LMFDB - Embedded newform 27.22.c.a.19.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [27,22,Mod(10,27)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(27, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([2]))

N = Newforms(chi, 22, names="a")

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

chi := DirichletCharacter("27.10");

S:= CuspForms(chi, 22);

N := Newforms(S);

Level:	$ N $	$=$	$ 27 = 3^{3} $
Weight:	$ k $	$=$	$ 22 $
Character orbit:	$[\chi]$	$=$	27.c (of order $3$, degree $2$, not 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:	$75.4588829575$
Analytic rank:	$0$
Dimension:	$40$
Relative dimension:	$20$ over $\Q(\zeta_{3})$
Twist minimal:	no (minimal twist has level 9)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			19.4
Character	$\chi$	$=$	27.19
Dual form			27.22.c.a.10.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-991.417 + 1717.18i) q^{2} +(-917239. - 1.58870e6i) q^{4} +(-5.12169e6 - 8.87103e6i) q^{5} +(4.75645e8 - 8.23841e8i) q^{7} -5.20838e8 q^{8} +O(q^{10})$	\(q+(-991.417 + 1717.18i) q^{2} +(-917239. - 1.58870e6i) q^{4} +(-5.12169e6 - 8.87103e6i) q^{5} +(4.75645e8 - 8.23841e8i) q^{7} -5.20838e8 q^{8} +2.03109e10 q^{10} +(4.33867e10 - 7.51480e10i) q^{11} +(-2.62920e11 - 4.55390e11i) q^{13} +(9.43125e11 + 1.63354e12i) q^{14} +(2.43996e12 - 4.22613e12i) q^{16} +9.08695e12 q^{17} -8.79971e12 q^{19} +(-9.39564e12 + 1.62737e13i) q^{20} +(8.60286e13 + 1.49006e14i) q^{22} +(1.93036e13 + 3.34348e13i) q^{23} +(1.85955e14 - 3.22084e14i) q^{25} +1.04265e15 q^{26} -1.74512e15 q^{28} +(-1.44890e14 + 2.50957e14i) q^{29} +(-3.02092e15 - 5.23239e15i) q^{31} +(4.29189e15 + 7.43378e15i) q^{32} +(-9.00895e15 + 1.56040e16i) q^{34} -9.74443e15 q^{35} -4.41709e16 q^{37} +(8.72418e15 - 1.51107e16i) q^{38} +(2.66757e15 + 4.62037e15i) q^{40} +(4.43133e16 + 7.67528e16i) q^{41} +(-3.63458e16 + 6.29527e16i) q^{43} -1.59184e17 q^{44} -7.65517e16 q^{46} +(-3.59772e17 + 6.23144e17i) q^{47} +(-1.73203e17 - 2.99997e17i) q^{49} +(3.68718e17 + 6.38638e17i) q^{50} +(-4.82320e17 + 8.35403e17i) q^{52} -5.36630e17 q^{53} -8.88854e17 q^{55} +(-2.47734e17 + 4.29088e17i) q^{56} +(-2.87293e17 - 4.97606e17i) q^{58} +(-2.68634e18 - 4.65287e18i) q^{59} +(-1.08619e18 + 1.88134e18i) q^{61} +1.19800e19 q^{62} -6.78630e18 q^{64} +(-2.69319e18 + 4.66474e18i) q^{65} +(-9.14762e18 - 1.58441e19i) q^{67} +(-8.33490e18 - 1.44365e19i) q^{68} +(9.66079e18 - 1.67330e19i) q^{70} +1.88011e19 q^{71} +7.15740e19 q^{73} +(4.37918e19 - 7.58496e19i) q^{74} +(8.07144e18 + 1.39801e19i) q^{76} +(-4.12733e19 - 7.14875e19i) q^{77} +(3.71050e19 - 6.42678e19i) q^{79} -4.99869e19 q^{80} -1.75732e20 q^{82} +(2.14787e19 - 3.72022e19i) q^{83} +(-4.65406e19 - 8.06106e19i) q^{85} +(-7.20676e19 - 1.24825e20i) q^{86} +(-2.25974e19 + 3.91399e19i) q^{88} +1.01476e20 q^{89} -5.00225e20 q^{91} +(3.54121e19 - 6.13355e19i) q^{92} +(-7.13369e20 - 1.23559e21i) q^{94} +(4.50694e19 + 7.80625e19i) q^{95} +(-4.98241e20 + 8.62978e20i) q^{97} +6.86866e20 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q - 1023 q^{2} - 19922945 q^{4} - 32234853 q^{5} - 189623959 q^{7} + 1296271662 q^{8}+O(q^{10}) $ 40 * q - 1023 * q^2 - 19922945 * q^4 - 32234853 * q^5 - 189623959 * q^7 + 1296271662 * q^8	$ 40 q - 1023 q^{2} - 19922945 q^{4} - 32234853 q^{5} - 189623959 q^{7} + 1296271662 q^{8} + 4194300 q^{10} - 146068576386 q^{11} - 177565977277 q^{13} - 1549677244440 q^{14} - 18691699769345 q^{16} + 18615603749598 q^{17} - 9768733723954 q^{19} - 76202257650204 q^{20} + 86758343554047 q^{22} - 356460494884095 q^{23} - 13\!\cdots\!29 q^{25}+ \cdots - 53\!\cdots\!86 q^{98}+O(q^{100}) $ 40 * q - 1023 * q^2 - 19922945 * q^4 - 32234853 * q^5 - 189623959 * q^7 + 1296271662 * q^8 + 4194300 * q^10 - 146068576386 * q^11 - 177565977277 * q^13 - 1549677244440 * q^14 - 18691699769345 * q^16 + 18615603749598 * q^17 - 9768733723954 * q^19 - 76202257650204 * q^20 + 86758343554047 * q^22 - 356460494884095 * q^23 - 1379841857082329 * q^25 - 4509080239093464 * q^26 + 1599477148286972 * q^28 + 2772828270755157 * q^29 + 3064842508546901 * q^31 - 9763241440878495 * q^32 + 5532390311666553 * q^34 + 57889578635103594 * q^35 + 30082698487879388 * q^37 - 38173338977409867 * q^38 - 43546396391926176 * q^40 - 4985514195953106 * q^41 - 41986108659289660 * q^43 - 309819550937094042 * q^44 - 741003239171632200 * q^46 - 971751895603333665 * q^47 - 1393736132530446381 * q^49 - 1504393427506051923 * q^50 - 892509168437820382 * q^52 + 6400936694928489300 * q^53 + 3526658855224378230 * q^55 - 9313401575284840590 * q^56 - 985520139125952432 * q^58 - 11335149505478767926 * q^59 - 333769931007960067 * q^61 + 61644391774413093852 * q^62 + 25609201125502545922 * q^64 - 24815104795645584999 * q^65 + 14325054629523996728 * q^67 - 98193137232148637751 * q^68 - 23664205955002266174 * q^70 + 217438227096249463920 * q^71 - 4831088596512341626 * q^73 - 284989967381657148240 * q^74 + 45502930505046158765 * q^76 - 209785238565183158133 * q^77 + 45386959469213650259 * q^79 + 998031008510384761248 * q^80 + 228516181628552966154 * q^82 - 224083700347690062915 * q^83 - 135764416394391341394 * q^85 + 210501162447733500423 * q^86 + 409557505702705259691 * q^88 - 281885809391320932720 * q^89 - 387169009858825345418 * q^91 - 160981359902419031922 * q^92 + 1246412695298803268064 * q^94 - 583111881346045719228 * q^95 - 658984791485125488346 * q^97 - 5342632206895563334686 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/27\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{2}{3}\right)$

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 $

$2$	−991.417	+	1717.18i	−0.684607	+	1.18577i	0.288953	+	0.957343i	$0.406693\pi$
$2$	−991.417	+	1717.18i	−0.684607	+	1.18577i	−0.973560	+	0.228431i	$0.926640\pi$
$3$		0			0
$3$		0			0
$4$	−917239.	−	1.58870e6i	−0.437374	−	0.757554i
$5$	−5.12169e6	−	8.87103e6i	−0.234546	−	0.406246i	0.724594	−	0.689176i	$-0.242027\pi$
$5$	−5.12169e6	−	8.87103e6i	−0.234546	−	0.406246i	−0.959141	+	0.282929i	$0.908694\pi$
$6$		0			0
$7$	4.75645e8	−	8.23841e8i	0.636434	−	1.10234i	−0.349775	−	0.936834i	$-0.613742\pi$
$7$	4.75645e8	−	8.23841e8i	0.636434	−	1.10234i	0.986209	−	0.165503i	$-0.0529246\pi$
$8$	−5.20838e8			−0.171497
$9$		0			0
$10$	2.03109e10			0.642288
$11$	4.33867e10	−	7.51480e10i	0.504352	−	0.873563i	−0.495636	−	0.868531i	$-0.665065\pi$
$11$	4.33867e10	−	7.51480e10i	0.504352	−	0.873563i	0.999987	−	0.00503232i	$-0.00160184\pi$
$12$		0			0
$13$	−2.62920e11	−	4.55390e11i	−0.528954	−	0.916175i	−0.999430	−	0.0337620i	$-0.989251\pi$
$13$	−2.62920e11	−	4.55390e11i	−0.528954	−	0.916175i	0.470476	−	0.882413i	$-0.344082\pi$
$14$	9.43125e11	+	1.63354e12i	0.871415	+	1.50933i
$15$		0			0
$16$	2.43996e12	−	4.22613e12i	0.554782	−	0.960911i
$17$	9.08695e12			1.09321			0.546606	−	0.837390i	$-0.315920\pi$
$17$	9.08695e12			1.09321			0.546606	+	0.837390i	$0.315920\pi$
$18$		0			0
$19$	−8.79971e12			−0.329273			−0.164636	−	0.986354i	$-0.552645\pi$
$19$	−8.79971e12			−0.329273			−0.164636	+	0.986354i	$0.552645\pi$
$20$	−9.39564e12	+	1.62737e13i	−0.205169	+	0.355363i
$21$		0			0
$22$	8.60286e13	+	1.49006e14i	0.690566	+	1.19609i
$23$	1.93036e13	+	3.34348e13i	0.0971620	+	0.168289i	0.910509	−	0.413490i	$-0.135690\pi$
$23$	1.93036e13	+	3.34348e13i	0.0971620	+	0.168289i	−0.813347	+	0.581779i	$0.802357\pi$
$24$		0			0
$25$	1.85955e14	−	3.22084e14i	0.389976	−	0.675458i
$26$	1.04265e15			1.44850
$27$		0			0
$28$	−1.74512e15			−1.11344
$29$	−1.44890e14	+	2.50957e14i	−0.0639528	+	0.110770i	−0.896229	−	0.443592i	$-0.853704\pi$
$29$	−1.44890e14	+	2.50957e14i	−0.0639528	+	0.110770i	0.832276	+	0.554361i	$0.187037\pi$
$30$		0			0
$31$	−3.02092e15	−	5.23239e15i	−0.661975	−	1.14657i	−0.980096	−	0.198525i	$-0.936385\pi$
$31$	−3.02092e15	−	5.23239e15i	−0.661975	−	1.14657i	0.318121	−	0.948050i	$-0.396948\pi$
$32$	4.29189e15	+	7.43378e15i	0.673867	+	1.16717i
$33$		0			0
$34$	−9.00895e15	+	1.56040e16i	−0.748421	+	1.29630i
$35$	−9.74443e15			−0.597093
$36$		0			0
$37$	−4.41709e16			−1.51014			−0.755071	−	0.655642i	$-0.772398\pi$
$37$	−4.41709e16			−1.51014			−0.755071	+	0.655642i	$0.772398\pi$
$38$	8.72418e15	−	1.51107e16i	0.225422	−	0.390443i
