LMFDB - Embedded newform 124.6.f.a.33.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [124,6,Mod(33,124)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(124, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 8]))

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

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

chi := DirichletCharacter("124.33");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 124 = 2^{2} \cdot 31 $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	124.f (of order $5$, degree $4$, 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:	$19.8875936568$
Analytic rank:	$0$
Dimension:	$56$
Relative dimension:	$14$ over $\Q(\zeta_{5})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			33.4
Character	$\chi$	$=$	124.33
Dual form			124.6.f.a.109.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-13.2483 + 9.62542i) q^{3} -92.0437 q^{5} +(-28.3654 - 87.2998i) q^{7} +(7.77640 - 23.9333i) q^{9} +O(q^{10})$	\(q+(-13.2483 + 9.62542i) q^{3} -92.0437 q^{5} +(-28.3654 - 87.2998i) q^{7} +(7.77640 - 23.9333i) q^{9} +(-174.475 - 536.979i) q^{11} +(-861.205 + 625.702i) q^{13} +(1219.42 - 885.959i) q^{15} +(224.644 - 691.383i) q^{17} +(2057.18 + 1494.63i) q^{19} +(1216.09 + 883.541i) q^{21} +(-724.896 + 2231.00i) q^{23} +5347.05 q^{25} +(-1102.33 - 3392.62i) q^{27} +(-3182.25 - 2312.04i) q^{29} +(-432.878 + 5333.08i) q^{31} +(7480.14 + 5434.64i) q^{33} +(2610.86 + 8035.40i) q^{35} +4450.80 q^{37} +(5386.81 - 16578.9i) q^{39} +(14394.3 + 10458.0i) q^{41} +(-5606.66 - 4073.47i) q^{43} +(-715.768 + 2202.91i) q^{45} +(7960.82 - 5783.87i) q^{47} +(6780.49 - 4926.31i) q^{49} +(3678.71 + 11321.9i) q^{51} +(8339.60 - 25666.7i) q^{53} +(16059.3 + 49425.5i) q^{55} -41640.5 q^{57} +(15018.7 - 10911.8i) q^{59} -24735.2 q^{61} -2309.95 q^{63} +(79268.5 - 57591.9i) q^{65} -72940.4 q^{67} +(-11870.7 - 36534.3i) q^{69} +(-7985.67 + 24577.4i) q^{71} +(-20363.9 - 62673.6i) q^{73} +(-70839.0 + 51467.6i) q^{75} +(-41929.1 + 30463.3i) q^{77} +(-9521.37 + 29303.8i) q^{79} +(52206.5 + 37930.3i) q^{81} +(69945.4 + 50818.3i) q^{83} +(-20677.1 + 63637.5i) q^{85} +64413.6 q^{87} +(-9653.07 - 29709.1i) q^{89} +(79052.1 + 57434.7i) q^{91} +(-45598.3 - 74820.7i) q^{93} +(-189350. - 137571. i) q^{95} +(-23820.9 - 73313.1i) q^{97} -14208.5 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 56 q + 2 q^{3} - 58 q^{5} + 104 q^{7} - 1234 q^{9}+O(q^{10}) $ 56 * q + 2 * q^3 - 58 * q^5 + 104 * q^7 - 1234 * q^9	$ 56 q + 2 q^{3} - 58 q^{5} + 104 q^{7} - 1234 q^{9} - 509 q^{11} - 117 q^{13} + 89 q^{15} - 3504 q^{17} + 262 q^{19} + 352 q^{21} - 2448 q^{23} + 49618 q^{25} + 14324 q^{27} - 9888 q^{29} - 12771 q^{31} + 27699 q^{33} + 13840 q^{35} + 76096 q^{37} + 33520 q^{39} - 4843 q^{41} - 40778 q^{43} + 56692 q^{45} + 38922 q^{47} - 17126 q^{49} - 69292 q^{51} - 41728 q^{53} - 172096 q^{55} + 57066 q^{57} - 58198 q^{59} + 176328 q^{61} - 37444 q^{63} + 143863 q^{65} + 9812 q^{67} - 9250 q^{69} - 67356 q^{71} - 63512 q^{73} - 198012 q^{75} - 74257 q^{77} + 137651 q^{79} + 196077 q^{81} + 156427 q^{83} + 238828 q^{85} - 558144 q^{87} - 99292 q^{89} - 243609 q^{91} - 325925 q^{93} - 75077 q^{95} - 476340 q^{97} + 745812 q^{99}+O(q^{100}) $ 56 * q + 2 * q^3 - 58 * q^5 + 104 * q^7 - 1234 * q^9 - 509 * q^11 - 117 * q^13 + 89 * q^15 - 3504 * q^17 + 262 * q^19 + 352 * q^21 - 2448 * q^23 + 49618 * q^25 + 14324 * q^27 - 9888 * q^29 - 12771 * q^31 + 27699 * q^33 + 13840 * q^35 + 76096 * q^37 + 33520 * q^39 - 4843 * q^41 - 40778 * q^43 + 56692 * q^45 + 38922 * q^47 - 17126 * q^49 - 69292 * q^51 - 41728 * q^53 - 172096 * q^55 + 57066 * q^57 - 58198 * q^59 + 176328 * q^61 - 37444 * q^63 + 143863 * q^65 + 9812 * q^67 - 9250 * q^69 - 67356 * q^71 - 63512 * q^73 - 198012 * q^75 - 74257 * q^77 + 137651 * q^79 + 196077 * q^81 + 156427 * q^83 + 238828 * q^85 - 558144 * q^87 - 99292 * q^89 - 243609 * q^91 - 325925 * q^93 - 75077 * q^95 - 476340 * q^97 + 745812 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$63$	$65$
$\chi(n)$	$1$	$e\left(\frac{4}{5}\right)$

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
$3$	−13.2483	+	9.62542i	−0.849876	+	0.617471i	−0.925112	−	0.379695i	$-0.876029\pi$
$3$	−13.2483	+	9.62542i	−0.849876	+	0.617471i	0.0752359	+	0.997166i	$0.476029\pi$
$4$		0			0
$5$	−92.0437			−1.64653			−0.823264	−	0.567659i	$-0.807849\pi$
$5$	−92.0437			−1.64653			−0.823264	+	0.567659i	$0.807849\pi$
$6$		0			0
$7$	−28.3654	−	87.2998i	−0.218799	−	0.673393i	−0.998862	−	0.0476923i	$-0.984813\pi$
$7$	−28.3654	−	87.2998i	−0.218799	−	0.673393i	0.780064	−	0.625700i	$-0.215187\pi$
$8$		0			0
$9$	7.77640	−	23.9333i	0.0320016	−	0.0984909i
$10$		0			0
$11$	−174.475	−	536.979i	−0.434762	−	1.33806i	−0.893330	−	0.449401i	$-0.851638\pi$
$11$	−174.475	−	536.979i	−0.434762	−	1.33806i	0.458568	−	0.888659i	$-0.348362\pi$
$12$		0			0
$13$	−861.205	+	625.702i	−1.41334	+	1.02685i	−0.420518	+	0.907284i	$0.638152\pi$
$13$	−861.205	+	625.702i	−1.41334	+	1.02685i	−0.992826	+	0.119571i	$0.961848\pi$
$14$		0			0
$15$	1219.42	−	885.959i	1.39934	−	1.01668i
$16$		0			0
$17$	224.644	−	691.383i	0.188527	−	0.580225i	−0.811465	−	0.584402i	$-0.801329\pi$
$17$	224.644	−	691.383i	0.188527	−	0.580225i	0.999991	+	0.00417619i	$0.00132933\pi$
$18$		0			0
$19$	2057.18	+	1494.63i	1.30734	+	0.949837i	0.999998	−	0.00176259i	$-0.000561050\pi$
$19$	2057.18	+	1494.63i	1.30734	+	0.949837i	0.307340	+	0.951600i	$0.400561\pi$
$20$		0			0
$21$	1216.09	+	883.541i	0.601752	+	0.437198i
$22$		0			0
$23$	−724.896	+	2231.00i	−0.285730	+	0.879387i	0.700449	+	0.713703i	$0.252983\pi$
$23$	−724.896	+	2231.00i	−0.285730	+	0.879387i	−0.986179	+	0.165684i	$0.947017\pi$
$24$		0			0
$25$	5347.05			1.71105
$26$		0			0
$27$	−1102.33	−	3392.62i	−0.291006	−	0.895624i
$28$		0			0
$29$	−3182.25	−	2312.04i	−0.702650	−	0.510505i	0.178144	−	0.984004i	$-0.442991\pi$
$29$	−3182.25	−	2312.04i	−0.702650	−	0.510505i	−0.880794	+	0.473499i	$0.842991\pi$
$30$		0			0
$31$	−432.878	+	5333.08i	−0.0809023	+	0.996722i
$31$	−432.878	+	5333.08i	−0.0809023	+	0.996722i
$32$		0			0
$33$	7480.14	+	5434.64i	1.19571	+	0.868732i
$34$		0			0
$35$	2610.86	+	8035.40i	0.360258	+	1.10876i
$36$		0			0
$37$	4450.80			0.534483			0.267241	−	0.963630i	$-0.413888\pi$
$37$	4450.80			0.534483			0.267241	+	0.963630i	$0.413888\pi$
$38$		0			0
$39$	5386.81	−	16578.9i	0.567114	−	1.74540i
$40$		0			0
$41$	14394.3	+	10458.0i	1.33730	+	0.971607i	0.999539	+	0.0303761i	$0.00967050\pi$
$41$	14394.3	+	10458.0i	1.33730	+	0.971607i	0.337764	+	0.941231i	$0.390329\pi$
$42$		0			0
$43$	−5606.66	−	4073.47i	−0.462416	−	0.335965i	0.332062	−	0.943257i	$-0.392256\pi$
$43$	−5606.66	−	4073.47i	−0.462416	−	0.335965i	−0.794478	+	0.607293i	$0.792256\pi$
$44$		0			0
$45$	−715.768	+	2202.91i	−0.0526916	+	0.162168i
$46$		0			0
$47$	7960.82	−	5783.87i	0.525670	−	0.381921i	−0.293066	−	0.956092i	$-0.594675\pi$
$47$	7960.82	−	5783.87i	0.525670	−	0.381921i	0.818736	+	0.574171i	$0.194675\pi$
$48$		0			0
$49$	6780.49	−	4926.31i	0.403432	−	0.293111i
$50$		0			0
$51$	3678.71	+	11321.9i	0.198048	+	0.609529i
$52$		0			0
