LMFDB - Embedded newform 354.5.b.a.119.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [354,5,Mod(119,354)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(354, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 0]))

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

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

chi := DirichletCharacter("354.119");

S:= CuspForms(chi, 5);

N := Newforms(S);

Level:	$ N $	$=$	$ 354 = 2 \cdot 3 \cdot 59 $
Weight:	$ k $	$=$	$ 5 $
Character orbit:	$[\chi]$	$=$	354.b (of order $2$, degree $1$, 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:	$36.5929669317$
Analytic rank:	$0$
Dimension:	$76$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			119.2
Character	$\chi$	$=$	354.119
Dual form			354.5.b.a.119.40

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.82843i q^{2} +(-8.91789 + 1.21294i) q^{3} -8.00000 q^{4} +12.8667i q^{5} +(3.43072 + 25.2236i) q^{6} -25.0597 q^{7} +22.6274i q^{8} +(78.0575 - 21.6338i) q^{9} +O(q^{10})$	\(q-2.82843i q^{2} +(-8.91789 + 1.21294i) q^{3} -8.00000 q^{4} +12.8667i q^{5} +(3.43072 + 25.2236i) q^{6} -25.0597 q^{7} +22.6274i q^{8} +(78.0575 - 21.6338i) q^{9} +36.3926 q^{10} -201.283i q^{11} +(71.3431 - 9.70354i) q^{12} -240.058 q^{13} +70.8796i q^{14} +(-15.6066 - 114.744i) q^{15} +64.0000 q^{16} +141.072i q^{17} +(-61.1895 - 220.780i) q^{18} -563.150 q^{19} -102.934i q^{20} +(223.480 - 30.3960i) q^{21} -569.315 q^{22} -283.363i q^{23} +(-27.4457 - 201.789i) q^{24} +459.448 q^{25} +678.985i q^{26} +(-669.868 + 287.607i) q^{27} +200.478 q^{28} +208.217i q^{29} +(-324.545 + 44.1421i) q^{30} -801.603 q^{31} -181.019i q^{32} +(244.145 + 1795.02i) q^{33} +399.012 q^{34} -322.436i q^{35} +(-624.460 + 173.070i) q^{36} +1509.92 q^{37} +1592.83i q^{38} +(2140.81 - 291.176i) q^{39} -291.140 q^{40} +2338.62i q^{41} +(-85.9729 - 632.097i) q^{42} +2310.64 q^{43} +1610.27i q^{44} +(278.355 + 1004.34i) q^{45} -801.473 q^{46} +556.559i q^{47} +(-570.745 + 77.6283i) q^{48} -1773.01 q^{49} -1299.51i q^{50} +(-171.112 - 1258.06i) q^{51} +1920.46 q^{52} -4898.80i q^{53} +(813.475 + 1894.67i) q^{54} +2589.85 q^{55} -567.037i q^{56} +(5022.11 - 683.069i) q^{57} +588.928 q^{58} -453.188i q^{59} +(124.853 + 917.951i) q^{60} +5170.61 q^{61} +2267.27i q^{62} +(-1956.10 + 542.137i) q^{63} -512.000 q^{64} -3088.75i q^{65} +(5077.09 - 690.546i) q^{66} -4426.93 q^{67} -1128.58i q^{68} +(343.703 + 2527.00i) q^{69} -911.988 q^{70} +4088.22i q^{71} +(489.516 + 1766.24i) q^{72} +959.240 q^{73} -4270.71i q^{74} +(-4097.30 + 557.283i) q^{75} +4505.20 q^{76} +5044.10i q^{77} +(-823.570 - 6055.12i) q^{78} +8802.67 q^{79} +823.470i q^{80} +(5624.96 - 3377.36i) q^{81} +6614.62 q^{82} +9213.19i q^{83} +(-1787.84 + 243.168i) q^{84} -1815.13 q^{85} -6535.48i q^{86} +(-252.556 - 1856.86i) q^{87} +4554.52 q^{88} +10798.0i q^{89} +(2840.71 - 787.308i) q^{90} +6015.78 q^{91} +2266.91i q^{92} +(7148.60 - 972.297i) q^{93} +1574.19 q^{94} -7245.89i q^{95} +(219.566 + 1614.31i) q^{96} +8347.83 q^{97} +5014.83i q^{98} +(-4354.51 - 15711.7i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 76 q - 608 q^{4} - 64 q^{6} - 184 q^{7} + 168 q^{9}+O(q^{10}) $ 76 * q - 608 * q^4 - 64 * q^6 - 184 * q^7 + 168 * q^9	$ 76 q - 608 q^{4} - 64 q^{6} - 184 q^{7} + 168 q^{9} + 256 q^{10} - 200 q^{13} - 26 q^{15} + 4864 q^{16} - 512 q^{18} + 616 q^{19} + 330 q^{21} + 640 q^{22} + 512 q^{24} - 10540 q^{25} - 354 q^{27} + 1472 q^{28} - 832 q^{30} - 3920 q^{31} - 188 q^{33} + 2560 q^{34} - 1344 q^{36} - 1440 q^{37} + 8204 q^{39} - 2048 q^{40} - 5760 q^{42} - 1944 q^{43} + 3886 q^{45} + 4864 q^{46} + 33636 q^{49} - 7544 q^{51} + 1600 q^{52} + 3392 q^{54} - 10536 q^{55} - 12182 q^{57} - 7168 q^{58} + 208 q^{60} + 6360 q^{61} + 10860 q^{63} - 38912 q^{64} + 19712 q^{66} + 30744 q^{67} - 34208 q^{69} - 23808 q^{70} + 4096 q^{72} + 4032 q^{73} + 22324 q^{75} - 4928 q^{76} + 12864 q^{78} - 29824 q^{79} - 22584 q^{81} + 13184 q^{82} - 2640 q^{84} + 9240 q^{85} + 32850 q^{87} - 5120 q^{88} - 16448 q^{90} - 31160 q^{91} - 1780 q^{93} + 5248 q^{94} - 4096 q^{96} + 77504 q^{97} - 15412 q^{99}+O(q^{100}) $ 76 * q - 608 * q^4 - 64 * q^6 - 184 * q^7 + 168 * q^9 + 256 * q^10 - 200 * q^13 - 26 * q^15 + 4864 * q^16 - 512 * q^18 + 616 * q^19 + 330 * q^21 + 640 * q^22 + 512 * q^24 - 10540 * q^25 - 354 * q^27 + 1472 * q^28 - 832 * q^30 - 3920 * q^31 - 188 * q^33 + 2560 * q^34 - 1344 * q^36 - 1440 * q^37 + 8204 * q^39 - 2048 * q^40 - 5760 * q^42 - 1944 * q^43 + 3886 * q^45 + 4864 * q^46 + 33636 * q^49 - 7544 * q^51 + 1600 * q^52 + 3392 * q^54 - 10536 * q^55 - 12182 * q^57 - 7168 * q^58 + 208 * q^60 + 6360 * q^61 + 10860 * q^63 - 38912 * q^64 + 19712 * q^66 + 30744 * q^67 - 34208 * q^69 - 23808 * q^70 + 4096 * q^72 + 4032 * q^73 + 22324 * q^75 - 4928 * q^76 + 12864 * q^78 - 29824 * q^79 - 22584 * q^81 + 13184 * q^82 - 2640 * q^84 + 9240 * q^85 + 32850 * q^87 - 5120 * q^88 - 16448 * q^90 - 31160 * q^91 - 1780 * q^93 + 5248 * q^94 - 4096 * q^96 + 77504 * q^97 - 15412 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/354\mathbb{Z}\right)^\times$.

$n$	$61$	$119$
$\chi(n)$	$1$	$-1$

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 $

$2$		−	2.82843i		−	0.707107i
$2$		−	2.82843i		−	0.707107i
$3$	−8.91789	+	1.21294i	−0.990877	+	0.134771i
$3$	−8.91789	+	1.21294i	−0.990877	+	0.134771i
$4$	−8.00000			−0.500000
$5$			12.8667i			0.514669i	0.966322	+	0.257334i	$0.0828441\pi$
$5$			12.8667i			0.514669i	−0.966322	+	0.257334i	$0.917156\pi$
$6$	3.43072	+	25.2236i	0.0952977	+	0.700656i
$7$	−25.0597			−0.511423			−0.255712	−	0.966753i	$-0.582310\pi$
$7$	−25.0597			−0.511423			−0.255712	+	0.966753i	$0.582310\pi$
$8$			22.6274i			0.353553i
$9$	78.0575	−	21.6338i	0.963673	−	0.267084i
$10$	36.3926			0.363926
$11$		−	201.283i		−	1.66350i	−0.555152	−	0.831749i	$-0.687340\pi$
$11$		−	201.283i		−	1.66350i	0.555152	−	0.831749i	$-0.312660\pi$
$12$	71.3431	−	9.70354i	0.495438	−	0.0673857i
$13$	−240.058			−1.42046			−0.710230	−	0.703970i	$-0.751409\pi$
$13$	−240.058			−1.42046			−0.710230	+	0.703970i	$0.751409\pi$
$14$			70.8796i			0.361631i
$15$	−15.6066	−	114.744i	−0.0693626	−	0.509973i
$16$	64.0000			0.250000
$17$			141.072i			0.488138i	0.969758	+	0.244069i	$0.0784824\pi$
$17$			141.072i			0.488138i	−0.969758	+	0.244069i	$0.921518\pi$
$18$	−61.1895	−	220.780i	−0.188857	−	0.681420i
$19$	−563.150			−1.55997			−0.779987	−	0.625796i	$-0.784774\pi$
$19$	−563.150			−1.55997			−0.779987	+	0.625796i	$0.784774\pi$
$20$		−	102.934i		−	0.257334i
$21$	223.480	−	30.3960i	0.506757	−	0.0689252i
$22$	−569.315			−1.17627
$23$		−	283.363i		−	0.535659i	−0.963466	−	0.267829i	$-0.913694\pi$
$23$		−	283.363i		−	0.535659i	0.963466	−	0.267829i	$-0.0863063\pi$
$24$	−27.4457	−	201.789i	−0.0476489	−	0.350328i
$25$	459.448			0.735116
$26$			678.985i			1.00442i
$27$	−669.868	+	287.607i	−0.918886	+	0.394522i
$28$	200.478			0.255712
$29$			208.217i			0.247583i	0.992308	+	0.123792i	$0.0395054\pi$
$29$			208.217i			0.247583i	−0.992308	+	0.123792i	$0.960495\pi$
$30$	−324.545	+	44.1421i	−0.360605	+	0.0490467i
$31$	−801.603			−0.834134			−0.417067	−	0.908876i	$-0.636942\pi$
$31$	−801.603			−0.834134			−0.417067	+	0.908876i	$0.636942\pi$
$32$		−	181.019i		−	0.176777i
$33$	244.145	+	1795.02i	0.224192	+	1.64832i
$34$	399.012			0.345166
$35$		−	322.436i		−	0.263213i
$36$	−624.460	+	173.070i	−0.481837	+	0.133542i
$37$	1509.92			1.10294			0.551469	−	0.834195i	$-0.314067\pi$
$37$	1509.92			1.10294			0.551469	+	0.834195i	$0.314067\pi$
$38$			1592.83i			1.10307i
$39$	2140.81	−	291.176i	1.40750	−	0.191437i
$40$	−291.140			−0.181963
$41$			2338.62i			1.39121i	0.718426	+	0.695604i	$0.244863\pi$
$41$			2338.62i			1.39121i	−0.718426	+	0.695604i	$0.755137\pi$
