LMFDB - Embedded newform 6.25.b.a.5.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6,25,Mod(5,6)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 25, names="a")

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

chi := DirichletCharacter("6.5");

S:= CuspForms(chi, 25);

N := Newforms(S);

Level:	$ N $	$=$	$ 6 = 2 \cdot 3 $
Weight:	$ k $	$=$	$ 25 $
Character orbit:	$[\chi]$	$=$	6.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:	$21.8980291355$
Analytic rank:	$0$
Dimension:	$8$
Coefficient field:	$\mathbb{Q}[x]/(x^{8} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} + 9921984x^{6} + 31297402621425x^{4} + 35629505313218665424x^{2} + 11190322069687119538557504 $ x^8 + 9921984x^6 + 31297402621425x^4 + 35629505313218665424*x^2 + 11190322069687119538557504
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{53}\cdot 3^{32}\cdot 17^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			5.2
Root			$1694.95i$ of defining polynomial
Character	$\chi$	$=$	6.5
Dual form			6.25.b.a.5.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2896.31i q^{2} +(-317945. + 425841. i) q^{3} -8.38861e6 q^{4} -6.76938e7i q^{5} +(1.23337e9 + 9.20867e8i) q^{6} -2.41596e10 q^{7} +2.42960e10i q^{8} +(-8.02515e10 - 2.70788e11i) q^{9} +O(q^{10})$	\(q-2896.31i q^{2} +(-317945. + 425841. i) q^{3} -8.38861e6 q^{4} -6.76938e7i q^{5} +(1.23337e9 + 9.20867e8i) q^{6} -2.41596e10 q^{7} +2.42960e10i q^{8} +(-8.02515e10 - 2.70788e11i) q^{9} -1.96062e11 q^{10} +4.00004e12i q^{11} +(2.66712e12 - 3.57221e12i) q^{12} +2.67023e13 q^{13} +6.99737e13i q^{14} +(2.88268e13 + 2.15229e13i) q^{15} +7.03687e13 q^{16} -6.60084e14i q^{17} +(-7.84286e14 + 2.32433e14i) q^{18} -3.05285e14 q^{19} +5.67857e14i q^{20} +(7.68142e15 - 1.02881e16i) q^{21} +1.15854e16 q^{22} -7.66067e14i q^{23} +(-1.03462e16 - 7.72479e15i) q^{24} +5.50222e16 q^{25} -7.73381e16i q^{26} +(1.40828e17 + 5.19213e16i) q^{27} +2.02665e17 q^{28} -4.00191e17i q^{29} +(6.23370e16 - 8.34913e16i) q^{30} +1.08492e18 q^{31} -2.03810e17i q^{32} +(-1.70338e18 - 1.27179e18i) q^{33} -1.91181e18 q^{34} +1.63546e18i q^{35} +(6.73199e17 + 2.27153e18i) q^{36} +2.67466e18 q^{37} +8.84200e17i q^{38} +(-8.48986e18 + 1.13709e19i) q^{39} +1.64469e18 q^{40} +3.10777e19i q^{41} +(-2.97976e19 - 2.22478e19i) q^{42} -2.43678e19 q^{43} -3.35548e19i q^{44} +(-1.83307e19 + 5.43253e18i) q^{45} -2.21877e18 q^{46} -3.79896e19i q^{47} +(-2.23734e19 + 2.99659e19i) q^{48} +3.92105e20 q^{49} -1.59361e20i q^{50} +(2.81091e20 + 2.09870e20i) q^{51} -2.23995e20 q^{52} -8.82597e19i q^{53} +(1.50380e20 - 4.07882e20i) q^{54} +2.70778e20 q^{55} -5.86982e20i q^{56} +(9.70638e19 - 1.30003e20i) q^{57} -1.15908e21 q^{58} +1.88092e21i q^{59} +(-2.41817e20 - 1.80547e20i) q^{60} -1.92240e21 q^{61} -3.14226e21i q^{62} +(1.93884e21 + 6.54213e21i) q^{63} -5.90296e20 q^{64} -1.80758e21i q^{65} +(-3.68351e21 + 4.93352e21i) q^{66} -7.96234e21 q^{67} +5.53718e21i q^{68} +(3.26223e20 + 2.43567e20i) q^{69} +4.73678e21 q^{70} -2.04327e22i q^{71} +(6.57907e21 - 1.94979e21i) q^{72} +3.28296e22 q^{73} -7.74666e21i q^{74} +(-1.74940e22 + 2.34307e22i) q^{75} +2.56092e21 q^{76} -9.66394e22i q^{77} +(3.29337e22 + 2.45893e22i) q^{78} +5.13170e21 q^{79} -4.76353e21i q^{80} +(-6.68858e22 + 4.34623e22i) q^{81} +9.00105e22 q^{82} +1.14963e21i q^{83} +(-6.44364e22 + 8.63032e22i) q^{84} -4.46836e22 q^{85} +7.05766e22i q^{86} +(1.70418e23 + 1.27239e23i) q^{87} -9.71851e22 q^{88} -3.69857e23i q^{89} +(1.57343e22 + 5.30913e22i) q^{90} -6.45117e23 q^{91} +6.42623e21i q^{92} +(-3.44945e23 + 4.62003e23i) q^{93} -1.10030e23 q^{94} +2.06659e22i q^{95} +(8.67905e22 + 6.48003e22i) q^{96} +1.10819e24 q^{97} -1.13566e24i q^{98} +(1.08316e24 - 3.21010e23i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 131880 q^{3} - 67108864 q^{4} + 33718272 q^{6} - 10160794640 q^{7} + 295169053896 q^{9}+O(q^{10}) $ 8 * q - 131880 * q^3 - 67108864 * q^4 + 33718272 * q^6 - 10160794640 * q^7 + 295169053896 * q^9	$ 8 q - 131880 q^{3} - 67108864 q^{4} + 33718272 q^{6} - 10160794640 q^{7} + 295169053896 q^{9} - 1863369424896 q^{10} + 1106289623040 q^{12} + 50568363679120 q^{13} - 348034956760512 q^{15} + 562949953421312 q^{16} - 514738292981760 q^{18} - 978083631341264 q^{19} + 36\!\cdots\!36 q^{21}+ \cdots + 69\!\cdots\!44 q^{99}+O(q^{100}) $ 8 * q - 131880 * q^3 - 67108864 * q^4 + 33718272 * q^6 - 10160794640 * q^7 + 295169053896 * q^9 - 1863369424896 * q^10 + 1106289623040 * q^12 + 50568363679120 * q^13 - 348034956760512 * q^15 + 562949953421312 * q^16 - 514738292981760 * q^18 - 978083631341264 * q^19 + 3640012304241936 * q^21 - 336450979430400 * q^22 - 282849366245376 * q^24 + 7630618767014024 * q^25 - 86594528606057640 * q^27 + 85234923203461120 * q^28 - 725410188900237312 * q^30 + 3092119786822709104 * q^31 - 8158685952668529600 * q^33 + 3821138032531341312 * q^34 - 2476057486864416768 * q^36 + 22590293223992782480 * q^37 - 40190176581881465040 * q^39 + 15631075664637984768 * q^40 - 79119883835565342720 * q^42 + 226487466371803896880 * q^43 - 347709996757177504128 * q^45 + 139842130561120468992 * q^46 - 9280229982150328320 * q^48 + 104686700473616731800 * q^49 + 558091874936566543104 * q^51 - 424198180105575464960 * q^52 + 334066775626796728320 * q^54 - 2212687664250467338368 * q^55 + 3588879995640760725840 * q^57 - 1867706355469718323200 * q^58 + 2919528822560885047296 * q^60 - 6507010783838092385648 * q^61 + 10112982777612899380080 * q^63 - 4722366482869645213696 * q^64 - 1924112442339530440704 * q^66 - 7042120118150060144720 * q^67 - 4323335967368731345536 * q^69 + 16481910236435553583104 * q^70 + 4317937762413135790080 * q^72 + 36259820324758576687120 * q^73 - 108081978448612908655272 * q^75 + 8204760174538377920512 * q^76 - 74188898027329578270720 * q^78 + 316807052777330015315824 * q^79 - 268518660504396776813304 * q^81 + 83114941529654645882880 * q^82 - 30534636335462338265088 * q^84 - 222512862545524200678912 * q^85 + 449461577201807342128320 * q^87 + 2822355377657688883200 * q^88 + 612683975543382025371648 * q^90 - 1196839602335690774367520 * q^91 + 873237537450828783745680 * q^93 - 1298887117621773403422720 * q^94 + 2372712456480891076608 * q^96 + 816517576248201265716880 * q^97 + 695858883367208922313344 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/6\mathbb{Z}\right)^\times$.

$n$	$5$
$\chi(n)$	$-1$

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 $

$2$		−	2896.31i		−	0.707107i
$2$		−	2896.31i		−	0.707107i
$3$	−317945.	+	425841.i	−0.598270	+	0.801295i
$3$	−317945.	+	425841.i	−0.598270	+	0.801295i
$4$	−8.38861e6			−0.500000
$5$		−	6.76938e7i		−	0.277274i	−0.990343	−	0.138637i	$-0.955728\pi$
$5$		−	6.76938e7i		−	0.277274i	0.990343	−	0.138637i	$-0.0442721\pi$
$6$	1.23337e9	+	9.20867e8i	0.566601	+	0.423040i
$7$	−2.41596e10			−1.74547			−0.872736	−	0.488192i	$-0.837657\pi$
$7$	−2.41596e10			−1.74547			−0.872736	+	0.488192i	$0.837657\pi$
$8$			2.42960e10i			0.353553i
$9$	−8.02515e10	−	2.70788e11i	−0.284147	−	0.958781i
$10$	−1.96062e11			−0.196062
$11$			4.00004e12i			1.27454i	0.770642	+	0.637268i	$0.219936\pi$
$11$			4.00004e12i			1.27454i	−0.770642	+	0.637268i	$0.780064\pi$
$12$	2.66712e12	−	3.57221e12i	0.299135	−	0.400647i
$13$	2.67023e13			1.14612			0.573058	−	0.819515i	$-0.305757\pi$
$13$	2.67023e13			1.14612			0.573058	+	0.819515i	$0.305757\pi$
$14$			6.99737e13i			1.23424i
$15$	2.88268e13	+	2.15229e13i	0.222178	+	0.165885i
$16$	7.03687e13			0.250000
$17$		−	6.60084e14i		−	1.13295i	−0.824078	−	0.566477i	$-0.808306\pi$
$17$		−	6.60084e14i		−	1.13295i	0.824078	−	0.566477i	$-0.191694\pi$
$18$	−7.84286e14	+	2.32433e14i	−0.677960	+	0.200922i
$19$	−3.05285e14			−0.137931			−0.0689656	−	0.997619i	$-0.521970\pi$
$19$	−3.05285e14			−0.137931			−0.0689656	+	0.997619i	$0.521970\pi$
$20$			5.67857e14i			0.138637i
$21$	7.68142e15	−	1.02881e16i	1.04426	−	1.39864i
$22$	1.15854e16			0.901234
$23$		−	7.66067e14i		−	0.0349569i	−0.999847	−	0.0174784i	$-0.994436\pi$
$23$		−	7.66067e14i		−	0.0349569i	0.999847	−	0.0174784i	$-0.00556384\pi$
$24$	−1.03462e16	−	7.72479e15i	−0.283301	−	0.211520i
$25$	5.50222e16			0.923119
$26$		−	7.73381e16i		−	0.810426i
$27$	1.40828e17	+	5.19213e16i	0.938263	+	0.345924i
$28$	2.02665e17			0.872736
$29$		−	4.00191e17i		−	1.13107i	−0.824723	−	0.565537i	$-0.808669\pi$
$29$		−	4.00191e17i		−	1.13107i	0.824723	−	0.565537i	$-0.191331\pi$
$30$	6.23370e16	−	8.34913e16i	0.117298	−	0.157104i
$31$	1.08492e18			1.37739			0.688696	−	0.725051i	$-0.258184\pi$
$31$	1.08492e18			1.37739			0.688696	+	0.725051i	$0.258184\pi$
$32$		−	2.03810e17i		−	0.176777i
