LMFDB - Embedded newform 147.6.c.d.146.36

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:	$40$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			146.36
Character	$\chi$	$=$	147.146
Dual form			147.6.c.d.146.35

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+7.35335i q^{2} +(-15.5875 - 0.174581i) q^{3} -22.0717 q^{4} -89.2354 q^{5} +(1.28375 - 114.620i) q^{6} +73.0063i q^{8} +(242.939 + 5.44254i) q^{9} -656.179i q^{10} -623.266i q^{11} +(344.042 + 3.85329i) q^{12} -535.808i q^{13} +(1390.96 + 15.5788i) q^{15} -1243.13 q^{16} -1065.74 q^{17} +(-40.0209 + 1786.41i) q^{18} +1092.24i q^{19} +1969.58 q^{20} +4583.09 q^{22} +812.382i q^{23} +(12.7455 - 1137.98i) q^{24} +4837.96 q^{25} +3939.98 q^{26} +(-3785.86 - 127.248i) q^{27} +6065.90i q^{29} +(-114.556 + 10228.2i) q^{30} +3242.58i q^{31} -6805.00i q^{32} +(-108.810 + 9715.14i) q^{33} -7836.77i q^{34} +(-5362.08 - 120.126i) q^{36} +5076.62 q^{37} -8031.61 q^{38} +(-93.5417 + 8351.90i) q^{39} -6514.75i q^{40} +6218.38 q^{41} -16533.7 q^{43} +13756.5i q^{44} +(-21678.8 - 485.668i) q^{45} -5973.73 q^{46} +27489.9 q^{47} +(19377.3 + 217.027i) q^{48} +35575.2i q^{50} +(16612.2 + 186.058i) q^{51} +11826.2i q^{52} -16694.7i q^{53} +(935.698 - 27838.7i) q^{54} +55617.4i q^{55} +(190.684 - 17025.2i) q^{57} -44604.7 q^{58} +28687.9 q^{59} +(-30700.7 - 343.850i) q^{60} -20080.9i q^{61} -23843.8 q^{62} +10259.2 q^{64} +47813.1i q^{65} +(-71438.8 - 800.118i) q^{66} -24962.8 q^{67} +23522.7 q^{68} +(141.826 - 12663.0i) q^{69} +12012.4i q^{71} +(-397.340 + 17736.1i) q^{72} -40436.7i q^{73} +37330.1i q^{74} +(-75411.7 - 844.614i) q^{75} -24107.6i q^{76} +(-61414.4 - 687.844i) q^{78} +70993.8 q^{79} +110932. q^{80} +(58989.8 + 2644.41i) q^{81} +45725.9i q^{82} -3633.62 q^{83} +95101.9 q^{85} -121578. i q^{86} +(1058.99 - 94552.1i) q^{87} +45502.3 q^{88} +82294.5 q^{89} +(3571.28 - 159412. i) q^{90} -17930.6i q^{92} +(566.091 - 50543.6i) q^{93} +202143. i q^{94} -97466.4i q^{95} +(-1188.02 + 106073. i) q^{96} +54668.6i q^{97} +(3392.15 - 151416. i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q - 640 q^{4} + 440 q^{9} - 3176 q^{15} + 3552 q^{16} - 4544 q^{18} + 21088 q^{22} + 30104 q^{25} + 44664 q^{30} - 59320 q^{36} - 26224 q^{37} - 16216 q^{39} + 21584 q^{43} - 27680 q^{46} + 95784 q^{51}+ \cdots - 258480 q^{99}+O(q^{100}) $ 40 * q - 640 * q^4 + 440 * q^9 - 3176 * q^15 + 3552 * q^16 - 4544 * q^18 + 21088 * q^22 + 30104 * q^25 + 44664 * q^30 - 59320 * q^36 - 26224 * q^37 - 16216 * q^39 + 21584 * q^43 - 27680 * q^46 + 95784 * q^51 - 130304 * q^57 - 131376 * q^58 + 329208 * q^60 + 53968 * q^64 - 187632 * q^67 + 606736 * q^72 + 70312 * q^78 - 597424 * q^79 + 755256 * q^81 + 108112 * q^85 - 1673072 * q^88 + 590480 * q^93 - 258480 * q^99

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 $

$2$			7.35335i			1.29990i	0.759977	+	0.649950i	$0.225210\pi$
$2$			7.35335i			1.29990i	−0.759977	+	0.649950i	$0.774790\pi$
$3$	−15.5875	−	0.174581i	−0.999937	−	0.0111993i
$3$	−15.5875	−	0.174581i	−0.999937	−	0.0111993i
$4$	−22.0717			−0.689740
$5$	−89.2354			−1.59629			−0.798146	−	0.602464i	$-0.794186\pi$
$5$	−89.2354			−1.59629			−0.798146	+	0.602464i	$0.794186\pi$
$6$	1.28375	−	114.620i	0.0145580	−	1.29982i
$7$		0			0
$7$		0			0
$8$			73.0063i			0.403306i
$9$	242.939	+	5.44254i	0.999749	+	0.0223973i
$10$		−	656.179i		−	2.07502i
$11$		−	623.266i		−	1.55307i	−0.630073	−	0.776536i	$-0.716975\pi$
$11$		−	623.266i		−	1.55307i	0.630073	−	0.776536i	$-0.283025\pi$
$12$	344.042	+	3.85329i	0.689697	+	0.00772464i
$13$		−	535.808i		−	0.879328i	−0.898162	−	0.439664i	$-0.855098\pi$
$13$		−	535.808i		−	0.879328i	0.898162	−	0.439664i	$-0.144902\pi$
$14$		0			0
$15$	1390.96	+	15.5788i	1.59619	+	0.0178774i
$16$	−1243.13			−1.21400
$17$	−1065.74			−0.894395			−0.447198	−	0.894435i	$-0.647578\pi$
$17$	−1065.74			−0.894395			−0.447198	+	0.894435i	$0.647578\pi$
$18$	−40.0209	+	1786.41i	−0.0291142	+	1.29957i
$19$			1092.24i			0.694118i	0.937843	+	0.347059i	$0.112820\pi$
$19$			1092.24i			0.694118i	−0.937843	+	0.347059i	$0.887180\pi$
$20$	1969.58			1.10103
$21$		0			0
$22$	4583.09			2.01884
$23$			812.382i			0.320214i	0.987100	+	0.160107i	$0.0511840\pi$
$23$			812.382i			0.320214i	−0.987100	+	0.160107i	$0.948816\pi$
$24$	12.7455	−	1137.98i	0.00451677	−	0.403281i
$25$	4837.96			1.54815
$26$	3939.98			1.14304
$27$	−3785.86	−	127.248i	−0.999436	−	0.0335924i
$28$		0			0
$29$			6065.90i			1.33937i	0.742646	+	0.669685i	$0.233571\pi$
$29$			6065.90i			1.33937i	−0.742646	+	0.669685i	$0.766429\pi$
$30$	−114.556	+	10228.2i	−0.0232389	+	2.07489i
$31$			3242.58i			0.606019i	0.952988	+	0.303009i	$0.0979914\pi$
$31$			3242.58i			0.606019i	−0.952988	+	0.303009i	$0.902009\pi$
$32$		−	6805.00i		−	1.17477i
$33$	−108.810	+	9715.14i	−0.0173934	+	1.55297i
$34$		−	7836.77i		−	1.16262i
$35$		0			0
$36$	−5362.08	−	120.126i	−0.689567	−	0.0154483i
$37$	5076.62			0.609635			0.304818	−	0.952411i	$-0.401405\pi$
$37$	5076.62			0.609635			0.304818	+	0.952411i	$0.401405\pi$
$38$	−8031.61			−0.902285
$39$	−93.5417	+	8351.90i	−0.00984790	+	0.879273i
$40$		−	6514.75i		−	0.643795i
$41$	6218.38			0.577720			0.288860	−	0.957371i	$-0.406724\pi$
$41$	6218.38			0.577720			0.288860	+	0.957371i	$0.406724\pi$
$42$		0			0
$43$	−16533.7			−1.36364			−0.681818	−	0.731522i	$-0.738811\pi$
$43$	−16533.7			−1.36364			−0.681818	+	0.731522i	$0.738811\pi$
$44$			13756.5i			1.07122i
$45$	−21678.8	−	485.668i	−1.59589	−	0.0357526i
$46$	−5973.73			−0.416247
$47$	27489.9			1.81522			0.907610	−	0.419814i	$-0.137905\pi$
$47$	27489.9			1.81522			0.907610	+	0.419814i	$0.137905\pi$
$48$	19377.3	+	217.027i	1.21392	+	0.0135960i
$49$		0			0
$50$			35575.2i			2.01244i
$51$	16612.2	+	186.058i	0.894339	+	0.0100166i
$52$			11826.2i			0.606508i
$53$		−	16694.7i		−	0.816373i	−0.912899	−	0.408187i	$-0.866161\pi$
$53$		−	16694.7i		−	0.816373i	0.912899	−	0.408187i	$-0.133839\pi$
$54$	935.698	−	27838.7i	0.0436668	−	1.29917i
$55$			55617.4i			2.47916i
$56$		0			0
$57$	190.684	−	17025.2i	0.00777367	−	0.694075i
$58$	−44604.7			−1.74105
$59$	28687.9			1.07292			0.536462	−	0.843925i	$-0.319760\pi$
$59$	28687.9			1.07292			0.536462	+	0.843925i	$0.319760\pi$
$60$	−30700.7	−	343.850i	−1.10096	−	0.0123308i
$61$		−	20080.9i		−	0.690968i	−0.938425	−	0.345484i	$-0.887715\pi$
$61$		−	20080.9i		−	0.690968i	0.938425	−	0.345484i	$-0.112285\pi$
$62$	−23843.8			−0.787764
$63$		0			0
$64$	10259.2			0.313086
$65$			47813.1i			1.40366i
$66$	−71438.8	−	800.118i	−2.01871	−	0.0226097i
$67$	−24962.8			−0.679370			−0.339685	−	0.940539i	$-0.610320\pi$
$67$	−24962.8			−0.679370			−0.339685	+	0.940539i	$0.610320\pi$
$68$	23522.7			0.616901
$69$	141.826	−	12663.0i	0.00358619	−	0.320194i
$70$		0			0
$71$			12012.4i			0.282802i	0.989952	+	0.141401i	$0.0451607\pi$
$71$			12012.4i			0.282802i	−0.989952	+	0.141401i	$0.954839\pi$
$72$	−397.340	+	17736.1i	−0.00903297	+	0.403205i
$73$		−	40436.7i		−	0.888114i	−0.895999	−	0.444057i	$-0.853539\pi$
$73$		−	40436.7i		−	0.888114i	0.895999	−	0.444057i	$-0.146461\pi$
