LMFDB - Embedded newform 33.9.b.a.23.14

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [33,9,Mod(23,33)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(33, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 0]))

N = Newforms(chi, 9, names="a")

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

chi := DirichletCharacter("33.23");

S:= CuspForms(chi, 9);

N := Newforms(S);

Level:	$ N $	$=$	$ 33 = 3 \cdot 11 $
Weight:	$ k $	$=$	$ 9 $
Character orbit:	$[\chi]$	$=$	33.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:	$13.4434941320$
Analytic rank:	$0$
Dimension:	$26$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			23.14
Character	$\chi$	$=$	33.23
Dual form			33.9.b.a.23.13

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+0.463681i q^{2} +(-38.1388 - 71.4593i) q^{3} +255.785 q^{4} +649.991i q^{5} +(33.1343 - 17.6842i) q^{6} -831.270 q^{7} +237.305i q^{8} +(-3651.86 + 5450.75i) q^{9} +O(q^{10})$	\(q+0.463681i q^{2} +(-38.1388 - 71.4593i) q^{3} +255.785 q^{4} +649.991i q^{5} +(33.1343 - 17.6842i) q^{6} -831.270 q^{7} +237.305i q^{8} +(-3651.86 + 5450.75i) q^{9} -301.389 q^{10} +4414.43i q^{11} +(-9755.34 - 18278.2i) q^{12} +43155.7 q^{13} -385.444i q^{14} +(46447.9 - 24789.9i) q^{15} +65370.9 q^{16} +104893. i q^{17} +(-2527.41 - 1693.30i) q^{18} +75962.6 q^{19} +166258. i q^{20} +(31703.7 + 59401.9i) q^{21} -2046.89 q^{22} -31800.2i q^{23} +(16957.6 - 9050.53i) q^{24} -31863.9 q^{25} +20010.5i q^{26} +(528784. + 53074.1i) q^{27} -212626. q^{28} +33557.3i q^{29} +(11494.6 + 21537.0i) q^{30} +1.04649e6 q^{31} +91061.3i q^{32} +(315452. - 168361. i) q^{33} -48636.8 q^{34} -540318. i q^{35} +(-934091. + 1.39422e6i) q^{36} -475780. q^{37} +35222.4i q^{38} +(-1.64591e6 - 3.08388e6i) q^{39} -154246. q^{40} -958455. i q^{41} +(-27543.5 + 14700.4i) q^{42} -5.21676e6 q^{43} +1.12914e6i q^{44} +(-3.54294e6 - 2.37368e6i) q^{45} +14745.1 q^{46} +4.32434e6i q^{47} +(-2.49317e6 - 4.67136e6i) q^{48} -5.07379e6 q^{49} -14774.7i q^{50} +(7.49557e6 - 4.00049e6i) q^{51} +1.10386e7 q^{52} +1.46582e7i q^{53} +(-24609.4 + 245187. i) q^{54} -2.86934e6 q^{55} -197264. i q^{56} +(-2.89713e6 - 5.42824e6i) q^{57} -15559.9 q^{58} -1.53022e7i q^{59} +(1.18807e7 - 6.34089e6i) q^{60} -6.61576e6 q^{61} +485239. i q^{62} +(3.03568e6 - 4.53104e6i) q^{63} +1.66927e7 q^{64} +2.80509e7i q^{65} +(78065.8 + 146269. i) q^{66} -8.92426e6 q^{67} +2.68300e7i q^{68} +(-2.27242e6 + 1.21282e6i) q^{69} +250535. q^{70} +1.10930e7i q^{71} +(-1.29349e6 - 866604. i) q^{72} +8.31278e6 q^{73} -220610. i q^{74} +(1.21525e6 + 2.27697e6i) q^{75} +1.94301e7 q^{76} -3.66958e6i q^{77} +(1.42994e6 - 763177. i) q^{78} +7.01564e7 q^{79} +4.24905e7i q^{80} +(-1.63746e7 - 3.98107e7i) q^{81} +444417. q^{82} -7.67533e7i q^{83} +(8.10932e6 + 1.51941e7i) q^{84} -6.81794e7 q^{85} -2.41891e6i q^{86} +(2.39798e6 - 1.27984e6i) q^{87} -1.04757e6 q^{88} +8.67620e6i q^{89} +(1.10063e6 - 1.64279e6i) q^{90} -3.58741e7 q^{91} -8.13402e6i q^{92} +(-3.99120e7 - 7.47817e7i) q^{93} -2.00511e6 q^{94} +4.93751e7i q^{95} +(6.50718e6 - 3.47297e6i) q^{96} -1.38818e8 q^{97} -2.35262e6i q^{98} +(-2.40619e7 - 1.61209e7i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 26 q - 35 q^{3} - 2596 q^{4} - 3746 q^{6} + 7156 q^{7} + 9011 q^{9}+O(q^{10}) $ 26 * q - 35 * q^3 - 2596 * q^4 - 3746 * q^6 + 7156 * q^7 + 9011 * q^9	\( 26 q - 35 q^{3} - 2596 q^{4} - 3746 q^{6} + 7156 q^{7} + 9011 q^{9} - 31836 q^{10} - 28900 q^{12} - 131624 q^{13} + 71041 q^{15} + 311972 q^{16} - 675394 q^{18} + 134608 q^{19} + 490306 q^{21} - 59088 q^{24} - 2324740 q^{25} + 2011426 q^{27} - 1996688 q^{28} - 324146 q^{30} + 964738 q^{31} - 512435 q^{33} + 9219648 q^{34} - 6887660 q^{36} - 5721542 q^{37} - 5782712 q^{39} + 8363496 q^{40} + 10350076 q^{42} + 4260820 q^{43} + 6595181 q^{45} - 39680292 q^{46} + 22674164 q^{48} + 20017254 q^{49} - 7985018 q^{51} + 48711952 q^{52} - 18774176 q^{54} - 4304454 q^{55} + 15476796 q^{57} - 16060008 q^{58} - 26730016 q^{60} + 58840 q^{61} - 42877282 q^{63} - 57365836 q^{64} - 10395110 q^{66} - 63186734 q^{67} + 100738079 q^{69} + 50969160 q^{70} + 48890880 q^{72} - 21879656 q^{73} - 122009926 q^{75} - 119289368 q^{76} - 123440744 q^{78} + 117211444 q^{79} + 138667019 q^{81} + 121755480 q^{82} - 28504816 q^{84} + 28880604 q^{85} + 14774868 q^{87} + 90481380 q^{88} + 189044834 q^{90} + 192183008 q^{91} - 113622071 q^{93} - 453996696 q^{94} + 11988416 q^{96} + 24314206 q^{97} - 57905155 q^{99}+O(q^{100}) \) 26 * q - 35 * q^3 - 2596 * q^4 - 3746 * q^6 + 7156 * q^7 + 9011 * q^9 - 31836 * q^10 - 28900 * q^12 - 131624 * q^13 + 71041 * q^15 + 311972 * q^16 - 675394 * q^18 + 134608 * q^19 + 490306 * q^21 - 59088 * q^24 - 2324740 * q^25 + 2011426 * q^27 - 1996688 * q^28 - 324146 * q^30 + 964738 * q^31 - 512435 * q^33 + 9219648 * q^34 - 6887660 * q^36 - 5721542 * q^37 - 5782712 * q^39 + 8363496 * q^40 + 10350076 * q^42 + 4260820 * q^43 + 6595181 * q^45 - 39680292 * q^46 + 22674164 * q^48 + 20017254 * q^49 - 7985018 * q^51 + 48711952 * q^52 - 18774176 * q^54 - 4304454 * q^55 + 15476796 * q^57 - 16060008 * q^58 - 26730016 * q^60 + 58840 * q^61 - 42877282 * q^63 - 57365836 * q^64 - 10395110 * q^66 - 63186734 * q^67 + 100738079 * q^69 + 50969160 * q^70 + 48890880 * q^72 - 21879656 * q^73 - 122009926 * q^75 - 119289368 * q^76 - 123440744 * q^78 + 117211444 * q^79 + 138667019 * q^81 + 121755480 * q^82 - 28504816 * q^84 + 28880604 * q^85 + 14774868 * q^87 + 90481380 * q^88 + 189044834 * q^90 + 192183008 * q^91 - 113622071 * q^93 - 453996696 * q^94 + 11988416 * q^96 + 24314206 * q^97 - 57905155 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/33\mathbb{Z}\right)^\times$.

$n$	$13$	$23$
$\chi(n)$	$1$	$-1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$			0.463681i			0.0289801i	0.999895	+	0.0144900i	$0.00461248\pi$
$2$			0.463681i			0.0289801i	−0.999895	+	0.0144900i	$0.995388\pi$
$3$	−38.1388	−	71.4593i	−0.470850	−	0.882213i
$3$	−38.1388	−	71.4593i	−0.470850	−	0.882213i
$4$	255.785			0.999160
$5$			649.991i			1.03999i	0.854170	+	0.519993i	$0.174066\pi$
$5$			649.991i			1.03999i	−0.854170	+	0.519993i	$0.825934\pi$
$6$	33.1343	−	17.6842i	0.0255666	−	0.0136453i
$7$	−831.270			−0.346218			−0.173109	−	0.984903i	$-0.555381\pi$
$7$	−831.270			−0.346218			−0.173109	+	0.984903i	$0.555381\pi$
$8$			237.305i			0.0579358i
$9$	−3651.86	+	5450.75i	−0.556601	+	0.830780i
$10$	−301.389			−0.0301389
$11$			4414.43i			0.301511i
$11$			4414.43i			0.301511i
$12$	−9755.34	−	18278.2i	−0.470454	−	0.881472i
$13$	43155.7			1.51100			0.755501	−	0.655147i	$-0.227393\pi$
$13$	43155.7			1.51100			0.755501	+	0.655147i	$0.227393\pi$
$14$		−	385.444i		−	0.0100334i
$15$	46447.9	−	24789.9i	0.917490	−	0.489677i
$16$	65370.9			0.997481
$17$			104893.i			1.25589i	0.778259	+	0.627943i	$0.216103\pi$
$17$			104893.i			1.25589i	−0.778259	+	0.627943i	$0.783897\pi$
$18$	−2527.41	−	1693.30i	−0.0240760	−	0.0161303i
$19$	75962.6			0.582889			0.291444	−	0.956588i	$-0.405864\pi$
$19$	75962.6			0.582889			0.291444	+	0.956588i	$0.405864\pi$
$20$			166258.i			1.03911i
$21$	31703.7	+	59401.9i	0.163017	+	0.305438i
$22$	−2046.89			−0.00873781
$23$		−	31800.2i		−	0.113637i	−0.998385	−	0.0568183i	$-0.981904\pi$
$23$		−	31800.2i		−	0.113637i	0.998385	−	0.0568183i	$-0.0180956\pi$
$24$	16957.6	−	9050.53i	0.0511117	−	0.0272790i
$25$	−31863.9			−0.0815716
$26$			20010.5i			0.0437889i
$27$	528784.	+	53074.1i	0.995001	+	0.0998683i
$28$	−212626.			−0.345927
$29$			33557.3i			0.0474455i	0.999719	+	0.0237227i	$0.00755189\pi$
$29$			33557.3i			0.0474455i	−0.999719	+	0.0237227i	$0.992448\pi$
$30$	11494.6	+	21537.0i	0.0141909	+	0.0265889i
$31$	1.04649e6			1.13316			0.566578	−	0.824008i	$-0.308267\pi$
$31$	1.04649e6			1.13316			0.566578	+	0.824008i	$0.308267\pi$
$32$			91061.3i			0.0868428i
$33$	315452.	−	168361.i	0.265997	−	0.141967i
$34$	−48636.8			−0.0363956
$35$		−	540318.i		−	0.360062i
$36$	−934091.	+	1.39422e6i	−0.556134	+	0.830082i
$37$	−475780.			−0.253863			−0.126931	−	0.991911i	$-0.540513\pi$
$37$	−475780.			−0.253863			−0.126931	+	0.991911i	$0.540513\pi$
$38$			35222.4i			0.0168921i
$39$	−1.64591e6	−	3.08388e6i	−0.711455	−	1.33303i
$40$	−154246.			−0.0602524
$41$		−	958455.i		−	0.339185i	−0.985514	−	0.169592i	$-0.945755\pi$
$41$		−	958455.i		−	0.339185i	0.985514	−	0.169592i	$-0.0542451\pi$
$42$	−27543.5	+	14700.4i	−0.00885162	+	0.00472423i
