LMFDB - Embedded newform 19.7.b.b.18.1

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			18.1
Root			$-14.9269i$ of defining polynomial
Character	$\chi$	$=$	19.18
Dual form			19.7.b.b.18.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-14.9269i q^{2} -33.0827i q^{3} -158.814 q^{4} +159.622 q^{5} -493.824 q^{6} +445.794 q^{7} +1415.28i q^{8} -365.466 q^{9} +O(q^{10})$	\(q-14.9269i q^{2} -33.0827i q^{3} -158.814 q^{4} +159.622 q^{5} -493.824 q^{6} +445.794 q^{7} +1415.28i q^{8} -365.466 q^{9} -2382.67i q^{10} -1700.61 q^{11} +5253.99i q^{12} +439.288i q^{13} -6654.34i q^{14} -5280.74i q^{15} +10961.7 q^{16} +569.044 q^{17} +5455.29i q^{18} +(6482.51 + 2241.20i) q^{19} -25350.2 q^{20} -14748.1i q^{21} +25385.0i q^{22} -2746.30 q^{23} +46821.3 q^{24} +9854.28 q^{25} +6557.23 q^{26} -12026.7i q^{27} -70798.1 q^{28} +26932.8i q^{29} -78825.3 q^{30} -29892.3i q^{31} -73047.0i q^{32} +56260.9i q^{33} -8494.09i q^{34} +71158.6 q^{35} +58041.0 q^{36} +52516.0i q^{37} +(33454.3 - 96764.0i) q^{38} +14532.9 q^{39} +225910. i q^{40} -27399.8i q^{41} -220144. q^{42} +67448.4 q^{43} +270081. q^{44} -58336.5 q^{45} +40993.9i q^{46} -66319.6 q^{47} -362643. i q^{48} +81083.1 q^{49} -147094. i q^{50} -18825.5i q^{51} -69765.0i q^{52} +59959.3i q^{53} -179522. q^{54} -271456. q^{55} +630922. i q^{56} +(74145.1 - 214459. i) q^{57} +402024. q^{58} -396359. i q^{59} +838654. i q^{60} -73557.7 q^{61} -446201. q^{62} -162922. q^{63} -388819. q^{64} +70120.2i q^{65} +839803. q^{66} +160211. i q^{67} -90372.0 q^{68} +90855.2i q^{69} -1.06218e6i q^{70} +259957. i q^{71} -517236. i q^{72} +291024. q^{73} +783903. q^{74} -326006. i q^{75} +(-1.02951e6 - 355934. i) q^{76} -758123. q^{77} -216931. i q^{78} +917363. i q^{79} +1.74973e6 q^{80} -664300. q^{81} -408996. q^{82} +681097. q^{83} +2.34219e6i q^{84} +90832.1 q^{85} -1.00680e6i q^{86} +891010. q^{87} -2.40684e6i q^{88} +242644. i q^{89} +870786. i q^{90} +195832. i q^{91} +436151. q^{92} -988920. q^{93} +989949. i q^{94} +(1.03475e6 + 357746. i) q^{95} -2.41659e6 q^{96} +1.24569e6i q^{97} -1.21032e6i q^{98} +621516. q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$		−	14.9269i		−	1.86587i	−0.360047	−	0.932934i	$-0.617239\pi$
$2$		−	14.9269i		−	1.86587i	0.360047	−	0.932934i	$-0.382761\pi$
$3$		−	33.0827i		−	1.22529i	−0.790360	−	0.612643i	$-0.790106\pi$
$3$		−	33.0827i		−	1.22529i	0.790360	−	0.612643i	$-0.209894\pi$
$4$	−158.814			−2.48146
$5$	159.622			1.27698			0.638489	−	0.769631i	$-0.279560\pi$
$5$	159.622			1.27698			0.638489	+	0.769631i	$0.279560\pi$
$6$	−493.824			−2.28622
$7$	445.794			1.29969			0.649845	−	0.760067i	$-0.274834\pi$
$7$	445.794			1.29969			0.649845	+	0.760067i	$0.274834\pi$
$8$			1415.28i			2.76422i
$9$	−365.466			−0.501325
$10$		−	2382.67i		−	2.38267i
$11$	−1700.61			−1.27770			−0.638848	−	0.769333i	$-0.720589\pi$
$11$	−1700.61			−1.27770			−0.638848	+	0.769333i	$0.720589\pi$
$12$			5253.99i			3.04050i
$13$			439.288i			0.199949i	0.994990	+	0.0999746i	$0.0318762\pi$
$13$			439.288i			0.199949i	−0.994990	+	0.0999746i	$0.968124\pi$
$14$		−	6654.34i		−	2.42505i
$15$		−	5280.74i		−	1.56466i
$16$	10961.7			2.67620
$17$	569.044			0.115824			0.0579121	−	0.998322i	$-0.481556\pi$
$17$	569.044			0.115824			0.0579121	+	0.998322i	$0.481556\pi$
$18$			5455.29i			0.935407i
$19$	6482.51	+	2241.20i	0.945110	+	0.326754i
$19$	6482.51	+	2241.20i	0.945110	+	0.326754i
$20$	−25350.2			−3.16878
$21$		−	14748.1i		−	1.59249i
$22$			25385.0i			2.38401i
$23$	−2746.30			−0.225717			−0.112859	−	0.993611i	$-0.536001\pi$
$23$	−2746.30			−0.225717			−0.112859	+	0.993611i	$0.536001\pi$
$24$	46821.3			3.38695
$25$	9854.28			0.630674
$26$	6557.23			0.373079
$27$		−	12026.7i		−	0.611019i
$28$	−70798.1			−3.22513
$29$			26932.8i			1.10430i	0.833745	+	0.552150i	$0.186193\pi$
$29$			26932.8i			1.10430i	−0.833745	+	0.552150i	$0.813807\pi$
$30$	−78825.3			−2.91946
$31$		−	29892.3i		−	1.00340i	−0.865041	−	0.501701i	$-0.832708\pi$
$31$		−	29892.3i		−	1.00340i	0.865041	−	0.501701i	$-0.167292\pi$
$32$		−	73047.0i		−	2.22922i
$33$			56260.9i			1.56554i
$34$		−	8494.09i		−	0.216113i
$35$	71158.6			1.65968
$36$	58041.0			1.24402
$37$			52516.0i			1.03678i	0.855144	+	0.518390i	$0.173468\pi$
$37$			52516.0i			1.03678i	−0.855144	+	0.518390i	$0.826532\pi$
$38$	33454.3	−	96764.0i	0.609679	−	1.76345i
$39$	14532.9			0.244995
$40$			225910.i			3.52984i
$41$		−	27399.8i		−	0.397554i	−0.980045	−	0.198777i	$-0.936303\pi$
$41$		−	27399.8i		−	0.397554i	0.980045	−	0.198777i	$-0.0636970\pi$
$42$	−220144.			−2.97138
$43$	67448.4			0.848332			0.424166	−	0.905584i	$-0.360567\pi$
$43$	67448.4			0.848332			0.424166	+	0.905584i	$0.360567\pi$
$44$	270081.			3.17056
$45$	−58336.5			−0.640181
$46$			40993.9i			0.421159i
$47$	−66319.6			−0.638776			−0.319388	−	0.947624i	$-0.603477\pi$
$47$	−66319.6			−0.638776			−0.319388	+	0.947624i	$0.603477\pi$
$48$		−	362643.i		−	3.27911i
$49$	81083.1			0.689195
$50$		−	147094.i		−	1.17675i
$51$		−	18825.5i		−	0.141918i
$52$		−	69765.0i		−	0.496167i
$53$			59959.3i			0.402744i	0.979515	+	0.201372i	$0.0645399\pi$
$53$			59959.3i			0.402744i	−0.979515	+	0.201372i	$0.935460\pi$
$54$	−179522.			−1.14008
$55$	−271456.			−1.63159
$56$			630922.i			3.59262i
$57$	74145.1	−	214459.i	0.400367	−	1.15803i
$58$	402024.			2.06048
$59$		−	396359.i		−	1.92989i	−0.262452	−	0.964945i	$-0.584531\pi$
$59$		−	396359.i		−	1.92989i	0.262452	−	0.964945i	$-0.415469\pi$
$60$			838654.i			3.88266i
$61$	−73557.7			−0.324070			−0.162035	−	0.986785i	$-0.551806\pi$
$61$	−73557.7			−0.324070			−0.162035	+	0.986785i	$0.551806\pi$
$62$	−446201.			−1.87222
$63$	−162922.			−0.651567
$64$	−388819.			−1.48323
$65$			70120.2i			0.255331i
$66$	839803.			2.92110
$67$			160211.i			0.532681i	0.963879	+	0.266341i	$0.0858146\pi$
$67$			160211.i			0.532681i	−0.963879	+	0.266341i	$0.914185\pi$
$68$	−90372.0			−0.287413
$69$			90855.2i			0.276568i
$70$		−	1.06218e6i		−	3.09674i
$71$			259957.i			0.726317i	0.931727	+	0.363158i	$0.118302\pi$
$71$			259957.i			0.726317i	−0.931727	+	0.363158i	$0.881698\pi$
$72$		−	517236.i		−	1.38577i
$73$	291024.			0.748101			0.374051	−	0.927408i	$-0.377969\pi$
$73$	291024.			0.748101			0.374051	+	0.927408i	$0.377969\pi$
$74$	783903.			1.93449
$75$		−	326006.i		−	0.772755i
$76$	−1.02951e6	−	355934.i	−2.34525	−	0.810827i
$77$	−758123.			−1.66061
$78$		−	216931.i		−	0.457128i
$79$			917363.i			1.86063i	0.366761	+	0.930315i	$0.380467\pi$
$79$			917363.i			1.86063i	−0.366761	+	0.930315i	$0.619533\pi$
$80$	1.74973e6			3.41745
$81$	−664300.			−1.25000
$82$	−408996.			−0.741784
$83$	681097.			1.19117			0.595586	−	0.803291i	$-0.296920\pi$
