LMFDB - Embedded newform 33.8.d.b.32.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [33,8,Mod(32,33)]

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, 1]))

N = Newforms(chi, 8, names="a")

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

chi := DirichletCharacter("33.32");

S:= CuspForms(chi, 8);

N := Newforms(S);

Level:	$ N $	$=$	$ 33 = 3 \cdot 11 $
Weight:	$ k $	$=$	$ 8 $
Character orbit:	$[\chi]$	$=$	33.d (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:	$10.3087058410$
Analytic rank:	$0$
Dimension:	$24$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			32.11
Character	$\chi$	$=$	33.32
Dual form			33.8.d.b.32.12

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-4.00282 q^{2} +(34.4918 - 31.5803i) q^{3} -111.977 q^{4} +109.310i q^{5} +(-138.065 + 126.410i) q^{6} +1222.62i q^{7} +960.586 q^{8} +(192.374 - 2178.52i) q^{9} +O(q^{10})$	\(q-4.00282 q^{2} +(34.4918 - 31.5803i) q^{3} -111.977 q^{4} +109.310i q^{5} +(-138.065 + 126.410i) q^{6} +1222.62i q^{7} +960.586 q^{8} +(192.374 - 2178.52i) q^{9} -437.547i q^{10} +(4400.12 + 355.132i) q^{11} +(-3862.31 + 3536.28i) q^{12} +2120.46i q^{13} -4893.92i q^{14} +(3452.03 + 3770.30i) q^{15} +10488.1 q^{16} +23816.2 q^{17} +(-770.039 + 8720.23i) q^{18} +46749.5i q^{19} -12240.2i q^{20} +(38610.6 + 42170.4i) q^{21} +(-17612.9 - 1421.53i) q^{22} +47997.7i q^{23} +(33132.4 - 30335.6i) q^{24} +66176.4 q^{25} -8487.80i q^{26} +(-62163.0 - 81216.5i) q^{27} -136906. i q^{28} -169761. q^{29} +(-13817.9 - 15091.8i) q^{30} -74372.3 q^{31} -164937. q^{32} +(162983. - 126708. i) q^{33} -95331.9 q^{34} -133644. q^{35} +(-21541.6 + 243945. i) q^{36} +277920. q^{37} -187130. i q^{38} +(66964.5 + 73138.4i) q^{39} +105001. i q^{40} -145178. q^{41} +(-154551. - 168800. i) q^{42} -264460. i q^{43} +(-492714. - 39766.8i) q^{44} +(238134. + 21028.4i) q^{45} -192126. i q^{46} +1.20856e6i q^{47} +(361753. - 331216. i) q^{48} -671255. q^{49} -264892. q^{50} +(821465. - 752122. i) q^{51} -237443. i q^{52} -1.78576e6i q^{53} +(248827. + 325095. i) q^{54} +(-38819.4 + 480976. i) q^{55} +1.17443e6i q^{56} +(1.47636e6 + 1.61248e6i) q^{57} +679523. q^{58} -388411. i q^{59} +(-386550. - 422188. i) q^{60} +2.73323e6i q^{61} +297699. q^{62} +(2.66350e6 + 235200. i) q^{63} -682260. q^{64} -231787. q^{65} +(-652393. + 507188. i) q^{66} -455681. q^{67} -2.66688e6 q^{68} +(1.51578e6 + 1.65553e6i) q^{69} +534954. q^{70} -2.64004e6i q^{71} +(184792. - 2.09266e6i) q^{72} +2.47259e6i q^{73} -1.11246e6 q^{74} +(2.28254e6 - 2.08987e6i) q^{75} -5.23489e6i q^{76} +(-434191. + 5.37967e6i) q^{77} +(-268047. - 292760. i) q^{78} -4.90350e6i q^{79} +1.14645e6i q^{80} +(-4.70895e6 - 838183. i) q^{81} +581120. q^{82} +2.93766e6 q^{83} +(-4.32352e6 - 4.72213e6i) q^{84} +2.60334e6i q^{85} +1.05859e6i q^{86} +(-5.85538e6 + 5.36110e6i) q^{87} +(4.22669e6 + 341135. i) q^{88} -2.83818e6i q^{89} +(-953206. - 84172.8i) q^{90} -2.59251e6 q^{91} -5.37467e6i q^{92} +(-2.56524e6 + 2.34870e6i) q^{93} -4.83765e6i q^{94} -5.11018e6 q^{95} +(-5.68897e6 + 5.20875e6i) q^{96} +6.00627e6 q^{97} +2.68691e6 q^{98} +(1.62013e6 - 9.51744e6i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 120 q^{3} + 1788 q^{4} - 5940 q^{9}+O(q^{10}) $ 24 * q + 120 * q^3 + 1788 * q^4 - 5940 * q^9	$ 24 q + 120 q^{3} + 1788 q^{4} - 5940 q^{9} - 6936 q^{12} + 23160 q^{15} + 5844 q^{16} - 17556 q^{22} - 34704 q^{25} + 7560 q^{27} + 131328 q^{31} + 28644 q^{33} - 436080 q^{34} - 302832 q^{36} + 1072488 q^{37} - 100296 q^{42} - 1854252 q^{45} + 3172548 q^{48} - 1169304 q^{49} - 4401936 q^{55} - 2920440 q^{58} + 1981452 q^{60} + 14578596 q^{64} + 2895156 q^{66} + 7729200 q^{67} - 4614108 q^{69} - 6924504 q^{70} - 4375800 q^{75} - 26237448 q^{78} + 22367340 q^{81} - 23600232 q^{82} - 25179660 q^{88} + 9380640 q^{91} + 25396908 q^{93} + 72948360 q^{97} + 53650080 q^{99}+O(q^{100}) $ 24 * q + 120 * q^3 + 1788 * q^4 - 5940 * q^9 - 6936 * q^12 + 23160 * q^15 + 5844 * q^16 - 17556 * q^22 - 34704 * q^25 + 7560 * q^27 + 131328 * q^31 + 28644 * q^33 - 436080 * q^34 - 302832 * q^36 + 1072488 * q^37 - 100296 * q^42 - 1854252 * q^45 + 3172548 * q^48 - 1169304 * q^49 - 4401936 * q^55 - 2920440 * q^58 + 1981452 * q^60 + 14578596 * q^64 + 2895156 * q^66 + 7729200 * q^67 - 4614108 * q^69 - 6924504 * q^70 - 4375800 * q^75 - 26237448 * q^78 + 22367340 * q^81 - 23600232 * q^82 - 25179660 * q^88 + 9380640 * q^91 + 25396908 * q^93 + 72948360 * q^97 + 53650080 * 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 $

$2$	−4.00282			−0.353802			−0.176901	−	0.984229i	$-0.556607\pi$
$2$	−4.00282			−0.353802			−0.176901	+	0.984229i	$0.556607\pi$
$3$	34.4918	−	31.5803i	0.737551	−	0.675292i
$3$	34.4918	−	31.5803i	0.737551	−	0.675292i
$4$	−111.977			−0.874824
$5$			109.310i			0.391079i	0.980696	+	0.195539i	$0.0626457\pi$
$5$			109.310i			0.391079i	−0.980696	+	0.195539i	$0.937354\pi$
$6$	−138.065	+	126.410i	−0.260947	+	0.238920i
$7$			1222.62i			1.34725i	0.739073	+	0.673625i	$0.235264\pi$
$7$			1222.62i			1.34725i	−0.739073	+	0.673625i	$0.764736\pi$
$8$	960.586			0.663317
$9$	192.374	−	2178.52i	0.0879626	−	0.996124i
$10$		−	437.547i		−	0.138365i
$11$	4400.12	+	355.132i	0.996759	+	0.0804480i
$11$	4400.12	+	355.132i	0.996759	+	0.0804480i
$12$	−3862.31	+	3536.28i	−0.645227	+	0.590761i
$13$			2120.46i			0.267687i	0.991002	+	0.133844i	$0.0427320\pi$
$13$			2120.46i			0.267687i	−0.991002	+	0.133844i	$0.957268\pi$
$14$		−	4893.92i		−	0.476660i
$15$	3452.03	+	3770.30i	0.264092	+	0.288440i
$16$	10488.1			0.640141
$17$	23816.2			1.17571			0.587856	−	0.808965i	$-0.299972\pi$
$17$	23816.2			1.17571			0.587856	+	0.808965i	$0.299972\pi$
$18$	−770.039	+	8720.23i	−0.0311214	+	0.352431i
$19$			46749.5i			1.56365i	0.623498	+	0.781825i	$0.285711\pi$
$19$			46749.5i			1.56365i	−0.623498	+	0.781825i	$0.714289\pi$
$20$		−	12240.2i		−	0.342125i
$21$	38610.6	+	42170.4i	0.909786	+	0.993665i
$22$	−17612.9	−	1421.53i	−0.352656	−	0.0284627i
$23$			47997.7i			0.822571i	0.911507	+	0.411286i	$0.134920\pi$
$23$			47997.7i			0.822571i	−0.911507	+	0.411286i	$0.865080\pi$
$24$	33132.4	−	30335.6i	0.489230	−	0.447933i
$25$	66176.4			0.847058
$26$		−	8487.80i		−	0.0947083i
$27$	−62163.0	−	81216.5i	−0.607797	−	0.794092i
$28$		−	136906.i		−	1.17861i
$29$	−169761.			−1.29254			−0.646272	−	0.763107i	$-0.723673\pi$
$29$	−169761.			−1.29254			−0.646272	+	0.763107i	$0.723673\pi$
$30$	−13817.9	−	15091.8i	−0.0934364	−	0.102051i
$31$	−74372.3			−0.448379			−0.224189	−	0.974546i	$-0.571973\pi$
$31$	−74372.3			−0.448379			−0.224189	+	0.974546i	$0.571973\pi$
$32$	−164937.			−0.889801
$33$	162983.	−	126708.i	0.789486	−	0.613768i
$34$	−95331.9			−0.415970
$35$	−133644.			−0.526880
$36$	−21541.6	+	243945.i	−0.0769518	+	0.871433i
$37$	277920.			0.902015			0.451008	−	0.892520i	$-0.351065\pi$
$37$	277920.			0.902015			0.451008	+	0.892520i	$0.351065\pi$
$38$		−	187130.i		−	0.553223i
$39$	66964.5	+	73138.4i	0.180767	+	0.197433i
$40$			105001.i			0.259409i
$41$	−145178.			−0.328970			−0.164485	−	0.986380i	$-0.552596\pi$
$41$	−145178.			−0.328970			−0.164485	+	0.986380i	$0.552596\pi$
$42$	−154551.	−	168800.i	−0.321885	−	0.351561i
$43$		−	264460.i		−	0.507249i	−0.967303	−	0.253624i	$-0.918377\pi$
$43$		−	264460.i		−	0.507249i	0.967303	−	0.253624i	$-0.0816227\pi$
$44$	−492714.	−	39766.8i	−0.871988	−	0.0703778i
$45$	238134.	+	21028.4i	0.389563	+	0.0344003i
$46$		−	192126.i		−	0.291028i
$47$			1.20856e6i			1.69795i	0.528430	+	0.848977i	$0.322781\pi$
$47$			1.20856e6i			1.69795i	−0.528430	+	0.848977i	$0.677219\pi$
$48$	361753.	−	331216.i	0.472136	−	0.432282i
$49$	−671255.			−0.815082
$50$	−264892.			−0.299691
$51$	821465.	−	752122.i	0.867148	−	0.793949i
$52$		−	237443.i		−	0.234179i
$53$		−	1.78576e6i		−	1.64762i	−0.566866	−	0.823810i	$-0.691844\pi$
$53$		−	1.78576e6i		−	1.64762i	0.566866	−	0.823810i	$-0.308156\pi$
$54$	248827.	+	325095.i	0.215040	+	0.280952i
$55$	−38819.4	+	480976.i	−0.0314615	+	0.389811i
$56$			1.17443e6i			0.893654i
$57$	1.47636e6	+	1.61248e6i	1.05592	+	1.15327i
$58$	679523.			0.457305
$59$		−	388411.i		−	0.246212i	−0.992394	−	0.123106i	$-0.960714\pi$