$53$	8339.60	−	25666.7i	0.407808	−	1.25510i	−0.510720	−	0.859747i	$-0.670621\pi$
$53$	8339.60	−	25666.7i	0.407808	−	1.25510i	0.918528	−	0.395356i	$-0.129379\pi$
$54$		0			0
$55$	16059.3	+	49425.5i	0.715848	+	2.20315i
$56$		0			0
$57$	−41640.5			−1.69757
$58$		0			0
$59$	15018.7	−	10911.8i	0.561699	−	0.408098i	−0.270381	−	0.962753i	$-0.587150\pi$
$59$	15018.7	−	10911.8i	0.561699	−	0.408098i	0.832080	+	0.554655i	$0.187150\pi$
$60$		0			0
$61$	−24735.2			−0.851121			−0.425560	−	0.904930i	$-0.639923\pi$
$61$	−24735.2			−0.851121			−0.425560	+	0.904930i	$0.639923\pi$
$62$		0			0
$63$	−2309.95			−0.0733250
$64$		0			0
$65$	79268.5	−	57591.9i	2.32711	−	1.69074i
$66$		0			0
$67$	−72940.4			−1.98510			−0.992548	−	0.121858i	$-0.961115\pi$
$67$	−72940.4			−1.98510			−0.992548	+	0.121858i	$0.961115\pi$
$68$		0			0
$69$	−11870.7	−	36534.3i	−0.300161	−	0.923800i
$70$		0			0
$71$	−7985.67	+	24577.4i	−0.188003	+	0.578615i	−0.999987	−	0.00506517i	$-0.998388\pi$
$71$	−7985.67	+	24577.4i	−0.188003	+	0.578615i	0.811984	+	0.583680i	$0.198388\pi$
$72$		0			0
$73$	−20363.9	−	62673.6i	−0.447254	−	1.37650i	−0.879993	−	0.474986i	$-0.842453\pi$
$73$	−20363.9	−	62673.6i	−0.447254	−	1.37650i	0.432740	−	0.901519i	$-0.357547\pi$
$74$		0			0
$75$	−70839.0	+	51467.6i	−1.45418	+	1.05653i
$76$		0			0
$77$	−41929.1	+	30463.3i	−0.805914	+	0.585531i
$78$		0			0
$79$	−9521.37	+	29303.8i	−0.171645	+	0.528269i	−0.999464	−	0.0327255i	$-0.989581\pi$
$79$	−9521.37	+	29303.8i	−0.171645	+	0.528269i	0.827819	+	0.560995i	$0.189581\pi$
$80$		0			0
$81$	52206.5	+	37930.3i	0.884122	+	0.642352i
$82$		0			0
$83$	69945.4	+	50818.3i	1.11446	+	0.809701i	0.983360	−	0.181668i	$-0.0581497\pi$
$83$	69945.4	+	50818.3i	1.11446	+	0.809701i	0.131098	+	0.991369i	$0.458150\pi$
$84$		0			0
$85$	−20677.1	+	63637.5i	−0.310414	+	0.955357i
$86$		0			0
$87$	64413.6			0.912388
$88$		0			0
$89$	−9653.07	−	29709.1i	−0.129179	−	0.397571i	0.865461	−	0.500977i	$-0.167026\pi$
$89$	−9653.07	−	29709.1i	−0.129179	−	0.397571i	−0.994639	+	0.103406i	$0.967026\pi$
$90$		0			0
$91$	79052.1	+	57434.7i	1.00071	+	0.727061i
$92$		0			0
$93$	−45598.3	−	74820.7i	−0.546690	−	0.897045i
$94$		0			0
$95$	−189350.	−	137571.i	−2.15257	−	1.56393i
$96$		0			0
$97$	−23820.9	−	73313.1i	−0.257056	−	0.791138i	−0.993418	−	0.114549i	$-0.963458\pi$
$97$	−23820.9	−	73313.1i	−0.257056	−	0.791138i	0.736361	−	0.676588i	$-0.236542\pi$
$98$		0			0
$99$	−14208.5			−0.145700
$100$		0			0
$101$	−2057.60	+	6332.65i	−0.0200705	+	0.0617707i	−0.960590	−	0.277969i	$-0.910339\pi$
$101$	−2057.60	+	6332.65i	−0.0200705	+	0.0617707i	0.940520	+	0.339739i	$0.110339\pi$
$102$		0			0
$103$	80773.3	+	58685.3i	0.750196	+	0.545050i	0.895888	−	0.444280i	$-0.146541\pi$
$103$	80773.3	+	58685.3i	0.750196	+	0.545050i	−0.145691	+	0.989330i	$0.546541\pi$
$104$		0			0
$105$	−111933.	−	81324.4i	−0.990802	−	0.719859i
$106$		0			0
$107$	15125.4	−	46551.2i	0.127717	−	0.393072i	−0.866670	−	0.498883i	$-0.833744\pi$
$107$	15125.4	−	46551.2i	0.127717	−	0.393072i	0.994386	+	0.105811i	$0.0337439\pi$
$108$		0			0
$109$	−123288.	+	89573.8i	−0.993925	+	0.722129i	−0.960777	−	0.277322i	$-0.910553\pi$
$109$	−123288.	+	89573.8i	−0.993925	+	0.722129i	−0.0331477	+	0.999450i	$0.510553\pi$
$110$		0			0
$111$	−58965.3	+	42840.8i	−0.454244	+	0.330028i
$112$		0			0
$113$	4869.15	+	14985.7i	0.0358721	+	0.110403i	0.967389	−	0.253294i	$-0.0815142\pi$
$113$	4869.15	+	14985.7i	0.0358721	+	0.110403i	−0.931517	+	0.363698i	$0.881514\pi$
$114$		0			0
$115$	66722.1	−	205350.i	0.470463	−	1.44794i
$116$		0			0
$117$	8278.03	+	25477.2i	0.0559065	+	0.172063i
$118$		0			0
$119$	−66729.8			−0.431969
$120$		0			0
$121$	−127612.	+	92715.5i	−0.792369	+	0.575690i
$122$		0			0
$123$	−291362.			−1.73648
$124$		0			0
$125$	−204525.			−1.17077
$126$		0			0
$127$	98684.9	−	71698.8i	0.542927	−	0.394460i	−0.282244	−	0.959343i	$-0.591079\pi$
$127$	98684.9	−	71698.8i	0.542927	−	0.394460i	0.825171	+	0.564883i	$0.191079\pi$
$128$		0			0
$129$	113487.			0.600445
$130$		0			0
$131$	−43866.1	−	135006.i	−0.223332	−	0.687345i	−0.998457	−	0.0555366i	$-0.982313\pi$
$131$	−43866.1	−	135006.i	−0.223332	−	0.687345i	0.775125	−	0.631808i	$-0.217687\pi$
$132$		0			0
$133$	72128.0	−	221987.i	0.353570	−	1.08818i
$134$		0			0
$135$	101462.	+	312269.i	0.479149	+	1.47467i
$136$		0			0
$137$	222904.	−	161949.i	1.01465	−	0.737185i	0.0494693	−	0.998776i	$-0.484247\pi$
$137$	222904.	−	161949.i	1.01465	−	0.737185i	0.965179	+	0.261591i	$0.0842470\pi$
$138$		0			0
$139$	159305.	−	115742.i	0.699345	−	0.508104i	−0.180374	−	0.983598i	$-0.557731\pi$
$139$	159305.	−	115742.i	0.699345	−	0.508104i	0.879719	+	0.475494i	$0.157731\pi$
$140$		0			0
$141$	−49794.7	+	153252.i	−0.210929	+	0.649172i
$142$		0			0
$143$	486247.	+	353279.i	1.98846	+	1.44470i
$144$		0			0
$145$	292906.	+	212809.i	1.15693	+	0.840561i
$146$		0			0
$147$	−42411.8	+	130530.i	−0.161880	+	0.498215i
$148$		0			0
$149$	316369.			1.16742			0.583711	−	0.811961i	$-0.301600\pi$
$149$	316369.			1.16742			0.583711	+	0.811961i	$0.301600\pi$
$150$		0			0
$151$	49592.2	+	152629.i	0.176999	+	0.544748i	0.999719	−	0.0236994i	$-0.00754446\pi$
$151$	49592.2	+	152629.i	0.176999	+	0.544748i	−0.822720	+	0.568447i	$0.807544\pi$
$152$		0			0
$153$	−14800.2	−	10752.9i	−0.0511138	−	0.0371363i
$154$		0			0
$155$	39843.7	−	490877.i	0.133208	−	1.64113i
$156$		0			0
$157$	467158.	+	339410.i	1.51257	+	1.09894i	0.965022	+	0.262168i	$0.0844374\pi$
$157$	467158.	+	339410.i	1.51257	+	1.09894i	0.547545	+	0.836776i	$0.315563\pi$
$158$		0			0
$159$	136567.	+	420310.i	0.428404	+	1.31849i
$160$		0			0
$161$	215328.			0.654690
$162$		0			0
$163$	−133562.	+	411062.i	−0.393744	+	1.21182i	0.536191	+	0.844096i	$0.319863\pi$
$163$	−133562.	+	411062.i	−0.393744	+	1.21182i	−0.929935	+	0.367723i	$0.880137\pi$
$164$		0			0
$165$	−688500.	−	500224.i	−1.96877	−	1.43039i
$166$		0			0
$167$	148090.	+	107594.i	0.410899	+	0.298536i	0.773966	−	0.633228i	$-0.218270\pi$
$167$	148090.	+	107594.i	0.410899	+	0.298536i	−0.363067	+	0.931763i	$0.618270\pi$
$168$		0			0
$169$	235435.	−	724594.i	0.634094	−	1.95154i
$170$		0			0
$171$	51768.8	−	37612.2i	0.135387	−	0.0983646i
$172$		0			0
$173$	−306952.	+	223014.i	−0.779750	+	0.566522i	−0.904904	−	0.425616i	$-0.860058\pi$
$173$	−306952.	+	223014.i	−0.779750	+	0.566522i	0.125154	+	0.992137i	$0.460058\pi$
$174$		0			0
$175$	−151671.	−	466796.i	−0.374376	−	1.15221i
$176$		0			0
$177$	−93941.9	+	289123.i	−0.225386	+	0.693666i
$178$		0			0
$179$	51996.8	+	160030.i	0.121295	+	0.373309i	0.993208	−	0.116353i	$-0.0371203\pi$
$179$	51996.8	+	160030.i	0.121295	+	0.373309i	−0.871913	+	0.489662i	$0.837120\pi$
$180$		0			0
$181$	566183.			1.28458			0.642288	−	0.766463i	$-0.277985\pi$
$181$	566183.			1.28458			0.642288	+	0.766463i	$0.277985\pi$
$182$		0			0
$183$	327699.	−	238087.i	0.723347	−	0.525542i
$184$		0			0
$185$	−409668.			−0.880041
$186$		0			0
$187$	−410453.			−0.858340
$188$		0			0
$189$	−264907.	+	192466.i	−0.539435	+	0.391922i
$190$		0			0
$191$	527348.			1.04596			0.522979	−	0.852346i	$-0.324821\pi$
$191$	527348.			1.04596			0.522979	+	0.852346i	$0.324821\pi$
