LMFDB - Embedded newform 124.5.o.a.17.9

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			17.9
Character	$\chi$	$=$	124.17
Dual form			124.5.o.a.73.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(6.45809 + 5.81489i) q^{3} +(4.44246 - 7.69456i) q^{5} +(6.90219 - 65.6700i) q^{7} +(-0.572828 - 5.45009i) q^{9} +O(q^{10})$	\(q+(6.45809 + 5.81489i) q^{3} +(4.44246 - 7.69456i) q^{5} +(6.90219 - 65.6700i) q^{7} +(-0.572828 - 5.45009i) q^{9} +(-9.13834 - 20.5251i) q^{11} +(54.6820 - 257.259i) q^{13} +(73.4328 - 23.8598i) q^{15} +(-91.9936 + 206.621i) q^{17} +(193.842 - 41.2025i) q^{19} +(426.439 - 383.967i) q^{21} +(271.912 + 374.254i) q^{23} +(273.029 + 472.900i) q^{25} +(441.739 - 608.001i) q^{27} +(-463.035 - 150.449i) q^{29} +(-241.675 - 930.115i) q^{31} +(60.3347 - 185.691i) q^{33} +(-474.639 - 344.845i) q^{35} +(569.121 - 328.582i) q^{37} +(1849.07 - 1343.43i) q^{39} +(1383.77 + 1536.83i) q^{41} +(182.899 + 860.473i) q^{43} +(-44.4808 - 19.8041i) q^{45} +(-1158.36 - 3565.06i) q^{47} +(-1916.37 - 407.338i) q^{49} +(-1795.58 + 799.444i) q^{51} +(1056.52 - 111.045i) q^{53} +(-198.528 - 20.8661i) q^{55} +(1491.44 + 861.083i) q^{57} +(-1916.56 + 2128.56i) q^{59} +1550.97i q^{61} -361.861 q^{63} +(-1736.57 - 1563.62i) q^{65} +(-2982.79 + 5166.34i) q^{67} +(-420.218 + 3998.10i) q^{69} +(771.080 + 7336.33i) q^{71} +(-2518.59 - 5656.85i) q^{73} +(-986.617 + 4641.67i) q^{75} +(-1410.95 + 458.447i) q^{77} +(-1856.81 + 4170.46i) q^{79} +(5954.06 - 1265.57i) q^{81} +(-2360.15 + 2125.09i) q^{83} +(1181.18 + 1625.76i) q^{85} +(-2115.48 - 3664.12i) q^{87} +(-3117.25 + 4290.52i) q^{89} +(-16516.8 - 5366.62i) q^{91} +(3847.76 - 7412.08i) q^{93} +(544.102 - 1674.57i) q^{95} +(9328.76 + 6777.74i) q^{97} +(-106.629 + 61.5621i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$3$	6.45809	+	5.81489i	0.717566	+	0.646099i	0.944765	−	0.327749i	$-0.106290\pi$
$3$	6.45809	+	5.81489i	0.717566	+	0.646099i	−0.227199	+	0.973848i	$0.572957\pi$
$4$		0			0
$5$	4.44246	−	7.69456i	0.177698	−	0.307782i	−0.763393	−	0.645934i	$-0.776468\pi$
$5$	4.44246	−	7.69456i	0.177698	−	0.307782i	0.941092	+	0.338151i	$0.109802\pi$
$6$		0			0
$7$	6.90219	−	65.6700i	0.140861	−	1.34020i	−0.664442	−	0.747340i	$-0.731331\pi$
$7$	6.90219	−	65.6700i	0.140861	−	1.34020i	0.805303	−	0.592864i	$-0.202003\pi$
$8$		0			0
$9$	−0.572828	−	5.45009i	−0.00707195	−	0.0672851i
$10$		0			0
$11$	−9.13834	−	20.5251i	−0.0755235	−	0.169629i	0.871838	−	0.489794i	$-0.162928\pi$
$11$	−9.13834	−	20.5251i	−0.0755235	−	0.169629i	−0.947362	+	0.320166i	$0.896261\pi$
$12$		0			0
$13$	54.6820	−	257.259i	0.323562	−	1.52224i	−0.452603	−	0.891712i	$-0.649505\pi$
$13$	54.6820	−	257.259i	0.323562	−	1.52224i	0.776166	−	0.630529i	$-0.217162\pi$
$14$		0			0
$15$	73.4328	−	23.8598i	0.326368	−	0.106043i
$16$		0			0
$17$	−91.9936	+	206.621i	−0.318317	+	0.714952i	−0.999858	−	0.0168279i	$-0.994643\pi$
$17$	−91.9936	+	206.621i	−0.318317	+	0.714952i	0.681541	+	0.731780i	$0.261310\pi$
$18$		0			0
$19$	193.842	−	41.2025i	0.536960	−	0.114134i	0.0685533	−	0.997647i	$-0.478162\pi$
$19$	193.842	−	41.2025i	0.536960	−	0.114134i	0.468406	+	0.883513i	$0.344828\pi$
$20$		0			0
$21$	426.439	−	383.967i	0.966981	−	0.870674i
$22$		0			0
$23$	271.912	+	374.254i	0.514010	+	0.707475i	0.984589	−	0.174883i	$-0.0559548\pi$
$23$	271.912	+	374.254i	0.514010	+	0.707475i	−0.470579	+	0.882358i	$0.655955\pi$
$24$		0			0
$25$	273.029	+	472.900i	0.436847	+	0.756641i
$26$		0			0
$27$	441.739	−	608.001i	0.605952	−	0.834021i
$28$		0			0
$29$	−463.035	−	150.449i	−0.550577	−	0.178893i	0.0204998	−	0.999790i	$-0.493474\pi$
$29$	−463.035	−	150.449i	−0.550577	−	0.178893i	−0.571077	+	0.820896i	$0.693474\pi$
$30$		0			0
$31$	−241.675	−	930.115i	−0.251483	−	0.967862i
$31$	−241.675	−	930.115i	−0.251483	−	0.967862i
$32$		0			0
$33$	60.3347	−	185.691i	0.0554038	−	0.170515i
$34$		0			0
$35$	−474.639	−	344.845i	−0.387460	−	0.281506i
$36$		0			0
$37$	569.121	−	328.582i	0.415720	−	0.240016i	−0.277524	−	0.960719i	$-0.589514\pi$
$37$	569.121	−	328.582i	0.415720	−	0.240016i	0.693245	+	0.720702i	$0.256181\pi$
$38$		0			0
$39$	1849.07	−	1343.43i	1.21570	−	0.883255i
$40$		0			0
$41$	1383.77	+	1536.83i	0.823183	+	0.914237i	0.997515	−	0.0704496i	$-0.0224434\pi$
$41$	1383.77	+	1536.83i	0.823183	+	0.914237i	−0.174332	+	0.984687i	$0.555777\pi$
$42$		0			0
$43$	182.899	+	860.473i	0.0989179	+	0.465372i	0.999527	+	0.0307427i	$0.00978725\pi$
$43$	182.899	+	860.473i	0.0989179	+	0.465372i	−0.900609	+	0.434629i	$0.856879\pi$
$44$		0			0
$45$	−44.4808	−	19.8041i	−0.0219658	−	0.00977982i
$46$		0			0
$47$	−1158.36	−	3565.06i	−0.524382	−	1.61388i	−0.765535	−	0.643394i	$-0.777526\pi$
$47$	−1158.36	−	3565.06i	−0.524382	−	1.61388i	0.241153	−	0.970487i	$-0.422474\pi$
$48$		0			0
$49$	−1916.37	−	407.338i	−0.798156	−	0.169653i
$50$		0			0
$51$	−1795.58	+	799.444i	−0.690343	+	0.307360i
$52$		0			0
$53$	1056.52	−	111.045i	0.376120	−	0.0395318i	0.0854175	−	0.996345i	$-0.472778\pi$
$53$	1056.52	−	111.045i	0.376120	−	0.0395318i	0.290703	+	0.956813i	$0.406111\pi$
$54$		0			0
$55$	−198.528	−	20.8661i	−0.0656291	−	0.00689790i
$56$		0			0
$57$	1491.44	+	861.083i	0.459046	+	0.265030i
$58$		0			0
$59$	−1916.56	+	2128.56i	−0.550578	+	0.611479i	−0.952628	−	0.304139i	$-0.901631\pi$
$59$	−1916.56	+	2128.56i	−0.550578	+	0.611479i	0.402049	+	0.915618i	$0.368298\pi$
$60$		0			0
$61$			1550.97i			0.416815i	0.978042	+	0.208408i	$0.0668281\pi$
$61$			1550.97i			0.416815i	−0.978042	+	0.208408i	$0.933172\pi$
$62$		0			0
$63$	−361.861			−0.0911719
$64$		0			0
$65$	−1736.57	−	1563.62i	−0.411023	−	0.370086i
$66$		0			0
$67$	−2982.79	+	5166.34i	−0.664466	+	1.15089i	0.314964	+	0.949104i	$0.398007\pi$
$67$	−2982.79	+	5166.34i	−0.664466	+	1.15089i	−0.979430	+	0.201785i	$0.935326\pi$
$68$		0			0
$69$	−420.218	+	3998.10i	−0.0882625	+	0.839761i
$70$		0			0
$71$	771.080	+	7336.33i	0.152962	+	1.45533i	0.754401	+	0.656414i	$0.227928\pi$
$71$	771.080	+	7336.33i	0.152962	+	1.45533i	−0.601439	+	0.798919i	$0.705406\pi$
$72$		0			0
$73$	−2518.59	−	5656.85i	−0.472620	−	1.06152i	−0.979854	−	0.199714i	$-0.935999\pi$
$73$	−2518.59	−	5656.85i	−0.472620	−	1.06152i	0.507234	−	0.861808i	$-0.330668\pi$
$74$		0			0
$75$	−986.617	+	4641.67i	−0.175399	+	0.825185i
$76$		0			0
$77$	−1410.95	+	458.447i	−0.237975	+	0.0773228i
$78$		0			0
$79$	−1856.81	+	4170.46i	−0.297518	+	0.668236i	−0.999012	−	0.0444392i	$-0.985850\pi$
$79$	−1856.81	+	4170.46i	−0.297518	+	0.668236i	0.701494	+	0.712675i	$0.252517\pi$
$80$		0			0
$81$	5954.06	−	1265.57i	0.907493	−	0.192894i
$82$		0			0
$83$	−2360.15	+	2125.09i	−0.342597	+	0.308475i	−0.822410	−	0.568895i	$-0.807371\pi$
$83$	−2360.15	+	2125.09i	−0.342597	+	0.308475i	0.479813	+	0.877371i	$0.340704\pi$