$83$	681097.			1.19117			0.595586	+	0.803291i	$0.296920\pi$
$84$			2.34219e6i			3.95171i
$85$	90832.1			0.147905
$86$		−	1.00680e6i		−	1.58288i
$87$	891010.			1.35308
$88$		−	2.40684e6i		−	3.53183i
$89$			242644.i			0.344191i	0.985080	+	0.172095i	$0.0550537\pi$
$89$			242644.i			0.344191i	−0.985080	+	0.172095i	$0.944946\pi$
$90$			870786.i			1.19449i
$91$			195832.i			0.259872i
$92$	436151.			0.560110
$93$	−988920.			−1.22945
$94$			989949.i			1.19187i
$95$	1.03475e6	+	357746.i	1.20688	+	0.417257i
$96$	−2.41659e6			−2.73143
$97$			1.24569e6i			1.36488i	0.730941	+	0.682440i	$0.239081\pi$
$97$			1.24569e6i			1.36488i	−0.730941	+	0.682440i	$0.760919\pi$
$98$		−	1.21032e6i		−	1.28595i
$99$	621516.			0.640541
$100$	−1.56499e6			−1.56499
$101$	−1.34311e6			−1.30361			−0.651807	−	0.758385i	$-0.725989\pi$
$101$	−1.34311e6			−1.30361			−0.651807	+	0.758385i	$0.725989\pi$
$102$	−281007.			−0.264800
$103$		−	1.37650e6i		−	1.25969i	−0.776719	−	0.629847i	$-0.783117\pi$
$103$		−	1.37650e6i		−	1.25969i	0.776719	−	0.629847i	$-0.216883\pi$
$104$	−621715.			−0.552703
$105$		−	2.35412e6i		−	2.03358i
$106$	895009.			0.751466
$107$		−	920616.i		−	0.751497i	−0.926722	−	0.375748i	$-0.877386\pi$
$107$		−	920616.i		−	0.751497i	0.926722	−	0.375748i	$-0.122614\pi$
$108$			1.91000e6i			1.51622i
$109$		−	385747.i		−	0.297868i	−0.988847	−	0.148934i	$-0.952416\pi$
$109$		−	385747.i		−	0.297868i	0.988847	−	0.148934i	$-0.0475841\pi$
$110$			4.05200e6i			3.04433i
$111$	1.73737e6			1.27035
$112$	4.88666e6			3.47823
$113$			620853.i			0.430282i	0.976583	+	0.215141i	$0.0690212\pi$
$113$			620853.i			0.430282i	−0.976583	+	0.215141i	$0.930979\pi$
$114$	−3.20122e6	−	1.10676e6i	−2.16073	−	0.747031i
$115$	−438371.			−0.288236
$116$		−	4.27729e6i		−	2.74028i
$117$		−	160545.i		−	0.100240i
$118$	−5.91643e6			−3.60092
$119$	253676.			0.150536
$120$	7.47372e6			4.32507
$121$	1.12052e6			0.632506
$122$			1.09799e6i			0.604671i
$123$	−906461.			−0.487118
$124$			4.74731e6i			2.48990i
$125$	−921136.			−0.471622
$126$			2.43193e6i			1.21574i
$127$			1.13559e6i			0.554385i	0.960814	+	0.277193i	$0.0894041\pi$
$127$			1.13559e6i			0.554385i	−0.960814	+	0.277193i	$0.910596\pi$
$128$			1.12887e6i			0.538288i
$129$		−	2.23138e6i		−	1.03945i
$130$	1.04668e6			0.476414
$131$	−370425.			−0.164773			−0.0823866	−	0.996600i	$-0.526254\pi$
$131$	−370425.			−0.164773			−0.0823866	+	0.996600i	$0.526254\pi$
$132$		−	8.93500e6i		−	3.88484i
$133$	2.88986e6	+	999114.i	1.22835	+	0.424679i
$134$	2.39146e6			0.993913
$135$		−	1.91973e6i		−	0.780258i
$136$			805356.i			0.320163i
$137$	−2.35314e6			−0.915136			−0.457568	−	0.889175i	$-0.651279\pi$
$137$	−2.35314e6			−0.915136			−0.457568	+	0.889175i	$0.651279\pi$
$138$	1.35619e6			0.516040
$139$	2.91982e6			1.08720			0.543602	−	0.839343i	$-0.317060\pi$
$139$	2.91982e6			1.08720			0.543602	+	0.839343i	$0.317060\pi$
$140$	−1.13010e7			−4.11843
$141$			2.19403e6i			0.782683i
$142$	3.88036e6			1.35521
$143$		−	747059.i		−	0.255474i
$144$	−4.00613e6			−1.34165
$145$			4.29907e6i			1.41017i
$146$		−	4.34410e6i		−	1.39586i
$147$		−	2.68245e6i		−	0.844461i
$148$		−	8.34026e6i		−	2.57273i
$149$	−1.34951e6			−0.407961			−0.203980	−	0.978975i	$-0.565388\pi$
$149$	−1.34951e6			−0.407961			−0.203980	+	0.978975i	$0.565388\pi$
$150$	−4.86628e6			−1.44186
$151$			5.87074e6i			1.70515i	0.522607	+	0.852574i	$0.324960\pi$
$151$			5.87074e6i			1.70515i	−0.522607	+	0.852574i	$0.675040\pi$
$152$	−3.17193e6	+	9.17455e6i	−0.903218	+	2.61249i
$153$	−207966.			−0.0580656
$154$			1.13165e7i			3.09848i
$155$		−	4.77148e6i		−	1.28132i
$156$	−2.30802e6			−0.607946
$157$	−673724.			−0.174094			−0.0870469	−	0.996204i	$-0.527743\pi$
$157$	−673724.			−0.174094			−0.0870469	+	0.996204i	$0.527743\pi$
$158$	1.36934e7			3.47169
$159$	1.98362e6			0.493476
$160$		−	1.16599e7i		−	2.84666i
$161$	−1.22429e6			−0.293363
$162$			9.91597e6i			2.33233i
$163$	−4.36326e6			−1.00751			−0.503754	−	0.863847i	$-0.668048\pi$
$163$	−4.36326e6			−1.00751			−0.503754	+	0.863847i	$0.668048\pi$
$164$			4.35147e6i			0.986517i
$165$			8.98049e6i			1.99916i
$166$		−	1.01667e7i		−	2.22257i
$167$			2.14529e6i			0.460613i	0.973118	+	0.230306i	$0.0739728\pi$
$167$			2.14529e6i			0.460613i	−0.973118	+	0.230306i	$0.926027\pi$
$168$	2.08726e7			4.40199
$169$	4.63383e6			0.960020
$170$		−	1.35585e6i		−	0.275971i
$171$	−2.36914e6	−	819084.i	−0.473807	−	0.163810i
$172$	−1.07117e7			−2.10511
$173$		−	3.44402e6i		−	0.665161i	−0.943075	−	0.332581i	$-0.892081\pi$
$173$		−	3.44402e6i		−	0.665161i	0.943075	−	0.332581i	$-0.107919\pi$
$174$		−	1.33001e7i		−	2.52468i
$175$	4.39297e6			0.819680
$176$	−1.86416e7			−3.41937
$177$	−1.31126e7			−2.36467
$178$	3.62193e6			0.642214
$179$		−	9.69997e6i		−	1.69126i	−0.533767	−	0.845632i	$-0.679224\pi$
$179$		−	9.69997e6i		−	1.69126i	0.533767	−	0.845632i	$-0.320776\pi$
$180$	9.26464e6			1.58859
$181$		−	6.17944e6i		−	1.04211i	−0.853523	−	0.521055i	$-0.825539\pi$
$181$		−	6.17944e6i		−	1.04211i	0.853523	−	0.521055i	$-0.174461\pi$
$182$	2.92317e6			0.484887
$183$			2.43349e6i			0.397078i
$184$		−	3.88679e6i		−	0.623932i
$185$			8.38272e6i			1.32395i
$186$			1.47616e7i			2.29400i
$187$	−967724.			−0.147988
$188$	1.05325e7			1.58510
$189$		−	5.36142e6i		−	0.794136i
$190$	5.34005e6	−	1.54457e7i	0.778547	−	2.25189i
$191$	6.71701e6			0.963998			0.481999	−	0.876172i	$-0.339911\pi$
$191$	6.71701e6			0.963998			0.481999	+	0.876172i	$0.339911\pi$
$192$			1.28632e7i			1.81738i
$193$			5.48205e6i			0.762555i	0.924461	+	0.381278i	$0.124516\pi$
$193$			5.48205e6i			0.762555i	−0.924461	+	0.381278i	$0.875484\pi$
$194$	1.85943e7			2.54669
$195$	2.31977e6			0.312853
$196$	−1.28771e7			−1.71021
$197$	−8.07614e6			−1.05634			−0.528172	−	0.849137i	$-0.677122\pi$
$197$	−8.07614e6			−1.05634			−0.528172	+	0.849137i	$0.677122\pi$
$198$		−	9.27734e6i		−	1.19516i
$199$	−7.76482e6			−0.985309			−0.492654	−	0.870225i	$-0.663973\pi$
$199$	−7.76482e6			−0.985309			−0.492654	+	0.870225i	$0.663973\pi$
$200$			1.39465e7i			1.74332i
$201$	5.30021e6			0.652687
$202$			2.00486e7i			2.43237i
$203$			1.20065e7i			1.43525i
$204$			2.98975e6i			0.352164i
$205$		−	4.37363e6i		−	0.507668i
$206$	−2.05470e7			−2.35042
$207$	1.00368e6			0.113158
$208$			4.81535e6i			0.535104i
$209$	−1.10242e7	−	3.81142e6i	−1.20756	−	0.417492i
$210$	−3.51398e7			−3.79439
$211$		−	6.10034e6i		−	0.649392i	−0.945818	−	0.324696i	$-0.894738\pi$
$211$		−	6.10034e6i		−	0.649392i	0.945818	−	0.324696i	$-0.105262\pi$
$212$		−	9.52235e6i		−	0.999394i
$213$	8.60008e6			0.889946
$214$	−1.37420e7			−1.40219
$215$	1.07663e7			1.08330
