LMFDB - Embedded newform 33.9.b.a.23.2

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			23.2
Character	$\chi$	$=$	33.23
Dual form			33.9.b.a.23.25

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-27.8469i q^{2} +(-68.6229 + 43.0336i) q^{3} -519.450 q^{4} +436.996i q^{5} +(1198.35 + 1910.94i) q^{6} -547.160 q^{7} +7336.27i q^{8} +(2857.21 - 5906.19i) q^{9} +O(q^{10})$	\(q-27.8469i q^{2} +(-68.6229 + 43.0336i) q^{3} -519.450 q^{4} +436.996i q^{5} +(1198.35 + 1910.94i) q^{6} -547.160 q^{7} +7336.27i q^{8} +(2857.21 - 5906.19i) q^{9} +12169.0 q^{10} -4414.43i q^{11} +(35646.2 - 22353.8i) q^{12} +24475.4 q^{13} +15236.7i q^{14} +(-18805.5 - 29987.9i) q^{15} +71313.3 q^{16} +103244. i q^{17} +(-164469. - 79564.6i) q^{18} +51453.1 q^{19} -226998. i q^{20} +(37547.7 - 23546.3i) q^{21} -122928. q^{22} -382919. i q^{23} +(-315706. - 503437. i) q^{24} +199659. q^{25} -681564. i q^{26} +(58094.2 + 528256. i) q^{27} +284223. q^{28} +663503. i q^{29} +(-835072. + 523676. i) q^{30} +1.75560e6 q^{31} -107768. i q^{32} +(189969. + 302931. i) q^{33} +2.87503e6 q^{34} -239107. i q^{35} +(-1.48418e6 + 3.06797e6i) q^{36} -159583. q^{37} -1.43281e6i q^{38} +(-1.67957e6 + 1.05326e6i) q^{39} -3.20592e6 q^{40} -679433. i q^{41} +(-655691. - 1.04559e6i) q^{42} +6.20692e6 q^{43} +2.29308e6i q^{44} +(2.58098e6 + 1.24859e6i) q^{45} -1.06631e7 q^{46} +3.90685e6i q^{47} +(-4.89373e6 + 3.06887e6i) q^{48} -5.46542e6 q^{49} -5.55990e6i q^{50} +(-4.44297e6 - 7.08492e6i) q^{51} -1.27137e7 q^{52} +5.24913e6i q^{53} +(1.47103e7 - 1.61775e6i) q^{54} +1.92909e6 q^{55} -4.01412e6i q^{56} +(-3.53086e6 + 2.21421e6i) q^{57} +1.84765e7 q^{58} +1.59934e7i q^{59} +(9.76853e6 + 1.55772e7i) q^{60} +1.39605e7 q^{61} -4.88882e7i q^{62} +(-1.56335e6 + 3.23163e6i) q^{63} +1.52552e7 q^{64} +1.06956e7i q^{65} +(8.43569e6 - 5.29004e6i) q^{66} -2.43344e7 q^{67} -5.36302e7i q^{68} +(1.64784e7 + 2.62770e7i) q^{69} -6.65839e6 q^{70} -9.07174e6i q^{71} +(4.33294e7 + 2.09613e7i) q^{72} -2.81023e7 q^{73} +4.44389e6i q^{74} +(-1.37012e7 + 8.59207e6i) q^{75} -2.67273e7 q^{76} +2.41540e6i q^{77} +(2.93302e7 + 4.67709e7i) q^{78} +1.11829e7 q^{79} +3.11636e7i q^{80} +(-2.67194e7 - 3.37505e7i) q^{81} -1.89201e7 q^{82} -6.75805e7i q^{83} +(-1.95042e7 + 1.22311e7i) q^{84} -4.51173e7 q^{85} -1.72844e8i q^{86} +(-2.85529e7 - 4.55315e7i) q^{87} +3.23854e7 q^{88} +1.58030e7i q^{89} +(3.47694e7 - 7.18723e7i) q^{90} -1.33920e7 q^{91} +1.98907e8i q^{92} +(-1.20475e8 + 7.55500e7i) q^{93} +1.08794e8 q^{94} +2.24848e7i q^{95} +(4.63764e6 + 7.39535e6i) q^{96} +1.31349e8 q^{97} +1.52195e8i q^{98} +(-2.60724e7 - 1.26130e7i) 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 $

$2$		−	27.8469i		−	1.74043i	−0.492671	−	0.870216i	$-0.663979\pi$
$2$		−	27.8469i		−	1.74043i	0.492671	−	0.870216i	$-0.336021\pi$
$3$	−68.6229	+	43.0336i	−0.847197	+	0.531279i
$3$	−68.6229	+	43.0336i	−0.847197	+	0.531279i
$4$	−519.450			−2.02910
$5$			436.996i			0.699194i	0.936900	+	0.349597i	$0.113681\pi$
$5$			436.996i			0.699194i	−0.936900	+	0.349597i	$0.886319\pi$
$6$	1198.35	+	1910.94i	0.924655	+	1.47449i
$7$	−547.160			−0.227888			−0.113944	−	0.993487i	$-0.536349\pi$
$7$	−547.160			−0.227888			−0.113944	+	0.993487i	$0.536349\pi$
$8$			7336.27i			1.79108i
$9$	2857.21	−	5906.19i	0.435485	−	0.900196i
$10$	12169.0			1.21690
$11$		−	4414.43i		−	0.301511i
$11$		−	4414.43i		−	0.301511i
$12$	35646.2	−	22353.8i	1.71905	−	1.07802i
$13$	24475.4			0.856951			0.428476	−	0.903553i	$-0.359051\pi$
$13$	24475.4			0.856951			0.428476	+	0.903553i	$0.359051\pi$
$14$			15236.7i			0.396624i
$15$	−18805.5	−	29987.9i	−0.371467	−	0.592355i
$16$	71313.3			1.08815
$17$			103244.i			1.23615i	0.786120	+	0.618074i	$0.212087\pi$
$17$			103244.i			1.23615i	−0.786120	+	0.618074i	$0.787913\pi$
$18$	−164469.	−	79564.6i	−1.56673	−	0.757931i
$19$	51453.1			0.394818			0.197409	−	0.980321i	$-0.436747\pi$
$19$	51453.1			0.394818			0.197409	+	0.980321i	$0.436747\pi$
$20$		−	226998.i		−	1.41874i
$21$	37547.7	−	23546.3i	0.193066	−	0.121072i
$22$	−122928.			−0.524760
$23$		−	382919.i		−	1.36834i	−0.729321	−	0.684172i	$-0.760164\pi$
$23$		−	382919.i		−	1.36834i	0.729321	−	0.684172i	$-0.239836\pi$
$24$	−315706.	−	503437.i	−0.951565	−	1.51740i
$25$	199659.			0.511128
$26$		−	681564.i		−	1.49147i
$27$	58094.2	+	528256.i	0.109315	+	0.994007i
$28$	284223.			0.462409
$29$			663503.i			0.938104i	0.883171	+	0.469052i	$0.155404\pi$
$29$			663503.i			0.938104i	−0.883171	+	0.469052i	$0.844596\pi$
$30$	−835072.	+	523676.i	−1.03095	+	0.646513i
$31$	1.75560e6			1.90099			0.950495	−	0.310739i	$-0.100577\pi$
$31$	1.75560e6			1.90099			0.950495	+	0.310739i	$0.100577\pi$
$32$		−	107768.i		−	0.102775i
$33$	189969.	+	302931.i	0.160187	+	0.255439i
$34$	2.87503e6			2.15143
$35$		−	239107.i		−	0.159338i
$36$	−1.48418e6	+	3.06797e6i	−0.883643	+	1.82659i
$37$	−159583.			−0.0851490			−0.0425745	−	0.999093i	$-0.513556\pi$
$37$	−159583.			−0.0851490			−0.0425745	+	0.999093i	$0.513556\pi$
$38$		−	1.43281e6i		−	0.687154i
$39$	−1.67957e6	+	1.05326e6i	−0.726006	+	0.455281i
$40$	−3.20592e6			−1.25231
$41$		−	679433.i		−	0.240443i	−0.992747	−	0.120221i	$-0.961640\pi$
$41$		−	679433.i		−	0.240443i	0.992747	−	0.120221i	$-0.0383604\pi$
$42$	−655691.	−	1.04559e6i	−0.210718	−	0.336019i
$43$	6.20692e6			1.81553			0.907763	−	0.419483i	$-0.137789\pi$
$43$	6.20692e6			1.81553			0.907763	+	0.419483i	$0.137789\pi$
$44$			2.29308e6i			0.611797i
$45$	2.58098e6	+	1.24859e6i	0.629411	+	0.304488i
$46$	−1.06631e7			−2.38151
$47$			3.90685e6i			0.800636i	0.916376	+	0.400318i	$0.131100\pi$
$47$			3.90685e6i			0.800636i	−0.916376	+	0.400318i	$0.868900\pi$
$48$	−4.89373e6	+	3.06887e6i	−0.921881	+	0.578114i
$49$	−5.46542e6			−0.948067
$50$		−	5.55990e6i		−	0.889584i
$51$	−4.44297e6	−	7.08492e6i	−0.656739	−	1.04726i
$52$	−1.27137e7			−1.73884
$53$			5.24913e6i			0.665248i	0.943060	+	0.332624i	$0.107934\pi$
$53$			5.24913e6i			0.665248i	−0.943060	+	0.332624i	$0.892066\pi$
$54$	1.47103e7	−	1.61775e6i	1.73000	−	0.190255i
$55$	1.92909e6			0.210815
$56$		−	4.01412e6i		−	0.408167i
$57$	−3.53086e6	+	2.21421e6i	−0.334489	+	0.209759i
$58$	1.84765e7			1.63271
$59$			1.59934e7i			1.31987i	0.751321	+	0.659937i	$0.229417\pi$
$59$			1.59934e7i			1.31987i	−0.751321	+	0.659937i	$0.770583\pi$
$60$	9.76853e6	+	1.55772e7i	0.753745	+	1.20195i
$61$	1.39605e7			1.00828			0.504142	−	0.863621i	$-0.331809\pi$
$61$	1.39605e7			1.00828			0.504142	+	0.863621i	$0.331809\pi$
$62$		−	4.88882e7i		−	3.30854i
$63$	−1.56335e6	+	3.23163e6i	−0.0992419	+	0.205144i
$64$	1.52552e7			0.909280
$65$			1.06956e7i			0.599175i
$66$	8.43569e6	−	5.29004e6i	0.444575	−	0.278794i
$67$	−2.43344e7			−1.20760			−0.603798	−	0.797137i	$-0.706347\pi$
$67$	−2.43344e7			−1.20760			−0.603798	+	0.797137i	$0.706347\pi$
$68$		−	5.36302e7i		−	2.50827i
$69$	1.64784e7	+	2.62770e7i	0.726973	+	1.15926i
$70$	−6.65839e6			−0.277317
$71$		−	9.07174e6i		−	0.356991i	−0.983941	−	0.178495i	$-0.942877\pi$
$71$		−	9.07174e6i		−	0.356991i	0.983941	−	0.178495i	$-0.0571230\pi$
$72$	4.33294e7	+	2.09613e7i	1.61233	+	0.779989i
$73$	−2.81023e7			−0.989579			−0.494790	−	0.869013i	$-0.664755\pi$
$73$	−2.81023e7			−0.989579			−0.494790	+	0.869013i	$0.664755\pi$
$74$			4.44389e6i			0.148196i
$75$	−1.37012e7	+	8.59207e6i	−0.433026	+	0.271552i
$76$	−2.67273e7			−0.801127
$77$			2.41540e6i			0.0687110i
$78$	2.93302e7	+	4.67709e7i	0.792385	+	1.26356i
$79$	1.11829e7			0.287107			0.143554	−	0.989643i	$-0.454147\pi$
$79$	1.11829e7			0.287107			0.143554	+	0.989643i	$0.454147\pi$
$80$			3.11636e7i			0.760830i
$81$	−2.67194e7	−	3.37505e7i	−0.620706	−	0.784043i
