LMFDB - Embedded newform 19.7.b.b.18.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [19,7,Mod(18,19)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(19, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 7, names="a")

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

chi := DirichletCharacter("19.18");

S:= CuspForms(chi, 7);

N := Newforms(S);

Level:	$ N $	$=$	$ 19 $
Weight:	$ k $	$=$	$ 7 $
Character orbit:	$[\chi]$	$=$	19.b (of order $2$, degree $1$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$4.37102758878$
Analytic rank:	$0$
Dimension:	$8$
Coefficient field:	$\mathbb{Q}[x]/(x^{8} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} + 483x^{6} + 75582x^{4} + 4242376x^{2} + 71047680 $ x^8 + 483x^6 + 75582x^4 + 4242376*x^2 + 71047680
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2^{3}\cdot 29 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			18.7
Root			$12.8592i$ of defining polynomial
Character	$\chi$	$=$	19.18
Dual form			19.7.b.b.18.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+12.8592i q^{2} -21.6433i q^{3} -101.358 q^{4} -216.848 q^{5} +278.315 q^{6} -134.238 q^{7} -480.398i q^{8} +260.567 q^{9} +O(q^{10})$	\(q+12.8592i q^{2} -21.6433i q^{3} -101.358 q^{4} -216.848 q^{5} +278.315 q^{6} -134.238 q^{7} -480.398i q^{8} +260.567 q^{9} -2788.49i q^{10} -610.546 q^{11} +2193.73i q^{12} +3172.26i q^{13} -1726.19i q^{14} +4693.32i q^{15} -309.417 q^{16} -4960.26 q^{17} +3350.68i q^{18} +(4433.12 - 5233.86i) q^{19} +21979.4 q^{20} +2905.36i q^{21} -7851.11i q^{22} -10967.2 q^{23} -10397.4 q^{24} +31398.3 q^{25} -40792.7 q^{26} -21417.5i q^{27} +13606.2 q^{28} +43660.1i q^{29} -60352.2 q^{30} +2147.30i q^{31} -34724.3i q^{32} +13214.2i q^{33} -63784.9i q^{34} +29109.3 q^{35} -26410.7 q^{36} -32215.6i q^{37} +(67303.1 + 57006.3i) q^{38} +68658.3 q^{39} +104174. i q^{40} -1442.23i q^{41} -37360.5 q^{42} +64084.1 q^{43} +61883.9 q^{44} -56503.6 q^{45} -141030. i q^{46} -96956.3 q^{47} +6696.80i q^{48} -99629.1 q^{49} +403756. i q^{50} +107356. i q^{51} -321536. i q^{52} +58504.5i q^{53} +275411. q^{54} +132396. q^{55} +64487.7i q^{56} +(-113278. - 95947.5i) q^{57} -561433. q^{58} -78833.1i q^{59} -475707. i q^{60} -12464.6 q^{61} -27612.5 q^{62} -34978.0 q^{63} +426723. q^{64} -687901. i q^{65} -169924. q^{66} +557643. i q^{67} +502764. q^{68} +237368. i q^{69} +374322. i q^{70} +375099. i q^{71} -125176. i q^{72} -678557. q^{73} +414266. q^{74} -679562. i q^{75} +(-449334. + 530496. i) q^{76} +81958.6 q^{77} +882889. i q^{78} -441287. i q^{79} +67096.6 q^{80} -273592. q^{81} +18545.9 q^{82} -286505. q^{83} -294482. i q^{84} +1.07562e6 q^{85} +824069. i q^{86} +944950. q^{87} +293305. i q^{88} -372535. i q^{89} -726589. i q^{90} -425839. i q^{91} +1.11162e6 q^{92} +46474.6 q^{93} -1.24678e6i q^{94} +(-961316. + 1.13495e6i) q^{95} -751549. q^{96} -392760. i q^{97} -1.28115e6i q^{98} -159088. q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 454 q^{4} + 108 q^{5} - 358 q^{6} - 140 q^{7} - 1052 q^{9}+O(q^{10}) $ 8 * q - 454 * q^4 + 108 * q^5 - 358 * q^6 - 140 * q^7 - 1052 * q^9	$ 8 q - 454 q^{4} + 108 q^{5} - 358 q^{6} - 140 q^{7} - 1052 q^{9} - 2024 q^{11} + 11546 q^{16} + 6008 q^{17} + 20552 q^{19} - 10732 q^{20} - 50252 q^{23} + 64310 q^{24} + 78492 q^{25} - 37522 q^{26} - 135818 q^{28} - 187696 q^{30} + 210800 q^{35} + 35052 q^{36} + 103318 q^{38} + 43724 q^{39} - 429970 q^{42} + 260800 q^{43} + 693512 q^{44} - 191012 q^{45} - 100248 q^{47} - 301872 q^{49} + 390202 q^{54} - 52480 q^{55} - 186860 q^{57} - 405186 q^{58} - 54548 q^{61} - 1461908 q^{62} - 137408 q^{63} - 858058 q^{64} + 1539556 q^{66} + 1243910 q^{68} + 479968 q^{73} + 2645844 q^{74} - 2569288 q^{76} - 1755300 q^{77} + 2344672 q^{80} - 4279648 q^{81} + 1847172 q^{82} + 483040 q^{83} + 2111780 q^{85} + 2802652 q^{87} + 3905498 q^{92} + 1507528 q^{93} - 2383888 q^{95} - 8462238 q^{96} + 528224 q^{99}+O(q^{100}) $ 8 * q - 454 * q^4 + 108 * q^5 - 358 * q^6 - 140 * q^7 - 1052 * q^9 - 2024 * q^11 + 11546 * q^16 + 6008 * q^17 + 20552 * q^19 - 10732 * q^20 - 50252 * q^23 + 64310 * q^24 + 78492 * q^25 - 37522 * q^26 - 135818 * q^28 - 187696 * q^30 + 210800 * q^35 + 35052 * q^36 + 103318 * q^38 + 43724 * q^39 - 429970 * q^42 + 260800 * q^43 + 693512 * q^44 - 191012 * q^45 - 100248 * q^47 - 301872 * q^49 + 390202 * q^54 - 52480 * q^55 - 186860 * q^57 - 405186 * q^58 - 54548 * q^61 - 1461908 * q^62 - 137408 * q^63 - 858058 * q^64 + 1539556 * q^66 + 1243910 * q^68 + 479968 * q^73 + 2645844 * q^74 - 2569288 * q^76 - 1755300 * q^77 + 2344672 * q^80 - 4279648 * q^81 + 1847172 * q^82 + 483040 * q^83 + 2111780 * q^85 + 2802652 * q^87 + 3905498 * q^92 + 1507528 * q^93 - 2383888 * q^95 - 8462238 * q^96 + 528224 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/19\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$-1$

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 $

$2$			12.8592i			1.60740i	0.595037	+	0.803698i	$0.297137\pi$
$2$			12.8592i			1.60740i	−0.595037	+	0.803698i	$0.702863\pi$
$3$		−	21.6433i		−	0.801604i	−0.916165	−	0.400802i	$-0.868732\pi$
$3$		−	21.6433i		−	0.801604i	0.916165	−	0.400802i	$-0.131268\pi$
$4$	−101.358			−1.58372
$5$	−216.848			−1.73479			−0.867394	−	0.497622i	$-0.834207\pi$
$5$	−216.848			−1.73479			−0.867394	+	0.497622i	$0.834207\pi$
$6$	278.315			1.28850
$7$	−134.238			−0.391365			−0.195682	−	0.980667i	$-0.562692\pi$
$7$	−134.238			−0.391365			−0.195682	+	0.980667i	$0.562692\pi$
$8$		−	480.398i		−	0.938277i
$9$	260.567			0.357431
$10$		−	2788.49i		−	2.78849i
$11$	−610.546			−0.458712			−0.229356	−	0.973343i	$-0.573662\pi$
$11$	−610.546			−0.458712			−0.229356	+	0.973343i	$0.573662\pi$
$12$			2193.73i			1.26952i
$13$			3172.26i			1.44391i	0.691941	+	0.721954i	$0.256756\pi$
$13$			3172.26i			1.44391i	−0.691941	+	0.721954i	$0.743244\pi$
$14$		−	1726.19i		−	0.629079i
$15$			4693.32i			1.39061i
$16$	−309.417			−0.0755412
$17$	−4960.26			−1.00962			−0.504810	−	0.863231i	$-0.668437\pi$
$17$	−4960.26			−1.00962			−0.504810	+	0.863231i	$0.668437\pi$
$18$			3350.68i			0.574533i
$19$	4433.12	−	5233.86i	0.646322	−	0.763065i
$19$	4433.12	−	5233.86i	0.646322	−	0.763065i
$20$	21979.4			2.74743
$21$			2905.36i			0.313720i
$22$		−	7851.11i		−	0.737332i
$23$	−10967.2			−0.901393			−0.450696	−	0.892677i	$-0.648824\pi$
$23$	−10967.2			−0.901393			−0.450696	+	0.892677i	$0.648824\pi$
$24$	−10397.4			−0.752127
$25$	31398.3			2.00949
$26$	−40792.7			−2.32093
$27$		−	21417.5i		−	1.08812i
$28$	13606.2			0.619814
$29$			43660.1i			1.79016i	0.445909	+	0.895078i	$0.352881\pi$
$29$			43660.1i			1.79016i	−0.445909	+	0.895078i	$0.647119\pi$
$30$	−60352.2			−2.23527
$31$			2147.30i			0.0720787i	0.999350	+	0.0360393i	$0.0114742\pi$
$31$			2147.30i			0.0720787i	−0.999350	+	0.0360393i	$0.988526\pi$
$32$		−	34724.3i		−	1.05970i
$33$			13214.2i			0.367705i
$34$		−	63784.9i		−	1.62286i
$35$	29109.3			0.678935
$36$	−26410.7			−0.566072
$37$		−	32215.6i		−	0.636006i	−0.948090	−	0.318003i	$-0.896988\pi$
$37$		−	32215.6i		−	0.636006i	0.948090	−	0.318003i	$-0.103012\pi$
$38$	67303.1	+	57006.3i	1.22655	+	1.03890i
$39$	68658.3			1.15744
$40$			104174.i			1.62771i
$41$		−	1442.23i		−	0.0209258i	−0.999945	−	0.0104629i	$-0.996669\pi$
