LMFDB - Embedded newform 147.6.c.d.146.35

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

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

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

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 $

$2$		−	7.35335i		−	1.29990i	−0.759977	−	0.649950i	$-0.774790\pi$
$2$		−	7.35335i		−	1.29990i	0.759977	−	0.649950i	$-0.225210\pi$
$3$	−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	$0.283025\pi$
$11$			623.266i			1.55307i	−0.630073	+	0.776536i	$0.716975\pi$
$12$	344.042	−	3.85329i	0.689697	−	0.00772464i
$13$			535.808i			0.879328i	0.898162	+	0.439664i	$0.144902\pi$
$13$			535.808i			0.879328i	−0.898162	+	0.439664i	$0.855098\pi$
$14$		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	$-0.887180\pi$
$19$		−	1092.24i		−	0.694118i	0.937843	−	0.347059i	$-0.112820\pi$
$20$	1969.58			1.10103
$21$		0			0
$22$	4583.09			2.01884
$23$		−	812.382i		−	0.320214i	−0.987100	−	0.160107i	$-0.948816\pi$
$23$		−	812.382i		−	0.320214i	0.987100	−	0.160107i	$-0.0511840\pi$
$24$	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	$-0.766429\pi$
$29$		−	6065.90i		−	1.33937i	0.742646	−	0.669685i	$-0.233571\pi$
$30$	−114.556	−	10228.2i	−0.0232389	−	2.07489i
$31$		−	3242.58i		−	0.606019i	−0.952988	−	0.303009i	$-0.902009\pi$
$31$		−	3242.58i		−	0.606019i	0.952988	−	0.303009i	$-0.0979914\pi$
$32$			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	$0.133839\pi$
$53$			16694.7i			0.816373i	−0.912899	+	0.408187i	$0.866161\pi$
$54$	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	$0.112285\pi$
$61$			20080.9i			0.690968i	−0.938425	+	0.345484i	$0.887715\pi$
$62$	−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	$-0.954839\pi$
$71$		−	12012.4i		−	0.282802i	0.989952	−	0.141401i	$-0.0451607\pi$
$72$	−397.340	−	17736.1i	−0.00903297	−	0.403205i
$73$			40436.7i			0.888114i	0.895999	+	0.444057i	$0.146461\pi$
$73$			40436.7i			0.888114i	−0.895999	+	0.444057i	$0.853539\pi$
$74$		−	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	$-0.904690\pi$
$97$		−	54668.6i		−	0.589941i	0.955506	−	0.294970i	$-0.0953097\pi$
$98$		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	$-0.836231\pi$
$103$		−	105967.i		−	0.984190i	0.870541	−	0.492095i	$-0.163769\pi$
$104$	39117.3			0.354639
$105$		0			0
$106$	122762.			1.06120
$107$			139609.i			1.17883i	0.807829	+	0.589417i	$0.200643\pi$
$107$			139609.i			1.17883i	−0.807829	+	0.589417i	$0.799357\pi$
$108$	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	$0.0676350\pi$
$113$			57249.9i			0.421773i	−0.977511	+	0.210886i	$0.932365\pi$
$114$	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	$-0.802085\pi$
$137$		−	255922.i		−	1.16495i	0.812849	−	0.582474i	$-0.197915\pi$
$138$	93115.3	−	1042.90i	0.416220	−	0.00466169i
$139$		−	27558.0i		−	0.120979i	−0.998169	−	0.0604895i	$-0.980734\pi$
$139$		−	27558.0i		−	0.120979i	0.998169	−	0.0604895i	$-0.0192662\pi$
$140$		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	$-0.920662\pi$
$149$		−	133697.i		−	0.493352i	0.969098	−	0.246676i	$-0.0793383\pi$
$150$	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	$-0.680788\pi$
$157$		−	520723.i		−	1.68600i	0.537914	−	0.843000i	$-0.319212\pi$
$158$		−	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	$0.127700\pi$
$179$			334805.i			0.781015i	−0.920600	+	0.390507i	$0.872300\pi$
$180$	478487.	−	10719.5i	1.10075	−	0.0246600i
$181$			87252.4i			0.197962i	0.995089	+	0.0989808i	$0.0315583\pi$
