LMFDB - Embedded newform 147.6.c.c.146.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [147,6,Mod(146,147)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(147, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("147.146");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 147 = 3 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	147.c (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:	$23.5764215125$
Analytic rank:	$0$
Dimension:	$16$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 171 x^{14} + 21495 x^{12} - 1128902 x^{10} + 42970860 x^{8} - 655075344 x^{6} + \cdots + 90230547456 $ x^16 - 171x^14 + 21495x^12 - 1128902x^10 + 42970860x^8 - 655075344x^6 + 7244325760x^4 - 29387167488*x^2 + 90230547456
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 2^{12}\cdot 3^{8}\cdot 7^{4} $
Twist minimal:	no (minimal twist has level 21)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			146.6
Root			$-3.16536 + 1.82752i$ of defining polynomial
Character	$\chi$	$=$	147.146
Dual form			147.6.c.c.146.12

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-3.65505i q^{2} +(15.5635 - 0.882561i) q^{3} +18.6406 q^{4} -74.3244 q^{5} +(-3.22580 - 56.8851i) q^{6} -185.094i q^{8} +(241.442 - 27.4714i) q^{9} +O(q^{10})$	\(q-3.65505i q^{2} +(15.5635 - 0.882561i) q^{3} +18.6406 q^{4} -74.3244 q^{5} +(-3.22580 - 56.8851i) q^{6} -185.094i q^{8} +(241.442 - 27.4714i) q^{9} +271.659i q^{10} +39.3914i q^{11} +(290.113 - 16.4515i) q^{12} -589.288i q^{13} +(-1156.74 + 65.5958i) q^{15} -80.0263 q^{16} -1237.51 q^{17} +(-100.409 - 882.482i) q^{18} -2767.79i q^{19} -1385.45 q^{20} +143.977 q^{22} +463.253i q^{23} +(-163.357 - 2880.70i) q^{24} +2399.11 q^{25} -2153.88 q^{26} +(3733.43 - 640.637i) q^{27} -5294.57i q^{29} +(239.756 + 4227.95i) q^{30} +2846.74i q^{31} -5630.50i q^{32} +(34.7653 + 613.066i) q^{33} +4523.16i q^{34} +(4500.64 - 512.084i) q^{36} +7847.11 q^{37} -10116.4 q^{38} +(-520.083 - 9171.36i) q^{39} +13757.0i q^{40} -12162.5 q^{41} +5350.18 q^{43} +734.281i q^{44} +(-17945.0 + 2041.79i) q^{45} +1693.21 q^{46} -6755.99 q^{47} +(-1245.49 + 70.6281i) q^{48} -8768.86i q^{50} +(-19259.9 + 1092.18i) q^{51} -10984.7i q^{52} -16011.8i q^{53} +(-2341.56 - 13645.9i) q^{54} -2927.74i q^{55} +(-2442.74 - 43076.3i) q^{57} -19351.9 q^{58} -7746.64 q^{59} +(-21562.4 + 1222.75i) q^{60} -5617.58i q^{61} +10405.0 q^{62} -23140.6 q^{64} +43798.5i q^{65} +(2240.79 - 127.069i) q^{66} -12887.4 q^{67} -23068.0 q^{68} +(408.849 + 7209.82i) q^{69} +60637.7i q^{71} +(-5084.79 - 44689.5i) q^{72} +51641.4i q^{73} -28681.6i q^{74} +(37338.5 - 2117.36i) q^{75} -51593.3i q^{76} +(-33521.7 + 1900.93i) q^{78} +67372.2 q^{79} +5947.90 q^{80} +(57539.6 - 13265.5i) q^{81} +44454.5i q^{82} +8712.06 q^{83} +91977.1 q^{85} -19555.1i q^{86} +(-4672.78 - 82401.9i) q^{87} +7291.11 q^{88} +18112.0 q^{89} +(7462.85 + 65589.9i) q^{90} +8635.34i q^{92} +(2512.42 + 44305.1i) q^{93} +24693.4i q^{94} +205714. i q^{95} +(-4969.26 - 87630.1i) q^{96} +18641.1i q^{97} +(1082.14 + 9510.75i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 172 q^{4} + 1212 q^{9}+O(q^{10}) $ 16 * q - 172 * q^4 + 1212 * q^9	$ 16 q - 172 q^{4} + 1212 q^{9} + 1188 q^{15} + 5716 q^{16} + 876 q^{18} - 21900 q^{22} + 13156 q^{25} - 900 q^{30} - 15132 q^{36} + 20932 q^{37} + 34836 q^{39} + 111052 q^{43} - 163392 q^{46} - 63192 q^{51} - 31368 q^{57} + 83412 q^{58} - 120132 q^{60} - 158884 q^{64} + 204404 q^{67} - 661728 q^{72} - 277512 q^{78} + 502616 q^{79} - 358524 q^{81} + 205152 q^{85} + 719028 q^{88} - 35352 q^{93} + 215472 q^{99}+O(q^{100}) $ 16 * q - 172 * q^4 + 1212 * q^9 + 1188 * q^15 + 5716 * q^16 + 876 * q^18 - 21900 * q^22 + 13156 * q^25 - 900 * q^30 - 15132 * q^36 + 20932 * q^37 + 34836 * q^39 + 111052 * q^43 - 163392 * q^46 - 63192 * q^51 - 31368 * q^57 + 83412 * q^58 - 120132 * q^60 - 158884 * q^64 + 204404 * q^67 - 661728 * q^72 - 277512 * q^78 + 502616 * q^79 - 358524 * q^81 + 205152 * q^85 + 719028 * q^88 - 35352 * q^93 + 215472 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/147\mathbb{Z}\right)^\times$.

$n$	$50$	$52$
$\chi(n)$	$-1$	$-1$

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 $

$2$		−	3.65505i		−	0.646127i	−0.946377	−	0.323064i	$-0.895287\pi$
$2$		−	3.65505i		−	0.646127i	0.946377	−	0.323064i	$-0.104713\pi$
$3$	15.5635	−	0.882561i	0.998396	−	0.0566163i
$3$	15.5635	−	0.882561i	0.998396	−	0.0566163i
$4$	18.6406			0.582520
$5$	−74.3244			−1.32955			−0.664777	−	0.747042i	$-0.731474\pi$
$5$	−74.3244			−1.32955			−0.664777	+	0.747042i	$0.731474\pi$
$6$	−3.22580	−	56.8851i	−0.0365813	−	0.645091i
$7$		0			0
$7$		0			0
$8$		−	185.094i		−	1.02251i
$9$	241.442	−	27.4714i	0.993589	−	0.113051i
$10$			271.659i			0.859061i
$11$			39.3914i			0.0981567i	0.998795	+	0.0490783i	$0.0156284\pi$
$11$			39.3914i			0.0981567i	−0.998795	+	0.0490783i	$0.984372\pi$
$12$	290.113	−	16.4515i	0.581586	−	0.0329801i
$13$		−	589.288i		−	0.967096i	−0.875318	−	0.483548i	$-0.839348\pi$
$13$		−	589.288i		−	0.967096i	0.875318	−	0.483548i	$-0.160652\pi$
$14$		0			0
$15$	−1156.74	+	65.5958i	−1.32742	+	0.0752745i
$16$	−80.0263			−0.0781507
$17$	−1237.51			−1.03855			−0.519274	−	0.854608i	$-0.673797\pi$
$17$	−1237.51			−1.03855			−0.519274	+	0.854608i	$0.673797\pi$
$18$	−100.409	−	882.482i	−0.0730453	−	0.641985i
$19$		−	2767.79i		−	1.75893i	−0.475964	−	0.879465i	$-0.657901\pi$
$19$		−	2767.79i		−	1.75893i	0.475964	−	0.879465i	$-0.342099\pi$
$20$	−1385.45			−0.774492
$21$		0			0
$22$	143.977			0.0634217
$23$			463.253i			0.182599i	0.995823	+	0.0912997i	$0.0291021\pi$
$23$			463.253i			0.182599i	−0.995823	+	0.0912997i	$0.970898\pi$
$24$	−163.357	−	2880.70i	−0.0578907	−	1.02087i
$25$	2399.11			0.767716
$26$	−2153.88			−0.624867
$27$	3733.43	−	640.637i	0.985595	−	0.169123i
$28$		0			0
$29$		−	5294.57i		−	1.16906i	−0.811373	−	0.584529i	$-0.801279\pi$
$29$		−	5294.57i		−	1.16906i	0.811373	−	0.584529i	$-0.198721\pi$
$30$	239.756	+	4227.95i	0.0486369	+	0.857683i
$31$			2846.74i			0.532039i	0.963968	+	0.266019i	$0.0857085\pi$
$31$			2846.74i			0.532039i	−0.963968	+	0.266019i	$0.914291\pi$
$32$		−	5630.50i		−	0.972014i
$33$	34.7653	+	613.066i	0.00555727	+	0.0979992i
$34$			4523.16i			0.671034i
$35$		0			0
$36$	4500.64	−	512.084i	0.578785	−	0.0658545i
$37$	7847.11			0.942336			0.471168	−	0.882044i	$-0.343833\pi$
$37$	7847.11			0.942336			0.471168	+	0.882044i	$0.343833\pi$
$38$	−10116.4			−1.13649
$39$	−520.083	−	9171.36i	−0.0547534	−	0.965544i
$40$			13757.0i			1.35948i
$41$	−12162.5			−1.12996			−0.564980	−	0.825105i	$-0.691116\pi$
$41$	−12162.5			−1.12996			−0.564980	+	0.825105i	$0.691116\pi$
$42$		0			0
$43$	5350.18			0.441262			0.220631	−	0.975357i	$-0.429188\pi$
$43$	5350.18			0.441262			0.220631	+	0.975357i	$0.429188\pi$
$44$			734.281i			0.0571782i
$45$	−17945.0	+	2041.79i	−1.32103	+	0.150307i
$46$	1693.21			0.117982
$47$	−6755.99			−0.446112			−0.223056	−	0.974806i	$-0.571603\pi$
$47$	−6755.99			−0.446112			−0.223056	+	0.974806i	$0.571603\pi$
$48$	−1245.49	+	70.6281i	−0.0780253	+	0.00442460i
$49$		0			0
$50$		−	8768.86i		−	0.496042i
$51$	−19259.9	+	1092.18i	−1.03688	+	0.0587987i
$52$		−	10984.7i		−	0.563352i
$53$		−	16011.8i		−	0.782977i	−0.920183	−	0.391489i	$-0.871960\pi$
$53$		−	16011.8i		−	0.782977i	0.920183	−	0.391489i	$-0.128040\pi$