$82$	−1.89201e7			−0.418474
$83$		−	6.75805e7i		−	1.42400i	−0.702181	−	0.711999i	$-0.747790\pi$
$83$		−	6.75805e7i		−	1.42400i	0.702181	−	0.711999i	$-0.252210\pi$
$84$	−1.95042e7	+	1.22311e7i	−0.391751	+	0.245668i
$85$	−4.51173e7			−0.864306
$86$		−	1.72844e8i		−	3.15980i
$87$	−2.85529e7	−	4.55315e7i	−0.498395	−	0.794758i
$88$	3.23854e7			0.540032
$89$			1.58030e7i			0.251871i	0.992038	+	0.125936i	$0.0401933\pi$
$89$			1.58030e7i			0.251871i	−0.992038	+	0.125936i	$0.959807\pi$
$90$	3.47694e7	−	7.18723e7i	0.529941	−	1.09545i
$91$	−1.33920e7			−0.195289
$92$			1.98907e8i			2.77651i
$93$	−1.20475e8	+	7.55500e7i	−1.61051	+	1.00996i
$94$	1.08794e8			1.39345
$95$			2.24848e7i			0.276054i
$96$	4.63764e6	+	7.39535e6i	0.0546025	+	0.0870711i
$97$	1.31349e8			1.48367			0.741837	−	0.670580i	$-0.233955\pi$
$97$	1.31349e8			1.48367			0.741837	+	0.670580i	$0.233955\pi$
$98$			1.52195e8i			1.65005i
$99$	−2.60724e7	−	1.26130e7i	−0.271419	−	0.131304i
$100$	−1.03713e8			−1.03713
$101$			2.40300e7i			0.230924i	0.993312	+	0.115462i	$0.0368348\pi$
$101$			2.40300e7i			0.230924i	−0.993312	+	0.115462i	$0.963165\pi$
$102$	−1.97293e8	+	1.23723e8i	−1.82268	+	1.14301i
$103$	9.87201e7			0.877116			0.438558	−	0.898703i	$-0.355489\pi$
$103$	9.87201e7			0.877116			0.438558	+	0.898703i	$0.355489\pi$
$104$			1.79558e8i			1.53487i
$105$	1.02896e7	+	1.64082e7i	0.0846531	+	0.134991i
$106$	1.46172e8			1.15782
$107$			2.55779e8i			1.95133i	0.219272	+	0.975664i	$0.429632\pi$
$107$			2.55779e8i			1.95133i	−0.219272	+	0.975664i	$0.570368\pi$
$108$	−3.01771e7	−	2.74403e8i	−0.221810	−	2.01694i
$109$	−1.91845e8			−1.35908			−0.679541	−	0.733638i	$-0.737821\pi$
$109$	−1.91845e8			−1.35908			−0.679541	+	0.733638i	$0.737821\pi$
$110$		−	5.37191e7i		−	0.366909i
$111$	1.09511e7	−	6.86744e6i	0.0721380	−	0.0452379i
$112$	−3.90198e7			−0.247978
$113$		−	6.28120e7i		−	0.385238i	−0.981274	−	0.192619i	$-0.938302\pi$
$113$		−	6.28120e7i		−	0.385238i	0.981274	−	0.192619i	$-0.0616982\pi$
$114$	6.16590e7	+	9.83236e7i	0.365071	+	0.582155i
$115$	1.67334e8			0.956737
$116$		−	3.44657e8i		−	1.90351i
$117$	6.99314e7	−	1.44556e8i	0.373189	−	0.771424i
$118$	4.45367e8			2.29715
$119$		−	5.64912e7i		−	0.281704i
$120$	2.20000e8	−	1.37962e8i	1.06096	−	0.665328i
$121$	−1.94872e7			−0.0909091
$122$		−	3.88758e8i		−	1.75485i
$123$	2.92385e7	+	4.66247e7i	0.127742	+	0.203702i
$124$	−9.11949e8			−3.85730
$125$			2.57952e8i			1.05657i
$126$	8.99909e7	+	4.35346e7i	0.357040	+	0.172724i
$127$	1.49894e8			0.576195			0.288098	−	0.957601i	$-0.406977\pi$
$127$	1.49894e8			0.576195			0.288098	+	0.957601i	$0.406977\pi$
$128$		−	4.52399e8i		−	1.68532i
$129$	−4.25937e8	+	2.67106e8i	−1.53811	+	0.964551i
$130$	2.97841e8			1.04282
$131$		−	2.74109e8i		−	0.930760i	−0.885111	−	0.465380i	$-0.845918\pi$
$131$		−	2.74109e8i		−	0.930760i	0.885111	−	0.465380i	$-0.154082\pi$
$132$	−9.86793e7	−	1.57358e8i	−0.325035	−	0.518313i
$133$	−2.81531e7			−0.0899745
$134$			6.77638e8i			2.10174i
$135$	−2.30846e8	+	2.53870e7i	−0.695003	+	0.0764321i
$136$	−7.57428e8			−2.21404
$137$			2.01061e8i			0.570749i	0.958416	+	0.285375i	$0.0921180\pi$
$137$			2.01061e8i			0.570749i	−0.958416	+	0.285375i	$0.907882\pi$
$138$	7.31733e8	−	4.58872e8i	2.01761	−	1.26525i
$139$	5.53194e8			1.48190			0.740948	−	0.671562i	$-0.234376\pi$
$139$	5.53194e8			1.48190			0.740948	+	0.671562i	$0.234376\pi$
$140$			1.24204e8i			0.323313i
$141$	−1.68126e8	−	2.68100e8i	−0.425362	−	0.678297i
$142$	−2.52620e8			−0.621318
$143$		−	1.08045e8i		−	0.258381i
$144$	2.03757e8	−	4.21190e8i	0.473874	−	0.979552i
$145$	−2.89948e8			−0.655916
$146$			7.82562e8i			1.72229i
$147$	3.75053e8	−	2.35197e8i	0.803199	−	0.503688i
$148$	8.28954e7			0.172776
$149$		−	2.99772e8i		−	0.608199i	−0.952640	−	0.304099i	$-0.901645\pi$
$149$		−	2.99772e8i		−	0.608199i	0.952640	−	0.304099i	$-0.0983555\pi$
$150$	2.39263e8	+	3.81537e8i	0.472618	+	0.753653i
$151$	8.05160e6			0.0154873			0.00774363	−	0.999970i	$-0.497535\pi$
$151$	8.05160e6			0.0154873			0.00774363	+	0.999970i	$0.497535\pi$
$152$			3.77474e8i			0.707152i
$153$	6.09780e8	+	2.94991e8i	1.11278	+	0.538323i
$154$	6.72614e7			0.119587
$155$			7.67192e8i			1.32916i
$156$	8.72455e8	−	5.47119e8i	1.47314	−	0.923811i
$157$	7.69557e8			1.26661			0.633304	−	0.773903i	$-0.281698\pi$
$157$	7.69557e8			1.26661			0.633304	+	0.773903i	$0.281698\pi$
$158$		−	3.11408e8i		−	0.499691i
$159$	−2.25889e8	−	3.60210e8i	−0.353432	−	0.563596i
$160$	4.70941e7			0.0718600
$161$			2.09518e8i			0.311830i
$162$	−9.39847e8	+	7.44052e8i	−1.36457	+	1.08030i
$163$	1.18822e9			1.68324			0.841620	−	0.540070i	$-0.181602\pi$
$163$	1.18822e9			1.68324			0.841620	+	0.540070i	$0.181602\pi$
$164$			3.52932e8i			0.487883i
$165$	−1.32380e8	+	8.30156e7i	−0.178602	+	0.112002i
$166$	−1.88191e9			−2.47837
$167$		−	7.03123e8i		−	0.903993i	−0.892020	−	0.451997i	$-0.850712\pi$
$167$		−	7.03123e8i		−	0.903993i	0.892020	−	0.451997i	$-0.149288\pi$
$168$	1.72742e8	+	2.75461e8i	0.216851	+	0.345798i
$169$	−2.16686e8			−0.265634
$170$			1.25638e9i			1.50427i
$171$	1.47013e8	−	3.03892e8i	0.171937	−	0.355414i
$172$	−3.22419e9			−3.68389
$173$			1.02435e7i			0.0114357i	0.999984	+	0.00571786i	$0.00182006\pi$
$173$			1.02435e7i			0.0114357i	−0.999984	+	0.00571786i	$0.998180\pi$
$174$	−1.26791e9	+	7.95111e8i	−1.38322	+	0.867423i
$175$	−1.09246e8			−0.116480
$176$		−	3.14807e8i		−	0.328091i
$177$	−6.88254e8	−	1.09751e9i	−0.701222	−	1.11819i
$178$	4.40064e8			0.438365
$179$		−	2.45065e8i		−	0.238709i	−0.992852	−	0.119355i	$-0.961917\pi$
$179$		−	2.45065e8i		−	0.238709i	0.992852	−	0.119355i	$-0.0380825\pi$
$180$	−1.34069e9	−	6.48581e8i	−1.27714	−	0.617837i
$181$	−3.06322e8			−0.285407			−0.142703	−	0.989765i	$-0.545580\pi$
$181$	−3.06322e8			−0.285407			−0.142703	+	0.989765i	$0.545580\pi$
$182$			3.72925e8i			0.339888i
$183$	−9.58013e8	+	6.00773e8i	−0.854215	+	0.535681i
$184$	2.80920e9			2.45082
$185$		−	6.97371e7i		−	0.0595357i
$186$	2.10383e9	+	3.35485e9i	1.75776	+	2.80299i
$187$	4.55764e8			0.372712
$188$		−	2.02941e9i		−	1.62457i
$189$	−3.17869e7	−	2.89041e8i	−0.0249115	−	0.226523i
$190$	6.26132e8			0.480454
$191$		−	1.97196e9i		−	1.48172i	−0.671662	−	0.740858i	$-0.734419\pi$
$191$		−	1.97196e9i		−	1.48172i	0.671662	−	0.740858i	$-0.265581\pi$
$192$	−1.04686e9	+	6.56486e8i	−0.770339	+	0.483082i
$193$	4.66893e8			0.336502			0.168251	−	0.985744i	$-0.446188\pi$
$193$	4.66893e8			0.336502			0.168251	+	0.985744i	$0.446188\pi$
$194$		−	3.65765e9i		−	2.58223i
$195$	−4.60273e8	−	7.33967e8i	−0.318329	−	0.507619i
$196$	2.83901e9			1.92372
$197$			6.52815e8i			0.433436i	0.976234	+	0.216718i	$0.0695353\pi$
$197$			6.52815e8i			0.433436i	−0.976234	+	0.216718i	$0.930465\pi$
$198$	−3.51232e8	+	7.26037e8i	−0.228525	+	0.472387i
$199$	−1.49810e9			−0.955275			−0.477638	−	0.878557i	$-0.658507\pi$
$199$	−1.49810e9			−0.955275			−0.477638	+	0.878557i	$0.658507\pi$
$200$			1.46476e9i			0.915473i
$201$	1.66990e9	−	1.04720e9i	1.02307	−	0.641571i
$202$	6.69161e8			0.401907
$203$		−	3.63042e8i		−	0.213783i
$204$	2.30790e9	+	3.68027e9i	1.33259	+	2.12500i
$205$	2.96910e8			0.168116
$206$		−	2.74905e9i		−	1.52656i
$207$	−2.26159e9	−	1.09408e9i	−1.23178	−	0.595892i
$208$	1.74542e9			0.932495
$209$		−	2.27136e8i		−	0.119042i
$210$	4.56918e8	−	2.86534e8i	0.234942	−	0.147333i
$211$	−2.49980e9			−1.26118			−0.630588	−	0.776118i	$-0.717186\pi$
$211$	−2.49980e9			−1.26118			−0.630588	+	0.776118i	$0.717186\pi$
$212$		−	2.72666e9i		−	1.34986i
$213$	3.90390e8	+	6.22529e8i	0.189662	+	0.302441i
$214$	7.12266e9			3.39615
$215$			2.71240e9i			1.26940i
$216$	−3.87543e9	+	4.26195e8i	−1.78035	+	0.195791i