$84$		0			0
$85$	1181.18	+	1625.76i	0.163485	+	0.225018i
$86$		0			0
$87$	−2115.48	−	3664.12i	−0.279492	−	0.484095i
$88$		0			0
$89$	−3117.25	+	4290.52i	−0.393542	+	0.541665i	−0.959109	−	0.283038i	$-0.908658\pi$
$89$	−3117.25	+	4290.52i	−0.393542	+	0.541665i	0.565566	+	0.824703i	$0.308658\pi$
$90$		0			0
$91$	−16516.8	−	5366.62i	−1.99454	−	0.648064i
$92$		0			0
$93$	3847.76	−	7412.08i	0.444879	−	0.856987i
$94$		0			0
$95$	544.102	−	1674.57i	0.0602883	−	0.185548i
$96$		0			0
$97$	9328.76	+	6777.74i	0.991472	+	0.720347i	0.960243	−	0.279166i	$-0.0900579\pi$
$97$	9328.76	+	6777.74i	0.991472	+	0.720347i	0.0312290	+	0.999512i	$0.490058\pi$
$98$		0			0
$99$	−106.629	+	61.5621i	−0.0108794	+	0.00628121i
$100$		0			0
$101$	10794.2	−	7842.47i	1.05815	−	0.768794i	0.0844082	−	0.996431i	$-0.473100\pi$
$101$	10794.2	−	7842.47i	1.05815	−	0.768794i	0.973746	+	0.227637i	$0.0731000\pi$
$102$		0			0
$103$	−8077.21	−	8970.65i	−0.761355	−	0.845570i	0.230483	−	0.973076i	$-0.425969\pi$
$103$	−8077.21	−	8970.65i	−0.761355	−	0.845570i	−0.991838	+	0.127506i	$0.959303\pi$
$104$		0			0
$105$	−1060.02	−	4987.02i	−0.0961472	−	0.452337i
$106$		0			0
$107$	−10673.4	−	4752.10i	−0.932255	−	0.415067i	−0.116321	−	0.993212i	$-0.537110\pi$
$107$	−10673.4	−	4752.10i	−0.932255	−	0.415067i	−0.815934	+	0.578145i	$0.803777\pi$
$108$		0			0
$109$	2401.30	+	7390.46i	0.202113	+	0.622040i	0.999820	+	0.0189941i	$0.00604638\pi$
$109$	2401.30	+	7390.46i	0.202113	+	0.622040i	−0.797707	+	0.603046i	$0.793954\pi$
$110$		0			0
$111$	5586.10	+	1187.36i	0.453381	+	0.0963690i
$112$		0			0
$113$	12862.8	−	5726.90i	1.00735	−	0.448500i	0.164341	−	0.986404i	$-0.447450\pi$
$113$	12862.8	−	5726.90i	1.00735	−	0.448500i	0.843006	+	0.537903i	$0.180784\pi$
$114$		0			0
$115$	4087.68	−	429.632i	0.309087	−	0.0324864i
$116$		0			0
$117$	−1433.41	−	150.657i	−0.104712	−	0.0110057i
$118$		0			0
$119$	12933.8	+	7467.36i	0.913342	+	0.527318i
$120$		0			0
$121$	9458.97	−	10505.3i	0.646061	−	0.717523i
$122$		0			0
$123$			17971.5i			1.18788i
$124$		0			0
$125$	10404.8			0.665904
$126$		0			0
$127$	−4976.08	−	4480.48i	−0.308518	−	0.277790i	0.500298	−	0.865854i	$-0.333224\pi$
$127$	−4976.08	−	4480.48i	−0.308518	−	0.277790i	−0.808815	+	0.588063i	$0.799891\pi$
$128$		0			0
$129$	−3822.38	+	6620.55i	−0.229696	+	0.397846i
$130$		0			0
$131$	1039.18	−	9887.12i	0.0605547	−	0.576139i	−0.921610	−	0.388117i	$-0.873126\pi$
$131$	1039.18	−	9887.12i	0.0605547	−	0.576139i	0.982165	−	0.188022i	$-0.0602077\pi$
$132$		0			0
$133$	−1367.83	−	13014.0i	−0.0773265	−	0.735712i
$134$		0			0
$135$	−2715.90	−	6100.01i	−0.149020	−	0.334705i
$136$		0			0
$137$	−2850.51	+	13410.6i	−0.151873	+	0.714508i	0.834636	+	0.550802i	$0.185678\pi$
$137$	−2850.51	+	13410.6i	−0.151873	+	0.714508i	−0.986509	+	0.163706i	$0.947655\pi$
$138$		0			0
$139$	−6111.16	+	1985.64i	−0.316296	+	0.102771i	−0.462863	−	0.886430i	$-0.653178\pi$
$139$	−6111.16	+	1985.64i	−0.316296	+	0.102771i	0.146567	+	0.989201i	$0.453178\pi$
$140$		0			0
$141$	13249.7	−	29759.2i	0.666449	−	1.49687i
$142$		0			0
$143$	−5779.95	+	1228.57i	−0.282652	+	0.0600796i
$144$		0			0
$145$	−3214.66	+	2894.49i	−0.152897	+	0.137669i
$146$		0			0
$147$	−10007.5	−	13774.1i	−0.463117	−	0.637425i
$148$		0			0
$149$	15564.6	+	26958.7i	0.701078	+	1.21430i	0.968088	+	0.250609i	$0.0806309\pi$
$149$	15564.6	+	26958.7i	0.701078	+	1.21430i	−0.267010	+	0.963694i	$0.586036\pi$
$150$		0			0
$151$	11056.2	−	15217.6i	0.484902	−	0.667410i	−0.494536	−	0.869157i	$-0.664662\pi$
$151$	11056.2	−	15217.6i	0.484902	−	0.667410i	0.979438	+	0.201747i	$0.0646619\pi$
$152$		0			0
$153$	1178.80	+	383.015i	0.0503567	+	0.0163619i
$154$		0			0
$155$	−8230.46	−	2272.41i	−0.342579	−	0.0945854i
$156$		0			0
$157$	−6130.90	+	18869.0i	−0.248728	+	0.765506i	0.746273	+	0.665640i	$0.231841\pi$
$157$	−6130.90	+	18869.0i	−0.248728	+	0.765506i	−0.995001	+	0.0998659i	$0.968159\pi$
$158$		0			0
$159$	7468.83	+	5426.42i	0.295432	+	0.214644i
$160$		0			0
$161$	26454.0	−	15273.3i	1.02056	−	0.589223i
$162$		0			0
$163$	22895.0	−	16634.2i	0.861720	−	0.626076i	−0.0666326	−	0.997778i	$-0.521226\pi$
$163$	22895.0	−	16634.2i	0.861720	−	0.626076i	0.928352	+	0.371702i	$0.121226\pi$
$164$		0			0
$165$	−1160.78	−	1289.17i	−0.0426365	−	0.0473526i
$166$		0			0
$167$	5831.76	+	27436.3i	0.209106	+	0.983767i	0.950025	+	0.312173i	$0.101057\pi$
$167$	5831.76	+	27436.3i	0.209106	+	0.983767i	−0.740919	+	0.671594i	$0.765610\pi$
$168$		0			0
$169$	−37100.2	−	16518.1i	−1.29898	−	0.578343i
$170$		0			0
$171$	−335.596	−	1032.86i	−0.0114769	−	0.0353222i
$172$		0			0
$173$	46913.1	+	9971.68i	1.56748	+	0.333178i	0.908139	−	0.418668i	$-0.137503\pi$
$173$	46913.1	+	9971.68i	1.56748	+	0.333178i	0.659339	+	0.751846i	$0.270836\pi$
$174$		0			0
$175$	32939.9	−	14665.8i	1.07559	−	0.478882i
$176$		0			0
$177$	−24754.7	+	2601.82i	−0.790152	+	0.0830483i
$178$		0			0
$179$	−33409.7	−	3511.50i	−1.04272	−	0.109594i	−0.432344	−	0.901709i	$-0.642313\pi$
$179$	−33409.7	−	3511.50i	−1.04272	−	0.109594i	−0.610372	+	0.792115i	$0.708980\pi$
$180$		0			0
$181$	−30108.1	−	17382.9i	−0.919022	−	0.530598i	−0.0356993	−	0.999363i	$-0.511366\pi$
$181$	−30108.1	−	17382.9i	−0.919022	−	0.530598i	−0.883323	+	0.468765i	$0.844699\pi$
$182$		0			0
$183$	−9018.72	+	10016.3i	−0.269304	+	0.299092i
$184$		0			0
$185$		−	5838.85i		−	0.170602i
$186$		0			0
$187$	5081.58			0.145317
$188$		0			0
$189$	−36878.5	−	33205.5i	−1.03240	−	0.929580i
$190$		0			0
$191$	−26427.6	+	45773.9i	−0.724420	+	1.25473i	0.234792	+	0.972046i	$0.424559\pi$
$191$	−26427.6	+	45773.9i	−0.724420	+	1.25473i	−0.959212	+	0.282687i	$0.908774\pi$
$192$		0			0
$193$	−679.761	+	6467.49i	−0.0182491	+	0.173629i	−0.999850	−	0.0173151i	$-0.994488\pi$
$193$	−679.761	+	6467.49i	−0.0182491	+	0.173629i	0.981601	+	0.190944i	$0.0611548\pi$
$194$		0			0
$195$	−2122.68	−	20195.9i	−0.0558232	−	0.531123i
$196$		0			0
$197$	12797.0	+	28742.6i	0.329744	+	0.740617i	0.999999	−	0.00151424i	$-0.000481997\pi$
$197$	12797.0	+	28742.6i	0.329744	+	0.740617i	−0.670255	+	0.742131i	$0.733815\pi$
$198$		0			0
$199$	3564.92	−	16771.6i	0.0900208	−	0.423515i	−0.909941	−	0.414738i	$-0.863873\pi$
$199$	3564.92	−	16771.6i	0.0900208	−	0.423515i	0.999961	−	0.00877626i	$-0.00279361\pi$
$200$		0			0
$201$	−49304.8	+	16020.1i	−1.22039	+	0.396527i
$202$		0			0
$203$	−13076.0	+	29369.1i	−0.317308	+	0.712686i
$204$		0			0
$205$	17972.6	−	3820.19i	0.427664	−	0.0909029i
$206$		0			0
$207$	1883.96	−	1696.33i	0.0439674	−	0.0395885i
$208$		0			0
$209$	−2617.08	−	3602.10i	−0.0599135	−	0.0824639i
$210$		0			0
$211$	25060.5	+	43406.1i	0.562892	+	0.974958i	0.997242	+	0.0742138i	$0.0236447\pi$
