LMFDB - Embedded newform 21.30.c.a.20.16

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [21,30,Mod(20,21)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(21, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 30, names="a")

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

chi := DirichletCharacter("21.20");

S:= CuspForms(chi, 30);

N := Newforms(S);

Level:	$ N $	$=$	$ 21 = 3 \cdot 7 $
Weight:	$ k $	$=$	$ 30 $
Character orbit:	$[\chi]$	$=$	21.c (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:	$111.883889004$
Analytic rank:	$0$
Dimension:	$76$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			20.16
Character	$\chi$	$=$	21.20
Dual form			21.30.c.a.20.15

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+18452.1i q^{2} +(-2.07416e6 - 8.02049e6i) q^{3} +1.96390e8 q^{4} +1.42232e10 q^{5} +(1.47995e11 - 3.82726e10i) q^{6} +(-7.69210e11 - 1.62118e12i) q^{7} +1.35302e13i q^{8} +(-6.00261e13 + 3.32715e13i) q^{9} +O(q^{10})$	\(q+18452.1i q^{2} +(-2.07416e6 - 8.02049e6i) q^{3} +1.96390e8 q^{4} +1.42232e10 q^{5} +(1.47995e11 - 3.82726e10i) q^{6} +(-7.69210e11 - 1.62118e12i) q^{7} +1.35302e13i q^{8} +(-6.00261e13 + 3.32715e13i) q^{9} +2.62448e14i q^{10} -5.94684e14i q^{11} +(-4.07344e14 - 1.57515e15i) q^{12} -8.49314e15i q^{13} +(2.99142e16 - 1.41935e16i) q^{14} +(-2.95012e16 - 1.14077e17i) q^{15} -1.44225e17 q^{16} +5.80016e17 q^{17} +(-6.13930e17 - 1.10761e18i) q^{18} +6.04886e18i q^{19} +2.79330e18 q^{20} +(-1.14072e19 + 9.53202e18i) q^{21} +1.09732e19 q^{22} +9.96781e19i q^{23} +(1.08519e20 - 2.80638e19i) q^{24} +1.60352e19 q^{25} +1.56716e20 q^{26} +(3.91358e20 + 4.12428e20i) q^{27} +(-1.51065e20 - 3.18384e20i) q^{28} -2.86579e20i q^{29} +(2.10496e21 - 5.44359e20i) q^{30} +8.36937e20i q^{31} +4.60272e21i q^{32} +(-4.76966e21 + 1.23347e21i) q^{33} +1.07025e22i q^{34} +(-1.09406e22 - 2.30584e22i) q^{35} +(-1.17885e22 + 6.53420e21i) q^{36} +8.80010e21 q^{37} -1.11614e23 q^{38} +(-6.81191e22 + 1.76161e22i) q^{39} +1.92443e23i q^{40} +2.50655e23 q^{41} +(-1.75886e23 - 2.10487e23i) q^{42} +5.32643e23 q^{43} -1.16790e23i q^{44} +(-8.53764e23 + 4.73228e23i) q^{45} -1.83927e24 q^{46} +5.56873e23 q^{47} +(2.99146e23 + 1.15676e24i) q^{48} +(-2.03654e24 + 2.49405e24i) q^{49} +2.95884e23i q^{50} +(-1.20305e24 - 4.65201e24i) q^{51} -1.66797e24i q^{52} +1.36208e24i q^{53} +(-7.61018e24 + 7.22138e24i) q^{54} -8.45832e24i q^{55} +(2.19349e25 - 1.04076e25i) q^{56} +(4.85149e25 - 1.25463e25i) q^{57} +5.28799e24 q^{58} +9.64829e24 q^{59} +(-5.79374e24 - 2.24036e25i) q^{60} -9.57504e25i q^{61} -1.54433e25 q^{62} +(1.00112e26 + 7.17203e25i) q^{63} -1.62360e26 q^{64} -1.20800e26i q^{65} +(-2.27601e25 - 8.80103e25i) q^{66} +3.55994e26 q^{67} +1.13910e26 q^{68} +(7.99467e26 - 2.06748e26i) q^{69} +(4.25476e26 - 2.01878e26i) q^{70} -3.70662e26i q^{71} +(-4.50171e26 - 8.12167e26i) q^{72} +7.35668e26i q^{73} +1.62380e26i q^{74} +(-3.32596e25 - 1.28610e26i) q^{75} +1.18794e27i q^{76} +(-9.64090e26 + 4.57437e26i) q^{77} +(-3.25055e26 - 1.25694e27i) q^{78} -3.26329e27 q^{79} -2.05134e27 q^{80} +(2.49614e27 - 3.99432e27i) q^{81} +4.62511e27i q^{82} -5.72323e27 q^{83} +(-2.24026e27 + 1.87200e27i) q^{84} +8.24969e27 q^{85} +9.82840e27i q^{86} +(-2.29850e27 + 5.94410e26i) q^{87} +8.04621e27 q^{88} +2.49217e28 q^{89} +(-8.73206e27 - 1.57538e28i) q^{90} +(-1.37689e28 + 6.53301e27i) q^{91} +1.95758e28i q^{92} +(6.71265e27 - 1.73594e27i) q^{93} +1.02755e28i q^{94} +8.60343e28i q^{95} +(3.69161e28 - 9.54678e27i) q^{96} -5.99578e28i q^{97} +(-4.60206e28 - 3.75785e28i) q^{98} +(1.97860e28 + 3.56966e28i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 76 q - 20401094660 q^{4} + 1962751543872 q^{7} - 89581451225964 q^{9}+O(q^{10}) $ 76 * q - 20401094660 * q^4 + 1962751543872 * q^7 - 89581451225964 * q^9	$ 76 q - 20401094660 q^{4} + 1962751543872 q^{7} - 89581451225964 q^{9} - 11\!\cdots\!48 q^{15}+ \cdots - 23\!\cdots\!24 q^{99}+O(q^{100}) $ 76 * q - 20401094660 * q^4 + 1962751543872 * q^7 - 89581451225964 * q^9 - 116668222909200048 * q^15 + 4964525139713333892 * q^16 + 1542346202347854996 * q^18 + 33840646982361357348 * q^21 - 9870996616978150672 * q^22 + 3225406746743103424612 * q^25 - 3181907581338093199564 * q^28 + 5113912044496410095244 * q^30 - 85758641407134848258352 * q^36 - 17812771227715200149976 * q^37 + 388095283792424641491696 * q^39 + 804036587819434104664956 * q^42 + 2391536152977907871782320 * q^43 - 1070985628070611677307000 * q^46 - 512656982878691867441540 * q^49 - 961431915936904000664400 * q^51 + 20345422731681279280765248 * q^57 - 40096240109469024574169272 * q^58 - 164991837955115951799442596 * q^60 - 360764839802574990409097184 * q^63 - 1608343949909674725081473028 * q^64 + 483978610969894046870693264 * q^67 - 656026306765550013508448520 * q^70 + 1937172856654554597960695124 * q^72 - 8054141680325499868559088636 * q^78 - 11740735193468750125742145952 * q^79 + 18477545939654446572971367132 * q^81 - 7249045143271847568431965452 * q^84 + 14576359553686844022629140848 * q^85 - 1685535263940707754634995584 * q^88 + 44135166284535829618726469040 * q^91 + 226499776928895503792863540632 * q^93 - 231093384978708762520959066624 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/21\mathbb{Z}\right)^\times$.

$n$	$8$	$10$
$\chi(n)$	$-1$	$-1$

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 $

$2$			18452.1i			0.796363i	0.917307	+	0.398182i	$0.130359\pi$
$2$			18452.1i			0.796363i	−0.917307	+	0.398182i	$0.869641\pi$
$3$	−2.07416e6	−	8.02049e6i	−0.250371	−	0.968150i
$3$	−2.07416e6	−	8.02049e6i	−0.250371	−	0.968150i
$4$	1.96390e8			0.365805
$5$	1.42232e10			1.04216			0.521078	−	0.853509i	$-0.325530\pi$
$5$	1.42232e10			1.04216			0.521078	+	0.853509i	$0.325530\pi$
$6$	1.47995e11	−	3.82726e10i	0.770999	−	0.199386i
$7$	−7.69210e11	−	1.62118e12i	−0.428670	−	0.903461i
$7$	−7.69210e11	−	1.62118e12i	−0.428670	−	0.903461i
$8$			1.35302e13i			1.08768i
$9$	−6.00261e13	+	3.32715e13i	−0.874629	+	0.484793i
$10$			2.62448e14i			0.829935i
$11$		−	5.94684e14i		−	0.472163i	−0.971733	−	0.236082i	$-0.924137\pi$
$11$		−	5.94684e14i		−	0.472163i	0.971733	−	0.236082i	$-0.0758633\pi$
$12$	−4.07344e14	−	1.57515e15i	−0.0915870	−	0.354154i
$13$		−	8.49314e15i		−	0.598260i	−0.954212	−	0.299130i	$-0.903304\pi$
$13$		−	8.49314e15i		−	0.598260i	0.954212	−	0.299130i	$-0.0966964\pi$
$14$	2.99142e16	−	1.41935e16i	0.719483	−	0.341377i
$15$	−2.95012e16	−	1.14077e17i	−0.260925	−	1.00896i
$16$	−1.44225e17			−0.500381
$17$	5.80016e17			0.835470			0.417735	−	0.908569i	$-0.362824\pi$
$17$	5.80016e17			0.835470			0.417735	+	0.908569i	$0.362824\pi$
$18$	−6.13930e17	−	1.10761e18i	−0.386071	−	0.696523i
$19$			6.04886e18i			1.73679i	0.495875	+	0.868394i	$0.334847\pi$
$19$			6.04886e18i			1.73679i	−0.495875	+	0.868394i	$0.665153\pi$
$20$	2.79330e18			0.381226
$21$	−1.14072e19	+	9.53202e18i	−0.767359	+	0.641217i
$22$	1.09732e19			0.376014
$23$			9.96781e19i			1.79286i	0.443186	+	0.896430i	$0.353848\pi$
$23$			9.96781e19i			1.79286i	−0.443186	+	0.896430i	$0.646152\pi$
$24$	1.08519e20	−	2.80638e19i	1.05303	−	0.272323i
$25$	1.60352e19			0.0860884
$26$	1.56716e20			0.476432
$27$	3.91358e20	+	4.12428e20i	0.688334	+	0.725394i
$28$	−1.51065e20	−	3.18384e20i	−0.156810	−	0.330491i
$29$		−	2.86579e20i		−	0.178843i	−0.995994	−	0.0894217i	$-0.971498\pi$
$29$		−	2.86579e20i		−	0.178843i	0.995994	−	0.0894217i	$-0.0285019\pi$
$30$	2.10496e21	−	5.44359e20i	0.803501	−	0.207791i
$31$			8.36937e20i			0.198586i	0.995058	+	0.0992929i	$0.0316581\pi$
$31$			8.36937e20i			0.198586i	−0.995058	+	0.0992929i	$0.968342\pi$
$32$			4.60272e21i			0.689192i
$33$	−4.76966e21	+	1.23347e21i	−0.457125	+	0.118216i
$34$			1.07025e22i			0.665338i
$35$	−1.09406e22	−	2.30584e22i	−0.446741	−	0.941547i
$36$	−1.17885e22	+	6.53420e21i	−0.319944	+	0.177340i
$37$	8.80010e21			0.160532			0.0802662	−	0.996773i	$-0.474423\pi$
$37$	8.80010e21			0.160532			0.0802662	+	0.996773i	$0.474423\pi$
$38$	−1.11614e23			−1.38311
$39$	−6.81191e22	+	1.76161e22i	−0.579205	+	0.149787i
$40$			1.92443e23i			1.13353i
$41$	2.50655e23			1.03207			0.516036	−	0.856567i	$-0.327407\pi$
$41$	2.50655e23			1.03207			0.516036	+	0.856567i	$0.327407\pi$
$42$	−1.75886e23	−	2.10487e23i	−0.510642	−	0.611097i
$43$	5.32643e23			1.09937			0.549685	−	0.835372i	$-0.314748\pi$
$43$	5.32643e23			1.09937			0.549685	+	0.835372i	$0.314748\pi$
$44$		−	1.16790e23i		−	0.172720i
$45$	−8.53764e23	+	4.73228e23i	−0.911500	+	0.505230i
$46$	−1.83927e24			−1.42777
$47$	5.56873e23			0.316473			0.158237	−	0.987401i	$-0.449419\pi$
$47$	5.56873e23			0.316473			0.158237	+	0.987401i	$0.449419\pi$