$43$	−5.21676e6			−1.52590			−0.762952	−	0.646456i	$-0.776251\pi$
$43$	−5.21676e6			−1.52590			−0.762952	+	0.646456i	$0.776251\pi$
$44$			1.12914e6i			0.301258i
$45$	−3.54294e6	−	2.37368e6i	−0.864000	−	0.578857i
$46$	14745.1			0.00329320
$47$			4.32434e6i			0.886192i	0.896474	+	0.443096i	$0.146120\pi$
$47$			4.32434e6i			0.886192i	−0.896474	+	0.443096i	$0.853880\pi$
$48$	−2.49317e6	−	4.67136e6i	−0.469664	−	0.879991i
$49$	−5.07379e6			−0.880133
$50$		−	14774.7i		−	0.00236395i
$51$	7.49557e6	−	4.00049e6i	1.10796	−	0.591333i
$52$	1.10386e7			1.50973
$53$			1.46582e7i			1.85771i	0.370442	+	0.928856i	$0.379206\pi$
$53$			1.46582e7i			1.85771i	−0.370442	+	0.928856i	$0.620794\pi$
$54$	−24609.4	+	245187.i	−0.00289419	+	0.0288352i
$55$	−2.86934e6			−0.313568
$56$		−	197264.i		−	0.0200584i
$57$	−2.89713e6	−	5.42824e6i	−0.274453	−	0.514232i
$58$	−15559.9			−0.00137497
$59$		−	1.53022e7i		−	1.26284i	−0.775443	−	0.631418i	$-0.782473\pi$
$59$		−	1.53022e7i		−	1.26284i	0.775443	−	0.631418i	$-0.217527\pi$
$60$	1.18807e7	−	6.34089e6i	0.916719	−	0.489266i
$61$	−6.61576e6			−0.477815			−0.238908	−	0.971042i	$-0.576789\pi$
$61$	−6.61576e6			−0.477815			−0.238908	+	0.971042i	$0.576789\pi$
$62$			485239.i			0.0328389i
$63$	3.03568e6	−	4.53104e6i	0.192705	−	0.287631i
$64$	1.66927e7			0.994964
$65$			2.80509e7i			1.57142i
$66$	78065.8	+	146269.i	0.00411420	+	0.00770862i
$67$	−8.92426e6			−0.442867			−0.221433	−	0.975176i	$-0.571074\pi$
$67$	−8.92426e6			−0.442867			−0.221433	+	0.975176i	$0.571074\pi$
$68$			2.68300e7i			1.25483i
$69$	−2.27242e6	+	1.21282e6i	−0.100252	+	0.0535058i
$70$	250535.			0.0104346
$71$			1.10930e7i			0.436532i	0.975889	+	0.218266i	$0.0700401\pi$
$71$			1.10930e7i			0.436532i	−0.975889	+	0.218266i	$0.929960\pi$
$72$	−1.29349e6	−	866604.i	−0.0481319	−	0.0322471i
$73$	8.31278e6			0.292722			0.146361	−	0.989231i	$-0.453244\pi$
$73$	8.31278e6			0.292722			0.146361	+	0.989231i	$0.453244\pi$
$74$		−	220610.i		−	0.00735696i
$75$	1.21525e6	+	2.27697e6i	0.0384080	+	0.0719636i
$76$	1.94301e7			0.582399
$77$		−	3.66958e6i		−	0.104389i
$78$	1.42994e6	−	763177.i	0.0386312	−	0.0206180i
$79$	7.01564e7			1.80119			0.900593	−	0.434663i	$-0.143133\pi$
$79$	7.01564e7			1.80119			0.900593	+	0.434663i	$0.143133\pi$
$80$			4.24905e7i			1.03737i
$81$	−1.63746e7	−	3.98107e7i	−0.380391	−	0.924826i
$82$	444417.			0.00982959
$83$		−	7.67533e7i		−	1.61728i	−0.588305	−	0.808639i	$-0.700204\pi$
$83$		−	7.67533e7i		−	1.61728i	0.588305	−	0.808639i	$-0.299796\pi$
$84$	8.10932e6	+	1.51941e7i	0.162880	+	0.305182i
$85$	−6.81794e7			−1.30610
$86$		−	2.41891e6i		−	0.0442208i
$87$	2.39798e6	−	1.27984e6i	0.0418570	−	0.0223397i
$88$	−1.04757e6			−0.0174683
$89$			8.67620e6i			0.138283i	0.997607	+	0.0691416i	$0.0220260\pi$
$89$			8.67620e6i			0.138283i	−0.997607	+	0.0691416i	$0.977974\pi$
$90$	1.10063e6	−	1.64279e6i	0.0167753	−	0.0250388i
$91$	−3.58741e7			−0.523136
$92$		−	8.13402e6i		−	0.113541i
$93$	−3.99120e7	−	7.47817e7i	−0.533546	−	0.999686i
$94$	−2.00511e6			−0.0256819
$95$			4.93751e7i			0.606196i
$96$	6.50718e6	−	3.47297e6i	0.0766139	−	0.0408899i
$97$	−1.38818e8			−1.56805			−0.784025	−	0.620729i	$-0.786837\pi$
$97$	−1.38818e8			−1.56805			−0.784025	+	0.620729i	$0.786837\pi$
$98$		−	2.35262e6i		−	0.0255063i
$99$	−2.40619e7	−	1.61209e7i	−0.250490	−	0.167822i
$100$	−8.15031e6			−0.0815031
$101$			9.38822e7i			0.902189i	0.892476	+	0.451095i	$0.148966\pi$
$101$			9.38822e7i			0.902189i	−0.892476	+	0.451095i	$0.851034\pi$
$102$	1.85495e6	+	3.47555e6i	0.0171369	+	0.0321087i
$103$	−7.99315e7			−0.710181			−0.355091	−	0.934832i	$-0.615550\pi$
$103$	−7.99315e7			−0.710181			−0.355091	+	0.934832i	$0.615550\pi$
$104$			1.02411e7i			0.0875411i
$105$	−3.86107e7	+	2.06071e7i	−0.317652	+	0.169535i
$106$	−6.79674e6			−0.0538366
$107$		−	1.39281e8i		−	1.06257i	−0.847195	−	0.531283i	$-0.821710\pi$
$107$		−	1.39281e8i		−	1.06257i	0.847195	−	0.531283i	$-0.178290\pi$
$108$	1.35255e8	+	1.35756e7i	0.994165	+	0.0997844i
$109$	1.68855e8			1.19621			0.598104	−	0.801418i	$-0.295921\pi$
$109$	1.68855e8			1.19621			0.598104	+	0.801418i	$0.295921\pi$
$110$		−	1.33046e6i		−	0.00908721i
$111$	1.81457e7	+	3.39989e7i	0.119531	+	0.223961i
$112$	−5.43409e7			−0.345346
$113$		−	2.75504e8i		−	1.68972i	−0.534989	−	0.844859i	$-0.679684\pi$
$113$		−	2.75504e8i		−	1.68972i	0.534989	−	0.844859i	$-0.320316\pi$
$114$	2.51697e6	−	1.34334e6i	0.0149025	−	0.00795366i
$115$	2.06699e7			0.118181
$116$			8.58345e6i			0.0474056i
$117$	−1.57599e8	+	2.35231e8i	−0.841026	+	1.25531i
$118$	7.09536e6			0.0365971
$119$		−	8.71942e7i		−	0.434810i
$120$	5.88277e6	+	1.10223e7i	0.0283698	+	0.0531555i
$121$	−1.94872e7			−0.0909091
$122$		−	3.06760e6i		−	0.0138471i
$123$	−6.84905e7	+	3.65544e7i	−0.299233	+	0.159705i
$124$	2.67677e8			1.13220
$125$			2.33192e8i			0.955153i
$126$	2.10096e6	+	1.40759e6i	0.00833556	+	0.00558461i
$127$	3.70029e8			1.42240			0.711199	−	0.702991i	$-0.248153\pi$
$127$	3.70029e8			1.42240			0.711199	+	0.702991i	$0.248153\pi$
$128$			3.10518e7i			0.115677i
$129$	1.98961e8	+	3.72786e8i	0.718471	+	1.34617i
$130$	−1.30067e7			−0.0455399
$131$		−	4.53608e8i		−	1.54027i	−0.637883	−	0.770133i	$-0.720190\pi$
$131$		−	4.53608e8i		−	1.54027i	0.637883	−	0.770133i	$-0.279810\pi$
$132$	8.06878e7	−	4.30642e7i	0.265774	−	0.141847i
$133$	−6.31454e7			−0.201807
$134$		−	4.13801e6i		−	0.0128343i
$135$	−3.44977e7	+	3.43705e8i	−0.103862	+	1.03479i
$136$	−2.48916e7			−0.0727607
$137$			7.47078e7i			0.212072i	0.994362	+	0.106036i	$0.0338159\pi$
$137$			7.47078e7i			0.212072i	−0.994362	+	0.106036i	$0.966184\pi$
$138$	−562363.	−	1.05368e6i	−0.00155060	−	0.00290530i
$139$	−2.84891e7			−0.0763167			−0.0381584	−	0.999272i	$-0.512149\pi$
$139$	−2.84891e7			−0.0763167			−0.0381584	+	0.999272i	$0.512149\pi$
$140$		−	1.38205e8i		−	0.359760i
$141$	3.09014e8	−	1.64925e8i	0.781811	−	0.417263i
$142$	−5.14362e6			−0.0126507
$143$			1.90508e8i			0.455584i
$144$	−2.38725e8	+	3.56320e8i	−0.555199	+	0.828687i
$145$	−2.18119e7			−0.0493426
$146$			3.85448e6i			0.00848309i
$147$	1.93508e8	+	3.62570e8i	0.414410	+	0.776465i
$148$	−1.21697e8			−0.253650
$149$		−	6.68520e8i		−	1.35634i	−0.734904	−	0.678171i	$-0.762773\pi$
$149$		−	6.68520e8i		−	1.35634i	0.734904	−	0.678171i	$-0.237227\pi$
$150$	−1.05579e6	+	563489.i	−0.00208551	+	0.00111307i
$151$	−1.10269e7			−0.0212103			−0.0106051	−	0.999944i	$-0.503376\pi$
$151$	−1.10269e7			−0.0212103			−0.0106051	+	0.999944i	$0.503376\pi$
$152$			1.80263e7i			0.0337701i
$153$	−5.71744e8	−	3.83054e8i	−1.04336	−	0.699027i
$154$	1.70151e6			0.00302519
$155$			6.80212e8i			1.17847i
$156$	−4.20999e8	−	7.88810e8i	−0.710858	−	1.33191i
$157$	−8.31454e8			−1.36848			−0.684242	−	0.729255i	$-0.739867\pi$
$157$	−8.31454e8			−1.36848			−0.684242	+	0.729255i	$0.739867\pi$
$158$			3.25302e7i			0.0521985i
$159$	1.04747e9	−	5.59048e8i	1.63890	−	0.874703i
$160$	−5.91891e7			−0.0903154
$161$			2.64345e7i			0.0393431i
$162$	1.84595e7	−	7.59258e6i	0.0268015	−	0.0110237i
$163$	−1.27899e8			−0.181183			−0.0905916	−	0.995888i	$-0.528876\pi$
$163$	−1.27899e8			−0.181183			−0.0905916	+	0.995888i	$0.528876\pi$
$164$		−	2.45158e8i		−	0.338900i
$165$	1.09433e8	+	2.05041e8i	0.147643	+	0.276634i
$166$	3.55891e7			0.0468688
$167$		−	1.99112e8i		−	0.255995i	−0.991774	−	0.127998i	$-0.959145\pi$
$167$		−	1.99112e8i		−	0.255995i	0.991774	−	0.127998i	$-0.0408550\pi$
$168$	−1.40964e7	+	7.52343e6i	−0.0176958	+	0.00944450i
$169$	1.04669e9			1.28313
$170$		−	3.16135e7i		−	0.0378510i
$171$	−2.77405e8	+	4.14053e8i	−0.324436	+	0.484252i
$172$	−1.33437e9			−1.52462
$173$		−	1.14200e9i		−	1.27492i	−0.770485	−	0.637458i	$-0.779986\pi$
$173$		−	1.14200e9i		−	1.27492i	0.770485	−	0.637458i	$-0.220014\pi$
$174$	593435.	+	1.11190e6i	0.000647405	+	0.00121302i
$175$	2.64875e7			0.0282416
$176$			2.88575e8i			0.300752i
$177$	−1.09349e9	+	5.83610e8i	−1.11409	+	0.594606i
$178$	−4.02299e6			−0.00400746
$179$			6.15680e8i			0.599712i	0.953984	+	0.299856i	$0.0969387\pi$
$179$			6.15680e8i			0.599712i	−0.953984	+	0.299856i	$0.903061\pi$
$180$	−9.06231e8	−	6.07151e8i	−0.863274	−	0.578371i
$181$	1.28354e8			0.119590			0.0597951	−	0.998211i	$-0.480955\pi$
$181$	1.28354e8			0.119590			0.0597951	+	0.998211i	$0.480955\pi$
$182$		−	1.66341e7i		−	0.0151605i
$183$	2.52317e8	+	4.72757e8i	0.224979	+	0.421535i
$184$	7.54634e6			0.00658363
$185$		−	3.09253e8i		−	0.264014i
