LMFDB - Embedded newform 124.5.o.a.13.4

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			13.4
Character	$\chi$	$=$	124.13
Dual form			124.5.o.a.105.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-3.55268 - 7.97945i) q^{3} +(-12.5017 - 21.6535i) q^{5} +(17.4290 + 19.3568i) q^{7} +(3.14955 - 3.49793i) q^{9} +O(q^{10})$	\(q+(-3.55268 - 7.97945i) q^{3} +(-12.5017 - 21.6535i) q^{5} +(17.4290 + 19.3568i) q^{7} +(3.14955 - 3.49793i) q^{9} +(-41.1889 - 193.779i) q^{11} +(-116.787 - 12.2748i) q^{13} +(-128.369 + 176.684i) q^{15} +(-103.675 + 487.755i) q^{17} +(39.4065 + 374.928i) q^{19} +(92.5373 - 207.842i) q^{21} +(-651.023 + 211.530i) q^{23} +(-0.0834765 + 0.144586i) q^{25} +(-711.975 - 231.335i) q^{27} +(-338.570 - 466.002i) q^{29} +(573.385 + 771.201i) q^{31} +(-1399.92 + 1017.10i) q^{33} +(201.253 - 619.392i) q^{35} +(942.801 + 544.326i) q^{37} +(316.961 + 975.505i) q^{39} +(-2741.04 - 1220.39i) q^{41} +(-528.783 + 55.5773i) q^{43} +(-115.117 - 24.4689i) q^{45} +(1346.10 + 977.997i) q^{47} +(180.055 - 1713.11i) q^{49} +(4260.34 - 905.563i) q^{51} +(-3637.75 - 3275.45i) q^{53} +(-3681.06 + 3314.44i) q^{55} +(2851.72 - 1646.44i) q^{57} +(5502.99 - 2450.09i) q^{59} -1493.50i q^{61} +122.602 q^{63} +(1194.24 + 2682.31i) q^{65} +(1079.60 + 1869.93i) q^{67} +(4000.77 + 4443.30i) q^{69} +(908.888 - 1009.42i) q^{71} +(-1437.83 - 6764.45i) q^{73} +(1.45028 + 0.152430i) q^{75} +(3033.06 - 4174.65i) q^{77} +(-1044.53 + 4914.12i) q^{79} +(643.643 + 6123.85i) q^{81} +(-1715.26 + 3852.54i) q^{83} +(11857.7 - 3852.81i) q^{85} +(-2515.61 + 4357.16i) q^{87} +(-2696.12 - 876.021i) q^{89} +(-1797.88 - 2474.57i) q^{91} +(4116.70 - 7315.12i) q^{93} +(7625.87 - 5540.52i) q^{95} +(1587.10 - 4884.60i) q^{97} +(-807.550 - 466.239i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/124\mathbb{Z}\right)^\times$.

$n$	$63$	$65$
$\chi(n)$	$1$	$e\left(\frac{11}{30}\right)$

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
$3$	−3.55268	−	7.97945i	−0.394742	−	0.886605i	−0.996150	−	0.0876631i	$-0.972060\pi$
$3$	−3.55268	−	7.97945i	−0.394742	−	0.886605i	0.601408	−	0.798942i	$-0.294607\pi$
$4$		0			0
$5$	−12.5017	−	21.6535i	−0.500067	−	0.866141i	−1.00000		7.71089e-5i	$-0.999975\pi$
$5$	−12.5017	−	21.6535i	−0.500067	−	0.866141i	0.499933	−	0.866064i	$-0.333358\pi$
$6$		0			0
$7$	17.4290	+	19.3568i	0.355694	+	0.395038i	0.894262	−	0.447544i	$-0.147701\pi$
$7$	17.4290	+	19.3568i	0.355694	+	0.395038i	−0.538568	+	0.842582i	$0.681035\pi$
$8$		0			0
$9$	3.14955	−	3.49793i	0.0388833	−	0.0431843i
$10$		0			0
$11$	−41.1889	−	193.779i	−0.340404	−	1.60148i	−0.731977	−	0.681329i	$-0.761402\pi$
$11$	−41.1889	−	193.779i	−0.340404	−	1.60148i	0.391573	−	0.920147i	$-0.371931\pi$
$12$		0			0
$13$	−116.787	−	12.2748i	−0.691048	−	0.0726320i	−0.247507	−	0.968886i	$-0.579611\pi$
$13$	−116.787	−	12.2748i	−0.691048	−	0.0726320i	−0.443541	+	0.896254i	$0.646278\pi$
$14$		0			0
$15$	−128.369	+	176.684i	−0.570528	+	0.785264i
$16$		0			0
$17$	−103.675	+	487.755i	−0.358739	+	1.68773i	0.315265	+	0.949004i	$0.397907\pi$
$17$	−103.675	+	487.755i	−0.358739	+	1.68773i	−0.674003	+	0.738728i	$0.735427\pi$
$18$		0			0
$19$	39.4065	+	374.928i	0.109159	+	1.03858i	0.902760	+	0.430144i	$0.141537\pi$
$19$	39.4065	+	374.928i	0.109159	+	1.03858i	−0.793601	+	0.608438i	$0.791796\pi$
$20$		0			0
$21$	92.5373	−	207.842i	0.209835	−	0.471298i
$22$		0			0
$23$	−651.023	+	211.530i	−1.23067	+	0.399868i	−0.850956	−	0.525237i	$-0.823977\pi$
$23$	−651.023	+	211.530i	−1.23067	+	0.399868i	−0.379711	+	0.925105i	$0.623977\pi$
$24$		0			0
$25$	−0.0834765	+	0.144586i	−0.000133562	+	0.000231337i
$26$		0			0
$27$	−711.975	−	231.335i	−0.976646	−	0.317332i
$28$		0			0
$29$	−338.570	−	466.002i	−0.402581	−	0.554105i	0.558809	−	0.829297i	$-0.311259\pi$
$29$	−338.570	−	466.002i	−0.402581	−	0.554105i	−0.961389	+	0.275192i	$0.911259\pi$
$30$		0			0
$31$	573.385	+	771.201i	0.596655	+	0.802498i
$31$	573.385	+	771.201i	0.596655	+	0.802498i
$32$		0			0
$33$	−1399.92	+	1017.10i	−1.28551	+	0.933974i
$34$		0			0
$35$	201.253	−	619.392i	0.164288	−	0.505626i
$36$		0			0
$37$	942.801	+	544.326i	0.688679	+	0.397609i	0.803117	−	0.595822i	$-0.203173\pi$
$37$	942.801	+	544.326i	0.688679	+	0.397609i	−0.114438	+	0.993430i	$0.536507\pi$
$38$		0			0
$39$	316.961	+	975.505i	0.208390	+	0.641357i
$40$		0			0
$41$	−2741.04	−	1220.39i	−1.63060	−	0.725991i	−0.631811	−	0.775122i	$-0.717688\pi$
$41$	−2741.04	−	1220.39i	−1.63060	−	0.725991i	−0.998792	+	0.0491309i	$0.984355\pi$
$42$		0			0
$43$	−528.783	+	55.5773i	−0.285983	+	0.0300580i	−0.246434	−	0.969160i	$-0.579259\pi$
$43$	−528.783	+	55.5773i	−0.285983	+	0.0300580i	−0.0395492	+	0.999218i	$0.512592\pi$
$44$		0			0
$45$	−115.117	−	24.4689i	−0.0568479	−	0.0120834i
$46$		0			0
$47$	1346.10	+	977.997i	0.609369	+	0.442733i	0.849192	−	0.528084i	$-0.177089\pi$
$47$	1346.10	+	977.997i	0.609369	+	0.442733i	−0.239823	+	0.970817i	$0.577089\pi$
$48$		0			0
$49$	180.055	−	1713.11i	0.0749916	−	0.713497i
$50$		0			0
$51$	4260.34	−	905.563i	1.63796	−	0.348159i
$52$		0			0
$53$	−3637.75	−	3275.45i	−1.29503	−	1.16605i	−0.975869	−	0.218355i	$-0.929931\pi$
$53$	−3637.75	−	3275.45i	−1.29503	−	1.16605i	−0.319165	−	0.947699i	$-0.603402\pi$
$54$		0			0
$55$	−3681.06	+	3314.44i	−1.21688	+	1.09568i
$56$		0			0
$57$	2851.72	−	1646.44i	0.877722	−	0.506753i
$58$		0			0
$59$	5502.99	−	2450.09i	1.58086	−	0.703846i	0.586508	−	0.809943i	$-0.300502\pi$
$59$	5502.99	−	2450.09i	1.58086	−	0.703846i	0.994356	+	0.106097i	$0.0338355\pi$
$60$		0			0
$61$		−	1493.50i		−	0.401372i	−0.979656	−	0.200686i	$-0.935683\pi$
$61$		−	1493.50i		−	0.401372i	0.979656	−	0.200686i	$-0.0643171\pi$
$62$		0			0
$63$	122.602			0.0308900
$64$		0			0
$65$	1194.24	+	2682.31i	0.282660	+	0.634866i
$66$		0			0
$67$	1079.60	+	1869.93i	0.240500	+	0.416558i	0.960857	−	0.277046i	$-0.0893553\pi$
$67$	1079.60	+	1869.93i	0.240500	+	0.416558i	−0.720357	+	0.693604i	$0.756022\pi$
$68$		0			0
$69$	4000.77	+	4443.30i	0.840321	+	0.933271i
$70$		0			0
$71$	908.888	−	1009.42i	0.180299	−	0.200242i	−0.646220	−	0.763151i	$-0.723651\pi$
$71$	908.888	−	1009.42i	0.180299	−	0.200242i	0.826519	+	0.562909i	$0.190318\pi$
$72$		0			0
$73$	−1437.83	−	6764.45i	−0.269812	−	1.26937i	−0.879184	−	0.476482i	$-0.841912\pi$
$73$	−1437.83	−	6764.45i	−0.269812	−	1.26937i	0.609372	−	0.792884i	$-0.291422\pi$
$74$		0			0
$75$	1.45028	+	0.152430i	0.000257827	+	2.70987e-5i
$76$		0			0
$77$	3033.06	−	4174.65i	0.511564	−	0.704107i
$78$		0			0
$79$	−1044.53	+	4914.12i	−0.167366	+	0.787393i	0.811736	+	0.584024i	$0.198523\pi$
$79$	−1044.53	+	4914.12i	−0.167366	+	0.787393i	−0.979102	+	0.203369i	$0.934811\pi$
$80$		0			0
$81$	643.643	+	6123.85i	0.0981013	+	0.933372i
$82$		0			0