$48$	2.99146e23	+	1.15676e24i	0.125281	+	0.484444i
$49$	−2.03654e24	+	2.49405e24i	−0.632484	+	0.774573i
$50$			2.95884e23i			0.0685577i
$51$	−1.20305e24	−	4.65201e24i	−0.209177	−	0.808860i
$52$		−	1.66797e24i		−	0.218847i
$53$			1.36208e24i			0.135582i	0.997700	+	0.0677910i	$0.0215951\pi$
$53$			1.36208e24i			0.135582i	−0.997700	+	0.0677910i	$0.978405\pi$
$54$	−7.61018e24	+	7.22138e24i	−0.577677	+	0.548164i
$55$		−	8.45832e24i		−	0.492068i
$56$	2.19349e25	−	1.04076e25i	0.982674	−	0.466255i
$57$	4.85149e25	−	1.25463e25i	1.68147	−	0.434841i
$58$	5.28799e24			0.142424
$59$	9.64829e24			0.202813			0.101407	−	0.994845i	$-0.467666\pi$
$59$	9.64829e24			0.202813			0.101407	+	0.994845i	$0.467666\pi$
$60$	−5.79374e24	−	2.24036e25i	−0.0954479	−	0.369084i
$61$		−	9.57504e25i		−	1.24125i	−0.784109	−	0.620623i	$-0.786880\pi$
$61$		−	9.57504e25i		−	1.24125i	0.784109	−	0.620623i	$-0.213120\pi$
$62$	−1.54433e25			−0.158147
$63$	1.00112e26	+	7.17203e25i	0.812919	+	0.582377i
$64$	−1.62360e26			−1.04923
$65$		−	1.20800e26i		−	0.623480i
$66$	−2.27601e25	−	8.80103e25i	−0.0941429	−	0.364038i
$67$	3.55994e26			1.18402			0.592009	−	0.805931i	$-0.298335\pi$
$67$	3.55994e26			1.18402			0.592009	+	0.805931i	$0.298335\pi$
$68$	1.13910e26			0.305619
$69$	7.99467e26	−	2.06748e26i	1.73576	−	0.448880i
$70$	4.25476e26	−	2.01878e26i	0.749814	−	0.355768i
$71$		−	3.70662e26i		−	0.531779i	−0.964003	−	0.265890i	$-0.914334\pi$
$71$		−	3.70662e26i		−	0.531779i	0.964003	−	0.265890i	$-0.0856657\pi$
$72$	−4.50171e26	−	8.12167e26i	−0.527298	−	0.951314i
$73$			7.35668e26i			0.705506i	0.935717	+	0.352753i	$0.114754\pi$
$73$			7.35668e26i			0.705506i	−0.935717	+	0.352753i	$0.885246\pi$
$74$			1.62380e26i			0.127842i
$75$	−3.32596e25	−	1.28610e26i	−0.0215540	−	0.0833465i
$76$			1.18794e27i			0.635326i
$77$	−9.64090e26	+	4.57437e26i	−0.426581	+	0.202402i
$78$	−3.25055e26	−	1.25694e27i	−0.119285	−	0.461258i
$79$	−3.26329e27			−0.995548			−0.497774	−	0.867307i	$-0.665849\pi$
$79$	−3.26329e27			−0.995548			−0.497774	+	0.867307i	$0.665849\pi$
$80$	−2.05134e27			−0.521475
$81$	2.49614e27	−	3.99432e27i	0.529952	−	0.848028i
$82$			4.62511e27i			0.821905i
$83$	−5.72323e27			−0.853118			−0.426559	−	0.904460i	$-0.640274\pi$
$83$	−5.72323e27			−0.853118			−0.426559	+	0.904460i	$0.640274\pi$
$84$	−2.24026e27	+	1.87200e27i	−0.280704	+	0.234561i
$85$	8.24969e27			0.870690
$86$			9.82840e27i			0.875498i
$87$	−2.29850e27	+	5.94410e26i	−0.173147	+	0.0447772i
$88$	8.04621e27			0.513562
$89$	2.49217e28			1.35027			0.675137	−	0.737692i	$-0.264084\pi$
$89$	2.49217e28			1.35027			0.675137	+	0.737692i	$0.264084\pi$
$90$	−8.73206e27	−	1.57538e28i	−0.402346	−	0.725885i
$91$	−1.37689e28	+	6.53301e27i	−0.540504	+	0.256456i
$92$			1.95758e28i			0.655837i
$93$	6.71265e27	−	1.73594e27i	0.192261	−	0.0497201i
$94$			1.02755e28i			0.252028i
$95$			8.60343e28i			1.81000i
$96$	3.69161e28	−	9.54678e27i	0.667241	−	0.172554i
$97$		−	5.99578e28i		−	0.932514i	−0.884649	−	0.466257i	$-0.845602\pi$
$97$		−	5.99578e28i		−	0.932514i	0.884649	−	0.466257i	$-0.154398\pi$
$98$	−4.60206e28	−	3.75785e28i	−0.616842	−	0.503687i
$99$	1.97860e28	+	3.56966e28i	0.228902	+	0.412968i
$100$	3.14916e27			0.0314916
$101$	−1.39958e29			−1.21154			−0.605771	−	0.795639i	$-0.707135\pi$
$101$	−1.39958e29			−1.21154			−0.605771	+	0.795639i	$0.707135\pi$
$102$	8.58395e28	−	2.21987e28i	0.644147	−	0.166581i
$103$			3.03637e28i			0.197795i	0.995098	+	0.0988974i	$0.0315316\pi$
$103$			3.03637e28i			0.197795i	−0.995098	+	0.0988974i	$0.968468\pi$
$104$	1.14914e29			0.650713
$105$	−1.62247e29	+	1.35576e29i	−0.799708	+	0.668248i
$106$	−2.51332e28			−0.107972
$107$		−	1.59865e29i		−	0.599363i	−0.954039	−	0.299681i	$-0.903120\pi$
$107$		−	1.59865e29i		−	0.599363i	0.954039	−	0.299681i	$-0.0968804\pi$
$108$	7.68588e28	+	8.09969e28i	0.251796	+	0.265353i
$109$	4.25375e29			1.21924			0.609618	−	0.792695i	$-0.291323\pi$
$109$	4.25375e29			1.21924			0.609618	+	0.792695i	$0.291323\pi$
$110$	1.56074e29			0.391865
$111$	−1.82528e28	−	7.05811e28i	−0.0401926	−	0.155419i
$112$	1.10939e29	+	2.33815e29i	0.214498	+	0.452075i
$113$		−	1.80203e29i		−	0.306284i	−0.988204	−	0.153142i	$-0.951061\pi$
$113$		−	1.80203e29i		−	0.306284i	0.988204	−	0.153142i	$-0.0489392\pi$
$114$	2.31506e29	+	8.95202e29i	0.346291	+	1.33906i
$115$			1.41774e30i			1.86844i
$116$		−	5.62813e28i		−	0.0654219i
$117$	2.82580e29	+	5.09810e29i	0.290032	+	0.523255i
$118$			1.78031e29i			0.161513i
$119$	−4.46154e29	−	9.40310e29i	−0.358141	−	0.754815i
$120$	1.54349e30	−	3.99158e29i	1.09743	−	0.283803i
$121$	1.23266e30			0.777062
$122$	1.76680e30			0.988483
$123$	−5.19898e29	−	2.01037e30i	−0.258401	−	0.999201i
$124$			1.64366e29i			0.0726438i
$125$	−2.42121e30			−0.952438
$126$	−1.32339e30	+	1.84727e30i	−0.463784	+	0.647379i
$127$	5.06814e30			1.58378			0.791889	−	0.610664i	$-0.209098\pi$
$127$	5.06814e30			1.58378			0.791889	+	0.610664i	$0.209098\pi$
$128$		−	5.24822e29i		−	0.146375i
$129$	−1.10479e30	−	4.27206e30i	−0.275250	−	1.06436i
$130$	2.22901e30			0.496516
$131$	5.95650e30			1.18729			0.593646	−	0.804726i	$-0.297688\pi$
$131$	5.95650e30			1.18729			0.593646	+	0.804726i	$0.297688\pi$
$132$	−9.36714e29	+	2.42241e29i	−0.167219	+	0.0432440i
$133$	9.80629e30	−	4.65284e30i	1.56912	−	0.744509i
$134$			6.56885e30i			0.942909i
$135$	5.56636e30	+	5.86606e30i	0.717351	+	0.755973i
$136$			7.84775e30i			0.908722i
$137$			1.44951e31i			1.50929i	0.656135	+	0.754643i	$0.272190\pi$
$137$			1.44951e31i			1.50929i	−0.656135	+	0.754643i	$0.727810\pi$
$138$	3.81494e30	+	1.47519e31i	0.357471	+	1.38229i
$139$			9.54377e30i			0.805388i	0.915335	+	0.402694i	$0.131926\pi$
$139$			9.54377e30i			0.805388i	−0.915335	+	0.402694i	$0.868074\pi$
$140$	−2.14863e30	−	4.52844e30i	−0.163420	−	0.344423i
$141$	−1.15504e30	−	4.46639e30i	−0.0792356	−	0.306394i
$142$	6.83949e30			0.423490
$143$	−5.05074e30			−0.282476
$144$	8.65727e30	−	4.79859e30i	0.437648	−	0.242581i
$145$		−	4.07607e30i		−	0.186383i
$146$	−1.35746e31			−0.561839
$147$	2.42276e31	+	1.11610e31i	0.908259	+	0.418409i
$148$	1.72825e30			0.0587236
$149$			6.12997e31i			1.88911i	0.328350	+	0.944556i	$0.393507\pi$
$149$			6.12997e31i			1.88911i	−0.328350	+	0.944556i	$0.606493\pi$
$150$	2.37313e30	−	6.13710e29i	0.0663741	−	0.0171648i
$151$	4.05710e31			1.03051			0.515253	−	0.857038i	$-0.327698\pi$
$151$	4.05710e31			1.03051			0.515253	+	0.857038i	$0.327698\pi$
$152$	−8.18425e31			−1.88906
$153$	−3.48161e31	+	1.92980e31i	−0.730726	+	0.405030i
$154$	−8.44068e30	−	1.77895e31i	−0.161186	−	0.339714i
$155$			1.19039e31i			0.206957i
$156$	−1.33779e31	+	3.45963e30i	−0.211876	+	0.0547928i
$157$			3.16864e31i			0.457434i	0.973493	+	0.228717i	$0.0734531\pi$
$157$			3.16864e31i			0.457434i	−0.973493	+	0.228717i	$0.926547\pi$
$158$		−	6.02145e31i		−	0.792818i
$159$	1.09245e31	−	2.82516e30i	0.131264	−	0.0339458i
$160$			6.54655e31i			0.718245i
$161$	1.61596e32	−	7.66734e31i	1.61978	−	0.768545i
$162$	7.37037e31	+	4.60591e31i	0.675338	+	0.422034i
$163$	−3.46471e31			−0.290367			−0.145183	−	0.989405i	$-0.546377\pi$
$163$	−3.46471e31			−0.290367			−0.145183	+	0.989405i	$0.546377\pi$
$164$	4.92262e31			0.377538
$165$	−6.78398e31	+	1.75439e31i	−0.476395	+	0.123199i
$166$		−	1.05606e32i		−	0.679392i
$167$	3.29770e32			1.94457			0.972283	−	0.233806i	$-0.0751180\pi$
$167$	3.29770e32			1.94457			0.972283	+	0.233806i	$0.0751180\pi$
$168$	−1.28970e32	−	1.54342e32i	−0.697437	−	0.834640i
$169$	1.29405e32			0.642085
$170$			1.52224e32i			0.693385i
$171$	−2.01255e32	−	3.63090e32i	−0.841982	−	1.51904i
$172$	1.04606e32			0.402155
$173$	2.87798e30			0.0101723			0.00508615	−	0.999987i	$-0.498381\pi$
$173$	2.87798e30			0.0101723			0.00508615	+	0.999987i	$0.498381\pi$
$174$	−1.09681e31	−	4.24122e31i	−0.0356589	−	0.137888i
$175$	−1.23344e31	−	2.59960e31i	−0.0369035	−	0.0777775i
$176$			8.57684e31i			0.236262i
$177$	−2.00121e31	−	7.73840e31i	−0.0507785	−	0.196354i
$178$			4.59858e32i			1.07531i
$179$		−	7.33880e32i		−	1.58218i	−0.611699	−	0.791091i	$-0.709514\pi$
$179$		−	7.33880e32i		−	1.58218i	0.611699	−	0.791091i	$-0.290486\pi$
$180$	−1.67671e32	+	9.29373e31i	−0.333431	+	0.184816i
$181$		−	5.69172e32i		−	1.04449i	−0.852795	−	0.522245i	$-0.825095\pi$
$181$		−	5.69172e32i		−	1.04449i	0.852795	−	0.522245i	$-0.174905\pi$
$182$	−1.20548e32	−	2.54065e32i	−0.204232	−	0.430438i
$183$	−7.67965e32	+	1.98601e32i	−1.20171	+	0.310772i
$184$	−1.34867e33			−1.95005
$185$	1.25166e32			0.167300
$186$	3.20318e31	+	1.23863e32i	0.0395953	+	0.153110i
$187$		−	3.44926e32i		−	0.394478i
$188$	1.09364e32			0.115768
$189$	3.67584e32	−	9.51705e32i	0.360297	−	0.932838i