$59$		−	388411.i		−	0.246212i	0.992394	−	0.123106i	$-0.0392855\pi$
$60$	−386550.	−	422188.i	−0.231034	−	0.252334i
$61$			2.73323e6i			1.54178i	0.636970	+	0.770889i	$0.280187\pi$
$61$			2.73323e6i			1.54178i	−0.636970	+	0.770889i	$0.719813\pi$
$62$	297699.			0.158638
$63$	2.66350e6	+	235200.i	1.34203	+	0.118508i
$64$	−682260.			−0.325327
$65$	−231787.			−0.104687
$66$	−652393.	+	507188.i	−0.279322	+	0.217153i
$67$	−455681.			−0.185097			−0.0925485	−	0.995708i	$-0.529501\pi$
$67$	−455681.			−0.185097			−0.0925485	+	0.995708i	$0.529501\pi$
$68$	−2.66688e6			−1.02854
$69$	1.51578e6	+	1.65553e6i	0.555475	+	0.606688i
$70$	534954.			0.186412
$71$		−	2.64004e6i		−	0.875399i	−0.899121	−	0.437699i	$-0.855793\pi$
$71$		−	2.64004e6i		−	0.875399i	0.899121	−	0.437699i	$-0.144207\pi$
$72$	184792.	−	2.09266e6i	0.0583471	−	0.660746i
$73$			2.47259e6i			0.743912i	0.928250	+	0.371956i	$0.121313\pi$
$73$			2.47259e6i			0.743912i	−0.928250	+	0.371956i	$0.878687\pi$
$74$	−1.11246e6			−0.319135
$75$	2.28254e6	−	2.08987e6i	0.624748	−	0.572011i
$76$		−	5.23489e6i		−	1.36792i
$77$	−434191.	+	5.37967e6i	−0.108384	+	1.34288i
$78$	−268047.	−	292760.i	−0.0639557	−	0.0698522i
$79$		−	4.90350e6i		−	1.11895i	−0.828847	−	0.559476i	$-0.811002\pi$
$79$		−	4.90350e6i		−	1.11895i	0.828847	−	0.559476i	$-0.188998\pi$
$80$			1.14645e6i			0.250345i
$81$	−4.70895e6	−	838183.i	−0.984525	−	0.175243i
$82$	581120.			0.116390
$83$	2.93766e6			0.563934			0.281967	−	0.959424i	$-0.409013\pi$
$83$	2.93766e6			0.563934			0.281967	+	0.959424i	$0.409013\pi$
$84$	−4.32352e6	−	4.72213e6i	−0.795903	−	0.869282i
$85$			2.60334e6i			0.459796i
$86$			1.05859e6i			0.179466i
$87$	−5.85538e6	+	5.36110e6i	−0.953317	+	0.872844i
$88$	4.22669e6	+	341135.i	0.661167	+	0.0533625i
$89$		−	2.83818e6i		−	0.426752i	−0.976970	−	0.213376i	$-0.931554\pi$
$89$		−	2.83818e6i		−	0.426752i	0.976970	−	0.213376i	$-0.0684459\pi$
$90$	−953206.	−	84172.8i	−0.137828	−	0.0121709i
$91$	−2.59251e6			−0.360641
$92$		−	5.37467e6i		−	0.719605i
$93$	−2.56524e6	+	2.34870e6i	−0.330702	+	0.302786i
$94$		−	4.83765e6i		−	0.600740i
$95$	−5.11018e6			−0.611510
$96$	−5.68897e6	+	5.20875e6i	−0.656273	+	0.600875i
$97$	6.00627e6			0.668195			0.334098	−	0.942538i	$-0.391568\pi$
$97$	6.00627e6			0.668195			0.334098	+	0.942538i	$0.391568\pi$
$98$	2.68691e6			0.288378
$99$	1.62013e6	−	9.51744e6i	0.167814	−	0.985819i
$100$	−7.41026e6			−0.741026
$101$	8.46529e6			0.817555			0.408778	−	0.912634i	$-0.365955\pi$
$101$	8.46529e6			0.817555			0.408778	+	0.912634i	$0.365955\pi$
$102$	−3.28817e6	+	3.01061e6i	−0.306799	+	0.280901i
$103$	−1.94396e6			−0.175290			−0.0876448	−	0.996152i	$-0.527934\pi$
$103$	−1.94396e6			−0.175290			−0.0876448	+	0.996152i	$0.527934\pi$
$104$			2.03688e6i			0.177561i
$105$	−4.60964e6	+	4.22052e6i	−0.388601	+	0.355798i
$106$			7.14806e6i			0.582932i
$107$	1.41698e7			1.11820			0.559100	−	0.829100i	$-0.311147\pi$
$107$	1.41698e7			1.11820			0.559100	+	0.829100i	$0.311147\pi$
$108$	6.96085e6	+	9.09442e6i	0.531715	+	0.694691i
$109$		−	6.10341e6i		−	0.451419i	−0.974195	−	0.225709i	$-0.927530\pi$
$109$		−	6.10341e6i		−	0.451419i	0.974195	−	0.225709i	$-0.0724700\pi$
$110$	155387.	−	1.92526e6i	0.0111311	−	0.137916i
$111$	9.58597e6	−	8.77679e6i	0.665282	−	0.609123i
$112$			1.28229e7i			0.862429i
$113$		−	1.22402e7i		−	0.798018i	−0.916947	−	0.399009i	$-0.869354\pi$
$113$		−	1.22402e7i		−	0.798018i	0.916947	−	0.399009i	$-0.130646\pi$
$114$	−5.90961e6	−	6.45445e6i	−0.373587	−	0.408030i
$115$	−5.24662e6			−0.321690
$116$	1.90094e7			1.13075
$117$	4.61946e6	+	407921.i	0.266649	+	0.0235465i
$118$			1.55474e6i			0.0871105i
$119$			2.91181e7i			1.58398i
$120$	3.31597e6	+	3.62169e6i	0.175177	+	0.191327i
$121$	1.92349e7	+	3.12524e6i	0.987056	+	0.160374i
$122$		−	1.09406e7i		−	0.545484i
$123$	−5.00744e6	+	4.58475e6i	−0.242632	+	0.222151i
$124$	8.32802e6			0.392252
$125$			1.57736e7i			0.722345i
$126$	−1.06615e7	−	941465.i	−0.474813	−	0.0419283i
$127$			2.11440e7i			0.915954i	0.888964	+	0.457977i	$0.151426\pi$
$127$			2.11440e7i			0.915954i	−0.888964	+	0.457977i	$0.848574\pi$
$128$	2.38429e7			1.00490
$129$	−8.35172e6	−	9.12172e6i	−0.342541	−	0.374122i
$130$	927799.			0.0370384
$131$	−1.27606e7			−0.495932			−0.247966	−	0.968769i	$-0.579762\pi$
$131$	−1.27606e7			−0.495932			−0.247966	+	0.968769i	$0.579762\pi$
$132$	−1.82505e7	+	1.41884e7i	−0.690661	+	0.536939i
$133$	−5.71569e7			−2.10663
$134$	1.82401e6			0.0654878
$135$	8.87776e6	−	6.79502e6i	0.310553	−	0.237696i
$136$	2.28775e7			0.779871
$137$		−	5.51362e7i		−	1.83195i	−0.401231	−	0.915977i	$-0.631418\pi$
$137$		−	5.51362e7i		−	1.83195i	0.401231	−	0.915977i	$-0.368582\pi$
$138$	−6.06740e6	−	6.62679e6i	−0.196529	−	0.214648i
$139$		−	4.06905e7i		−	1.28511i	−0.766238	−	0.642556i	$-0.777874\pi$
$139$		−	4.06905e7i		−	1.28511i	0.766238	−	0.642556i	$-0.222126\pi$
$140$	1.49651e7			0.460928
$141$	3.81666e7	+	4.16855e7i	1.14661	+	1.25233i
$142$			1.05676e7i			0.309718i
$143$	−753041.	+	9.33026e6i	−0.0215349	+	0.266819i
$144$	2.01763e6	−	2.28485e7i	0.0563084	−	0.637659i
$145$		−	1.85566e7i		−	0.505486i
$146$		−	9.89732e6i		−	0.263198i
$147$	−2.31528e7	+	2.11984e7i	−0.601164	+	0.550418i
$148$	−3.11208e7			−0.789104
$149$	−6.75543e7			−1.67302			−0.836510	−	0.547952i	$-0.815408\pi$
$149$	−6.75543e7			−1.67302			−0.836510	+	0.547952i	$0.815408\pi$
$150$	−9.13661e6	+	8.36536e6i	−0.221037	+	0.202379i
$151$		−	1.36035e7i		−	0.321538i	−0.986992	−	0.160769i	$-0.948603\pi$
$151$		−	1.36035e7i		−	0.321538i	0.986992	−	0.160769i	$-0.0513974\pi$
$152$			4.49069e7i			1.03720i
$153$	4.58162e6	−	5.18841e7i	0.103419	−	1.17116i
$154$	1.73799e6	−	2.15338e7i	0.0383464	−	0.475115i
$155$		−	8.12962e6i		−	0.175351i
$156$	−7.49852e6	−	8.18985e6i	−0.158139	−	0.172719i
$157$	3.48346e7			0.718394			0.359197	−	0.933262i	$-0.383051\pi$
$157$	3.48346e7			0.718394			0.359197	+	0.933262i	$0.383051\pi$
$158$			1.96278e7i			0.395888i
$159$	−5.63947e7	−	6.15941e7i	−1.11262	−	1.21520i
$160$		−	1.80292e7i		−	0.347982i
$161$	−5.86830e7			−1.10821
$162$	1.88491e7	+	3.35510e6i	0.348327	+	0.0620015i
$163$	2.81808e7			0.509680			0.254840	−	0.966983i	$-0.417977\pi$
$163$	2.81808e7			0.509680			0.254840	+	0.966983i	$0.417977\pi$
$164$	1.62566e7			0.287791
$165$	1.38504e7	+	1.78157e7i	0.240032	+	0.308751i
$166$	−1.17589e7			−0.199521
$167$	−4.89635e7			−0.813514			−0.406757	−	0.913536i	$-0.633340\pi$
$167$	−4.89635e7			−0.813514			−0.406757	+	0.913536i	$0.633340\pi$
$168$	3.70888e7	+	4.05083e7i	0.603477	+	0.659115i
$169$	5.82522e7			0.928344
$170$		−	1.04207e7i		−	0.162677i
$171$	1.01845e8	+	8.99340e6i	1.55759	+	0.137543i
$172$			2.96136e7i			0.443753i
$173$	−7.15181e7			−1.05016			−0.525079	−	0.851054i	$-0.675964\pi$
$173$	−7.15181e7			−1.05016			−0.525079	+	0.851054i	$0.675964\pi$
$174$	2.34380e7	−	2.14595e7i	0.337286	−	0.308814i
$175$			8.09085e7i			1.14120i
$176$	4.61487e7	+	3.72464e6i	0.638066	+	0.0514980i
$177$	−1.22661e7	−	1.33970e7i	−0.166265	−	0.181594i
$178$			1.13607e7i			0.150986i
$179$			7.34908e7i			0.957740i	0.877886	+	0.478870i	$0.158953\pi$
$179$			7.34908e7i			0.957740i	−0.877886	+	0.478870i	$0.841047\pi$
$180$	−2.66656e7	−	2.35471e6i	−0.340799	−	0.0300942i
$181$	−1.48438e8			−1.86068			−0.930339	−	0.366701i	$-0.880487\pi$
$181$	−1.48438e8			−1.86068			−0.930339	+	0.366701i	$0.880487\pi$
$182$	1.03773e7			0.127596
$183$	8.63161e7	+	9.42741e7i	1.04115	+	1.13714i
$184$			4.61060e7i			0.545626i
$185$			3.03794e7i			0.352759i
$186$	1.02682e7	−	9.40140e6i	0.117003	−	0.107127i
$187$	1.04794e8	+	8.45789e6i	1.17190	+	0.0945837i
$188$		−	1.35331e8i		−	1.48541i
$189$	9.92968e7	−	7.60016e7i	1.06984	−	0.818854i
$190$	2.04551e7			0.216354
$191$		−	2.49136e7i		−	0.258714i	−0.991598	−	0.129357i	$-0.958709\pi$
$191$		−	2.49136e7i		−	0.258714i	0.991598	−	0.129357i	$-0.0412913\pi$
$192$	−2.35324e7	+	2.15460e7i	−0.239945	+	0.219691i
$193$		−	1.20213e8i		−	1.20365i	−0.798629	−	0.601824i	$-0.794441\pi$
$193$		−	1.20213e8i		−	1.20365i	0.798629	−	0.601824i	$-0.205559\pi$
$194$	−2.40420e7			−0.236409
$195$	−7.99474e6	+	7.31988e6i	−0.0772117	+	0.0706940i
$196$	7.51654e7			0.713053