$192$		0			0
$193$	8295.00	+	25529.4i	0.0160296	+	0.0493341i	0.958751	−	0.284246i	$-0.0917432\pi$
$193$	8295.00	+	25529.4i	0.0160296	+	0.0493341i	−0.942722	+	0.333580i	$0.891743\pi$
$194$		0			0
$195$	−495822.	+	1.52598e6i	−0.933769	+	2.87385i
$196$		0			0
$197$	−218877.	−	673633.i	−0.401822	−	1.23668i	−0.923520	−	0.383551i	$-0.874701\pi$
$197$	−218877.	−	673633.i	−0.401822	−	1.23668i	0.521698	−	0.853130i	$-0.325299\pi$
$198$		0			0
$199$	−158671.	+	115281.i	−0.284030	+	0.206360i	−0.720673	−	0.693275i	$-0.756167\pi$
$199$	−158671.	+	115281.i	−0.284030	+	0.206360i	0.436643	+	0.899635i	$0.356167\pi$
$200$		0			0
$201$	966333.	−	702082.i	1.68708	−	1.22574i
$202$		0			0
$203$	−111575.	+	343392.i	−0.190032	+	0.584857i
$204$		0			0
$205$	−1.32490e6	−	962597.i	−2.20191	−	1.59978i
$206$		0			0
$207$	47758.1	+	34698.3i	0.0774678	+	0.0562836i
$208$		0			0
$209$	443657.	−	1.36544e6i	0.702558	−	2.16225i
$210$		0			0
$211$	−815651.			−1.26124			−0.630620	−	0.776091i	$-0.717199\pi$
$211$	−815651.			−1.26124			−0.630620	+	0.776091i	$0.717199\pi$
$212$		0			0
$213$	−130771.	−	402473.i	−0.197498	−	0.607837i
$214$		0			0
$215$	516058.	+	374938.i	0.761381	+	0.553176i
$216$		0			0
$217$	477856.	−	113485.i	0.688887	−	0.163602i
$218$		0			0
$219$	873046.	+	634305.i	1.23006	+	0.893692i
$220$		0			0
$221$	239135.	+	735983.i	0.329354	+	1.01365i
$222$		0			0
$223$	212826.			0.286592			0.143296	−	0.989680i	$-0.454230\pi$
$223$	212826.			0.286592			0.143296	+	0.989680i	$0.454230\pi$
$224$		0			0
$225$	41580.8	−	127972.i	0.0547565	−	0.168523i
$226$		0			0
$227$	−63464.5	−	46109.7i	−0.0817460	−	0.0593919i	0.546162	−	0.837680i	$-0.316088\pi$
$227$	−63464.5	−	46109.7i	−0.0817460	−	0.0593919i	−0.627908	+	0.778288i	$0.716088\pi$
$228$		0			0
$229$	200408.	+	145605.i	0.252538	+	0.183480i	0.706851	−	0.707363i	$-0.250115\pi$
$229$	200408.	+	145605.i	0.252538	+	0.183480i	−0.454313	+	0.890842i	$0.650115\pi$
$230$		0			0
$231$	262266.	−	807171.i	0.323379	−	0.995257i
$232$		0			0
$233$	−1.16280e6	+	844827.i	−1.40319	+	1.01948i	−0.408922	+	0.912569i	$0.634095\pi$
$233$	−1.16280e6	+	844827.i	−1.40319	+	1.01948i	−0.994269	+	0.106908i	$0.965905\pi$
$234$		0			0
$235$	−732743.	+	532369.i	−0.865530	+	0.628844i
$236$		0			0
$237$	−155919.	−	479871.i	−0.180314	−	0.554949i
$238$		0			0
$239$	−96453.4	+	296853.i	−0.109225	+	0.336161i	−0.990699	−	0.136073i	$-0.956552\pi$
$239$	−96453.4	+	296853.i	−0.109225	+	0.336161i	0.881474	+	0.472233i	$0.156552\pi$
$240$		0			0
$241$	318919.	+	981530.i	0.353702	+	1.08858i	0.956758	+	0.290884i	$0.0939492\pi$
$241$	318919.	+	981530.i	0.353702	+	1.08858i	−0.603057	+	0.797698i	$0.706051\pi$
$242$		0			0
$243$	−189908.			−0.206313
$244$		0			0
$245$	−624101.	+	453436.i	−0.664262	+	0.482615i
$246$		0			0
$247$	−2.70684e6			−2.82306
$248$		0			0
$249$	−1.41580e6			−1.44712
$250$		0			0
$251$	−2924.60	+	2124.85i	−0.00293010	+	0.00212884i	−0.589249	−	0.807951i	$-0.700576\pi$
$251$	−2924.60	+	2124.85i	−0.00293010	+	0.00212884i	0.586319	+	0.810080i	$0.300576\pi$
$252$		0			0
$253$	1.32448e6			1.30090
$254$		0			0
$255$	−338603.	−	1.04211e6i	−0.326092	−	1.00361i
$256$		0			0
$257$	435118.	−	1.33916e6i	0.410936	−	1.26473i	−0.504899	−	0.863178i	$-0.668470\pi$
$257$	435118.	−	1.33916e6i	0.410936	−	1.26473i	0.915836	−	0.401553i	$-0.131530\pi$
$258$		0			0
$259$	−126249.	−	388554.i	−0.116944	−	0.359917i
$260$		0			0
$261$	−80081.1	+	58182.4i	−0.0727661	+	0.0528676i
$262$		0			0
$263$	671297.	−	487726.i	0.598447	−	0.434797i	−0.246880	−	0.969046i	$-0.579406\pi$
$263$	671297.	−	487726.i	0.598447	−	0.434797i	0.845327	+	0.534249i	$0.179406\pi$
$264$		0			0
$265$	−767608.	+	2.36245e6i	−0.671467	+	2.06656i
$266$		0			0
$267$	413849.	+	300679.i	0.355274	+	0.258122i
$268$		0			0
$269$	−699557.	−	508258.i	−0.589444	−	0.428256i	0.252672	−	0.967552i	$-0.418691\pi$
$269$	−699557.	−	508258.i	−0.589444	−	0.428256i	−0.842117	+	0.539296i	$0.818691\pi$
$270$		0			0
$271$	−221680.	+	682262.i	−0.183360	+	0.564324i	−0.999916	−	0.0129421i	$-0.995880\pi$
$271$	−221680.	+	682262.i	−0.183360	+	0.564324i	0.816556	+	0.577266i	$0.195880\pi$
$272$		0			0
$273$	−1.60014e6			−1.29942
$274$		0			0
$275$	−932926.	−	2.87125e6i	−0.743902	−	2.28949i
$276$		0			0
$277$	1.61041e6	+	1.17003e6i	1.26106	+	0.916215i	0.998809	−	0.0487844i	$-0.0155347\pi$
$277$	1.61041e6	+	1.17003e6i	1.26106	+	0.916215i	0.262252	+	0.964999i	$0.415535\pi$
$278$		0			0
$279$	124272.	+	51832.4i	0.0955790	+	0.0398649i
$280$		0			0
$281$	−495164.	−	359757.i	−0.374096	−	0.271797i	0.384811	−	0.922995i	$-0.374266\pi$
$281$	−495164.	−	359757.i	−0.374096	−	0.271797i	−0.758907	+	0.651199i	$0.774266\pi$
$282$		0			0
$283$	−193147.	−	594445.i	−0.143358	−	0.441210i	0.853438	−	0.521194i	$-0.174513\pi$
$283$	−193147.	−	594445.i	−0.143358	−	0.441210i	−0.996796	+	0.0799837i	$0.974513\pi$
$284$		0			0
$285$	3.83274e6			2.79510
$286$		0			0
$287$	504686.	−	1.55326e6i	0.361673	−	1.11312i
$288$		0			0
$289$	721142.	+	523941.i	0.507898	+	0.369009i
$290$		0			0
$291$	1.02125e6	+	741984.i	0.706970	+	0.513644i
$292$		0			0
$293$	70083.0	−	215693.i	0.0476918	−	0.146780i	−0.924375	−	0.381486i	$-0.875413\pi$
$293$	70083.0	−	215693.i	0.0476918	−	0.146780i	0.972067	+	0.234705i	$0.0754125\pi$
$294$		0			0
$295$	−1.38238e6	+	1.00436e6i	−0.924853	+	0.671945i
$296$		0			0
$297$	−1.62944e6	+	1.18385e6i	−1.07188	+	0.778767i
$298$		0			0
$299$	−771657.	−	2.37492e6i	−0.499168	−	1.53628i
$300$		0			0
$301$	−196578.	+	605006.i	−0.125060	+	0.384896i
$302$		0			0
$303$	−33694.8	−	103702.i	−0.0210842	−	0.0648904i
$304$		0			0
$305$	2.27672e6			1.40139
$306$		0			0
$307$	226043.	−	164230.i	0.136882	−	0.0994504i	−0.517237	−	0.855842i	$-0.673040\pi$
$307$	226043.	−	164230.i	0.136882	−	0.0994504i	0.654119	+	0.756392i	$0.273040\pi$
$308$		0			0
$309$	−1.63498e6			−0.974126
$310$		0			0
$311$	1.03137e6			0.604663			0.302331	−	0.953203i	$-0.402235\pi$
$311$	1.03137e6			0.604663			0.302331	+	0.953203i	$0.402235\pi$
$312$		0			0
$313$	−7690.28	+	5587.32i	−0.00443692	+	0.00322361i	−0.590002	−	0.807402i	$-0.700873\pi$
$313$	−7690.28	+	5587.32i	−0.00443692	+	0.00322361i	0.585565	+	0.810626i	$0.300873\pi$
$314$		0			0
$315$	212617.			0.120732
$316$		0			0
$317$	−263736.	−	811695.i	−0.147408	−	0.453675i	0.849905	−	0.526936i	$-0.176659\pi$
$317$	−263736.	−	811695.i	−0.147408	−	0.453675i	−0.997313	+	0.0732613i	$0.976659\pi$
$318$		0			0
$319$	−686293.	+	2.11219e6i	−0.377601	+	1.16214i
$320$		0			0
$321$	247690.	+	762311.i	0.134167	+	0.412923i
$322$		0			0
$323$	1.49549e6	−	1.08654e6i	0.797588	−	0.579481i
$324$		0			0
$325$	−4.60490e6	+	3.34566e6i	−2.41831	+	1.75700i
$326$		0			0
$327$	771162.	−	2.37339e6i	0.398819	−	1.22744i
$328$		0			0
$329$	−730743.	−	530916.i	−0.372199	−	0.270418i
$330$		0			0
$331$	2.82788e6	+	2.05457e6i	1.41870	+	1.03075i	0.991984	+	0.126360i	$0.0403293\pi$
$331$	2.82788e6	+	2.05457e6i	1.41870	+	1.03075i	0.426715	+	0.904386i	$0.359671\pi$
$332$		0			0
$333$	34611.2	−	106522.i	0.0171043	−	0.0526417i
$334$		0			0
$335$	6.71371e6			3.26851
$336$		0			0
