LMFDB - Embedded newform 76.6.k.a.3.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [76,6,Mod(3,76)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(76, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([9, 13]))

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

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

chi := DirichletCharacter("76.3");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 76 = 2^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	76.k (of order $18$, degree $6$, 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:	$12.1891703058$
Analytic rank:	$0$
Dimension:	$288$
Relative dimension:	$48$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			3.11
Character	$\chi$	$=$	76.3
Dual form			76.6.k.a.51.11

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-4.39545 - 3.56091i) q^{2} +(16.7807 - 6.10766i) q^{3} +(6.63988 + 31.3035i) q^{4} +(16.0499 - 91.0237i) q^{5} +(-95.5073 - 32.9085i) q^{6} +(-124.031 + 71.6095i) q^{7} +(82.2838 - 161.237i) q^{8} +(58.1382 - 48.7837i) q^{9} +O(q^{10})$	\(q+(-4.39545 - 3.56091i) q^{2} +(16.7807 - 6.10766i) q^{3} +(6.63988 + 31.3035i) q^{4} +(16.0499 - 91.0237i) q^{5} +(-95.5073 - 32.9085i) q^{6} +(-124.031 + 71.6095i) q^{7} +(82.2838 - 161.237i) q^{8} +(58.1382 - 48.7837i) q^{9} +(-394.673 + 342.937i) q^{10} +(-133.511 - 77.0826i) q^{11} +(302.613 + 484.740i) q^{12} +(350.614 - 963.304i) q^{13} +(800.168 + 126.908i) q^{14} +(-286.613 - 1625.46i) q^{15} +(-935.824 + 415.703i) q^{16} +(856.907 + 719.031i) q^{17} +(-429.258 + 7.40153i) q^{18} +(-1336.24 - 831.007i) q^{19} +(2955.93 - 101.966i) q^{20} +(-1643.96 + 1959.20i) q^{21} +(312.356 + 814.232i) q^{22} +(-2278.74 + 401.804i) q^{23} +(395.996 - 3208.22i) q^{24} +(-5091.17 - 1853.03i) q^{25} +(-4971.34 + 2985.65i) q^{26} +(-1492.06 + 2584.32i) q^{27} +(-3065.18 - 3407.14i) q^{28} +(-777.405 - 926.476i) q^{29} +(-4528.34 + 8165.24i) q^{30} +(389.629 + 674.858i) q^{31} +(5593.64 + 1505.18i) q^{32} +(-2711.20 - 478.057i) q^{33} +(-1206.09 - 6211.83i) q^{34} +(4527.47 + 12439.1i) q^{35} +(1913.13 + 1496.01i) q^{36} -11079.2i q^{37} +(2914.21 + 8410.86i) q^{38} -18306.3i q^{39} +(-13355.7 - 10077.6i) q^{40} +(-3298.60 - 9062.83i) q^{41} +(14202.5 - 2757.55i) q^{42} +(-1983.83 - 349.803i) q^{43} +(1526.46 - 4691.18i) q^{44} +(-3507.36 - 6074.93i) q^{45} +(11446.9 + 6348.28i) q^{46} +(5098.24 + 6075.84i) q^{47} +(-13164.8 + 12691.5i) q^{48} +(1852.35 - 3208.36i) q^{49} +(15779.5 + 26274.1i) q^{50} +(18771.1 + 6832.11i) q^{51} +(32482.9 + 4579.24i) q^{52} +(26991.9 - 4759.41i) q^{53} +(15760.8 - 6046.15i) q^{54} +(-9159.18 + 10915.5i) q^{55} +(1340.34 + 25890.7i) q^{56} +(-27498.4 - 5783.57i) q^{57} +(117.949 + 6840.54i) q^{58} +(6979.50 + 5856.50i) q^{59} +(48979.7 - 19764.9i) q^{60} +(6770.78 + 38399.0i) q^{61} +(690.511 - 4353.73i) q^{62} +(-3717.58 + 10214.0i) q^{63} +(-19226.8 - 26534.4i) q^{64} +(-82056.2 - 47375.1i) q^{65} +(10214.6 + 11755.6i) q^{66} +(46745.5 - 39224.1i) q^{67} +(-16818.5 + 31598.5i) q^{68} +(-35784.7 + 20660.3i) q^{69} +(24394.3 - 70797.3i) q^{70} +(12204.6 - 69215.5i) q^{71} +(-3081.91 - 13388.1i) q^{72} +(38015.3 - 13836.4i) q^{73} +(-39452.0 + 48698.0i) q^{74} -96750.9 q^{75} +(17141.0 - 47346.7i) q^{76} +22079.4 q^{77} +(-65187.1 + 80464.4i) q^{78} +(36009.8 - 13106.5i) q^{79} +(22818.9 + 91854.2i) q^{80} +(-12456.0 + 70641.6i) q^{81} +(-17773.1 + 51581.2i) q^{82} +(-17886.3 + 10326.7i) q^{83} +(-72245.5 - 38453.0i) q^{84} +(79202.1 - 66458.5i) q^{85} +(7474.21 + 8601.79i) q^{86} +(-18704.0 - 10798.7i) q^{87} +(-23414.4 + 15184.3i) q^{88} +(35736.7 - 98185.7i) q^{89} +(-6215.84 + 39191.4i) q^{90} +(25494.6 + 144587. i) q^{91} +(-27708.4 - 68664.7i) q^{92} +(10660.0 + 8944.83i) q^{93} +(-773.511 - 44860.4i) q^{94} +(-97087.8 + 108291. i) q^{95} +(103058. - 8906.16i) q^{96} +(-97164.9 + 115797. i) q^{97} +(-19566.6 + 7506.13i) q^{98} +(-11522.5 + 2031.72i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 288 q - 6 q^{2} + 24 q^{4} - 12 q^{5} + 264 q^{6} - 9 q^{8} + 54 q^{9}+O(q^{10}) $ 288 * q - 6 * q^2 + 24 * q^4 - 12 * q^5 + 264 * q^6 - 9 * q^8 + 54 * q^9	\( 288 q - 6 q^{2} + 24 q^{4} - 12 q^{5} + 264 q^{6} - 9 q^{8} + 54 q^{9} - 657 q^{10} - 9 q^{12} + 336 q^{13} - 2163 q^{14} + 1824 q^{16} - 12 q^{17} - 10242 q^{20} - 7842 q^{21} - 102 q^{22} - 11856 q^{24} - 12 q^{25} + 1317 q^{26} + 6660 q^{28} - 12 q^{29} - 40692 q^{30} - 3351 q^{32} - 8604 q^{33} - 15756 q^{34} + 81783 q^{36} + 50400 q^{38} + 39246 q^{40} - 29082 q^{41} - 123081 q^{42} - 39651 q^{44} - 6 q^{45} - 112554 q^{46} - 68403 q^{48} + 259302 q^{49} + 154188 q^{50} - 36867 q^{52} - 26280 q^{53} + 172605 q^{54} - 12 q^{57} + 229740 q^{58} - 136062 q^{60} + 169296 q^{61} + 35076 q^{62} + 63795 q^{64} - 189918 q^{65} + 73644 q^{66} + 59706 q^{68} - 200898 q^{69} - 177831 q^{70} - 188502 q^{72} + 397428 q^{73} - 530703 q^{74} - 53022 q^{76} + 159804 q^{77} - 618237 q^{78} + 18045 q^{80} - 110160 q^{81} + 155859 q^{82} + 733851 q^{84} - 645108 q^{85} + 616836 q^{86} + 598383 q^{88} - 226320 q^{89} + 546366 q^{90} - 754308 q^{92} + 558942 q^{93} - 454530 q^{96} - 177198 q^{97} - 76791 q^{98}+O(q^{100}) \) 288 * q - 6 * q^2 + 24 * q^4 - 12 * q^5 + 264 * q^6 - 9 * q^8 + 54 * q^9 - 657 * q^10 - 9 * q^12 + 336 * q^13 - 2163 * q^14 + 1824 * q^16 - 12 * q^17 - 10242 * q^20 - 7842 * q^21 - 102 * q^22 - 11856 * q^24 - 12 * q^25 + 1317 * q^26 + 6660 * q^28 - 12 * q^29 - 40692 * q^30 - 3351 * q^32 - 8604 * q^33 - 15756 * q^34 + 81783 * q^36 + 50400 * q^38 + 39246 * q^40 - 29082 * q^41 - 123081 * q^42 - 39651 * q^44 - 6 * q^45 - 112554 * q^46 - 68403 * q^48 + 259302 * q^49 + 154188 * q^50 - 36867 * q^52 - 26280 * q^53 + 172605 * q^54 - 12 * q^57 + 229740 * q^58 - 136062 * q^60 + 169296 * q^61 + 35076 * q^62 + 63795 * q^64 - 189918 * q^65 + 73644 * q^66 + 59706 * q^68 - 200898 * q^69 - 177831 * q^70 - 188502 * q^72 + 397428 * q^73 - 530703 * q^74 - 53022 * q^76 + 159804 * q^77 - 618237 * q^78 + 18045 * q^80 - 110160 * q^81 + 155859 * q^82 + 733851 * q^84 - 645108 * q^85 + 616836 * q^86 + 598383 * q^88 - 226320 * q^89 + 546366 * q^90 - 754308 * q^92 + 558942 * q^93 - 454530 * q^96 - 177198 * q^97 - 76791 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/76\mathbb{Z}\right)^\times$.

$n$	$21$	$39$
$\chi(n)$	$e\left(\frac{13}{18}\right)$	$-1$

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 $

$2$	−4.39545	−	3.56091i	−0.777012	−	0.629485i
$2$	−4.39545	−	3.56091i	−0.777012	−	0.629485i
$3$	16.7807	−	6.10766i	1.07648	−	0.391807i	0.257884	−	0.966176i	$-0.416975\pi$
$3$	16.7807	−	6.10766i	1.07648	−	0.391807i	0.818596	+	0.574369i	$0.194753\pi$
$4$	6.63988	+	31.3035i	0.207496	+	0.978236i
$5$	16.0499	−	91.0237i	0.287110	−	1.62828i	−0.410540	−	0.911842i	$-0.634660\pi$
$5$	16.0499	−	91.0237i	0.287110	−	1.62828i	0.697650	−	0.716439i	$-0.254229\pi$
$6$	−95.5073	−	32.9085i	−1.08307	−	0.373190i
$7$	−124.031	+	71.6095i	−0.956723	+	0.552364i	−0.895163	−	0.445739i	$-0.852941\pi$
$7$	−124.031	+	71.6095i	−0.956723	+	0.552364i	−0.0615602	+	0.998103i	$0.519608\pi$
$8$	82.2838	−	161.237i	0.454558	−	0.890717i
$9$	58.1382	−	48.7837i	0.239252	−	0.200756i
$10$	−394.673	+	342.937i	−1.24807	+	1.08446i
$11$	−133.511	−	77.0826i	−0.332686	−	0.192077i	0.324347	−	0.945938i	$-0.394856\pi$
$11$	−133.511	−	77.0826i	−0.332686	−	0.192077i	−0.657033	+	0.753862i	$0.728189\pi$
$12$	302.613	+	484.740i	0.606645	+	0.971753i
$13$	350.614	−	963.304i	0.575401	−	1.58090i	−0.220442	−	0.975400i	$-0.570750\pi$
$13$	350.614	−	963.304i	0.575401	−	1.58090i	0.795844	−	0.605502i	$-0.207028\pi$
$14$	800.168	+	126.908i	1.09109	+	0.173049i
$15$	−286.613	−	1625.46i	−0.328903	−	1.86530i
$16$	−935.824	+	415.703i	−0.913891	+	0.405960i
$17$	856.907	+	719.031i	0.719137	+	0.603428i	0.927146	−	0.374699i	$-0.122254\pi$
$17$	856.907	+	719.031i	0.719137	+	0.603428i	−0.208009	+	0.978127i	$0.566698\pi$
$18$	−429.258	+	7.40153i	−0.312275	+	0.00538444i
$19$	−1336.24	−	831.007i	−0.849179	−	0.528106i
$19$	−1336.24	−	831.007i	−0.849179	−	0.528106i
$20$	2955.93	−	101.966i	1.65242	−	0.0570010i
$21$	−1643.96	+	1959.20i	−0.813473	+	0.969460i
$22$	312.356	+	814.232i	0.137592	+	0.358667i
$23$	−2278.74	+	401.804i	−0.898205	+	0.158378i	−0.603643	−	0.797255i	$-0.706285\pi$
$23$	−2278.74	+	401.804i	−0.898205	+	0.158378i	−0.294562	+	0.955632i	$0.595174\pi$
$24$	395.996	−	3208.22i	0.140334	−	1.13694i
$25$	−5091.17	−	1853.03i	−1.62917	−	0.592971i
$26$	−4971.34	+	2985.65i	−1.44225	+	0.866174i
$27$	−1492.06	+	2584.32i	−0.393891	+	0.682239i
$28$	−3065.18	−	3407.14i	−0.738859	−	0.821287i
$29$	−777.405	−	926.476i	−0.171653	−	0.204569i	0.673358	−	0.739316i	$-0.264851\pi$
$29$	−777.405	−	926.476i	−0.171653	−	0.204569i	−0.845012	+	0.534748i	$0.820407\pi$
$30$	−4528.34	+	8165.24i	−0.918619	+	1.65640i
$31$	389.629	+	674.858i	0.0728194	+	0.126127i	0.900136	−	0.435609i	$-0.143467\pi$
$31$	389.629	+	674.858i	0.0728194	+	0.126127i	−0.827317	+	0.561736i	$0.810134\pi$
$32$	5593.64	+	1505.18i	0.965650	+	0.259845i
$33$	−2711.20	−	478.057i	−0.433387	−	0.0764178i
$34$	−1206.09	−	6211.83i	−0.178929	−	0.921557i
$35$	4527.47	+	12439.1i	0.624720	+	1.71640i
$36$	1913.13	+	1496.01i	0.246031	+	0.192389i
$37$		−	11079.2i		−	1.33047i	−0.746636	−	0.665233i	$-0.768332\pi$
$37$		−	11079.2i		−	1.33047i	0.746636	−	0.665233i	$-0.231668\pi$
$38$	2914.21	+	8410.86i	0.327388	+	0.944890i
$39$		−	18306.3i		−	1.92726i
$40$	−13355.7	−	10077.6i	−1.31983	−	0.995882i
$41$	−3298.60	−	9062.83i	−0.306457	−	0.841984i	−0.993340	−	0.115216i	$-0.963244\pi$
$41$	−3298.60	−	9062.83i	−0.306457	−	0.841984i	0.686883	−	0.726768i	$-0.258978\pi$
$42$	14202.5	−	2757.55i	1.24234	−	0.241212i
$43$	−1983.83	−	349.803i	−0.163619	−	0.0288505i	0.0912384	−	0.995829i	$-0.470917\pi$
$43$	−1983.83	−	349.803i	−0.163619	−	0.0288505i	−0.254858	+	0.966979i	$0.582029\pi$
$44$	1526.46	−	4691.18i	0.118865	−	0.365301i
$45$	−3507.36	−	6074.93i	−0.258196	−	0.447208i
$46$	11446.9	+	6348.28i	0.797613	+	0.442345i
$47$	5098.24	+	6075.84i	0.336647	+	0.401201i	0.907637	−	0.419757i	$-0.137885\pi$
$47$	5098.24	+	6075.84i	0.336647	+	0.401201i	−0.570989	+	0.820958i	$0.693440\pi$