$211$	25060.5	+	43406.1i	0.562892	+	0.974958i	−0.434350	+	0.900744i	$0.643022\pi$
$212$		0			0
$213$	−37680.3	+	51862.5i	−0.830529	+	1.14313i
$214$		0			0
$215$	7433.48	+	2415.28i	0.160811	+	0.0522506i
$216$		0			0
$217$	−62748.7	+	9450.96i	−1.33256	+	0.200704i
$218$		0			0
$219$	16628.7	−	51177.8i	0.346712	−	1.06707i
$220$		0			0
$221$	48124.7	+	34964.6i	0.985333	+	0.715887i
$222$		0			0
$223$	−58339.8	+	33682.5i	−1.17315	+	0.677321i	−0.954421	−	0.298463i	$-0.903526\pi$
$223$	−58339.8	+	33682.5i	−1.17315	+	0.677321i	−0.218734	+	0.975785i	$0.570193\pi$
$224$		0			0
$225$	2420.95	−	1758.92i	0.0478213	−	0.0347442i
$226$		0			0
$227$	14795.5	+	16432.1i	0.287130	+	0.318890i	0.869403	−	0.494103i	$-0.164503\pi$
$227$	14795.5	+	16432.1i	0.287130	+	0.318890i	−0.582274	+	0.812993i	$0.697837\pi$
$228$		0			0
$229$	10212.7	+	48046.8i	0.194746	+	0.916207i	0.961615	+	0.274403i	$0.0884803\pi$
$229$	10212.7	+	48046.8i	0.194746	+	0.916207i	−0.766869	+	0.641804i	$0.778186\pi$
$230$		0			0
$231$	−11777.9	−	5243.86i	−0.220721	−	0.0982713i
$232$		0			0
$233$	16877.5	+	51943.6i	0.310883	+	0.956798i	0.977416	+	0.211323i	$0.0677773\pi$
$233$	16877.5	+	51943.6i	0.310883	+	0.956798i	−0.666534	+	0.745475i	$0.732223\pi$
$234$		0			0
$235$	−32577.6	−	6924.58i	−0.589906	−	0.125388i
$236$		0			0
$237$	−36242.2	+	16136.1i	−0.645235	+	0.287277i
$238$		0			0
$239$	54662.0	−	5745.20i	0.956951	−	0.100580i	0.386839	−	0.922147i	$-0.373567\pi$
$239$	54662.0	−	5745.20i	0.956951	−	0.100580i	0.570111	+	0.821568i	$0.306900\pi$
$240$		0			0
$241$	59992.0	+	6305.41i	1.03290	+	0.108562i	0.605781	−	0.795632i	$-0.292861\pi$
$241$	59992.0	+	6305.41i	1.03290	+	0.108562i	0.427122	+	0.904194i	$0.359528\pi$
$242$		0			0
$243$	−6907.39	−	3987.98i	−0.116977	−	0.0675368i
$244$		0			0
$245$	−11647.7	+	12936.1i	−0.194047	+	0.215511i
$246$		0			0
$247$		−	52120.7i		−	0.854312i
$248$		0			0
$249$	−27599.2			−0.445141
$250$		0			0
$251$	18604.0	+	16751.1i	0.295297	+	0.265887i	0.803440	−	0.595386i	$-0.203001\pi$
$251$	18604.0	+	16751.1i	0.295297	+	0.265887i	−0.508142	+	0.861273i	$0.669668\pi$
$252$		0			0
$253$	5196.77	−	9001.06i	0.0811881	−	0.140622i
$254$		0			0
$255$	−1825.42	+	17367.7i	−0.0280726	+	0.267093i
$256$		0			0
$257$	−9436.51	−	89782.4i	−0.142871	−	1.35933i	−0.797472	−	0.603356i	$-0.793830\pi$
$257$	−9436.51	−	89782.4i	−0.142871	−	1.35933i	0.654601	−	0.755975i	$-0.272837\pi$
$258$		0			0
$259$	−17649.8	−	39642.1i	−0.263112	−	0.590959i
$260$		0			0
$261$	−554.723	+	2609.77i	−0.00814320	+	0.0383107i
$262$		0			0
$263$	80890.5	−	26282.9i	1.16946	−	0.379981i	0.341020	−	0.940056i	$-0.389228\pi$
$263$	80890.5	−	26282.9i	1.16946	−	0.379981i	0.828442	+	0.560075i	$0.189228\pi$
$264$		0			0
$265$	3839.11	−	8622.78i	0.0546687	−	0.122788i
$266$		0			0
$267$	−45080.4	+	9582.14i	−0.632361	+	0.134413i
$268$		0			0
$269$	8517.12	−	7668.85i	0.117703	−	0.105980i	−0.608177	−	0.793801i	$-0.708099\pi$
$269$	8517.12	−	7668.85i	0.117703	−	0.105980i	0.725881	+	0.687821i	$0.241432\pi$
$270$		0			0
$271$	−32331.4	−	44500.4i	−0.440237	−	0.605934i	0.530028	−	0.847980i	$-0.322181\pi$
$271$	−32331.4	−	44500.4i	−0.440237	−	0.605934i	−0.970265	+	0.242046i	$0.922181\pi$
$272$		0			0
$273$	−75460.4	−	130701.i	−1.01250	−	1.75370i
$274$		0			0
$275$	7211.27	−	9925.47i	0.0953557	−	0.131246i
$276$		0			0
$277$	−78354.0	−	25458.7i	−1.02118	−	0.331801i	−0.249881	−	0.968277i	$-0.580392\pi$
$277$	−78354.0	−	25458.7i	−1.02118	−	0.331801i	−0.771297	+	0.636476i	$0.780392\pi$
$278$		0			0
$279$	−4930.77	+	1849.95i	−0.0633442	+	0.0237657i
$280$		0			0
$281$	22718.2	−	69919.4i	0.287714	−	0.885493i	−0.697858	−	0.716236i	$-0.745863\pi$
$281$	22718.2	−	69919.4i	0.287714	−	0.885493i	0.985572	−	0.169257i	$-0.0541367\pi$
$282$		0			0
$283$	45716.2	+	33214.7i	0.570817	+	0.414723i	0.835402	−	0.549640i	$-0.185235\pi$
$283$	45716.2	+	33214.7i	0.570817	+	0.414723i	−0.264585	+	0.964362i	$0.585235\pi$
$284$		0			0
$285$	13251.3	−	7650.65i	0.163143	−	0.0941908i
$286$		0			0
$287$	110475.	−	80264.7i	1.34122	−	0.974452i
$288$		0			0
$289$	21657.0	+	24052.6i	0.259300	+	0.287982i
$290$		0			0
$291$	20834.2	+	98017.0i	0.246031	+	1.15748i
$292$		0			0
$293$	147706.	+	65762.8i	1.72053	+	0.766029i	0.997139	+	0.0755882i	$0.0240834\pi$
$293$	147706.	+	65762.8i	1.72053	+	0.766029i	0.723389	+	0.690440i	$0.242583\pi$
$294$		0			0
$295$	7864.08	+	24203.1i	0.0903657	+	0.278117i
$296$		0			0
$297$	−16516.0	−	3510.59i	−0.187237	−	0.0397985i
$298$		0			0
$299$	111149.	−	49486.7i	1.24326	−	0.553536i
$300$		0			0
$301$	57769.6	−	6071.83i	0.637627	−	0.0670173i
$302$		0			0
$303$	115313.	+	12119.9i	1.25601	+	0.132012i
$304$		0			0
$305$	11934.0	+	6890.11i	0.128288	+	0.0740673i
$306$		0			0
$307$	−74323.0	+	82544.1i	−0.788582	+	0.875809i	−0.994711	−	0.102716i	$-0.967247\pi$
$307$	−74323.0	+	82544.1i	−0.788582	+	0.875809i	0.206129	+	0.978525i	$0.433913\pi$
$308$		0			0
$309$		−	104901.i		−	1.09866i
$310$		0			0
$311$	−33799.9			−0.349458			−0.174729	−	0.984617i	$-0.555905\pi$
$311$	−33799.9			−0.349458			−0.174729	+	0.984617i	$0.555905\pi$
$312$		0			0
$313$	−119758.	−	107830.i	−1.22240	−	1.10066i	−0.991825	−	0.127604i	$-0.959271\pi$
$313$	−119758.	−	107830.i	−1.22240	−	1.10066i	−0.230579	−	0.973054i	$-0.574062\pi$
$314$		0			0
$315$	−1607.55	+	2784.36i	−0.0162011	+	0.0280611i
$316$		0			0
$317$	−3572.45	+	33989.6i	−0.0355507	+	0.338242i	0.962261	+	0.272127i	$0.0877271\pi$
$317$	−3572.45	+	33989.6i	−0.0355507	+	0.338242i	−0.997812	+	0.0661151i	$0.978940\pi$
$318$		0			0
$319$	1143.40	+	10878.7i	0.0112361	+	0.106904i
$320$		0			0
$321$	−41296.8	−	92754.1i	−0.400780	−	0.900167i
$322$		0			0
$323$	−9318.97	+	43842.3i	−0.0893229	+	0.420231i
$324$		0			0
$325$	136588.	−	44380.0i	1.29314	−	0.420166i
$326$		0			0
$327$	−27466.9	+	61691.6i	−0.256870	+	0.576939i
$328$		0			0
$329$	−242113.	+	51462.7i	−2.23679	+	0.475445i
$330$		0			0
$331$	87178.2	−	78495.6i	0.795704	−	0.716455i	−0.167310	−	0.985904i	$-0.553508\pi$
$331$	87178.2	−	78495.6i	0.795704	−	0.716455i	0.963015	+	0.269449i	$0.0868415\pi$
$332$		0			0
$333$	−2116.81	−	2913.54i	−0.0190895	−	0.0262744i
$334$		0			0
$335$	26501.8	+	45902.5i	0.236149	+	0.409022i
$336$		0			0
$337$	4299.83	−	5918.21i	0.0378610	−	0.0521112i	−0.789667	−	0.613536i	$-0.789747\pi$
$337$	4299.83	−	5918.21i	0.0378610	−	0.0521112i	0.827528	+	0.561425i	$0.189747\pi$
$338$		0			0
$339$	116371.	+	37811.1i	1.01261	+	0.329018i
$340$		0			0
$341$	−16882.2	+	13460.1i	−0.145184	+	0.115755i
$342$		0			0
$343$	9015.17	−	27745.8i	0.0766277	−	0.235836i
$344$		0			0
$345$	28896.8	+	20994.8i	0.242780	+	0.176390i
$346$		0			0
$347$	50367.3	−	29079.6i	0.418302	−	0.241507i	−0.276049	−	0.961144i	$-0.589025\pi$