$41$		−	1442.23i		−	0.0209258i	0.999945	−	0.0104629i	$-0.00333051\pi$
$42$	−37360.5			−0.504272
$43$	64084.1			0.806019			0.403009	−	0.915196i	$-0.367964\pi$
$43$	64084.1			0.806019			0.403009	+	0.915196i	$0.367964\pi$
$44$	61883.9			0.726474
$45$	−56503.6			−0.620067
$46$		−	141030.i		−	1.44890i
$47$	−96956.3			−0.933862			−0.466931	−	0.884294i	$-0.654640\pi$
$47$	−96956.3			−0.933862			−0.466931	+	0.884294i	$0.654640\pi$
$48$			6696.80i			0.0605541i
$49$	−99629.1			−0.846833
$50$			403756.i			3.23005i
$51$			107356.i			0.809315i
$52$		−	321536.i		−	2.28675i
$53$			58504.5i			0.392972i	0.980507	+	0.196486i	$0.0629531\pi$
$53$			58504.5i			0.392972i	−0.980507	+	0.196486i	$0.937047\pi$
$54$	275411.			1.74904
$55$	132396.			0.795768
$56$			64487.7i			0.367209i
$57$	−113278.	−	95947.5i	−0.611676	−	0.518095i
$58$	−561433.			−2.87749
$59$		−	78833.1i		−	0.383842i	−0.981410	−	0.191921i	$-0.938528\pi$
$59$		−	78833.1i		−	0.383842i	0.981410	−	0.191921i	$-0.0614718\pi$
$60$		−	475707.i		−	2.20235i
$61$	−12464.6			−0.0549145			−0.0274573	−	0.999623i	$-0.508741\pi$
$61$	−12464.6			−0.0549145			−0.0274573	+	0.999623i	$0.508741\pi$
$62$	−27612.5			−0.115859
$63$	−34978.0			−0.139886
$64$	426723.			1.62782
$65$		−	687901.i		−	2.50487i
$66$	−169924.			−0.591049
$67$			557643.i			1.85410i	0.374943	+	0.927048i	$0.377662\pi$
$67$			557643.i			1.85410i	−0.374943	+	0.927048i	$0.622338\pi$
$68$	502764.			1.59896
$69$			237368.i			0.722560i
$70$			374322.i			1.09132i
$71$			375099.i			1.04802i	0.851712	+	0.524011i	$0.175565\pi$
$71$			375099.i			1.04802i	−0.851712	+	0.524011i	$0.824435\pi$
$72$		−	125176.i		−	0.335369i
$73$	−678557.			−1.74429			−0.872143	−	0.489252i	$-0.837270\pi$
$73$	−678557.			−1.74429			−0.872143	+	0.489252i	$0.837270\pi$
$74$	414266.			1.02231
$75$		−	679562.i		−	1.61081i
$76$	−449334.	+	530496.i	−1.02360	+	1.20848i
$77$	81958.6			0.179524
$78$			882889.i			1.86047i
$79$		−	441287.i		−	0.895035i	−0.894275	−	0.447517i	$-0.852308\pi$
$79$		−	441287.i		−	0.895035i	0.894275	−	0.447517i	$-0.147692\pi$
$80$	67096.6			0.131048
$81$	−273592.			−0.514812
$82$	18545.9			0.0336361
$83$	−286505.			−0.501069			−0.250535	−	0.968108i	$-0.580606\pi$
$83$	−286505.			−0.501069			−0.250535	+	0.968108i	$0.580606\pi$
$84$		−	294482.i		−	0.496846i
$85$	1.07562e6			1.75148
$86$			824069.i			1.29559i
$87$	944950.			1.43500
$88$			293305.i			0.430399i
$89$		−	372535.i		−	0.528442i	−0.964462	−	0.264221i	$-0.914885\pi$
$89$		−	372535.i		−	0.528442i	0.964462	−	0.264221i	$-0.0851148\pi$
$90$		−	726589.i		−	0.996693i
$91$		−	425839.i		−	0.565095i
$92$	1.11162e6			1.42756
$93$	46474.6			0.0577786
$94$		−	1.24678e6i		−	1.50109i
$95$	−961316.	+	1.13495e6i	−1.12123	+	1.32376i
$96$	−751549.			−0.849461
$97$		−	392760.i		−	0.430341i	−0.976577	−	0.215170i	$-0.930969\pi$
$97$		−	392760.i		−	0.430341i	0.976577	−	0.215170i	$-0.0690307\pi$
$98$		−	1.28115e6i		−	1.36120i
$99$	−159088.			−0.163958
$100$	−3.18248e6			−3.18248
$101$	825999.			0.801707			0.400853	−	0.916142i	$-0.368714\pi$
$101$	825999.			0.801707			0.400853	+	0.916142i	$0.368714\pi$
$102$	−1.38052e6			−1.30089
$103$			700092.i			0.640683i	0.947302	+	0.320342i	$0.103798\pi$
$103$			700092.i			0.640683i	−0.947302	+	0.320342i	$0.896202\pi$
$104$	1.52395e6			1.35478
$105$		−	630023.i		−	0.544237i
$106$	−752320.			−0.631662
$107$			1.15315e6i			0.941315i	0.882316	+	0.470657i	$0.155983\pi$
$107$			1.15315e6i			0.941315i	−0.882316	+	0.470657i	$0.844017\pi$
$108$			2.17084e6i			1.72329i
$109$		−	1.22013e6i		−	0.942160i	−0.882090	−	0.471080i	$-0.843864\pi$
$109$		−	1.22013e6i		−	0.942160i	0.882090	−	0.471080i	$-0.156136\pi$
$110$			1.70250e6i			1.27911i
$111$	−697252.			−0.509825
$112$	41535.5			0.0295642
$113$			1.42763e6i			0.989422i	0.869058	+	0.494711i	$0.164726\pi$
$113$			1.42763e6i			0.989422i	−0.869058	+	0.494711i	$0.835274\pi$
$114$	1.23381e6	−	1.45666e6i	0.832783	−	0.983206i
$115$	2.37823e6			1.56372
$116$		−	4.42532e6i		−	2.83511i
$117$			826588.i			0.516097i
$118$	1.01373e6			0.616987
$119$	665856.			0.395130
$120$	2.25466e6			1.30478
$121$	−1.39879e6			−0.789583
$122$		−	160284.i		−	0.0882695i
$123$	−31214.6			−0.0167742
$124$		−	217646.i		−	0.114153i
$125$	−3.42041e6			−1.75125
$126$		−	449789.i		−	0.224852i
$127$			1.69677e6i			0.828347i	0.910198	+	0.414174i	$0.135929\pi$
$127$			1.69677e6i			0.828347i	−0.910198	+	0.414174i	$0.864071\pi$
$128$			3.26495e6i			1.55685i
$129$		−	1.38699e6i		−	0.646108i
$130$	8.84583e6			4.02632
$131$	976074.			0.434179			0.217090	−	0.976152i	$-0.430344\pi$
$131$	976074.			0.434179			0.217090	+	0.976152i	$0.430344\pi$
$132$		−	1.33937e6i		−	0.582344i
$133$	−595094.	+	702584.i	−0.252948	+	0.298637i
$134$	−7.17083e6			−2.98027
$135$			4.64435e6i			1.88766i
$136$			2.38290e6i			0.947303i
$137$	−1.17898e6			−0.458505			−0.229253	−	0.973367i	$-0.573628\pi$
$137$	−1.17898e6			−0.458505			−0.229253	+	0.973367i	$0.573628\pi$
$138$	−3.05235e6			−1.16144
$139$	4.38059e6			1.63113			0.815565	−	0.578665i	$-0.196426\pi$
$139$	4.38059e6			1.63113			0.815565	+	0.578665i	$0.196426\pi$
$140$	−2.95048e6			−1.07525
$141$			2.09846e6i			0.748587i
$142$	−4.82346e6			−1.68459
$143$		−	1.93681e6i		−	0.662338i
$144$	−80623.8			−0.0270008
$145$		−	9.46763e6i		−	3.10554i
$146$		−	8.72568e6i		−	2.80376i
$147$			2.15630e6i			0.678825i
$148$			3.26532e6i			1.00726i
$149$	−878444.			−0.265555			−0.132778	−	0.991146i	$-0.542390\pi$
$149$	−878444.			−0.265555			−0.132778	+	0.991146i	$0.542390\pi$
$150$	8.73861e6			2.58922
$151$			98177.8i			0.0285156i	0.999898	+	0.0142578i	$0.00453855\pi$
$151$			98177.8i			0.0285156i	−0.999898	+	0.0142578i	$0.995461\pi$
$152$	−2.51433e6	−	2.12966e6i	−0.715966	−	0.606429i
$153$	−1.29248e6			−0.360869
$154$			1.05392e6i			0.288566i
$155$		−	465638.i		−	0.125041i
$156$	−6.95909e6			−1.83307
$157$	2.56108e6			0.661797			0.330899	−	0.943666i	$-0.392648\pi$
$157$	2.56108e6			0.661797			0.330899	+	0.943666i	$0.392648\pi$
$158$	5.67459e6			1.43868
$159$	1.26623e6			0.315008
$160$			7.52991e6i			1.83836i
$161$	1.47222e6			0.352774
$162$		−	3.51817e6i		−	0.827508i
$163$	2.58901e6			0.597821			0.298910	−	0.954281i	$-0.403377\pi$
$163$	2.58901e6			0.597821			0.298910	+	0.954281i	$0.403377\pi$
$164$			146182.i			0.0331407i
$165$		−	2.86549e6i		−	0.637891i
$166$		−	3.68422e6i		−	0.805417i
$167$		−	5.42647e6i		−	1.16511i	−0.812790	−	0.582556i	$-0.802053\pi$
$167$		−	5.42647e6i		−	1.16511i	0.812790	−	0.582556i	$-0.197947\pi$
$168$	1.39573e6			0.294356
$169$	−5.23645e6			−1.08487
$170$			1.38316e7i			2.81532i
$171$	1.15513e6	−	1.36377e6i	0.231015	−	0.272743i
$172$	−6.49546e6			−1.27651
$173$		−	1.02784e6i		−	0.198512i	−0.995062	−	0.0992562i	$-0.968354\pi$
$173$		−	1.02784e6i		−	0.198512i	0.995062	−	0.0992562i	$-0.0316463\pi$
$174$			1.21513e7i			2.30661i
$175$	−4.21484e6			−0.786443
$176$	188913.			0.0346517
$177$	−1.70621e6			−0.307689
$178$	4.79050e6			0.849416
$179$		−	2.69303e6i		−	0.469550i	−0.972050	−	0.234775i	$-0.924565\pi$
$179$		−	2.69303e6i		−	0.469550i	0.972050	−	0.234775i	$-0.0754354\pi$
$180$	5.72711e6			0.982015
$181$		−	1.25185e6i		−	0.211113i	−0.994413	−	0.105557i	$-0.966338\pi$