$54$	−2341.56	−	13645.9i	−0.109275	−	0.636820i
$55$		−	2927.74i		−	0.130505i
$56$		0			0
$57$	−2442.74	−	43076.3i	−0.0995841	−	1.75611i
$58$	−19351.9			−0.755360
$59$	−7746.64			−0.289723			−0.144862	−	0.989452i	$-0.546274\pi$
$59$	−7746.64			−0.289723			−0.144862	+	0.989452i	$0.546274\pi$
$60$	−21562.4	+	1222.75i	−0.773250	+	0.0438489i
$61$		−	5617.58i		−	0.193297i	−0.995319	−	0.0966484i	$-0.969188\pi$
$61$		−	5617.58i		−	0.193297i	0.995319	−	0.0966484i	$-0.0308122\pi$
$62$	10405.0			0.343765
$63$		0			0
$64$	−23140.6			−0.706195
$65$			43798.5i			1.28581i
$66$	2240.79	−	127.069i	0.0633199	−	0.00359070i
$67$	−12887.4			−0.350734			−0.175367	−	0.984503i	$-0.556111\pi$
$67$	−12887.4			−0.350734			−0.175367	+	0.984503i	$0.556111\pi$
$68$	−23068.0			−0.604975
$69$	408.849	+	7209.82i	0.0103381	+	0.182306i
$70$		0			0
$71$			60637.7i			1.42757i	0.700366	+	0.713784i	$0.253020\pi$
$71$			60637.7i			1.42757i	−0.700366	+	0.713784i	$0.746980\pi$
$72$	−5084.79	−	44689.5i	−0.115596	−	1.01595i
$73$			51641.4i			1.13420i	0.823648	+	0.567101i	$0.191935\pi$
$73$			51641.4i			1.13420i	−0.823648	+	0.567101i	$0.808065\pi$
$74$		−	28681.6i		−	0.608869i
$75$	37338.5	−	2117.36i	0.766484	−	0.0434652i
$76$		−	51593.3i		−	1.02461i
$77$		0			0
$78$	−33521.7	+	1900.93i	−0.623864	+	0.0353776i
$79$	67372.2			1.21454			0.607272	−	0.794494i	$-0.292264\pi$
$79$	67372.2			1.21454			0.607272	+	0.794494i	$0.292264\pi$
$80$	5947.90			0.103906
$81$	57539.6	−	13265.5i	0.974439	−	0.224652i
$82$			44454.5i			0.730097i
$83$	8712.06			0.138812			0.0694058	−	0.997589i	$-0.477890\pi$
$83$	8712.06			0.138812			0.0694058	+	0.997589i	$0.477890\pi$
$84$		0			0
$85$	91977.1			1.38081
$86$		−	19555.1i		−	0.285112i
$87$	−4672.78	−	82401.9i	−0.0661877	−	1.16718i
$88$	7291.11			0.100366
$89$	18112.0			0.242378			0.121189	−	0.992629i	$-0.461329\pi$
$89$	18112.0			0.242378			0.121189	+	0.992629i	$0.461329\pi$
$90$	7462.85	+	65589.9i	0.0971177	+	0.853554i
$91$		0			0
$92$			8635.34i			0.106368i
$93$	2512.42	+	44305.1i	0.0301221	+	0.531185i
$94$			24693.4i			0.288245i
$95$			205714.i			2.33859i
$96$	−4969.26	−	87630.1i	−0.0550318	−	0.970454i
$97$			18641.1i			0.201160i	0.994929	+	0.100580i	$0.0320698\pi$
$97$			18641.1i			0.201160i	−0.994929	+	0.100580i	$0.967930\pi$
$98$		0			0
$99$	1082.14	+	9510.75i	0.0110967	+	0.0975274i
$100$	44721.0			0.447210
$101$	170598.			1.66407			0.832034	−	0.554725i	$-0.187176\pi$
$101$	170598.			1.66407			0.832034	+	0.554725i	$0.187176\pi$
$102$	3991.96	+	70395.9i	0.0379914	+	0.669957i
$103$			58887.8i			0.546931i	0.961882	+	0.273465i	$0.0881699\pi$
$103$			58887.8i			0.546931i	−0.961882	+	0.273465i	$0.911830\pi$
$104$	−109074.			−0.988864
$105$		0			0
$106$	−58523.7			−0.505903
$107$		−	147582.i		−	1.24616i	−0.782157	−	0.623082i	$-0.785880\pi$
$107$		−	147582.i		−	1.24616i	0.782157	−	0.623082i	$-0.214120\pi$
$108$	69593.5	−	11941.9i	0.574129	−	0.0985175i
$109$	26156.0			0.210865			0.105433	−	0.994426i	$-0.466377\pi$
$109$	26156.0			0.210865			0.105433	+	0.994426i	$0.466377\pi$
$110$	−10701.0			−0.0843226
$111$	122128.	−	6925.56i	0.940824	−	0.0533516i
$112$		0			0
$113$			19094.4i			0.140672i	0.997523	+	0.0703362i	$0.0224072\pi$
$113$			19094.4i			0.140672i	−0.997523	+	0.0703362i	$0.977593\pi$
$114$	−157446.	+	8928.33i	−1.13467	+	0.0643440i
$115$		−	34431.0i		−	0.242776i
$116$		−	98694.2i		−	0.681000i
$117$	−16188.6	−	142279.i	−0.109331	−	0.960896i
$118$			28314.3i			0.187198i
$119$		0			0
$120$	12141.4	+	214106.i	0.0769688	+	1.35730i
$121$	159499.			0.990365
$122$	−20532.5			−0.124894
$123$	−189290.	+	10734.1i	−1.12815	+	0.0639741i
$124$			53065.0i			0.309923i
$125$	53951.2			0.308835
$126$		0			0
$127$	−42178.1			−0.232048			−0.116024	−	0.993246i	$-0.537015\pi$
$127$	−42178.1			−0.232048			−0.116024	+	0.993246i	$0.537015\pi$
$128$		−	95596.2i		−	0.515722i
$129$	83267.2	−	4721.86i	0.440555	−	0.0249827i
$130$	160085.			0.830794
$131$	283072.			1.44118			0.720590	−	0.693361i	$-0.243871\pi$
$131$	283072.			1.44118			0.720590	+	0.693361i	$0.243871\pi$
$132$	648.048	+	11427.9i	0.00323722	+	0.0570865i
$133$		0			0
$134$			47104.0i			0.226619i
$135$	−277485.	+	47615.0i	−1.31040	+	0.224858i
$136$			229055.i			1.06192i
$137$			263686.i			1.20029i	0.799891	+	0.600145i	$0.204890\pi$
$137$			263686.i			1.20029i	−0.799891	+	0.600145i	$0.795110\pi$
$138$	26352.2	−	1494.36i	0.117793	−	0.00667972i
$139$		−	363744.i		−	1.59683i	−0.602108	−	0.798415i	$-0.705672\pi$
$139$		−	363744.i		−	1.59683i	0.602108	−	0.798415i	$-0.294328\pi$
$140$		0			0
$141$	−105147.	+	5962.57i	−0.445397	+	0.0252572i
$142$	221634.			0.922390
$143$	23212.9			0.0949269
$144$	−19321.7	+	2198.43i	−0.0776497	+	0.00883501i
$145$			393516.i			1.55433i
$146$	188752.			0.732839
$147$		0			0
$148$	146275.			0.548929
$149$			385877.i			1.42391i	0.702224	+	0.711957i	$0.252191\pi$
$149$			385877.i			1.42391i	−0.702224	+	0.711957i	$0.747809\pi$
$150$	−7739.06	−	136474.i	−0.0280841	−	0.495246i
$151$	−276533.			−0.986970			−0.493485	−	0.869754i	$-0.664277\pi$
$151$	−276533.			−0.986970			−0.493485	+	0.869754i	$0.664277\pi$
$152$	−512300.			−1.79852
$153$	−298787.	+	33996.1i	−1.03189	+	0.117409i
$154$		0			0
$155$		−	211582.i		−	0.707375i
$156$	−9694.67	−	170960.i	−0.0318949	−	0.562449i
$157$			378991.i			1.22710i	0.789656	+	0.613550i	$0.210259\pi$
$157$			378991.i			1.22710i	−0.789656	+	0.613550i	$0.789741\pi$
$158$		−	246248.i		−	0.784749i
$159$	−14131.3	−	249198.i	−0.0443293	−	0.781722i
$160$			418484.i			1.29235i
$161$		0			0
$162$	−48486.0	−	210310.i	−0.145154	−	0.629611i
$163$	−231513.			−0.682505			−0.341252	−	0.939972i	$-0.610851\pi$
$163$	−231513.			−0.682505			−0.341252	+	0.939972i	$0.610851\pi$
$164$	−226717.			−0.658224
$165$	−2583.91	−	45565.8i	−0.00738869	−	0.130295i
$166$		−	31843.0i		−	0.0896899i
$167$	173708.			0.481981			0.240990	−	0.970527i	$-0.422528\pi$
$167$	173708.			0.481981			0.240990	+	0.970527i	$0.422528\pi$
$168$		0			0
$169$	24032.3			0.0647260
$170$		−	336181.i		−	0.892176i
$171$	−76034.9	−	668260.i	−0.198849	−	1.74765i
$172$	99730.7			0.257044
$173$	490510.			1.24604			0.623021	−	0.782205i	$-0.285905\pi$
$173$	490510.			1.24604			0.623021	+	0.782205i	$0.285905\pi$
$174$	−301183.	+	17079.2i	−0.754148	+	0.0427657i
$175$		0			0
$176$		−	3152.35i		−	0.00767101i
$177$	−120564.	+	6836.88i	−0.289259	+	0.0164031i
$178$		−	66200.4i		−	0.156607i
$179$		−	641321.i		−	1.49604i	−0.663677	−	0.748019i	$-0.731005\pi$
$179$		−	641321.i		−	1.49604i	0.663677	−	0.748019i	$-0.268995\pi$
$180$	−334507.	+	38060.3i	−0.769527	+	0.0875571i
$181$		−	46939.3i		−	0.106498i	−0.998581	−	0.0532489i	$-0.983042\pi$
$181$		−	46939.3i		−	0.106498i	0.998581	−	0.0532489i	$-0.0169577\pi$
$182$		0			0
$183$	−4957.85	−	87428.9i	−0.0109437	−	0.192987i
$184$	85745.4			0.186709
$185$	−583232.			−1.25289
$186$	161937.	−	9183.01i	0.343213	−	0.0194627i
$187$		−	48747.3i		−	0.101940i
$188$	−125936.			−0.259869
$189$		0			0
$190$	751894.			1.51103
$191$			761400.i			1.51018i	0.655620	+	0.755091i	$0.272407\pi$
$191$			761400.i			1.51018i	−0.655620	+	0.755091i	$0.727593\pi$
$192$	−360148.	+	20423.0i	−0.705062	+	0.0399821i
$193$	556313.			1.07504			0.537522	−	0.843250i	$-0.319361\pi$
$193$	556313.			1.07504			0.537522	+	0.843250i	$0.319361\pi$
