LMFDB - Embedded newform 27.7.d.a.8.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [27,7,Mod(8,27)]

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([1]))

N = Newforms(chi, 7, names="a")

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

chi := DirichletCharacter("27.8");

S:= CuspForms(chi, 7);

N := Newforms(S);

Level:	$ N $	$=$	$ 27 = 3^{3} $
Weight:	$ k $	$=$	$ 7 $
Character orbit:	$[\chi]$	$=$	27.d (of order $6$, 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:	$6.21146025774$
Analytic rank:	$0$
Dimension:	$10$
Relative dimension:	$5$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{10} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} - x^{9} + 75 x^{8} - 2 x^{7} + 4610 x^{6} - 2412 x^{5} + 66932 x^{4} - 174032 x^{3} + \cdots + 1982464 $ x^10 - x^9 + 75x^8 - 2x^7 + 4610x^6 - 2412x^5 + 66932x^4 - 174032x^3 + 870720x^2 - 1272832x + 1982464
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{2}\cdot 3^{14} $
Twist minimal:	no (minimal twist has level 9)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			8.1
Root			$-3.54866 - 6.14646i$ of defining polynomial
Character	$\chi$	$=$	27.8
Dual form			27.7.d.a.17.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-10.6460 - 6.14646i) q^{2} +(43.5579 + 75.4444i) q^{4} +(157.562 - 90.9682i) q^{5} +(83.3541 - 144.373i) q^{7} -284.159i q^{8} +O(q^{10})$	\(q+(-10.6460 - 6.14646i) q^{2} +(43.5579 + 75.4444i) q^{4} +(157.562 - 90.9682i) q^{5} +(83.3541 - 144.373i) q^{7} -284.159i q^{8} -2236.53 q^{10} +(-1488.57 - 859.428i) q^{11} +(-279.116 - 483.444i) q^{13} +(-1774.77 + 1024.66i) q^{14} +(1041.13 - 1803.29i) q^{16} -5319.63i q^{17} -1409.91 q^{19} +(13726.1 + 7924.76i) q^{20} +(10564.9 + 18298.9i) q^{22} +(-3657.39 + 2111.59i) q^{23} +(8737.93 - 15134.5i) q^{25} +6862.31i q^{26} +14522.9 q^{28} +(2799.35 + 1616.21i) q^{29} +(-22229.2 - 38502.0i) q^{31} +(-37917.4 + 21891.6i) q^{32} +(-32696.9 + 56632.7i) q^{34} -30330.3i q^{35} +6453.68 q^{37} +(15009.9 + 8665.95i) q^{38} +(-25849.5 - 44772.6i) q^{40} +(53284.9 - 30764.1i) q^{41} +(-11382.6 + 19715.3i) q^{43} -149739. i q^{44} +51915.3 q^{46} +(38957.3 + 22492.0i) q^{47} +(44928.7 + 77818.8i) q^{49} +(-186048. + 107415. i) q^{50} +(24315.4 - 42115.6i) q^{52} +72344.4i q^{53} -312722. q^{55} +(-41025.1 - 23685.9i) q^{56} +(-19867.9 - 34412.2i) q^{58} +(175718. - 101451. i) q^{59} +(181034. - 313560. i) q^{61} +546522. i q^{62} +404959. q^{64} +(-87956.1 - 50781.5i) q^{65} +(244451. + 423401. i) q^{67} +(401337. - 231712. i) q^{68} +(-186424. + 322895. i) q^{70} -152912. i q^{71} +17880.2 q^{73} +(-68705.7 - 39667.3i) q^{74} +(-61412.6 - 106370. i) q^{76} +(-248157. + 143274. i) q^{77} +(146033. - 252936. i) q^{79} -378839. i q^{80} -756360. q^{82} +(-356275. - 205696. i) q^{83} +(-483917. - 838170. i) q^{85} +(242359. - 139926. i) q^{86} +(-244215. + 422992. i) q^{88} +758118. i q^{89} -93062.0 q^{91} +(-318616. - 183953. i) q^{92} +(-276492. - 478899. i) q^{94} +(-222148. + 128257. i) q^{95} +(-477655. + 827322. i) q^{97} -1.10461e6i q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q + 3 q^{2} + 127 q^{4} + 219 q^{5} - 121 q^{7}+O(q^{10}) $ 10 * q + 3 * q^2 + 127 * q^4 + 219 * q^5 - 121 * q^7	$ 10 q + 3 q^{2} + 127 q^{4} + 219 q^{5} - 121 q^{7} - 132 q^{10} - 483 q^{11} - 841 q^{13} - 12174 q^{14} - 1985 q^{16} + 6176 q^{19} + 63186 q^{20} + 3471 q^{22} - 53565 q^{23} + 8452 q^{25} - 22660 q^{28} + 80679 q^{29} - 24601 q^{31} - 218295 q^{32} + 7425 q^{34} + 12764 q^{37} + 371877 q^{38} + 54150 q^{40} - 232251 q^{41} - 93271 q^{43} + 112512 q^{46} + 142887 q^{47} + 86238 q^{49} - 318459 q^{50} + 186920 q^{52} - 419982 q^{55} - 342546 q^{56} - 380658 q^{58} + 995061 q^{59} - 59305 q^{61} + 403066 q^{64} - 1642029 q^{65} + 158513 q^{67} + 1693791 q^{68} - 304788 q^{70} + 933896 q^{73} - 595182 q^{74} + 666641 q^{76} + 2198883 q^{77} + 468707 q^{79} - 2038470 q^{82} - 3008337 q^{83} - 1189944 q^{85} - 1905549 q^{86} - 349773 q^{88} - 211778 q^{91} + 973788 q^{92} + 809124 q^{94} + 2562954 q^{95} + 336029 q^{97}+O(q^{100}) $ 10 * q + 3 * q^2 + 127 * q^4 + 219 * q^5 - 121 * q^7 - 132 * q^10 - 483 * q^11 - 841 * q^13 - 12174 * q^14 - 1985 * q^16 + 6176 * q^19 + 63186 * q^20 + 3471 * q^22 - 53565 * q^23 + 8452 * q^25 - 22660 * q^28 + 80679 * q^29 - 24601 * q^31 - 218295 * q^32 + 7425 * q^34 + 12764 * q^37 + 371877 * q^38 + 54150 * q^40 - 232251 * q^41 - 93271 * q^43 + 112512 * q^46 + 142887 * q^47 + 86238 * q^49 - 318459 * q^50 + 186920 * q^52 - 419982 * q^55 - 342546 * q^56 - 380658 * q^58 + 995061 * q^59 - 59305 * q^61 + 403066 * q^64 - 1642029 * q^65 + 158513 * q^67 + 1693791 * q^68 - 304788 * q^70 + 933896 * q^73 - 595182 * q^74 + 666641 * q^76 + 2198883 * q^77 + 468707 * q^79 - 2038470 * q^82 - 3008337 * q^83 - 1189944 * q^85 - 1905549 * q^86 - 349773 * q^88 - 211778 * q^91 + 973788 * q^92 + 809124 * q^94 + 2562954 * q^95 + 336029 * q^97

Display 100 coefficients 10 coefficients

Character values

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

$n$	$2$
$\chi(n)$	$e\left(\frac{1}{6}\right)$

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 $

$2$	−10.6460	−	6.14646i	−1.33075	−	0.768307i	−0.345333	−	0.938480i	$-0.612234\pi$
$2$	−10.6460	−	6.14646i	−1.33075	−	0.768307i	−0.985414	+	0.170173i	$0.945567\pi$
$3$		0			0
$3$		0			0
$4$	43.5579	+	75.4444i	0.680592	+	1.17882i
$5$	157.562	−	90.9682i	1.26049	−	0.727746i	0.287323	−	0.957834i	$-0.407235\pi$
$5$	157.562	−	90.9682i	1.26049	−	0.727746i	0.973170	+	0.230088i	$0.0739014\pi$
$6$		0			0
$7$	83.3541	−	144.373i	0.243015	−	0.420914i	−0.718557	−	0.695468i	$-0.755197\pi$
$7$	83.3541	−	144.373i	0.243015	−	0.420914i	0.961572	+	0.274554i	$0.0885303\pi$
$8$		−	284.159i		−	0.554999i
$9$		0			0
$10$	−2236.53			−2.23653
$11$	−1488.57	−	859.428i	−1.11839	−	0.645701i	−0.177398	−	0.984139i	$-0.556768\pi$
$11$	−1488.57	−	859.428i	−1.11839	−	0.645701i	−0.940989	+	0.338438i	$0.890101\pi$
$12$		0			0
$13$	−279.116	−	483.444i	−0.127044	−	0.220047i	0.795486	−	0.605972i	$-0.207216\pi$
$13$	−279.116	−	483.444i	−0.127044	−	0.220047i	−0.922530	+	0.385925i	$0.873882\pi$
$14$	−1774.77	+	1024.66i	−0.646782	+	0.373420i
$15$		0			0
$16$	1041.13	−	1803.29i	0.254182	−	0.440256i
$17$		−	5319.63i		−	1.08277i	−0.840776	−	0.541383i	$-0.817901\pi$
$17$		−	5319.63i		−	1.08277i	0.840776	−	0.541383i	$-0.182099\pi$
$18$		0			0
$19$	−1409.91			−0.205556			−0.102778	−	0.994704i	$-0.532773\pi$
$19$	−1409.91			−0.205556			−0.102778	+	0.994704i	$0.532773\pi$
$20$	13726.1	+	7924.76i	1.71576	+	0.990595i
$21$		0			0
$22$	10564.9	+	18298.9i	0.992193	+	1.71853i
$23$	−3657.39	+	2111.59i	−0.300599	+	0.173551i	−0.642712	−	0.766108i	$-0.722191\pi$
$23$	−3657.39	+	2111.59i	−0.300599	+	0.173551i	0.342113	+	0.939659i	$0.388857\pi$
$24$		0			0
$25$	8737.93	−	15134.5i	0.559228	−	0.968611i
$26$			6862.31i			0.390436i
$27$		0			0
$28$	14522.9			0.661575
$29$	2799.35	+	1616.21i	0.114779	+	0.0662679i	0.556291	−	0.830988i	$-0.312224\pi$
$29$	2799.35	+	1616.21i	0.114779	+	0.0662679i	−0.441511	+	0.897256i	$0.645557\pi$
$30$		0			0
$31$	−22229.2	−	38502.0i	−0.746170	−	1.29240i	−0.949646	−	0.313325i	$-0.898557\pi$
$31$	−22229.2	−	38502.0i	−0.746170	−	1.29240i	0.203476	−	0.979080i	$-0.434776\pi$
$32$	−37917.4	+	21891.6i	−1.15715	+	0.668079i
$33$		0			0
$34$	−32696.9	+	56632.7i	−0.831897	+	1.44089i
$35$		−	30330.3i		−	0.707412i
$36$		0			0
$37$	6453.68			0.127410			0.0637048	−	0.997969i	$-0.479708\pi$