$186$	3.46748e7	−	1.85064e7i	0.0289709	−	0.0154622i
$187$	−4.63042e8			−0.378664
$188$			1.10610e9i			0.885448i
$189$	−4.39562e8	−	4.41189e7i	−0.344487	−	0.0345762i
$190$	−2.28943e7			−0.0175676
$191$			1.24168e9i			0.932986i	0.884525	+	0.466493i	$0.154483\pi$
$191$			1.24168e9i			0.932986i	−0.884525	+	0.466493i	$0.845517\pi$
$192$	−6.36641e8	−	1.19285e9i	−0.468479	−	0.877771i
$193$	2.13484e9			1.53864			0.769318	−	0.638866i	$-0.220596\pi$
$193$	2.13484e9			1.53864			0.769318	+	0.638866i	$0.220596\pi$
$194$		−	6.43674e7i		−	0.0454422i
$195$	2.00450e9	−	1.06983e9i	1.38633	−	0.739904i
$196$	−1.29780e9			−0.879394
$197$			9.17198e7i			0.0608973i	0.999536	+	0.0304487i	$0.00969361\pi$
$197$			9.17198e7i			0.0608973i	−0.999536	+	0.0304487i	$0.990306\pi$
$198$	7.47494e6	−	1.11571e7i	0.00486348	−	0.00725920i
$199$	−272964.			−0.000174058			−8.70290e−5	−	1.00000i	$-0.500028\pi$
$199$	−272964.			−0.000174058			−8.70290e−5		1.00000i	$0.500028\pi$
$200$		−	7.56146e6i		−	0.00472591i
$201$	3.40361e8	+	6.37721e8i	0.208524	+	0.390703i
$202$	−4.35314e7			−0.0261455
$203$		−	2.78951e7i		−	0.0164265i
$204$	1.91725e9	−	1.02327e9i	1.10703	−	0.590837i
$205$	6.22988e8			0.352748
$206$		−	3.70627e7i		−	0.0205811i
$207$	1.73335e8	+	1.16130e8i	0.0944071	+	0.0632503i
$208$	2.82113e9			1.50720
$209$			3.35332e8i			0.175748i
$210$	−9.55512e6	−	1.79031e7i	−0.00491314	−	0.00920556i
$211$	2.45761e9			1.23989			0.619944	−	0.784646i	$-0.287155\pi$
$211$	2.45761e9			1.23989			0.619944	+	0.784646i	$0.287155\pi$
$212$			3.74936e9i			1.85615i
$213$	7.92699e8	−	4.23075e8i	0.385115	−	0.205541i
$214$	6.45818e7			0.0307932
$215$		−	3.39085e9i		−	1.58692i
$216$	−1.25947e7	+	1.25483e8i	−0.00578594	+	0.0576461i
$217$	−8.69918e8			−0.392319
$218$			7.82946e7i			0.0346662i
$219$	−3.17040e8	−	5.94025e8i	−0.137828	−	0.258243i
$220$	−7.33934e8			−0.313304
$221$			4.52673e9i			1.89765i
$222$	−1.57646e7	+	8.41381e6i	−0.00649041	+	0.00346402i
$223$	−3.21507e9			−1.30008			−0.650042	−	0.759898i	$-0.725249\pi$
$223$	−3.21507e9			−1.30008			−0.650042	+	0.759898i	$0.725249\pi$
$224$		−	7.56965e7i		−	0.0300666i
$225$	1.16363e8	−	1.73682e8i	0.0454028	−	0.0677681i
$226$	1.27746e8			0.0489681
$227$			4.88497e9i			1.83975i	0.392215	+	0.919874i	$0.371709\pi$
$227$			4.88497e9i			1.83975i	−0.392215	+	0.919874i	$0.628291\pi$
$228$	−7.41042e8	−	1.38846e9i	−0.274223	−	0.513800i
$229$	−1.14386e9			−0.415942			−0.207971	−	0.978135i	$-0.566686\pi$
$229$	−1.14386e9			−0.415942			−0.207971	+	0.978135i	$0.566686\pi$
$230$			9.58422e6i			0.00342488i
$231$	−2.62226e8	+	1.39953e8i	−0.0920931	+	0.0491514i
$232$	−7.96331e6			−0.00274879
$233$			2.06400e9i			0.700304i	0.936693	+	0.350152i	$0.113870\pi$
$233$			2.06400e9i			0.700304i	−0.936693	+	0.350152i	$0.886130\pi$
$234$	−1.09072e8	−	7.30755e7i	−0.0363790	−	0.0243730i
$235$	−2.81078e9			−0.921628
$236$		−	3.91408e9i		−	1.26178i
$237$	−2.67568e9	−	5.01332e9i	−0.848088	−	1.58903i
$238$	4.04303e7			0.0126008
$239$		−	3.60302e9i		−	1.10427i	−0.833755	−	0.552134i	$-0.813814\pi$
$239$		−	3.60302e9i		−	1.10427i	0.833755	−	0.552134i	$-0.186186\pi$
$240$	3.03634e9	−	1.62054e9i	0.915179	−	0.488444i
$241$	1.93455e9			0.573470			0.286735	−	0.958010i	$-0.407430\pi$
$241$	1.93455e9			0.573470			0.286735	+	0.958010i	$0.407430\pi$
$242$		−	9.03583e6i		−	0.00263455i
$243$	−2.22034e9	+	2.68845e9i	−0.636787	+	0.771040i
$244$	−1.69221e9			−0.477414
$245$		−	3.29792e9i		−	0.915326i
$246$	−1.69496e7	−	3.17577e7i	−0.00462826	−	0.00867180i
$247$	3.27822e9			0.880747
$248$			2.48338e8i			0.0656503i
$249$	−5.48474e9	+	2.92728e9i	−1.42679	+	0.761495i
$250$	−1.08127e8			−0.0276804
$251$		−	2.48100e8i		−	0.0625074i	−0.999511	−	0.0312537i	$-0.990050\pi$
$251$		−	2.48100e8i		−	0.0625074i	0.999511	−	0.0312537i	$-0.00994999\pi$
$252$	7.76481e8	−	1.15897e9i	0.192543	−	0.287389i
$253$	1.40380e8			0.0342627
$254$			1.71575e8i			0.0412212i
$255$	2.60028e9	+	4.87205e9i	0.614979	+	1.15226i
$256$	4.25894e9			0.991612
$257$		−	5.63936e9i		−	1.29270i	−0.763042	−	0.646349i	$-0.776295\pi$
$257$		−	5.63936e9i		−	1.29270i	0.763042	−	0.646349i	$-0.223705\pi$
$258$	−1.72854e8	+	9.22545e7i	−0.0390121	+	0.0208213i
$259$	3.95501e8			0.0878919
$260$			7.17499e9i			1.57010i
$261$	−1.82912e8	−	1.22546e8i	−0.0394167	−	0.0264082i
$262$	2.10330e8			0.0446370
$263$		−	7.53017e9i		−	1.57392i	−0.617006	−	0.786959i	$-0.711655\pi$
$263$		−	7.53017e9i		−	1.57392i	0.617006	−	0.786959i	$-0.288345\pi$
$264$	3.99529e7	+	7.48583e7i	0.00822494	+	0.0154108i
$265$	−9.52773e9			−1.93199
$266$		−	2.92793e7i		−	0.00584837i
$267$	6.19995e8	−	3.30900e8i	0.121995	−	0.0651106i
$268$	−2.28269e9			−0.442495
$269$		−	6.86100e9i		−	1.31032i	−0.755489	−	0.655161i	$-0.772601\pi$
$269$		−	6.86100e9i		−	1.31032i	0.755489	−	0.655161i	$-0.227399\pi$
$270$	−1.59370e8	−	1.59959e7i	−0.0299882	−	0.00300992i
$271$	−3.01473e9			−0.558947			−0.279474	−	0.960153i	$-0.590160\pi$
$271$	−3.01473e9			−0.558947			−0.279474	+	0.960153i	$0.590160\pi$
$272$			6.85694e9i			1.25272i
$273$	1.36819e9	+	2.56353e9i	0.246319	+	0.461518i
$274$	−3.46406e7			−0.00614586
$275$		−	1.40661e8i		−	0.0245948i
$276$	−5.81251e8	+	3.10222e8i	−0.100168	+	0.0534609i
$277$	−1.63933e9			−0.278449			−0.139225	−	0.990261i	$-0.544461\pi$
$277$	−1.63933e9			−0.278449			−0.139225	+	0.990261i	$0.544461\pi$
$278$		−	1.32099e7i		−	0.00221166i
$279$	−3.82165e9	+	5.70417e9i	−0.630716	+	0.941403i
$280$	1.28220e8			0.0208605
$281$		−	1.15302e10i		−	1.84932i	−0.380798	−	0.924658i	$-0.624351\pi$
$281$		−	1.15302e10i		−	1.84932i	0.380798	−	0.924658i	$-0.375649\pi$
$282$	7.64726e7	+	1.43284e8i	0.0120923	+	0.0226569i
$283$	4.61179e9			0.718991			0.359496	−	0.933147i	$-0.382949\pi$
$283$	4.61179e9			0.718991			0.359496	+	0.933147i	$0.382949\pi$
$284$			2.83743e9i			0.436166i
$285$	3.52831e9	−	1.88311e9i	0.534795	−	0.285427i
$286$	−8.83349e7			−0.0132029
$287$			7.96735e8i			0.117432i
$288$	−4.96352e8	−	3.32543e8i	−0.0721473	−	0.0483368i
$289$	−4.02675e9			−0.577249
$290$		−	1.01138e7i		−	0.00142995i
$291$	5.29437e9	+	9.91986e9i	0.738316	+	1.38336i
$292$	2.12628e9			0.292476
$293$			3.62605e9i			0.491997i	0.969270	+	0.245999i	$0.0791159\pi$
$293$			3.62605e9i			0.491997i	−0.969270	+	0.245999i	$0.920884\pi$
$294$	−1.68117e8	+	8.97262e7i	−0.0225020	+	0.0120096i
$295$	9.94633e9			1.31333
$296$		−	1.12905e8i		−	0.0147077i
$297$	−2.34292e8	+	2.33428e9i	−0.0301114	+	0.300004i
$298$	3.09980e8			0.0393069
$299$		−	1.37236e9i		−	0.171705i
$300$	3.10843e8	+	5.82415e8i	0.0383757	+	0.0719031i
$301$	4.33653e9			0.528295
$302$		−	5.11297e6i		−	0.000614675i
$303$	6.70875e9	−	3.58056e9i	0.795923	−	0.424796i
$304$	4.96575e9			0.581421
$305$		−	4.30019e9i		−	0.496922i
$306$	1.77615e8	−	2.65107e8i	0.0202578	−	0.0302368i
$307$	−3.76730e9			−0.424108			−0.212054	−	0.977258i	$-0.568015\pi$
$307$	−3.76730e9			−0.424108			−0.212054	+	0.977258i	$0.568015\pi$
$308$		−	9.38623e8i		−	0.104301i
$309$	3.04850e9	+	5.71185e9i	0.334389	+	0.626531i
$310$	−3.15401e8			−0.0341520
$311$			1.22053e10i			1.30469i	0.757924	+	0.652343i	$0.226214\pi$
$311$			1.22053e10i			1.30469i	−0.757924	+	0.652343i	$0.773786\pi$
$312$	7.31820e8	−	3.90582e8i	0.0772299	−	0.0412187i
$313$	−1.33667e9			−0.139267			−0.0696335	−	0.997573i	$-0.522183\pi$
$313$	−1.33667e9			−0.139267			−0.0696335	+	0.997573i	$0.522183\pi$
$314$		−	3.85529e8i		−	0.0396587i
$315$	2.94514e9	+	1.97317e9i	0.299132	+	0.200411i
$316$	1.79449e10			1.79967
$317$		−	1.19962e10i		−	1.18797i	−0.804475	−	0.593986i	$-0.797553\pi$
$317$		−	1.19962e10i		−	1.18797i	0.804475	−	0.593986i	$-0.202447\pi$
$318$	2.59220e8	+	4.85690e8i	0.0253489	+	0.0474953i
$319$	−1.48136e8			−0.0143053
$320$			1.08501e10i			1.03475i
$321$	−9.95290e9	+	5.31200e9i	−0.937409	+	0.500309i
$322$	−1.22572e7			−0.00114016
$323$			7.96794e9i			0.732042i
$324$	−4.18837e9	−	1.01830e10i	−0.380071	−	0.924049i
$325$	−1.37511e9			−0.123255
$326$		−	5.93045e7i		−	0.00525070i
$327$	−6.43992e9	−	1.20662e10i	−0.563234	−	1.05531i
$328$	2.27446e8			0.0196509
$329$		−	3.59469e9i		−	0.306816i
$330$	−9.50736e7	+	5.07421e7i	−0.00801686	+	0.00427871i
$331$	1.21367e9			0.101108			0.0505542	−	0.998721i	$-0.483901\pi$
$331$	1.21367e9			0.101108			0.0505542	+	0.998721i	$0.483901\pi$
$332$		−	1.96324e10i		−	1.61592i
$333$	1.73748e9	−	2.59336e9i	0.141300	−	0.210904i
$334$	9.23245e7			0.00741876
$335$		−	5.80069e9i		−	0.460575i
