LMFDB - Embedded newform 33.9.b.a.23.5

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			23.5
Character	$\chi$	$=$	33.23
Dual form			33.9.b.a.23.22

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-22.5549i q^{2} +(76.8411 - 25.6211i) q^{3} -252.723 q^{4} +1149.93i q^{5} +(-577.881 - 1733.14i) q^{6} +3915.62 q^{7} -73.9026i q^{8} +(5248.12 - 3937.51i) q^{9} +O(q^{10})$	\(q-22.5549i q^{2} +(76.8411 - 25.6211i) q^{3} -252.723 q^{4} +1149.93i q^{5} +(-577.881 - 1733.14i) q^{6} +3915.62 q^{7} -73.9026i q^{8} +(5248.12 - 3937.51i) q^{9} +25936.5 q^{10} +4414.43i q^{11} +(-19419.6 + 6475.05i) q^{12} +10789.7 q^{13} -88316.4i q^{14} +(29462.4 + 88361.7i) q^{15} -66364.1 q^{16} +58982.1i q^{17} +(-88810.1 - 118371. i) q^{18} +45205.4 q^{19} -290614. i q^{20} +(300881. - 100323. i) q^{21} +99567.0 q^{22} -247409. i q^{23} +(-1893.47 - 5678.76i) q^{24} -931708. q^{25} -243360. i q^{26} +(302388. - 437025. i) q^{27} -989569. q^{28} -132724. i q^{29} +(1.99299e6 - 664522. i) q^{30} +228406. q^{31} +1.47792e6i q^{32} +(113103. + 339210. i) q^{33} +1.33034e6 q^{34} +4.50268e6i q^{35} +(-1.32632e6 + 995101. i) q^{36} +943932. q^{37} -1.01960e6i q^{38} +(829092. - 276444. i) q^{39} +84982.6 q^{40} -1.19879e6i q^{41} +(-2.26276e6 - 6.78633e6i) q^{42} -5.64585e6 q^{43} -1.11563e6i q^{44} +(4.52785e6 + 6.03496e6i) q^{45} -5.58029e6 q^{46} -2.93576e6i q^{47} +(-5.09949e6 + 1.70032e6i) q^{48} +9.56729e6 q^{49} +2.10146e7i q^{50} +(1.51119e6 + 4.53225e6i) q^{51} -2.72681e6 q^{52} -7.26329e6i q^{53} +(-9.85706e6 - 6.82033e6i) q^{54} -5.07627e6 q^{55} -289375. i q^{56} +(3.47363e6 - 1.15821e6i) q^{57} -2.99357e6 q^{58} +1.19288e7i q^{59} +(-7.44584e6 - 2.23311e7i) q^{60} +8.48061e6 q^{61} -5.15167e6i q^{62} +(2.05496e7 - 1.54178e7i) q^{63} +1.63450e7 q^{64} +1.24074e7i q^{65} +(7.65084e6 - 2.55102e6i) q^{66} -3.04522e7 q^{67} -1.49062e7i q^{68} +(-6.33890e6 - 1.90112e7i) q^{69} +1.01558e8 q^{70} +2.17031e7i q^{71} +(-290992. - 387850. i) q^{72} +4.63687e7 q^{73} -2.12903e7i q^{74} +(-7.15935e7 + 2.38714e7i) q^{75} -1.14245e7 q^{76} +1.72852e7i q^{77} +(-6.23516e6 - 1.87001e7i) q^{78} -6.98447e7 q^{79} -7.63139e7i q^{80} +(1.20388e7 - 4.13290e7i) q^{81} -2.70387e7 q^{82} +8.83537e6i q^{83} +(-7.60396e7 + 2.53539e7i) q^{84} -6.78252e7 q^{85} +1.27341e8i q^{86} +(-3.40052e6 - 1.01986e7i) q^{87} +326238. q^{88} +7.69239e7i q^{89} +(1.36118e8 - 1.02125e8i) q^{90} +4.22484e7 q^{91} +6.25261e7i q^{92} +(1.75510e7 - 5.85201e6i) q^{93} -6.62157e7 q^{94} +5.19829e7i q^{95} +(3.78658e7 + 1.13565e8i) q^{96} -7.58060e7 q^{97} -2.15789e8i q^{98} +(1.73819e7 + 2.31674e7i) 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 $

$2$		−	22.5549i		−	1.40968i	−0.709366	−	0.704841i	$-0.751019\pi$
$2$		−	22.5549i		−	1.40968i	0.709366	−	0.704841i	$-0.248981\pi$
$3$	76.8411	−	25.6211i	0.948656	−	0.316310i
$3$	76.8411	−	25.6211i	0.948656	−	0.316310i
$4$	−252.723			−0.987201
$5$			1149.93i			1.83988i	0.392054	+	0.919942i	$0.371765\pi$
$5$			1149.93i			1.83988i	−0.392054	+	0.919942i	$0.628235\pi$
$6$	−577.881	−	1733.14i	−0.445896	−	1.33730i
$7$	3915.62			1.63083			0.815415	−	0.578877i	$-0.196509\pi$
$7$	3915.62			1.63083			0.815415	+	0.578877i	$0.196509\pi$
$8$		−	73.9026i		−	0.0180426i
$9$	5248.12	−	3937.51i	0.799896	−	0.600139i
$10$	25936.5			2.59365
$11$			4414.43i			0.301511i
$11$			4414.43i			0.301511i
$12$	−19419.6	+	6475.05i	−0.936514	+	0.312261i
$13$	10789.7			0.377777			0.188889	−	0.981999i	$-0.439511\pi$
$13$	10789.7			0.377777			0.188889	+	0.981999i	$0.439511\pi$
$14$		−	88316.4i		−	2.29895i
$15$	29462.4	+	88361.7i	0.581974	+	1.74542i
$16$	−66364.1			−1.01264
$17$			58982.1i			0.706195i	0.935587	+	0.353098i	$0.114872\pi$
$17$			58982.1i			0.706195i	−0.935587	+	0.353098i	$0.885128\pi$
$18$	−88810.1	−	118371.i	−0.846004	−	1.12760i
$19$	45205.4			0.346877			0.173439	−	0.984845i	$-0.444512\pi$
$19$	45205.4			0.346877			0.173439	+	0.984845i	$0.444512\pi$
$20$		−	290614.i		−	1.81634i
$21$	300881.	−	100323.i	1.54710	−	0.515848i
$22$	99567.0			0.425035
$23$		−	247409.i		−	0.884107i	−0.896989	−	0.442053i	$-0.854250\pi$
$23$		−	247409.i		−	0.884107i	0.896989	−	0.442053i	$-0.145750\pi$
$24$	−1893.47	−	5678.76i	−0.00570706	−	0.0171162i
$25$	−931708.			−2.38517
$26$		−	243360.i		−	0.532545i
$27$	302388.	−	437025.i	0.568996	−	0.822340i
$28$	−989569.			−1.60996
$29$		−	132724.i		−	0.187653i	−0.995589	−	0.0938266i	$-0.970090\pi$
$29$		−	132724.i		−	0.187653i	0.995589	−	0.0938266i	$-0.0299099\pi$
$30$	1.99299e6	−	664522.i	2.46048	−	0.820397i
$31$	228406.			0.247321			0.123660	−	0.992325i	$-0.460537\pi$
$31$	228406.			0.247321			0.123660	+	0.992325i	$0.460537\pi$
$32$			1.47792e6i			1.40945i
$33$	113103.	+	339210.i	0.0953710	+	0.286031i
$34$	1.33034e6			0.995510
$35$			4.50268e6i			3.00054i
$36$	−1.32632e6	+	995101.i	−0.789658	+	0.592457i
$37$	943932.			0.503656			0.251828	−	0.967772i	$-0.418968\pi$
$37$	943932.			0.503656			0.251828	+	0.967772i	$0.418968\pi$
$38$		−	1.01960e6i		−	0.488986i
$39$	829092.	−	276444.i	0.358381	−	0.119495i
$40$	84982.6			0.0331963
$41$		−	1.19879e6i		−	0.424238i	−0.977244	−	0.212119i	$-0.931964\pi$
$41$		−	1.19879e6i		−	0.424238i	0.977244	−	0.212119i	$-0.0680364\pi$
$42$	−2.26276e6	−	6.78633e6i	−0.727181	−	2.18091i
$43$	−5.64585e6			−1.65141			−0.825705	−	0.564102i	$-0.809223\pi$
$43$	−5.64585e6			−1.65141			−0.825705	+	0.564102i	$0.809223\pi$
$44$		−	1.11563e6i		−	0.297652i
$45$	4.52785e6	+	6.03496e6i	1.10419	+	1.47172i
$46$	−5.58029e6			−1.24631
$47$		−	2.93576e6i		−	0.601629i	−0.953683	−	0.300815i	$-0.902741\pi$
$47$		−	2.93576e6i		−	0.601629i	0.953683	−	0.300815i	$-0.0972585\pi$
$48$	−5.09949e6	+	1.70032e6i	−0.960642	+	0.320307i
$49$	9.56729e6			1.65960
$50$			2.10146e7i			3.36233i
$51$	1.51119e6	+	4.53225e6i	0.223377	+	0.669936i
$52$	−2.72681e6			−0.372942
$53$		−	7.26329e6i		−	0.920514i	−0.887786	−	0.460257i	$-0.847757\pi$
$53$		−	7.26329e6i		−	0.920514i	0.887786	−	0.460257i	$-0.152243\pi$
$54$	−9.85706e6	−	6.82033e6i	−1.15924	−	0.802103i
$55$	−5.07627e6			−0.554746
$56$		−	289375.i		−	0.0294244i
$57$	3.47363e6	−	1.15821e6i	0.329067	−	0.109721i
$58$	−2.99357e6			−0.264531
$59$			1.19288e7i			0.984442i	0.870470	+	0.492221i	$0.163815\pi$
$59$			1.19288e7i			0.984442i	−0.870470	+	0.492221i	$0.836185\pi$
$60$	−7.44584e6	−	2.23311e7i	−0.574525	−	1.72308i
$61$	8.48061e6			0.612502			0.306251	−	0.951951i	$-0.400925\pi$
$61$	8.48061e6			0.612502			0.306251	+	0.951951i	$0.400925\pi$
$62$		−	5.15167e6i		−	0.348643i
$63$	2.05496e7	−	1.54178e7i	1.30449	−	0.978724i
$64$	1.63450e7			0.974240
$65$			1.24074e7i			0.695066i
$66$	7.65084e6	−	2.55102e6i	0.403212	−	0.134443i
$67$	−3.04522e7			−1.51119			−0.755596	−	0.655038i	$-0.772653\pi$
$67$	−3.04522e7			−1.51119			−0.755596	+	0.655038i	$0.772653\pi$
$68$		−	1.49062e7i		−	0.697156i
$69$	−6.33890e6	−	1.90112e7i	−0.279652	−	0.838713i
$70$	1.01558e8			4.22980
$71$			2.17031e7i			0.854062i	0.904237	+	0.427031i	$0.140440\pi$
$71$			2.17031e7i			0.854062i	−0.904237	+	0.427031i	$0.859560\pi$
$72$	−290992.	−	387850.i	−0.0108281	−	0.0144322i
$73$	4.63687e7			1.63280			0.816401	−	0.577485i	$-0.195966\pi$
$73$	4.63687e7			1.63280			0.816401	+	0.577485i	$0.195966\pi$
$74$		−	2.12903e7i		−	0.709994i
$75$	−7.15935e7	+	2.38714e7i	−2.26271	+	0.754454i
$76$	−1.14245e7			−0.342437
$77$			1.72852e7i			0.491714i
$78$	−6.23516e6	−	1.87001e7i	−0.168449	−	0.505202i
$79$	−6.98447e7			−1.79318			−0.896592	−	0.442857i	$-0.853965\pi$
$79$	−6.98447e7			−1.79318			−0.896592	+	0.442857i	$0.853965\pi$
$80$		−	7.63139e7i		−	1.86313i
$81$	1.20388e7	−	4.13290e7i	0.279667	−	0.960097i