$39$		0			0
$40$	2.66757e15	+	4.62037e15i	0.0402241	+	0.0696702i
$41$	4.43133e16	+	7.67528e16i	0.515589	+	0.893026i	0.999836	+	0.0180947i	$0.00576004\pi$
$41$	4.43133e16	+	7.67528e16i	0.515589	+	0.893026i	−0.484248	+	0.874931i	$0.660907\pi$
$42$		0			0
$43$	−3.63458e16	+	6.29527e16i	−0.256469	+	0.444217i	−0.965294	−	0.261167i	$-0.915893\pi$
$43$	−3.63458e16	+	6.29527e16i	−0.256469	+	0.444217i	0.708824	+	0.705385i	$0.249226\pi$
$44$	−1.59184e17			−0.882361
$45$		0			0
$46$	−7.65517e16			−0.266071
$47$	−3.59772e17	+	6.23144e17i	−0.997701	+	1.72807i	−0.440157	+	0.897921i	$0.645077\pi$
$47$	−3.59772e17	+	6.23144e17i	−0.997701	+	1.72807i	−0.557544	+	0.830147i	$0.688256\pi$
$48$		0			0
$49$	−1.73203e17	−	2.99997e17i	−0.310097	−	0.537103i
$50$	3.68718e17	+	6.38638e17i	0.533961	+	0.924847i
$51$		0			0
$52$	−4.82320e17	+	8.35403e17i	−0.462701	+	0.801421i
$53$	−5.36630e17			−0.421481			−0.210740	−	0.977542i	$-0.567587\pi$
$53$	−5.36630e17			−0.421481			−0.210740	+	0.977542i	$0.567587\pi$
$54$		0			0
$55$	−8.88854e17			−0.473175
$56$	−2.47734e17	+	4.29088e17i	−0.109147	+	0.189048i
$57$		0			0
$58$	−2.87293e17	−	4.97606e17i	−0.0875651	−	0.151667i
$59$	−2.68634e18	−	4.65287e18i	−0.684249	−	1.18515i	−0.973672	−	0.227953i	$-0.926797\pi$
$59$	−2.68634e18	−	4.65287e18i	−0.684249	−	1.18515i	0.289423	−	0.957201i	$-0.406536\pi$
$60$		0			0
$61$	−1.08619e18	+	1.88134e18i	−0.194959	+	0.337679i	−0.946887	−	0.321566i	$-0.895791\pi$
$61$	−1.08619e18	+	1.88134e18i	−0.194959	+	0.337679i	0.751928	+	0.659245i	$0.229124\pi$
$62$	1.19800e19			1.81277
$63$		0			0
$64$	−6.78630e18			−0.735772
$65$	−2.69319e18	+	4.66474e18i	−0.248128	+	0.429771i
$66$		0			0
$67$	−9.14762e18	−	1.58441e19i	−0.613088	−	1.06190i	−0.990717	−	0.135942i	$-0.956594\pi$
$67$	−9.14762e18	−	1.58441e19i	−0.613088	−	1.06190i	0.377629	−	0.925957i	$-0.376739\pi$
$68$	−8.33490e18	−	1.44365e19i	−0.478142	−	0.828167i
$69$		0			0
$70$	9.66079e18	−	1.67330e19i	0.408774	−	0.708017i
$71$	1.88011e19			0.685442			0.342721	−	0.939437i	$-0.388651\pi$
$71$	1.88011e19			0.685442			0.342721	+	0.939437i	$0.388651\pi$
$72$		0			0
$73$	7.15740e19			1.94924			0.974619	−	0.223869i	$-0.0718689\pi$
$73$	7.15740e19			1.94924			0.974619	+	0.223869i	$0.0718689\pi$
$74$	4.37918e19	−	7.58496e19i	1.03385	−	1.79069i
$75$		0			0
$76$	8.07144e18	+	1.39801e19i	0.144015	+	0.249442i
$77$	−4.12733e19	−	7.14875e19i	−0.641973	−	1.11193i
$78$		0			0
$79$	3.71050e19	−	6.42678e19i	0.440908	−	0.763675i	−0.556849	−	0.830614i	$-0.687990\pi$
$79$	3.71050e19	−	6.42678e19i	0.440908	−	0.763675i	0.997757	+	0.0669386i	$0.0213232\pi$
$80$	−4.99869e19			−0.520488
$81$		0			0
$82$	−1.75732e20			−1.41190
$83$	2.14787e19	−	3.72022e19i	0.151946	−	0.263178i	−0.779997	−	0.625783i	$-0.784779\pi$
$83$	2.14787e19	−	3.72022e19i	0.151946	−	0.263178i	0.931943	+	0.362606i	$0.118113\pi$
$84$		0			0
$85$	−4.65406e19	−	8.06106e19i	−0.256409	−	0.444113i
$86$	−7.20676e19	−	1.24825e20i	−0.351161	−	0.608229i
$87$		0			0
$88$	−2.25974e19	+	3.91399e19i	−0.0864951	+	0.149814i
$89$	1.01476e20			0.344958			0.172479	−	0.985013i	$-0.444822\pi$
$89$	1.01476e20			0.344958			0.172479	+	0.985013i	$0.444822\pi$
$90$		0			0
$91$	−5.00225e20			−1.34658
$92$	3.54121e19	−	6.13355e19i	0.0849922	−	0.147211i
$93$		0			0
$94$	−7.13369e20	−	1.23559e21i	−1.36607	−	2.36610i
$95$	4.50694e19	+	7.80625e19i	0.0772297	+	0.133766i
$96$		0			0
$97$	−4.98241e20	+	8.62978e20i	−0.686019	+	1.18822i	0.287097	+	0.957902i	$0.407310\pi$
$97$	−4.98241e20	+	8.62978e20i	−0.686019	+	1.18822i	−0.973115	+	0.230318i	$0.926023\pi$
$98$	6.86866e20			0.849177
$99$		0			0
$100$	−6.82261e20			−0.682261
$101$	4.70250e20	−	8.14498e20i	0.423599	−	0.733695i	−0.572690	−	0.819772i	$-0.694100\pi$
$101$	4.70250e20	−	8.14498e20i	0.423599	−	0.733695i	0.996288	+	0.0860775i	$0.0274333\pi$
$102$		0			0
$103$	2.17081e19	+	3.75996e19i	0.0159159	+	0.0275672i	0.873874	−	0.486153i	$-0.161600\pi$
$103$	2.17081e19	+	3.75996e19i	0.0159159	+	0.0275672i	−0.857958	+	0.513720i	$0.828267\pi$
$104$	1.36938e20	+	2.37184e20i	0.0907142	+	0.157122i
$105$		0			0
$106$	5.32024e20	−	9.21492e20i	0.288549	−	0.499781i
$107$	−1.58939e21			−0.781088			−0.390544	−	0.920584i	$-0.627713\pi$
$107$	−1.58939e21			−0.781088			−0.390544	+	0.920584i	$0.627713\pi$
$108$		0			0
$109$	−3.48277e20			−0.140911			−0.0704557	−	0.997515i	$-0.522445\pi$
$109$	−3.48277e20			−0.140911			−0.0704557	+	0.997515i	$0.522445\pi$
$110$	8.81225e20	−	1.52633e21i	0.323939	−	0.561079i
$111$		0			0
$112$	−2.32111e21	−	4.02027e21i	−0.706165	−	1.22311i
$113$	−2.24899e21	−	3.89537e21i	−0.623253	−	1.07951i	−0.988876	−	0.148743i	$-0.952477\pi$
$113$	−2.24899e21	−	3.89537e21i	−0.623253	−	1.07951i	0.365623	−	0.930763i	$-0.380856\pi$
$114$		0			0
$115$	1.97734e20	−	3.42486e20i	0.0455779	−	0.0789433i
$116$	5.31595e20			0.111885
$117$		0			0
$118$	1.06531e22			1.87377
$119$	4.32216e21	−	7.48620e21i	0.695757	−	1.20509i
$120$		0			0
$121$	−6.46889e19	−	1.12044e20i	−0.00874144	−	0.0151406i
$122$	−2.15374e21	−	3.73039e21i	−0.266941	−	0.462355i
$123$		0			0
$124$	−5.54182e21	+	9.59871e21i	−0.579061	+	1.00296i
$125$	−8.69405e21			−0.834962
$126$		0			0
$127$	1.85658e22			1.50930			0.754650	−	0.656128i	$-0.227807\pi$
$127$	1.85658e22			1.50930			0.754650	+	0.656128i	$0.227807\pi$
$128$	−2.27270e21	+	3.93643e21i	−0.170152	+	0.294712i
$129$		0			0
$130$	−5.34014e21	−	9.24940e21i	−0.339741	−	0.588448i
$131$	1.45973e22	+	2.52833e22i	0.856889	+	1.48418i	0.874881	+	0.484337i	$0.160939\pi$
$131$	1.45973e22	+	2.52833e22i	0.856889	+	1.48418i	−0.0179922	+	0.999838i	$0.505727\pi$
$132$		0			0
$133$	−4.18554e21	+	7.24956e21i	−0.209560	+	0.362969i
$134$	3.62764e22			1.67890
$135$		0			0
$136$	−4.73283e21			−0.187483
$137$	−1.27026e22	+	2.20015e22i	−0.465935	+	0.807024i	−0.999243	−	0.0388974i	$-0.987615\pi$
$137$	−1.27026e22	+	2.20015e22i	−0.465935	+	0.807024i	0.533308	+	0.845921i	$0.320949\pi$
$138$		0			0
$139$	−4.06090e21	−	7.03369e21i	−0.127929	−	0.221579i	0.794945	−	0.606681i	$-0.207499\pi$
$139$	−4.06090e21	−	7.03369e21i	−0.127929	−	0.221579i	−0.922874	+	0.385102i	$0.874166\pi$
$140$	8.93797e21	+	1.54810e22i	0.261153	+	0.452330i
$141$		0			0
$142$	−1.86397e22	+	3.22850e22i	−0.469259	+	0.812780i
$143$	−4.56289e22			−1.06711
$144$		0			0
$145$	2.96833e21			0.0599996
$146$	−7.09596e22	+	1.22906e23i	−1.33446	+	2.31136i
$147$		0			0
$148$	4.05153e22	+	7.01745e22i	0.660497	+	1.14401i
$149$	−4.23323e22	−	7.33217e22i	−0.643008	−	1.11372i	−0.984758	−	0.173932i	$-0.944353\pi$
$149$	−4.23323e22	−	7.33217e22i	−0.643008	−	1.11372i	0.341750	−	0.939791i	$-0.388980\pi$
$150$		0			0
$151$	−7.13475e22	+	1.23578e23i	−0.942152	+	1.63186i	−0.180797	+	0.983520i	$0.557868\pi$
$151$	−7.13475e22	+	1.23578e23i	−0.942152	+	1.63186i	−0.761355	+	0.648335i	$0.775466\pi$
$152$	4.58322e21			0.0564694
$153$		0			0
$154$	1.63676e23			1.75800
$155$	−3.09445e22	+	5.35974e22i	−0.310528	+	0.537850i
$156$		0			0
$157$	−8.73884e22	−	1.51361e23i	−0.766491	−	1.32760i	−0.939454	−	0.342674i	$-0.888667\pi$
$157$	−8.73884e22	−	1.51361e23i	−0.766491	−	1.32760i	0.172963	−	0.984928i	$-0.444666\pi$
$158$	7.35731e22	+	1.27432e23i	0.603698	+	1.04563i
$159$		0			0
$160$	4.39635e22	−	7.61470e22i	0.316106	−	0.547511i
$161$	3.67267e22			0.247349
$162$		0			0
$163$	2.02629e23			1.19876			0.599378	−	0.800466i	$-0.295414\pi$
$163$	2.02629e23			1.19876			0.599378	+	0.800466i	$0.295414\pi$
$164$	8.12917e22	−	1.40801e23i	0.451010	−	0.781172i
$165$		0			0
$166$	4.25887e22	+	7.37658e22i	0.208046	+	0.360347i
$167$	1.06878e22	+	1.85119e22i	0.0490193	+	0.0849038i	0.889494	−	0.456947i	$-0.151057\pi$
$167$	1.06878e22	+	1.85119e22i	0.0490193	+	0.0849038i	−0.840475	+	0.541851i	$0.817724\pi$
$168$		0			0
$169$	−1.47211e22	+	2.54977e22i	−0.0595839	+	0.103202i
$170$	1.84564e23			0.702157
$171$		0			0
$172$	1.33351e23			0.448691
$173$	1.95528e23	−	3.38664e23i	0.619048	−	1.07222i	−0.370612	−	0.928788i	$-0.620852\pi$
$173$	1.95528e23	−	3.38664e23i	0.619048	−	1.07222i	0.989660	−	0.143435i	$-0.0458148\pi$
$174$		0			0
$175$	−1.76897e23	−	3.06395e23i	−0.496388	−	0.859769i
$176$	−2.11723e23	−	3.66716e23i	−0.559611	−	0.969274i
$177$		0			0
$178$	−1.00605e23	+	1.74252e23i	−0.236161	+	0.409042i