$217$	−9.60597e8			−0.433214
$218$			5.34230e9i			2.36539i
$219$	1.92846e9	−	1.20934e9i	0.838368	−	0.525743i
$220$	−1.00206e9			−0.427765
$221$			2.52694e9i			1.05932i
$222$	−1.91237e8	−	3.04953e8i	−0.0787335	−	0.125551i
$223$	2.07469e9			0.838946			0.419473	−	0.907768i	$-0.362215\pi$
$223$	2.07469e9			0.838946			0.419473	+	0.907768i	$0.362215\pi$
$224$			5.89663e7i			0.0234214i
$225$	5.70470e8	−	1.17923e9i	0.222588	−	0.460116i
$226$	−1.74912e9			−0.670480
$227$		−	1.27579e9i		−	0.480479i	−0.970714	−	0.240239i	$-0.922774\pi$
$227$		−	1.27579e9i		−	0.480479i	0.970714	−	0.240239i	$-0.0772260\pi$
$228$	1.83411e9	−	1.15017e9i	0.678712	−	0.425622i
$229$	−3.04232e8			−0.110627			−0.0553137	−	0.998469i	$-0.517616\pi$
$229$	−3.04232e8			−0.110627			−0.0553137	+	0.998469i	$0.517616\pi$
$230$		−	4.65973e9i		−	1.66514i
$231$	−1.03943e8	−	1.65752e8i	−0.0365047	−	0.0582117i
$232$	−4.86764e9			−1.68022
$233$			1.46280e9i			0.496318i	0.968719	+	0.248159i	$0.0798256\pi$
$233$			1.46280e9i			0.496318i	−0.968719	+	0.248159i	$0.920174\pi$
$234$	−4.02544e9	−	1.94737e9i	−1.34261	−	0.649510i
$235$	−1.70728e9			−0.559800
$236$		−	8.30777e9i		−	2.67816i
$237$	−7.67401e8	+	4.81239e8i	−0.243237	+	0.152534i
$238$	−1.57310e9			−0.490286
$239$			1.66655e9i			0.510771i	0.966839	+	0.255386i	$0.0822024\pi$
$239$			1.66655e9i			0.510771i	−0.966839	+	0.255386i	$0.917798\pi$
$240$	−1.34108e9	−	2.13854e9i	−0.404213	−	0.644573i
$241$	−4.41606e9			−1.30908			−0.654540	−	0.756027i	$-0.727138\pi$
$241$	−4.41606e9			−1.30908			−0.654540	+	0.756027i	$0.727138\pi$
$242$			5.42657e8i			0.158221i
$243$	3.28597e9	+	1.16623e9i	0.942406	+	0.334470i
$244$	−7.25181e9			−2.04591
$245$		−	2.38837e9i		−	0.662882i
$246$	1.29835e9	−	8.14201e8i	0.354530	−	0.222327i
$247$	1.25934e9			0.338340
$248$			1.28796e10i			3.40483i
$249$	2.90824e9	+	4.63758e9i	0.756541	+	1.20641i
$250$	7.18316e9			1.83889
$251$			2.80923e9i			0.707770i	0.935289	+	0.353885i	$0.115140\pi$
$251$			2.80923e9i			0.707770i	−0.935289	+	0.353885i	$0.884860\pi$
$252$	8.12085e8	−	1.67867e9i	0.201372	−	0.416259i
$253$	−1.69037e9			−0.412571
$254$		−	4.17409e9i		−	1.00283i
$255$	3.09608e9	−	1.94156e9i	0.732237	−	0.459188i
$256$	−8.69257e9			−2.02390
$257$			6.76785e9i			1.55138i	0.631113	+	0.775691i	$0.282598\pi$
$257$			6.76785e9i			1.55138i	−0.631113	+	0.775691i	$0.717402\pi$
$258$	7.43809e9	+	1.18610e10i	1.67874	+	2.67697i
$259$	8.73175e7			0.0194045
$260$		−	5.55586e9i		−	1.21579i
$261$	3.91877e9	+	1.89577e9i	0.844477	+	0.408530i
$262$	−7.63308e9			−1.61992
$263$			3.68017e9i			0.769210i	0.923081	+	0.384605i	$0.125662\pi$
$263$			3.68017e9i			0.769210i	−0.923081	+	0.384605i	$0.874338\pi$
$264$	−2.22238e9	+	1.39366e9i	−0.457513	+	0.286908i
$265$	−2.29385e9			−0.465137
$266$			7.83977e8i			0.156595i
$267$	−6.80059e8	−	1.08445e9i	−0.133814	−	0.213385i
$268$	1.26405e10			2.45034
$269$		−	4.92486e9i		−	0.940557i	−0.882518	−	0.470279i	$-0.844153\pi$
$269$		−	4.92486e9i		−	0.940557i	0.882518	−	0.470279i	$-0.155847\pi$
$270$	7.06948e8	+	6.42834e9i	0.133025	+	1.20961i
$271$	−2.97605e9			−0.551776			−0.275888	−	0.961190i	$-0.588972\pi$
$271$	−2.97605e9			−0.551776			−0.275888	+	0.961190i	$0.588972\pi$
$272$			7.36269e9i			1.34512i
$273$	9.18996e8	−	5.76305e8i	0.165449	−	0.103753i
$274$	5.59892e9			0.993350
$275$		−	8.81382e8i		−	0.154111i
$276$	−8.55969e9	−	1.36496e10i	−1.47510	−	2.35225i
$277$	7.62931e9			1.29588			0.647942	−	0.761689i	$-0.275630\pi$
$277$	7.62931e9			1.29588			0.647942	+	0.761689i	$0.275630\pi$
$278$		−	1.54047e10i		−	2.57914i
$279$	5.01614e9	−	1.03689e10i	0.827852	−	1.71126i
$280$	1.75415e9			0.285388
$281$			4.39132e9i			0.704319i	0.935940	+	0.352159i	$0.114553\pi$
$281$			4.39132e9i			0.704319i	−0.935940	+	0.352159i	$0.885447\pi$
$282$	−7.46574e9	+	4.68179e9i	−1.18053	+	0.740313i
$283$	7.30165e9			1.13835			0.569174	−	0.822217i	$-0.307263\pi$
$283$	7.30165e9			1.13835			0.569174	+	0.822217i	$0.307263\pi$
$284$			4.71231e9i			0.724371i
$285$	−9.67603e8	−	1.54297e9i	−0.146662	−	0.233872i
$286$	−3.00871e9			−0.449694
$287$			3.71759e8i			0.0547941i
$288$	−6.36498e8	−	3.07916e8i	−0.0925181	−	0.0447571i
$289$	−3.68362e9			−0.528060
$290$			8.07416e9i			1.14158i
$291$	−9.01353e9	+	5.65241e9i	−1.25696	+	0.788245i
$292$	1.45977e10			2.00796
$293$			8.50421e9i			1.15389i	0.816784	+	0.576944i	$0.195755\pi$
$293$			8.50421e9i			1.15389i	−0.816784	+	0.576944i	$0.804245\pi$
$294$	−6.54950e9	−	1.04441e10i	−0.876635	−	1.39791i
$295$	−6.98905e9			−0.922848
$296$		−	1.17074e9i		−	0.152509i
$297$	2.33195e9	−	2.56453e8i	0.299704	−	0.0329596i
$298$	−8.34771e9			−1.05853
$299$		−	9.37208e9i		−	1.17260i
$300$	7.11710e9	−	4.46315e9i	0.878655	−	0.551007i
$301$	−3.39618e9			−0.413738
$302$		−	2.24212e8i		−	0.0269545i
$303$	−1.03410e9	−	1.64901e9i	−0.122685	−	0.195638i
$304$	3.66929e9			0.429623
$305$			6.10070e9i			0.704986i
$306$	8.21459e9	−	1.69805e10i	0.936914	−	1.93671i
$307$	−3.21375e9			−0.361792			−0.180896	−	0.983502i	$-0.557900\pi$
$307$	−3.21375e9			−0.361792			−0.180896	+	0.983502i	$0.557900\pi$
$308$		−	1.25468e9i		−	0.139422i
$309$	−6.77446e9	+	4.24828e9i	−0.743089	+	0.465993i
$310$	2.13639e10			2.31331
$311$			2.58582e9i			0.276412i	0.990403	+	0.138206i	$0.0441337\pi$
$311$			2.58582e9i			0.276412i	−0.990403	+	0.138206i	$0.955866\pi$
$312$	−7.72704e9	−	1.23218e10i	−0.815445	−	1.30034i
$313$	−9.49462e9			−0.989236			−0.494618	−	0.869110i	$-0.664692\pi$
$313$	−9.49462e9			−0.989236			−0.494618	+	0.869110i	$0.664692\pi$
$314$		−	2.14298e10i		−	2.20445i
$315$	−1.41221e9	−	6.83179e8i	−0.143436	−	0.0693893i
$316$	−5.80894e9			−0.582570
$317$			1.73018e10i			1.71338i	0.515832	+	0.856690i	$0.327483\pi$
$317$			1.73018e10i			1.71338i	−0.515832	+	0.856690i	$0.672517\pi$
$318$	−1.00307e10	+	6.29031e9i	−0.980900	+	0.615125i
$319$	2.92899e9			0.282849
$320$			6.66646e9i			0.635763i
$321$	−1.10071e10	−	1.75523e10i	−1.03670	−	1.65316i
$322$	5.83442e9			0.542718
$323$			5.31224e9i			0.488054i
$324$	1.38794e10	+	1.75317e10i	1.25948	+	1.59090i
$325$	4.88674e9			0.438012
$326$		−	3.30882e10i		−	2.92957i
$327$	1.31650e10	−	8.25580e9i	1.15141	−	0.722052i
$328$	4.98451e9			0.430652
$329$		−	2.13767e9i		−	0.182456i
$330$	2.31173e9	+	3.68636e9i	0.194931	+	0.310844i
$331$	1.84970e10			1.54095			0.770477	−	0.637468i	$-0.220018\pi$
$331$	1.84970e10			1.54095			0.770477	+	0.637468i	$0.220018\pi$
$332$			3.51047e10i			2.88944i
$333$	−4.55963e8	+	9.42527e8i	−0.0370811	+	0.0766508i
$334$	−1.95798e10			−1.57334
$335$		−	1.06340e10i		−	0.844343i
$336$	2.67765e9	−	1.67916e9i	0.210086	−	0.131745i
$337$	−1.44393e10			−1.11951			−0.559754	−	0.828659i	$-0.689104\pi$
$337$	−1.44393e10			−1.11951			−0.559754	+	0.828659i	$0.689104\pi$
$338$			6.03403e9i			0.462318i
$339$	2.70303e9	+	4.31035e9i	0.204669	+	0.326372i
$340$	2.34362e10			1.75377
$341$		−	7.74999e9i		−	0.573170i
$342$	−8.46244e9	−	4.09385e9i	−0.618574	−	0.299245i
$343$	6.14473e9			0.443942
$344$			4.55357e10i			3.25176i
$345$	−1.14829e10	+	7.20098e9i	−0.810544	+	0.508295i
$346$	2.85249e8			0.0199031
$347$		−	1.66531e10i		−	1.14862i	−0.818637	−	0.574311i	$-0.805270\pi$
$347$		−	1.66531e10i		−	1.14862i	0.818637	−	0.574311i	$-0.194730\pi$
$348$	1.48318e10	+	2.36514e10i	1.01129	+	1.61265i
$349$	−1.65028e10			−1.11238			−0.556192	−	0.831054i	$-0.687738\pi$
$349$	−1.65028e10			−1.11238			−0.556192	+	0.831054i	$0.687738\pi$
$350$			3.04216e9i			0.202726i
$351$	1.42188e9	+	1.29293e10i	0.0936773	+	0.851816i
$352$	−4.75734e8			−0.0309880
$353$			1.34905e10i			0.868820i	0.900715	+	0.434410i	$0.143043\pi$
$353$			1.34905e10i			0.868820i	−0.900715	+	0.434410i	$0.856957\pi$
