LMFDB - Embedded newform 124.5.o.a.17.8

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			17.8
Character	$\chi$	$=$	124.17
Dual form			124.5.o.a.73.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(6.29564 + 5.66862i) q^{3} +(-3.44300 + 5.96345i) q^{5} +(-1.27725 + 12.1523i) q^{7} +(-0.964961 - 9.18099i) q^{9} +O(q^{10})$	\(q+(6.29564 + 5.66862i) q^{3} +(-3.44300 + 5.96345i) q^{5} +(-1.27725 + 12.1523i) q^{7} +(-0.964961 - 9.18099i) q^{9} +(89.5477 + 201.127i) q^{11} +(-26.7824 + 126.001i) q^{13} +(-55.4804 + 18.0267i) q^{15} +(65.2583 - 146.573i) q^{17} +(-600.230 + 127.583i) q^{19} +(-76.9277 + 69.2660i) q^{21} +(320.675 + 441.371i) q^{23} +(288.792 + 500.202i) q^{25} +(449.308 - 618.419i) q^{27} +(-1124.34 - 365.320i) q^{29} +(-296.718 + 914.046i) q^{31} +(-576.355 + 1773.84i) q^{33} +(-68.0718 - 49.4571i) q^{35} +(1419.79 - 819.717i) q^{37} +(-882.865 + 641.439i) q^{39} +(-142.389 - 158.139i) q^{41} +(196.383 + 923.911i) q^{43} +(58.0727 + 25.8557i) q^{45} +(872.597 + 2685.58i) q^{47} +(2202.49 + 468.153i) q^{49} +(1241.71 - 552.844i) q^{51} +(-1444.67 + 151.841i) q^{53} +(-1507.73 - 158.468i) q^{55} +(-4502.05 - 2599.26i) q^{57} +(4204.20 - 4669.24i) q^{59} -3022.96i q^{61} +112.802 q^{63} +(-659.190 - 593.537i) q^{65} +(2935.13 - 5083.80i) q^{67} +(-483.112 + 4596.50i) q^{69} +(-674.698 - 6419.32i) q^{71} +(-1582.76 - 3554.94i) q^{73} +(-1017.33 + 4786.14i) q^{75} +(-2558.53 + 831.316i) q^{77} +(3275.14 - 7356.09i) q^{79} +(5602.85 - 1190.92i) q^{81} +(4141.04 - 3728.61i) q^{83} +(649.394 + 893.814i) q^{85} +(-5007.58 - 8673.39i) q^{87} +(-4477.12 + 6162.22i) q^{89} +(-1496.99 - 486.402i) q^{91} +(-7049.41 + 4072.52i) q^{93} +(1305.76 - 4018.71i) q^{95} +(9278.48 + 6741.21i) q^{97} +(1760.14 - 1016.22i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$3$	6.29564	+	5.66862i	0.699516	+	0.629847i	0.940147	−	0.340770i	$-0.110688\pi$
$3$	6.29564	+	5.66862i	0.699516	+	0.629847i	−0.240631	+	0.970617i	$0.577354\pi$
$4$		0			0
$5$	−3.44300	+	5.96345i	−0.137720	+	0.238538i	−0.926633	−	0.375967i	$-0.877311\pi$
$5$	−3.44300	+	5.96345i	−0.137720	+	0.238538i	0.788913	+	0.614505i	$0.210644\pi$
$6$		0			0
$7$	−1.27725	+	12.1523i	−0.0260664	+	0.248005i	0.973728	+	0.227715i	$0.0731256\pi$
$7$	−1.27725	+	12.1523i	−0.0260664	+	0.248005i	−0.999794	+	0.0202899i	$0.993541\pi$
$8$		0			0
$9$	−0.964961	−	9.18099i	−0.0119131	−	0.113346i
$10$		0			0
$11$	89.5477	+	201.127i	0.740063	+	1.66221i	0.749281	+	0.662252i	$0.230399\pi$
$11$	89.5477	+	201.127i	0.740063	+	1.66221i	−0.00921822	+	0.999958i	$0.502934\pi$
$12$		0			0
$13$	−26.7824	+	126.001i	−0.158476	+	0.745569i	0.825088	+	0.565005i	$0.191126\pi$
$13$	−26.7824	+	126.001i	−0.158476	+	0.745569i	−0.983563	+	0.180564i	$0.942208\pi$
$14$		0			0
$15$	−55.4804	+	18.0267i	−0.246580	+	0.0801186i
$16$		0			0
$17$	65.2583	−	146.573i	0.225807	−	0.507172i	−0.764741	−	0.644338i	$-0.777133\pi$
$17$	65.2583	−	146.573i	0.225807	−	0.507172i	0.990548	+	0.137167i	$0.0437996\pi$
$18$		0			0
$19$	−600.230	+	127.583i	−1.66269	+	0.353415i	−0.940895	−	0.338697i	$-0.890014\pi$
$19$	−600.230	+	127.583i	−1.66269	+	0.353415i	−0.721790	+	0.692112i	$0.756680\pi$
$20$		0			0
$21$	−76.9277	+	69.2660i	−0.174439	+	0.157066i
$22$		0			0
$23$	320.675	+	441.371i	0.606191	+	0.834350i	0.996257	−	0.0864366i	$-0.0275480\pi$
$23$	320.675	+	441.371i	0.606191	+	0.834350i	−0.390067	+	0.920787i	$0.627548\pi$
$24$		0			0
$25$	288.792	+	500.202i	0.462066	+	0.800323i
$26$		0			0
$27$	449.308	−	618.419i	0.616334	−	0.848311i
$28$		0			0
$29$	−1124.34	−	365.320i	−1.33691	−	0.434388i	−0.448640	−	0.893713i	$-0.648091\pi$
$29$	−1124.34	−	365.320i	−1.33691	−	0.434388i	−0.888268	+	0.459325i	$0.848091\pi$
$30$		0			0
$31$	−296.718	+	914.046i	−0.308760	+	0.951140i
$31$	−296.718	+	914.046i	−0.308760	+	0.951140i
$32$		0			0
$33$	−576.355	+	1773.84i	−0.529252	+	1.62887i
$34$		0			0
$35$	−68.0718	−	49.4571i	−0.0555688	−	0.0403731i
$36$		0			0
$37$	1419.79	−	819.717i	1.03710	−	0.598771i	0.118090	−	0.993003i	$-0.462323\pi$
$37$	1419.79	−	819.717i	1.03710	−	0.598771i	0.919011	+	0.394232i	$0.128989\pi$
$38$		0			0
$39$	−882.865	+	641.439i	−0.580450	+	0.421722i
$40$		0			0
$41$	−142.389	−	158.139i	−0.0847048	−	0.0940742i	0.699302	−	0.714826i	$-0.253494\pi$
$41$	−142.389	−	158.139i	−0.0847048	−	0.0940742i	−0.784007	+	0.620752i	$0.786827\pi$
$42$		0			0
$43$	196.383	+	923.911i	0.106211	+	0.499681i	0.998807	+	0.0488255i	$0.0155478\pi$
$43$	196.383	+	923.911i	0.106211	+	0.499681i	−0.892597	+	0.450856i	$0.851119\pi$
$44$		0			0
$45$	58.0727	+	25.8557i	0.0286779	+	0.0127682i
$46$		0			0
$47$	872.597	+	2685.58i	0.395019	+	1.21574i	0.928947	+	0.370213i	$0.120715\pi$
$47$	872.597	+	2685.58i	0.395019	+	1.21574i	−0.533928	+	0.845530i	$0.679285\pi$
$48$		0			0
$49$	2202.49	+	468.153i	0.917320	+	0.194982i
$50$		0			0
$51$	1241.71	−	552.844i	0.477396	−	0.212551i
$52$		0			0
$53$	−1444.67	+	151.841i	−0.514300	+	0.0540552i	−0.358124	−	0.933674i	$-0.616583\pi$
$53$	−1444.67	+	151.841i	−0.514300	+	0.0540552i	−0.156176	+	0.987729i	$0.549917\pi$
$54$		0			0
$55$	−1507.73	−	158.468i	−0.498421	−	0.0523862i
$56$		0			0
$57$	−4502.05	−	2599.26i	−1.38567	−	0.800018i
$58$		0			0
$59$	4204.20	−	4669.24i	1.20776	−	1.34135i	0.283786	−	0.958888i	$-0.408410\pi$
$59$	4204.20	−	4669.24i	1.20776	−	1.34135i	0.923971	−	0.382462i	$-0.124924\pi$
$60$		0			0
$61$		−	3022.96i		−	0.812406i	−0.913783	−	0.406203i	$-0.866853\pi$
$61$		−	3022.96i		−	0.812406i	0.913783	−	0.406203i	$-0.133147\pi$
$62$		0			0
$63$	112.802			0.0284208
$64$		0			0
$65$	−659.190	−	593.537i	−0.156021	−	0.140482i
$66$		0			0
$67$	2935.13	−	5083.80i	0.653850	−	1.13250i	−0.328331	−	0.944563i	$-0.606486\pi$
$67$	2935.13	−	5083.80i	0.653850	−	1.13250i	0.982181	−	0.187939i	$-0.0601807\pi$
$68$		0			0
$69$	−483.112	+	4596.50i	−0.101473	+	0.965449i
$70$		0			0
$71$	−674.698	−	6419.32i	−0.133842	−	1.27342i	−0.830906	−	0.556413i	$-0.812177\pi$
$71$	−674.698	−	6419.32i	−0.133842	−	1.27342i	0.697064	−	0.717009i	$-0.254489\pi$
$72$		0			0
$73$	−1582.76	−	3554.94i	−0.297009	−	0.667093i	0.701973	−	0.712203i	$-0.252303\pi$
$73$	−1582.76	−	3554.94i	−0.297009	−	0.667093i	−0.998982	+	0.0451107i	$0.985636\pi$
$74$		0			0
$75$	−1017.33	+	4786.14i	−0.180858	+	0.850870i
$76$		0			0
$77$	−2558.53	+	831.316i	−0.431528	+	0.140212i
$78$		0			0
$79$	3275.14	−	7356.09i	0.524779	−	1.17867i	−0.435642	−	0.900120i	$-0.643479\pi$
$79$	3275.14	−	7356.09i	0.524779	−	1.17867i	0.960421	−	0.278552i	$-0.0898545\pi$
$80$		0			0
$81$	5602.85	−	1190.92i	0.853963	−	0.181515i
$82$		0			0
$83$	4141.04	−	3728.61i	0.601109	−	0.541241i	−0.311410	−	0.950276i	$-0.600801\pi$
$83$	4141.04	−	3728.61i	0.601109	−	0.541241i	0.912519	+	0.409034i	$0.134134\pi$