$179$	−8.21918e23			−1.81916			−0.909582	−	0.415525i	$-0.863598\pi$
$179$	−8.21918e23			−1.81916			−0.909582	+	0.415525i	$0.863598\pi$
$180$		0			0
$181$	−7.25876e23			−1.42968			−0.714838	−	0.699290i	$-0.753500\pi$
$181$	−7.25876e23			−1.42968			−0.714838	+	0.699290i	$0.753500\pi$
$182$	4.95932e23	−	8.58979e23i	0.921876	−	1.59674i
$183$		0			0
$184$	−1.00541e22	−	1.74141e22i	−0.0166630	−	0.0288612i
$185$	2.26230e23	+	3.91841e23i	0.354198	+	0.613490i
$186$		0			0
$187$	3.94253e23	−	6.82866e23i	0.551363	−	0.954989i
$188$	1.31999e24			1.74547
$189$		0			0
$190$	−1.78730e23			−0.211488
$191$	−8.78441e23	+	1.52150e24i	−0.983699	+	1.70382i	−0.336119	+	0.941820i	$0.609114\pi$
$191$	−8.78441e23	+	1.52150e24i	−0.983699	+	1.70382i	−0.647581	+	0.761997i	$0.724219\pi$
$192$		0			0
$193$	−6.29757e23	−	1.09077e24i	−0.632151	−	1.09492i	−0.987111	−	0.160036i	$-0.948839\pi$
$193$	−6.29757e23	−	1.09077e24i	−0.632151	−	1.09492i	0.354960	−	0.934882i	$-0.384495\pi$
$194$	−9.87929e23	−	1.71114e24i	−0.939307	−	1.62693i
$195$		0			0
$196$	−3.17738e23	+	5.50338e23i	−0.271256	+	0.469830i
$197$	9.65242e22			0.0781162			0.0390581	−	0.999237i	$-0.487564\pi$
$197$	9.65242e22			0.0781162			0.0390581	+	0.999237i	$0.487564\pi$
$198$		0			0
$199$	−1.00060e24			−0.728286			−0.364143	−	0.931343i	$-0.618638\pi$
$199$	−1.00060e24			−0.728286			−0.364143	+	0.931343i	$0.618638\pi$
$200$	−9.68525e22	+	1.67753e23i	−0.0668799	+	0.115839i
$201$		0			0
$202$	9.32429e23	+	1.61501e24i	0.579998	+	1.00459i
$203$	1.37832e23	+	2.38733e23i	0.0814035	+	0.140995i
$204$		0			0
$205$	4.53918e23	−	7.86209e23i	0.241859	−	0.418912i
$206$	−8.60872e22			−0.0435846
$207$		0			0
$208$	−2.56605e24			−1.17382
$209$	−3.81791e23	+	6.61281e23i	−0.166069	+	0.287640i
$210$		0			0
$211$	4.90200e23	+	8.49052e23i	0.192934	+	0.334171i	0.946221	−	0.323521i	$-0.104866\pi$
$211$	4.90200e23	+	8.49052e23i	0.192934	+	0.334171i	−0.753288	+	0.657691i	$0.771533\pi$
$212$	4.92218e23	+	8.52546e23i	0.184345	+	0.319294i
$213$		0			0
$214$	1.57574e24	−	2.72927e24i	0.534738	−	0.926194i
$215$	7.44607e23			0.240615
$216$		0			0
$217$	−5.74755e24			−1.68521
$218$	3.45287e23	−	5.98055e23i	0.0964689	−	0.167089i
$219$		0			0
$220$	8.15292e23	+	1.41213e24i	0.206954	+	0.358456i
$221$	−2.38914e24	−	4.13810e24i	−0.578258	−	1.00157i
$222$		0			0
$223$	1.00530e24	−	1.74124e24i	0.221359	−	0.383404i	−0.733862	−	0.679298i	$-0.762284\pi$
$223$	1.00530e24	−	1.74124e24i	0.221359	−	0.383404i	0.955221	+	0.295894i	$0.0956176\pi$
$224$	8.16567e24			1.71549
$225$		0			0
$226$	8.91876e24			1.70673
$227$	−7.42968e23	+	1.28686e24i	−0.135737	+	0.235104i	−0.925879	−	0.377821i	$-0.876674\pi$
$227$	−7.42968e23	+	1.28686e24i	−0.135737	+	0.235104i	0.790142	+	0.612924i	$0.210007\pi$
$228$		0			0
$229$	1.42720e24	+	2.47198e24i	0.237800	+	0.411882i	0.960083	−	0.279716i	$-0.0902403\pi$
$229$	1.42720e24	+	2.47198e24i	0.237800	+	0.411882i	−0.722283	+	0.691598i	$0.756907\pi$
$230$	3.92074e23	+	6.79093e23i	0.0624060	+	0.108090i
$231$		0			0
$232$	7.54643e22	−	1.30708e23i	0.0109677	−	0.0189967i
$233$	−5.64192e24			−0.783772			−0.391886	−	0.920014i	$-0.628177\pi$
$233$	−5.64192e24			−0.783772			−0.391886	+	0.920014i	$0.628177\pi$
$234$		0			0
$235$	7.37057e24			0.936028
$236$	−4.92802e24	+	8.53559e24i	−0.598545	+	1.03671i
$237$		0			0
$238$	8.57013e24	+	1.48439e25i	0.952641	+	1.65002i
$239$	−2.68700e24	−	4.65402e24i	−0.285818	−	0.495052i	0.686989	−	0.726668i	$-0.258932\pi$
$239$	−2.68700e24	−	4.65402e24i	−0.285818	−	0.495052i	−0.972807	+	0.231616i	$0.925599\pi$
$240$		0			0
$241$	−2.05963e23	+	3.56738e23i	−0.0200729	+	0.0347672i	−0.875887	−	0.482516i	$-0.839723\pi$
$241$	−2.05963e23	+	3.56738e23i	−0.0200729	+	0.0347672i	0.855814	+	0.517283i	$0.173056\pi$
$242$	2.56535e23			0.0239378
$243$		0			0
$244$	3.98520e24			0.341080
$245$	−1.77419e24	+	3.07298e24i	−0.145464	+	0.251951i
$246$		0			0
$247$	2.31362e24	+	4.00730e24i	0.174170	+	0.301671i
$248$	1.57341e24	+	2.72523e24i	0.113527	+	0.196635i
$249$		0			0
$250$	8.61943e24	−	1.49293e25i	0.571621	−	0.990077i
$251$	9.06680e24			0.576607			0.288304	−	0.957539i	$-0.406909\pi$
$251$	9.06680e24			0.576607			0.288304	+	0.957539i	$0.406909\pi$
$252$		0			0
$253$	3.35008e24			0.196015
$254$	−1.84065e25	+	3.18810e25i	−1.03328	+	1.78969i
$255$		0			0
$256$	−1.16223e25	−	2.01305e25i	−0.600861	−	1.04072i
$257$	4.58351e24	+	7.93887e24i	0.227458	+	0.393968i	0.957054	−	0.289910i	$-0.0936254\pi$
$257$	4.58351e24	+	7.93887e24i	0.227458	+	0.393968i	−0.729596	+	0.683878i	$0.760292\pi$
$258$		0			0
$259$	−2.10097e25	+	3.63898e25i	−0.961106	+	1.66469i
$260$	9.88118e24			0.434099
$261$		0			0
$262$	−5.78881e25			−2.34653
$263$	−9.89072e24	+	1.71312e25i	−0.385206	+	0.667196i	−0.991798	−	0.127818i	$-0.959203\pi$
$263$	−9.89072e24	+	1.71312e25i	−0.385206	+	0.667196i	0.606592	+	0.795013i	$0.292536\pi$
$264$		0			0
$265$	2.74845e24	+	4.76046e24i	0.0988568	+	0.171225i
$266$	−8.29923e24	−	1.43747e25i	−0.286933	−	0.496982i
$267$		0			0
$268$	−1.67811e25	+	2.90657e25i	−0.536297	+	0.928893i
$269$	1.02928e25			0.316327			0.158163	−	0.987413i	$-0.449443\pi$
$269$	1.02928e25			0.316327			0.158163	+	0.987413i	$0.449443\pi$
$270$		0			0
$271$	4.42626e25			1.25852			0.629258	−	0.777196i	$-0.283359\pi$
$271$	4.42626e25			1.25852			0.629258	+	0.777196i	$0.283359\pi$
$272$	2.21718e25	−	3.84026e25i	0.606494	−	1.05048i
$273$		0			0
$274$	−2.51871e25	−	4.36253e25i	−0.637965	−	1.10499i
$275$	−1.61360e25	−	2.79483e25i	−0.393370	−	0.681337i
$276$		0			0
$277$	3.78887e24	−	6.56251e24i	0.0855996	−	0.148263i	−0.820047	−	0.572296i	$-0.806053\pi$
$277$	3.78887e24	−	6.56251e24i	0.0855996	−	0.148263i	0.905647	+	0.424033i	$0.139386\pi$
$278$	1.61042e25			0.350323
$279$		0			0
$280$	5.07527e24			0.102400
$281$	1.15316e24	−	1.99733e24i	0.0224116	−	0.0388180i	−0.854602	−	0.519283i	$-0.826199\pi$
$281$	1.15316e24	−	1.99733e24i	0.0224116	−	0.0388180i	0.877014	+	0.480465i	$0.159532\pi$
$282$		0			0
$283$	−4.98262e24	−	8.63015e24i	−0.0898876	−	0.155690i	0.817576	−	0.575821i	$-0.195317\pi$
$283$	−4.98262e24	−	8.63015e24i	−0.0898876	−	0.155690i	−0.907463	+	0.420131i	$0.861984\pi$
$284$	−1.72451e25	−	2.98694e25i	−0.299794	−	0.519259i
$285$		0			0
$286$	4.52372e25	−	7.83532e25i	0.730554	−	1.26536i
$287$	8.43095e25			1.31255
$288$		0			0
$289$	1.34807e25			0.195112
$290$	−2.94285e24	+	5.09717e24i	−0.0410761	+	0.0711460i
$291$		0			0
$292$	−6.56504e25	−	1.13710e26i	−0.852546	−	1.47665i
$293$	−4.53913e25	−	7.86201e25i	−0.568673	−	0.984971i	−0.996698	−	0.0812038i	$-0.974124\pi$
$293$	−4.53913e25	−	7.86201e25i	−0.568673	−	0.984971i	0.428024	−	0.903767i	$-0.359210\pi$
$294$		0			0
$295$	−2.75172e25	+	4.76611e25i	−0.320976	+	0.555947i
$296$	2.30059e25			0.258986
$297$		0			0
$298$	1.67876e26			1.76083
$299$	1.01506e25	−	1.75813e25i	0.102788	−	0.178035i
$300$		0			0
$301$	3.45754e25	+	5.98863e25i	0.326451	+	0.565430i
$302$	−1.41470e26	−	2.45034e26i	−1.29001	−	2.23436i
$303$		0			0
$304$	−2.14709e25	+	3.71887e25i	−0.182675	+	0.316402i
$305$	2.22526e25			0.182908
$306$		0			0
$307$	−2.92837e25			−0.224736			−0.112368	−	0.993667i	$-0.535844\pi$
$307$	−2.92837e25			−0.224736			−0.112368	+	0.993667i	$0.535844\pi$
$308$	−7.57150e25	+	1.31142e26i	−0.561565	+	0.972658i
$309$		0			0
$310$	−6.13578e25	−	1.06275e26i	−0.425179	−	0.736432i
$311$	−3.88592e25	−	6.73062e25i	−0.260322	−	0.450890i	0.706006	−	0.708206i	$-0.250495\pi$
$311$	−3.88592e25	−	6.73062e25i	−0.260322	−	0.450890i	−0.966327	+	0.257316i	$0.917162\pi$
$312$		0			0
$313$	−5.96248e25	+	1.03273e26i	−0.373432	+	0.646803i	−0.990091	−	0.140427i	$-0.955152\pi$
$313$	−5.96248e25	+	1.03273e26i	−0.373432	+	0.646803i	0.616659	+	0.787230i	$0.288486\pi$
$314$	3.46553e26			2.09898
$315$		0			0
$316$	−1.36137e26			−0.771366
$317$	−2.28158e25	+	3.95182e25i	−0.125059	+	0.216608i	−0.921756	−	0.387771i	$-0.873245\pi$
$317$	−2.28158e25	+	3.95182e25i	−0.125059	+	0.216608i	0.796697	+	0.604379i	$0.206579\pi$
$318$		0			0
$319$	1.25726e25	+	2.17764e25i	0.0645094	+	0.111734i
$320$	3.47573e25	+	6.02015e25i	0.172573	+	0.298904i
$321$		0			0
$322$	−3.64114e25	+	6.30664e25i	−0.169337	+	0.293300i
$323$	−7.99625e25			−0.359965
$324$		0			0
$325$	−1.95565e26			−0.825117