$194$	68133.9			0.129975
$195$	38654.8	+	681656.i	0.0727976	+	1.28374i
$196$		0			0
$197$		−	545896.i		−	1.00218i	−0.865396	−	0.501088i	$-0.832933\pi$
$197$		−	545896.i		−	1.00218i	0.865396	−	0.501088i	$-0.167067\pi$
$198$	34762.2	−	3955.26i	0.0630151	−	0.00716988i
$199$		−	211201.i		−	0.378062i	−0.981971	−	0.189031i	$-0.939465\pi$
$199$		−	211201.i		−	0.378062i	0.981971	−	0.189031i	$-0.0605346\pi$
$200$		−	444061.i		−	0.784996i
$201$	−200572.	+	11373.9i	−0.350171	+	0.0198573i
$202$		−	623544.i		−	1.07520i
$203$		0			0
$204$	−359017.	+	20358.9i	−0.604004	+	0.0342514i
$205$	903969.			1.50234
$206$	215238.			0.353387
$207$	12726.2	+	111849.i	0.0206430	+	0.181429i
$208$			47158.6i			0.0755792i
$209$	109027.			0.172651
$210$		0			0
$211$	−670640.			−1.03701			−0.518506	−	0.855074i	$-0.673512\pi$
$211$	−670640.			−1.03701			−0.518506	+	0.855074i	$0.673512\pi$
$212$		−	298469.i		−	0.456100i
$213$	53516.5	+	943732.i	0.0808236	+	1.42528i
$214$	−539420.			−0.805180
$215$	−397649.			−0.586683
$216$	−118578.	−	691035.i	−0.172930	−	1.00778i
$217$		0			0
$218$		−	95601.5i		−	0.136246i
$219$	45576.7	+	803718.i	0.0642144	+	1.13238i
$220$		−	54575.0i		−	0.0760216i
$221$			729250.i			1.00437i
$222$	−25313.2	−	446384.i	−0.0344719	−	0.607892i
$223$			18729.0i			0.0252204i	0.999920	+	0.0126102i	$0.00401406\pi$
$223$			18729.0i			0.0252204i	−0.999920	+	0.0126102i	$0.995986\pi$
$224$		0			0
$225$	579247.	−	65906.9i	0.762794	−	0.0867910i
$226$	69790.8			0.0908923
$227$	−447047.			−0.575822			−0.287911	−	0.957657i	$-0.592961\pi$
$227$	−447047.			−0.575822			−0.287911	+	0.957657i	$0.592961\pi$
$228$	−45534.2	−	802970.i	−0.0580097	−	1.02297i
$229$			22000.4i			0.0277231i	0.999904	+	0.0138616i	$0.00441241\pi$
$229$			22000.4i			0.0277231i	−0.999904	+	0.0138616i	$0.995588\pi$
$230$	−125847.			−0.156864
$231$		0			0
$232$	−979993.			−1.19537
$233$		−	533090.i		−	0.643296i	−0.946859	−	0.321648i	$-0.895763\pi$
$233$		−	533090.i		−	0.643296i	0.946859	−	0.321648i	$-0.104237\pi$
$234$	−520036.	+	59170.0i	−0.620861	+	0.0706418i
$235$	502135.			0.593131
$236$	−144402.			−0.168770
$237$	1.04854e6	−	59460.1i	1.21259	−	0.0687629i
$238$		0			0
$239$		−	269068.i		−	0.304697i	−0.988327	−	0.152348i	$-0.951316\pi$
$239$		−	269068.i		−	0.304697i	0.988327	−	0.152348i	$-0.0486836\pi$
$240$	92569.9	−	5249.39i	0.103739	−	0.00588275i
$241$		−	266824.i		−	0.295926i	−0.988993	−	0.147963i	$-0.952728\pi$
$241$		−	266824.i		−	0.295926i	0.988993	−	0.147963i	$-0.0472716\pi$
$242$		−	582977.i		−	0.639902i
$243$	883808.	−	257239.i	0.960157	−	0.279461i
$244$		−	104715.i		−	0.112599i
$245$		0			0
$246$	39233.8	+	691865.i	0.0413354	+	0.728926i
$247$	−1.63102e6			−1.70105
$248$	526914.			0.544014
$249$	135590.	−	7688.92i	0.138589	−	0.00785899i
$250$		−	197194.i		−	0.199546i
$251$	−947580.			−0.949361			−0.474681	−	0.880158i	$-0.657436\pi$
$251$	−947580.			−0.949361			−0.474681	+	0.880158i	$0.657436\pi$
$252$		0			0
$253$	−18248.2			−0.0179233
$254$			154163.i			0.149932i
$255$	1.43148e6	−	81175.4i	1.37859	−	0.0781761i
$256$	−1.08991e6			−1.03942
$257$	526317.			0.497066			0.248533	−	0.968623i	$-0.420052\pi$
$257$	526317.			0.497066			0.248533	+	0.968623i	$0.420052\pi$
$258$	−17258.6	−	304346.i	−0.0161420	−	0.284654i
$259$		0			0
$260$			816432.i			0.749008i
$261$	−145449.	−	1.27833e6i	−0.132163	−	1.16156i
$262$		−	1.03464e6i		−	0.931186i
$263$			1.36537e6i			1.21720i	0.793477	+	0.608601i	$0.208269\pi$
$263$			1.36537e6i			1.21720i	−0.793477	+	0.608601i	$0.791731\pi$
$264$	113475.	−	6434.85i	0.100205	−	0.00568236i
$265$			1.19006e6i			1.04101i
$266$		0			0
$267$	281886.	−	15985.0i	0.241989	−	0.0137225i
$268$	−240229.			−0.204310
$269$	29229.0			0.0246283			0.0123141	−	0.999924i	$-0.496080\pi$
$269$	29229.0			0.0246283			0.0123141	+	0.999924i	$0.496080\pi$
$270$	174035.	+	1.01422e6i	0.145287	+	0.846686i
$271$		−	423724.i		−	0.350477i	−0.984526	−	0.175239i	$-0.943930\pi$
$271$		−	423724.i		−	0.350477i	0.984526	−	0.175239i	$-0.0560697\pi$
$272$	99033.3			0.0811632
$273$		0			0
$274$	963785.			0.775540
$275$			94504.4i			0.0753564i
$276$	7621.21	+	134396.i	0.00602215	+	0.106197i
$277$	−746981.			−0.584938			−0.292469	−	0.956275i	$-0.594477\pi$
$277$	−746981.			−0.584938			−0.292469	+	0.956275i	$0.594477\pi$
$278$	−1.32950e6			−1.03175
$279$	78203.9	+	687323.i	0.0601475	+	0.528628i
$280$		0			0
$281$			841921.i			0.636071i	0.948079	+	0.318035i	$0.103023\pi$
$281$			841921.i			0.636071i	−0.948079	+	0.318035i	$0.896977\pi$
$282$	21793.5	+	384315.i	0.0163194	+	0.287783i
$283$			1.39274e6i			1.03373i	0.856068	+	0.516863i	$0.172900\pi$
$283$			1.39274e6i			1.03373i	−0.856068	+	0.516863i	$0.827100\pi$
$284$			1.13033e6i			0.831587i
$285$	181555.	+	3.20162e6i	0.132403	+	2.33484i
$286$		−	84844.2i		−	0.0613348i
$287$		0			0
$288$	−154678.	−	1.35944e6i	−0.109887	−	0.965782i
$289$	111574.			0.0785809
$290$	1.43832e6			1.00429
$291$	16451.9	+	290119.i	0.0113889	+	0.200837i
$292$			962628.i			0.660696i
$293$	−537097.			−0.365497			−0.182748	−	0.983160i	$-0.558499\pi$
$293$	−537097.			−0.365497			−0.182748	+	0.983160i	$0.558499\pi$
$294$		0			0
$295$	575764.			0.385203
$296$		−	1.45245e6i		−	0.963547i
$297$	25235.6	+	147065.i	0.0166006	+	0.0967427i
$298$	1.41040e6			0.920029
$299$	272990.			0.176591
$300$	696013.	−	39469.0i	0.446492	−	0.0253194i
$301$		0			0
$302$			1.01074e6i			0.637708i
$303$	2.65510e6	−	150563.i	1.66140	−	0.0942134i
$304$			221496.i			0.137462i
$305$			417523.i			0.256999i
$306$	124257.	+	1.09208e6i	0.0758610	+	0.666732i
$307$			511397.i			0.309679i	0.987940	+	0.154840i	$0.0494861\pi$
$307$			511397.i			0.309679i	−0.987940	+	0.154840i	$0.950514\pi$
$308$		0			0
$309$	51972.1	+	916497.i	0.0309652	+	0.546053i
$310$	−773342.			−0.457054
$311$	2.41299e6			1.41467			0.707335	−	0.706878i	$-0.249897\pi$
$311$	2.41299e6			1.41467			0.707335	+	0.706878i	$0.249897\pi$
$312$	−1.69756e6	+	96264.1i	−0.987278	+	0.0559858i
$313$		−	2.72163e6i		−	1.57025i	−0.619339	−	0.785124i	$-0.712599\pi$
$313$		−	2.72163e6i		−	1.57025i	0.619339	−	0.785124i	$-0.287401\pi$
$314$	1.38523e6			0.792862
$315$		0			0
$316$	1.25586e6			0.707495
$317$			1.65080e6i			0.922672i	0.887226	+	0.461336i	$0.152630\pi$
$317$			1.65080e6i			0.922672i	−0.887226	+	0.461336i	$0.847370\pi$
$318$	−910831.	+	51650.7i	−0.505091	+	0.0286424i
$319$	208561.			0.114751
$320$	1.71991e6			0.938925
$321$	−130250.	−	2.29689e6i	−0.0705532	−	1.24416i
$322$		0			0
$323$			3.42516e6i			1.82673i
$324$	1.07258e6	−	247277.i	0.567630	−	0.130865i
$325$		−	1.41377e6i		−	0.742455i
$326$			846190.i			0.440985i
$327$	407078.	−	23084.3i	0.210527	−	0.0119384i
$328$			2.25120e6i			1.15539i
$329$		0			0
$330$	−166545.	+	9444.31i	−0.0841873	+	0.00477403i
$331$	−2.62569e6			−1.31727			−0.658633	−	0.752464i	$-0.728865\pi$
$331$	−2.62569e6			−1.31727			−0.658633	+	0.752464i	$0.728865\pi$
$332$	162398.			0.0808605
$333$	1.89462e6	−	215571.i	0.936295	−	0.106532i
$334$		−	634912.i		−	0.311421i
$335$	957847.			0.466320
$336$		0			0
$337$	−3.01254e6			−1.44497			−0.722483	−	0.691388i	$-0.756999\pi$
$337$	−3.01254e6			−1.44497			−0.722483	+	0.691388i	$0.756999\pi$
$338$		−	87839.2i		−	0.0418212i
$339$	16851.9	+	297174.i	0.00796436	+	0.140447i
$340$	1.71451e6			0.804347
$341$	−112137.			−0.0522232
$342$	−2.44252e6	+	277911.i	−1.12921	+	0.128482i