$74$			37330.1i			0.792465i
$75$	−75411.7	−	844.614i	−1.54805	−	0.0173383i
$76$		−	24107.6i		−	0.478762i
$77$		0			0
$78$	−61414.4	−	687.844i	−1.14297	−	0.0128013i
$79$	70993.8			1.27983			0.639916	−	0.768445i	$-0.278969\pi$
$79$	70993.8			1.27983			0.639916	+	0.768445i	$0.278969\pi$
$80$	110932.			1.93790
$81$	58989.8	+	2644.41i	0.998997	+	0.0447834i
$82$			45725.9i			0.750978i
$83$	−3633.62			−0.0578954			−0.0289477	−	0.999581i	$-0.509216\pi$
$83$	−3633.62			−0.0578954			−0.0289477	+	0.999581i	$0.509216\pi$
$84$		0			0
$85$	95101.9			1.42772
$86$		−	121578.i		−	1.77259i
$87$	1058.99	−	94552.1i	0.0150001	−	1.33929i
$88$	45502.3			0.626364
$89$	82294.5			1.10128			0.550638	−	0.834744i	$-0.314385\pi$
$89$	82294.5			1.10128			0.550638	+	0.834744i	$0.314385\pi$
$90$	3571.28	−	159412.i	0.0464748	−	2.07450i
$91$		0			0
$92$		−	17930.6i		−	0.220865i
$93$	566.091	−	50543.6i	0.00678702	−	0.605981i
$94$			202143.i			2.35960i
$95$		−	97466.4i		−	1.10802i
$96$	−1188.02	+	106073.i	−0.0131567	+	1.17470i
$97$			54668.6i			0.589941i	0.955506	+	0.294970i	$0.0953097\pi$
$97$			54668.6i			0.589941i	−0.955506	+	0.294970i	$0.904690\pi$
$98$		0			0
$99$	3392.15	−	151416.i	0.0347846	−	1.55268i
$100$	−106782.			−1.06782
$101$	−51188.1			−0.499305			−0.249652	−	0.968336i	$-0.580316\pi$
$101$	−51188.1			−0.499305			−0.249652	+	0.968336i	$0.580316\pi$
$102$	−1368.15	+	122155.i	−0.0130206	+	1.16255i
$103$			105967.i			0.984190i	0.870541	+	0.492095i	$0.163769\pi$
$103$			105967.i			0.984190i	−0.870541	+	0.492095i	$0.836231\pi$
$104$	39117.3			0.354639
$105$		0			0
$106$	122762.			1.06120
$107$		−	139609.i		−	1.17883i	−0.807829	−	0.589417i	$-0.799357\pi$
$107$		−	139609.i		−	1.17883i	0.807829	−	0.589417i	$-0.200643\pi$
$108$	83560.3	+	2808.58i	0.689351	+	0.0231701i
$109$	227786.			1.83637			0.918185	−	0.396152i	$-0.129655\pi$
$109$	227786.			1.83637			0.918185	+	0.396152i	$0.129655\pi$
$110$	−408974.			−3.22265
$111$	−79131.6	−	886.278i	−0.609597	−	0.00682752i
$112$		0			0
$113$		−	57249.9i		−	0.421773i	−0.977511	−	0.210886i	$-0.932365\pi$
$113$		−	57249.9i		−	0.421773i	0.977511	−	0.210886i	$-0.0676350\pi$
$114$	125193.	+	1402.16i	0.902228	+	0.0101050i
$115$		−	72493.3i		−	0.511155i
$116$		−	133885.i		−	0.923817i
$117$	2916.16	−	130169.i	0.0196946	−	0.879107i
$118$			210952.i			1.39469i
$119$		0			0
$120$	−1137.35	+	101548.i	−0.00721008	+	0.643754i
$121$	−227409.			−1.41203
$122$	147662.			0.898189
$123$	−96928.8	−	1085.61i	−0.577684	−	0.00647009i
$124$		−	71569.2i		−	0.417996i
$125$	−152857.			−0.875005
$126$		0			0
$127$	−13454.4			−0.0740208			−0.0370104	−	0.999315i	$-0.511783\pi$
$127$	−13454.4			−0.0740208			−0.0370104	+	0.999315i	$0.511783\pi$
$128$		−	142321.i		−	0.767790i
$129$	257719.	+	2886.46i	1.36355	+	0.0152718i
$130$	−351586.			−1.82462
$131$	166402.			0.847188			0.423594	−	0.905852i	$-0.360768\pi$
$131$	166402.			0.847188			0.423594	+	0.905852i	$0.360768\pi$
$132$	2401.62	−	214430.i	0.0119969	−	1.07115i
$133$		0			0
$134$		−	183560.i		−	0.883113i
$135$	337833.	+	11355.0i	1.59539	+	0.0536233i
$136$		−	77805.8i		−	0.360715i
$137$			255922.i			1.16495i	0.812849	+	0.582474i	$0.197915\pi$
$137$			255922.i			1.16495i	−0.812849	+	0.582474i	$0.802085\pi$
$138$	93115.3	+	1042.90i	0.416220	+	0.00466169i
$139$			27558.0i			0.120979i	0.998169	+	0.0604895i	$0.0192662\pi$
$139$			27558.0i			0.120979i	−0.998169	+	0.0604895i	$0.980734\pi$
$140$		0			0
$141$	−428499.	−	4799.21i	−1.81511	−	0.0203293i
$142$	−88331.0			−0.367614
$143$	−333951.			−1.36566
$144$	−302006.	−	6765.81i	−1.21369	−	0.0271903i
$145$		−	541293.i		−	2.13802i
$146$	297345.			1.15446
$147$		0			0
$148$	−112050.			−0.420490
$149$			133697.i			0.493352i	0.969098	+	0.246676i	$0.0793383\pi$
$149$			133697.i			0.493352i	−0.969098	+	0.246676i	$0.920662\pi$
$150$	6210.74	−	554528.i	0.0225380	−	2.01231i
$151$	74200.2			0.264827			0.132414	−	0.991195i	$-0.457727\pi$
$151$	74200.2			0.264827			0.132414	+	0.991195i	$0.457727\pi$
$152$	−79740.3			−0.279942
$153$	−258910.	−	5800.34i	−0.894171	−	0.0200320i
$154$		0			0
$155$		−	289353.i		−	0.967383i
$156$	2064.62	−	184341.i	0.00679250	−	0.606470i
$157$			520723.i			1.68600i	0.537914	+	0.843000i	$0.319212\pi$
$157$			520723.i			1.68600i	−0.537914	+	0.843000i	$0.680788\pi$
$158$			522042.i			1.66365i
$159$	−2914.57	+	260228.i	−0.00914285	+	0.816322i
$160$			607247.i			1.87528i
$161$		0			0
$162$	−19445.3	+	433772.i	−0.0582139	+	1.29860i
$163$	15304.1			0.0451169			0.0225585	−	0.999746i	$-0.492819\pi$
$163$	15304.1			0.0451169			0.0225585	+	0.999746i	$0.492819\pi$
$164$	−137250.			−0.398477
$165$	9709.71	−	866935.i	0.0277649	−	2.47900i
$166$		−	26719.2i		−	0.0752582i
$167$	−40217.2			−0.111589			−0.0557943	−	0.998442i	$-0.517769\pi$
$167$	−40217.2			−0.111589			−0.0557943	+	0.998442i	$0.517769\pi$
$168$		0			0
$169$	84202.7			0.226782
$170$			699317.i			1.85589i
$171$	−5944.55	+	265347.i	−0.0155464	+	0.693944i
$172$	364927.			0.940555
$173$	102252.			0.259750			0.129875	−	0.991530i	$-0.458542\pi$
$173$	102252.			0.259750			0.129875	+	0.991530i	$0.458542\pi$
$174$	695274.	+	7787.11i	1.74094	+	0.0194986i
$175$		0			0
$176$			774803.i			1.88543i
$177$	−447172.	−	5008.35i	−1.07286	−	0.0120160i
$178$			605140.i			1.43155i
$179$		−	334805.i		−	0.781015i	−0.920600	−	0.390507i	$-0.872300\pi$
$179$		−	334805.i		−	0.781015i	0.920600	−	0.390507i	$-0.127700\pi$
$180$	478487.	+	10719.5i	1.10075	+	0.0246600i
$181$		−	87252.4i		−	0.197962i	−0.995089	−	0.0989808i	$-0.968442\pi$
$181$		−	87252.4i		−	0.197962i	0.995089	−	0.0989808i	$-0.0315583\pi$
$182$		0			0
$183$	−3505.73	+	313010.i	−0.00773839	+	0.690925i
$184$	−59309.0			−0.129144
$185$	−453014.			−0.973156
$186$	371665.	+	4162.66i	0.787715	+	0.00882244i
$187$			664240.i			1.38906i
$188$	−606750.			−1.25203
$189$		0			0
$190$	716704.			1.44031
$191$			573929.i			1.13835i	0.822217	+	0.569174i	$0.192737\pi$
$191$			573929.i			1.13835i	−0.822217	+	0.569174i	$0.807263\pi$
$192$	−159915.	−	1791.06i	−0.313066	−	0.00350636i
$193$	−32676.0			−0.0631445			−0.0315722	−	0.999501i	$-0.510051\pi$
$193$	−32676.0			−0.0631445			−0.0315722	+	0.999501i	$0.510051\pi$
$194$	−401997.			−0.766864
$195$	8347.23	−	745285.i	0.0157201	−	1.40358i
$196$		0			0
$197$		−	1.03884e6i		−	1.90714i	−0.301179	−	0.953568i	$-0.597380\pi$
$197$		−	1.03884e6i		−	1.90714i	0.301179	−	0.953568i	$-0.402620\pi$
$198$	1.11341e6	+	24943.6i	2.01833	+	0.0452165i
$199$		−	613372.i		−	1.09797i	−0.835832	−	0.548986i	$-0.815014\pi$
$199$		−	613372.i		−	1.09797i	0.835832	−	0.548986i	$-0.184986\pi$
$200$			353202.i			0.624378i
$201$	389107.	+	4358.02i	0.679327	+	0.00760850i
$202$		−	376404.i		−	0.649046i
$203$		0			0
$204$	−366660.	−	4106.61i	−0.616862	−	0.00690889i
$205$	−554900.			−0.922210
$206$	−779215.			−1.27935
$207$	−4421.42	+	197359.i	−0.00717193	+	0.320134i
$208$			666081.i			1.06750i
$209$	680755.			1.07802
$210$		0			0
$211$	271530.			0.419867			0.209934	−	0.977716i	$-0.432675\pi$