$84$		0			0
$85$	649.394	+	893.814i	0.0898815	+	0.123711i
$86$		0			0
$87$	−5007.58	−	8673.39i	−0.661591	−	1.14591i
$88$		0			0
$89$	−4477.12	+	6162.22i	−0.565221	+	0.777960i	−0.991979	−	0.126406i	$-0.959656\pi$
$89$	−4477.12	+	6162.22i	−0.565221	+	0.777960i	0.426758	+	0.904366i	$0.359656\pi$
$90$		0			0
$91$	−1496.99	−	486.402i	−0.180774	−	0.0587371i
$92$		0			0
$93$	−7049.41	+	4072.52i	−0.815055	+	0.470866i
$94$		0			0
$95$	1305.76	−	4018.71i	0.144682	−	0.445286i
$96$		0			0
$97$	9278.48	+	6741.21i	0.986128	+	0.716464i	0.959070	−	0.283170i	$-0.0913859\pi$
$97$	9278.48	+	6741.21i	0.986128	+	0.716464i	0.0270586	+	0.999634i	$0.491386\pi$
$98$		0			0
$99$	1760.14	−	1016.22i	0.179588	−	0.103685i
$100$		0			0
$101$	−4402.76	+	3198.79i	−0.431601	+	0.313576i	−0.782289	−	0.622916i	$-0.785948\pi$
$101$	−4402.76	+	3198.79i	−0.431601	+	0.313576i	0.350688	+	0.936492i	$0.385948\pi$
$102$		0			0
$103$	11358.5	+	12614.9i	1.07065	+	1.18907i	0.981182	+	0.193084i	$0.0618489\pi$
$103$	11358.5	+	12614.9i	1.07065	+	1.18907i	0.0894645	+	0.995990i	$0.471484\pi$
$104$		0			0
$105$	−148.202	−	697.238i	−0.0134424	−	0.0632415i
$106$		0			0
$107$	−1941.60	−	864.454i	−0.169586	−	0.0755047i	0.320188	−	0.947354i	$-0.396254\pi$
$107$	−1941.60	−	864.454i	−0.169586	−	0.0755047i	−0.489774	+	0.871849i	$0.662921\pi$
$108$		0			0
$109$	422.755	+	1301.11i	0.0355824	+	0.109511i	0.967270	−	0.253749i	$-0.0816636\pi$
$109$	422.755	+	1301.11i	0.0355824	+	0.109511i	−0.931688	+	0.363260i	$0.881664\pi$
$110$		0			0
$111$	13585.2	+	2887.62i	1.10260	+	0.234365i
$112$		0			0
$113$	−73.7815	+	32.8496i	−0.00577817	+	0.00257261i	−0.409624	−	0.912255i	$-0.634340\pi$
$113$	−73.7815	+	32.8496i	−0.00577817	+	0.00257261i	0.403846	+	0.914827i	$0.367673\pi$
$114$		0			0
$115$	−3736.18	+	392.688i	−0.282509	+	0.0296929i
$116$		0			0
$117$	1182.66	+	124.302i	0.0863949	+	0.00908047i
$118$		0			0
$119$	1697.84	+	980.247i	0.119895	+	0.0692216i
$120$		0			0
$121$	−22636.7	+	25140.6i	−1.54612	+	1.71713i
$122$		0			0
$123$		−	1802.73i		−	0.119157i
$124$		0			0
$125$	−8280.98			−0.529983
$126$		0			0
$127$	−6759.62	−	6086.39i	−0.419098	−	0.377357i	0.432430	−	0.901668i	$-0.357656\pi$
$127$	−6759.62	−	6086.39i	−0.419098	−	0.377357i	−0.851527	+	0.524311i	$0.824323\pi$
$128$		0			0
$129$	−4000.94	+	6929.84i	−0.240427	+	0.416431i
$130$		0			0
$131$	1094.06	−	10409.3i	0.0637529	−	0.606569i	−0.915273	−	0.402834i	$-0.868025\pi$
$131$	1094.06	−	10409.3i	0.0637529	−	0.606569i	0.979026	−	0.203735i	$-0.0653080\pi$
$132$		0			0
$133$	−783.773	−	7457.10i	−0.0443085	−	0.421567i
$134$		0			0
$135$	2140.94	+	4808.64i	0.117473	+	0.263849i
$136$		0			0
$137$	1164.16	−	5476.93i	0.0620256	−	0.291807i	−0.936192	−	0.351489i	$-0.885675\pi$
$137$	1164.16	−	5476.93i	0.0620256	−	0.291807i	0.998217	+	0.0596820i	$0.0190087\pi$
$138$		0			0
$139$	11327.1	−	3680.38i	0.586256	−	0.190486i	−0.000845261	−	1.00000i	$-0.500269\pi$
$139$	11327.1	−	3680.38i	0.586256	−	0.190486i	0.587101	+	0.809514i	$0.300269\pi$
$140$		0			0
$141$	−9729.96	+	21853.9i	−0.489410	+	1.09923i
$142$		0			0
$143$	−27740.6	+	5896.44i	−1.35657	+	0.288348i
$144$		0			0
$145$	6049.67	−	5447.15i	0.287737	−	0.259080i
$146$		0			0
$147$	11212.3	+	15432.4i	0.518871	+	0.714165i
$148$		0			0
$149$	11315.8	+	19599.6i	0.509699	+	0.882825i	0.999937	+	0.0112360i	$0.00357662\pi$
$149$	11315.8	+	19599.6i	0.509699	+	0.882825i	−0.490238	+	0.871589i	$0.663090\pi$
$150$		0			0
$151$	−7475.53	+	10289.2i	−0.327860	+	0.451260i	−0.940847	−	0.338833i	$-0.889968\pi$
$151$	−7475.53	+	10289.2i	−0.327860	+	0.451260i	0.612987	+	0.790093i	$0.289968\pi$
$152$		0			0
$153$	−1408.65	−	457.699i	−0.0601757	−	0.0195523i
$154$		0			0
$155$	−4429.26	−	4916.52i	−0.184361	−	0.204642i
$156$		0			0
$157$	1234.03	−	3797.97i	0.0500643	−	0.154082i	−0.922899	−	0.385042i	$-0.874187\pi$
$157$	1234.03	−	3797.97i	0.0500643	−	0.154082i	0.972963	+	0.230960i	$0.0741868\pi$
$158$		0			0
$159$	−9955.86	−	7233.35i	−0.393808	−	0.286118i
$160$		0			0
$161$	−5773.24	+	3333.18i	−0.222724	+	0.128590i
$162$		0			0
$163$	41901.0	−	30442.8i	1.57706	−	1.14580i	0.657096	−	0.753807i	$-0.271784\pi$
$163$	41901.0	−	30442.8i	1.57706	−	1.14580i	0.919967	−	0.391997i	$-0.128216\pi$
$164$		0			0
$165$	−8593.80	−	9544.39i	−0.315659	−	0.350574i
$166$		0			0
$167$	8178.15	+	38475.2i	0.293239	+	1.37958i	0.840133	+	0.542380i	$0.182477\pi$
$167$	8178.15	+	38475.2i	0.293239	+	1.37958i	−0.546894	+	0.837202i	$0.684190\pi$
$168$		0			0
$169$	10932.8	+	4867.59i	0.382787	+	0.170428i
$170$		0			0
$171$	1750.53	+	5387.59i	0.0598657	+	0.184248i
$172$		0			0
$173$	−49986.5	−	10625.0i	−1.67017	−	0.355005i	−0.726825	−	0.686823i	$-0.759005\pi$
$173$	−49986.5	−	10625.0i	−1.67017	−	0.355005i	−0.943344	+	0.331818i	$0.892338\pi$
$174$		0			0
$175$	−6447.44	+	2870.59i	−0.210529	+	0.0937334i
$176$		0			0
$177$	52936.3	−	5563.83i	1.68969	−	0.177594i
$178$		0			0
$179$	−13156.5	−	1382.81i	−0.410616	−	0.0431574i	−0.103031	−	0.994678i	$-0.532854\pi$
$179$	−13156.5	−	1382.81i	−0.410616	−	0.0431574i	−0.307585	+	0.951521i	$0.599521\pi$
$180$		0			0
$181$	−3338.67	−	1927.58i	−0.101910	−	0.0588377i	0.448179	−	0.893944i	$-0.352073\pi$
$181$	−3338.67	−	1927.58i	−0.101910	−	0.0588377i	−0.550089	+	0.835106i	$0.685406\pi$
$182$		0			0
$183$	17136.0	−	19031.5i	0.511692	−	0.568291i
$184$		0			0
$185$			11289.1i			0.329851i
$186$		0			0
$187$	35323.5			1.01014
$188$		0			0
$189$	6941.31	+	6249.98i	0.194320	+	0.174967i
$190$		0			0
$191$	−32043.6	+	55501.1i	−0.878363	+	1.52137i	−0.0252267	+	0.999682i	$0.508031\pi$
$191$	−32043.6	+	55501.1i	−0.878363	+	1.52137i	−0.853136	+	0.521688i	$0.825303\pi$
$192$		0			0
$193$	1542.42	−	14675.2i	0.0414084	−	0.393975i	−0.954114	−	0.299445i	$-0.903198\pi$
$193$	1542.42	−	14675.2i	0.0414084	−	0.393975i	0.995522	−	0.0945300i	$-0.0301348\pi$
$194$		0			0
$195$	−785.485	−	7473.40i	−0.0206571	−	0.196539i
$196$		0			0
$197$	−21401.6	−	48068.9i	−0.551461	−	1.23860i	−0.947320	−	0.320290i	$-0.896220\pi$
$197$	−21401.6	−	48068.9i	−0.551461	−	1.23860i	0.395859	−	0.918311i	$-0.370447\pi$
$198$		0			0
$199$	1447.97	−	6812.14i	0.0365639	−	0.172019i	−0.956077	−	0.293116i	$-0.905308\pi$
$199$	1447.97	−	6812.14i	0.0365639	−	0.172019i	0.992641	+	0.121097i	$0.0386411\pi$
$200$		0			0
$201$	47296.7	−	15367.6i	1.17068	−	0.380378i
$202$		0			0
$203$	5875.53	−	13196.7i	0.142579	−	0.320237i
$204$		0			0
$205$	1433.30	−	304.657i	0.0341058	−	0.00724941i
$206$		0			0
$207$	3742.79	−	3370.02i	0.0873483	−	0.0786487i
$208$		0			0
$209$	−79409.5	−	109298.i	−1.81794	−	2.50218i
$210$		0			0
$211$	4815.67	+	8340.99i	0.108166	+	0.187350i	0.915027	−	0.403392i	$-0.132169\pi$
$211$	4815.67	+	8340.99i	0.108166	+	0.187350i	−0.806861	+	0.590741i	$0.798835\pi$