$343$		0			0
$344$		−	990285.i		−	0.451195i
$345$	−30387.5	−	535866.i	−0.0137451	−	0.242386i
$346$		−	1.79284e6i		−	0.805101i
$347$		−	2.90956e6i		−	1.29719i	−0.761134	−	0.648595i	$-0.775357\pi$
$347$		−	2.90956e6i		−	1.29719i	0.761134	−	0.648595i	$-0.224643\pi$
$348$	−87103.7	−	1.53602e6i	−0.0385557	−	0.679907i
$349$		−	3.93286e6i		−	1.72840i	−0.503147	−	0.864201i	$-0.667824\pi$
$349$		−	3.93286e6i		−	1.72840i	0.503147	−	0.864201i	$-0.332176\pi$
$350$		0			0
$351$	−377520.	−	2.20007e6i	−0.163558	−	0.953165i
$352$	221793.			0.0954096
$353$	−1.93598e6			−0.826922			−0.413461	−	0.910522i	$-0.635680\pi$
$353$	−1.93598e6			−0.826922			−0.413461	+	0.910522i	$0.635680\pi$
$354$	24989.1	+	440669.i	0.0105985	+	0.186898i
$355$		−	4.50686e6i		−	1.89803i
$356$	337620.			0.141190
$357$		0			0
$358$	−2.34406e6			−0.966631
$359$		−	1.39251e6i		−	0.570247i	−0.958491	−	0.285123i	$-0.907965\pi$
$359$		−	1.39251e6i		−	0.570247i	0.958491	−	0.285123i	$-0.0920346\pi$
$360$	377924.	+	3.32152e6i	0.153691	+	1.35077i
$361$	−5.18454e6			−2.09383
$362$	−171565.			−0.0688111
$363$	2.48236e6	−	140768.i	0.988777	−	0.0560708i
$364$		0			0
$365$		−	3.83821e6i		−	1.50798i
$366$	−319557.	+	18121.2i	−0.124694	+	0.00707105i
$367$		−	985240.i		−	0.381836i	−0.981606	−	0.190918i	$-0.938854\pi$
$367$		−	985240.i		−	0.381836i	0.981606	−	0.190918i	$-0.0611465\pi$
$368$		−	37072.5i		−	0.0142703i
$369$	−2.93654e6	+	334120.i	−1.12272	+	0.127743i
$370$			2.13174e6i			0.809524i
$371$		0			0
$372$	46833.1	+	825875.i	0.0175467	+	0.309426i
$373$	2.51585e6			0.936296			0.468148	−	0.883650i	$-0.344921\pi$
$373$	2.51585e6			0.936296			0.468148	+	0.883650i	$0.344921\pi$
$374$	−178173.			−0.0658664
$375$	839667.	−	47615.2i	0.308339	−	0.0174851i
$376$			1.25049e6i			0.456154i
$377$	−3.12003e6			−1.13059
$378$		0			0
$379$	−627888.			−0.224535			−0.112268	−	0.993678i	$-0.535811\pi$
$379$	−627888.			−0.224535			−0.112268	+	0.993678i	$0.535811\pi$
$380$			3.83464e6i			1.36228i
$381$	−656437.	+	37224.8i	−0.231676	+	0.0131377i
$382$	2.78295e6			0.975770
$383$	−3.10523e6			−1.08167			−0.540837	−	0.841127i	$-0.681893\pi$
$383$	−3.10523e6			−1.08167			−0.540837	+	0.841127i	$0.681893\pi$
$384$	−84369.5	−	1.48781e6i	−0.0291983	−	0.514895i
$385$		0			0
$386$		−	2.03335e6i		−	0.694615i
$387$	1.29176e6	−	146977.i	0.438434	−	0.0498852i
$388$			347481.i			0.117180i
$389$			669791.i			0.224422i	0.993684	+	0.112211i	$0.0357932\pi$
$389$			669791.i			0.224422i	−0.993684	+	0.112211i	$0.964207\pi$
$390$	2.49148e6	−	141285.i	0.829462	−	0.0470365i
$391$		−	573281.i		−	0.189638i
$392$		0			0
$393$	4.40558e6	−	249828.i	1.43887	−	0.0815943i
$394$	−1.99527e6			−0.647533
$395$	−5.00740e6			−1.61480
$396$	20171.7	+	177286.i	0.00646405	+	0.0568117i
$397$			3.49472e6i			1.11285i	0.830898	+	0.556425i	$0.187827\pi$
$397$			3.49472e6i			1.11285i	−0.830898	+	0.556425i	$0.812173\pi$
$398$	−771949.			−0.244276
$399$		0			0
$400$	−191992.			−0.0599975
$401$		−	2.81146e6i		−	0.873115i	−0.899676	−	0.436558i	$-0.856198\pi$
$401$		−	2.81146e6i		−	0.873115i	0.899676	−	0.436558i	$-0.143802\pi$
$402$	41572.1	+	733101.i	0.0128303	+	0.226255i
$403$	1.67755e6			0.514532
$404$	3.18006e6			0.969353
$405$	−4.27660e6	+	985950.i	−1.29557	+	0.298688i
$406$		0			0
$407$			309109.i			0.0924965i
$408$	202155.	+	3.56489e6i	0.0601222	+	1.06022i
$409$		−	2.79035e6i		−	0.824803i	−0.911002	−	0.412402i	$-0.864690\pi$
$409$		−	2.79035e6i		−	0.824803i	0.911002	−	0.412402i	$-0.135310\pi$
$410$		−	3.30405e6i		−	0.970704i
$411$	232719.	+	4.10387e6i	0.0679560	+	1.19836i
$412$			1.09771e6i			0.318598i
$413$		0			0
$414$	408813.	−	46514.9i	0.117226	−	0.0133380i
$415$	−647518.			−0.184557
$416$	−3.31799e6			−0.940030
$417$	−321026.	−	5.66111e6i	−0.0904066	−	1.59427i
$418$		−	398499.i		−	0.111554i
$419$	3.40729e6			0.948144			0.474072	−	0.880486i	$-0.342784\pi$
$419$	3.40729e6			0.948144			0.474072	+	0.880486i	$0.342784\pi$
$420$		0			0
$421$	3.77099e6			1.03693			0.518465	−	0.855099i	$-0.326504\pi$
$421$	3.77099e6			1.03693			0.518465	+	0.855099i	$0.326504\pi$
$422$			2.45122e6i			0.670041i
$423$	−1.63118e6	+	185596.i	−0.443252	+	0.0504334i
$424$	−2.96368e6			−0.800601
$425$	−2.96892e6			−0.797309
$426$	3.44938e6	−	195605.i	0.920911	−	0.0522223i
$427$		0			0
$428$		−	2.75103e6i		−	0.725915i
$429$	361273.	−	20486.8i	0.0947746	−	0.00537441i
$430$			1.45342e6i			0.379071i
$431$		−	3.00701e6i		−	0.779726i	−0.920873	−	0.389863i	$-0.872522\pi$
$431$		−	3.00701e6i		−	0.779726i	0.920873	−	0.389863i	$-0.127478\pi$
$432$	−298773.	+	51267.8i	−0.0770249	+	0.0132171i
$433$			1.50880e6i			0.386734i	0.981126	+	0.193367i	$0.0619408\pi$
$433$			1.50880e6i			0.386734i	−0.981126	+	0.193367i	$0.938059\pi$
$434$		0			0
$435$	347302.	+	6.12447e6i	0.0880002	+	1.55183i
$436$	487565.			0.122833
$437$	1.28219e6			0.321179
$438$	2.93763e6	−	166585.i	0.731664	−	0.0414906i
$439$			1.97163e6i			0.488275i	0.969741	+	0.244138i	$0.0785049\pi$
$439$			1.97163e6i			0.488275i	−0.969741	+	0.244138i	$0.921495\pi$
$440$	−541907.			−0.133442
$441$		0			0
$442$	2.66544e6			0.648954
$443$		−	2.13681e6i		−	0.517316i	−0.965969	−	0.258658i	$-0.916720\pi$
$443$		−	2.13681e6i		−	0.517316i	0.965969	−	0.258658i	$-0.0832803\pi$
$444$	2.27655e6	−	129097.i	0.548049	−	0.0310784i
$445$	−1.34617e6			−0.322254
$446$	68455.3			0.0162956
$447$	340560.	+	6.00558e6i	0.0806167	+	1.42163i
$448$		0			0
$449$		−	5.91347e6i		−	1.38429i	−0.721759	−	0.692144i	$-0.756666\pi$
$449$		−	5.91347e6i		−	1.38429i	0.721759	−	0.692144i	$-0.243334\pi$
$450$	−240893.	−	2.11717e6i	−0.0560780	−	0.492862i
$451$		−	479098.i		−	0.110913i
$452$			355931.i			0.0819445i
$453$	−4.30380e6	+	244057.i	−0.985387	+	0.0558786i
$454$			1.63398e6i			0.372054i
$455$		0			0
$456$	−7.97316e6	+	452136.i	−1.79564	+	0.101826i
$457$	−7.51891e6			−1.68409			−0.842044	−	0.539410i	$-0.818647\pi$
$457$	−7.51891e6			−1.68409			−0.842044	+	0.539410i	$0.818647\pi$
$458$	80412.5			0.0179126
$459$	−4.62016e6	+	792795.i	−1.02359	+	0.175642i
$460$		−	641816.i		−	0.141422i
$461$	−929187.			−0.203634			−0.101817	−	0.994803i	$-0.532466\pi$
$461$	−929187.			−0.203634			−0.101817	+	0.994803i	$0.532466\pi$
$462$		0			0
$463$	1.21496e6			0.263396			0.131698	−	0.991290i	$-0.457957\pi$
$463$	1.21496e6			0.263396			0.131698	+	0.991290i	$0.457957\pi$
$464$			423705.i			0.0913627i
$465$	−186734.	−	3.29295e6i	−0.0400489	−	0.706240i
$466$	−1.94847e6			−0.415651
$467$	3.03117e6			0.643159			0.321580	−	0.946883i	$-0.395786\pi$
$467$	3.03117e6			0.643159			0.321580	+	0.946883i	$0.395786\pi$
$468$	−301765.	−	2.65217e6i	−0.0636876	−	0.559741i
$469$		0			0
$470$		−	1.83532e6i		−	0.383238i
$471$	334483.	+	5.89841e6i	0.0694739	+	1.22513i
$472$			1.43386e6i			0.296245i
$473$			210751.i			0.0433129i
$474$	−217329.	−	3.83248e6i	−0.0444296	−	0.783490i
$475$		−	6.64023e6i		−	1.35036i
$476$		0			0
$477$	−439865.	−	3.86591e6i	−0.0885164	−	0.777958i
$478$	−983457.			−0.196873
$479$	81905.2			0.0163107			0.00815535	−	0.999967i	$-0.497404\pi$
$479$	81905.2			0.0163107			0.00815535	+	0.999967i	$0.497404\pi$
$480$	369337.	+	6.51305e6i	0.0731678	+	1.29027i
$481$		−	4.62421e6i		−	0.911329i
$482$	−975255.			−0.191206
$483$		0			0
$484$	2.97317e6			0.576907
$485$		−	1.38549e6i		−	0.267453i
