LMFDB - Embedded newform 100.11.b.e.51.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [100,11,Mod(51,100)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(100, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 11, names="a")

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

chi := DirichletCharacter("100.51");

S:= CuspForms(chi, 11);

N := Newforms(S);

Level:	$ N $	$=$	$ 100 = 2^{2} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 11 $
Character orbit:	$[\chi]$	$=$	100.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:	$63.5357252674$
Analytic rank:	$0$
Dimension:	$20$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} + 199481 x^{18} + 16413464051 x^{16} + 725560177607766 x^{14} + \cdots + 21\!\cdots\!25 $ x^20 + 199481x^18 + 16413464051x^16 + 725560177607766x^14 + 18834574233849489621x^12 + 294503164498899790078095x^10 + 2731275057520962661290869385x^8 + 14154171070179138865031966998950x^6 + 35770310815174676049504613026680775x^4 + 31929367165777304447910767061760715625*x^2 + 2155644618924695638814066662020965503125
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 2^{97}\cdot 3^{4}\cdot 5^{29} $
Twist minimal:	no (minimal twist has level 20)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			51.11
Root			$40.2810i$ of defining polynomial
Character	$\chi$	$=$	100.51
Dual form			100.11.b.e.51.12

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.770283 - 31.9907i) q^{2} +80.5620i q^{3} +(-1022.81 - 49.2838i) q^{4} +(2577.24 + 62.0555i) q^{6} -345.112i q^{7} +(-2364.48 + 32682.6i) q^{8} +52558.8 q^{9} +O(q^{10})$	\(q+(0.770283 - 31.9907i) q^{2} +80.5620i q^{3} +(-1022.81 - 49.2838i) q^{4} +(2577.24 + 62.0555i) q^{6} -345.112i q^{7} +(-2364.48 + 32682.6i) q^{8} +52558.8 q^{9} -167110. i q^{11} +(3970.40 - 82399.9i) q^{12} -95695.6 q^{13} +(-11040.4 - 265.834i) q^{14} +(1.04372e6 + 100816. i) q^{16} -2.26205e6 q^{17} +(40485.1 - 1.68139e6i) q^{18} +1.35682e6i q^{19} +27802.9 q^{21} +(-5.34596e6 - 128722. i) q^{22} +7.72397e6i q^{23} +(-2.63297e6 - 190487. i) q^{24} +(-73712.7 + 3.06137e6i) q^{26} +8.99135e6i q^{27} +(-17008.4 + 352985. i) q^{28} -6.87281e6 q^{29} -4.09489e7i q^{31} +(4.02915e6 - 3.33116e7i) q^{32} +1.34627e7 q^{33} +(-1.74242e6 + 7.23647e7i) q^{34} +(-5.37578e7 - 2.59030e6i) q^{36} +4.60291e7 q^{37} +(4.34058e7 + 1.04514e6i) q^{38} -7.70943e6i q^{39} +1.22306e7 q^{41} +(21416.1 - 889435. i) q^{42} +2.14512e8i q^{43} +(-8.23580e6 + 1.70922e8i) q^{44} +(2.47095e8 + 5.94964e6i) q^{46} +1.55391e8i q^{47} +(-8.12196e6 + 8.40840e7i) q^{48} +2.82356e8 q^{49} -1.82235e8i q^{51} +(9.78788e7 + 4.71625e6i) q^{52} +5.32341e7 q^{53} +(2.87640e8 + 6.92588e6i) q^{54} +(1.12791e7 + 816010. i) q^{56} -1.09309e8 q^{57} +(-5.29401e6 + 2.19866e8i) q^{58} +9.05250e8i q^{59} +7.30533e8 q^{61} +(-1.30998e9 - 3.15422e7i) q^{62} -1.81387e7i q^{63} +(-1.06256e9 - 1.54555e8i) q^{64} +(1.03701e7 - 4.30681e8i) q^{66} -5.67307e8i q^{67} +(2.31366e9 + 1.11483e8i) q^{68} -6.22259e8 q^{69} +2.07599e9i q^{71} +(-1.24274e8 + 1.71776e9i) q^{72} +3.04740e9 q^{73} +(3.54554e7 - 1.47250e9i) q^{74} +(6.68695e7 - 1.38778e9i) q^{76} -5.76715e7 q^{77} +(-2.46630e8 - 5.93845e6i) q^{78} -2.49153e9i q^{79} +2.37918e9 q^{81} +(9.42105e6 - 3.91267e8i) q^{82} -6.00897e9i q^{83} +(-2.84372e7 - 1.37023e6i) q^{84} +(6.86238e9 + 1.65235e8i) q^{86} -5.53687e8i q^{87} +(5.46157e9 + 3.95128e8i) q^{88} +5.14975e9 q^{89} +3.30257e7i q^{91} +(3.80667e8 - 7.90018e9i) q^{92} +3.29892e9 q^{93} +(4.97108e9 + 1.19695e8i) q^{94} +(2.68365e9 + 3.24596e8i) q^{96} -6.01008e9 q^{97} +(2.17494e8 - 9.03278e9i) q^{98} -8.78308e9i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q - 22 q^{2} - 644 q^{4} - 14784 q^{6} - 3448 q^{8} - 414868 q^{9}+O(q^{10}) $ 20 * q - 22 * q^2 - 644 * q^4 - 14784 * q^6 - 3448 * q^8 - 414868 * q^9	\( 20 q - 22 q^{2} - 644 q^{4} - 14784 q^{6} - 3448 q^{8} - 414868 q^{9} - 1329640 q^{12} + 278864 q^{13} - 2240504 q^{14} + 4261360 q^{16} + 1921656 q^{17} + 3556082 q^{18} + 4157512 q^{21} + 5811280 q^{22} - 19112144 q^{24} + 25066884 q^{26} + 87415400 q^{28} - 66014888 q^{29} + 33171328 q^{32} - 85980560 q^{33} - 27236084 q^{34} + 355456476 q^{36} + 153620656 q^{37} - 250352720 q^{38} + 477406160 q^{41} + 570662040 q^{42} + 339141040 q^{44} - 897549304 q^{46} + 479727360 q^{48} + 333772012 q^{49} + 110465096 q^{52} + 1669491824 q^{53} + 706139792 q^{54} - 1362290224 q^{56} - 3973032960 q^{57} - 2075027916 q^{58} - 4283166080 q^{61} - 1664032240 q^{62} + 340459456 q^{64} + 1884031760 q^{66} - 3042411896 q^{68} - 5321669928 q^{69} - 1632326712 q^{72} - 2474287656 q^{73} + 188682276 q^{74} + 2323171200 q^{76} - 410885040 q^{77} + 19914223760 q^{78} + 9939722652 q^{81} + 3197757116 q^{82} + 2383099552 q^{84} + 19648321456 q^{86} - 2774318240 q^{88} + 3011851592 q^{89} + 27349072440 q^{92} + 11861394640 q^{93} + 15684681576 q^{94} - 1990377984 q^{96} + 39984502056 q^{97} - 38416891998 q^{98}+O(q^{100}) \) 20 * q - 22 * q^2 - 644 * q^4 - 14784 * q^6 - 3448 * q^8 - 414868 * q^9 - 1329640 * q^12 + 278864 * q^13 - 2240504 * q^14 + 4261360 * q^16 + 1921656 * q^17 + 3556082 * q^18 + 4157512 * q^21 + 5811280 * q^22 - 19112144 * q^24 + 25066884 * q^26 + 87415400 * q^28 - 66014888 * q^29 + 33171328 * q^32 - 85980560 * q^33 - 27236084 * q^34 + 355456476 * q^36 + 153620656 * q^37 - 250352720 * q^38 + 477406160 * q^41 + 570662040 * q^42 + 339141040 * q^44 - 897549304 * q^46 + 479727360 * q^48 + 333772012 * q^49 + 110465096 * q^52 + 1669491824 * q^53 + 706139792 * q^54 - 1362290224 * q^56 - 3973032960 * q^57 - 2075027916 * q^58 - 4283166080 * q^61 - 1664032240 * q^62 + 340459456 * q^64 + 1884031760 * q^66 - 3042411896 * q^68 - 5321669928 * q^69 - 1632326712 * q^72 - 2474287656 * q^73 + 188682276 * q^74 + 2323171200 * q^76 - 410885040 * q^77 + 19914223760 * q^78 + 9939722652 * q^81 + 3197757116 * q^82 + 2383099552 * q^84 + 19648321456 * q^86 - 2774318240 * q^88 + 3011851592 * q^89 + 27349072440 * q^92 + 11861394640 * q^93 + 15684681576 * q^94 - 1990377984 * q^96 + 39984502056 * q^97 - 38416891998 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/100\mathbb{Z}\right)^\times$.