$83$	−1715.26	+	3852.54i	−0.248986	+	0.559231i	−0.994194	−	0.107600i	$-0.965683\pi$
$83$	−1715.26	+	3852.54i	−0.248986	+	0.559231i	0.745208	+	0.666832i	$0.232350\pi$
$84$		0			0
$85$	11857.7	−	3852.81i	1.64121	−	0.533261i
$86$		0			0
$87$	−2515.61	+	4357.16i	−0.332356	+	0.575658i
$88$		0			0
$89$	−2696.12	−	876.021i	−0.340376	−	0.110595i	0.133841	−	0.991003i	$-0.457269\pi$
$89$	−2696.12	−	876.021i	−0.340376	−	0.110595i	−0.474217	+	0.880408i	$0.657269\pi$
$90$		0			0
$91$	−1797.88	−	2474.57i	−0.217109	−	0.298825i
$92$		0			0
$93$	4116.70	−	7315.12i	0.475974	−	0.845777i
$94$		0			0
$95$	7625.87	−	5540.52i	0.844972	−	0.613908i
$96$		0			0
$97$	1587.10	−	4884.60i	0.168679	−	0.519141i	−0.830609	−	0.556856i	$-0.812008\pi$
$97$	1587.10	−	4884.60i	0.168679	−	0.519141i	0.999289	+	0.0377143i	$0.0120077\pi$
$98$		0			0
$99$	−807.550	−	466.239i	−0.0823947	−	0.0475706i
$100$		0			0
$101$	−978.984	−	3013.00i	−0.0959694	−	0.295364i	0.891536	−	0.452950i	$-0.149629\pi$
$101$	−978.984	−	3013.00i	−0.0959694	−	0.295364i	−0.987505	+	0.157587i	$0.949629\pi$
$102$		0			0
$103$	−7774.56	−	3461.46i	−0.732827	−	0.326276i	0.00617318	−	0.999981i	$-0.498035\pi$
$103$	−7774.56	−	3461.46i	−0.732827	−	0.326276i	−0.739000	+	0.673705i	$0.764702\pi$
$104$		0			0
$105$	−5657.39	+	594.616i	−0.513142	+	0.0539334i
$106$		0			0
$107$	−14815.6	−	3149.16i	−1.29406	−	0.275060i	−0.491102	−	0.871102i	$-0.663406\pi$
$107$	−14815.6	−	3149.16i	−1.29406	−	0.275060i	−0.802953	+	0.596042i	$0.796739\pi$
$108$		0			0
$109$	−7080.39	−	5144.21i	−0.595942	−	0.432977i	0.248494	−	0.968633i	$-0.420064\pi$
$109$	−7080.39	−	5144.21i	−0.595942	−	0.432977i	−0.844436	+	0.535656i	$0.820064\pi$
$110$		0			0
$111$	993.954	−	9456.85i	0.0806716	−	0.767539i
$112$		0			0
$113$	20191.6	−	4291.87i	1.58130	−	0.336116i	0.668243	−	0.743943i	$-0.267047\pi$
$113$	20191.6	−	4291.87i	1.58130	−	0.336116i	0.913059	+	0.407827i	$0.133713\pi$
$114$		0			0
$115$	12719.3	+	11452.5i	0.961758	+	0.865971i
$116$		0			0
$117$	−410.763	+	369.853i	−0.0300068	+	0.0270182i
$118$		0			0
$119$	−11248.4	+	6494.24i	−0.794319	+	0.458600i
$120$		0			0
$121$	−22478.4	+	10008.0i	−1.53531	+	0.683562i
$122$		0			0
$123$			26207.7i			1.73228i
$124$		0			0
$125$	−15622.9			−0.999866
$126$		0			0
$127$	5719.91	+	12847.1i	0.354635	+	0.796523i	0.999481	+	0.0322107i	$0.0102548\pi$
$127$	5719.91	+	12847.1i	0.354635	+	0.796523i	−0.644846	+	0.764312i	$0.723079\pi$
$128$		0			0
$129$	2322.07	+	4021.95i	0.139539	+	0.241689i
$130$		0			0
$131$	−4205.23	−	4670.38i	−0.245046	−	0.272151i	0.608058	−	0.793893i	$-0.291949\pi$
$131$	−4205.23	−	4670.38i	−0.245046	−	0.272151i	−0.853103	+	0.521742i	$0.825282\pi$
$132$		0			0
$133$	−6570.61	+	7297.40i	−0.371452	+	0.412539i
$134$		0			0
$135$	3891.66	+	18308.8i	0.213534	+	1.00460i
$136$		0			0
$137$	−12812.2	−	1346.62i	−0.682626	−	0.0717469i	−0.243133	−	0.969993i	$-0.578175\pi$
$137$	−12812.2	−	1346.62i	−0.682626	−	0.0717469i	−0.439493	+	0.898246i	$0.644842\pi$
$138$		0			0
$139$	702.718	−	967.209i	0.0363707	−	0.0500600i	−0.790444	−	0.612534i	$-0.790150\pi$
$139$	702.718	−	967.209i	0.0363707	−	0.0500600i	0.826815	+	0.562474i	$0.190150\pi$
$140$		0			0
$141$	3021.62	−	14215.6i	0.151985	−	0.715035i
$142$		0			0
$143$	2431.74	+	23136.4i	0.118917	+	1.13142i
$144$		0			0
$145$	−5857.89	+	13157.0i	−0.278616	+	0.625781i
$146$		0			0
$147$	−14309.3	+	4649.38i	−0.662193	+	0.215159i
$148$		0			0
$149$	13346.9	−	23117.5i	0.601185	−	1.04128i	−0.391457	−	0.920197i	$-0.628029\pi$
$149$	13346.9	−	23117.5i	0.601185	−	1.04128i	0.992642	−	0.121087i	$-0.0386380\pi$
$150$		0			0
$151$	−35033.0	−	11382.9i	−1.53647	−	0.499229i	−0.586070	−	0.810260i	$-0.699326\pi$
$151$	−35033.0	−	11382.9i	−1.53647	−	0.499229i	−0.950400	+	0.311031i	$0.899326\pi$
$152$		0			0
$153$	1379.60	+	1898.86i	0.0589346	+	0.0811165i
$154$		0			0
$155$	9530.95	−	22057.1i	0.396710	−	0.918090i
$156$		0			0
$157$	3491.02	−	2536.38i	0.141629	−	0.102900i	−0.514714	−	0.857362i	$-0.672102\pi$
$157$	3491.02	−	2536.38i	0.141629	−	0.102900i	0.656344	+	0.754462i	$0.272102\pi$
$158$		0			0
$159$	−13212.5	+	40663.8i	−0.522625	+	1.60847i
$160$		0			0
$161$	−15441.2	−	8915.00i	−0.595704	−	0.343930i
$162$		0			0
$163$	−8500.91	−	26163.1i	−0.319956	−	0.984723i	−0.973666	−	0.227978i	$-0.926788\pi$
$163$	−8500.91	−	26163.1i	−0.319956	−	0.984723i	0.653710	−	0.756745i	$-0.273212\pi$
$164$		0			0
$165$	39525.0	+	17597.7i	1.45179	+	0.646379i
$166$		0			0
$167$	48266.6	−	5073.03i	1.73067	−	0.181901i	0.813815	−	0.581124i	$-0.197387\pi$
$167$	48266.6	−	5073.03i	1.73067	−	0.181901i	0.916854	+	0.399223i	$0.130720\pi$
$168$		0			0
$169$	−14448.3	−	3071.09i	−0.505876	−	0.107527i
$170$		0			0
$171$	1435.58	+	1043.01i	0.0490949	+	0.0356695i
$172$		0			0
$173$	1279.64	−	12174.9i	0.0427558	−	0.406794i	−0.952123	−	0.305716i	$-0.901104\pi$
$173$	1279.64	−	12174.9i	0.0427558	−	0.406794i	0.994879	−	0.101078i	$-0.0322292\pi$
$174$		0			0
$175$	−4.25363	+	0.904138i	−0.000138894	+	2.95229e-5i
$176$		0			0
$177$	−39100.7	−	35206.4i	−1.24807	−	1.12376i
$178$		0			0
$179$	20670.4	−	18611.7i	0.645125	−	0.580873i	−0.280250	−	0.959927i	$-0.590417\pi$
$179$	20670.4	−	18611.7i	0.645125	−	0.580873i	0.925374	+	0.379054i	$0.123751\pi$
$180$		0			0
$181$	−39832.2	+	22997.1i	−1.21584	+	0.701966i	−0.964026	−	0.265809i	$-0.914361\pi$
$181$	−39832.2	+	22997.1i	−1.21584	+	0.701966i	−0.251815	+	0.967775i	$0.581028\pi$
$182$		0			0
$183$	−11917.3	+	5305.94i	−0.355858	+	0.158438i
$184$		0			0
$185$		−	27220.0i		−	0.795324i
$186$		0			0
$187$	98786.7			2.82498
$188$		0			0
$189$	−7931.09	−	17813.5i	−0.222029	−	0.498685i
$190$		0			0
$191$	−8192.84	−	14190.4i	−0.224578	−	0.388981i	0.731615	−	0.681719i	$-0.238767\pi$
$191$	−8192.84	−	14190.4i	−0.224578	−	0.388981i	−0.956193	+	0.292738i	$0.905434\pi$
$192$		0			0
$193$	−14927.1	−	16578.2i	−0.400738	−	0.445065i	0.508675	−	0.860959i	$-0.330135\pi$
$193$	−14927.1	−	16578.2i	−0.400738	−	0.445065i	−0.909413	+	0.415894i	$0.863469\pi$
$194$		0			0
$195$	17160.6	−	19058.8i	0.451297	−	0.501216i
$196$		0			0
$197$	9157.77	+	43083.9i	0.235970	+	1.11015i	0.923381	+	0.383884i	$0.125414\pi$
$197$	9157.77	+	43083.9i	0.235970	+	1.11015i	−0.687411	+	0.726269i	$0.741253\pi$
$198$		0			0
$199$	24335.5	+	2557.76i	0.614516	+	0.0645883i	0.406673	−	0.913574i	$-0.366689\pi$
$199$	24335.5	+	2557.76i	0.614516	+	0.0645883i	0.207843	+	0.978162i	$0.433356\pi$
$200$		0			0
$201$	11085.5	−	15257.9i	0.274387	−	0.377661i
$202$		0			0
$203$	3119.39	−	14675.6i	0.0756969	−	0.356126i
$204$		0			0
$205$	7841.85	+	74610.2i	0.186600	+	1.77538i
$206$		0			0
$207$	−1310.51	+	2943.46i	−0.0305844	+	0.0686937i
$208$		0			0
$209$	71030.0	−	23079.0i	1.62611	−	0.528354i
$210$		0			0