$42$	−85.9729	−	632.097i	−0.0487375	−	0.358332i
$43$	2310.64			1.24967			0.624836	−	0.780756i	$-0.285166\pi$
$43$	2310.64			1.24967			0.624836	+	0.780756i	$0.285166\pi$
$44$			1610.27i			0.831749i
$45$	278.355	+	1004.34i	0.137459	+	0.495972i
$46$	−801.473			−0.378768
$47$			556.559i			0.251951i	0.992033	+	0.125975i	$0.0402060\pi$
$47$			556.559i			0.251951i	−0.992033	+	0.125975i	$0.959794\pi$
$48$	−570.745	+	77.6283i	−0.247719	+	0.0336928i
$49$	−1773.01			−0.738446
$50$		−	1299.51i		−	0.519806i
$51$	−171.112	−	1258.06i	−0.0657870	−	0.483685i
$52$	1920.46			0.710230
$53$		−	4898.80i		−	1.74397i	−0.489536	−	0.871983i	$-0.662834\pi$
$53$		−	4898.80i		−	1.74397i	0.489536	−	0.871983i	$-0.337166\pi$
$54$	813.475	+	1894.67i	0.278969	+	0.649751i
$55$	2589.85			0.856150
$56$		−	567.037i		−	0.180815i
$57$	5022.11	−	683.069i	1.54574	−	0.210240i
$58$	588.928			0.175068
$59$		−	453.188i		−	0.130189i
$59$		−	453.188i		−	0.130189i
$60$	124.853	+	917.951i	0.0346813	+	0.254987i
$61$	5170.61			1.38957			0.694787	−	0.719215i	$-0.255499\pi$
$61$	5170.61			1.38957			0.694787	+	0.719215i	$0.255499\pi$
$62$			2267.27i			0.589822i
$63$	−1956.10	+	542.137i	−0.492845	+	0.136593i
$64$	−512.000			−0.125000
$65$		−	3088.75i		−	0.731066i
$66$	5077.09	−	690.546i	1.16554	−	0.158528i
$67$	−4426.93			−0.986172			−0.493086	−	0.869981i	$-0.664131\pi$
$67$	−4426.93			−0.986172			−0.493086	+	0.869981i	$0.664131\pi$
$68$		−	1128.58i		−	0.244069i
$69$	343.703	+	2527.00i	0.0721914	+	0.530772i
$70$	−911.988			−0.186120
$71$			4088.22i			0.810994i	0.914096	+	0.405497i	$0.132902\pi$
$71$			4088.22i			0.810994i	−0.914096	+	0.405497i	$0.867098\pi$
$72$	489.516	+	1766.24i	0.0944283	+	0.340710i
$73$	959.240			0.180004			0.0900019	−	0.995942i	$-0.471313\pi$
$73$	959.240			0.180004			0.0900019	+	0.995942i	$0.471313\pi$
$74$		−	4270.71i		−	0.779895i
$75$	−4097.30	+	557.283i	−0.728410	+	0.0990726i
$76$	4505.20			0.779987
$77$			5044.10i			0.850751i
$78$	−823.570	−	6055.12i	−0.135367	−	0.995253i
$79$	8802.67			1.41046			0.705229	−	0.708979i	$-0.250844\pi$
$79$	8802.67			1.41046			0.705229	+	0.708979i	$0.250844\pi$
$80$			823.470i			0.128667i
$81$	5624.96	−	3377.36i	0.857333	−	0.514763i
$82$	6614.62			0.983732
$83$			9213.19i			1.33738i	0.743543	+	0.668688i	$0.233144\pi$
$83$			9213.19i			1.33738i	−0.743543	+	0.668688i	$0.766856\pi$
$84$	−1787.84	+	243.168i	−0.253379	+	0.0344626i
$85$	−1815.13			−0.251229
$86$		−	6535.48i		−	0.883651i
$87$	−252.556	−	1856.86i	−0.0333671	−	0.245324i
$88$	4554.52			0.588135
$89$			10798.0i			1.36321i	0.731719	+	0.681607i	$0.238719\pi$
$89$			10798.0i			1.36321i	−0.731719	+	0.681607i	$0.761281\pi$
$90$	2840.71	−	787.308i	0.350705	−	0.0971985i
$91$	6015.78			0.726456
$92$			2266.91i			0.267829i
$93$	7148.60	−	972.297i	0.826524	−	0.112417i
$94$	1574.19			0.178156
$95$		−	7245.89i		−	0.802869i
$96$	219.566	+	1614.31i	0.0238244	+	0.175164i
$97$	8347.83			0.887218			0.443609	−	0.896220i	$-0.353698\pi$
$97$	8347.83			0.887218			0.443609	+	0.896220i	$0.353698\pi$
$98$			5014.83i			0.522160i
$99$	−4354.51	−	15711.7i	−0.444293	−	1.60307i
$100$	−3675.58			−0.367558
$101$			1043.49i			0.102293i	0.998691	+	0.0511465i	$0.0162875\pi$
$101$			1043.49i			0.102293i	−0.998691	+	0.0511465i	$0.983712\pi$
$102$	−3558.34	+	483.978i	−0.342017	+	0.0465185i
$103$	16403.0			1.54614			0.773071	−	0.634320i	$-0.218720\pi$
$103$	16403.0			1.54614			0.773071	+	0.634320i	$0.218720\pi$
$104$		−	5431.88i		−	0.502208i
$105$	391.097	+	2875.45i	0.0354736	+	0.260812i
$106$	−13855.9			−1.23317
$107$		−	5455.76i		−	0.476528i	−0.971200	−	0.238264i	$-0.923422\pi$
$107$		−	5455.76i		−	0.476528i	0.971200	−	0.238264i	$-0.0765783\pi$
$108$	5358.95	−	2300.85i	0.459443	−	0.197261i
$109$	−1400.00			−0.117836			−0.0589178	−	0.998263i	$-0.518765\pi$
$109$	−1400.00			−0.117836			−0.0589178	+	0.998263i	$0.518765\pi$
$110$		−	7325.21i		−	0.605389i
$111$	−13465.3	+	1831.45i	−1.09288	+	0.148644i
$112$	−1603.82			−0.127856
$113$			25071.7i			1.96348i	0.190229	+	0.981740i	$0.439077\pi$
$113$			25071.7i			1.96348i	−0.190229	+	0.981740i	$0.560923\pi$
$114$	−1932.01	−	14204.7i	−0.148662	−	1.09300i
$115$	3645.96			0.275687
$116$		−	1665.74i		−	0.123792i
$117$	−18738.3	+	5193.35i	−1.36886	+	0.379381i
$118$	−1281.81			−0.0920575
$119$		−	3535.23i		−	0.249645i
$120$	2596.36	−	353.137i	0.180303	−	0.0245234i
$121$	−25873.9			−1.76722
$122$		−	14624.7i		−	0.982577i
$123$	−2836.61	−	20855.6i	−0.187495	−	1.37852i
$124$	6412.82			0.417067
$125$			13953.3i			0.893010i
$126$	1533.39	+	5532.69i	0.0965856	+	0.348494i
$127$	12295.9			0.762347			0.381174	−	0.924503i	$-0.375520\pi$
$127$	12295.9			0.762347			0.381174	+	0.924503i	$0.375520\pi$
$128$			1448.15i			0.0883883i
$129$	−20606.1	+	2802.68i	−1.23827	+	0.168420i
$130$	−8736.31			−0.516941
$131$		−	9864.35i		−	0.574812i	−0.957809	−	0.287406i	$-0.907207\pi$
$131$		−	9864.35i		−	0.574812i	0.957809	−	0.287406i	$-0.0927929\pi$
$132$	−1953.16	−	14360.2i	−0.112096	−	0.824160i
$133$	14112.4			0.797807
$134$			12521.2i			0.697329i
$135$	−3700.55	−	8619.00i	−0.203048	−	0.472922i
$136$	−3192.09			−0.172583
$137$			13596.1i			0.724390i	0.932102	+	0.362195i	$0.117972\pi$
$137$			13596.1i			0.724390i	−0.932102	+	0.362195i	$0.882028\pi$
$138$	7147.45	−	972.140i	0.375312	−	0.0510471i
$139$	13490.0			0.698204			0.349102	−	0.937085i	$-0.386487\pi$
$139$	13490.0			0.698204			0.349102	+	0.937085i	$0.386487\pi$
$140$			2579.49i			0.131607i
$141$	−675.074	−	4963.33i	−0.0339557	−	0.249652i
$142$	11563.2			0.573459
$143$			48319.6i			2.36293i
$144$	4995.68	−	1384.56i	0.240918	−	0.0667709i
$145$	−2679.07			−0.127423
$146$		−	2713.14i		−	0.127282i
$147$	15811.5	−	2150.56i	0.731709	−	0.0995214i
$148$	−12079.4			−0.551469
$149$		−	20517.9i		−	0.924189i	−0.886831	−	0.462095i	$-0.847098\pi$
$149$		−	20517.9i		−	0.924189i	0.886831	−	0.462095i	$-0.152902\pi$
$150$	1576.24	+	11588.9i	0.0700549	+	0.515063i
$151$	−35446.9			−1.55462			−0.777311	−	0.629117i	$-0.783417\pi$
$151$	−35446.9			−1.55462			−0.777311	+	0.629117i	$0.783417\pi$
$152$		−	12742.6i		−	0.551534i
$153$	3051.92	+	11011.7i	0.130374	+	0.470406i
$154$	14266.9			0.601572
$155$		−	10314.0i		−	0.429302i
$156$	−17126.5	+	2329.41i	−0.703750	+	0.0957186i
$157$	16047.4			0.651038			0.325519	−	0.945535i	$-0.394461\pi$
$157$	16047.4			0.651038			0.325519	+	0.945535i	$0.394461\pi$
$158$		−	24897.7i		−	0.997345i
$159$	5941.96	+	43687.0i	0.235037	+	1.72805i
$160$	2329.12			0.0909814
$161$			7101.01i			0.273948i
$162$	−9552.61	−	15909.8i	−0.363992	−	0.606226i
$163$	38091.1			1.43367			0.716833	−	0.697245i	$-0.245591\pi$
$163$	38091.1			1.43367			0.716833	+	0.697245i	$0.245591\pi$
$164$		−	18709.0i		−	0.695604i
$165$	−23096.0	+	3141.34i	−0.848339	+	0.115384i
$166$	26058.8			0.945668
$167$		−	41883.4i		−	1.50179i	−0.660421	−	0.750895i	$-0.729622\pi$
$167$		−	41883.4i		−	1.50179i	0.660421	−	0.750895i	$-0.270378\pi$
$168$	687.783	+	5056.77i	0.0243687	+	0.179166i
$169$	29066.6			1.01770
$170$			5133.97i			0.177646i
$171$	−43958.1	+	12183.1i	−1.50330	+	0.416643i
$172$	−18485.1			−0.624836
$173$			33004.6i			1.10276i	0.834253	+	0.551382i	$0.185899\pi$
$173$			33004.6i			1.10276i	−0.834253	+	0.551382i	$0.814101\pi$
$174$	−5251.99	+	714.335i	−0.173471	+	0.0235941i
$175$	−11513.6			−0.375956
$176$		−	12882.1i		−	0.415874i
$177$	549.690	+	4041.48i	0.0175457	+	0.129001i
$178$	30541.4			0.963938
$179$		−	30794.8i		−	0.961107i	−0.876966	−	0.480553i	$-0.840436\pi$
$179$		−	30794.8i		−	0.961107i	0.876966	−	0.480553i	$-0.159564\pi$
$180$	−2226.84	−	8034.75i	−0.0687297	−	0.247986i
$181$	−39969.3			−1.22003			−0.610014	−	0.792391i	$-0.708836\pi$
$181$	−39969.3			−1.22003			−0.610014	+	0.792391i	$0.708836\pi$