$181$		−	1.25185e6i		−	0.211113i	0.994413	−	0.105557i	$-0.0336624\pi$
$182$	5.47594e6			0.908331
$183$			269774.i			0.0440197i
$184$			5.26864e6i			0.845756i
$185$			6.98590e6i			1.10333i
$186$			597625.i			0.0928731i
$187$	3.02847e6			0.463125
$188$	9.82733e6			1.47898
$189$			2.87505e6i			0.425853i
$190$	−1.45946e7	−	1.23617e7i	−2.12780	−	1.80226i
$191$	−1.59280e6			−0.228592			−0.114296	−	0.993447i	$-0.536461\pi$
$191$	−1.59280e6			−0.228592			−0.114296	+	0.993447i	$0.536461\pi$
$192$		−	9.23570e6i		−	1.30487i
$193$			8.49629e6i			1.18184i	0.806731	+	0.590918i	$0.201234\pi$
$193$			8.49629e6i			1.18184i	−0.806731	+	0.590918i	$0.798766\pi$
$194$	5.05057e6			0.691728
$195$	−1.48884e7			−2.00792
$196$	1.00982e7			1.34115
$197$	−8.44740e6			−1.10490			−0.552452	−	0.833545i	$-0.686308\pi$
$197$	−8.44740e6			−1.10490			−0.552452	+	0.833545i	$0.686308\pi$
$198$		−	2.04574e6i		−	0.263545i
$199$	6.30988e6			0.800685			0.400343	−	0.916366i	$-0.368891\pi$
$199$	6.30988e6			0.800685			0.400343	+	0.916366i	$0.368891\pi$
$200$		−	1.50837e7i		−	1.88546i
$201$	1.20693e7			1.48625
$202$			1.06217e7i			1.28866i
$203$		−	5.86086e6i		−	0.700605i
$204$		−	1.08815e7i		−	1.28173i
$205$			312745.i			0.0363019i
$206$	−9.00260e6			−1.02983
$207$	−2.85770e6			−0.322185
$208$		−	981552.i		−	0.109075i
$209$	−2.70662e6	+	3.19551e6i	−0.296476	+	0.350027i
$210$	8.10157e6			0.874805
$211$			279028.i			0.0297031i	0.999890	+	0.0148515i	$0.00472756\pi$
$211$			279028.i			0.0297031i	−0.999890	+	0.0148515i	$0.995272\pi$
$212$		−	5.92992e6i		−	0.622360i
$213$	8.11838e6			0.840099
$214$	−1.48286e7			−1.51307
$215$	−1.38965e7			−1.39827
$216$	−1.02889e7			−1.02096
$217$		−	288249.i		−	0.0282091i
$218$	1.56898e7			1.51443
$219$			1.46862e7i			1.39823i
$220$	−1.34194e7			−1.26028
$221$		−	1.57353e7i		−	1.45780i
$222$		−	8.96609e6i		−	0.819491i
$223$			1.67228e7i			1.50798i	0.656886	+	0.753990i	$0.271873\pi$
$223$			1.67228e7i			1.50798i	−0.656886	+	0.753990i	$0.728127\pi$
$224$			4.66133e6i			0.414730i
$225$	8.18135e6			0.718253
$226$	−1.83582e7			−1.59039
$227$		−	1.16656e7i		−	0.997312i	−0.866800	−	0.498656i	$-0.833827\pi$
$227$		−	1.16656e7i		−	0.997312i	0.866800	−	0.498656i	$-0.166173\pi$
$228$	1.14817e7	+	9.72508e6i	0.968726	+	0.820519i
$229$	221475.			0.0184424			0.00922120	−	0.999957i	$-0.497065\pi$
$229$	221475.			0.0184424			0.00922120	+	0.999957i	$0.497065\pi$
$230$			3.05821e7i			2.51353i
$231$		−	1.77385e6i		−	0.143907i
$232$	2.09742e7			1.67966
$233$	5.10799e6			0.403815			0.201907	−	0.979405i	$-0.435286\pi$
$233$	5.10799e6			0.403815			0.201907	+	0.979405i	$0.435286\pi$
$234$	−1.06292e7			−0.829573
$235$	2.10248e7			1.62005
$236$			7.99040e6i			0.607900i
$237$	−9.55091e6			−0.717463
$238$			8.56236e6i			0.635130i
$239$	−1.49282e7			−1.09349			−0.546745	−	0.837299i	$-0.684133\pi$
$239$	−1.49282e7			−1.09349			−0.546745	+	0.837299i	$0.684133\pi$
$240$		−	1.45219e6i		−	0.105049i
$241$		−	9.74453e6i		−	0.696161i	−0.937465	−	0.348080i	$-0.886834\pi$
$241$		−	9.74453e6i		−	0.696161i	0.937465	−	0.348080i	$-0.113166\pi$
$242$		−	1.79873e7i		−	1.26917i
$243$		−	9.69192e6i		−	0.675446i
$244$	1.26339e6			0.0869695
$245$	2.16044e7			1.46908
$246$		−	401394.i		−	0.0269628i
$247$	1.66032e7	+	1.40630e7i	1.10179	+	0.933229i
$248$	1.03156e6			0.0676298
$249$			6.20091e6i			0.401659i
$250$		−	4.39836e7i		−	2.81495i
$251$	1.28110e7			0.810141			0.405071	−	0.914285i	$-0.367247\pi$
$251$	1.28110e7			0.810141			0.405071	+	0.914285i	$0.367247\pi$
$252$	3.54532e6			0.221541
$253$	6.69600e6			0.413480
$254$	−2.18191e7			−1.33148
$255$		−	2.32801e7i		−	1.40399i
$256$	−1.46743e7			−0.874657
$257$			2.69491e7i			1.58761i	0.608171	+	0.793806i	$0.291903\pi$
$257$			2.69491e7i			1.58761i	−0.608171	+	0.793806i	$0.708097\pi$
$258$	1.78356e7			1.03855
$259$			4.32456e6i			0.248910i
$260$			6.97245e7i			3.96703i
$261$			1.13764e7i			0.639857i
$262$			1.25515e7i			0.697898i
$263$	1.63453e7			0.898514			0.449257	−	0.893403i	$-0.351689\pi$
$263$	1.63453e7			0.898514			0.449257	+	0.893403i	$0.351689\pi$
$264$	6.34809e6			0.345010
$265$		−	1.26866e7i		−	0.681723i
$266$	−9.03465e6	−	7.65242e6i	−0.480028	−	0.406588i
$267$	−8.06290e6			−0.423601
$268$		−	5.65218e7i		−	2.93638i
$269$			6.31414e6i			0.324383i	0.986759	+	0.162191i	$0.0518562\pi$
$269$			6.31414e6i			0.324383i	−0.986759	+	0.162191i	$0.948144\pi$
$270$	−5.97226e7			−3.03422
$271$	−1.25433e7			−0.630238			−0.315119	−	0.949052i	$-0.602044\pi$
$271$	−1.25433e7			−0.630238			−0.315119	+	0.949052i	$0.602044\pi$
$272$	1.53479e6			0.0762679
$273$	−9.21657e6			−0.452982
$274$		−	1.51607e7i		−	0.737000i
$275$	−1.91701e7			−0.921777
$276$		−	2.40592e7i		−	1.14434i
$277$	−2.04081e7			−0.960202			−0.480101	−	0.877213i	$-0.659400\pi$
$277$	−2.04081e7			−0.960202			−0.480101	+	0.877213i	$0.659400\pi$
$278$			5.63308e7i			2.62187i
$279$			559515.i			0.0257631i
$280$		−	1.39841e7i		−	0.637029i
$281$		−	2.63413e7i		−	1.18719i	−0.804765	−	0.593593i	$-0.797709\pi$
$281$		−	2.63413e7i		−	1.18719i	0.804765	−	0.593593i	$-0.202291\pi$
$282$	−2.69844e7			−1.20328
$283$	−3.93597e7			−1.73657			−0.868285	−	0.496066i	$-0.834777\pi$
$283$	−3.93597e7			−1.73657			−0.868285	+	0.496066i	$0.834777\pi$
$284$		−	3.80194e7i		−	1.65978i
$285$	2.45642e7	+	2.08061e7i	1.06113	+	0.898784i
$286$	2.49058e7			1.06464
$287$			193602.i			0.00818963i
$288$		−	9.04801e6i		−	0.378770i
$289$	466619.			0.0193317
$290$	1.21746e8			4.99184
$291$	−8.50063e6			−0.344963
$292$	6.87774e7			2.76247
$293$			6.79927e6i			0.270308i	0.990825	+	0.135154i	$0.0431530\pi$
$293$			6.79927e6i			0.270308i	−0.990825	+	0.135154i	$0.956847\pi$
$294$	−2.77283e7			−1.09114
$295$			1.70948e7i			0.665885i
$296$	−1.54763e7			−0.596749
$297$			1.30764e7i			0.499135i
$298$		−	1.12961e7i		−	0.426853i
$299$		−	3.47910e7i		−	1.30153i
$300$			6.88793e7i			2.55109i
$301$	−8.60254e6			−0.315448
$302$	−1.26249e6			−0.0458359
$303$		−	1.78774e7i		−	0.642651i
$304$	−1.37168e6	+	1.61944e6i	−0.0488240	+	0.0576428i
$305$	2.70292e6			0.0952651
$306$		−	1.66202e7i		−	0.580060i
$307$		−	3.78588e7i		−	1.30843i	−0.756308	−	0.654216i	$-0.772999\pi$
$307$		−	3.78588e7i		−	1.30843i	0.756308	−	0.654216i	$-0.227001\pi$
$308$	−8.30718e6			−0.284316
$309$	1.51523e7			0.513574
$310$	5.98772e6			0.200991
$311$	−1.46077e7			−0.485626			−0.242813	−	0.970073i	$-0.578070\pi$
$311$	−1.46077e7			−0.485626			−0.242813	+	0.970073i	$0.578070\pi$
$312$		−	3.29833e7i		−	1.08600i
$313$	−1.50273e7			−0.490059			−0.245030	−	0.969516i	$-0.578798\pi$
$313$	−1.50273e7			−0.490059			−0.245030	+	0.969516i	$0.578798\pi$
$314$			3.29334e7i			1.06377i
$315$	7.58494e6			0.242672
$316$			4.47281e7i			1.41749i
$317$			1.48184e7i			0.465183i	0.972575	+	0.232591i	$0.0747205\pi$
$317$			1.48184e7i			0.465183i	−0.972575	+	0.232591i	$0.925279\pi$
$318$			1.62827e7i			0.506343i
$319$		−	2.66565e7i		−	0.821166i
$320$	−9.25343e7			−2.82392
$321$	2.49580e7			0.754562
$322$			1.89316e7i			0.567047i
$323$	−2.19895e7	+	2.59613e7i	−0.652539	+	0.770405i
$324$	2.77309e7			0.815321
$325$			9.96036e7i			2.90152i
$326$			3.32925e7i			0.960935i
$327$	−2.64075e7			−0.755240
$328$	−692843.			−0.0196342
$329$	1.30152e7			0.365481
$330$	3.68478e7			1.02534