$216$	1.70211e7			1.68899
$217$		−	1.33258e7i		−	1.30411i
$218$	−5.75803e6			−0.555782
$219$		−	9.62787e6i		−	0.916638i
$220$	4.31109e7			4.04873
$221$			249974.i			0.0231589i
$222$		−	2.59337e7i		−	2.37031i
$223$		−	3.09709e6i		−	0.279279i	−0.990202	−	0.139640i	$-0.955406\pi$
$223$		−	3.09709e6i		−	0.279279i	0.990202	−	0.139640i	$-0.0445944\pi$
$224$		−	3.25639e7i		−	2.89729i
$225$	−3.60140e6			−0.316173
$226$	9.26744e6			0.802850
$227$		−	1.26462e6i		−	0.108114i	−0.998538	−	0.0540569i	$-0.982785\pi$
$227$		−	1.26462e6i		−	0.108114i	0.998538	−	0.0540569i	$-0.0172152\pi$
$228$	−1.17753e7	+	3.40590e7i	−0.993495	+	2.87361i
$229$	1.06635e7			0.887958			0.443979	−	0.896037i	$-0.353566\pi$
$229$	1.06635e7			0.887958			0.443979	+	0.896037i	$0.353566\pi$
$230$			6.54355e6i			0.537811i
$231$			2.50808e7i			2.03472i
$232$	−3.81174e7			−3.05252
$233$	2.85242e6			0.225500			0.112750	−	0.993623i	$-0.464034\pi$
$233$	2.85242e6			0.225500			0.112750	+	0.993623i	$0.464034\pi$
$234$	−2.39645e6			−0.187034
$235$	−1.05861e7			−0.815703
$236$			6.29472e7i			4.78895i
$237$	3.03489e7			2.27980
$238$		−	3.78661e6i		−	0.280879i
$239$	−1.78416e7			−1.30689			−0.653445	−	0.756974i	$-0.726677\pi$
$239$	−1.78416e7			−1.30689			−0.653445	+	0.756974i	$0.726677\pi$
$240$		−	5.78859e7i		−	4.18735i
$241$			5.72052e6i			0.408681i	0.978900	+	0.204340i	$0.0655049\pi$
$241$			5.72052e6i			0.408681i	−0.978900	+	0.204340i	$0.934495\pi$
$242$		−	1.67260e7i		−	1.18017i
$243$			1.32094e7i			0.920586i
$244$	1.16820e7			0.804167
$245$	1.29427e7			0.880087
$246$			1.35307e7i			0.908897i
$247$	−984535.	+	2.84769e6i	−0.0653341	+	0.188974i
$248$	4.23060e7			2.77362
$249$		−	2.25325e7i		−	1.45953i
$250$			1.37498e7i			0.879984i
$251$	7.46125e6			0.471835			0.235918	−	0.971773i	$-0.424190\pi$
$251$	7.46125e6			0.471835			0.235918	+	0.971773i	$0.424190\pi$
$252$	2.58743e7			1.61684
$253$	4.67040e6			0.288398
$254$	1.69509e7			1.03441
$255$		−	3.00497e6i		−	0.181226i
$256$	−8.03380e6			−0.478852
$257$		−	8.46675e6i		−	0.498790i	−0.968402	−	0.249395i	$-0.919768\pi$
$257$		−	8.46675e6i		−	0.498790i	0.968402	−	0.249395i	$-0.0802317\pi$
$258$	−3.33076e7			−1.93948
$259$			2.34113e7i			1.34749i
$260$		−	1.11360e7i		−	0.633594i
$261$		−	9.84302e6i		−	0.553614i
$262$			5.52932e6i			0.307445i
$263$	−3.14002e7			−1.72610			−0.863049	−	0.505121i	$-0.831448\pi$
$263$	−3.14002e7			−1.72610			−0.863049	+	0.505121i	$0.831448\pi$
$264$	−7.96248e7			−4.32750
$265$			9.57083e6i			0.514295i
$266$	1.49137e7	−	4.31368e7i	0.792394	−	2.29194i
$267$	8.02731e6			0.421732
$268$		−	2.54437e7i		−	1.32183i
$269$			6.30864e6i			0.324100i	0.986783	+	0.162050i	$0.0518105\pi$
$269$			6.30864e6i			0.324100i	−0.986783	+	0.162050i	$0.948189\pi$
$270$	−2.86557e7			−1.45586
$271$	1.43606e7			0.721545			0.360772	−	0.932654i	$-0.382513\pi$
$271$	1.43606e7			0.721545			0.360772	+	0.932654i	$0.382513\pi$
$272$	6.23769e6			0.309968
$273$	6.47865e6			0.318417
$274$			3.51252e7i			1.70752i
$275$	−1.67583e7			−0.805809
$276$		−	1.44291e7i		−	0.686294i
$277$	9.38558e6			0.441593			0.220796	−	0.975320i	$-0.429134\pi$
$277$	9.38558e6			0.441593			0.220796	+	0.975320i	$0.429134\pi$
$278$		−	4.35839e7i		−	2.02858i
$279$			1.09246e7i			0.503030i
$280$			1.00709e8i			4.58770i
$281$			3.93600e7i			1.77393i	0.461837	+	0.886965i	$0.347190\pi$
$281$			3.93600e7i			1.77393i	−0.461837	+	0.886965i	$0.652810\pi$
$282$	3.27502e7			1.46038
$283$	−2.61094e7			−1.15196			−0.575980	−	0.817464i	$-0.695379\pi$
$283$	−2.61094e7			−1.15196			−0.575980	+	0.817464i	$0.695379\pi$
$284$		−	4.12847e7i		−	1.80233i
$285$	1.18352e7	−	3.42324e7i	0.511259	−	1.47878i
$286$	−1.11513e7			−0.476681
$287$		−	1.22147e7i		−	0.516698i
$288$			2.66962e7i			1.11756i
$289$	−2.38138e7			−0.986585
$290$	6.41720e7			2.63119
$291$	4.12108e7			1.67237
$292$	−4.62186e7			−1.85639
$293$		−	1.58306e7i		−	0.629354i	−0.949199	−	0.314677i	$-0.898104\pi$
$293$		−	1.58306e7i		−	0.629354i	0.949199	−	0.314677i	$-0.101896\pi$
$294$	−4.00408e7			−1.57565
$295$		−	6.32677e7i		−	2.46443i
$296$	−7.43248e7			−2.86588
$297$			2.04527e7i			0.780697i
$298$			2.01441e7i			0.761201i
$299$		−	1.20642e6i		−	0.0451320i
$300$			5.17742e7i			1.91756i
$301$	3.00681e7			1.10257
$302$	8.76322e7			3.18158
$303$			4.44339e7i			1.59730i
$304$	7.10593e7	+	2.45674e7i	2.52930	+	0.874458i
$305$	−1.17414e7			−0.413830
$306$			3.10430e6i			0.108343i
$307$		−	5.21895e7i		−	1.80371i	−0.432034	−	0.901857i	$-0.642204\pi$
$307$		−	5.21895e7i		−	1.80371i	0.432034	−	0.901857i	$-0.357796\pi$
$308$	1.20400e8			4.12074
$309$	−4.55384e7			−1.54349
$310$	−7.12237e7			−2.39078
$311$	−5.40593e7			−1.79717			−0.898585	−	0.438800i	$-0.855404\pi$
$311$	−5.40593e7			−1.79717			−0.898585	+	0.438800i	$0.855404\pi$
$312$			2.05680e7i			0.677219i
$313$	2.48919e7			0.811754			0.405877	−	0.913928i	$-0.366966\pi$
$313$	2.48919e7			0.811754			0.405877	+	0.913928i	$0.366966\pi$
$314$			1.00566e7i			0.324836i
$315$	−2.60061e7			−0.832038
$316$		−	1.45690e8i		−	4.61709i
$317$			3.78290e7i			1.18754i	0.804636	+	0.593769i	$0.202361\pi$
$317$			3.78290e7i			1.18754i	−0.804636	+	0.593769i	$0.797639\pi$
$318$		−	2.96093e7i		−	0.920761i
$319$		−	4.58022e7i		−	1.41096i
$320$	−6.20642e7			−1.89405
$321$	−3.04565e7			−0.920798
$322$			1.82748e7i			0.547376i
$323$	3.68883e6	+	1.27534e6i	0.109466	+	0.0378460i
$324$	1.05500e8			3.10183
$325$			4.32887e6i			0.126103i
$326$			6.51302e7i			1.87988i
$327$	−1.27616e7			−0.364973
$328$	3.87784e7			1.09893
$329$	−2.95649e7			−0.830211
$330$	1.34051e8			3.73018
$331$			6.04318e7i			1.66641i	0.552964	+	0.833205i	$0.313497\pi$
$331$			6.04318e7i			1.66641i	−0.552964	+	0.833205i	$0.686503\pi$
$332$	−1.08168e8			−2.95585
$333$		−	1.91928e7i		−	0.519764i
$334$	3.20226e7			0.859442
$335$			2.55732e7i			0.680222i
$336$		−	1.61664e8i		−	4.26182i
$337$		−	5.31644e7i		−	1.38909i	−0.719449	−	0.694546i	$-0.755605\pi$
$337$		−	5.31644e7i		−	1.38909i	0.719449	−	0.694546i	$-0.244395\pi$
$338$		−	6.91690e7i		−	1.79127i
$339$	2.05395e7			0.527219
$340$	−1.44254e7			−0.367021
$341$			5.08353e7i			1.28204i
$342$	−1.22264e7	+	3.53640e7i	−0.305648	+	0.884062i
$343$	−1.63009e7			−0.403950
$344$			9.54582e7i			2.34497i
$345$			1.45025e7i			0.353172i
$346$	−5.14087e7			−1.24110
$347$	−1.73896e7			−0.416200			−0.208100	−	0.978108i	$-0.566728\pi$
$347$	−1.73896e7			−0.416200			−0.208100	+	0.978108i	$0.566728\pi$
$348$	−1.41505e8			−3.35763
$349$	5.87325e7			1.38166			0.690832	−	0.723015i	$-0.257244\pi$
$349$	5.87325e7			1.38166			0.690832	+	0.723015i	$0.257244\pi$
$350$		−	6.55737e7i		−	1.52942i
$351$	5.28319e6			0.122173