$33$	−1.70338e18	−	1.27179e18i	−1.02128	−	0.762517i
$34$	−1.91181e18			−0.801119
$35$			1.63546e18i			0.483974i
$36$	6.73199e17	+	2.27153e18i	0.142074	+	0.479390i
$37$	2.67466e18			0.406302			0.203151	−	0.979147i	$-0.434882\pi$
$37$	2.67466e18			0.406302			0.203151	+	0.979147i	$0.434882\pi$
$38$			8.84200e17i			0.0975320i
$39$	−8.48986e18	+	1.13709e19i	−0.685686	+	0.918377i
$40$	1.64469e18			0.0980311
$41$			3.10777e19i			1.37734i	0.725074	+	0.688671i	$0.241806\pi$
$41$			3.10777e19i			1.37734i	−0.725074	+	0.688671i	$0.758194\pi$
$42$	−2.97976e19	−	2.22478e19i	−0.988987	−	0.738406i
$43$	−2.43678e19			−0.609810			−0.304905	−	0.952383i	$-0.598625\pi$
$43$	−2.43678e19			−0.609810			−0.304905	+	0.952383i	$0.598625\pi$
$44$		−	3.35548e19i		−	0.637268i
$45$	−1.83307e19	+	5.43253e18i	−0.265845	+	0.0787866i
$46$	−2.21877e18			−0.0247182
$47$		−	3.79896e19i		−	0.326957i	−0.986547	−	0.163478i	$-0.947729\pi$
$47$		−	3.79896e19i		−	0.326957i	0.986547	−	0.163478i	$-0.0522714\pi$
$48$	−2.23734e19	+	2.99659e19i	−0.149567	+	0.200324i
$49$	3.92105e20			2.04668
$50$		−	1.59361e20i		−	0.652744i
$51$	2.81091e20	+	2.09870e20i	0.907830	+	0.677811i
$52$	−2.23995e20			−0.573058
$53$		−	8.82597e19i		−	0.179660i	−0.995957	−	0.0898301i	$-0.971368\pi$
$53$		−	8.82597e19i		−	0.179660i	0.995957	−	0.0898301i	$-0.0286324\pi$
$54$	1.50380e20	−	4.07882e20i	0.244605	−	0.663452i
$55$	2.70778e20			0.353396
$56$		−	5.86982e20i		−	0.617118i
$57$	9.70638e19	−	1.30003e20i	0.0825200	−	0.110524i
$58$	−1.15908e21			−0.799791
$59$			1.88092e21i			1.05718i	0.848879	+	0.528588i	$0.177278\pi$
$59$			1.88092e21i			1.05718i	−0.848879	+	0.528588i	$0.822722\pi$
$60$	−2.41817e20	−	1.80547e20i	−0.111089	−	0.0829423i
$61$	−1.92240e21			−0.724244			−0.362122	−	0.932131i	$-0.617948\pi$
$61$	−1.92240e21			−0.724244			−0.362122	+	0.932131i	$0.617948\pi$
$62$		−	3.14226e21i		−	0.973963i
$63$	1.93884e21	+	6.54213e21i	0.495971	+	1.67353i
$64$	−5.90296e20			−0.125000
$65$		−	1.80758e21i		−	0.317788i
$66$	−3.68351e21	+	4.93352e21i	−0.539181	+	0.722154i
$67$	−7.96234e21			−0.973068			−0.486534	−	0.873662i	$-0.661739\pi$
$67$	−7.96234e21			−0.973068			−0.486534	+	0.873662i	$0.661739\pi$
$68$			5.53718e21i			0.566477i
$69$	3.26223e20	+	2.43567e20i	0.0280108	+	0.0209136i
$70$	4.73678e21			0.342221
$71$		−	2.04327e22i		−	1.24516i	−0.782557	−	0.622579i	$-0.786085\pi$
$71$		−	2.04327e22i		−	1.24516i	0.782557	−	0.622579i	$-0.213915\pi$
$72$	6.57907e21	−	1.94979e21i	0.338980	−	0.100461i
$73$	3.28296e22			1.43348			0.716740	−	0.697340i	$-0.245633\pi$
$73$	3.28296e22			1.43348			0.716740	+	0.697340i	$0.245633\pi$
$74$		−	7.74666e21i		−	0.287299i
$75$	−1.74940e22	+	2.34307e22i	−0.552274	+	0.739691i
$76$	2.56092e21			0.0689656
$77$		−	9.66394e22i		−	2.22467i
$78$	3.29337e22	+	2.45893e22i	0.649390	+	0.484853i
$79$	5.13170e21			0.0868433			0.0434216	−	0.999057i	$-0.486174\pi$
$79$	5.13170e21			0.0868433			0.0434216	+	0.999057i	$0.486174\pi$
$80$		−	4.76353e21i		−	0.0693185i
$81$	−6.68858e22	+	4.34623e22i	−0.838521	+	0.544870i
$82$	9.00105e22			0.973928
$83$			1.14963e21i			0.0107552i	0.999986	+	0.00537761i	$0.00171175\pi$
$83$			1.14963e21i			0.0107552i	−0.999986	+	0.00537761i	$0.998288\pi$
$84$	−6.44364e22	+	8.63032e22i	−0.522132	+	0.699319i
$85$	−4.46836e22			−0.314138
$86$			7.05766e22i			0.431201i
$87$	1.70418e23	+	1.27239e23i	0.906324	+	0.676688i
$88$	−9.71851e22			−0.450617
$89$		−	3.69857e23i		−	1.49745i	−0.662879	−	0.748727i	$-0.730665\pi$
$89$		−	3.69857e23i		−	1.49745i	0.662879	−	0.748727i	$-0.269335\pi$
$90$	1.57343e22	+	5.30913e22i	0.0557105	+	0.187981i
$91$	−6.45117e23			−2.00051
$92$			6.42623e21i			0.0174784i
$93$	−3.44945e23	+	4.62003e23i	−0.824051	+	1.10370i
$94$	−1.10030e23			−0.231193
$95$			2.06659e22i			0.0382447i
$96$	8.67905e22	+	6.48003e22i	0.141650	+	0.105760i
$97$	1.10819e24			1.59718			0.798592	−	0.601873i	$-0.205579\pi$
$97$	1.10819e24			1.59718			0.798592	+	0.601873i	$0.205579\pi$
$98$		−	1.13566e24i		−	1.44722i
$99$	1.08316e24	−	3.21010e23i	1.22200	−	0.362156i
$100$	−4.61560e23			−0.461560
$101$			1.86377e24i			1.65400i	0.562202	+	0.827000i	$0.309954\pi$
$101$			1.86377e24i			1.65400i	−0.562202	+	0.827000i	$0.690046\pi$
$102$	6.07849e23	−	8.14126e23i	0.479285	−	0.641933i
$103$	1.22843e24			0.861594			0.430797	−	0.902449i	$-0.358232\pi$
$103$	1.22843e24			0.861594			0.430797	+	0.902449i	$0.358232\pi$
$104$			6.48759e23i			0.405213i
$105$	−6.96444e23	−	5.19985e23i	−0.387806	−	0.289547i
$106$	−2.55627e23			−0.127039
$107$		−	3.55456e24i		−	1.57827i	−0.614220	−	0.789134i	$-0.710529\pi$
$107$		−	3.55456e24i		−	1.57827i	0.614220	−	0.789134i	$-0.289471\pi$
$108$	−1.18135e24	−	4.35547e23i	−0.469131	−	0.172962i
$109$	2.18543e23			0.0776995			0.0388497	−	0.999245i	$-0.487631\pi$
$109$	2.18543e23			0.0776995			0.0388497	+	0.999245i	$0.487631\pi$
$110$		−	7.84257e23i		−	0.249889i
$111$	−8.50396e23	+	1.13898e24i	−0.243078	+	0.325567i
$112$	−1.70008e24			−0.436368
$113$			5.66320e24i			1.30653i	0.757128	+	0.653267i	$0.226602\pi$
$113$			5.66320e24i			1.30653i	−0.757128	+	0.653267i	$0.773398\pi$
$114$	−3.76529e23	−	2.81127e23i	−0.0781519	−	0.0583504i
$115$	−5.18580e22			−0.00969263
$116$			3.35705e24i			0.565537i
$117$	−2.14290e24	−	7.23066e24i	−0.325666	−	1.09887i
$118$	5.44774e24			0.747536
$119$			1.59474e25i			1.97754i
$120$	−5.22921e23	+	7.00376e23i	−0.0586490	+	0.0785518i
$121$	−6.15061e24			−0.624444
$122$			5.56786e24i			0.512118i
$123$	−1.32341e25	−	9.88098e24i	−1.10366	−	0.824022i
$124$	−9.10097e24			−0.688696
$125$		−	7.75953e24i		−	0.533231i
$126$	1.89480e25	−	5.61549e24i	1.18336	−	0.350705i
$127$	1.31873e25			0.749051			0.374526	−	0.927217i	$-0.377806\pi$
$127$	1.31873e25			0.749051			0.374526	+	0.927217i	$0.377806\pi$
$128$			1.70968e24i			0.0883883i
$129$	7.74761e24	−	1.03768e25i	0.364831	−	0.488638i
$130$	−5.23531e24			−0.224710
$131$		−	2.72828e25i		−	1.06815i	−0.845436	−	0.534077i	$-0.820659\pi$
$131$		−	2.72828e25i		−	1.06815i	0.845436	−	0.534077i	$-0.179341\pi$
$132$	1.42890e25	+	1.06686e25i	0.510640	+	0.381258i
$133$	7.37556e24			0.240755
$134$			2.30614e25i			0.688063i
$135$	3.51475e24	−	9.53320e24i	0.0959156	−	0.260156i
$136$	1.60374e25			0.400559
$137$		−	1.88032e25i		−	0.430115i	−0.976601	−	0.215058i	$-0.931006\pi$
$137$		−	1.88032e25i		−	0.430115i	0.976601	−	0.215058i	$-0.0689939\pi$
$138$	7.05445e23	−	9.44841e23i	0.0147882	−	0.0198066i
$139$	4.16312e24			0.0800279			0.0400140	−	0.999199i	$-0.487260\pi$
$139$	4.16312e24			0.0800279			0.0400140	+	0.999199i	$0.487260\pi$
$140$		−	1.37192e25i		−	0.241987i
$141$	1.61775e25	+	1.20786e25i	0.261989	+	0.195608i
$142$	−5.91793e25			−0.880460
$143$			1.06810e26i			1.46077i
$144$	−5.64720e24	−	1.90550e25i	−0.0710368	−	0.239695i
$145$	−2.70905e25			−0.313618
$146$		−	9.50848e25i		−	1.01362i
$147$	−1.24668e26	+	1.66974e26i	−1.22446	+	1.63999i
$148$	−2.24367e25			−0.203151
$149$		−	9.17379e25i		−	0.766149i	−0.923717	−	0.383075i	$-0.874865\pi$
$149$		−	9.17379e25i		−	0.766149i	0.923717	−	0.383075i	$-0.125135\pi$
$150$	6.78626e25	+	5.06681e25i	0.523040	+	0.390517i
$151$	1.86184e26			1.32501			0.662505	−	0.749058i	$-0.269493\pi$
$151$	1.86184e26			1.32501			0.662505	+	0.749058i	$0.269493\pi$
$152$		−	7.41721e24i		−	0.0487660i
$153$	−1.78743e26	+	5.29727e25i	−1.08625	+	0.321925i
$154$	−2.79898e26			−1.57308
$155$		−	7.34424e25i		−	0.381915i
$156$	7.12181e25	−	9.53863e25i	0.342843	−	0.459188i
$157$	1.58923e26			0.708584			0.354292	−	0.935135i	$-0.384722\pi$
$157$	1.58923e26			0.708584			0.354292	+	0.935135i	$0.384722\pi$
$158$		−	1.48630e25i		−	0.0614075i
$159$	3.75846e25	+	2.80617e25i	0.143961	+	0.107485i
$160$	−1.37967e25			−0.0490156
$161$			1.85079e25i			0.0610163i
$162$	1.25880e26	+	1.93722e26i	0.385281	+	0.592924i
$163$	4.86804e26			1.38390			0.691948	−	0.721948i	$-0.256753\pi$
$163$	4.86804e26			1.38390			0.691948	+	0.721948i	$0.256753\pi$
$164$		−	2.60698e26i		−	0.688671i
$165$	−8.60926e25	+	1.15308e26i	−0.211426	+	0.283174i
$166$	3.32967e24			0.00760509
$167$		−	6.29000e26i		−	1.33676i	−0.743821	−	0.668379i	$-0.766989\pi$
$167$		−	6.29000e26i		−	1.33676i	0.743821	−	0.668379i	$-0.233011\pi$
$168$	2.49961e26	+	1.86628e26i	0.494493	+	0.369203i
$169$	1.70212e26			0.313582
$170$			1.29418e26i			0.222129i
$171$	2.44996e25	+	8.26675e25i	0.0391927	+	0.132246i
$172$	2.04412e26			0.304905
$173$		−	1.85146e26i		−	0.257609i	−0.991670	−	0.128805i	$-0.958886\pi$
$173$		−	1.85146e26i		−	0.257609i	0.991670	−	0.128805i	$-0.0411140\pi$
$174$	3.68523e26	−	4.93582e26i	0.478490	−	0.640868i
$175$	−1.32931e27			−1.61128
$176$			2.81478e26i			0.318634i