$337$	−808850.	−	2.48939e6i	−0.387966	−	1.19404i	−0.934306	−	0.356472i	$-0.883979\pi$
$337$	−808850.	−	2.48939e6i	−0.387966	−	1.19404i	0.546340	−	0.837563i	$-0.316021\pi$
$338$		0			0
$339$	−208751.	−	151667.i	−0.0986575	−	0.0716789i
$340$		0			0
$341$	2.93928e6	−	698044.i	1.36885	−	0.325085i
$342$		0			0
$343$	−1.87051e6	−	1.35901e6i	−0.858471	−	0.623716i
$344$		0			0
$345$	1.09262e6	+	3.36275e6i	0.494223	+	1.52106i
$346$		0			0
$347$	−2.95197e6			−1.31610			−0.658049	−	0.752975i	$-0.728618\pi$
$347$	−2.95197e6			−1.31610			−0.658049	+	0.752975i	$0.728618\pi$
$348$		0			0
$349$	457409.	−	1.40776e6i	0.201021	−	0.618679i	−0.798832	−	0.601554i	$-0.794549\pi$
$349$	457409.	−	1.40776e6i	0.201021	−	0.618679i	0.999853	−	0.0171254i	$-0.00545145\pi$
$350$		0			0
$351$	3.07210e6	+	2.23201e6i	1.33097	+	0.967004i
$352$		0			0
$353$	−2.17281e6	−	1.57864e6i	−0.928078	−	0.674288i	0.0174438	−	0.999848i	$-0.494447\pi$
$353$	−2.17281e6	−	1.57864e6i	−0.928078	−	0.674288i	−0.945521	+	0.325560i	$0.894447\pi$
$354$		0			0
$355$	735031.	−	2.26219e6i	0.309553	−	0.952705i
$356$		0			0
$357$	884053.	−	642302.i	0.367120	−	0.266728i
$358$		0			0
$359$	−2.03806e6	+	1.48074e6i	−0.834605	+	0.606376i	−0.920858	−	0.389897i	$-0.872511\pi$
$359$	−2.03806e6	+	1.48074e6i	−0.834605	+	0.606376i	0.0862532	+	0.996273i	$0.472511\pi$
$360$		0			0
$361$	1.23292e6	+	3.79453e6i	0.497927	+	1.53246i
$362$		0			0
$363$	798209.	−	2.45664e6i	0.317944	−	0.978530i
$364$		0			0
$365$	1.87437e6	+	5.76872e6i	0.736416	+	2.26645i
$366$		0			0
$367$	−2.10281e6			−0.814956			−0.407478	−	0.913215i	$-0.633592\pi$
$367$	−2.10281e6			−0.814956			−0.407478	+	0.913215i	$0.633592\pi$
$368$		0			0
$369$	362231.	−	263176.i	0.138490	−	0.100619i
$370$		0			0
$371$	−2.47725e6			−0.934405
$372$		0			0
$373$	1.34967e6			0.502293			0.251146	−	0.967949i	$-0.419192\pi$
$373$	1.34967e6			0.502293			0.251146	+	0.967949i	$0.419192\pi$
$374$		0			0
$375$	2.70960e6	−	1.96864e6i	0.995010	−	0.722917i
$376$		0			0
$377$	4.18721e6			1.51730
$378$		0			0
$379$	1.03693e6	+	3.19135e6i	0.370811	+	1.14124i	0.946262	+	0.323401i	$0.104826\pi$
$379$	1.03693e6	+	3.19135e6i	0.370811	+	1.14124i	−0.575451	+	0.817836i	$0.695174\pi$
$380$		0			0
$381$	−617272.	+	1.89977e6i	−0.217853	+	0.670483i
$382$		0			0
$383$	548952.	+	1.68950e6i	0.191222	+	0.588520i	1.00000		0.000406223i	$0.000129305\pi$
$383$	548952.	+	1.68950e6i	0.191222	+	0.588520i	−0.808778	+	0.588114i	$0.799871\pi$
$384$		0			0
$385$	3.85931e6	−	2.80395e6i	1.32696	−	0.964093i
$386$		0			0
$387$	−141091.	+	102509.i	−0.0478876	+	0.0347923i
$388$		0			0
$389$	−141860.	+	436601.i	−0.0475321	+	0.146289i	−0.972006	−	0.234957i	$-0.924505\pi$
$389$	−141860.	+	436601.i	−0.0475321	+	0.146289i	0.924474	+	0.381246i	$0.124505\pi$
$390$		0			0
$391$	1.37963e6	+	1.00236e6i	0.456375	+	0.331576i
$392$		0			0
$393$	1.88064e6	+	1.36636e6i	0.614220	+	0.446257i
$394$		0			0
$395$	876382.	−	2.69723e6i	0.282619	−	0.869811i
$396$		0			0
$397$	−1.46234e6			−0.465662			−0.232831	−	0.972517i	$-0.574799\pi$
$397$	−1.46234e6			−0.465662			−0.232831	+	0.972517i	$0.574799\pi$
$398$		0			0
$399$	1.18115e6	+	3.63520e6i	0.371426	+	1.14313i
$400$		0			0
$401$	−2.09193e6	−	1.51988e6i	−0.649661	−	0.472007i	0.213494	−	0.976944i	$-0.431515\pi$
$401$	−2.09193e6	−	1.51988e6i	−0.649661	−	0.472007i	−0.863156	+	0.504938i	$0.831515\pi$
$402$		0			0
$403$	−2.96412e6	−	4.86373e6i	−0.909146	−	1.49179i
$404$		0			0
$405$	−4.80528e6	−	3.49124e6i	−1.45573	−	1.05765i
$406$		0			0
$407$	−776554.	−	2.38999e6i	−0.232373	−	0.715170i
$408$		0			0
$409$	2.86382e6			0.846521			0.423260	−	0.906008i	$-0.360886\pi$
$409$	2.86382e6			0.846521			0.423260	+	0.906008i	$0.360886\pi$
$410$		0			0
$411$	−1.39426e6	+	4.29108e6i	−0.407135	+	1.25303i
$412$		0			0
$413$	−1.37861e6	−	1.00162e6i	−0.397709	−	0.288953i
$414$		0			0
$415$	−6.43803e6	−	4.67750e6i	−1.83499	−	1.33320i
$416$		0			0
$417$	−996446.	+	3.06675e6i	−0.280617	+	0.863650i
$418$		0			0
$419$	3.21185e6	−	2.33354e6i	0.893758	−	0.649353i	−0.0430970	−	0.999071i	$-0.513722\pi$
$419$	3.21185e6	−	2.33354e6i	0.893758	−	0.649353i	0.936855	+	0.349718i	$0.113722\pi$
$420$		0			0
$421$	1.58566e6	−	1.15205e6i	0.436019	−	0.316786i	−0.348032	−	0.937483i	$-0.613150\pi$
$421$	1.58566e6	−	1.15205e6i	0.436019	−	0.316786i	0.784051	+	0.620696i	$0.213150\pi$
$422$		0			0
$423$	−76520.6	−	235506.i	−0.0207935	−	0.0639958i
$424$		0			0
$425$	1.20118e6	−	3.69686e6i	0.322579	−	0.992797i
$426$		0			0
$427$	701625.	+	2.15938e6i	0.186224	+	0.573138i
$428$		0			0
$429$	−9.84239e6			−2.58201
$430$		0			0
$431$	−161326.	+	117210.i	−0.0418323	+	0.0303929i	−0.608505	−	0.793550i	$-0.708230\pi$
$431$	−161326.	+	117210.i	−0.0418323	+	0.0303929i	0.566673	+	0.823943i	$0.308230\pi$
$432$		0			0
$433$	−754619.			−0.193423			−0.0967115	−	0.995312i	$-0.530832\pi$
$433$	−754619.			−0.193423			−0.0967115	+	0.995312i	$0.530832\pi$
$434$		0			0
$435$	−5.92887e6			−1.50227
$436$		0			0
$437$	−4.82576e6	+	3.50612e6i	−1.20882	+	0.878259i
$438$		0			0
$439$	−1.77757e6			−0.440215			−0.220107	−	0.975476i	$-0.570641\pi$
$439$	−1.77757e6			−0.440215			−0.220107	+	0.975476i	$0.570641\pi$
$440$		0			0
$441$	−65175.1	−	200588.i	−0.0159582	−	0.0491144i
$442$		0			0
$443$	−534709.	+	1.64566e6i	−0.129452	+	0.398411i	−0.994686	−	0.102957i	$-0.967170\pi$
$443$	−534709.	+	1.64566e6i	−0.129452	+	0.398411i	0.865234	+	0.501368i	$0.167170\pi$
$444$		0			0
$445$	888505.	+	2.73454e6i	0.212696	+	0.654611i
$446$		0			0
$447$	−4.19133e6	+	3.04518e6i	−0.992164	+	0.720849i
$448$		0			0
$449$	5.48320e6	−	3.98378e6i	1.28357	−	0.932565i	0.283911	−	0.958851i	$-0.408368\pi$
$449$	5.48320e6	−	3.98378e6i	1.28357	−	0.932565i	0.999654	+	0.0262858i	$0.00836799\pi$
$450$		0			0
$451$	3.10431e6	−	9.55408e6i	0.718660	−	2.21181i
$452$		0			0
$453$	−2.12613e6	−	1.54472e6i	−0.486793	−	0.353676i
$454$		0			0
$455$	−7.27625e6	−	5.28650e6i	−1.64770	−	1.19713i
$456$		0			0
$457$	1.17573e6	−	3.61853e6i	0.263341	−	0.810479i	−0.728730	−	0.684801i	$-0.759889\pi$
$457$	1.17573e6	−	3.61853e6i	0.263341	−	0.810479i	0.992071	−	0.125678i	$-0.0401108\pi$
$458$		0			0
$459$	−2.59323e6			−0.574526
$460$		0			0
$461$	−1.13408e6	−	3.49035e6i	−0.248538	−	0.764922i	−0.995034	−	0.0995320i	$-0.968265\pi$
$461$	−1.13408e6	−	3.49035e6i	−0.248538	−	0.764922i	0.746496	−	0.665390i	$-0.231735\pi$
$462$		0			0
$463$	−1.18017e6	−	857447.i	−0.255855	−	0.185889i	0.452463	−	0.891783i	$-0.350546\pi$
$463$	−1.18017e6	−	857447.i	−0.255855	−	0.185889i	−0.708318	+	0.705894i	$0.750546\pi$
$464$		0			0
$465$	4.19704e6	+	6.88677e6i	0.900140	+	1.47701i
$466$		0			0
$467$	3.51845e6	+	2.55630e6i	0.746550	+	0.542400i	0.894755	−	0.446556i	$-0.147350\pi$
$467$	3.51845e6	+	2.55630e6i	0.746550	+	0.542400i	−0.148206	+	0.988957i	$0.547350\pi$
$468$		0			0
$469$	2.06899e6	+	6.36769e6i	0.434336	+	1.33675i
$470$		0			0
$471$	−9.45599e6			−1.96406
$472$		0			0
$473$	−1.20915e6	+	3.72138e6i	−0.248500	+	0.764805i
$474$		0			0
$475$	1.09998e7	+	7.99184e6i	2.23693	+	1.62522i
$476$		0			0
$477$	−549435.	−	399188.i	−0.110566	−	0.0803307i
$478$		0			0