$352$			1.24225e8i			2.84826i
$353$	7.21844e7			1.64104			0.820520	−	0.571618i	$-0.193684\pi$
$353$	7.21844e7			1.64104			0.820520	+	0.571618i	$0.193684\pi$
$354$			1.95731e8i			4.41216i
$355$			4.14949e7i			0.927491i
$356$		−	3.85351e7i		−	0.854097i
$357$		−	8.39230e6i		−	0.184449i
$358$	−1.44791e8			−3.15567
$359$	2.58410e6			0.0558504			0.0279252	−	0.999610i	$-0.491110\pi$
$359$	2.58410e6			0.0558504			0.0279252	+	0.999610i	$0.491110\pi$
$360$		−	8.25624e7i		−	1.76960i
$361$	3.69999e7	+	2.90572e7i	0.786464	+	0.617636i
$362$	−9.22401e7			−1.94444
$363$		−	3.70700e7i		−	0.775001i
$364$		−	3.11008e7i		−	0.644863i
$365$	4.64539e7			0.955309
$366$	3.63245e7			0.740895
$367$	2.11836e7			0.428551			0.214275	−	0.976773i	$-0.431261\pi$
$367$	2.11836e7			0.428551			0.214275	+	0.976773i	$0.431261\pi$
$368$	−3.01042e7			−0.604065
$369$			1.00137e7i			0.199304i
$370$	1.25128e8			2.47031
$371$			2.67295e7i			0.523442i
$372$	1.57054e8			3.05084
$373$			5.14538e6i			0.0991496i	0.998770	+	0.0495748i	$0.0157866\pi$
$373$			5.14538e6i			0.0991496i	−0.998770	+	0.0495748i	$0.984213\pi$
$374$			1.44452e7i			0.276126i
$375$			3.04737e7i			0.577871i
$376$		−	9.38607e7i		−	1.76571i
$377$	−1.18313e7			−0.220804
$378$	−8.00297e7			−1.48175
$379$		−	7.33294e7i		−	1.34698i	−0.739197	−	0.673489i	$-0.764795\pi$
$379$		−	7.33294e7i		−	1.34698i	0.739197	−	0.673489i	$-0.235205\pi$
$380$	−1.64333e8	−	5.68150e7i	−2.99484	−	1.03541i
$381$	3.75685e7			0.679281
$382$		−	1.00265e8i		−	1.79869i
$383$		−	110690.i		−	0.00197020i	−1.00000		0.000985101i	$-0.999686\pi$
$383$		−	110690.i		−	0.00197020i	1.00000		0.000985101i	$-0.000313567\pi$
$384$	3.73462e7			0.659557
$385$	−1.21013e8			−2.12056
$386$	8.18303e7			1.42283
$387$	−2.46501e7			−0.425290
$388$		−	1.97833e8i		−	3.38690i
$389$	5.72855e7			0.973186			0.486593	−	0.873629i	$-0.338239\pi$
$389$	5.72855e7			0.973186			0.486593	+	0.873629i	$0.338239\pi$
$390$		−	3.46270e7i		−	0.583743i
$391$	−1.56277e6			−0.0261435
$392$			1.14755e8i			1.90508i
$393$			1.22547e7i			0.201894i
$394$			1.20552e8i			1.97100i
$395$			1.46432e8i			2.37598i
$396$	−9.87053e7			−1.58948
$397$	−8.20397e7			−1.31115			−0.655575	−	0.755130i	$-0.727574\pi$
$397$	−8.20397e7			−1.31115			−0.655575	+	0.755130i	$0.727574\pi$
$398$			1.15905e8i			1.83846i
$399$	3.30534e7	−	9.56044e7i	0.520353	−	1.50508i
$400$	1.08020e8			1.68781
$401$		−	6.27155e6i		−	0.0972617i	−0.998817	−	0.0486309i	$-0.984514\pi$
$401$		−	6.27155e6i		−	0.0972617i	0.998817	−	0.0486309i	$-0.0154858\pi$
$402$		−	7.91159e7i		−	1.21783i
$403$	1.31314e7			0.200629
$404$	2.13305e8			3.23487
$405$	−1.06037e8			−1.59622
$406$	1.79220e8			2.67798
$407$		−	8.93094e7i		−	1.32469i
$408$	2.66434e7			0.392291
$409$		−	2.96714e7i		−	0.433678i	−0.976207	−	0.216839i	$-0.930425\pi$
$409$		−	2.96714e7i		−	0.433678i	0.976207	−	0.216839i	$-0.0695747\pi$
$410$	−6.52849e7			−0.947242
$411$			7.78482e7i			1.12130i
$412$			2.18607e8i			3.12589i
$413$		−	1.76694e8i		−	2.50826i
$414$		−	1.49819e7i		−	0.211138i
$415$	1.08718e8			1.52110
$416$	3.20887e7			0.445730
$417$		−	9.65955e7i		−	1.33214i
$418$	−5.68928e7	+	1.64558e8i	−0.778984	+	2.25315i
$419$	6.59835e7			0.897002			0.448501	−	0.893782i	$-0.351958\pi$
$419$	6.59835e7			0.897002			0.448501	+	0.893782i	$0.351958\pi$
$420$			3.73867e8i			5.04625i
$421$		−	1.93760e7i		−	0.259668i	−0.991536	−	0.129834i	$-0.958556\pi$
$421$		−	1.93760e7i		−	0.259668i	0.991536	−	0.129834i	$-0.0414444\pi$
$422$	−9.10595e7			−1.21168
$423$	2.42376e7			0.320234
$424$	−8.48590e7			−1.11327
$425$	5.60752e6			0.0730472
$426$		−	1.28373e8i		−	1.66052i
$427$	−3.27916e7			−0.421190
$428$			1.46206e8i			1.86481i
$429$	−2.47148e7			−0.313029
$430$		−	1.60707e8i		−	2.02130i
$431$		−	1.45675e8i		−	1.81951i	−0.415147	−	0.909755i	$-0.636270\pi$
$431$		−	1.45675e8i		−	1.81951i	0.415147	−	0.909755i	$-0.363730\pi$
$432$		−	1.31833e8i		−	1.63521i
$433$			9.54378e7i			1.17559i	0.809009	+	0.587796i	$0.200004\pi$
$433$			9.54378e7i			1.17559i	−0.809009	+	0.587796i	$0.799996\pi$
$434$	−1.98914e8			−2.43330
$435$	1.42225e8			1.72786
$436$			6.12619e7i			0.739148i
$437$	−1.78029e7	−	6.15503e6i	−0.213328	−	0.0737540i
$438$	−1.43715e8			−1.71033
$439$			1.14060e7i			0.134816i	0.997726	+	0.0674078i	$0.0214729\pi$
$439$			1.14060e7i			0.134816i	−0.997726	+	0.0674078i	$0.978527\pi$
$440$		−	3.84185e8i		−	4.51007i
$441$	−2.96331e7			−0.345511
$442$	3.73135e6			0.0432115
$443$	1.16201e7			0.133659			0.0668294	−	0.997764i	$-0.478712\pi$
$443$	1.16201e7			0.133659			0.0668294	+	0.997764i	$0.478712\pi$
$444$	−2.75918e8			−3.15233
$445$			3.87313e7i			0.439524i
$446$	−4.62301e7			−0.521099
$447$			4.46456e7i			0.499869i
$448$	−1.73333e8			−1.92774
$449$			2.46346e7i			0.272148i	0.990699	+	0.136074i	$0.0434486\pi$
$449$			2.46346e7i			0.272148i	−0.990699	+	0.136074i	$0.956551\pi$
$450$			5.37579e7i			0.589936i
$451$			4.65965e7i			0.507954i
$452$		−	9.86000e7i		−	1.06773i
$453$	1.94220e8			2.08929
$454$	−1.88769e7			−0.201726
$455$			3.12592e7i			0.331851i
$456$	3.03519e8	+	1.04936e8i	3.20104	+	1.10670i
$457$	−2.23961e7			−0.234652			−0.117326	−	0.993093i	$-0.537432\pi$
$457$	−2.23961e7			−0.234652			−0.117326	+	0.993093i	$0.537432\pi$
$458$		−	1.59173e8i		−	1.65681i
$459$		−	6.84372e6i		−	0.0707708i
$460$	6.96194e7			0.715248
$461$	−6.33431e7			−0.646541			−0.323271	−	0.946307i	$-0.604782\pi$
$461$	−6.33431e7			−0.646541			−0.323271	+	0.946307i	$0.604782\pi$
$462$	3.74379e8			3.79652
$463$	−1.35759e8			−1.36781			−0.683903	−	0.729573i	$-0.739719\pi$
$463$	−1.35759e8			−1.36781			−0.683903	+	0.729573i	$0.739719\pi$
$464$			2.95229e8i			2.95533i
$465$	−1.57854e8			−1.56999
$466$		−	4.25780e7i		−	0.420753i
$467$	−1.60120e8			−1.57215			−0.786075	−	0.618131i	$-0.787890\pi$
$467$	−1.60120e8			−1.57215			−0.786075	+	0.618131i	$0.787890\pi$
$468$			2.54967e7i			0.248741i
$469$			7.14210e7i			0.692321i
$470$			1.58018e8i			1.52199i
$471$			2.22886e7i			0.213315i
$472$	5.60958e8			5.33463
$473$	−1.14704e8			−1.08391
$474$		−	4.53016e8i		−	4.25381i
$475$	6.38804e7	+	2.20854e7i	0.596056	+	0.206075i
$476$	−4.02873e7			−0.373548
$477$		−	2.19131e7i		−	0.201906i
$478$			2.66320e8i			2.43849i
$479$	1.15981e8			1.05531			0.527654	−	0.849460i	$-0.323072\pi$
$479$	1.15981e8			1.05531			0.527654	+	0.849460i	$0.323072\pi$
$480$	−3.85742e8			−3.48797
$481$	−2.30697e7			−0.207303
$482$	8.53898e7			0.762544
$483$			4.05027e7i			0.359453i
$484$	−1.77954e8			−1.56954
$485$			1.98840e8i			1.74292i
$486$	1.97176e8			1.71769
$487$			9.87991e7i			0.855394i	0.903922	+	0.427697i	$0.140675\pi$