$336$	2.07250e9	+	3.88316e9i	0.162606	+	0.304669i
$337$	−1.27229e10			−0.986434			−0.493217	−	0.869906i	$-0.664179\pi$
$337$	−1.27229e10			−0.986434			−0.493217	+	0.869906i	$0.664179\pi$
$338$			4.85329e8i			0.0371852i
$339$	−1.96873e10	+	1.05074e10i	−1.49069	+	0.795603i
$340$	−1.74393e10			−1.30501
$341$			4.61967e9i			0.341659i
$342$	−1.91989e8	−	1.28627e8i	−0.0140337	−	0.00940219i
$343$	9.00979e9			0.650936
$344$		−	1.23796e9i		−	0.0884044i
$345$	−7.88324e8	−	1.47705e9i	−0.0556453	−	0.104261i
$346$	5.29524e8			0.0369471
$347$			1.72507e10i			1.18984i	0.803786	+	0.594919i	$0.202816\pi$
$347$			1.72507e10i			1.18984i	−0.803786	+	0.594919i	$0.797184\pi$
$348$	6.13367e8	−	3.27363e8i	0.0418219	−	0.0223209i
$349$	−1.81850e10			−1.22578			−0.612888	−	0.790170i	$-0.709992\pi$
$349$	−1.81850e10			−1.22578			−0.612888	+	0.790170i	$0.709992\pi$
$350$			1.22817e7i			0.000818442i
$351$	2.28201e10	+	2.29045e9i	1.50345	+	0.150901i
$352$	−4.01984e8			−0.0261841
$353$		−	1.60479e9i		−	0.103352i	−0.998664	−	0.0516762i	$-0.983544\pi$
$353$		−	1.60479e9i		−	0.103352i	0.998664	−	0.0516762i	$-0.0164564\pi$
$354$	−2.70609e8	−	5.07029e8i	−0.0172317	−	0.0322864i
$355$	−7.21037e9			−0.453988
$356$			2.21924e9i			0.138167i
$357$	−6.23084e9	+	3.32549e9i	−0.383595	+	0.204730i
$358$	−2.85479e8			−0.0173797
$359$		−	2.19165e10i		−	1.31945i	−0.751507	−	0.659725i	$-0.770673\pi$
$359$		−	2.19165e10i		−	1.31945i	0.751507	−	0.659725i	$-0.229327\pi$
$360$	5.63285e8	−	8.40757e8i	0.0335365	−	0.0500565i
$361$	−1.12132e10			−0.660241
$362$			5.95154e7i			0.00346573i
$363$	7.43218e8	+	1.39254e9i	0.0428045	+	0.0802012i
$364$	−9.17605e9			−0.522697
$365$			5.40324e9i			0.304427i
$366$	−2.19208e8	+	1.16995e8i	−0.0122161	+	0.00651991i
$367$	2.66903e10			1.47126			0.735629	−	0.677385i	$-0.236887\pi$
$367$	2.66903e10			1.47126			0.735629	+	0.677385i	$0.236887\pi$
$368$		−	2.07881e9i		−	0.113350i
$369$	5.22430e9	+	3.50014e9i	0.281788	+	0.188791i
$370$	1.43395e8			0.00765114
$371$		−	1.21849e10i		−	0.643173i
$372$	−1.02089e10	−	1.91280e10i	−0.533098	−	0.998846i
$373$	−1.19076e10			−0.615162			−0.307581	−	0.951522i	$-0.599520\pi$
$373$	−1.19076e10			−0.615162			−0.307581	+	0.951522i	$0.599520\pi$
$374$		−	2.14704e8i		−	0.0109737i
$375$	1.66637e10	−	8.89366e9i	0.842649	−	0.449734i
$376$	−1.02619e9			−0.0513422
$377$			1.44819e9i			0.0716902i
$378$	2.04571e7	−	2.03817e8i	0.00100202	−	0.00998326i
$379$	2.09110e10			1.01349			0.506744	−	0.862097i	$-0.330849\pi$
$379$	2.09110e10			1.01349			0.506744	+	0.862097i	$0.330849\pi$
$380$			1.26294e10i			0.605687i
$381$	−1.41125e10	−	2.64420e10i	−0.669735	−	1.25486i
$382$	−5.75742e8			−0.0270380
$383$			8.11163e9i			0.376975i	0.982076	+	0.188488i	$0.0603585\pi$
$383$			8.11163e9i			0.376975i	−0.982076	+	0.188488i	$0.939641\pi$
$384$	2.21894e9	−	1.18428e9i	0.102052	−	0.0544665i
$385$	2.38520e9			0.108563
$386$			9.89884e8i			0.0445898i
$387$	1.90509e10	−	2.84352e10i	0.849319	−	1.26769i
$388$	−3.55077e10			−1.56673
$389$			2.20202e9i			0.0961664i	0.998843	+	0.0480832i	$0.0153113\pi$
$389$			2.20202e9i			0.0961664i	−0.998843	+	0.0480832i	$0.984689\pi$
$390$	4.96058e8	+	9.29446e8i	0.0214425	+	0.0401759i
$391$	3.33561e9			0.142715
$392$		−	1.20404e9i		−	0.0509912i
$393$	−3.24145e10	+	1.73001e10i	−1.35884	+	0.725234i
$394$	−4.25287e7			−0.00176481
$395$			4.56010e10i			1.87321i
$396$	−6.15468e9	−	4.12348e9i	−0.250279	−	0.167681i
$397$	1.81707e10			0.731493			0.365747	−	0.930714i	$-0.380814\pi$
$397$	1.81707e10			0.731493			0.365747	+	0.930714i	$0.380814\pi$
$398$		−	126568.i		−	5.04421e-6i
$399$	2.40829e9	+	4.51233e9i	0.0950206	+	0.178037i
$400$	−2.08297e9			−0.0813662
$401$			4.26261e10i			1.64854i	0.566200	+	0.824268i	$0.308413\pi$
$401$			4.26261e10i			1.64854i	−0.566200	+	0.824268i	$0.691587\pi$
$402$	−2.95699e8	+	1.57819e8i	−0.0113226	+	0.00604303i
$403$	4.51622e10			1.71220
$404$			2.40136e10i			0.901431i
$405$	2.58766e10	−	1.06433e10i	0.961806	−	0.395601i
$406$	1.29344e7			0.000476040
$407$		−	2.10030e9i		−	0.0765425i
$408$	9.49336e8	+	1.77873e9i	0.0342594	+	0.0641905i
$409$	−1.92596e10			−0.688263			−0.344131	−	0.938921i	$-0.611827\pi$
$409$	−1.92596e10			−0.688263			−0.344131	+	0.938921i	$0.611827\pi$
$410$			2.88867e8i			0.0102226i
$411$	5.33856e9	−	2.84927e9i	0.187093	−	0.0998541i
$412$	−2.04453e10			−0.709585
$413$			1.27203e10i			0.437217i
$414$	−5.38472e7	+	8.03721e7i	−0.00183300	+	0.00273592i
$415$	4.98890e10			1.68195
$416$			3.92982e9i			0.131220i
$417$	1.08654e9	+	2.03581e9i	0.0359337	+	0.0673276i
$418$	−1.55487e8			−0.00509317
$419$		−	1.31277e10i		−	0.425925i	−0.977060	−	0.212963i	$-0.931689\pi$
$419$		−	1.31277e10i		−	0.425925i	0.977060	−	0.212963i	$-0.0683112\pi$
$420$	−9.87605e9	+	5.27099e9i	−0.317385	+	0.169393i
$421$	4.99077e10			1.58869			0.794346	−	0.607466i	$-0.207814\pi$
$421$	4.99077e10			1.58869			0.794346	+	0.607466i	$0.207814\pi$
$422$			1.13955e9i			0.0359320i
$423$	−2.35709e10	−	1.57919e10i	−0.736231	−	0.493255i
$424$	−3.47847e9			−0.107628
$425$		−	3.34230e9i		−	0.102445i
$426$	1.96172e8	+	3.67560e8i	0.00595659	+	0.0111606i
$427$	5.49948e9			0.165428
$428$		−	3.56259e10i		−	1.06167i
$429$	1.36136e10	−	7.26575e9i	0.401923	−	0.214512i
$430$	1.57227e9			0.0459890
$431$			5.19660e10i			1.50595i	0.658050	+	0.752975i	$0.271382\pi$
$431$			5.19660e10i			1.50595i	−0.658050	+	0.752975i	$0.728618\pi$
$432$	3.45671e10	+	3.46950e9i	0.992494	+	0.0996167i
$433$	−3.51552e10			−1.00009			−0.500043	−	0.866001i	$-0.666683\pi$
$433$	−3.51552e10			−1.00009			−0.500043	+	0.866001i	$0.666683\pi$
$434$		−	4.03364e8i		−	0.0113694i
$435$	8.31882e8	+	1.55867e9i	0.0232330	+	0.0435307i
$436$	4.31905e10			1.19520
$437$		−	2.41563e9i		−	0.0662375i
$438$	2.75438e8	−	1.47005e8i	0.00748389	−	0.00399426i
$439$	−2.78675e10			−0.750308			−0.375154	−	0.926963i	$-0.622410\pi$
$439$	−2.78675e10			−0.750308			−0.375154	+	0.926963i	$0.622410\pi$
$440$		−	6.80909e8i		−	0.0181668i
$441$	1.85288e10	−	2.76560e10i	0.489883	−	0.731197i
$442$	−2.09896e9			−0.0549939
$443$		−	7.13519e10i		−	1.85264i	−0.376740	−	0.926319i	$-0.622955\pi$
$443$		−	7.13519e10i		−	1.85264i	0.376740	−	0.926319i	$-0.377045\pi$
$444$	4.64140e9	+	8.69641e9i	0.119431	+	0.223773i
$445$	−5.63946e9			−0.143813
$446$		−	1.49077e9i		−	0.0376765i
$447$	−4.77720e10	+	2.54966e10i	−1.19658	+	0.638634i
$448$	−1.38762e10			−0.344475
$449$			2.72252e10i			0.669863i	0.942242	+	0.334932i	$0.108713\pi$
$449$			2.72252e10i			0.669863i	−0.942242	+	0.334932i	$0.891287\pi$
$450$	8.05331e7	+	5.39551e7i	0.00196392	+	0.00131578i
$451$	4.23103e9			0.102268
$452$		−	7.04698e10i		−	1.68830i
$453$	4.20554e8	+	7.87975e8i	0.00998685	+	0.0187120i
$454$	−2.26507e9			−0.0533160
$455$		−	2.33178e10i		−	0.544055i
$456$	1.28815e9	−	6.87502e8i	0.0297924	−	0.0159006i
$457$	−8.26157e10			−1.89408			−0.947039	−	0.321119i	$-0.895941\pi$
$457$	−8.26157e10			−1.89408			−0.947039	+	0.321119i	$0.895941\pi$
$458$		−	5.30388e8i		−	0.0120540i
$459$	−5.56709e9	+	5.54657e10i	−0.125423	+	1.24961i
$460$	5.28704e9			0.118081
$461$			1.73061e10i			0.383173i	0.981476	+	0.191586i	$0.0613632\pi$
$461$			1.73061e10i			0.383173i	−0.981476	+	0.191586i	$0.938637\pi$
$462$	−6.48937e7	−	1.21589e8i	−0.00142441	−	0.00266886i
$463$	−3.11536e10			−0.677930			−0.338965	−	0.940799i	$-0.610077\pi$
$463$	−3.11536e10			−0.677930			−0.338965	+	0.940799i	$0.610077\pi$
$464$			2.19367e9i			0.0473260i
$465$	4.86075e10	−	2.59425e10i	1.03966	−	0.554881i
$466$	−9.57039e8			−0.0202949
$467$			4.46334e10i			0.938410i	0.883089	+	0.469205i	$0.155459\pi$
$467$			4.46334e10i			0.938410i	−0.883089	+	0.469205i	$0.844541\pi$
$468$	−4.03114e10	+	6.01686e10i	−0.840319	+	1.25426i
$469$	7.41846e9			0.153328
$470$		−	1.30331e9i		−	0.0267088i
$471$	3.17107e10	+	5.94151e10i	0.644351	+	1.20730i
$472$	3.63130e9			0.0731634
$473$		−	2.30290e10i		−	0.460077i
$474$	2.32458e9	−	1.24066e9i	0.0460502	−	0.0245776i
$475$	−2.42047e9			−0.0475472
$476$		−	2.23030e10i		−	0.434445i
$477$	−7.98983e10	−	5.35298e10i	−1.54335	−	1.03400i
$478$	1.67065e9			0.0320018
$479$		−	2.84370e10i		−	0.540184i	−0.962835	−	0.270092i	$-0.912946\pi$
$479$		−	2.84370e10i		−	0.540184i	0.962835	−	0.270092i	$-0.0870541\pi$
$480$	2.25740e9	+	4.22961e9i	0.0425250	+	0.0796774i
$481$	−2.05326e10			−0.383588
$482$			8.97012e8i			0.0166192i
$483$	1.88899e9	−	1.00818e9i	0.0347090	−	0.0185247i
$484$	−4.98453e9			−0.0908327