$37$	6453.68			0.127410			0.0637048	+	0.997969i	$0.479708\pi$
$38$	15009.9	+	8665.95i	0.273543	+	0.157930i
$39$		0			0
$40$	−25849.5	−	44772.6i	−0.403898	−	0.699572i
$41$	53284.9	−	30764.1i	0.773130	−	0.446367i	−0.0608599	−	0.998146i	$-0.519384\pi$
$41$	53284.9	−	30764.1i	0.773130	−	0.446367i	0.833990	+	0.551779i	$0.186051\pi$
$42$		0			0
$43$	−11382.6	+	19715.3i	−0.143165	+	0.247970i	−0.928687	−	0.370865i	$-0.879061\pi$
$43$	−11382.6	+	19715.3i	−0.143165	+	0.247970i	0.785522	+	0.618834i	$0.212395\pi$
$44$		−	149739.i		−	1.75783i
$45$		0			0
$46$	51915.3			0.533362
$47$	38957.3	+	22492.0i	0.375228	+	0.216638i	0.675740	−	0.737140i	$-0.263824\pi$
$47$	38957.3	+	22492.0i	0.375228	+	0.216638i	−0.300512	+	0.953778i	$0.597158\pi$
$48$		0			0
$49$	44928.7	+	77818.8i	0.381888	+	0.661449i
$50$	−186048.	+	107415.i	−1.48838	+	0.859317i
$51$		0			0
$52$	24315.4	−	42115.6i	0.172931	−	0.299525i
$53$			72344.4i			0.485934i	0.970035	+	0.242967i	$0.0781207\pi$
$53$			72344.4i			0.485934i	−0.970035	+	0.242967i	$0.921879\pi$
$54$		0			0
$55$	−312722.			−1.87962
$56$	−41025.1	−	23685.9i	−0.233607	−	0.134873i
$57$		0			0
$58$	−19867.9	−	34412.2i	−0.101828	−	0.176372i
$59$	175718.	−	101451.i	0.855580	−	0.493969i	−0.00694996	−	0.999976i	$-0.502212\pi$
$59$	175718.	−	101451.i	0.855580	−	0.493969i	0.862530	+	0.506007i	$0.168879\pi$
$60$		0			0
$61$	181034.	−	313560.i	0.797574	−	1.38144i	−0.123617	−	0.992330i	$-0.539450\pi$
$61$	181034.	−	313560.i	0.797574	−	1.38144i	0.921192	−	0.389109i	$-0.127217\pi$
$62$			546522.i			2.29315i
$63$		0			0
$64$	404959.			1.54480
$65$	−87956.1	−	50781.5i	−0.320277	−	0.184912i
$66$		0			0
$67$	244451.	+	423401.i	0.812769	+	1.40776i	0.910919	+	0.412586i	$0.135374\pi$
$67$	244451.	+	423401.i	0.812769	+	1.40776i	−0.0981496	+	0.995172i	$0.531292\pi$
$68$	401337.	−	231712.i	1.27639	−	0.736922i
$69$		0			0
$70$	−186424.	+	322895.i	−0.543510	+	0.941386i
$71$		−	152912.i		−	0.427234i	−0.976917	−	0.213617i	$-0.931475\pi$
$71$		−	152912.i		−	0.427234i	0.976917	−	0.213617i	$-0.0685245\pi$
$72$		0			0
$73$	17880.2			0.0459625			0.0229812	−	0.999736i	$-0.492684\pi$
$73$	17880.2			0.0459625			0.0229812	+	0.999736i	$0.492684\pi$
$74$	−68705.7	−	39667.3i	−0.169550	−	0.0978897i
$75$		0			0
$76$	−61412.6	−	106370.i	−0.139900	−	0.242313i
$77$	−248157.	+	143274.i	−0.543569	+	0.313830i
$78$		0			0
$79$	146033.	−	252936.i	0.296189	−	0.513015i	−0.679072	−	0.734072i	$-0.737617\pi$
$79$	146033.	−	252936.i	0.296189	−	0.513015i	0.975261	+	0.221057i	$0.0709508\pi$
$80$		−	378839.i		−	0.739919i
$81$		0			0
$82$	−756360.			−1.37179
$83$	−356275.	−	205696.i	−0.623091	−	0.359742i	0.154980	−	0.987918i	$-0.450469\pi$
$83$	−356275.	−	205696.i	−0.623091	−	0.359742i	−0.778072	+	0.628176i	$0.783802\pi$
$84$		0			0
$85$	−483917.	−	838170.i	−0.787979	−	1.36482i
$86$	242359.	−	139926.i	0.381034	−	0.219990i
$87$		0			0
$88$	−244215.	+	422992.i	−0.358363	+	0.620703i
$89$			758118.i			1.07539i	0.843139	+	0.537696i	$0.180705\pi$
$89$			758118.i			1.07539i	−0.843139	+	0.537696i	$0.819295\pi$
$90$		0			0
$91$	−93062.0			−0.123495
$92$	−318616.	−	183953.i	−0.409170	−	0.236235i
$93$		0			0
$94$	−276492.	−	478899.i	−0.332889	−	0.576581i
$95$	−222148.	+	128257.i	−0.259102	+	0.149593i
$96$		0			0
$97$	−477655.	+	827322.i	−0.523358	+	0.906483i	0.476272	+	0.879298i	$0.341988\pi$
$97$	−477655.	+	827322.i	−0.523358	+	0.906483i	−0.999630	+	0.0271849i	$0.991346\pi$
$98$		−	1.10461e6i		−	1.17363i
$99$		0			0
$100$	1.52242e6			1.52242
$101$	−508685.	−	293690.i	−0.493725	−	0.285052i	0.232393	−	0.972622i	$-0.425344\pi$
$101$	−508685.	−	293690.i	−0.493725	−	0.285052i	−0.726119	+	0.687570i	$0.758678\pi$
$102$		0			0
$103$	626445.	+	1.08504e6i	0.573286	+	0.992961i	0.996226	+	0.0868028i	$0.0276650\pi$
$103$	626445.	+	1.08504e6i	0.573286	+	0.992961i	−0.422939	+	0.906158i	$0.639002\pi$
$104$	−137375.	+	79313.6i	−0.122126	+	0.0705095i
$105$		0			0
$106$	444662.	−	770177.i	0.373347	−	0.646655i
$107$			1.16410e6i			0.950250i	0.879918	+	0.475125i	$0.157597\pi$
$107$			1.16410e6i			0.950250i	−0.879918	+	0.475125i	$0.842403\pi$
$108$		0			0
$109$	2.04060e6			1.57572			0.787858	−	0.615857i	$-0.211190\pi$
$109$	2.04060e6			1.57572			0.787858	+	0.615857i	$0.211190\pi$
$110$	3.32924e6	+	1.92213e6i	2.50130	+	1.44413i
$111$		0			0
$112$	−173565.	−	300623.i	−0.123540	−	0.213977i
$113$	1.99955e6	−	1.15444e6i	1.38579	−	0.800087i	0.392954	−	0.919558i	$-0.371453\pi$
$113$	1.99955e6	−	1.15444e6i	1.38579	−	0.800087i	0.992838	+	0.119471i	$0.0381199\pi$
$114$		0			0
$115$	−384176.	+	665412.i	−0.252602	+	0.437519i
$116$			281594.i			0.180405i
$117$		0			0
$118$	−2.49425e6			−1.51808
$119$	−768014.	−	443413.i	−0.455752	−	0.263128i
$120$		0			0
$121$	591452.	+	1.02442e6i	0.333859	+	0.578261i
$122$	−3.85457e6	+	2.22544e6i	−2.12274	+	1.22556i
$123$		0			0
$124$	1.93651e6	−	3.35413e6i	1.01567	−	1.75920i
$125$		−	336740.i		−	0.172411i
$126$		0			0
$127$	−2.62583e6			−1.28190			−0.640952	−	0.767581i	$-0.721460\pi$
$127$	−2.62583e6			−1.28190			−0.640952	+	0.767581i	$0.721460\pi$
$128$	−1.88447e6	−	1.08800e6i	−0.898585	−	0.518798i
$129$		0			0
$130$	624252.	+	1.08124e6i	0.284138	+	0.492142i
$131$	−3.03542e6	+	1.75250e6i	−1.35022	+	0.779551i	−0.988280	−	0.152650i	$-0.951219\pi$
$131$	−3.03542e6	+	1.75250e6i	−1.35022	+	0.779551i	−0.361941	+	0.932201i	$0.617886\pi$
$132$		0			0
$133$	−117522.	+	203554.i	−0.0499532	+	0.0865214i
$134$		−	6.01003e6i		−	2.49783i
$135$		0			0
$136$	−1.51162e6			−0.600934
$137$	4.35807e6	+	2.51613e6i	1.69486	+	0.978525i	0.950491	+	0.310753i	$0.100581\pi$
$137$	4.35807e6	+	2.51613e6i	1.69486	+	0.978525i	0.744365	+	0.667773i	$0.232752\pi$
$138$		0			0
$139$	−458059.	−	793381.i	−0.170560	−	0.295418i	0.768056	−	0.640383i	$-0.221224\pi$
$139$	−458059.	−	793381.i	−0.170560	−	0.295418i	−0.938616	+	0.344964i	$0.887891\pi$
$140$	2.28825e6	−	1.32112e6i	0.833911	−	0.481459i
$141$		0			0
$142$	−939866.	+	1.62790e6i	−0.328247	+	0.568541i
$143$			959522.i			0.328131i
$144$		0			0
$145$	588094.			0.192905
$146$	−190352.	−	109900.i	−0.0611644	−	0.0353133i
$147$		0			0
$148$	281108.	+	486894.i	0.0867139	+	0.150193i
$149$	4.68451e6	−	2.70460e6i	1.41614	−	0.817608i	0.420181	−	0.907440i	$-0.361967\pi$
$149$	4.68451e6	−	2.70460e6i	1.41614	−	0.817608i	0.995957	+	0.0898326i	$0.0286332\pi$
$150$		0			0
$151$	41828.2	−	72448.6i	0.0121489	−	0.0210426i	−0.859887	−	0.510484i	$-0.829466\pi$
$151$	41828.2	−	72448.6i	0.0121489	−	0.0210426i	0.872036	+	0.489442i	$0.162799\pi$
$152$			400639.i			0.114083i
$153$		0			0
$154$	3.52250e6			0.964470
$155$	−7.00492e6	−	4.04429e6i	−1.88108	−	1.08604i
$156$		0			0
$157$	−3.55663e6	−	6.16027e6i	−0.919052	−	1.59185i	−0.800858	−	0.598855i	$-0.795623\pi$
$157$	−3.55663e6	−	6.16027e6i	−0.919052	−	1.59185i	−0.118195	−	0.992990i	$-0.537711\pi$
$158$	−3.10932e6	+	1.79517e6i	−0.788306	+	0.455129i
$159$		0			0
$160$	−3.98288e6	+	6.89855e6i	−0.972383	+	1.68422i
$161$			704040.i			0.168702i
$162$		0			0
$163$	3.40623e6			0.786523			0.393262	−	0.919427i	$-0.371347\pi$
$163$	3.40623e6			0.786523			0.393262	+	0.919427i	$0.371347\pi$
$164$	4.64195e6	+	2.68003e6i	1.05237	+	0.607587i
$165$		0			0
$166$	2.52860e6	+	4.37966e6i	0.552784	+	0.957451i
$167$	2.33573e6	−	1.34853e6i	0.501502	−	0.289542i	−0.227832	−	0.973701i	$-0.573164\pi$
$167$	2.33573e6	−	1.34853e6i	0.501502	−	0.289542i	0.729334	+	0.684158i	$0.239830\pi$
$168$		0			0
$169$	2.25759e6	−	3.91026e6i	0.467719	−	0.810114i
$170$			1.18975e7i			2.42164i