$211$	271530.			0.419867			0.209934	+	0.977716i	$0.432675\pi$
$212$			368480.i			0.563086i
$213$	2097.12	−	187242.i	0.00316720	−	0.282784i
$214$	1.02659e6			1.53237
$215$	1.47539e6			2.17676
$216$	9289.90	−	276391.i	0.0135480	−	0.403079i
$217$		0			0
$218$			1.67499e6i			2.38710i
$219$	−7059.46	+	630306.i	−0.00994629	+	0.888058i
$220$		−	1.22757e6i		−	1.70997i
$221$			571033.i			0.786467i
$222$	6517.11	−	581882.i	0.00887509	−	0.792415i
$223$		−	284455.i		−	0.383046i	−0.981488	−	0.191523i	$-0.938657\pi$
$223$		−	284455.i		−	0.383046i	0.981488	−	0.191523i	$-0.0613427\pi$
$224$		0			0
$225$	1.17533e6	+	26330.8i	1.54776	+	0.0346743i
$226$	420978.			0.548263
$227$	682203.			0.878716			0.439358	−	0.898312i	$-0.355206\pi$
$227$	682203.			0.878716			0.439358	+	0.898312i	$0.355206\pi$
$228$	−4208.71	+	375776.i	−0.00536182	+	0.478731i
$229$			83147.7i			0.104776i	0.998627	+	0.0523879i	$0.0166832\pi$
$229$			83147.7i			0.104776i	−0.998627	+	0.0523879i	$0.983317\pi$
$230$	533068.			0.664451
$231$		0			0
$232$	−442849.			−0.540176
$233$		−	1.05091e6i		−	1.26816i	−0.773266	−	0.634081i	$-0.781378\pi$
$233$		−	1.05091e6i		−	1.26816i	0.773266	−	0.634081i	$-0.218622\pi$
$234$	957175.	+	21443.5i	1.14275	+	0.0256010i
$235$	−2.45308e6			−2.89762
$236$	−633191.			−0.740039
$237$	−1.10661e6	−	12394.1i	−1.27975	−	0.0143333i
$238$		0			0
$239$		−	457976.i		−	0.518618i	−0.965794	−	0.259309i	$-0.916505\pi$
$239$		−	457976.i		−	0.518618i	0.965794	−	0.259309i	$-0.0834948\pi$
$240$	−1.72914e6	−	19366.5i	−1.93777	−	0.0217032i
$241$			636671.i			0.706110i	0.935603	+	0.353055i	$0.114857\pi$
$241$			636671.i			0.706110i	−0.935603	+	0.353055i	$0.885143\pi$
$242$		−	1.67222e6i		−	1.83550i
$243$	−919040.	−	51518.2i	−0.998433	−	0.0559687i
$244$			443219.i			0.476589i
$245$		0			0
$246$	7982.85	−	712751.i	0.00841047	−	0.750931i
$247$	585230.			0.610358
$248$	−236728.			−0.244411
$249$	56638.9	+	634.359i	0.0578917	+	0.000648390i
$250$		−	1.12401e6i		−	1.13742i
$251$	−703922.			−0.705245			−0.352623	−	0.935766i	$-0.614710\pi$
$251$	−703922.			−0.705245			−0.352623	+	0.935766i	$0.614710\pi$
$252$		0			0
$253$	506330.			0.497316
$254$		−	98934.6i		−	0.0962197i
$255$	−1.48240e6	−	16602.9i	−1.42763	−	0.0159895i
$256$	1.37483e6			1.31114
$257$	−560078.			−0.528951			−0.264475	−	0.964392i	$-0.585199\pi$
$257$	−560078.			−0.528951			−0.264475	+	0.964392i	$0.585199\pi$
$258$	−21225.1	+	1.89509e6i	−0.0198519	+	1.77248i
$259$		0			0
$260$		−	1.05532e6i		−	0.968164i
$261$	−33013.9	+	1.47364e6i	−0.0299982	+	1.33903i
$262$			1.22361e6i			1.10126i
$263$		−	1.32317e6i		−	1.17958i	−0.807558	−	0.589788i	$-0.799211\pi$
$263$		−	1.32317e6i		−	1.17958i	0.807558	−	0.589788i	$-0.200789\pi$
$264$	−709266.	−	7943.82i	−0.626324	−	0.00701487i
$265$			1.48976e6i			1.30317i
$266$		0			0
$267$	−1.28276e6	−	14367.0i	−1.10121	−	0.0123336i
$268$	550971.			0.468589
$269$	803833.			0.677306			0.338653	−	0.940911i	$-0.390029\pi$
$269$	803833.			0.677306			0.338653	+	0.940911i	$0.390029\pi$
$270$	−83497.4	+	2.48420e6i	−0.0697050	+	2.07385i
$271$		−	1.59491e6i		−	1.31921i	−0.751613	−	0.659604i	$-0.770724\pi$
$271$		−	1.59491e6i		−	1.31921i	0.751613	−	0.659604i	$-0.229276\pi$
$272$	1.32486e6			1.08579
$273$		0			0
$274$	−1.88188e6			−1.51432
$275$		−	3.01534e6i		−	2.40438i
$276$	−3130.34	+	279494.i	−0.00247354	+	0.220851i
$277$	−1.16511e6			−0.912366			−0.456183	−	0.889886i	$-0.650784\pi$
$277$	−1.16511e6			−0.912366			−0.456183	+	0.889886i	$0.650784\pi$
$278$	−202643.			−0.157261
$279$	−17647.9	+	787749.i	−0.0135732	+	0.605867i
$280$		0			0
$281$			976585.i			0.737810i	0.929467	+	0.368905i	$0.120267\pi$
$281$			976585.i			0.737810i	−0.929467	+	0.368905i	$0.879733\pi$
$282$	35290.3	−	3.15090e6i	0.0264260	−	2.35946i
$283$		−	423342.i		−	0.314214i	−0.987582	−	0.157107i	$-0.949783\pi$
$283$		−	423342.i		−	0.314214i	0.987582	−	0.157107i	$-0.0502167\pi$
$284$		−	265133.i		−	0.195060i
$285$	−17015.7	+	1.51926e6i	−0.0124091	+	1.10795i
$286$		−	2.45565e6i		−	1.77522i
$287$		0			0
$288$	37036.5	−	1.65320e6i	0.0263117	−	1.17448i
$289$	−284052.			−0.200057
$290$	3.98032e6			2.77922
$291$	9544.07	−	852145.i	0.00660695	−	0.589904i
$292$			892506.i			0.612568i
$293$	−1.12726e6			−0.767108			−0.383554	−	0.923518i	$-0.625300\pi$
$293$	−1.12726e6			−0.767108			−0.383554	+	0.923518i	$0.625300\pi$
$294$		0			0
$295$	−2.55998e6			−1.71270
$296$			370625.i			0.245870i
$297$	−79309.3	+	2.35959e6i	−0.0521714	+	1.55219i
$298$	−983121.			−0.641308
$299$	435281.			0.281573
$300$	1.66446e6	+	18642.1i	1.06775	+	0.0119589i
$301$		0			0
$302$			545620.i			0.344249i
$303$	797894.	+	8936.45i	0.499273	+	0.00559189i
$304$		−	1.35780e6i		−	0.842659i
$305$			1.79193e6i			1.10299i
$306$	42651.9	−	1.90386e6i	0.0260396	−	1.16233i
$307$		−	3.05776e6i		−	1.85165i	−0.377957	−	0.925823i	$-0.623373\pi$
$307$		−	3.05776e6i		−	1.85165i	0.377957	−	0.925823i	$-0.376627\pi$
$308$		0			0
$309$	18499.8	−	1.65176e6i	0.0110223	−	0.984128i
$310$	2.12771e6			1.25750
$311$	726942.			0.426186			0.213093	−	0.977032i	$-0.431646\pi$
$311$	726942.			0.426186			0.213093	+	0.977032i	$0.431646\pi$
$312$	−609741.	−	6829.13i	−0.354616	−	0.00397172i
$313$			1.96896e6i			1.13600i	0.823030	+	0.567998i	$0.192282\pi$
$313$			1.96896e6i			1.13600i	−0.823030	+	0.567998i	$0.807718\pi$
$314$	−3.82905e6			−2.19163
$315$		0			0
$316$	−1.56695e6			−0.882752
$317$			332011.i			0.185568i	0.995686	+	0.0927841i	$0.0295766\pi$
$317$			332011.i			0.185568i	−0.995686	+	0.0927841i	$0.970423\pi$
$318$	−1.91355e6	−	21431.8i	−1.06114	−	0.0118848i
$319$	3.78067e6			2.08014
$320$	−915484.			−0.499776
$321$	−24373.0	+	2.17615e6i	−0.0132022	+	1.17876i
$322$		0			0
$323$		−	1.16404e6i		−	0.620816i
$324$	−1.30200e6	−	58366.7i	−0.689048	−	0.0308889i
$325$		−	2.59222e6i		−	1.36133i
$326$			112536.i			0.0586475i
$327$	−3.55060e6	−	39767.0i	−1.83625	−	0.0205661i
$328$			453980.i			0.232998i
$329$		0			0
$330$	6.37487e6	+	71398.9i	3.22245	+	0.0360916i
$331$	−465032.			−0.233299			−0.116650	−	0.993173i	$-0.537215\pi$
$331$	−465032.			−0.233299			−0.116650	+	0.993173i	$0.537215\pi$
$332$	80200.1			0.0399328
$333$	1.23331e6	+	27629.7i	0.609482	+	0.0136542i
$334$		−	295731.i		−	0.145054i
$335$	2.22757e6			1.08447
$336$		0			0
$337$	3.03028e6			1.45348			0.726739	−	0.686913i	$-0.241035\pi$
$337$	3.03028e6			1.45348			0.726739	+	0.686913i	$0.241035\pi$
$338$			619172.i			0.294795i
$339$	−9994.72	+	892382.i	−0.00472358	+	0.421747i
$340$	−2.09906e6			−0.984754
$341$	2.02099e6			0.941191
$342$	−1.95119e6	−	43712.4i	−0.902058	−	0.0202087i
$343$		0			0
$344$		−	1.20706e6i		−	0.549963i
$345$	−12655.9	+	1.12999e6i	−0.00572461	+	0.511123i
$346$			751892.i			0.337649i
$347$			891627.i			0.397521i	0.980048	+	0.198760i	$0.0636915\pi$
$347$			891627.i			0.397521i	−0.980048	+	0.198760i	$0.936308\pi$
$348$	−23373.7	+	2.08693e6i	−0.0103462	+	0.923759i
$349$		−	484753.i		−	0.213038i	−0.994311	−	0.106519i	$-0.966030\pi$
$349$		−	484753.i		−	0.213038i	0.994311	−	0.106519i	$-0.0339705\pi$
$350$		0			0