$177$	−8.00974e26	−	5.98030e26i	−0.847109	−	0.632476i
$178$	−1.07122e27			−1.05886
$179$			1.47704e27i			1.36507i	0.730853	+	0.682535i	$0.239123\pi$
$179$			1.47704e27i			1.36507i	−0.730853	+	0.682535i	$0.760877\pi$
$180$	1.53769e26	−	4.55714e25i	0.132922	−	0.0393933i
$181$	−6.65463e26			−0.538246			−0.269123	−	0.963106i	$-0.586734\pi$
$181$	−6.65463e26			−0.538246			−0.269123	+	0.963106i	$0.586734\pi$
$182$			1.86846e27i			1.41458i
$183$	6.11216e26	−	8.18635e26i	0.433293	−	0.580333i
$184$	1.86124e25			0.0123591
$185$		−	1.81058e26i		−	0.112657i
$186$	1.33810e27	+	9.99067e26i	0.780431	+	0.582692i
$187$	2.64036e27			1.44399
$188$			3.18680e26i			0.163478i
$189$	−3.40235e27	−	1.25440e27i	−1.63771	−	0.603800i
$190$	5.98549e25			0.0270431
$191$			2.76451e27i			1.17279i	0.810027	+	0.586393i	$0.199452\pi$
$191$			2.76451e27i			1.17279i	−0.810027	+	0.586393i	$0.800548\pi$
$192$	1.87682e26	−	2.51372e26i	0.0747837	−	0.100162i
$193$	7.06698e26			0.264573			0.132287	−	0.991212i	$-0.457768\pi$
$193$	7.06698e26			0.264573			0.132287	+	0.991212i	$0.457768\pi$
$194$		−	3.20967e27i		−	1.12938i
$195$	7.69742e26	+	5.74711e26i	0.254642	+	0.190123i
$196$	−3.28921e27			−1.02334
$197$		−	4.71662e27i		−	1.38050i	−0.723571	−	0.690250i	$-0.757501\pi$
$197$		−	4.71662e27i		−	1.38050i	0.723571	−	0.690250i	$-0.242499\pi$
$198$	−9.29743e26	−	3.13718e27i	−0.256083	−	0.864085i
$199$	2.25704e27			0.585197			0.292598	−	0.956235i	$-0.405480\pi$
$199$	2.25704e27			0.585197			0.292598	+	0.956235i	$0.405480\pi$
$200$			1.33682e27i			0.326372i
$201$	2.53159e27	−	3.39069e27i	0.582157	−	0.779714i
$202$	5.39805e27			1.16955
$203$			9.66845e27i			1.97426i
$204$	−2.35796e27	−	1.76052e27i	−0.453915	−	0.338906i
$205$	2.10377e27			0.381901
$206$		−	3.55791e27i		−	0.609239i
$207$	−2.07442e26	+	6.14780e25i	−0.0335160	+	0.00993289i
$208$	1.87901e27			0.286529
$209$		−	1.22115e27i		−	0.175798i
$210$	−1.50604e27	+	2.01712e27i	−0.204741	+	0.274220i
$211$	3.37907e27			0.433918			0.216959	−	0.976181i	$-0.430386\pi$
$211$	3.37907e27			0.433918			0.216959	+	0.976181i	$0.430386\pi$
$212$			7.40376e26i			0.0898301i
$213$	8.70106e27	+	6.49646e27i	0.997739	+	0.744940i
$214$	−1.02951e28			−1.11600
$215$			1.64955e27i			0.169084i
$216$	−1.26148e27	+	3.42156e27i	−0.122302	+	0.331726i
$217$	−2.62112e28			−2.40420
$218$		−	6.32967e26i		−	0.0549418i
$219$	−1.04380e28	+	1.39802e28i	−0.857608	+	1.14864i
$220$	−2.27145e27			−0.176698
$221$		−	1.76258e28i		−	1.29850i
$222$	3.29884e27	+	2.46301e27i	0.230211	+	0.171882i
$223$	1.36332e28			0.901443			0.450722	−	0.892665i	$-0.351167\pi$
$223$	1.36332e28			0.901443			0.450722	+	0.892665i	$0.351167\pi$
$224$			4.92396e27i			0.308559i
$225$	−4.41562e27	−	1.48993e28i	−0.262302	−	0.885069i
$226$	1.64024e28			0.923859
$227$		−	6.82027e27i		−	0.364327i	−0.983268	−	0.182164i	$-0.941690\pi$
$227$		−	6.82027e27i		−	0.364327i	0.983268	−	0.182164i	$-0.0583100\pi$
$228$	−8.14231e26	+	1.09054e27i	−0.0412600	+	0.0552618i
$229$	−2.90439e28			−1.39646			−0.698231	−	0.715872i	$-0.746029\pi$
$229$	−2.90439e28			−1.39646			−0.698231	+	0.715872i	$0.746029\pi$
$230$			1.50197e26i			0.00685372i
$231$	4.11530e28	+	3.07260e28i	1.78262	+	1.33095i
$232$	9.72304e27			0.399895
$233$		−	8.69231e27i		−	0.339519i	−0.985486	−	0.169760i	$-0.945701\pi$
$233$		−	8.69231e27i		−	0.339519i	0.985486	−	0.169760i	$-0.0542991\pi$
$234$	−2.09422e28	+	6.20650e27i	−0.777021	+	0.230280i
$235$	−2.57166e27			−0.0906566
$236$		−	1.57783e28i		−	0.528588i
$237$	−1.63160e27	+	2.18529e27i	−0.0519557	+	0.0695871i
$238$	4.61885e28			1.39833
$239$		−	3.86579e28i		−	1.11292i	−0.830875	−	0.556459i	$-0.812160\pi$
$239$		−	3.86579e28i		−	1.11292i	0.830875	−	0.556459i	$-0.187840\pi$
$240$	2.02851e27	+	1.51454e27i	0.0555445	+	0.0414711i
$241$	1.20605e28			0.314168			0.157084	−	0.987585i	$-0.449791\pi$
$241$	1.20605e28			0.314168			0.157084	+	0.987585i	$0.449791\pi$
$242$			1.78141e28i			0.441549i
$243$	2.75798e27	−	4.23013e28i	0.0650603	−	0.997881i
$244$	1.61262e28			0.362122
$245$		−	2.65431e28i		−	0.567490i
$246$	−2.86184e28	+	3.83302e28i	−0.582672	+	0.780404i
$247$	−8.15181e27			−0.158085
$248$			2.63592e28i			0.486981i
$249$	−4.89557e26	−	3.65518e26i	−0.00861810	−	0.00643452i
$250$	−2.24740e28			−0.377051
$251$			8.43194e28i			1.34848i	0.738515	+	0.674238i	$0.235528\pi$
$251$			8.43194e28i			1.34848i	−0.738515	+	0.674238i	$0.764472\pi$
$252$	−1.62642e28	−	5.48793e28i	−0.247986	−	0.836763i
$253$	3.06430e27			0.0445538
$254$		−	3.81945e28i		−	0.529659i
$255$	1.42069e28	−	1.90281e28i	0.187939	−	0.251717i
$256$	4.95176e27			0.0625000
$257$			5.82077e28i			0.701105i	0.936543	+	0.350553i	$0.114006\pi$
$257$			5.82077e28i			0.701105i	−0.936543	+	0.350553i	$0.885994\pi$
$258$	−3.00544e28	−	2.24395e28i	−0.345519	−	0.257974i
$259$	−6.46188e28			−0.709189
$260$			1.51631e28i			0.158894i
$261$	−1.08367e29	+	3.21159e28i	−1.08445	+	0.321392i
$262$	−7.90195e28			−0.755299
$263$			1.33775e29i			1.22153i	0.791810	+	0.610767i	$0.209139\pi$
$263$			1.33775e29i			1.22153i	−0.791810	+	0.610767i	$0.790861\pi$
$264$	3.08995e28	−	4.13854e28i	0.269590	−	0.361077i
$265$	−5.97464e27			−0.0498151
$266$		−	2.13619e28i		−	0.170240i
$267$	1.57500e29	+	1.17594e29i	1.19990	+	0.895881i
$268$	6.67930e28			0.486534
$269$		−	4.31823e28i		−	0.300800i	−0.988625	−	0.150400i	$-0.951944\pi$
$269$		−	4.31823e28i		−	0.300800i	0.988625	−	0.150400i	$-0.0480562\pi$
$270$	−2.76111e28	−	1.01798e28i	−0.183958	−	0.0678226i
$271$	1.25855e28			0.0802119			0.0401059	−	0.999195i	$-0.487230\pi$
$271$	1.25855e28			0.0802119			0.0401059	+	0.999195i	$0.487230\pi$
$272$		−	4.64493e28i		−	0.283238i
$273$	2.05112e29	−	2.74717e29i	1.19685	−	1.60300i
$274$	−5.44599e28			−0.304137
$275$			2.20091e29i			1.17655i
$276$	−2.73655e27	−	2.04319e27i	−0.0140054	−	0.0104568i
$277$	9.17464e28			0.449606			0.224803	−	0.974404i	$-0.427826\pi$
$277$	9.17464e28			0.449606			0.224803	+	0.974404i	$0.427826\pi$
$278$		−	1.20577e28i		−	0.0565883i
$279$	−8.70665e28	−	2.93783e29i	−0.391382	−	1.32062i
$280$	−3.97350e28			−0.171111
$281$		−	2.21314e28i		−	0.0913131i	−0.998957	−	0.0456566i	$-0.985462\pi$
$281$		−	2.21314e28i		−	0.0913131i	0.998957	−	0.0456566i	$-0.0145380\pi$
$282$	3.49834e28	−	4.68551e28i	0.138316	−	0.185254i
$283$	3.26573e28			0.123749			0.0618747	−	0.998084i	$-0.480292\pi$
$283$	3.26573e28			0.123749			0.0618747	+	0.998084i	$0.480292\pi$
$284$			1.71402e29i			0.622579i
$285$	−8.80039e27	−	6.57062e27i	−0.0306453	−	0.0228806i
$286$	3.09356e29			1.03292
$287$		−	7.50824e29i		−	2.40411i
$288$	−5.51892e28	+	1.63560e28i	−0.169490	+	0.0502306i
$289$	−9.62619e28			−0.283583
$290$			7.84623e28i			0.221761i
$291$	−3.52344e29	+	4.71914e29i	−0.955546	+	1.27981i
$292$	−2.75395e29			−0.716740
$293$			3.37056e29i			0.841958i	0.907070	+	0.420979i	$0.138313\pi$
$293$			3.37056e29i			0.841958i	−0.907070	+	0.420979i	$0.861687\pi$
$294$	4.83609e29	+	3.61076e29i	1.15965	+	0.865827i
$295$	1.27327e29			0.293127
$296$			6.49837e28i			0.143649i
$297$	−2.07687e29	+	5.63319e29i	−0.440892	+	1.19585i
$298$	−2.65701e29			−0.541749
$299$		−	2.04557e28i		−	0.0400646i
$300$	1.46751e29	−	1.96551e29i	0.276137	−	0.369845i
$301$	5.88716e29			1.06441
$302$		−	5.39247e29i		−	0.936923i
$303$	−7.93669e29	−	5.92576e29i	−1.32534	−	0.989538i
$304$	−2.14825e28			−0.0344828
$305$			1.30134e29i			0.200814i
$306$	1.53425e29	+	5.17694e29i	0.227636	+	0.768097i
$307$	−6.58441e29			−0.939412			−0.469706	−	0.882823i	$-0.655640\pi$
$307$	−6.58441e29			−0.939412			−0.469706	+	0.882823i	$0.655640\pi$
$308$			8.10670e29i			1.11233i
$309$	−3.90572e29	+	5.23115e29i	−0.515466	+	0.690391i
$310$	−2.12712e29			−0.270054
$311$		−	1.25703e30i		−	1.53540i	−0.640810	−	0.767700i	$-0.721401\pi$
$311$		−	1.25703e30i		−	1.53540i	0.640810	−	0.767700i	$-0.278599\pi$
$312$	−2.76268e29	−	2.06270e29i	−0.324695	−	0.242427i
$313$	−4.01699e29			−0.454328			−0.227164	−	0.973857i	$-0.572945\pi$
$313$	−4.01699e29			−0.454328			−0.227164	+	0.973857i	$0.572945\pi$
$314$		−	4.60291e29i		−	0.501045i
$315$	4.42862e29	−	1.31248e29i	0.464025	−	0.137520i
$316$	−4.30478e28			−0.0434216
$317$		−	4.83365e29i		−	0.469422i	−0.972065	−	0.234711i	$-0.924586\pi$
$317$		−	4.83365e29i		−	0.469422i	0.972065	−	0.234711i	$-0.0754144\pi$
$318$	8.12755e28	−	1.08857e29i	0.0760036	−	0.101796i
$319$	1.60078e30			1.44160
$320$			3.99594e28i			0.0346592i
$321$	1.51368e30	+	1.13016e30i	1.26466	+	0.944230i
$322$	5.36045e28			0.0431450
$323$			2.01514e29i			0.156270i
$324$	5.61079e29	−	3.64588e29i	0.419260	−	0.272435i
$325$	1.46922e30			1.05800
$326$		−	1.40994e30i		−	0.978562i