$82$	−2.70387e7			−0.598040
$83$			8.83537e6i			0.186171i	0.995658	+	0.0930856i	$0.0296730\pi$
$83$			8.83537e6i			0.186171i	−0.995658	+	0.0930856i	$0.970327\pi$
$84$	−7.60396e7	+	2.53539e7i	−1.52729	+	0.509245i
$85$	−6.78252e7			−1.29932
$86$			1.27341e8i			2.32796i
$87$	−3.40052e6	−	1.01986e7i	−0.0593566	−	0.178018i
$88$	326238.			0.00544006
$89$			7.69239e7i			1.22603i	0.790071	+	0.613015i	$0.210043\pi$
$89$			7.69239e7i			1.22603i	−0.790071	+	0.613015i	$0.789957\pi$
$90$	1.36118e8	−	1.02125e8i	2.07465	−	1.55655i
$91$	4.22484e7			0.616090
$92$			6.25261e7i			0.872791i
$93$	1.75510e7	−	5.85201e6i	0.234622	−	0.0782300i
$94$	−6.62157e7			−0.848105
$95$			5.19829e7i			0.638214i
$96$	3.78658e7	+	1.13565e8i	0.445823	+	1.33708i
$97$	−7.58060e7			−0.856282			−0.428141	−	0.903712i	$-0.640831\pi$
$97$	−7.58060e7			−0.856282			−0.428141	+	0.903712i	$0.640831\pi$
$98$		−	2.15789e8i		−	2.33951i
$99$	1.73819e7	+	2.31674e7i	0.180949	+	0.241178i
$100$	2.35465e8			2.35465
$101$			3.70649e7i			0.356186i	0.984014	+	0.178093i	$0.0569929\pi$
$101$			3.70649e7i			0.356186i	−0.984014	+	0.178093i	$0.943007\pi$
$102$	1.02224e8	−	3.40847e7i	0.944396	−	0.314890i
$103$	−1.75448e8			−1.55884			−0.779418	−	0.626505i	$-0.784485\pi$
$103$	−1.75448e8			−1.55884			−0.779418	+	0.626505i	$0.784485\pi$
$104$		−	797387.i		−	0.00681609i
$105$	1.15364e8	+	3.45991e8i	0.949100	+	2.84648i
$106$	−1.63823e8			−1.29763
$107$		−	1.64592e8i		−	1.25566i	−0.778349	−	0.627832i	$-0.783942\pi$
$107$		−	1.64592e8i		−	1.25566i	0.778349	−	0.627832i	$-0.216058\pi$
$108$	−7.64205e7	+	1.10447e8i	−0.561714	+	0.811815i
$109$	−4.33509e6			−0.0307109			−0.0153554	−	0.999882i	$-0.504888\pi$
$109$	−4.33509e6			−0.0307109			−0.0153554	+	0.999882i	$0.504888\pi$
$110$			1.14495e8i			0.782015i
$111$	7.25328e7	−	2.41846e7i	0.477796	−	0.159311i
$112$	−2.59857e8			−1.65144
$113$		−	1.18225e8i		−	0.725097i	−0.931965	−	0.362548i	$-0.881907\pi$
$113$		−	1.18225e8i		−	0.725097i	0.931965	−	0.362548i	$-0.118093\pi$
$114$	−2.61233e7	−	7.83474e7i	−0.154671	−	0.463880i
$115$	2.84503e8			1.62665
$116$			3.35424e7i			0.185251i
$117$	5.66256e7	−	4.24845e7i	0.302182	−	0.226719i
$118$	2.69054e8			1.38775
$119$			2.30952e8i			1.15168i
$120$	6.53016e6	−	2.17735e6i	0.0314919	−	0.0105003i
$121$	−1.94872e7			−0.0909091
$122$		−	1.91279e8i		−	0.863433i
$123$	−3.07144e7	−	9.21167e7i	−0.134191	−	0.402456i
$124$	−5.77235e7			−0.244155
$125$		−	6.22207e8i		−	2.54856i
$126$	−3.47747e8	−	4.63495e8i	−1.37969	−	1.83892i
$127$	−3.94161e8			−1.51516			−0.757580	−	0.652742i	$-0.773619\pi$
$127$	−3.94161e8			−1.51516			−0.757580	+	0.652742i	$0.773619\pi$
$128$			9.68577e6i			0.0360823i
$129$	−4.33833e8	+	1.44653e8i	−1.56662	+	0.522358i
$130$	2.79847e8			0.979822
$131$			2.30318e8i			0.782064i	0.920377	+	0.391032i	$0.127882\pi$
$131$			2.30318e8i			0.782064i	−0.920377	+	0.391032i	$0.872118\pi$
$132$	−2.85837e7	−	8.57262e7i	−0.0941504	−	0.282370i
$133$	1.77007e8			0.565697
$134$			6.86847e8i			2.13030i
$135$	5.02547e8	+	3.47724e8i	1.51301	+	1.04689i
$136$	4.35893e6			0.0127416
$137$		−	4.69461e8i		−	1.33265i	−0.745660	−	0.666327i	$-0.767866\pi$
$137$		−	4.69461e8i		−	1.33265i	0.745660	−	0.666327i	$-0.232134\pi$
$138$	−4.28796e8	+	1.42973e8i	−1.18232	+	0.394220i
$139$	1.29973e8			0.348172			0.174086	−	0.984730i	$-0.444303\pi$
$139$	1.29973e8			0.348172			0.174086	+	0.984730i	$0.444303\pi$
$140$		−	1.13793e9i		−	2.96213i
$141$	−7.52174e7	−	2.25587e8i	−0.190301	−	0.570739i
$142$	4.89512e8			1.20395
$143$			4.76303e7i			0.113904i
$144$	−3.48286e8	+	2.61309e8i	−0.810003	+	0.607722i
$145$	1.52622e8			0.345260
$146$		−	1.04584e9i		−	2.30173i
$147$	7.35161e8	−	2.45125e8i	1.57439	−	0.524949i
$148$	−2.38554e8			−0.497210
$149$			4.35789e8i			0.884160i	0.896976	+	0.442080i	$0.145759\pi$
$149$			4.35789e8i			0.884160i	−0.896976	+	0.442080i	$0.854241\pi$
$150$	5.38417e8	+	1.61478e9i	1.06354	+	3.18970i
$151$	2.43204e8			0.467803			0.233902	−	0.972260i	$-0.424851\pi$
$151$	2.43204e8			0.467803			0.233902	+	0.972260i	$0.424851\pi$
$152$		−	3.34079e6i		−	0.00625858i
$153$	2.32243e8	+	3.09545e8i	0.423815	+	0.564883i
$154$	3.89867e8			0.693159
$155$			2.62650e8i			0.455042i
$156$	−2.09531e8	+	6.98639e7i	−0.353794	+	0.117965i
$157$	3.89652e8			0.641325			0.320663	−	0.947194i	$-0.396094\pi$
$157$	3.89652e8			0.641325			0.320663	+	0.947194i	$0.396094\pi$
$158$			1.57534e9i			2.52782i
$159$	−1.86094e8	−	5.58120e8i	−0.291168	−	0.873251i
$160$	−1.69950e9			−2.59323
$161$		−	9.68761e8i		−	1.44183i
$162$	−9.32172e8	−	2.71533e8i	−1.35343	−	0.394242i
$163$	7.15593e8			1.01371			0.506857	−	0.862030i	$-0.330807\pi$
$163$	7.15593e8			1.01371			0.506857	+	0.862030i	$0.330807\pi$
$164$			3.02963e8i			0.418808i
$165$	−3.90066e8	+	1.30060e8i	−0.526263	+	0.175472i
$166$	1.99281e8			0.262442
$167$			5.85510e8i			0.752781i	0.926461	+	0.376391i	$0.122835\pi$
$167$			5.85510e8i			0.752781i	−0.926461	+	0.376391i	$0.877165\pi$
$168$	−7.41410e6	−	2.22359e7i	−0.00930725	−	0.0279137i
$169$	−6.99313e8			−0.857284
$170$			1.52979e9i			1.83162i
$171$	2.37243e8	−	1.77997e8i	0.277466	−	0.208174i
$172$	1.42684e9			1.63027
$173$		−	5.06333e8i		−	0.565264i	−0.959228	−	0.282632i	$-0.908792\pi$
$173$		−	5.06333e8i		−	0.565264i	0.959228	−	0.282632i	$-0.0912076\pi$
$174$	−2.30029e8	+	7.66985e7i	−0.250949	+	0.0836739i
$175$	−3.64822e9			−3.88981
$176$		−	2.92959e8i		−	0.305321i
$177$	3.05630e8	+	9.16625e8i	0.311389	+	0.933897i
$178$	1.73501e9			1.72831
$179$			1.75132e8i			0.170590i	0.996356	+	0.0852950i	$0.0271833\pi$
$179$			1.75132e8i			0.170590i	−0.996356	+	0.0852950i	$0.972817\pi$
$180$	−1.14429e9	−	1.52517e9i	−1.09005	−	1.45288i
$181$	−5.53770e8			−0.515959			−0.257980	−	0.966150i	$-0.583057\pi$
$181$	−5.53770e8			−0.515959			−0.257980	+	0.966150i	$0.583057\pi$
$182$		−	9.52907e8i		−	0.868491i
$183$	6.51659e8	−	2.17283e8i	0.581054	−	0.193741i
$184$	−1.82842e7			−0.0159516
$185$			1.08545e9i			0.926668i
$186$	−1.31992e8	−	3.95860e8i	−0.110279	−	0.330743i
$187$	−2.60372e8			−0.212926
$188$			7.41935e8i			0.593929i
$189$	1.18404e9	−	1.71123e9i	0.927936	−	1.34110i
$190$	1.17247e9			0.899678
$191$		−	2.01892e9i		−	1.51700i	−0.651674	−	0.758499i	$-0.725933\pi$
$191$		−	2.01892e9i		−	1.51700i	0.651674	−	0.758499i	$-0.274067\pi$
$192$	1.25597e9	−	4.18778e8i	0.924219	−	0.308162i
$193$	7.34195e8			0.529154			0.264577	−	0.964365i	$-0.414768\pi$
$193$	7.34195e8			0.529154			0.264577	+	0.964365i	$0.414768\pi$
$194$			1.70980e9i			1.20708i
$195$	3.17890e8	+	9.53396e8i	0.219856	+	0.659379i
$196$	−2.41788e9			−1.63836
$197$		−	5.24637e8i		−	0.348333i	−0.984716	−	0.174166i	$-0.944277\pi$
$197$		−	5.24637e8i		−	0.348333i	0.984716	−	0.174166i	$-0.0557231\pi$
$198$	5.22539e8	−	3.92046e8i	0.339984	−	0.255080i
$199$	2.80022e8			0.178558			0.0892792	−	0.996007i	$-0.471544\pi$
$199$	2.80022e8			0.178558			0.0892792	+	0.996007i	$0.471544\pi$
$200$			6.88557e7i			0.0430348i
$201$	−2.33998e9	+	7.80220e8i	−1.43360	+	0.478005i
$202$	8.35995e8			0.502109
$203$		−	5.19695e8i		−	0.306030i
$204$	−3.81912e8	−	1.14541e9i	−0.220518	−	0.661362i
$205$	1.37853e9			0.780548
$206$			3.95722e9i			2.19746i
$207$	−9.74177e8	−	1.29843e9i	−0.530587	−	0.707193i
$208$	−7.16048e8			−0.382551
$209$			1.99556e8i			0.104587i
$210$	7.80379e9	−	2.60202e9i	4.01263	−	1.33793i
$211$	−1.06462e9			−0.537114			−0.268557	−	0.963264i	$-0.586547\pi$
$211$	−1.06462e9			−0.537114			−0.268557	+	0.963264i	$0.586547\pi$
$212$			1.83560e9i			0.908732i
$213$	5.56059e8	+	1.66769e9i	0.270148	+	0.810211i
$214$	−3.71236e9			−1.77009
$215$		−	6.49231e9i		−	3.03840i
$216$	−3.22973e7	−	2.23473e7i	−0.0148372	−	0.0102662i