$211$	−6680.53	+	11571.0i	−0.150053	+	0.259900i	−0.931247	−	0.364389i	$-0.881278\pi$
$211$	−6680.53	+	11571.0i	−0.150053	+	0.259900i	0.781193	+	0.624289i	$0.214611\pi$
$212$		0			0
$213$	−11283.6	−	3666.27i	−0.248708	−	0.0808100i
$214$		0			0
$215$	7814.11	+	10755.2i	0.169045	+	0.232671i
$216$		0			0
$217$	−4934.50	+	24540.2i	−0.104791	+	0.521144i
$218$		0			0
$219$	−48868.4	+	35505.0i	−1.01892	+	0.740289i
$220$		0			0
$221$	18095.1	−	55690.8i	0.370489	−	1.14025i
$222$		0			0
$223$	73886.5	+	42658.4i	1.48578	+	0.857817i	0.999869	−	0.0161904i	$-0.00515380\pi$
$223$	73886.5	+	42658.4i	1.48578	+	0.857817i	0.485913	+	0.874007i	$0.338487\pi$
$224$		0			0
$225$	0.242837	+	0.747374i	4.79677e−6	+	1.47629e-5i
$226$		0			0
$227$	−35295.7	−	15714.6i	−0.684967	−	0.304967i	0.0345889	−	0.999402i	$-0.488988\pi$
$227$	−35295.7	−	15714.6i	−0.684967	−	0.304967i	−0.719556	+	0.694435i	$0.755654\pi$
$228$		0			0
$229$	50833.7	−	5342.84i	0.969351	−	0.101883i	0.393400	−	0.919367i	$-0.371299\pi$
$229$	50833.7	−	5342.84i	0.969351	−	0.101883i	0.575951	+	0.817484i	$0.304632\pi$
$230$		0			0
$231$	−44086.9	−	9370.96i	−0.826201	−	0.175614i
$232$		0			0
$233$	12030.2	+	8740.43i	0.221595	+	0.160998i	0.693044	−	0.720895i	$-0.256269\pi$
$233$	12030.2	+	8740.43i	0.221595	+	0.160998i	−0.471449	+	0.881893i	$0.656269\pi$
$234$		0			0
$235$	4348.62	−	41374.3i	0.0787437	−	0.749196i
$236$		0			0
$237$	42922.8	−	9123.53i	0.764173	−	0.162430i
$238$		0			0
$239$	−24010.6	−	21619.3i	−0.420347	−	0.378482i	0.431639	−	0.902046i	$-0.357935\pi$
$239$	−24010.6	−	21619.3i	−0.420347	−	0.378482i	−0.851986	+	0.523564i	$0.824602\pi$
$240$		0			0
$241$	14571.3	−	13120.1i	0.250880	−	0.225893i	−0.534089	−	0.845428i	$-0.679345\pi$
$241$	14571.3	−	13120.1i	0.250880	−	0.225893i	0.784969	+	0.619535i	$0.212679\pi$
$242$		0			0
$243$	−5935.59	+	3426.92i	−0.100520	+	0.0580351i
$244$		0			0
$245$	−39345.8	+	17517.9i	−0.655490	+	0.291843i
$246$		0			0
$247$		−	44270.5i		−	0.725638i
$248$		0			0
$249$	36834.9			0.594102
$250$		0			0
$251$	−44059.3	−	98958.9i	−0.699343	−	1.57075i	−0.816309	−	0.577615i	$-0.803983\pi$
$251$	−44059.3	−	98958.9i	−0.699343	−	1.57075i	0.116966	−	0.993136i	$-0.462683\pi$
$252$		0			0
$253$	67805.0	+	117442.i	1.05930	+	1.83477i
$254$		0			0
$255$	−72869.9	−	80930.3i	−1.12065	−	1.24460i
$256$		0			0
$257$	−4452.26	+	4944.74i	−0.0674085	+	0.0748647i	−0.775906	−	0.630849i	$-0.782707\pi$
$257$	−4452.26	+	4944.74i	−0.0674085	+	0.0748647i	0.708497	+	0.705714i	$0.249373\pi$
$258$		0			0
$259$	5895.62	+	27736.7i	0.0878881	+	0.413481i
$260$		0			0
$261$	−2696.38	−	283.401i	−0.0395823	−	0.00416026i
$262$		0			0
$263$	12557.9	−	17284.5i	0.181554	−	0.249888i	−0.708534	−	0.705677i	$-0.750643\pi$
$263$	12557.9	−	17284.5i	0.181554	−	0.249888i	0.890088	+	0.455789i	$0.150643\pi$
$264$		0			0
$265$	−25447.0	+	119719.i	−0.362364	+	1.70479i
$266$		0			0
$267$	2588.27	+	24625.7i	0.0363067	+	0.345435i
$268$		0			0
$269$	4124.37	−	9263.49i	0.0569971	−	0.128018i	−0.882802	−	0.469746i	$-0.844346\pi$
$269$	4124.37	−	9263.49i	0.0569971	−	0.128018i	0.939799	+	0.341728i	$0.111012\pi$
$270$		0			0
$271$	1095.53	−	355.960i	0.0149172	−	0.00484688i	−0.301549	−	0.953451i	$-0.597504\pi$
$271$	1095.53	−	355.960i	0.0149172	−	0.00484688i	0.316466	+	0.948604i	$0.397504\pi$
$272$		0			0
$273$	−13358.4	+	23137.4i	−0.179238	+	0.310448i
$274$		0			0
$275$	31.4559	+	10.2206i	0.000415946	+	0.000135149i
$276$		0			0
$277$	−3898.68	−	5366.07i	−0.0508110	−	0.0699353i	0.782855	−	0.622204i	$-0.213762\pi$
$277$	−3898.68	−	5366.07i	−0.0508110	−	0.0699353i	−0.833666	+	0.552268i	$0.813762\pi$
$278$		0			0
$279$	4503.51	+	423.275i	0.0578552	+	0.00543768i
$280$		0			0
$281$	35634.3	−	25889.9i	0.451290	−	0.327881i	−0.338815	−	0.940853i	$-0.610026\pi$
$281$	35634.3	−	25889.9i	0.451290	−	0.327881i	0.790105	+	0.612972i	$0.210026\pi$
$282$		0			0
$283$	−40511.0	+	124680.i	−0.505825	+	1.55677i	0.293554	+	0.955943i	$0.405162\pi$
$283$	−40511.0	+	124680.i	−0.505825	+	1.55677i	−0.799379	+	0.600827i	$0.794838\pi$
$284$		0			0
$285$	−71302.5	−	41166.5i	−0.877840	−	0.506821i
$286$		0			0
$287$	−24150.7	−	74328.2i	−0.293201	−	0.902380i
$288$		0			0
$289$	−150856.	−	67165.3i	−1.80620	−	0.804173i
$290$		0			0
$291$	−44614.9	+	4689.21i	−0.526858	+	0.0553750i
$292$		0			0
$293$	25845.4	+	5493.62i	0.301057	+	0.0639916i	0.355963	−	0.934500i	$-0.384153\pi$
$293$	25845.4	+	5493.62i	0.301057	+	0.0639916i	−0.0549066	+	0.998491i	$0.517486\pi$
$294$		0			0
$295$	−121850.	−	88528.9i	−1.40017	−	1.01728i
$296$		0			0
$297$	−15502.2	+	147494.i	−0.175744	+	1.67210i
$298$		0			0
$299$	78627.6	−	16712.8i	0.879493	−	0.186942i
$300$		0			0
$301$	−10291.9	−	9266.91i	−0.113596	−	0.102283i
$302$		0			0
$303$	−20564.1	+	18516.0i	−0.223988	+	0.201679i
$304$		0			0
$305$	−32339.6	+	18671.3i	−0.347645	+	0.200713i
$306$		0			0
$307$	125357.	−	55812.4i	1.33006	−	0.592180i	0.386165	−	0.922430i	$-0.373800\pi$
$307$	125357.	−	55812.4i	1.33006	−	0.592180i	0.943894	+	0.330250i	$0.107133\pi$
$308$		0			0
$309$			74334.1i			0.778523i
$310$		0			0
$311$	82600.0			0.854002			0.427001	−	0.904251i	$-0.359570\pi$
$311$	82600.0			0.854002			0.427001	+	0.904251i	$0.359570\pi$
$312$		0			0
$313$	−47780.5	−	107317.i	−0.487711	−	1.09542i	−0.975006	−	0.222179i	$-0.928683\pi$
$313$	−47780.5	−	107317.i	−0.487711	−	1.09542i	0.487295	−	0.873237i	$-0.337983\pi$
$314$		0			0
$315$	−1532.73	−	2654.77i	−0.0154470	−	0.0267551i
$316$		0			0
$317$	96864.8	+	107579.i	0.963935	+	1.07056i	0.997468	+	0.0711204i	$0.0226574\pi$
$317$	96864.8	+	107579.i	0.963935	+	1.07056i	−0.0335330	+	0.999438i	$0.510676\pi$
$318$		0			0
$319$	−76355.9	+	84801.8i	−0.750345	+	0.833343i
$320$		0			0
$321$	27506.6	+	129409.i	0.266948	+	1.25589i
$322$		0			0
$323$	−186958.	−	19650.1i	−1.79201	−	0.188348i
$324$		0			0
$325$	11.5237	−	15.8611i	0.000109101	−	0.000150164i
$326$		0			0
$327$	−15893.6	+	74773.3i	−0.148637	+	0.699280i
$328$		0			0
$329$	4530.17	+	43101.7i	0.0418526	+	0.398201i
$330$		0			0
$331$	−68101.1	+	152958.i	−0.621582	+	1.39610i	0.278527	+	0.960429i	$0.410154\pi$
$331$	−68101.1	+	152958.i	−0.621582	+	1.39610i	−0.900108	+	0.435667i	$0.856513\pi$
$332$		0			0
$333$	4873.41	−	1583.47i	0.0439485	−	0.0142797i
$334$		0			0
$335$	26993.7	−	46754.5i	0.240532	−	0.416614i
$336$		0			0
$337$	−129701.	−	42142.4i	−1.14205	−	0.371073i	−0.323905	−	0.946090i	$-0.604996\pi$
$337$	−129701.	−	42142.4i	−1.14205	−	0.371073i	−0.818142	+	0.575016i	$0.804996\pi$
$338$		0			0
$339$	−105981.	−	145871.i	−0.922209	−	1.26931i
$340$		0			0
$341$	125825.	−	142875.i	1.08208	−	1.22870i
$342$		0			0
$343$	86893.9	−	63132.1i	0.738586	−	0.536614i
$344$		0			0
$345$	46196.9	−	142180.i	0.388128	−	1.19453i
$346$		0			0