$347$	50367.3	−	29079.6i	0.418302	−	0.241507i	0.694351	+	0.719637i	$0.255692\pi$
$348$		0			0
$349$	−26666.0	+	19374.0i	−0.218931	+	0.159063i	−0.691845	−	0.722046i	$-0.743202\pi$
$349$	−26666.0	+	19374.0i	−0.218931	+	0.159063i	0.472914	+	0.881108i	$0.343202\pi$
$350$		0			0
$351$	−132259.	−	146888.i	−1.07352	−	1.19226i
$352$		0			0
$353$	49659.0	+	233627.i	0.398519	+	1.87488i	0.478502	+	0.878087i	$0.341180\pi$
$353$	49659.0	+	233627.i	0.398519	+	1.87488i	−0.0799832	+	0.996796i	$0.525487\pi$
$354$		0			0
$355$	59875.4	+	26658.2i	0.475107	+	0.211531i
$356$		0			0
$357$	40106.1	+	123434.i	0.314683	+	0.968495i
$358$		0			0
$359$	−110001.	−	23381.5i	−0.853512	−	0.181420i	−0.239676	−	0.970853i	$-0.577041\pi$
$359$	−110001.	−	23381.5i	−0.853512	−	0.181420i	−0.613836	+	0.789433i	$0.710374\pi$
$360$		0			0
$361$	−83176.9	+	37032.7i	−0.638246	+	0.284166i
$362$		0			0
$363$	122174.	−	12841.0i	0.927182	−	0.0974507i
$364$		0			0
$365$	−54715.7	−	5750.85i	−0.410702	−	0.0431665i
$366$		0			0
$367$	−140439.	−	81082.3i	−1.04269	−	0.601996i	−0.122095	−	0.992518i	$-0.538961\pi$
$367$	−140439.	−	81082.3i	−1.04269	−	0.601996i	−0.920594	+	0.390522i	$0.872295\pi$
$368$		0			0
$369$	7583.22	−	8422.01i	0.0556930	−	0.0618534i
$370$		0			0
$371$		−	70148.2i		−	0.509646i
$372$		0			0
$373$	31861.3			0.229006			0.114503	−	0.993423i	$-0.463472\pi$
$373$	31861.3			0.229006			0.114503	+	0.993423i	$0.463472\pi$
$374$		0			0
$375$	67194.8	+	60502.5i	0.477830	+	0.430240i
$376$		0			0
$377$	−64024.1	+	110893.i	−0.450465	+	0.780228i
$378$		0			0
$379$	16706.8	−	158955.i	0.116310	−	1.10661i	−0.768239	−	0.640163i	$-0.778867\pi$
$379$	16706.8	−	158955.i	0.116310	−	1.10661i	0.884548	−	0.466448i	$-0.154467\pi$
$380$		0			0
$381$	−6082.46	−	57870.7i	−0.0419015	−	0.398666i
$382$		0			0
$383$	25816.6	+	57985.0i	0.175995	+	0.395292i	0.979907	−	0.199457i	$-0.0639179\pi$
$383$	25816.6	+	57985.0i	0.175995	+	0.395292i	−0.803911	+	0.594749i	$0.797251\pi$
$384$		0			0
$385$	−2740.56	+	12893.3i	−0.0184892	+	0.0869847i
$386$		0			0
$387$	4584.88	−	1489.72i	0.0306130	−	0.00994678i
$388$		0			0
$389$	−83572.2	+	187706.i	−0.552285	+	1.24045i	0.394593	+	0.918856i	$0.370886\pi$
$389$	−83572.2	+	187706.i	−0.552285	+	1.24045i	−0.946877	+	0.321595i	$0.895781\pi$
$390$		0			0
$391$	−102343.	+	21753.7i	−0.669428	+	0.142291i
$392$		0			0
$393$	64203.7	−	57809.2i	0.415695	−	0.374293i
$394$		0			0
$395$	23841.1	+	32814.4i	0.152803	+	0.210315i
$396$		0			0
$397$	−49011.4	−	84890.1i	−0.310968	−	0.538612i	0.667604	−	0.744516i	$-0.267320\pi$
$397$	−49011.4	−	84890.1i	−0.310968	−	0.538612i	−0.978572	+	0.205904i	$0.933987\pi$
$398$		0			0
$399$	66841.5	−	91999.5i	0.419856	−	0.577882i
$400$		0			0
$401$	−137760.	−	44760.8i	−0.856708	−	0.278361i	−0.152455	−	0.988310i	$-0.548718\pi$
$401$	−137760.	−	44760.8i	−0.856708	−	0.278361i	−0.704253	+	0.709949i	$0.748718\pi$
$402$		0			0
$403$	−252496.	+	11312.4i	−1.55469	+	0.0696539i
$404$		0			0
$405$	16712.6	−	51436.2i	0.101891	−	0.313587i
$406$		0			0
$407$	−11945.0	−	8678.54i	−0.0721102	−	0.0523911i
$408$		0			0
$409$	−6075.66	+	3507.78i	−0.0363201	+	0.0209694i	−0.518050	−	0.855350i	$-0.673342\pi$
$409$	−6075.66	+	3507.78i	−0.0363201	+	0.0209694i	0.481730	+	0.876320i	$0.340009\pi$
$410$		0			0
$411$	−96390.0	+	70031.5i	−0.570622	+	0.414581i
$412$		0			0
$413$	126554.	+	140552.i	0.741952	+	0.824021i
$414$		0			0
$415$	5866.76	+	27600.9i	0.0340645	+	0.160261i
$416$		0			0
$417$	−51012.7	−	22712.3i	−0.293363	−	0.130614i
$418$		0			0
$419$	24280.3	+	74727.1i	0.138301	+	0.425647i	0.996089	−	0.0883568i	$-0.0281616\pi$
$419$	24280.3	+	74727.1i	0.138301	+	0.425647i	−0.857788	+	0.514004i	$0.828162\pi$
$420$		0			0
$421$	29131.2	+	6192.02i	0.164359	+	0.0349356i	0.289356	−	0.957222i	$-0.406559\pi$
$421$	29131.2	+	6192.02i	0.164359	+	0.0349356i	−0.124997	+	0.992157i	$0.539892\pi$
$422$		0			0
$423$	−18766.4	+	8355.33i	−0.104882	+	0.0466964i
$424$		0			0
$425$	−122828.	+	12909.8i	−0.680017	+	0.0714727i
$426$		0			0
$427$	101852.	+	10705.1i	0.558617	+	0.0587130i
$428$		0			0
$429$	−44471.5	−	25675.6i	−0.241639	−	0.139510i
$430$		0			0
$431$	70230.4	−	77998.7i	0.378068	−	0.419887i	−0.523839	−	0.851817i	$-0.675501\pi$
$431$	70230.4	−	77998.7i	0.378068	−	0.419887i	0.901907	+	0.431930i	$0.142167\pi$
$432$		0			0
$433$			145452.i			0.775787i	0.921704	+	0.387894i	$0.126797\pi$
$433$			145452.i			0.775787i	−0.921704	+	0.387894i	$0.873203\pi$
$434$		0			0
$435$	−37591.7			−0.198661
$436$		0			0
$437$	68128.2	+	61342.9i	0.356750	+	0.321219i
$438$		0			0
$439$	−153950.	+	266649.i	−0.798822	+	1.38360i	0.121562	+	0.992584i	$0.461210\pi$
$439$	−153950.	+	266649.i	−0.798822	+	1.38360i	−0.920384	+	0.391016i	$0.872124\pi$
$440$		0			0
$441$	−1122.28	+	10677.7i	−0.00577062	+	0.0549038i
$442$		0			0
$443$	−33064.0	−	314583.i	−0.168480	−	1.60298i	−0.673041	−	0.739605i	$-0.735012\pi$
$443$	−33064.0	−	314583.i	−0.168480	−	1.60298i	0.504561	−	0.863376i	$-0.331654\pi$
$444$		0			0
$445$	19165.5	+	43046.3i	0.0967830	+	0.217378i
$446$		0			0
$447$	−56244.3	+	264609.i	−0.281490	+	1.32431i
$448$		0			0
$449$	−192170.	+	62439.7i	−0.953218	+	0.309719i	−0.744023	−	0.668154i	$-0.767085\pi$
$449$	−192170.	+	62439.7i	−0.953218	+	0.309719i	−0.209196	+	0.977874i	$0.567085\pi$
$450$		0			0
$451$	18898.2	−	42446.1i	0.0929111	−	0.208682i
$452$		0			0
$453$	159891.	−	33985.9i	0.779162	−	0.165616i
$454$		0			0
$455$	−114669.	+	103248.i	−0.553888	+	0.498723i
$456$		0			0
$457$	−156309.	−	215141.i	−0.748432	−	1.03013i	−0.998089	−	0.0617944i	$-0.980318\pi$
$457$	−156309.	−	215141.i	−0.748432	−	1.03013i	0.249656	−	0.968334i	$-0.419682\pi$
$458$		0			0
$459$	84988.7	+	147205.i	0.403400	+	0.698709i
$460$		0			0
$461$	−29185.7	+	40170.7i	−0.137331	+	0.189020i	−0.872143	−	0.489251i	$-0.837270\pi$
$461$	−29185.7	+	40170.7i	−0.137331	+	0.189020i	0.734812	+	0.678271i	$0.237270\pi$
$462$		0			0
$463$	309649.	+	100611.i	1.44446	+	0.469335i	0.923286	−	0.384112i	$-0.125493\pi$
$463$	309649.	+	100611.i	1.44446	+	0.469335i	0.521179	+	0.853448i	$0.325493\pi$
$464$		0			0
$465$	−39939.2	−	62534.7i	−0.184711	−	0.289211i
$466$		0			0
$467$	6523.54	−	20077.4i	0.0299123	−	0.0920606i	−0.934986	−	0.354685i	$-0.884588\pi$
$467$	6523.54	−	20077.4i	0.0299123	−	0.0920606i	0.964898	+	0.262625i	$0.0845881\pi$
$468$		0			0
$469$	318685.	+	231539.i	1.44883	+	1.05263i
$470$		0			0
$471$	−149315.	+	86206.9i	−0.673071	+	0.388598i
$472$		0			0
$473$	15989.9	−	11617.3i	0.0714698	−	0.0519258i
$474$		0			0
$475$	72409.3	+	80418.7i	0.320928	+	0.356426i
$476$		0			0
$477$	−1210.41	−	5694.53i	−0.00531980	−	0.0250277i
$478$		0			0
$479$	−237640.	−	105804.i	−1.03573	−	0.461138i	−0.182796	−	0.983151i	$-0.558515\pi$