$48$	−13164.8	+	12691.5i	−0.824727	+	0.795077i
$49$	1852.35	−	3208.36i	0.110213	−	0.190894i
$50$	15779.5	+	26274.1i	0.892622	+	1.48629i
$51$	18771.1	+	6832.11i	1.01056	+	0.367815i
$52$	32482.9	+	4579.24i	1.66589	+	0.234847i
$53$	26991.9	−	4759.41i	1.31991	−	0.232736i	0.531067	−	0.847330i	$-0.321791\pi$
$53$	26991.9	−	4759.41i	1.31991	−	0.232736i	0.788843	+	0.614594i	$0.210680\pi$
$54$	15760.8	−	6046.15i	0.735517	−	0.282159i
$55$	−9159.18	+	10915.5i	−0.408272	+	0.486560i
$56$	1340.34	+	25890.7i	0.0571141	+	1.10325i
$57$	−27498.4	−	5783.57i	−1.12104	−	0.235781i
$58$	117.949	+	6840.54i	0.00460388	+	0.267006i
$59$	6979.50	+	5856.50i	0.261032	+	0.219032i	0.763906	−	0.645328i	$-0.223279\pi$
$59$	6979.50	+	5856.50i	0.261032	+	0.219032i	−0.502873	+	0.864360i	$0.667724\pi$
$60$	48979.7	−	19764.9i	1.75646	−	0.708788i
$61$	6770.78	+	38399.0i	0.232978	+	1.32128i	0.846831	+	0.531862i	$0.178507\pi$
$61$	6770.78	+	38399.0i	0.232978	+	1.32128i	−0.613854	+	0.789420i	$0.710381\pi$
$62$	690.511	−	4353.73i	0.0228135	−	0.143841i
$63$	−3717.58	+	10214.0i	−0.118007	+	0.324222i
$64$	−19226.8	−	26534.4i	−0.586754	−	0.809765i
$65$	−82056.2	−	47375.1i	−2.40895	−	1.39081i
$66$	10214.6	+	11755.6i	0.288643	+	0.332188i
$67$	46745.5	−	39224.1i	1.27219	−	1.06750i	0.277922	−	0.960604i	$-0.410354\pi$
$67$	46745.5	−	39224.1i	1.27219	−	1.06750i	0.994271	−	0.106893i	$-0.0340902\pi$
$68$	−16818.5	+	31598.5i	−0.441076	+	0.828694i
$69$	−35784.7	+	20660.3i	−0.904846	+	0.522413i
$70$	24394.3	−	70797.3i	0.595036	−	1.72692i
$71$	12204.6	−	69215.5i	0.287327	−	1.62951i	−0.409526	−	0.912299i	$-0.634306\pi$
$71$	12204.6	−	69215.5i	0.287327	−	1.62951i	0.696853	−	0.717214i	$-0.254583\pi$
$72$	−3081.91	−	13388.1i	−0.0700631	−	0.304361i
$73$	38015.3	−	13836.4i	0.834931	−	0.303890i	0.111050	−	0.993815i	$-0.464579\pi$
$73$	38015.3	−	13836.4i	0.834931	−	0.303890i	0.723881	+	0.689925i	$0.242356\pi$
$74$	−39452.0	+	48698.0i	−0.837509	+	1.03379i
$75$	−96750.9			−1.98610
$76$	17141.0	−	47346.7i	0.340410	−	0.940277i
$77$	22079.4			0.424385
$78$	−65187.1	+	80464.4i	−1.21318	+	1.49750i
$79$	36009.8	−	13106.5i	0.649163	−	0.236276i	0.00361210	−	0.999993i	$-0.498850\pi$
$79$	36009.8	−	13106.5i	0.649163	−	0.236276i	0.645550	+	0.763718i	$0.276628\pi$
$80$	22818.9	+	91854.2i	0.398631	+	1.60463i
$81$	−12456.0	+	70641.6i	−0.210944	+	1.19632i
$82$	−17773.1	+	51581.2i	−0.291896	+	0.847142i
$83$	−17886.3	+	10326.7i	−0.284987	+	0.164538i	−0.635679	−	0.771953i	$-0.719280\pi$
$83$	−17886.3	+	10326.7i	−0.284987	+	0.164538i	0.350692	+	0.936491i	$0.385946\pi$
$84$	−72245.5	−	38453.0i	−1.11715	−	0.594609i
$85$	79202.1	−	66458.5i	1.18902	−	0.997707i
$86$	7474.21	+	8601.79i	0.108973	+	0.125413i
$87$	−18704.0	−	10798.7i	−0.264933	−	0.152959i
$88$	−23414.4	+	15184.3i	−0.322311	+	0.209020i
$89$	35736.7	−	98185.7i	0.478233	−	1.31393i	−0.432759	−	0.901509i	$-0.642460\pi$
$89$	35736.7	−	98185.7i	0.478233	−	1.31393i	0.910992	−	0.412424i	$-0.135318\pi$
$90$	−6215.84	+	39191.4i	−0.0808898	+	0.510017i
$91$	25494.6	+	144587.i	0.322734	+	1.83032i
$92$	−27708.4	−	68664.7i	−0.341305	−	0.845793i
$93$	10660.0	+	8944.83i	0.127806	+	0.107242i
$94$	−773.511	−	44860.4i	−0.00902915	−	0.523653i
$95$	−97087.8	+	108291.i	−1.10371	+	1.23108i
$96$	103058.	−	8906.16i	1.14131	−	0.0986308i
$97$	−97164.9	+	115797.i	−1.04853	+	1.24959i	−0.0810286	+	0.996712i	$0.525820\pi$
$97$	−97164.9	+	115797.i	−1.04853	+	1.24959i	−0.967499	+	0.252875i	$0.918624\pi$
$98$	−19566.6	+	7506.13i	−0.205802	+	0.0789498i
$99$	−11522.5	+	2031.72i	−0.118156	+	0.0208342i
$100$	24201.8	−	171676.i	0.242018	−	1.71676i
$101$	133986.	+	48766.9i	1.30694	+	0.475687i	0.899251	−	0.437434i	$-0.144113\pi$
$101$	133986.	+	48766.9i	1.30694	+	0.475687i	0.407689	+	0.913121i	$0.366335\pi$
$102$	−58178.7	−	96872.2i	−0.553686	−	0.921932i
$103$	77083.5	−	133513.i	0.715927	−	1.24002i	−0.246675	−	0.969098i	$-0.579338\pi$
$103$	77083.5	−	133513.i	0.715927	−	1.24002i	0.962601	−	0.270923i	$-0.0873288\pi$
$104$	−126470.	−	135796.i	−1.14658	−	1.23113i
$105$	151948.	+	181084.i	1.34500	+	1.60290i
$106$	−135589.	−	75196.1i	−1.17209	−	0.650026i
$107$	46758.7	+	80988.4i	0.394823	+	0.683854i	0.993079	−	0.117451i	$-0.0374724\pi$
$107$	46758.7	+	80988.4i	0.394823	+	0.683854i	−0.598255	+	0.801306i	$0.704139\pi$
$108$	−90805.4	−	29547.1i	−0.749121	−	0.243756i
$109$	−13402.1	−	2363.14i	−0.108045	−	0.0190513i	0.119364	−	0.992851i	$-0.461914\pi$
$109$	−13402.1	−	2363.14i	−0.108045	−	0.0190513i	−0.227409	+	0.973799i	$0.573026\pi$
$110$	79127.7	−	15363.4i	0.623515	−	0.121062i
$111$	−67667.9	−	185916.i	−0.521285	−	1.43222i
$112$	86303.2	−	118574.i	0.650102	−	0.893192i
$113$			43856.3i			0.323100i	0.986865	+	0.161550i	$0.0516492\pi$
$113$			43856.3i			0.323100i	−0.986865	+	0.161550i	$0.948351\pi$
$114$	100273.	+	123341.i	0.722640	+	0.888882i
$115$			213868.i			1.50800i
$116$	23840.1	−	30487.2i	0.164499	−	0.210365i
$117$	−26609.5	−	73109.0i	−0.179710	−	0.493749i
$118$	−9823.57	−	50595.3i	−0.0649478	−	0.334507i
$119$	−157773.	−	27819.6i	−1.02133	−	0.180087i
$120$	−285669.	−	87536.7i	−1.81096	−	0.554929i
$121$	−68642.1	−	118892.i	−0.426213	−	0.738223i
$122$	106975.	−	192891.i	0.650701	−	1.17331i
$123$	−110705.	−	131933.i	−0.659790	−	0.786307i
$124$	−18538.3	+	16677.7i	−0.108272	+	0.0974054i
$125$	−105964.	+	183536.i	−0.606575	+	1.05062i
$126$	52711.4	−	31657.0i	0.295786	−	0.177641i
$127$	70212.0	+	25555.1i	0.386280	+	0.140594i	0.527858	−	0.849333i	$-0.322995\pi$
$127$	70212.0	+	25555.1i	0.386280	+	0.140594i	−0.141578	+	0.989927i	$0.545218\pi$
$128$	−9976.37	+	185095.i	−0.0538205	+	0.998551i
$129$	−35426.5	+	6246.65i	−0.187436	+	0.0330501i
$130$	191975.	+	500429.i	0.996290	+	2.59707i
$131$	177679.	−	211749.i	0.904601	−	1.07806i	−0.0920063	−	0.995758i	$-0.529328\pi$
$131$	177679.	−	211749.i	0.904601	−	1.07806i	0.996607	−	0.0823031i	$-0.0262276\pi$
$132$	−3037.13	−	88044.3i	−0.0151715	−	0.439811i
$133$	225243.	+	7383.70i	1.10414	+	0.0361947i
$134$	−345141.	+	5951.14i	−1.66048	+	0.0286311i
$135$	211287.	+	177291.i	0.997786	+	0.837242i
$136$	186444.	−	79000.6i	0.864373	−	0.366255i
$137$	15368.6	+	87159.8i	0.0699574	+	0.396748i	0.999600	+	0.0282852i	$0.00900466\pi$
$137$	15368.6	+	87159.8i	0.0699574	+	0.396748i	−0.929643	+	0.368463i	$0.879884\pi$
$138$	230859.	+	36614.7i	1.03193	+	0.163666i
$139$	33972.2	−	93337.9i	0.149138	−	0.409752i	−0.842518	−	0.538668i	$-0.818928\pi$
$139$	33972.2	−	93337.9i	0.149138	−	0.409752i	0.991655	+	0.128916i	$0.0411498\pi$
$140$	−359327.	+	224320.i	−1.54942	+	0.967270i
$141$	122661.	+	70818.3i	0.519587	+	0.299984i
$142$	−300115.	+	260774.i	−1.24901	+	1.08528i
$143$	−121065.	+	101585.i	−0.495083	+	0.415424i
$144$	−34127.6	+	69821.3i	−0.137151	+	0.280596i
$145$	−96808.5	+	55892.4i	−0.382379	+	0.220766i
$146$	−216364.	−	74551.6i	−0.840046	−	0.289451i
$147$	11488.0	−	65151.9i	0.0438483	−	0.248676i
$148$	346818.	−	73564.5i	1.30151	−	0.276067i
$149$	54324.2	−	19772.4i	0.200460	−	0.0729615i	−0.239839	−	0.970813i	$-0.577095\pi$
$149$	54324.2	−	19772.4i	0.200460	−	0.0729615i	0.440299	+	0.897851i	$0.354872\pi$
$150$	425263.	+	344521.i	1.54323	+	1.25022i
$151$	−108360.			−0.386747			−0.193373	−	0.981125i	$-0.561943\pi$
$151$	−108360.			−0.386747			−0.193373	+	0.981125i	$0.561943\pi$
$152$	−243940.	+	147072.i	−0.856394	+	0.516323i
$153$	84896.1			0.293197
$154$	−97048.7	−	78622.6i	−0.329752	−	0.267144i
$155$	67681.5	−	24634.1i	0.226277	−	0.0823582i
$156$	573052.	−	121552.i	1.88531	−	0.399898i
$157$	39843.7	−	225965.i	0.129006	−	0.731630i	−0.849841	−	0.527039i	$-0.823302\pi$
$157$	39843.7	−	225965.i	0.129006	−	0.731630i	0.978847	−	0.204592i	$-0.0655866\pi$
$158$	−204950.	−	70618.8i	−0.653139	−	0.225049i
$159$	423874.	−	244724.i	1.32967	−	0.767685i
$160$	226785.	−	484996.i	0.700348	−	1.49775i
$161$	253862.	−	213016.i	0.771851	−	0.647660i
$162$	306298.	−	266147.i	0.916973	−	0.796770i
$163$	−406106.	−	234465.i	−1.19721	−	0.691209i	−0.237277	−	0.971442i	$-0.576255\pi$
$163$	−406106.	−	234465.i	−1.19721	−	0.691209i	−0.959932	+	0.280233i	$0.909588\pi$
$164$	261796.	−	163434.i	0.760070	−	0.474496i
$165$	−87029.0	+	239110.i	−0.248859	+	0.683736i
$166$	115391.	+	18301.2i	0.325013	+	0.0515477i
$167$	102386.	+	580660.i	0.284086	+	1.61113i	0.708532	+	0.705679i	$0.249358\pi$
$167$	102386.	+	580660.i	0.284086	+	1.61113i	−0.424446	+	0.905453i	$0.639531\pi$
$168$	180624.	+	426277.i	0.493743	+	1.16525i
$169$	−520598.	−	436833.i	−1.40212	−	1.17652i
$170$	−584781.	+	10083.2i	−1.55193	+	0.0267593i
$171$	−118226.	+	16873.3i	−0.309188	+	0.0441276i
$172$	−2222.33	−	64423.7i	−0.00572779	−	0.166044i
$173$	−166399.	+	198306.i	−0.422703	+	0.503757i	−0.934802	−	0.355169i	$-0.884423\pi$
$173$	−166399.	+	198306.i	−0.422703	+	0.503757i	0.512100	+	0.858926i	$0.328868\pi$
$174$	43759.0	+	114068.i	0.109571	+	0.285622i
$175$	764159.	−	134742.i	1.88620	−	0.332589i
$176$	156986.	+	16634.8i	0.382015	+	0.0404795i
$177$	152890.	+	55647.5i	0.366814	+	0.133509i
$178$	−506709.	+	304315.i	−1.19869	+	0.719902i
$179$	−24647.3	+	42690.4i	−0.0574959	+	0.0995858i	−0.893341	−	0.449380i	$-0.851645\pi$
$179$	−24647.3	+	42690.4i	−0.0574959	+	0.0995858i	0.835845	+	0.548966i	$0.184978\pi$
$180$	166878.	−	150130.i	0.383901	−	0.345370i
$181$	3244.97	+	3867.20i	0.00736231	+	0.00877406i	0.769713	−	0.638390i	$-0.220399\pi$
$181$	3244.97	+	3867.20i	0.00736231	+	0.00877406i	−0.762351	+	0.647164i	$0.775955\pi$
$182$	402801.	−	726309.i	0.901389	−	1.62534i
$183$	348146.	+	603007.i	0.768483	+	1.33105i
$184$	−122718.	+	400479.i	−0.267216	+	0.872038i
$185$	−1.00847e6	−	177820.i	−2.16637	−	0.381990i
$186$	−15003.9	−	77275.9i	−0.0317996	−	0.163780i
$187$	−58981.8	−	162051.i	−0.123343	−	0.338882i
$188$	−156344.	+	199936.i	−0.322616	+	0.412568i
$189$		−	427382.i		−	0.870285i
$190$	812360.	−	130269.i	1.63254	−	0.261792i
$191$			430244.i			0.853357i	0.904403	+	0.426679i	$0.140316\pi$
$191$			430244.i			0.853357i	−0.904403	+	0.426679i	$0.859684\pi$
$192$	−484701.	−	327834.i	−0.948900	−	0.641802i
$193$	68876.0	+	189235.i	0.133099	+	0.365686i	0.988282	−	0.152640i	$-0.0487775\pi$
$193$	68876.0	+	189235.i	0.133099	+	0.365686i	−0.855183	+	0.518326i	$0.826555\pi$
$194$	839424.	−	162982.i	1.60132	−	0.310911i