$327$	−6.94845e28	+	9.30644e28i	−0.0464852	+	0.0622602i
$328$	−7.55063e29			−0.486964
$329$			9.17814e29i			0.570694i
$330$	3.33969e29	+	2.49351e29i	0.200234	+	0.149501i
$331$	−1.33834e29			−0.0773802			−0.0386901	−	0.999251i	$-0.512319\pi$
$331$	−1.33834e29			−0.0773802			−0.0386901	+	0.999251i	$0.512319\pi$
$332$		−	9.64375e27i		−	0.00537761i
$333$	−2.14646e29	−	7.24267e29i	−0.115449	−	0.389554i
$334$	−1.82178e30			−0.945230
$335$			5.39001e29i			0.269806i
$336$	5.40532e29	−	7.23964e29i	0.261066	−	0.349660i
$337$	2.49698e26			0.000116374			5.81870e−5	−	1.00000i	$-0.499981\pi$
$337$	2.49698e26			0.000116374			5.81870e−5		1.00000i	$0.499981\pi$
$338$		−	4.92988e29i		−	0.221736i
$339$	−2.41162e30	−	1.80059e30i	−1.04692	−	0.781660i
$340$	3.74833e29			0.157069
$341$			4.33973e30i			1.75554i
$342$	2.39431e29	−	7.09584e28i	0.0935118	−	0.0277134i
$343$	−4.84457e30			−1.82694
$344$		−	5.92040e29i		−	0.215600i
$345$	1.64880e28	−	2.20833e28i	0.00579880	−	0.00776665i
$346$	−5.36241e29			−0.182157
$347$		−	1.01133e30i		−	0.331847i	−0.986139	−	0.165923i	$-0.946940\pi$
$347$		−	1.01133e30i		−	0.331847i	0.986139	−	0.165923i	$-0.0530605\pi$
$348$	−1.42957e30	−	1.06736e30i	−0.453162	−	0.338344i
$349$	4.79831e30			1.46955			0.734773	−	0.678314i	$-0.237289\pi$
$349$	4.79831e30			1.46955			0.734773	+	0.678314i	$0.237289\pi$
$350$			3.85010e30i			1.13935i
$351$	3.76044e30	+	1.38642e30i	1.07536	+	0.396469i
$352$	8.15247e29			0.225308
$353$		−	4.36735e29i		−	0.116660i	−0.998297	−	0.0583300i	$-0.981422\pi$
$353$		−	4.36735e29i		−	0.116660i	0.998297	−	0.0583300i	$-0.0185776\pi$
$354$	−1.73208e30	+	2.31987e30i	−0.447228	+	0.598997i
$355$	−1.38316e30			−0.345250
$356$			3.10258e30i			0.748727i
$357$	−6.79104e30	−	5.07038e30i	−1.58459	−	1.18310i
$358$	4.27796e30			0.965250
$359$			1.36292e30i			0.297397i	0.988883	+	0.148699i	$0.0475084\pi$
$359$			1.36292e30i			0.297397i	−0.988883	+	0.148699i	$0.952492\pi$
$360$	−1.31989e29	−	4.45362e29i	−0.0278553	−	0.0939904i
$361$	−4.80556e30			−0.980975
$362$			1.92739e30i			0.380597i
$363$	1.95556e30	−	2.61918e30i	0.373586	−	0.500364i
$364$	5.41163e30			1.00026
$365$		−	2.22236e30i		−	0.397467i
$366$	−2.37102e30	−	1.77027e30i	−0.410358	−	0.306385i
$367$	1.44710e30			0.242384			0.121192	−	0.992629i	$-0.461328\pi$
$367$	1.44710e30			0.242384			0.121192	+	0.992629i	$0.461328\pi$
$368$		−	5.39071e28i		−	0.00873922i
$369$	8.41546e30	−	2.49403e30i	1.32057	−	0.391368i
$370$	−5.24401e29			−0.0796604
$371$			2.13232e30i			0.313592i
$372$	2.89361e30	−	3.87556e30i	0.412026	−	0.551848i
$373$	2.12953e30			0.293614			0.146807	−	0.989165i	$-0.453100\pi$
$373$	2.12953e30			0.293614			0.146807	+	0.989165i	$0.453100\pi$
$374$		−	7.64731e30i		−	1.02106i
$375$	3.30433e30	+	2.46710e30i	0.427275	+	0.319016i
$376$	9.22996e29			0.115597
$377$		−	1.06860e31i		−	1.29634i
$378$	−3.63312e30	+	9.85426e30i	−0.426951	+	1.15804i
$379$	−4.51756e30			−0.514320			−0.257160	−	0.966369i	$-0.582787\pi$
$379$	−4.51756e30			−0.514320			−0.257160	+	0.966369i	$0.582787\pi$
$380$		−	1.73358e29i		−	0.0191224i
$381$	−4.19284e30	+	5.61570e30i	−0.448135	+	0.600211i
$382$	8.00689e30			0.829284
$383$		−	5.00583e30i		−	0.502448i	−0.967929	−	0.251224i	$-0.919167\pi$
$383$		−	5.00583e30i		−	0.502448i	0.967929	−	0.251224i	$-0.0808330\pi$
$384$	−7.28051e29	−	5.43584e29i	−0.0708251	−	0.0528801i
$385$	−6.54189e30			−0.616843
$386$		−	2.04681e30i		−	0.187082i
$387$	1.95555e30	+	6.59850e30i	0.173276	+	0.584674i
$388$	−9.29620e30			−0.798592
$389$			7.79334e30i			0.649125i	0.945864	+	0.324563i	$0.105217\pi$
$389$			7.79334e30i			0.649125i	−0.945864	+	0.324563i	$0.894783\pi$
$390$	1.66454e30	−	2.22941e30i	0.134437	−	0.180059i
$391$	−5.05668e29			−0.0396045
$392$			9.52658e30i			0.723609i
$393$	1.16181e31	+	8.67443e30i	0.855906	+	0.639044i
$394$	−1.36608e31			−0.976161
$395$		−	3.47384e29i		−	0.0240794i
$396$	−9.08623e30	+	2.69282e30i	−0.611001	+	0.181078i
$397$	−1.68507e31			−1.09934			−0.549669	−	0.835383i	$-0.685246\pi$
$397$	−1.68507e31			−1.09934			−0.549669	+	0.835383i	$0.685246\pi$
$398$		−	6.53708e30i		−	0.413797i
$399$	−2.34502e30	+	3.14082e30i	−0.144036	+	0.192916i
$400$	3.87184e30			0.230780
$401$			1.09723e31i			0.634693i	0.948310	+	0.317346i	$0.102792\pi$
$401$			1.09723e31i			0.634693i	−0.948310	+	0.317346i	$0.897208\pi$
$402$	−9.82049e30	−	7.33226e30i	−0.551341	−	0.411647i
$403$	2.89699e31			1.57865
$404$		−	1.56344e31i		−	0.827000i
$405$	2.94213e30	+	4.52776e30i	0.151078	+	0.232500i
$406$	2.80028e31			1.39601
$407$			1.06988e31i			0.517846i
$408$	−5.09901e30	+	6.82938e30i	−0.239643	+	0.320966i
$409$	−3.46568e31			−1.58164			−0.790822	−	0.612046i	$-0.790347\pi$
$409$	−3.46568e31			−1.58164			−0.790822	+	0.612046i	$0.790347\pi$
$410$		−	6.09316e30i		−	0.270045i
$411$	8.00717e30	+	5.97838e30i	0.344649	+	0.257325i
$412$	−1.03048e31			−0.430797
$413$		−	4.54423e31i		−	1.84527i
$414$	1.78059e29	+	6.00815e29i	0.00702362	+	0.0236994i
$415$	7.78225e28			0.00298214
$416$		−	5.44219e30i		−	0.202607i
$417$	−1.32364e30	+	1.77283e30i	−0.0478783	+	0.0641260i
$418$	−3.53684e30			−0.124308
$419$			4.32637e30i			0.147759i	0.997267	+	0.0738797i	$0.0235381\pi$
$419$			4.32637e30i			0.147759i	−0.997267	+	0.0738797i	$0.976462\pi$
$420$	5.84219e30	+	4.36195e30i	0.193903	+	0.144773i
$421$	5.35766e31			1.72818			0.864092	−	0.503334i	$-0.167893\pi$
$421$	5.35766e31			1.72818			0.864092	+	0.503334i	$0.167893\pi$
$422$		−	9.78683e30i		−	0.306826i
$423$	−1.02871e31	+	3.04872e30i	−0.313480	+	0.0929039i
$424$	2.14436e30			0.0635195
$425$		−	3.63193e31i		−	1.04585i
$426$	1.88158e31	−	2.52010e31i	0.526752	−	0.705508i
$427$	4.64443e31			1.26415
$428$			2.98178e31i			0.789134i
$429$	−4.54842e31	−	3.39598e31i	−1.17051	−	0.873932i
$430$	4.77760e30			0.119561
$431$			7.38282e31i			1.79678i	0.439197	+	0.898391i	$0.355263\pi$
$431$			7.38282e31i			1.79678i	−0.439197	+	0.898391i	$0.644737\pi$
$432$	9.90990e30	+	3.65364e30i	0.234566	+	0.0864809i
$433$	2.54475e30			0.0585856			0.0292928	−	0.999571i	$-0.490674\pi$
$433$	2.54475e30			0.0585856			0.0292928	+	0.999571i	$0.490674\pi$
$434$			7.59158e31i			1.70003i
$435$	8.61327e30	−	1.15362e31i	0.187628	−	0.251300i
$436$	−1.83327e30			−0.0388497
$437$			2.33869e29i			0.00482164i
$438$	4.04910e31	+	3.02317e31i	0.812212	+	0.606420i
$439$	−6.51383e31			−1.27134			−0.635671	−	0.771960i	$-0.719276\pi$
$439$	−6.51383e31			−1.27134			−0.635671	+	0.771960i	$0.719276\pi$
$440$			6.57883e30i			0.124944i
$441$	−3.14670e31	−	1.06177e32i	−0.581557	−	1.96231i
$442$	−5.10496e31			−0.918175
$443$		−	3.26967e31i		−	0.572347i	−0.958178	−	0.286173i	$-0.907617\pi$
$443$		−	3.26967e31i		−	0.572347i	0.958178	−	0.286173i	$-0.0923833\pi$
$444$	7.13364e30	−	9.55447e30i	0.121539	−	0.162784i
$445$	−2.50370e31			−0.415205
$446$		−	3.94859e31i		−	0.637417i
$447$	3.90657e31	+	2.91676e31i	0.613912	+	0.458364i
$448$	1.42613e31			0.218184
$449$			7.64915e31i			1.13935i	0.821870	+	0.569675i	$0.192931\pi$
$449$			7.64915e31i			1.13935i	−0.821870	+	0.569675i	$0.807069\pi$
$450$	−4.31531e31	+	1.27890e31i	−0.625838	+	0.185475i
$451$	−1.24312e32			−1.75547
$452$		−	4.75064e31i		−	0.653267i
$453$	−5.91963e31	+	7.92848e31i	−0.792713	+	1.06172i
$454$	−1.97536e31			−0.257618
$455$			4.36704e31i			0.554690i
$456$	3.15855e30	+	2.35826e30i	0.0390760	+	0.0291752i
$457$	5.89189e31			0.710003			0.355001	−	0.934866i	$-0.384480\pi$
$457$	5.89189e31			0.710003			0.355001	+	0.934866i	$0.384480\pi$
$458$			8.41201e31i			0.987448i
$459$	3.42724e31	−	9.29584e31i	0.391915	−	1.06301i
$460$	4.35016e29			0.00484631
$461$			4.35731e31i			0.472941i	0.971639	+	0.236470i	$0.0759907\pi$
$461$			4.35731e31i			0.472941i	−0.971639	+	0.236470i	$0.924009\pi$
$462$	8.89920e31	−	1.19192e32i	0.941125	−	1.26050i
$463$	1.14041e32			1.17514			0.587569	−	0.809174i	$-0.300085\pi$
$463$	1.14041e32			1.17514			0.587569	+	0.809174i	$0.300085\pi$
$464$		−	2.81609e31i		−	0.282769i
$465$	3.12748e31	+	2.33506e31i	0.306026	+	0.228488i
$466$	−2.51756e31			−0.240076
$467$		−	2.25380e31i		−	0.209466i	−0.994500	−	0.104733i	$-0.966601\pi$
$467$		−	2.25380e31i		−	0.209466i	0.994500	−	0.104733i	$-0.0333988\pi$
$468$	1.79760e31	+	6.06552e31i	0.162833	+	0.549437i
$469$	1.92367e32			1.69846
$470$			7.44833e30i			0.0641039i
$471$	−5.05288e31	+	6.76760e31i	−0.423924	+	0.567785i
$472$	−4.56989e31			−0.373768
$473$		−	9.74722e31i		−	0.777225i
$474$	6.32927e30	+	4.72561e30i	0.0492055	+	0.0367382i
$475$	−1.67975e31			−0.127327
$476$		−	1.33776e32i		−	0.988770i
$477$	−2.38997e31	+	7.08298e30i	−0.172255	+	0.0510499i
$478$	−1.11965e32			−0.786951