$479$	−237640.	−	105804.i	−1.03573	−	0.461138i	−0.852938	+	0.522012i	$0.825181\pi$
$480$		0			0
$481$	−53409.9	−	164379.i	−0.230851	−	0.710486i
$482$		0			0
$483$	259655.	+	55191.4i	1.11302	+	0.236579i
$484$		0			0
$485$	93594.3	−	41670.9i	0.397893	−	0.177153i
$486$		0			0
$487$	−167436.	+	17598.3i	−0.705978	+	0.0742013i	−0.450712	−	0.892669i	$-0.648830\pi$
$487$	−167436.	+	17598.3i	−0.705978	+	0.0742013i	−0.255266	+	0.966871i	$0.582163\pi$
$488$		0			0
$489$	244584.	+	25706.8i	1.02285	+	0.107506i
$490$		0			0
$491$	−179543.	−	103659.i	−0.744741	−	0.429976i	0.0790497	−	0.996871i	$-0.474811\pi$
$491$	−179543.	−	103659.i	−0.744741	−	0.429976i	−0.823790	+	0.566894i	$0.808145\pi$
$492$		0			0
$493$	73682.3	−	81832.5i	0.303158	−	0.336691i
$494$		0			0
$495$			1093.95i			0.00446464i
$496$		0			0
$497$	487099.			1.97199
$498$		0			0
$499$	−116504.	−	104901.i	−0.467888	−	0.421288i	0.401166	−	0.916005i	$-0.368605\pi$
$499$	−116504.	−	104901.i	−0.467888	−	0.421288i	−0.869054	+	0.494717i	$0.835272\pi$
$500$		0			0
$501$	−121877.	+	211097.i	−0.485563	+	0.841021i
$502$		0			0
$503$	41032.6	−	390399.i	0.162179	−	1.54303i	−0.546479	−	0.837473i	$-0.684032\pi$
$503$	41032.6	−	390399.i	0.162179	−	1.54303i	0.708657	−	0.705553i	$-0.249301\pi$
$504$		0			0
$505$	−12391.4	−	117897.i	−0.0485891	−	0.462295i
$506$		0			0
$507$	−143546.	−	322409.i	−0.558437	−	1.25427i
$508$		0			0
$509$	97113.4	−	456883.i	0.374838	−	1.76347i	−0.236034	−	0.971745i	$-0.575848\pi$
$509$	97113.4	−	456883.i	0.374838	−	1.76347i	0.610872	−	0.791730i	$-0.290819\pi$
$510$		0			0
$511$	−388869.	+	126351.i	−1.48923	+	0.483880i
$512$		0			0
$513$	60576.6	−	136057.i	0.230181	−	0.516996i
$514$		0			0
$515$	−104908.	+	22298.9i	−0.395543	+	0.0840753i
$516$		0			0
$517$	−62587.7	+	56354.2i	−0.234157	+	0.210836i
$518$		0			0
$519$	244985.	+	337192.i	0.909503	+	1.25182i
$520$		0			0
$521$	−245165.	−	424639.i	−0.903199	−	1.56439i	−0.823316	−	0.567583i	$-0.807879\pi$
$521$	−245165.	−	424639.i	−0.903199	−	1.56439i	−0.0798832	−	0.996804i	$-0.525455\pi$
$522$		0			0
$523$	10660.9	−	14673.5i	0.0389756	−	0.0536453i	−0.789084	−	0.614285i	$-0.789445\pi$
$523$	10660.9	−	14673.5i	0.0389756	−	0.0536453i	0.828060	+	0.560639i	$0.189445\pi$
$524$		0			0
$525$	298008.	+	96828.8i	1.08121	+	0.351306i
$526$		0			0
$527$	214414.	+	35629.5i	0.772026	+	0.128289i
$528$		0			0
$529$	20345.4	−	62616.6i	0.0727033	−	0.223758i
$530$		0			0
$531$	12698.7	+	9226.14i	0.0450371	+	0.0327214i
$532$		0			0
$533$	471031.	−	271950.i	1.65804	−	0.957270i
$534$		0			0
$535$	−83981.4	+	61016.1i	−0.293410	+	0.213175i
$536$		0			0
$537$	−195344.	−	216951.i	−0.677408	−	0.752338i
$538$		0			0
$539$	9151.85	+	43056.1i	0.0315015	+	0.148203i
$540$		0			0
$541$	322411.	+	143546.i	1.10158	+	0.490454i	0.875286	−	0.483606i	$-0.160673\pi$
$541$	322411.	+	143546.i	1.10158	+	0.490454i	0.226291	+	0.974060i	$0.427340\pi$
$542$		0			0
$543$	−93361.0	−	287336.i	−0.316640	−	0.974518i
$544$		0			0
$545$	67534.0	+	14354.8i	0.227368	+	0.0483286i
$546$		0			0
$547$	492389.	−	219226.i	1.64563	−	0.732684i	0.646102	−	0.763251i	$-0.276398\pi$
$547$	492389.	−	219226.i	1.64563	−	0.732684i	0.999533	+	0.0305670i	$0.00973129\pi$
$548$		0			0
$549$	8452.92	−	888.438i	0.0280454	−	0.00294769i
$550$		0			0
$551$	−95954.8	−	10085.3i	−0.316056	−	0.0332188i
$552$		0			0
$553$	261058.	+	150722.i	0.853663	+	0.492863i
$554$		0			0
$555$	33952.3	−	37707.8i	0.110226	−	0.122418i
$556$		0			0
$557$			228233.i			0.735645i	0.929896	+	0.367823i	$0.119897\pi$
$557$			228233.i			0.735645i	−0.929896	+	0.367823i	$0.880103\pi$
$558$		0			0
$559$	231365.			0.740414
$560$		0			0
$561$	32817.3	+	29548.8i	0.104274	+	0.0938889i
$562$		0			0
$563$	−16240.7	+	28129.7i	−0.0512374	+	0.0887458i	−0.890507	−	0.454970i	$-0.849650\pi$
$563$	−16240.7	+	28129.7i	−0.0512374	+	0.0887458i	0.839269	+	0.543716i	$0.182983\pi$
$564$		0			0
$565$	13076.6	−	124415.i	0.0409635	−	0.389742i
$566$		0			0
$567$	−42014.2	−	399738.i	−0.130686	−	1.24340i
$568$		0			0
$569$	−89054.0	−	200018.i	−0.275061	−	0.617797i	0.722206	−	0.691678i	$-0.243128\pi$
$569$	−89054.0	−	200018.i	−0.275061	−	0.617797i	−0.997267	+	0.0738811i	$0.976461\pi$
$570$		0			0
$571$	−110884.	+	521670.i	−0.340094	+	1.60001i	0.392768	+	0.919637i	$0.371517\pi$
$571$	−110884.	+	521670.i	−0.340094	+	1.60001i	−0.732862	+	0.680377i	$0.761816\pi$
$572$		0			0
$573$	−436842.	+	141939.i	−1.33050	+	0.432306i
$574$		0			0
$575$	−102745.	+	230769.i	−0.310760	+	0.697979i
$576$		0			0
$577$	89899.1	−	19108.6i	0.270025	−	0.0573956i	−0.0709092	−	0.997483i	$-0.522590\pi$
$577$	89899.1	−	19108.6i	0.270025	−	0.0573956i	0.340934	+	0.940087i	$0.389257\pi$
$578$		0			0
$579$	−41997.7	+	37814.9i	−0.125276	+	0.112799i
$580$		0			0
$581$	123264.	+	169659.i	0.365161	+	0.502601i
$582$		0			0
$583$	−11934.1	−	20670.4i	−0.0351117	−	0.0608152i
$584$		0			0
$585$	−7527.09	+	10360.1i	−0.0219946	+	0.0302729i
$586$		0			0
$587$	−461214.	−	149858.i	−1.33852	−	0.434913i	−0.449708	−	0.893176i	$-0.648472\pi$
$587$	−461214.	−	149858.i	−1.33852	−	0.434913i	−0.888817	+	0.458263i	$0.848472\pi$
$588$		0			0
$589$	−85169.9	−	170338.i	−0.245502	−	0.491000i
$590$		0			0
$591$	−84490.7	+	260036.i	−0.241899	+	0.744488i
$592$		0			0
$593$	241293.	+	175310.i	0.686176	+	0.498536i	0.875401	−	0.483398i	$-0.160598\pi$
$593$	241293.	+	175310.i	0.686176	+	0.498536i	−0.189225	+	0.981934i	$0.560598\pi$
$594$		0			0
$595$	114916.	−	66346.8i	0.324599	−	0.187407i
$596$		0			0
$597$	120548.	−	87583.0i	0.338228	−	0.245737i
$598$		0			0
$599$	−163425.	−	181502.i	−0.455475	−	0.505856i	0.471041	−	0.882111i	$-0.343878\pi$
$599$	−163425.	−	181502.i	−0.455475	−	0.505856i	−0.926516	+	0.376255i	$0.877212\pi$
$600$		0			0
$601$	−84189.6	−	396081.i	−0.233083	−	1.09657i	−0.926577	−	0.376105i	$-0.877263\pi$
$601$	−84189.6	−	396081.i	−0.233083	−	1.09657i	0.693494	−	0.720462i	$-0.256070\pi$
$602$		0			0
$603$	29865.6	+	13297.0i	0.0821367	+	0.0365696i
$604$		0			0
$605$	−38812.2	−	119452.i	−0.106037	−	0.326349i
$606$		0			0
$607$	−218023.	−	46342.3i	−0.591733	−	0.125777i	−0.0976941	−	0.995216i	$-0.531147\pi$
$607$	−218023.	−	46342.3i	−0.591733	−	0.125777i	−0.494039	+	0.869440i	$0.664480\pi$
$608$		0			0
$609$	−255224.	+	113633.i	−0.688156	+	0.306387i
$610$		0			0
$611$	−980485.	+	103053.i	−2.62639	+	0.276044i
$612$		0			0
$613$	732331.	+	76971.1i	1.94889	+	0.204836i	0.995341	−	0.0964149i	$-0.0307376\pi$
$613$	732331.	+	76971.1i	1.94889	+	0.204836i	0.953545	+	0.301251i	$0.0974042\pi$
$614$		0			0
$615$	138283.	+	79837.5i	0.365609	+	0.211085i
$616$		0			0
$617$	7941.54	−	8819.97i	0.0208610	−	0.0231684i	−0.732624	−	0.680634i	$-0.761705\pi$
$617$	7941.54	−	8819.97i	0.0208610	−	0.0231684i	0.753485	+	0.657465i	$0.228371\pi$