$212$		0			0
$213$	32141.1	−	44238.4i	0.708437	−	0.975079i
$214$		0			0
$215$	−6185.84	−	2009.90i	−0.133820	−	0.0434808i
$216$		0			0
$217$	−10728.7	−	4773.27i	−0.227839	−	0.101367i
$218$		0			0
$219$	10187.1	−	31352.7i	0.212404	−	0.653712i
$220$		0			0
$221$	16720.5	+	12148.2i	0.342346	+	0.248729i
$222$		0			0
$223$	−35680.9	+	20600.4i	−0.717506	+	0.414252i	−0.813834	−	0.581097i	$-0.802624\pi$
$223$	−35680.9	+	20600.4i	−0.717506	+	0.414252i	0.0963281	+	0.995350i	$0.469290\pi$
$224$		0			0
$225$	4313.67	−	3134.07i	0.0852084	−	0.0619075i
$226$		0			0
$227$	−50645.9	−	56247.9i	−0.982861	−	1.09158i	−0.995790	−	0.0916618i	$-0.970782\pi$
$227$	−50645.9	−	56247.9i	−0.982861	−	1.09158i	0.0129288	−	0.999916i	$-0.495885\pi$
$228$		0			0
$229$	2856.23	+	13437.5i	0.0544655	+	0.256240i	0.996953	−	0.0780004i	$-0.0248535\pi$
$229$	2856.23	+	13437.5i	0.0544655	+	0.256240i	−0.942488	+	0.334241i	$0.891520\pi$
$230$		0			0
$231$	−20820.0	−	9269.66i	−0.390172	−	0.173716i
$232$		0			0
$233$	17973.3	+	55316.2i	0.331068	+	1.01892i	0.968627	+	0.248520i	$0.0799441\pi$
$233$	17973.3	+	55316.2i	0.331068	+	1.01892i	−0.637559	+	0.770401i	$0.720056\pi$
$234$		0			0
$235$	−19019.6	−	4042.75i	−0.344403	−	0.0732051i
$236$		0			0
$237$	62318.1	−	27745.8i	1.10947	−	0.493970i
$238$		0			0
$239$	79933.4	−	8401.33i	1.39937	−	0.147080i	0.625401	−	0.780304i	$-0.284936\pi$
$239$	79933.4	−	8401.33i	1.39937	−	0.147080i	0.773968	+	0.633224i	$0.218269\pi$
$240$		0			0
$241$	58343.8	+	6132.18i	1.00453	+	0.105580i	0.592481	−	0.805584i	$-0.298148\pi$
$241$	58343.8	+	6132.18i	1.00453	+	0.105580i	0.412044	+	0.911164i	$0.364815\pi$
$242$		0			0
$243$	−11597.3	−	6695.70i	−0.196401	−	0.113392i
$244$		0			0
$245$	−10375.0	+	11522.6i	−0.172844	+	0.191963i
$246$		0			0
$247$		−	79046.5i		−	1.29565i
$248$		0			0
$249$	47206.6			0.761385
$250$		0			0
$251$	−45650.3	−	41103.8i	−0.724597	−	0.652430i	0.221927	−	0.975063i	$-0.428765\pi$
$251$	−45650.3	−	41103.8i	−0.724597	−	0.652430i	−0.946524	+	0.322633i	$0.895432\pi$
$252$		0			0
$253$	−60056.1	+	104020.i	−0.938245	+	1.62509i
$254$		0			0
$255$	−978.342	+	9308.30i	−0.0150456	+	0.143150i
$256$		0			0
$257$	2652.16	+	25233.6i	0.0401544	+	0.382044i	0.996082	+	0.0884398i	$0.0281881\pi$
$257$	2652.16	+	25233.6i	0.0401544	+	0.382044i	−0.955927	+	0.293604i	$0.905145\pi$
$258$		0			0
$259$	8147.98	+	18300.7i	0.121465	+	0.272814i
$260$		0			0
$261$	−2269.06	+	10675.1i	−0.0333092	+	0.156708i
$262$		0			0
$263$	−44631.7	+	14501.7i	−0.645255	+	0.209656i	−0.613321	−	0.789834i	$-0.710167\pi$
$263$	−44631.7	+	14501.7i	−0.645255	+	0.209656i	−0.0319344	+	0.999490i	$0.510167\pi$
$264$		0			0
$265$	4068.50	−	9138.00i	0.0579352	−	0.130125i
$266$		0			0
$267$	−63117.6	+	13416.1i	−0.885377	+	0.188193i
$268$		0			0
$269$	−22227.7	+	20013.9i	−0.307178	+	0.276585i	−0.808273	−	0.588808i	$-0.799597\pi$
$269$	−22227.7	+	20013.9i	−0.307178	+	0.276585i	0.501095	+	0.865392i	$0.332931\pi$
$270$		0			0
$271$	50088.2	+	68940.5i	0.682020	+	0.938720i	0.999956	−	0.00939224i	$-0.00298969\pi$
$271$	50088.2	+	68940.5i	0.682020	+	0.938720i	−0.317936	+	0.948112i	$0.602990\pi$
$272$		0			0
$273$	−6667.29	−	11548.1i	−0.0894590	−	0.154948i
$274$		0			0
$275$	−74743.6	+	102876.i	−0.988345	+	1.36034i
$276$		0			0
$277$	−34682.1	−	11268.9i	−0.452007	−	0.146866i	0.0741616	−	0.997246i	$-0.476372\pi$
$277$	−34682.1	−	11268.9i	−0.452007	−	0.146866i	−0.526169	+	0.850380i	$0.676372\pi$
$278$		0			0
$279$	8678.17	+	1842.15i	0.111486	+	0.0236656i
$280$		0			0
$281$	19092.0	−	58759.2i	0.241791	−	0.744155i	−0.754357	−	0.656464i	$-0.772051\pi$
$281$	19092.0	−	58759.2i	0.241791	−	0.744155i	0.996148	−	0.0876907i	$-0.0279487\pi$
$282$		0			0
$283$	128007.	+	93002.2i	1.59830	+	1.16124i	0.890664	+	0.454663i	$0.150240\pi$
$283$	128007.	+	93002.2i	1.59830	+	1.16124i	0.707640	+	0.706573i	$0.249760\pi$
$284$		0			0
$285$	31001.1	−	17898.5i	0.381670	−	0.220357i
$286$		0			0
$287$	2103.61	−	1528.36i	0.0255389	−	0.0185551i
$288$		0			0
$289$	38661.6	+	42938.0i	0.462897	+	0.514099i
$290$		0			0
$291$	20200.6	+	95036.5i	0.238550	+	1.12229i
$292$		0			0
$293$	−85787.7	−	38195.1i	−0.999286	−	0.444911i	−0.159131	−	0.987257i	$-0.550869\pi$
$293$	−85787.7	−	38195.1i	−0.999286	−	0.444911i	−0.840155	+	0.542347i	$0.817536\pi$
$294$		0			0
$295$	13369.7	+	41147.7i	0.153631	+	0.472826i
$296$		0			0
$297$	164615.	+	34990.1i	1.86620	+	0.396673i
$298$		0			0
$299$	−64201.7	+	28584.4i	−0.718132	+	0.319733i
$300$		0			0
$301$	−11478.4	+	1206.43i	−0.126692	+	0.0133159i
$302$		0			0
$303$	−45850.9	−	4819.13i	−0.499417	−	0.0524908i
$304$		0			0
$305$	18027.3	+	10408.1i	0.193790	+	0.111885i
$306$		0			0
$307$	−58495.3	+	64965.6i	−0.620646	+	0.689297i	−0.968716	−	0.248171i	$-0.920170\pi$
$307$	−58495.3	+	64965.6i	−0.620646	+	0.689297i	0.348070	+	0.937468i	$0.386837\pi$
$308$		0			0
$309$			143806.i			1.50612i
$310$		0			0
$311$	−76084.4			−0.786637			−0.393319	−	0.919402i	$-0.628673\pi$
$311$	−76084.4			−0.786637			−0.393319	+	0.919402i	$0.628673\pi$
$312$		0			0
$313$	−16748.8	−	15080.7i	−0.170960	−	0.153933i	0.579209	−	0.815179i	$-0.303361\pi$
$313$	−16748.8	−	15080.7i	−0.170960	−	0.153933i	−0.750169	+	0.661246i	$0.770028\pi$
$314$		0			0
$315$	−388.378	+	672.691i	−0.00391412	+	0.00677945i
$316$		0			0
$317$	12388.2	−	117866.i	0.123279	−	1.17292i	−0.741566	−	0.670880i	$-0.765917\pi$
$317$	12388.2	−	117866.i	0.123279	−	1.17292i	0.864845	−	0.502039i	$-0.167417\pi$
$318$		0			0
$319$	−27206.1	−	258849.i	−0.267353	−	2.54370i
$320$		0			0
$321$	−7323.33	−	16448.5i	−0.0710720	−	0.159630i
$322$		0			0
$323$	−20469.8	+	96303.0i	−0.196205	+	0.923071i
$324$		0			0
$325$	−70760.5	+	22991.5i	−0.669922	+	0.217671i
$326$		0			0
$327$	−4713.97	+	10587.7i	−0.0440850	+	0.0990165i
$328$		0			0
$329$	−33750.3	+	7173.86i	−0.311807	+	0.0662767i
$330$		0			0
$331$	62739.3	−	56490.7i	0.572643	−	0.515610i	−0.331151	−	0.943578i	$-0.607437\pi$
$331$	62739.3	−	56490.7i	0.572643	−	0.515610i	0.903794	+	0.427968i	$0.140770\pi$
$332$		0			0
$333$	−8895.86	−	12244.1i	−0.0802231	−	0.110418i
$334$		0			0
$335$	20211.3	+	35007.0i	0.180096	+	0.311936i
$336$		0			0
$337$	−1322.48	+	1820.24i	−0.0116448	+	0.0160276i	−0.814800	−	0.579743i	$-0.803153\pi$
$337$	−1322.48	+	1820.24i	−0.0116448	+	0.0160276i	0.803155	+	0.595770i	$0.203153\pi$
$338$		0			0
$339$	−650.714	−	211.430i	−0.00566228	−	0.00183978i
$340$		0			0
$341$	−210410.	+	22172.4i	−1.80950	+	0.190680i
$342$		0			0
$343$	−17568.3	+	54069.6i	−0.149328	+	0.459584i
$344$		0			0
$345$	−25747.6	−	18706.8i	−0.216321	−	0.157167i
$346$		0			0
$347$	89831.3	−	51864.1i	0.746052	−	0.430733i	−0.0782139	−	0.996937i	$-0.524922\pi$