$326$	−2.00890e26	+	3.47951e26i	−0.820678	+	1.42146i
$327$		0			0
$328$	−2.30800e25	−	3.99758e25i	−0.0884222	−	0.153152i
$329$	3.42248e26	+	5.92791e26i	1.26994	+	2.19960i
$330$		0			0
$331$	1.30259e26	−	2.25615e26i	0.453538	−	0.785551i	−0.545065	−	0.838394i	$-0.683495\pi$
$331$	1.30259e26	−	2.25615e26i	0.453538	−	0.785551i	0.998603	+	0.0528427i	$0.0168282\pi$
$332$	−7.88045e25			−0.265828
$333$		0			0
$334$	−4.23844e25			−0.134236
$335$	−9.37026e25	+	1.62298e26i	−0.287595	+	0.498129i
$336$		0			0
$337$	2.29871e26	+	3.98148e26i	0.662781	+	1.14797i	0.979882	+	0.199578i	$0.0639572\pi$
$337$	2.29871e26	+	3.98148e26i	0.662781	+	1.14797i	−0.317101	+	0.948392i	$0.602709\pi$
$338$	−2.91895e25	−	5.05576e25i	−0.0815832	−	0.141306i
$339$		0			0
$340$	−8.53776e25	+	1.47878e26i	−0.224293	+	0.388487i
$341$	−5.24272e26			−1.33547
$342$		0			0
$343$	2.01806e26			0.483444
$344$	1.89303e25	−	3.27882e25i	0.0439838	−	0.0761822i
$345$		0			0
$346$	3.87699e26	+	6.71515e26i	0.847610	+	1.46810i
$347$	−1.05372e26	−	1.82509e26i	−0.223493	−	0.387102i	0.732373	−	0.680904i	$-0.238413\pi$
$347$	−1.05372e26	−	1.82509e26i	−0.223493	−	0.387102i	−0.955866	+	0.293802i	$0.905079\pi$
$348$		0			0
$349$	−1.67205e26	+	2.89608e26i	−0.333875	+	0.578288i	−0.983268	−	0.182165i	$-0.941690\pi$
$349$	−1.67205e26	+	2.89608e26i	−0.333875	+	0.578288i	0.649393	+	0.760453i	$0.275023\pi$
$350$	7.01515e26			1.35932
$351$		0			0
$352$	7.44844e26			1.35946
$353$	−2.50279e26	+	4.33496e26i	−0.443394	+	0.767981i	−0.997939	−	0.0641726i	$-0.979559\pi$
$353$	−2.50279e26	+	4.33496e26i	−0.443394	+	0.767981i	0.554545	+	0.832154i	$0.312893\pi$
$354$		0			0
$355$	−9.62935e25	−	1.66785e26i	−0.160768	−	0.278458i
$356$	−9.30773e25	−	1.61215e26i	−0.150876	−	0.261324i
$357$		0			0
$358$	8.14864e26	−	1.41139e27i	1.24541	−	2.15712i
$359$	−7.99086e26			−1.18605			−0.593023	−	0.805185i	$-0.702066\pi$
$359$	−7.99086e26			−1.18605			−0.593023	+	0.805185i	$0.702066\pi$
$360$		0			0
$361$	−6.36775e26			−0.891580
$362$	7.19646e26	−	1.24646e27i	0.978766	−	1.69527i
$363$		0			0
$364$	4.58826e26	+	7.94710e26i	0.588957	+	1.02010i
$365$	−3.66580e26	−	6.34935e26i	−0.457187	−	0.791870i
$366$		0			0
$367$	2.23349e26	−	3.86852e26i	0.263021	−	0.455566i	−0.704022	−	0.710178i	$-0.748614\pi$
$367$	2.23349e26	−	3.86852e26i	0.263021	−	0.455566i	0.967043	+	0.254612i	$0.0819477\pi$
$368$	1.88400e26			0.215615
$369$		0			0
$370$	−8.97152e26			−0.969947
$371$	−2.55245e26	+	4.42097e26i	−0.268245	+	0.464614i
$372$		0			0
$373$	6.66261e26	+	1.15400e27i	0.661761	+	1.14620i	0.980152	+	0.198245i	$0.0635242\pi$
$373$	6.66261e26	+	1.15400e27i	0.661761	+	1.14620i	−0.318391	+	0.947959i	$0.603142\pi$
$374$	7.81738e26	+	1.35401e27i	0.754934	+	1.30758i
$375$		0			0
$376$	1.87383e26	−	3.24557e26i	0.171103	−	0.296359i
$377$	1.52378e26			0.135312
$378$		0			0
$379$	−8.18217e26			−0.687317			−0.343658	−	0.939095i	$-0.611666\pi$
$379$	−8.18217e26			−0.687317			−0.343658	+	0.939095i	$0.611666\pi$
$380$	8.26789e25	−	1.43204e26i	0.0675565	−	0.117011i
$381$		0			0
$382$	−1.74180e27	−	3.01689e27i	−1.34689	−	2.33289i
$383$	−7.23953e26	−	1.25392e27i	−0.544657	−	0.943373i	−0.998628	−	0.0523572i	$-0.983327\pi$
$383$	−7.23953e26	−	1.25392e27i	−0.544657	−	0.943373i	0.453972	−	0.891016i	$-0.350007\pi$
$384$		0			0
$385$	−4.22779e26	+	7.32274e26i	−0.301145	+	0.521598i
$386$	2.49741e27			1.73110
$387$		0			0
$388$	1.82802e27			1.20019
$389$	2.66956e26	−	4.62381e26i	0.170596	−	0.295481i	−0.768032	−	0.640411i	$-0.778764\pi$
$389$	2.66956e26	−	4.62381e26i	0.170596	−	0.295481i	0.938628	+	0.344930i	$0.112097\pi$
$390$		0			0
$391$	1.75411e26	+	3.03821e26i	0.106219	+	0.183976i
$392$	9.02108e25	+	1.56250e26i	0.0531808	+	0.0921118i
$393$		0			0
$394$	−9.56958e25	+	1.65750e26i	−0.0534789	+	0.0926282i
$395$	−7.60162e26			−0.413653
$396$		0			0
$397$	−2.65812e27			−1.37175			−0.685874	−	0.727720i	$-0.740580\pi$
$397$	−2.65812e27			−1.37175			−0.685874	+	0.727720i	$0.740580\pi$
$398$	9.92010e26	−	1.71821e27i	0.498590	−	0.863583i
$399$		0			0
$400$	−9.07445e26	−	1.57174e27i	−0.432704	−	0.749465i
$401$	−6.40064e26	−	1.10862e27i	−0.297309	−	0.514954i	0.678211	−	0.734868i	$-0.262756\pi$
$401$	−6.40064e26	−	1.10862e27i	−0.297309	−	0.514954i	−0.975519	+	0.219914i	$0.929422\pi$
$402$		0			0
$403$	−1.58852e27	+	2.75140e27i	−0.700309	+	1.21297i
$404$	−1.72533e27			−0.741084
$405$		0			0
$406$	−5.46598e26			−0.222918
$407$	−1.91643e27	+	3.31935e27i	−0.761643	+	1.31920i
$408$		0			0
$409$	−7.97868e26	−	1.38195e27i	−0.301187	−	0.521671i	0.675218	−	0.737618i	$-0.264050\pi$
$409$	−7.97868e26	−	1.38195e27i	−0.301187	−	0.521671i	−0.976405	+	0.215947i	$0.930716\pi$
$410$	9.00044e26	+	1.55892e27i	0.331156	+	0.573580i
$411$		0			0
$412$	3.98231e25	−	6.89756e25i	0.0139224	−	0.0241143i
$413$	−5.11097e27			−1.74192
$414$		0			0
$415$	−4.40030e26			−0.142553
$416$	2.25684e27	−	3.90897e27i	0.712889	−	1.23476i
$417$		0			0
$418$	−7.57027e26	−	1.31121e27i	−0.227384	−	0.393841i
$419$	1.69855e27	+	2.94197e27i	0.497542	+	0.861768i	0.999996	−	0.00283577i	$-0.000902655\pi$
$419$	1.69855e27	+	2.94197e27i	0.497542	+	0.861768i	−0.502454	+	0.864604i	$0.667569\pi$
$420$		0			0
$421$	1.35380e27	−	2.34486e27i	0.377219	−	0.653362i	−0.613438	−	0.789743i	$-0.710214\pi$
$421$	1.35380e27	−	2.34486e27i	0.377219	−	0.653362i	0.990656	+	0.136381i	$0.0435471\pi$
$422$	−1.94397e27			−0.528335
$423$		0			0
$424$	2.79497e26			0.0722829
$425$	1.68976e27	−	2.92676e27i	0.426326	−	0.738419i
$426$		0			0
$427$	1.03328e27	+	1.78970e27i	0.248157	+	0.429821i
$428$	1.45785e27	+	2.52507e27i	0.341627	+	0.591716i
$429$		0			0
$430$	−7.38216e26	+	1.27863e27i	−0.164727	+	0.285316i
$431$	−2.25771e26			−0.0491650			−0.0245825	−	0.999698i	$-0.507826\pi$
$431$	−2.25771e26			−0.0491650			−0.0245825	+	0.999698i	$0.507826\pi$
$432$		0			0
$433$	5.59341e27			1.16026			0.580128	−	0.814525i	$-0.303003\pi$
$433$	5.59341e27			1.16026			0.580128	+	0.814525i	$0.303003\pi$
$434$	5.69821e27	−	9.86960e27i	1.15371	−	1.99828i
$435$		0			0
$436$	3.19453e26	+	5.53309e26i	0.0616309	+	0.106748i
$437$	−1.69866e26	−	2.94217e26i	−0.0319928	−	0.0554131i
$438$		0			0
$439$	6.02107e26	−	1.04288e27i	0.108093	−	0.187222i	−0.806905	−	0.590681i	$-0.798859\pi$
$439$	6.02107e26	−	1.04288e27i	0.108093	−	0.187222i	0.914998	+	0.403459i	$0.132192\pi$
$440$	4.62949e26			0.0811484
$441$		0			0
$442$	9.47452e27			1.58352
$443$	−2.54542e27	+	4.40880e27i	−0.415451	+	0.719583i	−0.995476	−	0.0950163i	$-0.969710\pi$
$443$	−2.54542e27	+	4.40880e27i	−0.415451	+	0.719583i	0.580024	+	0.814599i	$0.303043\pi$
$444$		0			0
$445$	−5.19727e26	−	9.00193e26i	−0.0809086	−	0.140138i
$446$	1.99335e27	+	3.45258e27i	0.303087	+	0.524962i
$447$		0			0
$448$	−3.22787e27	+	5.59083e27i	−0.468270	+	0.811068i
$449$	3.77519e27			0.534998			0.267499	−	0.963558i	$-0.413803\pi$
$449$	3.77519e27			0.534998			0.267499	+	0.963558i	$0.413803\pi$
$450$		0			0
$451$	7.69043e27			1.04015
$452$	−4.12573e27	+	7.14597e27i	−0.545189	+	0.944295i
$453$		0			0
$454$	−1.47318e27	−	2.55163e27i	−0.185853	−	0.321907i
$455$	2.56200e27	+	4.43752e27i	0.315834	+	0.547041i
$456$		0			0
$457$	−4.48980e27	+	7.77655e27i	−0.528575	+	0.915518i	0.470870	+	0.882203i	$0.343940\pi$
$457$	−4.48980e27	+	7.77655e27i	−0.528575	+	0.915518i	−0.999445	+	0.0333159i	$0.989393\pi$
$458$	−5.65980e27			−0.651199
$459$		0			0
$460$	−7.25479e26			−0.0797384
$461$	5.18452e27	−	8.97985e27i	0.556992	−	0.964738i	−0.440754	−	0.897628i	$-0.645289\pi$
$461$	5.18452e27	−	8.97985e27i	0.556992	−	0.964738i	0.997746	−	0.0671098i	$-0.0213778\pi$
$462$		0			0
$463$	2.28325e27	+	3.95470e27i	0.234397	+	0.405988i	0.959097	−	0.283077i	$-0.0913551\pi$
$463$	2.28325e27	+	3.95470e27i	0.234397	+	0.405988i	−0.724700	+	0.689064i	$0.758022\pi$
$464$	7.07051e26	+	1.22465e27i	0.0709598	+	0.122906i
$465$		0			0
$466$	5.59349e27	−	9.68821e27i	0.536576	−	0.929376i
$467$	−9.25506e27			−0.868064			−0.434032	−	0.900897i	$-0.642910\pi$
$467$	−9.25506e27			−0.868064			−0.434032	+	0.900897i	$0.642910\pi$
$468$		0			0
$469$	−1.74041e28			−1.56076
$470$	−7.30731e27	+	1.26566e28i	−0.640811	+	1.10992i
$471$		0			0
$472$	1.39915e27	+	2.42339e27i	0.117347	+	0.203251i
$473$	3.15385e27	+	5.46262e27i	0.258701	+	0.448084i