$n$	$51$	$77$
$\chi(n)$	$-1$	$1$

Coefficient data

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

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

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

$2$	0.770283	−	31.9907i	0.0240713	−	0.999710i
$2$	0.770283	−	31.9907i	0.0240713	−	0.999710i
$3$			80.5620i			0.331531i	0.986165	+	0.165765i	$0.0530095\pi$
$3$			80.5620i			0.331531i	−0.986165	+	0.165765i	$0.946991\pi$
$4$	−1022.81	−	49.2838i	−0.998841	−	0.0481287i
$5$		0			0
$5$		0			0
$6$	2577.24	+	62.0555i	0.331435	+	0.00798039i
$7$		−	345.112i		−	0.0205338i	−0.999947	−	0.0102669i	$-0.996732\pi$
$7$		−	345.112i		−	0.0205338i	0.999947	−	0.0102669i	$-0.00326812\pi$
$8$	−2364.48	+	32682.6i	−0.0721582	+	0.997393i
$9$	52558.8			0.890087
$10$		0			0
$11$		−	167110.i		−	1.03762i	−0.854890	−	0.518810i	$-0.826375\pi$
$11$		−	167110.i		−	1.03762i	0.854890	−	0.518810i	$-0.173625\pi$
$12$	3970.40	−	82399.9i	0.0159562	−	0.331147i
$13$	−95695.6			−0.257736			−0.128868	−	0.991662i	$-0.541134\pi$
$13$	−95695.6			−0.257736			−0.128868	+	0.991662i	$0.541134\pi$
$14$	−11040.4	−	265.834i	−0.0205279	−	0.000494277i
$15$		0			0
$16$	1.04372e6	+	100816.i	0.995367	+	0.0961459i
$17$	−2.26205e6			−1.59315			−0.796577	−	0.604537i	$-0.793358\pi$
$17$	−2.26205e6			−1.59315			−0.796577	+	0.604537i	$0.793358\pi$
$18$	40485.1	−	1.68139e6i	0.0214256	−	0.889829i
$19$			1.35682e6i			0.547969i	0.961734	+	0.273984i	$0.0883417\pi$
$19$			1.35682e6i			0.547969i	−0.961734	+	0.273984i	$0.911658\pi$
$20$		0			0
$21$	27802.9			0.00680760
$22$	−5.34596e6	−	128722.i	−1.03732	−	0.0249769i
$23$			7.72397e6i			1.20006i	0.799979	+	0.600028i	$0.204844\pi$
$23$			7.72397e6i			1.20006i	−0.799979	+	0.600028i	$0.795156\pi$
$24$	−2.63297e6	−	190487.i	−0.330667	−	0.0239227i
$25$		0			0
$26$	−73712.7	+	3.06137e6i	−0.00620406	+	0.257662i
$27$			8.99135e6i			0.626622i
$28$	−17008.4	+	352985.i	−0.000988267	+	0.0205100i
$29$	−6.87281e6			−0.335077			−0.167538	−	0.985866i	$-0.553582\pi$
$29$	−6.87281e6			−0.335077			−0.167538	+	0.985866i	$0.553582\pi$
$30$		0			0
$31$		−	4.09489e7i		−	1.43032i	−0.698961	−	0.715160i	$-0.746354\pi$
$31$		−	4.09489e7i		−	1.43032i	0.698961	−	0.715160i	$-0.253646\pi$
$32$	4.02915e6	−	3.33116e7i	0.120078	−	0.992764i
$33$	1.34627e7			0.344003
$34$	−1.74242e6	+	7.23647e7i	−0.0383494	+	1.59269i
$35$		0			0
$36$	−5.37578e7	−	2.59030e6i	−0.889056	−	0.0428388i
$37$	4.60291e7			0.663779			0.331889	−	0.943318i	$-0.392314\pi$
$37$	4.60291e7			0.663779			0.331889	+	0.943318i	$0.392314\pi$
$38$	4.34058e7	+	1.04514e6i	0.547810	+	0.0131903i
$39$		−	7.70943e6i		−	0.0854475i
$40$		0			0
$41$	1.22306e7			0.105567			0.0527837	−	0.998606i	$-0.483191\pi$
$41$	1.22306e7			0.105567			0.0527837	+	0.998606i	$0.483191\pi$
$42$	21416.1	−	889435.i	0.000163868	−	0.00680562i
$43$			2.14512e8i			1.45918i	0.683886	+	0.729589i	$0.260289\pi$
$43$			2.14512e8i			1.45918i	−0.683886	+	0.729589i	$0.739711\pi$
$44$	−8.23580e6	+	1.70922e8i	−0.0499393	+	1.03642i
$45$		0			0
$46$	2.47095e8	+	5.94964e6i	1.19971	+	0.0288870i
$47$			1.55391e8i			0.677544i	0.940869	+	0.338772i	$0.110012\pi$
$47$			1.55391e8i			0.677544i	−0.940869	+	0.338772i	$0.889988\pi$
$48$	−8.12196e6	+	8.40840e7i	−0.0318753	+	0.329995i
$49$	2.82356e8			0.999578
$50$		0			0
$51$		−	1.82235e8i		−	0.528180i
$52$	9.78788e7	+	4.71625e6i	0.257438	+	0.0124045i
$53$	5.32341e7			0.127295			0.0636474	−	0.997972i	$-0.479727\pi$
$53$	5.32341e7			0.127295			0.0636474	+	0.997972i	$0.479727\pi$
$54$	2.87640e8	+	6.92588e6i	0.626441	+	0.0150836i
$55$		0			0
$56$	1.12791e7	+	816010.i	0.0204803	+	0.00148168i
$57$	−1.09309e8			−0.181669
$58$	−5.29401e6	+	2.19866e8i	−0.00806574	+	0.334980i
$59$			9.05250e8i			1.26622i	0.774062	+	0.633109i	$0.218222\pi$
$59$			9.05250e8i			1.26622i	−0.774062	+	0.633109i	$0.781778\pi$
$60$		0			0
$61$	7.30533e8			0.864950			0.432475	−	0.901646i	$-0.357640\pi$
$61$	7.30533e8			0.864950			0.432475	+	0.901646i	$0.357640\pi$
$62$	−1.30998e9	−	3.15422e7i	−1.42991	−	0.0344297i
$63$		−	1.81387e7i		−	0.0182769i
$64$	−1.06256e9	−	1.54555e8i	−0.989586	−	0.143940i
$65$		0			0
$66$	1.03701e7	−	4.30681e8i	0.00828061	−	0.343903i
$67$		−	5.67307e8i		−	0.420188i	−0.977681	−	0.210094i	$-0.932623\pi$
$67$		−	5.67307e8i		−	0.420188i	0.977681	−	0.210094i	$-0.0673770\pi$
$68$	2.31366e9	+	1.11483e8i	1.59131	+	0.0766765i
$69$	−6.22259e8			−0.397856
$70$		0			0
$71$			2.07599e9i			1.15063i	0.817934	+	0.575313i	$0.195120\pi$
$71$			2.07599e9i			1.15063i	−0.817934	+	0.575313i	$0.804880\pi$
$72$	−1.24274e8	+	1.71776e9i	−0.0642271	+	0.887767i
$73$	3.04740e9			1.46999			0.734996	−	0.678071i	$-0.237184\pi$
$73$	3.04740e9			1.46999			0.734996	+	0.678071i	$0.237184\pi$
$74$	3.54554e7	−	1.47250e9i	0.0159780	−	0.663587i
$75$		0			0
$76$	6.68695e7	−	1.38778e9i	0.0263730	−	0.547334i
$77$	−5.76715e7			−0.0213063
$78$	−2.46630e8	−	5.93845e6i	−0.0854228	−	0.00205684i
$79$		−	2.49153e9i		−	0.809711i	−0.914381	−	0.404855i	$-0.867322\pi$
$79$		−	2.49153e9i		−	0.809711i	0.914381	−	0.404855i	$-0.132678\pi$
$80$		0			0
$81$	2.37918e9			0.682343
$82$	9.42105e6	−	3.91267e8i	0.00254115	−	0.105537i
$83$		−	6.00897e9i		−	1.52549i	−0.646699	−	0.762745i	$-0.723851\pi$
$83$		−	6.00897e9i		−	1.52549i	0.646699	−	0.762745i	$-0.276149\pi$
$84$	−2.84372e7	−	1.37023e6i	−0.00679971	−	0.000327641i
$85$		0			0
$86$	6.86238e9	+	1.65235e8i	1.45876	+	0.0351244i
$87$		−	5.53687e8i		−	0.111088i
$88$	5.46157e9	+	3.95128e8i	1.03491	+	0.0748728i
$89$	5.14975e9			0.922223			0.461111	−	0.887342i	$-0.347451\pi$
$89$	5.14975e9			0.922223			0.461111	+	0.887342i	$0.347451\pi$
$90$		0			0
$91$			3.30257e7i			0.00529231i
$92$	3.80667e8	−	7.90018e9i	0.0577572	−	1.19867i
$93$	3.29892e9			0.474195
$94$	4.97108e9	+	1.19695e8i	0.677348	+	0.0163094i
$95$		0			0
$96$	2.68365e9	+	3.24596e8i	0.329132	+	0.0398095i
$97$	−6.01008e9			−0.699877			−0.349938	−	0.936773i	$-0.613797\pi$
$97$	−6.01008e9			−0.699877			−0.349938	+	0.936773i	$0.613797\pi$
$98$	2.17494e8	−	9.03278e9i	0.0240612	−	0.999289i
$99$		−	8.78308e9i		−	0.923572i
$100$		0			0
$101$	1.41252e10			1.34396			0.671980	−	0.740569i	$-0.265444\pi$
$101$	1.41252e10			1.34396			0.671980	+	0.740569i	$0.265444\pi$
$102$	−5.82984e9	−	1.40373e8i	−0.528027	−	0.0127140i
$103$			1.31381e10i			1.13330i	0.823957	+	0.566652i	$0.191762\pi$
$103$			1.31381e10i			1.13330i	−0.823957	+	0.566652i	$0.808238\pi$
$104$	2.26271e8	−	3.12758e9i	0.0185978	−	0.257064i
$105$		0			0
$106$	4.10053e7	−	1.70300e9i	0.00306416	−	0.127258i
$107$			1.84954e10i			1.31870i	0.751836	+	0.659350i	$0.229168\pi$
$107$			1.84954e10i			1.31870i	−0.751836	+	0.659350i	$0.770832\pi$
$108$	4.43128e8	−	9.19647e9i	0.0301585	−	0.625896i
$109$	−9.29496e9			−0.604108			−0.302054	−	0.953291i	$-0.597672\pi$
$109$	−9.29496e9			−0.604108			−0.302054	+	0.953291i	$0.597672\pi$
$110$		0			0
$111$			3.70819e9i			0.220063i
$112$	3.47929e7	−	3.60200e8i	0.00197424	−	0.0204387i
$113$	2.83775e10			1.54021			0.770107	−	0.637914i	$-0.220203\pi$
$113$	2.83775e10			1.54021			0.770107	+	0.637914i	$0.220203\pi$
$114$	−8.41985e7	+	3.49686e9i	−0.00437301	+	0.181616i
$115$		0			0
$116$	7.02960e9	+	3.38718e8i	0.334688	+	0.0161268i
$117$	−5.02964e9			−0.229408
$118$	2.89596e10	+	6.97299e8i	1.26585	+	0.0304796i
$119$			7.80661e8i			0.0327135i
$120$		0			0
$121$	−1.98821e9			−0.0766543
$122$	5.62717e8	−	2.33703e10i	0.0208205	−	0.864699i
$123$			9.85325e8i			0.0349989i
$124$	−2.01812e9	+	4.18830e10i	−0.0688395	+	1.42866i
$125$		0			0
$126$	−5.80269e8	−	1.39719e7i	−0.0182716	−	0.000439949i
$127$			2.03618e10i			0.616306i	0.951337	+	0.308153i	$0.0997109\pi$
$127$			2.03618e10i			0.616306i	−0.951337	+	0.308153i	$0.900289\pi$
$128$	−5.76279e9	+	3.38730e10i	−0.167719	+	0.985835i
$129$	−1.72815e10			−0.483763
$130$		0			0
$131$			3.67281e10i			0.952010i	0.879442	+	0.476005i	$0.157916\pi$
$131$			3.67281e10i			0.952010i	−0.879442	+	0.476005i	$0.842084\pi$
$132$	−1.37698e10	−	6.63493e8i	−0.343604	−	0.0165564i
$133$	4.68256e8			0.0112519
$134$	−1.81485e10	−	4.36987e8i	−0.420066	−	0.0101145i
$135$		0			0
$136$	5.34858e9	−	7.39297e10i	0.114959	−	1.58900i
$137$	−3.94095e10			−0.816578			−0.408289	−	0.912853i	$-0.633874\pi$
$137$	−3.94095e10			−0.816578			−0.408289	+	0.912853i	$0.633874\pi$
$138$	−4.79315e8	+	1.99065e10i	−0.00957692	+	0.397740i
$139$			2.13638e10i			0.411723i	0.978581	+	0.205861i	$0.0659996\pi$
$139$			2.13638e10i			0.411723i	−0.978581	+	0.205861i	$0.934000\pi$
$140$		0			0
$141$	−1.25186e10			−0.224627
$142$	6.64125e10	+	1.59910e9i	1.15029	+	0.0276971i
$143$			1.59917e10i			0.267432i
$144$	5.48565e10	+	5.29878e9i	0.885964	+	0.0855783i
$145$		0			0
$146$	2.34736e9	−	9.74885e10i	0.0353847	−	1.46957i
$147$			2.27472e10i			0.331391i
$148$	−4.70791e10	−	2.26849e9i	−0.663010	−	0.0319468i
$149$	8.44522e10			1.14995			0.574976	−	0.818170i	$-0.305011\pi$
$149$	8.44522e10			1.14995			0.574976	+	0.818170i	$0.305011\pi$
$150$		0			0
$151$			1.37451e11i			1.75091i	0.483298	+	0.875456i	$0.339439\pi$
$151$			1.37451e11i			1.75091i	−0.483298	+	0.875456i	$0.660561\pi$
$152$	−4.43445e10	−	3.20819e9i	−0.546540	−	0.0395405i
$153$	−1.18891e11			−1.41805
$154$	−4.44234e7	+	1.84495e9i	−0.000512871	+	0.0213001i
$155$		0			0
$156$	−3.79950e8	+	7.88531e9i	−0.00411248	+	0.0853485i