$479$	1.46678e6	−	4.51430e6i	0.292097	−	0.898983i	−0.692084	−	0.721817i	$-0.743307\pi$
$479$	1.46678e6	−	4.51430e6i	0.292097	−	0.898983i	0.984181	−	0.177166i	$-0.0566929\pi$
$480$		0			0
$481$	−3.83305e6	+	2.78487e6i	−0.755408	+	0.548836i
$482$		0			0
$483$	−2.85272e6	+	2.07262e6i	−0.556405	+	0.404252i
$484$		0			0
$485$	2.19256e6	+	6.74801e6i	0.423250	+	1.30263i
$486$		0			0
$487$	2.94565e6	−	9.06579e6i	0.562807	−	1.73214i	−0.111573	−	0.993756i	$-0.535589\pi$
$487$	2.94565e6	−	9.06579e6i	0.562807	−	1.73214i	0.674380	−	0.738385i	$-0.264411\pi$
$488$		0			0
$489$	−2.18718e6	−	6.73144e6i	−0.413630	−	1.27302i
$490$		0			0
$491$	9.30320e6			1.74152			0.870760	−	0.491708i	$-0.163627\pi$
$491$	9.30320e6			1.74152			0.870760	+	0.491708i	$0.163627\pi$
$492$		0			0
$493$	−2.31338e6	+	1.68077e6i	−0.428676	+	0.311452i
$494$		0			0
$495$	1.30780e6			0.239899
$496$		0			0
$497$	2.37212e6			0.430770
$498$		0			0
$499$	−1.35464e6	+	984205.i	−0.243542	+	0.176943i	−0.702860	−	0.711329i	$-0.748094\pi$
$499$	−1.35464e6	+	984205.i	−0.243542	+	0.176943i	0.459318	+	0.888272i	$0.348094\pi$
$500$		0			0
$501$	−2.99757e6			−0.533550
$502$		0			0
$503$	2.45593e6	+	7.55857e6i	0.432808	+	1.33205i	0.895316	+	0.445431i	$0.146950\pi$
$503$	2.45593e6	+	7.55857e6i	0.432808	+	1.33205i	−0.462508	+	0.886615i	$0.653050\pi$
$504$		0			0
$505$	189390.	−	582881.i	0.0330467	−	0.101707i
$506$		0			0
$507$	3.85542e6	+	1.18658e7i	0.666119	+	2.05010i
$508$		0			0
$509$	1.36110e6	−	988894.i	0.232860	−	0.169182i	−0.465237	−	0.885186i	$-0.654031\pi$
$509$	1.36110e6	−	988894.i	0.232860	−	0.169182i	0.698096	+	0.716004i	$0.254031\pi$
$510$		0			0
$511$	−4.89377e6	+	3.55553e6i	−0.829070	+	0.602354i
$512$		0			0
$513$	2.80302e6	−	8.62680e6i	0.470254	−	1.44729i
$514$		0			0
$515$	−7.43468e6	−	5.40161e6i	−1.23522	−	0.897439i
$516$		0			0
$517$	−4.49478e6	−	3.26565e6i	−0.739575	−	0.537333i
$518$		0			0
$519$	1.91998e6	−	5.90909e6i	0.312880	−	0.962946i
$520$		0			0
$521$	9.32928e6			1.50575			0.752877	−	0.658161i	$-0.228666\pi$
$521$	9.32928e6			1.50575			0.752877	+	0.658161i	$0.228666\pi$
$522$		0			0
$523$	94723.1	+	291528.i	0.0151426	+	0.0466042i	0.958342	−	0.285622i	$-0.0922002\pi$
$523$	94723.1	+	291528.i	0.0151426	+	0.0466042i	−0.943200	+	0.332226i	$0.892200\pi$
$524$		0			0
$525$	6.50249e6	+	4.72434e6i	1.02963	+	0.748070i
$526$		0			0
$527$	3.58996e6	+	1.49733e6i	0.563071	+	0.234850i
$528$		0			0
$529$	755224.	+	548702.i	0.117337	+	0.0852506i
$530$		0			0
$531$	−144363.	−	444302.i	−0.0222187	−	0.0683821i
$532$		0			0
$533$	−1.89400e7			−2.88777
$534$		0			0
$535$	−1.39220e6	+	4.28475e6i	−0.210289	+	0.647203i
$536$		0			0
$537$	−2.22922e6	−	1.61962e6i	−0.333593	−	0.242370i
$538$		0			0
$539$	−3.82835e6	−	2.78146e6i	−0.567597	−	0.412383i
$540$		0			0
$541$	756259.	−	2.32753e6i	0.111091	−	0.341902i	−0.880021	−	0.474935i	$-0.842472\pi$
$541$	756259.	−	2.32753e6i	0.111091	−	0.341902i	0.991112	+	0.133033i	$0.0424717\pi$
$542$		0			0
$543$	−7.50093e6	+	5.44975e6i	−1.09173	+	0.793189i
$544$		0			0
$545$	1.13479e7	−	8.24470e6i	1.63653	−	1.18901i
$546$		0			0
$547$	1.01170e6	+	3.11370e6i	0.144572	+	0.444947i	0.996956	−	0.0779700i	$-0.0248439\pi$
$547$	1.01170e6	+	3.11370e6i	0.144572	+	0.444947i	−0.852384	+	0.522917i	$0.824844\pi$
$548$		0			0
$549$	−192351.	+	591995.i	−0.0272373	+	0.0838277i
$550$		0			0
$551$	−3.09082e6	−	9.51256e6i	−0.433705	−	1.33481i
$552$		0			0
$553$	2.82829e6			0.393288
$554$		0			0
$555$	5.42739e6	−	3.94323e6i	0.747926	−	0.543400i
$556$		0			0
$557$	−3.94441e6			−0.538696			−0.269348	−	0.963043i	$-0.586808\pi$
$557$	−3.94441e6			−0.538696			−0.269348	+	0.963043i	$0.586808\pi$
$558$		0			0
$559$	7.37726e6			0.998540
$560$		0			0
$561$	5.43779e6	−	3.95078e6i	0.729483	−	0.530000i
$562$		0			0
$563$	3.85028e6			0.511943			0.255971	−	0.966684i	$-0.417605\pi$
$563$	3.85028e6			0.511943			0.255971	+	0.966684i	$0.417605\pi$
$564$		0			0
$565$	−448175.	−	1.37934e6i	−0.0590645	−	0.181782i
$566$		0			0
$567$	1.83044e6	−	5.63353e6i	0.239111	−	0.735907i
$568$		0			0
$569$	1.62949e6	+	5.01506e6i	0.210995	+	0.649375i	0.999414	+	0.0342364i	$0.0108999\pi$
$569$	1.62949e6	+	5.01506e6i	0.210995	+	0.649375i	−0.788419	+	0.615138i	$0.789100\pi$
$570$		0			0
$571$	486359.	−	353360.i	0.0624262	−	0.0453553i	−0.556135	−	0.831092i	$-0.687716\pi$
$571$	486359.	−	353360.i	0.0624262	−	0.0453553i	0.618561	+	0.785737i	$0.287716\pi$
$572$		0			0
$573$	−6.98645e6	+	5.07595e6i	−0.888935	+	0.645849i
$574$		0			0
$575$	−3.87605e6	+	1.19293e7i	−0.488900	+	1.50468i
$576$		0			0
$577$	−6.14981e6	−	4.46810e6i	−0.768993	−	0.558706i	0.132662	−	0.991161i	$-0.457647\pi$
$577$	−6.14981e6	−	4.46810e6i	−0.768993	−	0.558706i	−0.901655	+	0.432455i	$0.857647\pi$
$578$		0			0
$579$	−355625.	−	258377.i	−0.0440855	−	0.0320300i
$580$		0			0
$581$	2.45240e6	−	7.54770e6i	0.301405	−	0.927629i
$582$		0			0
$583$	−1.52375e7			−1.85670
$584$		0			0
$585$	−761941.	−	2.34501e6i	−0.0920516	−	0.283306i
$586$		0			0
$587$	3.93517e6	+	2.85907e6i	0.471377	+	0.342476i	0.797978	−	0.602687i	$-0.205903\pi$
$587$	3.93517e6	+	2.85907e6i	0.471377	+	0.342476i	−0.326601	+	0.945162i	$0.605903\pi$
$588$		0			0
$589$	−8.86148e6	+	1.03241e7i	−1.05249	+	1.22621i
$590$		0			0
$591$	9.38373e6	+	6.81768e6i	1.10511	+	0.802912i
$592$		0			0
$593$	1.17540e6	+	3.61750e6i	0.137261	+	0.422447i	0.995935	−	0.0900760i	$-0.0287110\pi$
$593$	1.17540e6	+	3.61750e6i	0.137261	+	0.422447i	−0.858674	+	0.512523i	$0.828711\pi$
$594$		0			0
$595$	6.14206e6			0.711249
$596$		0			0
$597$	992483.	−	3.05455e6i	0.113969	−	0.350761i
$598$		0			0
$599$	2.79219e6	+	2.02864e6i	0.317964	+	0.231014i	0.735306	−	0.677735i	$-0.237038\pi$
$599$	2.79219e6	+	2.02864e6i	0.317964	+	0.231014i	−0.417342	+	0.908749i	$0.637038\pi$
$600$		0			0
$601$	1.09047e7	+	7.92274e6i	1.23148	+	0.894724i	0.997000	−	0.0773964i	$-0.0246607\pi$
$601$	1.09047e7	+	7.92274e6i	1.23148	+	0.894724i	0.234482	+	0.972121i	$0.424661\pi$
$602$		0			0
$603$	−567214.	+	1.74570e6i	−0.0635263	+	0.195514i
$604$		0			0
$605$	1.17459e7	−	8.53388e6i	1.30466	−	0.947890i
$606$		0			0
$607$	1.13899e7	−	8.27524e6i	1.25472	−	0.911609i	0.256236	−	0.966614i	$-0.417518\pi$
$607$	1.13899e7	−	8.27524e6i	1.25472	−	0.911609i	0.998486	+	0.0550052i	$0.0175175\pi$
$608$		0			0
$609$	−1.82712e6	−	5.62330e6i	−0.199629	−	0.614395i
$610$		0			0
$611$	−3.23691e6	+	9.96219e6i	−0.350774	+	1.07957i
$612$		0			0
$613$	709444.	+	2.18345e6i	0.0762548	+	0.234688i	0.981917	−	0.189312i	$-0.0606257\pi$
$613$	709444.	+	2.18345e6i	0.0762548	+	0.234688i	−0.905662	+	0.424000i	$0.860626\pi$
$614$		0			0
$615$	2.68180e7			2.85916
$616$		0			0
$617$	1.21664e7	−	8.83941e6i	1.28662	−	0.934783i	0.286886	−	0.957965i	$-0.407380\pi$
$617$	1.21664e7	−	8.83941e6i	1.28662	−	0.934783i	0.999731	+	0.0231821i	$0.00737975\pi$
$618$		0			0
$619$	4.32863e6			0.454071			0.227036	−	0.973886i	$-0.427097\pi$
$619$	4.32863e6			0.454071			0.227036	+	0.973886i	$0.427097\pi$
$620$		0			0
$621$	8.36801e6			0.870749
$622$		0			0
$623$	−2.31979e6	+	1.68542e6i	−0.239457	+	0.173976i
$624$		0			0
$625$	2.11575e6			0.216653
$626$		0			0