$197$	−4.14742e6			−0.0386497			−0.0193248	−	0.999813i	$-0.506152\pi$
$197$	−4.14742e6			−0.0386497			−0.0193248	+	0.999813i	$0.506152\pi$
$198$	−6.48509e6	+	3.80966e7i	−0.0593729	+	0.348785i
$199$	−9.24021e7			−0.831181			−0.415591	−	0.909552i	$-0.636425\pi$
$199$	−9.24021e7			−0.831181			−0.415591	+	0.909552i	$0.636425\pi$
$200$	6.35681e7			0.561868
$201$	−1.57173e7	+	1.43905e7i	−0.136519	+	0.124994i
$202$	−3.38850e7			−0.289253
$203$		−	2.07553e8i		−	1.74138i
$204$	−9.19855e7	+	8.42207e7i	−0.758602	+	0.694565i
$205$		−	1.58693e7i		−	0.128653i
$206$	7.78130e6			0.0620179
$207$	1.04564e8	+	9.23353e6i	0.819383	+	0.0723555i
$208$			2.22395e7i			0.171357i
$209$	−1.66022e7	+	2.05703e8i	−0.125792	+	1.55858i
$210$	1.84515e7	−	1.68940e7i	0.137488	−	0.125882i
$211$			1.87679e8i			1.37539i	0.725998	+	0.687697i	$0.241378\pi$
$211$			1.87679e8i			1.37539i	−0.725998	+	0.687697i	$0.758622\pi$
$212$			1.99965e8i			1.44138i
$213$	−8.33731e7	−	9.10598e7i	−0.591149	−	0.645651i
$214$	−5.67190e7			−0.395622
$215$	2.89081e7			0.198374
$216$	−5.97129e7	−	7.80154e7i	−0.403162	−	0.526735i
$217$		−	9.09290e7i		−	0.604078i
$218$			2.44308e7i			0.159713i
$219$	7.80850e7	+	8.52841e7i	0.502358	+	0.548673i
$220$	4.34689e6	−	5.38585e7i	0.0275233	−	0.341016i
$221$			5.05012e7i			0.314723i
$222$	−3.83709e7	+	3.51319e7i	−0.235378	+	0.215509i
$223$	1.30741e8			0.789486			0.394743	−	0.918791i	$-0.370834\pi$
$223$	1.30741e8			0.789486			0.394743	+	0.918791i	$0.370834\pi$
$224$		−	2.01655e8i		−	1.19878i
$225$	1.27306e7	−	1.44167e8i	0.0745094	−	0.843774i
$226$			4.89951e7i			0.282341i
$227$	9.28062e7			0.526607			0.263303	−	0.964713i	$-0.415188\pi$
$227$	9.28062e7			0.526607			0.263303	+	0.964713i	$0.415188\pi$
$228$	−1.65319e8	−	1.80561e8i	−0.923744	−	1.00891i
$229$	1.34034e8			0.737548			0.368774	−	0.929519i	$-0.379778\pi$
$229$	1.34034e8			0.737548			0.368774	+	0.929519i	$0.379778\pi$
$230$	2.10013e7			0.113815
$231$	1.54915e8	+	1.99267e8i	0.826899	+	1.06364i
$232$	−1.63070e8			−0.857367
$233$	−2.92681e8			−1.51582			−0.757912	−	0.652357i	$-0.773780\pi$
$233$	−2.92681e8			−1.51582			−0.757912	+	0.652357i	$0.773780\pi$
$234$	−1.84909e7	−	1.63283e6i	−0.0943412	−	0.00833079i
$235$	−1.32107e8			−0.664033
$236$			4.34933e7i			0.215392i
$237$	−1.54854e8	−	1.69131e8i	−0.755619	−	0.825284i
$238$		−	1.16555e8i		−	0.560416i
$239$	1.46957e8			0.696301			0.348150	−	0.937439i	$-0.386810\pi$
$239$	1.46957e8			0.696301			0.348150	+	0.937439i	$0.386810\pi$
$240$	3.62051e7	+	3.95431e7i	0.169056	+	0.184642i
$241$		−	1.89917e8i		−	0.873987i	−0.899465	−	0.436993i	$-0.856043\pi$
$241$		−	1.89917e8i		−	0.873987i	0.899465	−	0.436993i	$-0.143957\pi$
$242$	−7.69939e7	−	1.25098e7i	−0.349223	−	0.0567409i
$243$	−1.88891e8	+	1.19799e8i	−0.844478	+	0.535591i
$244$		−	3.06060e8i		−	1.34878i
$245$		−	7.33747e7i		−	0.318761i
$246$	2.00439e7	−	1.83519e7i	0.0858438	−	0.0785974i
$247$	−9.91303e7			−0.418569
$248$	−7.14409e7			−0.297417
$249$	1.01325e8	−	9.27721e7i	0.415930	−	0.380820i
$250$		−	6.31386e7i		−	0.255567i
$251$			3.24261e6i			0.0129430i	0.999979	+	0.00647152i	$0.00205996\pi$
$251$			3.24261e6i			0.0129430i	−0.999979	+	0.00647152i	$0.997940\pi$
$252$	−2.98252e8	−	2.63371e7i	−1.17404	−	0.103673i
$253$	−1.70455e7	+	2.11196e8i	−0.0661742	+	0.819905i
$254$		−	8.46355e7i		−	0.324067i
$255$	8.22143e7	+	8.97941e7i	0.310496	+	0.339123i
$256$	−8.10939e6			−0.0302098
$257$		−	1.05823e8i		−	0.388877i	−0.980915	−	0.194438i	$-0.937712\pi$
$257$		−	1.05823e8i		−	0.388877i	0.980915	−	0.194438i	$-0.0622884\pi$
$258$	3.34304e7	+	3.65126e7i	0.121192	+	0.132365i
$259$			3.39790e8i			1.21524i
$260$	2.59549e7			0.0915824
$261$	−3.26577e7	+	3.69829e8i	−0.113696	+	1.28753i
$262$	5.10784e7			0.175462
$263$	3.07575e8			1.04257			0.521286	−	0.853382i	$-0.325452\pi$
$263$	3.07575e8			1.04257			0.521286	+	0.853382i	$0.325452\pi$
$264$	1.56560e8	−	1.21714e8i	0.523680	−	0.407123i
$265$	1.95201e8			0.644349
$266$	2.28788e8			0.745330
$267$	−8.96305e7	−	9.78941e7i	−0.288182	−	0.314751i
$268$	5.10261e7			0.161927
$269$			4.26870e7i			0.133709i	0.997763	+	0.0668547i	$0.0212964\pi$
$269$			4.26870e7i			0.133709i	−0.997763	+	0.0668547i	$0.978704\pi$
$270$	−3.55360e7	+	2.71992e7i	−0.109874	+	0.0840976i
$271$			3.52259e8i			1.07515i	0.843216	+	0.537575i	$0.180660\pi$
$271$			3.52259e8i			1.07515i	−0.843216	+	0.537575i	$0.819340\pi$
$272$	2.49786e8			0.752622
$273$	−8.94204e7	+	8.18721e7i	−0.265991	+	0.243538i
$274$			2.20700e8i			0.648150i
$275$	2.91184e8	+	2.35013e7i	0.844312	+	0.0681441i
$276$	−1.69733e8	−	1.85382e8i	−0.485943	−	0.530745i
$277$		−	1.55624e8i		−	0.439944i	−0.975506	−	0.219972i	$-0.929403\pi$
$277$		−	1.55624e8i		−	0.439944i	0.975506	−	0.219972i	$-0.0705966\pi$
$278$			1.62877e8i			0.454676i
$279$	−1.43073e7	+	1.62022e8i	−0.0394406	+	0.446641i
$280$	−1.28377e8			−0.349489
$281$	4.39187e8			1.18080			0.590401	−	0.807110i	$-0.298970\pi$
$281$	4.39187e8			1.18080			0.590401	+	0.807110i	$0.298970\pi$
$282$	−1.52774e8	−	1.66859e8i	−0.405675	−	0.443076i
$283$			1.58759e7i			0.0416375i	0.999783	+	0.0208188i	$0.00662730\pi$
$283$			1.58759e7i			0.0416375i	−0.999783	+	0.0208188i	$0.993373\pi$
$284$			2.95625e8i			0.765820i
$285$	−1.76259e8	+	1.61381e8i	−0.451020	+	0.412947i
$286$	3.01429e6	−	3.73473e7i	0.00761909	−	0.0944014i
$287$		−	1.77497e8i		−	0.443205i
$288$	−3.17296e7	+	3.59319e8i	−0.0782692	+	0.886351i
$289$	1.56873e8			0.382301
$290$			7.42785e7i			0.178842i
$291$	2.07167e8	−	1.89679e8i	0.492828	−	0.451227i
$292$		−	2.76874e8i		−	0.650792i
$293$	−2.57850e8			−0.598866			−0.299433	−	0.954117i	$-0.596798\pi$
$293$	−2.57850e8			−0.598866			−0.299433	+	0.954117i	$0.596798\pi$
$294$	9.26765e7	−	8.48533e7i	0.212693	−	0.194739i
$295$	4.24571e7			0.0962883
$296$	2.66966e8			0.598322
$297$	−2.44682e8	−	3.79438e8i	−0.541944	−	0.840415i
$298$	2.70408e8			0.591918
$299$	−1.01777e8			−0.220192
$300$	−2.55594e8	+	2.34018e8i	−0.546544	+	0.500409i
$301$	3.23334e8			0.683390
$302$			5.44524e7i			0.113761i
$303$	2.91983e8	−	2.67336e8i	0.602989	−	0.552088i
$304$			4.90312e8i			1.00096i
$305$	−2.98769e8			−0.602956
$306$	−1.83394e7	+	2.07683e8i	−0.0365898	+	0.414358i
$307$		−	7.64094e8i		−	1.50717i	−0.657350	−	0.753586i	$-0.728323\pi$
$307$		−	7.64094e8i		−	1.50717i	0.657350	−	0.753586i	$-0.271677\pi$
$308$	4.86196e7	−	6.02402e8i	0.0948165	−	1.17479i
$309$	−6.70506e7	+	6.13906e7i	−0.129285	+	0.118372i
$310$			3.25414e7i			0.0620397i
$311$		−	5.44516e8i		−	1.02648i	−0.858246	−	0.513239i	$-0.828446\pi$
$311$		−	5.44516e8i		−	1.02648i	0.858246	−	0.513239i	$-0.171554\pi$
$312$	6.43252e7	+	7.02557e7i	0.119906	+	0.130961i
$313$	−8.08038e8			−1.48945			−0.744726	−	0.667370i	$-0.767420\pi$
$313$	−8.08038e8			−1.48945			−0.744726	+	0.667370i	$0.767420\pi$
$314$	−1.39437e8			−0.254169
$315$	−2.57097e7	+	2.91147e8i	−0.0463458	+	0.524838i
$316$			5.49082e8i			0.978886i
$317$			5.79791e7i			0.102227i	0.998693	+	0.0511133i	$0.0162770\pi$
$317$			5.79791e7i			0.102227i	−0.998693	+	0.0511133i	$0.983723\pi$
$318$	2.25738e8	+	2.46550e8i	0.393649	+	0.429942i
$319$	−7.46970e8	−	6.02876e7i	−1.28836	−	0.103983i
$320$		−	7.45777e7i		−	0.127228i
$321$	4.88741e8	−	4.47485e8i	0.824729	−	0.755111i
$322$	2.34897e8			0.392087
$323$			1.11340e9i			1.83840i
$324$	5.27297e8	+	9.38576e7i	0.861286	+	0.153307i
$325$			1.40324e8i			0.226746i
$326$	−1.12803e8			−0.180326
$327$	−1.92747e8	−	2.10518e8i	−0.304839	−	0.332944i
$328$	−1.39456e8			−0.218211
$329$	−1.47761e9			−2.28757
$330$	−5.54406e7	−	7.13129e7i	−0.0849238	−	0.109237i
$331$	7.09518e8			1.07539			0.537695	−	0.843140i	$-0.319295\pi$
$331$	7.09518e8			1.07539			0.537695	+	0.843140i	$0.319295\pi$
$332$	−3.28952e8			−0.493343
$333$	5.34647e7	−	6.05455e8i	0.0793436	−	0.898519i
$334$	1.95992e8			0.287823
$335$		−	4.98104e7i		−	0.0723875i
$336$	4.04951e8	+	4.42286e8i	0.582391	+	0.636085i
$337$		−	1.08138e9i		−	1.53912i	−0.638576	−	0.769559i	$-0.720476\pi$
$337$		−	1.08138e9i		−	1.53912i	0.638576	−	0.769559i	$-0.279524\pi$
$338$	−2.33173e8			−0.328450
$339$	−3.86547e8	−	4.22186e8i	−0.538895	−	0.588579i
$340$		−	2.91516e8i		−	0.402241i
$341$	−3.27247e8	−	2.64120e7i	−0.446925	−	0.0360712i