$487$			9.87991e7i			0.855394i	−0.903922	+	0.427697i	$0.859325\pi$
$488$		−	1.04105e8i		−	0.895799i
$489$			1.44349e8i			1.23449i
$490$		−	1.93195e8i		−	1.64213i
$491$	−1.66715e8			−1.40841			−0.704206	−	0.709996i	$-0.748697\pi$
$491$	−1.66715e8			−1.40841			−0.704206	+	0.709996i	$0.748697\pi$
$492$	1.43958e8			1.20876
$493$			1.53259e7i			0.127905i
$494$	4.25073e7	+	1.46961e7i	0.352600	+	0.121905i
$495$	9.92078e7			0.817957
$496$		−	3.27671e8i		−	2.68530i
$497$			1.15887e8i			0.943987i
$498$	−3.36342e8			−2.72328
$499$	1.89230e8			1.52296			0.761479	−	0.648189i	$-0.224473\pi$
$499$	1.89230e8			1.52296			0.761479	+	0.648189i	$0.224473\pi$
$500$	1.46289e8			1.17031
$501$	7.09719e7			0.564382
$502$		−	1.11374e8i		−	0.880383i
$503$	1.32915e8			1.04441			0.522203	−	0.852821i	$-0.325110\pi$
$503$	1.32915e8			1.04441			0.522203	+	0.852821i	$0.325110\pi$
$504$		−	2.30581e8i		−	1.80107i
$505$	−2.14391e8			−1.66469
$506$		−	6.97148e7i		−	0.538113i
$507$		−	1.53300e8i		−	1.17630i
$508$		−	1.80348e8i		−	1.37569i
$509$		−	1.41670e8i		−	1.07430i	−0.843488	−	0.537148i	$-0.819501\pi$
$509$		−	1.41670e8i		−	1.07430i	0.843488	−	0.537148i	$-0.180499\pi$
$510$	−4.48551e7			−0.338143
$511$	1.29737e8			0.972300
$512$			1.92168e8i			1.43176i
$513$	2.69543e7	−	7.79631e7i	0.199653	−	0.577480i
$514$	−1.26383e8			−0.930676
$515$		−	2.19720e8i		−	1.60860i
$516$			3.54373e8i			2.57936i
$517$	1.12784e8			0.816161
$518$	3.49459e8			2.51424
$519$	−1.13937e8			−0.815013
$520$	−9.92396e7			−0.705789
$521$			6.06347e7i			0.428754i	0.976751	+	0.214377i	$0.0687721\pi$
$521$			6.06347e7i			0.428754i	−0.976751	+	0.214377i	$0.931228\pi$
$522$	−1.46926e8			−1.03297
$523$		−	7.90109e7i		−	0.552309i	−0.961113	−	0.276154i	$-0.910940\pi$
$523$		−	7.90109e7i		−	0.552309i	0.961113	−	0.276154i	$-0.0890601\pi$
$524$	5.88286e7			0.408879
$525$		−	1.45332e8i		−	1.00434i
$526$			4.68709e8i			3.22067i
$527$		−	1.70101e7i		−	0.116218i
$528$			6.16715e8i			4.18970i
$529$	−1.40494e8			−0.949052
$530$	1.42863e8			0.959606
$531$			1.44856e8i			0.967502i
$532$	−4.58949e8	−	1.58673e8i	−3.04811	−	1.05382i
$533$	1.20364e7			0.0794907
$534$		−	1.19823e8i		−	0.786896i
$535$		−	1.46951e8i		−	0.959645i
$536$	−2.26743e8			−1.47245
$537$	−3.20901e8			−2.07228
$538$	9.41687e7			0.604727
$539$	−1.37891e8			−0.880581
$540$			3.04879e8i			1.93618i
$541$	1.11613e8			0.704895			0.352448	−	0.935832i	$-0.385349\pi$
$541$	1.11613e8			0.704895			0.352448	+	0.935832i	$0.385349\pi$
$542$		−	2.14359e8i		−	1.34631i
$543$	−2.04433e8			−1.27688
$544$		−	4.15669e7i		−	0.258197i
$545$		−	6.15738e7i		−	0.380370i
$546$		−	9.67065e7i		−	0.594125i
$547$		−	1.81019e8i		−	1.10602i	−0.833176	−	0.553008i	$-0.813480\pi$
$547$		−	1.81019e8i		−	1.10602i	0.833176	−	0.553008i	$-0.186520\pi$
$548$	3.73710e8			2.27088
$549$	2.68828e7			0.162464
$550$			2.50150e8i			1.50353i
$551$	−6.03618e7	+	1.74592e8i	−0.360834	+	1.04368i
$552$	−1.28585e8			−0.764495
$553$			4.08955e8i			2.41824i
$554$		−	1.40098e8i		−	0.823954i
$555$	2.77323e8			1.62221
$556$	−4.63707e8			−2.69786
$557$	2.25990e8			1.30775			0.653873	−	0.756604i	$-0.273143\pi$
$557$	2.25990e8			1.30775			0.653873	+	0.756604i	$0.273143\pi$
$558$	1.63071e8			0.938589
$559$			2.96293e7i			0.169623i
$560$	7.80020e8			4.44162
$561$			3.20149e7i			0.181328i
$562$	5.87525e8			3.30992
$563$		−	3.26109e8i		−	1.82742i	−0.406370	−	0.913709i	$-0.633206\pi$
$563$		−	3.26109e8i		−	1.82742i	0.406370	−	0.913709i	$-0.366794\pi$
$564$		−	3.48442e8i		−	1.94220i
$565$			9.91020e7i			0.549461i
$566$			3.89733e8i			2.14941i
$567$	−2.96141e8			−1.62461
$568$	−3.67911e8			−2.00770
$569$		−	1.86517e8i		−	1.01247i	−0.862396	−	0.506234i	$-0.831037\pi$
$569$		−	1.86517e8i		−	1.01247i	0.862396	−	0.506234i	$-0.168963\pi$
$570$	−5.10985e8	−	1.76664e8i	−2.75921	−	0.953943i
$571$	8.66919e7			0.465662			0.232831	−	0.972517i	$-0.425201\pi$
$571$	8.66919e7			0.465662			0.232831	+	0.972517i	$0.425201\pi$
$572$			1.18643e8i			0.633950i
$573$		−	2.22217e8i		−	1.18117i
$574$	−1.82328e8			−0.964090
$575$	−2.70628e7			−0.142354
$576$	1.42100e8			0.743579
$577$	−1.74442e8			−0.908079			−0.454039	−	0.890982i	$-0.650017\pi$
$577$	−1.74442e8			−0.908079			−0.454039	+	0.890982i	$0.650017\pi$
$578$			3.55467e8i			1.84084i
$579$	1.81361e8			0.934348
$580$		−	6.82751e8i		−	3.49928i
$581$	3.03629e8			1.54816
$582$		−	6.15151e8i		−	3.12042i
$583$		−	1.01967e8i		−	0.514584i
$584$			4.11880e8i			2.06791i
$585$		−	2.56266e7i		−	0.128004i
$586$	−2.36303e8			−1.17429
$587$	−6.77908e6			−0.0335164			−0.0167582	−	0.999860i	$-0.505335\pi$
$587$	−6.77908e6			−0.0335164			−0.0167582	+	0.999860i	$0.505335\pi$
$588$			4.26010e8i			2.09550i
$589$	6.69948e7	−	1.93777e8i	0.327865	−	0.948324i
$590$	−9.44394e8			−4.59830
$591$			2.67181e8i			1.29432i
$592$			5.75665e8i			2.77463i
$593$	4.99086e7			0.239338			0.119669	−	0.992814i	$-0.461817\pi$
$593$	4.99086e7			0.239338			0.119669	+	0.992814i	$0.461817\pi$
$594$	3.05297e8			1.45668
$595$	4.04924e7			0.192231
$596$	2.14321e8			1.01234
$597$			2.56881e8i			1.20728i
$598$	−1.80082e7			−0.0842104
$599$			1.34986e8i			0.628072i	0.949411	+	0.314036i	$0.101681\pi$
$599$			1.34986e8i			0.628072i	−0.949411	+	0.314036i	$0.898319\pi$
$600$	4.61390e8			2.13606
$601$		−	9.31195e7i		−	0.428960i	−0.976728	−	0.214480i	$-0.931194\pi$
$601$		−	9.31195e7i		−	0.428960i	0.976728	−	0.214480i	$-0.0688057\pi$
$602$		−	4.48824e8i		−	2.05725i
$603$		−	5.85516e7i		−	0.267047i
$604$		−	9.32354e8i		−	4.23126i
$605$	1.78860e8			0.807697
$606$	6.63262e8			2.98035
$607$			2.08533e8i			0.932415i	0.884675	+	0.466207i	$0.154380\pi$
$607$			2.08533e8i			0.932415i	−0.884675	+	0.466207i	$0.845620\pi$
$608$	1.63713e8	−	4.73528e8i	0.728405	−	2.10685i
$609$	3.97207e8			1.75859
$610$			1.75264e8i			0.772152i
$611$		−	2.91334e7i		−	0.127723i
$612$	3.30279e7			0.144088
$613$	3.14675e8			1.36609			0.683047	−	0.730374i	$-0.260654\pi$
$613$	3.14675e8			1.36609			0.683047	+	0.730374i	$0.260654\pi$
$614$	−7.79029e8			−3.36549
$615$	−1.44691e8			−0.622039
$616$		−	1.07295e9i		−	4.59028i
$617$	−4.21738e7			−0.179551			−0.0897753	−	0.995962i	$-0.528615\pi$
$617$	−4.21738e7			−0.179551			−0.0897753	+	0.995962i	$0.528615\pi$
$618$			6.79750e8i			2.87994i
$619$	−2.07102e7			−0.0873198			−0.0436599	−	0.999046i	$-0.513902\pi$
$619$	−2.07102e7			−0.0873198			−0.0436599	+	0.999046i	$0.513902\pi$
$620$			7.57777e8i			3.17955i
$621$			3.30290e7i			0.137918i
$622$			8.06940e8i			3.35328i
$623$			1.08169e8i			0.447341i
$624$	1.59305e8			0.655655
$625$	−3.01007e8			−1.23292
$626$		−	3.71559e8i		−	1.51463i
$627$	−1.26092e8	+	3.64712e8i	−0.511547	+	1.47961i
$628$	1.06997e8			0.432007