$474$		0			0
$475$	−1.63635e27	+	2.83424e27i	−0.128408	+	0.222410i
$476$	−1.58578e28			−1.21722
$477$		0			0
$478$	1.06558e28			0.782693
$479$	−3.74662e27	+	6.48933e27i	−0.269226	+	0.466312i	−0.968662	−	0.248382i	$-0.920101\pi$
$479$	−3.74662e27	+	6.48933e27i	−0.269226	+	0.466312i	0.699436	+	0.714695i	$0.253434\pi$
$480$		0			0
$481$	1.16134e28	+	2.01150e28i	0.798796	+	1.38355i
$482$	−4.08390e26	−	7.07352e26i	−0.0274841	−	0.0476038i
$483$		0			0
$484$	−1.18670e26	+	2.05543e26i	−0.00764656	+	0.0132442i
$485$	1.02073e28			0.643613
$486$		0			0
$487$	5.44040e27			0.328531			0.164266	−	0.986416i	$-0.447475\pi$
$487$	5.44040e27			0.328531			0.164266	+	0.986416i	$0.447475\pi$
$488$	5.65731e26	−	9.79875e26i	0.0334350	−	0.0579112i
$489$		0			0
$490$	−3.51792e27	−	6.09321e27i	−0.199171	−	0.344975i
$491$	5.47514e27	+	9.48322e27i	0.303417	+	0.525533i	0.976908	−	0.213662i	$-0.0685392\pi$
$491$	5.47514e27	+	9.48322e27i	0.303417	+	0.525533i	−0.673491	+	0.739196i	$0.735206\pi$
$492$		0			0
$493$	−1.31661e27	+	2.28043e27i	−0.0699140	+	0.121095i
$494$	−9.17503e27			−0.476952
$495$		0			0
$496$	−2.94837e28			−1.46901
$497$	8.94265e27	−	1.54891e28i	0.436239	−	0.755588i
$498$		0			0
$499$	−8.45745e27	−	1.46487e28i	−0.395534	−	0.685085i	0.597635	−	0.801768i	$-0.296107\pi$
$499$	−8.45745e27	−	1.46487e28i	−0.395534	−	0.685085i	−0.993169	+	0.116683i	$0.962774\pi$
$500$	7.97452e27	+	1.38123e28i	0.365191	+	0.632529i
$501$		0			0
$502$	−8.98898e27	+	1.55694e28i	−0.394749	+	0.683726i
$503$	1.50401e28			0.646827			0.323414	−	0.946258i	$-0.395169\pi$
$503$	1.50401e28			0.646827			0.323414	+	0.946258i	$0.395169\pi$
$504$		0			0
$505$	−9.63391e27			−0.397414
$506$	−3.32133e27	+	5.75271e27i	−0.134193	+	0.232430i
$507$		0			0
$508$	−1.70293e28	−	2.94956e28i	−0.660128	−	1.14338i
$509$	−3.82053e27	−	6.61735e27i	−0.145073	−	0.251274i	0.784327	−	0.620347i	$-0.213008\pi$
$509$	−3.82053e27	−	6.61735e27i	−0.145073	−	0.251274i	−0.929400	+	0.369074i	$0.879675\pi$
$510$		0			0
$511$	3.40438e28	−	5.89656e28i	1.24056	−	2.14872i
$512$	3.65579e28			1.30511
$513$		0			0
$514$	−1.81767e28			−0.622876
$515$	2.22365e26	−	3.85147e26i	0.00746603	−	0.0129315i
$516$		0			0
$517$	3.12187e28	+	5.40723e28i	1.00638	+	1.74311i
$518$	−4.16587e28	−	7.21549e28i	−1.31596	−	2.27931i
$519$		0			0
$520$	1.40271e27	−	2.42957e27i	0.0425534	−	0.0737046i
$521$	2.10509e28			0.625856			0.312928	−	0.949777i	$-0.398690\pi$
$521$	2.10509e28			0.625856			0.312928	+	0.949777i	$0.398690\pi$
$522$		0			0
$523$	−2.92433e28			−0.835138			−0.417569	−	0.908645i	$-0.637118\pi$
$523$	−2.92433e28			−0.835138			−0.417569	+	0.908645i	$0.637118\pi$
$524$	2.67785e28	−	4.63817e28i	0.749562	−	1.29828i
$525$		0			0
$526$	−1.96117e28	−	3.39684e28i	−0.527429	−	0.913534i
$527$	−2.74510e28	−	4.75465e28i	−0.723679	−	1.25345i
$528$		0			0
$529$	1.89905e28	−	3.28926e28i	0.481119	−	0.833323i
$530$	−1.08994e28			−0.270712
$531$		0			0
$532$	1.53566e28			0.366625
$533$	2.33016e28	−	4.03596e28i	0.545445	−	0.944738i
$534$		0			0
$535$	8.14035e27	+	1.40995e28i	0.183201	+	0.317314i
$536$	4.76443e27	+	8.25223e27i	0.105143	+	0.182113i
$537$		0			0
$538$	−1.02045e28	+	1.76747e28i	−0.216560	+	0.375092i
$539$	−3.00589e28			−0.625591
$540$		0			0
$541$	−3.57924e28			−0.716506			−0.358253	−	0.933625i	$-0.616627\pi$
$541$	−3.57924e28			−0.716506			−0.358253	+	0.933625i	$0.616627\pi$
$542$	−4.38827e28	+	7.60070e28i	−0.861590	+	1.49232i
$543$		0			0
$544$	3.90002e28	+	6.75503e28i	0.736679	+	1.27597i
$545$	1.78377e27	+	3.08957e27i	0.0330502	+	0.0572447i
$546$		0			0
$547$	2.48111e28	−	4.29740e28i	0.442363	−	0.766195i	−0.555501	−	0.831516i	$-0.687474\pi$
$547$	2.48111e28	−	4.29740e28i	0.442363	−	0.766195i	0.997864	+	0.0653206i	$0.0208070\pi$
$548$	4.66052e28			0.815152
$549$		0			0
$550$	6.39899e28			1.07722
$551$	1.27499e27	−	2.20835e27i	0.0210579	−	0.0364734i
$552$		0			0
$553$	−3.52976e28	−	6.11373e28i	−0.561218	−	0.972058i
$554$	7.51269e27	+	1.30124e28i	0.117204	+	0.203004i
$555$		0			0
$556$	−7.44964e27	+	1.29032e28i	−0.111905	+	0.193825i
$557$	−2.30026e28			−0.339076			−0.169538	−	0.985524i	$-0.554228\pi$
$557$	−2.30026e28			−0.339076			−0.169538	+	0.985524i	$0.554228\pi$
$558$		0			0
$559$	3.82240e28			0.542641
$560$	−2.37760e28	+	4.11812e28i	−0.331256	+	0.573753i
$561$		0			0
$562$	2.28652e27	+	3.96037e27i	0.0306863	+	0.0531502i
$563$	2.81067e28	+	4.86823e28i	0.370230	+	0.641258i	0.989601	−	0.143841i	$-0.0459454\pi$
$563$	2.81067e28	+	4.86823e28i	0.370230	+	0.641258i	−0.619370	+	0.785099i	$0.712612\pi$
$564$		0			0
$565$	−2.30373e28	+	3.99018e28i	−0.292363	+	0.506388i
$566$	1.97594e28			0.246151
$567$		0			0
$568$	−9.79233e27			−0.117552
$569$	−4.08714e28	+	7.07913e28i	−0.481660	+	0.834259i	−0.999778	−	0.0210497i	$-0.993299\pi$
$569$	−4.08714e28	+	7.07913e28i	−0.481660	+	0.834259i	0.518119	+	0.855309i	$0.326633\pi$
$570$		0			0
$571$	−3.14092e28	−	5.44024e28i	−0.356762	−	0.617929i	0.630656	−	0.776062i	$-0.282786\pi$
$571$	−3.14092e28	−	5.44024e28i	−0.356762	−	0.617929i	−0.987418	+	0.158133i	$0.949452\pi$
$572$	4.18526e28	+	7.24908e28i	0.466728	+	0.808397i
$573$		0			0
$574$	−8.35859e28	+	1.44775e29i	−0.898583	+	1.55639i
$575$	1.43584e28			0.151563
$576$		0			0
$577$	−1.12097e29			−1.14090			−0.570449	−	0.821333i	$-0.693231\pi$
$577$	−1.12097e29			−1.14090			−0.570449	+	0.821333i	$0.693231\pi$
$578$	−1.33650e28	+	2.31488e28i	−0.133575	+	0.231359i
$579$		0			0
$580$	−2.72267e27	−	4.71580e27i	−0.0262422	−	0.0454529i
$581$	−2.04325e28	−	3.53901e28i	−0.193407	−	0.334990i
$582$		0			0
$583$	−2.32826e28	+	4.03266e28i	−0.212575	+	0.368190i
$584$	−3.72784e28			−0.334289
$585$		0			0
$586$	1.80007e29			1.55727
$587$	−8.44683e28	+	1.46303e29i	−0.717784	+	1.24324i	0.244092	+	0.969752i	$0.421510\pi$
$587$	−8.44683e28	+	1.46303e29i	−0.717784	+	1.24324i	−0.961876	+	0.273486i	$0.911823\pi$
$588$		0			0
$589$	2.65832e28	+	4.60435e28i	0.217970	+	0.377536i
$590$	−5.45620e28	−	9.45041e28i	−0.439485	−	0.761210i
$591$		0			0
$592$	−1.07775e29	+	1.86672e29i	−0.837800	+	1.45111i
$593$	2.13722e29			1.63221			0.816104	−	0.577906i	$-0.196130\pi$
$593$	2.13722e29			1.63221			0.816104	+	0.577906i	$0.196130\pi$
$594$		0			0
$595$	−8.85471e28			−0.652749
$596$	−7.76578e28	+	1.34507e29i	−0.562470	+	0.974226i
$597$		0			0
$598$	2.01269e28	+	3.48609e28i	0.140739	+	0.243768i
$599$	−3.31530e28	−	5.74226e28i	−0.227793	−	0.394549i	0.729361	−	0.684129i	$-0.239818\pi$
$599$	−3.31530e28	−	5.74226e28i	−0.227793	−	0.394549i	−0.957154	+	0.289580i	$0.906484\pi$
$600$		0			0
$601$	1.28295e29	−	2.22213e29i	0.851192	−	1.47431i	−0.0289412	−	0.999581i	$-0.509214\pi$
$601$	1.28295e29	−	2.22213e29i	0.851192	−	1.47431i	0.880133	−	0.474727i	$-0.157453\pi$
$602$	−1.37114e29			−0.893964
$603$		0			0
$604$	2.61771e29			1.64829
$605$	−6.62633e26	+	1.14771e27i	−0.00410055	+	0.00710235i
$606$		0			0
$607$	−3.18566e28	−	5.51772e28i	−0.190422	−	0.329821i	0.754968	−	0.655762i	$-0.227652\pi$
$607$	−3.18566e28	−	5.51772e28i	−0.190422	−	0.329821i	−0.945390	+	0.325941i	$0.894319\pi$
$608$	−3.77674e28	−	6.54151e28i	−0.221886	−	0.384318i
$609$		0			0
$610$	−2.20616e28	+	3.82118e28i	−0.125220	+	0.216887i
$611$	3.78365e29			2.11095
$612$		0			0
$613$	2.43258e29			1.31139			0.655694	−	0.755027i	$-0.272376\pi$
$613$	2.43258e29			1.31139			0.655694	+	0.755027i	$0.272376\pi$
$614$	2.90323e28	−	5.02855e28i	0.153856	−	0.266486i
$615$		0			0
$616$	2.14967e28	+	3.72334e28i	0.110097	+	0.190693i
$617$	1.15217e28	+	1.99562e28i	0.0580127	+	0.100481i	0.893573	−	0.448917i	$-0.148190\pi$
$617$	1.15217e28	+	1.99562e28i	0.0580127	+	0.100481i	−0.835561	+	0.549398i	$0.814857\pi$
$618$		0			0
$619$	1.83063e29	−	3.17074e29i	0.890938	−	1.54315i	0.0521857	−	0.998637i	$-0.483381\pi$
$619$	1.83063e29	−	3.17074e29i	0.890938	−	1.54315i	0.838752	−	0.544513i	$-0.183285\pi$
$620$	1.13534e29			0.543267
$621$		0			0
$622$	1.54103e29			0.712872
$623$	4.82663e28	−	8.35997e28i	0.219543	−	0.380260i
$624$		0			0
$625$	−4.41421e28	−	7.64563e28i	−0.194139	−	0.336258i
$626$	−1.18226e29	−	2.04774e29i	−0.511308	−	0.885612i
$627$		0			0
$628$	−1.60312e29	+	2.77669e29i	−0.670486	+	1.16132i
$629$	−4.01379e29			−1.65091
$630$		0			0