$157$	1.68284e11			1.76418			0.882091	−	0.471079i	$-0.156135\pi$
$157$	1.68284e11			1.76418			0.882091	+	0.471079i	$0.156135\pi$
$158$	−7.97057e10	−	1.91918e9i	−0.809476	−	0.0194908i
$159$			4.28865e9i			0.0422022i
$160$		0			0
$161$	2.66563e9			0.0246417
$162$	1.83264e9	−	7.61117e10i	0.0164249	−	0.682145i
$163$		−	3.14917e10i		−	0.273689i	−0.990593	−	0.136845i	$-0.956304\pi$
$163$		−	3.14917e10i		−	0.273689i	0.990593	−	0.136845i	$-0.0436961\pi$
$164$	−1.25097e10	−	6.02772e8i	−0.105445	−	0.00508082i
$165$		0			0
$166$	−1.92231e11	−	4.62861e9i	−1.52505	−	0.0367206i
$167$			9.91909e10i			0.763642i	0.924236	+	0.381821i	$0.124703\pi$
$167$			9.91909e10i			0.763642i	−0.924236	+	0.381821i	$0.875297\pi$
$168$	−6.57395e7	+	9.08671e8i	−0.000491224	+	0.00678985i
$169$	−1.28701e11			−0.933572
$170$		0			0
$171$			7.13130e10i			0.487740i
$172$	1.05720e10	−	2.19405e11i	0.0702284	−	1.45749i
$173$	−1.01217e10			−0.0653166			−0.0326583	−	0.999467i	$-0.510397\pi$
$173$	−1.01217e10			−0.0653166			−0.0326583	+	0.999467i	$0.510397\pi$
$174$	−1.77129e10	−	4.26496e8i	−0.111056	−	0.00267404i
$175$		0			0
$176$	1.68474e10	−	1.74415e11i	0.0997629	−	1.03281i
$177$	−7.29288e10			−0.419791
$178$	3.96676e9	−	1.64744e11i	0.0221991	−	0.921956i
$179$		−	2.93205e11i		−	1.59553i	−0.602966	−	0.797767i	$-0.706015\pi$
$179$		−	2.93205e11i		−	1.59553i	0.602966	−	0.797767i	$-0.293985\pi$
$180$		0			0
$181$	−2.98370e11			−1.53590			−0.767949	−	0.640511i	$-0.778723\pi$
$181$	−2.98370e11			−1.53590			−0.767949	+	0.640511i	$0.778723\pi$
$182$	1.05652e9	+	2.54391e7i	0.00529077	+	0.000127393i
$183$			5.88532e10i			0.286758i
$184$	−2.52439e11	−	1.82632e10i	−1.19693	−	0.0865939i
$185$		0			0
$186$	2.54110e9	−	1.05535e11i	0.0114145	−	0.474058i
$187$			3.78011e11i			1.65309i
$188$	7.65828e9	−	1.58936e11i	0.0326093	−	0.676759i
$189$	3.10302e9			0.0128670
$190$		0			0
$191$			4.51966e11i			1.77803i	0.457880	+	0.889014i	$0.348609\pi$
$191$			4.51966e11i			1.77803i	−0.457880	+	0.889014i	$0.651391\pi$
$192$	1.24512e10	−	8.56020e10i	0.0477207	−	0.328079i
$193$	−2.81708e11			−1.05199			−0.525996	−	0.850487i	$-0.676307\pi$
$193$	−2.81708e11			−1.05199			−0.525996	+	0.850487i	$0.676307\pi$
$194$	−4.62946e9	+	1.92267e11i	−0.0168470	+	0.699674i
$195$		0			0
$196$	−2.88798e11	−	1.39156e10i	−0.998420	−	0.0481084i
$197$	1.40740e11			0.474336			0.237168	−	0.971469i	$-0.423781\pi$
$197$	1.40740e11			0.474336			0.237168	+	0.971469i	$0.423781\pi$
$198$	−2.80977e11	−	6.76545e9i	−0.923304	−	0.0222316i
$199$		−	4.94062e11i		−	1.58313i	−0.611087	−	0.791564i	$-0.709267\pi$
$199$		−	4.94062e11i		−	1.58313i	0.611087	−	0.791564i	$-0.290733\pi$
$200$		0			0
$201$	4.57034e10			0.139305
$202$	1.08804e10	−	4.51874e11i	0.0323509	−	1.34357i
$203$			2.37189e9i			0.00688040i
$204$	−8.98126e9	+	1.86393e11i	−0.0254206	+	0.527568i
$205$		0			0
$206$	4.20297e11	+	1.01201e10i	1.13298	+	0.0272801i
$207$			4.05962e11i			1.06815i
$208$	−9.98793e10	−	9.64768e9i	−0.256542	−	0.0247803i
$209$	2.26739e11			0.568583
$210$		0			0
$211$			3.76526e11i			0.900291i	0.892955	+	0.450146i	$0.148628\pi$
$211$			3.76526e11i			0.900291i	−0.892955	+	0.450146i	$0.851372\pi$
$212$	−5.44486e10	−	2.62358e9i	−0.127147	−	0.00612654i
$213$	−1.67246e11			−0.381468
$214$	5.91683e11	+	1.42467e10i	1.31832	+	0.0317429i
$215$		0			0
$216$	−2.93860e11	−	2.12599e10i	−0.624989	−	0.0452160i
$217$	−1.41319e10			−0.0293699
$218$	−7.15975e9	+	2.97352e11i	−0.0145417	+	0.603933i
$219$			2.45505e11i			0.487348i
$220$		0			0
$221$	2.16468e11			0.410614
$222$	1.18628e11	+	2.85636e9i	0.219999	+	0.00529722i
$223$			1.01270e11i			0.183636i	0.995776	+	0.0918178i	$0.0292677\pi$
$223$			1.01270e11i			0.183636i	−0.995776	+	0.0918178i	$0.970732\pi$
$224$	−1.14962e10	−	1.39051e9i	−0.0203852	−	0.00246566i
$225$		0			0
$226$	2.18587e10	−	9.07816e11i	0.0370750	−	1.53977i
$227$			6.65566e10i			0.110424i	0.998475	+	0.0552118i	$0.0175834\pi$
$227$			6.65566e10i			0.110424i	−0.998475	+	0.0552118i	$0.982417\pi$
$228$	1.11802e11	+	5.38714e9i	0.181458	+	0.00874348i
$229$	−3.57386e11			−0.567492			−0.283746	−	0.958900i	$-0.591577\pi$
$229$	−3.57386e11			−0.567492			−0.283746	+	0.958900i	$0.591577\pi$
$230$		0			0
$231$		−	4.64613e9i		−	0.00706369i
$232$	1.62506e10	−	2.24621e11i	0.0241785	−	0.334203i
$233$	5.97154e11			0.869574			0.434787	−	0.900533i	$-0.356824\pi$
$233$	5.97154e11			0.869574			0.434787	+	0.900533i	$0.356824\pi$
$234$	−3.87425e9	+	1.60902e11i	−0.00552215	+	0.229341i
$235$		0			0
$236$	4.46142e10	−	9.25902e11i	0.0609415	−	1.26475i
$237$	2.00722e11			0.268444
$238$	2.49739e10	+	6.01330e8i	0.0327041	+	0.000787459i
$239$			1.11084e12i			1.42450i	0.701928	+	0.712248i	$0.252323\pi$
$239$			1.11084e12i			1.42450i	−0.701928	+	0.712248i	$0.747677\pi$
$240$		0			0
$241$	3.11125e11			0.382692			0.191346	−	0.981523i	$-0.438715\pi$
$241$	3.11125e11			0.382692			0.191346	+	0.981523i	$0.438715\pi$
$242$	−1.53149e9	+	6.36044e10i	−0.00184517	+	0.0766321i
$243$			7.22602e11i			0.852840i
$244$	−7.47199e11	−	3.60035e10i	−0.863947	−	0.0416289i
$245$		0			0
$246$	3.15213e10	+	7.58979e8i	0.0349887	+	0.000842469i
$247$		−	1.29842e11i		−	0.141231i
$248$	1.33831e12	+	9.68228e10i	1.42659	+	0.103209i
$249$	4.84095e11			0.505747
$250$		0			0
$251$			1.51632e12i			1.52203i	0.648737	+	0.761013i	$0.275298\pi$
$251$			1.51632e12i			1.52203i	−0.648737	+	0.761013i	$0.724702\pi$
$252$	−8.93942e8	+	1.85525e10i	−0.000879644	+	0.0182557i
$253$	1.29075e12			1.24520
$254$	6.51387e11	+	1.56843e10i	0.616128	+	0.0148353i
$255$		0			0
$256$	1.07918e12	+	2.10448e11i	0.981512	+	0.191401i
$257$	−1.58328e12			−1.41219			−0.706094	−	0.708118i	$-0.749544\pi$
$257$	−1.58328e12			−1.41219			−0.706094	+	0.708118i	$0.749544\pi$
$258$	−1.33116e10	+	5.52847e11i	−0.0116448	+	0.483623i
$259$		−	1.58852e10i		−	0.0136299i
$260$		0			0
$261$	−3.61226e11			−0.298247
$262$	1.17496e12	+	2.82910e10i	0.951735	+	0.0229162i
$263$		−	1.48239e12i		−	1.17810i	−0.808095	−	0.589052i	$-0.799501\pi$
$263$		−	1.48239e12i		−	1.17810i	0.808095	−	0.589052i	$-0.200499\pi$
$264$	−3.18323e10	+	4.39996e11i	−0.0248226	+	0.343106i
$265$		0			0
$266$	3.60690e8	−	1.49799e10i	0.000270848	−	0.0112486i
$267$			4.14874e11i			0.305745i
$268$	−2.79590e10	+	5.80249e11i	−0.0202231	+	0.419701i
$269$	−1.75617e12			−1.24682			−0.623411	−	0.781895i	$-0.714254\pi$
$269$	−1.75617e12			−1.24682			−0.623411	+	0.781895i	$0.714254\pi$
$270$		0			0
$271$		−	1.83455e12i		−	1.25512i	−0.778570	−	0.627558i	$-0.784055\pi$
$271$		−	1.83455e12i		−	1.25512i	0.778570	−	0.627558i	$-0.215945\pi$
$272$	−2.36094e12	−	2.28052e11i	−1.58577	−	0.153175i
$273$	−2.66062e9			−0.00175456
$274$	−3.03564e10	+	1.26074e12i	−0.0196561	+	0.816341i
$275$		0			0
$276$	6.36455e11	+	3.06673e10i	0.397395	+	0.0191483i
$277$	−5.98846e11			−0.367212			−0.183606	−	0.983000i	$-0.558777\pi$
$277$	−5.98846e11			−0.367212			−0.183606	+	0.983000i	$0.558777\pi$
$278$	6.83444e11	+	1.64562e10i	0.411603	+	0.00991071i
$279$		−	2.15222e12i		−	1.27311i
$280$		0			0
$281$	2.81093e12			1.60442			0.802211	−	0.597040i	$-0.203657\pi$
$281$	2.81093e12			1.60442			0.802211	+	0.597040i	$0.203657\pi$
$282$	−9.64289e9	+	4.00480e11i	−0.00540707	+	0.224562i
$283$			5.79586e11i			0.319290i	0.987174	+	0.159645i	$0.0510350\pi$
$283$			5.79586e11i			0.319290i	−0.987174	+	0.159645i	$0.948965\pi$
$284$	1.02313e11	−	2.12335e12i	0.0553781	−	1.14929i
$285$		0			0
$286$	5.11585e11	+	1.23181e10i	0.267355	+	0.00643745i
$287$		−	4.22094e9i		−	0.00216770i
$288$	2.11767e11	−	1.75082e12i	0.106880	−	0.883647i
$289$	3.10088e12			1.53814
$290$		0			0
$291$		−	4.84184e11i		−	0.232031i
$292$	−3.11692e12	−	1.50187e11i	−1.46829	−	0.0707489i
$293$	1.72641e12			0.799479			0.399739	−	0.916629i	$-0.369101\pi$
$293$	1.72641e12			0.799479			0.399739	+	0.916629i	$0.369101\pi$
$294$	7.27699e11	+	1.75218e10i	0.331295	+	0.00797703i
$295$		0			0
$296$	−1.08835e11	+	1.50435e12i	−0.0478971	+	0.662048i
$297$	1.50254e12			0.650196
$298$	6.50521e10	−	2.70169e12i	0.0276809	−	1.14962i
$299$		−	7.39150e11i		−	0.309298i
$300$		0			0
$301$	7.40305e10			0.0299625
$302$	4.39717e12	+	1.05876e11i	1.75040	+	0.0421468i
$303$			1.13795e12i			0.445564i
$304$	−1.36790e11	+	1.41614e12i	−0.0526850	+	0.545430i
$305$		0			0
$306$	−9.15794e10	+	3.80340e12i	−0.0341343	+	1.41764i
$307$		−	1.35975e12i		−	0.498616i	−0.968424	−	0.249308i	$-0.919797\pi$
$307$		−	1.35975e12i		−	0.498616i	0.968424	−	0.249308i	$-0.0802032\pi$
$308$	5.89872e10	+	2.84227e9i	0.0212816	+	0.00102544i
$309$	−1.05843e12			−0.375725
$310$		0			0
$311$		−	3.21142e11i		−	0.110381i	−0.998476	−	0.0551906i	$-0.982423\pi$
$311$		−	3.21142e11i		−	0.110381i	0.998476	−	0.0551906i	$-0.0175767\pi$
$312$	2.51964e11	+	1.82288e10i	0.0852248	+	0.00616574i
$313$	−2.93115e12			−0.975700			−0.487850	−	0.872927i	$-0.662219\pi$
$313$	−2.93115e12			−0.975700			−0.487850	+	0.872927i	$0.662219\pi$
$314$	1.29626e11	−	5.38351e12i	0.0424662	−	1.76367i
$315$		0			0
$316$	−1.22792e11	+	2.54837e12i	−0.0389704	+	0.808773i
$317$	2.71023e12			0.846663			0.423331	−	0.905975i	$-0.360861\pi$
$317$	2.71023e12			0.846663			0.423331	+	0.905975i	$0.360861\pi$
$318$	1.37197e11	+	3.30347e9i	0.0421899	+	0.00101586i
$319$			1.14851e12i			0.347682i
$320$		0			0
$321$	−1.49003e12			−0.437190