$351$	−68180.5	+	2.02849e6i	−0.0295388	+	0.878832i
$352$	−4.24132e6			−1.82450
$353$	2.40732e6			1.02825			0.514123	−	0.857717i	$-0.328118\pi$
$353$	2.40732e6			1.02825			0.514123	+	0.857717i	$0.328118\pi$
$354$	36828.1	−	3.28821e6i	0.0156197	−	1.39461i
$355$		−	1.07193e6i		−	0.451434i
$356$	−1.81638e6			−0.759594
$357$		0			0
$358$	2.46194e6			1.01524
$359$		−	1.39291e6i		−	0.570409i	−0.958467	−	0.285205i	$-0.907938\pi$
$359$		−	1.39291e6i		−	0.570409i	0.958467	−	0.285205i	$-0.0920616\pi$
$360$	35456.8	−	1.58269e6i	0.0144193	−	0.643633i
$361$	1.28311e6			0.518200
$362$	641597.			0.257330
$363$	3.54473e6	+	39701.2i	1.41194	+	0.0158138i
$364$		0			0
$365$			3.60839e6i			1.41769i
$366$	−2.30167e6	−	25778.8i	−0.898133	−	0.0100591i
$367$		−	1.58108e6i		−	0.612757i	−0.951910	−	0.306378i	$-0.900883\pi$
$367$		−	1.58108e6i		−	0.612757i	0.951910	−	0.306378i	$-0.0991173\pi$
$368$		−	1.00990e6i		−	0.388740i
$369$	1.51069e6	+	33843.8i	0.577575	+	0.0129394i
$370$		−	3.33117e6i		−	1.26501i
$371$		0			0
$372$	−12494.6	+	1.11558e6i	−0.00468128	+	0.417970i
$373$	4.32869e6			1.61096			0.805480	−	0.592623i	$-0.201908\pi$
$373$	4.32869e6			1.61096			0.805480	+	0.592623i	$0.201908\pi$
$374$	−4.88439e6			−1.80564
$375$	2.38266e6	+	26685.9i	0.874950	+	0.00979948i
$376$			2.00694e6i			0.732090i
$377$	3.25016e6			1.17774
$378$		0			0
$379$	2.71542e6			0.971045			0.485523	−	0.874224i	$-0.338629\pi$
$379$	2.71542e6			0.971045			0.485523	+	0.874224i	$0.338629\pi$
$380$			2.15125e6i			0.764243i
$381$	209720.	+	2348.87i	0.0740162	+	0.000828985i
$382$	−4.22030e6			−1.47974
$383$	−211659.			−0.0737291			−0.0368646	−	0.999320i	$-0.511737\pi$
$383$	−211659.			−0.0737291			−0.0368646	+	0.999320i	$0.511737\pi$
$384$	−24846.4	+	2.21842e6i	−0.00859875	+	0.767742i
$385$		0			0
$386$		−	240278.i		−	0.0820815i
$387$	−4.01668e6	−	89985.3i	−1.36329	−	0.0305418i
$388$		−	1.20663e6i		−	0.406906i
$389$			1.97112e6i			0.660449i	0.943902	+	0.330224i	$0.107124\pi$
$389$			1.97112e6i			0.660449i	−0.943902	+	0.330224i	$0.892876\pi$
$390$	5.48034e6	+	61380.1i	1.82451	+	0.0204346i
$391$		−	865789.i		−	0.286398i
$392$		0			0
$393$	−2.59378e6	−	29050.5i	−0.847135	−	0.00948795i
$394$	7.63892e6			2.47909
$395$	−6.33516e6			−2.04298
$396$	−74870.5	+	3.34200e6i	−0.0239923	+	1.07095i
$397$		−	2.40025e6i		−	0.764328i	−0.924095	−	0.382164i	$-0.875179\pi$
$397$		−	2.40025e6i		−	0.764328i	0.924095	−	0.382164i	$-0.124821\pi$
$398$	4.51034e6			1.42725
$399$		0			0
$400$	−6.01424e6			−1.87945
$401$			4.20251e6i			1.30511i	0.757740	+	0.652556i	$0.226303\pi$
$401$			4.20251e6i			1.30511i	−0.757740	+	0.652556i	$0.773697\pi$
$402$	−32046.0	+	2.86124e6i	−0.00989029	+	0.883058i
$403$	1.73740e6			0.532889
$404$	1.12981e6			0.344391
$405$	−5.26398e6	−	235975.i	−1.59469	−	0.0714873i
$406$		0			0
$407$		−	3.16408e6i		−	0.946807i
$408$	−13583.4	+	1.21280e6i	−0.00403978	+	0.360693i
$409$		−	2.47881e6i		−	0.732715i	−0.930474	−	0.366358i	$-0.880605\pi$
$409$		−	2.47881e6i		−	0.732715i	0.930474	−	0.366358i	$-0.119395\pi$
$410$		−	4.08037e6i		−	1.19878i
$411$	44679.1	−	3.98918e6i	0.0130467	−	1.16488i
$412$		−	2.33888e6i		−	0.678836i
$413$		0			0
$414$	−1.45125e6	−	32512.3i	−0.416142	−	0.00932280i
$415$	324247.			0.0924179
$416$	−3.64617e6			−1.03301
$417$	4811.08	−	429559.i	0.00135489	−	0.120971i
$418$			5.00582e6i			1.40131i
$419$	−1.55283e6			−0.432104			−0.216052	−	0.976382i	$-0.569318\pi$
$419$	−1.55283e6			−0.432104			−0.216052	+	0.976382i	$0.569318\pi$
$420$		0			0
$421$	−5.16901e6			−1.42135			−0.710677	−	0.703519i	$-0.751611\pi$
$421$	−5.16901e6			−1.42135			−0.710677	+	0.703519i	$0.751611\pi$
$422$			1.99666e6i			0.545785i
$423$	6.67838e6	+	149615.i	1.81476	+	0.0406560i
$424$	1.21882e6			0.329248
$425$	−5.15602e6			−1.38466
$426$	1.37686e6	+	15420.9i	0.367591	+	0.00411704i
$427$		0			0
$428$			3.08140e6i			0.813090i
$429$	5.20545e6	+	58301.3i	1.36557	+	0.0152945i
$430$			1.08491e7i			2.82957i
$431$		−	1.27104e6i		−	0.329584i	−0.986328	−	0.164792i	$-0.947305\pi$
$431$		−	1.27104e6i		−	0.329584i	0.986328	−	0.164792i	$-0.0526952\pi$
$432$	4.70633e6	+	158186.i	1.21331	+	0.0407812i
$433$			7.34053e6i			1.88151i	0.339082	+	0.940757i	$0.389884\pi$
$433$			7.34053e6i			1.88151i	−0.339082	+	0.940757i	$0.610116\pi$
$434$		0			0
$435$	−94499.3	+	8.43740e6i	−0.0239445	+	2.13789i
$436$	−5.02762e6			−1.26662
$437$	−887315.			−0.222267
$438$	−4.63486e6	−	51910.7i	−1.15439	−	0.0129292i
$439$		−	3.93669e6i		−	0.974923i	−0.873145	−	0.487461i	$-0.837923\pi$
$439$		−	3.93669e6i		−	0.974923i	0.873145	−	0.487461i	$-0.162077\pi$
$440$	−4.06042e6			−0.999859
$441$		0			0
$442$	−4.19900e6			−1.02233
$443$			6.00643e6i			1.45414i	0.686562	+	0.727071i	$0.259119\pi$
$443$			6.00643e6i			1.45414i	−0.686562	+	0.727071i	$0.740881\pi$
$444$	1.74657e6	+	19561.7i	0.420464	+	0.00470921i
$445$	−7.34359e6			−1.75796
$446$	2.09169e6			0.497922
$447$	23340.9	−	2.08400e6i	0.00552522	−	0.493321i
$448$		0			0
$449$			7.26371e6i			1.70037i	0.526487	+	0.850183i	$0.323509\pi$
$449$			7.26371e6i			1.70037i	−0.526487	+	0.850183i	$0.676491\pi$
$450$	−193620.	+	8.64261e6i	−0.0450732	+	2.01193i
$451$		−	3.87570e6i		−	0.897240i
$452$			1.26360e6i			0.290914i
$453$	−1.15659e6	−	12953.9i	−0.264811	−	0.00296589i
$454$			5.01647e6i			1.14224i
$455$		0			0
$456$	1.24295e6	+	13921.1i	0.279925	+	0.00313517i
$457$	−7.48597e6			−1.67671			−0.838354	−	0.545126i	$-0.816482\pi$
$457$	−7.48597e6			−1.67671			−0.838354	+	0.545126i	$0.816482\pi$
$458$	−611414.			−0.136198
$459$	4.03474e6	+	135613.i	0.893891	+	0.0300449i
$460$			1.60005e6i			0.352565i
$461$	7.34169e6			1.60895			0.804477	−	0.593984i	$-0.202446\pi$
$461$	7.34169e6			1.60895			0.804477	+	0.593984i	$0.202446\pi$
$462$		0			0
$463$	2.80093e6			0.607225			0.303613	−	0.952796i	$-0.401807\pi$
$463$	2.80093e6			0.607225			0.303613	+	0.952796i	$0.401807\pi$
$464$		−	7.54073e6i		−	1.62599i
$465$	−50515.4	+	4.51028e6i	−0.0108341	+	0.967322i
$466$	7.72769e6			1.64848
$467$	−739519.			−0.156912			−0.0784562	−	0.996918i	$-0.524999\pi$
$467$	−739519.			−0.156912			−0.0784562	+	0.996918i	$0.524999\pi$
$468$	−64364.5	+	2.87304e6i	−0.0135841	+	0.606356i
$469$		0			0
$470$		−	1.80383e7i		−	3.76662i
$471$	90908.1	−	8.11675e6i	0.0188821	−	1.68589i
$472$			2.09440e6i			0.432717i
$473$			1.03049e7i			2.11783i
$474$	91138.4	−	8.13732e6i	0.0186318	−	1.66355i
$475$			5.28421e6i			1.07460i
$476$		0			0
$477$	90861.6	−	4.05579e6i	0.0182845	−	0.816168i
$478$	3.36765e6			0.674151
$479$	−6.54705e6			−1.30379			−0.651894	−	0.758310i	$-0.726025\pi$
$479$	−6.54705e6			−1.30379			−0.651894	+	0.758310i	$0.726025\pi$
$480$	106014.	−	9.46545e6i	0.0210019	−	1.87516i
$481$		−	2.72009e6i		−	0.536069i
$482$	−4.68166e6			−0.917872
$483$		0			0
$484$	5.01930e6			0.973935
$485$		−	4.87837e6i		−	0.941717i
$486$	378831.	−	6.75802e6i	0.0727537	−	1.29786i
$487$	−6.11473e6			−1.16830			−0.584151	−	0.811645i	$-0.698572\pi$
$487$	−6.11473e6			−1.16830			−0.584151	+	0.811645i	$0.698572\pi$
$488$	1.46603e6			0.278672
$489$	−238553.	−	2671.80i	−0.0451141	−	0.000505280i