$181$			87252.4i			0.197962i	−0.995089	+	0.0989808i	$0.968442\pi$
$182$		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	$-0.807263\pi$
$191$		−	573929.i		−	1.13835i	0.822217	−	0.569174i	$-0.192737\pi$
$192$	−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	$0.402620\pi$
$197$			1.03884e6i			1.90714i	−0.301179	+	0.953568i	$0.597380\pi$
$198$	1.11341e6	−	24943.6i	2.01833	−	0.0452165i
$199$			613372.i			1.09797i	0.835832	+	0.548986i	$0.184986\pi$
$199$			613372.i			1.09797i	−0.835832	+	0.548986i	$0.815014\pi$
$200$		−	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	$0.0613427\pi$
$223$			284455.i			0.383046i	−0.981488	+	0.191523i	$0.938657\pi$
$224$		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	$-0.983317\pi$
$229$		−	83147.7i		−	0.104776i	0.998627	−	0.0523879i	$-0.0166832\pi$
$230$	533068.			0.664451
$231$		0			0
$232$	−442849.			−0.540176
$233$			1.05091e6i			1.26816i	0.773266	+	0.634081i	$0.218622\pi$
$233$			1.05091e6i			1.26816i	−0.773266	+	0.634081i	$0.781378\pi$
$234$	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	$0.0834948\pi$
$239$			457976.i			0.518618i	−0.965794	+	0.259309i	$0.916505\pi$
$240$	−1.72914e6	+	19366.5i	−1.93777	+	0.0217032i
$241$		−	636671.i		−	0.706110i	−0.935603	−	0.353055i	$-0.885143\pi$
$241$		−	636671.i		−	0.706110i	0.935603	−	0.353055i	$-0.114857\pi$
$242$			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	$0.200789\pi$
$263$			1.32317e6i			1.17958i	−0.807558	+	0.589788i	$0.799211\pi$
$264$	−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	$0.229276\pi$
$271$			1.59491e6i			1.31921i	−0.751613	+	0.659604i	$0.770724\pi$
$272$	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	$-0.879733\pi$
$281$		−	976585.i		−	0.737810i	0.929467	−	0.368905i	$-0.120267\pi$
$282$	35290.3	+	3.15090e6i	0.0264260	+	2.35946i
$283$			423342.i			0.314214i	0.987582	+	0.157107i	$0.0502167\pi$
$283$			423342.i			0.314214i	−0.987582	+	0.157107i	$0.949783\pi$
$284$			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	$0.376627\pi$
$307$			3.05776e6i			1.85165i	−0.377957	+	0.925823i	$0.623373\pi$
$308$		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	$-0.807718\pi$
$313$		−	1.96896e6i		−	1.13600i	0.823030	−	0.567998i	$-0.192282\pi$
$314$	−3.82905e6			−2.19163
$315$		0			0
$316$	−1.56695e6			−0.882752
$317$		−	332011.i		−	0.185568i	−0.995686	−	0.0927841i	$-0.970423\pi$
$317$		−	332011.i		−	0.185568i	0.995686	−	0.0927841i	$-0.0295766\pi$
$318$	−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	$-0.936308\pi$
$347$		−	891627.i		−	0.397521i	0.980048	−	0.198760i	$-0.0636915\pi$
$348$	−23373.7	−	2.08693e6i	−0.0103462	−	0.923759i
$349$			484753.i			0.213038i	0.994311	+	0.106519i	$0.0339705\pi$
$349$			484753.i			0.213038i	−0.994311	+	0.106519i	$0.966030\pi$
$350$		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	$0.0920616\pi$
$359$			1.39291e6i			0.570409i	−0.958467	+	0.285205i	$0.907938\pi$
$360$	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	$0.0991173\pi$
$367$			1.58108e6i			0.612757i	−0.951910	+	0.306378i	$0.900883\pi$
$368$			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	$-0.892876\pi$
$389$		−	1.97112e6i		−	0.660449i	0.943902	−	0.330224i	$-0.107124\pi$
$390$	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	$0.124821\pi$
$397$			2.40025e6i			0.764328i	−0.924095	+	0.382164i	$0.875179\pi$
$398$	4.51034e6			1.42725
$399$		0			0
$400$	−6.01424e6			−1.87945
$401$		−	4.20251e6i		−	1.30511i	−0.757740	−	0.652556i	$-0.773697\pi$