$322$	2.05329e9	−	8.52756e10i	0.000593159	−	0.0246346i
$323$		−	3.06921e12i		−	0.872999i
$324$	−2.43346e12	−	1.17255e11i	−0.681552	−	0.0328403i
$325$		0			0
$326$	−1.00744e12	−	2.42575e10i	−0.273610	−	0.00658807i
$327$		−	7.48821e11i		−	0.200281i
$328$	−2.89191e10	+	3.99729e11i	−0.00761756	+	0.105292i
$329$	5.36274e10			0.0139126
$330$		0			0
$331$		−	7.47010e12i		−	1.88012i	−0.341003	−	0.940062i	$-0.610767\pi$
$331$		−	7.47010e12i		−	1.88012i	0.341003	−	0.940062i	$-0.389233\pi$
$332$	−2.96145e11	+	6.14605e12i	−0.0734199	+	1.52372i
$333$	2.41923e12			0.590821
$334$	3.17319e12	+	7.64051e10i	0.763420	+	0.0183819i
$335$		0			0
$336$	2.90184e10	+	2.80299e9i	0.00677606	+	0.000654523i
$337$	−2.36492e12			−0.544085			−0.272043	−	0.962285i	$-0.587699\pi$
$337$	−2.36492e12			−0.544085			−0.272043	+	0.962285i	$0.587699\pi$
$338$	−9.91361e10	+	4.11723e12i	−0.0224723	+	0.933302i
$339$			2.28615e12i			0.510629i
$340$		0			0
$341$	−6.84295e12			−1.48413
$342$	2.28136e12	+	5.49312e10i	0.487599	+	0.0117406i
$343$		−	1.94930e11i		−	0.0410590i
$344$	−7.01079e12	−	5.07209e11i	−1.45537	−	0.105292i
$345$		0			0
$346$	−7.79658e9	+	3.23801e11i	−0.00157226	+	0.0652976i
$347$		−	8.77595e12i		−	1.74440i	−0.489147	−	0.872201i	$-0.662692\pi$
$347$		−	8.77595e12i		−	1.74440i	0.489147	−	0.872201i	$-0.337308\pi$
$348$	−2.72878e10	+	5.66319e11i	−0.00534654	+	0.110960i
$349$	−9.81518e11			−0.189571			−0.0947853	−	0.995498i	$-0.530216\pi$
$349$	−9.81518e11			−0.189571			−0.0947853	+	0.995498i	$0.530216\pi$
$350$		0			0
$351$		−	8.60433e11i		−	0.161503i
$352$	−5.56670e12	−	6.73309e11i	−1.03011	−	0.124595i
$353$	−8.89401e12			−1.62265			−0.811324	−	0.584597i	$-0.801253\pi$
$353$	−8.89401e12			−1.62265			−0.811324	+	0.584597i	$0.801253\pi$
$354$	−5.61758e10	+	2.33305e12i	−0.0101049	+	0.419669i
$355$		0			0
$356$	−5.26723e12	−	2.53799e11i	−0.921154	−	0.0443854i
$357$	−6.28916e10			−0.0108456
$358$	−9.37984e12	−	2.25851e11i	−1.59507	−	0.0384066i
$359$			8.74192e12i			1.46600i	0.680228	+	0.733001i	$0.261881\pi$
$359$			8.74192e12i			1.46600i	−0.680228	+	0.733001i	$0.738119\pi$
$360$		0			0
$361$	4.29009e12			0.699730
$362$	−2.29829e11	+	9.54508e12i	−0.0369711	+	1.53545i
$363$		−	1.60175e11i		−	0.0254133i
$364$	1.62763e9	−	3.37791e10i	0.000254712	−	0.00528618i
$365$		0			0
$366$	1.88276e12	+	4.53336e10i	0.286674	+	0.00690264i
$367$		−	1.06875e13i		−	1.60526i	−0.596478	−	0.802629i	$-0.703434\pi$
$367$		−	1.06875e13i		−	1.60526i	0.596478	−	0.802629i	$-0.296566\pi$
$368$	−7.78702e11	+	8.06165e12i	−0.115380	+	1.19450i
$369$	6.42827e11			0.0939642
$370$		0			0
$371$		−	1.83717e10i		−	0.00261385i
$372$	−3.37418e12	−	1.62584e11i	−0.473646	−	0.0228224i
$373$	−1.48573e12			−0.205776			−0.102888	−	0.994693i	$-0.532808\pi$
$373$	−1.48573e12			−0.205776			−0.102888	+	0.994693i	$0.532808\pi$
$374$	1.20928e13	+	2.91175e11i	1.65261	+	0.0397920i
$375$		0			0
$376$	−5.07859e12	−	3.67420e11i	−0.675778	−	0.0488904i
$377$	6.57698e11			0.0863614
$378$	2.39020e9	−	9.92679e10i	0.000309725	−	0.0128632i
$379$			4.09611e12i			0.523812i	0.965093	+	0.261906i	$0.0843511\pi$
$379$			4.09611e12i			0.523812i	−0.965093	+	0.261906i	$0.915649\pi$
$380$		0			0
$381$	−1.64038e12			−0.204325
$382$	1.44587e13	+	3.48141e11i	1.77751	+	0.0427995i
$383$			1.17512e12i			0.142590i	0.997455	+	0.0712951i	$0.0227132\pi$
$383$			1.17512e12i			0.142590i	−0.997455	+	0.0712951i	$0.977287\pi$
$384$	−2.72888e12	−	4.64262e11i	−0.326835	−	0.0556041i
$385$		0			0
$386$	−2.16995e11	+	9.01204e12i	−0.0253229	+	1.05169i
$387$			1.12745e13i			1.29880i
$388$	6.14719e12	+	2.96200e11i	0.699065	+	0.0336842i
$389$	−1.60662e12			−0.180370			−0.0901851	−	0.995925i	$-0.528746\pi$
$389$	−1.60662e12			−0.180370			−0.0901851	+	0.995925i	$0.528746\pi$
$390$		0			0
$391$		−	1.74720e13i		−	1.91187i
$392$	−6.67626e11	+	9.22813e12i	−0.0721278	+	0.996973i
$393$	−2.95889e12			−0.315621
$394$	1.08410e11	−	4.50237e12i	0.0114179	−	0.474199i
$395$		0			0
$396$	−4.32864e11	+	8.98345e12i	−0.0444503	+	0.922502i
$397$	6.57304e12			0.666521			0.333261	−	0.942835i	$-0.391851\pi$
$397$	6.57304e12			0.666521			0.333261	+	0.942835i	$0.391851\pi$
$398$	−1.58054e13	−	3.80567e11i	−1.58267	−	0.0381080i
$399$			3.77237e10i			0.00373035i
$400$		0			0
$401$	−1.11148e13			−1.07196			−0.535980	−	0.844231i	$-0.680058\pi$
$401$	−1.11148e13			−1.07196			−0.535980	+	0.844231i	$0.680058\pi$
$402$	3.52045e10	−	1.46208e12i	0.00335327	−	0.139265i
$403$			3.91863e12i			0.368645i
$404$	−1.44474e13	−	6.96142e11i	−1.34240	−	0.0646831i
$405$		0			0
$406$	7.58784e10	+	1.82702e9i	0.00687841	+	0.000165621i
$407$		−	7.69190e12i		−	0.688750i
$408$	5.95592e12	+	4.30892e11i	0.526803	+	0.0381125i
$409$	−1.05269e12			−0.0919783			−0.0459892	−	0.998942i	$-0.514644\pi$
$409$	−1.05269e12			−0.0919783			−0.0459892	+	0.998942i	$0.514644\pi$
$410$		0			0
$411$		−	3.17491e12i		−	0.270721i
$412$	6.47496e11	−	1.34378e13i	0.0545445	−	1.13199i
$413$	3.12413e11			0.0260003
$414$	1.29870e13	+	3.12706e11i	1.06784	+	0.0257119i
$415$		0			0
$416$	−3.85572e11	+	3.18778e12i	−0.0309484	+	0.255871i
$417$	−1.72111e12			−0.136499
$418$	1.74653e11	−	7.25353e12i	0.0136866	−	0.568418i
$419$		−	4.96270e12i		−	0.384280i	−0.981368	−	0.192140i	$-0.938457\pi$
$419$		−	4.96270e12i		−	0.384280i	0.981368	−	0.192140i	$-0.0615428\pi$
$420$		0			0
$421$	−4.69126e12			−0.354715			−0.177357	−	0.984147i	$-0.556755\pi$
$421$	−4.69126e12			−0.354715			−0.177357	+	0.984147i	$0.556755\pi$
$422$	1.20454e13	+	2.90032e11i	0.900031	+	0.0216712i
$423$			8.16717e12i			0.603073i
$424$	−1.25871e11	+	1.73983e12i	−0.00918537	+	0.126963i
$425$		0			0
$426$	−1.28827e11	+	5.35032e12i	−0.00918244	+	0.381357i
$427$		−	2.52116e11i		−	0.0177607i
$428$	9.11526e11	−	1.89174e13i	0.0634673	−	1.31717i
$429$	−1.28832e12			−0.0886620
$430$		0			0
$431$			9.67981e12i			0.650849i	0.945568	+	0.325425i	$0.105507\pi$
$431$			9.67981e12i			0.650849i	−0.945568	+	0.325425i	$0.894493\pi$
$432$	−9.06474e11	+	9.38443e12i	−0.0602472	+	0.623719i
$433$	1.28911e13			0.846936			0.423468	−	0.905911i	$-0.360813\pi$
$433$	1.28911e13			0.846936			0.423468	+	0.905911i	$0.360813\pi$
$434$	−1.08856e10	+	4.52091e11i	−0.000706974	+	0.0293614i
$435$		0			0
$436$	9.50701e12	+	4.58091e11i	0.603408	+	0.0290750i
$437$	−1.04801e13			−0.657593
$438$	7.85387e12	+	1.89108e11i	0.487207	+	0.0117311i
$439$		−	1.54725e13i		−	0.948936i	−0.880273	−	0.474468i	$-0.842640\pi$
$439$		−	1.54725e13i		−	0.948936i	0.880273	−	0.474468i	$-0.157360\pi$
$440$		0			0
$441$	1.48403e13			0.889712
$442$	1.66742e11	−	6.92498e12i	0.00988402	−	0.410495i
$443$		−	1.43716e13i		−	0.842340i	−0.906982	−	0.421170i	$-0.861620\pi$
$443$		−	1.43716e13i		−	0.842340i	0.906982	−	0.421170i	$-0.138380\pi$
$444$	1.82754e11	−	3.79279e12i	0.0105914	−	0.219808i
$445$		0			0
$446$	3.23970e12	+	7.80066e10i	0.183582	+	0.00442036i
$447$			6.80364e12i			0.381245i
$448$	−5.33387e10	+	3.66702e11i	−0.00295564	+	0.0203200i
$449$	1.18428e12			0.0648967			0.0324484	−	0.999473i	$-0.489670\pi$
$449$	1.18428e12			0.0648967			0.0324484	+	0.999473i	$0.489670\pi$
$450$		0			0
$451$		−	2.04386e12i		−	0.109539i
$452$	−2.90248e13	−	1.39855e12i	−1.53843	−	0.0741286i
$453$	−1.10734e13			−0.580481
$454$	2.12919e12	+	5.12674e10i	0.110392	+	0.00265804i
$455$		0			0
$456$	2.58458e11	−	3.57249e12i	0.0131089	−	0.181195i
$457$	−9.05816e12			−0.454422			−0.227211	−	0.973846i	$-0.572961\pi$
$457$	−9.05816e12			−0.454422			−0.227211	+	0.973846i	$0.572961\pi$
$458$	−2.75288e11	+	1.14330e13i	−0.0136603	+	0.567327i
$459$		−	2.03389e13i		−	0.998306i
$460$		0			0
$461$	3.36386e13			1.61560			0.807800	−	0.589457i	$-0.200658\pi$
$461$	3.36386e13			1.61560			0.807800	+	0.589457i	$0.200658\pi$
$462$	−1.48633e11	−	3.57884e9i	−0.00706165	−	0.000170033i
$463$		−	2.11734e13i		−	0.995143i	−0.867423	−	0.497572i	$-0.834225\pi$
$463$		−	2.11734e13i		−	0.995143i	0.867423	−	0.497572i	$-0.165775\pi$
$464$	−7.17327e12	−	6.92891e11i	−0.333524	−	0.0322162i
$465$		0			0
$466$	4.59977e11	−	1.91034e13i	0.0209318	−	0.869322i
$467$			1.26794e13i			0.570838i	0.958403	+	0.285419i	$0.0921328\pi$
$467$			1.26794e13i			0.570838i	−0.958403	+	0.285419i	$0.907867\pi$
$468$	5.14439e12	+	2.47880e11i	0.229142	+	0.0110411i
$469$	−1.95784e11			−0.00862807
$470$		0			0
$471$			1.35573e13i			0.584881i
$472$	−2.95859e13	−	2.14045e12i	−1.26292	−	0.0913681i
$473$	3.58470e13			1.51407
$474$	1.54613e11	−	6.42126e12i	0.00646181	−	0.268366i
$475$		0			0
$476$	3.84739e10	−	7.98470e11i	0.00157446	−	0.0326756i
$477$	2.79792e12			0.113303
$478$	3.55365e13	+	8.55660e11i	1.42408	+	0.0342895i
$479$			1.62583e13i			0.644760i	0.946610	+	0.322380i	$0.104483\pi$
$479$			1.62583e13i			0.644760i	−0.946610	+	0.322380i	$0.895517\pi$
$480$		0			0
$481$	−4.40478e12			−0.171080
$482$	2.39654e11	−	9.95311e12i	0.00921191	−	0.382581i
$483$			2.14749e11i			0.00816950i
$484$	2.03357e12	+	9.79868e10i	0.0765655	+	0.00368927i
$485$		0			0
$486$	2.31166e13	+	5.56608e11i	0.852593	+	0.0205290i
$487$		−	1.15134e13i		−	0.420300i	−0.977669	−	0.210150i	$-0.932605\pi$
$487$		−	1.15134e13i		−	0.420300i	0.977669	−	0.210150i	$-0.0673952\pi$
$488$	−1.72733e12	+	2.38757e13i	−0.0624132	+	0.862695i
$489$	2.53703e12			0.0907364
$490$		0			0
$491$			4.44463e13i			1.55750i	0.627334	+	0.778750i	$0.284146\pi$