$331$			5.51403e7i			1.52050i	0.649633	+	0.760248i	$0.274923\pi$
$331$			5.51403e7i			1.52050i	−0.649633	+	0.760248i	$0.725077\pi$
$332$	2.90397e7			0.793556
$333$		−	8.39432e6i		−	0.227328i
$334$	6.97799e7			1.87280
$335$		−	1.20924e8i		−	3.21646i
$336$		−	898967.i		−	0.0236988i
$337$		−	4.52028e6i		−	0.118107i	−0.998255	−	0.0590535i	$-0.981192\pi$
$337$		−	4.52028e6i		−	0.118107i	0.998255	−	0.0590535i	$-0.0188083\pi$
$338$		−	6.73365e7i		−	1.74381i
$339$	3.08987e7			0.793125
$340$	−1.09024e8			−2.77385
$341$		−	1.31102e6i		−	0.0330634i
$342$	1.75370e7	+	1.48540e7i	0.438406	+	0.371333i
$343$	2.91670e7			0.722786
$344$		−	3.07859e7i		−	0.756269i
$345$		−	5.14728e7i		−	1.25349i
$346$	1.32172e7			0.319088
$347$	−2.13638e7			−0.511317			−0.255658	−	0.966767i	$-0.582292\pi$
$347$	−2.13638e7			−0.511317			−0.255658	+	0.966767i	$0.582292\pi$
$348$	−9.57786e7			−2.27264
$349$	−2.39308e7			−0.562964			−0.281482	−	0.959567i	$-0.590826\pi$
$349$	−2.39308e7			−0.562964			−0.281482	+	0.959567i	$0.590826\pi$
$350$		−	5.41994e7i		−	1.26413i
$351$	6.79420e7			1.57115
$352$			2.12008e7i			0.486098i
$353$	−6.39808e7			−1.45454			−0.727270	−	0.686352i	$-0.759211\pi$
$353$	−6.39808e7			−1.45454			−0.727270	+	0.686352i	$0.759211\pi$
$354$		−	2.19404e7i		−	0.494579i
$355$		−	8.13396e7i		−	1.81810i
$356$			3.77596e7i			0.836907i
$357$		−	1.44113e7i		−	0.316738i
$358$	3.46301e7			0.754754
$359$	2.48683e7			0.537480			0.268740	−	0.963213i	$-0.413393\pi$
$359$	2.48683e7			0.537480			0.268740	+	0.963213i	$0.413393\pi$
$360$			2.71442e7i			0.581794i
$361$	−7.74071e6	−	4.64047e7i	−0.164535	−	0.986371i
$362$	1.60977e7			0.339342
$363$			3.02746e7i			0.632933i
$364$			4.31623e7i			0.894954i
$365$	1.47144e8			3.02596
$366$	−3.46908e6			−0.0707572
$367$	−8.86334e7			−1.79308			−0.896540	−	0.442964i	$-0.853927\pi$
$367$	−8.86334e7			−1.79308			−0.896540	+	0.442964i	$0.853927\pi$
$368$	3.39345e6			0.0680923
$369$		−	375797.i		−	0.00747953i
$370$	−8.98329e7			−1.77350
$371$		−	7.85354e6i		−	0.153796i
$372$	−4.71059e6			−0.0915053
$373$			3.66672e7i			0.706563i	0.935517	+	0.353282i	$0.114934\pi$
$373$			3.66672e7i			0.706563i	−0.935517	+	0.353282i	$0.885066\pi$
$374$			3.89436e7i			0.744425i
$375$			7.40289e7i			1.40381i
$376$			4.65776e7i			0.876221i
$377$	−1.38501e8			−2.58482
$378$	−3.69707e7			−0.684515
$379$			7.73753e7i			1.42130i	0.703548	+	0.710648i	$0.251598\pi$
$379$			7.73753e7i			1.42130i	−0.703548	+	0.710648i	$0.748402\pi$
$380$	9.74374e7	−	1.15037e8i	1.77572	−	2.09646i
$381$	3.67238e7			0.664007
$382$		−	2.04821e7i		−	0.367439i
$383$			5.70315e7i			1.01512i	0.861616	+	0.507561i	$0.169453\pi$
$383$			5.70315e7i			1.01512i	−0.861616	+	0.507561i	$0.830547\pi$
$384$	7.06644e7			1.24798
$385$	−1.77726e7			−0.311436
$386$	−1.09255e8			−1.89968
$387$	1.66982e7			0.288096
$388$			3.98095e7i			0.681541i
$389$	3.18945e7			0.541836			0.270918	−	0.962602i	$-0.412673\pi$
$389$	3.18945e7			0.541836			0.270918	+	0.962602i	$0.412673\pi$
$390$		−	1.91453e8i		−	3.22752i
$391$	5.44004e7			0.910064
$392$			4.78616e7i			0.794564i
$393$		−	2.11255e7i		−	0.348040i
$394$		−	1.08627e8i		−	1.77602i
$395$			9.56924e7i			1.55269i
$396$	1.61249e7			0.259664
$397$	2.92281e7			0.467121			0.233560	−	0.972342i	$-0.424962\pi$
$397$	2.92281e7			0.467121			0.233560	+	0.972342i	$0.424962\pi$
$398$			8.11398e7i			1.28702i
$399$	1.52062e7	+	1.28798e7i	0.239388	+	0.202764i
$400$	−9.71515e6			−0.151799
$401$		−	9.77290e7i		−	1.51562i	−0.652476	−	0.757810i	$-0.726270\pi$
$401$		−	9.77290e7i		−	1.51562i	0.652476	−	0.757810i	$-0.273730\pi$
$402$			1.55201e8i			2.38900i
$403$	−6.81179e6			−0.104075
$404$	−8.37219e7			−1.26968
$405$	5.93281e7			0.893090
$406$	7.53658e7			1.12615
$407$			1.96691e7i			0.291743i
$408$	5.15738e7			0.759362
$409$			6.60177e7i			0.964919i	0.875918	+	0.482459i	$0.160256\pi$
$409$			6.60177e7i			0.964919i	−0.875918	+	0.482459i	$0.839744\pi$
$410$	−4.02164e6			−0.0583515
$411$			2.55170e7i			0.367540i
$412$		−	7.09602e7i		−	1.01467i
$413$			1.05824e7i			0.150222i
$414$		−	3.67477e7i		−	0.517880i
$415$	6.21281e7			0.869249
$416$	1.10155e8			1.53011
$417$		−	9.48106e7i		−	1.30752i
$418$	−4.10916e7	−	3.48050e7i	−0.562632	−	0.476554i
$419$	5.57280e7			0.757586			0.378793	−	0.925482i	$-0.376339\pi$
$419$	5.57280e7			0.757586			0.378793	+	0.925482i	$0.376339\pi$
$420$			6.38581e7i			0.861922i
$421$			5.52129e7i			0.739937i	0.929044	+	0.369968i	$0.120631\pi$
$421$			5.52129e7i			0.739937i	−0.929044	+	0.369968i	$0.879369\pi$
$422$	−3.58808e6			−0.0477446
$423$	−2.52636e7			−0.333791
$424$	2.81054e7			0.368717
$425$	−1.55744e8			−2.02882
$426$			1.04396e8i			1.35037i
$427$	1.67322e6			0.0214916
$428$		−	1.16882e8i		−	1.49078i
$429$	−4.19190e7			−0.530933
$430$		−	1.78698e8i		−	2.24758i
$431$		−	9.53718e7i		−	1.19121i	−0.803278	−	0.595605i	$-0.796913\pi$
$431$		−	9.53718e7i		−	1.19121i	0.803278	−	0.595605i	$-0.203087\pi$
$432$			6.62694e6i			0.0821981i
$433$		−	4.42302e7i		−	0.544823i	−0.962181	−	0.272412i	$-0.912179\pi$
$433$		−	4.42302e7i		−	0.544823i	0.962181	−	0.272412i	$-0.0878212\pi$
$434$	3.70665e6			0.0453432
$435$	−2.04911e8			−2.48942
$436$			1.23670e8i			1.49212i
$437$	−4.86192e7	+	5.74010e7i	−0.582590	+	0.687821i
$438$	−1.88853e8			−2.24750
$439$		−	1.47409e7i		−	0.174234i	−0.996198	−	0.0871168i	$-0.972235\pi$
$439$		−	1.47409e7i		−	0.174234i	0.996198	−	0.0871168i	$-0.0277653\pi$
$440$		−	6.36027e7i		−	0.746651i
$441$	−2.59601e7			−0.302684
$442$	2.02342e8			2.34326
$443$	9.74634e7			1.12106			0.560532	−	0.828133i	$-0.310597\pi$
$443$	9.74634e7			1.12106			0.560532	+	0.828133i	$0.310597\pi$
$444$	7.06723e7			0.807422
$445$			8.07837e7i			0.916735i
$446$	−2.15042e8			−2.42392
$447$			1.90124e7i			0.212870i
$448$	−5.72825e7			−0.637072
$449$		−	1.46013e8i		−	1.61307i	−0.591189	−	0.806533i	$-0.701341\pi$
$449$		−	1.46013e8i		−	1.61307i	0.591189	−	0.806533i	$-0.298659\pi$
$450$			1.05205e8i			1.15452i
$451$			880547.i			0.00959893i
$452$		−	1.44703e8i		−	1.56697i
$453$	2.12489e6			0.0228582
$454$	1.50010e8			1.60308
$455$			9.23425e7i			0.980319i
$456$	−4.60930e7	+	5.44185e7i	−0.486116	+	0.573921i
$457$	1.43785e8			1.50648			0.753241	−	0.657744i	$-0.228489\pi$
$457$	1.43785e8			1.50648			0.753241	+	0.657744i	$0.228489\pi$
$458$			2.84798e6i			0.0296442i
$459$			1.06236e8i			1.09859i
$460$	−2.41054e8			−2.47651
$461$	5.83001e7			0.595068			0.297534	−	0.954711i	$-0.403836\pi$
$461$	5.83001e7			0.595068			0.297534	+	0.954711i	$0.403836\pi$
$462$	2.28103e7			0.231316
$463$	2.61228e7			0.263194			0.131597	−	0.991303i	$-0.457989\pi$
$463$	2.61228e7			0.263194			0.131597	+	0.991303i	$0.457989\pi$
$464$		−	1.35092e7i		−	0.135231i
$465$	−1.00779e7			−0.100234
$466$			6.56845e7i			0.649091i
$467$	5.61432e7			0.551248			0.275624	−	0.961266i	$-0.411116\pi$
$467$	5.61432e7			0.551248			0.275624	+	0.961266i	$0.411116\pi$
$468$		−	8.37816e7i		−	0.817355i
$469$		−	7.48570e7i		−	0.725628i
$470$			2.70362e8i			2.60407i
$471$		−	5.54303e7i		−	0.530499i
$472$	−3.78713e7			−0.360150
$473$	−3.91263e7			−0.369731
$474$		−	1.22817e8i		−	1.15325i
$475$	1.39192e8	−	1.64334e8i	1.29878	−	1.53337i
$476$	−6.74901e7			−0.625777
$477$			1.52443e7i			0.140460i