$195$	−1.66631e6	−	293815.i	−3.13811	−	0.553334i
$196$	112732.	+	36681.9i	0.209608	+	0.0682043i
$197$	279664.	+	484393.i	0.513418	+	0.889267i	0.999879	+	0.0155641i	$0.00495440\pi$
$197$	279664.	+	484393.i	0.513418	+	0.889267i	−0.486461	+	0.873703i	$0.661712\pi$
$198$	57881.1	+	32100.1i	0.104924	+	0.0581893i
$199$	−219359.	−	261422.i	−0.392665	−	0.467960i	0.533104	−	0.846050i	$-0.321026\pi$
$199$	−219359.	−	261422.i	−0.392665	−	0.467960i	−0.925769	+	0.378090i	$0.876581\pi$
$200$	−717698.	+	668410.i	−1.26872	+	1.18159i
$201$	544853.	−	943713.i	0.951238	−	1.64759i
$202$	−415273.	−	691463.i	−0.716070	−	1.19231i
$203$	162767.	+	59242.4i	0.277221	+	0.100900i
$204$	−89231.7	+	632965.i	−0.150122	+	1.06489i
$205$	−877874.	+	154793.i	−1.45897	+	0.257256i
$206$	−814242.	+	312360.i	−1.33686	+	0.512846i
$207$	−112880.	+	134526.i	−0.183102	+	0.218212i
$208$	72335.9	+	1.04723e6i	0.115930	+	1.67836i
$209$	114346.	+	213949.i	0.181074	+	0.338801i
$210$	−23053.7	−	1.33702e6i	−0.0360738	−	2.09213i
$211$	302263.	+	253629.i	0.467389	+	0.392186i	0.845841	−	0.533435i	$-0.179099\pi$
$211$	302263.	+	253629.i	0.467389	+	0.392186i	−0.378452	+	0.925621i	$0.623543\pi$
$212$	328209.	+	813341.i	0.501547	+	1.24289i
$213$	−217944.	−	1.23602e6i	−0.329152	−	1.86671i
$214$	82867.0	−	522484.i	0.123694	−	0.779899i
$215$	−63680.8	+	174961.i	−0.0939533	+	0.258135i
$216$	293916.	+	453222.i	0.428635	+	0.660962i
$217$	−96652.5	−	55802.3i	−0.139336	−	0.0804457i
$218$	50493.1	+	58110.5i	0.0719599	+	0.0828159i
$219$	553413.	−	464368.i	0.779720	−	0.654263i
$220$	−402509.	−	214237.i	−0.560685	−	0.298427i
$221$	993089.	−	573360.i	1.36775	−	0.789672i
$222$	−364599.	+	1.05814e6i	−0.496516	+	1.44099i
$223$	147235.	−	835009.i	0.198266	−	1.12442i	−0.709425	−	0.704781i	$-0.751045\pi$
$223$	147235.	−	835009.i	0.198266	−	1.12442i	0.907691	−	0.419640i	$-0.137844\pi$
$224$	−801572.	+	213869.i	−1.06739	+	0.284792i
$225$	−386389.	+	140634.i	−0.508825	+	0.185197i
$226$	156168.	−	192768.i	0.203386	−	0.251052i
$227$	−1.38385e6			−1.78248			−0.891241	−	0.453530i	$-0.850165\pi$
$227$	−1.38385e6			−1.78248			−0.891241	+	0.453530i	$0.850165\pi$
$228$	−1539.92	−	899200.i	−0.00196183	−	1.14556i
$229$	−326269.			−0.411137			−0.205569	−	0.978643i	$-0.565904\pi$
$229$	−326269.			−0.411137			−0.205569	+	0.978643i	$0.565904\pi$
$230$	761565.	−	940046.i	0.949265	−	1.17174i
$231$	370507.	−	134853.i	0.456842	−	0.166277i
$232$	−213350.	+	49112.6i	−0.260239	+	0.0599063i
$233$	−201508.	+	1.14281e6i	−0.243166	+	1.37906i	0.581547	+	0.813513i	$0.302448\pi$
$233$	−201508.	+	1.14281e6i	−0.243166	+	1.37906i	−0.824713	+	0.565552i	$0.808663\pi$
$234$	−143374.	+	416101.i	−0.171171	+	0.496774i
$235$	634872.	−	366543.i	0.749922	−	0.432968i
$236$	−136986.	+	257370.i	−0.160102	+	0.300800i
$237$	524219.	−	439872.i	0.606236	−	0.508692i
$238$	594419.	+	684094.i	0.680221	+	0.782841i
$239$	−333259.	−	192407.i	−0.377387	−	0.217885i	0.299294	−	0.954161i	$-0.403249\pi$
$239$	−333259.	−	192407.i	−0.377387	−	0.217885i	−0.676681	+	0.736276i	$0.736582\pi$
$240$	943931.	+	1.40200e6i	1.05782	+	1.57116i
$241$	−454179.	+	1.24785e6i	−0.503714	+	1.38394i	0.383908	+	0.923371i	$0.374578\pi$
$241$	−454179.	+	1.24785e6i	−0.503714	+	1.38394i	−0.887622	+	0.460572i	$0.847644\pi$
$242$	−121649.	+	767009.i	−0.133528	+	0.841903i
$243$	96515.5	+	547367.i	0.104853	+	0.594652i
$244$	−1.15707e6	+	466914.i	−1.24418	+	0.502068i
$245$	−262307.	−	220101.i	−0.279186	−	0.234265i
$246$	16796.3	+	974118.i	0.0176961	+	1.02630i
$247$	−1.26902e6	+	995839.i	−1.32350	+	1.03860i
$248$	140872.	−	7292.80i	0.145444	−	0.00752949i
$249$	−237072.	+	282532.i	−0.242316	+	0.288781i
$250$	1.11931e6	−	429392.i	1.13267	−	0.434514i
$251$	−1.02117e6	+	180060.i	−1.02309	+	0.180399i	−0.659930	−	0.751328i	$-0.729414\pi$
$251$	−1.02117e6	+	180060.i	−1.02309	+	0.180399i	−0.363162	+	0.931726i	$0.618303\pi$
$252$	−344417.	−	48553.9i	−0.341652	−	0.0481640i
$253$	335209.	+	122006.i	0.329241	+	0.119834i
$254$	−217614.	−	362345.i	−0.211642	−	0.352401i
$255$	923158.	−	1.59896e6i	0.889049	−	1.53988i
$256$	702957.	−	778051.i	0.670392	−	0.742007i
$257$	−772172.	−	920238.i	−0.729258	−	0.869096i	0.266237	−	0.963907i	$-0.414219\pi$
$257$	−772172.	−	920238.i	−0.729258	−	0.869096i	−0.995495	+	0.0948119i	$0.969775\pi$
$258$	177959.	+	98693.7i	0.166445	+	0.0923082i
$259$	793375.	+	1.37417e6i	0.734902	+	1.27289i
$260$	938167.	−	2.88321e6i	0.860690	−	2.64511i
$261$	−90393.9	−	15938.9i	−0.0821368	−	0.0144829i
$262$	−1.53500e6	+	298035.i	−1.38151	+	0.268234i
$263$	−487757.	−	1.34010e6i	−0.434825	−	1.19467i	−0.942817	−	0.333310i	$-0.891834\pi$
$263$	−487757.	−	1.34010e6i	−0.434825	−	1.19467i	0.507992	−	0.861362i	$-0.330388\pi$
$264$	−300168.	+	397809.i	−0.265066	+	0.351289i
$265$		−	2.53329e6i		−	2.21601i
$266$	−963751.	−	834525.i	−0.835143	−	0.723161i
$267$		−	1.86589e6i		−	1.60180i
$268$	1.53824e6	+	1.20286e6i	1.30824	+	1.02300i
$269$	299154.	+	821920.i	0.252066	+	0.692547i	0.999599	+	0.0283213i	$0.00901617\pi$
$269$	299154.	+	821920.i	0.252066	+	0.692547i	−0.747533	+	0.664225i	$0.768762\pi$
$270$	−297384.	−	1.53164e6i	−0.248261	−	1.27864i
$271$	2.03736e6	+	359242.i	1.68517	+	0.297142i	0.932478	−	0.361226i	$-0.117642\pi$
$271$	2.03736e6	+	359242.i	1.68517	+	0.297142i	0.752696	+	0.658368i	$0.228753\pi$
$272$	−1.10082e6	−	316667.i	−0.902180	−	0.259526i
$273$	1.31091e6	+	2.27056e6i	1.06455	+	1.84385i
$274$	242816.	−	437832.i	0.195389	−	0.352315i
$275$	536890.	+	639841.i	0.428108	+	0.510200i
$276$	−884347.	−	983006.i	−0.698795	−	0.776754i
$277$	−833170.	+	1.44309e6i	−0.652430	+	1.13004i	0.330101	+	0.943946i	$0.392917\pi$
$277$	−833170.	+	1.44309e6i	−0.652430	+	1.13004i	−0.982531	+	0.186097i	$0.940416\pi$
$278$	−481691.	+	289290.i	−0.373815	+	0.224502i
$279$	55574.4	+	20227.4i	0.0427429	+	0.0155572i
$280$	2.37818e6	+	293542.i	1.81280	+	0.223756i
$281$	2.51756e6	−	443914.i	1.90202	−	0.335377i	0.905906	−	0.423479i	$-0.139191\pi$
$281$	2.51756e6	−	443914.i	1.90202	−	0.335377i	0.996111	+	0.0881024i	$0.0280803\pi$
$282$	−286972.	−	748062.i	−0.214890	−	0.560164i
$283$	277863.	−	331144.i	0.206236	−	0.245783i	−0.653005	−	0.757354i	$-0.726492\pi$
$283$	277863.	−	331144.i	0.206236	−	0.245783i	0.859241	+	0.511571i	$0.170936\pi$
$284$	2.24773e6	−	77536.5i	1.65367	−	0.0570441i
$285$	−967790.	+	2.41018e6i	−0.705779	+	1.75767i
$286$	893870.	−	15412.7i	0.646188	−	0.0111420i
$287$	1.05811e6	+	887863.i	0.758277	+	0.636270i
$288$	398633.	−	185370.i	0.283199	−	0.131692i
$289$	−29270.4	−	166001.i	−0.0206150	−	0.116914i
$290$	624544.	+	99054.1i	0.436082	+	0.0691636i
$291$	−923244.	+	2.53659e6i	−0.639123	+	1.75597i
$292$	685546.	+	1.09814e6i	0.470521	+	0.753704i
$293$	306794.	+	177128.i	0.208775	+	0.120536i	0.600742	−	0.799443i	$-0.294872\pi$
$293$	306794.	+	177128.i	0.208775	+	0.120536i	−0.391967	+	0.919979i	$0.628205\pi$
$294$	−282495.	+	245464.i	−0.190608	+	0.165622i
$295$	645100.	−	541303.i	0.431591	−	0.362148i
$296$	−1.78638e6	−	911638.i	−1.18507	−	0.604774i
$297$	398412.	−	230023.i	0.262084	−	0.151314i
$298$	−309187.	−	106535.i	−0.201688	−	0.0694947i
$299$	−411900.	+	2.33600e6i	−0.266449	+	1.51110i
$300$	−642414.	−	3.02865e6i	−0.412109	−	1.94288i
$301$	271107.	−	98674.8i	0.172474	−	0.0627755i
$302$	476291.	+	385860.i	0.300507	+	0.243452i
$303$	2.54622e6			1.59327
$304$	1.59593e6	+	222198.i	0.990446	+	0.137898i
$305$	3.60389e6			2.21831
$306$	−373156.	−	302307.i	−0.227817	−	0.184563i
$307$	−1.35880e6	+	494562.i	−0.822828	+	0.299485i	−0.718912	−	0.695101i	$-0.755360\pi$
$307$	−1.35880e6	+	494562.i	−0.822828	+	0.299485i	−0.103916	+	0.994586i	$0.533137\pi$
$308$	146604.	+	691163.i	0.0880583	+	0.415149i
$309$	478063.	−	2.71123e6i	0.284832	−	1.61536i
$310$	−385210.	−	132730.i	−0.227664	−	0.0784449i
$311$	−433593.	+	250335.i	−0.254203	+	0.146764i	−0.621687	−	0.783265i	$-0.713553\pi$
$311$	−433593.	+	250335.i	−0.254203	+	0.146764i	0.367484	+	0.930030i	$0.380219\pi$
$312$	−2.95165e6	−	1.50631e6i	−1.71664	−	0.876050i
$313$	730007.	−	612549.i	0.421179	−	0.353411i	−0.407433	−	0.913235i	$-0.633576\pi$
$313$	730007.	−	612549.i	0.421179	−	0.353411i	0.828611	+	0.559824i	$0.189131\pi$
$314$	−979770.	+	851336.i	−0.560790	+	0.487278i
$315$	870045.	+	502321.i	0.494044	+	0.285236i
$316$	649381.	+	1.04021e6i	0.365832	+	0.586008i
$317$	225998.	−	620925.i	0.126316	−	0.347049i	−0.860374	−	0.509663i	$-0.829770\pi$
$317$	225998.	−	620925.i	0.126316	−	0.347049i	0.986690	+	0.162614i	$0.0519924\pi$
$318$	−2.73455e6	−	433706.i	−1.51642	−	0.240507i
$319$	32377.0	+	183619.i	0.0178139	+	0.101028i
$320$	−2.72385e6	+	1.32421e6i	−1.48699	+	0.722909i
$321$	1.27929e6	+	1.07345e6i	0.692958	+	0.581461i
$322$	−1.87437e6	+	32319.0i	−1.00743	+	0.0173707i
$323$	−547511.	−	1.67289e6i	−0.292002	−	0.892198i
$324$	−2.29404e6	+	79134.0i	−1.21405	+	0.0418794i
$325$	−3.57007e6	+	4.25464e6i	−1.87486	+	2.23437i
$326$	950106.	+	2.47668e6i	0.495140	+	1.29070i
$327$	−239329.	+	42200.1i	−0.123773	+	0.0218245i
$328$	−1.73268e6	−	213868.i	−0.889272	−	0.109764i
$329$	−1.06743e6	−	388512.i	−0.543687	−	0.197886i
$330$	1.23398e6	−	741094.i	0.623768	−	0.374618i
$331$	−482919.	+	836440.i	−0.242273	+	0.419628i	−0.961361	−	0.275290i	$-0.911226\pi$
$331$	−482919.	+	836440.i	−0.242273	+	0.419628i	0.719089	+	0.694918i	$0.244559\pi$
$332$	−442024.	−	491337.i	−0.220090	−	0.244644i
$333$	−540484.	−	644124.i	−0.267099	−	0.318316i
$334$	1.61765e6	−	2.91685e6i	0.793446	−	1.43070i
$335$	−2.82006e6	−	4.88449e6i	−1.37293	−	2.37798i
$336$	724013.	−	2.51686e6i	0.349863	−	1.21622i
$337$	−1.32288e6	−	233260.i	−0.634521	−	0.111883i	−0.152870	−	0.988246i	$-0.548852\pi$
$337$	−1.32288e6	−	233260.i	−0.634521	−	0.111883i	−0.481651	+	0.876363i	$0.659963\pi$
$338$	732736.	+	3.77388e6i	0.348864	+	1.79678i
$339$	267860.	+	735938.i	0.126593	+	0.347810i
$340$	2.60628e6	+	2.03803e6i	1.22271	+	0.956122i
$341$		−	120134.i		−	0.0559476i
$342$	579740.	+	346826.i	0.268021	+	0.160342i
$343$		−	1.87650e6i		−	0.861218i
$344$	−219639.	+	291084.i	−0.100072	+	0.132624i
$345$	1.30623e6	+	3.58885e6i	0.590845	+	1.62333i
$346$	1.43755e6	−	279114.i	0.645553	−	0.125341i
$347$	1.85117e6	+	326410.i	0.825318	+	0.145526i	0.570327	−	0.821417i	$-0.306816\pi$