$342$	−4.07666e8	−	3.59990e7i	−0.551079	−	0.0486630i
$343$			1.86190e8i			0.249131i
$344$		−	2.54037e8i		−	0.336467i
$345$	−1.80966e8	+	1.65690e8i	−0.237263	+	0.217234i
$346$	2.86274e8			0.371548
$347$	−1.13536e9			−1.45875			−0.729373	−	0.684116i	$-0.760188\pi$
$347$	−1.13536e9			−1.45875			−0.729373	+	0.684116i	$0.760188\pi$
$348$	6.55670e8	−	6.00323e8i	0.833985	−	0.763585i
$349$		−	4.72265e8i		−	0.594699i	−0.954769	−	0.297349i	$-0.903897\pi$
$349$		−	4.72265e8i		−	0.594699i	0.954769	−	0.297349i	$-0.0961026\pi$
$350$		−	3.23862e8i		−	0.403759i
$351$	1.72216e8	−	1.31814e8i	0.212568	−	0.162699i
$352$	−7.25742e8	−	5.85743e7i	−0.886917	−	0.0715827i
$353$			7.42425e8i			0.898341i	0.893446	+	0.449170i	$0.148280\pi$
$353$			7.42425e8i			0.898341i	−0.893446	+	0.449170i	$0.851720\pi$
$354$	4.90990e7	+	5.36258e7i	0.0588250	+	0.0642484i
$355$	2.88582e8			0.342350
$356$			3.17812e8i			0.373333i
$357$	9.19559e8	+	1.00434e9i	1.06965	+	1.16826i
$358$		−	2.94170e8i		−	0.338851i
$359$	−3.30727e8			−0.377259			−0.188630	−	0.982048i	$-0.560405\pi$
$359$	−3.30727e8			−0.377259			−0.188630	+	0.982048i	$0.560405\pi$
$360$	2.28748e8	+	2.01996e7i	0.258404	+	0.0228183i
$361$	−1.29165e9			−1.44500
$362$	5.94172e8			0.658312
$363$	7.62144e8	−	4.99649e8i	0.836304	−	0.548266i
$364$	2.90303e8			0.315498
$365$	−2.70278e8			−0.290928
$366$	−3.45508e8	−	3.77362e8i	−0.368361	−	0.402323i
$367$	3.33533e8			0.352215			0.176107	−	0.984371i	$-0.443649\pi$
$367$	3.33533e8			0.352215			0.176107	+	0.984371i	$0.443649\pi$
$368$			5.03403e8i			0.526561i
$369$	−2.79284e7	+	3.16273e8i	−0.0289371	+	0.327695i
$370$		−	1.21603e8i		−	0.124807i
$371$	2.18330e9			2.21976
$372$	2.87249e8	−	2.63001e8i	0.289306	−	0.264885i
$373$			1.45218e9i			1.44891i	0.689323	+	0.724454i	$0.257908\pi$
$373$			1.45218e9i			1.44891i	−0.689323	+	0.724454i	$0.742092\pi$
$374$	−4.19472e8	−	3.38554e7i	−0.414622	−	0.0334640i
$375$	4.98133e8	+	5.44059e8i	0.487793	+	0.532766i
$376$			1.16093e9i			1.12628i
$377$		−	3.59971e8i		−	0.345997i
$378$	−3.97467e8	+	3.04221e8i	−0.378512	+	0.289713i
$379$	9.82132e8			0.926686			0.463343	−	0.886179i	$-0.346650\pi$
$379$	9.82132e8			0.926686			0.463343	+	0.886179i	$0.346650\pi$
$380$	5.72225e8			0.534963
$381$	6.67732e8	+	7.29295e8i	0.618536	+	0.675563i
$382$			9.97247e7i			0.0915336i
$383$		−	1.26135e9i		−	1.14720i	−0.819136	−	0.573600i	$-0.805546\pi$
$383$		−	1.26135e9i		−	1.14720i	0.819136	−	0.573600i	$-0.194454\pi$
$384$	8.22385e8	−	7.52964e8i	0.741166	−	0.678602i
$385$	−5.88051e8	−	4.74613e7i	−0.525173	−	0.0423865i
$386$			4.81189e8i			0.425853i
$387$	−5.76133e8	−	5.08753e7i	−0.505282	−	0.0446189i
$388$	−6.72566e8			−0.584553
$389$		−	1.66191e9i		−	1.43148i	−0.698367	−	0.715740i	$-0.746090\pi$
$389$		−	1.66191e9i		−	1.43148i	0.698367	−	0.715740i	$-0.253910\pi$
$390$	3.20015e7	−	2.93001e7i	0.0273177	−	0.0250117i
$391$			1.14312e9i			0.967107i
$392$	−6.44798e8			−0.540658
$393$	−4.40137e8	+	4.02983e8i	−0.365775	+	0.334898i
$394$	1.66014e7			0.0136744
$395$	5.36001e8			0.437598
$396$	−1.81418e8	+	1.06574e9i	−0.146807	+	0.862418i
$397$	7.32753e8			0.587748			0.293874	−	0.955844i	$-0.405055\pi$
$397$	7.32753e8			0.587748			0.293874	+	0.955844i	$0.405055\pi$
$398$	3.69869e8			0.294074
$399$	−1.97145e9	+	1.80503e9i	−1.55374	+	1.42259i
$400$	6.94062e8			0.542236
$401$			1.66878e9i			1.29239i	0.763172	+	0.646195i	$0.223641\pi$
$401$			1.66878e9i			1.29239i	−0.763172	+	0.646195i	$0.776359\pi$
$402$	6.29135e7	−	5.76027e7i	0.0483006	−	0.0442234i
$403$		−	1.57703e8i		−	0.120025i
$404$	−9.47922e8			−0.715217
$405$	9.16216e7	−	5.14735e8i	0.0685339	−	0.385027i
$406$			8.30798e8i			0.616105i
$407$	1.22288e9	+	9.86982e7i	0.899091	+	0.0725653i
$408$	7.89087e8	−	7.22478e8i	0.575194	−	0.526640i
$409$		−	1.45762e9i		−	1.05345i	−0.850036	−	0.526725i	$-0.823420\pi$
$409$		−	1.45762e9i		−	1.05345i	0.850036	−	0.526725i	$-0.176580\pi$
$410$			6.35221e7i			0.0455178i
$411$	−1.74121e9	−	1.90175e9i	−1.23710	−	1.35116i
$412$	2.17679e8			0.153347
$413$	4.74879e8			0.331709
$414$	−4.18551e8	−	3.69601e7i	−0.289900	−	0.0255996i
$415$			3.21115e8i			0.220542i
$416$		−	3.49741e8i		−	0.238188i
$417$	−1.28502e9	−	1.40349e9i	−0.867826	−	0.947836i
$418$	6.64557e7	−	8.23393e8i	0.0445057	−	0.551430i
$419$			1.23610e9i			0.820930i	0.911876	+	0.410465i	$0.134634\pi$
$419$			1.23610e9i			0.820930i	−0.911876	+	0.410465i	$0.865366\pi$
$420$	5.16175e8	−	4.72603e8i	0.339958	−	0.311261i
$421$	8.73974e8			0.570836			0.285418	−	0.958403i	$-0.407868\pi$
$421$	8.73974e8			0.570836			0.285418	+	0.958403i	$0.407868\pi$
$422$		−	7.51245e8i		−	0.486618i
$423$	2.63288e9	+	2.32496e8i	1.69137	+	0.149356i
$424$		−	1.71537e9i		−	1.09289i
$425$	1.57607e9			0.995896
$426$	3.33727e8	+	3.64496e8i	0.209150	+	0.228433i
$427$	−3.34170e9			−2.07716
$428$	−1.58669e9			−0.978227
$429$	2.68678e8	+	3.45599e8i	0.164298	+	0.211335i
$430$	−1.15714e8			−0.0701852
$431$	6.46256e8			0.388807			0.194403	−	0.980922i	$-0.437723\pi$
$431$	6.46256e8			0.388807			0.194403	+	0.980922i	$0.437723\pi$
$432$	−6.51969e8	−	8.51804e8i	−0.389076	−	0.508331i
$433$	2.12078e9			1.25542			0.627709	−	0.778448i	$-0.283993\pi$
$433$	2.12078e9			1.25542			0.627709	+	0.778448i	$0.283993\pi$
$434$			3.63972e8i			0.213724i
$435$	−5.86021e8	−	6.40050e8i	−0.341351	−	0.372822i
$436$			6.83444e8i			0.394912i
$437$	−2.24387e9			−1.28621
$438$	−3.12560e8	−	3.41377e8i	−0.177735	−	0.194122i
$439$		−	6.05775e8i		−	0.341732i	−0.985294	−	0.170866i	$-0.945343\pi$
$439$		−	6.05775e8i		−	0.341732i	0.985294	−	0.170866i	$-0.0546565\pi$
$440$	−3.72893e7	+	4.62019e8i	−0.0208689	+	0.258568i
$441$	−1.29132e8	+	1.46234e9i	−0.0716967	+	0.811922i
$442$		−	2.02147e8i		−	0.111350i
$443$			9.79877e8i			0.535499i	0.963489	+	0.267750i	$0.0862800\pi$
$443$			9.79877e8i			0.535499i	−0.963489	+	0.267750i	$0.913720\pi$
$444$	−1.07341e9	+	9.82802e8i	−0.582005	+	0.532875i
$445$	3.10241e8			0.166893
$446$	−5.23332e8			−0.279322
$447$	−2.33007e9	+	2.13338e9i	−1.23394	+	1.12978i
$448$		−	8.34144e8i		−	0.438297i
$449$		−	3.50760e9i		−	1.82872i	−0.404898	−	0.914362i	$-0.632693\pi$
$449$		−	3.50760e9i		−	1.82872i	0.404898	−	0.914362i	$-0.367307\pi$
$450$	−5.09584e7	+	5.77073e8i	−0.0263616	+	0.298529i
$451$	−6.38799e8	−	5.15572e7i	−0.327904	−	0.0264650i
$452$			1.37062e9i			0.698125i
$453$	−4.29603e8	−	4.69211e8i	−0.217132	−	0.237151i
$454$	−3.71486e8			−0.186315
$455$		−	2.83387e8i		−	0.141039i
$456$	1.41817e9	+	1.54892e9i	0.700410	+	0.764985i
$457$		−	7.32171e8i		−	0.358844i	−0.983772	−	0.179422i	$-0.942577\pi$
$457$		−	7.32171e8i		−	0.358844i	0.983772	−	0.179422i	$-0.0574227\pi$
$458$	−5.36513e8			−0.260946
$459$	−1.48049e9	−	1.93427e9i	−0.714595	−	0.933625i
$460$	5.87504e8			0.281422
$461$	4.05721e9			1.92874			0.964372	−	0.264549i	$-0.0852232\pi$
$461$	4.05721e9			1.92874			0.964372	+	0.264549i	$0.0852232\pi$
$462$	−6.20098e8	−	7.97628e8i	−0.292559	−	0.376317i
$463$	3.64737e8			0.170784			0.0853918	−	0.996347i	$-0.472786\pi$
$463$	3.64737e8			0.170784			0.0853918	+	0.996347i	$0.472786\pi$
$464$	−1.78047e9			−0.827410
$465$	−2.56735e8	−	2.80405e8i	−0.118413	−	0.129331i
$466$	1.17155e9			0.536302
$467$			1.25335e9i			0.569459i	0.958608	+	0.284729i	$0.0919038\pi$
$467$			1.25335e9i			0.569459i	−0.958608	+	0.284729i	$0.908096\pi$
$468$	−5.17275e8	−	4.56780e7i	−0.233271	−	0.0205990i
$469$		−	5.57125e8i		−	0.249372i
$470$	5.28802e8			0.234937
$471$	1.20151e9	−	1.10009e9i	0.529852	−	0.485125i
$472$		−	3.73102e8i		−	0.163317i
$473$	9.39182e7	−	1.16366e9i	0.0408071	−	0.505604i
$474$	6.19852e8	+	6.77000e8i	0.267340	+	0.291988i
$475$			3.09371e9i			1.32450i
$476$		−	3.26058e9i		−	1.38570i
$477$	−3.89031e9	−	3.43534e8i	−1.64123	−	0.144929i
$478$	−5.88241e8			−0.246353
$479$	2.70060e9			1.12276			0.561378	−	0.827560i	$-0.310271\pi$
$479$	2.70060e9			1.12276			0.561378	+	0.827560i	$0.310271\pi$
$480$	−5.69367e8	−	6.21861e8i	−0.234989	−	0.256654i
$481$			5.89317e8i			0.241458i
$482$			7.60204e8i			0.309219i
$483$	−2.02408e9	+	1.85322e9i	−0.817360	+	0.748364i
$484$	−2.15388e9	−	3.49957e8i	−0.863500	−	0.140299i
$485$			6.56544e8i			0.261317i