$182$		−	17015.2i		−	0.513682i
$183$	−46110.9	+	6271.64i	−1.37690	+	0.187275i
$184$	6411.78			0.189384
$185$			19427.7i			0.567648i
$186$	−2750.07	−	20219.3i	−0.0794911	−	0.584441i
$187$	28395.4			0.812017
$188$		−	4452.47i		−	0.125975i
$189$	16786.7	−	7207.35i	0.469940	−	0.201768i
$190$	−20494.5			−0.567714
$191$			54759.6i			1.50104i	0.660846	+	0.750522i	$0.270198\pi$
$191$			54759.6i			1.50104i	−0.660846	+	0.750522i	$0.729802\pi$
$192$	4565.96	−	621.026i	0.123860	−	0.0168464i
$193$	−35026.2			−0.940326			−0.470163	−	0.882580i	$-0.655805\pi$
$193$	−35026.2			−0.940326			−0.470163	+	0.882580i	$0.655805\pi$
$194$		−	23611.2i		−	0.627358i
$195$	3746.48	+	27545.2i	0.0985267	+	0.724396i
$196$	14184.1			0.369223
$197$			64801.5i			1.66975i	0.550436	+	0.834877i	$0.314461\pi$
$197$			64801.5i			1.66975i	−0.550436	+	0.834877i	$0.685539\pi$
$198$	−44439.3	+	12316.4i	−1.13354	+	0.314162i
$199$	−20219.6			−0.510583			−0.255292	−	0.966864i	$-0.582172\pi$
$199$	−20219.6			−0.510583			−0.255292	+	0.966864i	$0.582172\pi$
$200$			10396.1i			0.259903i
$201$	39478.8	−	5369.61i	0.977175	−	0.132908i
$202$	2951.44			0.0723320
$203$		−	5217.87i		−	0.126620i
$204$	1368.90	+	10064.5i	0.0328935	+	0.241842i
$205$	−30090.4			−0.716011
$206$		−	46394.7i		−	1.09329i
$207$	−6130.22	−	22118.7i	−0.143066	−	0.516200i
$208$	−15363.7			−0.355115
$209$			113353.i			2.59501i
$210$	8133.01	−	1106.19i	0.184422	−	0.0250836i
$211$	−6475.86			−0.145456			−0.0727281	−	0.997352i	$-0.523171\pi$
$211$	−6475.86			−0.145456			−0.0727281	+	0.997352i	$0.523171\pi$
$212$			39190.4i			0.871983i
$213$	−4958.77	−	36458.3i	−0.109299	−	0.803595i
$214$	−15431.2			−0.336956
$215$			29730.4i			0.643167i
$216$	−6507.80	−	15157.4i	−0.139485	−	0.324875i
$217$	20088.0			0.426595
$218$			3959.81i			0.0833223i
$219$	−8554.40	+	1163.50i	−0.178362	+	0.0242594i
$220$	−20718.8			−0.428075
$221$		−	33865.4i		−	0.693380i
$222$	5180.12	+	38085.7i	0.105107	+	0.772780i
$223$	−49426.8			−0.993923			−0.496961	−	0.867773i	$-0.665551\pi$
$223$	−49426.8			−0.993923			−0.496961	+	0.867773i	$0.665551\pi$
$224$			4536.30i			0.0904077i
$225$	35863.4	−	9939.58i	0.708412	−	0.196337i
$226$	70913.4			1.38839
$227$		−	4963.92i		−	0.0963325i	−0.998839	−	0.0481662i	$-0.984662\pi$
$227$		−	4963.92i		−	0.0963325i	0.998839	−	0.0481662i	$-0.0153377\pi$
$228$	−40176.9	+	5464.55i	−0.772871	+	0.105120i
$229$	−30365.1			−0.579034			−0.289517	−	0.957173i	$-0.593495\pi$
$229$	−30365.1			−0.579034			−0.289517	+	0.957173i	$0.593495\pi$
$230$		−	10312.3i		−	0.194940i
$231$	−6118.21	−	44982.8i	−0.114657	−	0.842990i
$232$	−4711.42			−0.0875339
$233$		−	87897.3i		−	1.61906i	−0.587076	−	0.809532i	$-0.699721\pi$
$233$		−	87897.3i		−	1.61906i	0.587076	−	0.809532i	$-0.300279\pi$
$234$	14689.0	+	52999.9i	0.268263	+	0.967929i
$235$	−7161.09			−0.129671
$236$			3625.50i			0.0650945i
$237$	−78501.3	+	10677.1i	−1.39759	+	0.190089i
$238$	−9999.13			−0.176526
$239$			41544.5i			0.727307i	0.931534	+	0.363654i	$0.118471\pi$
$239$			41544.5i			0.727307i	−0.931534	+	0.363654i	$0.881529\pi$
$240$	−998.821	−	7343.61i	−0.0173406	−	0.127493i
$241$	−14783.9			−0.254540			−0.127270	−	0.991868i	$-0.540621\pi$
$241$	−14783.9			−0.254540			−0.127270	+	0.991868i	$0.540621\pi$
$242$			73182.5i			1.24962i
$243$	−46066.2	+	36941.7i	−0.780136	+	0.625610i
$244$	−41364.8			−0.694787
$245$		−	22812.8i		−	0.380055i
$246$	−58988.4	+	8023.15i	−0.974758	+	0.132579i
$247$	135189.			2.21588
$248$		−	18138.2i		−	0.294911i
$249$	−11175.1	−	82162.2i	−0.180240	−	1.32518i
$250$	39465.8			0.631453
$251$		−	91173.6i		−	1.44718i	−0.690232	−	0.723588i	$-0.742491\pi$
$251$		−	91173.6i		−	1.44718i	0.690232	−	0.723588i	$-0.257509\pi$
$252$	15648.8	−	4337.09i	0.246422	−	0.0682964i
$253$	−57036.3			−0.891067
$254$		−	34778.1i		−	0.539061i
$255$	16187.2	−	2201.65i	0.248937	−	0.0338585i
$256$	4096.00			0.0625000
$257$		−	7746.27i		−	0.117281i	−0.998279	−	0.0586403i	$-0.981323\pi$
$257$		−	7746.27i		−	0.117281i	0.998279	−	0.0586403i	$-0.0186765\pi$
$258$	7927.16	+	58282.7i	0.119091	+	0.875589i
$259$	−37838.3			−0.564068
$260$			24710.0i			0.365533i
$261$	4504.53	+	16252.9i	0.0661254	+	0.238589i
$262$	−27900.6			−0.406453
$263$			7113.25i			0.102839i	0.998677	+	0.0514194i	$0.0163745\pi$
$263$			7113.25i			0.102839i	−0.998677	+	0.0514194i	$0.983625\pi$
$264$	−40616.7	+	5524.37i	−0.582769	+	0.0792638i
$265$	63031.4			0.897564
$266$		−	39915.9i		−	0.564134i
$267$	−13097.4	−	96295.5i	−0.183722	−	1.35078i
$268$	35415.4			0.493086
$269$			35940.9i			0.496688i	0.968672	+	0.248344i	$0.0798864\pi$
$269$			35940.9i			0.496688i	−0.968672	+	0.248344i	$0.920114\pi$
$270$	−24378.2	+	10466.7i	−0.334406	+	0.143577i
$271$	−91125.2			−1.24079			−0.620397	−	0.784288i	$-0.713029\pi$
$271$	−91125.2			−1.24079			−0.620397	+	0.784288i	$0.713029\pi$
$272$			9028.60i			0.122035i
$273$	−53648.1	+	7296.79i	−0.719828	+	0.0979054i
$274$	38455.5			0.512221
$275$		−	92479.1i		−	1.22286i
$276$	−2749.63	−	20216.0i	−0.0360957	−	0.265386i
$277$	108770.			1.41759			0.708794	−	0.705416i	$-0.249240\pi$
$277$	108770.			1.41759			0.708794	+	0.705416i	$0.249240\pi$
$278$		−	38155.5i		−	0.493705i
$279$	−62571.1	+	17341.7i	−0.803833	+	0.222783i
$280$	7295.90			0.0930600
$281$		−	143037.i		−	1.81149i	−0.423826	−	0.905744i	$-0.639313\pi$
$281$		−	143037.i		−	1.81149i	0.423826	−	0.905744i	$-0.360687\pi$
$282$	−14038.4	+	1909.40i	−0.176531	+	0.0240103i
$283$	128718.			1.60718			0.803591	−	0.595183i	$-0.202920\pi$
$283$	128718.			1.60718			0.803591	+	0.595183i	$0.202920\pi$
$284$		−	32705.8i		−	0.405497i
$285$	8788.85	+	64618.1i	0.108204	+	0.795544i
$286$	136668.			1.67084
$287$		−	58605.2i		−	0.711496i
$288$	−3916.13	−	14129.9i	−0.0472141	−	0.170355i
$289$	63619.7			0.761721
$290$			7577.57i			0.0901018i
$291$	−74445.1	+	10125.4i	−0.879124	+	0.119572i
$292$	−7673.92			−0.0900019
$293$		−	82791.5i		−	0.964385i	−0.876065	−	0.482193i	$-0.839841\pi$
$293$		−	82791.5i		−	0.964385i	0.876065	−	0.482193i	$-0.160159\pi$
$294$	−6082.70	−	44721.7i	−0.0703723	−	0.517397i
$295$	5831.03			0.0670041
$296$			34165.6i			0.389948i
$297$	57890.4	+	134833.i	0.656287	+	1.52857i
$298$	−58033.4			−0.653500
$299$			68023.6i			0.760881i
$300$	32778.4	−	4458.27i	0.364205	−	0.0495363i
$301$	−57904.1			−0.639111
$302$			100259.i			1.09928i
$303$	−1265.69	−	9305.73i	−0.0137862	−	0.101360i
$304$	−36041.6			−0.389993
$305$			66528.7i			0.715170i
$306$	31145.9	−	8632.13i	0.332627	−	0.0921881i
$307$	41087.9			0.435950			0.217975	−	0.975954i	$-0.430055\pi$
$307$	41087.9			0.435950			0.217975	+	0.975954i	$0.430055\pi$
$308$		−	40352.8i		−	0.425376i
$309$	−146280.	+	19895.9i	−1.53204	+	0.208376i
$310$	−29172.4			−0.303563
$311$			841.823i			0.00870362i	0.999991	+	0.00435181i	$0.00138523\pi$
$311$			841.823i			0.00870362i	−0.999991	+	0.00435181i	$0.998615\pi$
$312$	6588.56	+	48440.9i	0.0676833	+	0.497626i
$313$	−31946.9			−0.326092			−0.163046	−	0.986618i	$-0.552132\pi$
$313$	−31946.9			−0.326092			−0.163046	+	0.986618i	$0.552132\pi$
$314$		−	45389.0i		−	0.460354i
$315$	−6975.51	−	25168.6i	−0.0703000	−	0.253652i
$316$	−70421.4			−0.705229
$317$			105298.i			1.04786i	0.851762	+	0.523929i	$0.175534\pi$
$317$			105298.i			1.04786i	−0.851762	+	0.523929i	$0.824466\pi$
$318$	123565.	−	16806.4i	1.22192	−	0.166196i
$319$	41910.7			0.411854
$320$		−	6587.76i		−	0.0643336i
$321$	6617.53	+	48653.9i	0.0642223	+	0.472180i
$322$	20084.7			0.193711
$323$		−	79444.7i		−	0.761483i
$324$	−44999.7	+	27018.9i	−0.428666	+	0.257381i
$325$	−110294.			−1.04420
$326$		−	107738.i		−	1.01376i
$327$	12485.1	−	1698.12i	0.116761	−	0.0158809i
$328$	−52916.9			−0.491866
$329$		−	13947.2i		−	0.128853i
$330$	8885.06	+	65325.4i	0.0815891	+	0.599866i