$190$	−1.58751e33			−1.44142
$191$			3.42751e32i			0.288400i	0.989549	+	0.144200i	$0.0460608\pi$
$191$			3.42751e32i			0.288400i	−0.989549	+	0.144200i	$0.953939\pi$
$192$	3.36761e32	+	1.30221e33i	0.262696	+	1.01581i
$193$	−1.82877e33			−1.32305			−0.661527	−	0.749922i	$-0.730091\pi$
$193$	−1.82877e33			−1.32305			−0.661527	+	0.749922i	$0.730091\pi$
$194$	1.10635e33			0.742620
$195$	−9.68873e32	+	2.50558e32i	−0.603622	+	0.156101i
$196$	−3.99956e32	+	4.89808e32i	−0.231366	+	0.283343i
$197$			3.52269e33i			1.89284i	0.322936	+	0.946421i	$0.395330\pi$
$197$			3.52269e33i			1.89284i	−0.322936	+	0.946421i	$0.604670\pi$
$198$	−6.58677e32	+	3.65094e32i	−0.328872	+	0.182289i
$199$		−	1.38664e33i		−	0.643566i	−0.946813	−	0.321783i	$-0.895718\pi$
$199$		−	1.38664e33i		−	0.643566i	0.946813	−	0.321783i	$-0.104282\pi$
$200$			2.16960e32i			0.0936364i
$201$	−7.38388e32	−	2.85525e33i	−0.296444	−	1.14631i
$202$		−	2.58253e33i		−	0.964828i
$203$	−4.64596e32	+	2.20439e32i	−0.161578	+	0.0766649i
$204$	−2.36266e32	−	9.13610e32i	−0.0765181	−	0.295885i
$205$	3.56512e33			1.07558
$206$	−5.60275e32			−0.157517
$207$	−3.31644e33	−	5.98329e33i	−0.869166	−	1.56809i
$208$			1.22492e33i			0.299358i
$209$	3.59716e33			0.820048
$210$	−2.50166e33	−	2.99380e33i	−0.532168	−	0.636858i
$211$	−1.79828e33			−0.357076			−0.178538	−	0.983933i	$-0.557137\pi$
$211$	−1.79828e33			−0.357076			−0.178538	+	0.983933i	$0.557137\pi$
$212$			2.67499e32i			0.0495966i
$213$	−2.97289e33	+	7.68811e32i	−0.514842	+	0.133142i
$214$	2.94986e33			0.477311
$215$	7.57590e33			1.14571
$216$	−5.58025e33	+	5.29515e33i	−0.788995	+	0.748685i
$217$	1.35683e33	−	6.43780e32i	0.179415	−	0.0851278i
$218$			7.84908e33i			0.970956i
$219$	5.90042e33	−	1.52589e33i	0.683035	−	0.176638i
$220$		−	1.66113e33i		−	0.180001i
$221$		−	4.92616e33i		−	0.499828i
$222$	1.30237e33	−	3.36803e32i	0.123770	−	0.0320079i
$223$			5.25094e33i			0.467538i	0.972292	+	0.233769i	$0.0751059\pi$
$223$			5.25094e33i			0.467538i	−0.972292	+	0.233769i	$0.924894\pi$
$224$	7.46184e33	−	3.54046e33i	0.622658	−	0.295436i
$225$	−9.62532e32	+	5.33516e32i	−0.0752954	+	0.0417351i
$226$	3.32513e33			0.243914
$227$	1.48134e34			1.01925			0.509625	−	0.860397i	$-0.329784\pi$
$227$	1.48134e34			1.01925			0.509625	+	0.860397i	$0.329784\pi$
$228$	9.52784e33	−	2.46397e33i	0.615091	−	0.159067i
$229$			1.43601e34i			0.870049i	0.900419	+	0.435024i	$0.143260\pi$
$229$			1.43601e34i			0.870049i	−0.900419	+	0.435024i	$0.856740\pi$
$230$	−2.61604e34			−1.48796
$231$	5.66854e33	+	6.78367e33i	0.302759	+	0.362319i
$232$	3.87748e33			0.194524
$233$		−	3.20974e34i		−	1.51290i	−0.654054	−	0.756448i	$-0.726933\pi$
$233$		−	3.20974e34i		−	1.51290i	0.654054	−	0.756448i	$-0.273067\pi$
$234$	−9.40708e33	+	5.21419e33i	−0.416701	+	0.230971i
$235$	7.92052e33			0.329814
$236$	1.89483e33			0.0741902
$237$	6.76857e33	+	2.61731e34i	0.249256	+	0.963840i
$238$	1.73507e34	−	8.23249e33i	0.601107	−	0.285210i
$239$			1.58327e31i			0.000516160i	1.00000		0.000258080i	$8.21494e-5\pi$
$239$			1.58327e31i			0.000516160i	−1.00000		0.000258080i	$0.999918\pi$
$240$	4.25481e33	+	1.64528e34i	0.130562	+	0.504866i
$241$			5.62480e34i			1.62503i	0.582943	+	0.812513i	$0.301901\pi$
$241$			5.62480e34i			1.62503i	−0.582943	+	0.812513i	$0.698099\pi$
$242$			2.27452e34i			0.618823i
$243$	−3.72138e34	−	1.17354e34i	−0.953703	−	0.300751i
$244$		−	1.88044e34i		−	0.454054i
$245$	−2.89661e34	+	3.54735e34i	−0.659147	+	0.807226i
$246$	3.70957e34	−	9.59322e33i	0.795727	−	0.205781i
$247$	5.13739e34			1.03905
$248$	−1.13239e34			−0.215997
$249$	1.18709e34	+	4.59031e34i	0.213596	+	0.825946i
$250$		−	4.46764e34i		−	0.758487i
$251$	7.44254e34			1.19248			0.596242	−	0.802805i	$-0.296660\pi$
$251$	7.44254e34			1.19248			0.596242	+	0.802805i	$0.296660\pi$
$252$	1.96610e34	+	1.40852e34i	0.297370	+	0.213037i
$253$	5.92770e34			0.846523
$254$			9.35179e34i			1.26126i
$255$	−1.71112e34	−	6.61666e34i	−0.217995	−	0.842958i
$256$	−7.74824e34			−0.932661
$257$	−4.10717e34			−0.467210			−0.233605	−	0.972332i	$-0.575052\pi$
$257$	−4.10717e34			−0.467210			−0.233605	+	0.972332i	$0.575052\pi$
$258$	7.88286e34	−	2.03857e34i	0.847614	−	0.219199i
$259$	−6.76912e33	−	1.42665e34i	−0.0688154	−	0.145035i
$260$		−	2.37239e34i		−	0.228072i
$261$	9.53491e33	+	1.72022e34i	0.0867021	+	0.156422i
$262$			1.09910e35i			0.945516i
$263$		−	1.34501e35i		−	1.09488i	−0.836844	−	0.547442i	$-0.815602\pi$
$263$		−	1.34501e35i		−	1.09488i	0.836844	−	0.547442i	$-0.184398\pi$
$264$	−1.66891e34	−	6.45345e34i	−0.128581	−	0.497205i
$265$			1.93731e34i			0.141297i
$266$	8.58549e34	+	1.80947e35i	0.592900	+	1.24959i
$267$	−5.16915e34	−	1.99884e35i	−0.338069	−	1.30727i
$268$	6.99138e34			0.433120
$269$	−1.95098e35			−1.14510			−0.572551	−	0.819869i	$-0.694046\pi$
$269$	−1.95098e35			−1.14510			−0.572551	+	0.819869i	$0.694046\pi$
$270$	−1.08241e35	+	1.02711e35i	−0.602030	+	0.571272i
$271$			9.52709e34i			0.502233i	0.967957	+	0.251117i	$0.0807978\pi$
$271$			9.52709e34i			0.502233i	−0.967957	+	0.251117i	$0.919202\pi$
$272$	−8.36529e34			−0.418053
$273$	8.09568e34	+	9.68828e34i	0.383614	+	0.459080i
$274$	−2.67464e35			−1.20194
$275$		−	9.53589e33i		−	0.0406478i
$276$	1.57008e35	−	4.06033e34i	0.634949	−	0.164203i
$277$	−4.33064e35			−1.66186			−0.830932	−	0.556374i	$-0.812192\pi$
$277$	−4.33064e35			−1.66186			−0.830932	+	0.556374i	$0.812192\pi$
$278$	−1.76103e35			−0.641382
$279$	−2.78462e34	−	5.02381e34i	−0.0962730	−	0.173689i
$280$	3.11985e35	−	1.48029e35i	1.02410	−	0.485910i
$281$		−	5.25747e35i		−	1.63884i	−0.573197	−	0.819418i	$-0.694297\pi$
$281$		−	5.25747e35i		−	1.63884i	0.573197	−	0.819418i	$-0.305703\pi$
$282$	8.24144e34	−	2.13130e34i	0.244001	−	0.0631004i
$283$			3.07978e34i			0.0866197i	0.999062	+	0.0433099i	$0.0137903\pi$
$283$			3.07978e34i			0.0866197i	−0.999062	+	0.0433099i	$0.986210\pi$
$284$		−	7.27943e34i		−	0.194528i
$285$	6.90037e35	−	1.78449e35i	1.75235	−	0.453172i
$286$		−	9.31968e34i		−	0.224954i
$287$	−1.92806e35	−	4.06357e35i	−0.442419	−	0.932438i
$288$	−1.53140e35	−	2.76284e35i	−0.334115	−	0.602787i
$289$	−1.45550e35			−0.301990
$290$	7.52122e34			0.148428
$291$	−4.80891e35	+	1.24362e35i	−0.902813	+	0.233474i
$292$			1.44478e35i			0.258078i
$293$	−1.26301e35			−0.214698			−0.107349	−	0.994221i	$-0.534236\pi$
$293$	−1.26301e35			−0.214698			−0.107349	+	0.994221i	$0.534236\pi$
$294$	−2.05944e35	+	4.47051e35i	−0.333205	+	0.723304i
$295$	1.37230e35			0.211363
$296$			1.19067e35i			0.174607i
$297$	2.45265e35	−	2.32734e35i	0.342505	−	0.325006i
$298$	−1.13111e36			−1.50442
$299$	8.46580e35			1.07260
$300$	−6.53186e33	−	2.52578e34i	−0.00788458	−	0.0304886i
$301$	−4.09714e35	−	8.63510e35i	−0.471267	−	0.993238i
$302$			7.48621e35i			0.820657i
$303$	2.90295e35	+	1.12253e36i	0.303335	+	1.17295i
$304$		−	8.72398e35i		−	0.869056i
$305$		−	1.36188e36i		−	1.29357i
$306$	−3.56089e35	−	6.42431e35i	−0.322551	−	0.581924i
$307$		−	3.26212e35i		−	0.281834i	−0.990021	−	0.140917i	$-0.954995\pi$
$307$		−	3.26212e35i		−	0.281834i	0.990021	−	0.140917i	$-0.0450051\pi$
$308$	−1.89338e35	+	8.98361e34i	−0.156046	+	0.0740398i
$309$	2.43532e35	−	6.29791e34i	0.191495	−	0.0495221i
$310$	−2.19653e35			−0.164813
$311$	1.78471e35			0.127803			0.0639015	−	0.997956i	$-0.479646\pi$
$311$	1.78471e35			0.127803			0.0639015	+	0.997956i	$0.479646\pi$
$312$	−2.38350e35	−	9.21667e35i	−0.162920	−	0.629988i
$313$			1.90751e36i			1.24473i	0.782728	+	0.622364i	$0.213827\pi$
$313$			1.90751e36i			1.24473i	−0.782728	+	0.622364i	$0.786173\pi$
$314$	−5.84682e35			−0.364284
$315$	1.42391e36	+	1.02009e36i	0.847188	+	0.606927i
$316$	−6.40877e35			−0.364177
$317$			2.91237e35i			0.158084i	0.996871	+	0.0790419i	$0.0251861\pi$
$317$			2.91237e35i			0.158084i	−0.996871	+	0.0790419i	$0.974814\pi$
$318$	5.21303e34	+	2.01581e35i	0.0270332	+	0.104534i
$319$	−1.70424e35			−0.0844434
$320$	−2.30928e36			−1.09346
$321$	−1.28220e36	+	3.31586e35i	−0.580273	+	0.150063i
$322$	1.41479e36	+	2.98179e36i	0.612041	+	1.28993i
$323$			3.50844e36i			1.45103i
$324$	4.90217e35	−	7.84445e35i	0.193859	−	0.310213i
$325$		−	1.36189e35i		−	0.0515032i
$326$		−	6.39313e35i		−	0.231238i
$327$	−8.82296e35	−	3.41172e36i	−0.305261	−	1.18040i
$328$			3.39142e36i			1.12256i
$329$	−4.28352e35	−	9.02790e35i	−0.135663	−	0.285921i
$330$	−3.23722e35	−	1.25179e36i	−0.0981115	−	0.379384i
$331$	5.82253e36			1.68891			0.844453	−	0.535630i	$-0.179926\pi$
$331$	5.82253e36			1.68891			0.844453	+	0.535630i	$0.179926\pi$
$332$	−1.12399e36			−0.312075
$333$	−5.28236e35	+	2.92793e35i	−0.140406	+	0.0778250i
$334$			6.08496e36i			1.54858i
$335$	5.06338e36			1.23393