$478$		−	1.91965e8i		−	1.75767i
$479$	−1.94372e8			−1.76859			−0.884295	−	0.466929i	$-0.845360\pi$
$479$	−1.94372e8			−1.76859			−0.884295	+	0.466929i	$0.845360\pi$
$480$	1.62972e8			1.47363
$481$	1.02196e8			0.918333
$482$	1.25307e8			1.11901
$483$		−	3.18638e7i		−	0.282785i
$484$	1.41780e8			1.25048
$485$			8.51695e7i			0.746550i
$486$	1.24630e8			1.08571
$487$			1.10939e8i			0.960497i	0.877133	+	0.480248i	$0.159453\pi$
$487$			1.10939e8i			0.960497i	−0.877133	+	0.480248i	$0.840547\pi$
$488$			5.98795e6i			0.0515250i
$489$		−	5.60347e7i		−	0.479215i
$490$			2.77815e8i			2.36139i
$491$	3.84300e7			0.324658			0.162329	−	0.986737i	$-0.448099\pi$
$491$	3.84300e7			0.324658			0.162329	+	0.986737i	$0.448099\pi$
$492$	3.16386e6			0.0265658
$493$		−	2.16566e8i		−	1.80738i
$494$	−1.80839e8	+	2.13503e8i	−1.50007	+	1.77102i
$495$	3.44980e7			0.284432
$496$		−	664409.i		−	0.00544491i
$497$		−	5.03526e7i		−	0.410159i
$498$	−7.97386e7			−0.645626
$499$	−2.24551e8			−1.80723			−0.903616	−	0.428344i	$-0.859097\pi$
$499$	−2.24551e8			−1.80723			−0.903616	+	0.428344i	$0.859097\pi$
$500$	3.46687e8			2.77349
$501$	−1.17447e8			−0.933959
$502$			1.64738e8i			1.30222i
$503$	1.77754e8			1.39674			0.698370	−	0.715737i	$-0.253909\pi$
$503$	1.77754e8			1.39674			0.698370	+	0.715737i	$0.253909\pi$
$504$			1.68034e7i			0.131252i
$505$	−1.79117e8			−1.39079
$506$			8.61051e7i			0.664626i
$507$			1.13334e8i			0.869635i
$508$		−	1.71982e8i		−	1.31187i
$509$			1.75276e8i			1.32914i	0.747228	+	0.664568i	$0.231384\pi$
$509$			1.75276e8i			1.32914i	−0.747228	+	0.664568i	$0.768616\pi$
$510$	2.99363e8			2.25677
$511$	9.10882e7			0.682652
$512$			2.02574e7i			0.150930i
$513$	−1.12096e8	−	9.49465e7i	−0.830308	−	0.703277i
$514$	−3.46543e8			−2.55192
$515$		−	1.51814e8i		−	1.11145i
$516$			1.40583e8i			1.02326i
$517$	5.91963e7			0.428374
$518$	−5.56103e7			−0.400098
$519$	−2.22459e7			−0.159128
$520$	−3.30466e8			−2.35026
$521$		−	1.55786e8i		−	1.10158i	−0.834644	−	0.550789i	$-0.814327\pi$
$521$		−	1.55786e8i		−	1.10158i	0.834644	−	0.550789i	$-0.185673\pi$
$522$	−1.46291e8			−1.02850
$523$		−	6.68971e7i		−	0.467630i	−0.972281	−	0.233815i	$-0.924879\pi$
$523$		−	6.68971e7i		−	0.467630i	0.972281	−	0.233815i	$-0.0751210\pi$
$524$	−9.89333e7			−0.687620
$525$			9.12232e7i			0.630416i
$526$			2.10187e8i			1.44427i
$527$		−	1.06511e7i		−	0.0727721i
$528$		−	4.08871e6i		−	0.0277769i
$529$	−2.77554e7			−0.187491
$530$	1.63139e8			1.09580
$531$		−	2.05413e7i		−	0.137197i
$532$	6.03178e7	−	7.12128e7i	0.400600	−	0.472958i
$533$	4.57513e6			0.0302150
$534$		−	1.03682e8i		−	0.680895i
$535$		−	2.50059e8i		−	1.63298i
$536$	2.67891e8			1.73966
$537$	−5.82861e7			−0.376393
$538$	−8.11947e7			−0.521412
$539$	6.08281e7			0.388453
$540$		−	4.70744e8i		−	2.98953i
$541$	−1.85229e7			−0.116981			−0.0584907	−	0.998288i	$-0.518629\pi$
$541$	−1.85229e7			−0.116981			−0.0584907	+	0.998288i	$0.518629\pi$
$542$		−	1.61297e8i		−	1.01304i
$543$	−2.70941e7			−0.169229
$544$			1.72242e8i			1.06990i
$545$			2.64582e8i			1.63445i
$546$		−	1.18517e8i		−	0.728122i
$547$			9.09744e7i			0.555850i	0.960603	+	0.277925i	$0.0896466\pi$
$547$			9.09744e7i			0.555850i	−0.960603	+	0.277925i	$0.910353\pi$
$548$	1.19499e8			0.726146
$549$	−3.24785e6			−0.0196281
$550$		−	2.46511e8i		−	1.48166i
$551$	2.28511e8	+	1.93551e8i	1.36601	+	1.15702i
$552$	1.14031e8			0.677961
$553$			5.92376e7i			0.350285i
$554$		−	2.62431e8i		−	1.54343i
$555$	1.51198e8			0.884438
$556$	−4.44010e8			−2.58326
$557$	−2.06452e8			−1.19468			−0.597342	−	0.801987i	$-0.703777\pi$
$557$	−2.06452e8			−1.19468			−0.597342	+	0.801987i	$0.703777\pi$
$558$	−7.19490e6			−0.0414116
$559$			2.03292e8i			1.16382i
$560$	−9.00692e6			−0.0512876
$561$		−	6.55460e7i		−	0.371243i
$562$	3.38728e8			1.90828
$563$			2.53968e8i			1.42316i	0.702606	+	0.711579i	$0.252020\pi$
$563$			2.53968e8i			1.42316i	−0.702606	+	0.711579i	$0.747980\pi$
$564$		−	2.12696e8i		−	1.18556i
$565$		−	3.09580e8i		−	1.71644i
$566$		−	5.06133e8i		−	2.79136i
$567$	3.67266e7			0.201480
$568$	1.80197e8			0.983335
$569$			3.38715e8i			1.83865i	0.393505	+	0.919323i	$0.371262\pi$
$569$			3.38715e8i			1.83865i	−0.393505	+	0.919323i	$0.628738\pi$
$570$	−2.67549e8	+	3.15875e8i	−1.44470	+	1.70565i
$571$	6.12557e7			0.329032			0.164516	−	0.986374i	$-0.447394\pi$
$571$	6.12557e7			0.329032			0.164516	+	0.986374i	$0.447394\pi$
$572$			1.96312e8i			1.04896i
$573$			3.44735e7i			0.183241i
$574$	−2.48956e6			−0.0131640
$575$	−3.44352e8			−1.81134
$576$	1.11190e8			0.581833
$577$	−1.60133e8			−0.833592			−0.416796	−	0.909000i	$-0.636847\pi$
$577$	−1.60133e8			−0.833592			−0.416796	+	0.909000i	$0.636847\pi$
$578$			6.00034e6i			0.0310737i
$579$	1.83888e8			0.947365
$580$			9.59624e8i			4.91832i
$581$	3.84599e7			0.196101
$582$		−	1.09311e8i		−	0.554492i
$583$		−	3.57197e7i		−	0.180261i
$584$			3.25977e8i			1.63662i
$585$		−	1.79244e8i		−	0.895319i
$586$	−8.74330e7			−0.434493
$587$	−2.31399e8			−1.14405			−0.572027	−	0.820235i	$-0.693843\pi$
$587$	−2.31399e8			−1.14405			−0.572027	+	0.820235i	$0.693843\pi$
$588$		−	2.18559e8i		−	1.07507i
$589$	1.12386e7	+	9.51923e6i	0.0550007	+	0.0465861i
$590$	−2.19826e8			−1.07034
$591$			1.82830e8i			0.885695i
$592$			9.96804e6i			0.0480446i
$593$	3.98181e8			1.90949			0.954743	−	0.297432i	$-0.0961301\pi$
$593$	3.98181e8			1.90949			0.954743	+	0.297432i	$0.0961301\pi$
$594$	−1.68151e8			−0.802308
$595$	−1.44390e8			−0.685466
$596$	8.90376e7			0.420567
$597$		−	1.36567e8i		−	0.641833i
$598$	4.47384e8			2.09207
$599$		−	5.91504e7i		−	0.275218i	−0.990487	−	0.137609i	$-0.956058\pi$
$599$		−	5.91504e7i		−	0.275218i	0.990487	−	0.137609i	$-0.0439418\pi$
$600$	−3.26460e8			−1.51139
$601$			8.49083e7i			0.391135i	0.980690	+	0.195567i	$0.0626549\pi$
$601$			8.49083e7i			0.391135i	−0.980690	+	0.195567i	$0.937345\pi$
$602$		−	1.10622e8i		−	0.507049i
$603$			1.45304e8i			0.662711i
$604$		−	9.95114e6i		−	0.0451609i
$605$	3.03327e8			1.36976
$606$	2.29888e8			1.03300
$607$		−	1.86731e8i		−	0.834931i	−0.908693	−	0.417466i	$-0.862918\pi$
$607$		−	1.86731e8i		−	0.834931i	0.908693	−	0.417466i	$-0.137082\pi$
$608$	−1.81742e8	−	1.53937e8i	−0.808621	−	0.684909i
$609$	−1.26848e8			−0.561608
$610$			3.47573e7i			0.153129i
$611$		−	3.07571e8i		−	1.34841i
$612$	1.31004e8			0.571517
$613$	−3.22574e7			−0.140039			−0.0700193	−	0.997546i	$-0.522306\pi$
$613$	−3.22574e7			−0.140039			−0.0700193	+	0.997546i	$0.522306\pi$
$614$	4.86832e8			2.10317
$615$	6.76884e6			0.0290997
$616$		−	3.93727e7i		−	0.168443i
$617$	7.13770e6			0.0303881			0.0151940	−	0.999885i	$-0.495163\pi$
$617$	7.13770e6			0.0303881			0.0151940	+	0.999885i	$0.495163\pi$
$618$			1.94846e8i			0.825518i
$619$	2.27364e8			0.958626			0.479313	−	0.877644i	$-0.340886\pi$
$619$	2.27364e8			0.958626			0.479313	+	0.877644i	$0.340886\pi$
$620$			4.71963e7i			0.198031i
$621$			2.34891e8i			0.980825i
$622$		−	1.87843e8i		−	0.780593i
$623$			5.00085e7i			0.206814i
$624$	−2.12440e7			−0.0874346
$625$	2.51112e8			1.02856
$626$		−	1.93239e8i		−	0.787719i
$627$	6.91614e7	+	5.85803e7i	0.280583	+	0.237656i
$628$	−2.59587e8			−1.04810
$629$			1.59798e8i			0.642124i
$630$			9.75360e7i			0.390071i