$627$	7.26522e6	+	2.23600e7i	0.738040	+	2.27145i
$628$		0			0
$629$	999846.	−	3.07721e6i	0.100764	−	0.310121i
$630$		0			0
$631$	−827509.	−	2.54681e6i	−0.0827370	−	0.254638i	0.901127	−	0.433555i	$-0.142741\pi$
$631$	−827509.	−	2.54681e6i	−0.0827370	−	0.254638i	−0.983864	+	0.178916i	$0.942741\pi$
$632$		0			0
$633$	1.08059e7	−	7.85098e6i	1.07190	−	0.778780i
$634$		0			0
$635$	−9.08333e6	+	6.59942e6i	−0.893945	+	0.649489i
$636$		0			0
$637$	−2.75698e6	+	8.48512e6i	−0.269207	+	0.828532i
$638$		0			0
$639$	526117.	+	382247.i	0.0509719	+	0.0370332i
$640$		0			0
$641$	−1.35283e7	−	9.82889e6i	−1.30046	−	0.944842i	−0.300504	−	0.953781i	$-0.597155\pi$
$641$	−1.35283e7	−	9.82889e6i	−1.30046	−	0.944842i	−0.999960	+	0.00893863i	$0.997155\pi$
$642$		0			0
$643$	−1.65017e6	+	5.07871e6i	−0.157399	+	0.484425i	−0.998396	−	0.0566151i	$-0.981969\pi$
$643$	−1.65017e6	+	5.07871e6i	−0.157399	+	0.484425i	0.840997	+	0.541040i	$0.181969\pi$
$644$		0			0
$645$	−1.04458e7			−0.988649
$646$		0			0
$647$	−3.89553e6	−	1.19892e7i	−0.365853	−	1.12598i	−0.949445	−	0.313932i	$-0.898354\pi$
$647$	−3.89553e6	−	1.19892e7i	−0.365853	−	1.12598i	0.583593	−	0.812046i	$-0.301646\pi$
$648$		0			0
$649$	−8.47978e6	−	6.16092e6i	−0.790265	−	0.574161i
$650$		0			0
$651$	−5.23842e6	+	6.10304e6i	−0.484448	+	0.564409i
$652$		0			0
$653$	−5.91907e6	−	4.30045e6i	−0.543213	−	0.394668i	0.282064	−	0.959396i	$-0.408981\pi$
$653$	−5.91907e6	−	4.30045e6i	−0.543213	−	0.394668i	−0.825277	+	0.564728i	$0.808981\pi$
$654$		0			0
$655$	4.03760e6	+	1.24264e7i	0.367722	+	1.13173i
$656$		0			0
$657$	−1.65834e6			−0.149886
$658$		0			0
$659$	4.30319e6	−	1.32439e7i	0.385991	−	1.18796i	−0.549768	−	0.835317i	$-0.685284\pi$
$659$	4.30319e6	−	1.32439e7i	0.385991	−	1.18796i	0.935759	−	0.352641i	$-0.114716\pi$
$660$		0			0
$661$	5.65205e6	+	4.10645e6i	0.503155	+	0.365564i	0.810221	−	0.586125i	$-0.199347\pi$
$661$	5.65205e6	+	4.10645e6i	0.503155	+	0.365564i	−0.307066	+	0.951688i	$0.599347\pi$
$662$		0			0
$663$	−1.02523e7	−	7.44871e6i	−0.905808	−	0.658108i
$664$		0			0
$665$	−6.63893e6	+	2.04325e7i	−0.582162	+	1.79171i
$666$		0			0
$667$	7.46496e6	−	5.42361e6i	0.649700	−	0.472035i
$668$		0			0
$669$	−2.81958e6	+	2.04854e6i	−0.243567	+	0.176962i
$670$		0			0
$671$	4.31568e6	+	1.32823e7i	0.370035	+	1.13885i
$672$		0			0
$673$	5.32115e6	−	1.63768e7i	0.452864	−	1.39377i	−0.420761	−	0.907172i	$-0.638237\pi$
$673$	5.32115e6	−	1.63768e7i	0.452864	−	1.39377i	0.873625	−	0.486600i	$-0.161763\pi$
$674$		0			0
$675$	−5.89420e6	−	1.81405e7i	−0.497927	−	1.53246i
$676$		0			0
$677$	−7.28582e6			−0.610952			−0.305476	−	0.952200i	$-0.598816\pi$
$677$	−7.28582e6			−0.610952			−0.305476	+	0.952200i	$0.598816\pi$
$678$		0			0
$679$	−5.72453e6	+	4.15911e6i	−0.476503	+	0.346199i
$680$		0			0
$681$	1.28462e6			0.106147
$682$		0			0
$683$	−4.83836e6			−0.396868			−0.198434	−	0.980114i	$-0.563586\pi$
$683$	−4.83836e6			−0.396868			−0.198434	+	0.980114i	$0.563586\pi$
$684$		0			0
$685$	−2.05169e7	+	1.49064e7i	−1.67065	+	1.21380i
$686$		0			0
$687$	−4.05657e6			−0.327919
$688$		0			0
$689$	8.87757e6	+	2.73223e7i	0.712436	+	2.19265i
$690$		0			0
$691$	−4.18981e6	+	1.28949e7i	−0.333810	+	1.02736i	0.633495	+	0.773746i	$0.281620\pi$
$691$	−4.18981e6	+	1.28949e7i	−0.333810	+	1.02736i	−0.967305	+	0.253615i	$0.918380\pi$
$692$		0			0
$693$	403029.	+	1.24040e6i	0.0318789	+	0.0981132i
$694$		0			0
$695$	−1.46630e7	+	1.06533e7i	−1.15149	+	0.836607i
$696$		0			0
$697$	1.04641e7	−	7.60261e6i	0.815868	−	0.592763i
$698$		0			0
$699$	7.27331e6	−	2.23850e7i	0.563040	−	1.73286i
$700$		0			0
$701$	3.54668e6	+	2.57682e6i	0.272601	+	0.198056i	0.715684	−	0.698425i	$-0.246115\pi$
$701$	3.54668e6	+	2.57682e6i	0.272601	+	0.198056i	−0.443083	+	0.896481i	$0.646115\pi$
$702$		0			0
$703$	9.15610e6	+	6.65229e6i	0.698750	+	0.507672i
$704$		0			0
$705$	4.58329e6	−	1.41059e7i	0.347300	−	1.06888i
$706$		0			0
$707$	611205.			0.0459873
$708$		0			0
$709$	−3.24139e6	−	9.97597e6i	−0.242167	−	0.745314i	−0.996089	−	0.0883506i	$-0.971840\pi$
$709$	−3.24139e6	−	9.97597e6i	−0.242167	−	0.745314i	0.753922	−	0.656964i	$-0.228160\pi$
$710$		0			0
$711$	627293.	+	455755.i	0.0465368	+	0.0338110i
$712$		0			0
$713$	−1.15843e7	−	4.83168e6i	−0.853388	−	0.355938i
$714$		0			0
$715$	−4.47560e7	−	3.25171e7i	−3.27406	−	2.37874i
$716$		0			0
$717$	−1.57950e6	−	4.86119e6i	−0.114742	−	0.353138i
$718$		0			0
$719$	1.76880e7			1.27602			0.638009	−	0.770029i	$-0.279758\pi$
$719$	1.76880e7			1.27602			0.638009	+	0.770029i	$0.279758\pi$
$720$		0			0
$721$	2.83204e6	−	8.71613e6i	0.202891	−	0.624433i
$722$		0			0
$723$	−1.36728e7	−	9.93384e6i	−0.972770	−	0.706759i
$724$		0			0
$725$	−1.70156e7	−	1.23626e7i	−1.20227	−	0.873502i
$726$		0			0
$727$	−3.13307e6	+	9.64259e6i	−0.219854	+	0.676640i	0.778920	+	0.627124i	$0.215768\pi$
$727$	−3.13307e6	+	9.64259e6i	−0.219854	+	0.676640i	−0.998773	+	0.0495164i	$0.984232\pi$
$728$		0			0
$729$	−1.01702e7	+	7.38911e6i	−0.708781	+	0.514960i
$730$		0			0
$731$	−4.07584e6	+	2.96127e6i	−0.282113	+	0.204967i
$732$		0			0
$733$	242994.	+	747859.i	0.0167046	+	0.0514115i	0.959061	−	0.283198i	$-0.0913955\pi$
$733$	242994.	+	747859.i	0.0167046	+	0.0514115i	−0.942357	+	0.334610i	$0.891395\pi$
$734$		0			0
$735$	3.90374e6	−	1.20145e7i	0.266540	−	0.820326i
$736$		0			0
$737$	1.27263e7	+	3.91675e7i	0.863044	+	2.65618i
$738$		0			0
$739$	2.60253e7			1.75301			0.876506	−	0.481392i	$-0.159868\pi$
$739$	2.60253e7			1.75301			0.876506	+	0.481392i	$0.159868\pi$
$740$		0			0
$741$	3.58609e7	−	2.60545e7i	2.39925	−	1.74316i
$742$		0			0
$743$	−4.49582e6			−0.298770			−0.149385	−	0.988779i	$-0.547729\pi$
$743$	−4.49582e6			−0.298770			−0.149385	+	0.988779i	$0.547729\pi$
$744$		0			0
$745$	−2.91198e7			−1.92219
$746$		0			0
$747$	1.76017e6	−	1.27884e6i	0.115413	−	0.0838522i
$748$		0			0
$749$	−4.49295e6			−0.292636
$750$		0			0
$751$	−7.77473e6	−	2.39282e7i	−0.503020	−	1.54814i	−0.804074	−	0.594530i	$-0.797338\pi$
$751$	−7.77473e6	−	2.39282e7i	−0.503020	−	1.54814i	0.301054	−	0.953607i	$-0.402662\pi$
$752$		0			0
$753$	18293.3	−	56301.0i	0.00117572	−	0.00361850i
$754$		0			0
$755$	−4.56465e6	−	1.40486e7i	−0.291434	−	0.896942i
$756$		0			0
$757$	3.19232e6	−	2.31935e6i	0.202473	−	0.147105i	−0.481929	−	0.876210i	$-0.660064\pi$
$757$	3.19232e6	−	2.31935e6i	0.202473	−	0.147105i	0.684401	+	0.729105i	$0.260064\pi$
$758$		0			0
$759$	−1.75470e7	+	1.27486e7i	−1.10560	+	0.803266i
$760$		0			0
$761$	3.14951e6	−	9.69320e6i	0.197143	−	0.606744i	−0.802802	−	0.596246i	$-0.796658\pi$
$761$	3.14951e6	−	9.69320e6i	0.197143	−	0.606744i	0.999945	−	0.0104982i	$-0.00334176\pi$
$762$		0			0
$763$	1.13169e7	+	8.22220e6i	0.703745	+	0.511301i
$764$		0			0
$765$	1.36226e6	+	989741.i	0.0841602	+	0.0611460i
$766$		0			0
$767$	−6.10671e6	+	1.87945e7i	−0.374816	+	1.15357i
$768$		0			0
$769$	199455.			0.0121627			0.00608135	−	0.999982i	$-0.498064\pi$
$769$	199455.			0.0121627			0.00608135	+	0.999982i	$0.498064\pi$
$770$		0			0
$771$	7.12538e6	+	2.19297e7i	0.431690	+	1.32861i
$772$		0			0
$773$	−2.43924e7	−	1.77221e7i	−1.46827	−	1.06676i	−0.981111	−	0.193445i	$-0.938034\pi$