$171$		0			0
$172$	−1.98322e6			−0.389749
$173$	−3.68413e6	−	2.12703e6i	−0.711535	−	0.410805i	0.100094	−	0.994978i	$-0.468086\pi$
$173$	−3.68413e6	−	2.12703e6i	−0.711535	−	0.410805i	−0.811629	+	0.584173i	$0.801419\pi$
$174$		0			0
$175$	−1.45668e6	−	2.52305e6i	−0.271801	−	0.470773i
$176$	−3.09959e6	+	1.78955e6i	−0.568547	+	0.328251i
$177$		0			0
$178$	4.65974e6	−	8.07090e6i	0.826231	−	1.43107i
$179$		−	4.17190e6i		−	0.727403i	−0.931516	−	0.363701i	$-0.881513\pi$
$179$		−	4.17190e6i		−	0.727403i	0.931516	−	0.363701i	$-0.118487\pi$
$180$		0			0
$181$	3.48525e6			0.587758			0.293879	−	0.955843i	$-0.405054\pi$
$181$	3.48525e6			0.587758			0.293879	+	0.955843i	$0.405054\pi$
$182$	990735.	+	572001.i	0.164340	+	0.0948818i
$183$		0			0
$184$	600029.	+	1.03928e6i	0.0963206	+	0.166832i
$185$	1.01685e6	−	587080.i	0.160599	−	0.0927218i
$186$		0			0
$187$	−4.57184e6	+	7.91866e6i	−0.699143	+	1.21095i
$188$			3.91882e6i			0.589768i
$189$		0			0
$190$	3.15330e6			0.459732
$191$	3.38874e6	+	1.95649e6i	0.486338	+	0.280787i	0.723054	−	0.690792i	$-0.242738\pi$
$191$	3.38874e6	+	1.95649e6i	0.486338	+	0.280787i	−0.236716	+	0.971579i	$0.576071\pi$
$192$		0			0
$193$	−71225.5	−	123366.i	−0.00990749	−	0.0171603i	0.861029	−	0.508556i	$-0.169820\pi$
$193$	−71225.5	−	123366.i	−0.00990749	−	0.0171603i	−0.870937	+	0.491395i	$0.836487\pi$
$194$	1.01702e7	−	5.87177e6i	1.39291	−	0.804199i
$195$		0			0
$196$	−3.91400e6	+	6.77924e6i	−0.519819	+	0.900353i
$197$			1.60395e6i			0.209793i	0.994483	+	0.104897i	$0.0334512\pi$
$197$			1.60395e6i			0.209793i	−0.994483	+	0.104897i	$0.966549\pi$
$198$		0			0
$199$	−6.37145e6			−0.808498			−0.404249	−	0.914649i	$-0.632467\pi$
$199$	−6.37145e6			−0.808498			−0.404249	+	0.914649i	$0.632467\pi$
$200$	−4.30062e6	−	2.48297e6i	−0.537578	−	0.310371i
$201$		0			0
$202$	3.61030e6	+	6.25323e6i	0.438015	+	0.758665i
$203$	466675.	−	269435.i	0.0557861	−	0.0322081i
$204$		0			0
$205$	5.59710e6	−	9.69447e6i	0.649683	−	1.12528i
$206$		−	1.54017e7i		−	1.76184i
$207$		0			0
$208$	−1.16238e6			−0.129169
$209$	2.09875e6	+	1.21172e6i	0.229891	+	0.132728i
$210$		0			0
$211$	4.04280e6	+	7.00233e6i	0.430363	+	0.745410i	0.996904	−	0.0786231i	$-0.0250524\pi$
$211$	4.04280e6	+	7.00233e6i	0.430363	+	0.745410i	−0.566542	+	0.824033i	$0.691719\pi$
$212$	−5.45798e6	+	3.15117e6i	−0.572828	+	0.330723i
$213$		0			0
$214$	7.15507e6	−	1.23930e7i	0.730084	−	1.26454i
$215$			4.14184e6i			0.416752i
$216$		0			0
$217$	−7.41156e6			−0.725322
$218$	−2.17242e7	−	1.25425e7i	−2.09688	−	1.21063i
$219$		0			0
$220$	−1.36215e7	−	2.35932e7i	−1.27926	−	2.21574i
$221$	−2.57174e6	+	1.48480e6i	−0.238260	+	0.137559i
$222$		0			0
$223$	−8.38450e6	+	1.45224e7i	−0.756071	+	1.30955i	0.188769	+	0.982021i	$0.439550\pi$
$223$	−8.38450e6	+	1.45224e7i	−0.756071	+	1.30955i	−0.944840	+	0.327532i	$0.893783\pi$
$224$			7.29902e6i			0.649412i
$225$		0			0
$226$	−2.83829e7			−2.45885
$227$	418528.	+	241637.i	0.0357806	+	0.0206579i	0.517784	−	0.855512i	$-0.326757\pi$
$227$	418528.	+	241637.i	0.0357806	+	0.0206579i	−0.482003	+	0.876170i	$0.660091\pi$
$228$		0			0
$229$	6.32135e6	+	1.09489e7i	0.526385	+	0.911725i	0.999527	+	0.0307393i	$0.00978616\pi$
$229$	6.32135e6	+	1.09489e7i	0.526385	+	0.911725i	−0.473143	+	0.880986i	$0.656881\pi$
$230$	8.17985e6	−	4.72264e6i	0.672298	−	0.388152i
$231$		0			0
$232$	459260.	−	795463.i	0.0367786	−	0.0637024i
$233$			9.13067e6i			0.721830i	0.932599	+	0.360915i	$0.117536\pi$
$233$			9.13067e6i			0.721830i	−0.932599	+	0.360915i	$0.882464\pi$
$234$		0			0
$235$	8.18423e6			0.630630
$236$	1.53078e7	+	8.83797e6i	1.16460	+	0.672382i
$237$		0			0
$238$	5.45084e6	+	9.44113e6i	0.404327	+	0.700314i
$239$	−9.51675e6	+	5.49450e6i	−0.697100	+	0.402471i	−0.806266	−	0.591553i	$-0.798515\pi$
$239$	−9.51675e6	+	5.49450e6i	−0.697100	+	0.402471i	0.109166	+	0.994023i	$0.465182\pi$
$240$		0			0
$241$	7.57250e6	−	1.31160e7i	0.540989	−	0.937020i	−0.457859	−	0.889025i	$-0.651383\pi$
$241$	7.57250e6	−	1.31160e7i	0.540989	−	0.937020i	0.998848	−	0.0479952i	$-0.0152832\pi$
$242$		−	1.45413e7i		−	1.02603i
$243$		0			0
$244$	3.15418e7			2.17129
$245$	1.41581e7	+	8.17417e6i	0.962733	+	0.555834i
$246$		0			0
$247$	393529.	+	681612.i	0.0261147	+	0.0452321i
$248$	−1.09407e7	+	6.31663e6i	−0.717283	+	0.414124i
$249$		0			0
$250$	−2.06976e6	+	3.58492e6i	−0.132464	+	0.229435i
$251$		−	1.62909e7i		−	1.03021i	−0.857128	−	0.515104i	$-0.827753\pi$
$251$		−	1.62909e7i		−	1.03021i	0.857128	−	0.515104i	$-0.172247\pi$
$252$		0			0
$253$	7.25905e6			0.448248
$254$	2.79545e7	+	1.61395e7i	1.70589	+	0.984895i
$255$		0			0
$256$	415992.	+	720520.i	0.0247951	+	0.0429463i
$257$	−1.21744e6	+	702891.i	−0.0717215	+	0.0414084i	−0.535432	−	0.844578i	$-0.679851\pi$
$257$	−1.21744e6	+	702891.i	−0.0717215	+	0.0414084i	0.463710	+	0.885987i	$0.346518\pi$
$258$		0			0
$259$	537940.	−	931740.i	0.0309624	−	0.0536285i
$260$		−	8.84772e6i		−	0.503398i
$261$		0			0
$262$	4.30867e7			2.39574
$263$	−4713.31	−	2721.23i	−0.000259095	−	0.000149588i	0.499870	−	0.866100i	$-0.333381\pi$
$263$	−4713.31	−	2721.23i	−0.000259095	−	0.000149588i	−0.500130	+	0.865951i	$0.666714\pi$
$264$		0			0
$265$	6.58104e6	+	1.13987e7i	0.353636	+	0.612516i
$266$	2.50227e6	−	1.44468e6i	0.132950	−	0.0767588i
$267$		0			0
$268$	−2.12955e7	+	3.68849e7i	−1.10633	+	1.91622i
$269$			1.35392e7i			0.695565i	0.937575	+	0.347782i	$0.113065\pi$
$269$			1.35392e7i			0.695565i	−0.937575	+	0.347782i	$0.886935\pi$
$270$		0			0
$271$	−2.84929e7			−1.43162			−0.715812	−	0.698293i	$-0.753943\pi$
$271$	−2.84929e7			−1.43162			−0.715812	+	0.698293i	$0.753943\pi$
$272$	−9.59283e6	−	5.53842e6i	−0.476694	−	0.275220i
$273$		0			0
$274$	−3.09306e7	−	5.35734e7i	−1.50362	−	2.60434i
$275$	−2.60141e7	+	1.50192e7i	−1.25087	+	0.722188i
$276$		0			0
$277$	−2.76602e6	+	4.79089e6i	−0.130142	+	0.225412i	−0.923731	−	0.383042i	$-0.874877\pi$
$277$	−2.76602e6	+	4.79089e6i	−0.130142	+	0.225412i	0.793589	+	0.608454i	$0.208210\pi$
$278$			1.12618e7i			0.524170i
$279$		0			0
$280$	−8.61864e6			−0.392613
$281$	−1.89478e7	−	1.09395e7i	−0.853966	−	0.493038i	0.00802086	−	0.999968i	$-0.497447\pi$
$281$	−1.89478e7	−	1.09395e7i	−0.853966	−	0.493038i	−0.861987	+	0.506930i	$0.830780\pi$
$282$		0			0
$283$	−2.49011e6	−	4.31300e6i	−0.109865	−	0.190292i	0.805850	−	0.592119i	$-0.201709\pi$
$283$	−2.49011e6	−	4.31300e6i	−0.109865	−	0.190292i	−0.915715	+	0.401827i	$0.868375\pi$
$284$	1.15363e7	−	6.66051e6i	0.503632	−	0.290772i
$285$		0			0
$286$	5.89766e6	−	1.02150e7i	0.252105	−	0.436659i
$287$		−	1.02572e7i		−	0.433895i
$288$		0			0
$289$	−4.16091e6			−0.172383
$290$	−6.26083e6	−	3.61469e6i	−0.256707	−	0.148210i
$291$		0			0
$292$	778822.	+	1.34896e6i	0.0312817	+	0.0541814i
$293$	1.56847e7	−	9.05555e6i	0.623552	−	0.360008i	−0.154699	−	0.987962i	$-0.549441\pi$
$293$	1.56847e7	−	9.05555e6i	0.623552	−	0.360008i	0.778251	+	0.627954i	$0.216107\pi$
$294$		0			0
$295$	1.84576e7	−	3.19695e7i	0.718968	−	1.24529i
$296$		−	1.83387e6i		−	0.0707122i
$297$		0			0
$298$	−6.64949e7			−2.51269
$299$	2.04167e6	+	1.17876e6i	0.0763788	+	0.0440973i
$300$		0			0
$301$	1.89758e6	+	3.28671e6i	0.0695826	+	0.120521i
$302$	−890604.	+	514191.i	−0.0323343	+	0.0186682i
$303$		0			0
$304$	−1.46790e6	+	2.54247e6i	−0.0522486	+	0.0904973i
$305$		−	6.58734e7i		−	2.32173i
$306$		0			0
$307$	1.92125e7			0.663999			0.332000	−	0.943280i	$-0.392277\pi$
$307$	1.92125e7			0.663999			0.332000	+	0.943280i	$0.392277\pi$
$308$	−2.16184e7	−	1.24814e7i	−0.739897	−	0.427180i