$631$	−1.66784e8			−0.663845			−0.331923	−	0.943307i	$-0.607697\pi$
$631$	−1.66784e8			−0.663845			−0.331923	+	0.943307i	$0.607697\pi$
$632$	−2.11993e8			−0.839790
$633$	6.03910e6			0.0238101
$634$	−1.90553e8			−0.747734
$635$		−	3.67943e8i		−	1.43701i
$636$	−1.28343e8			−0.498886
$637$		−	3.16050e8i		−	1.22275i
$638$	3.42781e8			1.31994
$639$			9.77383e7i			0.374595i
$640$		−	7.08000e8i		−	2.70081i
$641$		−	2.98503e8i		−	1.13338i	−0.823932	−	0.566689i	$-0.808224\pi$
$641$		−	2.98503e8i		−	1.13338i	0.823932	−	0.566689i	$-0.191776\pi$
$642$			3.20939e8i			1.21288i
$643$	2.52510e8			0.949829			0.474914	−	0.880032i	$-0.342479\pi$
$643$	2.52510e8			0.949829			0.474914	+	0.880032i	$0.342479\pi$
$644$	−1.49222e8			−0.558696
$645$			3.00767e8i			1.12086i
$646$	−3.33841e8	−	2.82766e8i	−1.23835	−	1.04889i
$647$	1.19544e8			0.441381			0.220690	−	0.975344i	$-0.429169\pi$
$647$	1.19544e8			0.441381			0.220690	+	0.975344i	$0.429169\pi$
$648$			1.31433e8i			0.483037i
$649$			4.81312e7i			0.176073i
$650$	−1.28082e9			−4.66389
$651$	−6.23867e6			−0.0226125
$652$	−2.62418e8			−0.946783
$653$	2.99786e8			1.07664			0.538322	−	0.842739i	$-0.319059\pi$
$653$	2.99786e8			1.07664			0.538322	+	0.842739i	$0.319059\pi$
$654$		−	3.39579e8i		−	1.21397i
$655$	−2.11660e8			−0.753209
$656$			446250.i			0.00158076i
$657$	−1.76809e8			−0.623461
$658$			1.67365e8i			0.587473i
$659$			2.88850e8i			1.00929i	0.863327	+	0.504646i	$0.168377\pi$
$659$			2.88850e8i			1.00929i	−0.863327	+	0.504646i	$0.831623\pi$
$660$			2.90441e8i			1.01024i
$661$			4.67718e8i			1.61950i	0.586777	+	0.809748i	$0.300396\pi$
$661$			4.67718e8i			1.61950i	−0.586777	+	0.809748i	$0.699604\pi$
$662$	−7.09059e8			−2.44404
$663$	−3.40563e8			−1.16858
$664$			1.37636e8i			0.470142i
$665$	1.29045e8	−	1.52354e8i	0.438811	−	0.518071i
$666$	1.07944e8			0.365406
$667$		−	4.78831e8i		−	1.61363i
$668$			5.50018e8i			1.84522i
$669$	3.61938e8			1.20880
$670$	1.55498e9			5.17013
$671$	7.61018e6			0.0251900
$672$	1.00887e8			0.332449
$673$			3.36632e8i			1.10436i	0.833725	+	0.552180i	$0.186204\pi$
$673$			3.36632e8i			1.10436i	−0.833725	+	0.552180i	$0.813796\pi$
$674$	5.81271e7			0.189845
$675$		−	6.72472e8i		−	2.18657i
$676$	5.30758e8			1.71813
$677$		−	5.79462e7i		−	0.186749i	−0.995631	−	0.0933747i	$-0.970235\pi$
$677$		−	5.79462e7i		−	0.186749i	0.995631	−	0.0933747i	$-0.0297655\pi$
$678$			3.97332e8i			1.27487i
$679$			5.27234e7i			0.168420i
$680$		−	5.16728e8i		−	1.64337i
$681$	−2.52483e8			−0.799449
$682$	1.68587e7			0.0531459
$683$			1.89792e8i			0.595683i	0.954615	+	0.297842i	$0.0962668\pi$
$683$			1.89792e8i			0.595683i	−0.954615	+	0.297842i	$0.903733\pi$
$684$	−1.17082e8	+	1.38230e8i	−0.365865	+	0.431949i
$685$	2.55660e8			0.795409
$686$			3.75064e8i			1.16180i
$687$		−	4.79344e6i		−	0.0147835i
$688$	−1.98287e7			−0.0608876
$689$	−1.85592e8			−0.567415
$690$	6.61897e8			2.01485
$691$	−6.07884e8			−1.84241			−0.921205	−	0.389077i	$-0.872794\pi$
$691$	−6.07884e8			−1.84241			−0.921205	+	0.389077i	$0.872794\pi$
$692$			1.04180e8i			0.314389i
$693$	2.13557e7			0.0641673
$694$		−	2.74721e8i		−	0.821889i
$695$	−9.49925e8			−2.82966
$696$		−	4.53952e8i		−	1.34642i
$697$			7.15383e6i			0.0211271i
$698$		−	3.07730e8i		−	0.904906i
$699$		−	1.10554e8i		−	0.323700i
$700$	4.27210e8			1.24551
$701$	2.97048e8			0.862328			0.431164	−	0.902273i	$-0.358103\pi$
$701$	2.97048e8			0.862328			0.431164	+	0.902273i	$0.358103\pi$
$702$			8.73678e8i			2.52546i
$703$	−1.68612e8	−	1.42816e8i	−0.485313	−	0.411064i
$704$	−2.60534e8			−0.746701
$705$		−	4.55047e8i		−	1.29864i
$706$		−	8.22740e8i		−	2.33802i
$707$	−1.10881e8			−0.313760
$708$	1.72939e8			0.487295
$709$	2.19795e8			0.616708			0.308354	−	0.951272i	$-0.400222\pi$
$709$	2.19795e8			0.616708			0.308354	+	0.951272i	$0.400222\pi$
$710$	1.04596e9			2.92240
$711$		−	1.14985e8i		−	0.319913i
$712$	−1.78965e8			−0.495825
$713$		−	2.35499e7i		−	0.0649712i
$714$	1.85318e8			0.509123
$715$			4.19995e8i			1.14902i
$716$			2.72961e8i			0.743638i
$717$			3.23096e8i			0.876546i
$718$			3.19785e8i			0.863944i
$719$	5.01794e8			1.35002			0.675008	−	0.737811i	$-0.264140\pi$
$719$	5.01794e8			1.35002			0.675008	+	0.737811i	$0.264140\pi$
$720$	1.74831e7			0.0468406
$721$		−	9.39791e7i		−	0.250741i
$722$	5.96726e8	−	9.95391e7i	1.58549	−	0.264474i
$723$	−2.10904e8			−0.558045
$724$			1.26885e8i			0.334345i
$725$			1.37085e9i			3.59730i
$726$	−3.89306e8			−1.01737
$727$	5.67690e7			0.147743			0.0738717	−	0.997268i	$-0.476464\pi$
$727$	5.67690e7			0.147743			0.0738717	+	0.997268i	$0.476464\pi$
$728$	−2.04572e8			−0.530215
$729$	−4.09214e8			−1.05625
$730$			1.89215e9i			4.86393i
$731$	−3.17874e8			−0.813772
$732$		−	2.73439e7i		−	0.0697151i
$733$	−5.79284e8			−1.47089			−0.735444	−	0.677585i	$-0.763026\pi$
$733$	−5.79284e8			−1.47089			−0.735444	+	0.677585i	$0.763026\pi$
$734$		−	1.13975e9i		−	2.88219i
$735$		−	4.67591e8i		−	1.17762i
$736$			3.80830e8i			0.955207i
$737$		−	3.40467e8i		−	0.850496i
$738$	4.83244e6			0.0120226
$739$	3.13387e8			0.776511			0.388255	−	0.921552i	$-0.373078\pi$
$739$	3.13387e8			0.776511			0.388255	+	0.921552i	$0.373078\pi$
$740$		−	7.08080e8i		−	1.74738i
$741$	3.04371e8	−	3.59348e8i	0.748081	−	0.883203i
$742$	1.00990e8			0.247210
$743$		−	4.31662e8i		−	1.05239i	−0.850363	−	0.526196i	$-0.823618\pi$
$743$		−	4.31662e8i		−	1.05239i	0.850363	−	0.526196i	$-0.176382\pi$
$744$		−	2.23263e7i		−	0.0542123i
$745$	1.90489e8			0.460682
$746$	−4.71510e8			−1.13573
$747$	−7.46537e7			−0.179098
$748$	−3.06960e8			−0.733462
$749$		−	1.54797e8i		−	0.368398i
$750$	−9.51951e8			−2.25648
$751$			6.89806e8i			1.62857i	0.580463	+	0.814287i	$0.302872\pi$
$751$			6.89806e8i			1.62857i	−0.580463	+	0.814287i	$0.697128\pi$
$752$	2.99999e7			0.0705450
$753$		−	2.77272e8i		−	0.649413i
$754$		−	1.78101e9i		−	4.15483i
$755$		−	2.12897e7i		−	0.0494685i
$756$		−	2.91410e8i		−	0.674434i
$757$	−5.51771e8			−1.27195			−0.635977	−	0.771708i	$-0.719403\pi$
$757$	−5.51771e8			−1.27195			−0.635977	+	0.771708i	$0.719403\pi$
$758$	−9.94982e8			−2.28459
$759$		−	1.44924e8i		−	0.331447i
$760$	5.45230e8	+	4.61814e8i	1.24205	+	1.05203i
$761$	1.04177e8			0.236383			0.118192	−	0.992991i	$-0.462290\pi$
$761$	1.04177e8			0.236383			0.118192	+	0.992991i	$0.462290\pi$
$762$			4.72237e8i			1.06732i
$763$			1.63787e8i			0.368729i
$764$	1.61444e8			0.362027
$765$	2.80272e8			0.626031
$766$	−7.33378e8			−1.63170
$767$	2.50079e8			0.554232
$768$			3.17601e8i			0.701129i
$769$	−5.46341e7			−0.120139			−0.0600696	−	0.998194i	$-0.519132\pi$
$769$	−5.46341e7			−0.120139			−0.0600696	+	0.998194i	$0.519132\pi$
$770$		−	2.28541e8i		−	0.500601i
$771$	5.83267e8			1.27264
$772$		−	8.61170e8i		−	1.87170i
$773$			5.46712e8i			1.18364i	0.806070	+	0.591821i	$0.201591\pi$
$773$			5.46712e8i			1.18364i	−0.806070	+	0.591821i	$0.798409\pi$
$774$			2.14725e8i			0.463084i
$775$			6.74214e7i			0.144841i
$776$	−1.88681e8			−0.403779
$777$	9.35979e7			0.199528
$778$			4.10137e8i			0.870945i
$779$	−7.54842e6	−	6.39358e6i	−0.0159678	−	0.0135248i
$780$	1.50907e9			3.17999
$781$		−	2.29015e8i		−	0.480740i
$782$			6.99544e8i			1.46283i
$783$	9.35091e8			1.94791
$784$	3.08269e7			0.0639708
$785$	−5.55367e8			−1.14808
$786$	2.71656e8			0.559438