$486$	7.56094e8	−	4.79535e8i	0.298778	−	0.189493i
$487$	2.03283e9			0.797536			0.398768	−	0.917052i	$-0.369438\pi$
$487$	2.03283e9			0.797536			0.398768	+	0.917052i	$0.369438\pi$
$488$			2.62550e9i			1.02269i
$489$	9.72009e8	−	8.89958e8i	0.375915	−	0.344182i
$490$			2.93706e8i			0.112778i
$491$	2.00888e9			0.765893			0.382947	−	0.923770i	$-0.374909\pi$
$491$	2.00888e9			0.765893			0.382947	+	0.923770i	$0.374909\pi$
$492$	5.60721e8	−	5.13388e8i	0.212260	−	0.194343i
$493$	−4.04307e9			−1.51966
$494$	3.96800e8			0.148091
$495$	1.04035e9	+	1.77096e8i	0.385533	+	0.0656283i
$496$	−7.80021e8			−0.287025
$497$	3.22776e9			1.17938
$498$	−4.05587e8	+	3.71350e8i	−0.147157	+	0.134735i
$499$	3.55159e9			1.27959			0.639796	−	0.768545i	$-0.279019\pi$
$499$	3.55159e9			1.27959			0.639796	+	0.768545i	$0.279019\pi$
$500$		−	1.76628e9i		−	0.631924i
$501$	−1.68884e9	+	1.54628e9i	−0.600008	+	0.549359i
$502$		−	1.29796e7i		−	0.00457928i
$503$	1.14279e9			0.400386			0.200193	−	0.979757i	$-0.435843\pi$
$503$	1.14279e9			0.400386			0.200193	+	0.979757i	$0.435843\pi$
$504$	2.55852e9	+	2.25930e8i	0.890190	+	0.0786081i
$505$			9.25339e8i			0.319728i
$506$	6.82301e7	−	8.45378e8i	0.0234126	−	0.290084i
$507$	2.00923e9	−	1.83962e9i	0.684701	−	0.626903i
$508$		−	2.36765e9i		−	0.801299i
$509$			3.34778e9i			1.12524i	0.826716	+	0.562619i	$0.190206\pi$
$509$			3.34778e9i			1.12524i	−0.826716	+	0.562619i	$0.809794\pi$
$510$	−3.29089e8	−	3.59429e8i	−0.109854	−	0.119983i
$511$	−3.02303e9			−1.00224
$512$	−3.01943e9			−0.994214
$513$	3.79683e9	−	2.90609e9i	1.24168	−	0.950382i
$514$			4.23588e8i			0.137586i
$515$		−	2.12493e8i		−	0.0685520i
$516$	9.35205e8	+	1.02143e9i	0.299663	+	0.327290i
$517$	−4.29198e8	+	5.31781e9i	−0.136597	+	1.69245i
$518$		−	1.36012e9i		−	0.429955i
$519$	−2.46679e9	+	2.25856e9i	−0.774545	+	0.709162i
$520$	−2.22651e8			−0.0694405
$521$			9.86635e8i			0.305650i	0.988253	+	0.152825i	$0.0488371\pi$
$521$			9.86635e8i			0.305650i	−0.988253	+	0.152825i	$0.951163\pi$
$522$	1.30723e8	−	1.48036e9i	0.0402258	−	0.455533i
$523$			4.45077e8i			0.136044i	0.997684	+	0.0680220i	$0.0216688\pi$
$523$			4.45077e8i			0.136044i	−0.997684	+	0.0680220i	$0.978331\pi$
$524$	1.42890e9			0.433853
$525$	2.55511e9	+	2.79068e9i	0.770641	+	0.841692i
$526$	−1.23117e9			−0.368865
$527$	−1.77126e9			−0.527165
$528$	1.70938e9	−	1.32892e9i	0.505382	−	0.392898i
$529$	1.10104e9			0.323377
$530$	−7.81353e8			−0.227972
$531$	−8.46162e8	−	7.47203e7i	−0.245258	−	0.0216575i
$532$	6.40028e9			1.84293
$533$		−	3.07843e8i		−	0.0880610i
$534$	3.58775e8	+	3.91852e8i	0.101959	+	0.111360i
$535$			1.54889e9i			0.437304i
$536$	−4.37721e8			−0.122778
$537$	2.32086e9	+	2.53483e9i	0.646754	+	0.706382i
$538$		−	1.70868e8i		−	0.0473067i
$539$	−2.95360e9	−	2.38384e8i	−0.812440	−	0.0655717i
$540$	−9.94109e8	+	7.60889e8i	−0.271679	+	0.207942i
$541$		−	1.92806e9i		−	0.523515i	−0.965134	−	0.261757i	$-0.915698\pi$
$541$		−	1.92806e9i		−	0.523515i	0.965134	−	0.261757i	$-0.0843021\pi$
$542$		−	1.41003e9i		−	0.380391i
$543$	−5.11991e9	+	4.68772e9i	−1.37234	+	1.25650i
$544$	−3.92817e9			−1.04615
$545$	6.67162e8			0.176540
$546$	3.57934e8	−	3.27719e8i	0.0941084	−	0.0861644i
$547$		−	4.64059e9i		−	1.21232i	−0.795342	−	0.606161i	$-0.792709\pi$
$547$		−	4.64059e9i		−	1.21232i	0.795342	−	0.606161i	$-0.207291\pi$
$548$			6.17401e9i			1.60264i
$549$	5.95440e9	+	5.25803e8i	1.53580	+	0.135619i
$550$	−1.16556e9	−	9.40716e7i	−0.298720	−	0.0241095i
$551$		−	7.93626e9i		−	2.02109i
$552$	1.45604e9	+	1.59028e9i	0.368456	+	0.402427i
$553$	5.99511e9			1.50751
$554$			6.22935e8i			0.155653i
$555$	9.59389e8	+	1.04784e9i	0.238215	+	0.260178i
$556$			4.55642e9i			1.12425i
$557$	−5.07922e9			−1.24538			−0.622692	−	0.782467i	$-0.713961\pi$
$557$	−5.07922e9			−1.24538			−0.622692	+	0.782467i	$0.713961\pi$
$558$	5.72695e7	−	6.48543e8i	0.0139542	−	0.158023i
$559$	5.60776e8			0.135784
$560$	−1.40167e9			−0.337278
$561$	3.88165e9	−	3.01770e9i	0.928209	−	0.721615i
$562$	−1.75798e9			−0.417770
$563$	−6.69589e9			−1.58135			−0.790677	−	0.612233i	$-0.790271\pi$
$563$	−6.69589e9			−1.58135			−0.790677	+	0.612233i	$0.790271\pi$
$564$	−4.27380e9	−	4.66783e9i	−1.00308	−	1.09557i
$565$	1.33797e9			0.312088
$566$		−	6.35482e7i		−	0.0147315i
$567$	1.02478e9	−	5.75726e9i	0.236097	−	1.32640i
$568$		−	2.53598e9i		−	0.580667i
$569$	−2.78085e9			−0.632826			−0.316413	−	0.948621i	$-0.602479\pi$
$569$	−2.78085e9			−0.632826			−0.316413	+	0.948621i	$0.602479\pi$
$570$	7.05535e8	−	6.45978e8i	0.159572	−	0.146102i
$571$		−	5.94969e9i		−	1.33742i	−0.743523	−	0.668711i	$-0.766847\pi$
$571$		−	5.94969e9i		−	1.33742i	0.743523	−	0.668711i	$-0.233153\pi$
$572$	8.43236e7	−	1.04478e9i	0.0188392	−	0.233420i
$573$	−7.86778e8	−	8.59316e8i	−0.174707	−	0.190815i
$574$			7.10488e8i			0.156807i
$575$			3.17632e9i			0.696765i
$576$	−1.31249e8	+	1.48632e9i	−0.0286166	+	0.324066i
$577$	−6.95086e9			−1.50634			−0.753170	−	0.657826i	$-0.771476\pi$
$577$	−6.95086e9			−1.50634			−0.753170	+	0.657826i	$0.771476\pi$
$578$	−6.27933e8			−0.135259
$579$	−3.79634e9	−	4.14635e9i	−0.812813	−	0.887751i
$580$			2.07792e9i			0.442212i
$581$			3.59164e9i			0.759760i
$582$	−8.29252e8	+	7.59252e8i	−0.174364	+	0.159645i
$583$	6.34179e8	−	7.85755e9i	0.132548	−	1.64228i
$584$			2.37513e9i			0.493450i
$585$	−4.45898e7	+	5.04952e8i	−0.00920851	+	0.104281i
$586$	1.03212e9			0.211880
$587$		−	1.12550e9i		−	0.229675i	−0.993384	−	0.114837i	$-0.963365\pi$
$587$		−	1.12550e9i		−	0.229675i	0.993384	−	0.114837i	$-0.0366347\pi$
$588$	2.59259e9	−	2.37374e9i	0.525913	−	0.481519i
$589$		−	3.47687e9i		−	0.701107i
$590$	−1.69948e8			−0.0340670
$591$	−1.43052e8	+	1.30977e8i	−0.0285061	+	0.0260998i
$592$	2.91484e9			0.577416
$593$	−8.07737e9			−1.59066			−0.795332	−	0.606174i	$-0.792704\pi$
$593$	−8.07737e9			−1.59066			−0.795332	+	0.606174i	$0.792704\pi$
$594$	9.79417e8	+	1.51882e9i	0.191741	+	0.297341i
$595$	−3.18290e9			−0.619460
$596$	7.56456e9			1.46360
$597$	−3.18712e9	+	2.91808e9i	−0.613039	+	0.561290i
$598$	4.07395e8			0.0779043
$599$		−	9.80067e8i		−	0.186321i	−0.995651	−	0.0931605i	$-0.970303\pi$
$599$		−	9.80067e8i		−	0.186321i	0.995651	−	0.0931605i	$-0.0296970\pi$
$600$	2.19258e9	−	2.00750e9i	0.414406	−	0.379425i
$601$			9.63989e9i			1.81139i	0.423933	+	0.905694i	$0.360649\pi$
$601$			9.63989e9i			1.81139i	−0.423933	+	0.905694i	$0.639351\pi$
$602$	−1.29425e9			−0.241785
$603$	−8.76614e7	+	9.92712e8i	−0.0162816	+	0.184380i
$604$			1.52329e9i			0.281289i
$605$	−3.41620e8	+	2.10257e9i	−0.0627190	+	0.386017i
$606$	−1.16876e9	+	1.07010e9i	−0.213339	+	0.195330i
$607$		−	6.05495e9i		−	1.09888i	−0.835533	−	0.549440i	$-0.814841\pi$
$607$		−	6.05495e9i		−	1.09888i	0.835533	−	0.549440i	$-0.185159\pi$
$608$		−	7.71072e9i		−	1.39134i
$609$	−6.55459e9	−	7.15890e9i	−1.17594	−	1.28436i
$610$	1.19592e9			0.213327
$611$	−2.56270e9			−0.454520
$612$	−5.13039e8	+	5.80985e9i	−0.0904732	+	1.02455i
$613$			5.58146e9i			0.978670i	0.872096	+	0.489335i	$0.162760\pi$
$613$			5.58146e9i			0.978670i	−0.872096	+	0.489335i	$0.837240\pi$
$614$			3.05853e9i			0.533241i
$615$	−5.01158e8	−	5.47363e8i	−0.0868784	−	0.0948882i
$616$	−4.17078e8	+	5.16764e9i	−0.0718927	+	0.890757i
$617$			5.45812e7i			0.00935502i	0.999989	+	0.00467751i	$0.00148890\pi$
$617$			5.45812e7i			0.00935502i	−0.999989	+	0.00467751i	$0.998511\pi$
$618$	2.68391e8	−	2.45735e8i	0.0457413	−	0.0418801i
$619$	7.68114e9			1.30169			0.650846	−	0.759209i	$-0.274414\pi$
$619$	7.68114e9			1.30169			0.650846	+	0.759209i	$0.274414\pi$
$620$			9.10334e8i			0.153402i
$621$	3.89821e9	−	2.98368e9i	0.653197	−	0.499956i
$622$			2.17960e9i			0.363170i
$623$	3.47002e9			0.574941
$624$	7.02328e8	+	7.67080e8i	0.115716	+	0.126385i
$625$	3.44583e9			0.564564
$626$	3.23443e9			0.526972
$627$	5.92353e9	+	7.61939e9i	0.959719	+	1.23448i
$628$	−3.90069e9			−0.628468
$629$	6.61900e9			1.06051
$630$	1.02911e8	−	1.16541e9i	0.0163973	−	0.185689i
$631$	4.50974e8			0.0714577			0.0357288	−	0.999362i	$-0.488625\pi$
$631$	4.50974e8			0.0714577			0.0357288	+	0.999362i	$0.488625\pi$
$632$		−	4.71023e9i		−	0.742220i
$633$	5.92695e9	+	6.47340e9i	0.928792	+	1.01442i