$347$	89831.3	−	51864.1i	0.746052	−	0.430733i	0.824265	+	0.566204i	$0.191588\pi$
$348$		0			0
$349$	160242.	−	116423.i	1.31561	−	0.955843i	0.315630	−	0.948882i	$-0.397784\pi$
$349$	160242.	−	116423.i	1.31561	−	0.955843i	0.999976	−	0.00696100i	$-0.00221577\pi$
$350$		0			0
$351$	65888.0	+	73176.0i	0.534801	+	0.593956i
$352$		0			0
$353$	29347.8	+	138071.i	0.235519	+	1.10803i	0.923886	+	0.382667i	$0.124995\pi$
$353$	29347.8	+	138071.i	0.235519	+	1.10803i	−0.688367	+	0.725362i	$0.741672\pi$
$354$		0			0
$355$	40604.3	+	18078.2i	0.322192	+	0.143449i
$356$		0			0
$357$	5132.33	+	15795.7i	0.0402697	+	0.123937i
$358$		0			0
$359$	36368.9	+	7730.46i	0.282190	+	0.0599814i	0.346832	−	0.937927i	$-0.387257\pi$
$359$	36368.9	+	7730.46i	0.282190	+	0.0599814i	−0.0646423	+	0.997909i	$0.520591\pi$
$360$		0			0
$361$	224944.	−	100152.i	1.72608	−	0.768499i
$362$		0			0
$363$	−285025.	+	29957.3i	−2.16306	+	0.227347i
$364$		0			0
$365$	26649.1	+	2800.94i	0.200031	+	0.0210241i
$366$		0			0
$367$	−85902.6	−	49595.9i	−0.637785	−	0.368225i	0.145976	−	0.989288i	$-0.453368\pi$
$367$	−85902.6	−	49595.9i	−0.637785	−	0.368225i	−0.783761	+	0.621063i	$0.786701\pi$
$368$		0			0
$369$	−1314.47	+	1459.87i	−0.00965380	+	0.0107216i
$370$		0			0
$371$		−	17749.9i		−	0.128958i
$372$		0			0
$373$	15879.5			0.114135			0.0570675	−	0.998370i	$-0.481825\pi$
$373$	15879.5			0.114135			0.0570675	+	0.998370i	$0.481825\pi$
$374$		0			0
$375$	−52134.1	−	46941.8i	−0.370732	−	0.333808i
$376$		0			0
$377$	76143.2	−	131884.i	0.535733	−	0.927917i
$378$		0			0
$379$	−16374.1	+	155789.i	−0.113993	+	1.08457i	0.776669	+	0.629909i	$0.216908\pi$
$379$	−16374.1	+	155789.i	−0.113993	+	1.08457i	−0.890662	+	0.454666i	$0.849759\pi$
$380$		0			0
$381$	−8054.72	−	76635.5i	−0.0554882	−	0.527935i
$382$		0			0
$383$	−71300.3	−	160143.i	−0.486064	−	1.09172i	−0.975564	−	0.219715i	$-0.929487\pi$
$383$	−71300.3	−	160143.i	−0.486064	−	1.09172i	0.489500	−	0.872003i	$-0.337179\pi$
$384$		0			0
$385$	3851.50	−	18119.9i	0.0259841	−	0.122246i
$386$		0			0
$387$	8292.92	−	2694.53i	0.0553714	−	0.0179912i
$388$		0			0
$389$	−28018.5	+	62930.6i	−0.185159	+	0.415875i	−0.982146	−	0.188123i	$-0.939760\pi$
$389$	−28018.5	+	62930.6i	−0.185159	+	0.415875i	0.796986	+	0.603998i	$0.206426\pi$
$390$		0			0
$391$	85619.6	−	18199.0i	0.560041	−	0.119040i
$392$		0			0
$393$	65894.4	−	59331.6i	0.426642	−	0.384150i
$394$		0			0
$395$	32591.4	+	44858.2i	0.208886	+	0.287506i
$396$		0			0
$397$	−47870.5	−	82914.1i	−0.303729	−	0.526074i	0.673248	−	0.739416i	$-0.264898\pi$
$397$	−47870.5	−	82914.1i	−0.303729	−	0.526074i	−0.976978	+	0.213342i	$0.931565\pi$
$398$		0			0
$399$	37337.1	−	51390.2i	0.234528	−	0.322801i
$400$		0			0
$401$	1636.72	+	531.802i	0.0101785	+	0.00330720i	0.314102	−	0.949389i	$-0.398297\pi$
$401$	1636.72	+	531.802i	0.0101785	+	0.00330720i	−0.303923	+	0.952697i	$0.598297\pi$
$402$		0			0
$403$	−107224.	−	61867.1i	−0.660209	−	0.380934i
$404$		0			0
$405$	−12188.6	+	37512.7i	−0.0743094	+	0.228701i
$406$		0			0
$407$	292006.	+	212155.i	1.76280	+	1.28075i
$408$		0			0
$409$	51683.3	−	29839.4i	0.308961	−	0.178379i	−0.337500	−	0.941325i	$-0.609581\pi$
$409$	51683.3	−	29839.4i	0.308961	−	0.178379i	0.646461	+	0.762947i	$0.276248\pi$
$410$		0			0
$411$	38375.8	−	27881.6i	0.227182	−	0.165057i
$412$		0			0
$413$	51372.0	+	57054.4i	0.301180	+	0.334494i
$414$		0			0
$415$	7977.78	+	37532.5i	0.0463218	+	0.217927i
$416$		0			0
$417$	92173.8	+	41038.4i	0.530073	+	0.236004i
$418$		0			0
$419$	−50286.1	−	154765.i	−0.286431	−	0.881544i	−0.985966	−	0.166946i	$-0.946610\pi$
$419$	−50286.1	−	154765.i	−0.286431	−	0.881544i	0.699535	−	0.714598i	$-0.253390\pi$
$420$		0			0
$421$	−85020.0	−	18071.6i	−0.479686	−	0.101960i	−0.0382782	−	0.999267i	$-0.512187\pi$
$421$	−85020.0	−	18071.6i	−0.479686	−	0.101960i	−0.441407	+	0.897307i	$0.645521\pi$
$422$		0			0
$423$	23814.2	−	10602.8i	0.133093	−	0.0592569i
$424$		0			0
$425$	92161.9	−	9686.61i	0.510239	−	0.0536283i
$426$		0			0
$427$	36735.8	+	3861.09i	0.201481	+	0.0211765i
$428$		0			0
$429$	−208069.	−	120129.i	−1.13056	−	0.652729i
$430$		0			0
$431$	244920.	−	272012.i	1.31847	−	1.46431i	0.531901	−	0.846806i	$-0.321478\pi$
$431$	244920.	−	272012.i	1.31847	−	1.46431i	0.786569	−	0.617503i	$-0.211856\pi$
$432$		0			0
$433$		−	303575.i		−	1.61916i	−0.587010	−	0.809580i	$-0.699695\pi$
$433$		−	303575.i		−	1.61916i	0.587010	−	0.809580i	$-0.300305\pi$
$434$		0			0
$435$	68964.4			0.364457
$436$		0			0
$437$	−248790.	−	224011.i	−1.30278	−	1.17303i
$438$		0			0
$439$	−140275.	+	242963.i	−0.727866	+	1.26070i	0.229918	+	0.973210i	$0.426154\pi$
$439$	−140275.	+	242963.i	−0.727866	+	1.26070i	−0.957784	+	0.287490i	$0.907179\pi$
$440$		0			0
$441$	2172.79	−	20672.8i	0.0111723	−	0.106297i
$442$		0			0
$443$	−1518.09	−	14443.7i	−0.00773555	−	0.0735988i	0.989973	−	0.141256i	$-0.0451142\pi$
$443$	−1518.09	−	14443.7i	−0.00773555	−	0.0735988i	−0.997709	+	0.0676575i	$0.978447\pi$
$444$		0			0
$445$	−21333.4	−	47915.6i	−0.107731	−	0.241967i
$446$		0			0
$447$	−39862.3	+	187537.i	−0.199502	+	0.938583i
$448$		0			0
$449$	−135804.	+	44125.5i	−0.673629	+	0.218875i	−0.625804	−	0.779980i	$-0.715229\pi$
$449$	−135804.	+	44125.5i	−0.673629	+	0.218875i	−0.0478253	+	0.998856i	$0.515229\pi$
$450$		0			0
$451$	19055.4	−	42799.2i	0.0936841	−	0.210418i
$452$		0			0
$453$	−105389.	+	22401.1i	−0.513568	+	0.109162i
$454$		0			0
$455$	8054.77	−	7252.55i	0.0389072	−	0.0350322i
$456$		0			0
$457$	153352.	+	211071.i	0.734271	+	1.01064i	0.998928	+	0.0462946i	$0.0147413\pi$
$457$	153352.	+	211071.i	0.734271	+	1.01064i	−0.264657	+	0.964343i	$0.585259\pi$
$458$		0			0
$459$	−61322.2	−	106213.i	−0.291067	−	0.504142i
$460$		0			0
$461$	66930.4	−	92121.7i	0.314935	−	0.433471i	−0.621977	−	0.783035i	$-0.713670\pi$
$461$	66930.4	−	92121.7i	0.314935	−	0.433471i	0.936912	+	0.349564i	$0.113670\pi$
$462$		0			0
$463$	−160018.	−	51993.1i	−0.746462	−	0.242540i	−0.0890037	−	0.996031i	$-0.528368\pi$
$463$	−160018.	−	51993.1i	−0.746462	−	0.242540i	−0.657458	+	0.753491i	$0.728368\pi$
$464$		0			0
$465$	−15.1443	−	56060.5i	−7.00394e−5	−	0.259269i
$466$		0			0
$467$	62066.7	−	191022.i	0.284593	−	0.875888i	−0.701927	−	0.712249i	$-0.747677\pi$
$467$	62066.7	−	191022.i	0.284593	−	0.875888i	0.986520	−	0.163639i	$-0.0523233\pi$
$468$		0			0
$469$	58030.8	+	42161.8i	0.263823	+	0.191679i
$470$		0			0
$471$	29298.3	−	16915.4i	0.132069	−	0.0762500i
$472$		0			0
$473$	−168238.	+	122232.i	−0.751972	+	0.546340i
$474$		0			0
$475$	−237158.	−	263391.i	−1.05112	−	1.16738i
$476$		0			0
$477$	2788.10	+	13117.0i	0.0122538	+	0.0576497i
$478$		0			0
$479$	34195.3	+	15224.7i	0.149038	+	0.0663558i	0.479900	−	0.877323i	$-0.340673\pi$
$479$	34195.3	+	15224.7i	0.149038	+	0.0663558i	−0.330862	+	0.943679i	$0.607340\pi$