$217$	8.94351e8			0.403338
$218$			9.77776e7i			0.0432926i
$219$	3.56302e9	−	1.18802e9i	1.54897	−	0.516472i
$220$	1.28289e9			0.547646
$221$			6.36399e8i			0.266784i
$222$	−5.45481e8	−	1.63597e9i	−0.224578	−	0.673540i
$223$	9.72548e6			0.00393271			0.00196635	−	0.999998i	$-0.499374\pi$
$223$	9.72548e6			0.00393271			0.00196635	+	0.999998i	$0.499374\pi$
$224$			5.78696e9i			2.29857i
$225$	−4.88972e9	+	3.66861e9i	−1.90789	+	1.43143i
$226$	−2.66656e9			−1.02216
$227$		−	3.21261e9i		−	1.20992i	−0.796258	−	0.604958i	$-0.793190\pi$
$227$		−	3.21261e9i		−	1.20992i	0.796258	−	0.604958i	$-0.206810\pi$
$228$	−8.77868e8	+	2.92707e8i	−0.324855	+	0.108316i
$229$	3.23612e9			1.17675			0.588374	−	0.808589i	$-0.299768\pi$
$229$	3.23612e9			1.17675			0.588374	+	0.808589i	$0.299768\pi$
$230$		−	6.41693e9i		−	2.29306i
$231$	4.42867e8	+	1.32822e9i	0.155534	+	0.466467i
$232$	−9.80862e6			−0.00338576
$233$			5.54259e8i			0.188057i	0.995570	+	0.0940283i	$0.0299744\pi$
$233$			5.54259e8i			0.188057i	−0.995570	+	0.0940283i	$0.970026\pi$
$234$	−9.58234e8	−	1.27718e9i	−0.319601	−	0.425981i
$235$	3.37591e9			1.10693
$236$		−	3.01470e9i		−	0.971842i
$237$	−5.36694e9	+	1.78950e9i	−1.70111	+	0.567202i
$238$	5.20909e9			1.62351
$239$			1.12837e9i			0.345827i	0.984937	+	0.172913i	$0.0553181\pi$
$239$			1.12837e9i			0.345827i	−0.984937	+	0.172913i	$0.944682\pi$
$240$	−1.95525e9	−	5.86404e9i	−0.589327	−	1.76747i
$241$	−7.30212e8			−0.216462			−0.108231	−	0.994126i	$-0.534519\pi$
$241$	−7.30212e8			−0.216462			−0.108231	+	0.994126i	$0.534519\pi$
$242$			4.39531e8i			0.128153i
$243$	−1.33824e8	−	3.48422e9i	−0.0383802	−	0.999263i
$244$	−2.14325e9			−0.604663
$245$			1.10017e10i			3.05348i
$246$	−2.07768e9	+	6.92761e8i	−0.567334	+	0.189166i
$247$	4.87752e8			0.131042
$248$		−	1.68798e7i		−	0.00446232i
$249$	2.26372e8	+	6.78920e8i	0.0588878	+	0.176612i
$250$	−1.40338e10			−3.59265
$251$		−	2.06213e9i		−	0.519542i	−0.965670	−	0.259771i	$-0.916353\pi$
$251$		−	2.06213e9i		−	0.519542i	0.965670	−	0.259771i	$-0.0836471\pi$
$252$	−5.19338e9	+	3.89644e9i	−1.28780	+	0.966197i
$253$	1.09217e9			0.266568
$254$			8.89026e9i			2.13589i
$255$	−5.21176e9	+	1.73776e9i	−1.23260	+	0.410987i
$256$	4.40279e9			1.02510
$257$			4.53683e9i			1.03997i	0.854176	+	0.519984i	$0.174062\pi$
$257$			4.53683e9i			1.03997i	−0.854176	+	0.519984i	$0.825938\pi$
$258$	3.26263e9	+	9.78506e9i	0.736358	+	2.20844i
$259$	3.69608e9			0.821377
$260$		−	3.13563e9i		−	0.686170i
$261$	−5.22600e8	−	6.96549e8i	−0.112618	−	0.150103i
$262$	5.19480e9			1.10246
$263$			4.46196e9i			0.932616i	0.884623	+	0.466308i	$0.154416\pi$
$263$			4.46196e9i			0.932616i	−0.884623	+	0.466308i	$0.845584\pi$
$264$	2.50685e7	−	8.35857e6i	0.00516074	−	0.00172074i
$265$	8.35226e9			1.69364
$266$		−	3.99238e9i		−	0.797453i
$267$	1.97087e9	+	5.91092e9i	0.387806	+	1.16308i
$268$	7.69599e9			1.49185
$269$		−	7.90752e9i		−	1.51019i	−0.655616	−	0.755095i	$-0.727591\pi$
$269$		−	7.90752e9i		−	1.51019i	0.655616	−	0.755095i	$-0.272409\pi$
$270$	7.84288e9	−	1.13349e10i	1.47578	−	2.13286i
$271$	2.16951e9			0.402239			0.201120	−	0.979567i	$-0.435542\pi$
$271$	2.16951e9			0.402239			0.201120	+	0.979567i	$0.435542\pi$
$272$		−	3.91429e9i		−	0.715118i
$273$	3.24641e9	−	1.08245e9i	0.584458	−	0.194875i
$274$	−1.05886e10			−1.87862
$275$		−	4.11296e9i		−	0.719157i
$276$	1.60199e9	+	4.80458e9i	0.276072	+	0.827978i
$277$	−4.10849e9			−0.697852			−0.348926	−	0.937150i	$-0.613454\pi$
$277$	−4.10849e9			−0.697852			−0.348926	+	0.937150i	$0.613454\pi$
$278$		−	2.93153e9i		−	0.490812i
$279$	1.19870e9	−	8.99351e8i	0.197831	−	0.148427i
$280$	3.32760e8			0.0541376
$281$			7.44750e9i			1.19450i	0.802056	+	0.597249i	$0.203739\pi$
$281$			7.44750e9i			1.19450i	−0.802056	+	0.597249i	$0.796261\pi$
$282$	−5.08809e9	+	1.69652e9i	−0.804560	+	0.268264i
$283$	1.67900e9			0.261762			0.130881	−	0.991398i	$-0.458219\pi$
$283$	1.67900e9			0.261762			0.130881	+	0.991398i	$0.458219\pi$
$284$		−	5.48489e9i		−	0.843131i
$285$	1.33186e9	+	3.99442e9i	0.201873	+	0.605445i
$286$	1.07430e9			0.160568
$287$		−	4.69403e9i		−	0.691859i
$288$	5.81931e9	+	7.75628e9i	0.845865	+	1.12741i
$289$	3.49687e9			0.501289
$290$		−	3.44238e9i		−	0.486707i
$291$	−5.82502e9	+	1.94223e9i	−0.812317	+	0.270850i
$292$	−1.17185e10			−1.61190
$293$		−	4.60811e9i		−	0.625248i	−0.949877	−	0.312624i	$-0.898792\pi$
$293$		−	4.60811e9i		−	0.625248i	0.949877	−	0.312624i	$-0.101208\pi$
$294$	−5.52876e9	−	1.65815e10i	−0.740011	−	2.21939i
$295$	−1.37173e10			−1.81126
$296$		−	6.97590e7i		−	0.00908728i
$297$	1.92922e9	+	1.33487e9i	0.247945	+	0.171559i
$298$	9.82917e9			1.24638
$299$		−	2.66947e9i		−	0.333995i
$300$	1.80934e10	−	6.03286e9i	2.23375	−	0.744798i
$301$	−2.21070e10			−2.69317
$302$		−	5.48545e9i		−	0.659454i
$303$	9.49644e8	+	2.84811e9i	0.112665	+	0.337898i
$304$	−3.00001e9			−0.351260
$305$			9.75208e9i			1.12693i
$306$	6.98176e9	−	5.23821e9i	0.796304	−	0.597444i
$307$	7.37360e9			0.830092			0.415046	−	0.909800i	$-0.363765\pi$
$307$	7.37360e9			0.830092			0.415046	+	0.909800i	$0.363765\pi$
$308$		−	4.36838e9i		−	0.485420i
$309$	−1.34816e10	+	4.49518e9i	−1.47880	+	0.493075i
$310$	5.92405e9			0.641464
$311$		−	8.05082e9i		−	0.860594i	−0.902687	−	0.430297i	$-0.858409\pi$
$311$		−	8.05082e9i		−	0.860594i	0.902687	−	0.430297i	$-0.141591\pi$
$312$	−2.04299e7	−	6.12721e7i	−0.00215600	−	0.00646613i
$313$	−6.20634e9			−0.646633			−0.323317	−	0.946291i	$-0.604798\pi$
$313$	−6.20634e9			−0.646633			−0.323317	+	0.946291i	$0.604798\pi$
$314$		−	8.78856e9i		−	0.904064i
$315$	1.77293e10	+	2.36306e10i	1.80074	+	2.40012i
$316$	1.76514e10			1.77023
$317$		−	3.18406e9i		−	0.315315i	−0.987494	−	0.157657i	$-0.949606\pi$
$317$		−	3.18406e9i		−	0.315315i	0.987494	−	0.157657i	$-0.0503941\pi$
$318$	−1.25883e10	+	4.19732e9i	−1.23100	+	0.410453i
$319$	5.85899e8			0.0565796
$320$			1.87956e10i			1.79249i
$321$	−4.21703e9	−	1.26474e10i	−0.397179	−	1.19119i
$322$	−2.18503e10			−2.03252
$323$			2.66631e9i			0.244963i
$324$	−3.04248e9	+	1.04448e10i	−0.276088	+	0.947809i
$325$	−1.00528e10			−0.901064
$326$		−	1.61401e10i		−	1.42901i
$327$	−3.33113e8	+	1.11070e8i	−0.0291341	+	0.00971416i
$328$	−8.85940e7			−0.00765436
$329$		−	1.14953e10i		−	0.981155i
$330$	2.93348e9	+	8.79791e9i	0.247359	+	0.741863i
$331$	1.56083e10			1.30030			0.650150	−	0.759806i	$-0.274706\pi$
$331$	1.56083e10			1.30030			0.650150	+	0.759806i	$0.274706\pi$
$332$		−	2.23290e9i		−	0.183788i
$333$	4.95387e9	−	3.71674e9i	0.402872	−	0.302263i
$334$	1.32061e10			1.06118
$335$		−	3.50179e10i		−	2.78042i
$336$	−1.99677e10	+	6.65781e9i	−1.56664	+	0.522365i
$337$	1.13380e9			0.0879057			0.0439528	−	0.999034i	$-0.486005\pi$
$337$	1.13380e9			0.0879057			0.0439528	+	0.999034i	$0.486005\pi$
$338$			1.57729e10i			1.20850i
$339$	−3.02906e9	−	9.08455e9i	−0.229355	−	0.687868i
$340$	1.71410e10			1.28269
$341$			1.00828e9i			0.0745700i
$342$	−4.01469e9	−	5.35099e9i	−0.293459	−	0.391138i
$343$	1.48891e10			1.07570
$344$			4.17243e8i			0.0297958i
$345$	2.18615e10	−	7.28928e9i	1.54313	−	0.514527i
$346$	−1.14203e10			−0.796842
$347$			1.53856e10i			1.06120i	0.847623	+	0.530600i	$0.178033\pi$
$347$			1.53856e10i			1.06120i	−0.847623	+	0.530600i	$0.821967\pi$
$348$	8.59392e8	+	2.57743e9i	0.0585969	+	0.175740i
$349$	1.63974e10			1.10528			0.552641	−	0.833419i	$-0.313620\pi$
$349$	1.63974e10			1.10528			0.552641	+	0.833419i	$0.313620\pi$
$350$			8.22852e10i			5.48339i
$351$	3.26267e9	−	4.71537e9i	0.214954	−	0.310661i
$352$	−6.52415e9			−0.424965
$353$		−	1.26112e10i		−	0.812193i	−0.913830	−	0.406096i	$-0.866890\pi$