$485$		−	9.02308e10i		−	1.63075i
$486$	−1.24658e9	−	1.02953e9i	−0.0223448	−	0.0184541i
$487$	−8.77522e10			−1.56006			−0.780031	−	0.625741i	$-0.784797\pi$
$487$	−8.77522e10			−1.56006			−0.780031	+	0.625741i	$0.784797\pi$
$488$		−	1.56995e9i		−	0.0276826i
$489$	4.87793e9	+	9.13960e9i	0.0853101	+	0.159842i
$490$	1.52918e9			0.0265262
$491$		−	4.84047e10i		−	0.832841i	−0.909172	−	0.416420i	$-0.863285\pi$
$491$		−	4.84047e10i		−	0.832841i	0.909172	−	0.416420i	$-0.136715\pi$
$492$	−1.75188e10	+	9.35006e9i	−0.298982	+	0.159571i
$493$	−3.51992e9			−0.0595861
$494$			1.52005e9i			0.0255241i
$495$	1.04784e10	−	1.56400e10i	0.174532	−	0.260506i
$496$	6.84103e10			1.13030
$497$		−	9.22129e9i		−	0.151135i
$498$	−1.35732e9	−	2.54317e9i	−0.0220682	−	0.0413483i
$499$	6.67276e10			1.07623			0.538113	−	0.842873i	$-0.319137\pi$
$499$	6.67276e10			1.07623			0.538113	+	0.842873i	$0.319137\pi$
$500$			5.96469e10i			0.954351i
$501$	−1.42284e10	+	7.59391e9i	−0.225843	+	0.120535i
$502$	1.15039e8			0.00181147
$503$			4.41867e10i			0.690271i	0.938553	+	0.345136i	$0.112167\pi$
$503$			4.41867e10i			0.690271i	−0.938553	+	0.345136i	$0.887833\pi$
$504$	1.07524e9	+	7.20382e8i	0.0166641	+	0.0111645i
$505$	−6.10226e10			−0.938264
$506$			6.50914e7i			0.000992936i
$507$	−3.99195e10	−	7.47956e10i	−0.604161	−	1.13199i
$508$	9.46479e10			1.42120
$509$			1.51164e10i			0.225204i	0.993640	+	0.112602i	$0.0359186\pi$
$509$			1.51164e10i			0.225204i	−0.993640	+	0.112602i	$0.964081\pi$
$510$	−2.25908e9	+	1.20570e9i	−0.0333926	+	0.0178221i
$511$	−6.91016e9			−0.101346
$512$			9.92405e9i			0.144414i
$513$	4.01678e10	+	4.03165e9i	0.579975	+	0.0582121i
$514$	2.61486e9			0.0374625
$515$		−	5.19548e10i		−	0.738579i
$516$	5.08913e10	+	9.53530e10i	0.717868	+	1.34504i
$517$	−1.90895e10			−0.267197
$518$			1.83386e8i			0.00254711i
$519$	−8.16065e10	+	4.35545e10i	−1.12475	+	0.600294i
$520$	−6.65661e9			−0.0910416
$521$		−	3.51670e8i		−	0.00477292i	−0.999997	−	0.00238646i	$-0.999240\pi$
$521$		−	3.51670e8i		−	0.00477292i	0.999997	−	0.00238646i	$-0.000759635\pi$
$522$	5.68224e7	−	8.48129e7i	0.000765311	−	0.00114230i
$523$	1.15691e10			0.154629			0.0773146	−	0.997007i	$-0.475365\pi$
$523$	1.15691e10			0.154629			0.0773146	+	0.997007i	$0.475365\pi$
$524$		−	1.16026e11i		−	1.53897i
$525$	−1.01020e9	−	1.89278e9i	−0.0132975	−	0.0249151i
$526$	3.49160e9			0.0456122
$527$			1.09770e11i			1.42311i
$528$	2.06214e10	−	1.10059e10i	0.265327	−	0.141609i
$529$	7.72997e10			0.987087
$530$		−	4.41783e9i		−	0.0559893i
$531$	8.34087e10	+	5.58816e10i	1.04914	+	0.702896i
$532$	−1.61517e10			−0.201637
$533$		−	4.13629e10i		−	0.512509i
$534$	1.53432e8	+	2.87480e8i	0.00188691	+	0.00353543i
$535$	9.05312e10			1.10505
$536$		−	2.11777e9i		−	0.0256578i
$537$	4.39961e10	−	2.34813e10i	0.529074	−	0.282374i
$538$	3.18131e9			0.0379732
$539$		−	2.23979e10i		−	0.265370i
$540$	−8.82399e9	+	8.79146e10i	−0.103774	+	1.03392i
$541$	1.29152e11			1.50770			0.753848	−	0.657049i	$-0.228196\pi$
$541$	1.29152e11			1.50770			0.753848	+	0.657049i	$0.228196\pi$
$542$		−	1.39787e9i		−	0.0161983i
$543$	−4.89528e9	−	9.17210e9i	−0.0563090	−	0.105504i
$544$	−9.55168e9			−0.109065
$545$			1.09754e11i			1.24404i
$546$	−1.18866e9	+	6.34406e8i	−0.0133748	+	0.00713833i
$547$	−6.65377e10			−0.743222			−0.371611	−	0.928388i	$-0.621195\pi$
$547$	−6.65377e10			−0.743222			−0.371611	+	0.928388i	$0.621195\pi$
$548$			1.91091e10i			0.211894i
$549$	2.41598e10	−	3.60608e10i	0.265953	−	0.396960i
$550$	6.52218e7			0.000712758
$551$			2.54910e9i			0.0276554i
$552$	−2.87809e8	−	5.39256e8i	−0.00309990	−	0.00580817i
$553$	−5.83188e10			−0.623603
$554$		−	7.60124e8i		−	0.00806948i
$555$	−2.20990e10	+	1.17945e10i	−0.232917	+	0.124311i
$556$	−7.28709e9			−0.0762526
$557$			3.91079e10i			0.406297i	0.979148	+	0.203149i	$0.0651175\pi$
$557$			3.91079e10i			0.406297i	−0.979148	+	0.203149i	$0.934883\pi$
$558$	−2.64492e9	−	1.77202e9i	−0.0272819	−	0.0182782i
$559$	−2.25133e11			−2.30564
$560$		−	3.53211e10i		−	0.359155i
$561$	1.76599e10	+	3.30886e10i	0.178294	+	0.334062i
$562$	5.34633e9			0.0535933
$563$			4.37934e10i			0.435889i	0.975961	+	0.217944i	$0.0699351\pi$
$563$			4.37934e10i			0.435889i	−0.975961	+	0.217944i	$0.930065\pi$
$564$	7.90411e10	−	4.21854e10i	0.781154	−	0.416913i
$565$	1.79075e11			1.75728
$566$			2.13840e9i			0.0208364i
$567$	1.36117e10	+	3.30934e10i	0.131698	+	0.320191i
$568$	−2.63243e9			−0.0252908
$569$		−	6.48473e10i		−	0.618647i	−0.950957	−	0.309324i	$-0.899897\pi$
$569$		−	6.48473e10i		−	0.618647i	0.950957	−	0.309324i	$-0.100103\pi$
$570$	8.73161e8	+	1.63601e9i	0.00827170	+	0.0154984i
$571$	−3.05163e10			−0.287070			−0.143535	−	0.989645i	$-0.545847\pi$
$571$	−3.05163e10			−0.287070			−0.143535	+	0.989645i	$0.545847\pi$
$572$			4.87291e10i			0.455202i
$573$	8.87293e10	−	4.73561e10i	0.823092	−	0.439296i
$574$	−3.69431e8			−0.00340318
$575$			1.01328e9i			0.00926953i
$576$	−6.09595e10	+	9.09879e10i	−0.553798	+	0.826597i
$577$	−1.20546e11			−1.08755			−0.543773	−	0.839232i	$-0.683005\pi$
$577$	−1.20546e11			−1.08755			−0.543773	+	0.839232i	$0.683005\pi$
$578$		−	1.86713e9i		−	0.0167287i
$579$	−8.14203e10	−	1.52554e11i	−0.724467	−	1.35741i
$580$	−5.57917e9			−0.0493012
$581$			6.38027e10i			0.559931i
$582$	−4.59965e9	+	2.45490e9i	−0.0400897	+	0.0213964i
$583$	−6.47077e10			−0.560121
$584$			1.97266e9i			0.0169591i
$585$	−1.52898e11	−	1.02438e11i	−1.30551	−	0.874655i
$586$	−1.68133e9			−0.0142581
$587$		−	1.51686e11i		−	1.27759i	−0.769375	−	0.638797i	$-0.779432\pi$
$587$		−	1.51686e11i		−	1.27759i	0.769375	−	0.638797i	$-0.220568\pi$
$588$	4.94966e10	+	9.27398e10i	0.414062	+	0.775813i
$589$	7.94944e10			0.660504
$590$			4.61192e9i			0.0380604i
$591$	6.55423e9	−	3.49809e9i	0.0537245	−	0.0286735i
$592$	−3.11022e10			−0.253223
$593$			6.17836e10i			0.499637i	0.968293	+	0.249819i	$0.0803710\pi$
$593$			6.17836e10i			0.499637i	−0.968293	+	0.249819i	$0.919629\pi$
$594$	−1.08236e9	−	1.08637e8i	−0.00869413	−	0.000872630i
$595$	5.66755e10			0.452197
$596$		−	1.70997e11i		−	1.35520i
$597$	1.04105e7	+	1.95058e7i	8.19551e−5	+	0.000153556i
$598$	6.36338e8			0.00497603
$599$		−	8.72409e10i		−	0.677661i	−0.940847	−	0.338831i	$-0.889969\pi$
$599$		−	8.72409e10i		−	0.677661i	0.940847	−	0.338831i	$-0.110031\pi$
$600$	−5.40337e8	+	2.88385e8i	−0.00416927	+	0.00222520i
$601$	2.06867e11			1.58560			0.792800	−	0.609482i	$-0.208622\pi$
$601$	2.06867e11			1.58560			0.792800	+	0.609482i	$0.208622\pi$
$602$			2.01077e9i			0.0153100i
$603$	3.25901e10	−	4.86439e10i	0.246500	−	0.367925i
$604$	−2.82052e9			−0.0211925
$605$		−	1.26665e10i		−	0.0945442i
$606$	1.66024e9	+	3.11072e9i	0.0123106	+	0.0230659i
$607$	−7.90355e10			−0.582193			−0.291097	−	0.956694i	$-0.594020\pi$
$607$	−7.90355e10			−0.582193			−0.291097	+	0.956694i	$0.594020\pi$
$608$			6.91726e9i			0.0506197i
$609$	−1.99337e9	+	1.06389e9i	−0.0144917	+	0.00773440i
$610$	1.99391e9			0.0144008
$611$			1.86620e11i			1.33904i
$612$	−1.46244e11	−	9.79794e10i	−1.04249	−	0.698440i
$613$	2.14208e11			1.51703			0.758513	−	0.651658i	$-0.225926\pi$
$613$	2.14208e11			1.51703			0.758513	+	0.651658i	$0.225926\pi$
$614$		−	1.74682e9i		−	0.0122907i
$615$	−2.37600e10	−	4.45183e10i	−0.166091	−	0.311199i
$616$	8.70809e8			0.00604784
$617$			1.13314e11i			0.781884i	0.920415	+	0.390942i	$0.127851\pi$
$617$			1.13314e11i			0.781884i	−0.920415	+	0.390942i	$0.872149\pi$
$618$	−2.64848e9	+	1.41353e9i	−0.0181569	+	0.00969060i
$619$	−2.75385e11			−1.87576			−0.937880	−	0.346961i	$-0.887214\pi$
$619$	−2.75385e11			−1.87576			−0.937880	+	0.346961i	$0.887214\pi$
$620$			1.73988e11i			1.17748i
$621$	1.68777e9	−	1.68154e10i	0.0113487	−	0.113069i
$622$	−5.65935e9			−0.0378099
$623$		−	7.21226e9i		−	0.0478762i
$624$	−1.07595e11	−	2.01596e11i	−0.709663	−	1.32967i
$625$	−1.64019e11			−1.07492
$626$		−	6.19790e8i		−	0.00403596i
$627$	2.39626e10	−	1.27892e10i	0.155047	−	0.0827507i
$628$	−2.12674e11			−1.36734
$629$		−	4.99059e10i		−	0.318823i
$630$	−9.14919e8	+	1.36560e9i	−0.00580792	+	0.00866887i
$631$	3.40330e10			0.214676			0.107338	−	0.994223i	$-0.465767\pi$
$631$	3.40330e10			0.214676			0.107338	+	0.994223i	$0.465767\pi$
$632$			1.66484e10i			0.104353i
$633$	−9.37303e10	−	1.75619e11i	−0.583801	−	1.09385i
$634$	5.56240e9			0.0344275
$635$			2.40516e11i			1.47927i
$636$	2.67926e11	−	1.42996e11i	1.63752	−	0.873968i
$637$	−2.18963e11			−1.32988