$401$		−	4.20251e6i		−	1.30511i	0.757740	−	0.652556i	$-0.226303\pi$
$402$	−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	$0.119395\pi$
$409$			2.47881e6i			0.732715i	−0.930474	+	0.366358i	$0.880605\pi$
$410$			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	$0.0526952\pi$
$431$			1.27104e6i			0.329584i	−0.986328	+	0.164792i	$0.947305\pi$
$432$	4.70633e6	−	158186.i	1.21331	−	0.0407812i
$433$		−	7.34053e6i		−	1.88151i	−0.339082	−	0.940757i	$-0.610116\pi$
$433$		−	7.34053e6i		−	1.88151i	0.339082	−	0.940757i	$-0.389884\pi$
$434$		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	$0.162077\pi$
$439$			3.93669e6i			0.974923i	−0.873145	+	0.487461i	$0.837923\pi$
$440$	−4.06042e6			−0.999859
$441$		0			0
$442$	−4.19900e6			−1.02233
$443$		−	6.00643e6i		−	1.45414i	−0.686562	−	0.727071i	$-0.740881\pi$
$443$		−	6.00643e6i		−	1.45414i	0.686562	−	0.727071i	$-0.259119\pi$
$444$	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	$-0.676491\pi$
$449$		−	7.26371e6i		−	1.70037i	0.526487	−	0.850183i	$-0.323509\pi$
$450$	−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	$-0.918858\pi$
$491$		−	2.69410e6i		−	0.504324i	0.967685	−	0.252162i	$-0.0811416\pi$
$492$	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	$-0.994931\pi$
$523$		−	199228.i		−	0.0318490i	0.999873	−	0.0159245i	$-0.00506914\pi$
$524$	−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	$-0.758063\pi$
$557$		−	1.00895e7i		−	1.37794i	0.724788	−	0.688971i	$-0.241937\pi$
$558$	−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	$-0.665591\pi$
$569$		−	1.34025e7i		−	1.73542i	0.497072	−	0.867709i	$-0.334409\pi$
$570$	−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	$-0.667103\pi$
$577$		−	1.38406e7i		−	1.73068i	0.501185	−	0.865340i	$-0.332897\pi$
$578$			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	$0.356475\pi$
$599$			1.58076e7i			1.80011i	−0.435773	+	0.900057i	$0.643525\pi$
$600$	61662.1	+	5.50552e6i	0.00699263	+	0.624339i
$601$		−	1.65411e6i		−	0.186800i	−0.995629	−	0.0934001i	$-0.970226\pi$
$601$		−	1.65411e6i		−	0.186800i	0.995629	−	0.0934001i	$-0.0297736\pi$
$602$		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	$-0.780276\pi$
$607$		−	1.15604e7i		−	1.27351i	0.771067	−	0.636755i	$-0.219724\pi$
$608$	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	$-0.853921\pi$
$617$		−	8.37776e6i		−	0.885962i	0.896531	−	0.442981i	$-0.146079\pi$
$618$	1.21460e7	−	136036.i	1.27927	−	0.0143279i
$619$			1.32169e7i			1.38645i	0.720721	+	0.693225i	$0.243811\pi$
$619$			1.32169e7i			1.38645i	−0.720721	+	0.693225i	$0.756189\pi$
$620$		−	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	$0.288433\pi$
$641$			1.63765e7i			1.57426i	−0.616789	+	0.787128i	$0.711567\pi$
$642$	−1.60020e7	+	179223.i	−1.53227	+	0.0171615i
$643$		−	1.82259e7i		−	1.73845i	−0.494417	−	0.869225i	$-0.664619\pi$
$643$		−	1.82259e7i		−	1.73845i	0.494417	−	0.869225i	$-0.335381\pi$
$644$		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	$-0.961486\pi$
$653$		−	2.63042e6i		−	0.241403i	0.992689	−	0.120701i	$-0.0385143\pi$
$654$	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	$0.312070\pi$
$659$			1.85224e7i			1.66144i	−0.556693	+	0.830718i	$0.687930\pi$
$660$	−214310.	−	1.91347e7i	−0.0191506	−	1.70987i
$661$			1.90277e7i			1.69388i	0.531692	+	0.846938i	$0.321556\pi$
$661$			1.90277e7i			1.69388i	−0.531692	+	0.846938i	$0.678444\pi$
$662$			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	$0.165638\pi$
$683$			1.21231e7i			0.994400i	−0.867636	+	0.497200i	$0.834362\pi$