$336$	1.64520e36	−	1.37476e36i	0.383972	−	0.320853i
$337$	−6.26685e36			−1.40093			−0.700463	−	0.713688i	$-0.747023\pi$
$337$	−6.26685e36			−1.40093			−0.700463	+	0.713688i	$0.747023\pi$
$338$			2.38779e36i			0.511333i
$339$	−1.44532e36	+	3.73770e35i	−0.296529	+	0.0766846i
$340$	1.62016e36			0.318503
$341$	4.97713e35			0.0937650
$342$	6.69978e36	−	3.71358e36i	1.20971	−	0.670524i
$343$	5.60983e36	+	1.38314e36i	0.970924	+	0.239388i
$344$			7.20678e36i			1.19576i
$345$	1.13710e37	−	2.94062e36i	1.80893	−	0.467802i
$346$			5.31048e34i			0.00810085i
$347$		−	1.25932e37i		−	1.84229i	−0.389216	−	0.921147i	$-0.627254\pi$
$347$		−	1.25932e37i		−	1.84229i	0.389216	−	0.921147i	$-0.372746\pi$
$348$	−4.51403e35	+	1.16736e35i	−0.0633382	+	0.0163797i
$349$			2.20712e36i			0.297069i	0.988907	+	0.148535i	$0.0474557\pi$
$349$			2.20712e36i			0.297069i	−0.988907	+	0.148535i	$0.952544\pi$
$350$	4.79681e35	−	2.27597e35i	0.0619392	−	0.0293886i
$351$	3.50281e36	−	3.32385e36i	0.433974	−	0.411802i
$352$	2.73717e36			0.325411
$353$	−2.62470e36			−0.299466			−0.149733	−	0.988727i	$-0.547841\pi$
$353$	−2.62470e36			−0.299466			−0.149733	+	0.988727i	$0.547841\pi$
$354$	1.42790e36	−	3.69265e35i	0.156369	−	0.0404382i
$355$		−	5.27200e36i		−	0.554197i
$356$	4.89437e36			0.493938
$357$	−6.61635e36	+	5.52873e36i	−0.641106	+	0.535718i
$358$	1.35416e37			1.25999
$359$			1.27051e37i			1.13529i	0.823272	+	0.567647i	$0.192146\pi$
$359$			1.27051e37i			1.13529i	−0.823272	+	0.567647i	$0.807854\pi$
$360$	−6.40288e36	−	1.15516e37i	−0.549527	−	0.991417i
$361$	−2.44589e37			−2.01643
$362$	1.05024e37			0.831794
$363$	−2.55673e36	−	9.88654e36i	−0.194554	−	0.752312i
$364$	−2.70408e36	+	1.28302e36i	−0.197719	+	0.0938129i
$365$			1.04636e37i			0.735247i
$366$	−3.66462e36	−	1.41706e37i	−0.247487	−	0.957000i
$367$			2.79469e37i			1.81416i	0.420961	+	0.907079i	$0.361693\pi$
$367$			2.79469e37i			1.81416i	−0.420961	+	0.907079i	$0.638307\pi$
$368$		−	1.43761e37i		−	0.897113i
$369$	−1.50458e37	+	8.33967e36i	−0.902681	+	0.500342i
$370$			2.30957e36i			0.133231i
$371$	2.20817e36	−	1.04772e36i	0.122493	−	0.0581199i
$372$	1.31830e36	−	3.40922e35i	0.0703301	−	0.0181879i
$373$	−1.04064e36			−0.0533975			−0.0266987	−	0.999644i	$-0.508499\pi$
$373$	−1.04064e36			−0.0533975			−0.0266987	+	0.999644i	$0.508499\pi$
$374$	6.36462e36			0.314148
$375$	5.02197e36	+	1.94193e37i	0.238463	+	0.922103i
$376$			7.53461e36i			0.344221i
$377$	−2.43395e36			−0.106995
$378$	1.75610e37	+	6.78271e36i	0.742878	+	0.286928i
$379$	−3.30692e37			−1.34634			−0.673171	−	0.739487i	$-0.735068\pi$
$379$	−3.30692e37			−1.34634			−0.673171	+	0.739487i	$0.735068\pi$
$380$			1.68963e37i			0.662109i
$381$	−1.05121e37	−	4.06490e37i	−0.396532	−	1.53334i
$382$	−6.32448e36			−0.229671
$383$	3.02407e37			1.05733			0.528665	−	0.848831i	$-0.322693\pi$
$383$	3.02407e37			1.05733			0.528665	+	0.848831i	$0.322693\pi$
$384$	−4.20933e36	+	1.08856e36i	−0.141713	+	0.0366481i
$385$	−1.37124e37	+	6.50622e36i	−0.444564	+	0.210935i
$386$		−	3.37446e37i		−	1.05363i
$387$	−3.19725e37	+	1.77219e37i	−0.961541	+	0.532967i
$388$		−	1.17751e37i		−	0.341118i
$389$			3.39257e37i			0.946804i	0.880846	+	0.473402i	$0.156974\pi$
$389$			3.39257e37i			0.946804i	−0.880846	+	0.473402i	$0.843026\pi$
$390$	−4.62332e36	−	1.78778e37i	−0.124313	−	0.480702i
$391$			5.78149e37i			1.49788i
$392$	−3.37451e37	−	2.75548e37i	−0.842486	−	0.687938i
$393$	−1.23547e37	−	4.77740e37i	−0.297263	−	1.14948i
$394$	−6.50011e37			−1.50739
$395$	−4.64144e37			−1.03752
$396$	3.88579e36	+	7.01046e36i	0.0837334	+	0.151066i
$397$		−	2.23970e37i		−	0.465293i	−0.972561	−	0.232647i	$-0.925261\pi$
$397$		−	2.23970e37i		−	0.465293i	0.972561	−	0.232647i	$-0.0747385\pi$
$398$	2.55864e37			0.512513
$399$	−5.76579e37	−	6.90005e37i	−1.11366	−	1.33274i
$400$	−2.31268e36			−0.0430770
$401$		−	4.69280e37i		−	0.843022i	−0.906823	−	0.421511i	$-0.861500\pi$
$401$		−	4.69280e37i		−	0.843022i	0.906823	−	0.421511i	$-0.138500\pi$
$402$	5.26854e37	−	1.36248e37i	0.912877	−	0.236077i
$403$	7.10822e36			0.118806
$404$	−2.74864e37			−0.443188
$405$	3.55031e37	−	5.68121e37i	0.552292	−	0.883777i
$406$	−4.06757e36	−	8.57277e36i	−0.0610531	−	0.128675i
$407$		−	5.23328e36i		−	0.0757975i
$408$	6.29428e37	−	1.62775e37i	0.879779	−	0.227517i
$409$			3.33078e37i			0.449322i	0.974437	+	0.224661i	$0.0721275\pi$
$409$			3.33078e37i			0.449322i	−0.974437	+	0.224661i	$0.927873\pi$
$410$			6.57840e37i			0.856553i
$411$	1.16257e38	−	3.00650e37i	1.46122	−	0.377881i
$412$			5.96314e36i			0.0723544i
$413$	−7.42156e36	−	1.56416e37i	−0.0869400	−	0.183234i
$414$	1.10404e38	−	6.11954e37i	1.24877	−	0.692172i
$415$	−8.14027e37			−0.889082
$416$	3.90916e37			0.412316
$417$	7.65457e37	−	1.97953e37i	0.779737	−	0.201646i
$418$			6.63753e37i			0.653056i
$419$	9.46607e37			0.899635			0.449817	−	0.893121i	$-0.351489\pi$
$419$	9.46607e37			0.899635			0.449817	+	0.893121i	$0.351489\pi$
$420$	−3.18637e37	+	2.66258e37i	−0.292537	+	0.244449i
$421$	1.02958e37			0.0913207			0.0456604	−	0.998957i	$-0.485461\pi$
$421$	1.02958e37			0.0913207			0.0456604	+	0.998957i	$0.485461\pi$
$422$		−	3.31820e37i		−	0.284362i
$423$	−3.34269e37	+	1.85280e37i	−0.276797	+	0.153424i
$424$	−1.84292e37			−0.147469
$425$	9.30069e36			0.0719243
$426$	−1.41862e37	−	5.48561e37i	−0.106029	−	0.410002i
$427$	−1.55229e38	+	7.36521e37i	−1.12142	+	0.532085i
$428$		−	3.13960e37i		−	0.219250i
$429$	1.04760e37	+	4.05094e37i	0.0707238	+	0.273479i
$430$			1.39791e38i			0.912405i
$431$			2.51935e37i			0.158989i	0.996835	+	0.0794947i	$0.0253307\pi$
$431$			2.51935e37i			0.158989i	−0.996835	+	0.0794947i	$0.974669\pi$
$432$	−5.64436e37	−	5.94825e37i	−0.344429	−	0.362974i
$433$			1.99861e38i			1.17938i	0.807629	+	0.589690i	$0.200750\pi$
$433$			1.99861e38i			1.17938i	−0.807629	+	0.589690i	$0.799250\pi$
$434$	1.18791e37	+	2.50363e37i	0.0677927	+	0.142879i
$435$	−3.26921e37	+	8.45442e36i	−0.180446	+	0.0466648i
$436$	8.35396e37			0.446003
$437$	−6.02939e38			−3.11382
$438$	2.81559e37	+	1.08875e38i	0.140668	+	0.543944i
$439$			1.19069e38i			0.575525i	0.957702	+	0.287762i	$0.0929113\pi$
$439$			1.19069e38i			0.575525i	−0.957702	+	0.287762i	$0.907089\pi$
$440$	1.14443e38			0.535211
$441$	3.92645e37	−	2.17467e38i	0.177681	−	0.984088i
$442$	9.08981e37			0.398045
$443$		−	1.43630e38i		−	0.608682i	−0.952563	−	0.304341i	$-0.901564\pi$
$443$		−	1.43630e38i		−	0.608682i	0.952563	−	0.304341i	$-0.0984362\pi$
$444$	−3.58467e36	−	1.38614e37i	−0.0147027	−	0.0568532i
$445$	3.54466e38			1.40720
$446$	−9.68910e37			−0.372330
$447$	4.91654e38	−	1.27145e38i	1.82894	−	0.472979i
$448$	1.24889e38	+	2.63215e38i	0.449773	+	0.947937i
$449$			2.17986e38i			0.760076i	0.924971	+	0.380038i	$0.124089\pi$
$449$			2.17986e38i			0.760076i	−0.924971	+	0.380038i	$0.875911\pi$
$450$	−9.84450e36	−	1.77608e37i	−0.0332363	−	0.0599625i
$451$		−	1.49060e38i		−	0.487307i
$452$		−	3.53901e37i		−	0.112040i
$453$	−8.41507e37	−	3.25399e38i	−0.258008	−	0.997684i
$454$			2.73339e38i			0.811693i
$455$	−1.95838e38	+	9.29203e37i	−0.563290	+	0.267267i
$456$	1.69754e38	+	6.56417e38i	0.472967	+	1.82890i
$457$	−2.43534e38			−0.657317			−0.328658	−	0.944449i	$-0.606596\pi$
$457$	−2.43534e38			−0.657317			−0.328658	+	0.944449i	$0.606596\pi$
$458$	−2.64975e38			−0.692875
$459$	2.26994e38	+	2.39215e38i	0.575082	+	0.606045i
$460$			2.78431e38i			0.683485i
$461$	6.88134e38			1.63685			0.818426	−	0.574612i	$-0.194847\pi$
$461$	6.88134e38			1.63685			0.818426	+	0.574612i	$0.194847\pi$
$462$	−1.25173e38	+	1.04597e38i	−0.288538	+	0.241106i
$463$	−6.65241e37			−0.148612			−0.0743062	−	0.997235i	$-0.523674\pi$
$463$	−6.65241e37			−0.148612			−0.0743062	+	0.997235i	$0.523674\pi$
$464$			4.13319e37i			0.0894899i
$465$	9.54754e37	−	2.46906e37i	0.200366	−	0.0518161i
$466$	5.92265e38			1.20481
$467$	3.60729e38			0.711355			0.355677	−	0.934609i	$-0.384250\pi$
$467$	3.60729e38			0.711355			0.355677	+	0.934609i	$0.384250\pi$
$468$	5.54959e37	+	1.00122e38i	0.106095	+	0.191409i
$469$	−2.73834e38	−	5.77131e38i	−0.507553	−	1.06971i
$470$			1.46150e38i			0.262652i
$471$	2.54141e38	−	6.57227e37i	0.442865	−	0.114528i
$472$			1.30544e38i			0.220595i
$473$		−	3.16755e38i		−	0.519082i
$474$	−4.82950e38	+	1.24894e38i	−0.767567	+	0.198498i
$475$			9.69949e37i			0.149517i
$476$	−8.76203e37	−	1.84668e38i	−0.131010	−	0.276115i
$477$	−4.53184e37	−	8.17602e37i	−0.0657292	−	0.118584i
$478$	−2.92146e35			−0.000411051
$479$	1.45237e38			0.198249			0.0991245	−	0.995075i	$-0.468396\pi$
$479$	1.45237e38			0.198249			0.0991245	+	0.995075i	$0.468396\pi$
$480$	5.25065e38	−	1.35786e38i	0.695369	−	0.179828i
$481$		−	7.47405e37i		−	0.0960400i