$638$		−	6.86879e7i		−	0.000414570i
$639$	−6.04653e10	−	4.05101e10i	−0.362662	−	0.242974i
$640$	−2.01834e10			−0.120302
$641$			2.06072e11i			1.22064i	0.792155	+	0.610320i	$0.208959\pi$
$641$			2.06072e11i			1.22064i	−0.792155	+	0.610320i	$0.791041\pi$
$642$	−2.46307e9	−	4.61497e9i	−0.0144990	−	0.0271662i
$643$	1.22928e11			0.719130			0.359565	−	0.933120i	$-0.382925\pi$
$643$	1.22928e11			0.719130			0.359565	+	0.933120i	$0.382925\pi$
$644$			6.76156e9i			0.0393100i
$645$	−2.42308e11	+	1.29323e11i	−1.40000	+	0.747200i
$646$	−3.69458e9			−0.0212146
$647$		−	9.90239e10i		−	0.565097i	−0.959253	−	0.282548i	$-0.908820\pi$
$647$		−	9.90239e10i		−	0.565097i	0.959253	−	0.282548i	$-0.0911797\pi$
$648$	9.44728e9	−	3.88577e9i	0.0535805	−	0.0220382i
$649$	6.75506e10			0.380759
$650$		−	6.37613e8i		−	0.00357193i
$651$	3.31777e10	+	6.21637e10i	0.184723	+	0.346109i
$652$	−3.27147e10			−0.181031
$653$			2.36684e11i			1.30172i	0.759199	+	0.650858i	$0.225591\pi$
$653$			2.36684e11i			1.30172i	−0.759199	+	0.650858i	$0.774409\pi$
$654$	5.59488e9	−	2.98607e9i	0.0305830	−	0.0163226i
$655$	2.94842e11			1.60186
$656$		−	6.26551e10i		−	0.338330i
$657$	−3.03571e10	+	4.53109e10i	−0.162929	+	0.243187i
$658$	1.66679e9			0.00889154
$659$		−	1.89365e11i		−	1.00405i	−0.864852	−	0.502027i	$-0.832588\pi$
$659$		−	1.89365e11i		−	1.00405i	0.864852	−	0.502027i	$-0.167412\pi$
$660$	2.79914e10	+	5.24464e10i	0.147519	+	0.276401i
$661$	−1.69454e10			−0.0887658			−0.0443829	−	0.999015i	$-0.514132\pi$
$661$	−1.69454e10			−0.0887658			−0.0443829	+	0.999015i	$0.514132\pi$
$662$			5.62753e8i			0.00293013i
$663$	3.23477e11	−	1.72644e11i	1.67413	−	0.893506i
$664$	1.82139e10			0.0936983
$665$		−	4.10440e10i		−	0.209876i
$666$	1.20249e9	+	8.05637e8i	0.00611201	+	0.00409489i
$667$	1.06713e9			0.00539155
$668$		−	5.09299e10i		−	0.255780i
$669$	1.22619e11	+	2.29747e11i	0.612144	+	1.14695i
$670$	2.68967e9			0.0133475
$671$		−	2.92048e10i		−	0.144067i
$672$	−5.40922e9	+	2.88698e9i	−0.0265251	+	0.0141568i
$673$	1.86567e11			0.909442			0.454721	−	0.890634i	$-0.349739\pi$
$673$	1.86567e11			0.909442			0.454721	+	0.890634i	$0.349739\pi$
$674$		−	5.89939e9i		−	0.0285869i
$675$	−1.68491e10	−	1.69115e9i	−0.0811638	−	0.00814642i
$676$	2.67727e11			1.28205
$677$		−	3.01974e11i		−	1.43752i	−0.695258	−	0.718760i	$-0.744710\pi$
$677$		−	3.01974e11i		−	1.43752i	0.695258	−	0.718760i	$-0.255290\pi$
$678$	−4.87208e9	−	9.12863e9i	−0.0230566	−	0.0432003i
$679$	1.15396e11			0.542887
$680$		−	1.61793e10i		−	0.0756701i
$681$	3.49076e11	−	1.86307e11i	1.62305	−	0.866245i
$682$	−2.14205e9			−0.00990131
$683$			1.83659e11i			0.843976i	0.906601	+	0.421988i	$0.138668\pi$
$683$			1.83659e11i			0.843976i	−0.906601	+	0.421988i	$0.861332\pi$
$684$	−7.09560e10	+	1.05909e11i	−0.324164	+	0.483846i
$685$	−4.85594e10			−0.220552
$686$			4.17767e9i			0.0188642i
$687$	4.36256e10	+	8.17397e10i	0.195846	+	0.366949i
$688$	−3.41024e11			−1.52206
$689$			6.32587e11i			2.80701i
$690$	6.84881e8	−	3.65531e8i	0.00302148	−	0.00161260i
$691$	1.81205e11			0.794799			0.397400	−	0.917646i	$-0.369913\pi$
$691$	1.81205e11			0.794799			0.397400	+	0.917646i	$0.369913\pi$
$692$		−	2.92106e11i		−	1.27385i
$693$	2.00020e10	+	1.34008e10i	0.0867240	+	0.0581028i
$694$	−7.99880e9			−0.0344816
$695$		−	1.85177e10i		−	0.0793684i
$696$	3.03711e8	+	5.69052e8i	0.00129427	+	0.00242502i
$697$	1.00535e11			0.425977
$698$		−	8.43203e9i		−	0.0355231i
$699$	1.47492e11	−	7.87187e10i	0.617818	−	0.329738i
$700$	6.77511e9			0.0282179
$701$			2.12324e10i			0.0879280i	0.999033	+	0.0439640i	$0.0139987\pi$
$701$			2.12324e10i			0.0879280i	−0.999033	+	0.0439640i	$0.986001\pi$
$702$	−1.06204e9	+	1.05812e10i	−0.00437312	+	0.0435700i
$703$	−3.61415e10			−0.147974
$704$			7.36889e10i			0.299993i
$705$	1.07200e11	+	2.00856e11i	0.433948	+	0.813072i
$706$	7.44113e8			0.00299516
$707$		−	7.80414e10i		−	0.312354i
$708$	−2.79698e11	+	1.49279e11i	−1.11316	+	0.594107i
$709$	−4.90836e10			−0.194246			−0.0971228	−	0.995272i	$-0.530964\pi$
$709$	−4.90836e10			−0.194246			−0.0971228	+	0.995272i	$0.530964\pi$
$710$		−	3.34331e9i		−	0.0131566i
$711$	−2.56201e11	+	3.82405e11i	−1.00254	+	1.49639i
$712$	−2.05891e9			−0.00801155
$713$		−	3.32787e10i		−	0.128768i
$714$	−1.54196e9	−	2.88912e9i	−0.00593310	−	0.0111166i
$715$	−1.23829e11			−0.473802
$716$			1.57482e11i			0.599209i
$717$	−2.57469e11	+	1.37415e11i	−0.974200	+	0.519944i
$718$	1.01623e10			0.0382378
$719$		−	4.27110e11i		−	1.59818i	−0.601214	−	0.799088i	$-0.705316\pi$
$719$		−	4.27110e11i		−	1.59818i	0.601214	−	0.799088i	$-0.294684\pi$
$720$	−2.31605e11	−	1.55169e11i	−0.861824	−	0.577399i
$721$	6.64447e10			0.245878
$722$		−	5.19936e9i		−	0.0191338i
$723$	−7.37813e10	−	1.38241e11i	−0.270018	−	0.505923i
$724$	3.28311e10			0.119490
$725$		−	1.06927e9i		−	0.00387020i
$726$	−6.45694e8	+	3.44616e8i	−0.00232424	+	0.00124048i
$727$	−3.02187e11			−1.08178			−0.540889	−	0.841094i	$-0.681912\pi$
$727$	−3.02187e11			−1.08178			−0.540889	+	0.841094i	$0.681912\pi$
$728$		−	8.51309e9i		−	0.0303083i
$729$	2.76796e11	+	5.61295e10i	0.980053	+	0.198738i
$730$	−2.50538e9			−0.00882230
$731$		−	5.47201e11i		−	1.91636i
$732$	6.45390e10	+	1.20924e11i	0.224790	+	0.421181i
$733$	2.32545e11			0.805547			0.402773	−	0.915300i	$-0.368046\pi$
$733$	2.32545e11			0.805547			0.402773	+	0.915300i	$0.368046\pi$
$734$			1.23758e10i			0.0426371i
$735$	−2.35667e11	+	1.25779e11i	−0.807513	+	0.430981i
$736$	2.89577e9			0.00986853
$737$		−	3.93955e10i		−	0.133529i
$738$	−1.62295e9	+	2.42241e9i	−0.00547116	+	0.00816623i
$739$	−7.16663e10			−0.240291			−0.120145	−	0.992756i	$-0.538336\pi$
$739$	−7.16663e10			−0.240291			−0.120145	+	0.992756i	$0.538336\pi$
$740$		−	7.91022e10i		−	0.263792i
$741$	−1.25028e11	−	2.34260e11i	−0.414699	−	0.777006i
$742$	5.64993e9			0.0186392
$743$		−	5.62589e11i		−	1.84602i	−0.384780	−	0.923008i	$-0.625723\pi$
$743$		−	5.62589e11i		−	1.84602i	0.384780	−	0.923008i	$-0.374277\pi$
$744$	1.77461e10	−	9.47132e9i	0.0579176	−	0.0309114i
$745$	4.34532e11			1.41058
$746$		−	5.52134e9i		−	0.0178274i
$747$	4.18363e11	+	2.80292e11i	1.34360	+	0.900179i
$748$	−1.18439e11			−0.378346
$749$			1.15780e11i			0.367879i
$750$	4.12382e9	+	7.72664e9i	0.0130333	+	0.0244200i
$751$	−5.17774e11			−1.62772			−0.813862	−	0.581058i	$-0.802639\pi$
$751$	−5.17774e11			−1.62772			−0.813862	+	0.581058i	$0.802639\pi$
$752$			2.82686e11i			0.883960i
$753$	−1.77290e10	+	9.46224e9i	−0.0551449	+	0.0294316i
$754$	−6.71498e8			−0.00207759
$755$		−	7.16740e9i		−	0.0220584i
$756$	−1.12433e11	−	1.12849e10i	−0.344198	−	0.0345472i
$757$	6.69784e10			0.203963			0.101981	−	0.994786i	$-0.467482\pi$
$757$	6.69784e10			0.203963			0.101981	+	0.994786i	$0.467482\pi$
$758$			9.69604e9i			0.0293709i
$759$	−5.35392e9	−	1.00314e10i	−0.0161326	−	0.0302271i
$760$	−1.17169e10			−0.0351205
$761$			4.30349e11i			1.28316i	0.767054	+	0.641582i	$0.221722\pi$
$761$			4.30349e11i			1.28316i	−0.767054	+	0.641582i	$0.778278\pi$
$762$	1.22607e10	−	6.54368e9i	0.0363659	−	0.0194090i
$763$	−1.40364e11			−0.414149
$764$			3.17602e11i			0.932202i
$765$	2.48982e11	−	3.71629e11i	0.726979	−	1.08508i
$766$	−3.76121e9			−0.0109248
$767$		−	6.60380e11i		−	1.90815i
$768$	−1.62431e11	−	3.04341e11i	−0.466900	−	0.874814i
$769$	−4.30496e11			−1.23102			−0.615509	−	0.788130i	$-0.711049\pi$
$769$	−4.30496e11			−1.23102			−0.615509	+	0.788130i	$0.711049\pi$
$770$			1.10597e9i			0.00314616i
$771$	−4.02984e11	+	2.15078e11i	−1.14044	+	0.608667i
$772$	5.46060e11			1.53734
$773$			2.25688e11i			0.632108i	0.948741	+	0.316054i	$0.102358\pi$
$773$			2.25688e11i			0.632108i	−0.948741	+	0.316054i	$0.897642\pi$
$774$	1.31849e10	+	8.83352e9i	0.0367377	+	0.0246133i
$775$	−3.33454e10			−0.0924334
$776$		−	3.29423e10i		−	0.0908462i
$777$	−1.50840e10	−	2.82622e10i	−0.0413839	−	0.0775394i
$778$	−1.02104e9			−0.00278691
$779$		−	7.28068e10i		−	0.197707i
$780$	5.12720e11	−	2.73646e11i	1.38517	−	0.739282i
$781$	−4.89693e10			−0.131619
$782$			1.54666e9i			0.00413588i
$783$	−1.78102e9	+	1.77446e10i	−0.00473830	+	0.0472083i
$784$	−3.31678e11			−0.877916
$785$		−	5.40438e11i		−	1.42321i
$786$	−8.02172e9	−	1.50300e10i	−0.0210173	−	0.0393794i
$787$	1.20189e11			0.313304			0.156652	−	0.987654i	$-0.449930\pi$
$787$	1.20189e11			0.313304			0.156652	+	0.987654i	$0.449930\pi$
$788$			2.34606e10i			0.0608462i
$789$	−5.38101e11	+	2.87192e11i	−1.38853	+	0.741079i