$490$		0			0
$491$			2.69410e6i			0.504324i	0.967685	+	0.252162i	$0.0811416\pi$
$491$			2.69410e6i			0.504324i	−0.967685	+	0.252162i	$0.918858\pi$
$492$	2.13938e6	+	23961.2i	0.398452	+	0.00446268i
$493$		−	6.46468e6i		−	1.19793i
$494$			4.30340e6i			0.793404i
$495$	−302700.	+	1.35116e7i	−0.0555264	+	2.47853i
$496$		−	4.03096e6i		−	0.735706i
$497$		0			0
$498$	−4664.66	+	416486.i	−0.000842843	+	0.0752535i
$499$	1.04559e6			0.187978			0.0939892	−	0.995573i	$-0.470038\pi$
$499$	1.04559e6			0.187978			0.0939892	+	0.995573i	$0.470038\pi$
$500$	3.37381e6			0.603526
$501$	626884.	+	7021.13i	0.111582	+	0.00124972i
$502$		−	5.17618e6i		−	0.916748i
$503$	4.84541e6			0.853908			0.426954	−	0.904273i	$-0.359587\pi$
$503$	4.84541e6			0.853908			0.426954	+	0.904273i	$0.359587\pi$
$504$		0			0
$505$	4.56779e6			0.797036
$506$			3.72322e6i			0.646461i
$507$	−1.31251e6	−	14700.2i	−0.226768	−	0.00253982i
$508$	296961.			0.0510552
$509$	1.90068e6			0.325172			0.162586	−	0.986694i	$-0.448016\pi$
$509$	1.90068e6			0.325172			0.162586	+	0.986694i	$0.448016\pi$
$510$	122087.	−	1.09006e7i	0.0207847	−	1.85577i
$511$		0			0
$512$			5.55532e6i			0.936556i
$513$	138985.	−	4.13506e6i	0.0233171	−	0.693727i
$514$		−	4.11844e6i		−	0.687583i
$515$		−	9.45604e6i		−	1.57105i
$516$	−5.68829e6	−	63709.1i	−0.940496	−	0.0105336i
$517$		−	1.71335e7i		−	2.81917i
$518$		0			0
$519$	−1.59385e6	−	17851.1i	−0.259733	−	0.00290903i
$520$	−3.49065e6			−0.566107
$521$	1.10379e7			1.78153			0.890766	−	0.454461i	$-0.150168\pi$
$521$	1.10379e7			1.78153			0.890766	+	0.454461i	$0.150168\pi$
$522$	−1.08362e7	−	242763.i	−1.74061	−	0.0389947i
$523$			199228.i			0.0318490i	0.999873	+	0.0159245i	$0.00506914\pi$
$523$			199228.i			0.0318490i	−0.999873	+	0.0159245i	$0.994931\pi$
$524$	−3.67277e6			−0.584340
$525$		0			0
$526$	9.72972e6			1.53333
$527$		−	3.45575e6i		−	0.542020i
$528$	135266.	−	1.20772e7i	0.0211155	−	1.88531i
$529$	5.77638e6			0.897463
$530$	−1.09547e7			−1.69399
$531$	6.96941e6	+	156135.i	1.07265	+	0.0240306i
$532$		0			0
$533$		−	3.33186e6i		−	0.508005i
$534$	105646.	−	9.43261e6i	0.0160324	−	1.43146i
$535$			1.24580e7i			1.88176i
$536$		−	1.82244e6i		−	0.273994i
$537$	−58450.4	+	5.21876e6i	−0.00874686	+	0.780966i
$538$			5.91086e6i			0.880431i
$539$		0			0
$540$	−7.45654e6	−	250625.i	−1.10041	−	0.0369862i
$541$	2.29138e6			0.336593			0.168296	−	0.985736i	$-0.446173\pi$
$541$	2.29138e6			0.336593			0.168296	+	0.985736i	$0.446173\pi$
$542$	1.17279e7			1.71484
$543$	−15232.6	+	1.36005e6i	−0.00221704	+	0.197949i
$544$			7.25237e6i			1.05071i
$545$	−2.03266e7			−2.93138
$546$		0			0
$547$	7.36525e6			1.05249			0.526247	−	0.850332i	$-0.323599\pi$
$547$	7.36525e6			1.05249			0.526247	+	0.850332i	$0.323599\pi$
$548$		−	5.64864e6i		−	0.803512i
$549$	109291.	−	4.87843e6i	0.0154758	−	0.690795i
$550$	2.21728e7			3.12546
$551$	−6.62541e6			−0.929681
$552$	924477.	+	10354.2i	0.129136	+	0.00144633i
$553$		0			0
$554$		−	8.56749e6i		−	1.18598i
$555$	7.06135e6	+	79087.4i	0.973095	+	0.0108987i
$556$		−	608251.i		−	0.0834441i
$557$			1.00895e7i			1.37794i	0.724788	+	0.688971i	$0.241937\pi$
$557$			1.00895e7i			1.37794i	−0.724788	+	0.688971i	$0.758063\pi$
$558$	−5.79259e6	−	129771.i	−0.787566	−	0.0176438i
$559$			8.85888e6i			1.19908i
$560$		0			0
$561$	115963.	−	1.03538e7i	0.0155566	−	1.38897i
$562$	−7.18117e6			−0.959079
$563$	−15191.7			−0.00201993			−0.00100996	−	0.999999i	$-0.500321\pi$
$563$	−15191.7			−0.00201993			−0.00100996	+	0.999999i	$0.500321\pi$
$564$	9.45770e6	+	105927.i	1.25195	+	0.0140219i
$565$			5.10872e6i			0.673273i
$566$	3.11298e6			0.408446
$567$		0			0
$568$	−876977.			−0.114056
$569$			1.34025e7i			1.73542i	0.497072	+	0.867709i	$0.334409\pi$
$569$			1.34025e7i			1.73542i	−0.497072	+	0.867709i	$0.665591\pi$
$570$	−1.11716e7	−	125123.i	−1.44022	−	0.0161305i
$571$	−1.05882e7			−1.35904			−0.679522	−	0.733655i	$-0.737813\pi$
$571$	−1.05882e7			−1.35904			−0.679522	+	0.733655i	$0.737813\pi$
$572$	7.37086e6			0.941950
$573$	100197.	−	8.94611e6i	0.0127488	−	1.13828i
$574$		0			0
$575$			3.93027e6i			0.495739i
$576$	2.49236e6	+	55836.1i	0.313007	+	0.00701228i
$577$			1.38406e7i			1.73068i	0.501185	+	0.865340i	$0.332897\pi$
$577$			1.38406e7i			1.73068i	−0.501185	+	0.865340i	$0.667103\pi$
$578$		−	2.08873e6i		−	0.260054i
$579$	509336.	+	5704.59i	0.0631405	+	0.000707177i
$580$			1.19473e7i			1.47468i
$581$		0			0
$582$	6.26612e6	+	70180.8i	0.766816	+	0.00858838i
$583$	−1.04052e7			−1.26789
$584$	2.95213e6			0.358182
$585$	−260225.	+	1.16157e7i	−0.0314383	+	1.40331i
$586$		−	8.28916e6i		−	0.997164i
$587$	9.67019e6			1.15835			0.579175	−	0.815203i	$-0.303375\pi$
$587$	9.67019e6			1.15835			0.579175	+	0.815203i	$0.303375\pi$
$588$		0			0
$589$	−3.54167e6			−0.420649
$590$		−	1.88244e7i		−	2.22634i
$591$	−181361.	+	1.61928e7i	−0.0213587	+	1.90702i
$592$	−6.31092e6			−0.740096
$593$	−4.23541e6			−0.494605			−0.247302	−	0.968938i	$-0.579544\pi$
$593$	−4.23541e6			−0.494605			−0.247302	+	0.968938i	$0.579544\pi$
$594$	−1.73509e7	−	583188.i	−2.01770	−	0.0678177i
$595$		0			0
$596$		−	2.95092e6i		−	0.340285i
$597$	−107083.	+	9.56092e6i	−0.0122966	+	1.09790i
$598$			3.20077e6i			0.366017i
$599$		−	1.58076e7i		−	1.80011i	−0.435773	−	0.900057i	$-0.643525\pi$
$599$		−	1.58076e7i		−	1.80011i	0.435773	−	0.900057i	$-0.356475\pi$
$600$	61662.1	−	5.50552e6i	0.00699263	−	0.624339i
$601$			1.65411e6i			0.186800i	0.995629	+	0.0934001i	$0.0297736\pi$
$601$			1.65411e6i			0.186800i	−0.995629	+	0.0934001i	$0.970226\pi$
$602$		0			0
$603$	−6.06444e6	−	135861.i	−0.679200	−	0.0152160i
$604$	−1.63773e6			−0.182662
$605$	2.02929e7			2.25401
$606$	−65712.8	+	5.86719e6i	−0.00726890	+	0.649006i
$607$			1.15604e7i			1.27351i	0.771067	+	0.636755i	$0.219724\pi$
$607$			1.15604e7i			1.27351i	−0.771067	+	0.636755i	$0.780276\pi$
$608$	7.43268e6			0.815430
$609$		0			0
$610$	−1.31766e7			−1.43377
$611$		−	1.47293e7i		−	1.59617i
$612$	5.71459e6	+	128023.i	0.616746	+	0.0138169i
$613$	2.51731e6			0.270574			0.135287	−	0.990806i	$-0.456804\pi$
$613$	2.51731e6			0.270574			0.135287	+	0.990806i	$0.456804\pi$
$614$	2.24848e7			2.40696
$615$	8.64949e6	+	96874.7i	0.922152	+	0.0103282i
$616$		0			0
$617$			8.37776e6i			0.885962i	0.896531	+	0.442981i	$0.146079\pi$
$617$			8.37776e6i			0.885962i	−0.896531	+	0.442981i	$0.853921\pi$
$618$	1.21460e7	+	136036.i	1.27927	+	0.0143279i
$619$		−	1.32169e7i		−	1.38645i	−0.720721	−	0.693225i	$-0.756189\pi$
$619$		−	1.32169e7i		−	1.38645i	0.720721	−	0.693225i	$-0.243811\pi$
$620$			6.38651e6i			0.667243i
$621$	103374.	−	3.07556e6i	0.0107568	−	0.320034i
$622$			5.34546e6i			0.553999i
$623$		0			0
$624$	116285.	−	1.03825e7i	0.0119553	−	1.06744i
$625$	−1.47837e6			−0.151385
$626$	−1.44785e7			−1.47668
$627$	−1.06112e7	−	118847.i	−1.07795	−	0.0120731i
$628$		−	1.14932e7i		−	1.16290i
$629$	−5.41036e6			−0.545255
$630$		0			0
$631$	−515624.			−0.0515536			−0.0257768	−	0.999668i	$-0.508206\pi$
$631$	−515624.			−0.0515536			−0.0257768	+	0.999668i	$0.508206\pi$