$354$	−3.05624e10	+	1.91657e10i	−1.94614	+	1.22043i
$355$	3.96431e9			0.249606
$356$		−	8.20886e9i		−	0.511073i
$357$	2.43102e9	+	3.87659e9i	0.149663	+	0.238658i
$358$	−6.82430e9			−0.415457
$359$		−	2.64012e10i		−	1.58944i	−0.606974	−	0.794722i	$-0.707617\pi$
$359$		−	2.64012e10i		−	1.58944i	0.606974	−	0.794722i	$-0.292383\pi$
$360$	−9.16001e9	+	1.89348e10i	−0.545363	+	1.12733i
$361$	−1.43361e10			−0.844119
$362$			8.53013e9i			0.496731i
$363$	1.33727e9	−	8.38604e8i	0.0770179	−	0.0482981i
$364$	6.95646e9			0.396262
$365$		−	1.22806e10i		−	0.691907i
$366$	1.67297e10	+	2.66777e10i	0.932315	+	1.48670i
$367$	−8.58724e9			−0.473357			−0.236679	−	0.971588i	$-0.576059\pi$
$367$	−8.58724e9			−0.473357			−0.236679	+	0.971588i	$0.576059\pi$
$368$		−	2.73072e10i		−	1.48897i
$369$	−4.01286e9	−	1.94129e9i	−0.216446	−	0.104709i
$370$	−1.94196e9			−0.103618
$371$		−	2.87211e9i		−	0.151602i
$372$	6.25806e10	−	3.92445e10i	3.26790	−	2.04931i
$373$	1.67293e10			0.864255			0.432127	−	0.901813i	$-0.357763\pi$
$373$	1.67293e10			0.864255			0.432127	+	0.901813i	$0.357763\pi$
$374$		−	1.26916e10i		−	0.648680i
$375$	−1.11006e10	−	1.77014e10i	−0.561334	−	0.895124i
$376$	−2.86617e10			−1.43401
$377$			1.62395e10i			0.803909i
$378$	−8.04889e9	+	8.85166e8i	−0.394247	+	0.0433568i
$379$	−5.48304e9			−0.265745			−0.132872	−	0.991133i	$-0.542420\pi$
$379$	−5.48304e9			−0.265745			−0.132872	+	0.991133i	$0.542420\pi$
$380$		−	1.16797e10i		−	0.560143i
$381$	−1.02862e10	+	6.45049e9i	−0.488151	+	0.306121i
$382$	−5.49130e10			−2.57882
$383$		−	8.28099e9i		−	0.384846i	−0.981312	−	0.192423i	$-0.938365\pi$
$383$		−	8.28099e9i		−	0.384846i	0.981312	−	0.192423i	$-0.0616346\pi$
$384$	1.94683e10	+	3.10449e10i	0.895374	+	1.42779i
$385$	−1.05552e9			−0.0480423
$386$		−	1.30015e10i		−	0.585659i
$387$	1.77345e10	−	3.66592e10i	0.790634	−	1.63433i
$388$	−6.82291e10			−3.01053
$389$		−	1.07122e10i		−	0.467821i	−0.972258	−	0.233910i	$-0.924848\pi$
$389$		−	1.07122e10i		−	0.467821i	0.972258	−	0.233910i	$-0.0751523\pi$
$390$	−2.04387e10	+	1.28172e10i	−0.883476	+	0.554030i
$391$	3.95341e10			1.69147
$392$		−	4.00958e10i		−	1.69807i
$393$	1.17959e10	+	1.88101e10i	0.494494	+	0.788537i
$394$	1.81789e10			0.754366
$395$			4.88687e9i			0.200744i
$396$	1.35433e10	+	6.55181e9i	0.550738	+	0.266428i
$397$	−1.54663e9			−0.0622620			−0.0311310	−	0.999515i	$-0.509911\pi$
$397$	−1.54663e9			−0.0622620			−0.0311310	+	0.999515i	$0.509911\pi$
$398$			4.17175e10i			1.66259i
$399$	1.93195e9	−	1.21153e9i	0.0762261	−	0.0478016i
$400$	1.42384e10			0.556186
$401$			2.28731e10i			0.884602i	0.896867	+	0.442301i	$0.145838\pi$
$401$			2.28731e10i			0.884602i	−0.896867	+	0.442301i	$0.854162\pi$
$402$	−2.91612e10	−	4.65015e10i	−1.11661	−	1.78059i
$403$	4.29691e10			1.62906
$404$		−	1.24824e10i		−	0.468568i
$405$	1.47488e10	−	1.16763e10i	0.548198	−	0.433994i
$406$	−1.01096e10			−0.372075
$407$			7.04468e8i			0.0256734i
$408$	5.19769e10	−	3.25949e10i	1.87573	−	1.17627i
$409$	1.31060e10			0.468356			0.234178	−	0.972194i	$-0.424760\pi$
$409$	1.31060e10			0.468356			0.234178	+	0.972194i	$0.424760\pi$
$410$		−	8.26802e9i		−	0.292594i
$411$	−8.65238e9	−	1.37974e10i	−0.303227	−	0.483537i
$412$	−5.12802e10			−1.77976
$413$		−	8.75095e9i		−	0.300784i
$414$	−3.04668e10	+	6.29782e10i	−1.03711	+	2.14382i
$415$	2.95324e10			0.995650
$416$		−	2.63766e9i		−	0.0880736i
$417$	−3.79618e10	+	2.38059e10i	−1.25546	+	0.787301i
$418$	−6.32504e9			−0.207185
$419$			5.10133e10i			1.65511i	0.561384	+	0.827556i	$0.310269\pi$
$419$			5.10133e10i			1.65511i	−0.561384	+	0.827556i	$0.689731\pi$
$420$	−5.34495e9	−	8.52325e9i	−0.171770	−	0.273910i
$421$	4.23853e10			1.34923			0.674616	−	0.738169i	$-0.264309\pi$
$421$	4.23853e10			1.34923			0.674616	+	0.738169i	$0.264309\pi$
$422$			6.96118e10i			2.19499i
$423$	2.30746e10	+	1.11627e10i	0.720730	+	0.348665i
$424$	−3.85090e10			−1.19151
$425$			2.06137e10i			0.631830i
$426$	1.73355e10	−	1.08711e10i	0.526379	−	0.330093i
$427$	−7.63865e9			−0.229776
$428$		−	1.32865e11i		−	3.95944i
$429$	4.64956e9	+	7.41435e9i	0.137272	+	0.218899i
$430$	7.55320e10			2.20931
$431$		−	3.73482e10i		−	1.08233i	−0.840915	−	0.541167i	$-0.817983\pi$
$431$		−	3.73482e10i		−	1.08233i	0.840915	−	0.541167i	$-0.182017\pi$
$432$	4.14289e9	+	3.76717e10i	0.118951	+	1.08163i
$433$	4.01849e10			1.14317			0.571586	−	0.820543i	$-0.306329\pi$
$433$	4.01849e10			1.14317			0.571586	+	0.820543i	$0.306329\pi$
$434$			2.67497e10i			0.753979i
$435$	1.98971e10	−	1.24775e10i	0.555690	−	0.348475i
$436$	9.96541e10			2.75771
$437$		−	1.97024e10i		−	0.540247i
$438$	−3.36765e10	−	5.37017e10i	−0.915020	−	1.45912i
$439$	−4.93682e10			−1.32920			−0.664598	−	0.747201i	$-0.731397\pi$
$439$	−4.93682e10			−1.32920			−0.664598	+	0.747201i	$0.731397\pi$
$440$			1.41523e10i			0.377587i
$441$	−1.56159e10	+	3.22798e10i	−0.412868	+	0.853446i
$442$	7.03676e10			1.84367
$443$		−	3.64202e10i		−	0.945644i	−0.881158	−	0.472822i	$-0.843235\pi$
$443$		−	3.64202e10i		−	0.945644i	0.881158	−	0.472822i	$-0.156765\pi$
$444$	−5.68853e9	+	3.56729e9i	−0.146375	+	0.0917924i
$445$	−6.90584e9			−0.176107
$446$		−	5.77737e10i		−	1.46013i
$447$	1.29003e10	+	2.05712e10i	0.323123	+	0.515264i
$448$	−8.34704e9			−0.207215
$449$		−	9.62654e9i		−	0.236856i	−0.992963	−	0.118428i	$-0.962214\pi$
$449$		−	9.62654e9i		−	0.236856i	0.992963	−	0.118428i	$-0.0377855\pi$
$450$	−3.28378e10	−	1.58858e10i	−0.800800	−	0.387400i
$451$	−2.99931e9			−0.0724962
$452$			3.26277e10i			0.781687i
$453$	−5.52524e8	+	3.46490e8i	−0.0131207	+	0.00822806i
$454$	−3.55267e10			−0.836241
$455$		−	5.85223e9i		−	0.136545i
$456$	−1.62441e10	−	2.59034e10i	−0.375695	−	0.599097i
$457$	1.61137e10			0.369429			0.184714	−	0.982792i	$-0.440864\pi$
$457$	1.61137e10			0.369429			0.184714	+	0.982792i	$0.440864\pi$
$458$			8.47191e9i			0.192539i
$459$	−5.45394e10	+	5.99790e9i	−1.22874	+	0.135129i
$460$	−8.69216e10			−1.94132
$461$			7.83528e9i			0.173481i	0.996231	+	0.0867403i	$0.0276450\pi$
$461$			7.83528e9i			0.173481i	−0.996231	+	0.0867403i	$0.972355\pi$
$462$	−4.61567e9	+	2.89450e9i	−0.101313	+	0.0635340i
$463$	−8.51522e10			−1.85299			−0.926493	−	0.376313i	$-0.877192\pi$
$463$	−8.51522e10			−1.85299			−0.926493	+	0.376313i	$0.877192\pi$
$464$			4.73166e10i			1.02080i
$465$	−3.30151e10	−	5.26470e10i	−0.706155	−	1.12606i
$466$	4.07344e10			0.863808
$467$		−	1.97669e10i		−	0.415595i	−0.978172	−	0.207797i	$-0.933370\pi$
$467$		−	1.97669e10i		−	0.415595i	0.978172	−	0.207797i	$-0.0666295\pi$
$468$	−3.63259e10	+	7.50898e10i	−0.757239	+	1.56530i
$469$	1.33148e10			0.275197
$470$			4.75424e10i			0.974293i
$471$	−5.28093e10	+	3.31168e10i	−1.07307	+	0.672923i
$472$	−1.17332e11			−2.36400
$473$		−	2.74000e10i		−	0.547402i
$474$	1.34010e10	+	2.13697e10i	0.265475	+	0.423337i
$475$	1.02731e10			0.201803
$476$			2.93443e10i			0.571606i
$477$	3.10023e10	+	1.49979e10i	0.598854	+	0.289705i
$478$	4.64082e10			0.888962
$479$			2.04853e10i			0.389136i	0.980889	+	0.194568i	$0.0623305\pi$
$479$			2.04853e10i			0.389136i	−0.980889	+	0.194568i	$0.937670\pi$
$480$	−3.23174e9	+	2.02663e9i	−0.0608795	+	0.0381777i
$481$	−3.90586e9			−0.0729686
$482$			1.22973e11i			2.27837i
$483$	−9.01631e9	−	1.43777e10i	−0.165669	−	0.264181i
$484$	1.01226e10			0.184464
$485$			5.73988e10i			1.03738i
$486$	3.24758e10	−	9.15040e10i	0.582123	−	1.64019i
$487$	2.98154e10			0.530060			0.265030	−	0.964240i	$-0.414618\pi$
$487$	2.98154e10			0.530060			0.265030	+	0.964240i	$0.414618\pi$
$488$			1.02418e11i			1.80592i
$489$	−8.15391e10	+	5.11334e10i	−1.42604	+	0.894271i
$490$	−6.65086e10			−1.15370