$309$		0			0
$310$	4.97161e7	+	8.61109e7i	1.66883	+	2.89050i
$311$	−7.62828e6	+	4.40419e6i	−0.253598	+	0.146415i	−0.621410	−	0.783485i	$-0.713440\pi$
$311$	−7.62828e6	+	4.40419e6i	−0.253598	+	0.146415i	0.367813	+	0.929900i	$0.380107\pi$
$312$		0			0
$313$	−4.39584e6	+	7.61381e6i	−0.143354	+	0.248296i	−0.928757	−	0.370688i	$-0.879122\pi$
$313$	−4.39584e6	+	7.61381e6i	−0.143354	+	0.248296i	0.785404	+	0.618984i	$0.212455\pi$
$314$			8.74428e7i			2.82446i
$315$		0			0
$316$	2.54435e7			0.806335
$317$	3.33247e6	+	1.92400e6i	0.104614	+	0.0603988i	0.551394	−	0.834245i	$-0.314096\pi$
$317$	3.33247e6	+	1.92400e6i	0.104614	+	0.0603988i	−0.446780	+	0.894644i	$0.647429\pi$
$318$		0			0
$319$	−2.77803e6	−	4.81168e6i	−0.0855784	−	0.148226i
$320$	6.38060e7	−	3.68384e7i	1.94720	−	1.12422i
$321$		0			0
$322$	4.32735e6	−	7.49519e6i	0.129615	−	0.224499i
$323$			7.50020e6i			0.222569i
$324$		0			0
$325$	−9.75560e6			−0.284187
$326$	−3.62627e7	−	2.09363e7i	−1.04666	−	0.604291i
$327$		0			0
$328$	−8.74190e6	−	1.51414e7i	−0.247733	−	0.429086i
$329$	6.49450e6	−	3.74960e6i	0.182372	−	0.105293i
$330$		0			0
$331$	508540.	−	880817.i	0.0140230	−	0.0242885i	−0.858929	−	0.512095i	$-0.828870\pi$
$331$	508540.	−	880817.i	0.0140230	−	0.0242885i	0.872952	+	0.487807i	$0.162203\pi$
$332$		−	3.58387e7i		−	0.979349i
$333$		0			0
$334$	−3.31548e7			−0.889829
$335$	7.70321e7	+	4.44745e7i	2.04898	+	1.18298i
$336$		0			0
$337$	−2.92475e7	−	5.06582e7i	−0.764187	−	1.32361i	−0.940675	−	0.339308i	$-0.889807\pi$
$337$	−2.92475e7	−	5.06582e7i	−0.764187	−	1.32361i	0.176489	−	0.984303i	$-0.443526\pi$
$338$	−4.80685e7	+	2.77524e7i	−1.24483	+	0.718704i
$339$		0			0
$340$	4.21568e7	−	7.30177e7i	1.07258	−	1.85777i
$341$			7.64174e7i			1.92721i
$342$		0			0
$343$	3.45930e7			0.857247
$344$	5.60230e6	+	3.23449e6i	0.137623	+	0.0794566i
$345$		0			0
$346$	2.61474e7	+	4.52887e7i	0.631249	+	1.09335i
$347$	1.49800e7	−	8.64871e6i	0.358528	−	0.206996i	−0.309907	−	0.950767i	$-0.600298\pi$
$347$	1.49800e7	−	8.64871e6i	0.358528	−	0.206996i	0.668435	+	0.743771i	$0.266964\pi$
$348$		0			0
$349$	−3.59193e7	+	6.22141e7i	−0.844990	+	1.46357i	0.0406390	+	0.999174i	$0.487061\pi$
$349$	−3.59193e7	+	6.22141e7i	−0.844990	+	1.46357i	−0.885629	+	0.464393i	$0.846273\pi$
$350$			3.58138e7i			0.835307i
$351$		0			0
$352$	7.52570e7			1.72552
$353$	−4.33051e7	−	2.50022e7i	−0.984497	−	0.568400i	−0.0808722	−	0.996724i	$-0.525771\pi$
$353$	−4.33051e7	−	2.50022e7i	−0.984497	−	0.568400i	−0.903625	+	0.428325i	$0.859104\pi$
$354$		0			0
$355$	−1.39101e7	−	2.40930e7i	−0.310918	−	0.538526i
$356$	−5.71958e7	+	3.30220e7i	−1.26769	+	0.731902i
$357$		0			0
$358$	−2.56424e7	+	4.44139e7i	−0.558869	+	0.967989i
$359$		−	4.05549e7i		−	0.876516i	−0.898849	−	0.438258i	$-0.855596\pi$
$359$		−	4.05549e7i		−	0.876516i	0.898849	−	0.438258i	$-0.144404\pi$
$360$		0			0
$361$	−4.50580e7			−0.957747
$362$	−3.71039e7	−	2.14219e7i	−0.782157	−	0.451578i
$363$		0			0
$364$	−4.05358e6	−	7.02101e6i	−0.0840494	−	0.145578i
$365$	2.81723e6	−	1.62653e6i	0.0579353	−	0.0334490i
$366$		0			0
$367$	1.31833e7	−	2.28341e7i	0.266701	−	0.461940i	−0.701307	−	0.712860i	$-0.747400\pi$
$367$	1.31833e7	−	2.28341e7i	0.266701	−	0.461940i	0.968008	+	0.250920i	$0.0807330\pi$
$368$			8.79377e6i			0.176454i
$369$		0			0
$370$	−1.44338e7			−0.284955
$371$	1.04446e7	+	6.03020e6i	0.204536	+	0.118089i
$372$		0			0
$373$	1.13842e7	+	1.97180e7i	0.219369	+	0.379958i	0.954615	−	0.297842i	$-0.0962669\pi$
$373$	1.13842e7	+	1.97180e7i	0.219369	+	0.379958i	−0.735246	+	0.677800i	$0.762934\pi$
$374$	9.73434e7	−	5.62012e7i	1.86077	−	1.07431i
$375$		0			0
$376$	6.39132e6	−	1.10701e7i	0.120234	−	0.208251i
$377$		−	1.80444e6i		−	0.0336758i
$378$		0			0
$379$	8.26212e7			1.51766			0.758829	−	0.651290i	$-0.225772\pi$
$379$	8.26212e7			1.51766			0.758829	+	0.651290i	$0.225772\pi$
$380$	−1.93525e7	−	1.11732e7i	−0.352685	−	0.203623i
$381$		0			0
$382$	−2.40510e7	−	4.16575e7i	−0.431462	−	0.747314i
$383$	4.76382e7	−	2.75039e7i	0.847928	−	0.489551i	−0.0120233	−	0.999928i	$-0.503827\pi$
$383$	4.76382e7	−	2.75039e7i	0.847928	−	0.489551i	0.859951	+	0.510376i	$0.170494\pi$
$384$		0			0
$385$	−2.60667e7	+	4.51488e7i	−0.456776	+	0.791160i
$386$			1.75114e6i			0.0304480i
$387$		0			0
$388$	−8.32225e7			−1.42477
$389$	−8.10301e6	−	4.67827e6i	−0.137657	−	0.0794762i	0.429590	−	0.903024i	$-0.358658\pi$
$389$	−8.10301e6	−	4.67827e6i	−0.137657	−	0.0794762i	−0.567247	+	0.823548i	$0.691991\pi$
$390$		0			0
$391$	1.12329e7	+	1.94560e7i	0.187915	+	0.325478i
$392$	2.21129e7	−	1.27669e7i	0.367103	−	0.211947i
$393$		0			0
$394$	9.85860e6	−	1.70756e7i	0.161186	−	0.279182i
$395$		−	5.31374e7i		−	0.862202i
$396$		0			0
$397$	2.76126e7			0.441301			0.220651	−	0.975353i	$-0.429182\pi$
$397$	2.76126e7			0.441301			0.220651	+	0.975353i	$0.429182\pi$
$398$	6.78303e7	+	3.91618e7i	1.07591	+	0.621175i
$399$		0			0
$400$	−1.81946e7	−	3.15140e7i	−0.284291	−	0.492407i
$401$	−5.58001e7	+	3.22162e7i	−0.865369	+	0.499621i	−0.865807	−	0.500379i	$-0.833194\pi$
$401$	−5.58001e7	+	3.22162e7i	−0.865369	+	0.499621i	0.000437241		1.00000i	$0.499861\pi$
$402$		0			0
$403$	−1.24090e7	+	2.14931e7i	−0.189593	+	0.328385i
$404$		−	5.11700e7i		−	0.776017i
$405$		0			0
$406$	−6.62428e6			−0.0989830
$407$	−9.60677e6	−	5.54647e6i	−0.142493	−	0.0822685i
$408$		0			0
$409$	−2.18221e7	−	3.77969e7i	−0.318952	−	0.552442i	0.661317	−	0.750106i	$-0.269998\pi$
$409$	−2.18221e7	−	3.77969e7i	−0.318952	−	0.552442i	−0.980270	+	0.197664i	$0.936664\pi$
$410$	−1.19173e8	+	6.88047e7i	−1.72913	+	0.998313i
$411$		0			0
$412$	−5.45732e7	+	9.45236e7i	−0.780347	+	1.35160i
$413$		−	3.38254e7i		−	0.480167i
$414$		0			0
$415$	−7.48471e7			−1.04720
$416$	2.11667e7	+	1.22206e7i	0.294018	+	0.169751i
$417$		0			0
$418$	−1.48955e7	−	2.57998e7i	−0.203951	−	0.353254i
$419$	−6.41948e7	+	3.70629e7i	−0.872686	+	0.503846i	−0.868240	−	0.496145i	$-0.834749\pi$
$419$	−6.41948e7	+	3.70629e7i	−0.872686	+	0.503846i	−0.00444624	+	0.999990i	$0.501415\pi$
$420$		0			0
$421$	3.28966e7	−	5.69785e7i	0.440864	−	0.763599i	−0.556890	−	0.830586i	$-0.688006\pi$
$421$	3.28966e7	−	5.69785e7i	0.440864	−	0.763599i	0.997754	+	0.0669877i	$0.0213388\pi$
$422$		−	9.93955e7i		−	1.32260i
$423$		0			0
$424$	2.05573e7			0.269693
$425$	−8.05102e7	−	4.64826e7i	−1.04878	−	0.605513i
$426$		0			0
$427$	−3.01799e7	−	5.22731e7i	−0.387645	−	0.671420i
$428$	−8.78247e7	+	5.07056e7i	−1.12017	+	0.646732i
$429$		0			0
$430$	2.54576e7	−	4.40939e7i	0.320193	−	0.554591i
$431$			5.53172e7i			0.690920i	0.938433	+	0.345460i	$0.112277\pi$
$431$			5.53172e7i			0.690920i	−0.938433	+	0.345460i	$0.887723\pi$
$432$		0			0
$433$	5.16421e7			0.636122			0.318061	−	0.948070i	$-0.396968\pi$
$433$	5.16421e7			0.636122			0.318061	+	0.948070i	$0.396968\pi$
$434$	7.89033e7	+	4.55549e7i	0.965220	+	0.557270i
$435$		0			0
$436$	8.88841e7	+	1.53952e8i	1.07242	+	1.85748i
$437$	5.15659e6	−	2.97716e6i	0.0617900	−	0.0356744i
$438$		0			0
$439$	7.20929e7	−	1.24869e8i	0.852116	−	1.47591i	−0.0271780	−	0.999631i	$-0.508652\pi$
$439$	7.20929e7	−	1.24869e8i	0.852116	−	1.47591i	0.879295	−	0.476278i	$-0.158015\pi$
$440$			8.88630e7i			1.04319i
$441$		0			0
$442$	3.65050e7			0.422751
$443$	1.19699e8	+	6.91083e7i	1.37683	+	0.794912i	0.991776	−	0.127983i	$-0.0408504\pi$
$443$	1.19699e8	+	6.91083e7i	1.37683	+	0.794912i	0.385051	+	0.922895i	$0.374184\pi$
$444$		0			0
$445$	6.89646e7	+	1.19450e8i	0.782612	+	1.35552i
$446$	1.78522e8	−	1.03070e8i	2.01228	−	1.16179i