$491$			4.44463e13i			1.55750i	−0.627334	+	0.778750i	$0.715854\pi$
$492$	4.85606e10	−	1.00780e12i	0.00168445	−	0.0349583i
$493$	1.55466e13			0.533829
$494$	−4.15375e12	−	1.00015e11i	−0.141190	−	0.00339963i
$495$		0			0
$496$	4.12831e12	−	4.27391e13i	0.137519	−	1.42369i
$497$	7.16449e11			0.0236267
$498$	3.72890e11	−	1.54865e13i	0.0121740	−	0.505601i
$499$			3.66572e13i			1.18483i	0.805633	+	0.592415i	$0.201825\pi$
$499$			3.66572e13i			1.18483i	−0.805633	+	0.592415i	$0.798175\pi$
$500$		0			0
$501$	−7.99102e12			−0.253171
$502$	4.85081e13	+	1.16799e12i	1.52158	+	0.0366372i
$503$			2.14439e13i			0.665983i	0.942930	+	0.332991i	$0.108058\pi$
$503$			2.14439e13i			0.665983i	−0.942930	+	0.332991i	$0.891942\pi$
$504$	5.92818e11	+	4.28885e10i	0.0182292	+	0.00131883i
$505$		0			0
$506$	9.94243e11	−	4.12920e13i	0.0299737	−	1.24484i
$507$		−	1.03684e13i		−	0.309508i
$508$	1.00351e12	−	2.08263e13i	0.0296620	−	0.615592i
$509$	2.89310e13			0.846788			0.423394	−	0.905946i	$-0.360839\pi$
$509$	2.89310e13			0.846788			0.423394	+	0.905946i	$0.360839\pi$
$510$		0			0
$511$		−	1.05169e12i		−	0.0301846i
$512$	7.56365e12	−	3.43618e13i	0.214972	−	0.976620i
$513$	−1.21997e13			−0.343370
$514$	−1.21957e12	+	5.06503e13i	−0.0339933	+	1.41178i
$515$		0			0
$516$	1.76757e13	+	8.51698e11i	0.483202	+	0.0232829i
$517$	2.59674e13			0.703033
$518$	−5.08178e11	−	1.22361e10i	−0.0136260	−	0.000328090i
$519$		−	8.15425e11i		−	0.0216545i
$520$		0			0
$521$	−4.43463e12			−0.115523			−0.0577616	−	0.998330i	$-0.518396\pi$
$521$	−4.43463e12			−0.115523			−0.0577616	+	0.998330i	$0.518396\pi$
$522$	−2.78246e11	+	1.15559e13i	−0.00717922	+	0.298161i
$523$			4.05278e13i			1.03573i	0.855464	+	0.517863i	$0.173272\pi$
$523$			4.05278e13i			1.03573i	−0.855464	+	0.517863i	$0.826728\pi$
$524$	1.81010e12	−	3.75660e13i	0.0458191	−	0.950907i
$525$		0			0
$526$	−4.74227e13	−	1.14186e12i	−1.17776	−	0.0283586i
$527$			9.26284e13i			2.27872i
$528$	1.40513e13	+	1.35726e12i	0.342409	+	0.0330745i
$529$	−1.82332e13			−0.440134
$530$		0			0
$531$			4.75788e13i			1.12704i
$532$	−4.78939e11	−	2.30775e10i	−0.0112389	−	0.000541539i
$533$	−1.17042e12			−0.0272085
$534$	1.32721e13	+	3.19570e11i	0.305657	+	0.00735970i
$535$		0			0
$536$	1.85410e13	+	1.34139e12i	0.419093	+	0.0303200i
$537$	2.36212e13			0.528969
$538$	−1.35275e12	+	5.61810e13i	−0.0300127	+	1.24646i
$539$		−	4.71844e13i		−	1.03718i
$540$		0			0
$541$	4.05839e13			0.875725			0.437863	−	0.899042i	$-0.355736\pi$
$541$	4.05839e13			0.875725			0.437863	+	0.899042i	$0.355736\pi$
$542$	−5.86887e13	−	1.41312e12i	−1.25475	−	0.0302123i
$543$		−	2.40373e13i		−	0.509198i
$544$	−9.11413e12	+	7.53527e13i	−0.191303	+	1.58163i
$545$		0			0
$546$	−2.04943e9	+	8.51151e10i	−4.22347e−5	+	0.00175406i
$547$			4.17118e13i			0.851769i	0.904777	+	0.425885i	$0.140037\pi$
$547$			4.17118e13i			0.851769i	−0.904777	+	0.425885i	$0.859963\pi$
$548$	4.03085e13	+	1.94225e12i	0.815632	+	0.0393009i
$549$	3.83959e13			0.769881
$550$		0			0
$551$		−	9.32520e12i		−	0.183612i
$552$	1.47132e12	−	2.03370e13i	0.0287086	−	0.396819i
$553$	−8.59855e11			−0.0166265
$554$	−4.61281e11	+	1.91575e13i	−0.00883928	+	0.367105i
$555$		0			0
$556$	1.05289e12	−	2.18512e13i	0.0198157	−	0.411245i
$557$	−9.55402e13			−1.78201			−0.891005	−	0.453994i	$-0.849999\pi$
$557$	−9.55402e13			−1.78201			−0.891005	+	0.453994i	$0.849999\pi$
$558$	−6.88511e13	−	1.65782e12i	−1.27274	−	0.0306455i
$559$		−	2.05278e13i		−	0.376083i
$560$		0			0
$561$	−3.04533e13			−0.548050
$562$	2.16521e12	−	8.99237e13i	0.0386206	−	1.60396i
$563$			4.37094e13i			0.772739i	0.922344	+	0.386369i	$0.126271\pi$
$563$			4.37094e13i			0.772739i	−0.922344	+	0.386369i	$0.873729\pi$
$564$	1.28042e13	+	6.16966e11i	0.224366	+	0.0108110i
$565$		0			0
$566$	1.85414e13	+	4.46445e11i	0.319198	+	0.00768574i
$567$		−	8.21084e11i		−	0.0140111i
$568$	−6.78488e13	−	4.90864e12i	−1.14763	−	0.0830271i
$569$	−1.14503e14			−1.91979			−0.959896	−	0.280356i	$-0.909548\pi$
$569$	−1.14503e14			−1.91979			−0.959896	+	0.280356i	$0.909548\pi$
$570$		0			0
$571$			5.05065e13i			0.832084i	0.909345	+	0.416042i	$0.136583\pi$
$571$			5.05065e13i			0.832084i	−0.909345	+	0.416042i	$0.863417\pi$
$572$	7.88131e11	−	1.63565e13i	0.0128712	−	0.267122i
$573$	−3.64113e13			−0.589471
$574$	−1.35031e11	−	3.25132e9i	−0.00216707	−	5.21795e-5i
$575$		0			0
$576$	−5.58469e13	−	8.12320e12i	−0.880818	−	0.128119i
$577$	3.55790e13			0.556308			0.278154	−	0.960537i	$-0.410278\pi$
$577$	3.55790e13			0.556308			0.278154	+	0.960537i	$0.410278\pi$
$578$	2.38856e12	−	9.91995e13i	0.0370251	−	1.53769i
$579$		−	2.26950e13i		−	0.348768i
$580$		0			0
$581$	−2.07377e12			−0.0313241
$582$	−1.54894e13	−	3.72959e11i	−0.231963	−	0.00558529i
$583$		−	8.89594e12i		−	0.132084i
$584$	−7.20552e12	+	9.95969e13i	−0.106072	+	1.46616i
$585$		0			0
$586$	1.32983e12	−	5.52292e13i	0.0192445	−	0.799247i
$587$			5.30294e13i			0.760897i	0.924802	+	0.380449i	$0.124230\pi$
$587$			5.30294e13i			0.760897i	−0.924802	+	0.380449i	$0.875770\pi$
$588$	1.12107e12	−	2.32661e13i	0.0159494	−	0.331007i
$589$	5.55604e13			0.783771
$590$		0			0
$591$			1.13383e13i			0.157257i
$592$	4.80414e13	+	4.64048e12i	0.660704	+	0.0638196i
$593$	−2.00349e13			−0.273221			−0.136610	−	0.990625i	$-0.543621\pi$
$593$	−2.00349e13			−0.273221			−0.136610	+	0.990625i	$0.543621\pi$
$594$	1.15738e12	−	4.80674e13i	0.0156511	−	0.650007i
$595$		0			0
$596$	−8.63789e13	−	4.16213e12i	−1.14862	−	0.0553457i
$597$	3.98026e13			0.524856
$598$	−2.36460e13	−	5.69355e11i	−0.309208	−	0.00744521i
$599$		−	6.78769e13i		−	0.880214i	−0.897945	−	0.440107i	$-0.854941\pi$
$599$		−	6.78769e13i		−	0.880214i	0.897945	−	0.440107i	$-0.145059\pi$
$600$		0			0
$601$	−1.12390e14			−1.43336			−0.716679	−	0.697403i	$-0.754339\pi$
$601$	−1.12390e14			−1.43336			−0.716679	+	0.697403i	$0.754339\pi$
$602$	5.70244e10	−	2.36829e12i	0.000721238	−	0.0299538i
$603$		−	2.98169e13i		−	0.374004i
$604$	6.77413e12	−	1.40587e14i	0.0842692	−	1.74888i
$605$		0			0
$606$	3.64039e13	+	8.76544e11i	0.445435	+	0.0107253i
$607$		−	5.32604e13i		−	0.646340i	−0.946341	−	0.323170i	$-0.895251\pi$
$607$		−	5.32604e13i		−	0.646340i	0.946341	−	0.323170i	$-0.104749\pi$
$608$	4.51981e13	+	5.46684e12i	0.544004	+	0.0657989i
$609$	−1.91084e11			−0.00228107
$610$		0			0
$611$		−	1.48703e13i		−	0.174628i
$612$	1.21603e14	+	5.85938e12i	1.41640	+	0.0682488i
$613$	−8.16071e13			−0.942813			−0.471407	−	0.881916i	$-0.656254\pi$
$613$	−8.16071e13			−0.942813			−0.471407	+	0.881916i	$0.656254\pi$
$614$	−4.34993e13	−	1.04739e12i	−0.498472	−	0.0120024i
$615$		0			0
$616$	1.36363e11	−	1.88485e12i	0.00153742	−	0.0212507i
$617$	9.91689e12			0.110905			0.0554523	−	0.998461i	$-0.482340\pi$
$617$	9.91689e12			0.110905			0.0554523	+	0.998461i	$0.482340\pi$
$618$	−8.15292e11	+	3.38600e13i	−0.00904421	+	0.375616i
$619$			4.79435e12i			0.0527565i	0.999652	+	0.0263783i	$0.00839743\pi$
$619$			4.79435e12i			0.0527565i	−0.999652	+	0.0263783i	$0.991603\pi$
$620$		0			0
$621$	−6.94489e13			−0.751982
$622$	−1.02736e13	−	2.47370e11i	−0.110349	−	0.00265703i
$623$		−	1.77724e12i		−	0.0189368i
$624$	7.77237e11	−	8.04648e12i	0.00821543	−	0.0850517i
$625$		0			0
$626$	−2.25782e12	+	9.37697e13i	−0.0234864	+	0.975418i
$627$			1.82665e13i			0.188503i
$628$	−1.72123e14	−	8.29366e12i	−1.76214	−	0.0849079i
$629$	−1.04120e14			−1.05750
$630$		0			0
$631$			7.60539e13i			0.760282i	0.924928	+	0.380141i	$0.124125\pi$
$631$			7.60539e13i			0.760282i	−0.924928	+	0.380141i	$0.875875\pi$
$632$	8.14295e13	+	5.89117e12i	0.807600	+	0.0584273i
$633$	−3.03337e13			−0.298474
$634$	2.08765e12	−	8.67023e13i	0.0203803	−	0.846417i
$635$		0			0
$636$	2.11361e11	−	4.38649e12i	0.00203114	−	0.0421533i
$637$	−2.70203e13			−0.257628
$638$	3.67417e13	+	8.84679e11i	0.347581	+	0.00836917i
$639$			1.09112e14i			1.02416i
$640$		0			0
$641$	1.81432e13			0.167657			0.0838287	−	0.996480i	$-0.473285\pi$
$641$	1.81432e13			0.167657			0.0838287	+	0.996480i	$0.473285\pi$
$642$	−1.14774e12	+	4.76672e13i	−0.0105237	+	0.437063i
$643$		−	1.38974e14i		−	1.26438i	−0.774812	−	0.632192i	$-0.782155\pi$
$643$		−	1.38974e14i		−	1.26438i	0.774812	−	0.632192i	$-0.217845\pi$
$644$	−2.72645e12	−	1.31373e11i	−0.0246132	−	0.00118598i
$645$		0			0
$646$	−9.81862e13	−	2.36416e12i	−0.872746	−	0.0210143i
$647$		−	1.35425e14i		−	1.19447i	−0.802065	−	0.597236i	$-0.796265\pi$
$647$		−	1.35425e14i		−	1.19447i	0.802065	−	0.597236i	$-0.203735\pi$
$648$	−5.62553e12	+	7.77578e13i	−0.0492366	+	0.680564i
$649$	1.51276e14			1.31385
$650$		0			0
$651$		−	1.13850e12i		−	0.00973704i
$652$	−1.55203e12	+	3.22101e13i	−0.0131723	+	0.273372i
$653$	6.82928e13			0.575187			0.287593	−	0.957753i	$-0.407145\pi$
$653$	6.82928e13			0.575187			0.287593	+	0.957753i	$0.407145\pi$
$654$	−2.39553e13	−	5.76804e11i	−0.200223	−	0.00482102i
$655$		0			0
$656$	1.27653e13	+	1.23305e12i	0.105078	+	0.0101499i
$657$	1.60168e14			1.30842
$658$	4.13083e10	−	1.71558e12i	0.000334894	−	0.0139085i
$659$			2.60660e13i			0.209724i	0.994487	+	0.104862i	$0.0334401\pi$
$659$			2.60660e13i			0.209724i	−0.994487	+	0.104862i	$0.966560\pi$
$660$		0			0
$661$	1.44276e14			1.14337			0.571686	−	0.820472i	$-0.306289\pi$
$661$	1.44276e14			1.14337			0.571686	+	0.820472i	$0.306289\pi$