$629$			2.98839e7i			0.120084i
$630$			3.88191e8i			1.55247i
$631$	2.34658e8			0.934000			0.467000	−	0.884257i	$-0.345335\pi$
$631$	2.34658e8			0.934000			0.467000	+	0.884257i	$0.345335\pi$
$632$	−1.29832e9			−5.14318
$633$	−2.01816e8			−0.795691
$634$	5.64672e8			2.21579
$635$			1.81266e8i			0.707938i
$636$	−3.15025e8			−1.22454
$637$			3.56189e7i			0.137804i
$638$	−6.83687e8			−2.63266
$639$		−	9.50054e7i		−	0.364121i
$640$			1.80193e8i			0.687382i
$641$		−	4.48685e8i		−	1.70360i	−0.523868	−	0.851799i	$-0.675512\pi$
$641$		−	4.48685e8i		−	1.70360i	0.523868	−	0.851799i	$-0.324488\pi$
$642$			4.54622e8i			1.71809i
$643$	−2.63984e7			−0.0992991			−0.0496495	−	0.998767i	$-0.515810\pi$
$643$	−2.63984e7			−0.0992991			−0.0496495	+	0.998767i	$0.515810\pi$
$644$	1.94433e8			0.727969
$645$		−	3.56177e8i		−	1.32735i
$646$	1.90370e7	−	5.50630e7i	0.0706156	−	0.204250i
$647$	2.06171e8			0.761229			0.380614	−	0.924734i	$-0.375713\pi$
$647$	2.06171e8			0.761229			0.380614	+	0.924734i	$0.375713\pi$
$648$		−	9.40170e8i		−	3.45526i
$649$			6.74053e8i			2.46581i
$650$	6.46168e7			0.235291
$651$	−4.40854e8			−1.59791
$652$	6.92946e8			2.50010
$653$	−1.04864e8			−0.376606			−0.188303	−	0.982111i	$-0.560299\pi$
$653$	−1.04864e8			−0.376606			−0.188303	+	0.982111i	$0.560299\pi$
$654$			1.90491e8i			0.680991i
$655$	−5.91281e7			−0.210412
$656$		−	3.00349e8i		−	1.06393i
$657$	−1.06359e8			−0.375042
$658$			4.41313e8i			1.54906i
$659$		−	1.00063e8i		−	0.349638i	−0.984601	−	0.174819i	$-0.944066\pi$
$659$		−	1.00063e8i		−	0.349638i	0.984601	−	0.174819i	$-0.0559340\pi$
$660$		−	1.42622e9i		−	4.96085i
$661$		−	3.79284e8i		−	1.31329i	−0.754201	−	0.656644i	$-0.771976\pi$
$661$		−	3.79284e8i		−	1.31329i	0.754201	−	0.656644i	$-0.228024\pi$
$662$	9.02063e8			3.10930
$663$	8.26983e6			0.0283763
$664$			9.63942e8i			3.29266i
$665$	4.61286e8	+	1.59481e8i	1.56858	+	0.542305i
$666$	−2.86490e8			−0.969811
$667$		−	7.39656e7i		−	0.249260i
$668$		−	3.40701e8i		−	1.14299i
$669$	−1.02460e8			−0.342197
$670$	3.81730e8			1.26921
$671$	1.25093e8			0.414063
$672$	−1.07730e9			−3.55001
$673$		−	3.66445e8i		−	1.20216i	−0.799187	−	0.601082i	$-0.794736\pi$
$673$		−	3.66445e8i		−	1.20216i	0.799187	−	0.601082i	$-0.205264\pi$
$674$	−7.93581e8			−2.59186
$675$		−	1.18514e8i		−	0.385354i
$676$	−7.35916e8			−2.38226
$677$		−	2.76020e8i		−	0.889560i	−0.895640	−	0.444780i	$-0.853282\pi$
$677$		−	2.76020e8i		−	0.889560i	0.895640	−	0.444780i	$-0.146718\pi$
$678$		−	3.06592e8i		−	0.983721i
$679$			5.55321e8i			1.77392i
$680$			1.28553e8i			0.408841i
$681$	−4.18370e7			−0.132470
$682$	7.58816e8			2.39212
$683$			1.05100e8i			0.329868i	0.986305	+	0.164934i	$0.0527412\pi$
$683$			1.05100e8i			0.329868i	−0.986305	+	0.164934i	$0.947259\pi$
$684$	3.76251e8	+	1.30082e8i	1.17574	+	0.406488i
$685$	−3.75613e8			−1.16861
$686$			2.43322e8i			0.753718i
$687$		−	3.52777e8i		−	1.08800i
$688$	7.39349e8			2.27031
$689$	−2.63394e7			−0.0805283
$690$	2.16478e8			0.658972
$691$	−3.03677e8			−0.920402			−0.460201	−	0.887815i	$-0.652223\pi$
$691$	−3.03677e8			−0.920402			−0.460201	+	0.887815i	$0.652223\pi$
$692$			5.46957e8i			1.65057i
$693$	2.77068e8			0.832505
$694$			2.59574e8i			0.776574i
$695$	4.66068e8			1.38834
$696$			1.26103e9i			3.74021i
$697$		−	1.55917e7i		−	0.0460464i
$698$		−	8.76697e8i		−	2.57800i
$699$		−	9.43659e7i		−	0.276302i
$700$	−6.97664e8			−2.03401
$701$	−4.26003e8			−1.23668			−0.618342	−	0.785909i	$-0.712195\pi$
$701$	−4.26003e8			−1.23668			−0.618342	+	0.785909i	$0.712195\pi$
$702$		−	7.88618e7i		−	0.227958i
$703$	−1.17699e8	+	3.40435e8i	−0.338772	+	0.979870i
$704$	6.61231e8			1.89511
$705$			3.50217e8i			0.999469i
$706$		−	1.07749e9i		−	3.06196i
$707$	−5.98752e8			−1.69429
$708$	2.08246e9			5.86783
$709$	4.72028e8			1.32443			0.662216	−	0.749313i	$-0.269616\pi$
$709$	4.72028e8			1.32443			0.662216	+	0.749313i	$0.269616\pi$
$710$	6.19392e8			1.73058
$711$		−	3.35265e8i		−	0.932781i
$712$	−3.43408e8			−0.951417
$713$			8.20935e7i			0.226485i
$714$	−1.25271e8			−0.344158
$715$		−	1.19247e8i		−	0.326235i
$716$			1.54049e9i			4.19681i
$717$			5.90247e8i			1.60131i
$718$		−	3.85728e7i		−	0.104210i
$719$	7.72222e7			0.207757			0.103879	−	0.994590i	$-0.466875\pi$
$719$	7.72222e7			0.207757			0.103879	+	0.994590i	$0.466875\pi$
$720$	−6.39468e8			−1.71325
$721$		−	6.13636e8i		−	1.63721i
$722$	4.33736e8	−	5.52295e8i	1.15243	−	1.46744i
$723$	1.89250e8			0.500751
$724$			9.81379e8i			2.58596i
$725$			2.65403e8i			0.696453i
$726$	−5.53341e8			−1.44605
$727$	−4.32964e8			−1.12680			−0.563402	−	0.826183i	$-0.690508\pi$
$727$	−4.32964e8			−1.12680			−0.563402	+	0.826183i	$0.690508\pi$
$728$	−2.77157e8			−0.718342
$729$	−4.72721e7			−0.122018
$730$		−	6.93415e8i		−	1.78248i
$731$	3.83811e7			0.0982574
$732$		−	3.86471e8i		−	0.985335i
$733$	−4.94099e8			−1.25459			−0.627296	−	0.778781i	$-0.715838\pi$
$733$	−4.94099e8			−1.25459			−0.627296	+	0.778781i	$0.715838\pi$
$734$		−	3.16207e8i		−	0.799619i
$735$		−	4.28179e8i		−	1.07836i
$736$			2.00609e8i			0.503173i
$737$		−	2.72457e8i		−	0.680605i
$738$	1.49474e8			0.371875
$739$	−6.00444e8			−1.48778			−0.743890	−	0.668302i	$-0.767022\pi$
$739$	−6.00444e8			−1.48778			−0.743890	+	0.668302i	$0.767022\pi$
$740$		−	1.33129e9i		−	3.28532i
$741$	9.42093e7	+	3.25711e7i	0.231547	+	0.0800530i
$742$	3.98989e8			0.976674
$743$			1.76594e8i			0.430536i	0.976555	+	0.215268i	$0.0690625\pi$
$743$			1.76594e8i			0.430536i	−0.976555	+	0.215268i	$0.930937\pi$
$744$		−	1.39960e9i		−	3.39848i
$745$	−2.15412e8			−0.520957
$746$	7.68048e7			0.185000
$747$	−2.48918e8			−0.597165
$748$	1.53688e8			0.367227
$749$		−	4.10405e8i		−	0.976713i
$750$	4.54879e8			1.07823
$751$			4.85737e8i			1.14678i	0.819281	+	0.573392i	$0.194373\pi$
$751$			4.85737e8i			1.14678i	−0.819281	+	0.573392i	$0.805627\pi$
$752$	−7.26976e8			−1.70949
$753$		−	2.46838e8i		−	0.578133i
$754$			1.76605e8i			0.411991i
$755$			9.37101e8i			2.17744i
$756$			8.51467e8i			1.97062i
$757$	6.87374e8			1.58455			0.792274	−	0.610166i	$-0.208897\pi$
$757$	6.87374e8			1.58455			0.792274	+	0.610166i	$0.208897\pi$
$758$	−1.09458e9			−2.51328
$759$		−	1.54510e8i		−	0.353370i
$760$	−5.06310e8	+	1.46446e9i	−1.15339	+	3.33609i
$761$	7.71555e8			1.75070			0.875352	−	0.483485i	$-0.160629\pi$
$761$	7.71555e8			1.75070			0.875352	+	0.483485i	$0.160629\pi$
$762$		−	5.60783e8i		−	1.26745i
$763$		−	1.71964e8i		−	0.387136i
$764$	−1.06675e9			−2.39213
$765$	−3.31960e7			−0.0741485
$766$	−1.65226e6			−0.00367614
$767$	1.74116e8			0.385880
$768$			2.65780e8i			0.586730i
$769$	−1.01084e8			−0.222281			−0.111141	−	0.993805i	$-0.535450\pi$