$482$	−1.03790e39			−1.29411
$483$	−9.50134e38	−	1.13705e39i	−1.14961	−	1.37577i
$484$	2.42082e38			0.284253
$485$		−	8.52792e38i		−	0.971824i
$486$	2.16543e38	−	6.86673e38i	0.239507	−	0.759494i
$487$	−8.71462e38			−0.935575			−0.467787	−	0.883841i	$-0.654949\pi$
$487$	−8.71462e38			−0.935575			−0.467787	+	0.883841i	$0.654949\pi$
$488$	1.29552e39			1.35008
$489$	7.18636e37	+	2.77887e38i	0.0726994	+	0.281119i
$490$	−6.54560e38	−	5.34486e38i	−0.642845	−	0.524920i
$491$			1.79712e38i			0.171355i	0.996323	+	0.0856774i	$0.0273054\pi$
$491$			1.79712e38i			0.171355i	−0.996323	+	0.0856774i	$0.972695\pi$
$492$	−1.02103e38	−	3.94818e38i	−0.0945244	−	0.365513i
$493$		−	1.66220e38i		−	0.149418i
$494$			9.47956e38i			0.827461i
$495$	2.81421e38	+	5.07720e38i	0.238551	+	0.430377i
$496$		−	1.20707e38i		−	0.0993686i
$497$	−6.00909e38	+	2.85116e38i	−0.480442	+	0.227958i
$498$	−8.47010e38	+	2.19043e38i	−0.657753	+	0.170100i
$499$	−1.63005e39			−1.22954			−0.614772	−	0.788705i	$-0.710752\pi$
$499$	−1.63005e39			−1.22954			−0.614772	+	0.788705i	$0.710752\pi$
$500$	−4.75501e38			−0.348407
$501$	−6.83996e38	−	2.64492e39i	−0.486863	−	1.88263i
$502$			1.37331e39i			0.949650i
$503$	2.35523e39			1.58233			0.791165	−	0.611602i	$-0.209475\pi$
$503$	2.35523e39			1.58233			0.791165	+	0.611602i	$0.209475\pi$
$504$	−9.70392e38	+	1.35453e39i	−0.633438	+	0.884193i
$505$	−1.99065e39			−1.26262
$506$			1.09379e39i			0.674140i
$507$	−2.68406e38	−	1.03789e39i	−0.160759	−	0.621635i
$508$	9.95333e38			0.579355
$509$	1.65401e39			0.935684			0.467842	−	0.883812i	$-0.345032\pi$
$509$	1.65401e39			0.935684			0.467842	+	0.883812i	$0.345032\pi$
$510$	1.22091e39	−	3.15737e38i	0.671301	−	0.173603i
$511$	1.19265e39	−	5.65883e38i	0.637397	−	0.302429i
$512$		−	1.71148e39i		−	0.889112i
$513$	−2.49472e39	+	2.36727e39i	−1.25986	+	1.19549i
$514$		−	7.57860e38i		−	0.372069i
$515$			4.31869e38i			0.206133i
$516$	−2.16969e38	−	8.38991e38i	−0.100688	−	0.389347i
$517$		−	3.31163e38i		−	0.149427i
$518$	2.63248e38	−	1.24905e38i	0.115500	−	0.0548021i
$519$	−5.96938e36	−	2.30828e37i	−0.00254685	−	0.00984831i
$520$	1.63445e39			0.678145
$521$	−4.32038e39			−1.74331			−0.871655	−	0.490120i	$-0.836953\pi$
$521$	−4.32038e39			−1.74331			−0.871655	+	0.490120i	$0.836953\pi$
$522$	−3.17417e38	+	1.75939e38i	−0.124569	+	0.0690464i
$523$		−	2.77177e39i		−	1.05799i	−0.848624	−	0.528996i	$-0.822569\pi$
$523$		−	2.77177e39i		−	1.05799i	0.848624	−	0.528996i	$-0.177431\pi$
$524$	1.16980e39			0.434317
$525$	−1.82917e38	+	1.52848e38i	−0.0660608	+	0.0552014i
$526$	2.48183e39			0.871925
$527$			4.85437e38i			0.165912i
$528$	6.87904e38	−	1.77897e38i	0.228737	−	0.0591530i
$529$	−6.84467e39			−2.21434
$530$	−3.57475e38			−0.112524
$531$	−5.79150e38	+	3.21013e38i	−0.177386	+	0.0983225i
$532$	1.92586e39	−	9.13773e38i	0.573992	−	0.272345i
$533$		−	2.12885e39i		−	0.617447i
$534$	3.68828e39	−	9.53817e38i	1.04106	−	0.269226i
$535$		−	2.27380e39i		−	0.624629i
$536$			4.81668e39i			1.28783i
$537$	−5.88608e39	+	1.52218e39i	−1.53179	+	0.396132i
$538$		−	3.59997e39i		−	0.911918i
$539$	1.48317e39	+	1.21110e39i	0.365725	+	0.298636i
$540$	1.09318e39	+	1.15204e39i	0.262411	+	0.276539i
$541$	1.72680e39			0.403535			0.201767	−	0.979433i	$-0.435332\pi$
$541$	1.72680e39			0.403535			0.201767	+	0.979433i	$0.435332\pi$
$542$	−1.75795e39			−0.399960
$543$	−4.56504e39	+	1.18055e39i	−1.01122	+	0.261510i
$544$			2.66965e39i			0.575799i
$545$	6.05020e39			1.27063
$546$	−1.78769e39	+	1.49382e39i	−0.365595	+	0.305496i
$547$	1.60545e39			0.319729			0.159864	−	0.987139i	$-0.448894\pi$
$547$	1.60545e39			0.319729			0.159864	+	0.987139i	$0.448894\pi$
$548$			2.84669e39i			0.552105i
$549$	3.18576e39	+	5.74752e39i	0.601747	+	1.08563i
$550$	1.75957e38			0.0323704
$551$	1.73348e39			0.310613
$552$	2.79735e39	+	1.08170e40i	0.488236	+	1.88794i
$553$	2.51015e39	+	5.29037e39i	0.426762	+	0.899439i
$554$		−	7.99095e39i		−	1.32345i
$555$	−2.59613e38	−	1.00389e39i	−0.0418870	−	0.161971i
$556$			1.87430e39i			0.294615i
$557$		−	8.65128e39i		−	1.32489i	−0.749110	−	0.662445i	$-0.769519\pi$
$557$		−	8.65128e39i		−	1.32489i	0.749110	−	0.662445i	$-0.230481\pi$
$558$	9.26999e38	−	5.13821e38i	0.138320	−	0.0766683i
$559$		−	4.52381e39i		−	0.657709i
$560$	1.57791e39	+	3.32560e39i	0.223541	+	0.471133i
$561$	−2.76648e39	+	7.15432e38i	−0.381914	+	0.0987659i
$562$	9.70115e39			1.30511
$563$	−9.08087e39			−1.19057			−0.595286	−	0.803514i	$-0.702961\pi$
$563$	−9.08087e39			−1.19057			−0.595286	+	0.803514i	$0.702961\pi$
$564$	−2.26839e38	−	8.77155e38i	−0.0289848	−	0.112080i
$565$		−	2.56307e39i		−	0.319196i
$566$	−5.68285e38			−0.0689808
$567$	−8.39556e39	−	9.74221e38i	−0.993335	−	0.115266i
$568$	5.01513e39			0.578404
$569$			3.11126e38i			0.0349791i	0.999847	+	0.0174896i	$0.00556738\pi$
$569$			3.11126e38i			0.0349791i	−0.999847	+	0.0174896i	$0.994433\pi$
$570$	3.29276e39	+	1.27326e40i	0.360889	+	1.39551i
$571$	1.18344e40			1.26452			0.632258	−	0.774758i	$-0.282128\pi$
$571$	1.18344e40			1.26452			0.632258	+	0.774758i	$0.282128\pi$
$572$	−9.91915e38			−0.103331
$573$	2.74903e39	−	7.10919e38i	0.279214	−	0.0722068i
$574$	7.49814e39	−	3.55768e39i	0.742559	−	0.352326i
$575$			1.59836e39i			0.154344i
$576$	9.74586e39	−	5.40197e39i	0.917686	−	0.508659i
$577$		−	1.59902e40i		−	1.46827i	−0.679004	−	0.734135i	$-0.737588\pi$
$577$		−	1.59902e40i		−	1.46827i	0.679004	−	0.734135i	$-0.262412\pi$
$578$		−	2.68570e39i		−	0.240494i
$579$	3.79315e39	+	1.46676e40i	0.331254	+	1.28091i
$580$		−	8.00500e38i		−	0.0681798i
$581$	4.40237e39	+	9.27838e39i	0.365706	+	0.770759i
$582$	−2.29474e39	−	8.87345e39i	−0.185930	−	0.718967i
$583$	8.10006e38			0.0640168
$584$	−9.95376e39			−0.767363
$585$	4.01919e39	+	7.25114e39i	0.302259	+	0.545313i
$586$		−	2.33053e39i		−	0.170977i
$587$	−2.27376e40			−1.62739			−0.813697	−	0.581289i	$-0.802548\pi$
$587$	−2.27376e40			−1.62739			−0.813697	+	0.581289i	$0.802548\pi$
$588$	4.75807e39	+	2.19191e39i	0.332246	+	0.153056i
$589$	−5.06252e39			−0.344901
$590$			2.53218e39i			0.168322i
$591$	2.82537e40	−	7.30662e39i	1.83255	−	0.473912i
$592$	−1.26919e39			−0.0803274
$593$	1.23686e39			0.0763886			0.0381943	−	0.999270i	$-0.487839\pi$
$593$	1.23686e39			0.0763886			0.0381943	+	0.999270i	$0.487839\pi$
$594$	4.29444e39	+	4.52565e39i	0.258823	+	0.272758i
$595$	−6.34574e39	−	1.33742e40i	−0.373239	−	0.786634i
$596$			1.20387e40i			0.691047i
$597$	−1.11215e40	+	2.87611e39i	−0.623069	+	0.161130i
$598$			1.56212e40i			0.854176i
$599$		−	1.09618e40i		−	0.585051i	−0.956258	−	0.292526i	$-0.905504\pi$
$599$		−	1.09618e40i		−	0.585051i	0.956258	−	0.292526i	$-0.0944957\pi$
$600$	1.74013e39	−	4.50009e38i	0.0906541	−	0.0234438i
$601$			6.61151e39i			0.336218i	0.985768	+	0.168109i	$0.0537661\pi$
$601$			6.61151e39i			0.336218i	−0.985768	+	0.168109i	$0.946234\pi$
$602$	1.59336e40	−	7.56010e39i	0.790978	−	0.375300i
$603$	−2.13690e40	+	1.18445e40i	−1.03558	+	0.574004i
$604$	7.96775e39			0.376964
$605$	1.75324e40			0.809819
$606$	−2.07131e40	+	5.35657e39i	−0.934098	+	0.241565i
$607$		−	3.43104e40i		−	1.51074i	−0.655299	−	0.755370i	$-0.727457\pi$
$607$		−	3.43104e40i		−	1.51074i	0.655299	−	0.755370i	$-0.272543\pi$
$608$	−2.78413e40			−1.19698
$609$	2.73168e39	+	3.26906e39i	0.114678	+	0.137237i
$610$	2.51295e40			1.03015
$611$		−	4.72960e39i		−	0.189333i
$612$	−6.83755e39	+	3.78994e39i	−0.267303	+	0.148162i
$613$	−3.03143e40			−1.15736			−0.578682	−	0.815553i	$-0.696433\pi$
$613$	−3.03143e40			−1.15736			−0.578682	+	0.815553i	$0.696433\pi$
$614$	6.01930e39			0.224442
$615$	−7.39462e39	−	2.85940e40i	−0.269294	−	1.04132i
$616$	−6.18922e39	−	1.30443e40i	−0.220148	−	0.463983i
$617$			5.05127e40i			1.75495i	0.479620	+	0.877476i	$0.340775\pi$
$617$			5.05127e40i			1.75495i	−0.479620	+	0.877476i	$0.659225\pi$
$618$	1.16210e39	+	4.49368e39i	0.0394376	+	0.152500i
$619$		−	2.70106e38i		−	0.00895405i	−0.999990	−	0.00447702i	$-0.998575\pi$
$619$		−	2.70106e38i		−	0.00895405i	0.999990	−	0.00447702i	$-0.00142509\pi$
$620$			2.33782e39i			0.0757061i
$621$	−4.11101e40	+	3.90098e40i	−1.30053	+	1.23409i
$622$			3.29316e39i			0.101778i
$623$	−1.91700e40	−	4.04025e40i	−0.578822	−	1.21992i
$624$	9.82449e39	−	2.54069e39i	0.289823	−	0.0749505i
$625$	−3.74241e40			−1.07868
$626$	−3.51976e40			−0.991255
$627$	−7.46109e39	−	2.88510e40i	−0.205316	−	0.793929i
$628$			6.22291e39i			0.167332i
$629$	5.10420e39			0.134120
$630$	−1.88229e40	+	2.62742e40i	−0.483335	+	0.674670i
$631$	−5.16581e40			−1.29632			−0.648160	−	0.761504i	$-0.724461\pi$
$631$	−5.16581e40			−1.29632			−0.648160	+	0.761504i	$0.724461\pi$
$632$		−	4.41530e40i		−	1.08284i