$447$		0			0
$448$	3.37550e7	−	5.84653e7i	0.375408	−	0.650226i
$449$			8.70368e7i			0.961532i	0.876849	+	0.480766i	$0.159641\pi$
$449$			8.70368e7i			0.961532i	−0.876849	+	0.480766i	$0.840359\pi$
$450$		0			0
$451$	−1.05758e8			−1.15288
$452$	1.74193e8	+	1.00570e8i	1.88632	+	1.08906i
$453$		0			0
$454$	−2.97043e6	−	5.14493e6i	−0.0317433	−	0.0549809i
$455$	−1.46630e7	+	8.46568e6i	−0.155664	+	0.0898727i
$456$		0			0
$457$	−5.39584e7	+	9.34587e7i	−0.565341	+	0.979200i	0.431677	+	0.902028i	$0.357922\pi$
$457$	−5.39584e7	+	9.34587e7i	−0.565341	+	0.979200i	−0.997018	+	0.0771712i	$0.975411\pi$
$458$		−	1.55416e8i		−	1.61770i
$459$		0			0
$460$	−6.69355e7			−0.687675
$461$	−9.05482e7	−	5.22780e7i	−0.924224	−	0.533601i	−0.0392436	−	0.999230i	$-0.512495\pi$
$461$	−9.05482e7	−	5.22780e7i	−0.924224	−	0.533601i	−0.884980	+	0.465629i	$0.845828\pi$
$462$		0			0
$463$	7.04837e7	+	1.22081e8i	0.710143	+	1.23000i	0.964803	+	0.262973i	$0.0847029\pi$
$463$	7.04837e7	+	1.22081e8i	0.710143	+	1.23000i	−0.254661	+	0.967030i	$0.581964\pi$
$464$	5.82897e6	−	3.36536e6i	0.0583496	−	0.0336882i
$465$		0			0
$466$	5.61213e7	−	9.72049e7i	0.554587	−	0.960573i
$467$			7.05545e7i			0.692746i	0.938097	+	0.346373i	$0.112587\pi$
$467$			7.05545e7i			0.692746i	−0.938097	+	0.346373i	$0.887413\pi$
$468$		0			0
$469$	8.15039e7			0.790060
$470$	−8.71291e7	−	5.03040e7i	−0.839208	−	0.484517i
$471$		0			0
$472$	−2.88282e7	−	4.99320e7i	−0.274152	−	0.474846i
$473$	3.38878e7	−	1.95651e7i	0.320228	−	0.184884i
$474$		0			0
$475$	−1.23197e7	+	2.13383e7i	−0.114953	+	0.199104i
$476$		−	7.72565e7i		−	0.716331i
$477$		0			0
$478$	1.35087e8			1.23689
$479$	−1.00661e8	−	5.81165e7i	−0.915912	−	0.528802i	−0.0335832	−	0.999436i	$-0.510692\pi$
$479$	−1.00661e8	−	5.81165e7i	−0.915912	−	0.528802i	−0.882328	+	0.470634i	$0.844025\pi$
$480$		0			0
$481$	−1.80133e6	−	3.11999e6i	−0.0161867	−	0.0280361i
$482$	−1.61233e8	+	9.30881e7i	−1.43984	+	0.831291i
$483$		0			0
$484$	−5.15247e7	+	8.92435e7i	−0.454443	+	0.787119i
$485$			1.73806e8i			1.52349i
$486$		0			0
$487$	−4.74498e7			−0.410816			−0.205408	−	0.978676i	$-0.565852\pi$
$487$	−4.74498e7			−0.410816			−0.205408	+	0.978676i	$0.565852\pi$
$488$	−8.91012e7	−	5.14426e7i	−0.766697	−	0.442653i
$489$		0			0
$490$	−1.00484e8	−	1.74044e8i	−0.854103	−	1.47935i
$491$	1.49100e8	−	8.60828e7i	1.25960	−	0.727230i	0.286603	−	0.958049i	$-0.407474\pi$
$491$	1.49100e8	−	8.60828e7i	1.25960	−	0.727230i	0.972997	+	0.230819i	$0.0741406\pi$
$492$		0			0
$493$	8.59763e6	−	1.48915e7i	0.0717526	−	0.124279i
$494$		−	9.67523e6i		−	0.0802566i
$495$		0			0
$496$	−9.25737e7			−0.758652
$497$	−2.20764e7	−	1.27458e7i	−0.179829	−	0.103824i
$498$		0			0
$499$	−4.15509e7	−	7.19683e7i	−0.334410	−	0.579215i	0.648961	−	0.760821i	$-0.275204\pi$
$499$	−4.15509e7	−	7.19683e7i	−0.334410	−	0.579215i	−0.983371	+	0.181607i	$0.941870\pi$
$500$	2.54051e7	−	1.46677e7i	0.203241	−	0.117341i
$501$		0			0
$502$	−1.00132e8	+	1.73433e8i	−0.791516	+	1.37095i
$503$		−	1.41492e8i		−	1.11180i	−0.831249	−	0.555901i	$-0.812374\pi$
$503$		−	1.41492e8i		−	1.11180i	0.831249	−	0.555901i	$-0.187626\pi$
$504$		0			0
$505$	−1.06866e8			−0.829782
$506$	−7.72797e7	−	4.46174e7i	−0.596504	−	0.344392i
$507$		0			0
$508$	−1.14375e8	−	1.98104e8i	−0.872452	−	1.51113i
$509$	2.73979e7	−	1.58182e7i	0.207761	−	0.119951i	−0.392509	−	0.919748i	$-0.628393\pi$
$509$	2.73979e7	−	1.58182e7i	0.207761	−	0.119951i	0.600270	+	0.799797i	$0.295060\pi$
$510$		0			0
$511$	1.49039e6	−	2.58142e6i	0.0111696	−	0.0193462i
$512$			1.29036e8i			0.961396i
$513$		0			0
$514$	1.72812e7			0.127258
$515$	1.97407e8	+	1.13973e8i	1.44525	+	0.834413i
$516$		0			0
$517$	−3.86605e7	−	6.69620e7i	−0.279767	−	0.484570i
$518$	−1.14538e7	+	6.61285e6i	−0.0824063	+	0.0475773i
$519$		0			0
$520$	−1.44300e7	+	2.49935e7i	−0.102626	+	0.177753i
$521$		−	1.72443e7i		−	0.121936i	−0.998140	−	0.0609681i	$-0.980581\pi$
$521$		−	1.72443e7i		−	0.121936i	0.998140	−	0.0609681i	$-0.0194188\pi$
$522$		0			0
$523$	1.85242e8			1.29489			0.647447	−	0.762111i	$-0.275837\pi$
$523$	1.85242e8			1.29489			0.647447	+	0.762111i	$0.275837\pi$
$524$	−2.64433e8	−	1.52670e8i	−1.83790	−	1.06111i
$525$		0			0
$526$	33451.8	+	57940.3i	0.000229860	+	0.000398129i
$527$	−2.04817e8	+	1.18251e8i	−1.39937	+	0.807928i
$528$		0			0
$529$	−6.51003e7	+	1.12757e8i	−0.439760	+	0.761687i
$530$		−	1.61800e8i		−	1.08681i
$531$		0			0
$532$	−2.04760e7			−0.135991
$533$	−2.97454e7	−	1.71735e7i	−0.196444	−	0.113417i
$534$		0			0
$535$	1.05896e8	+	1.83417e8i	0.691541	+	1.19778i
$536$	1.20314e8	−	6.94630e7i	0.781304	−	0.451086i
$537$		0			0
$538$	8.32184e7	−	1.44138e8i	0.534407	−	0.925621i
$539$		−	1.54452e8i		−	0.986341i
$540$		0			0
$541$	−6.24196e7			−0.394211			−0.197106	−	0.980382i	$-0.563154\pi$
$541$	−6.24196e7			−0.394211			−0.197106	+	0.980382i	$0.563154\pi$
$542$	3.03335e8	+	1.75131e8i	1.90513	+	1.09993i
$543$		0			0
$544$	1.16455e8	+	2.01707e8i	0.723373	+	1.25292i
$545$	3.21520e8	−	1.85630e8i	1.98618	−	1.14672i
$546$		0			0
$547$	−6.13250e7	+	1.06218e8i	−0.374693	+	0.648988i	−0.990281	−	0.139081i	$-0.955585\pi$
$547$	−6.13250e7	+	1.06218e8i	−0.374693	+	0.648988i	0.615588	+	0.788068i	$0.288919\pi$
$548$			4.38390e8i			2.66390i
$549$		0			0
$550$	3.69261e8			2.21945
$551$	−3.94683e6	−	2.27871e6i	−0.0235936	−	0.0136218i
$552$		0			0
$553$	−2.43449e7	−	4.21665e7i	−0.143957	−	0.249340i
$554$	5.88940e7	−	3.40024e7i	0.346371	−	0.199977i
$555$		0			0
$556$	3.99041e7	−	6.91160e7i	0.232163	−	0.402119i
$557$			1.65808e8i			0.959488i	0.877409	+	0.479744i	$0.159270\pi$
$557$			1.65808e8i			0.959488i	−0.877409	+	0.479744i	$0.840730\pi$
$558$		0			0
$559$	1.27083e7			0.0727534
$560$	−5.46943e7	−	3.15777e7i	−0.311442	−	0.179811i
$561$		0			0
$562$	1.34479e8	+	2.32924e8i	0.757609	+	1.31222i
$563$	−7.97550e6	+	4.60466e6i	−0.0446923	+	0.0258031i	−0.522180	−	0.852835i	$-0.674881\pi$
$563$	−7.97550e6	+	4.60466e6i	−0.0446923	+	0.0258031i	0.477487	+	0.878639i	$0.341548\pi$
$564$		0			0
$565$	2.10035e8	−	3.63792e8i	1.16452	−	2.01701i
$566$			6.12215e7i			0.337640i
$567$		0			0
$568$	−4.34514e7			−0.237115
$569$	−1.99300e8	−	1.15066e8i	−1.08186	−	0.624610i	−0.150459	−	0.988616i	$-0.548075\pi$
$569$	−1.99300e8	−	1.15066e8i	−1.08186	−	0.624610i	−0.931396	+	0.364006i	$0.881409\pi$
$570$		0			0
$571$	−1.08654e8	−	1.88194e8i	−0.583628	−	1.01087i	−0.995045	−	0.0994260i	$-0.968299\pi$
$571$	−1.08654e8	−	1.88194e8i	−0.583628	−	1.01087i	0.411417	−	0.911447i	$-0.365034\pi$
$572$	−7.23906e7	+	4.17947e7i	−0.386807	+	0.223323i
$573$		0			0
$574$	−6.30457e7	+	1.09198e8i	−0.333365	+	0.577405i
$575$			7.38039e7i			0.388218i
$576$		0			0
$577$	−2.72923e8			−1.42073			−0.710366	−	0.703833i	$-0.751470\pi$
$577$	−2.72923e8			−1.42073			−0.710366	+	0.703833i	$0.751470\pi$
$578$	4.42970e7	+	2.55749e7i	0.229398	+	0.132443i
$579$		0			0
$580$	2.56161e7	+	4.43684e7i	0.131289	+	0.227400i
$581$	−5.93940e7	+	3.42912e7i	−0.302841	+	0.174845i
$582$		0			0
$583$	6.21748e7	−	1.07690e8i	0.313768	−	0.543462i
$584$		−	5.08082e6i		−	0.0255091i
$585$		0			0
$586$	−2.22638e8			−1.10639
$587$	−2.25458e8	−	1.30168e8i	−1.11468	−	0.643561i	−0.174643	−	0.984632i	$-0.555877\pi$
$587$	−2.25458e8	−	1.30168e8i	−1.11468	−	0.643561i	−0.940038	+	0.341071i	$0.889210\pi$
$588$		0			0
$589$	3.13411e7	+	5.42844e7i	0.153380	+	0.265662i
$590$	−3.92999e8	+	2.26898e8i	−1.91353	+	1.10478i
$591$		0			0
$592$	6.71911e6	−	1.16378e7i	0.0323852	−	0.0560928i