$331$	29719.6			0.271261			0.135630	−	0.990760i	$-0.456694\pi$
$331$	29719.6			0.271261			0.135630	+	0.990760i	$0.456694\pi$
$332$		−	73705.5i		−	0.668688i
$333$	117861.	−	32665.3i	1.06287	−	0.294577i
$334$	−118464.			−1.06193
$335$		−	56960.0i		−	0.507552i
$336$	14302.7	−	1945.34i	0.126689	−	0.0172313i
$337$	−84997.9			−0.748426			−0.374213	−	0.927343i	$-0.622087\pi$
$337$	−84997.9			−0.748426			−0.374213	+	0.927343i	$0.622087\pi$
$338$		−	82212.9i		−	0.719625i
$339$	−30410.5	−	223586.i	−0.264621	−	1.94557i
$340$	14521.1			0.125615
$341$			161349.i			1.38758i
$342$	34458.9	+	124332.i	0.294611	+	1.06300i
$343$	104600.			0.889082
$344$			52283.9i			0.441826i
$345$	−32514.2	+	4422.33i	−0.273172	+	0.0371547i
$346$	93351.2			0.779772
$347$		−	54397.2i		−	0.451770i	−0.974154	−	0.225885i	$-0.927473\pi$
$347$		−	54397.2i		−	0.451770i	0.974154	−	0.225885i	$-0.0725273\pi$
$348$	2020.45	+	14854.9i	0.0166836	+	0.122662i
$349$	133423.			1.09542			0.547710	−	0.836668i	$-0.315500\pi$
$349$	133423.			1.09542			0.547710	+	0.836668i	$0.315500\pi$
$350$			32565.5i			0.265841i
$351$	160807.	−	69042.2i	1.30524	−	0.560403i
$352$	−36436.2			−0.294068
$353$		−	115584.i		−	0.927575i	−0.885946	−	0.463788i	$-0.846490\pi$
$353$		−	115584.i		−	0.927575i	0.885946	−	0.463788i	$-0.153510\pi$
$354$	11431.0	−	1554.76i	0.0912176	−	0.0124067i
$355$	−52602.0			−0.417393
$356$		−	86384.1i		−	0.681607i
$357$	4288.02	+	31526.8i	0.0336450	+	0.247368i
$358$	−87100.9			−0.679605
$359$		−	55132.1i		−	0.427775i	−0.976858	−	0.213888i	$-0.931387\pi$
$359$		−	55132.1i		−	0.427775i	0.976858	−	0.213888i	$-0.0686126\pi$
$360$	−22725.7	+	6298.47i	−0.175353	+	0.0485993i
$361$	186817.			1.43352
$362$			113050.i			0.862690i
$363$	230741.	−	31383.6i	1.75110	−	0.238171i
$364$	−48126.2			−0.363228
$365$			12342.3i			0.0926423i
$366$	17738.9	+	130421.i	0.132423	+	0.973613i
$367$	−52596.2			−0.390501			−0.195250	−	0.980753i	$-0.562552\pi$
$367$	−52596.2			−0.390501			−0.195250	+	0.980753i	$0.562552\pi$
$368$		−	18135.3i		−	0.133915i
$369$	50593.2	+	182547.i	0.371569	+	1.34067i
$370$	54949.9			0.401387
$371$			122763.i			0.891904i
$372$	−57188.8	+	7778.38i	−0.413262	+	0.0562087i
$373$	210391.			1.51220			0.756102	−	0.654454i	$-0.227102\pi$
$373$	210391.			1.51220			0.756102	+	0.654454i	$0.227102\pi$
$374$		−	80314.4i		−	0.574183i
$375$	−16924.5	−	124434.i	−0.120352	−	0.884863i
$376$	−12593.5			−0.0890780
$377$		−	49984.2i		−	0.351682i
$378$	−20385.5	−	47480.0i	−0.142671	−	0.332298i
$379$	158185.			1.10125			0.550627	−	0.834751i	$-0.314389\pi$
$379$	158185.			1.10125			0.550627	+	0.834751i	$0.314389\pi$
$380$			57967.2i			0.401435i
$381$	−109653.	+	14914.2i	−0.755392	+	0.102743i
$382$	154883.			1.06140
$383$			71514.6i			0.487525i	0.969835	+	0.243763i	$0.0783818\pi$
$383$			71514.6i			0.487525i	−0.969835	+	0.243763i	$0.921618\pi$
$384$	−1756.53	−	12914.5i	−0.0119122	−	0.0875820i
$385$	−64901.0			−0.437855
$386$			99069.0i			0.664911i
$387$	180363.	−	49987.9i	1.20428	−	0.333767i
$388$	−66782.7			−0.443609
$389$			235130.i			1.55385i	0.629593	+	0.776925i	$0.283222\pi$
$389$			235130.i			1.55385i	−0.629593	+	0.776925i	$0.716778\pi$
$390$	77909.5	−	10596.6i	0.512225	−	0.0696689i
$391$	39974.6			0.261476
$392$		−	40118.6i		−	0.261080i
$393$	11964.9	+	87969.2i	0.0774682	+	0.569568i
$394$	183286.			1.18069
$395$			113261.i			0.725919i
$396$	34836.1	+	125693.i	0.222146	+	0.801534i
$397$	−121055.			−0.768072			−0.384036	−	0.923318i	$-0.625466\pi$
$397$	−121055.			−0.768072			−0.384036	+	0.923318i	$0.625466\pi$
$398$			57189.7i			0.361037i
$399$	−125853.	+	17117.5i	−0.790528	+	0.107521i
$400$	29404.7			0.183779
$401$			140328.i			0.872679i	0.899782	+	0.436340i	$0.143725\pi$
$401$			140328.i			0.872679i	−0.899782	+	0.436340i	$0.856275\pi$
$402$	−15187.5	−	111663.i	−0.0939800	−	0.690967i
$403$	192431.			1.18485
$404$		−	8347.92i		−	0.0511465i
$405$	43455.5	+	72374.7i	0.264932	+	0.441242i
$406$	−14758.4			−0.0895337
$407$		−	303922.i		−	1.83473i
$408$	28466.7	−	3871.82i	0.171008	−	0.0232592i
$409$	210573.			1.25880			0.629398	−	0.777083i	$-0.283302\pi$
$409$	210573.			1.25880			0.629398	+	0.777083i	$0.283302\pi$
$410$			85108.4i			0.506296i
$411$	−16491.2	−	121248.i	−0.0976269	−	0.717781i
$412$	−131224.			−0.773071
$413$			11356.8i			0.0665816i
$414$	−62561.0	+	17338.9i	−0.365009	+	0.101163i
$415$	−118543.			−0.688306
$416$			43455.1i			0.251104i
$417$	−120302.	+	16362.6i	−0.691834	+	0.0940979i
$418$	320610.			1.83495
$419$			227178.i			1.29401i	0.762486	+	0.647005i	$0.223979\pi$
$419$			227178.i			1.29401i	−0.762486	+	0.647005i	$0.776021\pi$
$420$	−3128.77	−	23003.6i	−0.0177368	−	0.130406i
$421$	−106621.			−0.601561			−0.300781	−	0.953693i	$-0.597247\pi$
$421$	−106621.			−0.601561			−0.300781	+	0.953693i	$0.597247\pi$
$422$			18316.5i			0.102853i
$423$	12040.5	+	43443.6i	0.0672919	+	0.242798i
$424$	110847.			0.616585
$425$			64815.2i			0.358838i
$426$	−103120.	+	14025.5i	−0.568228	+	0.0772859i
$427$	−129574.			−0.710660
$428$			43646.1i			0.238264i
$429$	−58608.8	−	430909.i	−0.318455	−	2.34137i
$430$	84090.2			0.454787
$431$			5716.73i			0.0307747i	0.999882	+	0.0153873i	$0.00489813\pi$
$431$			5716.73i			0.0307747i	−0.999882	+	0.0153873i	$0.995102\pi$
$432$	−42871.6	+	18406.8i	−0.229722	+	0.0986306i
$433$	−54567.2			−0.291042			−0.145521	−	0.989355i	$-0.546486\pi$
$433$	−54567.2			−0.291042			−0.145521	+	0.989355i	$0.546486\pi$
$434$		−	56817.3i		−	0.301649i
$435$	23891.7	−	3249.56i	0.126261	−	0.0171730i
$436$	11200.0			0.0589178
$437$			159576.i			0.835613i
$438$	3290.88	+	24195.5i	0.0171540	+	0.126121i
$439$	111461.			0.578352			0.289176	−	0.957276i	$-0.406619\pi$
$439$	111461.			0.578352			0.289176	+	0.957276i	$0.406619\pi$
$440$			58601.7i			0.302695i
$441$	−138397.	+	38356.9i	−0.711621	+	0.197227i
$442$	−95785.8			−0.490294
$443$		−	287275.i		−	1.46383i	−0.681398	−	0.731914i	$-0.738627\pi$
$443$		−	287275.i		−	1.46383i	0.681398	−	0.731914i	$-0.261373\pi$
$444$	107723.	−	14651.6i	0.546438	−	0.0743222i
$445$	−138935.			−0.701603
$446$			139800.i			0.702809i
$447$	24887.0	+	182977.i	0.124554	+	0.915757i
$448$	12830.6			0.0639279
$449$			165830.i			0.822565i	0.911508	+	0.411282i	$0.134919\pi$
$449$			165830.i			0.822565i	−0.911508	+	0.411282i	$0.865081\pi$
$450$	−28113.4	−	101437.i	−0.138832	−	0.500923i
$451$	470725.			2.31427
$452$		−	200573.i		−	0.981740i
$453$	316112.	−	42995.1i	1.54044	−	0.209518i
$454$	−14040.1			−0.0681174
$455$			77403.3i			0.373884i
$456$	15456.1	+	113637.i	0.0743310	+	0.546502i
$457$	151641.			0.726078			0.363039	−	0.931774i	$-0.381739\pi$
$457$	151641.			0.726078			0.363039	+	0.931774i	$0.381739\pi$
$458$			85885.6i			0.409439i
$459$	−40573.3	−	94499.6i	−0.192581	−	0.448544i
$460$	−29167.7			−0.137843
$461$		−	112124.i		−	0.527589i	−0.964579	−	0.263795i	$-0.915026\pi$
$461$		−	112124.i		−	0.527589i	0.964579	−	0.263795i	$-0.0849742\pi$
$462$	−127230.	+	17304.9i	−0.596084	+	0.0810747i
$463$	−228365.			−1.06529			−0.532644	−	0.846340i	$-0.678801\pi$
$463$	−228365.			−1.06529			−0.532644	+	0.846340i	$0.678801\pi$
$464$			13325.9i			0.0618958i
$465$	12510.3	+	91979.0i	0.0578577	+	0.425386i
$466$	−248611.			−1.14485
$467$		−	144658.i		−	0.663297i	−0.943403	−	0.331649i	$-0.892395\pi$
$467$		−	144658.i		−	0.663297i	0.943403	−	0.331649i	$-0.107605\pi$
$468$	149906.	−	41546.8i	0.684429	−	0.189691i
$469$	110938.			0.504351
$470$			20254.6i			0.0916913i
$471$	−143109.	+	19464.6i	−0.645099	+	0.0877413i
$472$	10254.5			0.0460287
$473$		−	465093.i		−	2.07883i
$474$	30199.5	+	222035.i	0.134413	+	0.988246i
$475$	−258738.			−1.14676
$476$			28281.8i			0.124823i
$477$	−105979.	−	382388.i	−0.465785	−	1.68061i