$662$	−2.38974e14	−	5.75409e12i	−1.87958	−	0.0452571i
$663$			1.74391e13i			0.136131i
$664$	1.96389e14	+	1.42081e13i	1.52151	+	0.110077i
$665$		0			0
$666$	1.86349e12	−	7.73929e13i	0.0142219	−	0.590650i
$667$		−	5.30854e13i		−	0.402111i
$668$	4.88851e12	−	1.01454e14i	0.0367531	−	0.762757i
$669$	−8.15852e12			−0.0608809
$670$		0			0
$671$		−	1.22079e14i		−	0.897489i
$672$	1.12022e11	−	9.26161e11i	0.000817442	−	0.00675834i
$673$	−9.53562e13			−0.690675			−0.345337	−	0.938479i	$-0.612236\pi$
$673$	−9.53562e13			−0.690675			−0.345337	+	0.938479i	$0.612236\pi$
$674$	−1.82166e12	+	7.56555e13i	−0.0130969	+	0.543928i
$675$		0			0
$676$	1.31637e14	+	6.34287e12i	0.932490	+	0.0449316i
$677$	−1.36824e14			−0.962099			−0.481050	−	0.876693i	$-0.659744\pi$
$677$	−1.36824e14			−0.962099			−0.481050	+	0.876693i	$0.659744\pi$
$678$	7.31355e13	+	1.76098e12i	0.510481	+	0.0122915i
$679$			2.07415e12i			0.0143711i
$680$		0			0
$681$	−5.36193e12			−0.0366088
$682$	−5.27101e12	+	2.18911e14i	−0.0357250	+	1.48370i
$683$			9.14281e13i			0.615143i	0.951525	+	0.307572i	$0.0995164\pi$
$683$			9.14281e13i			0.615143i	−0.951525	+	0.307572i	$0.900484\pi$
$684$	3.51458e12	−	7.29399e13i	0.0234743	−	0.487175i
$685$		0			0
$686$	−6.23595e12	−	1.50151e11i	−0.0410471	−	0.000988345i
$687$		−	2.87917e13i		−	0.188141i
$688$	−2.16263e13	+	2.23890e14i	−0.140294	+	1.45242i
$689$	−5.09427e12			−0.0328085
$690$		0			0
$691$		−	8.12382e13i		−	0.515668i	−0.966189	−	0.257834i	$-0.916991\pi$
$691$		−	8.12382e13i		−	0.515668i	0.966189	−	0.257834i	$-0.0830088\pi$
$692$	1.03526e13	+	4.98836e11i	0.0652409	+	0.00314360i
$693$	−3.03114e12			−0.0189645
$694$	−2.80749e14	−	6.75996e12i	−1.74390	−	0.0419901i
$695$		0			0
$696$	1.80959e13	+	1.30918e12i	0.110799	+	0.00801593i
$697$	−2.76663e13			−0.168185
$698$	−7.56046e11	+	3.13995e13i	−0.00456322	+	0.189516i
$699$			4.81079e13i			0.288291i
$700$		0			0
$701$	1.02931e13			0.0608073			0.0304036	−	0.999538i	$-0.490321\pi$
$701$	1.02931e13			0.0608073			0.0304036	+	0.999538i	$0.490321\pi$
$702$	−2.75259e13	−	6.62777e11i	−0.161456	−	0.00388760i
$703$			6.24534e13i			0.363730i
$704$	−2.58276e13	+	1.77564e14i	−0.149355	+	1.02681i
$705$		0			0
$706$	−6.85091e12	+	2.84526e14i	−0.0390593	+	1.62218i
$707$		−	4.87476e12i		−	0.0275966i
$708$	7.45926e13	+	3.59421e12i	0.419304	+	0.0202040i
$709$	−6.64211e13			−0.370745			−0.185372	−	0.982668i	$-0.559349\pi$
$709$	−6.64211e13			−0.370745			−0.185372	+	0.982668i	$0.559349\pi$
$710$		0			0
$711$		−	1.30952e14i		−	0.720713i
$712$	−1.21765e13	+	1.68307e14i	−0.0665460	+	0.919819i
$713$	3.16288e14			1.71646
$714$	−4.84443e10	+	2.01195e12i	−0.000261067	+	0.0108424i
$715$		0			0
$716$	−1.44503e13	+	2.99894e14i	−0.0767910	+	1.59368i
$717$	−8.94914e13			−0.472265
$718$	2.79660e14	+	6.73375e12i	1.46558	+	0.0352886i
$719$			1.14349e14i			0.595097i	0.954707	+	0.297549i	$0.0961690\pi$
$719$			1.14349e14i			0.595097i	−0.954707	+	0.297549i	$0.903831\pi$
$720$		0			0
$721$	4.53411e12			0.0232711
$722$	3.30458e12	−	1.37243e14i	0.0168434	−	0.699527i
$723$			2.50648e13i			0.126874i
$724$	3.05177e14	+	1.47048e13i	1.53412	+	0.0739208i
$725$		0			0
$726$	−5.12410e12	−	1.23380e11i	−0.0254059	−	0.000611731i
$727$			6.85116e13i			0.337359i	0.985671	+	0.168680i	$0.0539503\pi$
$727$			6.85116e13i			0.337359i	−0.985671	+	0.168680i	$0.946050\pi$
$728$	−1.07937e12	−	7.80887e10i	−0.00527851	−	0.000381884i
$729$	8.22740e13			0.399600
$730$		0			0
$731$		−	4.85236e14i		−	2.32470i
$732$	2.90051e12	−	6.01959e13i	0.0138013	−	0.286425i
$733$	1.62363e14			0.767304			0.383652	−	0.923478i	$-0.374666\pi$
$733$	1.62363e14			0.767304			0.383652	+	0.923478i	$0.374666\pi$
$734$	−3.41900e14	−	8.23238e12i	−1.60479	−	0.0386407i
$735$		0			0
$736$	2.57298e14	+	3.11210e13i	1.19137	+	0.144100i
$737$	−9.48024e13			−0.435995
$738$	4.95159e11	−	2.05645e13i	0.00226184	−	0.0939369i
$739$			4.58877e13i			0.208197i	0.994567	+	0.104099i	$0.0331957\pi$
$739$			4.58877e13i			0.208197i	−0.994567	+	0.104099i	$0.966804\pi$
$740$		0			0
$741$	1.04604e13			0.0468226
$742$	−5.87725e11	−	1.41514e10i	−0.00261309	−	6.29188e-5i
$743$			1.13654e14i			0.501927i	0.967997	+	0.250963i	$0.0807473\pi$
$743$			1.13654e14i			0.501927i	−0.967997	+	0.250963i	$0.919253\pi$
$744$	−7.80024e12	+	1.07817e14i	−0.0342171	+	0.472959i
$745$		0			0
$746$	−1.14443e12	+	4.75295e13i	−0.00495331	+	0.205717i
$747$		−	3.15824e14i		−	1.35782i
$748$	1.86298e13	−	3.86634e14i	0.0795610	−	1.65117i
$749$	6.38300e12			0.0270779
$750$		0			0
$751$		−	6.48512e13i		−	0.271468i	−0.990745	−	0.135734i	$-0.956661\pi$
$751$		−	6.48512e13i		−	0.271468i	0.990745	−	0.135734i	$-0.0433392\pi$
$752$	−1.56660e13	+	1.62185e14i	−0.0651431	+	0.674405i
$753$	−1.22158e14			−0.504599
$754$	5.06613e11	−	2.10402e13i	0.00207883	−	0.0863363i
$755$		0			0
$756$	−3.17381e12	−	1.52929e11i	−0.0128520	−	0.000619270i
$757$	3.59034e14			1.44430			0.722148	−	0.691739i	$-0.243155\pi$
$757$	3.59034e14			1.44430			0.722148	+	0.691739i	$0.243155\pi$
$758$	1.31038e14	+	3.15517e12i	0.523661	+	0.0126089i
$759$			1.03985e14i			0.412823i
$760$		0			0
$761$	1.08335e14			0.424467			0.212233	−	0.977219i	$-0.431926\pi$
$761$	1.08335e14			0.424467			0.212233	+	0.977219i	$0.431926\pi$
$762$	−1.26356e12	+	5.24771e13i	−0.00491837	+	0.204265i
$763$			3.20780e12i			0.0124047i
$764$	2.22746e13	−	4.62277e14i	0.0855742	−	1.77597i
$765$		0			0
$766$	3.75931e13	+	9.05178e11i	0.142549	+	0.00343234i
$767$		−	8.66285e13i		−	0.326350i
$768$	−1.69541e13	+	8.69412e13i	−0.0634554	+	0.325402i
$769$	9.76902e13			0.363261			0.181631	−	0.983367i	$-0.441862\pi$
$769$	9.76902e13			0.363261			0.181631	+	0.983367i	$0.441862\pi$
$770$		0			0
$771$		−	1.27552e14i		−	0.468184i
$772$	2.88135e14	+	1.38836e13i	1.05077	+	0.0506311i
$773$	1.76068e14			0.637943			0.318972	−	0.947764i	$-0.396663\pi$
$773$	1.76068e14			0.637943			0.318972	+	0.947764i	$0.396663\pi$
$774$	3.60678e14	+	8.68453e12i	1.29842	+	0.0312638i
$775$		0			0
$776$	1.42107e13	−	1.96425e14i	0.0505019	−	0.698052i
$777$	1.27974e12			0.00451874
$778$	−1.23755e12	+	5.13969e13i	−0.00434175	+	0.180318i
$779$			1.65948e13i			0.0578476i
$780$		0			0
$781$	3.46918e14			1.19391
$782$	−5.58943e14	−	1.34584e13i	−1.91132	−	0.0460214i
$783$		−	6.17958e13i		−	0.209967i
$784$	2.94700e14	+	2.84661e13i	0.994948	+	0.0961054i
$785$		0			0
$786$	−2.27918e12	+	9.46570e13i	−0.00759742	+	0.315529i
$787$		−	1.51760e14i		−	0.502671i	−0.967900	−	0.251335i	$-0.919130\pi$
$787$		−	1.51760e14i		−	0.502671i	0.967900	−	0.251335i	$-0.0808697\pi$
$788$	−1.43951e14	−	6.93620e12i	−0.473786	−	0.0228292i
$789$	1.19424e14			0.390578
$790$		0			0
$791$		−	9.79340e12i		−	0.0316265i
$792$	2.87054e14	+	2.07674e13i	0.921164	+	0.0666433i
$793$	−6.99089e13			−0.222929
$794$	5.06310e12	−	2.10276e14i	0.0160441	−	0.666328i
$795$		0			0
$796$	−2.43493e13	+	5.05333e14i	−0.0761939	+	1.58129i
$797$	−4.10760e14			−1.27731			−0.638656	−	0.769493i	$-0.720509\pi$
$797$	−4.10760e14			−1.27731			−0.638656	+	0.769493i	$0.720509\pi$
$798$	1.20681e12	+	2.90579e10i	0.00372927	+	8.97945e-5i
$799$		−	3.51503e14i		−	1.07943i
$800$		0			0
$801$	2.70664e14			0.820859
$802$	−8.56152e12	+	3.55570e14i	−0.0258035	+	1.07165i
$803$		−	5.09250e14i		−	1.52529i
$804$	−4.67460e13	−	2.25244e12i	−0.139144	−	0.00670459i
$805$		0			0
$806$	1.25360e14	+	3.01845e12i	0.368539	+	0.00887379i
$807$		−	1.41480e14i		−	0.413360i
$808$	−3.33987e13	+	4.61647e14i	−0.0969778	+	1.34046i
$809$	−3.49456e14			−1.00844			−0.504220	−	0.863575i	$-0.668220\pi$
$809$	−3.49456e14			−1.00844			−0.504220	+	0.863575i	$0.668220\pi$
$810$		0			0
$811$			4.15248e14i			1.18360i	0.806086	+	0.591798i	$0.201582\pi$
$811$			4.15248e14i			1.18360i	−0.806086	+	0.591798i	$0.798418\pi$
$812$	1.16896e11	−	2.42600e12i	0.000331145	−	0.00687243i
$813$	1.47795e14			0.416110
$814$	−2.46069e14	−	5.92494e12i	−0.688550	−	0.0165791i
$815$		0			0
$816$	1.83723e13	−	1.90202e14i	0.0507823	−	0.525733i
$817$	−2.91055e14			−0.799584
$818$	−8.10872e11	+	3.36764e13i	−0.00221404	+	0.0919517i
$819$			1.73579e12i			0.00471062i
$820$		0			0
$821$	−6.64516e14			−1.78152			−0.890758	−	0.454478i	$-0.849826\pi$
$821$	−6.64516e14			−1.78152			−0.890758	+	0.454478i	$0.849826\pi$
$822$	−1.01568e14	−	2.44558e12i	−0.270642	−	0.00651662i
$823$		−	5.45678e14i		−	1.44523i	−0.691250	−	0.722615i	$-0.742940\pi$
$823$		−	5.45678e14i		−	1.44523i	0.691250	−	0.722615i	$-0.257060\pi$
$824$	−4.29387e14	−	3.10648e13i	−1.13035	−	0.0817772i
$825$		0			0
$826$	2.40646e11	−	9.99431e12i	0.000625862	−	0.0259928i
$827$		−	4.51590e13i		−	0.116739i	−0.998295	−	0.0583696i	$-0.981410\pi$
$827$		−	4.51590e13i		−	0.116739i	0.998295	−	0.0583696i	$-0.0185902\pi$
$828$	2.00074e13	−	4.15224e14i	0.0514089	−	1.06692i
$829$	3.08333e13			0.0787494			0.0393747	−	0.999225i	$-0.487463\pi$
$829$	3.08333e13			0.0787494			0.0393747	+	0.999225i	$0.487463\pi$
$830$		0			0
$831$		−	4.82443e13i		−	0.121742i
$832$	1.01682e14	+	1.47902e13i	0.255052	+	0.0370986i
$833$	−6.38704e14			−1.59248
$834$	−1.32574e12	+	5.50596e13i	−0.00328571	+	0.136459i
$835$		0			0
$836$	−2.31911e14	−	1.11745e13i	−0.567924	−	0.0273652i
$837$	3.68185e14			0.896271
$838$	−1.58760e14	−	3.82268e12i	−0.384169	−	0.00925014i
$839$			1.61246e14i			0.387863i	0.981015	+	0.193932i	$0.0621240\pi$