$769$	−1.01084e8			−0.222281			−0.111141	+	0.993805i	$0.535450\pi$
$770$			1.80636e9i			3.95669i
$771$	−2.80103e8			−0.611160
$772$		−	8.70625e8i		−	1.89225i
$773$			4.04573e8i			0.875909i	0.898997	+	0.437954i	$0.144297\pi$
$773$			4.04573e8i			0.875909i	−0.898997	+	0.437954i	$0.855703\pi$
$774$			3.67951e8i			0.793536i
$775$		−	2.94567e8i		−	0.632819i
$776$	−1.76300e9			−3.77282
$777$	7.74510e8			1.65106
$778$		−	8.55097e8i		−	1.81584i
$779$	6.14086e7	−	1.77620e8i	0.129902	−	0.375732i
$780$	−3.68411e8			−0.776334
$781$		−	4.42086e8i		−	0.928012i
$782$			2.33274e7i			0.0487804i
$783$	3.23912e8			0.674749
$784$	8.88809e8			1.84442
$785$	−1.07541e8			−0.222314
$786$	1.82925e8			0.376708
$787$		−	4.48190e8i		−	0.919470i	−0.888056	−	0.459735i	$-0.847944\pi$
$787$		−	4.48190e8i		−	0.919470i	0.888056	−	0.459735i	$-0.152056\pi$
$788$	1.28260e9			2.62128
$789$			1.03880e9i			2.11496i
$790$	2.18578e9			4.43327
$791$			2.76772e8i			0.559234i
$792$			8.79619e8i			1.77059i
$793$		−	3.23130e7i		−	0.0647975i
$794$			1.22460e9i			2.44643i
$795$	3.16629e8			0.630158
$796$	1.23316e9			2.44501
$797$			8.28284e8i			1.63608i	0.575162	+	0.818040i	$0.304939\pi$
$797$			8.28284e8i			1.63608i	−0.575162	+	0.818040i	$0.695061\pi$
$798$	−1.42708e9	−	4.93387e8i	−2.80828	−	0.970909i
$799$	−3.77388e7			−0.0739856
$800$		−	7.19825e8i		−	1.40591i
$801$		−	8.86780e7i		−	0.172551i
$802$	−9.36151e7			−0.181478
$803$	−4.94919e8			−0.955846
$804$	−8.41746e8			−1.61962
$805$	−1.95423e8			−0.374618
$806$		−	1.96011e8i		−	0.374348i
$807$	2.08707e8			0.397115
$808$		−	1.90088e9i		−	3.60347i
$809$	5.49140e8			1.03714			0.518570	−	0.855035i	$-0.326464\pi$
$809$	5.49140e8			1.03714			0.518570	+	0.855035i	$0.326464\pi$
$810$			1.58281e9i			2.97834i
$811$		−	4.97409e8i		−	0.932505i	−0.884652	−	0.466252i	$-0.845604\pi$
$811$		−	4.97409e8i		−	0.932505i	0.884652	−	0.466252i	$-0.154396\pi$
$812$		−	1.90679e9i		−	3.56152i
$813$		−	4.75086e8i		−	0.884099i
$814$	−1.33312e9			−2.47169
$815$	−6.96474e8			−1.28657
$816$		−	2.06360e8i		−	0.379800i
$817$	4.37234e8	+	1.51166e8i	0.801767	+	0.277196i
$818$	−4.42903e8			−0.809186
$819$		−	7.15700e7i		−	0.130280i
$820$			6.94592e8i			1.25976i
$821$	−2.38989e8			−0.431865			−0.215932	−	0.976408i	$-0.569279\pi$
$821$	−2.38989e8			−0.431865			−0.215932	+	0.976408i	$0.569279\pi$
$822$	1.16204e9			2.09220
$823$	−6.68644e8			−1.19949			−0.599743	−	0.800193i	$-0.704731\pi$
$823$	−6.68644e8			−1.19949			−0.599743	+	0.800193i	$0.704731\pi$
$824$	1.94813e9			3.48207
$825$			5.54410e8i			0.987346i
$826$	−2.63751e9			−4.68008
$827$		−	2.00405e8i		−	0.354317i	−0.984182	−	0.177158i	$-0.943310\pi$
$827$		−	2.00405e8i		−	0.354317i	0.984182	−	0.177158i	$-0.0566905\pi$
$828$	−1.59398e8			−0.280797
$829$		−	5.83575e8i		−	1.02431i	−0.858892	−	0.512157i	$-0.828846\pi$
$829$		−	5.83575e8i		−	1.02431i	0.858892	−	0.512157i	$-0.171154\pi$
$830$		−	1.62283e9i		−	2.83817i
$831$		−	3.10501e8i		−	0.541077i
$832$		−	1.70804e8i		−	0.296570i
$833$	4.61398e7			0.0798254
$834$	−1.44188e9			−2.48559
$835$			3.42435e8i			0.588192i
$836$	1.75080e9	+	6.05305e8i	2.99652	+	1.03599i
$837$	−3.59506e8			−0.613098
$838$		−	9.84932e8i		−	1.67369i
$839$		−	2.41664e8i		−	0.409190i	−0.978847	−	0.204595i	$-0.934412\pi$
$839$		−	2.41664e8i		−	0.409190i	0.978847	−	0.204595i	$-0.0655878\pi$
$840$	3.33174e9			5.62125
$841$	−1.30551e8			−0.219479
$842$	−2.89225e8			−0.484506
$843$	1.30214e9			2.17357
$844$			9.68818e8i			1.61144i
$845$	7.39663e8			1.22593
$846$		−	3.61793e8i		−	0.597515i
$847$	4.99522e8			0.822062
$848$			6.57256e8i			1.07782i
$849$			8.63770e8i			1.41148i
$850$		−	8.37031e7i		−	0.136296i
$851$		−	1.44225e8i		−	0.234019i
$852$	−1.36581e9			−2.20837
$853$	3.27850e8			0.528236			0.264118	−	0.964490i	$-0.414919\pi$
$853$	3.27850e8			0.528236			0.264118	+	0.964490i	$0.414919\pi$
$854$			4.89478e8i			0.785886i
$855$	−3.78167e8	−	1.30744e8i	−0.605042	−	0.209182i
$856$	1.30293e9			2.07730
$857$			5.60607e8i			0.890668i	0.895364	+	0.445334i	$0.146915\pi$
$857$			5.60607e8i			0.890668i	−0.895364	+	0.445334i	$0.853085\pi$
$858$			3.68916e8i			0.584071i
$859$	1.07374e9			1.69402			0.847010	−	0.531576i	$-0.178400\pi$
$859$	1.07374e9			1.69402			0.847010	+	0.531576i	$0.178400\pi$
$860$	−1.70983e9			−2.68818
$861$	−4.04095e8			−0.633102
$862$	−2.17449e9			−3.39496
$863$			5.66605e8i			0.881552i	0.897617	+	0.440776i	$0.145297\pi$
$863$			5.66605e8i			0.881552i	−0.897617	+	0.440776i	$0.854703\pi$
$864$	−8.78513e8			−1.36209
$865$		−	5.49742e8i		−	0.849397i
$866$	1.42459e9			2.19350
$867$			7.87824e8i			1.20885i
$868$			2.11632e9i			3.23611i
$869$		−	1.56008e9i		−	2.37732i
$870$		−	2.12298e9i		−	3.22396i
$871$	−7.03788e7			−0.106509
$872$	5.45940e8			0.823370
$873$		−	4.55257e8i		−	0.684249i
$874$	−9.18757e7	+	2.65743e8i	−0.137615	+	0.398041i
$875$	−4.10637e8			−0.612962
$876$			1.52904e9i			2.27460i
$877$			2.64799e8i			0.392571i	0.980547	+	0.196285i	$0.0628879\pi$
$877$			2.64799e8i			0.392571i	−0.980547	+	0.196285i	$0.937112\pi$
$878$	1.70257e8			0.251548
$879$	−5.23720e8			−0.771139
$880$	−2.97562e9			−4.36646
$881$	−3.11993e8			−0.456265			−0.228133	−	0.973630i	$-0.573262\pi$
$881$	−3.11993e8			−0.456265			−0.228133	+	0.973630i	$0.573262\pi$
$882$			4.42332e8i			0.644677i
$883$	7.80065e8			1.13305			0.566525	−	0.824045i	$-0.308288\pi$
$883$	7.80065e8			1.13305			0.566525	+	0.824045i	$0.308288\pi$
$884$		−	3.96994e7i		−	0.0574681i
$885$	−2.09307e9			−3.01963
$886$		−	1.73452e8i		−	0.249390i
$887$		−	2.78539e8i		−	0.399131i	−0.979885	−	0.199565i	$-0.936047\pi$
$887$		−	2.78539e8i		−	0.399131i	0.979885	−	0.199565i	$-0.0639530\pi$
$888$			2.45887e9i			3.51153i
$889$			5.06241e8i			0.720529i
$890$	5.78141e8			0.820094
$891$	1.12972e9			1.59712
$892$			4.91860e8i			0.693022i
$893$	−4.29917e8	−	1.48636e8i	−0.603713	−	0.208722i
$894$	6.66422e8			0.932689
$895$		−	1.54833e9i		−	2.15971i
$896$			5.03244e8i			0.699608i
$897$	−3.99116e7			−0.0552996
$898$	3.67719e8			0.507793
$899$	8.05084e8			1.10806
$900$	5.71952e8			0.784571
$901$			3.41195e7i			0.0466474i
$902$	6.95544e8			0.947774
$903$		−	9.94733e8i		−	1.35096i
$904$	−8.78680e8			−1.18939
$905$		−	9.86376e8i		−	1.33075i
$906$		−	2.89911e9i		−	3.89835i
$907$			1.08363e9i			1.45231i	0.687533	+	0.726153i	$0.258693\pi$
$907$			1.08363e9i			1.45231i	−0.687533	+	0.726153i	$0.741307\pi$
$908$			2.00838e8i			0.268281i
$909$	4.90863e8			0.653534
$910$	4.66604e8			0.619190
$911$		−	3.58900e8i		−	0.474699i	−0.971424	−	0.237350i	$-0.923721\pi$
$911$		−	3.58900e8i		−	0.474699i	0.971424	−	0.237350i	$-0.0762787\pi$