$347$	1.85117e6	+	326410.i	0.825318	+	0.145526i	0.254991	+	0.966943i	$0.417927\pi$
$348$	213847.	−	657203.i	0.0946575	−	0.290905i
$349$	−530922.	−	919583.i	−0.233328	−	0.404136i	0.725457	−	0.688267i	$-0.241628\pi$
$349$	−530922.	−	919583.i	−0.233328	−	0.404136i	−0.958785	+	0.284131i	$0.908295\pi$
$350$	−3.83862e6	−	2.12885e6i	−1.67496	−	0.928913i
$351$	1.96635e6	+	2.34340e6i	0.851908	+	1.01526i
$352$	−630790.	−	632131.i	−0.271349	−	0.271926i
$353$	−15935.4	+	27600.9i	−0.00680653	+	0.0117893i	−0.869409	−	0.494094i	$-0.835500\pi$
$353$	−15935.4	+	27600.9i	−0.00680653	+	0.0117893i	0.862602	+	0.505883i	$0.168833\pi$
$354$	−473865.	−	789023.i	−0.200977	−	0.334643i
$355$	−6.10437e6	−	2.22181e6i	−2.57081	−	0.935698i
$356$	3.31085e6	+	466744.i	1.38457	+	0.195188i
$357$	−2.81744e6	+	496791.i	−1.17000	+	0.206302i
$358$	260352.	−	99876.4i	0.107363	−	0.0411866i
$359$	446497.	−	532114.i	0.182845	−	0.217906i	−0.666834	−	0.745206i	$-0.732351\pi$
$359$	446497.	−	532114.i	0.182845	−	0.217906i	0.849679	+	0.527300i	$0.176796\pi$
$360$	−1.26810e6	+	65648.3i	−0.515701	+	0.0266973i
$361$	1.09495e6	+	2.22084e6i	0.442209	+	0.896912i
$362$	−492.331	−	28553.1i	−0.000197463	−	0.0114520i
$363$	−1.87801e6	−	1.57584e6i	−0.748050	−	0.627689i
$364$	−4.35681e6	+	1.75811e6i	−1.72352	+	0.695494i
$365$	−649300.	−	3.68236e6i	−0.255101	−	1.44675i
$366$	616994.	−	3.89020e6i	0.240757	−	1.51799i
$367$	502805.	−	1.38145e6i	0.194865	−	0.535388i	−0.803324	−	0.595542i	$-0.796937\pi$
$367$	502805.	−	1.38145e6i	0.194865	−	0.535388i	0.998189	+	0.0601546i	$0.0191594\pi$
$368$	1.96547e6	−	1.32330e6i	0.756566	−	0.509376i
$369$	−633893.	−	365978.i	−0.242354	−	0.139923i
$370$	3.79947e6	+	4.37266e6i	1.44284	+	1.66051i
$371$	−3.00703e6	+	2.52320e6i	−1.13423	+	0.951735i
$372$	−209224.	+	393090.i	−0.0783887	+	0.147277i
$373$	33405.8	−	19286.9i	0.0124323	−	0.00717777i	−0.493771	−	0.869592i	$-0.664382\pi$
$373$	33405.8	−	19286.9i	0.0124323	−	0.00717777i	0.506203	+	0.862414i	$0.331049\pi$
$374$	−317798.	+	922315.i	−0.117482	+	0.340958i
$375$	−657178.	+	3.72704e6i	−0.241326	+	1.36863i
$376$	1.39915e6	−	322081.i	0.510382	−	0.117489i
$377$	−1.16505e6	+	424042.i	−0.422173	+	0.153658i
$378$	−1.52187e6	+	1.87853e6i	−0.547832	+	0.676222i
$379$	594707.			0.212669			0.106335	−	0.994330i	$-0.466089\pi$
$379$	594707.			0.212669			0.106335	+	0.994330i	$0.466089\pi$
$380$	−4.03456e6	−	2.32015e6i	−1.43330	−	0.824247i
$381$	1.33429e6			0.470909
$382$	1.53206e6	−	1.89111e6i	0.537176	−	0.663069i
$383$	2.75138e6	−	1.00142e6i	0.958416	−	0.348835i	0.185004	−	0.982738i	$-0.440770\pi$
$383$	2.75138e6	−	1.00142e6i	0.958416	−	0.348835i	0.773413	+	0.633903i	$0.218548\pi$
$384$	963088.	+	3.16695e6i	0.333302	+	1.09601i
$385$	354373.	−	2.00975e6i	0.121845	−	0.691018i
$386$	371108.	−	1.07703e6i	0.126775	−	0.367927i
$387$	−132401.	+	76441.9i	−0.0449381	+	0.0259450i
$388$	−4.27001e6	−	2.27273e6i	−1.43996	−	0.766423i
$389$	3.14007e6	−	2.63483e6i	1.05212	−	0.882835i	0.0588062	−	0.998269i	$-0.481271\pi$
$389$	3.14007e6	−	2.63483e6i	1.05212	−	0.882835i	0.993315	+	0.115435i	$0.0368261\pi$
$390$	6.27792e6	+	7.22501e6i	2.09004	+	2.40534i
$391$	−2.24158e6	−	1.29418e6i	−0.741502	−	0.428106i
$392$	−364888.	−	562663.i	−0.119935	−	0.184941i
$393$	1.68827e6	−	4.63849e6i	0.551393	−	1.51494i
$394$	495629.	−	3.12498e6i	0.160848	−	1.01416i
$395$	−615047.	−	3.48811e6i	−0.198342	−	1.12486i
$396$	−140108.	−	347204.i	−0.0448977	−	0.111262i
$397$	−1.89007e6	−	1.58596e6i	−0.601870	−	0.505029i	0.290176	−	0.956973i	$-0.406286\pi$
$397$	−1.89007e6	−	1.58596e6i	−0.601870	−	0.505029i	−0.892046	+	0.451945i	$0.850730\pi$
$398$	33281.4	+	1.93018e6i	0.0105316	+	0.610788i
$399$	3.82483e6	−	1.25181e6i	1.20276	−	0.393645i
$400$	5.53475e6	−	382303.i	1.72961	−	0.119470i
$401$	−3.52210e6	+	4.19747e6i	−1.09381	+	1.30355i	−0.144392	+	0.989521i	$0.546123\pi$
$401$	−3.52210e6	+	4.19747e6i	−1.09381	+	1.30355i	−0.949414	+	0.314027i	$0.898322\pi$
$402$	−5.75534e6	+	2.20787e6i	−1.77626	+	0.681409i
$403$	786703.	−	138717.i	0.241295	−	0.0425468i
$404$	−636926.	+	4.51804e6i	−0.194149	+	1.37720i
$405$	6.23014e6	+	2.26758e6i	1.88738	+	0.686951i
$406$	−504477.	−	839995.i	−0.151889	−	0.252908i
$407$	−854012.	+	1.47919e6i	−0.255551	+	0.442628i
$408$	2.64614e6	−	2.46442e6i	0.786979	−	0.732933i
$409$	909717.	+	1.08416e6i	0.268904	+	0.320468i	0.883551	−	0.468335i	$-0.155146\pi$
$409$	909717.	+	1.08416e6i	0.268904	+	0.320468i	−0.614647	+	0.788803i	$0.710701\pi$
$410$	4.40985e6	+	2.44564e6i	1.29558	+	0.718511i
$411$	790238.	+	1.36873e6i	0.230756	+	0.399681i
$412$	4.69124e6	+	1.52648e6i	1.36159	+	0.443045i
$413$	−1.28506e6	−	226590.i	−0.370721	−	0.0653682i
$414$	975193.	−	189343.i	0.279634	−	0.0542937i
$415$	652897.	+	1.79382e6i	0.186091	+	0.511280i
$416$	3.41116e6	−	4.86064e6i	0.966426	−	1.37708i
$417$		−	1.77376e6i		−	0.499523i
$418$	259251.	−	1.34758e6i	0.0725739	−	0.377236i
$419$			3.54764e6i			0.987199i	0.869689	+	0.493600i	$0.164319\pi$
$419$			3.54764e6i			0.987199i	−0.869689	+	0.493600i	$0.835681\pi$
$420$	−4.65967e6	+	5.95888e6i	−1.28894	+	1.64832i
$421$	−2.09018e6	−	5.74273e6i	−0.574750	−	1.57911i	−0.796907	−	0.604101i	$-0.793532\pi$
$421$	−2.09018e6	−	5.74273e6i	−0.574750	−	1.57911i	0.222158	−	0.975011i	$-0.428690\pi$
$422$	−425432.	−	2.19114e6i	−0.116292	−	0.598948i
$423$	592805.	+	104527.i	0.161087	+	0.0284040i
$424$	1.45361e6	−	4.74372e6i	0.392674	−	1.28146i
$425$	−3.03027e6	−	5.24859e6i	−0.813784	−	1.40952i
$426$	−3.44340e6	+	6.20895e6i	−0.919314	+	1.65766i
$427$	−3.58952e6	−	4.27783e6i	−0.952724	−	1.13541i
$428$	−2.22475e6	+	2.00147e6i	−0.587046	+	0.528128i
$429$	−1.41110e6	+	2.44409e6i	−0.370181	+	0.641172i
$430$	902927.	−	542272.i	0.235495	−	0.141432i
$431$	4.76447e6	+	1.73412e6i	1.23544	+	0.449663i	0.875457	−	0.483297i	$-0.160561\pi$
$431$	4.76447e6	+	1.73412e6i	1.23544	+	0.449663i	0.359982	+	0.932959i	$0.382783\pi$
$432$	321992.	−	3.03872e6i	0.0830111	−	0.783396i
$433$	−2.36485e6	+	416987.i	−0.606156	+	0.106882i	−0.468298	−	0.883570i	$-0.655133\pi$
$433$	−2.36485e6	+	416987.i	−0.606156	+	0.106882i	−0.137858	+	0.990452i	$0.544022\pi$
$434$	226124.	+	589447.i	0.0576264	+	0.150217i
$435$	−1.28314e6	+	1.52919e6i	−0.325125	+	0.387469i
$436$	−15013.2	−	435223.i	−0.00378232	−	0.109647i
$437$	3.37884e6	+	1.35675e6i	0.846377	+	0.339856i
$438$	−4.08607e6	+	70454.6i	−1.01770	+	0.0175478i
$439$	1.76288e6	+	1.47923e6i	0.436578	+	0.366332i	0.834427	−	0.551119i	$-0.185799\pi$
$439$	1.76288e6	+	1.47923e6i	0.436578	+	0.366332i	−0.397849	+	0.917451i	$0.630243\pi$
$440$	1.00633e6	+	2.37497e6i	0.247804	+	0.584825i
$441$	−48823.6	−	276893.i	−0.0119546	−	0.0677977i
$442$	−6.40675e6	−	1.01612e6i	−1.55985	−	0.247395i
$443$	−157228.	+	431980.i	−0.0380645	+	0.104581i	−0.957269	−	0.289199i	$-0.906611\pi$
$443$	−157228.	+	431980.i	−0.0380645	+	0.104581i	0.919204	+	0.393781i	$0.128833\pi$
$444$	5.37053e6	−	3.35271e6i	1.29288	−	0.807120i
$445$	−8.36365e6	−	4.82876e6i	−2.00215	−	1.15594i
$446$	−3.62055e6	+	3.14595e6i	−0.861861	+	0.748883i
$447$	790833.	−	663588.i	0.187204	−	0.157083i
$448$	4.28483e6	+	1.91428e6i	1.00865	+	0.450619i
$449$	−1.38037e6	+	796954.i	−0.323131	+	0.186560i	−0.652787	−	0.757541i	$-0.726400\pi$
$449$	−1.38037e6	+	796954.i	−0.323131	+	0.186560i	0.329657	+	0.944101i	$0.393067\pi$
$450$	2.19914e6	+	757747.i	0.511943	+	0.176398i
$451$	−258187.	+	1.46425e6i	−0.0597713	+	0.338980i
$452$	−1.37286e6	+	291201.i	−0.316068	+	0.0670419i
$453$	−1.81835e6	+	661826.i	−0.416325	+	0.151530i
$454$	6.08265e6	+	4.92777e6i	1.38501	+	1.12205i
$455$	1.35700e7			3.07293
$456$	−3.19520e6	+	3.95787e6i	−0.719592	+	0.891352i
$457$	45794.3			0.0102570			0.00512850	−	0.999987i	$-0.498368\pi$
$457$	45794.3			0.0102570			0.00512850	+	0.999987i	$0.498368\pi$
$458$	1.43410e6	+	1.16181e6i	0.319459	+	0.258805i
$459$	−3.13676e6	+	1.14169e6i	−0.694943	+	0.252939i
$460$	−6.69484e6	+	1.42006e6i	−1.47518	+	0.312905i
$461$	301666.	−	1.71083e6i	0.0661111	−	0.374934i	−0.933745	−	0.357940i	$-0.883479\pi$
$461$	301666.	−	1.71083e6i	0.0661111	−	0.374934i	0.999856	−	0.0169943i	$-0.00540971\pi$
$462$	−2.10874e6	−	726599.i	−0.459641	−	0.158376i
$463$	−4.34124e6	+	2.50641e6i	−0.941155	+	0.543376i	−0.890322	−	0.455331i	$-0.849521\pi$
$463$	−4.34124e6	+	2.50641e6i	−0.941155	+	0.543376i	−0.0508327	+	0.998707i	$0.516188\pi$
$464$	1.11265e6	+	543848.i	0.239919	+	0.117269i
$465$	985284.	−	826752.i	0.211314	−	0.177314i
$466$	4.95516e6	−	4.30561e6i	1.05704	−	0.918480i
$467$	1.75674e6	+	1.01425e6i	0.372748	+	0.215206i	0.674658	−	0.738130i	$-0.264291\pi$
$467$	1.75674e6	+	1.01425e6i	0.372748	+	0.215206i	−0.301910	+	0.953336i	$0.597624\pi$
$468$	2.11189e6	−	1.31841e6i	0.445714	−	0.278250i
$469$	−2.98909e6	+	8.21245e6i	−0.627489	+	1.72401i
$470$	−4.09577e6	−	649598.i	−0.855246	−	0.135644i
$471$	−711513.	−	4.03519e6i	−0.147785	−	0.838131i
$472$	1.51858e6	−	643459.i	0.313750	−	0.132943i
$473$	237900.	+	199622.i	0.0488924	+	0.0410256i
$474$	−3.87052e6	+	66737.9i	−0.791267	+	0.0136435i
$475$	5.26312e6	+	6.70689e6i	1.07031	+	1.36391i
$476$	−176740.	−	5.12357e6i	−0.0357534	−	1.03647i
$477$	1.33708e6	−	1.59347e6i	0.269068	−	0.320663i
$478$	779678.	+	2.03242e6i	0.156079	+	0.406859i
$479$	−3.59992e6	+	634763.i	−0.716893	+	0.126408i	−0.520184	−	0.854054i	$-0.674137\pi$
$479$	−3.59992e6	+	634763.i	−0.716893	+	0.126408i	−0.196709	+	0.980462i	$0.563025\pi$
$480$	843405.	−	9.52368e6i	0.167083	−	1.88669i
$481$	−1.06726e7	−	3.88452e6i	−2.10334	−	0.765552i
$482$	6.43978e6	−	3.86755e6i	1.26256	−	0.758260i
$483$	2.95895e6	−	5.12505e6i	0.577125	−	0.999609i
$484$	3.26595e6	−	2.93817e6i	0.633718	−	0.570115i
$485$	8.98074e6	+	1.07028e7i	1.73364	+	2.06607i
$486$	1.52489e6	−	2.74960e6i	0.292852	−	0.528055i
$487$	−1.76108e6	−	3.05028e6i	−0.336478	−	0.582797i	0.647290	−	0.762244i	$-0.275902\pi$
$487$	−1.76108e6	−	3.05028e6i	−0.336478	−	0.582797i	−0.983768	+	0.179447i	$0.942569\pi$
$488$	6.74847e6	+	2.06792e6i	1.28279	+	0.393082i
$489$	−8.24675e6	−	1.45413e6i	−1.55959	−	0.274998i
$490$	369194.	+	1.90149e6i	0.0694647	+	0.357770i
$491$	−1.81146e6	−	4.97695e6i	−0.339098	−	0.931665i	−0.985651	−	0.168796i	$-0.946012\pi$