$790$	−2.11443e10			−0.0542857
$791$			2.29018e11i			0.585011i
$792$	3.82556e9	−	5.71001e9i	0.00972287	−	0.0145123i
$793$	−2.85508e11			−0.721980
$794$			8.42542e9i			0.0211987i
$795$	3.63376e11	+	6.80845e11i	0.909679	+	1.70443i
$796$	−6.98202e7			−0.000173912
$797$		−	4.17483e11i		−	1.03468i	−0.855781	−	0.517339i	$-0.826923\pi$
$797$		−	4.17483e11i		−	1.03468i	0.855781	−	0.517339i	$-0.173077\pi$
$798$	−2.09228e9	+	1.11668e9i	−0.00515951	+	0.00275370i
$799$	−4.53592e11			−1.11296
$800$		−	2.90157e9i		−	0.00708391i
$801$	−4.72918e10	−	3.16843e10i	−0.114883	−	0.0769686i
$802$	−1.97649e10			−0.0477746
$803$			3.66962e10i			0.0882589i
$804$	8.70592e10	+	1.63119e11i	0.208349	+	0.390375i
$805$	−1.71822e10			−0.0409163
$806$			2.09409e10i			0.0496197i
$807$	−4.90282e11	+	2.61670e11i	−1.15598	+	0.616965i
$808$	−2.22787e10			−0.0522690
$809$		−	4.05365e11i		−	0.946351i	−0.880968	−	0.473176i	$-0.843108\pi$
$809$		−	4.05365e11i		−	0.946351i	0.880968	−	0.473176i	$-0.156892\pi$
$810$	4.93511e9	+	1.19985e10i	0.0114645	+	0.0278732i
$811$	3.83222e10			0.0885865			0.0442932	−	0.999019i	$-0.485896\pi$
$811$	3.83222e10			0.0885865			0.0442932	+	0.999019i	$0.485896\pi$
$812$		−	7.13516e9i		−	0.0164127i
$813$	1.14978e11	+	2.15430e11i	0.263180	+	0.493111i
$814$	9.73867e8			0.00221821
$815$		−	8.31335e10i		−	0.188428i
$816$	4.89992e11	−	2.61516e11i	1.10517	−	0.589844i
$817$	−3.96279e11			−0.889432
$818$		−	8.93032e9i		−	0.0199459i
$819$	1.31007e11	−	1.95540e11i	0.291178	−	0.434611i
$820$	1.59351e11			0.352451
$821$			2.97651e11i			0.655140i	0.944827	+	0.327570i	$0.106230\pi$
$821$			2.97651e11i			0.655140i	−0.944827	+	0.327570i	$0.893770\pi$
$822$	1.32115e9	+	2.47539e9i	0.00289378	+	0.00542196i
$823$	9.20530e10			0.200650			0.100325	−	0.994955i	$-0.468012\pi$
$823$	9.20530e10			0.200650			0.100325	+	0.994955i	$0.468012\pi$
$824$		−	1.89681e10i		−	0.0411449i
$825$	−1.00515e10	+	5.36464e9i	−0.0216978	+	0.0115804i
$826$	−5.89815e9			−0.0126706
$827$			3.95331e11i			0.845159i	0.906326	+	0.422580i	$0.138875\pi$
$827$			3.95331e11i			0.845159i	−0.906326	+	0.422580i	$0.861125\pi$
$828$	4.43365e10	+	2.97043e10i	0.0943278	+	0.0631972i
$829$	8.27992e11			1.75311			0.876553	−	0.481305i	$-0.159837\pi$
$829$	8.27992e11			1.75311			0.876553	+	0.481305i	$0.159837\pi$
$830$			2.31326e10i			0.0487429i
$831$	6.25220e10	+	1.17145e11i	0.131108	+	0.245652i
$832$	7.20387e11			1.50339
$833$		−	5.32204e11i		−	1.10535i
$834$	−9.43967e8	+	5.03809e8i	−0.00195116	+	0.00104136i
$835$	1.29421e11			0.266232
$836$			8.57728e10i			0.175600i
$837$	5.53369e11	+	5.55417e10i	1.12749	+	0.113166i
$838$	6.08707e9			0.0123433
$839$			1.83018e11i			0.369357i	0.982799	+	0.184679i	$0.0591244\pi$
$839$			1.83018e11i			0.369357i	−0.982799	+	0.184679i	$0.940876\pi$
$840$	−4.89017e9	−	9.16252e9i	−0.00982215	−	0.0184034i
$841$	4.99120e11			0.997749
$842$			2.31413e10i			0.0460404i
$843$	−8.23939e11	+	4.39748e11i	−1.63149	+	0.870750i
$844$	6.28619e11			1.23885
$845$			6.80338e11i			1.33444i
$846$	7.32238e9	−	1.09294e10i	0.0142946	−	0.0213360i
$847$	1.61991e10			0.0314744
$848$			9.58222e11i			1.85303i
$849$	−1.75888e11	−	3.29555e11i	−0.338537	−	0.634304i
$850$	1.54976e9			0.00296885
$851$			1.51299e10i			0.0288481i
$852$	2.02761e11	−	1.08216e11i	0.384791	−	0.205369i
$853$	−4.43216e11			−0.837182			−0.418591	−	0.908175i	$-0.637476\pi$
$853$	−4.43216e11			−0.837182			−0.418591	+	0.908175i	$0.637476\pi$
$854$			2.55000e9i			0.00479412i
$855$	−2.69131e11	−	1.80311e11i	−0.503616	−	0.337409i
$856$	3.30520e10			0.0615605
$857$		−	2.91913e11i		−	0.541166i	−0.962697	−	0.270583i	$-0.912784\pi$
$857$		−	2.91913e11i		−	0.541166i	0.962697	−	0.270583i	$-0.0872165\pi$
$858$	3.36899e9	+	6.31235e9i	0.00621656	+	0.0116477i
$859$	1.85769e11			0.341194			0.170597	−	0.985341i	$-0.445430\pi$
$859$	1.85769e11			0.341194			0.170597	+	0.985341i	$0.445430\pi$
$860$		−	8.67328e11i		−	1.58559i
$861$	5.69341e10	−	3.03865e10i	0.103600	−	0.0552928i
$862$	−2.40956e10			−0.0436425
$863$			4.04477e11i			0.729207i	0.931163	+	0.364604i	$0.118796\pi$
$863$			4.04477e11i			0.729207i	−0.931163	+	0.364604i	$0.881204\pi$
$864$	−4.83300e9	+	4.81518e10i	−0.00867284	+	0.0864087i
$865$	7.42290e11			1.32590
$866$		−	1.63008e10i		−	0.0289826i
$867$	1.53575e11	+	2.87748e11i	0.271797	+	0.509256i
$868$	−2.22512e11			−0.391990
$869$			3.09700e11i			0.543078i
$870$	−7.22723e8	+	3.85728e8i	−0.00126152	+	0.000673293i
$871$	−3.85133e11			−0.669173
$872$			4.00700e10i			0.0693032i
$873$	5.06945e11	−	7.56664e11i	0.872778	−	1.30270i
$874$	1.12008e9			0.00191957
$875$		−	1.93845e11i		−	0.330691i
$876$	−8.10940e10	−	1.51943e11i	−0.137712	−	0.258026i
$877$	5.64450e11			0.954173			0.477086	−	0.878856i	$-0.341693\pi$
$877$	5.64450e11			0.954173			0.477086	+	0.878856i	$0.341693\pi$
$878$		−	1.29216e10i		−	0.0217440i
$879$	2.59115e11	−	1.38293e11i	0.434047	−	0.231657i
$880$	−1.87571e11			−0.312778
$881$		−	3.37942e11i		−	0.560969i	−0.959859	−	0.280484i	$-0.909505\pi$
$881$		−	3.37942e11i		−	0.560969i	0.959859	−	0.280484i	$-0.0904951\pi$
$882$	1.28235e10	+	8.59144e9i	0.0211901	+	0.0141968i
$883$	−1.07671e11			−0.177115			−0.0885574	−	0.996071i	$-0.528226\pi$
$883$	−1.07671e11			−0.177115			−0.0885574	+	0.996071i	$0.528226\pi$
$884$			1.15787e12i			1.89605i
$885$	−3.79341e11	−	7.10757e11i	−0.618382	−	1.15864i
$886$	3.30845e10			0.0536895
$887$		−	6.80937e11i		−	1.10005i	−0.835148	−	0.550025i	$-0.814618\pi$
$887$		−	6.80937e11i		−	1.10005i	0.835148	−	0.550025i	$-0.185382\pi$
$888$	−8.06810e9	+	4.30606e9i	−0.0129754	+	0.00692514i
$889$	−3.07594e11			−0.492460
$890$		−	2.61491e9i		−	0.00416770i
$891$	1.75742e11	−	7.22844e10i	0.278845	−	0.114692i
$892$	−8.22367e11			−1.29899
$893$			3.28488e11i			0.516551i
$894$	−1.18223e10	−	2.21510e10i	−0.0185076	−	0.0346771i
$895$	−4.00187e11			−0.623693
$896$		−	2.58124e10i		−	0.0400495i
$897$	−9.80680e10	+	5.23403e10i	−0.151481	+	0.0808474i
$898$	−1.26238e10			−0.0194127
$899$			3.51175e10i			0.0537631i
$900$	2.97638e10	−	4.44253e10i	0.0453647	−	0.0677112i
$901$	−1.53754e12			−2.33307
$902$			1.96185e9i			0.00296373i
$903$	−1.65390e11	−	3.09886e11i	−0.248748	−	0.466069i
$904$	6.53785e10			0.0978951
$905$			8.34291e10i			0.124372i
$906$	−3.65369e8	+	1.95003e8i	−0.000542274	+	0.000289419i
$907$	6.14742e11			0.908372			0.454186	−	0.890907i	$-0.349930\pi$
$907$	6.14742e11			0.908372			0.454186	+	0.890907i	$0.349930\pi$
$908$			1.24950e12i			1.83820i
$909$	−5.11728e11	−	3.42844e11i	−0.749521	−	0.502159i
$910$	1.08120e10			0.0157667
$911$		−	5.19358e11i		−	0.754038i	−0.926206	−	0.377019i	$-0.876949\pi$
$911$		−	5.19358e11i		−	0.754038i	0.926206	−	0.377019i	$-0.123051\pi$
$912$	−1.89388e11	−	3.54849e11i	−0.273762	−	0.512937i
$913$	3.38822e11			0.487628
$914$		−	3.83073e10i		−	0.0548905i
$915$	−3.07288e11	+	1.64004e11i	−0.438391	+	0.233975i
$916$	−2.92583e11			−0.415592
$917$			3.77071e11i			0.533268i
$918$	−2.57184e10	−	2.58135e9i	−0.0362137	−	0.00363477i
$919$	3.76611e11			0.527996			0.263998	−	0.964523i	$-0.414959\pi$
$919$	3.76611e11			0.527996			0.263998	+	0.964523i	$0.414959\pi$
$920$			4.90506e9i			0.00684688i
$921$	1.43680e11	+	2.69208e11i	0.199691	+	0.374154i
$922$	−8.02449e9			−0.0111044
$923$			4.78728e11i			0.659602i
$924$	−6.70734e10	+	3.57980e10i	−0.0920157	+	0.0491101i
$925$	1.51602e10			0.0207080
$926$		−	1.44453e10i		−	0.0196464i
$927$	2.91899e11	−	4.35687e11i	0.395288	−	0.590004i
$928$	−3.05577e9			−0.00412030
$929$			1.34697e12i			1.80841i	0.427101	+	0.904204i	$0.359535\pi$
$929$			1.34697e12i			1.80841i	−0.427101	+	0.904204i	$0.640465\pi$
$930$	1.20290e10	+	2.25383e10i	0.0160805	+	0.0301294i
$931$	−3.85419e11			−0.513020
$932$			5.27941e11i			0.699716i
$933$	8.72180e11	−	4.65495e11i	1.15101	−	0.614311i
$934$	−2.06957e10			−0.0271952
$935$		−	3.00973e11i		−	0.393805i
$936$	−5.58215e10	−	3.73989e10i	−0.0727274	−	0.0487255i
$937$	−7.59940e11			−0.985873			−0.492937	−	0.870065i	$-0.664077\pi$
$937$	−7.59940e11			−0.985873			−0.492937	+	0.870065i	$0.664077\pi$
$938$			3.43980e9i			0.00444347i
$939$	5.09792e10	+	9.55177e10i	0.0655738	+	0.122863i
$940$	−7.18956e11			−0.920854
$941$		−	7.21405e11i		−	0.920070i	−0.887901	−	0.460035i	$-0.847837\pi$
$941$		−	7.21405e11i		−	0.920070i	0.887901	−	0.460035i	$-0.152163\pi$
$942$	−2.75497e10	+	1.47036e10i	−0.0349875	+	0.0186733i
$943$	−3.04791e10			−0.0385438