$478$	117506.			0.514284
$479$			216999.i			0.945774i	0.881123	+	0.472887i	$0.156788\pi$
$479$			216999.i			0.945774i	−0.881123	+	0.472887i	$0.843212\pi$
$480$	−20770.9	+	2825.09i	−0.0901514	+	0.0122617i
$481$	−362468.			−1.56668
$482$			41815.2i			0.179987i
$483$	−8613.12	−	63326.1i	−0.0369204	−	0.271449i
$484$	206991.			0.883612
$485$			107409.i			0.456623i
$486$	104487.	+	130295.i	0.442373	+	0.551639i
$487$	134916.			0.568862			0.284431	−	0.958697i	$-0.408195\pi$
$487$	134916.			0.568862			0.284431	+	0.958697i	$0.408195\pi$
$488$			116997.i			0.491289i
$489$	−339692.	+	46202.3i	−1.42059	+	0.193217i
$490$	−64524.4			−0.268740
$491$			210221.i			0.871995i	0.899948	+	0.435998i	$0.143604\pi$
$491$			210221.i			0.871995i	−0.899948	+	0.435998i	$0.856396\pi$
$492$	22692.9	+	166844.i	0.0937475	+	0.689258i
$493$	−29373.6			−0.120855
$494$		−	382371.i		−	1.56686i
$495$	202158.	−	56028.3i	0.825049	−	0.228664i
$496$	−51302.6			−0.208533
$497$		−	102450.i		−	0.414761i
$498$	−232390.	+	31607.9i	−0.937041	+	0.127449i
$499$	−325092.			−1.30558			−0.652792	−	0.757537i	$-0.726403\pi$
$499$	−325092.			−1.30558			−0.652792	+	0.757537i	$0.726403\pi$
$500$		−	111626.i		−	0.446505i
$501$	50802.2	+	373512.i	0.202398	+	1.48809i
$502$	−257878.			−1.02331
$503$			46217.2i			0.182670i	0.995820	+	0.0913350i	$0.0291134\pi$
$503$			46217.2i			0.182670i	−0.995820	+	0.0913350i	$0.970887\pi$
$504$	−12267.1	−	44261.5i	−0.0482928	−	0.174247i
$505$	−13426.3			−0.0526469
$506$			161323.i			0.630080i
$507$	−259213.	+	35256.2i	−1.00842	+	0.137157i
$508$	−98367.2			−0.381174
$509$			205497.i			0.793176i	0.917997	+	0.396588i	$0.129806\pi$
$509$			205497.i			0.793176i	−0.917997	+	0.396588i	$0.870194\pi$
$510$	−6227.21	−	45784.2i	−0.0239416	−	0.176025i
$511$	−24038.3			−0.0920581
$512$		−	11585.2i		−	0.0441942i
$513$	377236.	−	161966.i	1.43344	−	0.615444i
$514$	−21909.8			−0.0829299
$515$			211053.i			0.795750i
$516$	164848.	−	22421.4i	0.619135	−	0.0842099i
$517$	112026.			0.419119
$518$			107023.i			0.398856i
$519$	−40032.7	−	294332.i	−0.148621	−	1.09270i
$520$	69890.5			0.258471
$521$		−	366676.i		−	1.35085i	−0.737429	−	0.675425i	$-0.763960\pi$
$521$		−	366676.i		−	1.35085i	0.737429	−	0.675425i	$-0.236040\pi$
$522$	45970.3	−	12740.7i	0.168708	−	0.0467577i
$523$	184873.			0.675881			0.337941	−	0.941167i	$-0.390270\pi$
$523$	184873.			0.675881			0.337941	+	0.941167i	$0.390270\pi$
$524$			78914.8i			0.287406i
$525$	102677.	−	13965.4i	0.372526	−	0.0506680i
$526$	20119.3			0.0727180
$527$		−	113084.i		−	0.407173i
$528$	15625.3	+	114881.i	0.0560479	+	0.412080i
$529$	199546.			0.713070
$530$		−	178280.i		−	0.634674i
$531$	−9804.16	−	35374.7i	−0.0347713	−	0.125460i
$532$	−112899.			−0.398903
$533$		−	561404.i		−	1.97615i
$534$	−272365.	+	37045.0i	−0.955144	+	0.129911i
$535$	70197.8			0.245254
$536$		−	100170.i		−	0.348665i
$537$	37352.3	+	274625.i	0.129530	+	0.952338i
$538$	101656.			0.351212
$539$			356877.i			1.22840i
$540$	29604.4	+	68952.0i	0.101524	+	0.236461i
$541$	−236927.			−0.809505			−0.404753	−	0.914426i	$-0.632642\pi$
$541$	−236927.			−0.809505			−0.404753	+	0.914426i	$0.632642\pi$
$542$			257741.i			0.877374i
$543$	356442.	−	48480.5i	1.20890	−	0.164425i
$544$	25536.8			0.0862915
$545$		−	18013.5i		−	0.0606462i
$546$	20638.4	+	151740.i	0.0692296	+	0.508995i
$547$	54395.5			0.181798			0.0908988	−	0.995860i	$-0.471026\pi$
$547$	54395.5			0.181798			0.0908988	+	0.995860i	$0.471026\pi$
$548$		−	108769.i		−	0.362195i
$549$	403605.	−	111860.i	1.33910	−	0.371132i
$550$	−261570.			−0.864696
$551$		−	117258.i		−	0.386223i
$552$	−57179.6	+	7777.12i	−0.187656	+	0.0255235i
$553$	−220593.			−0.721341
$554$		−	307648.i		−	1.00239i
$555$	−23564.7	−	173254.i	−0.0765026	−	0.562469i
$556$	−107920.			−0.349102
$557$			86937.6i			0.280219i	0.990136	+	0.140109i	$0.0447454\pi$
$557$			86937.6i			0.280219i	−0.990136	+	0.140109i	$0.955255\pi$
$558$	49049.7	+	176978.i	0.157532	+	0.568395i
$559$	−554687.			−1.77511
$560$		−	20635.9i		−	0.0658034i
$561$	−253227.	+	34442.0i	−0.804609	+	0.109437i
$562$	−404569.			−1.28091
$563$		−	146623.i		−	0.462580i	−0.972885	−	0.231290i	$-0.925705\pi$
$563$		−	146623.i		−	0.462580i	0.972885	−	0.231290i	$-0.0742946\pi$
$564$	5400.59	+	39706.7i	0.0169779	+	0.124826i
$565$	−322590.			−1.01054
$566$		−	364068.i		−	1.13645i
$567$	−140960.	+	84635.7i	−0.438460	+	0.263262i
$568$	−92505.9			−0.286730
$569$			584667.i			1.80586i	0.429789	+	0.902929i	$0.358588\pi$
$569$			584667.i			1.80586i	−0.429789	+	0.902929i	$0.641412\pi$
$570$	182768.	−	24858.6i	0.562535	−	0.0765116i
$571$	−420933.			−1.29104			−0.645521	−	0.763743i	$-0.723360\pi$
$571$	−420933.			−1.29104			−0.645521	+	0.763743i	$0.723360\pi$
$572$		−	386556.i		−	1.18147i
$573$	−66420.2	−	488340.i	−0.202298	−	1.48735i
$574$	−165761.			−0.503104
$575$		−	130191.i		−	0.393771i
$576$	−39965.5	+	11076.5i	−0.120459	+	0.0333854i
$577$	−263399.			−0.791157			−0.395578	−	0.918432i	$-0.629456\pi$
$577$	−263399.			−0.791157			−0.395578	+	0.918432i	$0.629456\pi$
$578$		−	179944.i		−	0.538618i
$579$	312360.	−	42484.7i	0.931747	−	0.126729i
$580$	21432.6			0.0637116
$581$		−	230880.i		−	0.683966i
$582$	28639.1	+	210562.i	0.0845498	+	0.621634i
$583$	−986046.			−2.90108
$584$			21705.1i			0.0636410i
$585$	−66821.3	−	241100.i	−0.195256	−	0.704508i
$586$	−234170.			−0.681923
$587$			467333.i			1.35628i	0.734931	+	0.678142i	$0.237215\pi$
$587$			467333.i			1.35628i	−0.734931	+	0.678142i	$0.762785\pi$
$588$	−126492.	+	17204.5i	−0.365855	+	0.0497607i
$589$	451423.			1.30123
$590$		−	16492.7i		−	0.0473791i
$591$	−78600.5	−	577893.i	−0.225035	−	1.65452i
$592$	96635.0			0.275735
$593$			141276.i			0.401754i	0.979616	+	0.200877i	$0.0643792\pi$
$593$			141276.i			0.401754i	−0.979616	+	0.200877i	$0.935621\pi$
$594$	381366.	−	163739.i	1.08086	−	0.464065i
$595$	45486.7			0.128485
$596$			164143.i			0.462095i
$597$	180316.	−	24525.2i	0.505925	−	0.0688120i
$598$	192400.			0.538024
$599$		−	82533.2i		−	0.230025i	−0.993364	−	0.115012i	$-0.963309\pi$
$599$		−	82533.2i		−	0.230025i	0.993364	−	0.115012i	$-0.0366908\pi$
$600$	−12609.9	−	92711.4i	−0.0350275	−	0.257532i
$601$	−519643.			−1.43865			−0.719326	−	0.694672i	$-0.755549\pi$
$601$	−519643.			−1.43865			−0.719326	+	0.694672i	$0.755549\pi$
$602$			163777.i			0.451920i
$603$	−345555.	+	95771.1i	−0.950348	+	0.263390i
$604$	283575.			0.777311
$605$		−	332912.i		−	0.909535i
$606$	−26320.6	+	3579.92i	−0.0716721	+	0.00974828i
$607$	−161923.			−0.439473			−0.219736	−	0.975559i	$-0.570520\pi$
$607$	−161923.			−0.439473			−0.219736	+	0.975559i	$0.570520\pi$
$608$			101941.i			0.275767i
$609$	6328.98	+	46532.4i	0.0170647	+	0.125465i
$610$	188172.			0.505702
$611$		−	133606.i		−	0.357886i
$612$	−24415.3	−	88093.8i	−0.0651868	−	0.235203i
$613$	705603.			1.87776			0.938878	−	0.344249i	$-0.111867\pi$
$613$	705603.			1.87776			0.938878	+	0.344249i	$0.111867\pi$
$614$		−	116214.i		−	0.308263i
$615$	268342.	−	36497.9i	0.709478	−	0.0964977i
$616$	−114135.			−0.300786
$617$			308297.i			0.809839i	0.914352	+	0.404920i	$0.132701\pi$
$617$			308297.i			0.809839i	−0.914352	+	0.404920i	$0.867299\pi$
$618$	56274.1	+	413743.i	0.147344	+	1.08331i
$619$	149166.			0.389303			0.194651	−	0.980873i	$-0.437642\pi$
$619$	149166.			0.389303			0.194651	+	0.980873i	$0.437642\pi$
$620$			82511.9i			0.214651i
$621$	81497.3	+	189816.i	0.211329	+	0.492210i
$622$	2381.04			0.00615439
$623$		−	270595.i		−	0.697179i
$624$	137012.	−	18635.3i	0.351875	−	0.0478593i
$625$	107622.			0.275512
$626$			90359.5i			0.230582i
$627$	−137490.	−	1.01087e6i	−0.349733	−	2.57134i
$628$	−128380.			−0.325519
$629$			213008.i			0.538386i
$630$	−71187.5	+	19729.7i	−0.179359	+	0.0497096i