$347$	−11180.9	−	6455.30i	−0.0928577	−	0.0536114i	0.452852	−	0.891586i	$-0.350407\pi$
$347$	−11180.9	−	6455.30i	−0.0928577	−	0.0536114i	−0.545710	+	0.837974i	$0.683740\pi$
$348$		0			0
$349$	64261.2	+	197776.i	0.527592	+	1.62376i	0.759133	+	0.650935i	$0.225623\pi$
$349$	64261.2	+	197776.i	0.527592	+	1.62376i	−0.231542	+	0.972825i	$0.574377\pi$
$350$		0			0
$351$	80309.9	+	35756.3i	0.651861	+	0.290227i
$352$		0			0
$353$	−154978.	+	16288.9i	−1.24372	+	0.130720i	−0.703432	−	0.710762i	$-0.748350\pi$
$353$	−154978.	+	16288.9i	−1.24372	+	0.130720i	−0.540285	+	0.841482i	$0.681683\pi$
$354$		0			0
$355$	−33220.2	−	7061.16i	−0.263600	−	0.0560299i
$356$		0			0
$357$	91782.2	+	66683.7i	0.720148	+	0.523218i
$358$		0			0
$359$	9766.14	−	92918.6i	0.0757764	−	0.720964i	−0.889003	−	0.457902i	$-0.848601\pi$
$359$	9766.14	−	92918.6i	0.0757764	−	0.720964i	0.964779	−	0.263062i	$-0.0847324\pi$
$360$		0			0
$361$	−11545.0	+	2453.98i	−0.0885893	+	0.0188302i
$362$		0			0
$363$	159717.	+	143810.i	1.21210	+	1.09138i
$364$		0			0
$365$	−128499.	+	115701.i	−0.964526	+	0.868463i
$366$		0			0
$367$	113725.	−	65658.9i	0.844349	−	0.487485i	−0.0143908	−	0.999896i	$-0.504581\pi$
$367$	113725.	−	65658.9i	0.844349	−	0.487485i	0.858740	+	0.512411i	$0.171248\pi$
$368$		0			0
$369$	−12901.9	+	5744.29i	−0.0947547	+	0.0421875i
$370$		0			0
$371$		−	127503.i		−	0.926345i
$372$		0			0
$373$	2338.29			0.0168067			0.00840333	−	0.999965i	$-0.497325\pi$
$373$	2338.29			0.0168067			0.00840333	+	0.999965i	$0.497325\pi$
$374$		0			0
$375$	55503.2	+	124662.i	0.394689	+	0.886487i
$376$		0			0
$377$	33820.5	+	58578.9i	0.237957	+	0.412153i
$378$		0			0
$379$	−12470.7	−	13850.1i	−0.0868185	−	0.0964217i	0.698170	−	0.715932i	$-0.253998\pi$
$379$	−12470.7	−	13850.1i	−0.0868185	−	0.0964217i	−0.784989	+	0.619510i	$0.787331\pi$
$380$		0			0
$381$	82191.9	−	91283.4i	0.566212	−	0.628842i
$382$		0			0
$383$	39996.6	+	188169.i	0.272663	+	1.28278i	0.874839	+	0.484413i	$0.160967\pi$
$383$	39996.6	+	188169.i	0.272663	+	1.28278i	−0.602177	+	0.798363i	$0.705700\pi$
$384$		0			0
$385$	−128314.	−	13486.4i	−0.865673	−	0.0909858i
$386$		0			0
$387$	−1471.02	+	2024.69i	−0.00982193	+	0.0135187i
$388$		0			0
$389$	14766.2	−	69469.7i	0.0975822	−	0.459088i	−0.902041	−	0.431650i	$-0.857932\pi$
$389$	14766.2	−	69469.7i	0.0975822	−	0.459088i	0.999623	−	0.0274385i	$-0.00873505\pi$
$390$		0			0
$391$	−35679.7	−	339470.i	−0.233382	−	2.22049i
$392$		0			0
$393$	−22327.2	+	50147.8i	−0.144561	+	0.324688i
$394$		0			0
$395$	119466.	−	38817.0i	0.765688	−	0.248787i
$396$		0			0
$397$	99134.3	−	171706.i	0.628989	−	1.08944i	−0.358766	−	0.933427i	$-0.616803\pi$
$397$	99134.3	−	171706.i	0.628989	−	1.08944i	0.987755	−	0.156013i	$-0.0498641\pi$
$398$		0			0
$399$	81572.5	+	26504.5i	0.512387	+	0.166485i
$400$		0			0
$401$	−186672.	−	256932.i	−1.16089	−	1.59782i	−0.707912	−	0.706300i	$-0.750363\pi$
$401$	−186672.	−	256932.i	−1.16089	−	1.59782i	−0.452975	−	0.891523i	$-0.649637\pi$
$402$		0			0
$403$	−57497.6	−	97104.5i	−0.354030	−	0.597901i
$404$		0			0
$405$	124556.	−	90495.5i	0.759374	−	0.551718i
$406$		0			0
$407$	66645.9	−	205115.i	0.402332	−	1.23825i
$408$		0			0
$409$	85654.0	+	49452.4i	0.512037	+	0.295624i	0.733670	−	0.679505i	$-0.237806\pi$
$409$	85654.0	+	49452.4i	0.512037	+	0.295624i	−0.221634	+	0.975130i	$0.571139\pi$
$410$		0			0
$411$	34772.4	+	107018.i	0.205850	+	0.633541i
$412$		0			0
$413$	143337.	+	63818.0i	0.840349	+	0.374147i
$414$		0			0
$415$	104865.	−	11021.7i	0.608883	−	0.0639961i
$416$		0			0
$417$	−10214.3	−	2171.12i	−0.0587405	−	0.0124857i
$418$		0			0
$419$	61595.9	+	44752.1i	0.350852	+	0.254909i	0.749226	−	0.662314i	$-0.230426\pi$
$419$	61595.9	+	44752.1i	0.350852	+	0.254909i	−0.398374	+	0.917223i	$0.630426\pi$
$420$		0			0
$421$	15268.4	−	145269.i	0.0861448	−	0.819613i	−0.863091	−	0.505048i	$-0.831475\pi$
$421$	15268.4	−	145269.i	0.0861448	−	0.819613i	0.949236	−	0.314565i	$-0.101859\pi$
$422$		0			0
$423$	7660.56	−	1628.30i	0.0428134	−	0.00910027i
$424$		0			0
$425$	−61.8678	−	55.7060i	−0.000342521	−	0.000308407i
$426$		0			0
$427$	28909.5	−	26030.3i	0.158557	−	0.142765i
$428$		0			0
$429$	175977.	−	101600.i	0.956182	−	0.552052i
$430$		0			0
$431$	−132202.	+	58860.3i	−0.711680	+	0.316861i	−0.730453	−	0.682963i	$-0.760691\pi$
$431$	−132202.	+	58860.3i	−0.711680	+	0.316861i	0.0187723	+	0.999824i	$0.494024\pi$
$432$		0			0
$433$			51107.3i			0.272588i	0.990668	+	0.136294i	$0.0435192\pi$
$433$			51107.3i			0.272588i	−0.990668	+	0.136294i	$0.956481\pi$
$434$		0			0
$435$	125797.			0.664802
$436$		0			0
$437$	−104963.	−	235751.i	−0.549635	−	1.23450i
$438$		0			0
$439$	16595.6	+	28744.4i	0.0861121	+	0.149151i	0.905865	−	0.423567i	$-0.139222\pi$
$439$	16595.6	+	28744.4i	0.0861121	+	0.149151i	−0.819752	+	0.572718i	$0.805889\pi$
$440$		0			0
$441$	−5425.23	−	6025.33i	−0.0278959	−	0.0309816i
$442$		0			0
$443$	−84755.4	+	94130.4i	−0.431877	+	0.479648i	−0.919322	−	0.393506i	$-0.871262\pi$
$443$	−84755.4	+	94130.4i	−0.431877	+	0.479648i	0.487445	+	0.873154i	$0.337929\pi$
$444$		0			0
$445$	14737.0	+	69332.1i	0.0744199	+	0.350118i
$446$		0			0
$447$	−231882.	−	24371.8i	−1.16052	−	0.121976i
$448$		0			0
$449$	11228.3	−	15454.4i	0.0556957	−	0.0766585i	−0.780261	−	0.625454i	$-0.784914\pi$
$449$	11228.3	−	15454.4i	0.0556957	−	0.0766585i	0.835956	+	0.548796i	$0.184914\pi$
$450$		0			0
$451$	−123585.	+	581423.i	−0.607594	+	2.85850i
$452$		0			0
$453$	33631.7	+	319984.i	0.163890	+	1.55931i
$454$		0			0
$455$	−31106.6	+	69866.6i	−0.150255	+	0.337479i
$456$		0			0
$457$	−136278.	+	44279.4i	−0.652519	+	0.212016i	−0.616524	−	0.787336i	$-0.711460\pi$
$457$	−136278.	+	44279.4i	−0.652519	+	0.212016i	−0.0359942	+	0.999352i	$0.511460\pi$
$458$		0			0
$459$	186649.	−	323285.i	0.885931	−	1.53448i
$460$		0			0
$461$	350994.	+	114045.i	1.65157	+	0.536628i	0.979080	−	0.203476i	$-0.0652240\pi$
$461$	350994.	+	114045.i	1.65157	+	0.536628i	0.672492	+	0.740105i	$0.265224\pi$
$462$		0			0
$463$	150962.	+	207781.i	0.704215	+	0.969268i	0.999902	+	0.0139837i	$0.00445129\pi$
$463$	150962.	+	207781.i	0.704215	+	0.969268i	−0.295688	+	0.955285i	$0.595549\pi$
$464$		0			0
$465$	−209864.	+	2310.13i	−0.970581	+	0.0106839i
$466$		0			0
$467$	−4643.51	+	3373.71i	−0.0212918	+	0.0154694i	−0.598380	−	0.801212i	$-0.704189\pi$
$467$	−4643.51	+	3373.71i	−0.0212918	+	0.0154694i	0.577088	+	0.816682i	$0.304189\pi$
$468$		0			0
$469$	−17379.5	+	53488.7i	−0.0790119	+	0.243174i
$470$		0			0
$471$	−32641.4	−	18845.5i	−0.147139	−	0.0849505i
$472$		0			0
$473$	32549.7	+	100178.i	0.145487	+	0.447763i
$474$		0			0
$475$	−57.4987	−	25.6001i	−0.000254842	−	0.000113463i
$476$		0			0
$477$	−22914.5	+	2408.42i	−0.100710	+	0.0105851i
$478$		0			0