$633$	3.72991e39	+	1.44230e40i	0.0894014	+	0.345703i
$634$	−5.37394e39			−0.125892
$635$	7.20852e40			1.65054
$636$	2.14547e39	−	5.54835e38i	0.0480169	−	0.0124175i
$637$	2.11823e40	+	1.72966e40i	0.463396	+	0.378390i
$638$		−	3.14468e39i		−	0.0672476i
$639$	1.23325e40	+	2.22494e40i	0.257803	+	0.465110i
$640$		−	7.46466e39i		−	0.152546i
$641$		−	6.95118e40i		−	1.38873i	−0.719624	−	0.694364i	$-0.755686\pi$
$641$		−	6.95118e40i		−	1.38873i	0.719624	−	0.694364i	$-0.244314\pi$
$642$	−6.11847e39	−	2.36593e40i	−0.119505	−	0.462108i
$643$		−	5.54425e40i		−	1.05873i	−0.848395	−	0.529363i	$-0.822431\pi$
$643$		−	5.54425e40i		−	1.05873i	0.848395	−	0.529363i	$-0.177569\pi$
$644$	3.17359e40	−	1.50579e40i	0.592524	−	0.281138i
$645$	−1.57136e40	−	6.07624e40i	−0.286853	−	1.10922i
$646$	−6.47381e40			−1.15555
$647$	2.56621e40			0.447899			0.223950	−	0.974601i	$-0.428105\pi$
$647$	2.56621e40			0.447899			0.223950	+	0.974601i	$0.428105\pi$
$648$	5.40440e40	+	3.37733e40i	0.922381	+	0.576416i
$649$		−	5.73769e39i		−	0.0957610i
$650$	2.51298e39			0.0410153
$651$	−7.97770e39	−	9.54710e39i	−0.127337	−	0.152387i
$652$	−6.80436e39			−0.106218
$653$			1.06252e41i			1.62217i	0.584927	+	0.811086i	$0.301123\pi$
$653$			1.06252e41i			1.62217i	−0.584927	+	0.811086i	$0.698877\pi$
$654$	6.29534e40	−	1.62802e40i	0.940031	−	0.243099i
$655$	8.47206e40			1.23734
$656$	−3.61507e40			−0.516430
$657$	−2.44768e40	−	4.41593e40i	−0.342024	−	0.617056i
$658$	1.66584e40	−	7.90400e39i	0.227697	−	0.108037i
$659$		−	2.27498e40i		−	0.304186i	−0.988366	−	0.152093i	$-0.951399\pi$
$659$		−	2.27498e40i		−	0.304186i	0.988366	−	0.152093i	$-0.0486012\pi$
$660$	−1.33231e40	+	3.44545e39i	−0.174268	+	0.0450670i
$661$			4.32277e40i			0.553148i	0.960993	+	0.276574i	$0.0891990\pi$
$661$			4.32277e40i			0.553148i	−0.960993	+	0.276574i	$0.910801\pi$
$662$			1.07438e41i			1.34498i
$663$	−3.95102e40	+	1.02176e40i	−0.483908	+	0.125142i
$664$		−	7.74366e40i		−	0.927917i
$665$	1.39477e41	−	6.61784e40i	1.63527	−	0.775894i
$666$	−5.40265e39	−	9.74707e39i	−0.0619770	−	0.111814i
$667$	2.85656e40			0.320641
$668$	6.47637e40			0.711333
$669$	4.21151e40	−	1.08913e40i	0.452647	−	0.117058i
$670$			9.34301e40i			0.982658i
$671$	−5.69412e40			−0.586071
$672$	−4.38733e40	−	5.25041e40i	−0.441922	−	0.528858i
$673$	8.48557e40			0.836494			0.418247	−	0.908333i	$-0.362645\pi$
$673$	8.48557e40			0.836494			0.418247	+	0.908333i	$0.362645\pi$
$674$		−	1.15637e41i		−	1.11565i
$675$	6.27550e39	+	6.61338e39i	0.0592576	+	0.0624480i
$676$	2.54138e40			0.234878
$677$	−1.82474e41			−1.65069			−0.825345	−	0.564628i	$-0.809020\pi$
$677$	−1.82474e41			−1.65069			−0.825345	+	0.564628i	$0.809020\pi$
$678$	−6.89684e39	−	2.66691e40i	−0.0610688	−	0.236145i
$679$	−9.72023e40	+	4.61201e40i	−0.842490	+	0.399741i
$680$			1.11620e41i			0.947029i
$681$	−3.07254e40	−	1.18811e41i	−0.255190	−	0.986786i
$682$			9.18386e39i			0.0746710i
$683$			5.83646e40i			0.464568i	0.972648	+	0.232284i	$0.0746199\pi$
$683$			5.83646e40i			0.464568i	−0.972648	+	0.232284i	$0.925380\pi$
$684$	−3.95245e40	−	7.13073e40i	−0.308002	−	0.555674i
$685$			2.06166e41i			1.57291i
$686$	−2.55219e40	+	1.03513e41i	−0.190640	+	0.773208i
$687$	1.15175e41	−	2.97852e40i	0.842338	−	0.217835i
$688$	−7.68205e40			−0.550104
$689$	1.15683e40			0.0811132
$690$	5.42607e40	+	2.09819e41i	0.372541	+	1.44056i
$691$			1.94591e41i			1.30825i	0.756386	+	0.654126i	$0.226963\pi$
$691$			1.94591e41i			1.30825i	−0.756386	+	0.654126i	$0.773037\pi$
$692$	5.65207e38			0.00372108
$693$	4.26509e40	−	5.95349e40i	0.274977	−	0.383831i
$694$	2.32371e41			1.46714
$695$			1.35743e41i			0.839340i
$696$	−8.04250e39	−	3.10992e40i	−0.0487031	−	0.188328i
$697$	1.45384e41			0.862266
$698$	−4.07261e40			−0.236575
$699$	−2.57437e41	+	6.65751e40i	−1.46471	+	0.378785i
$700$	−2.42236e39	−	5.10535e39i	−0.0134995	−	0.0284514i
$701$		−	1.57532e40i		−	0.0859922i	−0.999075	−	0.0429961i	$-0.986310\pi$
$701$		−	1.57532e40i		−	0.0859922i	0.999075	−	0.0429961i	$-0.0136903\pi$
$702$	6.13322e40	+	6.46343e40i	0.327944	+	0.345601i
$703$			5.32306e40i			0.278811i
$704$			9.65531e40i			0.495407i
$705$	−1.64284e40	−	6.35264e40i	−0.0825759	−	0.319310i
$706$		−	4.84313e40i		−	0.238483i
$707$	1.07657e41	+	2.26897e41i	0.519352	+	1.09458i
$708$	−3.93018e39	−	1.51975e40i	−0.0185751	−	0.0718272i
$709$	−1.39886e41			−0.647743			−0.323871	−	0.946101i	$-0.604985\pi$
$709$	−1.39886e41			−0.647743			−0.323871	+	0.946101i	$0.604985\pi$
$710$	9.72795e40			0.441342
$711$	1.95882e41	−	1.08574e41i	0.870735	−	0.482635i
$712$			3.37196e41i			1.46866i
$713$	−8.34243e40			−0.356037
$714$	−1.02017e41	−	1.22086e41i	−0.426626	−	0.510553i
$715$	−7.18377e40			−0.294384
$716$		−	1.44127e41i		−	0.578770i
$717$	1.26986e38	−	3.28394e37i	0.000499720	−	0.000129231i
$718$	−2.34436e41			−0.904106
$719$	2.17148e41			0.820703			0.410352	−	0.911927i	$-0.365406\pi$
$719$	2.17148e41			0.820703			0.410352	+	0.911927i	$0.365406\pi$
$720$	1.23134e41	−	6.82513e40i	0.456097	−	0.252807i
$721$	4.92250e40	−	2.33561e40i	0.178700	−	0.0847888i
$722$		−	4.51319e41i		−	1.60581i
$723$	4.51137e41	−	1.16667e41i	1.57327	−	0.406859i
$724$		−	1.11780e41i		−	0.382080i
$725$		−	4.59535e39i		−	0.0153964i
$726$	1.82428e41	−	4.71771e40i	0.599114	−	0.154935i
$727$		−	5.60200e41i		−	1.80341i	−0.432352	−	0.901705i	$-0.642316\pi$
$727$		−	5.60200e41i		−	1.80341i	0.432352	−	0.901705i	$-0.357684\pi$
$728$	−8.83930e40	−	1.86296e41i	−0.278941	−	0.587894i
$729$	−1.69365e40	+	3.22814e41i	−0.0523930	+	0.998627i
$730$	−1.93075e41			−0.585524
$731$	3.08942e41			0.918491
$732$	−1.50821e41	+	3.90034e40i	−0.439593	+	0.113682i
$733$			4.33300e41i			1.23817i	0.785324	+	0.619086i	$0.212497\pi$
$733$			4.33300e41i			1.23817i	−0.785324	+	0.619086i	$0.787503\pi$
$734$	−5.15679e41			−1.44473
$735$	3.44595e41	+	1.58745e41i	0.946547	+	0.436047i
$736$	−4.58791e41			−1.23562
$737$		−	2.11704e41i		−	0.559050i
$738$	−1.53885e41	−	2.77628e41i	−0.398454	−	0.718862i
$739$	1.68311e41			0.427335			0.213667	−	0.976906i	$-0.431459\pi$
$739$	1.68311e41			0.427335			0.213667	+	0.976906i	$0.431459\pi$
$740$	2.45813e40			0.0611991
$741$	−1.06557e41	−	4.12043e41i	−0.260148	−	1.00596i
$742$	1.93327e40	+	4.07455e40i	0.0462846	+	0.0975489i
$743$		−	2.21133e41i		−	0.519177i	−0.965719	−	0.259589i	$-0.916413\pi$
$743$		−	2.21133e41i		−	0.519177i	0.965719	−	0.259589i	$-0.0835870\pi$
$744$	2.34877e40	+	9.08236e40i	0.0540794	+	0.209118i
$745$			8.71879e41i			1.96875i
$746$		−	1.92019e40i		−	0.0425238i
$747$	3.43543e41	−	1.90421e41i	0.746161	−	0.413585i
$748$		−	6.77402e40i		−	0.144302i
$749$	−2.59171e41	+	1.22970e41i	−0.541501	+	0.256929i
$750$	−3.58327e41	+	9.26659e40i	−0.734329	+	0.189903i
$751$	4.36148e41			0.876707			0.438354	−	0.898803i	$-0.355562\pi$
$751$	4.36148e41			0.876707			0.438354	+	0.898803i	$0.355562\pi$
$752$	−8.03150e40			−0.158357
$753$	−1.54370e41	−	5.96928e41i	−0.298563	−	1.15450i
$754$		−	4.49116e40i		−	0.0852068i
$755$	5.77050e41			1.07395
$756$	7.21900e40	−	1.86905e41i	0.131799	−	0.341237i
$757$	2.26718e41			0.406065			0.203032	−	0.979172i	$-0.434920\pi$
$757$	2.26718e41			0.406065			0.203032	+	0.979172i	$0.434920\pi$
$758$		−	6.10197e41i		−	1.07218i
$759$	−1.22950e41	−	4.75430e41i	−0.211945	−	0.819561i
$760$	−1.16406e42			−1.96870
$761$	−7.74173e41			−1.28458			−0.642289	−	0.766463i	$-0.722015\pi$
$761$	−7.74173e41			−1.28458			−0.642289	+	0.766463i	$0.722015\pi$
$762$	7.50059e41	−	1.93971e41i	1.22109	−	0.315784i
$763$	−3.27203e41	−	6.89610e41i	−0.522650	−	1.10153i
$764$			6.73129e40i			0.105498i
$765$	−4.95197e41	+	2.74480e41i	−0.761530	+	0.422104i
$766$			5.58006e41i			0.842018i
$767$		−	8.19443e40i		−	0.121335i
$768$	1.60711e41	+	6.21447e41i	0.233511	+	0.902955i
$769$			4.65728e41i			0.664050i	0.943271	+	0.332025i	$0.107732\pi$
$769$			4.65728e41i			0.664050i	−0.943271	+	0.332025i	$0.892268\pi$
$770$	−1.20054e41	−	2.53024e41i	−0.167981	−	0.354035i
$771$	8.51892e40	+	3.29415e41i	0.116976	+	0.452329i
$772$	−3.59152e41			−0.483980
$773$	−4.47931e41			−0.592391			−0.296196	−	0.955127i	$-0.595718\pi$
$773$	−4.47931e41			−0.592391			−0.296196	+	0.955127i	$0.595718\pi$
$774$	−3.27006e41	−	5.89961e41i	−0.424435	−	0.765736i
$775$			1.34205e40i			0.0170959i
$776$	8.11242e41			1.01427
$777$	−1.00384e41	+	8.38827e40i	−0.123186	+	0.102936i
$778$	−6.26002e41			−0.754000
$779$			1.51618e42i			1.79249i
$780$	−1.90277e41	+	4.92071e40i	−0.220808	+	0.0571026i
$781$	−2.20427e41			−0.251087
$782$	−1.06681e42			−1.19286
$783$	1.18193e41	−	1.12155e41i	0.129732	−	0.123104i
$784$	2.93720e41	−	3.59705e41i	0.316483	−	0.387582i
$785$			4.50683e41i			0.476717i