$593$		−	1.03317e8i		−	0.495461i	−0.968829	−	0.247730i	$-0.920315\pi$
$593$		−	1.03317e8i		−	0.495461i	0.968829	−	0.247730i	$-0.0796847\pi$
$594$		0			0
$595$	−1.61346e8			−0.765962
$596$	4.08095e8	+	2.35614e8i	1.92762	+	1.11291i
$597$		0			0
$598$	−1.44904e7	−	2.50981e7i	−0.0677606	−	0.117365i
$599$	7.50671e7	−	4.33400e7i	0.349276	−	0.201655i	−0.315090	−	0.949062i	$-0.602035\pi$
$599$	7.50671e7	−	4.33400e7i	0.349276	−	0.201655i	0.664366	+	0.747407i	$0.268701\pi$
$600$		0			0
$601$	1.25884e8	−	2.18038e8i	0.579892	−	1.00440i	−0.415599	−	0.909548i	$-0.636428\pi$
$601$	1.25884e8	−	2.18038e8i	0.579892	−	1.00440i	0.995491	−	0.0948551i	$-0.0302388\pi$
$602$		−	4.66536e7i		−	0.213843i
$603$		0			0
$604$	7.28779e6			0.0330739
$605$	1.86380e8	+	1.07607e8i	0.841654	+	0.485929i
$606$		0			0
$607$	−1.32612e8	−	2.29691e8i	−0.592949	−	1.02702i	−0.993833	−	0.110888i	$-0.964630\pi$
$607$	−1.32612e8	−	2.29691e8i	−0.592949	−	1.02702i	0.400884	−	0.916129i	$-0.368703\pi$
$608$	5.34601e7	−	3.08652e7i	0.237859	−	0.137328i
$609$		0			0
$610$	−4.04888e8	+	7.01287e8i	−1.78380	+	3.08963i
$611$		−	2.51116e7i		−	0.110091i
$612$		0			0
$613$	1.81196e8			0.786625			0.393313	−	0.919405i	$-0.371329\pi$
$613$	1.81196e8			0.786625			0.393313	+	0.919405i	$0.371329\pi$
$614$	−2.04535e8	−	1.18088e8i	−0.883615	−	0.510155i
$615$		0			0
$616$	4.07126e7	+	7.05162e7i	0.174175	+	0.301680i
$617$	1.44378e8	−	8.33568e7i	0.614676	−	0.354883i	−0.160117	−	0.987098i	$-0.551187\pi$
$617$	1.44378e8	−	8.33568e7i	0.614676	−	0.354883i	0.774793	+	0.632215i	$0.217854\pi$
$618$		0			0
$619$	−2.00952e7	+	3.48060e7i	−0.0847269	+	0.146751i	−0.905275	−	0.424826i	$-0.860335\pi$
$619$	−2.00952e7	+	3.48060e7i	−0.0847269	+	0.146751i	0.820548	+	0.571578i	$0.193668\pi$
$620$		−	7.04643e8i		−	2.95661i
$621$		0			0
$622$	1.08281e8			0.449966
$623$	1.09452e8	+	6.31922e7i	0.452647	+	0.261336i
$624$		0			0
$625$	1.05898e8	+	1.83420e8i	0.433756	+	0.751288i
$626$	9.35959e7	−	5.40376e7i	0.381535	−	0.220279i
$627$		0			0
$628$	3.09839e8	−	5.36656e8i	1.25100	−	2.16679i
$629$		−	3.43312e7i		−	0.137955i
$630$		0			0
$631$	3.56910e8			1.42060			0.710298	−	0.703901i	$-0.248560\pi$
$631$	3.56910e8			1.42060			0.710298	+	0.703901i	$0.248560\pi$
$632$	−7.18742e7	−	4.14966e7i	−0.284723	−	0.164385i
$633$		0			0
$634$	−2.36516e7	−	4.09658e7i	−0.0928096	−	0.160751i
$635$	−4.13730e8	+	2.38867e8i	−1.61583	+	0.932900i
$636$		0			0
$637$	2.50807e7	−	4.34410e7i	0.0970333	−	0.168067i
$638$			6.83001e7i			0.263002i
$639$		0			0
$640$	−3.95893e8			−1.51021
$641$	−4.61294e7	−	2.66328e7i	−0.175148	−	0.101121i	0.409863	−	0.912147i	$-0.365576\pi$
$641$	−4.61294e7	−	2.66328e7i	−0.175148	−	0.101121i	−0.585011	+	0.811025i	$0.698910\pi$
$642$		0			0
$643$	−1.30620e6	−	2.26241e6i	−0.00491336	−	0.00851018i	0.863558	−	0.504249i	$-0.168231\pi$
$643$	−1.30620e6	−	2.26241e6i	−0.00491336	−	0.00851018i	−0.868472	+	0.495739i	$0.834897\pi$
$644$	−5.31159e7	+	3.06665e7i	−0.198869	+	0.114817i
$645$		0			0
$646$	4.60996e7	−	7.98469e7i	0.171002	−	0.296183i
$647$		−	3.01753e8i		−	1.11414i	−0.830467	−	0.557068i	$-0.811926\pi$
$647$		−	3.01753e8i		−	1.11414i	0.830467	−	0.557068i	$-0.188074\pi$
$648$		0			0
$649$	−3.48759e8			−1.27582
$650$	1.03858e8	+	5.99624e7i	0.378181	+	0.218343i
$651$		0			0
$652$	1.48368e8	+	2.56981e8i	0.535301	+	0.927169i
$653$	2.88988e8	−	1.66847e8i	1.03786	−	0.599210i	0.118636	−	0.992938i	$-0.462148\pi$
$653$	2.88988e8	−	1.66847e8i	1.03786	−	0.599210i	0.919227	+	0.393727i	$0.128815\pi$
$654$		0			0
$655$	−3.18844e8	+	5.52254e8i	−1.13463	+	1.96524i
$656$		−	1.28117e8i		−	0.453834i
$657$		0			0
$658$	−9.21871e7			−0.323588
$659$	1.01465e8	+	5.85808e7i	0.354536	+	0.204691i	0.666681	−	0.745343i	$-0.267714\pi$
$659$	1.01465e8	+	5.85808e7i	0.354536	+	0.204691i	−0.312145	+	0.950034i	$0.601048\pi$
$660$		0			0
$661$	−2.88517e7	−	4.99726e7i	−0.0999003	−	0.173032i	0.811743	−	0.584015i	$-0.198519\pi$
$661$	−2.88517e7	−	4.99726e7i	−0.0999003	−	0.173032i	−0.911643	+	0.410983i	$0.865186\pi$
$662$	−1.08278e7	+	6.25144e6i	−0.0373221	+	0.0215479i
$663$		0			0
$664$	−5.84504e7	+	1.01239e8i	−0.199656	+	0.345815i
$665$			4.27630e7i			0.145413i
$666$		0			0
$667$	−1.36511e7			−0.0460034
$668$	2.03478e8	+	1.17478e8i	0.682636	+	0.394120i
$669$		0			0
$670$	−5.46721e8	−	9.46949e8i	−1.81778	−	3.14849i
$671$	−5.38965e8	+	3.11172e8i	−1.78399	+	1.02999i
$672$		0			0
$673$	−2.35745e8	+	4.08322e8i	−0.773387	+	1.33955i	0.162310	+	0.986740i	$0.448106\pi$
$673$	−2.35745e8	+	4.08322e8i	−0.773387	+	1.33955i	−0.935697	+	0.352805i	$0.885228\pi$
$674$			7.19075e8i			2.34852i
$675$		0			0
$676$	3.93344e8			1.27330
$677$	3.33724e8	+	1.92676e8i	1.07553	+	0.620956i	0.929686	−	0.368353i	$-0.120078\pi$
$677$	3.33724e8	+	1.92676e8i	1.07553	+	0.620956i	0.145840	+	0.989308i	$0.453411\pi$
$678$		0			0
$679$	7.96289e7	+	1.37921e8i	0.254367	+	0.440577i
$680$	−2.38174e8	+	1.37510e8i	−0.757473	+	0.437327i
$681$		0			0
$682$	4.69696e8	−	8.13538e8i	1.48069	−	2.56463i
$683$			1.10409e7i			0.0346532i	0.999850	+	0.0173266i	$0.00551550\pi$
$683$			1.10409e7i			0.0346532i	−0.999850	+	0.0173266i	$0.994484\pi$
$684$		0			0
$685$	9.15553e8			2.84847
$686$	−3.68276e8	−	2.12624e8i	−1.14078	−	0.658629i
$687$		0			0
$688$	2.37016e7	+	4.10524e7i	0.0727801	+	0.126059i
$689$	3.49745e7	−	2.01925e7i	0.106928	−	0.0617352i
$690$		0			0
$691$	−1.43527e8	+	2.48595e8i	−0.435009	+	0.753457i	−0.997296	−	0.0734844i	$-0.976588\pi$
$691$	−1.43527e8	+	2.48595e8i	−0.435009	+	0.753457i	0.562287	+	0.826942i	$0.309921\pi$
$692$		−	3.70596e8i		−	1.11836i
$693$		0			0
$694$	−2.12636e8			−0.636147
$695$	−1.44345e8	−	8.33376e7i	−0.429979	−	0.248249i
$696$		0			0
$697$	−1.63653e8	−	2.83456e8i	−0.483311	−	0.837119i
$698$	7.64792e8	−	4.41553e8i	2.24894	−	1.29842i
$699$		0			0
$700$	1.26900e8	−	2.19797e8i	0.369971	−	0.640809i
$701$			6.53422e8i			1.89688i	0.316957	+	0.948440i	$0.397339\pi$
$701$			6.53422e8i			1.89688i	−0.316957	+	0.948440i	$0.602661\pi$
$702$		0			0
$703$	−9.09910e6			−0.0261898
$704$	−6.02811e8	−	3.48033e8i	−1.72768	−	0.997476i
$705$		0			0
$706$	3.07350e8	+	5.32345e8i	0.873411	+	1.51279i
$707$	−8.48020e7	+	4.89605e7i	−0.239965	+	0.138544i
$708$		0			0
$709$	−1.04127e8	+	1.80353e8i	−0.292162	+	0.506040i	−0.974321	−	0.225164i	$-0.927708\pi$
$709$	−1.04127e8	+	1.80353e8i	−0.292162	+	0.506040i	0.682158	+	0.731204i	$0.261041\pi$
$710$			3.41992e8i			0.955522i
$711$		0			0
$712$	2.15426e8			0.596841
$713$	1.62601e8	+	9.38779e7i	0.448596	+	0.258997i
$714$		0			0
$715$	8.72860e7	+	1.51184e8i	0.238796	+	0.413606i
$716$	3.14747e8	−	1.81719e8i	0.857476	−	0.495064i
$717$		0			0
$718$	−2.49269e8	+	4.31746e8i	−0.673434	+	1.16642i
$719$			9.36308e7i			0.251902i	0.992036	+	0.125951i	$0.0401982\pi$
$719$			9.36308e7i			0.251902i	−0.992036	+	0.125951i	$0.959802\pi$
$720$		0			0
$721$	2.08867e8			0.557268
$722$	4.79687e8	+	2.76947e8i	1.27452	+	0.735844i
$723$		0			0
$724$	1.51810e8	+	2.62943e8i	0.400023	+	0.692860i
$725$	4.89211e7	−	2.82446e7i	0.128376	−	0.0741176i
$726$		0			0
$727$	−2.44283e7	+	4.23111e7i	−0.0635755	+	0.110116i	−0.896061	−	0.443930i	$-0.853584\pi$
$727$	−2.44283e7	+	4.23111e7i	−0.0635755	+	0.110116i	0.832486	+	0.554047i	$0.186917\pi$
$728$			2.64444e7i			0.0685394i
$729$		0			0
$730$	−3.99895e7			−0.102796
$731$	1.04878e8	+	6.05515e7i	0.268493	+	0.155015i
$732$		0			0
$733$	1.37505e8	+	2.38166e8i	0.349146	+	0.604739i	0.986098	−	0.166165i	$-0.0531383\pi$
$733$	1.37505e8	+	2.38166e8i	0.349146	+	0.604739i	−0.636952	+	0.770904i	$0.719805\pi$