$479$	249107.	+	52949.4i	1.08571	+	0.230775i	0.715810	−	0.698295i	$-0.246058\pi$
$479$	249107.	+	52949.4i	1.08571	+	0.230775i	0.369903	+	0.929070i	$0.379391\pi$
$480$		0			0
$481$	−103425.	−	75143.0i	−0.447031	−	0.324787i
$482$		0			0
$483$	−16279.0	+	154885.i	−0.0697805	+	0.663917i
$484$		0			0
$485$	−125610.	+	26699.3i	−0.534000	+	0.113505i
$486$		0			0
$487$	−150970.	−	135934.i	−0.636552	−	0.573154i	0.286380	−	0.958116i	$-0.407548\pi$
$487$	−150970.	−	135934.i	−0.636552	−	0.573154i	−0.922932	+	0.384962i	$0.874215\pi$
$488$		0			0
$489$	−178566.	+	160782.i	−0.746761	+	0.672386i
$490$		0			0
$491$	−92611.4	+	53469.2i	−0.384151	+	0.221789i	−0.679623	−	0.733562i	$-0.737856\pi$
$491$	−92611.4	+	53469.2i	−0.384151	+	0.221789i	0.295472	+	0.955351i	$0.404523\pi$
$492$		0			0
$493$	262396.	−	116826.i	1.07960	−	0.480669i
$494$		0			0
$495$			23315.1i			0.0951539i
$496$		0			0
$497$	35380.2			0.143235
$498$		0			0
$499$	−67364.9	−	151304.i	−0.270541	−	0.607644i	0.726273	−	0.687406i	$-0.241251\pi$
$499$	−67364.9	−	151304.i	−0.270541	−	0.607644i	−0.996814	+	0.0797618i	$0.974584\pi$
$500$		0			0
$501$	−211956.	−	367118.i	−0.844442	−	1.46262i
$502$		0			0
$503$	−213486.	−	237100.i	−0.843787	−	0.937120i	0.154922	−	0.987927i	$-0.450487\pi$
$503$	−213486.	−	237100.i	−0.843787	−	0.937120i	−0.998709	+	0.0508066i	$0.983821\pi$
$504$		0			0
$505$	−53003.2	+	58866.0i	−0.207835	+	0.230825i
$506$		0			0
$507$	26824.7	+	126200.i	0.104356	+	0.490958i
$508$		0			0
$509$	−308972.	−	32474.3i	−1.19257	−	0.125344i	−0.512629	−	0.858610i	$-0.671328\pi$
$509$	−308972.	−	32474.3i	−1.19257	−	0.125344i	−0.679942	+	0.733266i	$0.737995\pi$
$510$		0			0
$511$	105879.	−	145729.i	0.405477	−	0.558091i
$512$		0			0
$513$	58677.4	−	276056.i	0.222965	−	1.04897i
$514$		0			0
$515$	22242.2	+	211621.i	0.0838617	+	0.797891i
$516$		0			0
$517$	134071.	−	301128.i	0.501594	−	1.12660i
$518$		0			0
$519$	−101695.	+	33042.8i	−0.377543	+	0.122671i
$520$		0			0
$521$	−87584.2	+	151700.i	−0.322664	+	0.558870i	−0.981037	−	0.193822i	$-0.937912\pi$
$521$	−87584.2	+	151700.i	−0.322664	+	0.558870i	0.658373	+	0.752692i	$0.271245\pi$
$522$		0			0
$523$	−408001.	−	132567.i	−1.49162	−	0.484656i	−0.554057	−	0.832479i	$-0.686921\pi$
$523$	−408001.	−	132567.i	−1.49162	−	0.484656i	−0.937560	+	0.347823i	$0.886921\pi$
$524$		0			0
$525$	22.3263	+	30.7295i	8.10025e−5	+	0.000111490i
$526$		0			0
$527$	−435603.	+	199717.i	−1.56845	+	0.719106i
$528$		0			0
$529$	152690.	−	110936.i	0.545631	−	0.396424i
$530$		0			0
$531$	8761.69	−	26965.7i	0.0310741	−	0.0956363i
$532$		0			0
$533$	305138.	+	176172.i	1.07409	+	0.620129i
$534$		0			0
$535$	117030.	+	360181.i	0.408873	+	1.25838i
$536$		0			0
$537$	−221947.	−	98817.1i	−0.769662	−	0.342676i
$538$		0			0
$539$	−339380.	+	35670.3i	−1.16818	+	0.122780i
$540$		0			0
$541$	241692.	+	51373.3i	0.825788	+	0.175527i	0.601374	−	0.798967i	$-0.294620\pi$
$541$	241692.	+	51373.3i	0.825788	+	0.175527i	0.224413	+	0.974494i	$0.427953\pi$
$542$		0			0
$543$	325015.	+	236137.i	1.10231	+	0.800875i
$544$		0			0
$545$	−22873.5	+	217627.i	−0.0770086	+	0.732688i
$546$		0			0
$547$	244017.	−	51867.4i	0.815539	−	0.173348i	0.218786	−	0.975773i	$-0.429790\pi$
$547$	244017.	−	51867.4i	0.815539	−	0.173348i	0.596754	+	0.802425i	$0.296457\pi$
$548$		0			0
$549$	−5224.17	−	4703.86i	−0.0173330	−	0.0156067i
$550$		0			0
$551$	161375.	−	145303.i	0.531538	−	0.478599i
$552$		0			0
$553$	−113327.	+	65429.4i	−0.370581	+	0.213955i
$554$		0			0
$555$	−217200.	+	96703.7i	−0.705138	+	0.313948i
$556$		0			0
$557$			109073.i			0.351567i	0.984429	+	0.175783i	$0.0562458\pi$
$557$			109073.i			0.351567i	−0.984429	+	0.175783i	$0.943754\pi$
$558$		0			0
$559$	62437.2			0.199811
$560$		0			0
$561$	−350957.	−	788263.i	−1.11514	−	2.50464i
$562$		0			0
$563$	−17435.9	−	30199.8i	−0.0550082	−	0.0952770i	0.837210	−	0.546881i	$-0.184185\pi$
$563$	−17435.9	−	30199.8i	−0.0550082	−	0.0952770i	−0.892218	+	0.451604i	$0.850852\pi$
$564$		0			0
$565$	−345363.	−	383565.i	−1.08188	−	1.20155i
$566$		0			0
$567$	−107320.	+	119191.i	−0.333823	+	0.370748i
$568$		0			0
$569$	15824.1	+	74446.4i	0.0488758	+	0.229943i	0.995805	−	0.0914992i	$-0.0291659\pi$
$569$	15824.1	+	74446.4i	0.0488758	+	0.229943i	−0.946929	+	0.321442i	$0.895833\pi$
$570$		0			0
$571$	2907.15	+	305.554i	0.00891652	+	0.000937164i	0.108986	−	0.994043i	$-0.465240\pi$
$571$	2907.15	+	305.554i	0.00891652	+	0.000937164i	−0.100069	+	0.994980i	$0.531906\pi$
$572$		0			0
$573$	−84125.1	+	115788.i	−0.256222	+	0.352659i
$574$		0			0
$575$	23.7609	−	111.786i	7.18667e−5	−	0.000338106i
$576$		0			0
$577$	−43374.0	−	412676.i	−0.130280	−	1.23953i	−0.842934	−	0.538017i	$-0.819174\pi$
$577$	−43374.0	−	412676.i	−0.130280	−	1.23953i	0.712654	−	0.701516i	$-0.247493\pi$
$578$		0			0
$579$	−79253.8	+	178007.i	−0.236408	+	0.530982i
$580$		0			0
$581$	−104468.	+	33943.8i	−0.309480	+	0.100556i
$582$		0			0
$583$	−484876.	+	839831.i	−1.42657	+	2.47090i
$584$		0			0
$585$	13143.8	+	4270.69i	0.0384070	+	0.0124792i
$586$		0			0
$587$	251530.	+	346201.i	0.729984	+	1.00474i	0.999133	+	0.0416379i	$0.0132576\pi$
$587$	251530.	+	346201.i	0.729984	+	1.00474i	−0.269149	+	0.963099i	$0.586742\pi$
$588$		0			0
$589$	−266550.	+	245369.i	−0.768330	+	0.707275i
$590$		0			0
$591$	311251.	−	226137.i	0.891120	−	0.647436i
$592$		0			0
$593$	−157535.	+	484843.i	−0.447990	+	1.37877i	0.431182	+	0.902265i	$0.358097\pi$
$593$	−157535.	+	484843.i	−0.447990	+	1.37877i	−0.879171	+	0.476506i	$0.841903\pi$
$594$		0			0
$595$	281246.	+	162378.i	0.794425	+	0.458661i
$596$		0			0
$597$	−66046.6	−	203270.i	−0.185311	−	0.570329i
$598$		0			0
$599$	325231.	+	144802.i	0.906438	+	0.403572i	0.806372	−	0.591409i	$-0.201428\pi$
$599$	325231.	+	144802.i	0.906438	+	0.403572i	0.100066	+	0.994981i	$0.468095\pi$
$600$		0			0
$601$	678145.	−	71275.9i	1.87747	−	0.197330i	0.904220	−	0.427068i	$-0.140454\pi$
$601$	678145.	−	71275.9i	1.87747	−	0.197330i	0.973253	+	0.229738i	$0.0737868\pi$
$602$		0			0
$603$	9941.14	+	2113.05i	0.0273402	+	0.00581134i
$604$		0			0
$605$	497727.	+	361620.i	1.35982	+	0.987965i
$606$		0			0
$607$	2715.08	−	25832.3i	0.00736895	−	0.0701108i	−0.990219	−	0.139519i	$-0.955444\pi$
$607$	2715.08	−	25832.3i	0.00736895	−	0.0701108i	0.997588	+	0.0694081i	$0.0221111\pi$
$608$		0			0
$609$	−128185.	+	27246.6i	−0.345624	+	0.0734646i
$610$		0			0
$611$	−145202.	−	130740.i	−0.388947	−	0.350209i
$612$		0			0
$613$	−62269.6	+	56067.8i	−0.165712	+	0.149208i	−0.747815	−	0.663907i	$-0.768897\pi$
$613$	−62269.6	+	56067.8i	−0.165712	+	0.149208i	0.582102	+	0.813115i	$0.302230\pi$
$614$		0			0
$615$	567489.	−	327640.i	1.50040	−	0.866256i
$616$		0			0
$617$	−436347.	+	194274.i	−1.14620	+	0.510322i	−0.889846	−	0.456260i	$-0.849189\pi$