$631$	−8.86516e28			−0.352678			−0.176339	−	0.984330i	$-0.556425\pi$
$631$	−8.86516e28			−0.352678			−0.176339	+	0.984330i	$0.556425\pi$
$632$	−1.93257e28	+	3.34731e28i	−0.0756146	+	0.130968i
$633$		0			0
$634$	−4.52400e28	−	7.83580e28i	−0.171232	−	0.296583i
$635$	−9.50885e28	−	1.64698e29i	−0.354001	−	0.613147i
$636$		0			0
$637$	−9.10770e28	+	1.57750e29i	−0.328053	+	0.568205i
$638$	−4.98588e28			−0.176654
$639$		0			0
$640$	4.65603e28			0.159634
$641$	1.06971e29	−	1.85278e29i	0.360790	−	0.624907i	−0.627301	−	0.778777i	$-0.715840\pi$
$641$	1.06971e29	−	1.85278e29i	0.360790	−	0.624907i	0.988091	+	0.153870i	$0.0491736\pi$
$642$		0			0
$643$	1.11303e29	+	1.92783e29i	0.363323	+	0.629295i	0.988506	−	0.151184i	$-0.0483086\pi$
$643$	1.11303e29	+	1.92783e29i	0.363323	+	0.629295i	−0.625182	+	0.780479i	$0.714975\pi$
$644$	−3.36871e28	−	5.83478e28i	−0.108184	−	0.187380i
$645$		0			0
$646$	7.92762e28	−	1.37310e29i	0.246434	−	0.426837i
$647$	−1.83534e29			−0.561333			−0.280666	−	0.959805i	$-0.590555\pi$
$647$	−1.83534e29			−0.561333			−0.280666	+	0.959805i	$0.590555\pi$
$648$		0			0
$649$	−4.66205e29			−1.38041
$650$	1.93886e29	−	3.35821e29i	0.564881	−	0.978403i
$651$		0			0
$652$	−1.85859e29	−	3.21917e29i	−0.524305	−	0.908123i
$653$	2.02294e29	+	3.50384e29i	0.561558	+	0.972647i	0.997361	+	0.0726051i	$0.0231313\pi$
$653$	2.02294e29	+	3.50384e29i	0.561558	+	0.972647i	−0.435803	+	0.900042i	$0.643535\pi$
$654$		0			0
$655$	1.49526e29	−	2.58987e29i	0.401960	−	0.696216i
$656$	4.32490e29			1.14416
$657$		0			0
$658$	−1.35724e30			−3.47764
$659$	−5.28360e28	+	9.15147e28i	−0.133240	+	0.230778i	−0.924924	−	0.380153i	$-0.875871\pi$
$659$	−5.28360e28	+	9.15147e28i	−0.133240	+	0.230778i	0.791684	+	0.610931i	$0.209205\pi$
$660$		0			0
$661$	−1.86167e29	−	3.22451e29i	−0.454766	−	0.787678i	0.543909	−	0.839144i	$-0.316944\pi$
$661$	−1.86167e29	−	3.22451e29i	−0.454766	−	0.787678i	−0.998675	+	0.0514664i	$0.983610\pi$
$662$	2.58282e29	+	4.47358e29i	0.620991	+	1.07559i
$663$		0			0
$664$	−1.11869e28	+	1.93763e28i	−0.0260583	+	0.0451343i
$665$	8.57482e28			0.196606
$666$		0			0
$667$	−1.11876e28			−0.0248551
$668$	1.96066e28	−	3.39596e28i	0.0428795	−	0.0742694i
$669$		0			0
$670$	−1.85797e29	−	3.21809e29i	−0.393779	−	0.682045i
$671$	9.42527e28	+	1.63251e29i	0.196656	+	0.340618i
$672$		0			0
$673$	−2.78672e29	+	4.82675e29i	−0.563554	+	0.976105i	0.433628	+	0.901092i	$0.357233\pi$
$673$	−2.78672e29	+	4.82675e29i	−0.563554	+	0.976105i	−0.997183	+	0.0750128i	$0.976100\pi$
$674$	−9.11591e29			−1.81498
$675$		0			0
$676$	5.40110e28			0.104242
$677$	4.71818e29	−	8.17213e29i	0.896589	−	1.55294i	0.0647636	−	0.997901i	$-0.479371\pi$
$677$	4.71818e29	−	8.17213e29i	0.896589	−	1.55294i	0.831825	−	0.555037i	$-0.187296\pi$
$678$		0			0
$679$	4.73971e29	+	8.20942e29i	0.873212	+	1.51245i
$680$	2.42401e28	+	4.19851e28i	0.0439735	+	0.0761643i
$681$		0			0
$682$	5.19772e29	−	9.00271e29i	0.914275	−	1.58357i
$683$	2.26004e29			0.391469			0.195735	−	0.980657i	$-0.437291\pi$
$683$	2.26004e29			0.391469			0.195735	+	0.980657i	$0.437291\pi$
$684$		0			0
$685$	2.60235e29			0.437134
$686$	−2.00074e29	+	3.46538e29i	−0.330969	+	0.573255i
$687$		0			0
$688$	1.77364e29	+	3.07204e29i	0.284569	+	0.492888i
$689$	1.41090e29	+	2.44376e29i	0.222944	+	0.386150i
$690$		0			0
$691$	−7.95101e28	+	1.37715e29i	−0.121872	+	0.211088i	−0.920506	−	0.390729i	$-0.872223\pi$
$691$	−7.95101e28	+	1.37715e29i	−0.121872	+	0.211088i	0.798634	+	0.601817i	$0.205556\pi$
$692$	−7.17383e29			−1.08302
$693$		0			0
$694$	4.17869e29			0.612021
$695$	−4.15974e28	+	7.20488e28i	−0.0600103	+	0.103941i
$696$		0			0
$697$	4.02672e29	+	6.97449e29i	0.563648	+	0.976266i
$698$	−3.31541e29	−	5.74245e29i	−0.457146	−	0.791800i
$699$		0			0
$700$	−3.24514e29	+	5.62075e29i	−0.434214	+	0.752081i
$701$	−8.48451e28			−0.111838			−0.0559188	−	0.998435i	$-0.517809\pi$
$701$	−8.48451e28			−0.111838			−0.0559188	+	0.998435i	$0.517809\pi$
$702$		0			0
$703$	3.88691e29			0.497249
$704$	−2.94435e29	+	5.09977e29i	−0.371088	+	0.642743i
$705$		0			0
$706$	−4.96262e29	−	8.59551e29i	−0.607102	−	1.05153i
$707$	−4.47344e29	−	7.74823e29i	−0.539186	−	0.933897i
$708$		0			0
$709$	7.40689e29	−	1.28291e30i	0.866663	−	1.50110i	0.00127715	−	0.999999i	$-0.499593\pi$
$709$	7.40689e29	−	1.28291e30i	0.866663	−	1.50110i	0.865386	−	0.501106i	$-0.167073\pi$
$710$	3.81868e29			0.440251
$711$		0			0
$712$	−5.28523e28			−0.0591594
$713$	1.16629e29	−	2.02008e29i	0.128638	−	0.222807i
$714$		0			0
$715$	2.33697e29	+	4.04775e29i	0.250288	+	0.433511i
$716$	7.53896e29	+	1.30579e30i	0.795655	+	1.37811i
$717$		0			0
$718$	7.92227e29	−	1.37218e30i	0.811976	−	1.40638i
$719$	3.93222e29			0.397178			0.198589	−	0.980083i	$-0.436364\pi$
$719$	3.93222e29			0.397178			0.198589	+	0.980083i	$0.436364\pi$
$720$		0			0
$721$	4.13014e28			0.0405177
$722$	6.31309e29	−	1.09346e30i	0.610382	−	1.05721i
$723$		0			0
$724$	6.65802e29	+	1.15320e30i	0.625303	+	1.08306i
$725$	5.38861e28	+	9.33335e28i	0.0498801	+	0.0863949i
$726$		0			0
$727$	−9.34415e29	+	1.61845e30i	−0.840289	+	1.45542i	0.0493615	+	0.998781i	$0.484281\pi$
$727$	−9.34415e29	+	1.61845e30i	−0.840289	+	1.45542i	−0.889650	+	0.456642i	$0.849052\pi$
$728$	2.60536e29			0.230934
$729$		0			0
$730$	1.45373e30			1.25197
$731$	−3.30272e29	+	5.72048e29i	−0.280375	+	0.485624i
$732$		0			0
$733$	7.82321e29	+	1.35502e30i	0.645347	+	1.11777i	0.984221	+	0.176942i	$0.0566204\pi$
$733$	7.82321e29	+	1.35502e30i	0.645347	+	1.11777i	−0.338875	+	0.940831i	$0.610046\pi$
$734$	4.42864e29	+	7.67064e29i	0.360132	+	0.623768i
$735$		0			0
$736$	−1.65698e29	+	2.86997e29i	−0.130948	+	0.226809i
$737$	−1.58754e30			−1.23685
$738$		0			0
$739$	−9.06934e29			−0.686766			−0.343383	−	0.939195i	$-0.611573\pi$
$739$	−9.06934e29			−0.686766			−0.343383	+	0.939195i	$0.611573\pi$
$740$	4.15014e29	−	7.18825e29i	0.309834	−	0.536649i
$741$		0			0
$742$	−5.06109e29	−	8.76606e29i	−0.367285	−	0.636156i
$743$	−2.65795e29	−	4.60370e29i	−0.190180	−	0.329401i	0.755130	−	0.655575i	$-0.227574\pi$
$743$	−2.65795e29	−	4.60370e29i	−0.190180	−	0.329401i	−0.945310	+	0.326174i	$0.894240\pi$
$744$		0			0
$745$	−4.33626e29	+	7.51063e29i	−0.301630	+	0.522439i
$746$	−2.64217e30			−1.81219
$747$		0			0
$748$	−1.44650e30			−0.964607
$749$	−7.55984e29	+	1.30940e30i	−0.497111	+	0.861021i
$750$		0			0
$751$	−3.97606e29	−	6.88674e29i	−0.254234	−	0.440346i	0.710453	−	0.703744i	$-0.248490\pi$
$751$	−3.97606e29	−	6.88674e29i	−0.254234	−	0.440346i	−0.964687	+	0.263398i	$0.915157\pi$
$752$	1.75566e30	+	3.04089e30i	1.10701	+	1.91740i
$753$		0			0
$754$	−1.51070e29	+	2.61661e29i	−0.0926358	+	0.160450i
$755$	1.46168e30			0.883913
$756$		0			0
$757$	1.04161e30			0.612630			0.306315	−	0.951930i	$-0.400904\pi$
$757$	1.04161e30			0.612630			0.306315	+	0.951930i	$0.400904\pi$
$758$	8.11195e29	−	1.40503e30i	0.470542	−	0.815003i
$759$		0			0
$760$	−2.34739e28	−	4.06579e28i	−0.0132447	−	0.0229405i
$761$	7.06690e29	+	1.22402e30i	0.393269	+	0.681163i	0.992879	−	0.119130i	$-0.0380107\pi$
$761$	7.06690e29	+	1.22402e30i	0.393269	+	0.681163i	−0.599609	+	0.800293i	$0.704677\pi$
$762$		0			0
$763$	−1.65656e29	+	2.86925e29i	−0.0896808	+	0.155332i
$764$	3.22296e30			1.72098
$765$		0			0
$766$	2.87096e30			1.49150
$767$	−1.41258e30	+	2.44666e30i	−0.723872	+	1.25378i
$768$		0			0
$769$	−1.62384e30	−	2.81258e30i	−0.809688	−	1.40242i	−0.913081	−	0.407779i	$-0.866303\pi$
$769$	−1.62384e30	−	2.81258e30i	−0.809688	−	1.40242i	0.103393	−	0.994641i	$-0.467030\pi$
$770$	−8.38300e29	−	1.45198e30i	−0.412332	−	0.714180i
$771$		0			0
$772$	−1.15527e30	+	2.00099e30i	−0.552973	+	0.957777i
$773$	−3.03297e30			−1.43213			−0.716067	−	0.698031i	$-0.754060\pi$
$773$	−3.03297e30			−1.43213			−0.716067	+	0.698031i	$0.754060\pi$
$774$		0			0
$775$	−2.24702e30			−1.03262
$776$	2.59503e29	−	4.49472e29i	0.117651	−	0.203777i
$777$		0			0
$778$	5.29329e29	+	9.16825e29i	0.233582	+	0.404577i
$779$	−3.89944e29	−	6.75403e29i	−0.169769	−	0.294049i
$780$		0			0
$781$	8.15718e29	−	1.41287e30i	0.345704	−	0.598777i
$782$	−6.95621e29			−0.290872
$783$		0			0
$784$	−1.69043e30			−0.688144
$785$	−8.95153e29	+	1.55045e30i	−0.359555	+	0.622768i
$786$		0			0