$634$		−	2.32080e8i		−	0.0361680i
$635$	−2.31124e9			−0.358210
$636$	6.31493e9	+	6.89715e9i	0.973350	+	1.06309i
$637$		−	1.42337e9i		−	0.218187i
$638$	2.98998e9	+	2.41320e8i	0.455823	+	0.0367893i
$639$	−5.75138e9	−	5.07875e8i	−0.872006	−	0.0770024i
$640$			2.60626e9i			0.392996i
$641$			7.36976e9i			1.10522i	0.833439	+	0.552612i	$0.186369\pi$
$641$			7.36976e9i			1.10522i	−0.833439	+	0.552612i	$0.813631\pi$
$642$	−1.95634e9	+	1.79120e9i	−0.291791	+	0.267160i
$643$	−1.07829e10			−1.59955			−0.799776	−	0.600299i	$-0.795048\pi$
$643$	−1.07829e10			−1.59955			−0.799776	+	0.600299i	$0.795048\pi$
$644$	6.57117e9			0.969487
$645$	9.97093e8	−	9.12925e8i	0.146311	−	0.133960i
$646$		−	4.45672e9i		−	0.650432i
$647$		−	1.43976e9i		−	0.208990i	−0.994525	−	0.104495i	$-0.966677\pi$
$647$		−	1.43976e9i		−	0.208990i	0.994525	−	0.104495i	$-0.0333227\pi$
$648$	−4.52335e9	−	8.05147e8i	−0.653053	−	0.116242i
$649$	1.37937e8	−	1.70905e9i	0.0198073	−	0.245414i
$650$		−	5.61692e8i		−	0.0802234i
$651$	−2.87156e9	−	3.13631e9i	−0.407929	−	0.445538i
$652$	−3.15562e9			−0.445880
$653$		−	8.56975e9i		−	1.20440i	−0.798344	−	0.602202i	$-0.794290\pi$
$653$		−	8.56975e9i		−	1.20440i	0.798344	−	0.602202i	$-0.205710\pi$
$654$	7.71532e8	+	8.42664e8i	0.107853	+	0.117797i
$655$		−	1.39486e9i		−	0.193948i
$656$	−1.52263e9			−0.210587
$657$	5.38659e9	+	4.75662e8i	0.741029	+	0.0654365i
$658$	5.91460e9			0.809347
$659$	2.28295e9			0.310741			0.155370	−	0.987856i	$-0.450343\pi$
$659$	2.28295e9			0.310741			0.155370	+	0.987856i	$0.450343\pi$
$660$	−1.55093e9	−	1.99495e9i	−0.209985	−	0.270103i
$661$	1.94943e9			0.262544			0.131272	−	0.991346i	$-0.458094\pi$
$661$	1.94943e9			0.262544			0.131272	+	0.991346i	$0.458094\pi$
$662$	−2.84007e9			−0.380475
$663$	1.59484e9	+	1.74188e9i	0.212530	+	0.232124i
$664$	2.82187e9			0.374067
$665$		−	6.24780e9i		−	0.823857i
$666$	−2.14009e8	+	2.42353e9i	−0.0280720	+	0.317898i
$667$		−	8.14816e9i		−	1.06321i
$668$	5.48281e9			0.711682
$669$	4.50950e9	−	4.12883e9i	0.582286	−	0.533133i
$670$			1.99382e8i			0.0256109i
$671$	−9.70656e8	+	1.20265e10i	−0.124033	+	1.53678i
$672$	−6.36831e9	−	6.95545e9i	−0.809528	−	0.884164i
$673$			1.53034e10i			1.93524i	0.252408	+	0.967621i	$0.418777\pi$
$673$			1.53034e10i			1.93524i	−0.252408	+	0.967621i	$0.581223\pi$
$674$			4.32855e9i			0.544543i
$675$	−4.11372e9	−	5.37461e9i	−0.514839	−	0.672642i
$676$	−6.52293e9			−0.812137
$677$	−4.84766e9			−0.600443			−0.300221	−	0.953870i	$-0.597061\pi$
$677$	−4.84766e9			−0.600443			−0.300221	+	0.953870i	$0.597061\pi$
$678$	1.54728e9	+	1.68993e9i	0.190662	+	0.208241i
$679$			7.34338e9i			0.900226i
$680$			2.50074e9i			0.304991i
$681$	3.20106e9	−	2.93084e9i	0.388399	−	0.355613i
$682$	1.30991e9	+	1.05722e8i	0.158123	+	0.0127621i
$683$		−	4.86318e9i		−	0.584047i	−0.956411	−	0.292023i	$-0.905672\pi$
$683$		−	4.86318e9i		−	0.584047i	0.956411	−	0.292023i	$-0.0943285\pi$
$684$	−1.14043e10	−	1.00706e9i	−1.36262	−	0.120326i
$685$	6.02692e9			0.716438
$686$		−	7.45286e8i		−	0.0881432i
$687$	4.62308e9	−	4.23283e9i	0.543979	−	0.498060i
$688$		−	2.77368e9i		−	0.324710i
$689$	3.78662e9			0.441046
$690$	7.24373e8	−	6.63226e8i	0.0839441	−	0.0768581i
$691$	−1.02045e10			−1.17657			−0.588285	−	0.808653i	$-0.700197\pi$
$691$	−1.02045e10			−1.17657			−0.588285	+	0.808653i	$0.700197\pi$
$692$	8.00841e9			0.918703
$693$	1.16362e10	+	1.98081e9i	1.32814	+	0.226087i
$694$	4.54463e9			0.516108
$695$	4.44787e9			0.502580
$696$	−5.62459e9	+	5.14980e9i	−0.632352	+	0.578973i
$697$	−3.45758e9			−0.386774
$698$			1.89039e9i			0.210406i
$699$	−1.00951e10	+	9.24294e9i	−1.11800	+	1.02362i
$700$		−	9.05993e9i		−	0.998347i
$701$	6.22431e9			0.682461			0.341231	−	0.939980i	$-0.389156\pi$
$701$	6.22431e9			0.682461			0.341231	+	0.939980i	$0.389156\pi$
$702$	−6.89349e8	+	5.27627e8i	−0.0752072	+	0.0575635i
$703$			1.29926e10i			1.41044i
$704$	−3.00203e9	−	2.42292e8i	−0.324273	−	0.0261719i
$705$	−4.55663e9	+	4.17199e9i	−0.489758	+	0.448416i
$706$		−	2.97179e9i		−	0.317835i
$707$			1.03498e10i			1.10145i
$708$	1.37353e9	+	1.50016e9i	0.145453	+	0.158863i
$709$	−1.48018e10			−1.55975			−0.779873	−	0.625938i	$-0.784716\pi$
$709$	−1.48018e10			−1.55975			−0.779873	+	0.625938i	$0.784716\pi$
$710$	−1.15514e9			−0.121124
$711$	−1.06824e10	−	9.43307e8i	−1.11461	−	0.0984260i
$712$		−	2.72632e9i		−	0.283072i
$713$		−	3.56970e9i		−	0.368823i
$714$	−3.68083e9	−	4.02018e9i	−0.378444	−	0.413335i
$715$	−1.01989e9	−	8.23148e7i	−0.104347	−	0.00842183i
$716$		−	8.22932e9i		−	0.837854i
$717$	5.06881e9	−	4.64093e9i	0.513557	−	0.470206i
$718$	1.32384e9			0.133475
$719$		−	8.33648e9i		−	0.836434i	−0.908347	−	0.418217i	$-0.862655\pi$
$719$		−	8.33648e9i		−	0.836434i	0.908347	−	0.418217i	$-0.137345\pi$
$720$	2.49756e9	+	2.20547e8i	0.249375	+	0.0220210i
$721$		−	2.37672e9i		−	0.236159i
$722$	5.17022e9			0.511245
$723$	−5.99764e9	−	6.55060e9i	−0.590196	−	0.644610i
$724$	1.66218e10			1.62777
$725$	−1.12342e10			−1.09486
$726$	−3.05072e9	+	2.00000e9i	−0.295886	+	0.193978i
$727$	9.61452e9			0.928019			0.464010	−	0.885830i	$-0.346410\pi$
$727$	9.61452e9			0.928019			0.464010	+	0.885830i	$0.346410\pi$
$728$	−2.49033e9			−0.239220
$729$	−2.73188e9	+	1.00973e10i	−0.261165	+	0.965294i
$730$	1.08187e9			0.102931
$731$		−	6.29844e9i		−	0.596379i
$732$	−9.66545e9	−	1.05566e10i	−0.910822	−	0.994796i
$733$		−	1.12849e10i		−	1.05836i	−0.848510	−	0.529179i	$-0.822500\pi$
$733$		−	1.12849e10i		−	1.05836i	0.848510	−	0.529179i	$-0.177500\pi$
$734$	−1.33507e9			−0.124614
$735$	−2.31719e9	−	2.53083e9i	−0.215257	−	0.235102i
$736$		−	7.91660e9i		−	0.731924i
$737$	−2.00505e9	−	1.61827e8i	−0.184497	−	0.0148907i
$738$	1.11792e8	−	1.26598e9i	0.0102380	−	0.115939i
$739$		−	1.23014e10i		−	1.12124i	−0.828072	−	0.560622i	$-0.810562\pi$
$739$		−	1.23014e10i		−	1.12124i	0.828072	−	0.560622i	$-0.189438\pi$
$740$		−	3.40181e9i		−	0.308602i
$741$	−3.41919e9	+	3.13056e9i	−0.308716	+	0.282656i
$742$	−8.73936e9			−0.785355
$743$	9.76414e9			0.873320			0.436660	−	0.899627i	$-0.356161\pi$
$743$	9.76414e9			0.873320			0.436660	+	0.899627i	$0.356161\pi$
$744$	−2.46413e9	+	2.25612e9i	−0.219360	+	0.200843i
$745$		−	7.38435e9i		−	0.654282i
$746$		−	5.81283e9i		−	0.512627i
$747$	5.65130e8	−	6.39976e9i	0.0496051	−	0.561748i
$748$	−1.17346e10	−	9.47093e8i	−1.02521	−	0.0827441i
$749$			1.73242e10i			1.50649i
$750$	−1.99394e9	−	2.17777e9i	−0.172582	−	0.188494i
$751$	1.89683e10			1.63413			0.817067	−	0.576543i	$-0.195599\pi$
$751$	1.89683e10			1.63413			0.817067	+	0.576543i	$0.195599\pi$
$752$			1.26755e10i			1.08693i
$753$	1.02402e8	+	1.11844e8i	0.00874033	+	0.00954616i
$754$			1.44090e9i			0.122415i
$755$	1.48700e9			0.125747
$756$	−1.11190e10	+	8.51047e9i	−0.935922	+	0.716353i
$757$	1.64301e9			0.137659			0.0688293	−	0.997628i	$-0.478074\pi$
$757$	1.64301e9			0.137659			0.0688293	+	0.997628i	$0.478074\pi$
$758$	−3.93129e9			−0.327864
$759$	6.08169e9	+	7.82284e9i	0.504868	+	0.649409i
$760$	−4.90877e9			−0.405625
$761$	−6.00825e9			−0.494199			−0.247099	−	0.968990i	$-0.579477\pi$
$761$	−6.00825e9			−0.494199			−0.247099	+	0.968990i	$0.579477\pi$
$762$	−2.67281e9	−	2.91923e9i	−0.218840	−	0.239016i
$763$	7.46215e9			0.608174
$764$			2.78976e9i			0.226329i
$765$	5.67144e9	+	5.00816e8i	0.458014	+	0.0404449i
$766$			5.04895e9i			0.405882i
$767$	8.23608e8			0.0659078
$768$	−2.79708e8	+	2.56097e8i	−0.0222813	+	0.0204004i
$769$			1.45317e10i			1.15232i	0.817336	+	0.576161i	$0.195450\pi$
$769$			1.45317e10i			1.15232i	−0.817336	+	0.576161i	$0.804550\pi$
$770$	2.35386e9	+	1.89979e8i	0.185807	+	0.0149964i
$771$	−3.34190e9	−	3.65001e9i	−0.262605	−	0.286816i
$772$			1.34611e10i			1.05298i
$773$		−	3.26721e9i		−	0.254418i	−0.991876	−	0.127209i	$-0.959398\pi$
$773$		−	3.26721e9i		−	0.254418i	0.991876	−	0.127209i	$-0.0406019\pi$
$774$	2.30615e9	+	2.03645e8i	0.178770	+	0.0157863i
$775$	−4.92169e9			−0.379803
$776$	5.76953e9			0.443226
$777$	1.07307e10	+	1.17200e10i	0.820641	+	0.896301i
$778$			6.65234e9i			0.506461i
$779$		−	6.78699e9i		−	0.514394i
$780$	8.95231e8	−	8.19661e8i	0.0675467	−	0.0618448i
$781$	9.37561e8	−	1.16165e10i	0.0704241	−	0.872561i