$912$	8.12757e8	−	2.35084e9i	1.07146	−	3.09912i
$913$	−1.15828e9			−1.52196
$914$			3.34305e8i			0.437829i
$915$			3.88439e8i			0.507060i
$916$	−1.69351e9			−2.20344
$917$	−1.65133e8			−0.214154
$918$	−1.02156e8			−0.132049
$919$	3.96276e8			0.510565			0.255282	−	0.966867i	$-0.417832\pi$
$919$	3.96276e8			0.510565			0.255282	+	0.966867i	$0.417832\pi$
$920$		−	6.20418e8i		−	0.796747i
$921$	−1.72657e9			−2.21007
$922$			9.45518e8i			1.20636i
$923$	−1.14196e8			−0.145226
$924$		−	3.98317e9i		−	5.04908i
$925$			5.17507e8i			0.653870i
$926$			2.02646e9i			2.55215i
$927$			5.03065e8i			0.631517i
$928$	1.96736e9			2.46173
$929$	7.38996e8			0.921711			0.460855	−	0.887475i	$-0.347543\pi$
$929$	7.38996e8			0.921711			0.460855	+	0.887475i	$0.347543\pi$
$930$			2.35627e9i			2.92939i
$931$	5.25622e8	+	1.81724e8i	0.651365	+	0.225197i
$932$	−4.53004e8			−0.559569
$933$			1.78843e9i			2.20205i
$934$			2.39010e9i			2.93342i
$935$	−1.54470e8			−0.188977
$936$	2.27216e8			0.277084
$937$	−2.42474e8			−0.294745			−0.147372	−	0.989081i	$-0.547082\pi$
$937$	−2.42474e8			−0.294745			−0.147372	+	0.989081i	$0.547082\pi$
$938$	1.06610e9			1.29178
$939$		−	8.23490e8i		−	0.994630i
$940$	1.68122e9			2.02414
$941$		−	7.76759e8i		−	0.932218i	−0.884727	−	0.466109i	$-0.845655\pi$
$941$		−	7.76759e8i		−	0.932218i	0.884727	−	0.466109i	$-0.154345\pi$
$942$	3.32701e8			0.398017
$943$			7.52483e7i			0.0897350i
$944$		−	4.34477e9i		−	5.16477i
$945$		−	8.55803e8i		−	1.01409i
$946$			1.71217e9i			2.02243i
$947$	−7.91274e8			−0.931702			−0.465851	−	0.884863i	$-0.654252\pi$
$947$	−7.91274e8			−0.931702			−0.465851	+	0.884863i	$0.654252\pi$
$948$	−4.81982e9			−5.65725
$949$			1.27844e8i			0.149582i
$950$	3.29668e8	−	9.53539e8i	0.384509	−	1.11216i
$951$	1.25149e9			1.45507
$952$			3.59023e8i			0.416113i
$953$			1.79542e8i			0.207437i	0.994607	+	0.103718i	$0.0330741\pi$
$953$			1.79542e8i			0.207437i	−0.994607	+	0.103718i	$0.966926\pi$
$954$	−3.27095e8			−0.376729
$955$	1.07219e9			1.23100
$956$	2.83348e9			3.24300
$957$	−1.51526e9			−1.72883
$958$		−	1.73124e9i		−	1.96906i
$959$	−1.04901e9			−1.18939
$960$			2.05325e9i			2.32075i
$961$	−6.04825e6			−0.00681490
$962$			3.44360e8i			0.386801i
$963$			3.36454e8i			0.376744i
$964$		−	9.08496e8i		−	1.01413i
$965$			8.75058e8i			0.973767i
$966$	6.04581e8			0.670692
$967$	−7.59012e8			−0.839400			−0.419700	−	0.907663i	$-0.637865\pi$
$967$	−7.59012e8			−0.839400			−0.419700	+	0.907663i	$0.637865\pi$
$968$			1.58585e9i			1.74838i
$969$	4.21918e7	−	1.22037e8i	0.0463721	−	0.134128i
$970$	2.96807e9			3.25206
$971$			9.72178e8i			1.06191i	0.847400	+	0.530956i	$0.178167\pi$
$971$			9.72178e8i			1.06191i	−0.847400	+	0.530956i	$0.821833\pi$
$972$		−	2.09783e9i		−	2.28440i
$973$	1.30164e9			1.41303
$974$	1.47477e9			1.59605
$975$	1.43211e8			0.154512
$976$	−8.06318e8			−0.867275
$977$			3.54587e8i			0.380224i	0.981762	+	0.190112i	$0.0608851\pi$
$977$			3.54587e8i			0.380224i	−0.981762	+	0.190112i	$0.939115\pi$
$978$	2.15468e9			2.30339
$979$		−	4.12643e8i		−	0.439771i
$980$	−2.05547e9			−2.18390
$981$			1.40977e8i			0.149329i
$982$			2.48854e9i			2.62791i
$983$			7.87276e8i			0.828832i	0.910088	+	0.414416i	$0.136014\pi$
$983$			7.87276e8i			0.828832i	−0.910088	+	0.414416i	$0.863986\pi$
$984$		−	1.28290e9i		−	1.34650i
$985$	−1.28913e9			−1.34893
$986$	2.28769e8			0.238653
$987$			9.78086e8i			1.01725i
$988$	1.56358e8	−	4.52252e8i	0.162124	−	0.468932i
$989$	−1.85234e8			−0.191483
$990$		−	1.48087e9i		−	1.52620i
$991$		−	1.87947e8i		−	0.193114i	−0.995327	−	0.0965571i	$-0.969217\pi$
$991$		−	1.87947e8i		−	0.193114i	0.995327	−	0.0965571i	$-0.0307830\pi$
$992$	−2.18355e9			−2.23680
$993$	1.99925e9			2.04183
$994$	1.72984e9			1.76136
$995$	−1.23944e9			−1.25822
$996$			3.57847e9i			3.62176i
$997$	−3.26970e8			−0.329930			−0.164965	−	0.986299i	$-0.552751\pi$
$997$	−3.26970e8			−0.329930			−0.164965	+	0.986299i	$0.552751\pi$
$998$		−	2.82462e9i		−	2.84164i
$999$	6.31594e8			0.633492

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	19.7.b.b.18.1	✓	8
3.2	odd	2		171.7.c.d.37.8		8
4.3	odd	2		304.7.e.d.113.7		8
19.18	odd	2	inner	19.7.b.b.18.8	yes	8
57.56	even	2		171.7.c.d.37.1		8
76.75	even	2		304.7.e.d.113.2		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
19.7.b.b.18.1	✓	8	1.1	even	1	trivial
19.7.b.b.18.8	yes	8	19.18	odd	2	inner
171.7.c.d.37.1		8	57.56	even	2
171.7.c.d.37.8		8	3.2	odd	2
304.7.e.d.113.2		8	76.75	even	2
304.7.e.d.113.7		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)

\(f(q)\)	\(=\)	\(q-14.9269i q^{2} -33.0827i q^{3} -158.814 q^{4} +159.622 q^{5} -493.824 q^{6} +445.794 q^{7} +1415.28i q^{8} -365.466 q^{9} +O(q^{10})\)	\(q-14.9269i q^{2} -33.0827i q^{3} -158.814 q^{4} +159.622 q^{5} -493.824 q^{6} +445.794 q^{7} +1415.28i q^{8} -365.466 q^{9} -2382.67i q^{10} -1700.61 q^{11} +5253.99i q^{12} +439.288i q^{13} -6654.34i q^{14} -5280.74i q^{15} +10961.7 q^{16} +569.044 q^{17} +5455.29i q^{18} +(6482.51 + 2241.20i) q^{19} -25350.2 q^{20} -14748.1i q^{21} +25385.0i q^{22} -2746.30 q^{23} +46821.3 q^{24} +9854.28 q^{25} +6557.23 q^{26} -12026.7i q^{27} -70798.1 q^{28} +26932.8i q^{29} -78825.3 q^{30} -29892.3i q^{31} -73047.0i q^{32} +56260.9i q^{33} -8494.09i q^{34} +71158.6 q^{35} +58041.0 q^{36} +52516.0i q^{37} +(33454.3 - 96764.0i) q^{38} +14532.9 q^{39} +225910. i q^{40} -27399.8i q^{41} -220144. q^{42} +67448.4 q^{43} +270081. q^{44} -58336.5 q^{45} +40993.9i q^{46} -66319.6 q^{47} -362643. i q^{48} +81083.1 q^{49} -147094. i q^{50} -18825.5i q^{51} -69765.0i q^{52} +59959.3i q^{53} -179522. q^{54} -271456. q^{55} +630922. i q^{56} +(74145.1 - 214459. i) q^{57} +402024. q^{58} -396359. i q^{59} +838654. i q^{60} -73557.7 q^{61} -446201. q^{62} -162922. q^{63} -388819. q^{64} +70120.2i q^{65} +839803. q^{66} +160211. i q^{67} -90372.0 q^{68} +90855.2i q^{69} -1.06218e6i q^{70} +259957. i q^{71} -517236. i q^{72} +291024. q^{73} +783903. q^{74} -326006. i q^{75} +(-1.02951e6 - 355934. i) q^{76} -758123. q^{77} -216931. i q^{78} +917363. i q^{79} +1.74973e6 q^{80} -664300. q^{81} -408996. q^{82} +681097. q^{83} +2.34219e6i q^{84} +90832.1 q^{85} -1.00680e6i q^{86} +891010. q^{87} -2.40684e6i q^{88} +242644. i q^{89} +870786. i q^{90} +195832. i q^{91} +436151. q^{92} -988920. q^{93} +989949. i q^{94} +(1.03475e6 + 357746. i) q^{95} -2.41659e6 q^{96} +1.24569e6i q^{97} -1.21032e6i q^{98} +621516. q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 454 q^{4} + 108 q^{5} - 358 q^{6} - 140 q^{7} - 1052 q^{9}+O(q^{10}) \) 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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