$839$			1.61246e14i			0.387863i	−0.981015	+	0.193932i	$0.937876\pi$
$840$		0			0
$841$	−3.73472e14			−0.887724
$842$	−3.61360e12	+	1.50077e14i	−0.00853846	+	0.354612i
$843$			2.26454e14i			0.531916i
$844$	1.85567e13	−	3.85116e14i	0.0433299	−	0.899248i
$845$		0			0
$846$	2.61274e14	+	6.29103e12i	0.602898	+	0.0145168i
$847$			6.86157e11i			0.00157401i
$848$	5.55614e13	+	5.36687e12i	0.126705	+	0.0122389i
$849$	−4.66926e13			−0.105855
$850$		0			0
$851$			3.55527e14i			0.796572i
$852$	1.71062e14	+	8.24253e12i	0.381026	+	0.0183596i
$853$	4.83432e14			1.07051			0.535254	−	0.844691i	$-0.320216\pi$
$853$	4.83432e14			1.07051			0.535254	+	0.844691i	$0.320216\pi$
$854$	−8.06536e12	−	1.94200e11i	−0.0177556	−	0.000427524i
$855$		0			0
$856$	−6.04479e14	−	4.37321e13i	−1.31526	−	0.0951550i
$857$	−3.50953e14			−0.759181			−0.379591	−	0.925155i	$-0.623935\pi$
$857$	−3.50953e14			−0.759181			−0.379591	+	0.925155i	$0.623935\pi$
$858$	−9.92372e11	+	4.12143e13i	−0.00213421	+	0.0886363i
$859$		−	2.20560e13i		−	0.0471586i	−0.999722	−	0.0235793i	$-0.992494\pi$
$859$		−	2.20560e13i		−	0.0471586i	0.999722	−	0.0235793i	$-0.00750622\pi$
$860$		0			0
$861$	3.40047e11			0.000718660
$862$	3.09664e14	+	7.45619e12i	0.650661	+	0.0156668i
$863$			4.34426e14i			0.907532i	0.891121	+	0.453766i	$0.149920\pi$
$863$			4.34426e14i			0.907532i	−0.891121	+	0.453766i	$0.850080\pi$
$864$	2.99517e14	+	3.62274e13i	0.622088	+	0.0752435i
$865$		0			0
$866$	9.92979e12	−	4.12396e14i	0.0203869	−	0.846690i
$867$			2.49813e14i			0.509941i
$868$	1.44543e13	+	6.96476e11i	0.0293359	+	0.00141354i
$869$	−4.16358e14			−0.840172
$870$		0			0
$871$			5.42888e13i			0.108298i
$872$	2.19778e13	−	3.03783e14i	0.0435914	−	0.602534i
$873$	−3.15882e14			−0.622951
$874$	−8.07262e12	+	3.35265e14i	−0.0158291	+	0.657403i
$875$		0			0
$876$	1.20994e13	−	2.51105e14i	0.0234554	−	0.486783i
$877$	7.88973e14			1.52077			0.760386	−	0.649471i	$-0.225010\pi$
$877$	7.88973e14			1.52077			0.760386	+	0.649471i	$0.225010\pi$
$878$	−4.94976e14	−	1.19182e13i	−0.948661	−	0.0228422i
$879$			1.39083e14i			0.265052i
$880$		0			0
$881$	−1.58307e14			−0.298277			−0.149139	−	0.988816i	$-0.547650\pi$
$881$	−1.58307e14			−0.298277			−0.149139	+	0.988816i	$0.547650\pi$
$882$	1.14312e13	−	4.74752e14i	0.0214166	−	0.889454i
$883$			8.37422e14i			1.56006i	0.625743	+	0.780029i	$0.284796\pi$
$883$			8.37422e14i			1.56006i	−0.625743	+	0.780029i	$0.715204\pi$
$884$	−2.21407e14	−	1.06684e13i	−0.410138	−	0.0197623i
$885$		0			0
$886$	−4.59759e14	−	1.10702e13i	−0.842096	−	0.0202763i
$887$			1.81020e14i			0.329692i	0.986319	+	0.164846i	$0.0527127\pi$
$887$			1.81020e14i			0.329692i	−0.986319	+	0.164846i	$0.947287\pi$
$888$	−1.21193e14	−	8.76795e12i	−0.219490	−	0.0158794i
$889$	7.02708e12			0.0126551
$890$		0			0
$891$		−	3.97584e14i		−	0.708012i
$892$	4.99098e12	−	1.03580e14i	0.00883815	−	0.183423i
$893$	−2.10839e14			−0.371273
$894$	2.17653e14	+	5.24073e12i	0.381134	+	0.00917707i
$895$		0			0
$896$	1.16900e13	+	1.98881e12i	0.0202430	+	0.00344392i
$897$	5.95475e13			0.102542
$898$	9.12231e11	−	3.78860e13i	0.00156215	−	0.0648779i
$899$			2.81434e14i			0.479267i
$900$		0			0
$901$	−1.20418e14			−0.202800
$902$	−6.53845e13	−	1.57435e12i	−0.109507	−	0.00263675i
$903$			5.96405e12i			0.00993350i
$904$	−6.70980e13	+	9.27449e14i	−0.111139	+	1.53620i
$905$		0			0
$906$	−8.52962e12	+	3.54245e14i	−0.0139730	+	0.580313i
$907$			9.90432e14i			1.61357i	0.590844	+	0.806786i	$0.298795\pi$
$907$			9.90432e14i			1.61357i	−0.590844	+	0.806786i	$0.701205\pi$
$908$	3.28016e12	−	6.80750e13i	0.00531455	−	0.110296i
$909$	7.42401e14			1.19624
$910$		0			0
$911$			2.52110e14i			0.401788i	0.979613	+	0.200894i	$0.0643847\pi$
$911$			2.52110e14i			0.401788i	−0.979613	+	0.200894i	$0.935615\pi$
$912$	−1.14087e14	−	1.10201e13i	−0.180827	−	0.0174667i
$913$	−1.00416e15			−1.58288
$914$	−6.97735e12	+	2.89777e14i	−0.0109385	+	0.454290i
$915$		0			0
$916$	3.65539e14	+	1.76133e13i	0.566834	+	0.0273127i
$917$	1.26753e13			0.0195484
$918$	−6.50656e14	−	1.56667e13i	−0.998017	−	0.0240306i
$919$		−	6.58794e14i		−	1.00501i	−0.864573	−	0.502507i	$-0.832411\pi$
$919$		−	6.58794e14i		−	1.00501i	0.864573	−	0.502507i	$-0.167589\pi$
$920$		0			0
$921$	1.09544e14			0.165307
$922$	2.59113e13	−	1.07612e15i	0.0388897	−	1.61513i
$923$		−	1.98663e14i		−	0.296558i
$924$	−2.28979e11	+	4.75213e12i	−0.000339967	+	0.00705551i
$925$		0			0
$926$	−6.77352e14	−	1.63095e13i	−0.994855	−	0.0239544i
$927$			6.90522e14i			1.00874i
$928$	−2.76915e13	+	2.28945e14i	−0.0402353	+	0.332652i
$929$	3.95978e14			0.572259			0.286129	−	0.958191i	$-0.407631\pi$
$929$	3.95978e14			0.572259			0.286129	+	0.958191i	$0.407631\pi$
$930$		0			0
$931$			3.83108e14i			0.547738i
$932$	−6.10777e14	−	2.94300e13i	−0.868566	−	0.0418515i
$933$	2.58719e13			0.0365948
$934$	4.05622e14	+	9.76669e12i	0.570673	+	0.0137408i
$935$		0			0
$936$	1.18925e13	−	1.64382e14i	0.0165537	−	0.228810i
$937$	6.67632e14			0.924356			0.462178	−	0.886787i	$-0.347068\pi$
$937$	6.67632e14			0.924356			0.462178	+	0.886787i	$0.347068\pi$
$938$	−1.50809e11	+	6.26328e12i	−0.000207689	+	0.00862557i
$939$		−	2.36139e14i		−	0.323475i
$940$		0			0
$941$	5.42638e14			0.735465			0.367733	−	0.929932i	$-0.380134\pi$
$941$	5.42638e14			0.735465			0.367733	+	0.929932i	$0.380134\pi$
$942$	4.33707e14	+	1.04429e13i	0.584711	+	0.0140789i
$943$			9.44691e13i			0.126687i
$944$	−9.12640e13	+	9.44826e14i	−0.121742	+	1.26035i
$945$		0			0
$946$	2.76123e13	−	1.14677e15i	0.0364457	−	1.51363i
$947$		−	8.96999e14i		−	1.17772i	−0.808235	−	0.588860i	$-0.799577\pi$
$947$		−	8.96999e14i		−	1.17772i	0.808235	−	0.588860i	$-0.200423\pi$
$948$	−2.05302e14	−	9.89237e12i	−0.268133	−	0.0129199i
$949$	−2.91623e14			−0.378870
$950$		0			0
$951$			2.18342e14i			0.280695i
$952$	−2.55140e13	−	1.84586e12i	−0.0326283	−	0.00236055i
$953$	6.68742e13			0.0850735			0.0425368	−	0.999095i	$-0.486456\pi$
$953$	6.68742e13			0.0850735			0.0425368	+	0.999095i	$0.486456\pi$
$954$	2.15519e12	−	8.95075e13i	0.00272737	−	0.113271i
$955$		0			0
$956$	5.47464e13	−	1.13618e15i	0.0685592	−	1.42285i
$957$	−9.25265e13			−0.115267
$958$	5.20116e14	+	1.25235e13i	0.644573	+	0.0155202i
$959$			1.36007e13i			0.0167675i
$960$		0			0
$961$	−8.57181e14			−1.04582
$962$	−3.39293e12	+	1.40912e14i	−0.00411812	+	0.171030i
$963$			9.72098e14i			1.17376i
$964$	−3.18223e14	−	1.53334e13i	−0.382249	−	0.0184185i
$965$		0			0
$966$	6.86997e12	+	1.65417e11i	0.00816713	+	0.000196651i
$967$			1.09537e15i			1.29547i	0.761865	+	0.647735i	$0.224284\pi$
$967$			1.09537e15i			1.29547i	−0.761865	+	0.647735i	$0.775716\pi$
$968$	4.70110e12	−	6.49800e13i	0.00553124	−	0.0764545i
$969$	2.47262e14			0.289426
$970$		0			0
$971$			8.64271e14i			1.00128i	0.865657	+	0.500638i	$0.166901\pi$
$971$			8.64271e14i			1.00128i	−0.865657	+	0.500638i	$0.833099\pi$
$972$	3.56126e13	−	7.39087e14i	0.0410461	−	0.851852i
$973$	7.37290e12			0.00845424
$974$	−3.68322e14	−	8.86858e12i	−0.420178	−	0.0101172i
$975$		0			0
$976$	7.62471e14	+	7.36497e13i	0.860943	+	0.0831614i
$977$	−9.80844e14			−1.10186			−0.550931	−	0.834551i	$-0.685727\pi$
$977$	−9.80844e14			−1.10186			−0.550931	+	0.834551i	$0.685727\pi$
$978$	1.95423e12	−	8.11615e13i	0.00218415	−	0.0907102i
$979$		−	8.60572e14i		−	0.956916i
$980$		0			0
$981$	−4.88531e14			−0.537709
$982$	1.42187e15	+	3.42362e13i	1.55705	+	0.0374911i
$983$		−	3.16524e14i		−	0.344858i	−0.985022	−	0.172429i	$-0.944839\pi$
$983$		−	3.16524e14i		−	0.344858i	0.985022	−	0.172429i	$-0.0551615\pi$
$984$	−3.22030e13	−	2.32978e12i	−0.0349076	−	0.00252546i
$985$		0			0
$986$	1.19753e13	−	4.97348e14i	0.0128500	−	0.533674i
$987$			4.32033e12i			0.00461244i
$988$	−6.39912e12	+	1.32804e14i	−0.00679729	+	0.141068i
$989$	−1.65688e15			−1.75110
$990$		0			0
$991$			1.51439e15i			1.58442i	0.610251	+	0.792208i	$0.291068\pi$
$991$			1.51439e15i			1.58442i	−0.610251	+	0.792208i	$0.708932\pi$
$992$	−1.36407e15	−	1.64989e14i	−1.41997	−	0.171750i
$993$	6.01807e14			0.623319
$994$	5.51869e11	−	2.29197e13i	0.000568727	−	0.0236199i
$995$		0			0
$996$	−4.95139e14	−	2.38580e13i	−0.505161	−	0.0243410i
$997$	−4.03612e14			−0.409721			−0.204861	−	0.978791i	$-0.565674\pi$
$997$	−4.03612e14			−0.409721			−0.204861	+	0.978791i	$0.565674\pi$
$998$	1.17269e15	+	2.82364e13i	1.18449	+	0.0285205i
$999$			4.13863e14i			0.415939i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	100.11.b.e.51.11		20
4.3	odd	2	inner	100.11.b.e.51.12		20
5.2	odd	4		100.11.d.c.99.40		40
5.3	odd	4		100.11.d.c.99.1		40
5.4	even	2		20.11.b.a.11.10	yes	20
15.14	odd	2		180.11.c.a.91.11		20
20.3	even	4		100.11.d.c.99.39		40
20.7	even	4		100.11.d.c.99.2		40
20.19	odd	2		20.11.b.a.11.9	✓	20
40.19	odd	2		320.11.b.d.191.9		20
40.29	even	2		320.11.b.d.191.12		20
60.59	even	2		180.11.c.a.91.12		20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
20.11.b.a.11.9	✓	20	20.19	odd	2
20.11.b.a.11.10	yes	20	5.4	even	2
100.11.b.e.51.11		20	1.1	even	1	trivial
100.11.b.e.51.12		20	4.3	odd	2	inner
100.11.d.c.99.1		40	5.3	odd	4
100.11.d.c.99.2		40	20.7	even	4
100.11.d.c.99.39		40	20.3	even	4
100.11.d.c.99.40		40	5.2	odd	4
180.11.c.a.91.11		20	15.14	odd	2
180.11.c.a.91.12		20	60.59	even	2
320.11.b.d.191.9		20	40.19	odd	2
320.11.b.d.191.12		20	40.29	even	2