$618$		0			0
$619$			630666.i			1.64596i	0.568074	+	0.822978i	$0.307689\pi$
$619$			630666.i			1.64596i	−0.568074	+	0.822978i	$0.692311\pi$
$620$		0			0
$621$	347661.			0.901514
$622$		0			0
$623$	260243.	+	234324.i	0.670506	+	0.603726i
$624$		0			0
$625$	−124421.	+	215503.i	−0.318517	+	0.551687i
$626$		0			0
$627$	4044.49	−	38480.8i	0.0102879	−	0.0978833i
$628$		0			0
$629$	15536.5	+	147820.i	0.0392691	+	0.373621i
$630$		0			0
$631$	−179876.	−	404008.i	−0.451766	−	1.01468i	−0.985600	−	0.169094i	$-0.945916\pi$
$631$	−179876.	−	404008.i	−0.451766	−	1.01468i	0.533833	−	0.845590i	$-0.320751\pi$
$632$		0			0
$633$	−90558.6	+	426045.i	−0.226007	+	1.06328i
$634$		0			0
$635$	−56581.4	+	18384.4i	−0.140322	+	0.0455934i
$636$		0			0
$637$	−209582.	+	470730.i	−0.516507	+	1.16009i
$638$		0			0
$639$	39542.0	−	8404.91i	0.0968405	−	0.0205841i
$640$		0			0
$641$	−382773.	+	344651.i	−0.931592	+	0.838809i	−0.987174	−	0.159645i	$-0.948965\pi$
$641$	−382773.	+	344651.i	−0.931592	+	0.838809i	0.0555827	+	0.998454i	$0.482298\pi$
$642$		0			0
$643$	456120.	+	627796.i	1.10321	+	1.51844i	0.831062	+	0.556179i	$0.187733\pi$
$643$	456120.	+	627796.i	1.10321	+	1.51844i	0.272146	+	0.962256i	$0.412267\pi$
$644$		0			0
$645$	33961.5	+	58823.0i	0.0816333	+	0.141393i
$646$		0			0
$647$	397859.	−	547606.i	0.950432	−	1.30816i	−0.000903715	−	1.00000i	$-0.500288\pi$
$647$	397859.	−	547606.i	0.950432	−	1.30816i	0.951335	−	0.308157i	$-0.0997123\pi$
$648$		0			0
$649$	61203.0	+	19886.1i	0.145306	+	0.0472128i
$650$		0			0
$651$	−460193.	−	303842.i	−1.08587	−	0.716945i
$652$		0			0
$653$	−45226.0	+	139191.i	−0.106062	+	0.326427i	−0.989978	−	0.141219i	$-0.954898\pi$
$653$	−45226.0	+	139191.i	−0.106062	+	0.326427i	0.883916	+	0.467646i	$0.154898\pi$
$654$		0			0
$655$	−71460.6	−	51919.1i	−0.166565	−	0.121017i
$656$		0			0
$657$	−29387.6	+	16967.0i	−0.0680822	+	0.0393073i
$658$		0			0
$659$	85062.3	−	61801.4i	0.195869	−	0.142307i	−0.485528	−	0.874221i	$-0.661373\pi$
$659$	85062.3	−	61801.4i	0.195869	−	0.142307i	0.681397	+	0.731914i	$0.261373\pi$
$660$		0			0
$661$	−362618.	−	402729.i	−0.829941	−	0.921742i	0.168006	−	0.985786i	$-0.446267\pi$
$661$	−362618.	−	402729.i	−0.829941	−	0.921742i	−0.997947	+	0.0640435i	$0.979600\pi$
$662$		0			0
$663$	107478.	+	505644.i	0.244508	+	1.15032i
$664$		0			0
$665$	−106214.	−	47289.4i	−0.240180	−	0.106935i
$666$		0			0
$667$	−69598.4	−	214202.i	−0.156440	−	0.481473i
$668$		0			0
$669$	−572624.	−	121715.i	−1.27943	−	0.271952i
$670$		0			0
$671$	31833.7	−	14173.3i	0.0707038	−	0.0314793i
$672$		0			0
$673$	163364.	−	17170.2i	0.360683	−	0.0379093i	0.0775461	−	0.996989i	$-0.475292\pi$
$673$	163364.	−	17170.2i	0.360683	−	0.0379093i	0.283137	+	0.959079i	$0.408625\pi$
$674$		0			0
$675$	408132.	+	42896.4i	0.895762	+	0.0941484i
$676$		0			0
$677$	7632.77	+	4406.78i	0.0166535	+	0.00961488i	0.508304	−	0.861178i	$-0.330273\pi$
$677$	7632.77	+	4406.78i	0.0166535	+	0.00961488i	−0.491650	+	0.870793i	$0.663606\pi$
$678$		0			0
$679$	509483.	−	565838.i	1.10507	−	1.22731i
$680$		0			0
$681$			192154.i			0.414339i
$682$		0			0
$683$	−659285.			−1.41329			−0.706645	−	0.707568i	$-0.749792\pi$
$683$	−659285.			−1.41329			−0.706645	+	0.707568i	$0.749792\pi$
$684$		0			0
$685$	90525.4	+	81509.4i	0.192925	+	0.173711i
$686$		0			0
$687$	−213433.	+	369676.i	−0.452217	+	0.783264i
$688$		0			0
$689$	29205.5	−	277872.i	0.0615214	−	0.585337i
$690$		0			0
$691$	44479.2	+	423192.i	0.0931540	+	0.886301i	0.936909	+	0.349573i	$0.113673\pi$
$691$	44479.2	+	423192.i	0.0931540	+	0.886301i	−0.843755	+	0.536728i	$0.819660\pi$
$692$		0			0
$693$	3306.81	+	7427.22i	0.00688562	+	0.0154654i
$694$		0			0
$695$	−11870.0	+	55843.8i	−0.0245742	+	0.115613i
$696$		0			0
$697$	−444840.	+	144537.i	−0.915669	+	0.297519i
$698$		0			0
$699$	−193050.	+	433597.i	−0.395108	+	0.887426i
$700$		0			0
$701$	−822128.	+	174749.i	−1.67303	+	0.355613i	−0.944273	−	0.329162i	$-0.893234\pi$
$701$	−822128.	+	174749.i	−1.67303	+	0.355613i	−0.728754	+	0.684775i	$0.759900\pi$
$702$		0			0
$703$	96781.4	−	87142.3i	0.195831	−	0.176327i
$704$		0			0
$705$	−170123.	−	234155.i	−0.342283	−	0.471112i
$706$		0			0
$707$	−440511.	−	762987.i	−0.881288	−	1.52644i
$708$		0			0
$709$	387554.	−	533423.i	0.770975	−	1.06116i	−0.225246	−	0.974302i	$-0.572319\pi$
$709$	387554.	−	533423.i	0.770975	−	1.06116i	0.996221	−	0.0868538i	$-0.0276813\pi$
$710$		0			0
$711$	23793.0	+	7730.82i	0.0470663	+	0.0152928i
$712$		0			0
$713$	282385.	−	343357.i	0.555473	−	0.675409i
$714$		0			0
$715$	−16223.9	+	49932.1i	−0.0317354	+	0.0976714i
$716$		0			0
$717$	386420.	+	280750.i	0.751659	+	0.546112i
$718$		0			0
$719$	446357.	−	257705.i	0.863426	−	0.498499i	−0.00173220	−	0.999998i	$-0.500551\pi$
$719$	446357.	−	257705.i	0.863426	−	0.498499i	0.865158	+	0.501499i	$0.167218\pi$
$720$		0			0
$721$	−644853.	+	468513.i	−1.24048	+	0.901263i
$722$		0			0
$723$	350768.	+	389568.i	0.671033	+	0.745258i
$724$		0			0
$725$	−55274.6	−	260047.i	−0.105160	−	0.494738i
$726$		0			0
$727$	713230.	+	317550.i	1.34946	+	0.600819i	0.948937	−	0.315467i	$-0.102161\pi$
$727$	713230.	+	317550.i	1.34946	+	0.600819i	0.400525	+	0.916286i	$0.368828\pi$
$728$		0			0
$729$	−173781.	−	534842.i	−0.326999	−	1.00640i
$730$		0			0
$731$	−194617.	−	41367.2i	−0.364206	−	0.0774143i
$732$		0			0
$733$	−541872.	+	241257.i	−1.00853	+	0.449027i	−0.843424	−	0.537249i	$-0.819464\pi$
$733$	−541872.	+	241257.i	−1.00853	+	0.449027i	−0.165107	+	0.986276i	$0.552797\pi$
$734$		0			0
$735$	−150444.	+	15812.3i	−0.278483	+	0.0292698i
$736$		0			0
$737$	133297.	+	14010.1i	0.245406	+	0.0257932i
$738$		0			0
$739$	−530295.	−	306166.i	−0.971021	−	0.560619i	−0.0714737	−	0.997442i	$-0.522770\pi$
$739$	−530295.	−	306166.i	−0.971021	−	0.560619i	−0.899547	+	0.436823i	$0.856104\pi$
$740$		0			0
$741$	303076.	−	336600.i	0.551970	−	0.613025i
$742$		0			0
$743$		−	433160.i		−	0.784641i	−0.919829	−	0.392320i	$-0.871672\pi$
$743$		−	433160.i		−	0.784641i	0.919829	−	0.392320i	$-0.128328\pi$
$744$		0			0
$745$	276581.			0.498321
$746$		0			0
$747$	12933.9	+	11645.7i	0.0231786	+	0.0208701i
$748$		0			0
$749$	−385740.	+	668122.i	−0.687593	+	1.19095i
$750$		0			0
$751$	−13192.8	+	125521.i	−0.0233915	+	0.222555i	0.976581	+	0.215150i	$0.0690239\pi$
$751$	−13192.8	+	125521.i	−0.0233915	+	0.222555i	−0.999973	+	0.00740534i	$0.997643\pi$
$752$		0			0
$753$	22740.4	+	216361.i	0.0401059	+	0.381583i
$754$		0			0
$755$	−67976.0	−	152677.i	−0.119251	−	0.267842i
$756$		0			0
$757$	−115358.	+	542716.i	−0.201306	+	0.947068i	0.755232	+	0.655458i	$0.227524\pi$
$757$	−115358.	+	542716.i	−0.201306	+	0.947068i	−0.956537	+	0.291610i	$0.905809\pi$
$758$		0			0
$759$	85901.4	−	27911.1i	0.149113	−	0.0484499i