$787$	−1.84731e30	−	3.19964e30i	−0.722447	−	1.25131i	−0.960016	−	0.279944i	$-0.909684\pi$
$787$	−1.84731e30	−	3.19964e30i	−0.722447	−	1.25131i	0.237570	−	0.971371i	$-0.423649\pi$
$788$	−8.85358e28	−	1.53349e29i	−0.0341660	−	0.0591772i
$789$		0			0
$790$	7.53637e29	−	1.30534e30i	0.283190	−	0.490499i
$791$	−4.27889e30			−1.58664
$792$		0			0
$793$	1.14233e30			0.412498
$794$	2.63531e30	−	4.56448e30i	0.939108	−	1.62658i
$795$		0			0
$796$	9.17787e29	+	1.58965e30i	0.318533	+	0.551716i
$797$	−2.88845e28	−	5.00295e28i	−0.00989356	−	0.0171362i	0.861036	−	0.508544i	$-0.169816\pi$
$797$	−2.88845e28	−	5.00295e28i	−0.00989356	−	0.0171362i	−0.870930	+	0.491407i	$0.836483\pi$
$798$		0			0
$799$	−3.26923e30	+	5.66248e30i	−1.09070	+	1.88914i
$800$	3.19240e30			1.05117
$801$		0			0
$802$	2.53828e30			0.814158
$803$	3.10536e30	−	5.37864e30i	0.983102	−	1.70278i
$804$		0			0
$805$	−1.88103e29	−	3.25803e29i	−0.0580147	−	0.100484i
$806$	−3.14977e30	−	5.45556e30i	−0.958872	−	1.66082i
$807$		0			0
$808$	−2.44924e29	+	4.24221e29i	−0.0726461	+	0.125827i
$809$	1.52694e30			0.447056			0.223528	−	0.974697i	$-0.428243\pi$
$809$	1.52694e30			0.447056			0.223528	+	0.974697i	$0.428243\pi$
$810$		0			0
$811$	3.21814e30			0.918092			0.459046	−	0.888412i	$-0.348191\pi$
$811$	3.21814e30			0.918092			0.459046	+	0.888412i	$0.348191\pi$
$812$	2.52851e29	−	4.37950e29i	0.0712075	−	0.123335i
$813$		0			0
$814$	−3.79996e30	−	6.58173e30i	−1.04285	−	1.80627i
$815$	−1.03780e30	−	1.79753e30i	−0.281164	−	0.486990i
$816$		0			0
$817$	3.19832e29	−	5.53966e29i	0.0844482	−	0.146269i
$818$	3.16408e30			0.824779
$819$		0			0
$820$	−1.66541e30			−0.423131
$821$	−3.10875e30	+	5.38451e30i	−0.779799	+	1.35065i	0.152259	+	0.988341i	$0.451345\pi$
$821$	−3.10875e30	+	5.38451e30i	−0.779799	+	1.35065i	−0.932057	+	0.362311i	$0.881988\pi$
$822$		0			0
$823$	−1.29631e30	−	2.24528e30i	−0.316965	−	0.548999i	0.662889	−	0.748718i	$-0.269330\pi$
$823$	−1.29631e30	−	2.24528e30i	−0.316965	−	0.548999i	−0.979853	+	0.199719i	$0.935997\pi$
$824$	−1.13064e28	−	1.95833e28i	−0.00272954	−	0.00472770i
$825$		0			0
$826$	5.06710e30	−	8.77647e30i	1.19253	−	2.06552i
$827$	7.60849e30			1.76804			0.884018	−	0.467454i	$-0.154829\pi$
$827$	7.60849e30			1.76804			0.884018	+	0.467454i	$0.154829\pi$
$828$		0			0
$829$	−2.02047e28			−0.00457752			−0.00228876	−	0.999997i	$-0.500729\pi$
$829$	−2.02047e28			−0.00457752			−0.00228876	+	0.999997i	$0.500729\pi$
$830$	4.36253e29	−	7.55612e29i	0.0975929	−	0.169036i
$831$		0			0
$832$	1.78425e30	+	3.09041e30i	0.389189	+	0.674095i
$833$	−1.57389e30	−	2.72605e30i	−0.339001	−	0.587167i
$834$		0			0
$835$	1.09480e29	−	1.89624e29i	0.0229946	−	0.0398278i
$836$	1.40077e30			0.290537
$837$		0			0
$838$	−6.73587e30			−1.36248
$839$	1.15540e30	−	2.00121e30i	0.230798	−	0.399753i	−0.727245	−	0.686377i	$-0.759200\pi$
$839$	1.15540e30	−	2.00121e30i	0.230798	−	0.399753i	0.958043	+	0.286624i	$0.0925331\pi$
$840$		0			0
$841$	2.52444e30	+	4.37245e30i	0.491820	+	0.851857i
$842$	2.68437e30	+	4.64946e30i	0.516494	+	0.894593i
$843$		0			0
$844$	8.99262e29	−	1.55757e30i	0.168768	−	0.292315i
$845$	3.01587e29			0.0559008
$846$		0			0
$847$	−1.23076e29			−0.0222534
$848$	−1.30935e30	+	2.26787e30i	−0.233830	+	0.405006i
$849$		0			0
$850$	3.35052e30	+	5.80327e30i	0.583732	+	1.01105i
$851$	−8.52658e29	−	1.47685e30i	−0.146728	−	0.254141i
$852$		0			0
$853$	−8.39063e29	+	1.45330e30i	−0.140874	+	0.244000i	−0.927826	−	0.373014i	$-0.878324\pi$
$853$	−8.39063e29	+	1.45330e30i	−0.140874	+	0.244000i	0.786952	+	0.617014i	$0.211658\pi$
$854$	−4.09766e30			−0.679561
$855$		0			0
$856$	8.27813e29			0.133955
$857$	−2.99518e30	+	5.18780e30i	−0.478766	+	0.829248i	−0.999704	−	0.0243474i	$-0.992249\pi$
$857$	−2.99518e30	+	5.18780e30i	−0.478766	+	0.829248i	0.520937	+	0.853595i	$0.325583\pi$
$858$		0			0
$859$	−1.15293e30	−	1.99694e30i	−0.179836	−	0.311484i	0.761988	−	0.647591i	$-0.224223\pi$
$859$	−1.15293e30	−	1.99694e30i	−0.179836	−	0.311484i	−0.941824	+	0.336106i	$0.890890\pi$
$860$	−6.82983e29	−	1.18296e30i	−0.105239	−	0.182279i
$861$		0			0
$862$	2.23833e29	−	3.87690e29i	0.0336587	−	0.0582986i
$863$	−5.11930e30			−0.760496			−0.380248	−	0.924884i	$-0.624161\pi$
$863$	−5.11930e30			−0.760496			−0.380248	+	0.924884i	$0.624161\pi$
$864$		0			0
$865$	−4.00573e30			−0.580782
$866$	−5.54540e30	+	9.60492e30i	−0.794319	+	1.37580i
$867$		0			0
$868$	5.27187e30	+	9.13115e30i	0.737069	+	1.27664i
$869$	−3.21973e30	−	5.57673e30i	−0.444746	−	0.770322i
$870$		0			0
$871$	−4.81017e30	+	8.33147e30i	−0.648590	+	1.12339i
$872$	1.81396e29			0.0241659
$873$		0			0
$874$	6.73633e29			0.0876099
$875$	−4.13528e30	+	7.16251e30i	−0.531398	+	0.920409i
$876$		0			0
$877$	3.43578e30	+	5.95095e30i	0.431052	+	0.746605i	0.996964	−	0.0778611i	$-0.0248091\pi$
$877$	3.43578e30	+	5.95095e30i	0.431052	+	0.746605i	−0.565912	+	0.824466i	$0.691476\pi$
$878$	1.19388e30	+	2.06786e30i	0.148002	+	0.256347i
$879$		0			0
$880$	−2.16877e30	+	3.75641e30i	−0.262509	+	0.454679i
$881$	5.75159e30			0.687924			0.343962	−	0.938984i	$-0.388231\pi$
$881$	5.75159e30			0.687924			0.343962	+	0.938984i	$0.388231\pi$
$882$		0			0
$883$	4.44146e30			0.518726			0.259363	−	0.965780i	$-0.416487\pi$
$883$	4.44146e30			0.518726			0.259363	+	0.965780i	$0.416487\pi$
$884$	−4.38282e30	+	7.59126e30i	−0.505830	+	0.876123i
$885$		0			0
$886$	−5.04714e30	−	8.74191e30i	−0.568842	−	0.985263i
$887$	2.42832e30	+	4.20597e30i	0.270463	+	0.468455i	0.968980	−	0.247138i	$-0.0794900\pi$
$887$	2.42832e30	+	4.20597e30i	0.270463	+	0.468455i	−0.698518	+	0.715593i	$0.746157\pi$
$888$		0			0
$889$	8.83074e30	−	1.52953e31i	0.960570	−	1.66376i
$890$	2.06106e30			0.221562
$891$		0			0
$892$	−3.68842e30			−0.387266
$893$	3.16589e30	−	5.48349e30i	0.328516	−	0.569006i
$894$		0			0
$895$	4.20961e30	+	7.29126e30i	0.426678	+	0.739028i
$896$	2.16200e30	+	3.74469e30i	0.216581	+	0.375130i
$897$		0			0
$898$	−3.74279e30	+	6.48270e30i	−0.366264	+	0.634387i
$899$	1.75081e30			0.169341
$900$		0			0
$901$	−4.87632e30			−0.460768
$902$	−7.62442e30	+	1.32059e31i	−0.712096	+	1.23339i
$903$		0			0
$904$	1.17136e30	+	2.02886e30i	0.106886	+	0.185133i
$905$	3.71772e30	+	6.43927e30i	0.335325	+	0.580800i
$906$		0			0
$907$	6.27820e30	−	1.08742e31i	0.553298	−	0.958339i	−0.444736	−	0.895662i	$-0.646703\pi$
$907$	6.27820e30	−	1.08742e31i	0.553298	−	0.958339i	0.998034	−	0.0626779i	$-0.0199641\pi$
$908$	2.72592e30			0.237471
$909$		0			0
$910$	−1.01600e31			−0.864890
$911$	−2.66932e30	+	4.62340e30i	−0.224625	+	0.389061i	−0.956207	−	0.292692i	$-0.905449\pi$
$911$	−2.66932e30	+	4.62340e30i	−0.224625	+	0.389061i	0.731582	+	0.681753i	$0.238782\pi$
$912$		0			0
$913$	−1.86378e30	−	3.22816e30i	−0.153268	−	0.265468i
$914$	−8.90252e30	−	1.54196e31i	−0.723732	−	1.25354i
$915$		0			0
$916$	2.61817e30	−	4.53480e30i	0.208015	−	0.360293i
$917$	2.77726e31			2.18141
$918$		0			0
$919$	1.80818e31			1.38813			0.694063	−	0.719914i	$-0.255819\pi$
$919$	1.80818e31			1.38813			0.694063	+	0.719914i	$0.255819\pi$
$920$	−1.02988e29	+	1.78380e29i	−0.00781650	+	0.0135386i
$921$		0			0
$922$	1.02800e31	+	1.78055e31i	0.762641	+	1.32093i
$923$	−4.94318e30	−	8.56184e30i	−0.362567	−	0.627985i
$924$		0			0
$925$	−8.21380e30	+	1.42267e31i	−0.588920	+	1.02004i
$926$	−9.05459e30			−0.641880
$927$		0			0
$928$	−2.48741e30			−0.172383
$929$	1.21602e31	−	2.10622e31i	0.833254	−	1.44324i	−0.0621901	−	0.998064i	$-0.519808\pi$
$929$	1.21602e31	−	2.10622e31i	0.833254	−	1.44324i	0.895444	−	0.445174i	$-0.146858\pi$
$930$		0			0
$931$	1.52414e30	+	2.63988e30i	0.102106	+	0.176853i
$932$	5.17499e30	+	8.96334e30i	0.342801	+	0.593749i
$933$		0			0
$934$	9.17562e30	−	1.58926e31i	0.594283	−	1.02933i
$935$	−8.07697e30			−0.517281
$936$		0			0
$937$	1.65121e31			1.03404			0.517018	−	0.855974i	$-0.327042\pi$
$937$	1.65121e31			1.03404			0.517018	+	0.855974i	$0.327042\pi$
$938$	1.72547e31	−	2.98860e31i	1.06851	−	1.85071i
$939$		0			0
$940$	−6.76058e30	−	1.17097e31i	−0.409394	−	0.709091i
$941$	−5.45424e30	−	9.44702e30i	−0.326620	−	0.565723i	0.655219	−	0.755439i	$-0.272576\pi$
$941$	−5.45424e30	−	9.44702e30i	−0.326620	−	0.565723i	−0.981839	+	0.189716i	$0.939243\pi$
$942$		0			0
$943$	−1.71081e30	+	2.96321e30i	−0.100191	+	0.173536i