$684$	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	$0.0577172\pi$
$691$			4.52687e6i			0.360664i	−0.983606	+	0.180332i	$0.942283\pi$
$692$	−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	$-0.872820\pi$
$701$		−	1.01222e7i		−	0.778001i	0.921237	−	0.389001i	$-0.127180\pi$
$702$	−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	$0.127924\pi$
$727$			1.11485e7i			0.782310i	−0.920325	+	0.391155i	$0.872076\pi$
$728$		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	$0.162064\pi$
$733$			1.41807e7i			0.974850i	−0.873165	+	0.487425i	$0.837936\pi$
$734$	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	$-0.967720\pi$
$743$		−	3.04678e6i		−	0.202474i	0.994862	−	0.101237i	$-0.0322800\pi$
$744$	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	$-0.814540\pi$
$769$		−	1.80464e7i		−	1.10046i	0.835012	−	0.550231i	$-0.185460\pi$
$770$		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	$0.169041\pi$
$787$			1.75995e7i			1.01289i	−0.862271	+	0.506447i	$0.830959\pi$
$788$		−	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	$0.144232\pi$
$809$			1.62985e7i			0.875541i	−0.899087	+	0.437770i	$0.855768\pi$
$810$	1.73521e6	+	3.87078e7i	0.0929264	+	2.07294i
$811$			2.19393e7i			1.17131i	0.810562	+	0.585653i	$0.199162\pi$
$811$			2.19393e7i			1.17131i	−0.810562	+	0.585653i	$0.800838\pi$
$812$		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	$-0.889974\pi$
$821$		−	1.30873e7i		−	0.677632i	0.940853	−	0.338816i	$-0.110026\pi$
$822$	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	$0.0425395\pi$
$827$			5.24134e6i			0.266489i	−0.991083	+	0.133244i	$0.957460\pi$
$828$	97588.3	+	4.35605e6i	0.00494677	+	0.220809i
$829$		−	1.62990e7i		−	0.823712i	−0.911249	−	0.411856i	$-0.864881\pi$
$829$		−	1.62990e7i		−	0.823712i	0.911249	−	0.411856i	$-0.135119\pi$
$830$		−	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	$-0.785542\pi$
$853$		−	2.65171e7i		−	1.24783i	0.781494	−	0.623913i	$-0.214458\pi$
$854$		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	$0.141233\pi$
$859$			1.85675e7i			0.858560i	−0.903171	+	0.429280i	$0.858767\pi$
$860$	−3.25644e7			−1.50140
$861$		0			0
$862$	9.34639e6			0.428426
$863$			2.57457e7i			1.17673i	0.808595	+	0.588366i	$0.200228\pi$
$863$			2.57457e7i			1.17673i	−0.808595	+	0.588366i	$0.799772\pi$
$864$	−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	$-0.739427\pi$
$911$		−	3.65820e7i		−	1.46040i	0.683234	−	0.730200i	$-0.260573\pi$
$912$	−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	$0.0475594\pi$
$937$			8.00107e6i			0.297714i	−0.988859	+	0.148857i	$0.952441\pi$
$938$		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	$0.0989088\pi$
$947$			1.68763e7i			0.611510i	−0.952110	+	0.305755i	$0.901091\pi$
$948$	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	$-0.889524\pi$
$953$		−	1.90733e7i		−	0.680288i	0.940373	−	0.340144i	$-0.110476\pi$
$954$	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	$-0.765864\pi$
$977$		−	4.00397e7i		−	1.34201i	0.741454	−	0.671003i	$-0.234136\pi$
$978$	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	$0.0780113\pi$
$997$			1.52307e7i			0.485268i	−0.970118	+	0.242634i	$0.921989\pi$
$998$		−	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.146.35	yes	40
3.2	odd	2	inner	147.6.c.d.146.6	yes	40
7.6	odd	2	inner	147.6.c.d.146.5	✓	40
21.20	even	2	inner	147.6.c.d.146.36	yes	40

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

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