$617$	−436347.	+	194274.i	−1.14620	+	0.510322i	−0.256356	+	0.966582i	$0.582522\pi$
$618$		0			0
$619$		−	255827.i		−	0.667675i	−0.942631	−	0.333838i	$-0.891656\pi$
$619$		−	255827.i		−	0.667675i	0.942631	−	0.333838i	$-0.108344\pi$
$620$		0			0
$621$	512447.			1.32882
$622$		0			0
$623$	−30033.6	−	67456.5i	−0.0773803	−	0.173799i
$624$		0			0
$625$	195365.	+	338382.i	0.500134	+	0.866257i
$626$		0			0
$627$	−436504.	−	484787.i	−1.11033	−	1.23315i
$628$		0			0
$629$	−363243.	+	403422.i	−0.918113	+	1.01967i
$630$		0			0
$631$	−80859.4	−	380414.i	−0.203082	−	0.955427i	−0.955100	−	0.296284i	$-0.904253\pi$
$631$	−80859.4	−	380414.i	−0.203082	−	0.955427i	0.752018	−	0.659143i	$-0.229081\pi$
$632$		0			0
$633$	116064.	+	12198.8i	0.289661	+	0.0304446i
$634$		0			0
$635$	206677.	−	284467.i	0.512560	−	0.705479i
$636$		0			0
$637$	−42056.1	+	197859.i	−0.103646	+	0.487614i
$638$		0			0
$639$	−668.300	−	6358.45i	−0.00163670	−	0.0155722i
$640$		0			0
$641$	303440.	−	681537.i	0.738511	−	1.65872i	−0.0137924	−	0.999905i	$-0.504390\pi$
$641$	303440.	−	681537.i	0.738511	−	1.65872i	0.752303	−	0.658817i	$-0.228943\pi$
$642$		0			0
$643$	209297.	−	68004.6i	0.506221	−	0.164481i	−0.0447618	−	0.998998i	$-0.514253\pi$
$643$	209297.	−	68004.6i	0.506221	−	0.164481i	0.550983	+	0.834516i	$0.314253\pi$
$644$		0			0
$645$	58059.5	−	100562.i	0.139558	−	0.241721i
$646$		0			0
$647$	−327313.	−	106351.i	−0.781907	−	0.254057i	−0.109253	−	0.994014i	$-0.534846\pi$
$647$	−327313.	−	106351.i	−0.781907	−	0.254057i	−0.672654	+	0.739957i	$0.734846\pi$
$648$		0			0
$649$	−701437.	−	965445.i	−1.66533	−	2.29212i
$650$		0			0
$651$	213348.	−	47808.8i	0.503415	−	0.112810i
$652$		0			0
$653$	495175.	−	359766.i	1.16127	−	0.843711i	0.171331	−	0.985214i	$-0.445193\pi$
$653$	495175.	−	359766.i	1.16127	−	0.843711i	0.989938	+	0.141502i	$0.0451933\pi$
$654$		0			0
$655$	−48557.8	+	149446.i	−0.113182	+	0.348338i
$656$		0			0
$657$	−28190.1	−	16275.5i	−0.0653079	−	0.0377055i
$658$		0			0
$659$	163601.	+	503514.i	0.376718	+	1.15942i	0.942312	+	0.334735i	$0.108647\pi$
$659$	163601.	+	503514.i	0.376718	+	1.15942i	−0.565594	+	0.824684i	$0.691353\pi$
$660$		0			0
$661$	694864.	+	309373.i	1.59037	+	0.708076i	0.995412	−	0.0956840i	$-0.0305038\pi$
$661$	694864.	+	309373.i	1.59037	+	0.708076i	0.594953	+	0.803760i	$0.297170\pi$
$662$		0			0
$663$	−508668.	+	53463.2i	−1.15720	+	0.121626i
$664$		0			0
$665$	240158.	+	51047.2i	0.543068	+	0.115433i
$666$		0			0
$667$	318991.	+	231760.i	0.717012	+	0.520939i
$668$		0			0
$669$	77895.3	−	741124.i	0.174044	−	1.65592i
$670$		0			0
$671$	−289409.	+	61515.8i	−0.642787	+	0.136629i
$672$		0			0
$673$	158439.	+	142659.i	0.349810	+	0.314970i	0.825239	−	0.564784i	$-0.191040\pi$
$673$	158439.	+	142659.i	0.349810	+	0.314970i	−0.475429	+	0.879754i	$0.657707\pi$
$674$		0			0
$675$	92.8809	−	83.6303i	0.000203854	−	0.000183551i
$676$		0			0
$677$	237899.	−	137351.i	0.519056	−	0.299677i	−0.217492	−	0.976062i	$-0.569788\pi$
$677$	237899.	−	137351.i	0.519056	−	0.299677i	0.736549	+	0.676385i	$0.236454\pi$
$678$		0			0
$679$	122212.	−	54412.3i	0.265078	−	0.118021i
$680$		0			0
$681$			337469.i			0.727678i
$682$		0			0
$683$	29139.1			0.0624647			0.0312323	−	0.999512i	$-0.490057\pi$
$683$	29139.1			0.0624647			0.0312323	+	0.999512i	$0.490057\pi$
$684$		0			0
$685$	131015.	+	294264.i	0.279216	+	0.627129i
$686$		0			0
$687$	−223229.	−	386644.i	−0.472973	−	0.819214i
$688$		0			0
$689$	384637.	+	427182.i	0.810238	+	0.899860i
$690$		0			0
$691$	243971.	−	270958.i	0.510955	−	0.567473i	−0.431369	−	0.902176i	$-0.641969\pi$
$691$	243971.	−	270958.i	0.510955	−	0.567473i	0.942324	+	0.334703i	$0.108636\pi$
$692$		0			0
$693$	−5049.85	−	23757.7i	−0.0105151	−	0.0494695i
$694$		0			0
$695$	−29728.6	−	3124.61i	−0.0615468	−	0.00646883i
$696$		0			0
$697$	879431.	−	1.21043e6i	1.81024	−	2.49158i
$698$		0			0
$699$	27004.5	−	127046.i	0.0552690	−	0.260020i
$700$		0			0
$701$	83613.6	+	795530.i	0.170153	+	1.61890i	0.662886	+	0.748721i	$0.269332\pi$
$701$	83613.6	+	795530.i	0.170153	+	1.61890i	−0.492732	+	0.870181i	$0.664002\pi$
$702$		0			0
$703$	−166931.	+	374933.i	−0.337774	+	0.758652i
$704$		0			0
$705$	−345594.	+	112290.i	−0.695324	+	0.225925i
$706$		0			0
$707$	41259.5	−	71463.6i	0.0825440	−	0.142970i
$708$		0			0
$709$	−745887.	−	242354.i	−1.48382	−	0.482122i	−0.548567	−	0.836106i	$-0.684827\pi$
$709$	−745887.	−	242354.i	−1.48382	−	0.482122i	−0.935251	+	0.353984i	$0.884827\pi$
$710$		0			0
$711$	13899.4	+	19130.9i	0.0274953	+	0.0378440i
$712$		0			0
$713$	−536419.	−	380781.i	−1.05518	−	0.749025i
$714$		0			0
$715$	470585.	−	341900.i	0.920504	−	0.668785i
$716$		0			0
$717$	−87207.8	+	268398.i	−0.169636	+	0.522085i
$718$		0			0
$719$	−576742.	−	332982.i	−1.11564	−	0.644114i	−0.175354	−	0.984505i	$-0.556107\pi$
$719$	−576742.	−	332982.i	−1.11564	−	0.644114i	−0.940284	+	0.340391i	$0.889440\pi$
$720$		0			0
$721$	−68499.8	−	210821.i	−0.131771	−	0.405548i
$722$		0			0
$723$	−156458.	−	69659.8i	−0.299311	−	0.133262i
$724$		0			0
$725$	95.6398	−	10.0522i	0.000181955	−	1.91242e-5i
$726$		0			0
$727$	907916.	+	192983.i	1.71782	+	0.365133i	0.958390	−	0.285461i	$-0.0921466\pi$
$727$	907916.	+	192983.i	1.71782	+	0.365133i	0.759426	+	0.650594i	$0.225480\pi$
$728$		0			0
$729$	451941.	+	328354.i	0.850407	+	0.617857i
$730$		0			0
$731$	27713.7	−	263678.i	0.0518633	−	0.493446i
$732$		0			0
$733$	−260276.	+	55323.4i	−0.484425	+	0.102968i	−0.443649	−	0.896201i	$-0.646316\pi$
$733$	−260276.	+	55323.4i	−0.484425	+	0.102968i	−0.0407760	+	0.999168i	$0.512983\pi$
$734$		0			0
$735$	279566.	+	251722.i	0.517499	+	0.465958i
$736$		0			0
$737$	317885.	−	286225.i	0.585241	−	0.526953i
$738$		0			0
$739$	744690.	−	429947.i	1.36360	−	0.787275i	0.373499	−	0.927631i	$-0.378158\pi$
$739$	744690.	−	429947.i	1.36360	−	0.787275i	0.990101	+	0.140356i	$0.0448248\pi$
$740$		0			0
$741$	−353254.	+	157279.i	−0.643355	+	0.286440i
$742$		0			0
$743$			843002.i			1.52704i	0.645784	+	0.763521i	$0.276531\pi$
$743$			843002.i			1.52704i	−0.645784	+	0.763521i	$0.723469\pi$
$744$		0			0
$745$	−667435.			−1.20253
$746$		0			0
$747$	8073.61	+	18133.6i	0.0144686	+	0.0324970i
$748$		0			0
$749$	−197264.	−	341671.i	−0.351628	−	0.609038i
$750$		0			0
$751$	−230724.	−	256245.i	−0.409084	−	0.454334i	0.503031	−	0.864268i	$-0.332218\pi$
$751$	−230724.	−	256245.i	−0.409084	−	0.454334i	−0.912115	+	0.409935i	$0.865551\pi$
$752$		0			0
$753$	−633108.	+	703138.i	−1.11658	+	1.24008i
$754$		0			0
$755$	191491.	+	900895.i	0.335934	+	1.58045i
$756$		0			0
$757$	−495385.	−	52067.0i	−0.864472	−	0.0908596i	−0.338096	−	0.941112i	$-0.609783\pi$
$757$	−495385.	−	52067.0i	−0.864472	−	0.0908596i	−0.526376	+	0.850252i	$0.676449\pi$
$758$		0			0