$632$			5.18299e6i			0.516164i
$633$	−4.23247e6	−	47403.9i	−0.419841	−	0.00470224i
$634$	−2.44139e6			−0.241220
$635$	1.20061e6			0.118159
$636$	64329.5	−	5.74368e6i	0.00630619	−	0.563050i
$637$		0			0
$638$			2.78006e7i			2.70397i
$639$	−65377.7	+	2.91827e6i	−0.00633400	+	0.282731i
$640$			1.27000e7i			1.22562i
$641$		−	1.63765e7i		−	1.57426i	−0.616789	−	0.787128i	$-0.711567\pi$
$641$		−	1.63765e7i		−	1.57426i	0.616789	−	0.787128i	$-0.288433\pi$
$642$	−1.60020e7	−	179223.i	−1.53227	−	0.0171615i
$643$			1.82259e7i			1.73845i	0.494417	+	0.869225i	$0.335381\pi$
$643$			1.82259e7i			1.73845i	−0.494417	+	0.869225i	$0.664619\pi$
$644$		0			0
$645$	−2.29976e7	−	257575.i	−2.17663	−	0.0243783i
$646$	8.55962e6			0.806999
$647$	−1.76450e7			−1.65715			−0.828575	−	0.559878i	$-0.810848\pi$
$647$	−1.76450e7			−1.65715			−0.828575	+	0.559878i	$0.810848\pi$
$648$	−193059.	+	4.30662e6i	−0.0180614	+	0.402902i
$649$		−	1.78802e7i		−	1.66633i
$650$	1.90615e7			1.76959
$651$		0			0
$652$	−337788.			−0.0311190
$653$			2.63042e6i			0.241403i	0.992689	+	0.120701i	$0.0385143\pi$
$653$			2.63042e6i			0.241403i	−0.992689	+	0.120701i	$0.961486\pi$
$654$	292420.	−	2.61088e7i	0.0267339	−	2.38695i
$655$	−1.48489e7			−1.35236
$656$	−7.73028e6			−0.701351
$657$	220078.	−	9.82365e6i	0.0198913	−	0.887891i
$658$		0			0
$659$		−	1.85224e7i		−	1.66144i	−0.556693	−	0.830718i	$-0.687930\pi$
$659$		−	1.85224e7i		−	1.66144i	0.556693	−	0.830718i	$-0.312070\pi$
$660$	−214310.	+	1.91347e7i	−0.0191506	+	1.70987i
$661$		−	1.90277e7i		−	1.69388i	−0.531692	−	0.846938i	$-0.678444\pi$
$661$		−	1.90277e7i		−	1.69388i	0.531692	−	0.846938i	$-0.321556\pi$
$662$		−	3.41954e6i		−	0.303266i
$663$	99691.2	−	8.90096e6i	0.00880792	−	0.786417i
$664$		−	265277.i		−	0.0233496i
$665$		0			0
$666$	−203171.	+	9.06894e6i	−0.0177491	+	0.792266i
$667$	−4.92783e6			−0.428885
$668$	887661.			0.0769672
$669$	−49660.3	+	4.43393e6i	−0.00428987	+	0.383022i
$670$			1.63801e7i			1.40971i
$671$	−1.25157e7			−1.07312
$672$		0			0
$673$	1.26436e7			1.07605			0.538024	−	0.842929i	$-0.319171\pi$
$673$	1.26436e7			1.07605			0.538024	+	0.842929i	$0.319171\pi$
$674$			2.22827e7i			1.88938i
$675$	−1.83158e7	−	615621.i	−1.54727	−	0.0520061i
$676$	−1.85850e6			−0.156421
$677$	7.13591e6			0.598381			0.299190	−	0.954193i	$-0.403283\pi$
$677$	7.13591e6			0.598381			0.299190	+	0.954193i	$0.403283\pi$
$678$	−6.56199e6	−	73494.7i	−0.548228	−	0.00614019i
$679$		0			0
$680$			6.94303e6i			0.575807i
$681$	−1.06338e7	−	119099.i	−0.878661	−	0.00984105i
$682$			1.48610e7i			1.22345i
$683$		−	1.21231e7i		−	0.994400i	−0.867636	−	0.497200i	$-0.834362\pi$
$683$		−	1.21231e7i		−	0.994400i	0.867636	−	0.497200i	$-0.165638\pi$
$684$	131206.	−	5.85667e6i	0.0107230	−	0.478641i
$685$		−	2.28373e7i		−	1.85960i
$686$		0			0
$687$	14516.0	−	1.29606e6i	0.00117342	−	0.104769i
$688$	2.05536e7			1.65545
$689$	−8.94515e6			−0.717860
$690$	−8.30919e6	−	93063.3i	−0.664409	−	0.00744142i
$691$		−	4.52687e6i		−	0.360664i	−0.983606	−	0.180332i	$-0.942283\pi$
$691$		−	4.52687e6i		−	0.360664i	0.983606	−	0.180332i	$-0.0577172\pi$
$692$	−2.25687e6			−0.179160
$693$		0			0
$694$	−6.55644e6			−0.516737
$695$		−	2.45915e6i		−	0.193118i
$696$	6.90290e6	+	77312.8i	0.540142	+	0.00604962i
$697$	−6.62718e6			−0.516710
$698$	3.56456e6			0.276928
$699$	−183468.	+	1.63810e7i	−0.0142026	+	1.26808i
$700$		0			0
$701$			1.01222e7i			0.778001i	0.921237	+	0.389001i	$0.127180\pi$
$701$			1.01222e7i			0.778001i	−0.921237	+	0.389001i	$0.872820\pi$
$702$	−1.49162e7	−	501355.i	−1.14239	−	0.0383974i
$703$			5.54488e6i			0.423159i
$704$		−	6.39420e6i		−	0.486245i
$705$	3.82373e7	+	428260.i	2.89744	+	0.0324515i
$706$			1.77018e7i			1.33662i
$707$		0			0
$708$	9.86985e6	+	110543.i	0.739993	+	0.00828796i
$709$	−1.56987e6			−0.117286			−0.0586431	−	0.998279i	$-0.518677\pi$
$709$	−1.56987e6			−0.117286			−0.0586431	+	0.998279i	$0.518677\pi$
$710$	7.88225e6			0.586820
$711$	1.72472e7	+	386387.i	1.27951	+	0.0286648i
$712$			6.00801e6i			0.444151i
$713$	−2.63421e6			−0.194056
$714$		0			0
$715$	2.98002e7			2.17999
$716$			7.38971e6i			0.538697i
$717$	−79953.6	+	7.13868e6i	−0.00580818	+	0.518585i
$718$	1.02425e7			0.741475
$719$	3.81731e6			0.275382			0.137691	−	0.990475i	$-0.456032\pi$
$719$	3.81731e6			0.275382			0.137691	+	0.990475i	$0.456032\pi$
$720$	2.69496e7	+	603750.i	1.93741	+	0.0434036i
$721$		0			0
$722$			9.43518e6i			0.673608i
$723$	111150.	−	9.92409e6i	0.00790797	−	0.706066i
$724$			1.92581e6i			0.136542i
$725$			2.93466e7i			2.07354i
$726$	−291937.	+	2.60656e7i	−0.0205564	+	1.83538i
$727$		−	1.11485e7i		−	0.782310i	−0.920325	−	0.391155i	$-0.872076\pi$
$727$		−	1.11485e7i		−	0.782310i	0.920325	−	0.391155i	$-0.127924\pi$
$728$		0			0
$729$	1.43165e7	+	963485.i	0.997743	+	0.0671469i
$730$	−2.65337e7			−1.84285
$731$	1.76206e7			1.21963
$732$	77377.4	−	6.90866e6i	0.00533748	−	0.476559i
$733$		−	1.41807e7i		−	0.974850i	−0.873165	−	0.487425i	$-0.837936\pi$
$733$		−	1.41807e7i		−	0.974850i	0.873165	−	0.487425i	$-0.162064\pi$
$734$	1.16262e7			0.796523
$735$		0			0
$736$	5.52826e6			0.376178
$737$			1.55585e7i			1.05511i
$738$	−248865.	+	1.11086e7i	−0.0168199	+	0.750790i
$739$	2.63965e7			1.77801			0.889006	−	0.457896i	$-0.151397\pi$
$739$	2.63965e7			1.77801			0.889006	+	0.457896i	$0.151397\pi$
$740$	9.99879e6			0.671225
$741$	−9.12226e6	−	102170.i	−0.610319	−	0.00683561i
$742$		0			0
$743$			3.04678e6i			0.202474i	0.994862	+	0.101237i	$0.0322800\pi$
$743$			3.04678e6i			0.202474i	−0.994862	+	0.101237i	$0.967720\pi$
$744$	3.69000e6	+	41328.2i	0.244396	+	0.00273725i
$745$		−	1.19305e7i		−	0.787533i
$746$			3.18304e7i			2.09409i
$747$	−882747.	−	19776.1i	−0.0578808	−	0.00129670i
$748$		−	1.46609e7i		−	0.958091i
$749$		0			0
$750$	−196230.	+	1.75205e7i	−0.0127383	+	1.13735i
$751$	1.26517e7			0.818559			0.409279	−	0.912409i	$-0.365780\pi$
$751$	1.26517e7			0.818559			0.409279	+	0.912409i	$0.365780\pi$
$752$	−3.41737e7			−2.20367
$753$	1.09724e7	+	122891.i	0.705201	+	0.00789829i
$754$			2.38995e7i			1.53095i
$755$	−6.62129e6			−0.422742
$756$		0			0
$757$	−1.58198e7			−1.00337			−0.501686	−	0.865050i	$-0.667287\pi$
$757$	−1.58198e7			−1.00337			−0.501686	+	0.865050i	$0.667287\pi$
$758$			1.99674e7i			1.26226i
$759$	−7.89240e6	−	88395.3i	−0.497284	−	0.00556961i
$760$	7.11566e6			0.446870
$761$	−6.50793e6			−0.407363			−0.203681	−	0.979037i	$-0.565291\pi$
$761$	−6.50793e6			−0.407363			−0.203681	+	0.979037i	$0.565291\pi$
$762$	−17272.1	+	1.54214e6i	−0.00107760	+	0.0962136i
$763$		0			0
$764$		−	1.26676e7i		−	0.785165i
$765$	2.31040e7	+	517596.i	1.42736	+	0.0319770i
$766$		−	1.55640e6i		−	0.0958405i
$767$		−	1.53712e7i		−	0.943452i
$768$	−2.14301e7	−	240018.i	−1.31105	−	0.0146839i
$769$			1.80464e7i			1.10046i	0.835012	+	0.550231i	$0.185460\pi$
$769$			1.80464e7i			1.10046i	−0.835012	+	0.550231i	$0.814540\pi$
$770$		0			0
$771$	8.73020e6	+	97778.7i	0.528918	+	0.00592391i
$772$	721214.			0.0435533
$773$	−8.59104e6			−0.517127			−0.258563	−	0.965994i	$-0.583249\pi$