$491$	−1.81146e6	−	4.97695e6i	−0.339098	−	0.931665i	0.646553	−	0.762869i	$-0.276210\pi$
$492$	3.39492e6	−	4.34149e6i	0.632290	−	0.808586i
$493$		−	1.35288e6i		−	0.250693i
$494$	9.12398e6	+	141692.i	1.68216	+	0.0261233i
$495$			1.08143e6i			0.198374i
$496$	−645165.	−	469578.i	−0.117752	−	0.0857044i
$497$	3.44274e6	+	9.45886e6i	0.625192	+	1.71770i
$498$	2.04811e6	−	397660.i	0.370066	−	0.0718520i
$499$	7.06243e6	+	1.24530e6i	1.26971	+	0.223883i	0.767603	−	0.640925i	$-0.221449\pi$
$499$	7.06243e6	+	1.24530e6i	1.26971	+	0.223883i	0.502102	+	0.864808i	$0.332560\pi$
$500$	−6.44891e6	−	2.09841e6i	−1.15362	−	0.375374i
$501$	5.26458e6	+	9.11853e6i	0.937065	+	1.62304i
$502$	5.12968e6	+	2.84485e6i	0.908513	+	0.503849i
$503$	538865.	+	642195.i	0.0949643	+	0.113174i	0.811434	−	0.584444i	$-0.198688\pi$
$503$	538865.	+	642195.i	0.0949643	+	0.113174i	−0.716469	+	0.697618i	$0.754243\pi$
$504$	1.34097e6	+	1.43985e6i	0.235149	+	0.252489i
$505$	6.58940e6	−	1.14132e7i	1.14979	−	1.99149i
$506$	−1.03894e6	−	1.72992e6i	−0.180391	−	0.300365i
$507$	−1.14040e7	−	4.15072e6i	−1.97032	−	0.717139i
$508$	−333766.	+	2.36757e6i	−0.0573829	+	0.407046i
$509$	8.77916e6	−	1.54800e6i	1.50196	−	0.264836i	0.638645	−	0.769501i	$-0.279495\pi$
$509$	8.77916e6	−	1.54800e6i	1.50196	−	0.264836i	0.863315	+	0.504665i	$0.168384\pi$
$510$	−9.75143e6	+	3.74085e6i	−1.66013	+	0.636861i
$511$	−3.72426e6	+	4.43840e6i	−0.630940	+	0.751925i
$512$	−5.86038e6	+	916714.i	−0.987986	+	0.154546i
$513$	4.14132e6	−	2.21335e6i	0.694778	−	0.371327i
$514$	117155.	+	6.79449e6i	0.0195593	+	1.13436i
$515$	−1.09156e7	−	9.15929e6i	−1.81355	−	1.52175i
$516$	−430770.	−	1.06750e6i	−0.0712231	−	0.176499i
$517$	−212329.	−	1.20418e6i	−0.0349368	−	0.198136i
$518$	1.40604e6	−	8.86521e6i	0.230236	−	1.45166i
$519$	−1.58109e6	+	4.34402e6i	−0.257655	+	0.707902i
$520$	−1.43905e7	+	9.33228e6i	−2.33382	+	1.51349i
$521$	−721654.	−	416647.i	−0.116476	−	0.0672472i	0.440630	−	0.897689i	$-0.354755\pi$
$521$	−721654.	−	416647.i	−0.116476	−	0.0672472i	−0.557106	+	0.830441i	$0.688088\pi$
$522$	340565.	+	391943.i	0.0547045	+	0.0629574i
$523$	3.52974e6	−	2.96180e6i	0.564271	−	0.473480i	−0.315468	−	0.948936i	$-0.602161\pi$
$523$	3.52974e6	−	2.96180e6i	0.564271	−	0.473480i	0.879739	+	0.475456i	$0.157717\pi$
$524$	7.80827e6	+	4.15598e6i	1.24230	+	0.661219i
$525$	1.20001e7	−	6.92828e6i	1.90015	−	1.09705i
$526$	−2.62807e6	+	7.62721e6i	−0.414164	+	1.20199i
$527$	−151367.	+	858446.i	−0.0237413	+	0.134644i
$528$	2.73593e6	−	679676.i	0.427091	−	0.106100i
$529$	−1.01697e6	+	370147.i	−0.158004	+	0.0575089i
$530$	−9.02082e6	+	1.11350e7i	−1.39494	+	1.72186i
$531$	691478.			0.106425
$532$	1.26445e6	+	7.09994e6i	0.193697	+	1.08762i
$533$	−9.88679e6			−1.50743
$534$	−6.64426e6	+	8.20141e6i	−1.00831	+	1.24462i
$535$	8.12234e6	−	2.95629e6i	1.22686	−	0.446542i
$536$	−2.47799e6	−	1.07646e7i	−0.372552	−	1.61840i
$537$	−152860.	+	866910.i	−0.0228748	+	0.129729i
$538$	1.61186e6	−	4.67797e6i	0.240089	−	0.696789i
$539$	−494617.	+	285567.i	−0.0733326	+	0.0423386i
$540$	−4.14690e6	+	7.79121e6i	−0.611983	+	1.14980i
$541$	6.09582e6	−	5.11500e6i	0.895444	−	0.751367i	−0.0738502	−	0.997269i	$-0.523529\pi$
$541$	6.09582e6	−	5.11500e6i	0.895444	−	0.751367i	0.969295	+	0.245902i	$0.0790842\pi$
$542$	−7.67588e6	−	8.83388e6i	−1.12235	−	1.29168i
$543$	78072.3	+	45075.1i	0.0113631	+	0.00656050i
$544$	3.71096e6	+	5.31180e6i	0.537638	+	0.769564i
$545$	−430204.	+	1.18198e6i	−0.0620416	+	0.170458i
$546$	2.32322e6	−	1.46481e7i	0.333510	−	2.10281i
$547$	−224660.	−	1.27411e6i	−0.0321039	−	0.182070i	0.964539	−	0.263940i	$-0.0850221\pi$
$547$	−224660.	−	1.27411e6i	−0.0321039	−	0.182070i	−0.996643	+	0.0818694i	$0.973911\pi$
$548$	−2.62636e6	+	1.05982e6i	−0.373597	+	0.150758i
$549$	2.26689e6	+	1.90215e6i	0.320996	+	0.269347i
$550$	−81457.6	−	4.72420e6i	−0.0114822	−	0.665919i
$551$	268889.	+	1.88402e6i	0.0377306	+	0.264366i
$552$	386705.	+	7.46983e6i	0.0540172	+	1.04343i
$553$	−3.52780e6	+	4.20427e6i	−0.490558	+	0.584625i
$554$	8.80087e6	−	3.37619e6i	1.21829	−	0.467361i
$555$	−1.80088e7	+	3.17544e6i	−2.48172	+	0.437594i
$556$	3.14738e6	+	443699.i	0.431780	+	0.0608697i
$557$	−182006.	−	66244.8i	−0.0248570	−	0.00904720i	0.329562	−	0.944134i	$-0.393099\pi$
$557$	−182006.	−	66244.8i	−0.0248570	−	0.00904720i	−0.354419	+	0.935087i	$0.615321\pi$
$558$	−172246.	−	286804.i	−0.0234188	−	0.0389942i
$559$	−1.03253e6	+	1.78839e6i	−0.139756	+	0.242065i
$560$	−9.40790e6	−	9.75874e6i	−1.26772	−	1.31499i
$561$	−1.97951e6	−	2.35908e6i	−0.265552	−	0.316473i
$562$	−1.26465e7	−	7.01361e6i	−1.68901	−	0.936700i
$563$	−2.92222e6	−	5.06143e6i	−0.388545	−	0.672980i	0.603709	−	0.797205i	$-0.293689\pi$
$563$	−2.92222e6	−	5.06143e6i	−0.388545	−	0.672980i	−0.992254	+	0.124225i	$0.960356\pi$
$564$	−1.40241e6	+	4.30995e6i	−0.185643	+	0.570524i
$565$	3.99197e6	+	703891.i	0.526097	+	0.0927651i
$566$	−2.40051e6	+	466082.i	−0.314965	+	0.0611535i
$567$	−3.51367e6	−	9.65374e6i	−0.458991	−	1.26107i
$568$	−1.01559e7	−	7.66315e6i	−1.32083	−	0.996635i
$569$			8.39424e6i			1.08693i	0.839432	+	0.543464i	$0.182888\pi$
$569$			8.39424e6i			1.08693i	−0.839432	+	0.543464i	$0.817112\pi$
$570$	1.28363e7	−	7.14761e6i	1.65483	−	0.921455i
$571$			4.92465e6i			0.632099i	0.948743	+	0.316050i	$0.102357\pi$
$571$			4.92465e6i			0.632099i	−0.948743	+	0.316050i	$0.897643\pi$
$572$	−3.98384e6	−	3.11524e6i	−0.509110	−	0.398109i
$573$	2.62778e6	+	7.21977e6i	0.334351	+	0.918622i
$574$	−1.48928e6	−	7.67040e6i	−0.188668	−	0.971714i
$575$	1.23460e7	+	2.17693e6i	1.55725	+	0.274584i
$576$	−2.41226e6	−	604709.i	−0.302947	−	0.0759434i
$577$	3.81666e6	+	6.61065e6i	0.477248	+	0.826617i	0.999660	−	0.0260758i	$-0.00830113\pi$
$577$	3.81666e6	+	6.61065e6i	0.477248	+	0.826617i	−0.522412	+	0.852693i	$0.674968\pi$
$578$	−462456.	+	833876.i	−0.0575773	+	0.103820i
$579$	2.31157e6	+	2.75482e6i	0.286557	+	0.341505i
$580$	−2.39243e6	−	2.65933e6i	−0.295304	−	0.328248i
$581$	1.47898e6	−	2.56166e6i	0.181769	−	0.314834i
$582$	1.30906e7	−	7.86187e6i	1.60197	−	0.962096i
$583$	−3.97059e6	−	1.44517e6i	−0.483819	−	0.176096i
$584$	897096.	−	7.26798e6i	0.108845	−	0.881823i
$585$	−7.08173e6	+	1.24870e6i	−0.855559	+	0.150858i
$586$	−717761.	−	1.87102e6i	−0.0863448	−	0.225079i
$587$	34254.9	−	40823.4i	0.00410324	−	0.00489005i	−0.763989	−	0.645229i	$-0.776762\pi$
$587$	34254.9	−	40823.4i	0.00410324	−	0.00489005i	0.768092	+	0.640339i	$0.221206\pi$
$588$	2.11576e6	−	72984.3i	0.252362	−	0.00870535i
$589$	40174.9	−	1.22555e6i	0.00477163	−	0.145561i
$590$	−4.76303e6	+	82127.2i	−0.563318	+	0.00971308i
$591$	7.65146e6	+	6.42033e6i	0.901105	+	0.756117i
$592$	4.60566e6	+	1.03682e7i	0.540116	+	1.21590i
$593$	1.56377e6	+	8.86856e6i	0.182615	+	1.03566i	0.928982	+	0.370125i	$0.120685\pi$
$593$	1.56377e6	+	8.86856e6i	0.182615	+	1.03566i	−0.746368	+	0.665534i	$0.768204\pi$
$594$	−2.57029e6	−	407653.i	−0.298893	−	0.0474050i
$595$	−5.06449e6	+	1.39146e7i	−0.586466	+	1.61130i
$596$	979653.	+	1.56925e6i	0.112968	+	0.180958i
$597$	−5.27766e6	−	3.04706e6i	−0.606046	−	0.349901i
$598$	1.01288e7	−	8.80102e6i	1.15825	−	1.00642i
$599$	1.08959e7	−	9.14278e6i	1.24079	−	1.04114i	0.243326	−	0.969944i	$-0.421761\pi$
$599$	1.08959e7	−	9.14278e6i	1.24079	−	1.04114i	0.997462	−	0.0712005i	$-0.0226830\pi$
$600$	−7.96103e6	+	1.55998e7i	−0.902799	+	1.76906i
$601$	−4.03311e6	+	2.32852e6i	−0.455464	+	0.262962i	−0.710135	−	0.704066i	$-0.751366\pi$
$601$	−4.03311e6	+	2.32852e6i	−0.455464	+	0.262962i	0.254671	+	0.967028i	$0.418033\pi$
$602$	−1.54301e6	−	531666.i	−0.173531	−	0.0597927i
$603$	804200.	−	4.56084e6i	0.0900680	−	0.510801i
$604$	−719498.	−	3.39205e6i	−0.0802485	−	0.378330i
$605$	−1.19236e7	+	4.33985e6i	−1.32440	+	0.482044i
$606$	−1.11918e7	−	9.06686e6i	−1.23799	−	1.00294i
$607$	−8.89638e6			−0.980035			−0.490017	−	0.871713i	$-0.663010\pi$
$607$	−8.89638e6			−0.980035			−0.490017	+	0.871713i	$0.663010\pi$
$608$	−6.22361e6	−	6.65963e6i	−0.682784	−	0.730620i
$609$	3.09317e6			0.337956
$610$	−1.58407e7	−	1.28331e7i	−1.72365	−	1.39639i
$611$	7.64040e6	−	2.78088e6i	0.827967	−	0.301355i
$612$	563700.	+	2.65755e6i	0.0608372	+	0.286815i
$613$	−2.56093e6	+	1.45237e7i	−0.275262	+	1.56109i	0.462867	+	0.886428i	$0.346821\pi$
$613$	−2.56093e6	+	1.45237e7i	−0.275262	+	1.56109i	−0.738129	+	0.674660i	$0.764290\pi$
$614$	7.73361e6	+	2.66473e6i	0.827869	+	0.285255i
$615$	−1.37859e7	+	7.95928e6i	−1.46976	+	0.848567i
$616$	1.81678e6	−	3.56001e6i	0.192908	−	0.378007i
$617$	−666101.	+	558925.i	−0.0704413	+	0.0591073i	−0.677328	−	0.735681i	$-0.736862\pi$
$617$	−666101.	+	558925.i	−0.0704413	+	0.0591073i	0.606887	+	0.794788i	$0.292418\pi$
$618$	−1.17557e7	+	1.02147e7i	−1.23817	+	1.07586i
$619$	1.17165e7	+	6.76451e6i	1.22905	+	0.709594i	0.966832	−	0.255414i	$-0.0822118\pi$
$619$	1.17165e7	+	6.76451e6i	1.22905	+	0.709594i	0.262221	+	0.965008i	$0.415545\pi$
$620$	1.22053e6	+	1.95511e6i	0.127517	+	0.204264i
$621$	2.36162e6	−	6.48850e6i	0.245743	−	0.675174i
$622$	2.79725e6	+	443651.i	0.289905	+	0.0459796i
$623$	2.59856e6	+	1.47372e7i	0.268234	+	1.52123i
$624$	7.61000e6	+	1.71315e7i	0.782389	+	1.76130i
$625$	2.03549e6	+	1.70798e6i	0.208435	+	0.174897i
$626$	−5.38994e6	+	92936.6i	−0.549728	+	0.00947875i
$627$	3.22553e6	+	2.89182e6i	0.327666	+	0.293767i
$628$	7.33806e6	−	253130.i	0.742475	−	0.0256121i
$629$	7.96628e6	−	9.49384e6i	0.802840	−	0.956787i
$630$	−2.03552e6	−	5.30608e6i	−0.204326	−	0.532626i
$631$	−137093.	+	24173.1i	−0.0137070	+	0.00241691i	−0.180497	−	0.983575i	$-0.557771\pi$
$631$	−137093.	+	24173.1i	−0.0137070	+	0.00241691i	0.166790	+	0.985992i	$0.446660\pi$
$632$	849772.	−	6.88457e6i	0.0846272	−	0.685621i
$633$	6.62125e6	+	2.40994e6i	0.656796	+	0.239054i
$634$	−3.20442e6	+	1.92448e6i	−0.316611	+	0.190148i
$635$	3.45302e6	−	5.98080e6i	0.339832	−	0.588606i
$636$	1.04752e7	+	1.16438e7i	1.02688	+	1.14144i
$637$	−2.44117e6	−	2.90927e6i	−0.238368	−	0.284076i
$638$	511539.	−	922379.i	0.0497539	−	0.0897135i
$639$	−2.66704e6	−	4.61945e6i	−0.258391	−	0.447547i
$640$	1.66879e7	+	3.87885e6i	1.61047	+	0.374329i
$641$	1.81525e7	+	3.20078e6i	1.74499	+	0.307688i	0.953027	−	0.302887i	$-0.0979504\pi$
$641$	1.81525e7	+	3.20078e6i	1.74499	+	0.307688i	0.791959	+	0.610575i	$0.209062\pi$