$759$	696230.	−	958279.i	1.20856	−	1.66344i
$760$		0			0
$761$	−185708.	+	873686.i	−0.320672	+	1.50864i	0.462378	+	0.886683i	$0.346996\pi$
$761$	−185708.	+	873686.i	−0.320672	+	1.50864i	−0.783050	+	0.621959i	$0.786337\pi$
$762$		0			0
$763$	−23828.4	−	226712.i	−0.0409304	−	0.389427i
$764$		0			0
$765$	23869.6	−	53612.1i	0.0407871	−	0.0916093i
$766$		0			0
$767$	−672752.	+	218590.i	−1.14357	+	0.371570i
$768$		0			0
$769$	−435745.	+	754733.i	−0.736851	+	1.27626i	0.217055	+	0.976159i	$0.430355\pi$
$769$	−435745.	+	754733.i	−0.736851	+	1.27626i	−0.953906	+	0.300104i	$0.902978\pi$
$770$		0			0
$771$	55273.7	+	17959.5i	0.0929844	+	0.0302125i
$772$		0			0
$773$	211072.	+	290516.i	0.353242	+	0.486196i	0.948250	−	0.317524i	$-0.102851\pi$
$773$	211072.	+	290516.i	0.353242	+	0.486196i	−0.595009	+	0.803719i	$0.702851\pi$
$774$		0			0
$775$	−159.369	+	18.5261i	−0.000265338	+	3.08446e-5i
$776$		0			0
$777$	200378.	−	145583.i	0.331901	−	0.241140i
$778$		0			0
$779$	349544.	−	1.07579e6i	0.576006	−	1.77276i
$780$		0			0
$781$	−233041.	−	134546.i	−0.382058	−	0.220581i
$782$		0			0
$783$	133251.	+	410105.i	0.217344	+	0.668916i
$784$		0			0
$785$	−98565.2	−	43884.0i	−0.159950	−	0.0712143i
$786$		0			0
$787$	−339475.	+	35680.3i	−0.548098	+	0.0576075i	−0.374531	−	0.927214i	$-0.622196\pi$
$787$	−339475.	+	35680.3i	−0.548098	+	0.0576075i	−0.173568	+	0.984822i	$0.555530\pi$
$788$		0			0
$789$	−182535.	−	38799.0i	−0.293219	−	0.0623255i
$790$		0			0
$791$	434997.	+	316044.i	0.695237	+	0.505120i
$792$		0			0
$793$	−18332.5	+	174422.i	−0.0291525	+	0.277367i
$794$		0			0
$795$	1.04569e6	−	222269.i	1.65451	−	0.351678i
$796$		0			0
$797$	−439039.	−	395312.i	−0.691172	−	0.622334i	0.246791	−	0.969069i	$-0.420624\pi$
$797$	−439039.	−	395312.i	−0.691172	−	0.622334i	−0.937963	+	0.346734i	$0.887291\pi$
$798$		0			0
$799$	−616580.	+	555171.i	−0.965819	+	0.869627i
$800$		0			0
$801$	−11555.8	+	6671.75i	−0.0180109	+	0.0103986i
$802$		0			0
$803$	−1.25158e6	+	557241.i	−1.94102	+	0.864196i
$804$		0			0
$805$			445809.i			0.687951i
$806$		0			0
$807$	−88570.0			−0.136000
$808$		0			0
$809$	488875.	+	1.09803e6i	0.746966	+	1.67771i	0.735262	+	0.677783i	$0.237059\pi$
$809$	488875.	+	1.09803e6i	0.746966	+	1.67771i	0.0117041	+	0.999932i	$0.496274\pi$
$810$		0			0
$811$	−458864.	−	794775.i	−0.697657	−	1.20838i	−0.969277	−	0.245973i	$-0.920893\pi$
$811$	−458864.	−	794775.i	−0.697657	−	1.20838i	0.271620	−	0.962405i	$-0.412441\pi$
$812$		0			0
$813$	−6732.43	−	7477.12i	−0.0101857	−	0.0113124i
$814$		0			0
$815$	−460248.	+	511157.i	−0.692910	+	0.769554i
$816$		0			0
$817$	−41675.0	−	196065.i	−0.0624355	−	0.293736i
$818$		0			0
$819$	−14318.4	−	1504.92i	−0.0213464	−	0.00224360i
$820$		0			0
$821$	239951.	−	330264.i	0.355988	−	0.489975i	−0.593037	−	0.805175i	$-0.702071\pi$
$821$	239951.	−	330264.i	0.355988	−	0.489975i	0.949025	+	0.315199i	$0.102071\pi$
$822$		0			0
$823$	−103225.	+	485635.i	−0.152400	+	0.716985i	0.833886	+	0.551937i	$0.186111\pi$
$823$	−103225.	+	485635.i	−0.152400	+	0.716985i	−0.986286	+	0.165048i	$0.947222\pi$
$824$		0			0
$825$	−30.1976	−	287.311i	−4.43675e−5	−	0.000422129i
$826$		0			0
$827$	−9705.69	+	21799.3i	−0.0141911	+	0.0318737i	−0.920502	−	0.390738i	$-0.872220\pi$
$827$	−9705.69	+	21799.3i	−0.0141911	+	0.0318737i	0.906311	+	0.422612i	$0.138887\pi$
$828$		0			0
$829$	−734578.	+	238679.i	−1.06888	+	0.347300i	−0.790051	−	0.613041i	$-0.789946\pi$
$829$	−734578.	+	238679.i	−1.06888	+	0.347300i	−0.278829	+	0.960341i	$0.589946\pi$
$830$		0			0
$831$	−28967.5	+	50173.2i	−0.0419478	+	0.0726557i
$832$		0			0
$833$	816908.	+	265430.i	1.17729	+	0.382525i
$834$		0			0
$835$	−713262.	−	981721.i	−1.02300	−	1.40804i
$836$		0			0
$837$	−229830.	−	681720.i	−0.328062	−	0.973094i
$838$		0			0
$839$	−369148.	+	268202.i	−0.524417	+	0.381011i	−0.818265	−	0.574841i	$-0.805064\pi$
$839$	−369148.	+	268202.i	−0.524417	+	0.381011i	0.293848	+	0.955852i	$0.405064\pi$
$840$		0			0
$841$	116034.	−	357115.i	0.164056	−	0.504913i
$842$		0			0
$843$	−333184.	−	192364.i	−0.468845	−	0.270688i
$844$		0			0
$845$	114128.	+	351251.i	0.159838	+	0.491931i
$846$		0			0
$847$	−585500.	−	260681.i	−0.816132	−	0.363365i
$848$		0			0
$849$	1.13880e6	−	119693.i	1.57991	−	0.166055i
$850$		0			0
$851$	−728927.	−	154938.i	−1.00653	−	0.213944i
$852$		0			0
$853$	630972.	+	458428.i	0.867186	+	0.630048i	0.929830	−	0.367988i	$-0.119953\pi$
$853$	630972.	+	458428.i	0.867186	+	0.630048i	−0.0626444	+	0.998036i	$0.519953\pi$
$854$		0			0
$855$	4637.71	−	44124.9i	0.00634412	−	0.0603603i
$856$		0			0
$857$	159942.	−	33996.6i	0.217771	−	0.0462886i	−0.0977340	−	0.995213i	$-0.531159\pi$
$857$	159942.	−	33996.6i	0.217771	−	0.0462886i	0.315505	+	0.948924i	$0.397826\pi$
$858$		0			0
$859$	−892244.	−	803380.i	−1.20920	−	1.08877i	−0.993678	−	0.112268i	$-0.964189\pi$
$859$	−892244.	−	803380.i	−1.20920	−	1.08877i	−0.215520	−	0.976499i	$-0.569145\pi$
$860$		0			0
$861$	−507298.	+	456773.i	−0.684316	+	0.616161i
$862$		0			0
$863$	1.12138e6	−	647430.i	1.50568	−	0.869304i	0.505700	−	0.862710i	$-0.331234\pi$
$863$	1.12138e6	−	647430.i	1.50568	−	0.869304i	0.999978	−	0.00659408i	$-0.00209898\pi$
$864$		0			0
$865$	−279628.	+	124498.i	−0.373722	+	0.166392i
$866$		0			0
$867$			1.44236e6i			1.91883i
$868$		0			0
$869$	995275.			1.31796
$870$		0			0
$871$	−103131.	−	231635.i	−0.135941	−	0.305329i
$872$		0			0
$873$	−12087.3	−	20935.8i	−0.0158599	−	0.0274702i
$874$		0			0
$875$	−272291.	−	302410.i	−0.355646	−	0.394985i
$876$		0			0
$877$	−605422.	+	672390.i	−0.787153	+	0.874222i	−0.994574	−	0.104030i	$-0.966826\pi$
$877$	−605422.	+	672390.i	−0.787153	+	0.874222i	0.207421	+	0.978252i	$0.433493\pi$
$878$		0			0
$879$	−47984.5	−	225749.i	−0.0621045	−	0.292179i
$880$		0			0
$881$	−1.17808e6	−	123821.i	−1.51783	−	0.159530i	−0.691359	−	0.722512i	$-0.742988\pi$
$881$	−1.17808e6	−	123821.i	−1.51783	−	0.159530i	−0.826470	+	0.562981i	$0.809654\pi$
$882$		0			0
$883$	−28785.6	+	39620.0i	−0.0369194	+	0.0508151i	−0.827078	−	0.562088i	$-0.809998\pi$
$883$	−28785.6	+	39620.0i	−0.0369194	+	0.0508151i	0.790158	+	0.612903i	$0.209998\pi$
$884$		0			0
$885$	−273519.	+	1.28681e6i	−0.349222	+	1.64296i
$886$		0			0
$887$	−30234.9	−	287666.i	−0.0384293	−	0.365630i	−0.996789	−	0.0800677i	$-0.974486\pi$
$887$	−30234.9	−	287666.i	−0.0384293	−	0.365630i	0.958360	−	0.285562i	$-0.0921803\pi$
$888$		0			0
$889$	−148988.	+	334632.i	−0.188515	+	0.423412i
$890$		0			0
$891$	1.16016e6	−	376959.i	1.46138	−	0.474831i
$892$		0			0
$893$	−313633.	+	543229.i	−0.393296	+	0.681209i
$894$		0			0
$895$	−661425.	−	214910.i	−0.825723	−	0.268294i
$896$		0			0
$897$	−412697.	−	568029.i	−0.512917	−	0.705969i
$898$		0			0
$899$	165250.	−	528304.i	0.204466	−	0.653679i