$480$		0			0
$481$	65259.9	+	200849.i	0.282069	+	0.868121i
$482$		0			0
$483$	−55240.8	−	11741.8i	−0.236791	−	0.0503316i
$484$		0			0
$485$	−72146.7	+	32121.8i	−0.306714	+	0.136558i
$486$		0			0
$487$	86711.5	−	9113.75i	0.365611	−	0.0384272i	0.0800579	−	0.996790i	$-0.474489\pi$
$487$	86711.5	−	9113.75i	0.365611	−	0.0384272i	0.285553	+	0.958363i	$0.407823\pi$
$488$		0			0
$489$	436363.	+	45863.6i	1.82486	+	0.191801i
$490$		0			0
$491$	129353.	+	74681.7i	0.536552	+	0.309779i	0.743680	−	0.668535i	$-0.233078\pi$
$491$	129353.	+	74681.7i	0.536552	+	0.309779i	−0.207128	+	0.978314i	$0.566412\pi$
$492$		0			0
$493$	−126918.	+	140957.i	−0.522193	+	0.579954i
$494$		0			0
$495$			13995.3i			0.0571180i
$496$		0			0
$497$	78871.0			0.319304
$498$		0			0
$499$	303672.	+	273428.i	1.21956	+	1.09810i	0.992248	+	0.124277i	$0.0396611\pi$
$499$	303672.	+	273428.i	1.21956	+	1.09810i	0.227314	+	0.973821i	$0.427006\pi$
$500$		0			0
$501$	−166615.	+	288585.i	−0.663800	+	1.14974i
$502$		0			0
$503$	6618.87	−	62974.4i	0.0261606	−	0.248902i	−0.973624	−	0.228158i	$-0.926730\pi$
$503$	6618.87	−	62974.4i	0.0261606	−	0.248902i	0.999785	−	0.0207440i	$-0.00660350\pi$
$504$		0			0
$505$	−3917.13	−	37269.0i	−0.0153598	−	0.146139i
$506$		0			0
$507$	41236.4	+	92618.5i	0.160422	+	0.360315i
$508$		0			0
$509$	−46784.6	+	220104.i	−0.180579	+	0.849557i	0.790810	+	0.612062i	$0.209660\pi$
$509$	−46784.6	+	220104.i	−0.180579	+	0.849557i	−0.971389	+	0.237495i	$0.923674\pi$
$510$		0			0
$511$	45222.1	−	14693.6i	0.173184	−	0.0562710i
$512$		0			0
$513$	−190788.	+	428517.i	−0.724965	+	1.62830i
$514$		0			0
$515$	−114335.	+	24302.8i	−0.431089	+	0.0916307i
$516$		0			0
$517$	−462004.	+	415990.i	−1.72848	+	1.55633i
$518$		0			0
$519$	−254468.	−	350245.i	−0.944711	−	1.30028i
$520$		0			0
$521$	−58640.1	−	101568.i	−0.216033	−	0.374180i	0.737559	−	0.675283i	$-0.235978\pi$
$521$	−58640.1	−	101568.i	−0.216033	−	0.374180i	−0.953592	+	0.301103i	$0.902645\pi$
$522$		0			0
$523$	209936.	−	288952.i	0.767509	−	1.05639i	−0.229043	−	0.973416i	$-0.573560\pi$
$523$	209936.	−	288952.i	0.767509	−	1.05639i	0.996552	−	0.0829693i	$-0.0264403\pi$
$524$		0			0
$525$	−56863.1	−	18475.9i	−0.206306	−	0.0670328i
$526$		0			0
$527$	114611.	+	103140.i	0.412671	+	0.371369i
$528$		0			0
$529$	−5500.47	+	16928.7i	−0.0196557	+	0.0604941i
$530$		0			0
$531$	−46925.1	−	34093.1i	−0.166424	−	0.120914i
$532$		0			0
$533$	23739.2	−	13705.8i	0.0835624	−	0.0482448i
$534$		0			0
$535$	11840.0	−	8602.29i	0.0413662	−	0.0300543i
$536$		0			0
$537$	−74990.3	−	83285.1i	−0.260050	−	0.288814i
$538$		0			0
$539$	103069.	+	484902.i	0.354773	+	1.66908i
$540$		0			0
$541$	314758.	+	140139.i	1.07543	+	0.478813i	0.866531	−	0.499124i	$-0.166345\pi$
$541$	314758.	+	140139.i	1.07543	+	0.478813i	0.208901	+	0.977937i	$0.433011\pi$
$542$		0			0
$543$	−10092.3	−	31061.0i	−0.0342289	−	0.105346i
$544$		0			0
$545$	−9214.63	−	1958.63i	−0.0310231	−	0.00659416i
$546$		0			0
$547$	−87421.6	+	38922.6i	−0.292176	+	0.130085i	−0.547590	−	0.836747i	$-0.684455\pi$
$547$	−87421.6	+	38922.6i	−0.292176	+	0.130085i	0.255414	+	0.966832i	$0.417788\pi$
$548$		0			0
$549$	−27753.8	+	2917.04i	−0.0920827	+	0.00967828i
$550$		0			0
$551$	721471.	+	75829.6i	2.37638	+	0.249767i
$552$		0			0
$553$	85210.0	+	49196.0i	0.278638	+	0.160872i
$554$		0			0
$555$	−63993.9	+	71072.4i	−0.207755	+	0.230736i
$556$		0			0
$557$			352576.i			1.13643i	0.822880	+	0.568215i	$0.192366\pi$
$557$			352576.i			1.13643i	−0.822880	+	0.568215i	$0.807634\pi$
$558$		0			0
$559$	−121673.			−0.389378
$560$		0			0
$561$	222384.	+	200236.i	0.706607	+	0.636232i
$562$		0			0
$563$	−91244.5	+	158040.i	−0.287866	+	0.498598i	−0.973300	−	0.229536i	$-0.926279\pi$
$563$	−91244.5	+	158040.i	−0.287866	+	0.498598i	0.685434	+	0.728134i	$0.259612\pi$
$564$		0			0
$565$	58.1325	−	553.094i	0.000182105	−	0.00173261i
$566$		0			0
$567$	7316.14	+	69608.4i	0.0227570	+	0.216519i
$568$		0			0
$569$	−31656.5	−	71101.7i	−0.0977774	−	0.219612i	0.858034	−	0.513594i	$-0.171686\pi$
$569$	−31656.5	−	71101.7i	−0.0977774	−	0.219612i	−0.955811	+	0.293982i	$0.905019\pi$
$570$		0			0
$571$	70280.3	−	330643.i	0.215557	−	1.01411i	−0.728682	−	0.684852i	$-0.759867\pi$
$571$	70280.3	−	330643.i	0.215557	−	1.01411i	0.944239	−	0.329262i	$-0.106800\pi$
$572$		0			0
$573$	−516350.	+	167772.i	−1.57266	+	0.510988i
$574$		0			0
$575$	−128166.	+	287866.i	−0.387649	+	0.870673i
$576$		0			0
$577$	−640174.	+	136073.i	−1.92286	+	0.408716i	−0.923150	+	0.384439i	$0.874395\pi$
$577$	−640174.	+	136073.i	−1.92286	+	0.408716i	−0.999705	+	0.0242766i	$0.992272\pi$
$578$		0			0
$579$	92898.6	−	83646.3i	0.277110	−	0.249511i
$580$		0			0
$581$	40021.9	+	55085.4i	0.118562	+	0.163187i
$582$		0			0
$583$	−159906.	−	276966.i	−0.470466	−	0.814871i
$584$		0			0
$585$	−4813.17	+	6624.75i	−0.0140643	+	0.0193579i
$586$		0			0
$587$	576540.	+	187329.i	1.67322	+	0.543662i	0.983577	−	0.180488i	$-0.0577677\pi$
$587$	576540.	+	187329.i	1.67322	+	0.543662i	0.689643	+	0.724150i	$0.257768\pi$
$588$		0			0
$589$	61482.7	−	586493.i	0.177224	−	1.69057i
$590$		0			0
$591$	137747.	−	423942.i	0.394374	−	1.21376i
$592$		0			0
$593$	−62167.4	−	45167.3i	−0.176788	−	0.128444i	0.495872	−	0.868396i	$-0.334848\pi$
$593$	−62167.4	−	45167.3i	−0.176788	−	0.128444i	−0.672660	+	0.739951i	$0.734848\pi$
$594$		0			0
$595$	−11691.3	+	6749.98i	−0.0330239	+	0.0190664i
$596$		0			0
$597$	47731.3	−	34678.9i	0.133923	−	0.0973007i
$598$		0			0
$599$	−166432.	−	184841.i	−0.463855	−	0.515163i	0.465149	−	0.885232i	$-0.346001\pi$
$599$	−166432.	−	184841.i	−0.463855	−	0.515163i	−0.929004	+	0.370069i	$0.879334\pi$
$600$		0			0
$601$	−16971.2	−	79843.1i	−0.0469854	−	0.221049i	0.948391	−	0.317105i	$-0.102711\pi$
$601$	−16971.2	−	79843.1i	−0.0469854	−	0.221049i	−0.995376	+	0.0960556i	$0.969377\pi$
$602$		0			0
$603$	−49506.6	−	22041.8i	−0.136153	−	0.0606194i
$604$		0			0
$605$	−71986.5	−	221552.i	−0.196671	−	0.605291i
$606$		0			0
$607$	−315851.	−	67136.1i	−0.857244	−	0.182213i	−0.241735	−	0.970342i	$-0.577716\pi$
$607$	−315851.	−	67136.1i	−0.857244	−	0.182213i	−0.615509	+	0.788130i	$0.711050\pi$
$608$		0			0
$609$	111797.	−	49775.3i	0.301437	−	0.134208i
$610$		0			0
$611$	−361756.	+	38022.1i	−0.969021	+	0.101848i
$612$		0			0
$613$	−433899.	−	45604.6i	−1.15470	−	0.121363i	−0.492236	−	0.870462i	$-0.663820\pi$
$613$	−433899.	−	45604.6i	−1.15470	−	0.121363i	−0.662459	+	0.749098i	$0.730487\pi$
$614$		0			0
$615$	10750.5	+	6206.81i	0.0284236	+	0.0164104i
$616$		0			0
$617$	218715.	−	242908.i	0.574525	−	0.638075i	−0.383915	−	0.923368i	$-0.625424\pi$
$617$	218715.	−	242908.i	0.574525	−	0.638075i	0.958440	+	0.285294i	$0.0920911\pi$
$618$		0			0