$773$	−8.59104e6			−0.517127			−0.258563	+	0.965994i	$0.583249\pi$
$774$	661693.	−	2.95360e7i	0.0397013	−	1.77215i
$775$			1.56875e7i			0.938207i
$776$	−3.99115e6			−0.237927
$777$		0			0
$778$	−1.44943e7			−0.858518
$779$			6.79195e6i			0.401006i
$780$	−184238.	+	1.64497e7i	−0.0108428	+	0.968103i
$781$	7.48689e6			0.439211
$782$	6.36645e6			0.372289
$783$	771873.	−	2.29646e7i	0.0449927	−	1.33861i
$784$		0			0
$785$		−	4.64669e7i		−	2.69135i
$786$	213619.	−	1.90730e7i	0.0123334	−	1.10119i
$787$		−	1.75995e7i		−	1.01289i	−0.862271	−	0.506447i	$-0.830959\pi$
$787$		−	1.75995e7i		−	1.01289i	0.862271	−	0.506447i	$-0.169041\pi$
$788$			2.29289e7i			1.31543i
$789$	−231000.	+	2.06249e7i	−0.0132105	+	1.17950i
$790$		−	4.65846e7i		−	2.65568i
$791$		0			0
$792$	1.10543e7	+	247648.i	0.626207	+	0.0140289i
$793$	−1.07595e7			−0.607587
$794$	1.76498e7			0.993550
$795$	260083.	−	2.32216e7i	0.0145947	−	1.30309i
$796$			1.35382e7i			0.757316i
$797$	−2.22022e7			−1.23808			−0.619042	−	0.785358i	$-0.712479\pi$
$797$	−2.22022e7			−1.23808			−0.619042	+	0.785358i	$0.712479\pi$
$798$		0			0
$799$	−2.92972e7			−1.62352
$800$		−	3.29223e7i		−	1.81872i
$801$	1.99926e7	+	447891.i	1.10100	+	0.0246656i
$802$	−3.09025e7			−1.69652
$803$	−2.52028e7			−1.37930
$804$	−8.58826e6	−	96188.9i	−0.468560	−	0.00524789i
$805$		0			0
$806$			1.27757e7i			0.692703i
$807$	−1.25297e7	−	140334.i	−0.677264	−	0.00758539i
$808$		−	3.73705e6i		−	0.201373i
$809$		−	1.62985e7i		−	0.875541i	−0.899087	−	0.437770i	$-0.855768\pi$
$809$		−	1.62985e7i		−	0.875541i	0.899087	−	0.437770i	$-0.144232\pi$
$810$	1.73521e6	−	3.87078e7i	0.0929264	−	2.07294i
$811$		−	2.19393e7i		−	1.17131i	−0.810562	−	0.585653i	$-0.800838\pi$
$811$		−	2.19393e7i		−	1.17131i	0.810562	−	0.585653i	$-0.199162\pi$
$812$		0			0
$813$	−278441.	+	2.48606e7i	−0.0147743	+	1.31913i
$814$	2.32666e7			1.23075
$815$	−1.36567e6			−0.0720198
$816$	−2.06512e7	−	231295.i	−1.08573	−	0.0121602i
$817$		−	1.80587e7i		−	0.946525i
$818$	1.82276e7			0.952457
$819$		0			0
$820$	1.22476e7			0.636085
$821$			1.30873e7i			0.677632i	0.940853	+	0.338816i	$0.110026\pi$
$821$			1.30873e7i			0.677632i	−0.940853	+	0.338816i	$0.889974\pi$
$822$	2.93338e7	+	328541.i	1.51422	+	0.0169594i
$823$	1.41992e7			0.730741			0.365371	−	0.930862i	$-0.380942\pi$
$823$	1.41992e7			0.730741			0.365371	+	0.930862i	$0.380942\pi$
$824$	−7.73628e6			−0.396930
$825$	−526419.	+	4.70015e7i	−0.0269275	+	2.40423i
$826$		0			0
$827$		−	5.24134e6i		−	0.266489i	−0.991083	−	0.133244i	$-0.957460\pi$
$827$		−	5.24134e6i		−	0.266489i	0.991083	−	0.133244i	$-0.0425395\pi$
$828$	97588.3	−	4.35605e6i	0.00494677	−	0.220809i
$829$			1.62990e7i			0.823712i	0.911249	+	0.411856i	$0.135119\pi$
$829$			1.62990e7i			0.823712i	−0.911249	+	0.411856i	$0.864881\pi$
$830$			2.38430e6i			0.120134i
$831$	1.81612e7	+	203406.i	0.912309	+	0.0102179i
$832$		−	5.49696e6i		−	0.275305i
$833$		0			0
$834$	3.15870e6	+	35377.6i	0.157251	+	0.00176122i
$835$	3.58880e6			0.178128
$836$	−1.50254e7			−0.743551
$837$	412611.	−	1.22759e7i	0.0203576	−	0.605677i
$838$		−	1.14185e7i		−	0.561692i
$839$	3.24297e7			1.59051			0.795257	−	0.606273i	$-0.207336\pi$
$839$	3.24297e7			1.59051			0.795257	+	0.606273i	$0.207336\pi$
$840$		0			0
$841$	−1.62840e7			−0.793910
$842$		−	3.80095e7i		−	1.84762i
$843$	170493.	−	1.52225e7i	0.00826299	−	0.737763i
$844$	−5.99313e6			−0.289599
$845$	−7.51387e6			−0.362011
$846$	−1.10017e6	+	4.91084e7i	−0.0528488	+	2.35901i
$847$		0			0
$848$			2.07537e7i			0.991076i
$849$	−73907.2	+	6.59883e6i	−0.00351899	+	0.314194i
$850$		−	3.79140e7i		−	1.79992i
$851$			4.12415e6i			0.195214i
$852$	−46287.1	+	4.13276e6i	−0.00218454	+	0.195048i
$853$			2.65171e7i			1.24783i	0.781494	+	0.623913i	$0.214458\pi$
$853$			2.65171e7i			1.24783i	−0.781494	+	0.623913i	$0.785542\pi$
$854$		0			0
$855$	530465.	−	2.36784e7i	0.0248165	−	1.10774i
$856$	1.01923e7			0.475432
$857$	−1.14566e7			−0.532848			−0.266424	−	0.963856i	$-0.585842\pi$
$857$	−1.14566e7			−0.532848			−0.266424	+	0.963856i	$0.585842\pi$
$858$	−428710.	+	3.82775e7i	−0.0198813	+	1.77511i
$859$		−	1.85675e7i		−	0.858560i	−0.903171	−	0.429280i	$-0.858767\pi$
$859$		−	1.85675e7i		−	0.858560i	0.903171	−	0.429280i	$-0.141233\pi$
$860$	−3.25644e7			−1.50140
$861$		0			0
$862$	9.34639e6			0.428426
$863$		−	2.57457e7i		−	1.17673i	−0.808595	−	0.588366i	$-0.799772\pi$
$863$		−	2.57457e7i		−	1.17673i	0.808595	−	0.588366i	$-0.200228\pi$
$864$	−865922.	+	2.57627e7i	−0.0394634	+	1.17411i
$865$	−9.12447e6			−0.414636
$866$	−5.39774e7			−2.44578
$867$	4.42766e6	+	49590.0i	0.200044	+	0.00224051i
$868$		0			0
$869$		−	4.42480e7i		−	1.98767i
$870$	−6.20431e7	−	694886.i	−2.77904	−	0.0311254i
$871$			1.33753e7i			0.597389i
$872$			1.66298e7i			0.740620i
$873$	−297536.	+	1.32811e7i	−0.0132131	+	0.589793i
$874$		−	6.52473e6i		−	0.288924i
$875$		0			0
$876$	155814.	−	1.39119e7i	0.00686036	−	0.612529i
$877$	3.36055e7			1.47540			0.737702	−	0.675127i	$-0.235911\pi$
$877$	3.36055e7			1.47540			0.737702	+	0.675127i	$0.235911\pi$
$878$	2.89479e7			1.26730
$879$	1.75712e7	+	196798.i	0.767060	+	0.00859111i
$880$		−	6.91399e7i		−	3.00969i
$881$	−2.02040e7			−0.876995			−0.438497	−	0.898732i	$-0.644489\pi$
$881$	−2.02040e7			−0.876995			−0.438497	+	0.898732i	$0.644489\pi$
$882$		0			0
$883$	−2.26260e7			−0.976575			−0.488287	−	0.872683i	$-0.662378\pi$
$883$	−2.26260e7			−0.976575			−0.488287	+	0.872683i	$0.662378\pi$
$884$		−	1.26037e7i		−	0.542458i
$885$	3.99036e7	+	446922.i	1.71259	+	0.0191811i
$886$	−4.41673e7			−1.89024
$887$	1.19883e7			0.511620			0.255810	−	0.966727i	$-0.417658\pi$
$887$	1.19883e7			0.511620			0.255810	+	0.966727i	$0.417658\pi$
$888$	64703.9	−	5.77710e6i	0.00275358	−	0.245854i
$889$		0			0
$890$		−	5.39999e7i		−	2.28517i
$891$	1.64817e6	−	3.67663e7i	0.0695517	−	1.55151i
$892$			6.27840e6i			0.264202i
$893$			3.00256e7i			1.25998i
$894$	1.53244e7	+	171634.i	0.641268	+	0.00718223i
$895$			2.98765e7i			1.24673i
$896$		0			0
$897$	−6.78493e6	−	75991.6i	−0.281556	−	0.00315344i
$898$	−5.34125e7			−2.21031
$899$	−1.96692e7			−0.811683
$900$	−2.59415e7	−	581166.i	−1.06755	−	0.0239163i
$901$			1.77922e7i			0.730160i
$902$	2.84994e7			1.16632
$903$		0			0
$904$	4.17960e6			0.170104
$905$			7.78601e6i			0.316005i
$906$	95254.7	−	8.50484e6i	0.00385537	−	0.344228i
$907$	−2.97148e7			−1.19937			−0.599686	−	0.800235i	$-0.704708\pi$
$907$	−2.97148e7			−1.19937			−0.599686	+	0.800235i	$0.704708\pi$
$908$	−1.50574e7			−0.606086
$909$	−1.24356e7	−	278593.i	−0.499179	−	0.0111831i
$910$		0			0
$911$			3.65820e7i			1.46040i	0.683234	+	0.730200i	$0.260573\pi$
$911$			3.65820e7i			1.46040i	−0.683234	+	0.730200i	$0.739427\pi$
$912$	−237045.	+	2.11647e7i	−0.00943723	+	0.842606i
$913$			2.26471e6i			0.0899156i
$914$		−	5.50469e7i		−	2.17955i
$915$	312835.	−	2.79316e7i	0.0123527	−	1.10292i
$916$		−	1.83521e6i		−	0.0722682i
$917$		0			0
$918$	−997212.	+	2.96689e7i	−0.0390554	+	1.16197i
$919$	2.19246e7			0.856332			0.428166	−	0.903700i	$-0.359160\pi$