$486$	−940222.	−	3.23036e6i	−0.180567	−	0.620383i
$487$	4.41516e6			0.843575			0.421787	−	0.906695i	$-0.361403\pi$
$487$	4.41516e6			0.843575			0.421787	+	0.906695i	$0.361403\pi$
$488$	−1.03978e6			−0.197648
$489$	−3.60314e6	+	204324.i	−0.681410	+	0.0386409i
$490$		0			0
$491$			9.60786e6i			1.79855i	0.437381	+	0.899276i	$0.355906\pi$
$491$			9.60786e6i			1.79855i	−0.437381	+	0.899276i	$0.644094\pi$
$492$	−3.52849e6	+	200091.i	−0.657168	+	0.0372662i
$493$			6.55209e6i			1.21412i
$494$			5.96147e6i			1.09910i
$495$	−80429.1	−	706880.i	−0.0147537	−	0.129668i
$496$		−	227814.i		−	0.0415792i
$497$		0			0
$498$	−28103.4	−	495587.i	−0.00507791	−	0.0895460i
$499$	1.00695e7			1.81032			0.905160	−	0.425071i	$-0.139751\pi$
$499$	1.00695e7			1.81032			0.905160	+	0.425071i	$0.139751\pi$
$500$	1.00568e6			0.179902
$501$	2.70350e6	−	153308.i	0.481208	−	0.0272880i
$502$			3.46345e6i			0.613408i
$503$	2.68345e6			0.472904			0.236452	−	0.971643i	$-0.424015\pi$
$503$	2.68345e6			0.472904			0.236452	+	0.971643i	$0.424015\pi$
$504$		0			0
$505$	−1.26796e7			−2.21247
$506$			66698.0i			0.0115808i
$507$	374026.	−	21210.0i	0.0646222	−	0.00366455i
$508$	−786227.			−0.135173
$509$	7.51287e6			1.28532			0.642661	−	0.766151i	$-0.277831\pi$
$509$	7.51287e6			1.28532			0.642661	+	0.766151i	$0.277831\pi$
$510$	−296700.	−	5.23213e6i	−0.0505117	−	0.890745i
$511$		0			0
$512$			924585.i			0.155873i
$513$	−1.77315e6	−	1.03333e7i	−0.297475	−	1.73359i
$514$		−	1.92371e6i		−	0.321168i
$515$		−	4.37680e6i		−	0.727174i
$516$	1.55215e6	−	88018.4i	0.256632	−	0.0145529i
$517$		−	266128.i		−	0.0437889i
$518$		0			0
$519$	7.63403e6	−	432905.i	1.24404	−	0.0705463i
$520$	8.10683e6			1.31475
$521$	9.46018e6			1.52688			0.763440	−	0.645878i	$-0.223509\pi$
$521$	9.46018e6			1.52688			0.763440	+	0.645878i	$0.223509\pi$
$522$	−4.67237e6	+	531624.i	−0.750517	+	0.0853942i
$523$			1.32587e6i			0.211957i	0.994368	+	0.105979i	$0.0337975\pi$
$523$			1.32587e6i			0.211957i	−0.994368	+	0.105979i	$0.966202\pi$
$524$	5.27664e6			0.839517
$525$		0			0
$526$	4.99051e6			0.786466
$527$		−	3.52287e6i		−	0.552548i
$528$	−2782.14	−	49061.4i	−0.000434304	−	0.00765871i
$529$	6.22174e6			0.966657
$530$	4.34974e6			0.672626
$531$	−1.87037e6	+	212811.i	−0.287866	+	0.0327535i
$532$		0			0
$533$			7.16721e6i			1.09278i
$534$	−58425.9	−	1.03031e6i	−0.00886650	−	0.156356i
$535$			1.09690e7i			1.65684i
$536$			2.38538e6i			0.358629i
$537$	−566005.	−	9.98116e6i	−0.0847002	−	1.49364i
$538$		−	106833.i		−	0.0159130i
$539$		0			0
$540$	−5.17249e6	+	887573.i	−0.763335	+	0.130984i
$541$	6.92295e6			1.01695			0.508473	−	0.861078i	$-0.330210\pi$
$541$	6.92295e6			1.01695			0.508473	+	0.861078i	$0.330210\pi$
$542$	−1.54873e6			−0.226453
$543$	−41426.8	−	730538.i	−0.00602951	−	0.106327i
$544$			6.96780e6i			1.00948i
$545$	−1.94403e6			−0.280357
$546$		0			0
$547$	−9.97756e6			−1.42579			−0.712896	−	0.701270i	$-0.752617\pi$
$547$	−9.97756e6			−1.42579			−0.712896	+	0.701270i	$0.752617\pi$
$548$			4.91528e6i			0.699193i
$549$	−154323.	−	1.35632e6i	−0.0218524	−	0.192058i
$550$	345418.			0.0486898
$551$	−1.46542e7			−2.05629
$552$	1.33449e6	−	75675.5i	0.186410	−	0.0105708i
$553$		0			0
$554$			2.73025e6i			0.377944i
$555$	−9.07710e6	+	514738.i	−1.25088	+	0.0709338i
$556$		−	6.78041e6i		−	0.930185i
$557$			1.25386e7i			1.71242i	0.516628	+	0.856210i	$0.327187\pi$
$557$			1.25386e7i			1.71242i	−0.516628	+	0.856210i	$0.672813\pi$
$558$	2.51220e6	−	285839.i	0.341561	−	0.0388629i
$559$		−	3.15280e6i		−	0.426743i
$560$		0			0
$561$	−43022.4	−	758676.i	−0.00577149	−	0.101777i
$562$	3.07726e6			0.410982
$563$	6.87659e6			0.914329			0.457164	−	0.889382i	$-0.348865\pi$
$563$	6.87659e6			0.914329			0.457164	+	0.889382i	$0.348865\pi$
$564$	−1.96000e6	+	111146.i	−0.259452	+	0.0147128i
$565$		−	1.41918e6i		−	0.187032i
$566$	5.09055e6			0.667918
$567$		0			0
$568$	1.12237e7			1.45970
$569$			2.64936e6i			0.343053i	0.985180	+	0.171526i	$0.0548699\pi$
$569$			2.64936e6i			0.343053i	−0.985180	+	0.171526i	$0.945130\pi$
$570$	1.17021e7	−	663592.i	1.50860	−	0.0855488i
$571$	1.09557e6			0.140621			0.0703105	−	0.997525i	$-0.477601\pi$
$571$	1.09557e6			0.140621			0.0703105	+	0.997525i	$0.477601\pi$
$572$	432703.			0.0552968
$573$	671982.	+	1.18500e7i	0.0855009	+	1.50776i
$574$		0			0
$575$			1.11140e6i			0.140184i
$576$	−5.58712e6	+	635704.i	−0.701668	+	0.0798360i
$577$		−	2.90428e6i		−	0.363161i	−0.983376	−	0.181581i	$-0.941879\pi$
$577$		−	2.90428e6i		−	0.363161i	0.983376	−	0.181581i	$-0.0581214\pi$
$578$		−	407807.i		−	0.0507733i
$579$	8.65816e6	−	490980.i	1.07332	−	0.0608650i
$580$			7.33539e6i			0.905426i
$581$		0			0
$582$	1.06040e6	−	60132.3i	0.129766	−	0.00735869i
$583$	630726.			0.0768545
$584$	9.55850e6			1.15973
$585$	1.20321e6	+	1.05748e7i	0.145362	+	1.27756i
$586$			1.96311e6i			0.236157i
$587$	2.80932e6			0.336516			0.168258	−	0.985743i	$-0.446186\pi$
$587$	2.80932e6			0.336516			0.168258	+	0.985743i	$0.446186\pi$
$588$		0			0
$589$	7.87916e6			0.935819
$590$		−	2.10444e6i		−	0.248890i
$591$	−481786.	−	8.49602e6i	−0.0567395	−	1.00057i
$592$	−627976.			−0.0736442
$593$	471223.			0.0550288			0.0275144	−	0.999621i	$-0.491241\pi$
$593$	471223.			0.0550288			0.0275144	+	0.999621i	$0.491241\pi$
$594$	537529.	−	92237.3i	0.0625081	−	0.0107261i
$595$		0			0
$596$			7.19300e6i			0.829458i
$597$	−186398.	−	3.28701e6i	−0.0214045	−	0.377455i
$598$		−	997791.i		−	0.114100i
$599$			1.73472e6i			0.197544i	0.995110	+	0.0987719i	$0.0314914\pi$
$599$			1.73472e6i			0.197544i	−0.995110	+	0.0987719i	$0.968509\pi$
$600$	−391911.	−	6.91112e6i	−0.0444436	−	0.783737i
$601$			3.42903e6i			0.387244i	0.981076	+	0.193622i	$0.0620235\pi$
$601$			3.42903e6i			0.387244i	−0.981076	+	0.193622i	$0.937976\pi$
$602$		0			0
$603$	−3.11156e6	+	354034.i	−0.348486	+	0.0396508i
$604$	−5.15475e6			−0.574930
$605$	−1.18547e7			−1.31674
$606$	−550316.	−	9.70451e6i	−0.0608738	−	1.07347i
$607$			9.81466e6i			1.08119i	0.841282	+	0.540597i	$0.181802\pi$
$607$			9.81466e6i			1.08119i	−0.841282	+	0.540597i	$0.818198\pi$
$608$	−1.55840e7			−1.70970
$609$		0			0
$610$	1.52607e6			0.166054
$611$			3.98122e6i			0.431433i
$612$	−5.56958e6	+	633709.i	−0.601096	+	0.0683930i
$613$	−2.75780e6			−0.296422			−0.148211	−	0.988956i	$-0.547352\pi$
$613$	−2.75780e6			−0.296422			−0.148211	+	0.988956i	$0.547352\pi$
$614$	1.86918e6			0.200092
$615$	1.40689e7	−	797808.i	1.49993	−	0.0850571i
$616$		0			0
$617$		−	5.46419e6i		−	0.577847i	−0.957352	−	0.288923i	$-0.906703\pi$
$617$		−	5.46419e6i		−	0.577847i	0.957352	−	0.288923i	$-0.0932973\pi$
$618$	3.34984e6	−	189960.i	0.352820	−	0.0200074i
$619$			4.24390e6i			0.445183i	0.974912	+	0.222591i	$0.0714516\pi$
$619$			4.24390e6i			0.445183i	−0.974912	+	0.222591i	$0.928548\pi$
$620$		−	3.94402e6i		−	0.412060i
$621$	296777.	+	1.72952e6i	0.0308817	+	0.179969i
$622$		−	8.81960e6i		−	0.914057i
$623$		0			0
$624$	41620.3	+	733950.i	0.00427901	+	0.0754580i
$625$	−1.15071e7			−1.17833
$626$	−9.94768e6			−1.01458
$627$	1.69684e6	−	96222.9i	0.172374	−	0.00977484i
$628$			7.06464e6i			0.714810i
$629$	−9.71088e6			−0.978660
$630$		0			0
$631$	1.97794e6			0.197761			0.0988804	−	0.995099i	$-0.468474\pi$
$631$	1.97794e6			0.197761			0.0988804	+	0.995099i	$0.468474\pi$
$632$		−	1.24702e7i		−	1.24188i