$782$		−	4.57572e9i		−	0.342165i
$783$	1.05529e10	+	1.37874e10i	0.785605	+	1.02640i
$784$	−7.04016e9			−0.521767
$785$			3.80777e9i			0.280948i
$786$	1.76179e9	−	1.61307e9i	0.129412	−	0.118488i
$787$			5.72577e9i			0.418719i	0.977839	+	0.209359i	$0.0671378\pi$
$787$			5.72577e9i			0.418719i	−0.977839	+	0.209359i	$0.932862\pi$
$788$	4.64417e8			0.0338117
$789$	1.06088e10	−	9.71331e9i	0.768951	−	0.704041i
$790$	−2.14551e9			−0.154823
$791$	1.49651e10			1.07513
$792$	1.55628e9	−	9.14232e9i	0.111314	−	0.653911i
$793$	−5.79569e9			−0.412714
$794$	−2.93308e9			−0.207947
$795$	6.73283e9	−	6.16449e9i	0.475240	−	0.435123i
$796$	1.03469e10			0.727137
$797$		−	2.15696e10i		−	1.50917i	−0.656202	−	0.754585i	$-0.727838\pi$
$797$		−	2.15696e10i		−	1.50917i	0.656202	−	0.754585i	$-0.272162\pi$
$798$	7.89134e9	−	7.22520e9i	0.549719	−	0.503315i
$799$			2.87833e10i			1.99631i
$800$	−1.09149e10			−0.753712
$801$	−6.18304e9	−	5.45993e8i	−0.425097	−	0.0375382i
$802$		−	6.67982e9i		−	0.457251i
$803$	−8.78095e8	+	1.08797e10i	−0.0598462	+	0.741501i
$804$	1.75998e9	−	1.61142e9i	0.119430	−	0.109348i
$805$		−	6.41462e9i		−	0.433397i
$806$			6.31257e8i			0.0424652i
$807$	1.34807e9	+	1.47235e9i	0.0902929	+	0.0986175i
$808$	8.13164e9			0.542298
$809$	−5.11270e9			−0.339492			−0.169746	−	0.985488i	$-0.554295\pi$
$809$	−5.11270e9			−0.339492			−0.169746	+	0.985488i	$0.554295\pi$
$810$	−3.66745e8	+	2.06039e9i	−0.0242475	+	0.136223i
$811$			5.16615e9i			0.340090i	0.985436	+	0.170045i	$0.0543914\pi$
$811$			5.16615e9i			0.340090i	−0.985436	+	0.170045i	$0.945609\pi$
$812$			2.32413e10i			1.52340i
$813$	1.11244e10	+	1.21501e10i	0.726040	+	0.792978i
$814$	−4.89497e9	−	3.95071e8i	−0.318101	−	0.0256738i
$815$			3.08044e9i			0.199325i
$816$	8.61557e9	−	7.88830e9i	0.555097	−	0.508239i
$817$	1.23634e10			0.793159
$818$			5.83460e9i			0.372713i
$819$	−4.98732e8	+	5.64784e9i	−0.0317230	+	0.359243i
$820$			1.77701e9i			0.112549i
$821$	−3.03208e10			−1.91222			−0.956112	−	0.293000i	$-0.905346\pi$
$821$	−3.03208e10			−1.91222			−0.956112	+	0.293000i	$0.905346\pi$
$822$	6.96976e9	+	7.61235e9i	0.437690	+	0.478043i
$823$	−2.47410e10			−1.54710			−0.773549	−	0.633737i	$-0.781520\pi$
$823$	−2.47410e10			−1.54710			−0.773549	+	0.633737i	$0.781520\pi$
$824$	−1.86734e9			−0.116273
$825$	1.07856e10	−	8.38506e9i	0.668740	−	0.519897i
$826$	−1.90085e9			−0.117360
$827$	1.43389e10			0.881549			0.440775	−	0.897618i	$-0.354704\pi$
$827$	1.43389e10			0.881549			0.440775	+	0.897618i	$0.354704\pi$
$828$	−1.17088e10	−	1.03395e9i	−0.716815	−	0.0632983i
$829$	−1.90275e9			−0.115996			−0.0579978	−	0.998317i	$-0.518472\pi$
$829$	−1.90275e9			−0.115996			−0.0579978	+	0.998317i	$0.518472\pi$
$830$		−	1.28536e9i		−	0.0780284i
$831$	−4.91465e9	−	5.36776e9i	−0.297091	−	0.324481i
$832$		−	1.44670e9i		−	0.0870858i
$833$	−1.59867e10			−0.958302
$834$	5.14369e9	+	5.61792e9i	0.307039	+	0.335347i
$835$		−	5.35219e9i		−	0.318148i
$836$	1.85908e9	−	2.30341e10i	0.110046	−	1.36348i
$837$	4.62320e9	+	6.04025e9i	0.272523	+	0.356054i
$838$		−	4.94790e9i		−	0.290447i
$839$		−	2.04432e10i		−	1.19504i	−0.801854	−	0.597520i	$-0.796153\pi$
$839$		−	2.04432e10i		−	1.19504i	0.801854	−	0.597520i	$-0.203847\pi$
$840$	−4.42795e9	+	4.05417e9i	−0.257766	+	0.236007i
$841$	1.15690e10			0.670671
$842$	−3.49836e9			−0.201963
$843$	1.51484e10	−	1.38696e10i	0.870901	−	0.797385i
$844$		−	2.10158e10i		−	1.20323i
$845$			6.36753e9i			0.363055i
$846$	−1.05389e10	−	9.30639e8i	−0.598411	−	0.0528427i
$847$	−3.82098e9	+	2.35170e10i	−0.216064	+	1.32981i
$848$		−	1.87291e10i		−	1.05471i
$849$	5.01364e8	+	5.47588e8i	0.0281175	+	0.0307098i
$850$	−6.30872e9			−0.352351
$851$			1.33395e10i			0.741972i
$852$	9.33591e9	+	1.01966e10i	0.517152	+	0.564831i
$853$		−	1.42872e10i		−	0.788182i	−0.919071	−	0.394091i	$-0.871059\pi$
$853$		−	1.42872e10i		−	0.788182i	0.919071	−	0.394091i	$-0.128941\pi$
$854$	1.33762e10			0.734904
$855$	−9.83067e8	+	1.11326e10i	−0.0537900	+	0.609140i
$856$	1.36113e10			0.741721
$857$	1.81913e9			0.0987261			0.0493631	−	0.998781i	$-0.484281\pi$
$857$	1.81913e9			0.0987261			0.0493631	+	0.998781i	$0.484281\pi$
$858$	−1.07547e9	−	1.38337e9i	−0.0581290	−	0.0747709i
$859$	2.20608e10			1.18753			0.593765	−	0.804638i	$-0.297641\pi$
$859$	2.20608e10			1.18753			0.593765	+	0.804638i	$0.297641\pi$
$860$	−3.23705e9			−0.173542
$861$	−5.60540e9	−	6.12220e9i	−0.299292	−	0.326886i
$862$	−2.58684e9			−0.137561
$863$			3.63377e10i			1.92451i	0.272155	+	0.962253i	$0.412264\pi$
$863$			3.63377e10i			1.92451i	−0.272155	+	0.962253i	$0.587736\pi$
$864$	1.02530e10	+	1.33956e10i	0.540818	+	0.706584i
$865$		−	7.81762e9i		−	0.410694i
$866$	−8.48910e9			−0.444170
$867$	5.41083e9	−	4.95408e9i	0.281966	−	0.258164i
$868$			1.01820e10i			0.528462i
$869$	1.74139e9	−	2.15760e10i	0.0900174	−	1.11533i
$870$	2.34574e9	+	2.56200e9i	0.120771	+	0.131905i
$871$		−	9.66252e8i		−	0.0495481i
$872$		−	5.86285e9i		−	0.299434i
$873$	1.15545e9	−	1.30848e10i	0.0587762	−	0.665605i
$874$	8.98181e9			0.455065
$875$	−1.92850e10			−0.973179
$876$	−8.74376e9	−	9.54990e9i	−0.439474	−	0.479992i
$877$			2.33325e9i			0.116805i	0.998293	+	0.0584026i	$0.0186007\pi$
$877$			2.33325e9i			0.116805i	−0.998293	+	0.0584026i	$0.981399\pi$
$878$			2.42481e9i			0.120906i
$879$	−8.89371e9	+	8.14296e9i	−0.441694	+	0.404409i
$880$	−4.07140e8	+	5.04451e9i	−0.0201398	+	0.249534i
$881$			3.35567e10i			1.65334i	0.562684	+	0.826672i	$0.309769\pi$
$881$			3.35567e10i			1.65334i	−0.562684	+	0.826672i	$0.690231\pi$
$882$	5.16892e8	−	5.85350e9i	0.0253665	−	0.287260i
$883$	−3.50787e10			−1.71467			−0.857335	−	0.514759i	$-0.827881\pi$
$883$	−3.50787e10			−1.71467			−0.857335	+	0.514759i	$0.827881\pi$
$884$		−	5.65499e9i		−	0.275327i
$885$	1.46442e9	−	1.34081e9i	0.0710175	−	0.0650227i
$886$		−	3.92227e9i		−	0.189461i
$887$	1.46423e10			0.704492			0.352246	−	0.935907i	$-0.385418\pi$
$887$	1.46423e10			0.704492			0.352246	+	0.935907i	$0.385418\pi$
$888$	9.20815e9	−	8.43086e9i	0.441293	−	0.404042i
$889$	−2.58510e10			−1.23402
$890$	−1.24184e9			−0.0590473
$891$	−2.04223e10	−	5.36041e9i	−0.967236	−	0.253878i
$892$	−1.46400e10			−0.690661
$893$	−5.64996e10			−2.65500
$894$	9.32685e9	−	8.53954e9i	0.436570	−	0.399718i
$895$	−8.03327e9			−0.374552
$896$			2.91508e10i			1.35385i
$897$	−3.51048e9	+	3.21415e9i	−0.162403	+	0.148694i
$898$			1.40403e10i			0.647007i
$899$	1.26255e10			0.579550
$900$	−1.42554e9	+	1.61434e10i	−0.0651826	+	0.738154i
$901$		−	4.25300e10i		−	1.93713i
$902$	2.55700e9	+	2.06374e8i	0.116013	+	0.00936337i
$903$	1.11524e10	−	1.02110e10i	0.504035	−	0.461488i
$904$		−	1.17577e10i		−	0.529339i
$905$		−	1.62258e10i		−	0.727671i
$906$	1.71962e9	+	1.87816e9i	0.0768218	+	0.0839044i
$907$	2.61701e10			1.16461			0.582303	−	0.812972i	$-0.302152\pi$
$907$	2.61701e10			1.16461			0.582303	+	0.812972i	$0.302152\pi$
$908$	−1.03922e10			−0.460688
$909$	1.62850e9	−	1.84418e10i	0.0719143	−	0.814386i
$910$			1.13435e9i			0.0499000i
$911$		−	3.40322e10i		−	1.49134i	−0.666317	−	0.745668i	$-0.732130\pi$
$911$		−	3.40322e10i		−	1.49134i	0.666317	−	0.745668i	$-0.267870\pi$
$912$	1.54842e10	+	1.69118e10i	0.675937	+	0.738256i
$913$	1.29261e10	+	1.04326e9i	0.562106	+	0.0453673i
$914$			2.93075e9i			0.126960i
$915$	−1.03051e10	+	9.43519e9i	−0.444711	+	0.407171i
$916$	−1.50088e10			−0.645225
$917$		−	1.56014e10i		−	0.668144i
$918$	5.92611e9	+	7.74252e9i	0.252825	+	0.330319i
$919$			6.48094e9i			0.275444i	0.990471	+	0.137722i	$0.0439781\pi$
$919$			6.48094e9i			0.275444i	−0.990471	+	0.137722i	$0.956022\pi$
$920$	−5.03983e9			−0.213382
$921$	−2.41303e10	−	2.63550e10i	−1.01778	−	1.11162i
$922$	−1.62403e10			−0.682394
$923$	5.59808e9			0.234333
$924$	−1.73470e10	−	2.23134e10i	−0.723391	−	0.930493i
$925$	1.83917e10			0.764059
$926$	−1.45998e9			−0.0604237
$927$	−3.73967e8	+	4.23495e9i	−0.0154189	+	0.174610i
$928$	2.79999e10			1.15011
$929$			2.19466e10i			0.898073i	0.893513	+	0.449037i	$0.148233\pi$
$929$			2.19466e10i			0.898073i	−0.893513	+	0.449037i	$0.851767\pi$
$930$	1.02766e9	+	1.12241e9i	0.0418949	+	0.0457575i
$931$		−	3.13808e10i		−	1.27450i