$353$		−	1.26112e10i		−	0.812193i	0.913830	−	0.406096i	$-0.133110\pi$
$354$	2.06744e10	−	6.89346e9i	1.31650	−	0.438959i
$355$	−2.49570e10			−1.57137
$356$		−	1.94405e10i		−	1.21034i
$357$	5.91724e9	+	1.77466e10i	0.364289	+	1.09255i
$358$	3.95009e9			0.240477
$359$			2.19263e10i			1.32004i	0.751247	+	0.660021i	$0.229453\pi$
$359$			2.19263e10i			1.32004i	−0.751247	+	0.660021i	$0.770547\pi$
$360$	4.45999e8	−	3.34620e8i	0.0265536	−	0.0199224i
$361$	−1.49400e10			−0.879676
$362$			1.24902e10i			0.727338i
$363$	−1.49742e9	+	4.99283e8i	−0.0862414	+	0.0287555i
$364$	−1.06772e10			−0.608205
$365$			5.33207e10i			3.00417i
$366$	−4.90079e9	−	1.46981e10i	−0.273112	−	0.819100i
$367$	−2.28590e10			−1.26006			−0.630032	−	0.776569i	$-0.716958\pi$
$367$	−2.28590e10			−1.26006			−0.630032	+	0.776569i	$0.716958\pi$
$368$			1.64191e10i			0.895278i
$369$	−4.72026e9	−	6.29141e9i	−0.254601	−	0.339346i
$370$	2.44823e10			1.30631
$371$		−	2.84403e10i		−	1.50120i
$372$	−4.43554e9	+	1.47894e9i	−0.231619	+	0.0772288i
$373$	−2.99575e9			−0.154764			−0.0773821	−	0.997002i	$-0.524656\pi$
$373$	−2.99575e9			−0.154764			−0.0773821	+	0.997002i	$0.524656\pi$
$374$			5.87267e9i			0.300158i
$375$	−1.59416e10	−	4.78111e10i	−0.806134	−	2.41771i
$376$	−2.16960e8			−0.0108550
$377$		−	1.43205e9i		−	0.0708911i
$378$	−3.85965e10	−	2.67058e10i	−1.89052	−	1.30809i
$379$	2.98747e10			1.44793			0.723965	−	0.689837i	$-0.242318\pi$
$379$	2.98747e10			1.44793			0.723965	+	0.689837i	$0.242318\pi$
$380$		−	1.31373e10i		−	0.630045i
$381$	−3.02878e10	+	1.00988e10i	−1.43737	+	0.479260i
$382$	−4.55365e10			−2.13848
$383$		−	3.15617e9i		−	0.146678i	−0.997307	−	0.0733390i	$-0.976634\pi$
$383$		−	3.15617e9i		−	0.146678i	0.997307	−	0.0733390i	$-0.0233655\pi$
$384$	2.48160e8	+	7.44265e8i	0.0114132	+	0.0342297i
$385$	−1.98768e10			−0.904696
$386$		−	1.65597e10i		−	0.745939i
$387$	−2.96301e10	+	2.22306e10i	−1.32096	+	0.991075i
$388$	1.91580e10			0.845322
$389$			1.92559e10i			0.840939i	0.907307	+	0.420470i	$0.138135\pi$
$389$			1.92559e10i			0.840939i	−0.907307	+	0.420470i	$0.861865\pi$
$390$	2.15038e10	−	7.16999e9i	0.929514	−	0.309927i
$391$	1.45927e10			0.624352
$392$		−	7.07048e8i		−	0.0299436i
$393$	5.90100e9	+	1.76979e10i	0.247375	+	0.741910i
$394$	−1.18331e10			−0.491038
$395$		−	8.03163e10i		−	3.29925i
$396$	−4.39280e9	−	5.85495e9i	−0.178633	−	0.238091i
$397$	2.73074e10			1.09930			0.549652	−	0.835394i	$-0.314760\pi$
$397$	2.73074e10			1.09930			0.549652	+	0.835394i	$0.314760\pi$
$398$		−	6.31588e9i		−	0.251710i
$399$	1.36014e10	−	4.53512e9i	0.536652	−	0.178936i
$400$	6.18320e10			2.41531
$401$		−	2.52479e10i		−	0.976446i	−0.872719	−	0.488223i	$-0.837645\pi$
$401$		−	2.52479e10i		−	0.976446i	0.872719	−	0.488223i	$-0.162355\pi$
$402$	1.75978e10	+	5.27781e10i	0.673835	+	2.02092i
$403$	2.46443e9			0.0934322
$404$		−	9.36717e9i		−	0.351628i
$405$	4.75254e10	+	1.38437e10i	1.76647	+	0.514555i
$406$	−1.17217e10			−0.431405
$407$			4.16692e9i			0.151858i
$408$	3.34945e8	−	1.11681e8i	0.0120874	−	0.00403030i
$409$	5.58994e9			0.199763			0.0998813	−	0.994999i	$-0.468154\pi$
$409$	5.58994e9			0.199763			0.0998813	+	0.994999i	$0.468154\pi$
$410$		−	3.10925e10i		−	1.10032i
$411$	−1.20281e10	−	3.60739e10i	−0.421531	−	1.26423i
$412$	4.43399e10			1.53888
$413$			4.67088e10i			1.60546i
$414$	−2.92860e10	+	2.19725e10i	−0.996917	+	0.747958i
$415$	−1.01600e10			−0.342533
$416$			1.59463e10i			0.532458i
$417$	9.98728e9	−	3.33005e9i	0.330296	−	0.110130i
$418$	4.50096e9			0.147435
$419$			6.04244e10i			1.96045i	0.197882	+	0.980226i	$0.436594\pi$
$419$			6.04244e10i			1.96045i	−0.197882	+	0.980226i	$0.563406\pi$
$420$	−2.91551e10	−	8.74401e10i	−0.936952	−	2.81004i
$421$	4.69811e10			1.49553			0.747765	−	0.663963i	$-0.231127\pi$
$421$	4.69811e10			1.49553			0.747765	+	0.663963i	$0.231127\pi$
$422$			2.40125e10i			0.757160i
$423$	−1.15596e10	−	1.54072e10i	−0.361061	−	0.481241i
$424$	−5.36776e8			−0.0166085
$425$		−	5.49541e10i		−	1.68440i
$426$	3.76147e10	−	1.25418e10i	1.14214	−	0.380823i
$427$	3.32068e10			0.998886
$428$			4.15963e10i			1.23959i
$429$	1.22034e9	+	3.65997e9i	0.0360290	+	0.108056i
$430$	−1.46433e11			−4.28318
$431$			1.81507e10i			0.525997i	0.964796	+	0.262999i	$0.0847115\pi$
$431$			1.81507e10i			0.525997i	−0.964796	+	0.262999i	$0.915288\pi$
$432$	−2.00677e10	+	2.90028e10i	−0.576186	+	0.832731i
$433$	1.21702e10			0.346214			0.173107	−	0.984903i	$-0.444619\pi$
$433$	1.21702e10			0.346214			0.173107	+	0.984903i	$0.444619\pi$
$434$		−	2.01720e10i		−	0.568578i
$435$	1.17277e10	−	3.91036e9i	0.327533	−	0.109209i
$436$	1.09558e9			0.0303178
$437$		−	1.11842e10i		−	0.306676i
$438$	−2.67956e10	−	8.03636e10i	−0.728060	−	2.18355i
$439$	1.20117e10			0.323403			0.161702	−	0.986840i	$-0.448302\pi$
$439$	1.20117e10			0.323403			0.161702	+	0.986840i	$0.448302\pi$
$440$			3.75150e8i			0.0100091i
$441$	5.02103e10	−	3.76713e10i	1.32751	−	0.995993i
$442$	1.43539e10			0.376081
$443$		−	2.70457e10i		−	0.702237i	−0.936331	−	0.351118i	$-0.885802\pi$
$443$		−	2.70457e10i		−	0.702237i	0.936331	−	0.351118i	$-0.114198\pi$
$444$	−1.83307e10	+	6.11201e9i	−0.471681	+	0.157272i
$445$	−8.84569e10			−2.25575
$446$		−	2.19357e8i		−	0.00554386i
$447$	1.11654e10	+	3.34865e10i	0.279669	+	0.838764i
$448$	6.40010e10			1.58882
$449$			3.69310e9i			0.0908669i	0.998967	+	0.0454335i	$0.0144669\pi$
$449$			3.69310e9i			0.0908669i	−0.998967	+	0.0454335i	$0.985533\pi$
$450$	8.27451e10	+	1.10287e11i	2.01787	+	2.68952i
$451$	5.29199e9			0.127913
$452$			2.98783e10i			0.715816i
$453$	1.86881e10	−	6.23116e9i	0.443784	−	0.147971i
$454$	−7.24602e10			−1.70559
$455$			4.85826e10i			1.13353i
$456$	−8.55949e7	−	2.56710e8i	−0.00197965	−	0.00593723i
$457$	1.76320e10			0.404239			0.202119	−	0.979361i	$-0.435217\pi$
$457$	1.76320e10			0.404239			0.202119	+	0.979361i	$0.435217\pi$
$458$		−	7.29905e10i		−	1.65884i
$459$	2.57767e10	+	1.78355e10i	0.580733	+	0.401822i
$460$	−7.19005e10			−1.60583
$461$			8.79885e10i			1.94815i	0.226226	+	0.974075i	$0.427361\pi$
$461$			8.79885e10i			1.94815i	−0.226226	+	0.974075i	$0.572639\pi$
$462$	2.99578e10	−	9.98881e9i	0.657570	−	0.219253i
$463$	−5.59098e10			−1.21665			−0.608323	−	0.793690i	$-0.708157\pi$
$463$	−5.59098e10			−1.21665			−0.608323	+	0.793690i	$0.708157\pi$
$464$			8.80808e9i			0.190024i
$465$	6.72939e9	+	2.01823e10i	0.143934	+	0.431678i
$466$	1.25012e10			0.265100
$467$			4.14532e10i			0.871545i	0.900057	+	0.435773i	$0.143525\pi$
$467$			4.14532e10i			0.871545i	−0.900057	+	0.435773i	$0.856475\pi$
$468$	−1.43106e10	+	1.07368e10i	−0.298315	+	0.223817i
$469$	−1.19239e11			−2.46450
$470$		−	7.61433e10i		−	1.56042i
$471$	2.99413e10	−	9.98331e9i	0.608397	−	0.202858i
$472$	8.81572e8			0.0177619
$473$		−	2.49232e10i		−	0.497919i
$474$	4.03619e10	+	1.21051e11i	0.799574	+	2.39803i
$475$	−4.21182e10			−0.827362
$476$		−	5.83669e10i		−	1.13694i
$477$	−2.85993e10	−	3.81186e10i	−0.552436	−	0.736315i
$478$	2.54502e10			0.487506
$479$		−	2.42011e10i		−	0.459719i	−0.973224	−	0.229860i	$-0.926173\pi$
$479$		−	2.42011e10i		−	0.459719i	0.973224	−	0.229860i	$-0.0738267\pi$
$480$	−1.30591e11	+	4.35430e10i	−2.46008	+	0.820263i
$481$	1.01847e10			0.190270
$482$			1.64699e10i			0.305142i
$483$	−2.48207e10	−	7.44407e10i	−0.456064	−	1.36780i
$484$	4.92486e9			0.0897455
$485$		−	8.71714e10i		−	1.57546i
$486$	−7.85861e10	+	3.01838e9i	−1.40864	+	0.0541039i
$487$	−3.27419e10			−0.582087			−0.291044	−	0.956710i	$-0.594002\pi$
$487$	−3.27419e10			−0.582087			−0.291044	+	0.956710i	$0.594002\pi$
$488$		−	6.26739e8i		−	0.0110511i
$489$	5.49870e10	−	1.83343e10i	0.961666	−	0.320648i
$490$	2.48142e11			4.30443