$633$	−1.04375e7	+	591881.i	−1.03535	+	0.0587118i
$634$	6.03376e6			0.596163
$635$	3.13486e6			0.308521
$636$	−263417.	−	4.64521e6i	−0.0258227	−	0.455368i
$637$		0			0
$638$		−	762299.i		−	0.0741436i
$639$	1.66580e6	+	1.46405e7i	0.161388	+	1.41842i
$640$			7.10513e6i			0.685681i
$641$		−	6.87312e6i		−	0.660707i	−0.943857	−	0.330353i	$-0.892832\pi$
$641$		−	6.87312e6i		−	0.660707i	0.943857	−	0.330353i	$-0.107168\pi$
$642$	−8.39524e6	+	476071.i	−0.803888	+	0.0455863i
$643$		−	4.81869e6i		−	0.459623i	−0.973235	−	0.229811i	$-0.926189\pi$
$643$		−	4.81869e6i		−	0.459623i	0.973235	−	0.229811i	$-0.0738109\pi$
$644$		0			0
$645$	−6.18878e6	+	350949.i	−0.585742	+	0.0332158i
$646$	1.25191e7			1.18030
$647$	7.50407e6			0.704752			0.352376	−	0.935859i	$-0.385374\pi$
$647$	7.50407e6			0.704752			0.352376	+	0.935859i	$0.385374\pi$
$648$	−2.45536e6	−	1.06502e7i	−0.229709	−	0.996372i
$649$		−	305151.i		−	0.0284383i
$650$	−5.16739e6			−0.479720
$651$		0			0
$652$	−4.31554e6			−0.397573
$653$		−	1.40288e7i		−	1.28747i	−0.765248	−	0.643735i	$-0.777384\pi$
$653$		−	1.40288e7i		−	1.28747i	0.765248	−	0.643735i	$-0.222616\pi$
$654$	−84374.1	−	1.48789e6i	−0.00771374	−	0.136027i
$655$	−2.10391e7			−1.91613
$656$	973319.			0.0883071
$657$	1.41866e6	+	1.24684e7i	0.128223	+	1.12693i
$658$		0			0
$659$		−	4.93455e6i		−	0.442623i	−0.975203	−	0.221311i	$-0.928966\pi$
$659$		−	4.93455e6i		−	0.442623i	0.975203	−	0.221311i	$-0.0710337\pi$
$660$	−48165.7	−	849375.i	−0.00430406	−	0.0758996i
$661$			1.83713e7i			1.63544i	0.575615	+	0.817721i	$0.304763\pi$
$661$			1.83713e7i			1.63544i	−0.575615	+	0.817721i	$0.695237\pi$
$662$			9.59702e6i			0.851121i
$663$	643608.	+	1.13496e7i	0.0568640	+	1.00276i
$664$		−	1.61255e6i		−	0.141936i
$665$		0			0
$666$	−787923.	−	6.92494e6i	−0.0688332	−	0.604965i
$667$	2.45273e6			0.213469
$668$	3.23804e6			0.280763
$669$	16529.5	+	291488.i	0.00142789	+	0.0251800i
$670$		−	3.50097e6i		−	0.301302i
$671$	221284.			0.0189734
$672$		0			0
$673$	5.27763e6			0.449160			0.224580	−	0.974456i	$-0.427899\pi$
$673$	5.27763e6			0.449160			0.224580	+	0.974456i	$0.427899\pi$
$674$			1.10110e7i			0.933632i
$675$	8.95691e6	−	1.53696e6i	0.756657	−	0.129838i
$676$	447978.			0.0377042
$677$	−1.37062e7			−1.14933			−0.574666	−	0.818388i	$-0.694868\pi$
$677$	−1.37062e7			−1.14933			−0.574666	+	0.818388i	$0.694868\pi$
$678$	1.08619e6	−	61594.6i	0.0907465	−	0.00514599i
$679$		0			0
$680$		−	1.70244e7i		−	1.41189i
$681$	−6.95759e6	+	394546.i	−0.574899	+	0.0326009i
$682$			409866.i			0.0337428i
$683$		−	1.56582e7i		−	1.28437i	−0.766549	−	0.642186i	$-0.778028\pi$
$683$		−	1.56582e7i		−	1.28437i	0.766549	−	0.642186i	$-0.221972\pi$
$684$	−1.41734e6	−	1.24568e7i	−0.115833	−	1.01804i
$685$		−	1.95983e7i		−	1.59585i
$686$		0			0
$687$	19416.7	+	342402.i	0.00156958	+	0.0276786i
$688$	−428155.			−0.0344850
$689$	−9.43554e6			−0.757214
$690$	−1.95861e6	+	111068.i	−0.156612	+	0.00888106i
$691$		−	4.22151e6i		−	0.336336i	−0.985758	−	0.168168i	$-0.946215\pi$
$691$		−	4.22151e6i		−	0.336336i	0.985758	−	0.168168i	$-0.0537850\pi$
$692$	9.14342e6			0.725844
$693$		0			0
$694$	−1.06346e7			−0.838150
$695$			2.70350e7i			2.12307i
$696$	−1.52521e7	+	864904.i	−1.19345	+	0.0676776i
$697$	1.50512e7			1.17352
$698$	−1.43748e7			−1.11677
$699$	−470485.	−	8.29673e6i	−0.0364211	−	0.642264i
$700$		0			0
$701$		−	2.08992e7i		−	1.60633i	−0.595758	−	0.803164i	$-0.703148\pi$
$701$		−	2.08992e7i		−	1.60633i	0.595758	−	0.803164i	$-0.296852\pi$
$702$	−8.04134e6	+	1.37985e6i	−0.615865	+	0.105679i
$703$		−	2.17191e7i		−	1.65750i
$704$		−	911541.i		−	0.0693177i
$705$	7.81495e6	−	443164.i	0.592179	−	0.0335809i
$706$			7.07610e6i			0.534297i
$707$		0			0
$708$	−2.24740e6	+	127444.i	−0.168499	+	0.00955511i
$709$	2.06100e6			0.153979			0.0769895	−	0.997032i	$-0.475469\pi$
$709$	2.06100e6			0.153979			0.0769895	+	0.997032i	$0.475469\pi$
$710$	−1.64728e7			−1.22637
$711$	1.62665e7	−	1.85081e6i	1.20676	−	0.137305i
$712$		−	3.35243e6i		−	0.247833i
$713$	−1.31876e6			−0.0971499
$714$		0			0
$715$	−1.72528e6			−0.126210
$716$		−	1.19546e7i		−	0.871472i
$717$	−237469.	−	4.18763e6i	−0.0172508	−	0.304208i
$718$	−5.08970e6			−0.368452
$719$	2.24934e7			1.62268			0.811339	−	0.584575i	$-0.198739\pi$
$719$	2.24934e7			1.62268			0.811339	+	0.584575i	$0.198739\pi$
$720$	1.43607e6	−	163397.i	0.103239	−	0.0117466i
$721$		0			0
$722$			1.89497e7i			1.35288i
$723$	−235489.	−	4.15271e6i	−0.0167542	−	0.295451i
$724$		−	874979.i		−	0.0620370i
$725$		−	1.27023e7i		−	0.897504i
$726$	−514513.	−	9.07314e6i	−0.0362289	−	0.638875i
$727$			2.23831e7i			1.57067i	0.619073	+	0.785334i	$0.287509\pi$
$727$			2.23831e7i			1.57067i	−0.619073	+	0.785334i	$0.712491\pi$
$728$		0			0
$729$	1.35281e7	−	4.78355e6i	0.942795	−	0.333374i
$730$	−1.40288e7			−0.974350
$731$	−6.62090e6			−0.458272
$732$	−92417.6	−	1.62973e6i	−0.00637495	−	0.112419i
$733$		−	1.24379e7i		−	0.855040i	−0.904006	−	0.427520i	$-0.859387\pi$
$733$		−	1.24379e7i		−	0.855040i	0.904006	−	0.427520i	$-0.140613\pi$
$734$	−3.60110e6			−0.246715
$735$		0			0
$736$	2.60835e6			0.177489
$737$		−	507652.i		−	0.0344269i
$738$	1.22123e6	+	1.07332e7i	0.0825382	+	0.725417i
$739$	−1.34548e7			−0.906291			−0.453145	−	0.891437i	$-0.649698\pi$
$739$	−1.34548e7			−0.906291			−0.453145	+	0.891437i	$0.649698\pi$
$740$	−1.08718e7			−0.729832
$741$	−2.53844e7	+	1.43948e6i	−1.69832	+	0.0963073i
$742$		0			0
$743$			1.80287e7i			1.19810i	0.800713	+	0.599049i	$0.204454\pi$
$743$			1.80287e7i			1.19810i	−0.800713	+	0.599049i	$0.795546\pi$
$744$	8.20060e6	−	465034.i	0.543142	−	0.0308001i
$745$		−	2.86801e7i		−	1.89317i
$746$		−	9.19556e6i		−	0.604966i
$747$	2.10346e6	−	239332.i	0.137922	−	0.0156928i
$748$		−	908680.i		−	0.0593823i
$749$		0			0
$750$	−174036.	−	3.06902e6i	−0.0112976	−	0.199226i
$751$	8.24075e6			0.533171			0.266586	−	0.963811i	$-0.414105\pi$
$751$	8.24075e6			0.533171			0.266586	+	0.963811i	$0.414105\pi$
$752$	540657.			0.0348640
$753$	−1.47476e7	+	836297.i	−0.947838	+	0.0537493i
$754$			1.14039e7i			0.730505i
$755$	2.05531e7			1.31223
$756$		0			0
$757$	−1.17983e7			−0.748308			−0.374154	−	0.927367i	$-0.622067\pi$
$757$	−1.17983e7			−0.748308			−0.374154	+	0.927367i	$0.622067\pi$
$758$			2.29496e6i			0.145078i
$759$	−284005.	+	16105.2i	−0.0178946	+	0.00101475i
$760$	3.80764e7			2.39123
$761$	1.22420e7			0.766286			0.383143	−	0.923689i	$-0.374842\pi$
$761$	1.22420e7			0.766286			0.383143	+	0.923689i	$0.374842\pi$
$762$	136058.	+	2.39931e6i	0.00848862	+	0.149692i
$763$		0			0
$764$			1.41930e7i			0.879711i
$765$	2.22072e7	−	2.52674e6i	1.37195	−	0.156101i
$766$			1.13498e7i			0.698899i
$767$			4.56500e6i			0.280190i
$768$	−1.69627e7	+	961910.i	−1.03775	+	0.0588479i
$769$			2.89879e6i			0.176767i	0.996087	+	0.0883834i	$0.0281701\pi$
$769$			2.89879e6i			0.176767i	−0.996087	+	0.0883834i	$0.971830\pi$
$770$		0			0
$771$	8.19131e6	−	464507.i	0.496269	−	0.0281421i
$772$	1.03700e7			0.626234
$773$	−3.49988e6			−0.210671			−0.105336	−	0.994437i	$-0.533592\pi$
$773$	−3.49988e6			−0.210671			−0.105336	+	0.994437i	$0.533592\pi$
$774$	−537207.	−	4.72144e6i	−0.0322322	−	0.283284i
$775$			6.82964e6i			0.408455i
$776$	3.45035e6			0.205688
$777$		0			0
$778$	2.44812e6			0.145005
$779$			3.36632e7i			1.98752i
$780$	720551.	+	1.27065e7i	0.0424061	+	0.747807i