$932$	3.27737e10			1.32608
$933$	−1.71960e10	−	1.87814e10i	−0.693171	−	0.757079i
$934$		−	5.01692e9i		−	0.201476i
$935$	−9.24530e8	+	1.14550e10i	−0.0369897	+	0.458306i
$936$	4.43739e9	+	3.91843e8i	0.176873	+	0.0156188i
$937$			1.70925e10i			0.678763i	0.940649	+	0.339381i	$0.110218\pi$
$937$			1.70925e10i			0.678763i	−0.940649	+	0.339381i	$0.889782\pi$
$938$			2.23007e9i			0.0882284i
$939$	−2.78707e10	+	2.55181e10i	−1.09855	+	1.00581i
$940$	1.47931e10			0.580912
$941$	1.77594e9			0.0694809			0.0347404	−	0.999396i	$-0.488940\pi$
$941$	1.77594e9			0.0694809			0.0347404	+	0.999396i	$0.488940\pi$
$942$	−4.80943e9	+	4.40345e9i	−0.187463	+	0.171638i
$943$		−	6.96820e9i		−	0.270601i
$944$		−	4.07368e9i		−	0.157610i
$945$	8.30772e9	+	1.08541e10i	0.320236	+	0.418392i
$946$	−3.75938e8	+	4.65791e9i	−0.0144377	+	0.178884i
$947$		−	1.44300e10i		−	0.552130i	−0.961139	−	0.276065i	$-0.910970\pi$
$947$		−	1.44300e10i		−	0.552130i	0.961139	−	0.276065i	$-0.0890305\pi$
$948$	1.73401e10	+	1.89388e10i	0.661033	+	0.721978i
$949$	−5.24301e9			−0.199136
$950$		−	1.23836e10i		−	0.468612i
$951$	1.83100e9	+	1.99981e9i	0.0690328	+	0.0753974i
$952$			2.79705e10i			1.05068i
$953$	−1.02914e10			−0.385168			−0.192584	−	0.981281i	$-0.561687\pi$
$953$	−1.02914e10			−0.385168			−0.192584	+	0.981281i	$0.561687\pi$
$954$	1.55722e10	+	1.37510e9i	0.580672	+	0.0512762i
$955$	2.72330e9			0.101178
$956$	−1.64558e10			−0.609140
$957$	−2.76683e10	+	2.15101e10i	−1.02045	+	0.793323i
$958$	−1.08100e10			−0.397234
$959$	6.74105e10			2.46810
$960$	−2.35518e9	−	2.57232e9i	−0.0859163	−	0.0938374i
$961$	−2.19814e10			−0.798956
$962$		−	2.35893e9i		−	0.0854283i
$963$	2.72590e9	−	3.08691e10i	0.0983597	−	1.11386i
$964$			2.12664e10i			0.764584i
$965$	1.31404e10			0.470721
$966$	8.10204e9	−	7.41812e9i	0.289184	−	0.264773i
$967$			3.34086e10i			1.18814i	0.804415	+	0.594068i	$0.202479\pi$
$967$			3.34086e10i			1.18814i	−0.804415	+	0.594068i	$0.797521\pi$
$968$	1.84768e10	+	3.00207e9i	0.654731	+	0.106379i
$969$	3.51613e10	+	3.84031e10i	1.24146	+	1.35592i
$970$		−	2.62802e9i		−	0.0924546i
$971$			8.05011e7i			0.00282185i	0.999999	+	0.00141093i	$0.000449112\pi$
$971$			8.05011e7i			0.00282185i	−0.999999	+	0.00141093i	$0.999551\pi$
$972$	2.11515e10	−	1.34148e10i	0.738769	−	0.468547i
$973$	4.97490e10			1.73137
$974$	−8.13706e9			−0.282170
$975$	4.43147e9	+	4.84003e9i	0.153120	+	0.167237i
$976$			2.86663e10i			0.986954i
$977$		−	1.75738e10i		−	0.602887i	−0.953484	−	0.301443i	$-0.902532\pi$
$977$		−	1.75738e10i		−	0.602887i	0.953484	−	0.301443i	$-0.0974684\pi$
$978$	−3.89078e9	+	3.56234e9i	−0.133000	+	0.121773i
$979$	1.00793e9	−	1.24883e10i	0.0343313	−	0.425368i
$980$			8.21631e9i			0.278860i
$981$	−1.32964e10	−	1.17414e9i	−0.449669	−	0.0397080i
$982$	−8.04117e9			−0.270975
$983$			1.12515e10i			0.377810i	0.981995	+	0.188905i	$0.0604939\pi$
$983$			1.12515e10i			0.377810i	−0.981995	+	0.188905i	$0.939506\pi$
$984$	−4.81008e9	+	4.40405e9i	−0.160942	+	0.147356i
$985$		−	4.53353e8i		−	0.0151151i
$986$	1.61837e10			0.537660
$987$	−5.09655e10	+	4.66633e10i	−1.68720	+	1.54477i
$988$	1.11004e10			0.366174
$989$	1.26935e10			0.417248
$990$	−4.16433e9	−	7.08884e8i	−0.136402	−	0.0232195i
$991$	−1.13350e10			−0.369969			−0.184985	−	0.982741i	$-0.559224\pi$
$991$	−1.13350e10			−0.369969			−0.184985	+	0.982741i	$0.559224\pi$
$992$	1.22667e10			0.398968
$993$	2.44726e10	−	2.24068e10i	0.793154	−	0.726201i
$994$	−1.29201e10			−0.417268
$995$		−	1.01004e10i		−	0.325057i
$996$	−1.13461e10	+	1.03884e10i	−0.363865	+	0.333150i
$997$			2.09177e10i			0.668469i	0.942490	+	0.334235i	$0.108478\pi$
$997$			2.09177e10i			0.668469i	−0.942490	+	0.334235i	$0.891522\pi$
$998$	−1.42164e10			−0.452723
$999$	−1.72763e10	−	2.25717e10i	−0.548242	−	0.716283i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	33.8.d.b.32.11	✓	24
3.2	odd	2	inner	33.8.d.b.32.14	yes	24
11.10	odd	2	inner	33.8.d.b.32.13	yes	24
33.32	even	2	inner	33.8.d.b.32.12	yes	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
33.8.d.b.32.11	✓	24	1.1	even	1	trivial
33.8.d.b.32.12	yes	24	33.32	even	2	inner
33.8.d.b.32.13	yes	24	11.10	odd	2	inner
33.8.d.b.32.14	yes	24	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:	\( k \)	\(=\)	\( 8 \)
Character orbit:	\([\chi]\)	\(=\)	33.d (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-4.00282 q^{2} +(34.4918 - 31.5803i) q^{3} -111.977 q^{4} +109.310i q^{5} +(-138.065 + 126.410i) q^{6} +1222.62i q^{7} +960.586 q^{8} +(192.374 - 2178.52i) q^{9} +O(q^{10})\)	\(q-4.00282 q^{2} +(34.4918 - 31.5803i) q^{3} -111.977 q^{4} +109.310i q^{5} +(-138.065 + 126.410i) q^{6} +1222.62i q^{7} +960.586 q^{8} +(192.374 - 2178.52i) q^{9} -437.547i q^{10} +(4400.12 + 355.132i) q^{11} +(-3862.31 + 3536.28i) q^{12} +2120.46i q^{13} -4893.92i q^{14} +(3452.03 + 3770.30i) q^{15} +10488.1 q^{16} +23816.2 q^{17} +(-770.039 + 8720.23i) q^{18} +46749.5i q^{19} -12240.2i q^{20} +(38610.6 + 42170.4i) q^{21} +(-17612.9 - 1421.53i) q^{22} +47997.7i q^{23} +(33132.4 - 30335.6i) q^{24} +66176.4 q^{25} -8487.80i q^{26} +(-62163.0 - 81216.5i) q^{27} -136906. i q^{28} -169761. q^{29} +(-13817.9 - 15091.8i) q^{30} -74372.3 q^{31} -164937. q^{32} +(162983. - 126708. i) q^{33} -95331.9 q^{34} -133644. q^{35} +(-21541.6 + 243945. i) q^{36} +277920. q^{37} -187130. i q^{38} +(66964.5 + 73138.4i) q^{39} +105001. i q^{40} -145178. q^{41} +(-154551. - 168800. i) q^{42} -264460. i q^{43} +(-492714. - 39766.8i) q^{44} +(238134. + 21028.4i) q^{45} -192126. i q^{46} +1.20856e6i q^{47} +(361753. - 331216. i) q^{48} -671255. q^{49} -264892. q^{50} +(821465. - 752122. i) q^{51} -237443. i q^{52} -1.78576e6i q^{53} +(248827. + 325095. i) q^{54} +(-38819.4 + 480976. i) q^{55} +1.17443e6i q^{56} +(1.47636e6 + 1.61248e6i) q^{57} +679523. q^{58} -388411. i q^{59} +(-386550. - 422188. i) q^{60} +2.73323e6i q^{61} +297699. q^{62} +(2.66350e6 + 235200. i) q^{63} -682260. q^{64} -231787. q^{65} +(-652393. + 507188. i) q^{66} -455681. q^{67} -2.66688e6 q^{68} +(1.51578e6 + 1.65553e6i) q^{69} +534954. q^{70} -2.64004e6i q^{71} +(184792. - 2.09266e6i) q^{72} +2.47259e6i q^{73} -1.11246e6 q^{74} +(2.28254e6 - 2.08987e6i) q^{75} -5.23489e6i q^{76} +(-434191. + 5.37967e6i) q^{77} +(-268047. - 292760. i) q^{78} -4.90350e6i q^{79} +1.14645e6i q^{80} +(-4.70895e6 - 838183. i) q^{81} +581120. q^{82} +2.93766e6 q^{83} +(-4.32352e6 - 4.72213e6i) q^{84} +2.60334e6i q^{85} +1.05859e6i q^{86} +(-5.85538e6 + 5.36110e6i) q^{87} +(4.22669e6 + 341135. i) q^{88} -2.83818e6i q^{89} +(-953206. - 84172.8i) q^{90} -2.59251e6 q^{91} -5.37467e6i q^{92} +(-2.56524e6 + 2.34870e6i) q^{93} -4.83765e6i q^{94} -5.11018e6 q^{95} +(-5.68897e6 + 5.20875e6i) q^{96} +6.00627e6 q^{97} +2.68691e6 q^{98} +(1.62013e6 - 9.51744e6i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 120 q^{3} + 1788 q^{4} - 5940 q^{9}+O(q^{10}) \) 24 * q + 120 * q^3 + 1788 * q^4 - 5940 * q^9	\( 24 q + 120 q^{3} + 1788 q^{4} - 5940 q^{9} - 6936 q^{12} + 23160 q^{15} + 5844 q^{16} - 17556 q^{22} - 34704 q^{25} + 7560 q^{27} + 131328 q^{31} + 28644 q^{33} - 436080 q^{34} - 302832 q^{36} + 1072488 q^{37} - 100296 q^{42} - 1854252 q^{45} + 3172548 q^{48} - 1169304 q^{49} - 4401936 q^{55} - 2920440 q^{58} + 1981452 q^{60} + 14578596 q^{64} + 2895156 q^{66} + 7729200 q^{67} - 4614108 q^{69} - 6924504 q^{70} - 4375800 q^{75} - 26237448 q^{78} + 22367340 q^{81} - 23600232 q^{82} - 25179660 q^{88} + 9380640 q^{91} + 25396908 q^{93} + 72948360 q^{97} + 53650080 q^{99}+O(q^{100}) \) 24 * q + 120 * q^3 + 1788 * q^4 - 5940 * q^9 - 6936 * q^12 + 23160 * q^15 + 5844 * q^16 - 17556 * q^22 - 34704 * q^25 + 7560 * q^27 + 131328 * q^31 + 28644 * q^33 - 436080 * q^34 - 302832 * q^36 + 1072488 * q^37 - 100296 * q^42 - 1854252 * q^45 + 3172548 * q^48 - 1169304 * q^49 - 4401936 * q^55 - 2920440 * q^58 + 1981452 * q^60 + 14578596 * q^64 + 2895156 * q^66 + 7729200 * q^67 - 4614108 * q^69 - 6924504 * q^70 - 4375800 * q^75 - 26237448 * q^78 + 22367340 * q^81 - 23600232 * q^82 - 25179660 * q^88 + 9380640 * q^91 + 25396908 * q^93 + 72948360 * q^97 + 53650080 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more