$491$		−	6.85569e10i		−	1.17957i	−0.807559	−	0.589787i	$-0.799212\pi$
$491$		−	6.85569e10i		−	1.17957i	0.807559	−	0.589787i	$-0.200788\pi$
$492$	7.76226e9	+	2.32801e10i	0.132473	+	0.397305i
$493$	7.82832e9			0.132520
$494$		−	1.10012e10i		−	0.184728i
$495$	−2.66409e10	+	1.99879e10i	−0.443739	+	0.332924i
$496$	−1.51579e10			−0.250446
$497$			8.49813e10i			1.39283i
$498$	1.53130e10	−	5.10580e9i	0.248967	−	0.0830130i
$499$	−4.01511e10			−0.647582			−0.323791	−	0.946129i	$-0.604958\pi$
$499$	−4.01511e10			−0.647582			−0.323791	+	0.946129i	$0.604958\pi$
$500$			1.57246e11i			2.51594i
$501$	1.50014e10	+	4.49913e10i	0.238112	+	0.714130i
$502$	−4.65111e10			−0.732389
$503$			1.24491e11i			1.94477i	0.233392	+	0.972383i	$0.425017\pi$
$503$			1.24491e11i			1.94477i	−0.233392	+	0.972383i	$0.574983\pi$
$504$	−1.13942e9	−	1.51867e9i	−0.0176587	−	0.0235365i
$505$	−4.26220e10			−0.655342
$506$		−	2.46338e10i		−	0.375776i
$507$	−5.37360e10	+	1.79172e10i	−0.813268	+	0.271168i
$508$	9.96137e10			1.49577
$509$			1.30811e11i			1.94882i	0.224775	+	0.974411i	$0.427835\pi$
$509$			1.30811e11i			1.94882i	−0.224775	+	0.974411i	$0.572165\pi$
$510$	3.91949e10	+	1.17551e11i	0.579361	+	1.73758i
$511$	1.81562e11			2.66282
$512$		−	9.68249e10i		−	1.40899i
$513$	1.36696e10	−	1.97559e10i	0.197372	−	0.285251i
$514$	1.02328e11			1.46602
$515$		−	2.01753e11i		−	2.86808i
$516$	1.09640e11	−	3.65572e10i	1.54657	−	0.515672i
$517$	1.29597e10			0.181398
$518$		−	8.33647e10i		−	1.15788i
$519$	−1.29728e10	−	3.89072e10i	−0.178799	−	0.536241i
$520$	9.16937e8			0.0125408
$521$		−	2.36101e10i		−	0.320440i	−0.987081	−	0.160220i	$-0.948780\pi$
$521$		−	2.36101e10i		−	0.320440i	0.987081	−	0.160220i	$-0.0512203\pi$
$522$	−1.57106e10	+	1.17872e10i	−0.211597	+	0.158755i
$523$	−1.06380e11			−1.42185			−0.710926	−	0.703267i	$-0.751724\pi$
$523$	−1.06380e11			−1.42185			−0.710926	+	0.703267i	$0.751724\pi$
$524$		−	5.82067e10i		−	0.772055i
$525$	−2.80333e11	+	9.34714e10i	−3.69009	+	1.23039i
$526$	1.00639e11			1.31469
$527$			1.34719e10i			0.174657i
$528$	−7.50594e9	−	2.25113e10i	−0.0965761	−	0.289645i
$529$	1.70996e10			0.218355
$530$		−	1.88384e11i		−	2.38749i
$531$	4.69699e10	+	6.26040e10i	0.590802	+	0.787451i
$532$	−4.47338e10			−0.558457
$533$		−	1.29346e10i		−	0.160267i
$534$	1.33320e11	−	4.44529e10i	1.63957	−	0.546682i
$535$	1.89269e11			2.31028
$536$			2.25050e9i			0.0272659i
$537$	4.48708e9	+	1.34573e10i	0.0539593	+	0.161831i
$538$	−1.78353e11			−2.12889
$539$			4.22341e10i			0.500390i
$540$	−1.27005e11	−	8.78781e10i	−1.49365	−	1.03349i
$541$	1.61955e10			0.189062			0.0945310	−	0.995522i	$-0.469865\pi$
$541$	1.61955e10			0.189062			0.0945310	+	0.995522i	$0.469865\pi$
$542$		−	4.89331e10i		−	0.567029i
$543$	−4.25523e10	+	1.41882e10i	−0.489468	+	0.163203i
$544$	−8.71706e10			−0.995347
$545$		−	4.98504e9i		−	0.0565045i
$546$	−2.44145e10	−	7.32225e10i	−0.274712	−	0.823899i
$547$	1.38866e11			1.55113			0.775565	−	0.631268i	$-0.217465\pi$
$547$	1.38866e11			1.55113			0.775565	+	0.631268i	$0.217465\pi$
$548$			1.18644e11i			1.31560i
$549$	4.45072e10	−	3.33925e10i	0.489938	−	0.367586i
$550$	−9.27674e10			−1.01378
$551$		−	5.99982e9i		−	0.0650926i
$552$	−1.40498e9	+	4.68461e8i	−0.0151326	+	0.00504565i
$553$	−2.73485e11			−2.92438
$554$			9.26667e10i			0.983749i
$555$	2.78105e10	+	8.34075e10i	0.293114	+	0.879089i
$556$	−3.28472e10			−0.343716
$557$		−	4.22621e10i		−	0.439066i	−0.975605	−	0.219533i	$-0.929547\pi$
$557$		−	4.22621e10i		−	0.439066i	0.975605	−	0.219533i	$-0.0704534\pi$
$558$	−2.02848e10	−	2.70366e10i	−0.209234	−	0.278879i
$559$	−6.09169e10			−0.623865
$560$		−	2.98816e11i		−	3.03845i
$561$	−2.00073e10	+	6.67103e9i	−0.201993	+	0.0673506i
$562$	1.67978e11			1.68386
$563$			9.51179e10i			0.946736i	0.880865	+	0.473368i	$0.156962\pi$
$563$			9.51179e10i			0.946736i	−0.880865	+	0.473368i	$0.843038\pi$
$564$	1.90092e10	+	5.70111e10i	0.187866	+	0.563434i
$565$	1.35950e11			1.33409
$566$		−	3.78698e10i		−	0.369000i
$567$	4.71392e10	−	1.61829e11i	0.456090	−	1.56575i
$568$	1.60392e9			0.0154095
$569$		−	2.84043e8i		−	0.00270979i	−0.999999	−	0.00135489i	$-0.999569\pi$
$569$		−	2.84043e8i		−	0.00270979i	0.999999	−	0.00135489i	$-0.000431276\pi$
$570$	9.00938e10	−	3.00400e10i	0.853485	−	0.284577i
$571$	1.57348e11			1.48019			0.740095	−	0.672502i	$-0.234780\pi$
$571$	1.57348e11			1.48019			0.740095	+	0.672502i	$0.234780\pi$
$572$		−	1.20373e10i		−	0.112446i
$573$	−5.17269e10	−	1.55136e11i	−0.479841	−	1.43911i
$574$	−1.05873e11			−0.975301
$575$			2.30513e11i			2.10875i
$576$	8.57807e10	−	6.43587e10i	0.779291	−	0.584679i
$577$	−7.14889e10			−0.644963			−0.322482	−	0.946576i	$-0.604517\pi$
$577$	−7.14889e10			−0.644963			−0.322482	+	0.946576i	$0.604517\pi$
$578$		−	7.88715e10i		−	0.706657i
$579$	5.64164e10	−	1.88109e10i	0.501985	−	0.167377i
$580$	−3.85713e10			−0.340841
$581$			3.45960e10i			0.303613i
$582$	4.38069e10	+	1.31383e11i	0.381813	+	1.14511i
$583$	3.20633e10			0.277545
$584$		−	3.42677e9i		−	0.0294600i
$585$	4.88541e10	+	6.51153e10i	0.417136	+	0.555981i
$586$	−1.03935e11			−0.881400
$587$		−	4.36499e10i		−	0.367647i	−0.982959	−	0.183823i	$-0.941153\pi$
$587$		−	4.36499e10i		−	0.367647i	0.982959	−	0.183823i	$-0.0588474\pi$
$588$	−1.85792e11	+	6.19487e10i	−1.55424	+	0.518231i
$589$	1.03252e10			0.0857899
$590$			3.09392e11i			2.55330i
$591$	−1.34418e10	−	4.03137e10i	−0.110181	−	0.330448i
$592$	−6.26432e10			−0.510020
$593$			2.03206e11i			1.64331i	0.569987	+	0.821653i	$0.306948\pi$
$593$			2.03206e11i			1.64331i	−0.569987	+	0.821653i	$0.693052\pi$
$594$	3.01078e10	−	4.35133e10i	0.241843	−	0.349523i
$595$	−2.65578e11			−2.11896
$596$		−	1.10134e11i		−	0.872843i
$597$	2.15172e10	−	7.17448e9i	0.169391	−	0.0564798i
$598$	−6.02097e10			−0.470827
$599$		−	9.26344e10i		−	0.719556i	−0.933038	−	0.359778i	$-0.882852\pi$
$599$		−	9.26344e10i		−	0.719556i	0.933038	−	0.359778i	$-0.117148\pi$
$600$	1.76416e9	+	5.29095e9i	0.0136123	+	0.0408252i
$601$	2.05053e11			1.57170			0.785848	−	0.618419i	$-0.212227\pi$
$601$	2.05053e11			1.57170			0.785848	+	0.618419i	$0.212227\pi$
$602$			4.98621e11i			3.79651i
$603$	−1.59817e11	+	1.19906e11i	−1.20880	+	0.906925i
$604$	−6.14634e10			−0.461816
$605$		−	2.24088e10i		−	0.167262i
$606$	6.42388e10	−	2.14191e10i	0.476329	−	0.158822i
$607$	1.17208e11			0.863380			0.431690	−	0.902022i	$-0.357918\pi$
$607$	1.17208e11			0.863380			0.431690	+	0.902022i	$0.357918\pi$
$608$			6.68097e10i			0.488906i
$609$	−1.33152e10	−	3.99340e10i	−0.0968005	−	0.290318i
$610$	2.19957e11			1.58862
$611$		−	3.16759e10i		−	0.227282i
$612$	−5.86932e10	−	7.82293e10i	−0.418390	−	0.557653i
$613$	1.57802e11			1.11756			0.558780	−	0.829316i	$-0.311269\pi$
$613$	1.57802e11			1.11756			0.558780	+	0.829316i	$0.311269\pi$
$614$		−	1.66311e11i		−	1.17017i
$615$	1.05928e11	−	3.53194e10i	0.740472	−	0.246895i
$616$	1.27742e9			0.00887181
$617$			3.70050e10i			0.255340i	0.991817	+	0.127670i	$0.0407499\pi$
$617$			3.70050e10i			0.255340i	−0.991817	+	0.127670i	$0.959250\pi$
$618$	1.01388e11	+	3.04077e11i	0.695079	+	2.08463i
$619$	−2.00591e11			−1.36631			−0.683155	−	0.730273i	$-0.739393\pi$
$619$	−2.00591e11			−1.36631			−0.683155	+	0.730273i	$0.739393\pi$
$620$		−	6.63779e10i		−	0.449218i
$621$	−1.08124e11	−	7.48136e10i	−0.727036	−	0.503053i
$622$	−1.81585e11			−1.21316
$623$			3.01205e11i			1.99945i
$624$	−5.50219e10	+	1.83459e10i	−0.362909	+	0.121005i
$625$	3.51544e11			2.30388
$626$			1.39983e11i			0.911547i
$627$	5.11284e9	+	1.53341e10i	0.0330820	+	0.0992174i
$628$	−9.84742e10			−0.633117
$629$			5.56751e10i			0.355679i
$630$	5.32986e11	−	3.99884e11i	3.38340	−	2.53847i