$619$			475933.i			1.24212i	0.783762	+	0.621062i	$0.213298\pi$
$619$			475933.i			1.24212i	−0.783762	+	0.621062i	$0.786702\pi$
$620$		0			0
$621$	417034.			1.08140
$622$		0			0
$623$	−69166.5	−	62277.8i	−0.178205	−	0.160456i
$624$		0			0
$625$	−151983.	+	263243.i	−0.389077	+	0.673901i
$626$		0			0
$627$	119634.	−	1.13824e6i	0.304313	−	2.89534i
$628$		0			0
$629$	−27494.8	−	261596.i	−0.0694944	−	0.661195i
$630$		0			0
$631$	−36859.1	−	82786.9i	−0.0925734	−	0.207923i	0.861324	−	0.508056i	$-0.169636\pi$
$631$	−36859.1	−	82786.9i	−0.0925734	−	0.207923i	−0.953897	+	0.300133i	$0.902969\pi$
$632$		0			0
$633$	−16964.2	+	79810.2i	−0.0423375	+	0.199182i
$634$		0			0
$635$	59569.3	−	19355.2i	0.147732	−	0.0480011i
$636$		0			0
$637$	−117976.	+	264977.i	−0.290746	+	0.653025i
$638$		0			0
$639$	−58284.7	+	12388.8i	−0.142742	+	0.0303408i
$640$		0			0
$641$	537208.	−	483704.i	1.30745	−	1.17724i	0.335507	−	0.942038i	$-0.391092\pi$
$641$	537208.	−	483704.i	1.30745	−	1.17724i	0.971947	−	0.235199i	$-0.0755742\pi$
$642$		0			0
$643$	171685.	+	236305.i	0.415252	+	0.571545i	0.964490	−	0.264121i	$-0.0850818\pi$
$643$	171685.	+	236305.i	0.415252	+	0.571545i	−0.549238	+	0.835666i	$0.685082\pi$
$644$		0			0
$645$	−27550.5	−	47718.8i	−0.0662231	−	0.114702i
$646$		0			0
$647$	184458.	−	253884.i	0.440644	−	0.606494i	−0.529711	−	0.848178i	$-0.677700\pi$
$647$	184458.	−	253884.i	0.440644	−	0.606494i	0.970355	+	0.241684i	$0.0776996\pi$
$648$		0			0
$649$	1.31559e6	+	427460.i	3.12342	+	1.01486i
$650$		0			0
$651$	−40486.4	−	90868.0i	−0.0955317	−	0.214412i
$652$		0			0
$653$	−74162.0	+	228247.i	−0.173922	+	0.535278i	−0.999583	−	0.0288898i	$-0.990803\pi$
$653$	−74162.0	+	228247.i	−0.173922	+	0.535278i	0.825660	+	0.564168i	$0.190803\pi$
$654$		0			0
$655$	58308.6	+	42363.7i	0.135910	+	0.0987441i
$656$		0			0
$657$	−31110.5	+	17961.7i	−0.0720737	+	0.0416118i
$658$		0			0
$659$	−427477.	+	310580.i	−0.984333	+	0.715160i	−0.958673	−	0.284511i	$-0.908169\pi$
$659$	−427477.	+	310580.i	−0.984333	+	0.715160i	−0.0256600	+	0.999671i	$0.508169\pi$
$660$		0			0
$661$	−255182.	−	283409.i	−0.584046	−	0.648649i	0.376615	−	0.926370i	$-0.377088\pi$
$661$	−255182.	−	283409.i	−0.584046	−	0.648649i	−0.960662	+	0.277720i	$0.910421\pi$
$662$		0			0
$663$	36403.1	+	171263.i	0.0828154	+	0.389616i
$664$		0			0
$665$	47168.6	+	21000.8i	0.106662	+	0.0474890i
$666$		0			0
$667$	−199306.	−	613400.i	−0.447990	−	1.37877i
$668$		0			0
$669$	−341410.	−	72568.9i	−0.762823	−	0.162143i
$670$		0			0
$671$	608000.	−	270699.i	1.35039	−	0.601232i
$672$		0			0
$673$	−783639.	+	82363.7i	−1.73016	+	0.181847i	−0.916646	−	0.399701i	$-0.869114\pi$
$673$	−783639.	+	82363.7i	−1.73016	+	0.181847i	−0.813512	+	0.581548i	$0.802447\pi$
$674$		0			0
$675$	439090.	+	46150.3i	0.963710	+	0.101290i
$676$		0			0
$677$	76097.7	+	43935.0i	0.166033	+	0.0958591i	0.580714	−	0.814108i	$-0.302773\pi$
$677$	76097.7	+	43935.0i	0.166033	+	0.0958591i	−0.414681	+	0.909967i	$0.636107\pi$
$678$		0			0
$679$	−93771.9	+	104144.i	−0.203392	+	0.225889i
$680$		0			0
$681$		−	641209.i		−	1.38263i
$682$		0			0
$683$	421236.			0.902991			0.451496	−	0.892273i	$-0.350891\pi$
$683$	421236.			0.902991			0.451496	+	0.892273i	$0.350891\pi$
$684$		0			0
$685$	28653.2	+	25799.5i	0.0610650	+	0.0549831i
$686$		0			0
$687$	−58190.3	+	100789.i	−0.123293	+	0.213549i
$688$		0			0
$689$	19559.5	−	186097.i	0.0412022	−	0.392013i
$690$		0			0
$691$	−48278.8	−	459342.i	−0.101112	−	0.962012i	−0.921019	−	0.389517i	$-0.872642\pi$
$691$	−48278.8	−	459342.i	−0.101112	−	0.962012i	0.819908	−	0.572495i	$-0.194025\pi$
$692$		0			0
$693$	10101.2	+	22687.6i	0.0210332	+	0.0472414i
$694$		0			0
$695$	−17051.3	+	80219.8i	−0.0353010	+	0.166078i
$696$		0			0
$697$	−32470.9	+	10550.4i	−0.0668387	+	0.0217172i
$698$		0			0
$699$	−200413.	+	450135.i	−0.410177	+	0.921274i
$700$		0			0
$701$	542243.	−	115257.i	1.10346	−	0.234548i	0.380052	−	0.924965i	$-0.375906\pi$
$701$	542243.	−	115257.i	1.10346	−	0.234548i	0.723412	+	0.690417i	$0.242573\pi$
$702$		0			0
$703$	−747619.	+	673159.i	−1.51276	+	1.36209i
$704$		0			0
$705$	−96824.1	−	133267.i	−0.194807	−	0.268129i
$706$		0			0
$707$	−33249.1	−	57589.1i	−0.0665183	−	0.115213i
$708$		0			0
$709$	383876.	−	528361.i	0.763658	−	1.05109i	−0.233243	−	0.972419i	$-0.574934\pi$
$709$	383876.	−	528361.i	0.763658	−	1.05109i	0.996901	−	0.0786668i	$-0.0250663\pi$
$710$		0			0
$711$	−70696.6	−	22970.7i	−0.139849	−	0.0454397i
$712$		0			0
$713$	−498583.	+	162149.i	−0.980751	+	0.318958i
$714$		0			0
$715$	60347.6	−	185731.i	0.118045	−	0.363306i
$716$		0			0
$717$	550856.	+	400220.i	1.07152	+	0.778504i
$718$		0			0
$719$	−294459.	+	170006.i	−0.569597	+	0.328857i	−0.756988	−	0.653428i	$-0.773330\pi$
$719$	−294459.	+	170006.i	−0.569597	+	0.328857i	0.187391	+	0.982285i	$0.439997\pi$
$720$		0			0
$721$	−167807.	+	121919.i	−0.322805	+	0.234531i
$722$		0			0
$723$	332551.	+	369335.i	0.636182	+	0.706552i
$724$		0			0
$725$	−141966.	−	667898.i	−0.270090	−	1.27067i
$726$		0			0
$727$	871246.	+	387904.i	1.64844	+	0.733931i	0.999635	−	0.0270274i	$-0.00860414\pi$
$727$	871246.	+	387904.i	1.64844	+	0.733931i	0.648801	+	0.760958i	$0.275271\pi$
$728$		0			0
$729$	−178432.	−	549156.i	−0.335750	−	1.03333i
$730$		0			0
$731$	148236.	+	31508.5i	0.277407	+	0.0589647i
$732$		0			0
$733$	−724650.	+	322635.i	−1.34872	+	0.600487i	−0.948745	−	0.316041i	$-0.897646\pi$
$733$	−724650.	+	322635.i	−1.34872	+	0.600487i	−0.399970	+	0.916528i	$0.630979\pi$
$734$		0			0
$735$	−130634.	+	13730.2i	−0.241814	+	0.0254157i
$736$		0			0
$737$	1.28533e6	+	135093.i	2.36635	+	0.248713i
$738$		0			0
$739$	−524567.	−	302859.i	−0.960532	−	0.554563i	−0.0641953	−	0.997937i	$-0.520448\pi$
$739$	−524567.	−	302859.i	−0.960532	−	0.554563i	−0.896337	+	0.443374i	$0.853781\pi$
$740$		0			0
$741$	448085.	−	497649.i	0.816064	−	0.906331i
$742$		0			0
$743$			598975.i			1.08500i	0.840055	+	0.542502i	$0.182523\pi$
$743$			598975.i			1.08500i	−0.840055	+	0.542502i	$0.817477\pi$
$744$		0			0
$745$	−155842.			−0.280783
$746$		0			0
$747$	−38228.3	−	34420.9i	−0.0685084	−	0.0616852i
$748$		0			0
$749$	12985.0	−	22490.6i	0.0231461	−	0.0400902i
$750$		0			0
$751$	45405.3	−	432003.i	0.0805058	−	0.765961i	−0.877570	−	0.479448i	$-0.840837\pi$
$751$	45405.3	−	432003.i	0.0805058	−	0.765961i	0.958076	−	0.286513i	$-0.0924963\pi$
$752$		0			0
$753$	−54396.6	−	517549.i	−0.0959361	−	0.912771i
$754$		0			0
$755$	−35620.8	−	80005.6i	−0.0624898	−	0.140354i
$756$		0			0
$757$	−135294.	+	636507.i	−0.236094	+	1.11074i	0.687147	+	0.726518i	$0.258863\pi$
$757$	−135294.	+	636507.i	−0.236094	+	1.11074i	−0.923242	+	0.384219i	$0.874471\pi$
$758$		0			0
$759$	−967744.	+	314439.i	−1.67987	+	0.545824i
$760$		0			0