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:	\( N \)	\(=\)	\( 100 = 2^{2} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 11 \)
Character orbit:	\([\chi]\)	\(=\)	100.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(0.770283 - 31.9907i) q^{2} +80.5620i q^{3} +(-1022.81 - 49.2838i) q^{4} +(2577.24 + 62.0555i) q^{6} -345.112i q^{7} +(-2364.48 + 32682.6i) q^{8} +52558.8 q^{9} +O(q^{10})\)	\(q+(0.770283 - 31.9907i) q^{2} +80.5620i q^{3} +(-1022.81 - 49.2838i) q^{4} +(2577.24 + 62.0555i) q^{6} -345.112i q^{7} +(-2364.48 + 32682.6i) q^{8} +52558.8 q^{9} -167110. i q^{11} +(3970.40 - 82399.9i) q^{12} -95695.6 q^{13} +(-11040.4 - 265.834i) q^{14} +(1.04372e6 + 100816. i) q^{16} -2.26205e6 q^{17} +(40485.1 - 1.68139e6i) q^{18} +1.35682e6i q^{19} +27802.9 q^{21} +(-5.34596e6 - 128722. i) q^{22} +7.72397e6i q^{23} +(-2.63297e6 - 190487. i) q^{24} +(-73712.7 + 3.06137e6i) q^{26} +8.99135e6i q^{27} +(-17008.4 + 352985. i) q^{28} -6.87281e6 q^{29} -4.09489e7i q^{31} +(4.02915e6 - 3.33116e7i) q^{32} +1.34627e7 q^{33} +(-1.74242e6 + 7.23647e7i) q^{34} +(-5.37578e7 - 2.59030e6i) q^{36} +4.60291e7 q^{37} +(4.34058e7 + 1.04514e6i) q^{38} -7.70943e6i q^{39} +1.22306e7 q^{41} +(21416.1 - 889435. i) q^{42} +2.14512e8i q^{43} +(-8.23580e6 + 1.70922e8i) q^{44} +(2.47095e8 + 5.94964e6i) q^{46} +1.55391e8i q^{47} +(-8.12196e6 + 8.40840e7i) q^{48} +2.82356e8 q^{49} -1.82235e8i q^{51} +(9.78788e7 + 4.71625e6i) q^{52} +5.32341e7 q^{53} +(2.87640e8 + 6.92588e6i) q^{54} +(1.12791e7 + 816010. i) q^{56} -1.09309e8 q^{57} +(-5.29401e6 + 2.19866e8i) q^{58} +9.05250e8i q^{59} +7.30533e8 q^{61} +(-1.30998e9 - 3.15422e7i) q^{62} -1.81387e7i q^{63} +(-1.06256e9 - 1.54555e8i) q^{64} +(1.03701e7 - 4.30681e8i) q^{66} -5.67307e8i q^{67} +(2.31366e9 + 1.11483e8i) q^{68} -6.22259e8 q^{69} +2.07599e9i q^{71} +(-1.24274e8 + 1.71776e9i) q^{72} +3.04740e9 q^{73} +(3.54554e7 - 1.47250e9i) q^{74} +(6.68695e7 - 1.38778e9i) q^{76} -5.76715e7 q^{77} +(-2.46630e8 - 5.93845e6i) q^{78} -2.49153e9i q^{79} +2.37918e9 q^{81} +(9.42105e6 - 3.91267e8i) q^{82} -6.00897e9i q^{83} +(-2.84372e7 - 1.37023e6i) q^{84} +(6.86238e9 + 1.65235e8i) q^{86} -5.53687e8i q^{87} +(5.46157e9 + 3.95128e8i) q^{88} +5.14975e9 q^{89} +3.30257e7i q^{91} +(3.80667e8 - 7.90018e9i) q^{92} +3.29892e9 q^{93} +(4.97108e9 + 1.19695e8i) q^{94} +(2.68365e9 + 3.24596e8i) q^{96} -6.01008e9 q^{97} +(2.17494e8 - 9.03278e9i) q^{98} -8.78308e9i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q - 22 q^{2} - 644 q^{4} - 14784 q^{6} - 3448 q^{8} - 414868 q^{9}+O(q^{10}) \) 20 * q - 22 * q^2 - 644 * q^4 - 14784 * q^6 - 3448 * q^8 - 414868 * q^9	\( 20 q - 22 q^{2} - 644 q^{4} - 14784 q^{6} - 3448 q^{8} - 414868 q^{9} - 1329640 q^{12} + 278864 q^{13} - 2240504 q^{14} + 4261360 q^{16} + 1921656 q^{17} + 3556082 q^{18} + 4157512 q^{21} + 5811280 q^{22} - 19112144 q^{24} + 25066884 q^{26} + 87415400 q^{28} - 66014888 q^{29} + 33171328 q^{32} - 85980560 q^{33} - 27236084 q^{34} + 355456476 q^{36} + 153620656 q^{37} - 250352720 q^{38} + 477406160 q^{41} + 570662040 q^{42} + 339141040 q^{44} - 897549304 q^{46} + 479727360 q^{48} + 333772012 q^{49} + 110465096 q^{52} + 1669491824 q^{53} + 706139792 q^{54} - 1362290224 q^{56} - 3973032960 q^{57} - 2075027916 q^{58} - 4283166080 q^{61} - 1664032240 q^{62} + 340459456 q^{64} + 1884031760 q^{66} - 3042411896 q^{68} - 5321669928 q^{69} - 1632326712 q^{72} - 2474287656 q^{73} + 188682276 q^{74} + 2323171200 q^{76} - 410885040 q^{77} + 19914223760 q^{78} + 9939722652 q^{81} + 3197757116 q^{82} + 2383099552 q^{84} + 19648321456 q^{86} - 2774318240 q^{88} + 3011851592 q^{89} + 27349072440 q^{92} + 11861394640 q^{93} + 15684681576 q^{94} - 1990377984 q^{96} + 39984502056 q^{97} - 38416891998 q^{98}+O(q^{100}) \) 20 * q - 22 * q^2 - 644 * q^4 - 14784 * q^6 - 3448 * q^8 - 414868 * q^9 - 1329640 * q^12 + 278864 * q^13 - 2240504 * q^14 + 4261360 * q^16 + 1921656 * q^17 + 3556082 * q^18 + 4157512 * q^21 + 5811280 * q^22 - 19112144 * q^24 + 25066884 * q^26 + 87415400 * q^28 - 66014888 * q^29 + 33171328 * q^32 - 85980560 * q^33 - 27236084 * q^34 + 355456476 * q^36 + 153620656 * q^37 - 250352720 * q^38 + 477406160 * q^41 + 570662040 * q^42 + 339141040 * q^44 - 897549304 * q^46 + 479727360 * q^48 + 333772012 * q^49 + 110465096 * q^52 + 1669491824 * q^53 + 706139792 * q^54 - 1362290224 * q^56 - 3973032960 * q^57 - 2075027916 * q^58 - 4283166080 * q^61 - 1664032240 * q^62 + 340459456 * q^64 + 1884031760 * q^66 - 3042411896 * q^68 - 5321669928 * q^69 - 1632326712 * q^72 - 2474287656 * q^73 + 188682276 * q^74 + 2323171200 * q^76 - 410885040 * q^77 + 19914223760 * q^78 + 9939722652 * q^81 + 3197757116 * q^82 + 2383099552 * q^84 + 19648321456 * q^86 - 2774318240 * q^88 + 3011851592 * q^89 + 27349072440 * q^92 + 11861394640 * q^93 + 15684681576 * q^94 - 1990377984 * q^96 + 39984502056 * q^97 - 38416891998 * q^98

Introduction

L-functions

Modular forms

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