$631$	−5.32618e10			−0.335968			−0.167984	−	0.985790i	$-0.553726\pi$
$631$	−5.32618e10			−0.335968			−0.167984	+	0.985790i	$0.553726\pi$
$632$			5.16170e9i			0.0323538i
$633$	−8.18070e10	+	2.72769e10i	−0.509537	+	0.169895i
$634$	−7.18161e10			−0.444493
$635$		−	4.53257e11i		−	2.78772i
$636$	4.70302e10	+	1.41050e11i	0.287441	+	0.862074i
$637$	1.03228e11			0.626961
$638$		−	1.32149e10i		−	0.0797592i
$639$	8.54563e10	+	1.13901e11i	0.512555	+	0.683161i
$640$	−1.11379e10			−0.0663873
$641$		−	2.38934e11i		−	1.41529i	−0.706566	−	0.707647i	$-0.749757\pi$
$641$		−	2.38934e11i		−	1.41529i	0.706566	−	0.707647i	$-0.250243\pi$
$642$	−2.85262e11	+	9.51147e10i	−1.67920	+	0.559896i
$643$	−6.17337e10			−0.361142			−0.180571	−	0.983562i	$-0.557795\pi$
$643$	−6.17337e10			−0.361142			−0.180571	+	0.983562i	$0.557795\pi$
$644$			2.44829e11i			1.42337i
$645$	−1.66340e11	−	4.98877e11i	−0.961078	−	2.88240i
$646$	6.01383e10			0.345320
$647$		−	1.11824e11i		−	0.638143i	−0.947731	−	0.319071i	$-0.896629\pi$
$647$		−	1.11824e11i		−	0.638143i	0.947731	−	0.319071i	$-0.103371\pi$
$648$	−3.05432e9	−	8.89696e8i	−0.0173227	−	0.00504593i
$649$	−5.26590e10			−0.296820
$650$			2.26741e11i			1.27021i
$651$	6.87230e10	−	2.29143e10i	0.382629	−	0.127580i
$652$	−1.80847e11			−1.00074
$653$		−	2.24385e11i		−	1.23408i	−0.786934	−	0.617038i	$-0.788333\pi$
$653$		−	2.24385e11i		−	1.23408i	0.786934	−	0.617038i	$-0.211667\pi$
$654$	2.50517e9	+	7.51334e9i	0.0136939	+	0.0410697i
$655$	−2.64849e11			−1.43891
$656$			7.95569e10i			0.429598i
$657$	2.43348e11	−	1.82577e11i	1.30607	−	0.979908i
$658$	−2.59276e11			−1.38312
$659$			1.87289e11i			0.993051i	0.868022	+	0.496525i	$0.165391\pi$
$659$			1.87289e11i			0.993051i	−0.868022	+	0.496525i	$0.834609\pi$
$660$	9.85789e10	−	3.28691e10i	0.519527	−	0.173226i
$661$	1.67039e11			0.875008			0.437504	−	0.899216i	$-0.355863\pi$
$661$	1.67039e11			0.875008			0.437504	+	0.899216i	$0.355863\pi$
$662$		−	3.52043e11i		−	1.83301i
$663$	1.63052e10	+	4.89016e10i	0.0843866	+	0.253087i
$664$	6.52957e8			0.00335902
$665$			2.03545e11i			1.04082i
$666$	−8.38307e10	−	1.11734e11i	−0.426095	−	0.567921i
$667$	−3.28371e10			−0.165906
$668$		−	1.47972e11i		−	0.743146i
$669$	7.47317e8	−	2.49178e8i	0.00373079	−	0.00124395i
$670$	−7.89824e11			−3.91950
$671$			3.74370e10i			0.184676i
$672$	1.48268e11	+	4.44676e11i	0.727061	+	2.18055i
$673$	2.15980e11			1.05282			0.526409	−	0.850232i	$-0.323538\pi$
$673$	2.15980e11			1.05282			0.526409	+	0.850232i	$0.323538\pi$
$674$		−	2.55727e10i		−	0.123919i
$675$	−2.81737e11	+	4.07180e11i	−1.35715	+	1.96142i
$676$	1.76733e11			0.846312
$677$			1.15271e11i			0.548738i	0.961624	+	0.274369i	$0.0884690\pi$
$677$			1.15271e11i			0.548738i	−0.961624	+	0.274369i	$0.911531\pi$
$678$	−2.04901e11	+	6.83201e10i	−0.969674	+	0.323318i
$679$	−2.96828e11			−1.39645
$680$			5.01246e9i			0.0234431i
$681$	−8.23107e10	−	2.46861e11i	−0.382708	−	1.14779i
$682$	2.27417e10			0.105120
$683$		−	6.94974e10i		−	0.319364i	−0.987169	−	0.159682i	$-0.948953\pi$
$683$		−	6.94974e10i		−	0.319364i	0.987169	−	0.159682i	$-0.0510468\pi$
$684$	−5.99569e10	+	4.49839e10i	−0.273914	+	0.205510i
$685$	5.39846e11			2.45193
$686$		−	3.35822e11i		−	1.51640i
$687$	2.48667e11	−	8.29131e10i	1.11633	−	0.372217i
$688$	3.74681e11			1.67228
$689$		−	7.83687e10i		−	0.347749i
$690$	−1.64409e11	−	4.93084e11i	−0.725319	−	2.17533i
$691$	−1.59299e11			−0.698717			−0.349358	−	0.936989i	$-0.613600\pi$
$691$	−1.59299e11			−0.698717			−0.349358	+	0.936989i	$0.613600\pi$
$692$			1.27962e11i			0.558029i
$693$	6.80607e10	+	9.07149e10i	0.295096	+	0.393320i
$694$	3.47021e11			1.49595
$695$			1.49460e11i			0.640597i
$696$	−7.53705e8	+	2.51308e8i	−0.00321192	+	0.00107095i
$697$	7.07074e10			0.299595
$698$		−	3.69842e11i		−	1.55810i
$699$	1.42007e10	+	4.25898e10i	0.0594842	+	0.178401i
$700$	9.21990e11			3.84002
$701$		−	2.60901e11i		−	1.08045i	−0.841521	−	0.540225i	$-0.818339\pi$
$701$		−	2.60901e11i		−	1.08045i	0.841521	−	0.540225i	$-0.181661\pi$
$702$	−1.06355e11	−	7.35893e10i	−0.437933	−	0.303016i
$703$	4.26708e10			0.174707
$704$			7.21540e10i			0.293744i
$705$	2.59409e11	−	8.64945e10i	1.05009	−	0.350132i
$706$	−2.84445e11			−1.14493
$707$			1.45132e11i			0.580879i
$708$	−7.72399e10	−	2.31653e11i	−0.307403	−	0.921944i
$709$	−9.15663e10			−0.362369			−0.181184	−	0.983449i	$-0.557993\pi$
$709$	−9.15663e10			−0.362369			−0.181184	+	0.983449i	$0.557993\pi$
$710$			5.62904e11i			2.21514i
$711$	−3.66553e11	+	2.75014e11i	−1.43436	+	1.07616i
$712$	5.68487e9			0.0221208
$713$		−	5.65098e10i		−	0.218658i
$714$	4.00272e11	−	1.33463e11i	1.54015	−	0.513531i
$715$	−5.47714e10			−0.209570
$716$		−	4.42600e10i		−	0.168407i
$717$	2.89100e10	+	8.67050e10i	0.109389	+	0.328071i
$718$	4.94546e11			1.86084
$719$		−	2.50226e11i		−	0.936303i	−0.883648	−	0.468151i	$-0.844920\pi$
$719$		−	2.50226e11i		−	0.936303i	0.883648	−	0.468151i	$-0.155080\pi$
$720$	−3.00487e11	−	4.00504e11i	−1.11814	−	1.49031i
$721$	−6.86989e11			−2.54219
$722$			3.36971e11i			1.24006i
$723$	−5.61103e10	+	1.87088e10i	−0.205348	+	0.0684690i
$724$	1.39951e11			0.509355
$725$			1.23660e11i			0.447586i
$726$	1.12613e10	+	3.37741e10i	0.0405360	+	0.121573i
$727$	1.63890e9			0.00586698			0.00293349	−	0.999996i	$-0.499066\pi$
$727$	1.63890e9			0.00586698			0.00293349	+	0.999996i	$0.499066\pi$
$728$		−	3.12226e9i		−	0.0111159i
$729$	−9.95526e10	−	2.64302e11i	−0.352487	−	0.935817i
$730$	1.20264e12			4.23492
$731$		−	3.33004e11i		−	1.16622i
$732$	−1.64690e11	+	5.49124e10i	−0.573617	+	0.191261i
$733$	2.18572e10			0.0757145			0.0378573	−	0.999283i	$-0.487947\pi$
$733$	2.18572e10			0.0757145			0.0378573	+	0.999283i	$0.487947\pi$
$734$			5.15582e11i			1.77629i
$735$	2.81875e11	+	8.45382e11i	0.965846	+	2.89670i
$736$	3.65650e11			1.24610
$737$		−	1.34429e11i		−	0.455642i
$738$	−1.41902e11	+	1.06465e11i	−0.478370	+	0.358907i
$739$	−2.40349e10			−0.0805870			−0.0402935	−	0.999188i	$-0.512829\pi$
$739$	−2.40349e10			−0.0805870			−0.0402935	+	0.999188i	$0.512829\pi$
$740$		−	2.74320e11i		−	0.914808i
$741$	3.74794e10	−	1.24968e10i	0.124314	−	0.0414500i
$742$	−6.41468e11			−2.11621
$743$		−	1.83045e11i		−	0.600625i	−0.953841	−	0.300313i	$-0.902909\pi$
$743$		−	1.83045e11i		−	0.600625i	0.953841	−	0.300313i	$-0.0970910\pi$
$744$	−4.32479e8	−	1.29706e9i	−0.00141148	−	0.00423320i
$745$	−5.01125e11			−1.62675
$746$			6.75689e10i			0.218168i
$747$	3.47893e10	+	4.63691e10i	0.111728	+	0.148918i
$748$	6.58022e10			0.210201
$749$		−	6.44480e11i		−	2.04777i
$750$	−1.07837e12	+	3.59562e11i	−3.40819	+	1.13639i
$751$	−3.26982e11			−1.02793			−0.513965	−	0.857811i	$-0.671824\pi$
$751$	−3.26982e11			−1.02793			−0.513965	+	0.857811i	$0.671824\pi$
$752$			1.94829e11i			0.609231i
$753$	−5.28340e10	−	1.58456e11i	−0.164336	−	0.492867i
$754$	−3.22997e10			−0.0999339
$755$			2.79667e11i			0.860704i
$756$	−2.99234e11	+	4.32467e11i	−0.916059	+	1.32393i
$757$	−1.24295e11			−0.378503			−0.189252	−	0.981929i	$-0.560606\pi$
$757$	−1.24295e11			−0.378503			−0.189252	+	0.981929i	$0.560606\pi$
$758$		−	6.73822e11i		−	2.04112i
$759$	8.39236e10	−	2.79826e10i	0.252882	−	0.0843182i
$760$	3.84167e9			0.0115151
$761$		−	3.24940e11i		−	0.968869i	−0.874828	−	0.484434i	$-0.839025\pi$
$761$		−	3.24940e11i		−	0.968869i	0.874828	−	0.484434i	$-0.160975\pi$
$762$	2.27778e11	+	6.83138e11i	0.675604	+	2.02623i
$763$	−1.69746e10			−0.0500842
$764$			5.10228e11i			1.49758i
$765$	−3.55954e11	+	2.67062e11i	−1.03932	+	0.779770i
$766$	−7.11871e10			−0.206769
$767$			1.28709e11i			0.371900i
$768$	3.38315e11	−	1.12804e11i	0.972472	−	0.324251i