$786$	8.81532e41	−	2.27971e41i	0.915401	−	0.236729i
$787$			1.28963e41i			0.131471i	0.997837	+	0.0657355i	$0.0209394\pi$
$787$			1.28963e41i			0.131471i	−0.997837	+	0.0657355i	$0.979061\pi$
$788$			6.91822e41i			0.692412i
$789$	−1.07877e42	+	2.78977e41i	−1.06001	+	0.274127i
$790$		−	8.56444e41i		−	0.826240i
$791$	−2.92141e41	+	1.38614e41i	−0.276716	+	0.131295i
$792$	−4.82983e41	+	2.67710e41i	−0.449176	+	0.248971i
$793$	−8.13221e41			−0.742587
$794$	4.13271e41			0.370543
$795$	1.55382e41	−	4.01829e40i	0.136797	−	0.0353768i
$796$		−	2.72322e41i		−	0.235420i
$797$	8.57515e41			0.727941			0.363970	−	0.931410i	$-0.381421\pi$
$797$	8.57515e41			0.727941			0.363970	+	0.931410i	$0.381421\pi$
$798$	1.27321e42	−	1.06391e42i	1.06135	−	0.886876i
$799$	3.22995e41			0.264404
$800$			7.38057e40i			0.0593315i
$801$	−1.49595e42	+	8.29182e41i	−1.18099	+	0.654604i
$802$	8.65922e41			0.671352
$803$	4.37490e41			0.333114
$804$	−1.45012e41	−	5.60743e41i	−0.108441	−	0.419325i
$805$	2.29842e42	−	1.09054e42i	1.68806	−	0.800944i
$806$			1.31162e41i			0.0946127i
$807$	4.04664e41	+	1.56478e42i	0.286700	+	1.10863i
$808$		−	1.89367e42i		−	1.31777i
$809$		−	2.05987e42i		−	1.40795i	−0.710225	−	0.703975i	$-0.751407\pi$
$809$		−	2.05987e42i		−	1.40795i	0.710225	−	0.703975i	$-0.248593\pi$
$810$	1.04830e42	+	6.55108e41i	0.703808	+	0.439825i
$811$		−	6.24704e41i		−	0.411976i	−0.978555	−	0.205988i	$-0.933959\pi$
$811$		−	6.24704e41i		−	0.411976i	0.978555	−	0.205988i	$-0.0660408\pi$
$812$	−9.12420e40	+	4.32921e40i	−0.0591061	+	0.0280444i
$813$	7.64119e41	−	1.97607e41i	0.486237	−	0.125745i
$814$	9.65651e40			0.0603624
$815$	−4.92794e41			−0.302608
$816$	1.73509e41	+	6.70937e41i	0.104668	+	0.404738i
$817$			3.22189e42i			1.90937i
$818$	−6.14599e41			−0.357824
$819$	6.09131e41	−	8.50263e41i	0.348413	−	0.486336i
$820$	7.00154e41			0.393453
$821$			1.08741e42i			0.600366i	0.953882	+	0.300183i	$0.0970478\pi$
$821$			1.08741e42i			0.600366i	−0.953882	+	0.300183i	$0.902952\pi$
$822$	5.54764e41	+	2.14520e42i	0.300931	+	1.16366i
$823$	−7.36285e41			−0.392418			−0.196209	−	0.980562i	$-0.562863\pi$
$823$	−7.36285e41			−0.392418			−0.196209	+	0.980562i	$0.562863\pi$
$824$	−4.10828e41			−0.215137
$825$	−7.64825e40	+	1.97789e40i	−0.0393532	+	0.0101770i
$826$	2.88621e41	−	1.36944e41i	0.145921	−	0.0692358i
$827$		−	9.88456e41i		−	0.491052i	−0.969390	−	0.245526i	$-0.921039\pi$
$827$		−	9.88456e41i		−	0.491052i	0.969390	−	0.245526i	$-0.0789607\pi$
$828$	−6.51317e41	−	1.17506e42i	−0.317945	−	0.573614i
$829$		−	1.67451e41i		−	0.0803242i	−0.999193	−	0.0401621i	$-0.987213\pi$
$829$		−	1.67451e41i		−	0.0803242i	0.999193	−	0.0401621i	$-0.0127874\pi$
$830$		−	1.50205e42i		−	0.708032i
$831$	8.98243e41	+	3.47339e42i	0.416082	+	1.60893i
$832$			1.37895e42i			0.627711i
$833$	−1.18123e42	+	1.44659e42i	−0.528421	+	0.647133i
$834$	3.65265e41	+	1.41243e42i	0.160583	+	0.620954i
$835$	4.69039e42			2.02654
$836$	7.06448e41			0.299978
$837$	−3.45177e41	+	3.27542e41i	−0.144053	+	0.136693i
$838$			1.74669e42i			0.716436i
$839$	4.42420e42			1.78355			0.891777	−	0.452476i	$-0.149459\pi$
$839$	4.42420e42			1.78355			0.891777	+	0.452476i	$0.149459\pi$
$840$	−1.83437e42	−	2.19524e42i	−0.726838	−	0.869824i
$841$	2.48556e42			0.968015
$842$			1.89979e41i			0.0727245i
$843$	−4.21675e42	+	1.09048e42i	−1.58664	+	0.410317i
$844$	−3.53164e41			−0.130620
$845$	1.84055e42			0.669153
$846$	−3.41881e41	−	6.16797e41i	−0.122181	−	0.220431i
$847$	−9.48174e41	−	1.99836e42i	−0.333103	−	0.702045i
$848$		−	1.96446e41i		−	0.0678426i
$849$	2.47014e41	−	6.38796e40i	0.0838609	−	0.0216870i
$850$			1.71617e41i			0.0572779i
$851$			8.77177e41i			0.287812i
$852$	−5.83846e41	+	1.50987e41i	−0.188332	+	0.0487041i
$853$		−	1.69671e42i		−	0.538079i	−0.963129	−	0.269040i	$-0.913294\pi$
$853$		−	1.69671e42i		−	0.538079i	0.963129	−	0.269040i	$-0.0867063\pi$
$854$	−1.35904e42	−	2.86429e42i	−0.423733	−	0.893056i
$855$	−2.86249e42	−	5.16430e42i	−0.877477	−	1.58308i
$856$	2.16302e42			0.651913
$857$	1.92041e42			0.569078			0.284539	−	0.958665i	$-0.408160\pi$
$857$	1.92041e42			0.569078			0.284539	+	0.958665i	$0.408160\pi$
$858$	−7.47484e41	+	1.93305e41i	−0.217789	+	0.0563219i
$859$			3.55424e42i			1.01823i	0.860699	+	0.509115i	$0.170027\pi$
$859$			3.55424e42i			1.01823i	−0.860699	+	0.509115i	$0.829973\pi$
$860$	1.48783e42			0.419108
$861$	−2.85927e42	+	2.38925e42i	−0.791971	+	0.661783i
$862$	−4.64874e41			−0.126613
$863$		−	2.71355e42i		−	0.726745i	−0.931644	−	0.363372i	$-0.881625\pi$
$863$		−	2.71355e42i		−	0.726745i	0.931644	−	0.363372i	$-0.118375\pi$
$864$	−1.89829e42	+	1.80131e42i	−0.499936	+	0.474394i
$865$	4.09341e40			0.0106011
$866$	−3.68786e42			−0.939216
$867$	3.01893e41	+	1.16738e42i	0.0756095	+	0.292372i
$868$	2.66467e41	−	1.26432e41i	0.0656308	−	0.0311402i
$869$			1.94062e42i			0.470061i
$870$	−1.56002e41	−	6.03238e41i	−0.0371621	−	0.143701i
$871$		−	3.02351e42i		−	0.708350i
$872$			5.75542e42i			1.32614i
$873$	1.99489e42	+	3.59903e42i	0.452076	+	0.815603i
$874$		−	1.11255e43i		−	2.47973i
$875$	1.86242e42	+	3.92521e42i	0.408282	+	0.860491i
$876$	1.15878e42	−	2.99670e41i	0.249858	−	0.0646151i
$877$	−5.87221e42			−1.24540			−0.622698	−	0.782462i	$-0.713963\pi$
$877$	−5.87221e42			−1.24540			−0.622698	+	0.782462i	$0.713963\pi$
$878$	−2.19708e42			−0.458327
$879$	2.61969e41	+	1.01300e42i	0.0537540	+	0.207859i
$880$			1.21990e42i			0.246222i
$881$	4.89337e42			0.971532			0.485766	−	0.874089i	$-0.338541\pi$
$881$	4.89337e42			0.971532			0.485766	+	0.874089i	$0.338541\pi$
$882$	4.01273e42	+	7.24514e41i	0.783692	+	0.141499i
$883$	−3.13901e42			−0.603063			−0.301531	−	0.953456i	$-0.597498\pi$
$883$	−3.13901e42			−0.603063			−0.301531	+	0.953456i	$0.597498\pi$
$884$		−	9.67449e41i		−	0.182840i
$885$	−2.84636e41	−	1.10065e42i	−0.0529191	−	0.204631i
$886$	2.65027e42			0.484732
$887$	−5.38191e42			−0.968376			−0.484188	−	0.874964i	$-0.660885\pi$
$887$	−5.38191e42			−0.968376			−0.484188	+	0.874964i	$0.660885\pi$
$888$	9.54978e41	−	2.46964e41i	0.169046	−	0.0437166i
$889$	−3.89846e42	−	8.21636e42i	−0.678919	−	1.43088i
$890$			6.54065e42i			1.12064i
$891$	−2.37536e42	−	1.48441e42i	−0.400408	−	0.250224i
$892$			1.03123e42i			0.171028i
$893$			3.36845e42i			0.549647i
$894$	2.34610e42	+	9.07206e42i	0.376663	+	1.45650i
$895$		−	1.04381e43i		−	1.64888i
$896$	−8.50831e41	+	4.03698e41i	−0.132244	+	0.0627467i
$897$	−1.75594e42	−	6.78999e42i	−0.268547	−	1.03843i
$898$	−4.02231e42			−0.605297
$899$	2.39848e41			0.0355158
$900$	−1.89032e41	+	1.04777e41i	−0.0275435	+	0.0152669i
$901$			7.90027e41i			0.113275i
$902$	2.75048e42			0.388073
$903$	−6.07596e42	+	5.07717e42i	−0.843612	+	0.704935i
$904$	2.43819e42			0.333138
$905$		−	8.09546e42i		−	1.08852i
$906$	6.00431e42	−	1.55276e42i	0.794519	−	0.205468i
$907$	7.97433e42			1.03846			0.519229	−	0.854635i	$-0.326219\pi$
$907$	7.97433e42			1.03846			0.519229	+	0.854635i	$0.326219\pi$
$908$	2.90921e42			0.372847
$909$	8.40115e42	−	4.65662e42i	1.05965	−	0.587347i
$910$	−1.71458e42	−	3.61363e42i	−0.212842	−	0.448583i
$911$		−	2.81789e42i		−	0.344276i	−0.985073	−	0.172138i	$-0.944932\pi$
$911$		−	2.81789e42i		−	0.344276i	0.985073	−	0.172138i	$-0.0550675\pi$
$912$	−6.99706e42	+	1.80949e42i	−0.841376	+	0.217586i
$913$			3.40351e42i			0.402811i
$914$		−	4.49372e42i		−	0.523463i
$915$	−1.09229e43	+	2.82475e42i	−1.25237	+	0.323872i
$916$			2.82019e42i			0.318268i
$917$	−4.58180e42	−	9.65655e42i	−0.508956	−	1.07267i
$918$	−4.41403e42	+	4.18852e42i	−0.482632	+	0.457974i
$919$	−5.60738e42			−0.603511			−0.301755	−	0.953385i	$-0.597573\pi$
$919$	−5.60738e42			−0.603511			−0.301755	+	0.953385i	$0.597573\pi$
$920$	−1.91824e43			−2.03226
$921$	−2.61638e42	+	6.76615e41i	−0.272858	+	0.0705630i
$922$			1.26975e43i			1.30353i
$923$	−3.14808e42			−0.318142
$924$	1.11325e42	+	1.33225e42i	0.110751	+	0.132538i
$925$	1.41112e41			0.0138200
$926$		−	1.22751e42i		−	0.118349i
$927$	−1.01025e42	−	1.82262e42i	−0.0958896	−	0.172997i
$928$	1.31904e42			0.123258
$929$	−5.54753e41			−0.0510355			−0.0255177	−	0.999674i	$-0.508123\pi$
$929$	−5.54753e41			−0.0510355			−0.0255177	+	0.999674i	$0.508123\pi$
$930$	4.55595e41	+	1.76172e42i	0.0412644	+	0.159564i
$931$	−1.50862e43	−	1.23187e43i	−1.34527	−	1.09849i
$932$		−	6.30361e42i		−	0.553425i
$933$	−3.70176e41	−	1.43142e42i	−0.0319981	−	0.123732i
$934$			6.65621e42i			0.566497i
$935$		−	4.90596e42i		−	0.411108i
$936$	−6.89784e42	+	3.82337e42i	−0.569133	+	0.315461i
$937$		−	1.97529e43i		−	1.60474i	−0.596824	−	0.802372i	$-0.703571\pi$
$937$		−	1.97529e43i		−	1.60474i	0.596824	−	0.802372i	$-0.296429\pi$
$938$	1.06493e43	−	5.05282e42i	0.851881	−	0.404197i