$760$		0			0
$761$	−421273.	+	946194.i	−0.727435	+	1.63385i	0.0451869	+	0.998979i	$0.485612\pi$
$761$	−421273.	+	946194.i	−0.727435	+	1.63385i	−0.772622	+	0.634867i	$0.781055\pi$
$762$		0			0
$763$	501905.	−	106683.i	0.862130	−	0.183251i
$764$		0			0
$765$	8183.90	−	7368.82i	0.0139842	−	0.0125914i
$766$		0			0
$767$	442789.	+	609447.i	0.752672	+	1.03596i
$768$		0			0
$769$	−281555.	−	487668.i	−0.476114	−	0.824653i	0.523512	−	0.852018i	$-0.324622\pi$
$769$	−281555.	−	487668.i	−0.476114	−	0.824653i	−0.999626	+	0.0273652i	$0.991288\pi$
$770$		0			0
$771$	461133.	−	634695.i	0.775742	−	1.06772i
$772$		0			0
$773$	1.12062e6	+	364110.i	1.87542	+	0.609360i	0.989299	+	0.145903i	$0.0466086\pi$
$773$	1.12062e6	+	364110.i	1.87542	+	0.609360i	0.886119	+	0.463458i	$0.153391\pi$
$774$		0			0
$775$	373867.	−	368237.i	0.622464	−	0.613089i
$776$		0			0
$777$	116530.	−	358644.i	0.193018	−	0.594048i
$778$		0			0
$779$	331555.	+	240889.i	0.546362	+	0.396955i
$780$		0			0
$781$	143532.	−	82868.4i	0.235314	−	0.135859i
$782$		0			0
$783$	−296014.	+	215067.i	−0.482824	+	0.350792i
$784$		0			0
$785$	117952.	+	130999.i	0.191411	+	0.212583i
$786$		0			0
$787$	146937.	+	691285.i	0.237237	+	1.11611i	0.921953	+	0.387302i	$0.126593\pi$
$787$	146937.	+	691285.i	0.237237	+	1.11611i	−0.684716	+	0.728810i	$0.740074\pi$
$788$		0			0
$789$	675231.	+	300632.i	1.08467	+	0.482927i
$790$		0			0
$791$	−287304.	−	884229.i	−0.459185	−	1.41323i
$792$		0			0
$793$	399000.	+	84810.2i	0.634493	+	0.134866i
$794$		0			0
$795$	74933.9	−	33362.7i	0.118562	−	0.0527870i
$796$		0			0
$797$	−715563.	+	75208.7i	−1.12650	+	0.118400i	−0.649398	−	0.760448i	$-0.724979\pi$
$797$	−715563.	+	75208.7i	−1.12650	+	0.118400i	−0.477101	+	0.878848i	$0.658313\pi$
$798$		0			0
$799$	843179.	+	88621.7i	1.32077	+	0.138818i
$800$		0			0
$801$	25169.4	+	14531.6i	0.0392290	+	0.0226489i
$802$		0			0
$803$	−93091.4	+	103389.i	−0.144371	+	0.160340i
$804$		0			0
$805$		−	271403.i		−	0.418816i
$806$		0			0
$807$	99597.9			0.152934
$808$		0			0
$809$	−309673.	−	278830.i	−0.473157	−	0.426033i	0.397740	−	0.917498i	$-0.369795\pi$
$809$	−309673.	−	278830.i	−0.473157	−	0.426033i	−0.870897	+	0.491465i	$0.836461\pi$
$810$		0			0
$811$	285579.	−	494638.i	0.434195	−	0.752049i	−0.563034	−	0.826434i	$-0.690366\pi$
$811$	285579.	−	494638.i	0.434195	−	0.752049i	0.997230	+	0.0743850i	$0.0236994\pi$
$812$		0			0
$813$	49965.6	−	475391.i	0.0755945	−	0.719234i
$814$		0			0
$815$	−26282.8	−	250064.i	−0.0395691	−	0.376475i
$816$		0			0
$817$	70907.2	+	159260.i	0.106230	+	0.238596i
$818$		0			0
$819$	−19787.3	+	93091.9i	−0.0294998	+	0.138786i
$820$		0			0
$821$	−1.01389e6	+	329431.i	−1.50419	+	0.488741i	−0.941237	−	0.337748i	$-0.890335\pi$
$821$	−1.01389e6	+	329431.i	−1.50419	+	0.488741i	−0.562953	+	0.826489i	$0.690335\pi$
$822$		0			0
$823$	−133352.	+	299513.i	−0.196879	+	0.442198i	−0.984826	−	0.173546i	$-0.944478\pi$
$823$	−133352.	+	299513.i	−0.196879	+	0.442198i	0.787947	+	0.615744i	$0.211144\pi$
$824$		0			0
$825$	104287.	−	22166.8i	0.153222	−	0.0325683i
$826$		0			0
$827$	117775.	−	106045.i	0.172204	−	0.155053i	−0.578522	−	0.815667i	$-0.696370\pi$
$827$	117775.	−	106045.i	0.172204	−	0.155053i	0.750726	+	0.660614i	$0.229704\pi$
$828$		0			0
$829$	−609656.	−	839119.i	−0.887106	−	1.22100i	−0.974402	−	0.224815i	$-0.927822\pi$
$829$	−609656.	−	839119.i	−0.887106	−	1.22100i	0.0872952	−	0.996182i	$-0.472178\pi$
$830$		0			0
$831$	−357977.	−	620035.i	−0.518386	−	0.897871i
$832$		0			0
$833$	260459.	−	358491.i	0.375361	−	0.516640i
$834$		0			0
$835$	237017.	+	77011.6i	0.339944	+	0.110455i
$836$		0			0
$837$	−672269.	−	263929.i	−0.959604	−	0.376736i
$838$		0			0
$839$	395937.	−	1.21857e6i	0.562474	−	1.73112i	−0.112865	−	0.993610i	$-0.536003\pi$
$839$	395937.	−	1.21857e6i	0.562474	−	1.73112i	0.675339	−	0.737508i	$-0.263997\pi$
$840$		0			0
$841$	−380436.	−	276403.i	−0.537885	−	0.390796i
$842$		0			0
$843$	553290.	−	319442.i	0.778570	−	0.449507i
$844$		0			0
$845$	−291915.	+	212089.i	−0.408830	+	0.297033i
$846$		0			0
$847$	−624592.	−	693680.i	−0.870622	−	0.966924i
$848$		0			0
$849$	102099.	+	480338.i	0.141647	+	0.666395i
$850$		0			0
$851$	277724.	+	123651.i	0.383490	+	0.170741i
$852$		0			0
$853$	107546.	+	330993.i	0.147808	+	0.454905i	0.997361	−	0.0725969i	$-0.0231286\pi$
$853$	107546.	+	330993.i	0.147808	+	0.454905i	−0.849554	+	0.527502i	$0.823129\pi$
$854$		0			0
$855$	−9438.25	−	2006.16i	−0.0129110	−	0.00274431i
$856$		0			0
$857$	838120.	−	373155.i	1.14115	−	0.508075i	0.252930	−	0.967485i	$-0.418606\pi$
$857$	838120.	−	373155.i	1.14115	−	0.508075i	0.888224	+	0.459410i	$0.151939\pi$
$858$		0			0
$859$	−273126.	+	28706.7i	−0.370149	+	0.0389042i	−0.287777	−	0.957697i	$-0.592916\pi$
$859$	−273126.	+	28706.7i	−0.370149	+	0.0389042i	−0.0823717	+	0.996602i	$0.526249\pi$
$860$		0			0
$861$	1.18019e6	+	124043.i	1.59201	+	0.167326i
$862$		0			0
$863$	70883.6	+	40924.7i	0.0951753	+	0.0549495i	0.546832	−	0.837242i	$-0.315834\pi$
$863$	70883.6	+	40924.7i	0.0951753	+	0.0549495i	−0.451657	+	0.892192i	$0.649167\pi$
$864$		0			0
$865$	285137.	−	316677.i	0.381084	−	0.423237i
$866$		0			0
$867$			281267.i			0.374180i
$868$		0			0
$869$	102567.			0.135821
$870$		0			0
$871$	1.16598e6	+	1.04985e6i	1.53693	+	1.38386i
$872$		0			0
$873$	31595.5	−	54725.1i	0.0414569	−	0.0718055i
$874$		0			0
$875$	71815.6	−	683280.i	0.0938000	−	0.892447i
$876$		0			0
$877$	−142909.	−	1.35969e6i	−0.185807	−	1.76783i	−0.548717	−	0.836008i	$-0.684884\pi$
$877$	−142909.	−	1.35969e6i	−0.185807	−	1.76783i	0.362911	−	0.931824i	$-0.381783\pi$
$878$		0			0
$879$	571493.	+	1.28359e6i	0.739662	+	1.66131i
$880$		0			0
$881$	276701.	−	1.30177e6i	0.356499	−	1.67720i	−0.325264	−	0.945623i	$-0.605453\pi$
$881$	276701.	−	1.30177e6i	0.356499	−	1.67720i	0.681763	−	0.731573i	$-0.261213\pi$
$882$		0			0
$883$	−216845.	+	70457.1i	−0.278117	+	0.0903657i	−0.444754	−	0.895653i	$-0.646709\pi$
$883$	−216845.	+	70457.1i	−0.278117	+	0.0903657i	0.166638	+	0.986018i	$0.446709\pi$
$884$		0			0
$885$	−89951.7	+	202035.i	−0.114848	+	0.257952i
$886$		0			0
$887$	−1.06555e6	+	226489.i	−1.35433	+	0.287873i	−0.827199	−	0.561909i	$-0.810067\pi$
$887$	−1.06555e6	+	226489.i	−1.35433	+	0.287873i	−0.527135	+	0.849782i	$0.676734\pi$
$888$		0			0
$889$	−328579.	+	295854.i	−0.415754	+	0.374346i
$890$		0			0
$891$	−80386.3	−	110642.i	−0.101257	−	0.139369i
$892$		0			0
$893$	−371429.	−	643333.i	−0.465771	−	0.806739i
$894$		0			0
$895$	−175440.	+	241473.i	−0.219020	+	0.301455i
$896$		0			0
$897$	1.00557e6	+	326729.i	1.24976	+	0.406072i
$898$		0			0
$899$	−28031.1	+	467036.i	−0.0346834	+	0.577871i
$900$		0			0
$901$	−74249.0	+	228515.i	−0.0914621	+	0.281491i
$902$		0			0