$491$		−	5.75739e10i		−	0.990604i	−0.868721	−	0.495302i	$-0.835057\pi$
$491$		−	5.75739e10i		−	0.990604i	0.868721	−	0.495302i	$-0.164943\pi$
$492$	−1.51879e10	−	2.42192e10i	−0.259202	−	0.413333i
$493$	−6.85029e10			−1.15963
$494$		−	3.50686e10i		−	0.588858i
$495$	5.51182e9	−	1.13936e10i	0.0918066	−	0.189775i
$496$	1.25198e11			2.06857
$497$			4.96369e9i			0.0813541i
$498$	1.29142e11	−	8.09854e10i	2.09967	−	1.31671i
$499$	5.31825e10			0.857761			0.428881	−	0.903361i	$-0.358908\pi$
$499$	5.31825e10			0.857761			0.428881	+	0.903361i	$0.358908\pi$
$500$		−	1.33993e11i		−	2.14389i
$501$	3.02579e10	+	4.82503e10i	0.480273	+	0.765860i
$502$	7.82283e10			1.23183
$503$			1.39894e10i			0.218538i	0.994012	+	0.109269i	$0.0348510\pi$
$503$			1.39894e10i			0.218538i	−0.994012	+	0.109269i	$0.965149\pi$
$504$	−2.37081e10	−	1.14692e10i	−0.367430	−	0.177750i
$505$	−1.05010e10			−0.161460
$506$			4.70715e10i			0.718052i
$507$	1.48696e10	−	9.32478e9i	0.225044	−	0.141126i
$508$	−7.78626e10			−1.16916
$509$		−	1.32599e11i		−	1.97547i	−0.156136	−	0.987736i	$-0.549904\pi$
$509$		−	1.32599e11i		−	1.97547i	0.156136	−	0.987736i	$-0.450096\pi$
$510$	−5.40665e10	−	8.62163e10i	−0.799185	−	1.27441i
$511$	1.53765e10			0.225514
$512$			1.26247e11i			1.83714i
$513$	2.98913e9	+	2.71804e10i	0.0431594	+	0.392452i
$514$	1.88464e11			2.70007
$515$			4.31403e10i			0.613274i
$516$	2.21253e11	−	1.38748e11i	3.12098	−	1.95717i
$517$	1.72465e10			0.241401
$518$		−	2.43152e9i		−	0.0337722i
$519$	−4.40814e8	−	7.02938e8i	−0.00607556	−	0.00968830i
$520$	−7.84662e10			−1.07317
$521$			8.84553e9i			0.120053i	0.998197	+	0.0600265i	$0.0191185\pi$
$521$			8.84553e9i			0.120053i	−0.998197	+	0.0600265i	$0.980881\pi$
$522$	5.27913e10	−	1.09126e11i	0.711018	−	1.46976i
$523$	−1.25242e11			−1.67396			−0.836979	−	0.547235i	$-0.815681\pi$
$523$	−1.25242e11			−1.67396			−0.836979	+	0.547235i	$0.815681\pi$
$524$			1.42386e11i			1.88861i
$525$	7.49676e9	−	4.70124e9i	0.0986817	−	0.0618836i
$526$	1.02481e11			1.33876
$527$			1.81256e11i			2.34990i
$528$	1.35473e10	+	2.16030e10i	0.174308	+	0.277957i
$529$	−6.83156e10			−0.872363
$530$			6.38765e10i			0.809539i
$531$	9.44600e10	+	4.56966e10i	1.18815	+	0.574785i
$532$	1.46241e10			0.182568
$533$		−	1.66294e10i		−	0.206048i
$534$	−3.01985e10	+	1.89375e10i	−0.371381	+	0.232894i
$535$	−1.11774e11			−1.36436
$536$		−	1.78524e11i		−	2.16290i
$537$	1.05460e10	+	1.68171e10i	0.126821	+	0.202234i
$538$	−1.37142e11			−1.63698
$539$			2.41267e10i			0.285853i
$540$	1.19913e11	−	1.31873e10i	1.41023	−	0.155088i
$541$	−3.11521e10			−0.363663			−0.181831	−	0.983330i	$-0.558202\pi$
$541$	−3.11521e10			−0.363663			−0.181831	+	0.983330i	$0.558202\pi$
$542$			8.28737e10i			0.960328i
$543$	2.10207e10	−	1.31822e10i	0.241796	−	0.151631i
$544$	1.11264e10			0.127046
$545$		−	8.38357e10i		−	0.950261i
$546$	−1.60483e10	−	2.55912e10i	−0.180575	−	0.287952i
$547$	−8.91436e10			−0.995728			−0.497864	−	0.867255i	$-0.665882\pi$
$547$	−8.91436e10			−0.995728			−0.497864	+	0.867255i	$0.665882\pi$
$548$		−	1.04441e11i		−	1.15811i
$549$	3.98883e10	−	8.24536e10i	0.439092	−	0.907654i
$550$	−2.45438e10			−0.268220
$551$			3.41393e10i			0.370380i
$552$	−1.92775e11	+	1.20890e11i	−2.07632	+	1.30207i
$553$	−6.11882e9			−0.0654285
$554$		−	2.12453e11i		−	2.25540i
$555$	3.00104e9	+	4.78557e9i	0.0316301	+	0.0504384i
$556$	−2.87357e11			−3.00692
$557$		−	2.92101e9i		−	0.0303468i	−0.999885	−	0.0151734i	$-0.995170\pi$
$557$		−	2.92101e9i		−	0.0303468i	0.999885	−	0.0151734i	$-0.00483002\pi$
$558$	−2.88743e11	−	1.39684e11i	−2.97834	−	1.44082i
$559$	1.51917e11			1.55582
$560$		−	1.70515e10i		−	0.173384i
$561$	−3.12759e10	+	1.96132e10i	−0.315761	+	0.198014i
$562$	1.22285e11			1.22582
$563$		−	1.89875e11i		−	1.88988i	−0.327248	−	0.944938i	$-0.606121\pi$
$563$		−	1.89875e11i		−	1.88988i	0.327248	−	0.944938i	$-0.393879\pi$
$564$	8.73331e10	+	1.39264e11i	0.863102	+	1.37633i
$565$	2.74486e10			0.269356
$566$		−	2.03328e11i		−	1.98122i
$567$	1.46198e10	+	1.84669e10i	0.141452	+	0.178674i
$568$	6.65527e10			0.639400
$569$		−	1.13089e11i		−	1.07887i	−0.842027	−	0.539436i	$-0.818637\pi$
$569$		−	1.13089e11i		−	1.07887i	0.842027	−	0.539436i	$-0.181363\pi$
$570$	−4.29670e10	+	2.69447e10i	−0.407039	+	0.255255i
$571$	−2.00781e9			−0.0188877			−0.00944384	−	0.999955i	$-0.503006\pi$
$571$	−2.00781e9			−0.0188877			−0.00944384	+	0.999955i	$0.503006\pi$
$572$			5.61239e10i			0.524281i
$573$	8.48606e10	+	1.35322e11i	0.787205	+	1.25530i
$574$	1.03523e10			0.0953654
$575$		−	7.64533e10i		−	0.699399i
$576$	4.35874e10	−	9.01000e10i	0.395978	−	0.818531i
$577$	2.58788e10			0.233475			0.116738	−	0.993163i	$-0.462756\pi$
$577$	2.58788e10			0.233475			0.116738	+	0.993163i	$0.462756\pi$
$578$			1.02577e11i			0.919052i
$579$	−3.20395e10	+	2.00921e10i	−0.285084	+	0.178777i
$580$	1.50614e11			1.33092
$581$			3.69774e10i			0.324513i
$582$	1.57402e11	+	2.50999e11i	1.37189	+	2.18766i
$583$	2.31719e10			0.200580
$584$		−	2.06166e11i		−	1.77242i
$585$	6.31705e10	+	3.05598e10i	0.539375	+	0.260931i
$586$	2.36816e11			2.00826
$587$			8.53959e10i			0.719257i	0.933095	+	0.359629i	$0.117097\pi$
$587$			8.53959e10i			0.719257i	−0.933095	+	0.359629i	$0.882903\pi$
$588$	−1.94821e11	+	1.22173e11i	−1.62977	+	1.02204i
$589$	9.03313e10			0.750546
$590$			1.94623e11i			1.60615i
$591$	−2.80930e10	−	4.47981e10i	−0.230276	−	0.367206i
$592$	−1.13804e10			−0.0926553
$593$		−	5.94424e10i		−	0.480704i	−0.970686	−	0.240352i	$-0.922737\pi$
$593$		−	5.94424e10i		−	0.480704i	0.970686	−	0.240352i	$-0.0772628\pi$
$594$	−7.14142e9	−	6.49376e10i	−0.0573639	−	0.521615i
$595$	2.46864e10			0.196965
$596$			1.55716e11i			1.23410i
$597$	1.02804e11	−	6.44687e10i	0.809306	−	0.507518i
$598$	−2.60983e11			−2.04084
$599$			2.46053e11i			1.91126i	0.294562	+	0.955632i	$0.404826\pi$
$599$			2.46053e11i			1.91126i	−0.294562	+	0.955632i	$0.595174\pi$
$600$	−6.30338e10	−	1.00516e11i	−0.486372	−	0.775586i
$601$	−1.62423e11			−1.24495			−0.622473	−	0.782641i	$-0.713872\pi$
$601$	−1.62423e11			−1.24495			−0.622473	+	0.782641i	$0.713872\pi$
$602$			9.45731e10i			0.720082i
$603$	−6.95286e10	+	1.43724e11i	−0.525889	+	1.08707i
$604$	−4.18240e9			−0.0314252
$605$		−	8.51582e9i		−	0.0635631i
$606$	−4.59198e10	+	2.87964e10i	−0.340494	+	0.213525i
$607$	−8.95997e10			−0.660012			−0.330006	−	0.943979i	$-0.607051\pi$
$607$	−8.95997e10			−0.660012			−0.330006	+	0.943979i	$0.607051\pi$
$608$		−	5.54500e9i		−	0.0405776i
$609$	1.56230e10	+	2.49130e10i	0.113579	+	0.181116i
$610$	1.69886e11			1.22698
$611$			9.56217e10i			0.686107i
$612$	−3.16750e11	−	1.53233e11i	−2.25793	−	1.09231i
$613$	1.55668e11			1.10245			0.551225	−	0.834357i	$-0.314161\pi$
$613$	1.55668e11			1.10245			0.551225	+	0.834357i	$0.314161\pi$
$614$			8.94930e10i			0.629674i
$615$	−2.03748e10	+	1.27771e10i	−0.142427	+	0.0893165i
$616$	−1.77200e10			−0.123067
$617$			4.95367e10i			0.341811i	0.985287	+	0.170906i	$0.0546693\pi$
$617$			4.95367e10i			0.341811i	−0.985287	+	0.170906i	$0.945331\pi$
$618$	1.18302e11	+	1.88648e11i	0.811030	+	1.29330i
$619$	3.39503e10			0.231250			0.115625	−	0.993293i	$-0.463113\pi$
$619$	3.39503e10			0.231250			0.115625	+	0.993293i	$0.463113\pi$
$620$		−	3.98518e11i		−	2.69700i
$621$	2.02279e11	−	2.22454e10i	1.36014	−	0.149580i
$622$	7.20072e10			0.481077
$623$		−	8.64676e9i		−	0.0573986i
$624$	−1.19776e11	+	7.51118e10i	−0.790007	+	0.495415i
$625$	−3.47320e10			−0.227620
$626$			2.64396e11i			1.72170i
$627$	9.77449e9	+	1.55867e10i	0.0632447	+	0.100852i
$628$	−3.99747e11			−2.57008
$629$		−	1.64760e10i		−	0.105257i
$630$	−1.90244e10	+	3.93257e10i	−0.120767	+	0.249640i