$787$		−	3.32410e8i		−	0.681946i	−0.940073	−	0.340973i	$-0.889244\pi$
$787$		−	3.32410e8i		−	0.681946i	0.940073	−	0.340973i	$-0.110756\pi$
$788$	8.56215e8			1.74986
$789$		−	3.53766e8i		−	0.720253i
$790$	−1.23053e9			−2.49580
$791$		−	1.91643e8i		−	0.387225i
$792$			7.64256e7i			0.153838i
$793$		−	3.95409e7i		−	0.0792915i
$794$			3.75849e8i			0.750848i
$795$	−2.74580e8			−0.546472
$796$	−6.39559e8			−1.26806
$797$		−	4.45080e8i		−	0.879149i	−0.898206	−	0.439575i	$-0.855129\pi$
$797$		−	4.45080e8i		−	0.879149i	0.898206	−	0.439575i	$-0.144871\pi$
$798$	−1.65624e8	+	1.95540e8i	−0.325922	+	0.384792i
$799$	4.80929e8			0.942845
$800$		−	1.09028e9i		−	2.12946i
$801$		−	9.70704e7i		−	0.188881i
$802$	1.25671e9			2.43620
$803$	4.14290e8			0.800125
$804$	−1.22332e9			−2.35381
$805$	−3.19249e8			−0.611987
$806$		−	8.75940e7i		−	0.167290i
$807$	1.36659e8			0.260026
$808$		−	3.96808e8i		−	0.752223i
$809$	6.28653e8			1.18731			0.593657	−	0.804718i	$-0.297684\pi$
$809$	6.28653e8			1.18731			0.593657	+	0.804718i	$0.297684\pi$
$810$			7.62910e8i			1.43555i
$811$			5.18077e8i			0.971252i	0.874167	+	0.485626i	$0.161408\pi$
$811$			5.18077e8i			0.971252i	−0.874167	+	0.485626i	$0.838592\pi$
$812$			5.94047e8i			1.10956i
$813$			2.71479e8i			0.505202i
$814$	−2.52928e8			−0.468947
$815$	−5.61423e8			−1.03709
$816$		−	3.32179e7i		−	0.0611366i
$817$	2.84093e8	−	3.35407e8i	0.520948	−	0.615044i
$818$	−8.48934e8			−1.55101
$819$		−	1.10960e8i		−	0.201982i
$820$		−	3.16993e7i		−	0.0574921i
$821$	−1.15009e8			−0.207828			−0.103914	−	0.994586i	$-0.533137\pi$
$821$	−1.15009e8			−0.207828			−0.103914	+	0.994586i	$0.533137\pi$
$822$	−3.28128e8			−0.590782
$823$	4.69442e8			0.842137			0.421068	−	0.907029i	$-0.361655\pi$
$823$	4.69442e8			0.842137			0.421068	+	0.907029i	$0.361655\pi$
$824$	3.36323e8			0.601138
$825$			4.14904e8i			0.738900i
$826$	−1.36081e8			−0.241467
$827$		−	8.21593e8i		−	1.45258i	−0.687388	−	0.726290i	$-0.741243\pi$
$827$		−	8.21593e8i		−	1.45258i	0.687388	−	0.726290i	$-0.258757\pi$
$828$	2.89652e8			0.510253
$829$			3.49058e7i			0.0612681i	0.999531	+	0.0306340i	$0.00975264\pi$
$829$			3.49058e7i			0.0612681i	−0.999531	+	0.0306340i	$0.990247\pi$
$830$			7.98917e8i			1.39723i
$831$			4.41698e8i			0.769702i
$832$			1.35368e9i			2.35042i
$833$	4.94186e8			0.854980
$834$	1.21919e9			2.10170
$835$			1.17672e9i			2.02122i
$836$	2.74339e8	−	3.23892e8i	0.469536	−	0.554346i
$837$	4.59897e7			0.0784304
$838$			7.16617e8i			1.21774i
$839$		−	4.05151e8i		−	0.686010i	−0.939334	−	0.343005i	$-0.888555\pi$
$839$		−	4.05151e8i		−	0.686010i	0.939334	−	0.343005i	$-0.111445\pi$
$840$	−3.02661e8			−0.510645
$841$	−1.31138e9			−2.20466
$842$	−7.09993e8			−1.18937
$843$	−5.70114e8			−0.951654
$844$		−	2.82819e7i		−	0.0470415i
$845$	1.13552e9			1.88202
$846$		−	3.24869e8i		−	0.536534i
$847$	1.87772e8			0.309015
$848$		−	1.81023e7i		−	0.0296856i
$849$			8.51874e8i			1.39204i
$850$		−	2.00273e9i		−	3.26112i
$851$			3.53316e8i			0.573291i
$852$	−8.22865e8			−1.33049
$853$	−5.18312e8			−0.835111			−0.417555	−	0.908651i	$-0.637113\pi$
$853$	−5.18312e8			−0.835111			−0.417555	+	0.908651i	$0.637113\pi$
$854$			2.15162e7i			0.0345456i
$855$	−2.50487e8	+	2.95732e8i	−0.400763	+	0.473151i
$856$	5.53971e8			0.883214
$857$			7.24971e8i			1.15180i	0.817519	+	0.575902i	$0.195349\pi$
$857$			7.24971e8i			1.15180i	−0.817519	+	0.575902i	$0.804651\pi$
$858$		−	5.39044e8i		−	0.853419i
$859$	−1.77192e8			−0.279554			−0.139777	−	0.990183i	$-0.544638\pi$
$859$	−1.77192e8			−0.279554			−0.139777	+	0.990183i	$0.544638\pi$
$860$	1.40853e9			2.21448
$861$	4.19019e6			0.00656484
$862$	1.22640e9			1.91475
$863$		−	3.44228e8i		−	0.535568i	−0.963479	−	0.267784i	$-0.913709\pi$
$863$		−	3.44228e8i		−	0.535568i	0.963479	−	0.267784i	$-0.0862913\pi$
$864$	−7.43708e8			−1.15308
$865$			2.22886e8i			0.344377i
$866$	5.68764e8			0.875747
$867$		−	1.00992e7i		−	0.0154963i
$868$			2.92165e7i			0.0446754i
$869$			2.69426e8i			0.410563i
$870$		−	2.63499e9i		−	4.00148i
$871$	−1.76899e9			−2.67714
$872$	−5.86145e8			−0.884007
$873$		−	1.02340e8i		−	0.153817i
$874$	−7.38130e8	−	6.25202e8i	−1.10560	−	0.936453i
$875$	4.59149e8			0.685377
$876$		−	1.48857e9i		−	2.21441i
$877$		−	7.37805e8i		−	1.09381i	−0.837194	−	0.546906i	$-0.815806\pi$
$877$		−	7.37805e8i		−	1.09381i	0.837194	−	0.546906i	$-0.184194\pi$
$878$	1.89556e8			0.280062
$879$	1.47159e8			0.216680
$880$	−4.09655e7			−0.0601133
$881$	7.86541e8			1.15025			0.575127	−	0.818064i	$-0.304953\pi$
$881$	7.86541e8			1.15025			0.575127	+	0.818064i	$0.304953\pi$
$882$		−	3.33825e8i		−	0.486534i
$883$	7.61345e8			1.10586			0.552929	−	0.833229i	$-0.313510\pi$
$883$	7.61345e8			1.10586			0.552929	+	0.833229i	$0.313510\pi$
$884$			1.59490e9i			2.30875i
$885$	3.69989e8			0.533776
$886$			1.25330e9i			1.80199i
$887$		−	1.05827e9i		−	1.51645i	−0.651995	−	0.758223i	$-0.726068\pi$
$887$		−	1.05827e9i		−	1.51645i	0.651995	−	0.758223i	$-0.273932\pi$
$888$			3.34958e8i			0.478357i
$889$		−	2.27772e8i		−	0.324186i
$890$	−1.03881e9			−1.47356
$891$	1.67041e8			0.236151
$892$		−	1.69500e9i		−	2.38822i
$893$	−4.29819e8	+	5.07456e8i	−0.603575	+	0.712597i
$894$	−2.44484e8			−0.342167
$895$			5.83979e8i			0.814570i
$896$		−	4.38281e8i		−	0.609297i
$897$	−7.52992e8			−1.04331
$898$	1.87760e9			2.59284
$899$	−9.37512e7			−0.129032
$900$	−8.29248e8			−1.13751
$901$		−	2.90198e8i		−	0.396752i
$902$	−1.13231e7			−0.0154293
$903$			1.86187e8i			0.252864i
$904$	6.85832e8			0.928352
$905$			2.71461e8i			0.366236i
$906$			2.73244e7i			0.0367422i
$907$		−	4.63722e8i		−	0.621493i	−0.950493	−	0.310747i	$-0.899421\pi$
$907$		−	4.63722e8i		−	0.621493i	0.950493	−	0.310747i	$-0.100579\pi$
$908$			1.18241e9i			1.57947i
$909$	2.15228e8			0.286555
$910$	−1.18745e9			−1.57576
$911$			8.15792e8i			1.07901i	0.841983	+	0.539503i	$0.181388\pi$
$911$			8.15792e8i			1.07901i	−0.841983	+	0.539503i	$0.818612\pi$
$912$	3.50501e7	+	2.96878e7i	0.0462067	+	0.0391375i
$913$	1.74924e8			0.229846
$914$			1.84895e9i			2.42152i
$915$		−	5.85001e7i		−	0.0763649i
$916$	−2.24483e7			−0.0292077
$917$	−1.31026e8			−0.169922
$918$	−1.36611e9			−1.76587
$919$	1.00276e9			1.29197			0.645984	−	0.763351i	$-0.276447\pi$
$919$	1.00276e9			1.29197			0.645984	+	0.763351i	$0.276447\pi$
$920$		−	1.14250e9i		−	1.46721i
$921$	−8.19389e8			−1.04884
$922$			7.49691e8i			0.956511i
$923$	−1.18991e9			−1.51325
$924$			1.79795e8i			0.227909i
$925$		−	1.01151e9i		−	1.27805i
$926$			3.35917e8i			0.423057i
$927$			1.82421e8i			0.229000i
$928$	1.51607e9			1.89703
$929$	−3.77625e8			−0.470992			−0.235496	−	0.971875i	$-0.575672\pi$
$929$	−3.77625e8			−0.470992			−0.235496	+	0.971875i	$0.575672\pi$
$930$		−	1.29594e8i		−	0.161115i
$931$	−4.41668e8	+	5.21445e8i	−0.547327	+	0.646189i
$932$	−5.17737e8			−0.639531
$933$			3.16160e8i			0.389280i
$934$			7.21956e8i			0.886074i
$935$	−6.56718e8			−0.803423
$936$	3.97091e8			0.484242
$937$	9.00225e7			0.109429			0.0547145	−	0.998502i	$-0.482575\pi$
$937$	9.00225e7			0.109429			0.0547145	+	0.998502i	$0.482575\pi$
$938$	9.62600e8			1.16637
$939$			3.25241e8i			0.392833i
$940$	−2.13104e9			−2.56572
$941$			5.96862e8i			0.716316i	0.933661	+	0.358158i	$0.116595\pi$