$761$	−137381.	+	308564.i	−0.237224	+	0.532814i	−0.992450	−	0.122651i	$-0.960861\pi$
$761$	−137381.	+	308564.i	−0.237224	+	0.532814i	0.755226	+	0.655465i	$0.227527\pi$
$762$		0			0
$763$	−16351.3	+	3475.59i	−0.0280869	+	0.00597006i
$764$		0			0
$765$	7579.46	−	6824.58i	0.0129514	−	0.0116615i
$766$		0			0
$767$	475731.	+	654787.i	0.808668	+	1.11304i
$768$		0			0
$769$	−467231.	−	809268.i	−0.790094	−	1.36848i	−0.925908	−	0.377749i	$-0.876698\pi$
$769$	−467231.	−	809268.i	−0.790094	−	1.36848i	0.135813	−	0.990734i	$-0.456635\pi$
$770$		0			0
$771$	−126343.	+	173896.i	−0.212541	+	0.292537i
$772$		0			0
$773$	26607.3	+	8645.23i	0.0445288	+	0.0144683i	0.331197	−	0.943562i	$-0.392548\pi$
$773$	26607.3	+	8645.23i	0.0445288	+	0.0144683i	−0.286668	+	0.958030i	$0.592548\pi$
$774$		0			0
$775$	−542897.	+	115550.i	−0.903886	+	0.192382i
$776$		0			0
$777$	−52442.8	+	161402.i	−0.0868648	+	0.267342i
$778$		0			0
$779$	105642.	+	76753.2i	0.174085	+	0.126480i
$780$		0			0
$781$	1.23068e6	−	710535.i	2.01764	−	1.16489i
$782$		0			0
$783$	−731096.	+	531172.i	−1.19248	+	0.866387i
$784$		0			0
$785$	18400.2	+	20435.5i	0.0298595	+	0.0331624i
$786$		0			0
$787$	−79453.9	−	373801.i	−0.128282	−	0.603519i	−0.994578	−	0.103989i	$-0.966839\pi$
$787$	−79453.9	−	373801.i	−0.128282	−	0.603519i	0.866297	−	0.499530i	$-0.166494\pi$
$788$		0			0
$789$	−363190.	−	161703.i	−0.583418	−	0.259754i
$790$		0			0
$791$	−304.960	−	938.569i	−0.000487404	−	0.00150008i
$792$		0			0
$793$	380897.	+	80962.1i	0.605705	+	0.128746i
$794$		0			0
$795$	77413.7	−	34466.8i	0.122485	−	0.0545339i
$796$		0			0
$797$	−777146.	+	81681.3i	−1.22345	+	0.128590i	−0.694140	−	0.719840i	$-0.744215\pi$
$797$	−777146.	+	81681.3i	−1.22345	+	0.128590i	−0.529309	+	0.848429i	$0.677549\pi$
$798$		0			0
$799$	450576.	+	47357.4i	0.705788	+	0.0741813i
$800$		0			0
$801$	60895.5	+	35158.1i	0.0949119	+	0.0547974i
$802$		0			0
$803$	573262.	−	636672.i	0.889042	−	0.987381i
$804$		0			0
$805$		−	45904.6i		−	0.0708377i
$806$		0			0
$807$	−253389.			−0.389082
$808$		0			0
$809$	526598.	+	474151.i	0.804605	+	0.724469i	0.964905	−	0.262599i	$-0.0845796\pi$
$809$	526598.	+	474151.i	0.804605	+	0.724469i	−0.160300	+	0.987068i	$0.551246\pi$
$810$		0			0
$811$	−268090.	+	464345.i	−0.407604	+	0.705991i	−0.994621	−	0.103584i	$-0.966969\pi$
$811$	−268090.	+	464345.i	−0.407604	+	0.705991i	0.587017	+	0.809575i	$0.300302\pi$
$812$		0			0
$813$	−75460.3	+	717956.i	−0.114166	+	1.08622i
$814$		0			0
$815$	37279.3	+	354689.i	0.0561245	+	0.533989i
$816$		0			0
$817$	−235750.	−	529503.i	−0.353189	−	0.793277i
$818$		0			0
$819$	−3021.11	+	14213.2i	−0.00450401	+	0.0211897i
$820$		0			0
$821$	−692270.	+	224932.i	−1.02704	+	0.333707i	−0.773621	−	0.633648i	$-0.781557\pi$
$821$	−692270.	+	224932.i	−1.02704	+	0.333707i	−0.253424	+	0.967355i	$0.581557\pi$
$822$		0			0
$823$	−75008.6	+	168472.i	−0.110742	+	0.248730i	−0.960412	−	0.278585i	$-0.910135\pi$
$823$	−75008.6	+	168472.i	−0.110742	+	0.248730i	0.849670	+	0.527315i	$0.176801\pi$
$824$		0			0
$825$	−1.05372e6	+	223976.i	−1.54817	+	0.329074i
$826$		0			0
$827$	−502198.	+	452181.i	−0.734284	+	0.661152i	−0.948911	−	0.315544i	$-0.897813\pi$
$827$	−502198.	+	452181.i	−0.734284	+	0.661152i	0.214627	+	0.976696i	$0.431146\pi$
$828$		0			0
$829$	691528.	+	951807.i	1.00624	+	1.38497i	0.921418	+	0.388572i	$0.127032\pi$
$829$	691528.	+	951807.i	1.00624	+	1.38497i	0.0848203	+	0.996396i	$0.472968\pi$
$830$		0			0
$831$	−154467.	−	267544.i	−0.223683	−	0.387430i
$832$		0			0
$833$	212349.	−	292273.i	0.306027	−	0.421210i
$834$		0			0
$835$	−257602.	−	83700.0i	−0.369468	−	0.120047i
$836$		0			0
$837$	431945.	+	594184.i	0.616564	+	0.848145i
$838$		0			0
$839$	−151000.	+	464730.i	−0.214513	+	0.660202i	0.784675	+	0.619907i	$0.212830\pi$
$839$	−151000.	+	464730.i	−0.214513	+	0.660202i	−0.999188	+	0.0402949i	$0.987170\pi$
$840$		0			0
$841$	558479.	+	405759.i	0.789614	+	0.573688i
$842$		0			0
$843$	453280.	−	261702.i	0.637840	−	0.368257i
$844$		0			0
$845$	−66669.2	+	48438.0i	−0.0933710	+	0.0678380i
$846$		0			0
$847$	−276602.	−	307198.i	−0.385557	−	0.428204i
$848$		0			0
$849$	278689.	+	1.31113e6i	0.386638	+	1.81899i
$850$		0			0
$851$	817091.	+	363792.i	1.12827	+	0.502336i
$852$		0			0
$853$	115095.	+	354227.i	0.158183	+	0.486837i	0.998469	−	0.0553053i	$-0.0176132\pi$
$853$	115095.	+	354227.i	0.158183	+	0.486837i	−0.840286	+	0.542143i	$0.817613\pi$
$854$		0			0
$855$	−38155.7	−	8110.25i	−0.0521948	−	0.0110943i
$856$		0			0
$857$	−289832.	+	129041.i	−0.394625	+	0.175698i	−0.594449	−	0.804134i	$-0.702630\pi$
$857$	−289832.	+	129041.i	−0.394625	+	0.175698i	0.199824	+	0.979832i	$0.435963\pi$
$858$		0			0
$859$	−236527.	+	24860.0i	−0.320549	+	0.0336910i	−0.263436	−	0.964677i	$-0.584856\pi$
$859$	−236527.	+	24860.0i	−0.320549	+	0.0336910i	−0.0571122	+	0.998368i	$0.518189\pi$
$860$		0			0
$861$	21907.3	+	2302.55i	0.0295517	+	0.00310601i
$862$		0			0
$863$	−1.17224e6	−	676794.i	−1.57397	−	0.908730i	−0.995675	−	0.0928997i	$-0.970386\pi$
$863$	−1.17224e6	−	676794.i	−1.57397	−	0.908730i	−0.578291	−	0.815830i	$-0.696280\pi$
$864$		0			0
$865$	235465.	−	261510.i	0.314698	−	0.349507i
$866$		0			0
$867$			489481.i			0.651174i
$868$		0			0
$869$	1.77279e6			2.34757
$870$		0			0
$871$	561955.	+	505986.i	0.740739	+	0.666964i
$872$		0			0
$873$	52937.6	−	91690.7i	0.0694602	−	0.120309i
$874$		0			0
$875$	10576.9	−	100633.i	0.0138148	−	0.131439i
$876$		0			0
$877$	−112474.	−	1.07012e6i	−0.146236	−	1.39134i	−0.783832	−	0.620973i	$-0.786738\pi$
$877$	−112474.	−	1.07012e6i	−0.146236	−	1.39134i	0.637596	−	0.770371i	$-0.279929\pi$
$878$		0			0
$879$	−323575.	−	726761.i	−0.418791	−	0.940620i
$880$		0			0
$881$	−153860.	+	723856.i	−0.198232	+	0.932610i	0.760728	+	0.649071i	$0.224842\pi$
$881$	−153860.	+	723856.i	−0.198232	+	0.932610i	−0.958961	+	0.283540i	$0.908491\pi$
$882$		0			0
$883$	−1.24673e6	+	405089.i	−1.59902	+	0.519552i	−0.966864	−	0.255293i	$-0.917828\pi$
$883$	−1.24673e6	+	405089.i	−1.59902	+	0.519552i	−0.632152	+	0.774844i	$0.717828\pi$
$884$		0			0
$885$	−149080.	+	334839.i	−0.190341	+	0.427514i
$886$		0			0
$887$	−318830.	+	67769.4i	−0.405240	+	0.0861364i	−0.406022	−	0.913863i	$-0.633084\pi$
$887$	−318830.	+	67769.4i	−0.405240	+	0.0861364i	0.000782149		1.00000i	$0.499751\pi$
$888$		0			0
$889$	82597.2	−	74370.9i	0.104511	−	0.0941021i
$890$		0			0
$891$	741249.	+	1.02024e6i	0.933703	+	1.28513i
$892$		0			0
$893$	−866391.	−	1.50063e6i	−1.08645	−	1.88179i
$894$		0			0
$895$	53544.2	−	73697.3i	0.0668447	−	0.0920038i
$896$		0			0
$897$	−566225.	−	183978.i	−0.703727	−	0.228655i
$898$		0			0
$899$	667532.	−	919301.i	0.825948	−	1.13747i
$900$		0			0
$901$	−72021.0	+	221658.i	−0.0887176	+	0.273045i