$769$	−4.03844e11			−1.15480			−0.577402	−	0.816460i	$-0.695933\pi$
$769$	−4.03844e11			−1.15480			−0.577402	+	0.816460i	$0.695933\pi$
$770$			4.48318e11i			1.27533i
$771$	1.16239e11	+	3.48615e11i	0.328953	+	0.986573i
$772$	−1.85548e11			−0.522382
$773$		−	2.43769e11i		−	0.682749i	−0.939927	−	0.341375i	$-0.889108\pi$
$773$		−	2.43769e11i		−	0.682749i	0.939927	−	0.341375i	$-0.110892\pi$
$774$	5.01408e11	+	6.68303e11i	1.39710	+	1.86213i
$775$	−2.12808e11			−0.589903
$776$			5.60226e9i			0.0154496i
$777$	2.84011e11	−	9.46977e10i	0.779204	−	0.259810i
$778$	4.34314e11			1.18546
$779$		−	5.41920e10i		−	0.147158i
$780$	−8.03384e10	−	2.40946e11i	−0.217042	−	0.650939i
$781$	−9.58070e10			−0.257509
$782$		−	3.29137e11i		−	0.880137i
$783$	−5.80036e10	−	4.01340e10i	−0.154315	−	0.106774i
$784$	−6.34924e11			−1.68057
$785$			4.48072e11i			1.17996i
$786$	3.99174e11	−	1.33096e11i	1.04586	−	0.348720i
$787$	6.09638e11			1.58918			0.794590	−	0.607147i	$-0.207686\pi$
$787$	6.09638e11			1.58918			0.794590	+	0.607147i	$0.207686\pi$
$788$			1.32588e11i			0.343874i
$789$	1.14320e11	+	3.42862e11i	0.294996	+	0.884731i
$790$	−1.81153e12			−4.65089
$791$		−	4.62925e11i		−	1.18251i
$792$	1.71213e9	−	1.28456e9i	0.00435148	−	0.00326479i
$793$	9.15032e10			0.231389
$794$		−	6.15915e11i		−	1.54967i
$795$	6.41797e11	−	2.13994e11i	1.60668	−	0.535715i
$796$	−7.07682e10			−0.176273
$797$			5.73745e11i			1.42196i	0.703215	+	0.710978i	$0.251747\pi$
$797$			5.73745e11i			1.42196i	−0.703215	+	0.710978i	$0.748253\pi$
$798$	−1.02289e11	−	3.06779e11i	−0.252242	−	0.756508i
$799$	1.73157e11			0.424868
$800$		−	1.37699e12i		−	3.36178i
$801$	3.02888e11	+	4.03706e11i	0.735788	+	0.980697i
$802$	−5.69464e11			−1.37648
$803$			2.04691e11i			0.492308i
$804$	5.91369e11	−	1.97180e11i	1.41525	−	0.471887i
$805$	1.11401e12			2.65280
$806$		−	5.55850e10i		−	0.131710i
$807$	−2.02600e11	−	6.07623e11i	−0.477688	−	1.43265i
$808$	2.73919e9			0.00642654
$809$			4.37464e11i			1.02129i	0.859792	+	0.510644i	$0.170593\pi$
$809$			4.37464e11i			1.02129i	−0.859792	+	0.510644i	$0.829407\pi$
$810$	3.12243e11	−	1.07193e12i	0.725359	−	2.49016i
$811$	4.30873e11			0.996015			0.498007	−	0.867173i	$-0.334065\pi$
$811$	4.30873e11			0.996015			0.498007	+	0.867173i	$0.334065\pi$
$812$			1.31339e11i			0.302114i
$813$	1.66708e11	−	5.55853e10i	0.381587	−	0.127232i
$814$	9.39845e10			0.214071
$815$			8.22880e11i			1.86512i
$816$	−1.00289e11	−	3.00779e11i	−0.226199	−	0.678401i
$817$	−2.55223e11			−0.572837
$818$		−	1.26081e11i		−	0.281602i
$819$	2.21724e11	−	1.66353e11i	0.492808	−	0.369740i
$820$	−3.48386e11			−0.770558
$821$			4.06889e11i			0.895578i	0.894139	+	0.447789i	$0.147789\pi$
$821$			4.06889e11i			0.895578i	−0.894139	+	0.447789i	$0.852211\pi$
$822$	−8.13643e11	+	2.71293e11i	−1.78216	+	0.594225i
$823$	4.40532e11			0.960236			0.480118	−	0.877204i	$-0.340594\pi$
$823$	4.40532e11			0.960236			0.480118	+	0.877204i	$0.340594\pi$
$824$			1.29661e10i			0.0281255i
$825$	−1.05379e11	−	3.16044e11i	−0.227476	−	0.682232i
$826$	1.05351e12			2.26318
$827$		−	3.02347e10i		−	0.0646373i	−0.999478	−	0.0323187i	$-0.989711\pi$
$827$		−	3.02347e10i		−	0.0646373i	0.999478	−	0.0323187i	$-0.0102891\pi$
$828$	2.46197e11	+	3.28145e11i	0.523796	+	0.698142i
$829$	−7.97129e11			−1.68776			−0.843879	−	0.536533i	$-0.819734\pi$
$829$	−7.97129e11			−1.68776			−0.843879	+	0.536533i	$0.819734\pi$
$830$			2.29159e11i			0.482863i
$831$	−3.15701e11	+	1.05264e11i	−0.662022	+	0.220738i
$832$	1.76358e11			0.368046
$833$			5.64299e11i			1.17200i
$834$	−7.51090e10	−	2.25262e11i	−0.155249	−	0.465612i
$835$	−6.73295e11			−1.38503
$836$		−	5.04324e10i		−	0.103249i
$837$	6.90672e10	−	9.98192e10i	0.140725	−	0.203382i
$838$	1.36287e12			2.76361
$839$			2.93373e11i			0.592069i	0.955177	+	0.296034i	$0.0956643\pi$
$839$			2.93373e11i			0.592069i	−0.955177	+	0.296034i	$0.904336\pi$
$840$	2.55696e10	−	8.52568e9i	0.0513579	−	0.0171243i
$841$	4.82631e11			0.964786
$842$		−	1.05965e12i		−	2.10822i
$843$	1.90813e11	+	5.72274e11i	0.377831	+	1.13317i
$844$	2.69056e11			0.530240
$845$		−	8.04160e11i		−	1.57730i
$846$	−3.47508e11	+	2.60725e11i	−0.678396	+	0.508981i
$847$	−7.63044e10			−0.148257
$848$			4.82022e11i			0.932144i
$849$	1.29017e11	−	4.30179e10i	0.248322	−	0.0827978i
$850$	−1.23948e12			−2.37446
$851$		−	2.33538e11i		−	0.445286i
$852$	−1.40529e11	−	4.21465e11i	−0.266691	−	0.799841i
$853$	2.43764e11			0.460441			0.230220	−	0.973139i	$-0.426055\pi$
$853$	2.43764e11			0.460441			0.230220	+	0.973139i	$0.426055\pi$
$854$		−	7.48977e11i		−	1.40811i
$855$	2.04683e11	+	2.72812e11i	0.383017	+	0.510505i
$856$	−1.21638e10			−0.0226555
$857$		−	5.57455e10i		−	0.103344i	−0.998664	−	0.0516721i	$-0.983545\pi$
$857$		−	5.57455e10i		−	0.103344i	0.998664	−	0.0516721i	$-0.0164551\pi$
$858$	8.25502e10	−	2.75247e10i	0.152324	−	0.0507894i
$859$	2.07252e10			0.0380651			0.0190326	−	0.999819i	$-0.493941\pi$
$859$	2.07252e10			0.0380651			0.0190326	+	0.999819i	$0.493941\pi$
$860$			1.64076e12i			2.99952i
$861$	−1.20266e11	−	3.60694e11i	−0.218842	−	0.656337i
$862$	4.09387e11			0.741489
$863$			3.75673e11i			0.677278i	0.940916	+	0.338639i	$0.109967\pi$
$863$			3.75673e11i			0.677278i	−0.940916	+	0.338639i	$0.890033\pi$
$864$	6.45886e11	+	4.46904e11i	1.15905	+	0.801972i
$865$	5.82246e11			1.04002
$866$		−	2.74497e11i		−	0.488052i
$867$	2.68703e11	−	8.95936e10i	0.475550	−	0.158563i
$868$	−2.26024e11			−0.398176
$869$		−	3.08324e11i		−	0.540665i
$870$	−8.81977e10	−	2.64517e11i	−0.153950	−	0.461717i
$871$	−3.28570e11			−0.570894
$872$			3.20375e8i			0.000554105i
$873$	−3.97839e11	+	2.98487e11i	−0.684936	+	0.513888i
$874$	−2.52259e11			−0.432316
$875$		−	2.43633e12i		−	4.15626i
$876$	−9.00460e11	+	3.00240e11i	−1.52914	+	0.509861i
$877$	−5.93586e11			−1.00343			−0.501713	−	0.865034i	$-0.667297\pi$
$877$	−5.93586e11			−1.00343			−0.501713	+	0.865034i	$0.667297\pi$
$878$		−	2.70922e11i		−	0.455896i
$879$	−1.18065e11	−	3.54092e11i	−0.197772	−	0.593145i
$880$	3.36882e11			0.561755
$881$			2.25330e11i			0.374038i	0.982356	+	0.187019i	$0.0598826\pi$
$881$			2.25330e11i			0.374038i	−0.982356	+	0.187019i	$0.940117\pi$
$882$	−8.49672e11	−	1.13249e12i	−1.40403	−	1.87137i
$883$	1.15095e12			1.89327			0.946634	−	0.322311i	$-0.104460\pi$
$883$	1.15095e12			1.89327			0.946634	+	0.322311i	$0.104460\pi$
$884$		−	1.60833e11i		−	0.263370i
$885$	−1.05405e12	+	3.51452e11i	−1.71826	+	0.572919i
$886$	−6.10013e11			−0.989930
$887$			4.60561e11i			0.744034i	0.928226	+	0.372017i	$0.121334\pi$
$887$			4.60561e11i			0.744034i	−0.928226	+	0.372017i	$0.878666\pi$
$888$	−1.78730e9	−	5.36036e9i	−0.00287440	−	0.00862070i
$889$	−1.54339e12			−2.47097
$890$			1.99514e12i			3.17989i
$891$	1.82444e11	+	5.31442e10i	0.289480	+	0.0843229i
$892$	−2.45786e9			−0.00388237
$893$		−	1.32712e11i		−	0.208691i
$894$	7.55284e11	−	2.51834e11i	1.18239	−	0.394244i
$895$	−2.01389e11			−0.313866
$896$			3.79258e10i			0.0588441i
$897$	−6.83948e10	−	2.05125e11i	−0.105646	−	0.316847i
$898$	8.32975e10			0.128093
$899$		−	3.03149e10i		−	0.0464106i
$900$	1.23575e12	−	9.27144e11i	1.88347	−	1.41311i
$901$	4.28404e11			0.650062
$902$		−	1.19360e11i		−	0.180316i
$903$	−1.69873e12	+	5.66406e11i	−2.55489	+	0.851876i
$904$	−8.73715e9			−0.0130827
$905$		−	6.36796e11i		−	0.949305i
$906$	−1.40543e11	−	4.21508e11i	−0.208592	−	0.625595i
$907$	−2.48086e10			−0.0366584			−0.0183292	−	0.999832i	$-0.505835\pi$
$907$	−2.48086e10			−0.0366584			−0.0183292	+	0.999832i	$0.505835\pi$
$908$			8.11903e11i			1.19443i
$909$	1.45943e11	+	1.94521e11i	0.213761	+	0.284912i
$910$	1.09577e12			1.59792
$911$			3.32037e11i			0.482074i	0.970516	+	0.241037i	$0.0774874\pi$