$642$	−1.80059e6	−	9.27374e6i	−0.172416	−	0.888009i
$643$	1.76771e6	+	4.85674e6i	0.168610	+	0.463253i	0.995003	−	0.0998408i	$-0.0318334\pi$
$643$	1.76771e6	+	4.85674e6i	0.168610	+	0.463253i	−0.826393	+	0.563093i	$0.809611\pi$
$644$	8.35376e6	+	6.53239e6i	0.793720	+	0.620665i
$645$			3.32491e6i			0.314688i
$646$	−3.55045e6	+	9.30274e6i	−0.334736	+	0.877060i
$647$			1.41229e7i			1.32637i	0.748455	+	0.663185i	$0.230796\pi$
$647$			1.41229e7i			1.32637i	−0.748455	+	0.663185i	$0.769204\pi$
$648$	1.03651e7	+	7.82103e6i	0.969698	+	0.731689i
$649$	−480406.	−	1.31990e6i	−0.0447710	−	0.123007i
$650$	3.08424e7	−	5.98837e6i	2.86329	−	0.555936i
$651$	−1.96271e6	−	346079.i	−0.181512	−	0.0320054i
$652$	4.64310e6	−	1.42694e7i	0.427749	−	1.31458i
$653$	−484506.	−	839190.i	−0.0444648	−	0.0770153i	0.842936	−	0.538013i	$-0.180825\pi$
$653$	−484506.	−	839190.i	−0.0444648	−	0.0770153i	−0.887401	+	0.460998i	$0.847492\pi$
$654$	1.20223e6	+	666739.i	0.109911	+	0.0609553i
$655$	−1.64225e7	−	1.95715e7i	−1.49567	−	1.78247i
$656$	6.85436e6	+	7.10997e6i	0.621881	+	0.645072i
$657$	1.53515e6	−	2.65895e6i	0.138751	−	0.240324i
$658$	3.30837e6	+	5.50870e6i	0.297885	+	0.496003i
$659$	1.09878e7	+	3.99922e6i	0.985590	+	0.358725i	0.784011	−	0.620747i	$-0.213171\pi$
$659$	1.09878e7	+	3.99922e6i	0.985590	+	0.358725i	0.201579	+	0.979472i	$0.435393\pi$
$660$	−8.06286e6	−	1.13665e6i	−0.720492	−	0.101571i
$661$	−1.26855e7	+	2.23679e6i	−1.12928	+	0.199123i	−0.706913	−	0.707300i	$-0.749913\pi$
$661$	−1.26855e7	+	2.23679e6i	−1.12928	+	0.199123i	−0.422370	+	0.906423i	$0.638802\pi$
$662$	5.10113e6	−	1.95690e6i	0.452399	−	0.173549i
$663$	1.31628e7	−	1.56868e7i	1.16296	−	1.38596i
$664$	193287.	+	3.73365e6i	0.0170131	+	0.328635i
$665$	4.28723e6	−	2.03839e7i	0.375943	−	1.78745i
$666$	82002.9	+	4.75583e6i	0.00716381	+	0.415471i
$667$	2.14377e6	+	1.79883e6i	0.186579	+	0.156558i
$668$	−1.74969e7	+	7.06056e6i	−1.51712	+	0.612207i
$669$	−2.62926e6	−	1.49113e7i	−0.227126	−	1.28810i
$670$	−4.99779e6	+	3.15115e7i	−0.430122	+	2.71195i
$671$	2.05592e6	−	5.64860e6i	0.176279	−	0.484322i
$672$	−1.21447e7	+	8.48459e6i	−1.03744	+	0.724782i
$673$	−1.16690e6	−	673709.i	−0.0993106	−	0.0573370i	0.449522	−	0.893269i	$-0.351594\pi$
$673$	−1.16690e6	−	673709.i	−0.0993106	−	0.0573370i	−0.548833	+	0.835932i	$0.684928\pi$
$674$	4.98403e6	+	5.73593e6i	0.422602	+	0.486356i
$675$	1.23851e7	−	1.03924e7i	1.04626	−	0.877920i
$676$	1.02177e7	−	1.91971e7i	0.859978	−	1.61573i
$677$	389727.	−	225009.i	0.0326805	−	0.0188681i	−0.483571	−	0.875305i	$-0.660660\pi$
$677$	389727.	−	225009.i	0.0326805	−	0.0188681i	0.516251	+	0.856437i	$0.327327\pi$
$678$	1.44325e6	−	4.18860e6i	0.120577	−	0.349941i
$679$	3.75935e6	−	2.13203e7i	0.312924	−	1.77468i
$680$	−4.19851e6	−	1.82388e7i	−0.348196	−	1.51260i
$681$	−2.32220e7	+	8.45210e6i	−1.91881	+	0.698388i
$682$	−427788.	+	528045.i	−0.0352182	+	0.0434720i
$683$	−5.09898e6			−0.418246			−0.209123	−	0.977889i	$-0.567061\pi$
$683$	−5.09898e6			−0.418246			−0.209123	+	0.977889i	$0.567061\pi$
$684$	−1.31320e6	−	3.58886e6i	−0.107323	−	0.293302i
$685$	8.18027e6			0.666103
$686$	−6.68204e6	+	8.24805e6i	−0.542124	+	0.669177i
$687$	−5.47500e6	+	1.99274e6i	−0.442581	+	0.161086i
$688$	2.00193e6	−	497332.i	0.161242	−	0.0400567i
$689$	4.87900e6	−	2.76702e7i	0.391546	−	2.22057i
$690$	7.03808e6	−	2.04260e7i	0.562771	−	1.63328i
$691$	2.03858e7	−	1.17697e7i	1.62417	−	0.937718i	0.638388	−	0.769715i	$-0.279602\pi$
$691$	2.03858e7	−	1.17697e7i	1.62417	−	0.937718i	0.985787	−	0.168003i	$-0.0537317\pi$
$692$	−7.31256e6	−	3.89214e6i	−0.580503	−	0.308975i
$693$	1.28366e6	−	1.07711e6i	0.101535	−	0.0851979i
$694$	−6.97438e6	−	8.02655e6i	−0.549676	−	0.632601i
$695$	−7.95071e6	−	4.59034e6i	−0.624373	−	0.360482i
$696$	−3.28019e6	+	2.12721e6i	−0.256671	+	0.166451i
$697$	3.68986e6	−	1.01378e7i	0.287692	−	0.790427i
$698$	−940914.	+	5.93254e6i	−0.0730990	+	0.460895i
$699$	3.59846e6	+	2.04079e7i	0.278563	+	1.57981i
$700$	9.29183e6	+	2.30262e7i	0.716731	+	1.77614i
$701$	1.63282e6	+	1.37010e6i	0.125500	+	0.105307i	0.703377	−	0.710817i	$-0.251674\pi$
$701$	1.63282e6	+	1.37010e6i	0.125500	+	0.105307i	−0.577878	+	0.816123i	$0.696119\pi$
$702$	−298337.	−	1.73023e7i	−0.0228488	−	1.32514i
$703$	−9.20688e6	+	1.48044e7i	−0.702626	+	1.12980i
$704$	521642.	+	5.02468e6i	0.0396681	+	0.382100i
$705$	8.41484e6	−	1.00284e7i	0.637637	−	0.759906i
$706$	168327.	−	64573.8i	0.0127099	−	0.00487579i
$707$	−2.01106e7	+	3.54604e6i	−1.51313	+	0.266806i
$708$	−726791.	+	5.15550e6i	−0.0544912	+	0.386534i
$709$	−1.70833e7	−	6.21781e6i	−1.27631	−	0.464539i	−0.387100	−	0.922038i	$-0.626523\pi$
$709$	−1.70833e7	−	6.21781e6i	−1.27631	−	0.464539i	−0.889210	+	0.457499i	$0.848745\pi$
$710$	1.89198e7	+	3.15029e7i	1.40854	+	2.34534i
$711$	1.45416e6	−	2.51868e6i	0.107880	−	0.186853i
$712$	−1.28906e7	−	1.38412e7i	−0.952958	−	1.02323i
$713$	−1.15902e6	−	1.38127e6i	−0.0853825	−	0.101755i
$714$	1.41530e7	+	7.84904e6i	1.03897	+	0.576197i
$715$	7.30360e6	+	1.26502e7i	0.534283	+	0.925406i
$716$	−1.50002e6	−	488089.i	−0.109349	−	0.0355809i
$717$	−6.76747e6	−	1.19329e6i	−0.491618	−	0.0866856i
$718$	−3.85736e6	+	748945.i	−0.279241	+	0.0542174i
$719$	−7.48251e6	−	2.05580e7i	−0.539791	−	1.48306i	−0.847090	−	0.531450i	$-0.821648\pi$
$719$	−7.48251e6	−	2.05580e7i	−0.539791	−	1.48306i	0.307299	−	0.951613i	$-0.400575\pi$
$720$	5.80764e6	+	4.22704e6i	0.417512	+	0.303882i
$721$			2.20797e7i			1.58181i
$722$	3.09541e6	−	1.36606e7i	0.220991	−	0.975276i
$723$			2.37136e7i			1.68715i
$724$	−99511.0	+	127257.i	−0.00705545	+	0.00902266i
$725$	2.24111e6	+	6.15740e6i	0.158350	+	0.435063i
$726$	2.64328e6	+	1.36139e7i	0.186123	+	0.958609i
$727$	−2.17401e7	−	3.83337e6i	−1.52555	−	0.268995i	−0.652937	−	0.757412i	$-0.726464\pi$
$727$	−2.17401e7	−	3.83337e6i	−1.52555	−	0.268995i	−0.872611	+	0.488417i	$0.837575\pi$
$728$	2.54106e7	+	7.78651e6i	1.77700	+	0.544521i
$729$	−3.75263e6	−	6.49975e6i	−0.261528	−	0.452979i
$730$	−1.02586e7	+	1.84977e7i	−0.712493	+	1.28473i
$731$	−1.44844e6	−	1.72619e6i	−0.100255	−	0.119480i
$732$	−1.65646e7	+	1.49021e7i	−1.14262	+	1.02795i
$733$	−7.71835e6	+	1.33686e7i	−0.530597	+	0.919020i	0.468766	+	0.883322i	$0.344699\pi$
$733$	−7.71835e6	+	1.33686e7i	−0.530597	+	0.919020i	−0.999363	+	0.0356979i	$0.988635\pi$
$734$	−7.12925e6	+	4.28163e6i	−0.488432	+	0.293338i
$735$	−5.74598e6	−	2.09137e6i	−0.392325	−	0.142795i
$736$	−1.33513e7	−	1.18237e6i	−0.908505	−	0.0804561i
$737$	−9.26453e6	+	1.63359e6i	−0.628282	+	0.110783i
$738$	1.48303e6	+	3.86587e6i	0.100232	+	0.261280i
$739$	7.15970e6	−	8.53260e6i	0.482263	−	0.574739i	−0.468969	−	0.883214i	$-0.655374\pi$
$739$	7.15970e6	−	8.53260e6i	0.482263	−	0.574739i	0.951232	+	0.308476i	$0.0998189\pi$
$740$	−1.12971e6	−	3.27493e7i	−0.0758378	−	2.19848i
$741$	−1.52127e7	+	2.44615e7i	−1.01779	+	1.63658i
$742$	2.22021e7	−	382822.i	1.48042	−	0.0255263i
$743$	1.29164e7	+	1.08381e7i	0.858358	+	0.720248i	0.961614	−	0.274407i	$-0.0884816\pi$
$743$	1.29164e7	+	1.08381e7i	0.858358	+	0.720248i	−0.103256	+	0.994655i	$0.532926\pi$
$744$	2.31939e6	−	982778.i	0.153618	−	0.0650913i
$745$	−927857.	−	5.26214e6i	−0.0612478	−	0.347353i
$746$	−215512.	−	34180.7i	−0.0141783	−	0.00224871i
$747$	−536105.	+	1.47294e6i	−0.0351518	+	0.0965789i
$748$	4.68114e6	−	2.92234e6i	0.305913	−	0.190975i
$749$	−1.15991e7	−	6.69673e6i	−0.755473	−	0.436173i
$750$	1.61602e7	−	1.40419e7i	1.04905	−	0.911531i
$751$	−3.99051e6	+	3.34843e6i	−0.258183	+	0.216641i	−0.762687	−	0.646768i	$-0.776120\pi$
$751$	−3.99051e6	+	3.34843e6i	−0.258183	+	0.216641i	0.504503	+	0.863410i	$0.331676\pi$
$752$	−7.29680e6	−	3.56656e6i	−0.470531	−	0.229988i
$753$	−1.60362e7	+	9.25850e6i	−1.03066	+	0.595049i
$754$	6.63088e6	+	2.28477e6i	0.424759	+	0.146357i
$755$	−1.73917e6	+	9.86333e6i	−0.111039	+	0.629733i
$756$	1.33786e7	−	2.83776e6i	0.851344	−	0.180581i
$757$	2.10019e7	−	7.64406e6i	1.33204	−	0.484824i	0.424746	−	0.905312i	$-0.360363\pi$
$757$	2.10019e7	−	7.64406e6i	1.33204	−	0.484824i	0.907298	+	0.420488i	$0.138141\pi$
$758$	−2.61400e6	−	2.11770e6i	−0.165247	−	0.133872i
$759$	6.37020e6			0.401373
$760$	9.47184e6	+	2.45648e7i	0.594840	+	1.54269i
$761$	−7.53166e6			−0.471443			−0.235721	−	0.971821i	$-0.575745\pi$
$761$	−7.53166e6			−0.471443			−0.235721	+	0.971821i	$0.575745\pi$
$762$	−5.86478e6	−	4.75127e6i	−0.365902	−	0.296430i
$763$	1.83150e6	−	666611.i	0.113892	−	0.0414535i
$764$	−1.34682e7	+	2.85677e6i	−0.834785	+	0.177068i
$765$	1.36258e6	−	7.72755e6i	0.0841796	−	0.477407i
$766$	−1.56595e7	−	5.39573e6i	−0.964288	−	0.332260i
$767$	8.08870e6	−	4.67001e6i	0.496467	−	0.286635i
$768$	7.04402e6	−	1.73496e7i	0.430940	−	1.06142i
$769$	−6.97754e6	+	5.85485e6i	−0.425487	+	0.357026i	−0.830246	−	0.557397i	$-0.811800\pi$
$769$	−6.97754e6	+	5.85485e6i	−0.425487	+	0.357026i	0.404758	+	0.914424i	$0.367356\pi$
$770$	−8.71415e6	+	7.57184e6i	−0.529661	+	0.460230i
$771$	−1.85781e7	−	1.07260e7i	−1.12555	−	0.649836i
$772$	−5.46641e6	+	3.41256e6i	−0.330110	+	0.206081i
$773$	4.70711e6	−	1.29327e7i	0.283339	−	0.778467i	−0.713620	−	0.700533i	$-0.752946\pi$
$773$	4.70711e6	−	1.29327e7i	0.283339	−	0.778467i	0.996959	−	0.0779336i	$-0.0248322\pi$
$774$	854165.	+	135472.i	0.0512494	+	0.00812827i
$775$	−733134.	−	4.15781e6i	−0.0438459	−	0.248663i
$776$	1.06756e7	+	2.51948e7i	0.636411	+	1.50195i
$777$	2.17063e7	+	1.82137e7i	1.28983	+	1.08230i
$778$	−2.31844e7	+	399760.i	−1.37324	+	0.0236783i
$779$	−3.12357e6	+	1.48512e7i	−0.184420	+	0.876837i
$780$	−1.86663e6	−	5.41122e7i	−0.109855	−	3.18463i
$781$	−6.96475e6	+	8.30027e6i	−0.408581	+	0.486928i
$782$	5.24430e6	+	1.36705e7i	0.306669	+	0.799408i
$783$	3.55424e6	−	626708.i	0.207177	−	0.0365310i
$784$	−399745.	+	3.77249e6i	−0.0232270	+	0.219198i
$785$	−1.99287e7	−	7.25344e6i	−1.15426	−	0.420116i
$786$	−2.39380e7	+	1.43765e7i	−1.38207	+	0.830033i
$787$	1.01269e7	−	1.75403e7i	0.582828	−	1.00949i	−0.412314	−	0.911042i	$-0.635279\pi$
$787$	1.01269e7	−	1.75403e7i	0.582828	−	1.00949i	0.995142	−	0.0984461i	$-0.0313872\pi$
$788$	−1.33063e7	+	1.19708e7i	−0.763380	+	0.686764i
$789$	−1.63698e7	−	1.95087e7i	−0.936161	−	1.11567i