$631$	9420.05			0.0236589			0.0118295	−	0.999930i	$-0.496234\pi$
$631$	9420.05			0.0236589			0.0118295	+	0.999930i	$0.496234\pi$
$632$			199182.i			0.498672i
$633$	57751.0	−	7854.84i	0.144129	−	0.0196033i
$634$	297829.			0.740948
$635$			158208.i			0.392356i
$636$	−47535.7	−	349496.i	−0.117518	−	0.864027i
$637$	425624.			1.04893
$638$		−	118541.i		−	0.291225i
$639$	88443.6	+	319116.i	0.216603	+	0.781533i
$640$	−18633.0			−0.0454907
$641$			221740.i			0.539669i	0.962907	+	0.269834i	$0.0869690\pi$
$641$			221740.i			0.539669i	−0.962907	+	0.269834i	$0.913031\pi$
$642$	137614.	−	18717.2i	0.333882	−	0.0454120i
$643$	300351.			0.726453			0.363226	−	0.931701i	$-0.381675\pi$
$643$	300351.			0.726453			0.363226	+	0.931701i	$0.381675\pi$
$644$		−	56808.1i		−	0.136974i
$645$	−36061.2	−	265132.i	−0.0866804	−	0.637299i
$646$	−224704.			−0.538450
$647$			303175.i			0.724243i	0.932131	+	0.362122i	$0.117947\pi$
$647$			303175.i			0.724243i	−0.932131	+	0.362122i	$0.882053\pi$
$648$	76420.9	+	127278.i	0.181996	+	0.303113i
$649$	−91219.0			−0.216569
$650$			311958.i			0.738363i
$651$	−179142.	+	24365.5i	−0.422703	+	0.0574928i
$652$	−304729.			−0.716833
$653$			556943.i			1.30612i	0.757304	+	0.653062i	$0.226516\pi$
$653$			556943.i			1.30612i	−0.757304	+	0.653062i	$0.773484\pi$
$654$	−4803.02	−	35313.1i	−0.0112295	−	0.0825621i
$655$	126922.			0.295838
$656$			149672.i			0.347802i
$657$	74875.9	−	20752.0i	0.173465	−	0.0480761i
$658$	−39448.7			−0.0911131
$659$			629693.i			1.44997i	0.688766	+	0.724984i	$0.258153\pi$
$659$			629693.i			1.44997i	−0.688766	+	0.724984i	$0.741847\pi$
$660$	184768.	−	25130.7i	0.424169	−	0.0576922i
$661$	−647930.			−1.48295			−0.741473	−	0.670983i	$-0.765872\pi$
$661$	−647930.			−1.48295			−0.741473	+	0.670983i	$0.765872\pi$
$662$		−	84059.7i		−	0.191810i
$663$	41076.8	+	302008.i	0.0934478	+	0.687055i
$664$	−208471.			−0.472834
$665$			181580.i			0.410606i
$666$	−92391.4	−	333361.i	−0.208297	−	0.751564i
$667$	59001.2			0.132620
$668$			335068.i			0.750895i
$669$	440783.	−	59951.8i	0.984855	−	0.133952i
$670$	−161107.			−0.358893
$671$		−	1.04076e6i		−	2.31155i
$672$	−5502.26	−	40454.2i	−0.0121844	−	0.0895829i
$673$	−105982.			−0.233992			−0.116996	−	0.993132i	$-0.537326\pi$
$673$	−105982.			−0.233992			−0.116996	+	0.993132i	$0.537326\pi$
$674$			240410.i			0.529217i
$675$	−307769.	+	132140.i	−0.675488	+	0.290020i
$676$	−232533.			−0.508852
$677$		−	792864.i		−	1.72990i	−0.501858	−	0.864950i	$-0.667350\pi$
$677$		−	792864.i		−	1.72990i	0.501858	−	0.864950i	$-0.332650\pi$
$678$	−632398.	+	86013.8i	−1.37572	+	0.187115i
$679$	−209195.			−0.453744
$680$		−	41071.8i		−	0.0888230i
$681$	6020.94	+	44267.7i	0.0129829	+	0.0954536i
$682$	456364.			0.981167
$683$		−	638326.i		−	1.36836i	−0.729312	−	0.684181i	$-0.760160\pi$
$683$		−	638326.i		−	1.36836i	0.729312	−	0.684181i	$-0.239840\pi$
$684$	351665.	−	97464.5i	0.751652	−	0.208322i
$685$	−174937.			−0.372820
$686$		−	295852.i		−	0.628676i
$687$	270793.	−	36831.2i	0.573752	−	0.0780372i
$688$	147881.			0.312418
$689$			1.17599e6i			2.47723i
$690$	12508.2	+	91964.2i	0.0262723	+	0.193161i
$691$	351927.			0.737049			0.368525	−	0.929618i	$-0.379863\pi$
$691$	351927.			0.737049			0.368525	+	0.929618i	$0.379863\pi$
$692$		−	264037.i		−	0.551382i
$693$	109123.	+	393730.i	0.227222	+	0.819846i
$694$	−153858.			−0.319450
$695$			173572.i			0.359344i
$696$	42016.0	−	5714.68i	0.0867353	−	0.0117971i
$697$	−329914.			−0.679102
$698$		−	377378.i		−	0.774579i
$699$	106614.	+	783859.i	0.218203	+	1.60429i
$700$	92109.1			0.187978
$701$			507680.i			1.03313i	0.856249	+	0.516564i	$0.172789\pi$
$701$			507680.i			1.03313i	−0.856249	+	0.516564i	$0.827211\pi$
$702$	−195281.	−	454831.i	−0.396265	−	0.922944i
$703$	−850313.			−1.72055
$704$			103057.i			0.207937i
$705$	63861.8	−	8685.98i	0.128488	−	0.0174759i
$706$	−326922.			−0.655895
$707$		−	26149.6i		−	0.0523150i
$708$	−4397.52	−	32331.8i	−0.00877287	−	0.0645006i
$709$	259628.			0.516487			0.258244	−	0.966080i	$-0.416856\pi$
$709$	259628.			0.516487			0.258244	+	0.966080i	$0.416856\pi$
$710$			148781.i			0.295141i
$711$	687115.	−	190435.i	1.35922	−	0.376710i
$712$	−244331.			−0.481969
$713$			227145.i			0.446811i
$714$	89171.1	−	12128.4i	0.174915	−	0.0237906i
$715$	−621714.			−1.21613
$716$			246359.i			0.480553i
$717$	−50391.1	−	370490.i	−0.0980202	−	0.720672i
$718$	−155937.			−0.302483
$719$		−	625261.i		−	1.20949i	−0.796418	−	0.604747i	$-0.793274\pi$
$719$		−	625261.i		−	1.20949i	0.796418	−	0.604747i	$-0.206726\pi$
$720$	17814.8	+	64278.0i	0.0343649	+	0.123993i
$721$	−411055.			−0.790732
$722$		−	528399.i		−	1.01365i
$723$	131841.	−	17932.0i	0.252217	−	0.0343047i
$724$	319755.			0.610014
$725$			95665.0i			0.182002i
$726$	−88766.1	−	652634.i	−0.168412	−	1.23822i
$727$	964760.			1.82537			0.912684	−	0.408666i	$-0.134006\pi$
$727$	964760.			1.82537			0.912684	+	0.408666i	$0.134006\pi$
$728$			136122.i			0.256841i
$729$	366006.	−	385317.i	0.688704	−	0.725042i
$730$	34909.2			0.0655080
$731$			325967.i			0.610012i
$732$	368887.	−	50173.2i	0.688448	−	0.0936374i
$733$	−548207.			−1.02032			−0.510161	−	0.860079i	$-0.670414\pi$
$733$	−548207.			−1.02032			−0.510161	+	0.860079i	$0.670414\pi$
$734$			148764.i			0.276126i
$735$	27670.6	+	203442.i	0.0512205	+	0.376588i
$736$	−51294.3			−0.0946920
$737$			891066.i			1.64049i
$738$	516321.	−	143099.i	0.947997	−	0.262739i
$739$	136919.			0.250712			0.125356	−	0.992112i	$-0.459993\pi$
$739$	136919.			0.250712			0.125356	+	0.992112i	$0.459993\pi$
$740$		−	155422.i		−	0.283824i
$741$	−1.20560e6	+	163976.i	−2.19566	+	0.298637i
$742$	347225.			0.630672
$743$			455927.i			0.825881i	0.910758	+	0.412941i	$0.135498\pi$
$743$			455927.i			0.825881i	−0.910758	+	0.412941i	$0.864502\pi$
$744$	22000.6	+	161754.i	0.0397455	+	0.292220i
$745$	263998.			0.475651
$746$		−	595077.i		−	1.06929i
$747$	199316.	+	719159.i	0.357191	+	1.28879i
$748$	−227163.			−0.406008
$749$			136720.i			0.243707i
$750$	−351952.	+	47869.8i	−0.625692	+	0.0851018i
$751$	−366011.			−0.648954			−0.324477	−	0.945894i	$-0.605188\pi$
$751$	−366011.			−0.648954			−0.324477	+	0.945894i	$0.605188\pi$
$752$			35619.8i			0.0629877i
$753$	110588.	+	813076.i	0.195038	+	1.43397i
$754$	−141377.			−0.248677
$755$		−	456085.i		−	0.800115i
$756$	−134294.	+	57658.8i	−0.234970	+	0.100884i
$757$	437889.			0.764138			0.382069	−	0.924134i	$-0.375212\pi$
$757$	437889.			0.764138			0.382069	+	0.924134i	$0.375212\pi$
$758$		−	447416.i		−	0.778705i
$759$	508644.	−	69181.7i	0.882938	−	0.120090i
$760$	163956.			0.283857
$761$		−	293801.i		−	0.507323i	−0.967293	−	0.253661i	$-0.918365\pi$
$761$		−	293801.i		−	0.507323i	0.967293	−	0.253661i	$-0.0816349\pi$
$762$	42183.8	+	310147.i	0.0726500	+	0.534143i
$763$	35083.7			0.0602638
$764$		−	438076.i		−	0.750522i
$765$	−141685.	+	39268.2i	−0.242103	+	0.0670992i
$766$	202274.			0.344733
$767$			108791.i			0.184928i
$768$	−36527.7	+	4968.21i	−0.0619298	+	0.00842321i
$769$	503747.			0.851843			0.425922	−	0.904760i	$-0.359950\pi$
$769$	503747.			0.851843			0.425922	+	0.904760i	$0.359950\pi$
$770$			183568.i			0.309610i
$771$	9395.77	+	69080.4i	0.0158061	+	0.116211i
$772$	280209.			0.470163
$773$			497928.i			0.833313i	0.909064	+	0.416656i	$0.136798\pi$
$773$			497928.i			0.833313i	−0.909064	+	0.416656i	$0.863202\pi$
$774$	−141387.	−	510144.i	−0.236009	−	0.851551i
$775$	−368294.			−0.613185
$776$			188890.i			0.313679i
$777$	337437.	−	45895.6i	0.558922	−	0.0760202i
$778$	665048.			1.09874
$779$		−	1.31699e6i		−	2.17025i
$780$	−29971.8	−	220361.i	−0.0492633	−	0.362198i
$781$	822890.			1.34909
$782$		−	113065.i		−	0.184891i
$783$	−59884.8	−	139478.i	−0.0976771	−	0.227501i
$784$	−113473.			−0.184612