$479$		−	8.30835e31i		−	0.569493i	−0.958603	−	0.284747i	$-0.908090\pi$
$479$		−	8.30835e31i		−	0.569493i	0.958603	−	0.284747i	$-0.0919095\pi$
$480$	4.38658e30	−	5.87518e30i	0.0293245	−	0.0392759i
$481$	7.14197e31			0.465669
$482$		−	3.49310e31i		−	0.222150i
$483$	−7.88140e30	−	5.88448e30i	−0.0488920	−	0.0365042i
$484$	5.15950e31			0.312222
$485$		−	7.50178e31i		−	0.442857i
$486$	−1.22518e32	−	7.98797e30i	−0.705609	−	0.0460046i
$487$	2.38724e32			1.34137			0.670686	−	0.741741i	$-0.266000\pi$
$487$	2.38724e32			1.34137			0.670686	+	0.741741i	$0.266000\pi$
$488$		−	4.67066e31i		−	0.256059i
$489$	−1.54777e32	+	2.07301e32i	−0.827942	+	1.10891i
$490$	−7.68769e31			−0.401276
$491$		−	1.30787e32i		−	0.666173i	−0.942896	−	0.333087i	$-0.891910\pi$
$491$		−	1.30787e32i		−	0.666173i	0.942896	−	0.333087i	$-0.108090\pi$
$492$	1.11016e32	+	8.28877e31i	0.551829	+	0.412011i
$493$	−2.64160e32			−1.28145
$494$			2.36102e31i			0.111783i
$495$	−2.17304e31	−	7.33235e31i	−0.100416	−	0.338829i
$496$	7.63444e31			0.344348
$497$			4.93645e32i			2.17339i
$498$	−1.05865e30	+	1.41791e30i	−0.00454989	+	0.00609392i
$499$	−2.33308e32			−0.978868			−0.489434	−	0.872040i	$-0.662797\pi$
$499$	−2.33308e32			−0.978868			−0.489434	+	0.872040i	$0.662797\pi$
$500$			6.50916e31i			0.266615i
$501$	2.67854e32	+	1.99987e32i	1.07114	+	0.799741i
$502$	2.44215e32			0.953516
$503$		−	3.12030e32i		−	1.18954i	−0.803895	−	0.594772i	$-0.797242\pi$
$503$		−	3.12030e32i		−	1.18954i	0.803895	−	0.594772i	$-0.202758\pi$
$504$	−1.58948e32	+	4.71062e31i	−0.591681	+	0.175352i
$505$	1.26166e32			0.458611
$506$		−	8.87516e30i		−	0.0315043i
$507$	−5.41182e31	+	7.24834e31i	−0.187606	+	0.251271i
$508$	−1.10623e32			−0.374526
$509$			7.26199e31i			0.240128i	0.992766	+	0.120064i	$0.0383099\pi$
$509$			7.26199e31i			0.240128i	−0.992766	+	0.120064i	$0.961690\pi$
$510$	−5.51113e31	−	4.11476e31i	−0.177991	−	0.132893i
$511$	−7.93151e32			−2.50210
$512$		−	1.43418e31i		−	0.0441942i
$513$	−4.29927e31	−	1.58508e31i	−0.129416	−	0.0477136i
$514$	1.68588e32			0.495756
$515$		−	8.31569e31i		−	0.238898i
$516$	−6.49917e31	+	8.70469e31i	−0.182415	+	0.244319i
$517$	1.51960e32			0.416719
$518$			1.87156e32i			0.501472i
$519$	7.88429e31	+	5.88663e31i	0.206421	+	0.154120i
$520$	4.39170e31			0.112355
$521$		−	6.64395e32i		−	1.66102i	−0.557007	−	0.830508i	$-0.688050\pi$
$521$		−	6.64395e32i		−	1.66102i	0.557007	−	0.830508i	$-0.311950\pi$
$522$	9.30177e31	+	3.13864e32i	0.227258	+	0.766824i
$523$	−5.25543e31			−0.125484			−0.0627420	−	0.998030i	$-0.519985\pi$
$523$	−5.25543e31			−0.125484			−0.0627420	+	0.998030i	$0.519985\pi$
$524$			2.28865e32i			0.534077i
$525$	4.22649e32	−	5.66076e32i	0.963980	−	1.29111i
$526$	3.87453e32			0.863755
$527$		−	7.16138e32i		−	1.56052i
$528$	−1.19865e32	−	8.94945e31i	−0.255320	−	0.190629i
$529$	4.79664e32			0.998778
$530$			1.73044e31i			0.0352246i
$531$	5.09332e32	−	1.50947e32i	1.01360	−	0.300393i
$532$	−6.18707e31			−0.120378
$533$			8.29845e32i			1.57859i
$534$	3.40589e32	−	4.56169e32i	0.633484	−	0.848459i
$535$	−2.40622e32			−0.437613
$536$		−	1.93453e32i		−	0.344031i
$537$	−6.28983e32	−	4.69616e32i	−1.09382	−	0.816680i
$538$	−1.25069e32			−0.212698
$539$			1.56844e33i			2.60856i
$540$	−2.94839e31	+	7.99703e31i	−0.0479578	+	0.130078i
$541$	−1.00798e32			−0.160356			−0.0801778	−	0.996781i	$-0.525549\pi$
$541$	−1.00798e32			−0.160356			−0.0801778	+	0.996781i	$0.525549\pi$
$542$		−	3.64515e31i		−	0.0567184i
$543$	2.11581e32	−	2.83381e32i	0.322016	−	0.431294i
$544$	−1.34531e32			−0.200280
$545$		−	1.47940e31i		−	0.0215440i
$546$	−7.95666e32	−	5.94067e32i	−1.13349	−	0.846298i
$547$	2.11119e32			0.294225			0.147113	−	0.989120i	$-0.453002\pi$
$547$	2.11119e32			0.294225			0.147113	+	0.989120i	$0.453002\pi$
$548$			1.57733e32i			0.215058i
$549$	1.54275e32	+	5.20562e32i	0.205792	+	0.694391i
$550$	6.37452e32			0.831946
$551$			1.22172e32i			0.156010i
$552$	−5.91771e30	+	7.92590e30i	−0.00739408	+	0.00990330i
$553$	−1.23980e32			−0.151583
$554$		−	2.65726e32i		−	0.317919i
$555$	7.71020e31	+	5.75666e31i	0.0902714	+	0.0673992i
$556$	−3.49228e31			−0.0400140
$557$		−	1.33948e32i		−	0.150201i	−0.997176	−	0.0751005i	$-0.976072\pi$
$557$		−	1.33948e32i		−	0.150201i	0.997176	−	0.0751005i	$-0.0239278\pi$
$558$	−8.50887e32	+	2.52171e32i	−0.933817	+	0.276749i
$559$	−6.50676e32			−0.698913
$560$			1.15085e32i			0.120994i
$561$	−8.39490e32	+	1.12437e33i	−0.863896	+	1.15706i
$562$	−6.40994e31			−0.0645681
$563$			6.33412e32i			0.624576i	0.949987	+	0.312288i	$0.101095\pi$
$563$			6.33412e32i			0.624576i	−0.949987	+	0.312288i	$0.898905\pi$
$564$	−1.35707e32	−	1.01323e32i	−0.130994	−	0.0978042i
$565$	3.83364e32			0.362268
$566$		−	9.45857e31i		−	0.0875040i
$567$	1.61593e33	−	1.05003e33i	1.46362	−	0.951055i
$568$	4.96432e32			0.440230
$569$			3.30678e32i			0.287116i	0.989642	+	0.143558i	$0.0458544\pi$
$569$			3.30678e32i			0.287116i	−0.989642	+	0.143558i	$0.954146\pi$
$570$	−1.90306e31	+	2.54887e31i	−0.0161791	+	0.0216695i
$571$	−1.57897e33			−1.31444			−0.657218	−	0.753700i	$-0.728267\pi$
$571$	−1.57897e33			−1.31444			−0.657218	+	0.753700i	$0.728267\pi$
$572$		−	8.95990e32i		−	0.730383i
$573$	−1.17724e33	−	8.78964e32i	−0.939747	−	0.701642i
$574$	−2.17462e33			−1.69997
$575$		−	4.21507e31i		−	0.0322694i
$576$	4.73721e31	+	1.59845e32i	0.0355184	+	0.119848i
$577$	2.68744e33			1.97346			0.986730	−	0.162371i	$-0.0519140\pi$
$577$	2.68744e33			1.97346			0.986730	+	0.162371i	$0.0519140\pi$
$578$			2.78804e32i			0.200523i
$579$	−2.24691e32	+	3.00941e32i	−0.158286	+	0.212001i
$580$	2.27251e32			0.156809
$581$		−	2.77745e31i		−	0.0187729i
$582$	1.36681e33	+	1.02050e33i	0.904966	+	0.675673i
$583$	3.53043e32			0.228984
$584$			7.97629e32i			0.506812i
$585$	−4.89471e32	+	1.45061e32i	−0.304689	+	0.0902986i
$586$	9.76218e32			0.595354
$587$		−	1.59247e33i		−	0.951510i	−0.879578	−	0.475755i	$-0.842175\pi$
$587$		−	1.59247e33i		−	0.951510i	0.879578	−	0.475755i	$-0.157825\pi$
$588$	1.04579e33	−	1.40068e33i	0.612232	−	0.819996i
$589$	−3.31210e32			−0.189985
$590$		−	3.68778e32i		−	0.207272i
$591$	2.00853e33	+	1.49963e33i	1.10619	+	0.825911i
$592$	1.88213e32			0.101575
$593$		−	2.89338e33i		−	1.53020i	−0.643910	−	0.765102i	$-0.722689\pi$
$593$		−	2.89338e33i		−	1.53020i	0.643910	−	0.765102i	$-0.277311\pi$
$594$	1.63155e33	+	6.01527e32i	0.845594	+	0.311758i
$595$	1.07954e33			0.548320
$596$			7.69553e32i			0.383075i
$597$	−7.17614e32	+	9.61139e32i	−0.350105	+	0.468915i
$598$	−5.92462e31			−0.0283300
$599$		−	1.27146e33i		−	0.595911i	−0.954580	−	0.297955i	$-0.903695\pi$
$599$		−	1.27146e33i		−	0.595911i	0.954580	−	0.297955i	$-0.0963047\pi$
$600$	−5.69272e32	−	4.25035e32i	−0.261520	−	0.195258i
$601$	−1.15108e33			−0.518337			−0.259169	−	0.965832i	$-0.583449\pi$
$601$	−1.15108e33			−0.518337			−0.259169	+	0.965832i	$0.583449\pi$
$602$		−	1.70510e33i		−	0.752649i
$603$	6.38990e32	+	2.15611e33i	0.276494	+	0.932959i
$604$	−1.56183e33			−0.662505
$605$			4.16358e32i			0.173142i
$606$	−1.71628e33	+	2.29871e33i	−0.699709	+	0.937158i
$607$	4.18715e32			0.167361			0.0836805	−	0.996493i	$-0.473332\pi$
$607$	4.18715e32			0.167361			0.0836805	+	0.996493i	$0.473332\pi$
$608$			6.22200e31i			0.0243830i
$609$	−4.11722e33	−	3.07404e33i	−1.58196	−	1.18114i
$610$	3.76910e32			0.141997
$611$		−	1.01441e33i		−	0.374731i
$612$	1.49940e33	−	4.44367e32i	0.543127	−	0.160963i
$613$	−3.03008e33			−1.07629			−0.538144	−	0.842853i	$-0.680874\pi$
$613$	−3.03008e33			−1.07629			−0.538144	+	0.842853i	$0.680874\pi$
$614$			1.90705e33i			0.664265i
$615$	−6.68882e32	+	8.95870e32i	−0.228480	+	0.306015i
$616$	2.34795e33			0.786540
$617$		−	3.78856e33i		−	1.24466i	−0.782753	−	0.622332i	$-0.786185\pi$
$617$		−	3.78856e33i		−	1.24466i	0.782753	−	0.622332i	$-0.213815\pi$
$618$	1.51510e33	+	1.13122e33i	0.488180	+	0.364489i
$619$	−2.01070e33			−0.635418			−0.317709	−	0.948188i	$-0.602913\pi$
$619$	−2.01070e33			−0.635418			−0.317709	+	0.948188i	$0.602913\pi$
$620$			6.16079e32i			0.190957i
$621$	3.97752e31	−	1.07884e32i	0.0120924	−	0.0327987i
$622$	−3.64075e33			−1.08569
$623$			8.93559e33i			2.61377i
$624$	−5.97421e32	+	8.00158e32i	−0.171422	+	0.229594i
$625$	2.75431e33			0.775268
$626$			1.16345e33i			0.321258i
$627$	5.20017e32	+	3.88260e32i	0.140866	+	0.105175i
$628$	−1.33314e33			−0.354292
$629$		−	1.76550e33i		−	0.460321i
$630$	−3.80134e32	−	1.28266e33i	−0.0972412	−	0.328115i
$631$	2.99733e33			0.752284			0.376142	−	0.926562i	$-0.377250\pi$
$631$	2.99733e33			0.752284			0.376142	+	0.926562i	$0.377250\pi$
$632$			1.24680e32i			0.0307037i
$633$	−1.07436e33	+	1.43895e33i	−0.259600	+	0.347696i