$631$	6.20903e10			0.391657			0.195829	−	0.980638i	$-0.437260\pi$
$631$	6.20903e10			0.391657			0.195829	+	0.980638i	$0.437260\pi$
$632$			8.20405e10i			0.514233i
$633$	1.71544e11	−	1.07576e11i	1.06846	−	0.670037i
$634$	4.81801e11			2.98202
$635$			6.55032e10i			0.402872i
$636$	1.17338e11	+	1.87111e11i	0.717151	+	1.14359i
$637$	−1.33768e11			−0.812447
$638$		−	8.15632e10i		−	0.492279i
$639$	−5.35794e10	−	2.59199e10i	−0.321362	−	0.155464i
$640$	1.97696e11			1.17836
$641$		−	3.97086e10i		−	0.235208i	−0.993061	−	0.117604i	$-0.962479\pi$
$641$		−	3.97086e10i		−	0.235208i	0.993061	−	0.117604i	$-0.0375214\pi$
$642$	−4.88778e11	+	3.06514e11i	−2.87721	+	1.80431i
$643$	−2.09828e11			−1.22749			−0.613746	−	0.789504i	$-0.710338\pi$
$643$	−2.09828e11			−1.22749			−0.613746	+	0.789504i	$0.710338\pi$
$644$		−	1.08834e11i		−	0.632734i
$645$	−1.16724e11	−	1.86133e11i	−0.674408	−	1.07544i
$646$	1.47929e11			0.849424
$647$		−	1.07186e11i		−	0.611674i	−0.952084	−	0.305837i	$-0.901064\pi$
$647$		−	1.07186e11i		−	0.611674i	0.952084	−	0.305837i	$-0.0989363\pi$
$648$	2.47603e11	−	1.96021e11i	1.40429	−	1.11174i
$649$	7.06017e10			0.397957
$650$		−	1.36081e11i		−	0.762330i
$651$	6.59190e10	−	4.13380e10i	0.367017	−	0.230158i
$652$	−6.17221e11			−3.41547
$653$			9.89775e10i			0.544357i	0.962247	+	0.272179i	$0.0877441\pi$
$653$			9.89775e10i			0.544357i	−0.962247	+	0.272179i	$0.912256\pi$
$654$	−2.29899e11	−	3.66604e11i	−1.25668	−	2.00395i
$655$	1.19784e11			0.650781
$656$		−	4.84526e10i		−	0.261639i
$657$	−8.02943e10	+	1.65977e11i	−0.430946	+	0.890815i
$658$	−5.95276e10			−0.317552
$659$		−	2.55460e11i		−	1.35450i	−0.735751	−	0.677252i	$-0.763170\pi$
$659$		−	2.55460e11i		−	1.35450i	0.735751	−	0.677252i	$-0.236830\pi$
$660$	6.87646e10	−	4.31225e10i	0.362401	−	0.227263i
$661$	−8.06734e10			−0.422595			−0.211298	−	0.977422i	$-0.567769\pi$
$661$	−8.06734e10			−0.422595			−0.211298	+	0.977422i	$0.567769\pi$
$662$		−	5.15085e11i		−	2.68193i
$663$	−1.08744e11	−	1.73406e11i	−0.562794	−	0.897451i
$664$	4.95789e11			2.55050
$665$		−	1.23028e10i		−	0.0629096i
$666$	2.62465e10	+	1.26972e10i	0.133406	+	0.0645371i
$667$	2.54068e11			1.28365
$668$			3.65237e11i			1.83429i
$669$	−1.42371e11	+	8.92815e10i	−0.710752	+	0.445715i
$670$	−2.96125e11			−1.46952
$671$		−	6.16278e10i		−	0.304009i
$672$	−2.53753e9	−	4.04644e9i	−0.0124433	−	0.0198425i
$673$	1.76698e11			0.861335			0.430667	−	0.902511i	$-0.358278\pi$
$673$	1.76698e11			0.861335			0.430667	+	0.902511i	$0.358278\pi$
$674$			4.02090e11i			1.94843i
$675$	1.15991e10	+	1.05471e11i	0.0558738	+	0.508065i
$676$	1.12558e11			0.538999
$677$		−	3.05832e11i		−	1.45589i	−0.685635	−	0.727946i	$-0.740475\pi$
$677$		−	3.05832e11i		−	1.45589i	0.685635	−	0.727946i	$-0.259525\pi$
$678$	1.20030e11	−	7.52710e10i	0.568029	−	0.356212i
$679$	−7.18687e10			−0.338112
$680$		−	3.30993e11i		−	1.54804i
$681$	5.49017e10	+	8.75482e10i	0.255269	+	0.407060i
$682$	−2.15813e11			−0.997564
$683$		−	1.30047e11i		−	0.597607i	−0.954315	−	0.298804i	$-0.903412\pi$
$683$		−	1.30047e11i		−	0.597607i	0.954315	−	0.298804i	$-0.0965876\pi$
$684$	−7.63657e10	+	1.57857e11i	−0.348878	+	0.721171i
$685$	−8.78628e10			−0.399064
$686$		−	1.71112e11i		−	0.772651i
$687$	2.08773e10	−	1.30922e10i	0.0937231	−	0.0587740i
$688$	4.42636e11			1.97557
$689$			1.28474e11i			0.570085i
$690$	2.00525e11	+	3.19764e11i	0.884652	+	1.41070i
$691$	−2.98938e11			−1.31120			−0.655600	−	0.755108i	$-0.727584\pi$
$691$	−2.98938e11			−1.31120			−0.655600	+	0.755108i	$0.727584\pi$
$692$		−	5.32098e9i		−	0.0232042i
$693$	1.42658e10	+	6.90131e9i	0.0618534	+	0.0299226i
$694$	−4.63738e11			−1.99910
$695$			2.41743e11i			1.03613i
$696$	3.34032e11	−	2.09472e11i	1.42348	−	0.892667i
$697$	7.01476e10			0.297222
$698$			4.59551e11i			1.93603i
$699$	−6.29494e10	−	1.00381e11i	−0.263684	−	0.420479i
$700$	5.67477e10			0.236350
$701$		−	2.65240e11i		−	1.09842i	−0.835686	−	0.549208i	$-0.814930\pi$
$701$		−	2.65240e11i		−	1.09842i	0.835686	−	0.549208i	$-0.185070\pi$
$702$	3.60040e11	−	3.95949e10i	1.48253	−	0.163039i
$703$	−8.21104e9			−0.0336184
$704$		−	6.73429e10i		−	0.274158i
$705$	1.17158e11	−	7.34704e10i	0.474261	−	0.297410i
$706$	3.75669e11			1.51212
$707$		−	1.31483e10i		−	0.0526249i
$708$	3.57514e11	+	5.70104e11i	1.42285	+	2.26893i
$709$	4.88627e10			0.193372			0.0966858	−	0.995315i	$-0.469176\pi$
$709$	4.88627e10			0.193372			0.0966858	+	0.995315i	$0.469176\pi$
$710$		−	1.10394e11i		−	0.434422i
$711$	3.19518e10	−	6.60481e10i	0.125031	−	0.258453i
$712$	−1.15935e11			−0.451122
$713$		−	6.72254e11i		−	2.60121i
$714$	1.07951e11	−	6.76964e10i	0.415369	−	0.260479i
$715$	4.72152e10			0.180658
$716$			1.27299e11i			0.484365i
$717$	−7.17176e10	−	1.14363e11i	−0.271362	−	0.432724i
$718$	−7.35191e11			−2.76632
$719$			6.44788e10i			0.241269i	0.992697	+	0.120635i	$0.0384929\pi$
$719$			6.44788e10i			0.241269i	−0.992697	+	0.120635i	$0.961507\pi$
$720$	1.84058e11	+	8.90411e10i	0.684897	+	0.331330i
$721$	−5.40157e10			−0.199885
$722$			3.99217e11i			1.46913i
$723$	3.03043e11	−	1.90039e11i	1.10905	−	0.695487i
$724$	1.59119e11			0.579120
$725$			1.32475e11i			0.479491i
$726$	−2.33525e10	−	3.72387e10i	−0.0840596	−	0.134044i
$727$	4.40257e11			1.57605			0.788023	−	0.615646i	$-0.211105\pi$
$727$	4.40257e11			1.57605			0.788023	+	0.615646i	$0.211105\pi$
$728$		−	9.82471e10i		−	0.349779i
$729$	−2.75680e11	+	6.13773e10i	−0.976101	+	0.217319i
$730$	−3.41977e11			−1.20422
$731$			6.40829e11i			2.24426i
$732$	4.97640e11	−	3.12072e11i	1.73329	−	1.08695i
$733$	−1.11976e11			−0.387889			−0.193945	−	0.981012i	$-0.562128\pi$
$733$	−1.11976e11			−0.387889			−0.193945	+	0.981012i	$0.562128\pi$
$734$			2.39128e11i			0.823846i
$735$	1.02780e11	+	1.63897e11i	0.352176	+	0.561592i
$736$	−4.12663e10			−0.140632
$737$			1.07423e11i			0.364104i
$738$	−5.40588e10	+	1.11746e11i	−0.182239	+	0.376709i
$739$	−1.59418e11			−0.534514			−0.267257	−	0.963625i	$-0.586117\pi$
$739$	−1.59418e11			−0.534514			−0.267257	+	0.963625i	$0.586117\pi$
$740$			3.62250e10i			0.120804i
$741$	−8.64193e10	+	5.41938e10i	−0.286641	+	0.179753i
$742$	−7.99795e10			−0.263853
$743$			1.90256e11i			0.624284i	0.950035	+	0.312142i	$0.101047\pi$
$743$			1.90256e11i			0.624284i	−0.950035	+	0.312142i	$0.898953\pi$
$744$	−5.54256e11	−	8.83836e11i	−1.80892	−	2.88456i
$745$	1.30999e11			0.425249
$746$		−	4.65859e11i		−	1.50418i
$747$	−3.99143e11	−	1.93092e11i	−1.28188	−	0.620129i
$748$	−2.36747e11			−0.756272
$749$		−	1.39952e11i		−	0.444685i
$750$	−4.92930e11	+	3.09118e11i	−1.55790	+	0.976964i
$751$	−4.88184e11			−1.53470			−0.767351	−	0.641228i	$-0.778425\pi$
$751$	−4.88184e11			−1.53470			−0.767351	+	0.641228i	$0.778425\pi$
$752$			2.78610e11i			0.871216i
$753$	−1.20891e11	−	1.92778e11i	−0.376024	−	0.599621i
$754$	4.52220e11			1.39915
$755$			3.51852e9i			0.0108286i
$756$	1.65117e10	+	1.50142e11i	0.0505481	+	0.459638i
$757$	9.19943e10			0.280141			0.140071	−	0.990141i	$-0.455267\pi$
$757$	9.19943e10			0.280141			0.140071	+	0.990141i	$0.455267\pi$
$758$			1.52686e11i			0.462511i
$759$	1.15998e11	−	7.27426e10i	0.349529	−	0.219190i
$760$	−1.64955e11			−0.494436
$761$		−	4.34813e11i		−	1.29647i	−0.761439	−	0.648236i	$-0.775507\pi$
$761$		−	4.34813e11i		−	1.29647i	0.761439	−	0.648236i	$-0.224493\pi$
$762$	1.79626e11	+	2.86438e11i	0.532782	+	0.849593i
$763$	1.04970e11			0.309719
$764$			1.02434e12i			3.00655i
$765$	−1.28910e11	+	2.66471e11i	−0.376392	+	0.778045i
$766$	−2.30600e11			−0.669798
$767$			3.91445e11i			1.13107i
$768$	5.96510e11	−	3.74073e11i	1.71464	−	1.07525i
$769$	1.72025e11			0.491911			0.245956	−	0.969281i	$-0.420898\pi$