$944$	−2.62182e31			−1.51844
$945$		0			0
$946$	−1.25071e31			−0.708435
$947$	1.44881e31	−	2.50942e31i	0.811592	−	1.40572i	−0.100157	−	0.994972i	$-0.531935\pi$
$947$	1.44881e31	−	2.50942e31i	0.811592	−	1.40572i	0.911749	−	0.410747i	$-0.134732\pi$
$948$		0			0
$949$	−1.88182e31	−	3.25941e31i	−1.03106	−	1.78584i
$950$	−3.24461e30	−	5.61983e30i	−0.175819	−	0.304527i
$951$		0			0
$952$	−2.25114e30	+	3.89910e30i	−0.119321	+	0.206669i
$953$	1.18340e31			0.620376			0.310188	−	0.950675i	$-0.399608\pi$
$953$	1.18340e31			0.620376			0.310188	+	0.950675i	$0.399608\pi$
$954$		0			0
$955$	1.79964e31			0.922892
$956$	−4.92925e30	+	8.53771e30i	−0.250019	+	0.433045i
$957$		0			0
$958$	−7.42892e30	−	1.28673e31i	−0.368627	−	0.638482i
$959$	1.20838e31	+	2.09298e31i	0.593074	+	1.02724i
$960$		0			0
$961$	−7.83919e30	+	1.35779e31i	−0.376423	+	0.651983i
$962$	−4.60548e31			−2.18744
$963$		0			0
$964$	7.55668e29			0.0351174
$965$	−6.45084e30	+	1.11732e31i	−0.296537	+	0.513618i
$966$		0			0
$967$	−1.20884e31	−	2.09377e31i	−0.543739	−	0.941784i	−0.998685	−	0.0512647i	$-0.983675\pi$
$967$	−1.20884e31	−	2.09377e31i	−0.543739	−	0.941784i	0.454946	−	0.890519i	$-0.349659\pi$
$968$	3.36924e28	+	5.83570e28i	0.00149914	+	0.00259658i
$969$		0			0
$970$	−1.01197e31	+	1.75279e31i	−0.440622	+	0.763179i
$971$	2.60921e31			1.12384			0.561922	−	0.827190i	$-0.310062\pi$
$971$	2.60921e31			1.12384			0.561922	+	0.827190i	$0.310062\pi$
$972$		0			0
$973$	−7.72619e30			−0.325672
$974$	−5.39371e30	+	9.34217e30i	−0.224915	+	0.389564i
$975$		0			0
$976$	5.30053e30	+	9.18079e30i	0.216320	+	0.374677i
$977$	−6.54896e30	−	1.13431e31i	−0.264411	−	0.457973i	0.702998	−	0.711192i	$-0.251844\pi$
$977$	−6.54896e30	−	1.13431e31i	−0.264411	−	0.457973i	−0.967409	+	0.253219i	$0.918511\pi$
$978$		0			0
$979$	4.40269e30	−	7.62568e30i	0.173980	−	0.301343i
$980$	6.50942e30			0.254489
$981$		0			0
$982$	−2.17126e31			−0.830885
$983$	−1.41740e31	+	2.45500e31i	−0.536636	+	0.929480i	0.462447	+	0.886647i	$0.346972\pi$
$983$	−1.41740e31	+	2.45500e31i	−0.536636	+	0.929480i	−0.999082	+	0.0428331i	$0.986362\pi$
$984$		0			0
$985$	−4.94368e29	−	8.56270e29i	−0.0183219	−	0.0317344i
$986$	−2.61062e30	−	4.52172e30i	−0.0957272	−	0.165804i
$987$		0			0
$988$	4.24428e30	−	7.35131e30i	0.152355	−	0.263886i
$989$	−2.80642e30			−0.0996762
$990$		0			0
$991$	−2.80586e31			−0.975646			−0.487823	−	0.872942i	$-0.662209\pi$
$991$	−2.80586e31			−0.975646			−0.487823	+	0.872942i	$0.662209\pi$
$992$	2.59310e31	−	4.49137e31i	0.892166	−	1.54528i
$993$		0			0
$994$	1.77318e31	+	3.07124e31i	0.597304	+	1.03456i
$995$	5.12475e30	+	8.87633e30i	0.170817	+	0.295863i
$996$		0			0
$997$	−2.54584e30	+	4.40952e30i	−0.0830868	+	0.143911i	−0.904574	−	0.426316i	$-0.859811\pi$
$997$	−2.54584e30	+	4.40952e30i	−0.0830868	+	0.143911i	0.821488	+	0.570226i	$0.193145\pi$
$998$	3.35394e31			1.08314
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	27.22.c.a.19.4		40
3.2	odd	2		9.22.c.a.7.17	yes	40
9.2	odd	6		81.22.a.c.1.4		20
9.4	even	3	inner	27.22.c.a.10.4		40
9.5	odd	6		9.22.c.a.4.17	✓	40
9.7	even	3		81.22.a.d.1.17		20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
9.22.c.a.4.17	✓	40	9.5	odd	6
9.22.c.a.7.17	yes	40	3.2	odd	2
27.22.c.a.10.4		40	9.4	even	3	inner
27.22.c.a.19.4		40	1.1	even	1	trivial
81.22.a.c.1.4		20	9.2	odd	6
81.22.a.d.1.17		20	9.7	even	3

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:	\( N \)	\(=\)	\( 27 = 3^{3} \)
Weight:	\( k \)	\(=\)	\( 22 \)
Character orbit:	\([\chi]\)	\(=\)	27.c (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-991.417 + 1717.18i) q^{2} +(-917239. - 1.58870e6i) q^{4} +(-5.12169e6 - 8.87103e6i) q^{5} +(4.75645e8 - 8.23841e8i) q^{7} -5.20838e8 q^{8} +O(q^{10})\)	\(q+(-991.417 + 1717.18i) q^{2} +(-917239. - 1.58870e6i) q^{4} +(-5.12169e6 - 8.87103e6i) q^{5} +(4.75645e8 - 8.23841e8i) q^{7} -5.20838e8 q^{8} +2.03109e10 q^{10} +(4.33867e10 - 7.51480e10i) q^{11} +(-2.62920e11 - 4.55390e11i) q^{13} +(9.43125e11 + 1.63354e12i) q^{14} +(2.43996e12 - 4.22613e12i) q^{16} +9.08695e12 q^{17} -8.79971e12 q^{19} +(-9.39564e12 + 1.62737e13i) q^{20} +(8.60286e13 + 1.49006e14i) q^{22} +(1.93036e13 + 3.34348e13i) q^{23} +(1.85955e14 - 3.22084e14i) q^{25} +1.04265e15 q^{26} -1.74512e15 q^{28} +(-1.44890e14 + 2.50957e14i) q^{29} +(-3.02092e15 - 5.23239e15i) q^{31} +(4.29189e15 + 7.43378e15i) q^{32} +(-9.00895e15 + 1.56040e16i) q^{34} -9.74443e15 q^{35} -4.41709e16 q^{37} +(8.72418e15 - 1.51107e16i) q^{38} +(2.66757e15 + 4.62037e15i) q^{40} +(4.43133e16 + 7.67528e16i) q^{41} +(-3.63458e16 + 6.29527e16i) q^{43} -1.59184e17 q^{44} -7.65517e16 q^{46} +(-3.59772e17 + 6.23144e17i) q^{47} +(-1.73203e17 - 2.99997e17i) q^{49} +(3.68718e17 + 6.38638e17i) q^{50} +(-4.82320e17 + 8.35403e17i) q^{52} -5.36630e17 q^{53} -8.88854e17 q^{55} +(-2.47734e17 + 4.29088e17i) q^{56} +(-2.87293e17 - 4.97606e17i) q^{58} +(-2.68634e18 - 4.65287e18i) q^{59} +(-1.08619e18 + 1.88134e18i) q^{61} +1.19800e19 q^{62} -6.78630e18 q^{64} +(-2.69319e18 + 4.66474e18i) q^{65} +(-9.14762e18 - 1.58441e19i) q^{67} +(-8.33490e18 - 1.44365e19i) q^{68} +(9.66079e18 - 1.67330e19i) q^{70} +1.88011e19 q^{71} +7.15740e19 q^{73} +(4.37918e19 - 7.58496e19i) q^{74} +(8.07144e18 + 1.39801e19i) q^{76} +(-4.12733e19 - 7.14875e19i) q^{77} +(3.71050e19 - 6.42678e19i) q^{79} -4.99869e19 q^{80} -1.75732e20 q^{82} +(2.14787e19 - 3.72022e19i) q^{83} +(-4.65406e19 - 8.06106e19i) q^{85} +(-7.20676e19 - 1.24825e20i) q^{86} +(-2.25974e19 + 3.91399e19i) q^{88} +1.01476e20 q^{89} -5.00225e20 q^{91} +(3.54121e19 - 6.13355e19i) q^{92} +(-7.13369e20 - 1.23559e21i) q^{94} +(4.50694e19 + 7.80625e19i) q^{95} +(-4.98241e20 + 8.62978e20i) q^{97} +6.86866e20 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q - 1023 q^{2} - 19922945 q^{4} - 32234853 q^{5} - 189623959 q^{7} + 1296271662 q^{8}+O(q^{10}) \) 40 * q - 1023 * q^2 - 19922945 * q^4 - 32234853 * q^5 - 189623959 * q^7 + 1296271662 * q^8	\( 40 q - 1023 q^{2} - 19922945 q^{4} - 32234853 q^{5} - 189623959 q^{7} + 1296271662 q^{8} + 4194300 q^{10} - 146068576386 q^{11} - 177565977277 q^{13} - 1549677244440 q^{14} - 18691699769345 q^{16} + 18615603749598 q^{17} - 9768733723954 q^{19} - 76202257650204 q^{20} + 86758343554047 q^{22} - 356460494884095 q^{23} - 13\!\cdots\!29 q^{25}+ \cdots - 53\!\cdots\!86 q^{98}+O(q^{100}) \) 40 * q - 1023 * q^2 - 19922945 * q^4 - 32234853 * q^5 - 189623959 * q^7 + 1296271662 * q^8 + 4194300 * q^10 - 146068576386 * q^11 - 177565977277 * q^13 - 1549677244440 * q^14 - 18691699769345 * q^16 + 18615603749598 * q^17 - 9768733723954 * q^19 - 76202257650204 * q^20 + 86758343554047 * q^22 - 356460494884095 * q^23 - 1379841857082329 * q^25 - 4509080239093464 * q^26 + 1599477148286972 * q^28 + 2772828270755157 * q^29 + 3064842508546901 * q^31 - 9763241440878495 * q^32 + 5532390311666553 * q^34 + 57889578635103594 * q^35 + 30082698487879388 * q^37 - 38173338977409867 * q^38 - 43546396391926176 * q^40 - 4985514195953106 * q^41 - 41986108659289660 * q^43 - 309819550937094042 * q^44 - 741003239171632200 * q^46 - 971751895603333665 * q^47 - 1393736132530446381 * q^49 - 1504393427506051923 * q^50 - 892509168437820382 * q^52 + 6400936694928489300 * q^53 + 3526658855224378230 * q^55 - 9313401575284840590 * q^56 - 985520139125952432 * q^58 - 11335149505478767926 * q^59 - 333769931007960067 * q^61 + 61644391774413093852 * q^62 + 25609201125502545922 * q^64 - 24815104795645584999 * q^65 + 14325054629523996728 * q^67 - 98193137232148637751 * q^68 - 23664205955002266174 * q^70 + 217438227096249463920 * q^71 - 4831088596512341626 * q^73 - 284989967381657148240 * q^74 + 45502930505046158765 * q^76 - 209785238565183158133 * q^77 + 45386959469213650259 * q^79 + 998031008510384761248 * q^80 + 228516181628552966154 * q^82 - 224083700347690062915 * q^83 - 135764416394391341394 * q^85 + 210501162447733500423 * q^86 + 409557505702705259691 * q^88 - 281885809391320932720 * q^89 - 387169009858825345418 * q^91 - 160981359902419031922 * q^92 + 1246412695298803268064 * q^94 - 583111881346045719228 * q^95 - 658984791485125488346 * q^97 - 5342632206895563334686 * q^98

Introduction

L-functions

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