$773$	−2.43924e7	−	1.77221e7i	−1.46827	−	1.06676i	−0.487157	−	0.873314i	$-0.661966\pi$
$774$		0			0
$775$	−2.31462e6	+	2.85162e7i	−0.138428	+	1.70545i
$776$		0			0
$777$	5.41258e6	+	3.93247e6i	0.321626	+	0.233675i
$778$		0			0
$779$	1.39807e7	+	4.30281e7i	0.825439	+	2.54044i
$780$		0			0
$781$	1.45908e7			0.855958
$782$		0			0
$783$	−4.33598e6	+	1.33448e7i	−0.252745	+	0.777870i
$784$		0			0
$785$	−4.29990e7	−	3.12406e7i	−2.49048	−	1.80944i
$786$		0			0
$787$	3.06645e6	+	2.22790e6i	0.176481	+	0.128221i	0.672519	−	0.740080i	$-0.265212\pi$
$787$	3.06645e6	+	2.22790e6i	0.176481	+	0.128221i	−0.496038	+	0.868301i	$0.665212\pi$
$788$		0			0
$789$	−4.19895e6	+	1.29230e7i	−0.240131	+	0.739047i
$790$		0			0
$791$	1.17013e6	−	850152.i	0.0664958	−	0.0483121i
$792$		0			0
$793$	2.13021e7	−	1.54769e7i	1.20293	−	0.873977i
$794$		0			0
$795$	−1.25701e7	−	3.86869e7i	−0.705379	−	2.17093i
$796$		0			0
$797$	−3.83563e6	+	1.18049e7i	−0.213890	+	0.658287i	0.785340	+	0.619064i	$0.212488\pi$
$797$	−3.83563e6	+	1.18049e7i	−0.213890	+	0.658287i	−0.999231	+	0.0392223i	$0.987512\pi$
$798$		0			0
$799$	−2.21052e6	−	6.80329e6i	−0.122498	−	0.377009i
$800$		0			0
$801$	−786103.			−0.0432910
$802$		0			0
$803$	−3.01014e7	+	2.18700e7i	−1.64740	+	1.19690i
$804$		0			0
$805$	−1.98196e7			−1.07797
$806$		0			0
$807$	1.41601e7			0.765390
$808$		0			0
$809$	2.42640e7	−	1.76289e7i	1.30344	−	0.947006i	0.303459	−	0.952844i	$-0.401858\pi$
$809$	2.42640e7	−	1.76289e7i	1.30344	−	0.947006i	0.999983	+	0.00583837i	$0.00185842\pi$
$810$		0			0
$811$	−2.05523e6			−0.109726			−0.0548629	−	0.998494i	$-0.517472\pi$
$811$	−2.05523e6			−0.109726			−0.0548629	+	0.998494i	$0.517472\pi$
$812$		0			0
$813$	−3.63018e6	−	1.11726e7i	−0.192620	−	0.592824i
$814$		0			0
$815$	1.22935e7	−	3.78356e7i	0.648311	−	1.99529i
$816$		0			0
$817$	−5.44557e6	−	1.67597e7i	−0.285422	−	0.878440i
$818$		0			0
$819$	1.98934e6	−	1.44534e6i	0.103633	−	0.0752941i
$820$		0			0
$821$	−4.21496e6	+	3.06235e6i	−0.218241	+	0.158561i	−0.691534	−	0.722344i	$-0.743065\pi$
$821$	−4.21496e6	+	3.06235e6i	−0.218241	+	0.158561i	0.473294	+	0.880905i	$0.343065\pi$
$822$		0			0
$823$	−3.53476e6	+	1.08789e7i	−0.181912	+	0.559866i	−0.999881	−	0.0153946i	$-0.995100\pi$
$823$	−3.53476e6	+	1.08789e7i	−0.181912	+	0.559866i	0.817970	+	0.575261i	$0.195100\pi$
$824$		0			0
$825$	3.99966e7	+	2.90593e7i	2.04592	+	1.48645i
$826$		0			0
$827$	1.89675e7	+	1.37807e7i	0.964375	+	0.700660i	0.954163	−	0.299288i	$-0.0967492\pi$
$827$	1.89675e7	+	1.37807e7i	0.964375	+	0.700660i	0.0102126	+	0.999948i	$0.496749\pi$
$828$		0			0
$829$	−1.24040e6	+	3.81755e6i	−0.0626866	+	0.192929i	−0.977495	−	0.210959i	$-0.932341\pi$
$829$	−1.24040e6	+	3.81755e6i	−0.0626866	+	0.192929i	0.914808	+	0.403888i	$0.132341\pi$
$830$		0			0
$831$	−3.25971e7			−1.63748
$832$		0			0
$833$	−1.88277e6	−	5.79458e6i	−0.0940125	−	0.289341i
$834$		0			0
$835$	−1.36308e7	−	9.90333e6i	−0.676557	−	0.491547i
$836$		0			0
$837$	1.85703e7	−	4.41022e6i	0.916231	−	0.217594i
$838$		0			0
$839$	7.34898e6	+	5.33935e6i	0.360431	+	0.261868i	0.753232	−	0.657755i	$-0.228494\pi$
$839$	7.34898e6	+	5.33935e6i	0.360431	+	0.261868i	−0.392801	+	0.919624i	$0.628494\pi$
$840$		0			0
$841$	−1.55711e6	−	4.79229e6i	−0.0759153	−	0.233643i
$842$		0			0
$843$	1.00229e7			0.485762
$844$		0			0
$845$	−2.16703e7	+	6.66943e7i	−1.04405	+	3.21327i
$846$		0			0
$847$	1.17138e7	+	8.51058e6i	0.561035	+	0.407616i
$848$		0			0
$849$	8.28064e6	+	6.01624e6i	0.394271	+	0.286455i
$850$		0			0
$851$	−3.22637e6	+	9.92974e6i	−0.152718	+	0.470017i
$852$		0			0
$853$	2.60766e7	−	1.89458e7i	1.22710	−	0.891537i	0.230426	−	0.973090i	$-0.425988\pi$
$853$	2.60766e7	−	1.89458e7i	1.22710	−	0.891537i	0.996669	+	0.0815531i	$0.0259880\pi$
$854$		0			0
$855$	−4.76499e6	+	3.46197e6i	−0.222919	+	0.161960i
$856$		0			0
$857$	1.00459e7	+	3.09181e7i	0.467236	+	1.43801i	0.856148	+	0.516731i	$0.172851\pi$
$857$	1.00459e7	+	3.09181e7i	0.467236	+	1.43801i	−0.388911	+	0.921275i	$0.627149\pi$
$858$		0			0
$859$	−1.71439e6	+	5.27634e6i	−0.0792730	+	0.243977i	−0.982837	−	0.184476i	$-0.940941\pi$
$859$	−1.71439e6	+	5.27634e6i	−0.0792730	+	0.243977i	0.903564	+	0.428453i	$0.140941\pi$
$860$		0			0
$861$	8.26460e6	+	2.54358e7i	0.379939	+	1.16933i
$862$		0			0
$863$	9.49802e6			0.434116			0.217058	−	0.976159i	$-0.430354\pi$
$863$	9.49802e6			0.434116			0.217058	+	0.976159i	$0.430354\pi$
$864$		0			0
$865$	2.82530e7	−	2.05270e7i	1.28388	−	0.932794i
$866$		0			0
$867$	−1.45970e7			−0.659503
$868$		0			0
$869$	1.73967e7			0.781481
$870$		0			0
$871$	6.28166e7	−	4.56390e7i	2.80562	−	2.03840i
$872$		0			0
$873$	−1.93986e6			−0.0861461
$874$		0			0
$875$	5.80145e6	+	1.78550e7i	0.256163	+	0.788389i
$876$		0			0
$877$	9.07060e6	−	2.79164e7i	0.398233	−	1.22563i	−0.528183	−	0.849131i	$-0.677126\pi$
$877$	9.07060e6	−	2.79164e7i	0.398233	−	1.22563i	0.926415	−	0.376503i	$-0.122874\pi$
$878$		0			0
$879$	1.14766e6	+	3.53214e6i	0.0501005	+	0.154193i
$880$		0			0
$881$	−3.54623e7	+	2.57649e7i	−1.53931	+	1.11838i	−0.588550	+	0.808461i	$0.700301\pi$
$881$	−3.54623e7	+	2.57649e7i	−1.53931	+	1.11838i	−0.950764	+	0.309916i	$0.899699\pi$
$882$		0			0
$883$	2.11765e6	−	1.53856e6i	0.0914013	−	0.0664069i	−0.541146	−	0.840929i	$-0.682009\pi$
$883$	2.11765e6	−	1.53856e6i	0.0914013	−	0.0664069i	0.632547	+	0.774522i	$0.282009\pi$
$884$		0			0
$885$	8.64676e6	−	2.66120e7i	0.371104	−	1.14214i
$886$		0			0
$887$	1.46050e7	+	1.06112e7i	0.623294	+	0.452849i	0.854070	−	0.520157i	$-0.174127\pi$
$887$	1.46050e7	+	1.06112e7i	0.623294	+	0.452849i	−0.230777	+	0.973007i	$0.574127\pi$
$888$		0			0
$889$	−9.05853e6	−	6.58141e6i	−0.384418	−	0.279296i
$890$		0			0
$891$	1.12590e7	−	3.46517e7i	0.475123	−	1.46228i
$892$		0			0
$893$	2.50216e7			1.04999
$894$		0			0
$895$	−4.78598e6	−	1.47297e7i	−0.199716	−	0.614663i
$896$		0			0
$897$	3.30827e7	+	2.40360e7i	1.37284	+	0.997426i
$898$		0			0
$899$	1.37078e7	−	1.59704e7i	0.565678	−	0.659046i
$900$		0			0
$901$	−1.58721e7	−	1.15317e7i	−0.651360	−	0.473241i
$902$		0			0
$903$	−3.21912e6	−	9.90742e6i	−0.131376	−	0.404335i
$904$		0			0
$905$	−5.21136e7			−2.11509
$906$		0			0
$907$	−8.01065e6	+	2.46543e7i	−0.323333	+	0.995116i	0.648855	+	0.760912i	$0.275248\pi$
$907$	−8.01065e6	+	2.46543e7i	−0.323333	+	0.995116i	−0.972188	+	0.234204i	$0.924752\pi$
$908$		0			0
$909$	135561.	+	98490.5i	0.00544156	+	0.00395353i
$910$		0			0
$911$	7.28134e6	+	5.29020e6i	0.290680	+	0.211192i	0.723562	−	0.690259i	$-0.242503\pi$
$911$	7.28134e6	+	5.29020e6i	0.290680	+	0.211192i	−0.432882	+	0.901451i	$0.642503\pi$
$912$		0			0
$913$	1.50846e7	−	4.64257e7i	0.598905	−	1.84324i
$914$		0			0
$915$	−3.01626e7	+	2.19144e7i	−1.19101	+	0.865320i
$916$		0			0
$917$	−1.05417e7	+	7.65900e6i	−0.413988	+	0.300780i
$918$		0			0
$919$	−1.74809e6	−	5.38008e6i	−0.0682772	−	0.210136i	0.911096	−	0.412193i	$-0.135237\pi$
$919$	−1.74809e6	−	5.38008e6i	−0.0682772	−	0.210136i	−0.979374	+	0.202058i	$0.935237\pi$
$920$		0			0
$921$	−1.41390e6	+	4.35152e6i	−0.0549248	+	0.169041i
$922$		0			0
$923$	−8.50081e6	−	2.61628e7i	−0.328440	−	1.01083i