$634$	−1.39997e33			−0.331932
$635$		−	8.92699e32i		−	0.207692i
$636$	−3.15282e32	−	2.35399e32i	−0.0719804	−	0.0537426i
$637$	1.04701e34			2.34573
$638$		−	4.63636e33i		−	1.01936i
$639$	−5.53292e33	+	1.63975e33i	−1.19383	+	0.353808i
$640$	1.15735e32			0.0245078
$641$			6.59215e33i			1.37003i	0.728528	+	0.685016i	$0.240205\pi$
$641$			6.59215e33i			1.37003i	−0.728528	+	0.685016i	$0.759795\pi$
$642$	3.27328e33	−	4.38408e33i	0.667672	−	0.894249i
$643$	1.70251e32			0.0340845			0.0170423	−	0.999855i	$-0.494575\pi$
$643$	1.70251e32			0.0340845			0.0170423	+	0.999855i	$0.494575\pi$
$644$		−	1.55255e32i		−	0.0305081i
$645$	−7.02445e32	−	5.24466e32i	−0.135486	−	0.101158i
$646$	5.83646e32			0.110499
$647$		−	2.44965e33i		−	0.455253i	−0.973749	−	0.227626i	$-0.926904\pi$
$647$		−	2.44965e33i		−	0.455253i	0.973749	−	0.227626i	$-0.0730965\pi$
$648$	−1.05596e33	−	1.62506e33i	−0.192640	−	0.296462i
$649$	−7.52378e33			−1.34741
$650$		−	4.25531e33i		−	0.748120i
$651$	8.33373e33	−	1.11618e34i	1.43836	−	1.92647i
$652$	−4.08361e33			−0.691948
$653$		−	1.61675e32i		−	0.0268958i	−0.999910	−	0.0134479i	$-0.995719\pi$
$653$		−	1.61675e32i		−	0.0268958i	0.999910	−	0.0134479i	$-0.00428073\pi$
$654$	2.69543e32	+	2.01249e32i	0.0440246	+	0.0328700i
$655$	−1.84688e33			−0.296171
$656$			2.18690e33i			0.344336i
$657$	−2.63463e33	−	8.88987e33i	−0.407319	−	1.37439i
$658$	2.65827e33			0.403542
$659$			1.23809e34i			1.84556i	0.385333	+	0.922778i	$0.374087\pi$
$659$			1.23809e34i			1.84556i	−0.385333	+	0.922778i	$0.625913\pi$
$660$	7.22197e32	−	9.67277e32i	0.105713	−	0.141587i
$661$	1.28758e34			1.85079			0.925395	−	0.379003i	$-0.123733\pi$
$661$	1.28758e34			1.85079			0.925395	+	0.379003i	$0.123733\pi$
$662$			3.87624e32i			0.0547160i
$663$	7.50577e33	+	5.60402e33i	1.04048	+	0.776850i
$664$	−2.79313e31			−0.00380254
$665$		−	4.99280e32i		−	0.0667551i
$666$	−2.09770e33	+	6.21681e32i	−0.275456	+	0.0816351i
$667$	−3.06573e32			−0.0395388
$668$			5.27643e33i			0.668379i
$669$	−4.33460e33	+	5.80556e33i	−0.539306	+	0.722322i
$670$	1.56111e33			0.190782
$671$		−	7.68967e33i		−	0.923076i
$672$	−2.09682e33	−	1.56555e33i	−0.247247	−	0.184601i
$673$	−4.97150e33			−0.575847			−0.287923	−	0.957653i	$-0.592965\pi$
$673$	−4.97150e33			−0.575847			−0.287923	+	0.957653i	$0.592965\pi$
$674$		−	7.23202e29i		−	8.22888e-5i
$675$	7.74868e33	+	2.85682e33i	0.866128	+	0.319329i
$676$	−1.42784e33			−0.156791
$677$			3.16889e33i			0.341856i	0.985283	+	0.170928i	$0.0546766\pi$
$677$			3.16889e33i			0.341856i	−0.985283	+	0.170928i	$0.945323\pi$
$678$	−5.21506e33	+	6.98481e33i	−0.552717	+	0.740284i
$679$	−2.67735e34			−2.78784
$680$		−	1.08563e33i		−	0.111065i
$681$	2.90435e33	+	2.16847e33i	0.291933	+	0.217966i
$682$	1.25692e34			1.24135
$683$		−	6.57986e33i		−	0.638510i	−0.947669	−	0.319255i	$-0.896567\pi$
$683$		−	6.57986e33i		−	0.638510i	0.947669	−	0.319255i	$-0.103433\pi$
$684$	−2.05517e32	−	6.93465e32i	−0.0195964	−	0.0661229i
$685$	−1.27286e33			−0.119260
$686$			1.40314e34i			1.29184i
$687$	9.23436e33	−	1.23681e34i	0.835461	−	1.11898i
$688$	−1.71473e33			−0.152453
$689$		−	2.35674e33i		−	0.205911i
$690$	−6.39599e31	−	4.77543e31i	−0.00549185	−	0.00410037i
$691$	−2.28870e34			−1.93131			−0.965657	−	0.259819i	$-0.916337\pi$
$691$	−2.28870e34			−1.93131			−0.965657	+	0.259819i	$0.916337\pi$
$692$			1.55312e33i			0.128805i
$693$	−2.61688e34	+	7.75546e33i	−2.13297	+	0.632133i
$694$	−2.92911e33			−0.234651
$695$		−	2.81818e32i		−	0.0221897i
$696$	−3.09139e33	+	4.14047e33i	−0.239245	+	0.320434i
$697$	2.05139e34			1.56046
$698$		−	1.38974e34i		−	1.03913i
$699$	3.70154e33	+	2.76368e33i	0.272055	+	0.203124i
$700$	1.11511e34			0.805640
$701$			2.42814e34i			1.72448i	0.506504	+	0.862238i	$0.330938\pi$
$701$			2.42814e34i			1.72448i	−0.506504	+	0.862238i	$0.669062\pi$
$702$	4.01550e33	−	1.08914e34i	0.280346	−	0.760393i
$703$	−8.16535e32			−0.0560417
$704$		−	2.36121e33i		−	0.159317i
$705$	8.17647e32	−	1.09512e33i	0.0542371	−	0.0726427i
$706$	−1.26492e33			−0.0824910
$707$		−	4.50279e34i		−	2.88701i
$708$	6.71906e33	+	5.01664e33i	0.423555	+	0.316238i
$709$	3.13216e34			1.94129			0.970643	−	0.240526i	$-0.0773201\pi$
$709$	3.13216e34			1.94129			0.970643	+	0.240526i	$0.0773201\pi$
$710$			4.00607e33i			0.244129i
$711$	−4.11827e32	−	1.38960e33i	−0.0246763	−	0.0832636i
$712$	8.98604e33			0.529430
$713$		−	8.31121e32i		−	0.0481493i
$714$	−1.46854e34	+	1.96689e34i	−0.836579	+	1.12048i
$715$	7.23040e33			0.405033
$716$		−	1.23903e34i		−	0.682535i
$717$	1.64621e34	+	1.22911e34i	0.891775	+	0.665825i
$718$	3.94744e33			0.210292
$719$		−	6.69265e33i		−	0.350632i	−0.984512	−	0.175316i	$-0.943905\pi$
$719$		−	6.69265e33i		−	0.350632i	0.984512	−	0.175316i	$-0.0560947\pi$
$720$	−1.28991e33	+	3.82281e32i	−0.0664612	+	0.0196966i
$721$	−2.96783e34			−1.50389
$722$			1.39184e34i			0.693654i
$723$	−3.83458e33	+	5.13586e33i	−0.187957	+	0.251741i
$724$	5.58231e33			0.269123
$725$		−	2.20194e34i		−	1.04412i
$726$	−7.58596e33	−	5.66389e33i	−0.353811	−	0.264165i
$727$	−3.17481e32			−0.0145648			−0.00728241	−	0.999973i	$-0.502318\pi$
$727$	−3.17481e32			−0.0145648			−0.00728241	+	0.999973i	$0.502318\pi$
$728$		−	1.56738e34i		−	0.707289i
$729$	1.71368e34	+	1.46240e34i	0.760674	+	0.649135i
$730$	−6.43665e33			−0.281051
$731$			1.60848e34i			0.690886i
$732$	−5.12726e33	+	6.86721e33i	−0.216647	+	0.290167i
$733$	9.81929e33			0.408162			0.204081	−	0.978954i	$-0.434579\pi$
$733$	9.81929e33			0.408162			0.204081	+	0.978954i	$0.434579\pi$
$734$		−	4.19123e33i		−	0.171392i
$735$	1.13031e34	+	8.43923e33i	0.454727	+	0.339512i
$736$	−1.56132e32			−0.00617956
$737$		−	3.18497e34i		−	1.24021i
$738$	−7.22348e33	−	2.43738e34i	−0.276739	−	0.933784i
$739$	−9.87359e33			−0.372171			−0.186085	−	0.982534i	$-0.559580\pi$
$739$	−9.87359e33			−0.372171			−0.186085	+	0.982534i	$0.559580\pi$
$740$			1.51883e33i			0.0563284i
$741$	2.59183e33	−	3.47138e33i	0.0945775	−	0.126673i
$742$	6.17585e33			0.221743
$743$			4.57424e34i			1.61604i	0.589153	+	0.808022i	$0.299462\pi$
$743$			4.57424e34i			1.61604i	−0.589153	+	0.808022i	$0.700538\pi$
$744$	−1.12248e34	−	8.38078e33i	−0.390216	−	0.291346i
$745$	−6.21009e33			−0.212433
$746$		−	6.16777e33i		−	0.207617i
$747$	3.11305e32	−	9.22592e31i	0.0103119	−	0.00305606i
$748$	−2.21490e34			−0.721995
$749$			8.58768e34i			2.75483i
$750$	7.14549e33	−	9.57035e33i	0.225578	−	0.302129i
$751$	−2.95235e34			−0.917253			−0.458626	−	0.888629i	$-0.651658\pi$
$751$	−2.95235e34			−0.917253			−0.458626	+	0.888629i	$0.651658\pi$
$752$		−	2.67328e33i		−	0.0817392i
$753$	−3.59067e34	−	2.68089e34i	−1.08053	−	0.806752i
$754$	−3.09500e34			−0.916653
$755$		−	1.26035e34i		−	0.367391i
$756$	2.85410e34	+	1.05226e34i	0.818856	+	0.301900i
$757$	2.19612e34			0.620163			0.310082	−	0.950710i	$-0.399644\pi$
$757$	2.19612e34			0.620163			0.310082	+	0.950710i	$0.399644\pi$
$758$			1.30843e34i			0.363679i
$759$	−9.74278e32	+	1.30490e33i	−0.0266552	+	0.0357007i
$760$	−5.02099e32			−0.0135215
$761$		−	4.02417e34i		−	1.06675i	−0.845880	−	0.533373i	$-0.820924\pi$
$761$		−	4.02417e34i		−	1.06675i	0.845880	−	0.533373i	$-0.179076\pi$
$762$	1.62648e34	+	1.21438e34i	0.424413	+	0.316879i
$763$	−5.27990e33			−0.135622
$764$		−	2.31904e34i		−	0.586393i
$765$	3.58593e33	+	1.20998e34i	0.0892615	+	0.301190i
$766$	−1.44984e34			−0.355284
$767$			5.02250e34i			1.21165i
$768$	−1.57439e33	+	2.10866e33i	−0.0373918	+	0.0500809i
$769$	−1.32227e34			−0.309175			−0.154587	−	0.987979i	$-0.549405\pi$
$769$	−1.32227e34			−0.309175			−0.154587	+	0.987979i	$0.549405\pi$
$770$			1.89473e34i			0.436174i
$771$	−2.47872e34	−	1.85069e34i	−0.561792	−	0.419450i
$772$	−5.92821e33			−0.132287
$773$			2.79581e33i			0.0614261i	0.999528	+	0.0307131i	$0.00977781\pi$
$773$			2.79581e33i			0.0614261i	−0.999528	+	0.0307131i	$0.990222\pi$
$774$	1.91113e34	−	5.66388e33i	0.413427	−	0.122524i
$775$	5.96947e34			1.27150
$776$			2.69247e34i			0.564690i
$777$	2.05452e34	−	2.75173e34i	0.424286	−	0.568269i
$778$	2.25719e34			0.459001
$779$		−	9.48754e33i		−	0.189978i
$780$	−6.45707e33	−	4.82103e33i	−0.127321	−	0.0950615i
$781$	8.17315e34			1.58700
$782$			1.46457e33i			0.0280046i
$783$	2.07784e34	−	5.63582e34i	0.391266	−	1.06125i
$784$	2.75919e34			0.511669
$785$		−	1.07581e34i		−	0.196472i
$786$	2.51238e34	−	3.36497e34i	0.451872	−	0.605217i
$787$	−1.02458e33			−0.0181489			−0.00907443	−	0.999959i	$-0.502889\pi$
$787$	−1.02458e33			−0.0181489			−0.00907443	+	0.999959i	$0.502889\pi$
$788$			3.95659e34i			0.690250i
$789$	−5.69668e34	−	4.25331e34i	−0.978809	−	0.730807i
$790$	−1.00613e33			−0.0170267