$790$	−9.71742e6	+	1.75219e7i	−0.553966	+	0.998881i
$791$	−3.14053e6	−	5.43956e6i	−0.178469	−	0.309117i
$792$	−620523.	+	2.02503e6i	−0.0351516	+	0.114714i
$793$	3.93639e7	+	6.94091e6i	2.22287	+	0.391953i
$794$	2.66026e6	+	1.37014e7i	0.149752	+	0.771282i
$795$	−1.54725e7	−	4.25103e7i	−0.868245	−	2.38548i
$796$	6.72691e6	−	8.60252e6i	0.376299	−	0.481219i
$797$		−	8.35859e6i		−	0.466109i	−0.972464	−	0.233054i	$-0.925128\pi$
$797$		−	8.35859e6i		−	0.466109i	0.972464	−	0.233054i	$-0.0748720\pi$
$798$	−2.12694e7	−	8.11761e6i	−1.18235	−	0.451254i
$799$			8.87222e6i			0.491661i
$800$	−2.56890e7	−	1.80283e7i	−1.41913	−	0.995935i
$801$	−2.71220e6	−	7.45171e6i	−0.149362	−	0.410369i
$802$	3.04280e7	−	5.90790e6i	1.67047	−	0.324337i
$803$	−6.14200e6	−	1.08300e6i	−0.336140	−	0.0592706i
$804$	3.31593e7	+	1.07897e7i	1.80911	+	0.588666i
$805$	−1.53150e7	−	2.65264e7i	−0.832966	−	1.44274i
$806$	−3.95187e6	−	2.19165e6i	−0.214272	−	0.118832i
$807$	1.00400e7	+	1.19652e7i	0.542689	+	0.646751i
$808$	1.88879e7	−	1.75908e7i	1.01778	−	0.947886i
$809$	−851333.	+	1.47455e6i	−0.0457328	+	0.0792116i	−0.887986	−	0.459871i	$-0.847896\pi$
$809$	−851333.	+	1.47455e6i	−0.0457328	+	0.0792116i	0.842253	+	0.539083i	$0.181229\pi$
$810$	−1.93096e7	−	3.21520e7i	−1.03409	−	1.72185i
$811$	−2.69393e7	−	9.80511e6i	−1.43825	−	0.523480i	−0.498966	−	0.866621i	$-0.666287\pi$
$811$	−2.69393e7	−	9.80511e6i	−1.43825	−	0.523480i	−0.939284	+	0.343141i	$0.888509\pi$
$812$	−773743.	+	5.48855e6i	−0.0411819	+	0.292124i
$813$	3.63824e7	−	6.41520e6i	1.93048	−	0.340395i
$814$	9.02103e6	−	3.46065e6i	0.477194	−	0.183061i
$815$	−2.78598e7	+	3.32021e7i	−1.46921	+	1.75094i
$816$	−2.04065e7	+	1.40955e6i	−1.07286	+	0.0741061i
$817$	2.36018e6	+	2.11600e6i	0.123706	+	0.110907i
$818$	−138023.	−	8.00478e6i	−0.00721223	−	0.418279i
$819$	8.53572e6	+	7.16232e6i	0.444662	+	0.373116i
$820$	−1.06745e7	−	2.64528e7i	−0.554389	−	1.37384i
$821$	696166.	+	3.94815e6i	0.0360458	+	0.204426i	0.997512	−	0.0704973i	$-0.0224586\pi$
$821$	696166.	+	3.94815e6i	0.0360458	+	0.204426i	−0.961466	+	0.274923i	$0.911348\pi$
$822$	1.40048e6	−	8.83015e6i	0.0722932	−	0.455815i
$823$	−1.23742e7	+	3.39980e7i	−0.636823	+	1.74966i	0.0246573	+	0.999696i	$0.492151\pi$
$823$	−1.23742e7	+	3.39980e7i	−0.636823	+	1.74966i	−0.661481	+	0.749962i	$0.730072\pi$
$824$	−1.51844e7	−	2.34146e7i	−0.779078	−	1.20135i
$825$	1.29173e7	+	7.45781e6i	0.660750	+	0.381484i
$826$	4.84153e6	+	5.57194e6i	0.246907	+	0.284156i
$827$	1.28539e7	−	1.07857e7i	0.653539	−	0.548384i	−0.254603	−	0.967046i	$-0.581945\pi$
$827$	1.28539e7	−	1.07857e7i	0.653539	−	0.548384i	0.908143	+	0.418661i	$0.137501\pi$
$828$	−4.96064e6	−	2.64032e6i	−0.251456	−	0.133839i
$829$	1.92277e6	−	1.11011e6i	0.0971718	−	0.0561022i	−0.450627	−	0.892713i	$-0.648799\pi$
$829$	1.92277e6	−	1.11011e6i	0.0971718	−	0.0561022i	0.547798	+	0.836610i	$0.315466\pi$
$830$	3.51785e6	−	1.02095e7i	0.177248	−	0.514412i
$831$	−5.16722e6	+	2.93048e7i	−0.259570	+	1.47209i
$832$	−3.23019e7	+	9.21788e6i	−1.61778	+	0.461661i
$833$	3.89420e6	−	1.41737e6i	0.194449	−	0.0707736i
$834$	−6.31621e6	+	7.79648e6i	−0.314442	+	0.388135i
$835$	5.44971e7			2.70494
$836$	−5.93812e6	+	5.00003e6i	−0.293855	+	0.247433i
$837$	−2.32539e6			−0.114732
$838$	1.26328e7	−	1.55935e7i	0.621428	−	0.767066i
$839$	−1.49800e7	+	5.45228e6i	−0.734696	+	0.267407i	−0.682151	−	0.731211i	$-0.738955\pi$
$839$	−1.49800e7	+	5.45228e6i	−0.734696	+	0.267407i	−0.0525445	+	0.998619i	$0.516733\pi$
$840$	4.17003e7	−	9.59930e6i	2.03911	−	0.469398i
$841$	3.30773e6	−	1.87590e7i	0.161265	−	0.914578i
$842$	−1.12620e7	+	3.26848e7i	−0.547440	+	1.58879i
$843$	3.95351e7	−	2.28256e7i	1.91608	−	1.10625i
$844$	−5.93249e6	+	1.11460e7i	−0.286669	+	0.538594i
$845$	−4.81177e7	+	4.03756e7i	−2.31827	+	1.94526i
$846$	−2.23343e6	−	2.57037e6i	−0.107287	−	0.123472i
$847$	1.70275e7	+	9.83085e6i	0.815536	+	0.470850i
$848$	−2.32812e7	+	1.56746e7i	−1.11177	+	0.748526i
$849$	2.64021e6	−	7.25391e6i	0.125710	−	0.345385i
$850$	−5.37033e6	+	3.38604e7i	−0.254949	+	1.60748i
$851$	4.45166e6	+	2.52466e7i	0.210716	+	1.19503i
$852$	3.72448e7	−	1.50295e7i	1.75779	−	0.709324i
$853$	2.03716e7	+	1.70938e7i	0.958635	+	0.804391i	0.980731	−	0.195365i	$-0.0625893\pi$
$853$	2.03716e7	+	1.70938e7i	0.958635	+	0.804391i	−0.0220952	+	0.999756i	$0.507034\pi$
$854$	544607.	+	3.15849e7i	0.0255528	+	1.48196i
$855$	−361646.	+	1.10322e7i	−0.0169188	+	0.516114i
$856$	1.69058e7	−	875196.i	0.788591	−	0.0408245i
$857$	1.93797e7	−	2.30959e7i	0.901355	−	1.07419i	−0.0955383	−	0.995426i	$-0.530457\pi$
$857$	1.93797e7	−	2.30959e7i	0.901355	−	1.07419i	0.996893	−	0.0787670i	$-0.0250983\pi$
$858$	1.49056e7	−	5.71809e6i	0.691243	−	0.265175i
$859$	−1.93039e7	+	3.40380e6i	−0.892610	+	0.157391i	−0.601098	−	0.799176i	$-0.705270\pi$
$859$	−1.93039e7	+	3.40380e6i	−0.892610	+	0.157391i	−0.291513	+	0.956567i	$0.594159\pi$
$860$	−5.89975e6	−	831711.i	−0.272011	−	0.0383465i
$861$	2.31786e7	+	8.43633e6i	1.06556	+	0.387834i
$862$	−1.47669e7	−	2.45881e7i	−0.676895	−	1.12708i
$863$	1.47149e6	−	2.54869e6i	0.0672558	−	0.116490i	−0.830437	−	0.557113i	$-0.811909\pi$
$863$	1.47149e6	−	2.54869e6i	0.0672558	−	0.116490i	0.897692	+	0.440623i	$0.145242\pi$
$864$	−1.22359e7	+	1.22099e7i	−0.557637	+	0.556454i
$865$	1.53799e7	+	1.83290e7i	0.698897	+	0.832912i
$866$	1.18794e7	+	6.58818e6i	0.538271	+	0.298518i
$867$	−1.50505e6	−	2.60683e6i	−0.0679992	−	0.117778i
$868$	1.10505e6	−	3.39609e6i	0.0497832	−	0.152996i
$869$	−5.81799e6	−	1.02587e6i	−0.261351	−	0.0460832i
$870$	1.10853e7	−	2.15231e6i	0.496532	−	0.0964067i
$871$	−2.13951e7	−	5.87827e7i	−0.955586	−	2.62545i
$872$	−1.48380e6	+	1.96646e6i	−0.0660821	+	0.0875777i
$873$			1.14723e7i			0.509464i
$874$	−1.00202e7	−	1.79952e7i	−0.443711	−	0.796854i
$875$		−	3.03522e7i		−	1.34020i
$876$	1.82110e7	+	1.42404e7i	0.801813	+	0.626993i
$877$	−4.60439e6	−	1.26505e7i	−0.202150	−	0.555402i	0.796647	−	0.604445i	$-0.206605\pi$
$877$	−4.60439e6	−	1.26505e7i	−0.202150	−	0.555402i	−0.998797	+	0.0490433i	$0.984383\pi$
$878$	−2.48124e6	−	1.27793e7i	−0.108625	−	0.559464i
$879$	6.23004e6	+	1.09852e6i	0.271969	+	0.0479554i
$880$	4.03377e6	−	1.40225e7i	0.175592	−	0.610405i
$881$	1.90696e6	+	3.30295e6i	0.0827754	+	0.143371i	0.904441	−	0.426599i	$-0.140288\pi$
$881$	1.90696e6	+	3.30295e6i	0.0827754	+	0.143371i	−0.821666	+	0.569970i	$0.806955\pi$
$882$	−771387.	+	1.39092e6i	−0.0333888	+	0.0602049i
$883$	4.52049e6	+	5.38731e6i	0.195112	+	0.232525i	0.854726	−	0.519079i	$-0.173725\pi$
$883$	4.52049e6	+	5.38731e6i	0.195112	+	0.232525i	−0.659614	+	0.751604i	$0.729280\pi$
$884$	2.45422e7	+	2.72802e7i	1.05629	+	1.17413i
$885$	7.51911e6	−	1.30235e7i	0.322707	−	0.558945i
$886$	2.22933e6	−	1.33887e6i	0.0954091	−	0.0573000i
$887$	−3.40129e7	−	1.23797e7i	−1.45156	−	0.528324i	−0.508532	−	0.861043i	$-0.669812\pi$
$887$	−3.40129e7	−	1.23797e7i	−1.45156	−	0.528324i	−0.943026	+	0.332719i	$0.892034\pi$
$888$	−3.55445e7	−	4.38731e6i	−1.51266	−	0.186709i
$889$	−1.05385e7	+	1.85822e6i	−0.447222	+	0.0788574i
$890$	1.95672e7	+	5.10067e7i	0.828046	+	2.15850i
$891$	7.10825e6	−	8.47128e6i	0.299963	−	0.357483i
$892$	2.71163e7	−	935392.i	1.14109	−	0.0393624i
$893$	−1.76338e6	−	1.23554e7i	−0.0739975	−	0.518477i
$894$	−5.83904e6	+	100680.i	−0.244342	+	0.00421309i
$895$	3.49025e6	+	2.92866e6i	0.145646	+	0.122212i
$896$	−1.20172e7	−	2.36720e7i	−0.500072	−	0.985065i
$897$	7.35554e6	+	4.17153e7i	0.305234	+	1.73107i
$898$	8.90520e6	+	1.41238e6i	0.368513	+	0.0584470i
$899$	322339.	−	885620.i	0.0133019	−	0.0365467i
$900$	−6.96793e6	−	1.11616e7i	−0.286746	−	0.459324i
$901$	2.65518e7	+	1.53297e7i	1.08964	+	0.629101i
$902$	6.34891e6	−	5.51665e6i	0.259826	−	0.225766i
$903$	3.94668e6	−	3.31166e6i	0.161069	−	0.135153i
$904$	7.07127e6	+	3.60867e6i	0.287790	+	0.146868i
$905$	404089.	−	233301.i	0.0164004	−	0.00946879i
$906$	1.03492e7	+	3.56596e6i	0.418876	+	0.144330i
$907$	−2.87327e6	+	1.62951e7i	−0.115974	+	0.657719i	0.870290	+	0.492540i	$0.163931\pi$
$907$	−2.87327e6	+	1.62951e7i	−0.115974	+	0.657719i	−0.986264	+	0.165179i	$0.947180\pi$
$908$	−9.18861e6	−	4.33195e7i	−0.369858	−	1.74369i
$909$	1.01687e7	−	3.70111e6i	0.408185	−	0.148567i
$910$	−5.96464e7	−	4.83217e7i	−2.38770	−	1.93437i
$911$	3.49885e7			1.39679			0.698393	−	0.715715i	$-0.253899\pi$
$911$	3.49885e7			1.39679			0.698393	+	0.715715i	$0.253899\pi$
$912$	2.81379e7	−	6.01879e6i	1.12022	−	0.239619i
$913$	3.18402e6			0.126415
$914$	−201286.	−	163069.i	−0.00796982	−	0.00645664i
$915$	6.04756e7	−	2.20113e7i	2.38796	−	0.869148i
$916$	−2.16638e6	−	1.02134e7i	−0.0853094	−	0.402189i
$917$	−6.87446e6	+	3.89870e7i	−0.269970	+	1.53108i
$918$	1.78529e7	+	6.15148e6i	0.699200	+	0.240920i
$919$	−7.62179e6	+	4.40045e6i	−0.297693	+	0.171873i	−0.641406	−	0.767202i	$-0.721649\pi$
$919$	−7.62179e6	+	4.40045e6i	−0.297693	+	0.171873i	0.343713	+	0.939075i	$0.388315\pi$
$920$	3.44835e7	+	1.75979e7i	1.34320	+	0.685474i
$921$	−1.97809e7	+	1.65982e7i	−0.768417	+	0.644779i
$922$	−7.41807e6	+	6.44567e6i	−0.287385	+	0.249713i
$923$	−6.23965e7	−	3.60247e7i	−2.41077	−	1.39186i
$924$	6.68151e6	+	1.07028e7i	0.257451	+	0.412397i
$925$	−2.05301e7	+	5.64060e7i	−0.788927	+	2.16756i
$926$	2.80068e7	+	4.44194e6i	1.07334	+	0.170233i
$927$	−2.03175e6	−	1.15226e7i	−0.0776551	−	0.440404i
$928$	−2.95402e6	−	6.35251e6i	−0.112601	−	0.242145i
$929$	1.05894e7	+	8.88556e6i	0.402561	+	0.337789i	0.821483	−	0.570234i	$-0.193147\pi$
$929$	1.05894e7	+	8.88556e6i	0.402561	+	0.337789i	−0.418921	+	0.908022i	$0.637592\pi$
$930$	−7.27475e6	+	125436.i	−0.275810	+	0.00475570i
$931$	−5.14134e6	+	2.74781e6i	−0.194403	+	0.103899i
$932$	−3.71120e7	+	1.28020e6i	−1.39951	+	0.0482767i
$933$	−5.74702e6	+	6.84903e6i	−0.216142	+	0.257588i
$934$	−4.10999e6	−	1.07137e7i	−0.154161	−	0.401857i
$935$	−1.56971e7	+	2.76783e6i	−0.587207	+	0.103540i
$936$	−1.39774e7	−	1.72525e6i	−0.521479	−	0.0643669i
$937$	−4.56145e6	−	1.66023e6i	−0.169728	−	0.0617760i	0.255758	−	0.966741i	$-0.417675\pi$
$937$	−4.56145e6	−	1.66023e6i	−0.169728	−	0.0617760i	−0.425487	+	0.904965i	$0.639897\pi$
$938$	4.23821e7	−	2.54535e7i	1.57281	−	0.944584i
$939$	8.50876e6	−	1.47376e7i	0.314922	−	0.545460i
$940$	1.56896e7	+	1.74399e7i	0.579151	+	0.643762i