$781$	−2.38860e6			−0.140125
$782$	−2.09537e6			−0.122530
$783$	−3.39190e6	−	1.97669e7i	−0.197715	−	1.15222i
$784$		0			0
$785$		−	2.81683e7i		−	1.63150i
$786$	−913134.	−	1.61026e7i	−0.0527203	−	0.929692i
$787$			2.48618e7i			1.43086i	0.698685	+	0.715429i	$0.253769\pi$
$787$			2.48618e7i			1.43086i	−0.698685	+	0.715429i	$0.746231\pi$
$788$		−	1.01758e7i		−	0.583788i
$789$	1.20503e6	+	2.12499e7i	0.0689134	+	1.21525i
$790$			1.83023e7i			1.04337i
$791$		0			0
$792$	1.76038e6	−	200297.i	0.0997226	−	0.0113465i
$793$	−3.31037e6			−0.186936
$794$	1.27734e7			0.719043
$795$	1.05030e6	+	1.85215e7i	0.0589382	+	1.03934i
$796$		−	3.93692e6i		−	0.220229i
$797$	4.51523e6			0.251787			0.125894	−	0.992044i	$-0.459820\pi$
$797$	4.51523e6			0.251787			0.125894	+	0.992044i	$0.459820\pi$
$798$		0			0
$799$	8.36060e6			0.463309
$800$		−	1.35082e7i		−	0.746230i
$801$	4.37301e6	−	497563.i	0.240824	−	0.0274010i
$802$	−1.02760e7			−0.564143
$803$	−2.03423e6			−0.111330
$804$	−3.73879e6	+	212017.i	−0.203982	+	0.0115673i
$805$		0			0
$806$		−	6.13152e6i		−	0.332453i
$807$	454905.	−	25796.4i	0.0245888	−	0.00139436i
$808$		−	3.15767e7i		−	1.70152i
$809$			3.23092e7i			1.73562i	0.496894	+	0.867811i	$0.334474\pi$
$809$			3.23092e7i			1.73562i	−0.496894	+	0.867811i	$0.665526\pi$
$810$	3.60369e6	+	1.56312e7i	0.192990	+	0.837103i
$811$		−	1.64891e7i		−	0.880329i	−0.897917	−	0.440164i	$-0.854920\pi$
$811$		−	1.64891e7i		−	0.880329i	0.897917	−	0.440164i	$-0.145080\pi$
$812$		0			0
$813$	−373962.	−	6.59461e6i	−0.0198427	−	0.349915i
$814$	1.12981e6			0.0597645
$815$	1.72070e7			0.907428
$816$	1.54130e6	−	87403.0i	0.0810330	−	0.00459516i
$817$		−	1.48081e7i		−	0.776150i
$818$	−1.01989e7			−0.532928
$819$		0			0
$820$	1.68506e7			0.875145
$821$		−	1.74100e7i		−	0.901449i	−0.892663	−	0.450724i	$-0.851166\pi$
$821$		−	1.74100e7i		−	0.901449i	0.892663	−	0.450724i	$-0.148834\pi$
$822$	1.49998e7	−	850599.i	0.774296	−	0.0439082i
$823$	1.58051e7			0.813387			0.406693	−	0.913565i	$-0.366682\pi$
$823$	1.58051e7			0.813387			0.406693	+	0.913565i	$0.366682\pi$
$824$	1.08998e7			0.559241
$825$	83405.9	+	1.47081e6i	0.00426640	+	0.0752355i
$826$		0			0
$827$			7.08010e6i			0.359978i	0.983669	+	0.179989i	$0.0576061\pi$
$827$			7.08010e6i			0.359978i	−0.983669	+	0.179989i	$0.942394\pi$
$828$	237225.	+	2.08494e6i	0.0120250	+	0.105686i
$829$			215839.i			0.0109080i	0.999985	+	0.00545399i	$0.00173607\pi$
$829$			215839.i			0.0109080i	−0.999985	+	0.00545399i	$0.998264\pi$
$830$			2.36671e6i			0.119248i
$831$	−1.16256e7	+	659256.i	−0.584000	+	0.0331170i
$832$			1.36365e7i			0.682958i
$833$		0			0
$834$	−2.06916e7	+	1.17336e6i	−1.03010	+	0.0584141i
$835$	−1.29108e7			−0.640820
$836$	2.03233e6			0.100572
$837$	1.82373e6	+	1.06281e7i	0.0899800	+	0.524375i
$838$		−	1.24538e7i		−	0.612621i
$839$	2.60061e7			1.27547			0.637735	−	0.770256i	$-0.279871\pi$
$839$	2.60061e7			1.27547			0.637735	+	0.770256i	$0.279871\pi$
$840$		0			0
$841$	−7.52137e6			−0.366697
$842$		−	1.37831e7i		−	0.669989i
$843$	743046.	+	1.31032e7i	0.0360120	+	0.635050i
$844$	−1.25012e7			−0.604080
$845$	−1.78619e6			−0.0860568
$846$	678363.	+	5.96204e6i	0.0325864	+	0.286397i
$847$		0			0
$848$			1.28136e6i			0.0611902i
$849$	1.22918e6	+	2.16759e7i	0.0585257	+	1.03207i
$850$			1.08516e7i			0.515163i
$851$			3.63520e6i			0.172070i
$852$	997581.	+	1.75918e7i	0.0470814	+	0.830253i
$853$		−	2.81393e7i		−	1.32416i	−0.749433	−	0.662080i	$-0.769674\pi$
$853$		−	2.81393e7i		−	1.32416i	0.749433	−	0.662080i	$-0.230326\pi$
$854$		0			0
$855$	5.65125e6	+	4.96680e7i	0.264380	+	2.32360i
$856$	−2.73166e7			−1.27421
$857$	−1.72530e6			−0.0802440			−0.0401220	−	0.999195i	$-0.512775\pi$
$857$	−1.72530e6			−0.0802440			−0.0401220	+	0.999195i	$0.512775\pi$
$858$	−74880.2	−	1.32047e6i	−0.00347255	−	0.0612364i
$859$		−	3.93753e7i		−	1.82071i	−0.413829	−	0.910354i	$-0.635809\pi$
$859$		−	3.93753e7i		−	1.82071i	0.413829	−	0.910354i	$-0.364191\pi$
$860$	−7.41242e6			−0.341754
$861$		0			0
$862$	−1.09908e7			−0.503802
$863$		−	3.69584e7i		−	1.68922i	−0.535382	−	0.844610i	$-0.679832\pi$
$863$		−	3.69584e7i		−	1.68922i	0.535382	−	0.844610i	$-0.320168\pi$
$864$	−3.60711e6	−	2.10211e7i	−0.164390	−	0.958012i
$865$	−3.64569e7			−1.65668
$866$	5.51474e6			0.249879
$867$	1.73647e6	−	98470.6i	0.0784549	−	0.00444896i
$868$		0			0
$869$			2.65389e6i			0.119215i
$870$	2.23852e7	−	1.26940e6i	1.00268	−	0.0568593i
$871$			7.59439e6i			0.339193i
$872$		−	4.84132e6i		−	0.215612i
$873$	512096.	+	4.50074e6i	0.0227413	+	0.199870i
$874$		−	4.68645e6i		−	0.207523i
$875$		0			0
$876$	849578.	+	1.49818e7i	0.0374062	+	0.659636i
$877$	−3.48022e7			−1.52795			−0.763973	−	0.645248i	$-0.776754\pi$
$877$	−3.48022e7			−1.52795			−0.763973	+	0.645248i	$0.776754\pi$
$878$	7.20641e6			0.315488
$879$	−8.35909e6	+	474021.i	−0.364911	+	0.0206931i
$880$			234296.i			0.0101990i
$881$	−2.98621e7			−1.29623			−0.648114	−	0.761544i	$-0.724442\pi$
$881$	−2.98621e7			−1.29623			−0.648114	+	0.761544i	$0.724442\pi$
$882$		0			0
$883$	−3.38129e7			−1.45942			−0.729710	−	0.683757i	$-0.760345\pi$
$883$	−3.38129e7			−1.45942			−0.729710	+	0.683757i	$0.760345\pi$
$884$			1.35937e7i			0.585068i
$885$	8.96088e6	−	508147.i	0.384585	−	0.0218088i
$886$	−7.81013e6			−0.334252
$887$	3.00116e7			1.28080			0.640398	−	0.768044i	$-0.278770\pi$
$887$	3.00116e7			1.28080			0.640398	+	0.768044i	$0.278770\pi$
$888$	−1.28188e6	−	2.26052e7i	−0.0545525	−	0.962001i
$889$		0			0
$890$			4.92030e6i			0.208217i
$891$	522547.	+	2.26657e6i	0.0220511	+	0.0956477i
$892$			349120.i			0.0146914i
$893$			1.86991e7i			0.784680i
$894$	2.19507e7	−	1.24476e6i	0.918553	−	0.0520886i
$895$			4.76658e7i			1.98906i
$896$		0			0
$897$	4.24866e6	−	240930.i	0.176308	−	0.00999793i
$898$	−2.16140e7			−0.894426
$899$	1.50723e7			0.621984
$900$	1.07975e7	−	1.22855e6i	0.444343	−	0.0505575i
$901$			1.98147e7i			0.813159i
$902$	−1.75112e6			−0.0716639
$903$		0			0
$904$	3.53425e6			0.143839
$905$			3.48874e6i			0.141595i
$906$	892039.	+	1.57306e7i	0.0361047	+	0.636685i
$907$	1.06507e7			0.429892			0.214946	−	0.976626i	$-0.431042\pi$
$907$	1.06507e7			0.429892			0.214946	+	0.976626i	$0.431042\pi$
$908$	−8.33324e6			−0.335428
$909$	4.11896e7	−	4.68657e6i	1.65340	−	0.188125i
$910$		0			0
$911$			1.33185e7i			0.531690i	0.964016	+	0.265845i	$0.0856509\pi$
$911$			1.33185e7i			0.531690i	−0.964016	+	0.265845i	$0.914349\pi$
$912$	195483.	+	3.44724e6i	0.00778257	+	0.137241i
$913$			343180.i			0.0136253i
$914$			2.74820e7i			1.08813i
$915$	368489.	+	6.49810e6i	0.0145503	+	0.256586i
$916$			410101.i			0.0161493i
$917$		0			0
$918$	2.89770e6	+	1.68869e7i	0.113487	+	0.661367i
$919$	1.18307e6			0.0462086			0.0231043	−	0.999733i	$-0.492645\pi$
$919$	1.18307e6			0.0462086			0.0231043	+	0.999733i	$0.492645\pi$
$920$	−6.37297e6			−0.248240
$921$	451339.	+	7.95910e6i	0.0175329	+	0.309182i
$922$			3.39622e6i			0.131574i
$923$	3.57331e7			1.38059
$924$		0			0
$925$	1.88261e7			0.723446
$926$		−	4.44073e6i		−	0.170187i
$927$	1.61773e6	+	1.42180e7i	0.0618310	+	0.543424i
$928$	−2.98111e7			−1.13634
$929$	9.48459e6			0.360561			0.180281	−	0.983615i	$-0.442299\pi$
$929$	9.48459e6			0.360561			0.180281	+	0.983615i	$0.442299\pi$
$930$	−1.20359e7	+	682522.i	−0.456321	+	0.0258767i
$931$		0			0
$932$		−	9.93714e6i		−	0.374733i