$939$	1.52992e43	−	3.95648e42i	1.20508	−	0.311643i
$940$	1.55551e42			0.120648
$941$	1.92905e43			1.47331			0.736654	−	0.676270i	$-0.236405\pi$
$941$	1.92905e43			1.47331			0.736654	+	0.676270i	$0.236405\pi$
$942$	1.21272e42	+	4.68944e42i	0.0912060	+	0.352681i
$943$			2.49848e43i			1.85036i
$944$	−1.39153e42			−0.101484
$945$	5.22823e42	−	1.35363e43i	0.375486	−	0.972162i
$946$	5.84479e42			0.413378
$947$		−	3.59108e41i		−	0.0250121i	−0.999922	−	0.0125060i	$-0.996019\pi$
$947$		−	3.59108e41i		−	0.0250121i	0.999922	−	0.0125060i	$-0.00398090\pi$
$948$	1.32928e42	+	5.14015e42i	0.0911792	+	0.352578i
$949$	6.24813e42			0.422076
$950$	−1.78976e42			−0.119070
$951$	2.33586e42	−	6.04072e41i	0.153049	−	0.0395796i
$952$	1.27226e43	−	6.03656e42i	0.820995	−	0.389542i
$953$			1.95662e43i			1.24354i	0.783199	+	0.621771i	$0.213586\pi$
$953$			1.95662e43i			1.24354i	−0.783199	+	0.621771i	$0.786414\pi$
$954$	1.50865e42	−	8.36221e41i	0.0944359	−	0.0523443i
$955$			4.87502e42i			0.300557i
$956$			3.10938e39i			0.000188814i
$957$	3.53486e41	+	1.36688e42i	0.0211422	+	0.0817538i
$958$			2.67992e42i			0.157878i
$959$	2.34991e43	−	1.11497e43i	1.36358	−	0.646986i
$960$	4.78982e42	+	1.85216e43i	0.273770	+	1.05863i
$961$	1.70614e43			0.960564
$962$	1.37912e42			0.0764828
$963$	5.31897e42	+	9.59610e42i	0.290567	+	0.524220i
$964$			1.10466e43i			0.594443i
$965$	−2.60109e43			−1.37883
$966$	2.09809e43	−	1.75320e43i	1.09561	−	0.915509i
$967$	−1.72136e43			−0.885498			−0.442749	−	0.896646i	$-0.645997\pi$
$967$	−1.72136e43			−0.885498			−0.442749	+	0.896646i	$0.645997\pi$
$968$			1.66782e43i			0.845192i
$969$	2.81394e43	−	7.27706e42i	1.40482	−	0.363296i
$970$	1.57358e43			0.773925
$971$	−1.64762e43			−0.798321			−0.399160	−	0.916881i	$-0.630698\pi$
$971$	−1.64762e43			−0.798321			−0.399160	+	0.916881i	$0.630698\pi$
$972$	−7.30842e42	−	2.30472e42i	−0.348869	−	0.110016i
$973$	1.54722e43	−	7.34116e42i	0.727637	−	0.345246i
$974$		−	1.60803e43i		−	0.745058i
$975$	−1.09231e42	+	2.82478e41i	−0.0498628	+	0.0128949i
$976$			1.38096e43i			0.621096i
$977$			8.85837e42i			0.392539i	0.980550	+	0.196270i	$0.0628827\pi$
$977$			8.85837e42i			0.392539i	−0.980550	+	0.196270i	$0.937117\pi$
$978$	−5.12760e42	+	1.32604e42i	−0.223873	+	0.0578951i
$979$		−	1.48205e43i		−	0.637550i
$980$	−5.68866e42	+	6.96664e42i	−0.241119	+	0.295288i
$981$	−2.55336e43	+	1.41529e43i	−1.06638	+	0.591077i
$982$	−3.31607e42			−0.136461
$983$	−3.78700e43			−1.53557			−0.767784	−	0.640709i	$-0.778640\pi$
$983$	−3.78700e43			−1.53557			−0.767784	+	0.640709i	$0.778640\pi$
$984$	2.72008e43	−	7.03433e42i	1.08681	−	0.281057i
$985$			5.01040e43i			1.97264i
$986$	3.06712e42			0.118991
$987$	−6.35235e42	+	5.30812e42i	−0.242849	+	0.202928i
$988$	1.00893e43			0.380090
$989$			5.30929e43i			1.97102i
$990$	−9.36851e42	+	5.19282e42i	−0.342736	+	0.189973i
$991$	−3.96609e43			−1.42986			−0.714932	−	0.699194i	$-0.753543\pi$
$991$	−3.96609e43			−1.42986			−0.714932	+	0.699194i	$0.753543\pi$
$992$	−3.85219e42			−0.136864
$993$	−1.20768e43	−	4.66995e43i	−0.422853	−	1.63511i
$994$	−5.26100e42	−	1.10880e43i	−0.181537	−	0.382606i
$995$		−	1.97224e43i		−	0.670696i
$996$	2.33133e42	+	9.01492e42i	0.0781345	+	0.302135i
$997$			2.98746e43i			0.986784i	0.869807	+	0.493392i	$0.164243\pi$
$997$			2.98746e43i			0.986784i	−0.869807	+	0.493392i	$0.835757\pi$
$998$		−	3.00779e43i		−	0.979163i
$999$	3.44399e42	+	3.62941e42i	0.110500	+	0.116449i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	21.30.c.a.20.16	yes	76
3.2	odd	2	inner	21.30.c.a.20.61	yes	76
7.6	odd	2	inner	21.30.c.a.20.62	yes	76
21.20	even	2	inner	21.30.c.a.20.15	✓	76

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
21.30.c.a.20.15	✓	76	21.20	even	2	inner
21.30.c.a.20.16	yes	76	1.1	even	1	trivial
21.30.c.a.20.61	yes	76	3.2	odd	2	inner
21.30.c.a.20.62	yes	76	7.6	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:	\( N \)	\(=\)	\( 21 = 3 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 30 \)
Character orbit:	\([\chi]\)	\(=\)	21.c (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+18452.1i q^{2} +(-2.07416e6 - 8.02049e6i) q^{3} +1.96390e8 q^{4} +1.42232e10 q^{5} +(1.47995e11 - 3.82726e10i) q^{6} +(-7.69210e11 - 1.62118e12i) q^{7} +1.35302e13i q^{8} +(-6.00261e13 + 3.32715e13i) q^{9} +O(q^{10})\)	\(q+18452.1i q^{2} +(-2.07416e6 - 8.02049e6i) q^{3} +1.96390e8 q^{4} +1.42232e10 q^{5} +(1.47995e11 - 3.82726e10i) q^{6} +(-7.69210e11 - 1.62118e12i) q^{7} +1.35302e13i q^{8} +(-6.00261e13 + 3.32715e13i) q^{9} +2.62448e14i q^{10} -5.94684e14i q^{11} +(-4.07344e14 - 1.57515e15i) q^{12} -8.49314e15i q^{13} +(2.99142e16 - 1.41935e16i) q^{14} +(-2.95012e16 - 1.14077e17i) q^{15} -1.44225e17 q^{16} +5.80016e17 q^{17} +(-6.13930e17 - 1.10761e18i) q^{18} +6.04886e18i q^{19} +2.79330e18 q^{20} +(-1.14072e19 + 9.53202e18i) q^{21} +1.09732e19 q^{22} +9.96781e19i q^{23} +(1.08519e20 - 2.80638e19i) q^{24} +1.60352e19 q^{25} +1.56716e20 q^{26} +(3.91358e20 + 4.12428e20i) q^{27} +(-1.51065e20 - 3.18384e20i) q^{28} -2.86579e20i q^{29} +(2.10496e21 - 5.44359e20i) q^{30} +8.36937e20i q^{31} +4.60272e21i q^{32} +(-4.76966e21 + 1.23347e21i) q^{33} +1.07025e22i q^{34} +(-1.09406e22 - 2.30584e22i) q^{35} +(-1.17885e22 + 6.53420e21i) q^{36} +8.80010e21 q^{37} -1.11614e23 q^{38} +(-6.81191e22 + 1.76161e22i) q^{39} +1.92443e23i q^{40} +2.50655e23 q^{41} +(-1.75886e23 - 2.10487e23i) q^{42} +5.32643e23 q^{43} -1.16790e23i q^{44} +(-8.53764e23 + 4.73228e23i) q^{45} -1.83927e24 q^{46} +5.56873e23 q^{47} +(2.99146e23 + 1.15676e24i) q^{48} +(-2.03654e24 + 2.49405e24i) q^{49} +2.95884e23i q^{50} +(-1.20305e24 - 4.65201e24i) q^{51} -1.66797e24i q^{52} +1.36208e24i q^{53} +(-7.61018e24 + 7.22138e24i) q^{54} -8.45832e24i q^{55} +(2.19349e25 - 1.04076e25i) q^{56} +(4.85149e25 - 1.25463e25i) q^{57} +5.28799e24 q^{58} +9.64829e24 q^{59} +(-5.79374e24 - 2.24036e25i) q^{60} -9.57504e25i q^{61} -1.54433e25 q^{62} +(1.00112e26 + 7.17203e25i) q^{63} -1.62360e26 q^{64} -1.20800e26i q^{65} +(-2.27601e25 - 8.80103e25i) q^{66} +3.55994e26 q^{67} +1.13910e26 q^{68} +(7.99467e26 - 2.06748e26i) q^{69} +(4.25476e26 - 2.01878e26i) q^{70} -3.70662e26i q^{71} +(-4.50171e26 - 8.12167e26i) q^{72} +7.35668e26i q^{73} +1.62380e26i q^{74} +(-3.32596e25 - 1.28610e26i) q^{75} +1.18794e27i q^{76} +(-9.64090e26 + 4.57437e26i) q^{77} +(-3.25055e26 - 1.25694e27i) q^{78} -3.26329e27 q^{79} -2.05134e27 q^{80} +(2.49614e27 - 3.99432e27i) q^{81} +4.62511e27i q^{82} -5.72323e27 q^{83} +(-2.24026e27 + 1.87200e27i) q^{84} +8.24969e27 q^{85} +9.82840e27i q^{86} +(-2.29850e27 + 5.94410e26i) q^{87} +8.04621e27 q^{88} +2.49217e28 q^{89} +(-8.73206e27 - 1.57538e28i) q^{90} +(-1.37689e28 + 6.53301e27i) q^{91} +1.95758e28i q^{92} +(6.71265e27 - 1.73594e27i) q^{93} +1.02755e28i q^{94} +8.60343e28i q^{95} +(3.69161e28 - 9.54678e27i) q^{96} -5.99578e28i q^{97} +(-4.60206e28 - 3.75785e28i) q^{98} +(1.97860e28 + 3.56966e28i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 76 q - 20401094660 q^{4} + 1962751543872 q^{7} - 89581451225964 q^{9}+O(q^{10}) \) 76 * q - 20401094660 * q^4 + 1962751543872 * q^7 - 89581451225964 * q^9	\( 76 q - 20401094660 q^{4} + 1962751543872 q^{7} - 89581451225964 q^{9} - 11\!\cdots\!48 q^{15}+ \cdots - 23\!\cdots\!24 q^{99}+O(q^{100}) \) 76 * q - 20401094660 * q^4 + 1962751543872 * q^7 - 89581451225964 * q^9 - 116668222909200048 * q^15 + 4964525139713333892 * q^16 + 1542346202347854996 * q^18 + 33840646982361357348 * q^21 - 9870996616978150672 * q^22 + 3225406746743103424612 * q^25 - 3181907581338093199564 * q^28 + 5113912044496410095244 * q^30 - 85758641407134848258352 * q^36 - 17812771227715200149976 * q^37 + 388095283792424641491696 * q^39 + 804036587819434104664956 * q^42 + 2391536152977907871782320 * q^43 - 1070985628070611677307000 * q^46 - 512656982878691867441540 * q^49 - 961431915936904000664400 * q^51 + 20345422731681279280765248 * q^57 - 40096240109469024574169272 * q^58 - 164991837955115951799442596 * q^60 - 360764839802574990409097184 * q^63 - 1608343949909674725081473028 * q^64 + 483978610969894046870693264 * q^67 - 656026306765550013508448520 * q^70 + 1937172856654554597960695124 * q^72 - 8054141680325499868559088636 * q^78 - 11740735193468750125742145952 * q^79 + 18477545939654446572971367132 * q^81 - 7249045143271847568431965452 * q^84 + 14576359553686844022629140848 * q^85 - 1685535263940707754634995584 * q^88 + 44135166284535829618726469040 * q^91 + 226499776928895503792863540632 * q^93 - 231093384978708762520959066624 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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