027	+	0.0282758i	−0.0309453	+	0.999521i	$0.509852\pi$
$984$		0			0
$985$	276782.	+	29091.0i	0.285276	+	0.0299837i
$986$		0			0
$987$	118557.	+	68448.9i	0.121701	+	0.0702639i
$988$		0			0
$989$	−464860.	+	516280.i	−0.475259	+	0.527828i
$990$		0			0
$991$			940795.i			0.957960i	0.877826	+	0.478980i	$0.158993\pi$
$991$			940795.i			0.957960i	−0.877826	+	0.478980i	$0.841007\pi$
$992$		0			0
$993$	61587.0			0.0624584
$994$		0			0
$995$	965639.	+	869466.i	0.975369	+	0.878226i
$996$		0			0
$997$	−434619.	+	752782.i	−0.437238	+	0.757319i	−0.997475	−	0.0710133i	$-0.977377\pi$
$997$	−434619.	+	752782.i	−0.437238	+	0.757319i	0.560237	+	0.828332i	$0.310710\pi$
$998$		0			0
$999$	−3395.85	+	32309.4i	−0.00340266	+	0.0323741i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	124.5.o.a.17.7	✓	88
31.11	odd	30	inner	124.5.o.a.73.7	yes	88

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
124.5.o.a.17.7	✓	88	1.1	even	1	trivial
124.5.o.a.73.7	yes	88	31.11	odd	30	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:	\( N \)	\(=\)	\( 124 = 2^{2} \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	124.o (of order \(30\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(3.32625 + 2.99497i) q^{3} +(10.0265 - 17.3665i) q^{5} +(0.840912 - 8.00074i) q^{7} +(-6.37270 - 60.6322i) q^{9} +O(q^{10})\)	\(q+(3.32625 + 2.99497i) q^{3} +(10.0265 - 17.3665i) q^{5} +(0.840912 - 8.00074i) q^{7} +(-6.37270 - 60.6322i) q^{9} +(-53.5258 - 120.221i) q^{11} +(-40.7018 + 191.487i) q^{13} +(85.3630 - 27.7361i) q^{15} +(210.863 - 473.607i) q^{17} +(-7.71531 + 1.63994i) q^{19} +(26.7591 - 24.0940i) q^{21} +(-324.598 - 446.771i) q^{23} +(111.437 + 193.014i) q^{25} +(373.496 - 514.073i) q^{27} +(1246.36 + 404.968i) q^{29} +(197.070 - 940.577i) q^{31} +(182.018 - 560.193i) q^{33} +(-130.513 - 94.8235i) q^{35} +(-44.2770 + 25.5633i) q^{37} +(-708.882 + 515.033i) q^{39} +(-2120.74 - 2355.32i) q^{41} +(-261.555 - 1230.52i) q^{43} +(-1116.86 - 497.260i) q^{45} +(1174.85 + 3615.80i) q^{47} +(2285.23 + 485.740i) q^{49} +(2119.82 - 943.807i) q^{51} +(-176.408 + 18.5412i) q^{53} +(-2624.49 - 275.845i) q^{55} +(-30.5747 - 17.6523i) q^{57} +(-1152.75 + 1280.26i) q^{59} +1725.27i q^{61} -490.461 q^{63} +(2917.36 + 2626.80i) q^{65} +(-3502.26 + 6066.09i) q^{67} +(258.371 - 2458.24i) q^{69} +(-244.506 - 2326.32i) q^{71} +(4261.62 + 9571.75i) q^{73} +(-207.405 + 975.763i) q^{75} +(-1006.87 + 327.151i) q^{77} +(-662.553 + 1488.12i) q^{79} +(-2048.37 + 435.395i) q^{81} +(-9367.73 + 8434.74i) q^{83} +(-6110.66 - 8410.60i) q^{85} +(2932.86 + 5079.85i) q^{87} +(1115.83 - 1535.80i) q^{89} +(1497.81 + 486.668i) q^{91} +(3472.51 - 2538.38i) q^{93} +(-48.8779 + 150.431i) q^{95} +(-1202.13 - 873.399i) q^{97} +(-6948.15 + 4011.52i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 88 q - 9 q^{3} + 3 q^{5} - 215 q^{7} - 254 q^{9}+O(q^{10}) \) 88 * q - 9 * q^3 + 3 * q^5 - 215 * q^7 - 254 * q^9	\( 88 q - 9 q^{3} + 3 q^{5} - 215 q^{7} - 254 q^{9} - 42 q^{11} + 6 q^{13} + 665 q^{15} - 585 q^{17} - 153 q^{19} - 402 q^{21} - 1365 q^{23} - 5933 q^{25} - 9225 q^{27} - 1140 q^{29} + 117 q^{31} + 5151 q^{33} + 2898 q^{35} + 6594 q^{37} + 3173 q^{39} - 9393 q^{41} - 5322 q^{43} + 2010 q^{45} - 5112 q^{47} - 5210 q^{49} - 1829 q^{51} + 7395 q^{53} + 10585 q^{55} + 40485 q^{57} + 5625 q^{59} - 14954 q^{63} - 17094 q^{65} + 8909 q^{67} - 35370 q^{69} - 11811 q^{71} - 22105 q^{73} + 79377 q^{75} + 71490 q^{77} + 219 q^{79} - 5422 q^{81} + 10545 q^{83} - 53630 q^{85} + 13732 q^{87} - 40305 q^{89} + 42760 q^{91} - 1028 q^{93} + 62319 q^{95} + 35201 q^{97} + 16197 q^{99}+O(q^{100}) \) 88 * q - 9 * q^3 + 3 * q^5 - 215 * q^7 - 254 * q^9 - 42 * q^11 + 6 * q^13 + 665 * q^15 - 585 * q^17 - 153 * q^19 - 402 * q^21 - 1365 * q^23 - 5933 * q^25 - 9225 * q^27 - 1140 * q^29 + 117 * q^31 + 5151 * q^33 + 2898 * q^35 + 6594 * q^37 + 3173 * q^39 - 9393 * q^41 - 5322 * q^43 + 2010 * q^45 - 5112 * q^47 - 5210 * q^49 - 1829 * q^51 + 7395 * q^53 + 10585 * q^55 + 40485 * q^57 + 5625 * q^59 - 14954 * q^63 - 17094 * q^65 + 8909 * q^67 - 35370 * q^69 - 11811 * q^71 - 22105 * q^73 + 79377 * q^75 + 71490 * q^77 + 219 * q^79 - 5422 * q^81 + 10545 * q^83 - 53630 * q^85 + 13732 * q^87 - 40305 * q^89 + 42760 * q^91 - 1028 * q^93 + 62319 * q^95 + 35201 * q^97 + 16197 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more