$933$	3.75545e7	−	2.12961e6i	1.41240	−	0.0800934i
$934$		−	1.10791e7i		−	0.415563i
$935$			3.62311e6i			0.135535i
$936$	−2.63350e7	+	2.99640e6i	−0.982524	+	0.111792i
$937$		−	1.67626e7i		−	0.623723i	−0.950128	−	0.311861i	$-0.899048\pi$
$937$		−	1.67626e7i		−	0.623723i	0.950128	−	0.311861i	$-0.100952\pi$
$938$		0			0
$939$	−2.40200e6	−	4.23580e7i	−0.0889016	−	1.56773i
$940$	9.36011e6			0.345510
$941$	4.11603e7			1.51532			0.757660	−	0.652650i	$-0.226343\pi$
$941$	4.11603e7			1.51532			0.757660	+	0.652650i	$0.226343\pi$
$942$	2.15590e7	−	1.22255e6i	0.791591	−	0.0448889i
$943$		−	5.63432e6i		−	0.206330i
$944$	619935.			0.0226421
$945$		0			0
$946$	770305.			0.0279856
$947$			2.24751e7i			0.814381i	0.913343	+	0.407190i	$0.133491\pi$
$947$			2.24751e7i			0.814381i	−0.913343	+	0.407190i	$0.866509\pi$
$948$	1.95455e7	−	1.10837e6i	0.706361	−	0.0400558i
$949$	3.04317e7			1.09688
$950$	−2.42703e7			−0.872503
$951$	1.45693e6	+	2.56922e7i	0.0522383	+	0.921192i
$952$		0			0
$953$			3.77762e6i			0.134737i	0.997728	+	0.0673683i	$0.0214603\pi$
$953$			3.77762e6i			0.134737i	−0.997728	+	0.0673683i	$0.978540\pi$
$954$	−1.41301e7	+	1.60773e6i	−0.502660	+	0.0571928i
$955$		−	5.65906e7i		−	2.00787i
$956$		−	5.01561e6i		−	0.177492i
$957$	3.24593e6	−	184068.i	0.114567	−	0.00649677i
$958$		−	299367.i		−	0.0105388i
$959$		0			0
$960$	2.67677e7	−	1.51793e6i	0.937419	−	0.0531585i
$961$	2.05252e7			0.716935
$962$	−1.69017e7			−0.588834
$963$	−4.05429e6	−	3.56326e7i	−0.140880	−	1.23817i
$964$		−	4.97378e6i		−	0.172383i
$965$	−4.13476e7			−1.42933
$966$		0			0
$967$	3.72823e7			1.28214			0.641072	−	0.767481i	$-0.278490\pi$
$967$	3.72823e7			1.28214			0.641072	+	0.767481i	$0.278490\pi$
$968$		−	2.95223e7i		−	1.01266i
$969$	3.02291e6	+	5.33073e7i	0.103423	+	1.82380i
$970$	−5.06401e6			−0.172809
$971$	−3.79173e7			−1.29059			−0.645296	−	0.763932i	$-0.723266\pi$
$971$	−3.79173e7			−1.29059			−0.645296	+	0.763932i	$0.723266\pi$
$972$	1.64747e7	−	4.79510e6i	0.559311	−	0.162792i
$973$		0			0
$974$		−	1.61376e7i		−	0.545056i
$975$	−1.24774e6	−	2.20031e7i	−0.0420350	−	0.741264i
$976$			449554.i			0.0151063i
$977$		−	2.56335e7i		−	0.859154i	−0.903030	−	0.429577i	$-0.858663\pi$
$977$		−	2.56335e7i		−	0.859154i	0.903030	−	0.429577i	$-0.141337\pi$
$978$	746814.	+	1.31696e7i	0.0249669	+	0.440278i
$979$			713459.i			0.0237910i
$980$		0			0
$981$	6.31517e6	−	718542.i	0.209514	−	0.0238385i
$982$	3.51172e7			1.16209
$983$	−3.49327e7			−1.15305			−0.576526	−	0.817079i	$-0.695592\pi$
$983$	−3.49327e7			−1.15305			−0.576526	+	0.817079i	$0.695592\pi$
$984$	1.98682e6	+	3.50365e7i	0.0654141	+	1.15354i
$985$			4.05733e7i			1.33245i
$986$	2.39482e7			0.784477
$987$		0			0
$988$	−3.04033e7			−0.990897
$989$			2.47849e6i			0.0805742i
$990$	−2.58368e6	+	293972.i	−0.0837820	+	0.00953275i
$991$	4.96071e7			1.60457			0.802286	−	0.596940i	$-0.203617\pi$
$991$	4.96071e7			1.60457			0.802286	+	0.596940i	$0.203617\pi$
$992$	1.60286e7			0.517149
$993$	−4.08648e7	+	2.31733e6i	−1.31515	+	0.0745787i
$994$		0			0
$995$			1.56974e7i			0.502654i
$996$	2.52748e6	−	143326.i	0.0807308	−	0.00457802i
$997$		−	9.02979e6i		−	0.287700i	−0.989600	−	0.143850i	$-0.954052\pi$
$997$		−	9.02979e6i		−	0.287700i	0.989600	−	0.143850i	$-0.0459483\pi$
$998$		−	3.68044e7i		−	1.16970i
$999$	2.92966e7	−	5.02715e6i	0.928761	−	0.159371i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	147.6.c.c.146.6		16
3.2	odd	2	inner	147.6.c.c.146.11		16
7.4	even	3		21.6.g.c.5.6	yes	16
7.5	odd	6		21.6.g.c.17.3	yes	16
7.6	odd	2	inner	147.6.c.c.146.5		16
21.5	even	6		21.6.g.c.17.6	yes	16
21.11	odd	6		21.6.g.c.5.3	✓	16
21.20	even	2	inner	147.6.c.c.146.12		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
21.6.g.c.5.3	✓	16	21.11	odd	6
21.6.g.c.5.6	yes	16	7.4	even	3
21.6.g.c.17.3	yes	16	7.5	odd	6
21.6.g.c.17.6	yes	16	21.5	even	6
147.6.c.c.146.5		16	7.6	odd	2	inner
147.6.c.c.146.6		16	1.1	even	1	trivial
147.6.c.c.146.11		16	3.2	odd	2	inner
147.6.c.c.146.12		16	21.20	even	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:	\( N \)	\(=\)	\( 147 = 3 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	147.c (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-3.65505i q^{2} +(15.5635 - 0.882561i) q^{3} +18.6406 q^{4} -74.3244 q^{5} +(-3.22580 - 56.8851i) q^{6} -185.094i q^{8} +(241.442 - 27.4714i) q^{9} +O(q^{10})\)	\(q-3.65505i q^{2} +(15.5635 - 0.882561i) q^{3} +18.6406 q^{4} -74.3244 q^{5} +(-3.22580 - 56.8851i) q^{6} -185.094i q^{8} +(241.442 - 27.4714i) q^{9} +271.659i q^{10} +39.3914i q^{11} +(290.113 - 16.4515i) q^{12} -589.288i q^{13} +(-1156.74 + 65.5958i) q^{15} -80.0263 q^{16} -1237.51 q^{17} +(-100.409 - 882.482i) q^{18} -2767.79i q^{19} -1385.45 q^{20} +143.977 q^{22} +463.253i q^{23} +(-163.357 - 2880.70i) q^{24} +2399.11 q^{25} -2153.88 q^{26} +(3733.43 - 640.637i) q^{27} -5294.57i q^{29} +(239.756 + 4227.95i) q^{30} +2846.74i q^{31} -5630.50i q^{32} +(34.7653 + 613.066i) q^{33} +4523.16i q^{34} +(4500.64 - 512.084i) q^{36} +7847.11 q^{37} -10116.4 q^{38} +(-520.083 - 9171.36i) q^{39} +13757.0i q^{40} -12162.5 q^{41} +5350.18 q^{43} +734.281i q^{44} +(-17945.0 + 2041.79i) q^{45} +1693.21 q^{46} -6755.99 q^{47} +(-1245.49 + 70.6281i) q^{48} -8768.86i q^{50} +(-19259.9 + 1092.18i) q^{51} -10984.7i q^{52} -16011.8i q^{53} +(-2341.56 - 13645.9i) q^{54} -2927.74i q^{55} +(-2442.74 - 43076.3i) q^{57} -19351.9 q^{58} -7746.64 q^{59} +(-21562.4 + 1222.75i) q^{60} -5617.58i q^{61} +10405.0 q^{62} -23140.6 q^{64} +43798.5i q^{65} +(2240.79 - 127.069i) q^{66} -12887.4 q^{67} -23068.0 q^{68} +(408.849 + 7209.82i) q^{69} +60637.7i q^{71} +(-5084.79 - 44689.5i) q^{72} +51641.4i q^{73} -28681.6i q^{74} +(37338.5 - 2117.36i) q^{75} -51593.3i q^{76} +(-33521.7 + 1900.93i) q^{78} +67372.2 q^{79} +5947.90 q^{80} +(57539.6 - 13265.5i) q^{81} +44454.5i q^{82} +8712.06 q^{83} +91977.1 q^{85} -19555.1i q^{86} +(-4672.78 - 82401.9i) q^{87} +7291.11 q^{88} +18112.0 q^{89} +(7462.85 + 65589.9i) q^{90} +8635.34i q^{92} +(2512.42 + 44305.1i) q^{93} +24693.4i q^{94} +205714. i q^{95} +(-4969.26 - 87630.1i) q^{96} +18641.1i q^{97} +(1082.14 + 9510.75i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 172 q^{4} + 1212 q^{9}+O(q^{10}) \) 16 * q - 172 * q^4 + 1212 * q^9	\( 16 q - 172 q^{4} + 1212 q^{9} + 1188 q^{15} + 5716 q^{16} + 876 q^{18} - 21900 q^{22} + 13156 q^{25} - 900 q^{30} - 15132 q^{36} + 20932 q^{37} + 34836 q^{39} + 111052 q^{43} - 163392 q^{46} - 63192 q^{51} - 31368 q^{57} + 83412 q^{58} - 120132 q^{60} - 158884 q^{64} + 204404 q^{67} - 661728 q^{72} - 277512 q^{78} + 502616 q^{79} - 358524 q^{81} + 205152 q^{85} + 719028 q^{88} - 35352 q^{93} + 215472 q^{99}+O(q^{100}) \) 16 * q - 172 * q^4 + 1212 * q^9 + 1188 * q^15 + 5716 * q^16 + 876 * q^18 - 21900 * q^22 + 13156 * q^25 - 900 * q^30 - 15132 * q^36 + 20932 * q^37 + 34836 * q^39 + 111052 * q^43 - 163392 * q^46 - 63192 * q^51 - 31368 * q^57 + 83412 * q^58 - 120132 * q^60 - 158884 * q^64 + 204404 * q^67 - 661728 * q^72 - 277512 * q^78 + 502616 * q^79 - 358524 * q^81 + 205152 * q^85 + 719028 * q^88 - 35352 * q^93 + 215472 * q^99

Introduction

L-functions

Modular forms

Varieties

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Groups

Database

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