$903$	408389.	+	296712.i	0.500839	+	0.363881i
$904$		0			0
$905$	−267508.	+	154446.i	−0.326617	+	0.188573i
$906$		0			0
$907$	−299898.	+	217889.i	−0.364551	+	0.264862i	−0.754948	−	0.655785i	$-0.772338\pi$
$907$	−299898.	+	217889.i	−0.364551	+	0.264862i	0.390397	+	0.920647i	$0.372338\pi$
$908$		0			0
$909$	−48925.4	−	54337.2i	−0.0592116	−	0.0657611i
$910$		0			0
$911$	2110.65	+	9929.83i	0.00254319	+	0.0119648i	0.979401	−	0.201925i	$-0.0647199\pi$
$911$	2110.65	+	9929.83i	0.00254319	+	0.0119648i	−0.976858	+	0.213890i	$0.931387\pi$
$912$		0			0
$913$	65185.4	+	29022.4i	0.0782003	+	0.0348170i
$914$		0			0
$915$	37005.8	+	113892.i	0.0442005	+	0.136035i
$916$		0			0
$917$	−642115.	−	136486.i	−0.763614	−	0.162311i
$918$		0			0
$919$	−460601.	+	205073.i	−0.545373	+	0.242816i	−0.660881	−	0.750491i	$-0.729817\pi$
$919$	−460601.	+	205073.i	−0.545373	+	0.242816i	0.115508	+	0.993307i	$0.463151\pi$
$920$		0			0
$921$	−959970.	+	100897.i	−1.13172	+	0.118948i
$922$		0			0
$923$	1.92950e6	+	202799.i	2.26486	+	0.238046i
$924$		0			0
$925$	310773.	+	179425.i	0.363212	+	0.209700i
$926$		0			0
$927$	−44264.0	+	49160.2i	−0.0515100	+	0.0572076i
$928$		0			0
$929$		−	37173.6i		−	0.0430728i	−0.999768	−	0.0215364i	$-0.993144\pi$
$929$		−	37173.6i		−	0.0430728i	0.999768	−	0.0215364i	$-0.00685578\pi$
$930$		0			0
$931$	−388258.			−0.447941
$932$		0			0
$933$	−218283.	−	196543.i	−0.250759	−	0.225784i
$934$		0			0
$935$	22574.7	−	39100.5i	0.0258225	−	0.0447259i
$936$		0			0
$937$	31157.9	−	296448.i	0.0354887	−	0.337652i	−0.962343	−	0.271837i	$-0.912369\pi$
$937$	31157.9	−	296448.i	0.0354887	−	0.337652i	0.997832	−	0.0658147i	$-0.0209646\pi$
$938$		0			0
$939$	−146385.	−	1.39276e6i	−0.166021	−	1.57959i
$940$		0			0
$941$	−346460.	−	778161.i	−0.391267	−	0.878801i	−0.996566	−	0.0828024i	$-0.973613\pi$
$941$	−346460.	−	778161.i	−0.391267	−	0.878801i	0.605299	−	0.795998i	$-0.293054\pi$
$942$		0			0
$943$	−198903.	+	935764.i	−0.223675	+	1.05231i
$944$		0			0
$945$	−419333.	+	136250.i	−0.469565	+	0.152571i
$946$		0			0
$947$	−207164.	+	465298.i	−0.231001	+	0.518838i	−0.991439	−	0.130574i	$-0.958318\pi$
$947$	−207164.	+	465298.i	−0.231001	+	0.518838i	0.760437	+	0.649412i	$0.224985\pi$
$948$		0			0
$949$	−1.59300e6	+	338602.i	−1.76881	+	0.375973i
$950$		0			0
$951$	−220717.	+	198735.i	−0.244048	+	0.219742i
$952$		0			0
$953$	981197.	+	1.35050e6i	1.08037	+	1.48699i	0.859118	+	0.511777i	$0.171013\pi$
$953$	981197.	+	1.35050e6i	1.08037	+	1.48699i	0.221247	+	0.975218i	$0.428987\pi$
$954$		0			0
$955$	234807.	+	406697.i	0.257456	+	0.445928i
$956$		0			0
$957$	−55874.2	+	76904.3i	−0.0610081	+	0.0839705i
$958$		0			0
$959$	860999.	+	279756.i	0.936193	+	0.304188i
$960$		0			0
$961$	−806707.	+	449571.i	−0.873513	+	0.486801i
$962$		0			0
$963$	−19785.4	+	60893.1i	−0.0213349	+	0.0656622i
$964$		0			0
$965$	46744.7	+	33962.0i	0.0501970	+	0.0364703i
$966$		0			0
$967$	−1.42214e6	+	821073.i	−1.52086	+	0.878069i	−0.521163	+	0.853457i	$0.674502\pi$
$967$	−1.42214e6	+	821073.i	−1.52086	+	0.878069i	−0.999697	+	0.0246123i	$0.992165\pi$
$968$		0			0
$969$	−315121.	+	228949.i	−0.335606	+	0.243832i
$970$		0			0
$971$	−387885.	−	430790.i	−0.411401	−	0.456907i	0.501458	−	0.865182i	$-0.332797\pi$
$971$	−387885.	−	430790.i	−0.411401	−	0.456907i	−0.912859	+	0.408275i	$0.866130\pi$
$972$		0			0
$973$	88216.3	+	415025.i	0.0931801	+	0.438378i
$974$		0			0
$975$	1.14016e6	+	507632.i	1.19938	+	0.533998i
$976$		0			0
$977$	422595.	+	1.30061e6i	0.442726	+	1.36257i	0.884959	+	0.465669i	$0.154186\pi$
$977$	422595.	+	1.30061e6i	0.442726	+	1.36257i	−0.442233	+	0.896900i	$0.645814\pi$
$978$		0			0
$979$	116550.	+	24773.4i	0.121603	+	0.0258476i
$980$		0			0
$981$	38903.1	−	17320.8i	0.0404247	−	0.0179982i
$982$		0			0
$983$	−1.88930e6	+	198573.i	−1.95521	+	0.205501i	−0.996803	−	0.0798994i	$-0.974540\pi$
$983$	−1.88930e6	+	198573.i	−1.95521	+	0.205501i	−0.958408	+	0.285400i	$0.907873\pi$
$984$		0			0
$985$	278012.	+	29220.2i	0.286544	+	0.0301169i
$986$		0			0
$987$	−1.86284e6	−	1.07551e6i	−1.91223	−	1.10403i
$988$		0			0
$989$	−272303.	+	302423.i	−0.278394	+	0.309188i
$990$		0			0
$991$		−	112690.i		−	0.114746i	−0.998353	−	0.0573730i	$-0.981728\pi$
$991$		−	112690.i		−	0.114746i	0.998353	−	0.0573730i	$-0.0182724\pi$
$992$		0			0
$993$	1.01945e6			1.03387
$994$		0			0
$995$	−113213.	−	101938.i	−0.114354	−	0.102965i
$996$		0			0
$997$	371842.	−	644048.i	0.374083	−	0.647930i	−0.616107	−	0.787663i	$-0.711291\pi$
$997$	371842.	−	644048.i	0.374083	−	0.647930i	0.990189	+	0.139733i	$0.0446243\pi$
$998$		0			0
$999$	51624.4	−	491174.i	0.0517278	−	0.492158i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	124.5.o.a.17.9	✓	88
31.11	odd	30	inner	124.5.o.a.73.9	yes	88

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
124.5.o.a.17.9	✓	88	1.1	even	1	trivial
124.5.o.a.73.9	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)

\(f(q)\)	\(=\)	\(q+(6.45809 + 5.81489i) q^{3} +(4.44246 - 7.69456i) q^{5} +(6.90219 - 65.6700i) q^{7} +(-0.572828 - 5.45009i) q^{9} +O(q^{10})\)	\(q+(6.45809 + 5.81489i) q^{3} +(4.44246 - 7.69456i) q^{5} +(6.90219 - 65.6700i) q^{7} +(-0.572828 - 5.45009i) q^{9} +(-9.13834 - 20.5251i) q^{11} +(54.6820 - 257.259i) q^{13} +(73.4328 - 23.8598i) q^{15} +(-91.9936 + 206.621i) q^{17} +(193.842 - 41.2025i) q^{19} +(426.439 - 383.967i) q^{21} +(271.912 + 374.254i) q^{23} +(273.029 + 472.900i) q^{25} +(441.739 - 608.001i) q^{27} +(-463.035 - 150.449i) q^{29} +(-241.675 - 930.115i) q^{31} +(60.3347 - 185.691i) q^{33} +(-474.639 - 344.845i) q^{35} +(569.121 - 328.582i) q^{37} +(1849.07 - 1343.43i) q^{39} +(1383.77 + 1536.83i) q^{41} +(182.899 + 860.473i) q^{43} +(-44.4808 - 19.8041i) q^{45} +(-1158.36 - 3565.06i) q^{47} +(-1916.37 - 407.338i) q^{49} +(-1795.58 + 799.444i) q^{51} +(1056.52 - 111.045i) q^{53} +(-198.528 - 20.8661i) q^{55} +(1491.44 + 861.083i) q^{57} +(-1916.56 + 2128.56i) q^{59} +1550.97i q^{61} -361.861 q^{63} +(-1736.57 - 1563.62i) q^{65} +(-2982.79 + 5166.34i) q^{67} +(-420.218 + 3998.10i) q^{69} +(771.080 + 7336.33i) q^{71} +(-2518.59 - 5656.85i) q^{73} +(-986.617 + 4641.67i) q^{75} +(-1410.95 + 458.447i) q^{77} +(-1856.81 + 4170.46i) q^{79} +(5954.06 - 1265.57i) q^{81} +(-2360.15 + 2125.09i) q^{83} +(1181.18 + 1625.76i) q^{85} +(-2115.48 - 3664.12i) q^{87} +(-3117.25 + 4290.52i) q^{89} +(-16516.8 - 5366.62i) q^{91} +(3847.76 - 7412.08i) q^{93} +(544.102 - 1674.57i) q^{95} +(9328.76 + 6777.74i) q^{97} +(-106.629 + 61.5621i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 88 q - 9 q^{3} + 3 q^{5} - 215 q^{7} - 254 q^{9}+O(q^{10}) \) 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

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