$785$			206478.i			0.335069i
$786$	248814.	−	33841.8i	0.402745	−	0.0547783i
$787$	−280438.			−0.452781			−0.226390	−	0.974037i	$-0.572692\pi$
$787$	−280438.			−0.452781			−0.226390	+	0.974037i	$0.572692\pi$
$788$		−	518412.i		−	0.834877i
$789$	−8627.96	−	63435.2i	−0.0138597	−	0.101901i
$790$	320352.			0.513302
$791$		−	628289.i		−	1.00417i
$792$	355515.	−	98531.4i	0.566770	−	0.157081i
$793$	−1.24124e6			−1.97383
$794$			342395.i			0.543109i
$795$	−562108.	+	76453.5i	−0.889375	+	0.120966i
$796$	161757.			0.255292
$797$		−	53774.4i		−	0.0846562i	−0.999104	−	0.0423281i	$-0.986523\pi$
$797$		−	53774.4i		−	0.0846562i	0.999104	−	0.0423281i	$-0.0134775\pi$
$798$	48415.7	+	355966.i	0.0760291	+	0.558988i
$799$	−78514.9			−0.122987
$800$		−	83168.9i		−	0.129951i
$801$	233602.	+	842867.i	0.364092	+	1.31369i
$802$	396907.			0.617077
$803$		−	193079.i		−	0.299436i
$804$	−315831.	+	42956.8i	−0.488588	+	0.0664539i
$805$	−91366.7			−0.140993
$806$		−	544276.i		−	0.837818i
$807$	−43594.2	−	320517.i	−0.0669394	−	0.492157i
$808$	−23611.5			−0.0361660
$809$			802389.i			1.22599i	0.790086	+	0.612996i	$0.210036\pi$
$809$			802389.i			1.22599i	−0.790086	+	0.612996i	$0.789964\pi$
$810$	204707.	−	122911.i	0.312005	−	0.187335i
$811$	−1.14963e6			−1.74790			−0.873952	−	0.486012i	$-0.838451\pi$
$811$	−1.14963e6			−1.74790			−0.873952	+	0.486012i	$0.838451\pi$
$812$			41743.0i			0.0633099i
$813$	812644.	−	110530.i	1.22947	−	0.167223i
$814$	−859621.			−1.29735
$815$			490107.i			0.737863i
$816$	−10951.2	−	80516.1i	−0.0164468	−	0.120921i
$817$	−1.30124e6			−1.94945
$818$		−	595589.i		−	0.890103i
$819$	469577.	−	130144.i	0.700066	−	0.194024i
$820$	240723.			0.358005
$821$			1.07989e6i			1.60211i	0.598592	+	0.801054i	$0.295727\pi$
$821$			1.07989e6i			1.60211i	−0.598592	+	0.801054i	$0.704273\pi$
$822$	−342942.	+	46644.3i	−0.507548	+	0.0690327i
$823$	649655.			0.959143			0.479571	−	0.877503i	$-0.340792\pi$
$823$	649655.			0.959143			0.479571	+	0.877503i	$0.340792\pi$
$824$			371158.i			0.546643i
$825$	112172.	+	824719.i	0.164807	+	1.21171i
$826$	32121.8			0.0470803
$827$			945793.i			1.38288i	0.722433	+	0.691441i	$0.243024\pi$
$827$			945793.i			1.38288i	−0.722433	+	0.691441i	$0.756976\pi$
$828$	49041.8	+	176949.i	0.0715328	+	0.258100i
$829$	−930350.			−1.35375			−0.676873	−	0.736100i	$-0.736666\pi$
$829$	−930350.			−1.35375			−0.676873	+	0.736100i	$0.736666\pi$
$830$			335292.i			0.486706i
$831$	−970000.	+	131932.i	−1.40465	+	0.191050i
$832$	122909.			0.177557
$833$		−	250122.i		−	0.360464i
$834$	46280.4	+	340267.i	0.0665373	+	0.489201i
$835$	538902.			0.772924
$836$		−	906822.i		−	1.29751i
$837$	536968.	−	230546.i	0.766474	−	0.329085i
$838$	642556.			0.915003
$839$			1.31291e6i			1.86513i	0.361000	+	0.932566i	$0.382435\pi$
$839$			1.31291e6i			1.86513i	−0.361000	+	0.932566i	$0.617565\pi$
$840$	−65064.1	+	8849.51i	−0.0922110	+	0.0125418i
$841$	663926.			0.938703
$842$			301571.i			0.425368i
$843$	173495.	+	1.27559e6i	0.244137	+	1.79496i
$844$	51806.8			0.0727281
$845$			373992.i			0.523780i
$846$	122877.	−	34055.6i	0.171684	−	0.0475826i
$847$	648394.			0.903799
$848$		−	313523.i		−	0.435991i
$849$	−1.14789e6	+	156127.i	−1.59252	+	0.216602i
$850$	183325.			0.253737
$851$		−	427857.i		−	0.590798i
$852$	39670.2	+	291666.i	0.0546494	+	0.401798i
$853$	442931.			0.608749			0.304375	−	0.952552i	$-0.401553\pi$
$853$	442931.			0.608749			0.304375	+	0.952552i	$0.401553\pi$
$854$			366491.i			0.502513i
$855$	−156756.	−	565597.i	−0.214433	−	0.773704i
$856$	123450.			0.168478
$857$		−	959443.i		−	1.30634i	−0.757209	−	0.653172i	$-0.773438\pi$
$857$		−	959443.i		−	1.30634i	0.757209	−	0.653172i	$-0.226562\pi$
$858$	−1.21879e6	+	165771.i	−1.65560	+	0.225182i
$859$	476722.			0.646070			0.323035	−	0.946387i	$-0.395297\pi$
$859$	476722.			0.646070			0.323035	+	0.946387i	$0.395297\pi$
$860$		−	237843.i		−	0.321583i
$861$	71084.7	+	522635.i	0.0958893	+	0.705005i
$862$	16169.4			0.0217610
$863$			737791.i			0.990631i	0.868713	+	0.495316i	$0.164948\pi$
$863$			737791.i			0.990631i	−0.868713	+	0.495316i	$0.835052\pi$
$864$	52062.4	+	121259.i	0.0697424	+	0.162438i
$865$	−424661.			−0.567558
$866$			154339.i			0.205798i
$867$	−567354.	+	77167.0i	−0.754772	+	0.102658i
$868$	−160704.			−0.213298
$869$		−	1.77183e6i		−	2.34629i
$870$	−9191.15	−	67575.9i	−0.0121431	−	0.0892798i
$871$	1.06272e6			1.40082
$872$		−	31678.5i		−	0.0416612i
$873$	651611.	−	180595.i	0.854988	−	0.236961i
$874$	451350.			0.590868
$875$		−	349665.i		−	0.456706i
$876$	68435.2	−	9308.02i	0.0891808	−	0.0121297i
$877$	−937901.			−1.21943			−0.609717	−	0.792620i	$-0.708717\pi$
$877$	−937901.			−1.21943			−0.609717	+	0.792620i	$0.708717\pi$
$878$		−	315258.i		−	0.408957i
$879$	100421.	+	738326.i	0.129971	+	0.955587i
$880$	165751.			0.214037
$881$			730926.i			0.941720i	0.882208	+	0.470860i	$0.156056\pi$
$881$			730926.i			0.941720i	−0.882208	+	0.470860i	$0.843944\pi$
$882$	108490.	+	391445.i	0.139460	+	0.503192i
$883$	1.23746e6			1.58712			0.793560	−	0.608492i	$-0.208225\pi$
$883$	1.23746e6			1.58712			0.793560	+	0.608492i	$0.208225\pi$
$884$			270923.i			0.346690i
$885$	−52000.5	+	7072.71i	−0.0663928	+	0.00903024i
$886$	−812535.			−1.03508
$887$		−	411756.i		−	0.523350i	−0.965156	−	0.261675i	$-0.915725\pi$
$887$		−	411756.i		−	0.523350i	0.965156	−	0.261675i	$-0.0842749\pi$
$888$	−41440.9	−	304685.i	−0.0525537	−	0.386390i
$889$	−308132.			−0.389882
$890$			392967.i			0.496108i
$891$	−679805.	−	1.13221e6i	−0.856306	−	1.42617i
$892$	395414.			0.496961
$893$		−	313426.i		−	0.393036i
$894$	517536.	−	70391.2i	0.647538	−	0.0880731i
$895$	396228.			0.494651
$896$		−	36290.4i		−	0.0452039i
$897$	−82508.6	−	606627.i	−0.102545	−	0.753940i
$898$	469038.			0.581641
$899$		−	166908.i		−	0.206517i
$900$	−286907.	+	79516.7i	−0.354206	+	0.0981687i
$901$	691083.			0.851296
$902$		−	1.33141e6i		−	1.63644i
$903$	516382.	−	70234.3i	0.633280	−	0.0861338i
$904$	−567307.			−0.694195
$905$		−	514274.i		−	0.627910i
$906$	−121608.	−	894099.i	−0.148152	−	1.08925i
$907$	860274.			1.04574			0.522868	−	0.852414i	$-0.324862\pi$
$907$	860274.			1.04574			0.522868	+	0.852414i	$0.324862\pi$
$908$			39711.3i			0.0481662i
$909$	22574.6	+	81452.3i	0.0273208	+	0.0985770i
$910$	218930.			0.264376
$911$			516100.i			0.621866i	0.950432	+	0.310933i	$0.100642\pi$
$911$			516100.i			0.621866i	−0.950432	+	0.310933i	$0.899358\pi$
$912$	321415.	−	43716.4i	0.386435	−	0.0525599i
$913$	1.85446e6			2.22472
$914$		−	428904.i		−	0.513415i
$915$	−80695.4	−	593296.i	−0.0963844	−	0.708645i
$916$	242921.			0.289517
$917$			247198.i			0.293972i
$918$	−267285.	+	114759.i	−0.317168	+	0.136176i
$919$	250109.			0.296141			0.148071	−	0.988977i	$-0.452694\pi$
$919$	250109.			0.296141			0.148071	+	0.988977i	$0.452694\pi$
$920$			82498.6i			0.0974700i
$921$	−366417.	+	49837.2i	−0.431973	+	0.0587536i
$922$	−317134.			−0.373062
$923$		−	981408.i		−	1.15198i
$924$	48945.6	+	359862.i	0.0573284	+	0.421495i
$925$	693730.			0.810788
$926$			645913.i			0.753272i
$927$	1.28038e6	−	354859.i	1.48998	−	0.412949i
$928$	37691.4			0.0437669
$929$			229734.i			0.266191i	0.991103	+	0.133095i	$0.0424917\pi$
$929$			229734.i			0.266191i	−0.991103	+	0.133095i	$0.957508\pi$
$930$	260156.	−	35384.4i	0.300793	−	0.0409115i
$931$	998471.			1.15196
$932$			703179.i			0.809532i
$933$	−1021.08	−	7507.29i	−0.00117300	−	0.00862422i
$934$	−409154.			−0.469022
$935$			365356.i			0.417919i
$936$	−117512.	−	423999.i	−0.134132	−	0.483965i
$937$	730809.			0.832385			0.416193	−	0.909276i	$-0.363364\pi$
$937$	730809.			0.832385			0.416193	+	0.909276i	$0.363364\pi$
$938$		−	313779.i		−	0.356630i
$939$	284899.	−	38749.8i	0.323117	−	0.0439479i
$940$	57288.7			0.0648355