$944$		−	1.00032e12i		−	1.25966i
$945$	2.86769e10	−	2.85712e11i	0.0359588	−	0.358262i
$946$	1.06781e10			0.0133331
$947$		−	3.20479e11i		−	0.398474i	−0.979951	−	0.199237i	$-0.936154\pi$
$947$		−	3.20479e11i		−	0.398474i	0.979951	−	0.199237i	$-0.0638464\pi$
$948$	−6.84399e11	−	1.28233e12i	−0.847376	−	1.58770i
$949$	3.58744e11			0.442303
$950$		−	1.12232e9i		−	0.00137792i
$951$	−8.57239e11	+	4.57521e11i	−1.04804	+	0.559356i
$952$	2.06916e10			0.0251911
$953$		−	6.13488e11i		−	0.743763i	−0.928280	−	0.371882i	$-0.878713\pi$
$953$		−	6.13488e11i		−	0.743763i	0.928280	−	0.371882i	$-0.121287\pi$
$954$	2.48207e10	−	3.70473e10i	0.0299655	−	0.0447263i
$955$	−8.07079e11			−0.970292
$956$		−	9.21597e11i		−	1.10334i
$957$	5.64974e9	+	1.05857e10i	0.00673567	+	0.0126204i
$958$	1.31857e10			0.0156545
$959$		−	6.21023e10i		−	0.0734232i
$960$	7.75343e11	−	4.13811e11i	0.912870	−	0.487212i
$961$	2.42258e11			0.284043
$962$		−	9.52059e9i		−	0.0111164i
$963$	7.59184e11	+	5.08633e11i	0.882758	+	0.591425i
$964$	4.94828e11			0.572989
$965$			1.38763e12i			1.60016i
$966$	4.67475e8	+	8.75890e8i	0.000536846	+	0.00100587i
$967$	9.10858e11			1.04171			0.520853	−	0.853647i	$-0.325614\pi$
$967$	9.10858e11			1.04171			0.520853	+	0.853647i	$0.325614\pi$
$968$		−	4.62440e9i		−	0.00526689i
$969$	5.69383e11	−	3.03888e11i	0.645817	−	0.344682i
$970$	4.18383e10			0.0472593
$971$		−	1.29844e12i		−	1.46065i	−0.683102	−	0.730323i	$-0.739369\pi$
$971$		−	1.29844e12i		−	1.46065i	0.683102	−	0.730323i	$-0.260631\pi$
$972$	−5.67929e11	+	6.87665e11i	−0.636252	+	0.770392i
$973$	2.36821e10			0.0264222
$974$		−	4.06890e10i		−	0.0452107i
$975$	5.24451e10	+	9.82645e10i	0.0580346	+	0.108737i
$976$	−4.32478e11			−0.476612
$977$			9.39096e11i			1.03070i	0.856980	+	0.515349i	$0.172338\pi$
$977$			9.39096e11i			1.03070i	−0.856980	+	0.515349i	$0.827662\pi$
$978$	−4.23786e9	+	2.26180e9i	−0.00463224	+	0.00247229i
$979$	−3.83005e10			−0.0416940
$980$		−	8.43559e11i		−	0.914558i
$981$	−6.16633e11	+	9.20384e11i	−0.665811	+	0.993786i
$982$	2.24443e10			0.0241358
$983$		−	8.21237e10i		−	0.0879538i	−0.999033	−	0.0439769i	$-0.985997\pi$
$983$		−	8.21237e10i		−	0.0879538i	0.999033	−	0.0439769i	$-0.0140028\pi$
$984$	−8.67453e9	−	1.62531e10i	−0.00925264	−	0.0173363i
$985$	−5.96171e10			−0.0633324
$986$		−	1.63212e9i		−	0.00172681i
$987$	−2.56874e11	+	1.37097e11i	−0.270677	+	0.144464i
$988$	8.38521e11			0.880007
$989$			1.65894e11i			0.173399i
$990$	7.25199e9	+	4.85865e9i	0.00754947	+	0.00505795i
$991$	1.37543e12			1.42608			0.713039	−	0.701125i	$-0.247318\pi$
$991$	1.37543e12			1.42608			0.713039	+	0.701125i	$0.247318\pi$
$992$			9.52951e10i			0.0984065i
$993$	−4.62878e10	−	8.67277e10i	−0.0476068	−	0.0891991i
$994$	4.27574e9			0.00437991
$995$		−	1.77425e8i		−	0.000181018i
$996$	−1.40291e12	+	7.48755e11i	−1.42559	+	0.760856i
$997$	−4.03195e11			−0.408070			−0.204035	−	0.978964i	$-0.565406\pi$
$997$	−4.03195e11			−0.408070			−0.204035	+	0.978964i	$0.565406\pi$
$998$			3.09403e10i			0.0311891i
$999$	−2.51585e11	−	2.52516e10i	−0.252594	−	0.0253528i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	33.9.b.a.23.14	yes	26
3.2	odd	2	inner	33.9.b.a.23.13	✓	26

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
33.9.b.a.23.13	✓	26	3.2	odd	2	inner
33.9.b.a.23.14	yes	26	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 33 = 3 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 9 \)
Character orbit:	\([\chi]\)	\(=\)	33.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+0.463681i q^{2} +(-38.1388 - 71.4593i) q^{3} +255.785 q^{4} +649.991i q^{5} +(33.1343 - 17.6842i) q^{6} -831.270 q^{7} +237.305i q^{8} +(-3651.86 + 5450.75i) q^{9} +O(q^{10})\)	\(q+0.463681i q^{2} +(-38.1388 - 71.4593i) q^{3} +255.785 q^{4} +649.991i q^{5} +(33.1343 - 17.6842i) q^{6} -831.270 q^{7} +237.305i q^{8} +(-3651.86 + 5450.75i) q^{9} -301.389 q^{10} +4414.43i q^{11} +(-9755.34 - 18278.2i) q^{12} +43155.7 q^{13} -385.444i q^{14} +(46447.9 - 24789.9i) q^{15} +65370.9 q^{16} +104893. i q^{17} +(-2527.41 - 1693.30i) q^{18} +75962.6 q^{19} +166258. i q^{20} +(31703.7 + 59401.9i) q^{21} -2046.89 q^{22} -31800.2i q^{23} +(16957.6 - 9050.53i) q^{24} -31863.9 q^{25} +20010.5i q^{26} +(528784. + 53074.1i) q^{27} -212626. q^{28} +33557.3i q^{29} +(11494.6 + 21537.0i) q^{30} +1.04649e6 q^{31} +91061.3i q^{32} +(315452. - 168361. i) q^{33} -48636.8 q^{34} -540318. i q^{35} +(-934091. + 1.39422e6i) q^{36} -475780. q^{37} +35222.4i q^{38} +(-1.64591e6 - 3.08388e6i) q^{39} -154246. q^{40} -958455. i q^{41} +(-27543.5 + 14700.4i) q^{42} -5.21676e6 q^{43} +1.12914e6i q^{44} +(-3.54294e6 - 2.37368e6i) q^{45} +14745.1 q^{46} +4.32434e6i q^{47} +(-2.49317e6 - 4.67136e6i) q^{48} -5.07379e6 q^{49} -14774.7i q^{50} +(7.49557e6 - 4.00049e6i) q^{51} +1.10386e7 q^{52} +1.46582e7i q^{53} +(-24609.4 + 245187. i) q^{54} -2.86934e6 q^{55} -197264. i q^{56} +(-2.89713e6 - 5.42824e6i) q^{57} -15559.9 q^{58} -1.53022e7i q^{59} +(1.18807e7 - 6.34089e6i) q^{60} -6.61576e6 q^{61} +485239. i q^{62} +(3.03568e6 - 4.53104e6i) q^{63} +1.66927e7 q^{64} +2.80509e7i q^{65} +(78065.8 + 146269. i) q^{66} -8.92426e6 q^{67} +2.68300e7i q^{68} +(-2.27242e6 + 1.21282e6i) q^{69} +250535. q^{70} +1.10930e7i q^{71} +(-1.29349e6 - 866604. i) q^{72} +8.31278e6 q^{73} -220610. i q^{74} +(1.21525e6 + 2.27697e6i) q^{75} +1.94301e7 q^{76} -3.66958e6i q^{77} +(1.42994e6 - 763177. i) q^{78} +7.01564e7 q^{79} +4.24905e7i q^{80} +(-1.63746e7 - 3.98107e7i) q^{81} +444417. q^{82} -7.67533e7i q^{83} +(8.10932e6 + 1.51941e7i) q^{84} -6.81794e7 q^{85} -2.41891e6i q^{86} +(2.39798e6 - 1.27984e6i) q^{87} -1.04757e6 q^{88} +8.67620e6i q^{89} +(1.10063e6 - 1.64279e6i) q^{90} -3.58741e7 q^{91} -8.13402e6i q^{92} +(-3.99120e7 - 7.47817e7i) q^{93} -2.00511e6 q^{94} +4.93751e7i q^{95} +(6.50718e6 - 3.47297e6i) q^{96} -1.38818e8 q^{97} -2.35262e6i q^{98} +(-2.40619e7 - 1.61209e7i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 26 q - 35 q^{3} - 2596 q^{4} - 3746 q^{6} + 7156 q^{7} + 9011 q^{9}+O(q^{10}) \) 26 * q - 35 * q^3 - 2596 * q^4 - 3746 * q^6 + 7156 * q^7 + 9011 * q^9	\( 26 q - 35 q^{3} - 2596 q^{4} - 3746 q^{6} + 7156 q^{7} + 9011 q^{9} - 31836 q^{10} - 28900 q^{12} - 131624 q^{13} + 71041 q^{15} + 311972 q^{16} - 675394 q^{18} + 134608 q^{19} + 490306 q^{21} - 59088 q^{24} - 2324740 q^{25} + 2011426 q^{27} - 1996688 q^{28} - 324146 q^{30} + 964738 q^{31} - 512435 q^{33} + 9219648 q^{34} - 6887660 q^{36} - 5721542 q^{37} - 5782712 q^{39} + 8363496 q^{40} + 10350076 q^{42} + 4260820 q^{43} + 6595181 q^{45} - 39680292 q^{46} + 22674164 q^{48} + 20017254 q^{49} - 7985018 q^{51} + 48711952 q^{52} - 18774176 q^{54} - 4304454 q^{55} + 15476796 q^{57} - 16060008 q^{58} - 26730016 q^{60} + 58840 q^{61} - 42877282 q^{63} - 57365836 q^{64} - 10395110 q^{66} - 63186734 q^{67} + 100738079 q^{69} + 50969160 q^{70} + 48890880 q^{72} - 21879656 q^{73} - 122009926 q^{75} - 119289368 q^{76} - 123440744 q^{78} + 117211444 q^{79} + 138667019 q^{81} + 121755480 q^{82} - 28504816 q^{84} + 28880604 q^{85} + 14774868 q^{87} + 90481380 q^{88} + 189044834 q^{90} + 192183008 q^{91} - 113622071 q^{93} - 453996696 q^{94} + 11988416 q^{96} + 24314206 q^{97} - 57905155 q^{99}+O(q^{100}) \) 26 * q - 35 * q^3 - 2596 * q^4 - 3746 * q^6 + 7156 * q^7 + 9011 * q^9 - 31836 * q^10 - 28900 * q^12 - 131624 * q^13 + 71041 * q^15 + 311972 * q^16 - 675394 * q^18 + 134608 * q^19 + 490306 * q^21 - 59088 * q^24 - 2324740 * q^25 + 2011426 * q^27 - 1996688 * q^28 - 324146 * q^30 + 964738 * q^31 - 512435 * q^33 + 9219648 * q^34 - 6887660 * q^36 - 5721542 * q^37 - 5782712 * q^39 + 8363496 * q^40 + 10350076 * q^42 + 4260820 * q^43 + 6595181 * q^45 - 39680292 * q^46 + 22674164 * q^48 + 20017254 * q^49 - 7985018 * q^51 + 48711952 * q^52 - 18774176 * q^54 - 4304454 * q^55 + 15476796 * q^57 - 16060008 * q^58 - 26730016 * q^60 + 58840 * q^61 - 42877282 * q^63 - 57365836 * q^64 - 10395110 * q^66 - 63186734 * q^67 + 100738079 * q^69 + 50969160 * q^70 + 48890880 * q^72 - 21879656 * q^73 - 122009926 * q^75 - 119289368 * q^76 - 123440744 * q^78 + 117211444 * q^79 + 138667019 * q^81 + 121755480 * q^82 - 28504816 * q^84 + 28880604 * q^85 + 14774868 * q^87 + 90481380 * q^88 + 189044834 * q^90 + 192183008 * q^91 - 113622071 * q^93 - 453996696 * q^94 + 11988416 * q^96 + 24314206 * q^97 - 57905155 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more