$941$			5.96862e8i			0.716316i	−0.933661	+	0.358158i	$0.883405\pi$
$942$	7.12788e8			0.852723
$943$			1.58173e7i			0.0188624i
$944$			2.43923e7i			0.0289959i
$945$		−	6.23450e8i		−	0.738764i
$946$		−	5.03132e8i		−	0.594304i
$947$	−4.97294e7			−0.0585549			−0.0292775	−	0.999571i	$-0.509321\pi$
$947$	−4.97294e7			−0.0585549			−0.0292775	+	0.999571i	$0.509321\pi$
$948$	9.68065e8			1.13626
$949$		−	2.15256e9i		−	2.51859i
$950$	2.11320e9	+	1.78990e9i	2.46473	+	2.08765i
$951$	3.20719e8			0.372893
$952$		−	3.19876e8i		−	0.370741i
$953$		−	9.85780e8i		−	1.13894i	−0.822012	−	0.569470i	$-0.807148\pi$
$953$		−	9.85780e8i		−	1.13894i	0.822012	−	0.569470i	$-0.192852\pi$
$954$	−1.96030e8			−0.225776
$955$	3.45397e8			0.396559
$956$	1.51310e9			1.73179
$957$	−5.76935e8			−0.658250
$958$		−	2.49946e9i		−	2.84283i
$959$	1.58264e8			0.179443
$960$			2.00275e9i			2.26367i
$961$	8.82893e8			0.994805
$962$			1.31416e9i			1.47613i
$963$			3.00473e8i			0.336455i
$964$			9.87689e8i			1.10253i
$965$		−	1.84241e9i		−	2.05024i
$966$	4.09742e8			0.454547
$967$	1.19229e9			1.31856			0.659282	−	0.751896i	$-0.270860\pi$
$967$	1.19229e9			1.31856			0.659282	+	0.751896i	$0.270860\pi$
$968$			6.71978e8i			0.740848i
$969$	5.61889e8	+	4.75925e8i	0.617560	+	0.523078i
$970$	−1.09521e9			−1.20000
$971$		−	3.55220e8i		−	0.388007i	−0.981001	−	0.194003i	$-0.937853\pi$
$971$		−	3.55220e8i		−	0.388007i	0.981001	−	0.194003i	$-0.0621473\pi$
$972$			9.82357e8i			1.06972i
$973$	−5.88043e8			−0.638367
$974$	−1.42658e9			−1.54390
$975$	2.15575e9			2.32587
$976$	3.85674e6			0.00414831
$977$		−	2.18008e8i		−	0.233770i	−0.993145	−	0.116885i	$-0.962709\pi$
$977$		−	2.18008e8i		−	0.233770i	0.993145	−	0.116885i	$-0.0372910\pi$
$978$	7.20561e8			0.770289
$979$			2.27450e8i			0.242403i
$980$	−2.18979e9			−2.32661
$981$		−	3.17924e8i		−	0.336757i
$982$			4.94178e8i			0.521854i
$983$		−	1.82201e8i		−	0.191819i	−0.995390	−	0.0959093i	$-0.969424\pi$
$983$		−	1.82201e8i		−	0.191819i	0.995390	−	0.0959093i	$-0.0305759\pi$
$984$			1.49954e7i			0.0157389i
$985$	1.83181e9			1.91677
$986$	2.78486e9			2.90517
$987$		−	2.81693e8i		−	0.292971i
$988$	−1.68287e9	−	1.42541e9i	−1.74494	−	1.47798i
$989$	−7.02826e8			−0.726539
$990$			4.43616e8i			0.457195i
$991$		−	1.11227e8i		−	0.114285i	−0.998366	−	0.0571426i	$-0.981801\pi$
$991$		−	1.11227e8i		−	0.114285i	0.998366	−	0.0571426i	$-0.0181990\pi$
$992$	7.45634e7			0.0763819
$993$	1.19342e9			1.21884
$994$	6.47492e8			0.659288
$995$	−1.36829e9			−1.38902
$996$		−	6.28514e8i		−	0.636117i
$997$	−1.68213e9			−1.69736			−0.848679	−	0.528908i	$-0.822602\pi$
$997$	−1.68213e9			−1.69736			−0.848679	+	0.528908i	$0.822602\pi$
$998$		−	2.88754e9i		−	2.90494i
$999$	−6.89978e8			−0.692052

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	19.7.b.b.18.7	yes	8
3.2	odd	2		171.7.c.d.37.2		8
4.3	odd	2		304.7.e.d.113.5		8
19.18	odd	2	inner	19.7.b.b.18.2	✓	8
57.56	even	2		171.7.c.d.37.7		8
76.75	even	2		304.7.e.d.113.4		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
19.7.b.b.18.2	✓	8	19.18	odd	2	inner
19.7.b.b.18.7	yes	8	1.1	even	1	trivial
171.7.c.d.37.2		8	3.2	odd	2
171.7.c.d.37.7		8	57.56	even	2
304.7.e.d.113.4		8	76.75	even	2
304.7.e.d.113.5		8	4.3	odd	2

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:	\( N \)	\(=\)	\( 19 \)
Weight:	\( k \)	\(=\)	\( 7 \)
Character orbit:	\([\chi]\)	\(=\)	19.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+12.8592i q^{2} -21.6433i q^{3} -101.358 q^{4} -216.848 q^{5} +278.315 q^{6} -134.238 q^{7} -480.398i q^{8} +260.567 q^{9} +O(q^{10})\)	\(q+12.8592i q^{2} -21.6433i q^{3} -101.358 q^{4} -216.848 q^{5} +278.315 q^{6} -134.238 q^{7} -480.398i q^{8} +260.567 q^{9} -2788.49i q^{10} -610.546 q^{11} +2193.73i q^{12} +3172.26i q^{13} -1726.19i q^{14} +4693.32i q^{15} -309.417 q^{16} -4960.26 q^{17} +3350.68i q^{18} +(4433.12 - 5233.86i) q^{19} +21979.4 q^{20} +2905.36i q^{21} -7851.11i q^{22} -10967.2 q^{23} -10397.4 q^{24} +31398.3 q^{25} -40792.7 q^{26} -21417.5i q^{27} +13606.2 q^{28} +43660.1i q^{29} -60352.2 q^{30} +2147.30i q^{31} -34724.3i q^{32} +13214.2i q^{33} -63784.9i q^{34} +29109.3 q^{35} -26410.7 q^{36} -32215.6i q^{37} +(67303.1 + 57006.3i) q^{38} +68658.3 q^{39} +104174. i q^{40} -1442.23i q^{41} -37360.5 q^{42} +64084.1 q^{43} +61883.9 q^{44} -56503.6 q^{45} -141030. i q^{46} -96956.3 q^{47} +6696.80i q^{48} -99629.1 q^{49} +403756. i q^{50} +107356. i q^{51} -321536. i q^{52} +58504.5i q^{53} +275411. q^{54} +132396. q^{55} +64487.7i q^{56} +(-113278. - 95947.5i) q^{57} -561433. q^{58} -78833.1i q^{59} -475707. i q^{60} -12464.6 q^{61} -27612.5 q^{62} -34978.0 q^{63} +426723. q^{64} -687901. i q^{65} -169924. q^{66} +557643. i q^{67} +502764. q^{68} +237368. i q^{69} +374322. i q^{70} +375099. i q^{71} -125176. i q^{72} -678557. q^{73} +414266. q^{74} -679562. i q^{75} +(-449334. + 530496. i) q^{76} +81958.6 q^{77} +882889. i q^{78} -441287. i q^{79} +67096.6 q^{80} -273592. q^{81} +18545.9 q^{82} -286505. q^{83} -294482. i q^{84} +1.07562e6 q^{85} +824069. i q^{86} +944950. q^{87} +293305. i q^{88} -372535. i q^{89} -726589. i q^{90} -425839. i q^{91} +1.11162e6 q^{92} +46474.6 q^{93} -1.24678e6i q^{94} +(-961316. + 1.13495e6i) q^{95} -751549. q^{96} -392760. i q^{97} -1.28115e6i q^{98} -159088. q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 454 q^{4} + 108 q^{5} - 358 q^{6} - 140 q^{7} - 1052 q^{9}+O(q^{10}) \) 8 * q - 454 * q^4 + 108 * q^5 - 358 * q^6 - 140 * q^7 - 1052 * q^9	\( 8 q - 454 q^{4} + 108 q^{5} - 358 q^{6} - 140 q^{7} - 1052 q^{9} - 2024 q^{11} + 11546 q^{16} + 6008 q^{17} + 20552 q^{19} - 10732 q^{20} - 50252 q^{23} + 64310 q^{24} + 78492 q^{25} - 37522 q^{26} - 135818 q^{28} - 187696 q^{30} + 210800 q^{35} + 35052 q^{36} + 103318 q^{38} + 43724 q^{39} - 429970 q^{42} + 260800 q^{43} + 693512 q^{44} - 191012 q^{45} - 100248 q^{47} - 301872 q^{49} + 390202 q^{54} - 52480 q^{55} - 186860 q^{57} - 405186 q^{58} - 54548 q^{61} - 1461908 q^{62} - 137408 q^{63} - 858058 q^{64} + 1539556 q^{66} + 1243910 q^{68} + 479968 q^{73} + 2645844 q^{74} - 2569288 q^{76} - 1755300 q^{77} + 2344672 q^{80} - 4279648 q^{81} + 1847172 q^{82} + 483040 q^{83} + 2111780 q^{85} + 2802652 q^{87} + 3905498 q^{92} + 1507528 q^{93} - 2383888 q^{95} - 8462238 q^{96} + 528224 q^{99}+O(q^{100}) \) 8 * q - 454 * q^4 + 108 * q^5 - 358 * q^6 - 140 * q^7 - 1052 * q^9 - 2024 * q^11 + 11546 * q^16 + 6008 * q^17 + 20552 * q^19 - 10732 * q^20 - 50252 * q^23 + 64310 * q^24 + 78492 * q^25 - 37522 * q^26 - 135818 * q^28 - 187696 * q^30 + 210800 * q^35 + 35052 * q^36 + 103318 * q^38 + 43724 * q^39 - 429970 * q^42 + 260800 * q^43 + 693512 * q^44 - 191012 * q^45 - 100248 * q^47 - 301872 * q^49 + 390202 * q^54 - 52480 * q^55 - 186860 * q^57 - 405186 * q^58 - 54548 * q^61 - 1461908 * q^62 - 137408 * q^63 - 858058 * q^64 + 1539556 * q^66 + 1243910 * q^68 + 479968 * q^73 + 2645844 * q^74 - 2569288 * q^76 - 1755300 * q^77 + 2344672 * q^80 - 4279648 * q^81 + 1847172 * q^82 + 483040 * q^83 + 2111780 * q^85 + 2802652 * q^87 + 3905498 * q^92 + 1507528 * q^93 - 2383888 * q^95 - 8462238 * q^96 + 528224 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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