$902$		0			0
$903$	−79103.0	−	57471.7i	−0.0970102	−	0.0704820i
$904$		0			0
$905$	22990.1	−	13273.3i	0.0280701	−	0.0162063i
$906$		0			0
$907$	−381718.	+	277334.i	−0.464011	+	0.337124i	−0.795103	−	0.606475i	$-0.792583\pi$
$907$	−381718.	+	277334.i	−0.464011	+	0.337124i	0.331092	+	0.943599i	$0.392583\pi$
$908$		0			0
$909$	33616.6	+	37335.0i	0.0406842	+	0.0451844i
$910$		0			0
$911$	177666.	+	835854.i	0.214076	+	1.00715i	0.945600	+	0.325332i	$0.105476\pi$
$911$	177666.	+	835854.i	0.214076	+	1.00715i	−0.731524	+	0.681816i	$0.761190\pi$
$912$		0			0
$913$	1.12075e6	+	498988.i	1.34452	+	0.598617i
$914$		0			0
$915$	54494.0	+	167715.i	0.0650889	+	0.200323i
$916$		0			0
$917$	125099.	+	26590.7i	0.148770	+	0.0316221i
$918$		0			0
$919$	1.01960e6	−	453955.i	1.20725	−	0.537504i	0.298329	−	0.954463i	$-0.403571\pi$
$919$	1.01960e6	−	453955.i	1.20725	−	0.537504i	0.908925	+	0.416959i	$0.136904\pi$
$920$		0			0
$921$	−736531.	+	77412.5i	−0.868304	+	0.0912624i
$922$		0			0
$923$	826912.	+	86911.9i	0.970634	+	0.102018i
$924$		0			0
$925$	820047.	+	473455.i	0.958419	+	0.553344i
$926$		0			0
$927$	104857.	−	116455.i	0.122022	−	0.135519i
$928$		0			0
$929$		−	990512.i		−	1.14770i	−0.818961	−	0.573850i	$-0.805449\pi$
$929$		−	990512.i		−	1.14770i	0.818961	−	0.573850i	$-0.194551\pi$
$930$		0			0
$931$	−1.38173e6			−1.59413
$932$		0			0
$933$	−479000.	−	431294.i	−0.550266	−	0.495461i
$934$		0			0
$935$	−121619.	+	210650.i	−0.139116	+	0.240956i
$936$		0			0
$937$	−9225.28	+	87772.7i	−0.0105075	+	0.0999724i	−0.998519	−	0.0544102i	$-0.982672\pi$
$937$	−9225.28	+	87772.7i	−0.0105075	+	0.0999724i	0.988011	+	0.154383i	$0.0493388\pi$
$938$		0			0
$939$	−19957.7	−	189885.i	−0.0226350	−	0.215357i
$940$		0			0
$941$	−166928.	−	374926.i	−0.188517	−	0.423415i	0.794418	−	0.607372i	$-0.207776\pi$
$941$	−166928.	−	374926.i	−0.188517	−	0.423415i	−0.982934	+	0.183956i	$0.941109\pi$
$942$		0			0
$943$	24137.4	−	113557.i	0.0271436	−	0.127700i
$944$		0			0
$945$	−61170.4	+	19875.5i	−0.0684979	+	0.0222563i
$946$		0			0
$947$	−7778.68	+	17471.2i	−0.00867373	+	0.0194815i	−0.917830	−	0.396973i	$-0.870061\pi$
$947$	−7778.68	+	17471.2i	−0.00867373	+	0.0194815i	0.909157	+	0.416454i	$0.136727\pi$
$948$		0			0
$949$	490316.	−	104220.i	0.544432	−	0.115723i
$950$		0			0
$951$	746127.	−	671816.i	0.824995	−	0.742829i
$952$		0			0
$953$	−624817.	−	859987.i	−0.687967	−	0.946905i	0.312028	−	0.950073i	$-0.398992\pi$
$953$	−624817.	−	859987.i	−0.687967	−	0.946905i	−0.999995	+	0.00316809i	$0.998992\pi$
$954$		0			0
$955$	−220652.	−	382180.i	−0.241936	−	0.419046i
$956$		0			0
$957$	1.29604e6	−	1.78384e6i	1.41512	−	1.94775i
$958$		0			0
$959$	65070.2	+	21142.6i	0.0707530	+	0.0229890i
$960$		0			0
$961$	−747437.	−	542428.i	−0.809334	−	0.587348i
$962$		0			0
$963$	−6062.98	+	18659.9i	−0.00653783	+	0.0201214i
$964$		0			0
$965$	82204.1	+	59724.8i	0.0882752	+	0.0641357i
$966$		0			0
$967$	1.29338e6	−	746730.i	1.38316	−	0.798566i	0.390625	−	0.920550i	$-0.372259\pi$
$967$	1.29338e6	−	746730.i	1.38316	−	0.798566i	0.992532	+	0.121984i	$0.0389255\pi$
$968$		0			0
$969$	−674776.	+	490254.i	−0.718642	+	0.522124i
$970$		0			0
$971$	−231099.	−	256661.i	−0.245109	−	0.272221i	0.608019	−	0.793922i	$-0.291964\pi$
$971$	−231099.	−	256661.i	−0.245109	−	0.272221i	−0.853128	+	0.521701i	$0.825298\pi$
$972$		0			0
$973$	30257.4	+	142350.i	0.0319600	+	0.150360i
$974$		0			0
$975$	−575813.	−	256368.i	−0.605720	−	0.269684i
$976$		0			0
$977$	−368889.	−	1.13532e6i	−0.386462	−	1.18941i	−0.935414	−	0.353553i	$-0.884973\pi$
$977$	−368889.	−	1.13532e6i	−0.386462	−	1.18941i	0.548953	−	0.835853i	$-0.315027\pi$
$978$		0			0
$979$	−1.64031e6	−	348658.i	−1.71143	−	0.363776i
$980$		0			0
$981$	11537.5	−	5136.83i	0.0119887	−	0.00533773i
$982$		0			0
$983$	−541224.	+	56885.0i	−0.560106	+	0.0588695i	−0.380352	−	0.924842i	$-0.624197\pi$
$983$	−541224.	+	56885.0i	−0.560106	+	0.0588695i	−0.179754	+	0.983712i	$0.557530\pi$
$984$		0			0
$985$	360342.	+	37873.5i	0.371401	+	0.0390358i
$986$		0			0
$987$	−253146.	−	146154.i	−0.259858	−	0.150029i
$988$		0			0
$989$	−344812.	+	382953.i	−0.352525	+	0.391519i
$990$		0			0
$991$			948329.i			0.965632i	0.875722	+	0.482816i	$0.160386\pi$
$991$			948329.i			0.965632i	−0.875722	+	0.482816i	$0.839614\pi$
$992$		0			0
$993$	715209.			0.725328
$994$		0			0
$995$	35638.5	+	32089.1i	0.0359976	+	0.0324124i
$996$		0			0
$997$	−53552.7	+	92755.9i	−0.0538754	+	0.0933150i	−0.891705	−	0.452616i	$-0.850491\pi$
$997$	−53552.7	+	92755.9i	−0.0538754	+	0.0933150i	0.837830	+	0.545931i	$0.183824\pi$
$998$		0			0
$999$	130995.	−	1.24633e6i	0.131257	−	1.24883i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	124.5.o.a.17.8	✓	88
31.11	odd	30	inner	124.5.o.a.73.8	yes	88

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
124.5.o.a.17.8	✓	88	1.1	even	1	trivial
124.5.o.a.73.8	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)

\(f(q)\)	\(=\)	\(q+(6.29564 + 5.66862i) q^{3} +(-3.44300 + 5.96345i) q^{5} +(-1.27725 + 12.1523i) q^{7} +(-0.964961 - 9.18099i) q^{9} +O(q^{10})\)	\(q+(6.29564 + 5.66862i) q^{3} +(-3.44300 + 5.96345i) q^{5} +(-1.27725 + 12.1523i) q^{7} +(-0.964961 - 9.18099i) q^{9} +(89.5477 + 201.127i) q^{11} +(-26.7824 + 126.001i) q^{13} +(-55.4804 + 18.0267i) q^{15} +(65.2583 - 146.573i) q^{17} +(-600.230 + 127.583i) q^{19} +(-76.9277 + 69.2660i) q^{21} +(320.675 + 441.371i) q^{23} +(288.792 + 500.202i) q^{25} +(449.308 - 618.419i) q^{27} +(-1124.34 - 365.320i) q^{29} +(-296.718 + 914.046i) q^{31} +(-576.355 + 1773.84i) q^{33} +(-68.0718 - 49.4571i) q^{35} +(1419.79 - 819.717i) q^{37} +(-882.865 + 641.439i) q^{39} +(-142.389 - 158.139i) q^{41} +(196.383 + 923.911i) q^{43} +(58.0727 + 25.8557i) q^{45} +(872.597 + 2685.58i) q^{47} +(2202.49 + 468.153i) q^{49} +(1241.71 - 552.844i) q^{51} +(-1444.67 + 151.841i) q^{53} +(-1507.73 - 158.468i) q^{55} +(-4502.05 - 2599.26i) q^{57} +(4204.20 - 4669.24i) q^{59} -3022.96i q^{61} +112.802 q^{63} +(-659.190 - 593.537i) q^{65} +(2935.13 - 5083.80i) q^{67} +(-483.112 + 4596.50i) q^{69} +(-674.698 - 6419.32i) q^{71} +(-1582.76 - 3554.94i) q^{73} +(-1017.33 + 4786.14i) q^{75} +(-2558.53 + 831.316i) q^{77} +(3275.14 - 7356.09i) q^{79} +(5602.85 - 1190.92i) q^{81} +(4141.04 - 3728.61i) q^{83} +(649.394 + 893.814i) q^{85} +(-5007.58 - 8673.39i) q^{87} +(-4477.12 + 6162.22i) q^{89} +(-1496.99 - 486.402i) q^{91} +(-7049.41 + 4072.52i) q^{93} +(1305.76 - 4018.71i) q^{95} +(9278.48 + 6741.21i) q^{97} +(1760.14 - 1016.22i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 88 q - 9 q^{3} + 3 q^{5} - 215 q^{7} - 254 q^{9}+O(q^{10}) \) 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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