$791$		−	1.36821e35i		−	2.28052i
$792$	7.79925e33	+	2.63165e34i	0.128041	+	0.432043i
$793$	−5.13324e34			−0.830068
$794$			4.88048e34i			0.777349i
$795$	1.89961e33	−	2.54425e33i	0.0298029	−	0.0399166i
$796$	−1.89334e34			−0.292598
$797$			1.28416e34i			0.195487i	0.995212	+	0.0977437i	$0.0311625\pi$
$797$			1.28416e34i			0.195487i	−0.995212	+	0.0977437i	$0.968837\pi$
$798$	9.09678e33	+	6.79191e33i	0.136412	+	0.101849i
$799$	−2.50763e34			−0.370427
$800$		−	1.12141e34i		−	0.163186i
$801$	−1.00153e35	+	2.96816e34i	−1.43573	+	0.425497i
$802$	3.17790e34			0.448795
$803$			1.31320e35i			1.82702i
$804$	−2.12365e34	+	2.84432e34i	−0.291078	+	0.389857i
$805$	1.25287e33			0.0169182
$806$		−	8.39057e34i		−	1.11627i
$807$	1.83888e34	+	1.37296e34i	0.241030	+	0.179960i
$808$	−4.52821e34			−0.584777
$809$		−	2.52757e34i		−	0.321604i	−0.986987	−	0.160802i	$-0.948592\pi$
$809$		−	2.52757e34i		−	0.321604i	0.986987	−	0.160802i	$-0.0514081\pi$
$810$	1.31138e34	−	8.52132e33i	0.164402	−	0.106828i
$811$	6.11893e34			0.755832			0.377916	−	0.925840i	$-0.376641\pi$
$811$	6.11893e34			0.755832			0.377916	+	0.925840i	$0.376641\pi$
$812$		−	8.11048e34i		−	0.987130i
$813$	−4.00149e33	+	5.35942e33i	−0.0479883	+	0.0642734i
$814$	3.09870e34			0.366173
$815$		−	3.29536e34i		−	0.383718i
$816$	1.97800e34	+	1.47683e34i	0.226957	+	0.169453i
$817$	7.43912e33			0.0841118
$818$			1.00377e35i			1.11839i
$819$	5.17716e34	+	1.74690e35i	0.568440	+	1.91805i
$820$	−1.76477e34			−0.190951
$821$			1.06023e35i			1.13053i	0.824910	+	0.565264i	$0.191226\pi$
$821$			1.06023e35i			1.13053i	−0.824910	+	0.565264i	$0.808774\pi$
$822$	1.73152e34	−	2.31912e34i	0.181956	−	0.243704i
$823$	2.36678e34			0.245110			0.122555	−	0.992462i	$-0.460891\pi$
$823$	2.36678e34			0.245110			0.122555	+	0.992462i	$0.460891\pi$
$824$			2.98459e34i			0.304620i
$825$	−9.37238e34	−	6.99769e34i	−0.942763	−	0.703894i
$826$	−1.31615e35			−1.30480
$827$			8.95156e34i			0.874647i	0.899304	+	0.437324i	$0.144074\pi$
$827$			8.95156e34i			0.874647i	−0.899304	+	0.437324i	$0.855926\pi$
$828$	1.74015e33	−	5.15715e32i	0.0167580	−	0.00496645i
$829$	−9.98135e34			−0.947404			−0.473702	−	0.880685i	$-0.657083\pi$
$829$	−9.98135e34			−0.947404			−0.473702	+	0.880685i	$0.657083\pi$
$830$		−	2.25398e32i		−	0.00210869i
$831$	−2.91703e34	+	3.90694e34i	−0.268985	+	0.360267i
$832$	−1.57623e34			−0.143264
$833$		−	2.58822e35i		−	2.31879i
$834$	5.13466e33	+	3.83368e33i	0.0453439	+	0.0338551i
$835$	−4.25794e34			−0.370648
$836$			1.02438e34i			0.0878992i
$837$	1.52787e35	+	5.63304e34i	1.29235	+	0.476472i
$838$	1.25305e34			0.104482
$839$		−	6.41910e34i		−	0.527631i	−0.964573	−	0.263816i	$-0.915019\pi$
$839$		−	6.41910e34i		−	0.527631i	0.964573	−	0.263816i	$-0.0849811\pi$
$840$	1.26336e34	−	1.69208e34i	0.102370	−	0.137110i
$841$	−3.49679e34			−0.279330
$842$		−	1.55174e35i		−	1.22201i
$843$	9.42446e33	+	7.03657e33i	0.0731687	+	0.0546299i
$844$	−2.83457e34			−0.216959
$845$		−	1.15223e34i		−	0.0869480i
$846$	8.83005e33	+	2.97947e34i	0.0656930	+	0.221664i
$847$	1.48596e35			1.08995
$848$		−	6.21072e33i		−	0.0449151i
$849$	−1.03832e34	+	1.39068e34i	−0.0740355	+	0.0991598i
$850$	−1.05192e35			−0.739528
$851$		−	2.04897e33i		−	0.0142030i
$852$	−7.29898e34	−	5.44963e34i	−0.498870	−	0.372470i
$853$	1.28735e35			0.867577			0.433788	−	0.901015i	$-0.357177\pi$
$853$	1.28735e35			0.867577			0.433788	+	0.901015i	$0.357177\pi$
$854$		−	1.34517e35i		−	0.893888i
$855$	5.59608e33	−	1.65847e33i	0.0366683	−	0.0108671i
$856$	8.63617e34			0.558002
$857$		−	1.19549e35i		−	0.761686i	−0.924640	−	0.380843i	$-0.875634\pi$
$857$		−	1.19549e35i		−	0.761686i	0.924640	−	0.380843i	$-0.124366\pi$
$858$	−9.83581e34	+	1.31736e35i	−0.617964	+	0.827672i
$859$	3.64373e33			0.0225750			0.0112875	−	0.999936i	$-0.496407\pi$
$859$	3.64373e33			0.0225750			0.0112875	+	0.999936i	$0.496407\pi$
$860$		−	1.38374e34i		−	0.0845422i
$861$	3.19731e35	+	2.38721e35i	1.92640	+	1.43831i
$862$	2.13829e35			1.27052
$863$			1.13114e35i			0.662808i	0.943489	+	0.331404i	$0.107522\pi$
$863$			1.13114e35i			0.662808i	−0.943489	+	0.331404i	$0.892478\pi$
$864$	1.05821e34	−	2.87021e34i	0.0611512	−	0.165863i
$865$	−1.25333e34			−0.0714284
$866$		−	7.37039e33i		−	0.0414263i
$867$	3.06060e34	−	4.09923e34i	0.169659	−	0.227234i
$868$	2.19876e35			1.20210
$869$			2.05270e34i			0.110685i
$870$	−3.34125e34	−	2.49467e34i	−0.177696	−	0.132673i
$871$	−2.12613e35			−1.11525
$872$			5.30971e33i			0.0274709i
$873$	−8.89342e34	−	3.00085e35i	−0.453835	−	1.53135i
$874$	6.77356e32			0.00340941
$875$			1.87467e35i			0.930740i
$876$	8.75605e34	−	1.17274e35i	0.428804	−	0.574320i
$877$	−2.74651e35			−1.32674			−0.663371	−	0.748291i	$-0.730875\pi$
$877$	−2.74651e35			−1.32674			−0.663371	+	0.748291i	$0.730875\pi$
$878$			1.88661e35i			0.898974i
$879$	−1.43532e35	−	1.07165e35i	−0.674657	−	0.503718i
$880$	1.90543e34			0.0883490
$881$			3.92641e33i			0.0179591i	0.999960	+	0.00897954i	$0.00285832\pi$
$881$			3.92641e33i			0.0179591i	−0.999960	+	0.00897954i	$0.997142\pi$
$882$	−3.07522e35	+	9.11382e34i	−1.38757	+	0.411223i
$883$	3.14107e35			1.39814			0.699068	−	0.715055i	$-0.253598\pi$
$883$	3.14107e35			1.39814			0.699068	+	0.715055i	$0.253598\pi$
$884$			1.47856e35i			0.649248i
$885$	−4.04830e34	+	5.42210e34i	−0.175369	+	0.234881i
$886$	−9.46997e34			−0.404710
$887$			1.36842e35i			0.576949i	0.957488	+	0.288474i	$0.0931480\pi$
$887$			1.36842e35i			0.576949i	−0.957488	+	0.288474i	$0.906852\pi$
$888$	−2.76727e34	−	2.06612e34i	−0.115105	−	0.0859410i
$889$	−3.18600e35			−1.30745
$890$			7.25149e34i			0.293594i
$891$	−1.73851e35	−	2.67546e35i	−0.694456	−	1.06873i
$892$	−1.14363e35			−0.450722
$893$			1.15977e34i			0.0450975i
$894$	8.44784e34	−	1.13146e35i	0.324112	−	0.434101i
$895$	9.99863e34			0.378498
$896$		−	4.13052e34i		−	0.154279i
$897$	8.71089e33	+	6.50380e33i	0.0321036	+	0.0239694i
$898$	2.21543e35			0.805642
$899$		−	4.34175e35i		−	1.55793i
$900$	3.70409e34	+	1.24985e35i	0.131151	+	0.442534i
$901$	−5.82588e34			−0.203547
$902$			3.60046e35i			1.24131i
$903$	−1.87179e35	+	2.50699e35i	−0.636802	+	0.852904i
$904$	−1.37593e35			−0.461930
$905$			4.50477e34i			0.149242i
$906$	2.29633e35	+	1.71451e35i	0.750752	+	0.560533i
$907$	−4.89113e35			−1.57805			−0.789027	−	0.614359i	$-0.789415\pi$
$907$	−4.89113e35			−1.57805			−0.789027	+	0.614359i	$0.789415\pi$
$908$			5.72126e34i			0.182164i
$909$	5.04686e35	−	1.49570e35i	1.58582	−	0.469979i
$910$	1.26483e35			0.392225
$911$			1.37776e35i			0.421652i	0.977524	+	0.210826i	$0.0676153\pi$
$911$			1.37776e35i			0.421652i	−0.977524	+	0.210826i	$0.932385\pi$
$912$	6.83026e33	−	9.14814e33i	0.0206300	−	0.0276309i
$913$	−4.59855e33			−0.0137079
$914$		−	1.70647e35i		−	0.502048i
$915$	−5.54166e34	−	4.13756e34i	−0.160911	−	0.120141i
$916$	2.43638e35			0.698231
$917$			6.59142e35i			1.86443i
$918$	−2.69236e35	−	9.92635e34i	−0.751660	−	0.277126i
$919$	5.77554e35			1.59150			0.795749	−	0.605626i	$-0.207077\pi$
$919$	5.77554e35			1.59150			0.795749	+	0.605626i	$0.207077\pi$
$920$		−	1.25994e33i		−	0.00342686i
$921$	2.09348e35	−	2.80391e35i	0.562022	−	0.752746i
$922$	1.26201e35			0.334420
$923$		−	5.45599e35i		−	1.42710i
$924$	−3.45217e35	−	2.57748e35i	−0.891308	−	0.665476i
$925$	1.47166e35			0.375065
$926$		−	3.30298e35i		−	0.830948i
$927$	−9.85832e34	−	3.32643e35i	−0.244820	−	0.826080i
$928$	−8.15628e34			−0.199948
$929$			4.96289e35i			1.20101i	0.799621	+	0.600504i	$0.205033\pi$
$929$			4.96289e35i			1.20101i	−0.799621	+	0.600504i	$0.794967\pi$
$930$	6.76307e34	−	9.05814e34i	0.161565	−	0.216393i
$931$	−1.19704e35			−0.282300
$932$			7.29164e34i			0.169760i
$933$	5.35295e35	+	3.99667e35i	1.23031	+	0.918583i
$934$	−6.52771e34			−0.148115
$935$		−	1.78736e35i		−	0.400381i
$936$	1.75676e35	−	5.20639e34i	0.388511	−	0.115140i
$937$	−6.65386e35			−1.45278			−0.726388	−	0.687284i	$-0.758803\pi$
$937$	−6.65386e35			−1.45278			−0.726388	+	0.687284i	$0.758803\pi$
$938$		−	5.57154e35i		−	1.20100i
$939$	1.27718e35	−	1.71060e35i	0.271810	−	0.364050i
$940$	2.15727e34			0.0453283
$941$			5.63970e35i			1.16999i	0.811038	+	0.584993i	$0.198903\pi$
$941$			5.63970e35i			1.16999i	−0.811038	+	0.584993i	$0.801097\pi$
$942$	1.96011e35	+	1.46347e35i	0.401485	+	0.299760i
$943$	2.38076e34			0.0481476
$944$			1.32358e35i			0.264294i
$945$	−8.49149e34	+	2.30318e35i	−0.167418	+	0.454095i
$946$	−2.82310e35			−0.549581
$947$		−	7.06990e35i		−	1.35898i	−0.733684	−	0.679491i	$-0.762201\pi$
$947$		−	7.06990e35i		−	1.35898i	0.733684	−	0.679491i	$-0.237799\pi$
$948$	1.36868e34	−	1.83315e34i	0.0259778	−	0.0347935i