$769$	1.72025e11			0.491911			0.245956	+	0.969281i	$0.420898\pi$
$770$			2.93930e10i			0.0836143i
$771$	−2.91245e11	−	4.64430e11i	−0.824217	−	1.31432i
$772$	−2.42528e11			−0.682797
$773$			6.62238e11i			1.85480i	0.374075	+	0.927399i	$0.377960\pi$
$773$			6.62238e11i			1.85480i	−0.374075	+	0.927399i	$0.622040\pi$
$774$	−1.02085e12	−	4.93851e11i	−2.84444	−	1.37604i
$775$	3.50523e11			0.971650
$776$			9.63609e11i			2.65738i
$777$	−5.99198e9	+	3.75759e9i	−0.0164394	+	0.0103092i
$778$	−2.98301e11			−0.814210
$779$		−	3.49590e10i		−	0.0949311i
$780$	2.39089e11	+	3.81259e11i	0.645923	+	1.03001i
$781$	−4.00465e10			−0.107637
$782$		−	1.10090e12i		−	2.94389i
$783$	−3.50499e11	+	3.85457e10i	−0.932482	+	0.102548i
$784$	−3.89757e11			−1.03164
$785$			3.36293e11i			0.885604i
$786$	5.23804e11	−	3.28479e11i	1.37239	−	0.860632i
$787$	5.41364e11			1.41121			0.705603	−	0.708607i	$-0.250676\pi$
$787$	5.41364e11			1.41121			0.705603	+	0.708607i	$0.250676\pi$
$788$		−	3.39105e11i		−	0.879487i
$789$	−1.58371e11	−	2.52544e11i	−0.408665	−	0.651672i
$790$	1.36084e11			0.349381
$791$			3.43683e10i			0.0877913i
$792$	9.25322e10	−	1.91275e11i	0.235175	−	0.486134i
$793$	3.41690e11			0.864051
$794$			4.30687e10i			0.108363i
$795$	1.57411e11	−	9.87125e10i	0.394063	−	0.247118i
$796$	7.78189e11			1.93835
$797$		−	5.31497e11i		−	1.31725i	−0.752472	−	0.658624i	$-0.771139\pi$
$797$		−	5.31497e11i		−	1.31725i	0.752472	−	0.658624i	$-0.228861\pi$
$798$	−3.37374e10	−	5.37988e10i	−0.0831954	−	0.132666i
$799$	−4.03360e11			−0.989705
$800$		−	2.15169e10i		−	0.0525315i
$801$	9.33353e10	+	4.51525e10i	0.226734	+	0.109686i
$802$	6.36945e11			1.53959
$803$			1.24056e11i			0.298369i
$804$	−8.67429e11	+	5.43967e11i	−2.07592	+	1.30181i
$805$	−9.15584e10			−0.218029
$806$		−	1.19656e12i		−	2.83526i
$807$	2.11935e11	+	3.37959e11i	0.499699	+	0.796837i
$808$	−1.76291e11			−0.413603
$809$			3.87254e11i			0.904070i	0.892000	+	0.452035i	$0.149302\pi$
$809$			3.87254e11i			0.904070i	−0.892000	+	0.452035i	$0.850698\pi$
$810$	−3.25148e11	−	4.10709e11i	−0.755337	−	0.954101i
$811$	−4.92898e10			−0.113939			−0.0569697	−	0.998376i	$-0.518144\pi$
$811$	−4.92898e10			−0.113939			−0.0569697	+	0.998376i	$0.518144\pi$
$812$			1.88582e11i			0.433788i
$813$	2.04225e11	−	1.28070e11i	0.467463	−	0.293147i
$814$	1.96172e10			0.0446828
$815$			5.19247e11i			1.17691i
$816$	−3.16843e11	−	5.05249e11i	−0.714634	−	1.13958i
$817$	3.19365e11			0.716803
$818$		−	3.64961e11i		−	0.815142i
$819$	−3.82637e10	+	7.90954e10i	−0.0850455	+	0.175799i
$820$	−1.54230e11			−0.341124
$821$		−	3.41151e11i		−	0.750887i	−0.926845	−	0.375443i	$-0.877490\pi$
$821$		−	3.41151e11i		−	0.750887i	0.926845	−	0.375443i	$-0.122510\pi$
$822$	−3.84215e11	+	2.40942e11i	−0.841563	+	0.527746i
$823$	−4.95910e11			−1.08094			−0.540472	−	0.841362i	$-0.681754\pi$
$823$	−4.95910e11			−1.08094			−0.540472	+	0.841362i	$0.681754\pi$
$824$			7.24238e11i			1.57099i
$825$	3.79291e10	+	6.04830e10i	0.0818760	+	0.130562i
$826$	−2.43687e11			−0.523494
$827$			4.21137e11i			0.900330i	0.892945	+	0.450165i	$0.148635\pi$
$827$			4.21137e11i			0.900330i	−0.892945	+	0.450165i	$0.851365\pi$
$828$	1.17478e12	+	5.68320e11i	2.49940	+	1.20913i
$829$	−8.32965e10			−0.176363			−0.0881817	−	0.996104i	$-0.528106\pi$
$829$	−8.32965e10			−0.176363			−0.0881817	+	0.996104i	$0.528106\pi$
$830$		−	8.22387e11i		−	1.73286i
$831$	−5.23546e11	+	3.28317e11i	−1.09787	+	0.688477i
$832$	3.73377e11			0.779209
$833$		−	5.64273e11i		−	1.17195i
$834$	6.62921e11	+	1.05712e12i	1.37024	+	2.18504i
$835$	3.07262e11			0.632066
$836$			1.17986e11i			0.241549i
$837$	1.01991e11	+	9.27409e11i	0.207806	+	1.88960i
$838$	1.42056e12			2.88061
$839$			7.90314e11i			1.59497i	0.603341	+	0.797484i	$0.293836\pi$
$839$			7.90314e11i			1.59497i	−0.603341	+	0.797484i	$0.706164\pi$
$840$	−1.20375e11	+	7.54876e10i	−0.241780	+	0.151621i
$841$	6.00103e10			0.119962
$842$		−	1.18030e12i		−	2.34825i
$843$	−1.88974e11	−	3.01345e11i	−0.374190	−	0.596697i
$844$	1.29852e12			2.55906
$845$		−	9.46909e10i		−	0.185730i
$846$	3.10847e11	−	6.42556e11i	0.606827	−	1.25438i
$847$	1.06626e10			0.0207171
$848$			3.74332e11i			0.723892i
$849$	−5.01061e11	+	3.14216e11i	−0.964405	+	0.604781i
$850$	5.74028e11			1.09966
$851$			6.11073e10i			0.116513i
$852$	−2.02788e11	−	3.23373e11i	−0.384843	−	0.613685i
$853$	8.00045e11			1.51119			0.755593	−	0.655041i	$-0.227349\pi$
$853$	8.00045e11			1.51119			0.755593	+	0.655041i	$0.227349\pi$
$854$			2.12713e11i			0.399910i
$855$	1.32799e11	+	6.42439e10i	0.248503	+	0.120217i
$856$	−1.87647e12			−3.49499
$857$			6.52509e11i			1.20966i	0.796355	+	0.604830i	$0.206759\pi$
$857$			6.52509e11i			1.20966i	−0.796355	+	0.604830i	$0.793241\pi$
$858$	2.06467e11	−	1.29476e11i	0.380979	−	0.238913i
$859$	4.21259e11			0.773706			0.386853	−	0.922141i	$-0.373562\pi$
$859$	4.21259e11			0.773706			0.386853	+	0.922141i	$0.373562\pi$
$860$		−	1.40896e12i		−	2.57575i
$861$	−1.59981e10	−	2.55112e10i	−0.0291110	−	0.0464214i
$862$	−1.04003e12			−1.88373
$863$		−	2.59945e11i		−	0.468638i	−0.972160	−	0.234319i	$-0.924714\pi$
$863$		−	2.59945e11i		−	0.468638i	0.972160	−	0.234319i	$-0.0752860\pi$
$864$	5.69291e10	−	6.26070e9i	0.102160	−	0.0112349i
$865$	−4.47636e9			−0.00799578
$866$		−	1.11902e12i		−	1.98961i
$867$	2.52781e11	−	1.58519e11i	0.447371	−	0.280547i
$868$	4.98982e11			0.879035
$869$		−	4.93659e10i		−	0.0865662i
$870$	−3.47460e11	−	5.54072e11i	−0.606496	−	0.967140i
$871$	−5.95594e11			−1.03485
$872$		−	1.40743e12i		−	2.43423i
$873$	3.75291e11	−	7.75769e11i	0.646117	−	1.33560i
$874$	−5.48650e11			−0.940263
$875$		−	1.41141e11i		−	0.240780i
$876$	−1.00174e12	+	6.28194e11i	−1.70113	+	1.06679i
$877$	−5.91454e11			−0.999822			−0.499911	−	0.866077i	$-0.666634\pi$
$877$	−5.91454e11			−0.999822			−0.499911	+	0.866077i	$0.666634\pi$
$878$			1.37475e12i			2.31338i
$879$	−3.65967e11	−	5.83584e11i	−0.613037	−	0.977570i
$880$	1.37570e11			0.229399
$881$		−	5.95489e11i		−	0.988485i	−0.869324	−	0.494242i	$-0.835446\pi$
$881$		−	5.95489e11i		−	0.988485i	0.869324	−	0.494242i	$-0.164554\pi$
$882$	8.98892e11	+	4.34854e11i	1.48536	+	0.718569i
$883$	1.07866e11			0.177436			0.0887182	−	0.996057i	$-0.471723\pi$
$883$	1.07866e11			0.177436			0.0887182	+	0.996057i	$0.471723\pi$
$884$		−	1.31262e12i		−	2.14947i
$885$	4.79609e11	−	3.00764e11i	0.781834	−	0.490290i
$886$	−1.01419e12			−1.64583
$887$			1.54871e11i			0.250193i	0.992145	+	0.125096i	$0.0399240\pi$
$887$			1.54871e11i			0.250193i	−0.992145	+	0.125096i	$0.960076\pi$
$888$	5.03814e10	+	8.03399e10i	0.0810248	+	0.129205i
$889$	−8.20161e10			−0.131308
$890$			1.92306e11i			0.306502i
$891$	−1.48989e11	+	1.17951e11i	−0.236398	+	0.187150i
$892$	−1.07770e12			−1.70231
$893$			2.01020e11i			0.316106i
$894$	5.72845e11	−	3.59232e11i	0.896782	−	0.562374i
$895$	1.07092e11			0.166904
$896$			2.47535e11i			0.384064i
$897$	4.03315e11	+	6.43140e11i	0.622980	+	0.993426i
$898$	−2.68069e11			−0.412232
$899$			1.16485e12i			1.78333i
$900$	−2.96331e11	+	6.12549e11i	−0.451655	+	0.933622i
$901$	−5.41942e11			−0.822344
$902$			8.35215e10i			0.126175i
$903$	2.33056e11	−	1.46150e11i	0.350517	−	0.219810i
$904$	4.60806e11			0.689993
$905$		−	1.33862e11i		−	0.199555i
$906$	9.64866e9	+	1.53861e10i	0.0143204	+	0.0228358i
$907$	2.97695e11			0.439889			0.219944	−	0.975512i	$-0.429412\pi$
$907$	2.97695e11			0.439889			0.219944	+	0.975512i	$0.429412\pi$
$908$			6.62707e11i			0.974941i
$909$	1.41926e11	+	6.86589e10i	0.207877	+	0.100564i
$910$	−1.62967e11			−0.237647
$911$		−	1.36126e10i		−	0.0197636i	−0.999951	−	0.00988182i	$-0.996854\pi$