$919$	2.19246e7			0.856332			0.428166	+	0.903700i	$0.359160\pi$
$920$	5.29246e6			0.206152
$921$	−533826.	+	4.76628e7i	−0.0207372	+	1.85153i
$922$			5.39860e7i			2.09148i
$923$	6.43632e6			0.248676
$924$		0			0
$925$	2.45605e7			0.943805
$926$			2.05962e7i			0.789332i
$927$	−576732.	+	2.57436e7i	−0.0220432	+	0.983943i
$928$	4.12784e7			1.57345
$929$	3.56775e7			1.35630			0.678148	−	0.734925i	$-0.262783\pi$
$929$	3.56775e7			1.35630			0.678148	+	0.734925i	$0.262783\pi$
$930$	−3.31657e7	−	371457.i	−1.25742	−	0.0140832i
$931$		0			0
$932$			2.31953e7i			0.874703i
$933$	−1.13312e7	−	126910.i	−0.426159	−	0.00477300i
$934$		−	5.43794e6i		−	0.203970i
$935$		−	5.92737e7i		−	2.21735i
$936$	9.50313e6	+	212898.i	0.354550	+	0.00794294i
$937$		−	8.00107e6i		−	0.297714i	−0.988859	−	0.148857i	$-0.952441\pi$
$937$		−	8.00107e6i		−	0.297714i	0.988859	−	0.148857i	$-0.0475594\pi$
$938$		0			0
$939$	343743.	−	3.06912e7i	0.0127224	−	1.13592i
$940$	5.41436e7			1.99861
$941$	1.66012e7			0.611175			0.305588	−	0.952164i	$-0.401147\pi$
$941$	1.66012e7			0.611175			0.305588	+	0.952164i	$0.401147\pi$
$942$	5.96853e7	+	668479.i	2.19149	+	0.0245448i
$943$			5.05170e6i			0.184994i
$944$	−3.56629e7			−1.30253
$945$		0			0
$946$	−7.57753e7			−2.75296
$947$		−	1.68763e7i		−	0.611510i	−0.952110	−	0.305755i	$-0.901091\pi$
$947$		−	1.68763e7i		−	0.611510i	0.952110	−	0.305755i	$-0.0989088\pi$
$948$	2.44249e7	+	273560.i	0.882696	+	0.00988624i
$949$	−2.16663e7			−0.780943
$950$	−3.88566e7			−1.39687
$951$	57962.6	−	5.17521e6i	0.00207824	−	0.185557i
$952$		0			0
$953$			1.90733e7i			0.680288i	0.940373	+	0.340144i	$0.110476\pi$
$953$			1.90733e7i			0.680288i	−0.940373	+	0.340144i	$0.889524\pi$
$954$	2.98236e7	+	668136.i	1.06094	+	0.0237681i
$955$		−	5.12148e7i		−	1.81714i
$956$			1.01083e7i			0.357712i
$957$	−5.89311e7	−	660031.i	−2.08001	−	0.0232962i
$958$		−	4.81428e7i		−	1.69479i
$959$		0			0
$960$	1.42701e7	+	159826.i	0.499745	+	0.00559717i
$961$	1.81148e7			0.632741
$962$	2.00018e7			0.696836
$963$	759826.	−	3.39164e7i	0.0264027	−	1.17854i
$964$		−	1.40524e7i		−	0.487033i
$965$	2.91585e6			0.100797
$966$		0			0
$967$	−9.76047e6			−0.335664			−0.167832	−	0.985816i	$-0.553677\pi$
$967$	−9.76047e6			−0.335664			−0.167832	+	0.985816i	$0.553677\pi$
$968$		−	1.66023e7i		−	0.569481i
$969$	−203219.	+	1.81445e7i	−0.00695274	+	0.620777i
$970$	3.58724e7			1.22414
$971$	1.21739e7			0.414363			0.207182	−	0.978303i	$-0.433571\pi$
$971$	1.21739e7			0.414363			0.207182	+	0.978303i	$0.433571\pi$
$972$	2.02848e7	+	1.13709e6i	0.688659	+	0.0386038i
$973$		0			0
$974$		−	4.49637e7i		−	1.51867i
$975$	−452551.	+	4.04062e7i	−0.0152460	+	1.36124i
$976$			2.49632e7i			0.838834i
$977$			4.00397e7i			1.34201i	0.741454	+	0.671003i	$0.234136\pi$
$977$			4.00397e7i			1.34201i	−0.741454	+	0.671003i	$0.765864\pi$
$978$	19646.7	−	1.75416e6i	0.000656814	−	0.0586438i
$979$		−	5.12913e7i		−	1.71036i
$980$		0			0
$981$	5.53380e7	+	1.23973e6i	1.83591	+	0.0411297i
$982$	−1.98106e7			−0.655571
$983$	−3.47290e7			−1.14633			−0.573164	−	0.819441i	$-0.694284\pi$
$983$	−3.47290e7			−1.14633			−0.573164	+	0.819441i	$0.694284\pi$
$984$	79256.2	−	7.07641e6i	0.00260943	−	0.232984i
$985$			9.27010e7i			3.04435i
$986$	4.75370e7			1.55718
$987$		0			0
$988$	−1.29170e7			−0.420988
$989$		−	1.34317e7i		−	0.436656i
$990$	−9.93557e7	−	2.22586e6i	−3.22185	−	0.0721787i
$991$	2.53964e7			0.821463			0.410732	−	0.911756i	$-0.365273\pi$
$991$	2.53964e7			0.821463			0.410732	+	0.911756i	$0.365273\pi$
$992$	2.20657e7			0.711933
$993$	7.24868e6	+	81185.6i	0.233285	+	0.00261280i
$994$		0			0
$995$			5.47345e7i			1.75268i
$996$	−1.25012e6	−	14001.4i	−0.0399303	−	0.000447221i
$997$		−	1.52307e7i		−	0.485268i	−0.970118	−	0.242634i	$-0.921989\pi$
$997$		−	1.52307e7i		−	0.485268i	0.970118	−	0.242634i	$-0.0780113\pi$
$998$			7.68855e6i			0.244353i
$999$	−1.92193e7	−	645989.i	−0.609291	−	0.0204791i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	147.6.c.d.146.36	yes	40
3.2	odd	2	inner	147.6.c.d.146.5	✓	40
7.6	odd	2	inner	147.6.c.d.146.6	yes	40
21.20	even	2	inner	147.6.c.d.146.35	yes	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
147.6.c.d.146.5	✓	40	3.2	odd	2	inner
147.6.c.d.146.6	yes	40	7.6	odd	2	inner
147.6.c.d.146.35	yes	40	21.20	even	2	inner
147.6.c.d.146.36	yes	40	1.1	even	1	trivial

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)

\(f(q)\)	\(=\)	\(q+7.35335i q^{2} +(-15.5875 - 0.174581i) q^{3} -22.0717 q^{4} -89.2354 q^{5} +(1.28375 - 114.620i) q^{6} +73.0063i q^{8} +(242.939 + 5.44254i) q^{9} -656.179i q^{10} -623.266i q^{11} +(344.042 + 3.85329i) q^{12} -535.808i q^{13} +(1390.96 + 15.5788i) q^{15} -1243.13 q^{16} -1065.74 q^{17} +(-40.0209 + 1786.41i) q^{18} +1092.24i q^{19} +1969.58 q^{20} +4583.09 q^{22} +812.382i q^{23} +(12.7455 - 1137.98i) q^{24} +4837.96 q^{25} +3939.98 q^{26} +(-3785.86 - 127.248i) q^{27} +6065.90i q^{29} +(-114.556 + 10228.2i) q^{30} +3242.58i q^{31} -6805.00i q^{32} +(-108.810 + 9715.14i) q^{33} -7836.77i q^{34} +(-5362.08 - 120.126i) q^{36} +5076.62 q^{37} -8031.61 q^{38} +(-93.5417 + 8351.90i) q^{39} -6514.75i q^{40} +6218.38 q^{41} -16533.7 q^{43} +13756.5i q^{44} +(-21678.8 - 485.668i) q^{45} -5973.73 q^{46} +27489.9 q^{47} +(19377.3 + 217.027i) q^{48} +35575.2i q^{50} +(16612.2 + 186.058i) q^{51} +11826.2i q^{52} -16694.7i q^{53} +(935.698 - 27838.7i) q^{54} +55617.4i q^{55} +(190.684 - 17025.2i) q^{57} -44604.7 q^{58} +28687.9 q^{59} +(-30700.7 - 343.850i) q^{60} -20080.9i q^{61} -23843.8 q^{62} +10259.2 q^{64} +47813.1i q^{65} +(-71438.8 - 800.118i) q^{66} -24962.8 q^{67} +23522.7 q^{68} +(141.826 - 12663.0i) q^{69} +12012.4i q^{71} +(-397.340 + 17736.1i) q^{72} -40436.7i q^{73} +37330.1i q^{74} +(-75411.7 - 844.614i) q^{75} -24107.6i q^{76} +(-61414.4 - 687.844i) q^{78} +70993.8 q^{79} +110932. q^{80} +(58989.8 + 2644.41i) q^{81} +45725.9i q^{82} -3633.62 q^{83} +95101.9 q^{85} -121578. i q^{86} +(1058.99 - 94552.1i) q^{87} +45502.3 q^{88} +82294.5 q^{89} +(3571.28 - 159412. i) q^{90} -17930.6i q^{92} +(566.091 - 50543.6i) q^{93} +202143. i q^{94} -97466.4i q^{95} +(-1188.02 + 106073. i) q^{96} +54668.6i q^{97} +(3392.15 - 151416. i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q - 640 q^{4} + 440 q^{9} - 3176 q^{15} + 3552 q^{16} - 4544 q^{18} + 21088 q^{22} + 30104 q^{25} + 44664 q^{30} - 59320 q^{36} - 26224 q^{37} - 16216 q^{39} + 21584 q^{43} - 27680 q^{46} + 95784 q^{51}+ \cdots - 258480 q^{99}+O(q^{100}) \) 40 * q - 640 * q^4 + 440 * q^9 - 3176 * q^15 + 3552 * q^16 - 4544 * q^18 + 21088 * q^22 + 30104 * q^25 + 44664 * q^30 - 59320 * q^36 - 26224 * q^37 - 16216 * q^39 + 21584 * q^43 - 27680 * q^46 + 95784 * q^51 - 130304 * q^57 - 131376 * q^58 + 329208 * q^60 + 53968 * q^64 - 187632 * q^67 + 606736 * q^72 + 70312 * q^78 - 597424 * q^79 + 755256 * q^81 + 108112 * q^85 - 1673072 * q^88 + 590480 * q^93 - 258480 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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