$941$		−	100273.i		−	0.113241i	−0.998396	−	0.0566206i	$-0.981967\pi$
$941$		−	100273.i		−	0.113241i	0.998396	−	0.0566206i	$-0.0180325\pi$
$942$	55054.3	+	404774.i	0.0620425	+	0.456154i
$943$	662680.			0.745213
$944$		−	29004.0i		−	0.0325472i
$945$	92734.9	+	215990.i	0.103844	+	0.241863i
$946$	−1.31548e6			−1.46995
$947$		−	1.70999e6i		−	1.90675i	−0.301790	−	0.953375i	$-0.597584\pi$
$947$		−	1.70999e6i		−	1.90675i	0.301790	−	0.953375i	$-0.402416\pi$
$948$	628010.	−	85417.0i	0.698795	−	0.0950447i
$949$	−230273.			−0.255688
$950$			731822.i			0.810883i
$951$	−127721.	−	939039.i	−0.141221	−	1.03830i
$952$	79993.0			0.0882629
$953$			168698.i			0.185747i	0.995678	+	0.0928737i	$0.0296053\pi$
$953$			168698.i			0.185747i	−0.995678	+	0.0928737i	$0.970395\pi$
$954$	−1.08156e6	+	299755.i	−1.18837	+	0.329359i
$955$	−704575.			−0.772540
$956$		−	332356.i		−	0.363654i
$957$	−373755.	+	50835.2i	−0.408097	+	0.0555061i
$958$	613767.			0.668763
$959$		−	340714.i		−	0.370470i
$960$	7990.57	+	58748.9i	0.00867032	+	0.0637466i
$961$	−280954.			−0.304221
$962$			1.02522e6i			1.10781i
$963$	−118029.	−	425864.i	−0.127273	−	0.459217i
$964$	118271.			0.127270
$965$		−	450672.i		−	0.483956i
$966$	−179113.	+	24361.6i	−0.191943	+	0.0261067i
$967$	224069.			0.239623			0.119811	−	0.992797i	$-0.461771\pi$
$967$	224069.			0.239623			0.119811	+	0.992797i	$0.461771\pi$
$968$		−	585460.i		−	0.624808i
$969$	96361.8	+	708479.i	0.102626	+	0.754535i
$970$	303799.			0.322881
$971$		−	1.80160e6i		−	1.91082i	−0.295283	−	0.955410i	$-0.595414\pi$
$971$		−	1.80160e6i		−	1.91082i	0.295283	−	0.955410i	$-0.404586\pi$
$972$	368530.	−	295533.i	0.390068	−	0.312805i
$973$	−338056.			−0.357078
$974$		−	381601.i		−	0.402246i
$975$	983589.	−	133780.i	1.03468	−	0.140729i
$976$	330919.			0.347394
$977$		−	567261.i		−	0.594284i	−0.954833	−	0.297142i	$-0.903967\pi$
$977$		−	567261.i		−	0.594284i	0.954833	−	0.297142i	$-0.0960335\pi$
$978$	130680.	+	960794.i	0.136625	+	1.00451i
$979$	2.17346e6			2.26770
$980$			182502.i			0.190028i
$981$	−109281.	+	30287.4i	−0.113555	+	0.0314719i
$982$	594596.			0.616594
$983$			1.17473e6i			1.21571i	0.794049	+	0.607854i	$0.207969\pi$
$983$			1.17473e6i			1.21571i	−0.794049	+	0.607854i	$0.792031\pi$
$984$	471907.	−	64185.2i	0.487379	−	0.0662895i
$985$	−833782.			−0.859370
$986$			83081.2i			0.0854573i
$987$	16917.2	+	124380.i	0.0173657	+	0.127678i
$988$	−1.08151e6			−1.10794
$989$		−	654752.i		−	0.669397i
$990$	−158472.	−	571788.i	−0.161690	−	0.583398i
$991$	−726533.			−0.739790			−0.369895	−	0.929074i	$-0.620606\pi$
$991$	−726533.			−0.739790			−0.369895	+	0.929074i	$0.620606\pi$
$992$			145106.i			0.147455i
$993$	−265036.	+	36048.1i	−0.268786	+	0.0365582i
$994$	−289772.			−0.293280
$995$		−	260160.i		−	0.262781i
$996$	89400.5	+	657298.i	0.0901200	+	0.662588i
$997$	1.46044e6			1.46924			0.734620	−	0.678479i	$-0.237360\pi$
$997$	1.46044e6			1.46924			0.734620	+	0.678479i	$0.237360\pi$
$998$			919499.i			0.923188i
$999$	−1.01145e6	+	434264.i	−1.01347	+	0.435134i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	354.5.b.a.119.2	✓	76
3.2	odd	2	inner	354.5.b.a.119.40	yes	76

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
354.5.b.a.119.2	✓	76	1.1	even	1	trivial
354.5.b.a.119.40	yes	76	3.2	odd	2	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:	\( N \)	\(=\)	\( 354 = 2 \cdot 3 \cdot 59 \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	354.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-2.82843i q^{2} +(-8.91789 + 1.21294i) q^{3} -8.00000 q^{4} +12.8667i q^{5} +(3.43072 + 25.2236i) q^{6} -25.0597 q^{7} +22.6274i q^{8} +(78.0575 - 21.6338i) q^{9} +O(q^{10})\)	\(q-2.82843i q^{2} +(-8.91789 + 1.21294i) q^{3} -8.00000 q^{4} +12.8667i q^{5} +(3.43072 + 25.2236i) q^{6} -25.0597 q^{7} +22.6274i q^{8} +(78.0575 - 21.6338i) q^{9} +36.3926 q^{10} -201.283i q^{11} +(71.3431 - 9.70354i) q^{12} -240.058 q^{13} +70.8796i q^{14} +(-15.6066 - 114.744i) q^{15} +64.0000 q^{16} +141.072i q^{17} +(-61.1895 - 220.780i) q^{18} -563.150 q^{19} -102.934i q^{20} +(223.480 - 30.3960i) q^{21} -569.315 q^{22} -283.363i q^{23} +(-27.4457 - 201.789i) q^{24} +459.448 q^{25} +678.985i q^{26} +(-669.868 + 287.607i) q^{27} +200.478 q^{28} +208.217i q^{29} +(-324.545 + 44.1421i) q^{30} -801.603 q^{31} -181.019i q^{32} +(244.145 + 1795.02i) q^{33} +399.012 q^{34} -322.436i q^{35} +(-624.460 + 173.070i) q^{36} +1509.92 q^{37} +1592.83i q^{38} +(2140.81 - 291.176i) q^{39} -291.140 q^{40} +2338.62i q^{41} +(-85.9729 - 632.097i) q^{42} +2310.64 q^{43} +1610.27i q^{44} +(278.355 + 1004.34i) q^{45} -801.473 q^{46} +556.559i q^{47} +(-570.745 + 77.6283i) q^{48} -1773.01 q^{49} -1299.51i q^{50} +(-171.112 - 1258.06i) q^{51} +1920.46 q^{52} -4898.80i q^{53} +(813.475 + 1894.67i) q^{54} +2589.85 q^{55} -567.037i q^{56} +(5022.11 - 683.069i) q^{57} +588.928 q^{58} -453.188i q^{59} +(124.853 + 917.951i) q^{60} +5170.61 q^{61} +2267.27i q^{62} +(-1956.10 + 542.137i) q^{63} -512.000 q^{64} -3088.75i q^{65} +(5077.09 - 690.546i) q^{66} -4426.93 q^{67} -1128.58i q^{68} +(343.703 + 2527.00i) q^{69} -911.988 q^{70} +4088.22i q^{71} +(489.516 + 1766.24i) q^{72} +959.240 q^{73} -4270.71i q^{74} +(-4097.30 + 557.283i) q^{75} +4505.20 q^{76} +5044.10i q^{77} +(-823.570 - 6055.12i) q^{78} +8802.67 q^{79} +823.470i q^{80} +(5624.96 - 3377.36i) q^{81} +6614.62 q^{82} +9213.19i q^{83} +(-1787.84 + 243.168i) q^{84} -1815.13 q^{85} -6535.48i q^{86} +(-252.556 - 1856.86i) q^{87} +4554.52 q^{88} +10798.0i q^{89} +(2840.71 - 787.308i) q^{90} +6015.78 q^{91} +2266.91i q^{92} +(7148.60 - 972.297i) q^{93} +1574.19 q^{94} -7245.89i q^{95} +(219.566 + 1614.31i) q^{96} +8347.83 q^{97} +5014.83i q^{98} +(-4354.51 - 15711.7i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 76 q - 608 q^{4} - 64 q^{6} - 184 q^{7} + 168 q^{9}+O(q^{10}) \) 76 * q - 608 * q^4 - 64 * q^6 - 184 * q^7 + 168 * q^9	\( 76 q - 608 q^{4} - 64 q^{6} - 184 q^{7} + 168 q^{9} + 256 q^{10} - 200 q^{13} - 26 q^{15} + 4864 q^{16} - 512 q^{18} + 616 q^{19} + 330 q^{21} + 640 q^{22} + 512 q^{24} - 10540 q^{25} - 354 q^{27} + 1472 q^{28} - 832 q^{30} - 3920 q^{31} - 188 q^{33} + 2560 q^{34} - 1344 q^{36} - 1440 q^{37} + 8204 q^{39} - 2048 q^{40} - 5760 q^{42} - 1944 q^{43} + 3886 q^{45} + 4864 q^{46} + 33636 q^{49} - 7544 q^{51} + 1600 q^{52} + 3392 q^{54} - 10536 q^{55} - 12182 q^{57} - 7168 q^{58} + 208 q^{60} + 6360 q^{61} + 10860 q^{63} - 38912 q^{64} + 19712 q^{66} + 30744 q^{67} - 34208 q^{69} - 23808 q^{70} + 4096 q^{72} + 4032 q^{73} + 22324 q^{75} - 4928 q^{76} + 12864 q^{78} - 29824 q^{79} - 22584 q^{81} + 13184 q^{82} - 2640 q^{84} + 9240 q^{85} + 32850 q^{87} - 5120 q^{88} - 16448 q^{90} - 31160 q^{91} - 1780 q^{93} + 5248 q^{94} - 4096 q^{96} + 77504 q^{97} - 15412 q^{99}+O(q^{100}) \) 76 * q - 608 * q^4 - 64 * q^6 - 184 * q^7 + 168 * q^9 + 256 * q^10 - 200 * q^13 - 26 * q^15 + 4864 * q^16 - 512 * q^18 + 616 * q^19 + 330 * q^21 + 640 * q^22 + 512 * q^24 - 10540 * q^25 - 354 * q^27 + 1472 * q^28 - 832 * q^30 - 3920 * q^31 - 188 * q^33 + 2560 * q^34 - 1344 * q^36 - 1440 * q^37 + 8204 * q^39 - 2048 * q^40 - 5760 * q^42 - 1944 * q^43 + 3886 * q^45 + 4864 * q^46 + 33636 * q^49 - 7544 * q^51 + 1600 * q^52 + 3392 * q^54 - 10536 * q^55 - 12182 * q^57 - 7168 * q^58 + 208 * q^60 + 6360 * q^61 + 10860 * q^63 - 38912 * q^64 + 19712 * q^66 + 30744 * q^67 - 34208 * q^69 - 23808 * q^70 + 4096 * q^72 + 4032 * q^73 + 22324 * q^75 - 4928 * q^76 + 12864 * q^78 - 29824 * q^79 - 22584 * q^81 + 13184 * q^82 - 2640 * q^84 + 9240 * q^85 + 32850 * q^87 - 5120 * q^88 - 16448 * q^90 - 31160 * q^91 - 1780 * q^93 + 5248 * q^94 - 4096 * q^96 + 77504 * q^97 - 15412 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more