$734$	−2.80698e8	+	1.62061e8i	−0.709824	+	0.409817i
$735$		0			0
$736$	9.24524e7	−	1.60132e8i	0.231891	−	0.401648i
$737$		−	8.40352e8i		−	2.09922i
$738$		0			0
$739$	−5.77851e8			−1.43180			−0.715901	−	0.698202i	$-0.753984\pi$
$739$	−5.77851e8			−1.43180			−0.715901	+	0.698202i	$0.753984\pi$
$740$	8.85838e7	+	5.11439e7i	0.218604	+	0.126211i
$741$		0			0
$742$	−7.41287e7	−	1.28395e8i	−0.181457	−	0.314294i
$743$	2.89368e8	−	1.67067e8i	0.705479	−	0.407308i	−0.103906	−	0.994587i	$-0.533134\pi$
$743$	2.89368e8	−	1.67067e8i	0.705479	−	0.407308i	0.809385	+	0.587279i	$0.199801\pi$
$744$		0			0
$745$	4.92066e8	−	8.52283e8i	1.19002	−	2.06118i
$746$		−	2.79889e8i		−	0.674171i
$747$		0			0
$748$	−7.96558e8			−1.90332
$749$	1.68065e8	+	9.70323e7i	0.399974	+	0.230925i
$750$		0			0
$751$	2.39478e7	+	4.14788e7i	0.0565387	+	0.0979280i	0.892909	−	0.450236i	$-0.148660\pi$
$751$	2.39478e7	+	4.14788e7i	0.0565387	+	0.0979280i	−0.836371	+	0.548164i	$0.815327\pi$
$752$	8.11192e7	−	4.68342e7i	0.190752	−	0.110131i
$753$		0			0
$754$	−1.10909e7	+	1.92100e7i	−0.0258734	+	0.0448140i
$755$		−	1.52202e7i		−	0.0353654i
$756$		0			0
$757$	2.50721e8			0.577967			0.288983	−	0.957334i	$-0.406683\pi$
$757$	2.50721e8			0.577967			0.288983	+	0.957334i	$0.406683\pi$
$758$	−8.79583e8	−	5.07828e8i	−2.01962	−	1.16603i
$759$		0			0
$760$	3.64454e7	+	6.31253e7i	0.0830237	+	0.143801i
$761$	−5.59560e8	+	3.23062e8i	−1.26967	+	0.733047i	−0.974926	−	0.222528i	$-0.928569\pi$
$761$	−5.59560e8	+	3.23062e8i	−1.26967	+	0.733047i	−0.294748	+	0.955575i	$0.595236\pi$
$762$		0			0
$763$	1.70092e8	−	2.94608e8i	0.382922	−	0.663241i
$764$			3.40882e8i			0.764406i
$765$		0			0
$766$	−6.76207e8			−1.50450
$767$	−9.80916e7	−	5.66332e7i	−0.217393	−	0.125512i
$768$		0			0
$769$	−3.50532e8	−	6.07140e8i	−0.770813	−	1.33509i	−0.937118	−	0.349013i	$-0.886517\pi$
$769$	−3.50532e8	−	6.07140e8i	−0.770813	−	1.33509i	0.166305	−	0.986074i	$-0.446816\pi$
$770$	5.55011e8	−	3.20436e8i	1.21571	−	0.701889i
$771$		0			0
$772$	6.20486e6	−	1.07471e7i	0.0134859	−	0.0233583i
$773$			5.51419e8i			1.19383i	0.802303	+	0.596917i	$0.203608\pi$
$773$			5.51419e8i			1.19383i	−0.802303	+	0.596917i	$0.796392\pi$
$774$		0			0
$775$	−7.76947e8			−1.66912
$776$	2.35091e8	+	1.35730e8i	0.503097	+	0.290463i
$777$		0			0
$778$	5.75096e7	+	9.96096e7i	0.122124	+	0.211525i
$779$	−7.51269e7	+	4.33745e7i	−0.158922	+	0.0917535i
$780$		0			0
$781$	−1.31417e8	+	2.27620e8i	−0.275866	+	0.477813i
$782$		−	2.76170e8i		−	0.577506i
$783$		0			0
$784$	1.87106e8			0.388276
$785$	−1.12078e9	−	6.47081e8i	−2.31692	−	1.33767i
$786$		0			0
$787$	3.32219e8	+	5.75420e8i	0.681554	+	1.18049i	0.974507	+	0.224359i	$0.0720289\pi$
$787$	3.32219e8	+	5.75420e8i	0.681554	+	1.18049i	−0.292952	+	0.956127i	$0.594638\pi$
$788$	−1.21009e8	+	6.98646e7i	−0.247308	+	0.142784i
$789$		0			0
$790$	−3.26607e8	+	5.65699e8i	−0.662436	+	1.14737i
$791$		−	3.84910e8i		−	0.777732i
$792$		0			0
$793$	−2.02119e8			−0.405309
$794$	−2.93963e8	−	1.69719e8i	−0.587260	−	0.339055i
$795$		0			0
$796$	−2.77527e8	−	4.80690e8i	−0.550257	−	0.953073i
$797$	−2.54833e8	+	1.47128e8i	−0.503361	+	0.290616i	−0.730101	−	0.683340i	$-0.760527\pi$
$797$	−2.54833e8	+	1.47128e8i	−0.503361	+	0.290616i	0.226739	+	0.973956i	$0.427194\pi$
$798$		0			0
$799$	1.19649e8	−	2.07239e8i	0.234568	−	0.406284i
$800$			7.65150e8i			1.49443i
$801$		0			0
$802$	7.92061e8			1.53545
$803$	−2.66159e7	−	1.53667e7i	−0.0514038	−	0.0296780i
$804$		0			0
$805$	6.40452e7	+	1.10930e8i	0.122772	+	0.212647i
$806$	2.64213e8	−	1.52543e8i	0.504602	−	0.291332i
$807$		0			0
$808$	−8.34547e7	+	1.44548e8i	−0.158204	+	0.274017i
$809$			1.97574e8i			0.373151i	0.982441	+	0.186575i	$0.0597389\pi$
$809$			1.97574e8i			0.373151i	−0.982441	+	0.186575i	$0.940261\pi$
$810$		0			0
$811$	4.90274e8			0.919129			0.459565	−	0.888144i	$-0.348005\pi$
$811$	4.90274e8			0.919129			0.459565	+	0.888144i	$0.348005\pi$
$812$	4.06547e7	+	2.34720e7i	0.0759351	+	0.0438412i
$813$		0			0
$814$	6.81823e7	+	1.18095e8i	0.126415	+	0.218957i
$815$	5.36691e8	−	3.09859e8i	0.991407	−	0.572389i
$816$		0			0
$817$	1.60485e7	−	2.77968e7i	0.0294285	−	0.0509717i
$818$			5.36514e8i			0.980214i
$819$		0			0
$820$	9.75191e8			1.76868
$821$	9.32855e8	+	5.38584e8i	1.68572	+	0.973249i	0.957734	+	0.287655i	$0.0928756\pi$
$821$	9.32855e8	+	5.38584e8i	1.68572	+	0.973249i	0.727983	+	0.685595i	$0.240458\pi$
$822$		0			0
$823$	−2.62590e8	−	4.54820e8i	−0.471063	−	0.815906i	0.528389	−	0.849002i	$-0.322796\pi$
$823$	−2.62590e8	−	4.54820e8i	−0.471063	−	0.815906i	−0.999452	+	0.0330969i	$0.989463\pi$
$824$	3.08323e8	−	1.78010e8i	0.551092	−	0.318173i
$825$		0			0
$826$	−2.07906e8	+	3.60104e8i	−0.368916	+	0.638981i
$827$		−	8.02753e8i		−	1.41927i	−0.704569	−	0.709636i	$-0.748860\pi$
$827$		−	8.02753e8i		−	1.41927i	0.704569	−	0.709636i	$-0.251140\pi$
$828$		0			0
$829$	−2.14734e8			−0.376909			−0.188455	−	0.982082i	$-0.560348\pi$
$829$	−2.14734e8			−0.376909			−0.188455	+	0.982082i	$0.560348\pi$
$830$	7.96820e8	+	4.60044e8i	1.39356	+	0.804573i
$831$		0			0
$832$	−1.13031e8	−	1.95775e8i	−0.196258	−	0.339928i
$833$	4.13967e8	−	2.39004e8i	0.716195	−	0.413495i
$834$		0			0
$835$	2.45347e8	−	4.24954e8i	0.421426	−	0.729932i
$836$			2.11119e8i			0.361334i
$837$		0			0
$838$	9.11222e8			1.54843
$839$	5.95132e8	+	3.43600e8i	1.00769	+	0.581791i	0.910515	−	0.413476i	$-0.135685\pi$
$839$	5.95132e8	+	3.43600e8i	1.00769	+	0.581791i	0.0971767	+	0.995267i	$0.469019\pi$
$840$		0			0
$841$	−2.92187e8	−	5.06083e8i	−0.491217	−	0.850813i
$842$	−7.00432e8	+	4.04395e8i	−1.17336	+	0.677438i
$843$		0			0
$844$	−3.52191e8	+	6.10013e8i	−0.585802	+	1.01464i
$845$		−	8.21477e8i		−	1.36152i
$846$		0			0
$847$	1.97200e8			0.324531
$848$	1.30458e8	+	7.53198e7i	0.213935	+	0.123516i
$849$		0			0
$850$	5.71406e8	+	9.89705e8i	0.930440	+	1.61157i
$851$	−2.36036e7	+	1.36275e7i	−0.0382992	+	0.0221120i
$852$		0			0
$853$	−9.41008e7	+	1.62987e8i	−0.151616	+	0.262607i	−0.931822	−	0.362916i	$-0.881781\pi$
$853$	−9.41008e7	+	1.62987e8i	−0.151616	+	0.262607i	0.780205	+	0.625523i	$0.215114\pi$
$854$			7.41997e8i			1.19132i
$855$		0			0
$856$	3.30789e8			0.527388
$857$	−1.45720e8	−	8.41315e7i	−0.231514	−	0.133665i	0.379756	−	0.925087i	$-0.376008\pi$
$857$	−1.45720e8	−	8.41315e7i	−0.231514	−	0.133665i	−0.611270	+	0.791422i	$0.709341\pi$
$858$		0			0
$859$	4.65765e8	+	8.06728e8i	0.734831	+	1.27276i	0.954798	+	0.297257i	$0.0960717\pi$
$859$	4.65765e8	+	8.06728e8i	0.734831	+	1.27276i	−0.219967	+	0.975507i	$0.570595\pi$
$860$	−3.12479e8	+	1.80410e8i	−0.491275	+	0.283638i
$861$		0			0
$862$	3.40004e8	−	5.88905e8i	0.530839	−	0.919440i
$863$			5.91095e8i			0.919656i	0.888008	+	0.459828i	$0.152089\pi$
$863$			5.91095e8i			0.919656i	−0.888008	+	0.459828i	$0.847911\pi$
$864$		0			0
$865$	−7.73969e8			−1.19585
$866$	−5.49781e8	−	3.17416e8i	−0.846517	−	0.488737i
$867$		0			0
$868$	−3.22832e8	−	5.59161e8i	−0.493648	−	0.855023i
$869$	−4.34761e8	+	2.51009e8i	−0.662508	+	0.382499i
$870$		0			0
$871$	1.36461e8	−	2.36357e8i	0.206515	−	0.357695i
$872$		−	5.79855e8i		−	0.874521i
$873$		0			0
$874$	−7.31958e7			−0.109636
$875$	−4.86163e7	−	2.80686e7i	−0.0725701	−	0.0418984i
$876$		0			0
$877$	3.18604e8	+	5.51838e8i	0.472337	+	0.818111i	0.999499	−	0.0316534i	$-0.0100773\pi$
$877$	3.18604e8	+	5.51838e8i	0.472337	+	0.818111i	−0.527162	+	0.849765i	$0.676744\pi$
$878$	−1.53500e9	+	8.86232e8i	−2.26790	+	1.30937i
$879$		0			0