$949$	8.76627e35			1.64294
$950$			4.86506e34i			0.0900337i
$951$	2.05836e35	+	1.53683e35i	0.376146	+	0.280841i
$952$	−3.87457e35			−0.699166
$953$		−	1.01676e36i		−	1.81177i	−0.423527	−	0.905883i	$-0.639208\pi$
$953$		−	1.01676e36i		−	1.81177i	0.423527	−	0.905883i	$-0.360792\pi$
$954$	2.05145e34	+	6.92208e34i	0.0360978	+	0.121803i
$955$	1.87141e35			0.325183
$956$			3.24286e35i			0.556459i
$957$	−5.08960e35	+	6.81678e35i	−0.862463	+	1.15514i
$958$	−2.40636e35			−0.402693
$959$			4.54278e35i			0.750755i
$960$	−1.70163e34	−	1.27049e34i	−0.0277723	−	0.0207356i
$961$	5.56638e35			0.897207
$962$		−	2.06854e35i		−	0.329278i
$963$	−9.62533e35	+	2.85259e35i	−1.51321	+	0.448461i
$964$	−1.01171e35			−0.157084
$965$		−	4.78391e34i		−	0.0733593i
$966$	−1.70433e34	+	2.28270e34i	−0.0258123	+	0.0345719i
$967$	−9.91788e35			−1.48355			−0.741773	−	0.670651i	$-0.766015\pi$
$967$	−9.91788e35			−1.48355			−0.741773	+	0.670651i	$0.766015\pi$
$968$		−	1.49435e35i		−	0.220774i
$969$	−8.58128e34	−	6.40703e34i	−0.125218	−	0.0934913i
$970$	−2.17275e35			−0.313147
$971$			1.14482e36i			1.62970i	0.579675	+	0.814848i	$0.303180\pi$
$971$			1.14482e36i			1.62970i	−0.579675	+	0.814848i	$0.696820\pi$
$972$	−2.31356e34	+	3.54849e35i	−0.0325302	+	0.498941i
$973$	−1.00579e35			−0.139687
$974$		−	6.91420e35i		−	0.948493i
$975$	−4.67131e35	+	6.25654e35i	−0.632970	+	0.847771i
$976$	−1.35277e35			−0.181061
$977$		−	1.52947e35i		−	0.202212i	−0.994876	−	0.101106i	$-0.967762\pi$
$977$		−	1.52947e35i		−	0.202212i	0.994876	−	0.101106i	$-0.0322380\pi$
$978$	6.00408e35	+	4.48282e35i	0.784116	+	0.585444i
$979$	1.47944e36			1.90856
$980$			2.22659e35i			0.283745i
$981$	−1.75384e34	−	5.91787e34i	−0.0220781	−	0.0744967i
$982$	−3.78800e35			−0.471056
$983$		−	8.83352e35i		−	1.08515i	−0.840006	−	0.542577i	$-0.817448\pi$
$983$		−	8.83352e35i		−	1.08515i	0.840006	−	0.542577i	$-0.182552\pi$
$984$	2.40068e35	−	3.21537e35i	0.291336	−	0.390202i
$985$	−3.19286e35			−0.382777
$986$			7.65088e35i			0.906125i
$987$	−3.90843e35	−	2.91814e35i	−0.457295	−	0.341429i
$988$	6.83824e34			0.0790425
$989$			1.86673e34i			0.0213171i
$990$	−2.12367e35	+	6.29379e34i	−0.239588	+	0.0710051i
$991$	−3.62104e35			−0.403598			−0.201799	−	0.979427i	$-0.564679\pi$
$991$	−3.62104e35			−0.403598			−0.201799	+	0.979427i	$0.564679\pi$
$992$		−	2.21117e35i		−	0.243491i
$993$	4.25518e34	−	5.69919e34i	0.0462942	−	0.0620043i
$994$	1.42975e36			1.53682
$995$		−	1.52788e35i		−	0.162260i
$996$	4.10671e33	+	3.06618e33i	0.00430905	+	0.00321726i
$997$	1.31697e35			0.136532			0.0682662	−	0.997667i	$-0.478253\pi$
$997$	1.31697e35			0.136532			0.0682662	+	0.997667i	$0.478253\pi$
$998$			6.75733e35i			0.692164i
$999$	3.76668e35	+	1.38872e35i	0.381218	+	0.140549i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6.25.b.a.5.2	✓	8
3.2	odd	2	inner	6.25.b.a.5.6	yes	8
4.3	odd	2		48.25.e.d.17.5		8
12.11	even	2		48.25.e.d.17.6		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6.25.b.a.5.2	✓	8	1.1	even	1	trivial
6.25.b.a.5.6	yes	8	3.2	odd	2	inner
48.25.e.d.17.5		8	4.3	odd	2
48.25.e.d.17.6		8	12.11	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:	\( N \)	\(=\)	\( 6 = 2 \cdot 3 \)
Weight:	\( k \)	\(=\)	\( 25 \)
Character orbit:	\([\chi]\)	\(=\)	6.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-2896.31i q^{2} +(-317945. + 425841. i) q^{3} -8.38861e6 q^{4} -6.76938e7i q^{5} +(1.23337e9 + 9.20867e8i) q^{6} -2.41596e10 q^{7} +2.42960e10i q^{8} +(-8.02515e10 - 2.70788e11i) q^{9} +O(q^{10})\)	\(q-2896.31i q^{2} +(-317945. + 425841. i) q^{3} -8.38861e6 q^{4} -6.76938e7i q^{5} +(1.23337e9 + 9.20867e8i) q^{6} -2.41596e10 q^{7} +2.42960e10i q^{8} +(-8.02515e10 - 2.70788e11i) q^{9} -1.96062e11 q^{10} +4.00004e12i q^{11} +(2.66712e12 - 3.57221e12i) q^{12} +2.67023e13 q^{13} +6.99737e13i q^{14} +(2.88268e13 + 2.15229e13i) q^{15} +7.03687e13 q^{16} -6.60084e14i q^{17} +(-7.84286e14 + 2.32433e14i) q^{18} -3.05285e14 q^{19} +5.67857e14i q^{20} +(7.68142e15 - 1.02881e16i) q^{21} +1.15854e16 q^{22} -7.66067e14i q^{23} +(-1.03462e16 - 7.72479e15i) q^{24} +5.50222e16 q^{25} -7.73381e16i q^{26} +(1.40828e17 + 5.19213e16i) q^{27} +2.02665e17 q^{28} -4.00191e17i q^{29} +(6.23370e16 - 8.34913e16i) q^{30} +1.08492e18 q^{31} -2.03810e17i q^{32} +(-1.70338e18 - 1.27179e18i) q^{33} -1.91181e18 q^{34} +1.63546e18i q^{35} +(6.73199e17 + 2.27153e18i) q^{36} +2.67466e18 q^{37} +8.84200e17i q^{38} +(-8.48986e18 + 1.13709e19i) q^{39} +1.64469e18 q^{40} +3.10777e19i q^{41} +(-2.97976e19 - 2.22478e19i) q^{42} -2.43678e19 q^{43} -3.35548e19i q^{44} +(-1.83307e19 + 5.43253e18i) q^{45} -2.21877e18 q^{46} -3.79896e19i q^{47} +(-2.23734e19 + 2.99659e19i) q^{48} +3.92105e20 q^{49} -1.59361e20i q^{50} +(2.81091e20 + 2.09870e20i) q^{51} -2.23995e20 q^{52} -8.82597e19i q^{53} +(1.50380e20 - 4.07882e20i) q^{54} +2.70778e20 q^{55} -5.86982e20i q^{56} +(9.70638e19 - 1.30003e20i) q^{57} -1.15908e21 q^{58} +1.88092e21i q^{59} +(-2.41817e20 - 1.80547e20i) q^{60} -1.92240e21 q^{61} -3.14226e21i q^{62} +(1.93884e21 + 6.54213e21i) q^{63} -5.90296e20 q^{64} -1.80758e21i q^{65} +(-3.68351e21 + 4.93352e21i) q^{66} -7.96234e21 q^{67} +5.53718e21i q^{68} +(3.26223e20 + 2.43567e20i) q^{69} +4.73678e21 q^{70} -2.04327e22i q^{71} +(6.57907e21 - 1.94979e21i) q^{72} +3.28296e22 q^{73} -7.74666e21i q^{74} +(-1.74940e22 + 2.34307e22i) q^{75} +2.56092e21 q^{76} -9.66394e22i q^{77} +(3.29337e22 + 2.45893e22i) q^{78} +5.13170e21 q^{79} -4.76353e21i q^{80} +(-6.68858e22 + 4.34623e22i) q^{81} +9.00105e22 q^{82} +1.14963e21i q^{83} +(-6.44364e22 + 8.63032e22i) q^{84} -4.46836e22 q^{85} +7.05766e22i q^{86} +(1.70418e23 + 1.27239e23i) q^{87} -9.71851e22 q^{88} -3.69857e23i q^{89} +(1.57343e22 + 5.30913e22i) q^{90} -6.45117e23 q^{91} +6.42623e21i q^{92} +(-3.44945e23 + 4.62003e23i) q^{93} -1.10030e23 q^{94} +2.06659e22i q^{95} +(8.67905e22 + 6.48003e22i) q^{96} +1.10819e24 q^{97} -1.13566e24i q^{98} +(1.08316e24 - 3.21010e23i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 131880 q^{3} - 67108864 q^{4} + 33718272 q^{6} - 10160794640 q^{7} + 295169053896 q^{9}+O(q^{10}) \) 8 * q - 131880 * q^3 - 67108864 * q^4 + 33718272 * q^6 - 10160794640 * q^7 + 295169053896 * q^9	\( 8 q - 131880 q^{3} - 67108864 q^{4} + 33718272 q^{6} - 10160794640 q^{7} + 295169053896 q^{9} - 1863369424896 q^{10} + 1106289623040 q^{12} + 50568363679120 q^{13} - 348034956760512 q^{15} + 562949953421312 q^{16} - 514738292981760 q^{18} - 978083631341264 q^{19} + 36\!\cdots\!36 q^{21}+ \cdots + 69\!\cdots\!44 q^{99}+O(q^{100}) \) 8 * q - 131880 * q^3 - 67108864 * q^4 + 33718272 * q^6 - 10160794640 * q^7 + 295169053896 * q^9 - 1863369424896 * q^10 + 1106289623040 * q^12 + 50568363679120 * q^13 - 348034956760512 * q^15 + 562949953421312 * q^16 - 514738292981760 * q^18 - 978083631341264 * q^19 + 3640012304241936 * q^21 - 336450979430400 * q^22 - 282849366245376 * q^24 + 7630618767014024 * q^25 - 86594528606057640 * q^27 + 85234923203461120 * q^28 - 725410188900237312 * q^30 + 3092119786822709104 * q^31 - 8158685952668529600 * q^33 + 3821138032531341312 * q^34 - 2476057486864416768 * q^36 + 22590293223992782480 * q^37 - 40190176581881465040 * q^39 + 15631075664637984768 * q^40 - 79119883835565342720 * q^42 + 226487466371803896880 * q^43 - 347709996757177504128 * q^45 + 139842130561120468992 * q^46 - 9280229982150328320 * q^48 + 104686700473616731800 * q^49 + 558091874936566543104 * q^51 - 424198180105575464960 * q^52 + 334066775626796728320 * q^54 - 2212687664250467338368 * q^55 + 3588879995640760725840 * q^57 - 1867706355469718323200 * q^58 + 2919528822560885047296 * q^60 - 6507010783838092385648 * q^61 + 10112982777612899380080 * q^63 - 4722366482869645213696 * q^64 - 1924112442339530440704 * q^66 - 7042120118150060144720 * q^67 - 4323335967368731345536 * q^69 + 16481910236435553583104 * q^70 + 4317937762413135790080 * q^72 + 36259820324758576687120 * q^73 - 108081978448612908655272 * q^75 + 8204760174538377920512 * q^76 - 74188898027329578270720 * q^78 + 316807052777330015315824 * q^79 - 268518660504396776813304 * q^81 + 83114941529654645882880 * q^82 - 30534636335462338265088 * q^84 - 222512862545524200678912 * q^85 + 449461577201807342128320 * q^87 + 2822355377657688883200 * q^88 + 612683975543382025371648 * q^90 - 1196839602335690774367520 * q^91 + 873237537450828783745680 * q^93 - 1298887117621773403422720 * q^94 + 2372712456480891076608 * q^96 + 816517576248201265716880 * q^97 + 695858883367208922313344 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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