$924$		0			0
$925$	2.37986e7			0.914530
$926$		0			0
$927$	2.03266e6	−	1.47681e6i	0.0776899	−	0.0564450i
$928$		0			0
$929$	−5.09085e7			−1.93531			−0.967656	−	0.252275i	$-0.918821\pi$
$929$	−5.09085e7			−1.93531			−0.967656	+	0.252275i	$0.918821\pi$
$930$		0			0
$931$	2.13117e7			0.805830
$932$		0			0
$933$	−1.36638e7	+	9.92737e6i	−0.513888	+	0.373362i
$934$		0			0
$935$	3.77796e7			1.41328
$936$		0			0
$937$	7.24272e6	+	2.22908e7i	0.269496	+	0.829424i	0.990623	+	0.136621i	$0.0436243\pi$
$937$	7.24272e6	+	2.22908e7i	0.269496	+	0.829424i	−0.721127	+	0.692803i	$0.756376\pi$
$938$		0			0
$939$	48102.5	−	148044.i	0.00178034	−	0.00547934i
$940$		0			0
$941$	8.08491e6	+	2.48828e7i	0.297647	+	0.916063i	0.982319	+	0.187212i	$0.0599452\pi$
$941$	8.08491e6	+	2.48828e7i	0.297647	+	0.916063i	−0.684673	+	0.728851i	$0.740055\pi$
$942$		0			0
$943$	−3.37662e7	+	2.45326e7i	−1.23653	+	0.898389i
$944$		0			0
$945$	2.43830e7	−	1.77153e7i	0.888195	−	0.645311i
$946$		0			0
$947$	3.59445e6	−	1.10626e7i	0.130244	−	0.400849i	−0.864576	−	0.502502i	$-0.832413\pi$
$947$	3.59445e6	−	1.10626e7i	0.130244	−	0.400849i	0.994820	+	0.101653i	$0.0324130\pi$
$948$		0			0
$949$	5.67525e7	+	4.12331e7i	2.04559	+	1.48621i
$950$		0			0
$951$	1.13069e7	+	8.21497e6i	0.405409	+	0.294547i
$952$		0			0
$953$	−1.50207e7	+	4.62289e7i	−0.535744	+	1.64885i	0.206292	+	0.978490i	$0.433860\pi$
$953$	−1.50207e7	+	4.62289e7i	−0.535744	+	1.64885i	−0.742036	+	0.670360i	$0.766140\pi$
$954$		0			0
$955$	−4.85391e7			−1.72220
$956$		0			0
$957$	−1.12386e7	−	3.45887e7i	−0.396671	−	1.22083i
$958$		0			0
$959$	−2.04609e7	−	1.48657e7i	−0.718419	−	0.521962i
$960$		0			0
$961$	−2.82544e7	−	4.61714e6i	−0.986910	−	0.161274i
$962$		0			0
$963$	−996503.	−	724002.i	−0.0346268	−	0.0251579i
$964$		0			0
$965$	−763502.	−	2.34982e6i	−0.0263932	−	0.0812299i
$966$		0			0
$967$	2.25009e7			0.773809			0.386904	−	0.922120i	$-0.373544\pi$
$967$	2.25009e7			0.773809			0.386904	+	0.922120i	$0.373544\pi$
$968$		0			0
$969$	−9.35428e6	+	2.87895e7i	−0.320038	+	0.984975i
$970$		0			0
$971$	−3.41224e7	−	2.47914e7i	−1.16143	−	0.843826i	−0.171470	−	0.985189i	$-0.554852\pi$
$971$	−3.41224e7	−	2.47914e7i	−1.16143	−	0.843826i	−0.989958	+	0.141363i	$0.954852\pi$
$972$		0			0
$973$	−1.46230e7	−	1.06242e7i	−0.495169	−	0.359761i
$974$		0			0
$975$	2.88035e7	−	8.86482e7i	0.970363	−	2.98647i
$976$		0			0
$977$	2.32835e7	−	1.69164e7i	0.780390	−	0.566986i	−0.124706	−	0.992194i	$-0.539799\pi$
$977$	2.32835e7	−	1.69164e7i	0.780390	−	0.566986i	0.905096	+	0.425207i	$0.139799\pi$
$978$		0			0
$979$	−1.42689e7	+	1.03670e7i	−0.475812	+	0.345697i
$980$		0			0
$981$	1.18506e6	+	3.64724e6i	0.0393159	+	0.121002i
$982$		0			0
$983$	−4.79274e6	+	1.47505e7i	−0.158198	+	0.486882i	−0.998471	−	0.0552811i	$-0.982395\pi$
$983$	−4.79274e6	+	1.47505e7i	−0.158198	+	0.486882i	0.840273	+	0.542163i	$0.182395\pi$
$984$		0			0
$985$	2.01462e7	+	6.20037e7i	0.661611	+	2.03623i
$986$		0			0
$987$	1.47914e7			0.483298
$988$		0			0
$989$	1.31522e7	−	9.55561e6i	0.427569	−	0.310647i
$990$		0			0
$991$	7.29731e6			0.236036			0.118018	−	0.993011i	$-0.462346\pi$
$991$	7.29731e6			0.236036			0.118018	+	0.993011i	$0.462346\pi$
$992$		0			0
$993$	−5.72406e7			−1.84217
$994$		0			0
$995$	1.46047e7	−	1.06109e7i	0.467664	−	0.339778i
$996$		0			0
$997$	9.61311e6			0.306285			0.153143	−	0.988204i	$-0.451061\pi$
$997$	9.61311e6			0.306285			0.153143	+	0.988204i	$0.451061\pi$
$998$		0			0
$999$	−4.90625e6	−	1.50999e7i	−0.155538	−	0.478696i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	124.6.f.a.33.4	✓	56
31.16	even	5	inner	124.6.f.a.109.4	yes	56

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
124.6.f.a.33.4	✓	56	1.1	even	1	trivial
124.6.f.a.109.4	yes	56	31.16	even	5	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:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	124.f (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-13.2483 + 9.62542i) q^{3} -92.0437 q^{5} +(-28.3654 - 87.2998i) q^{7} +(7.77640 - 23.9333i) q^{9} +O(q^{10})\)	\(q+(-13.2483 + 9.62542i) q^{3} -92.0437 q^{5} +(-28.3654 - 87.2998i) q^{7} +(7.77640 - 23.9333i) q^{9} +(-174.475 - 536.979i) q^{11} +(-861.205 + 625.702i) q^{13} +(1219.42 - 885.959i) q^{15} +(224.644 - 691.383i) q^{17} +(2057.18 + 1494.63i) q^{19} +(1216.09 + 883.541i) q^{21} +(-724.896 + 2231.00i) q^{23} +5347.05 q^{25} +(-1102.33 - 3392.62i) q^{27} +(-3182.25 - 2312.04i) q^{29} +(-432.878 + 5333.08i) q^{31} +(7480.14 + 5434.64i) q^{33} +(2610.86 + 8035.40i) q^{35} +4450.80 q^{37} +(5386.81 - 16578.9i) q^{39} +(14394.3 + 10458.0i) q^{41} +(-5606.66 - 4073.47i) q^{43} +(-715.768 + 2202.91i) q^{45} +(7960.82 - 5783.87i) q^{47} +(6780.49 - 4926.31i) q^{49} +(3678.71 + 11321.9i) q^{51} +(8339.60 - 25666.7i) q^{53} +(16059.3 + 49425.5i) q^{55} -41640.5 q^{57} +(15018.7 - 10911.8i) q^{59} -24735.2 q^{61} -2309.95 q^{63} +(79268.5 - 57591.9i) q^{65} -72940.4 q^{67} +(-11870.7 - 36534.3i) q^{69} +(-7985.67 + 24577.4i) q^{71} +(-20363.9 - 62673.6i) q^{73} +(-70839.0 + 51467.6i) q^{75} +(-41929.1 + 30463.3i) q^{77} +(-9521.37 + 29303.8i) q^{79} +(52206.5 + 37930.3i) q^{81} +(69945.4 + 50818.3i) q^{83} +(-20677.1 + 63637.5i) q^{85} +64413.6 q^{87} +(-9653.07 - 29709.1i) q^{89} +(79052.1 + 57434.7i) q^{91} +(-45598.3 - 74820.7i) q^{93} +(-189350. - 137571. i) q^{95} +(-23820.9 - 73313.1i) q^{97} -14208.5 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 56 q + 2 q^{3} - 58 q^{5} + 104 q^{7} - 1234 q^{9}+O(q^{10}) \) 56 * q + 2 * q^3 - 58 * q^5 + 104 * q^7 - 1234 * q^9	\( 56 q + 2 q^{3} - 58 q^{5} + 104 q^{7} - 1234 q^{9} - 509 q^{11} - 117 q^{13} + 89 q^{15} - 3504 q^{17} + 262 q^{19} + 352 q^{21} - 2448 q^{23} + 49618 q^{25} + 14324 q^{27} - 9888 q^{29} - 12771 q^{31} + 27699 q^{33} + 13840 q^{35} + 76096 q^{37} + 33520 q^{39} - 4843 q^{41} - 40778 q^{43} + 56692 q^{45} + 38922 q^{47} - 17126 q^{49} - 69292 q^{51} - 41728 q^{53} - 172096 q^{55} + 57066 q^{57} - 58198 q^{59} + 176328 q^{61} - 37444 q^{63} + 143863 q^{65} + 9812 q^{67} - 9250 q^{69} - 67356 q^{71} - 63512 q^{73} - 198012 q^{75} - 74257 q^{77} + 137651 q^{79} + 196077 q^{81} + 156427 q^{83} + 238828 q^{85} - 558144 q^{87} - 99292 q^{89} - 243609 q^{91} - 325925 q^{93} - 75077 q^{95} - 476340 q^{97} + 745812 q^{99}+O(q^{100}) \) 56 * q + 2 * q^3 - 58 * q^5 + 104 * q^7 - 1234 * q^9 - 509 * q^11 - 117 * q^13 + 89 * q^15 - 3504 * q^17 + 262 * q^19 + 352 * q^21 - 2448 * q^23 + 49618 * q^25 + 14324 * q^27 - 9888 * q^29 - 12771 * q^31 + 27699 * q^33 + 13840 * q^35 + 76096 * q^37 + 33520 * q^39 - 4843 * q^41 - 40778 * q^43 + 56692 * q^45 + 38922 * q^47 - 17126 * q^49 - 69292 * q^51 - 41728 * q^53 - 172096 * q^55 + 57066 * q^57 - 58198 * q^59 + 176328 * q^61 - 37444 * q^63 + 143863 * q^65 + 9812 * q^67 - 9250 * q^69 - 67356 * q^71 - 63512 * q^73 - 198012 * q^75 - 74257 * q^77 + 137651 * q^79 + 196077 * q^81 + 156427 * q^83 + 238828 * q^85 - 558144 * q^87 - 99292 * q^89 - 243609 * q^91 - 325925 * q^93 - 75077 * q^95 - 476340 * q^97 + 745812 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more