$911$			3.32037e11i			0.482074i	−0.970516	+	0.241037i	$0.922513\pi$
$912$	−2.30524e11	+	7.68636e10i	−0.333225	+	0.111107i
$913$	−3.90031e10			−0.0561327
$914$		−	3.97689e11i		−	0.569848i
$915$	2.49859e11	+	7.49361e11i	0.356460	+	1.06907i
$916$	−8.17845e11			−1.16169
$917$			9.01838e11i			1.27541i
$918$	4.02277e11	−	5.81390e11i	0.566441	−	0.818648i
$919$	−1.78901e11			−0.250813			−0.125407	−	0.992105i	$-0.540024\pi$
$919$	−1.78901e11			−0.250813			−0.125407	+	0.992105i	$0.540024\pi$
$920$		−	2.10255e10i		−	0.0293491i
$921$	5.66596e11	−	1.88920e11i	0.787472	−	0.262566i
$922$	1.98457e12			2.74627
$923$			2.34170e11i			0.322645i
$924$	−1.11923e11	−	3.35671e11i	−0.153543	−	0.460497i
$925$	−8.79469e11			−1.20131
$926$			1.26104e12i			1.71508i
$927$	−9.20773e11	+	6.90829e11i	−1.24691	+	0.935517i
$928$	1.96154e11			0.264488
$929$			9.33085e11i			1.25273i	0.779529	+	0.626366i	$0.215459\pi$
$929$			9.33085e11i			1.25273i	−0.779529	+	0.626366i	$0.784541\pi$
$930$	4.55211e11	−	1.51781e11i	0.608528	−	0.202901i
$931$	4.32493e11			0.575679
$932$		−	1.40074e11i		−	0.185650i
$933$	−2.06271e11	−	6.18634e11i	−0.272215	−	0.816408i
$934$	9.34972e11			1.22860
$935$		−	2.99409e11i		−	0.391759i
$936$	−3.13972e9	−	4.18478e9i	−0.00409060	−	0.00545217i
$937$	−6.69260e10			−0.0868233			−0.0434116	−	0.999057i	$-0.513823\pi$
$937$	−6.69260e10			−0.0868233			−0.0434116	+	0.999057i	$0.513823\pi$
$938$			2.68943e12i			3.47416i
$939$	−4.76902e11	+	1.59013e11i	−0.613432	+	0.204537i
$940$	−8.53172e11			−1.09276
$941$			5.51982e11i			0.703990i	0.936002	+	0.351995i	$0.114497\pi$
$941$			5.51982e11i			0.703990i	−0.936002	+	0.351995i	$0.885503\pi$
$942$	−2.25173e11	−	6.75323e11i	−0.285964	−	0.857646i
$943$	−2.96593e11			−0.375071
$944$		−	7.91646e11i		−	0.996881i
$945$	1.96779e12	+	1.36156e12i	2.46746	+	1.70729i
$946$	−5.62140e11			−0.701907
$947$			4.43446e11i			0.551368i	0.961248	+	0.275684i	$0.0889043\pi$
$947$			4.43446e11i			0.551368i	−0.961248	+	0.275684i	$0.911096\pi$
$948$	1.35635e12	−	4.52248e11i	1.67934	−	0.559942i
$949$	5.00304e11			0.616836
$950$			9.49972e11i			1.16632i
$951$	−8.15791e10	−	2.44667e11i	−0.0997371	−	0.299125i
$952$	1.70679e10			0.0207794
$953$		−	1.23342e12i		−	1.49534i	−0.664071	−	0.747670i	$-0.731173\pi$
$953$		−	1.23342e12i		−	1.49534i	0.664071	−	0.747670i	$-0.268827\pi$
$954$	−8.59762e11	+	6.45054e11i	−1.03797	+	0.778758i
$955$	2.32161e12			2.79110
$956$		−	2.85165e11i		−	0.341401i
$957$	4.50211e10	−	1.50114e10i	0.0536746	−	0.0178967i
$958$	−5.45853e11			−0.648058
$959$		−	1.83823e12i		−	2.17333i
$960$	4.81564e11	+	1.44428e12i	0.566982	+	1.70046i
$961$	−8.00722e11			−0.938832
$962$		−	2.29716e11i		−	0.268220i
$963$	−6.48083e11	−	8.63798e11i	−0.753573	−	1.00440i
$964$	1.84542e11			0.213691
$965$			8.44271e11i			0.973583i
$966$	−1.67900e12	+	5.59829e11i	−1.92816	+	0.642905i
$967$	5.38140e11			0.615445			0.307723	−	0.951476i	$-0.400433\pi$
$967$	5.38140e11			0.615445			0.307723	+	0.951476i	$0.400433\pi$
$968$			1.44015e9i			0.00164024i
$969$	6.83138e10	+	2.04882e11i	0.0774842	+	0.232386i
$970$	−1.96614e12			−2.22089
$971$		−	9.90219e11i		−	1.11392i	−0.830539	−	0.556961i	$-0.811967\pi$
$971$		−	9.90219e11i		−	1.11392i	0.830539	−	0.556961i	$-0.188033\pi$
$972$	3.38203e10	+	8.80543e11i	0.0378890	+	0.986474i
$973$	5.08925e11			0.567810
$974$			7.38490e11i			0.820557i
$975$	−7.72472e11	+	2.57565e11i	−0.854800	+	0.285016i
$976$	−5.62807e11			−0.620241
$977$		−	4.85991e11i		−	0.533396i	−0.963780	−	0.266698i	$-0.914067\pi$
$977$		−	4.85991e11i		−	0.533396i	0.963780	−	0.266698i	$-0.0859326\pi$
$978$	−4.13528e11	−	1.24023e12i	−0.452011	−	1.35564i
$979$	−3.39575e11			−0.369662
$980$		−	2.78038e12i		−	3.01440i
$981$	−2.27511e10	+	1.70695e10i	−0.0245655	+	0.0184308i
$982$	−1.54629e12			−1.66282
$983$		−	5.78550e11i		−	0.619622i	−0.950798	−	0.309811i	$-0.899734\pi$
$983$		−	5.78550e11i		−	0.619622i	0.950798	−	0.309811i	$-0.100266\pi$
$984$	−6.80767e9	+	2.26988e9i	−0.00726136	+	0.00242115i
$985$	6.03295e11			0.640892
$986$		−	1.76567e11i		−	0.186811i
$987$	−2.94523e11	−	8.83313e11i	−0.310349	−	0.930778i
$988$	−1.23266e11			−0.129365
$989$			1.39683e12i			1.46002i
$990$	4.50824e11	+	6.00882e11i	0.469317	+	0.625531i
$991$	−9.25342e11			−0.959417			−0.479709	−	0.877428i	$-0.659258\pi$
$991$	−9.25342e11			−0.959417			−0.479709	+	0.877428i	$0.659258\pi$
$992$			3.37565e11i			0.348586i
$993$	1.19936e12	−	3.99902e11i	1.23354	−	0.411298i
$994$	1.91674e12			1.96344
$995$			3.22005e11i			0.328527i
$996$	−5.72095e10	−	1.71579e11i	−0.0581341	−	0.174352i
$997$	1.89812e12			1.92107			0.960533	−	0.278165i	$-0.0897262\pi$
$997$	1.89812e12			1.92107			0.960533	+	0.278165i	$0.0897262\pi$
$998$			9.05603e11i			0.912884i
$999$	2.85434e11	−	4.12522e11i	0.286578	−	0.414176i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	33.9.b.a.23.5	✓	26
3.2	odd	2	inner	33.9.b.a.23.22	yes	26

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
33.9.b.a.23.5	✓	26	1.1	even	1	trivial
33.9.b.a.23.22	yes	26	3.2	odd	2	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q-22.5549i q^{2} +(76.8411 - 25.6211i) q^{3} -252.723 q^{4} +1149.93i q^{5} +(-577.881 - 1733.14i) q^{6} +3915.62 q^{7} -73.9026i q^{8} +(5248.12 - 3937.51i) q^{9} +O(q^{10})\)	\(q-22.5549i q^{2} +(76.8411 - 25.6211i) q^{3} -252.723 q^{4} +1149.93i q^{5} +(-577.881 - 1733.14i) q^{6} +3915.62 q^{7} -73.9026i q^{8} +(5248.12 - 3937.51i) q^{9} +25936.5 q^{10} +4414.43i q^{11} +(-19419.6 + 6475.05i) q^{12} +10789.7 q^{13} -88316.4i q^{14} +(29462.4 + 88361.7i) q^{15} -66364.1 q^{16} +58982.1i q^{17} +(-88810.1 - 118371. i) q^{18} +45205.4 q^{19} -290614. i q^{20} +(300881. - 100323. i) q^{21} +99567.0 q^{22} -247409. i q^{23} +(-1893.47 - 5678.76i) q^{24} -931708. q^{25} -243360. i q^{26} +(302388. - 437025. i) q^{27} -989569. q^{28} -132724. i q^{29} +(1.99299e6 - 664522. i) q^{30} +228406. q^{31} +1.47792e6i q^{32} +(113103. + 339210. i) q^{33} +1.33034e6 q^{34} +4.50268e6i q^{35} +(-1.32632e6 + 995101. i) q^{36} +943932. q^{37} -1.01960e6i q^{38} +(829092. - 276444. i) q^{39} +84982.6 q^{40} -1.19879e6i q^{41} +(-2.26276e6 - 6.78633e6i) q^{42} -5.64585e6 q^{43} -1.11563e6i q^{44} +(4.52785e6 + 6.03496e6i) q^{45} -5.58029e6 q^{46} -2.93576e6i q^{47} +(-5.09949e6 + 1.70032e6i) q^{48} +9.56729e6 q^{49} +2.10146e7i q^{50} +(1.51119e6 + 4.53225e6i) q^{51} -2.72681e6 q^{52} -7.26329e6i q^{53} +(-9.85706e6 - 6.82033e6i) q^{54} -5.07627e6 q^{55} -289375. i q^{56} +(3.47363e6 - 1.15821e6i) q^{57} -2.99357e6 q^{58} +1.19288e7i q^{59} +(-7.44584e6 - 2.23311e7i) q^{60} +8.48061e6 q^{61} -5.15167e6i q^{62} +(2.05496e7 - 1.54178e7i) q^{63} +1.63450e7 q^{64} +1.24074e7i q^{65} +(7.65084e6 - 2.55102e6i) q^{66} -3.04522e7 q^{67} -1.49062e7i q^{68} +(-6.33890e6 - 1.90112e7i) q^{69} +1.01558e8 q^{70} +2.17031e7i q^{71} +(-290992. - 387850. i) q^{72} +4.63687e7 q^{73} -2.12903e7i q^{74} +(-7.15935e7 + 2.38714e7i) q^{75} -1.14245e7 q^{76} +1.72852e7i q^{77} +(-6.23516e6 - 1.87001e7i) q^{78} -6.98447e7 q^{79} -7.63139e7i q^{80} +(1.20388e7 - 4.13290e7i) q^{81} -2.70387e7 q^{82} +8.83537e6i q^{83} +(-7.60396e7 + 2.53539e7i) q^{84} -6.78252e7 q^{85} +1.27341e8i q^{86} +(-3.40052e6 - 1.01986e7i) q^{87} +326238. q^{88} +7.69239e7i q^{89} +(1.36118e8 - 1.02125e8i) q^{90} +4.22484e7 q^{91} +6.25261e7i q^{92} +(1.75510e7 - 5.85201e6i) q^{93} -6.62157e7 q^{94} +5.19829e7i q^{95} +(3.78658e7 + 1.13565e8i) q^{96} -7.58060e7 q^{97} -2.15789e8i q^{98} +(1.73819e7 + 2.31674e7i) 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

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