$911$		−	1.36126e10i		−	0.0197636i	0.999951	−	0.00988182i	$-0.00314553\pi$
$912$	−2.51797e11	+	1.57903e11i	−0.363975	+	0.228250i
$913$	−2.98329e11			−0.429352
$914$		−	4.48717e11i		−	0.642966i
$915$	−2.62535e11	−	4.18648e11i	−0.374544	−	0.597262i
$916$	1.58033e11			0.224474
$917$			1.49981e11i			0.212109i
$918$	1.67023e11	+	1.51875e12i	0.235183	+	2.13854i
$919$	−1.19518e12			−1.67561			−0.837804	−	0.545971i	$-0.816161\pi$
$919$	−1.19518e12			−1.67561			−0.837804	+	0.545971i	$0.816161\pi$
$920$			1.22761e12i			1.71359i
$921$	2.20537e11	−	1.38299e11i	0.306509	−	0.192212i
$922$	2.18188e11			0.301931
$923$		−	2.22034e11i		−	0.305924i
$924$	5.39934e10	+	8.60998e10i	0.0740718	+	0.118118i
$925$	−3.18623e10			−0.0435221
$926$			2.37123e12i			3.22499i
$927$	2.82065e11	−	5.83060e11i	0.381970	−	0.789576i
$928$	7.15043e10			0.0964141
$929$			2.02927e11i			0.272443i	0.990678	+	0.136222i	$0.0434959\pi$
$929$			2.02927e11i			0.272443i	−0.990678	+	0.136222i	$0.956504\pi$
$930$	−1.46606e12	+	9.19367e11i	−1.95983	+	1.22902i
$931$	−2.81213e11			−0.374314
$932$		−	7.59850e11i		−	1.00708i
$933$	−1.11277e11	−	1.77447e11i	−0.146852	−	0.234176i
$934$	−5.50446e11			−0.723315
$935$			1.99167e11i			0.260598i
$936$	1.06050e12	+	5.13036e11i	1.38168	+	0.668412i
$937$	−4.03528e11			−0.523498			−0.261749	−	0.965136i	$-0.584299\pi$
$937$	−4.03528e11			−0.523498			−0.261749	+	0.965136i	$0.584299\pi$
$938$		−	3.70777e11i		−	0.478962i
$939$	6.51548e11	−	4.08588e11i	0.838078	−	0.525561i
$940$	8.86846e11			1.13589
$941$			4.51826e11i			0.576252i	0.957593	+	0.288126i	$0.0930322\pi$
$941$			4.51826e11i			0.576252i	−0.957593	+	0.288126i	$0.906968\pi$
$942$	9.22202e11	+	1.47058e12i	1.17118	+	1.86760i
$943$	−2.60168e11			−0.329008
$944$			1.14054e12i			1.43623i
$945$	1.26310e11	−	1.38907e10i	0.158383	−	0.0174180i
$946$	−7.63006e11			−0.952715
$947$		−	1.20525e12i		−	1.49857i	−0.662245	−	0.749287i	$-0.730396\pi$
$947$		−	1.20525e12i		−	1.49857i	0.662245	−	0.749287i	$-0.269604\pi$
$948$	3.98626e11	−	2.49980e11i	0.493552	−	0.309508i
$949$	−6.87815e11			−0.848021
$950$		−	2.86074e11i		−	0.351224i
$951$	−7.44558e11	−	1.18730e12i	−0.910283	−	1.45157i
$952$	4.14435e11			0.504555
$953$		−	6.97558e11i		−	0.845685i	−0.906203	−	0.422842i	$-0.861032\pi$
$953$		−	6.97558e11i		−	0.845685i	0.906203	−	0.422842i	$-0.138968\pi$
$954$	4.17644e11	−	8.63319e11i	0.504212	−	1.04226i
$955$	8.61739e11			1.03601
$956$		−	8.65689e11i		−	1.03641i
$957$	−2.00996e11	+	1.26045e11i	−0.239629	+	0.150272i
$958$	5.70453e11			0.677264
$959$		−	1.10013e11i		−	0.130067i
$960$	−2.86882e11	−	4.57472e11i	−0.337768	−	0.538616i
$961$	2.22926e12			2.61377
$962$			1.08766e11i			0.126997i
$963$	1.51068e12	+	7.30816e11i	1.75658	+	0.849773i
$964$	2.29392e12			2.65626
$965$			2.04030e11i			0.235280i
$966$	−4.00375e11	+	2.51076e11i	−0.459789	+	0.288335i
$967$	−1.41423e12			−1.61739			−0.808694	−	0.588229i	$-0.799825\pi$
$967$	−1.41423e12			−1.61739			−0.808694	+	0.588229i	$0.799825\pi$
$968$		−	1.42963e11i		−	0.162826i
$969$	−2.28605e11	−	3.64541e11i	−0.259293	−	0.413477i
$970$	1.59838e12			1.80548
$971$		−	1.04887e11i		−	0.117990i	−0.998258	−	0.0589948i	$-0.981210\pi$
$971$		−	1.04887e11i		−	0.117990i	0.998258	−	0.0589948i	$-0.0187895\pi$
$972$	−1.70690e12	−	6.05796e11i	−1.91224	−	0.678674i
$973$	−3.02686e11			−0.337707
$974$		−	8.30267e11i		−	0.922533i
$975$	−3.35343e11	+	2.10294e11i	−0.371082	+	0.232707i
$976$	9.95572e11			1.09717
$977$		−	1.14391e12i		−	1.25549i	−0.778421	−	0.627743i	$-0.783979\pi$
$977$		−	1.14391e12i		−	1.25549i	0.778421	−	0.627743i	$-0.216021\pi$
$978$	1.42391e12	+	2.27061e12i	1.55642	+	2.48192i
$979$	6.97611e10			0.0759421
$980$			1.24064e12i			1.34506i
$981$	−5.48143e11	+	1.13307e12i	−0.591859	+	1.22344i
$982$	−1.60326e12			−1.72408
$983$		−	3.69703e10i		−	0.0395948i	−0.999804	−	0.0197974i	$-0.993698\pi$
$983$		−	3.69703e10i		−	0.0395948i	0.999804	−	0.0197974i	$-0.00630212\pi$
$984$	−3.42052e11	+	2.14501e11i	−0.364847	+	0.228797i
$985$	−2.85278e11			−0.303056
$986$			1.90759e12i			2.01826i
$987$	9.19918e10	+	1.46693e11i	0.0969350	+	0.154576i
$988$	−6.54162e11			−0.686527
$989$		−	2.37675e12i		−	2.48426i
$990$	−3.17275e11	−	1.53487e11i	−0.330290	−	0.159783i
$991$	1.82119e11			0.188826			0.0944129	−	0.995533i	$-0.469903\pi$
$991$	1.82119e11			0.188826			0.0944129	+	0.995533i	$0.469903\pi$
$992$		−	1.89198e11i		−	0.195375i
$993$	−1.26932e12	+	7.95994e11i	−1.30549	+	0.818677i
$994$	1.38223e11			0.141591
$995$		−	6.54664e11i		−	0.667922i
$996$	−1.51068e12	−	2.40899e12i	−1.53510	−	2.44792i
$997$	7.11923e11			0.720530			0.360265	−	0.932850i	$-0.382686\pi$
$997$	7.11923e11			0.720530			0.360265	+	0.932850i	$0.382686\pi$
$998$		−	1.48097e12i		−	1.49287i
$999$	−9.27085e9	−	8.43007e10i	−0.00930803	−	0.0846388i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	33.9.b.a.23.2	✓	26
3.2	odd	2	inner	33.9.b.a.23.25	yes	26

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
33.9.b.a.23.2	✓	26	1.1	even	1	trivial
33.9.b.a.23.25	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)

\(f(q)\)	\(=\)	\(q-27.8469i q^{2} +(-68.6229 + 43.0336i) q^{3} -519.450 q^{4} +436.996i q^{5} +(1198.35 + 1910.94i) q^{6} -547.160 q^{7} +7336.27i q^{8} +(2857.21 - 5906.19i) q^{9} +O(q^{10})\)	\(q-27.8469i q^{2} +(-68.6229 + 43.0336i) q^{3} -519.450 q^{4} +436.996i q^{5} +(1198.35 + 1910.94i) q^{6} -547.160 q^{7} +7336.27i q^{8} +(2857.21 - 5906.19i) q^{9} +12169.0 q^{10} -4414.43i q^{11} +(35646.2 - 22353.8i) q^{12} +24475.4 q^{13} +15236.7i q^{14} +(-18805.5 - 29987.9i) q^{15} +71313.3 q^{16} +103244. i q^{17} +(-164469. - 79564.6i) q^{18} +51453.1 q^{19} -226998. i q^{20} +(37547.7 - 23546.3i) q^{21} -122928. q^{22} -382919. i q^{23} +(-315706. - 503437. i) q^{24} +199659. q^{25} -681564. i q^{26} +(58094.2 + 528256. i) q^{27} +284223. q^{28} +663503. i q^{29} +(-835072. + 523676. i) q^{30} +1.75560e6 q^{31} -107768. i q^{32} +(189969. + 302931. i) q^{33} +2.87503e6 q^{34} -239107. i q^{35} +(-1.48418e6 + 3.06797e6i) q^{36} -159583. q^{37} -1.43281e6i q^{38} +(-1.67957e6 + 1.05326e6i) q^{39} -3.20592e6 q^{40} -679433. i q^{41} +(-655691. - 1.04559e6i) q^{42} +6.20692e6 q^{43} +2.29308e6i q^{44} +(2.58098e6 + 1.24859e6i) q^{45} -1.06631e7 q^{46} +3.90685e6i q^{47} +(-4.89373e6 + 3.06887e6i) q^{48} -5.46542e6 q^{49} -5.55990e6i q^{50} +(-4.44297e6 - 7.08492e6i) q^{51} -1.27137e7 q^{52} +5.24913e6i q^{53} +(1.47103e7 - 1.61775e6i) q^{54} +1.92909e6 q^{55} -4.01412e6i q^{56} +(-3.53086e6 + 2.21421e6i) q^{57} +1.84765e7 q^{58} +1.59934e7i q^{59} +(9.76853e6 + 1.55772e7i) q^{60} +1.39605e7 q^{61} -4.88882e7i q^{62} +(-1.56335e6 + 3.23163e6i) q^{63} +1.52552e7 q^{64} +1.06956e7i q^{65} +(8.43569e6 - 5.29004e6i) q^{66} -2.43344e7 q^{67} -5.36302e7i q^{68} +(1.64784e7 + 2.62770e7i) q^{69} -6.65839e6 q^{70} -9.07174e6i q^{71} +(4.33294e7 + 2.09613e7i) q^{72} -2.81023e7 q^{73} +4.44389e6i q^{74} +(-1.37012e7 + 8.59207e6i) q^{75} -2.67273e7 q^{76} +2.41540e6i q^{77} +(2.93302e7 + 4.67709e7i) q^{78} +1.11829e7 q^{79} +3.11636e7i q^{80} +(-2.67194e7 - 3.37505e7i) q^{81} -1.89201e7 q^{82} -6.75805e7i q^{83} +(-1.95042e7 + 1.22311e7i) q^{84} -4.51173e7 q^{85} -1.72844e8i q^{86} +(-2.85529e7 - 4.55315e7i) q^{87} +3.23854e7 q^{88} +1.58030e7i q^{89} +(3.47694e7 - 7.18723e7i) q^{90} -1.33920e7 q^{91} +1.98907e8i q^{92} +(-1.20475e8 + 7.55500e7i) q^{93} +1.08794e8 q^{94} +2.24848e7i q^{95} +(4.63764e6 + 7.39535e6i) q^{96} +1.31349e8 q^{97} +1.52195e8i q^{98} +(-2.60724e7 - 1.26130e7i) 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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