$900$		0			0
$901$	1.97476e6	−	1.43475e6i	2.43257	−	1.76736i
$902$		0			0
$903$	−37380.8	+	115046.i	−0.0458431	+	0.141090i
$904$		0			0
$905$	995937.	+	575005.i	1.21600	+	0.702060i
$906$		0			0
$907$	−3034.76	−	9340.03i	−0.00368901	−	0.0113536i	0.949195	−	0.314688i	$-0.101900\pi$
$907$	−3034.76	−	9340.03i	−0.00368901	−	0.0113536i	−0.952884	+	0.303335i	$0.901900\pi$
$908$		0			0
$909$	−13622.6	−	6065.18i	−0.0164867	−	0.00734034i
$910$		0			0
$911$	−957548.	+	100642.i	−1.15378	+	0.121267i	−0.662037	−	0.749472i	$-0.730308\pi$
$911$	−957548.	+	100642.i	−1.15378	+	0.121267i	−0.491746	+	0.870739i	$0.663641\pi$
$912$		0			0
$913$	817190.	+	173699.i	0.980351	+	0.208380i
$914$		0			0
$915$	263879.	+	191719.i	0.315183	+	0.228994i
$916$		0			0
$917$	17111.0	−	162800.i	0.0203487	−	0.193605i
$918$		0			0
$919$	604417.	−	128473.i	0.715658	−	0.152118i	0.164329	−	0.986406i	$-0.447454\pi$
$919$	604417.	−	128473.i	0.715658	−	0.152118i	0.551329	+	0.834288i	$0.314121\pi$
$920$		0			0
$921$	−890704.	−	801993.i	−1.05006	−	0.945478i
$922$		0			0
$923$	−118537.	+	106731.i	−0.139139	+	0.125282i
$924$		0			0
$925$	−157.404	+	90.8770i	−0.000183963	+	0.000106211i
$926$		0			0
$927$	−36594.3	+	16292.8i	−0.0425847	+	0.0189599i
$928$		0			0
$929$		−	46572.6i		−	0.0539634i	−0.999636	−	0.0269817i	$-0.991410\pi$
$929$		−	46572.6i		−	0.0539634i	0.999636	−	0.0269817i	$-0.00858958\pi$
$930$		0			0
$931$	649387.			0.749211
$932$		0			0
$933$	−293451.	−	659102.i	−0.337111	−	0.757163i
$934$		0			0
$935$	−1.23500e6	−	2.13908e6i	−1.41268	−	2.44683i
$936$		0			0
$937$	272231.	+	302343.i	0.310069	+	0.344366i	0.877957	−	0.478740i	$-0.158906\pi$
$937$	272231.	+	302343.i	0.310069	+	0.344366i	−0.567888	+	0.823106i	$0.692240\pi$
$938$		0			0
$939$	−686580.	+	762524.i	−0.778681	+	0.864813i
$940$		0			0
$941$	−345651.	−	1.62616e6i	−0.390354	−	1.83647i	−0.532248	−	0.846588i	$-0.678653\pi$
$941$	−345651.	−	1.62616e6i	−0.390354	−	1.83647i	0.141894	−	0.989882i	$-0.454681\pi$
$942$		0			0
$943$	2.04263e6	+	214689.i	2.29703	+	0.241428i
$944$		0			0
$945$	−286574.	+	394435.i	−0.320902	+	0.441684i
$946$		0			0
$947$	−61197.7	+	287913.i	−0.0682394	+	0.321041i	−0.999006	−	0.0445724i	$-0.985807\pi$
$947$	−61197.7	+	287913.i	−0.0682394	+	0.321041i	0.930767	+	0.365614i	$0.119141\pi$
$948$		0			0
$949$	84887.4	+	807650.i	0.0942564	+	0.896790i
$950$		0			0
$951$	514294.	−	1.15512e6i	0.568657	−	1.27722i
$952$		0			0
$953$	484382.	−	157385.i	0.533337	−	0.173292i	−0.0299524	−	0.999551i	$-0.509536\pi$
$953$	484382.	−	157385.i	0.533337	−	0.173292i	0.563290	+	0.826260i	$0.309536\pi$
$954$		0			0
$955$	−204848.	+	354808.i	−0.224608	+	0.389033i
$956$		0			0
$957$	947939.	+	308004.i	1.03504	+	0.336304i
$958$		0			0
$959$	−197237.	−	271474.i	−0.214463	−	0.295183i
$960$		0			0
$961$	−265980.	+	884390.i	−0.288007	+	0.957628i
$962$		0			0
$963$	−57678.1	+	41905.6i	−0.0621954	+	0.0451876i
$964$		0			0
$965$	−172363.	+	530479.i	−0.185093	+	0.569658i
$966$		0			0
$967$	828079.	+	478091.i	0.885561	+	0.511279i	0.872488	−	0.488635i	$-0.162505\pi$
$967$	828079.	+	478091.i	0.885561	+	0.511279i	0.0130733	+	0.999915i	$0.495839\pi$
$968$		0			0
$969$	507406.	+	1.56164e6i	0.540391	+	1.66315i
$970$		0			0
$971$	−363495.	−	161838.i	−0.385531	−	0.171650i	0.204813	−	0.978801i	$-0.434341\pi$
$971$	−363495.	−	161838.i	−0.385531	−	0.171650i	−0.590344	+	0.807152i	$0.701008\pi$
$972$		0			0
$973$	30969.8	−	3255.05i	0.0327124	−	0.00343821i
$974$		0			0
$975$	−167.503	−	35.6038i	−0.000176203	−	3.74530e-5i
$976$		0			0
$977$	296711.	+	215573.i	0.310845	+	0.225842i	0.732259	−	0.681026i	$-0.238466\pi$
$977$	296711.	+	215573.i	0.310845	+	0.225842i	−0.421414	+	0.906868i	$0.638466\pi$
$978$		0			0
$979$	−58704.1	+	558532.i	−0.0612496	+	0.582751i
$980$		0			0
$981$	−40294.1	+	8564.77i	−0.0418700	+	0.00889975i
$982$		0			0
$983$	544527.	+	490294.i	0.563523	+	0.507399i	0.900932	−	0.433959i	$-0.142884\pi$
$983$	544527.	+	490294.i	0.563523	+	0.507399i	−0.337409	+	0.941358i	$0.609551\pi$
$984$		0			0
$985$	818431.	−	736919.i	0.843548	−	0.759534i
$986$		0			0
$987$	327833.	−	189275.i	0.336526	−	0.194293i
$988$		0			0
$989$	332494.	−	148036.i	0.339931	−	0.151347i
$990$		0			0
$991$		−	441555.i		−	0.449612i	−0.974404	−	0.224806i	$-0.927825\pi$
$991$		−	441555.i		−	0.449612i	0.974404	−	0.224806i	$-0.0721748\pi$
$992$		0			0
$993$	1.46246e6			1.48315
$994$		0			0
$995$	−248849.	−	558925.i	−0.251357	−	0.564556i
$996$		0			0
$997$	445558.	+	771728.i	0.448243	+	0.776380i	0.998272	−	0.0587660i	$-0.0187166\pi$
$997$	445558.	+	771728.i	0.448243	+	0.776380i	−0.550029	+	0.835146i	$0.685383\pi$
$998$		0			0
$999$	−545329.	−	605649.i	−0.546421	−	0.606863i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	124.5.o.a.13.4	✓	88
31.12	odd	30	inner	124.5.o.a.105.4	yes	88

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
124.5.o.a.13.4	✓	88	1.1	even	1	trivial
124.5.o.a.105.4	yes	88	31.12	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)

\(f(q)\)	\(=\)	\(q+(-3.55268 - 7.97945i) q^{3} +(-12.5017 - 21.6535i) q^{5} +(17.4290 + 19.3568i) q^{7} +(3.14955 - 3.49793i) q^{9} +O(q^{10})\)	\(q+(-3.55268 - 7.97945i) q^{3} +(-12.5017 - 21.6535i) q^{5} +(17.4290 + 19.3568i) q^{7} +(3.14955 - 3.49793i) q^{9} +(-41.1889 - 193.779i) q^{11} +(-116.787 - 12.2748i) q^{13} +(-128.369 + 176.684i) q^{15} +(-103.675 + 487.755i) q^{17} +(39.4065 + 374.928i) q^{19} +(92.5373 - 207.842i) q^{21} +(-651.023 + 211.530i) q^{23} +(-0.0834765 + 0.144586i) q^{25} +(-711.975 - 231.335i) q^{27} +(-338.570 - 466.002i) q^{29} +(573.385 + 771.201i) q^{31} +(-1399.92 + 1017.10i) q^{33} +(201.253 - 619.392i) q^{35} +(942.801 + 544.326i) q^{37} +(316.961 + 975.505i) q^{39} +(-2741.04 - 1220.39i) q^{41} +(-528.783 + 55.5773i) q^{43} +(-115.117 - 24.4689i) q^{45} +(1346.10 + 977.997i) q^{47} +(180.055 - 1713.11i) q^{49} +(4260.34 - 905.563i) q^{51} +(-3637.75 - 3275.45i) q^{53} +(-3681.06 + 3314.44i) q^{55} +(2851.72 - 1646.44i) q^{57} +(5502.99 - 2450.09i) q^{59} -1493.50i q^{61} +122.602 q^{63} +(1194.24 + 2682.31i) q^{65} +(1079.60 + 1869.93i) q^{67} +(4000.77 + 4443.30i) q^{69} +(908.888 - 1009.42i) q^{71} +(-1437.83 - 6764.45i) q^{73} +(1.45028 + 0.152430i) q^{75} +(3033.06 - 4174.65i) q^{77} +(-1044.53 + 4914.12i) q^{79} +(643.643 + 6123.85i) q^{81} +(-1715.26 + 3852.54i) q^{83} +(11857.7 - 3852.81i) q^{85} +(-2515.61 + 4357.16i) q^{87} +(-2696.12 - 876.021i) q^{89} +(-1797.88 - 2474.57i) q^{91} +(4116.70 - 7315.12i) q^{93} +(7625.87 - 5540.52i) q^{95} +(1587.10 - 4884.60i) q^{97} +(-807.550 - 466.239i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 88 q - 9 q^{3} + 3 q^{5} - 215 q^{7} - 254 q^{9}+O(q^{10}) \) 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