$941$	1.22274e7	+	1.45721e7i	0.450154	+	0.536472i	0.942624	−	0.333857i	$-0.108350\pi$
$941$	1.22274e7	+	1.45721e7i	0.450154	+	0.536472i	−0.492470	+	0.870329i	$0.663906\pi$
$942$	−1.12415e7	+	2.02701e7i	−0.412760	+	0.744266i
$943$	1.11581e7	+	1.93264e7i	0.408613	+	0.707738i
$944$	−8.96615e6	−	2.57925e6i	−0.327473	−	0.0942026i
$945$	−3.89019e7	−	6.85945e6i	−1.41707	−	0.249867i
$946$	−334841.	−	1.72456e6i	−0.0121650	−	0.0626544i
$947$	1.03835e7	+	2.85284e7i	0.376243	+	1.03372i	0.972901	+	0.231223i	$0.0742727\pi$
$947$	1.03835e7	+	2.85284e7i	0.376243	+	1.03372i	−0.596658	+	0.802496i	$0.703505\pi$
$948$	1.72503e7	+	1.34892e7i	0.623413	+	0.487490i
$949$		−	4.14715e7i		−	1.49480i
$950$	748857.	−	4.82212e7i	0.0269209	−	1.73352i
$951$		−	1.17999e7i		−	0.423083i
$952$	−1.74677e7	+	2.31497e7i	−0.624659	+	0.827853i
$953$	6.69263e6	+	1.83878e7i	0.238707	+	0.655841i	0.999973	+	0.00740132i	$0.00235593\pi$
$953$	6.69263e6	+	1.83878e7i	0.238707	+	0.655841i	−0.761266	+	0.648440i	$0.775422\pi$
$954$	−1.15513e7	+	2.24279e6i	−0.410921	+	0.0797845i
$955$	3.91624e7	+	6.90538e6i	1.38951	+	0.245007i
$956$	3.81023e6	−	1.17098e7i	0.134836	−	0.414384i
$957$	1.66479e6	+	2.88350e6i	0.0587597	+	0.101775i
$958$	1.80836e7	+	1.00289e7i	0.636606	+	0.353053i
$959$	−8.14766e6	−	9.71000e6i	−0.286079	−	0.340936i
$960$	−3.76201e7	+	3.88575e7i	−1.31747	+	1.36081i
$961$	1.40110e7	−	2.42677e7i	0.489395	−	0.847656i
$962$	3.30785e7	+	5.50784e7i	1.15241	+	1.91886i
$963$	6.66938e6	+	2.42746e6i	0.231750	+	0.0843502i
$964$	−4.20777e7	−	5.93186e6i	−1.45834	−	0.205588i
$965$	1.83303e7	−	3.23213e6i	0.633654	−	0.111730i
$966$	−3.12557e7	+	1.19903e7i	−1.07767	+	0.413417i
$967$	2.78695e7	−	3.32136e7i	0.958437	−	1.14222i	−0.0313276	−	0.999509i	$-0.509974\pi$
$967$	2.78695e7	−	3.32136e7i	0.958437	−	1.14222i	0.989764	−	0.142711i	$-0.0455821\pi$
$968$	−2.48178e7	+	1.28479e6i	−0.851286	+	0.0440702i
$969$	−1.94050e7	−	2.47282e7i	−0.663904	−	0.846025i
$970$	−1.36257e6	−	7.90233e7i	−0.0464974	−	2.69666i
$971$	3.89298e7	+	3.26660e7i	1.32506	+	1.11185i	0.985206	+	0.171376i	$0.0548212\pi$
$971$	3.89298e7	+	3.26660e7i	1.32506	+	1.11185i	0.339851	+	0.940479i	$0.389623\pi$
$972$	−1.64937e7	+	6.65573e6i	−0.559953	+	0.225959i
$973$	2.47026e6	+	1.40096e7i	0.0836491	+	0.474398i
$974$	−3.12103e6	+	1.96784e7i	−0.105415	+	0.664648i
$975$	−3.39222e7	+	9.32005e7i	−1.14281	+	3.13983i
$976$	−2.22989e7	−	3.31201e7i	−0.749304	−	1.11293i
$977$	−2.37278e7	−	1.36992e7i	−0.795281	−	0.459156i	0.0465376	−	0.998917i	$-0.485181\pi$
$977$	−2.37278e7	−	1.36992e7i	−0.795281	−	0.459156i	−0.841818	+	0.539761i	$0.818515\pi$
$978$	3.10701e7	+	3.57574e7i	1.03871	+	1.19542i
$979$	−1.23396e7	+	1.03542e7i	−0.411477	+	0.345271i
$980$	5.14827e6	−	9.67257e6i	0.171236	−	0.321719i
$981$	−894454.	+	516413.i	−0.0296747	+	0.0171327i
$982$	−9.76029e6	+	2.83264e7i	−0.322986	+	0.937373i
$983$	−3.48034e6	+	1.97380e7i	−0.114878	+	0.651508i	0.871932	+	0.489627i	$0.162867\pi$
$983$	−3.48034e6	+	1.97380e7i	−0.114878	+	0.651508i	−0.986810	+	0.161881i	$0.948244\pi$
$984$	−3.03818e7	+	6.99381e6i	−1.00029	+	0.230264i
$985$	4.85798e7	−	1.76816e7i	1.59538	−	0.580672i
$986$	−4.81749e6	+	5.94652e6i	−0.157808	+	0.194792i
$987$	−2.02851e7			−0.662802
$988$	−3.95994e7	−	3.31124e7i	−1.29061	−	1.07919i
$989$	4.66119e6			0.151533
$990$	3.85086e6	−	4.75335e6i	0.124873	−	0.154139i
$991$	−1.59979e7	+	5.82275e6i	−0.517461	+	0.188340i	−0.587531	−	0.809202i	$-0.699900\pi$
$991$	−1.59979e7	+	5.82275e6i	−0.517461	+	0.188340i	0.0700699	+	0.997542i	$0.477678\pi$
$992$	1.16366e6	+	4.36138e6i	0.0375447	+	0.140716i
$993$	−2.99501e6	+	1.69855e7i	−0.0963883	+	0.546645i
$994$	1.85497e7	−	5.38352e7i	0.595486	−	1.72822i
$995$	−2.73163e7	+	1.57711e7i	−0.874709	+	0.505013i
$996$	−1.04184e7	−	5.54523e6i	−0.332776	−	0.177121i
$997$	4.72372e7	−	3.96367e7i	1.50503	−	1.26287i	0.632248	−	0.774766i	$-0.282132\pi$
$997$	4.72372e7	−	3.96367e7i	1.50503	−	1.26287i	0.872784	−	0.488106i	$-0.162312\pi$
$998$	−2.66081e7	−	3.06223e7i	−0.845645	−	0.973221i
$999$	2.86321e7	+	1.65308e7i	0.907695	+	0.524058i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	76.6.k.a.3.11	✓	288
4.3	odd	2	inner	76.6.k.a.3.36	yes	288
19.13	odd	18	inner	76.6.k.a.51.36	yes	288
76.51	even	18	inner	76.6.k.a.51.11	yes	288

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
76.6.k.a.3.11	✓	288	1.1	even	1	trivial
76.6.k.a.3.36	yes	288	4.3	odd	2	inner
76.6.k.a.51.11	yes	288	76.51	even	18	inner
76.6.k.a.51.36	yes	288	19.13	odd	18	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 76 = 2^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	76.k (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-4.39545 - 3.56091i) q^{2} +(16.7807 - 6.10766i) q^{3} +(6.63988 + 31.3035i) q^{4} +(16.0499 - 91.0237i) q^{5} +(-95.5073 - 32.9085i) q^{6} +(-124.031 + 71.6095i) q^{7} +(82.2838 - 161.237i) q^{8} +(58.1382 - 48.7837i) q^{9} +O(q^{10})\)	\(q+(-4.39545 - 3.56091i) q^{2} +(16.7807 - 6.10766i) q^{3} +(6.63988 + 31.3035i) q^{4} +(16.0499 - 91.0237i) q^{5} +(-95.5073 - 32.9085i) q^{6} +(-124.031 + 71.6095i) q^{7} +(82.2838 - 161.237i) q^{8} +(58.1382 - 48.7837i) q^{9} +(-394.673 + 342.937i) q^{10} +(-133.511 - 77.0826i) q^{11} +(302.613 + 484.740i) q^{12} +(350.614 - 963.304i) q^{13} +(800.168 + 126.908i) q^{14} +(-286.613 - 1625.46i) q^{15} +(-935.824 + 415.703i) q^{16} +(856.907 + 719.031i) q^{17} +(-429.258 + 7.40153i) q^{18} +(-1336.24 - 831.007i) q^{19} +(2955.93 - 101.966i) q^{20} +(-1643.96 + 1959.20i) q^{21} +(312.356 + 814.232i) q^{22} +(-2278.74 + 401.804i) q^{23} +(395.996 - 3208.22i) q^{24} +(-5091.17 - 1853.03i) q^{25} +(-4971.34 + 2985.65i) q^{26} +(-1492.06 + 2584.32i) q^{27} +(-3065.18 - 3407.14i) q^{28} +(-777.405 - 926.476i) q^{29} +(-4528.34 + 8165.24i) q^{30} +(389.629 + 674.858i) q^{31} +(5593.64 + 1505.18i) q^{32} +(-2711.20 - 478.057i) q^{33} +(-1206.09 - 6211.83i) q^{34} +(4527.47 + 12439.1i) q^{35} +(1913.13 + 1496.01i) q^{36} -11079.2i q^{37} +(2914.21 + 8410.86i) q^{38} -18306.3i q^{39} +(-13355.7 - 10077.6i) q^{40} +(-3298.60 - 9062.83i) q^{41} +(14202.5 - 2757.55i) q^{42} +(-1983.83 - 349.803i) q^{43} +(1526.46 - 4691.18i) q^{44} +(-3507.36 - 6074.93i) q^{45} +(11446.9 + 6348.28i) q^{46} +(5098.24 + 6075.84i) q^{47} +(-13164.8 + 12691.5i) q^{48} +(1852.35 - 3208.36i) q^{49} +(15779.5 + 26274.1i) q^{50} +(18771.1 + 6832.11i) q^{51} +(32482.9 + 4579.24i) q^{52} +(26991.9 - 4759.41i) q^{53} +(15760.8 - 6046.15i) q^{54} +(-9159.18 + 10915.5i) q^{55} +(1340.34 + 25890.7i) q^{56} +(-27498.4 - 5783.57i) q^{57} +(117.949 + 6840.54i) q^{58} +(6979.50 + 5856.50i) q^{59} +(48979.7 - 19764.9i) q^{60} +(6770.78 + 38399.0i) q^{61} +(690.511 - 4353.73i) q^{62} +(-3717.58 + 10214.0i) q^{63} +(-19226.8 - 26534.4i) q^{64} +(-82056.2 - 47375.1i) q^{65} +(10214.6 + 11755.6i) q^{66} +(46745.5 - 39224.1i) q^{67} +(-16818.5 + 31598.5i) q^{68} +(-35784.7 + 20660.3i) q^{69} +(24394.3 - 70797.3i) q^{70} +(12204.6 - 69215.5i) q^{71} +(-3081.91 - 13388.1i) q^{72} +(38015.3 - 13836.4i) q^{73} +(-39452.0 + 48698.0i) q^{74} -96750.9 q^{75} +(17141.0 - 47346.7i) q^{76} +22079.4 q^{77} +(-65187.1 + 80464.4i) q^{78} +(36009.8 - 13106.5i) q^{79} +(22818.9 + 91854.2i) q^{80} +(-12456.0 + 70641.6i) q^{81} +(-17773.1 + 51581.2i) q^{82} +(-17886.3 + 10326.7i) q^{83} +(-72245.5 - 38453.0i) q^{84} +(79202.1 - 66458.5i) q^{85} +(7474.21 + 8601.79i) q^{86} +(-18704.0 - 10798.7i) q^{87} +(-23414.4 + 15184.3i) q^{88} +(35736.7 - 98185.7i) q^{89} +(-6215.84 + 39191.4i) q^{90} +(25494.6 + 144587. i) q^{91} +(-27708.4 - 68664.7i) q^{92} +(10660.0 + 8944.83i) q^{93} +(-773.511 - 44860.4i) q^{94} +(-97087.8 + 108291. i) q^{95} +(103058. - 8906.16i) q^{96} +(-97164.9 + 115797. i) q^{97} +(-19566.6 + 7506.13i) q^{98} +(-11522.5 + 2031.72i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 288 q - 6 q^{2} + 24 q^{4} - 12 q^{5} + 264 q^{6} - 9 q^{8} + 54 q^{9}+O(q^{10}) \) 288 * q - 6 * q^2 + 24 * q^4 - 12 * q^5 + 264 * q^6 - 9 * q^8 + 54 * q^9	\( 288 q - 6 q^{2} + 24 q^{4} - 12 q^{5} + 264 q^{6} - 9 q^{8} + 54 q^{9} - 657 q^{10} - 9 q^{12} + 336 q^{13} - 2163 q^{14} + 1824 q^{16} - 12 q^{17} - 10242 q^{20} - 7842 q^{21} - 102 q^{22} - 11856 q^{24} - 12 q^{25} + 1317 q^{26} + 6660 q^{28} - 12 q^{29} - 40692 q^{30} - 3351 q^{32} - 8604 q^{33} - 15756 q^{34} + 81783 q^{36} + 50400 q^{38} + 39246 q^{40} - 29082 q^{41} - 123081 q^{42} - 39651 q^{44} - 6 q^{45} - 112554 q^{46} - 68403 q^{48} + 259302 q^{49} + 154188 q^{50} - 36867 q^{52} - 26280 q^{53} + 172605 q^{54} - 12 q^{57} + 229740 q^{58} - 136062 q^{60} + 169296 q^{61} + 35076 q^{62} + 63795 q^{64} - 189918 q^{65} + 73644 q^{66} + 59706 q^{68} - 200898 q^{69} - 177831 q^{70} - 188502 q^{72} + 397428 q^{73} - 530703 q^{74} - 53022 q^{76} + 159804 q^{77} - 618237 q^{78} + 18045 q^{80} - 110160 q^{81} + 155859 q^{82} + 733851 q^{84} - 645108 q^{85} + 616836 q^{86} + 598383 q^{88} - 226320 q^{89} + 546366 q^{90} - 754308 q^{92} + 558942 q^{93} - 454530 q^{96} - 177198 q^{97} - 76791 q^{98}+O(q^{100}) \) 288 * q - 6 * q^2 + 24 * q^4 - 12 * q^5 + 264 * q^6 - 9 * q^8 + 54 * q^9 - 657 * q^10 - 9 * q^12 + 336 * q^13 - 2163 * q^14 + 1824 * q^16 - 12 * q^17 - 10242 * q^20 - 7842 * q^21 - 102 * q^22 - 11856 * q^24 - 12 * q^25 + 1317 * q^26 + 6660 * q^28 - 12 * q^29 - 40692 * q^30 - 3351 * q^32 - 8604 * q^33 - 15756 * q^34 + 81783 * q^36 + 50400 * q^38 + 39246 * q^40 - 29082 * q^41 - 123081 * q^42 - 39651 * q^44 - 6 * q^45 - 112554 * q^46 - 68403 * q^48 + 259302 * q^49 + 154188 * q^50 - 36867 * q^52 - 26280 * q^53 + 172605 * q^54 - 12 * q^57 + 229740 * q^58 - 136062 * q^60 + 169296 * q^61 + 35076 * q^62 + 63795 * q^64 - 189918 * q^65 + 73644 * q^66 + 59706 * q^68 - 200898 * q^69 - 177831 * q^70 - 188502 * q^72 + 397428 * q^73 - 530703 * q^74 - 53022 * q^76 + 159804 * q^77 - 618237 * q^78 + 18045 * q^80 - 110160 * q^81 + 155859 * q^82 + 733851 * q^84 - 645108 * q^85 + 616836 * q^86 + 598383 * q^88 - 226320 * q^89 + 546366 * q^90 - 754308 * q^92 + 558942 * q^93 - 454530 * q^96 - 177198 * q^97 - 76791 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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