$880$	−3.25584e8	+	5.63929e8i	−0.477766	+	0.827516i
$881$		−	2.46549e8i		−	0.360558i	−0.983615	−	0.180279i	$-0.942300\pi$
$881$		−	2.46549e8i		−	0.360558i	0.983615	−	0.180279i	$-0.0577001\pi$
$882$		0			0
$883$	−5.98776e7			−0.0869725			−0.0434863	−	0.999054i	$-0.513846\pi$
$883$	−5.98776e7			−0.0869725			−0.0434863	+	0.999054i	$0.513846\pi$
$884$	−2.24039e8	−	1.29349e8i	−0.324315	−	0.187243i
$885$		0			0
$886$	−8.49542e8	−	1.47145e9i	−1.22147	−	2.11565i
$887$	−1.40016e8	+	8.08385e7i	−0.200636	+	0.115837i	−0.596952	−	0.802277i	$-0.703622\pi$
$887$	−1.40016e8	+	8.08385e7i	−0.200636	+	0.115837i	0.396316	+	0.918114i	$0.370288\pi$
$888$		0			0
$889$	−2.18874e8	+	3.79100e8i	−0.311521	+	0.539571i
$890$		−	1.69555e9i		−	2.40514i
$891$		0			0
$892$	−1.46084e9			−2.05830
$893$	−5.49263e7	−	3.17117e7i	−0.0771304	−	0.0445313i
$894$		0			0
$895$	−3.79510e8	−	6.57331e8i	−0.529364	−	0.916886i
$896$	−3.14156e8	+	1.81378e8i	−0.436739	+	0.252151i
$897$		0			0
$898$	5.34968e8	−	9.26592e8i	0.738752	−	1.27956i
$899$		−	1.43708e8i		−	0.197788i
$900$		0			0
$901$	3.84846e8			0.526153
$902$	1.12590e9	+	6.50037e8i	1.53419	+	0.885764i
$903$		0			0
$904$	−3.28046e8	−	5.68192e8i	−0.444047	−	0.769113i
$905$	5.49142e8	−	3.17047e8i	0.740864	−	0.427738i
$906$		0			0
$907$	1.28962e8	−	2.23369e8i	0.172839	−	0.299365i	−0.766573	−	0.642158i	$-0.778039\pi$
$907$	1.28962e8	−	2.23369e8i	0.172839	−	0.299365i	0.939411	+	0.342792i	$0.111373\pi$
$908$			4.21008e7i			0.0562384i
$909$		0			0
$910$	2.08136e8			0.276199
$911$	1.36279e8	+	7.86807e7i	0.180249	+	0.104067i	0.587410	−	0.809290i	$-0.300148\pi$
$911$	1.36279e8	+	7.86807e7i	0.180249	+	0.104067i	−0.407160	+	0.913357i	$0.633481\pi$
$912$		0			0
$913$	3.53561e8	+	6.12386e8i	0.464571	+	0.804661i
$914$	1.14888e9	−	6.63306e8i	1.50465	−	0.868711i
$915$		0			0
$916$	−5.50689e8	+	9.53821e8i	−0.716506	+	1.24102i
$917$			5.84312e8i			0.757769i
$918$		0			0
$919$	−4.42108e8			−0.569616			−0.284808	−	0.958585i	$-0.591930\pi$
$919$	−4.42108e8			−0.569616			−0.284808	+	0.958585i	$0.591930\pi$
$920$	1.89083e8	+	1.09167e8i	0.242823	+	0.140194i
$921$		0			0
$922$	6.42649e8	+	1.11310e9i	0.819939	+	1.42018i
$923$	−7.39243e7	+	4.26802e7i	−0.0940118	+	0.0542777i
$924$		0			0
$925$	5.63918e7	−	9.76735e7i	0.0712510	−	0.123410i
$926$		−	1.73290e9i		−	2.18243i
$927$		0			0
$928$	−1.41525e8			−0.177089
$929$	−2.17771e8	−	1.25730e8i	−0.271614	−	0.156817i	0.358007	−	0.933719i	$-0.383456\pi$
$929$	−2.17771e8	−	1.25730e8i	−0.271614	−	0.156817i	−0.629621	+	0.776902i	$0.716790\pi$
$930$		0			0
$931$	−6.33454e7	−	1.09717e8i	−0.0784993	−	0.135965i
$932$	−6.88858e8	+	3.97712e8i	−0.850907	+	0.491271i
$933$		0			0
$934$	4.33660e8	−	7.51122e8i	0.532242	−	0.921870i
$935$			1.66357e9i			2.03519i
$936$		0			0
$937$	−7.37359e8			−0.896314			−0.448157	−	0.893955i	$-0.647920\pi$
$937$	−7.37359e8			−0.896314			−0.448157	+	0.893955i	$0.647920\pi$
$938$	−8.67689e8	−	5.00960e8i	−1.05137	−	0.607008i
$939$		0			0
$940$	3.56488e8	+	6.17455e8i	0.429201	+	0.743398i
$941$	8.22533e8	−	4.74890e8i	0.987153	−	0.569933i	0.0827308	−	0.996572i	$-0.473636\pi$
$941$	8.22533e8	−	4.74890e8i	0.987153	−	0.569933i	0.904422	+	0.426639i	$0.140303\pi$
$942$		0			0
$943$	−1.29922e8	+	2.25032e8i	−0.154935	+	0.268355i
$944$		−	4.22494e8i		−	0.502232i
$945$		0			0
$946$	−4.81025e8			−0.568191
$947$	3.88674e7	+	2.24401e7i	0.0457652	+	0.0264226i	0.522708	−	0.852512i	$-0.324922\pi$
$947$	3.88674e7	+	2.24401e7i	0.0457652	+	0.0264226i	−0.476943	+	0.878934i	$0.658255\pi$
$948$		0			0
$949$	−4.99065e6	−	8.64406e6i	−0.00583927	−	0.0101139i
$950$	2.62310e8	−	1.51445e8i	0.305946	−	0.176638i
$951$		0			0
$952$	−1.26000e8	+	2.18238e8i	−0.146036	+	0.252942i
$953$		−	4.94928e8i		−	0.571826i	−0.958256	−	0.285913i	$-0.907703\pi$
$953$		−	4.94928e8i		−	0.571826i	0.958256	−	0.285913i	$-0.0922968\pi$
$954$		0			0
$955$	7.11913e8			0.817367
$956$	−8.29059e8	−	4.78657e8i	−0.948881	−	0.547837i
$957$		0			0
$958$	7.14421e8	+	1.23741e9i	0.812564	+	1.40740i
$959$	7.26526e8	−	4.19460e8i	0.823750	−	0.475592i
$960$		0			0
$961$	−5.44519e8	+	9.43135e8i	−0.613540	+	1.06268i
$962$			4.42871e7i			0.0497453i
$963$		0			0
$964$	1.31937e9			1.47277
$965$	−2.24448e7	−	1.29585e7i	−0.0249766	−	0.0144203i
$966$		0			0
$967$	−2.98641e8	−	5.17262e8i	−0.330271	−	0.572046i	0.652294	−	0.757966i	$-0.273807\pi$
$967$	−2.98641e8	−	5.17262e8i	−0.330271	−	0.572046i	−0.982565	+	0.185920i	$0.940473\pi$
$968$	2.91100e8	−	1.68067e8i	0.320934	−	0.185291i
$969$		0			0
$970$	1.06829e9	−	1.85033e9i	1.17051	−	2.02737i
$971$			7.35847e8i			0.803767i	0.915691	+	0.401883i	$0.131644\pi$
$971$			7.35847e8i			0.803767i	−0.915691	+	0.401883i	$0.868356\pi$
$972$		0			0
$973$	−1.52724e8			−0.165794
$974$	5.05150e8	+	2.91648e8i	0.546692	+	0.315633i
$975$		0			0
$976$	−3.76960e8	−	6.52914e8i	−0.405458	−	0.702274i
$977$	−1.21385e9	+	7.00818e8i	−1.30161	+	0.751487i	−0.980681	−	0.195615i	$-0.937330\pi$
$977$	−1.21385e9	+	7.00818e8i	−1.30161	+	0.751487i	−0.320933	+	0.947102i	$0.603996\pi$
$978$		0			0
$979$	6.51547e8	−	1.12851e9i	0.694381	−	1.20270i
$980$			1.42420e9i			1.51318i
$981$		0			0
$982$	−2.11642e9			−2.23494
$983$	−1.14773e9	−	6.62641e8i	−1.20831	−	0.697618i	−0.245920	−	0.969290i	$-0.579090\pi$
$983$	−1.14773e9	−	6.62641e8i	−1.20831	−	0.697618i	−0.962390	+	0.271672i	$0.912424\pi$
$984$		0			0
$985$	1.45908e8	+	2.52721e8i	0.152676	+	0.264443i
$986$	−1.83060e8	+	1.05690e8i	−0.190969	+	0.110256i
$987$		0			0
$988$	−3.42826e7	+	5.93791e7i	−0.0355469	+	0.0615691i
$989$		−	9.61421e7i		−	0.0993859i
$990$		0			0
$991$	1.70571e9			1.75261			0.876303	−	0.481760i	$-0.160002\pi$
$991$	1.70571e9			1.75261			0.876303	+	0.481760i	$0.160002\pi$
$992$	1.68574e9	+	9.73264e8i	1.72686	+	0.997001i
$993$		0			0
$994$	1.56683e8	+	2.71384e8i	0.159538	+	0.276328i
$995$	−1.00390e9	+	5.79599e8i	−1.01911	+	0.588381i
$996$		0			0
$997$	−5.59983e7	+	9.69920e7i	−0.0565054	+	0.0978702i	−0.892894	−	0.450266i	$-0.851329\pi$
$997$	−5.59983e7	+	9.69920e7i	−0.0565054	+	0.0978702i	0.836389	+	0.548136i	$0.184662\pi$
$998$			1.02156e9i			1.02772i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	27.7.d.a.8.1		10
3.2	odd	2		9.7.d.a.2.5	✓	10
4.3	odd	2		432.7.q.a.305.5		10
9.2	odd	6		81.7.b.a.80.2		10
9.4	even	3		9.7.d.a.5.5	yes	10
9.5	odd	6	inner	27.7.d.a.17.1		10
9.7	even	3		81.7.b.a.80.9		10
12.11	even	2		144.7.q.a.65.3		10
36.23	even	6		432.7.q.a.17.5		10
36.31	odd	6		144.7.q.a.113.3		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
9.7.d.a.2.5	✓	10	3.2	odd	2
9.7.d.a.5.5	yes	10	9.4	even	3
27.7.d.a.8.1		10	1.1	even	1	trivial
27.7.d.a.17.1		10	9.5	odd	6	inner
81.7.b.a.80.2		10	9.2	odd	6
81.7.b.a.80.9		10	9.7	even	3
144.7.q.a.65.3		10	12.11	even	2
144.7.q.a.113.3		10	36.31	odd	6
432.7.q.a.17.5		10	36.23	even	6
432.7.q.a.305.5		10	4.3	odd	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:	\( N \)	\(=\)	\( 27 = 3^{3} \)
Weight:	\( k \)	\(=\)	\( 7 \)
Character orbit:	\([\chi]\)	\(=\)	27.d (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-10.6460 - 6.14646i) q^{2} +(43.5579 + 75.4444i) q^{4} +(157.562 - 90.9682i) q^{5} +(83.3541 - 144.373i) q^{7} -284.159i q^{8} +O(q^{10})\)	\(q+(-10.6460 - 6.14646i) q^{2} +(43.5579 + 75.4444i) q^{4} +(157.562 - 90.9682i) q^{5} +(83.3541 - 144.373i) q^{7} -284.159i q^{8} -2236.53 q^{10} +(-1488.57 - 859.428i) q^{11} +(-279.116 - 483.444i) q^{13} +(-1774.77 + 1024.66i) q^{14} +(1041.13 - 1803.29i) q^{16} -5319.63i q^{17} -1409.91 q^{19} +(13726.1 + 7924.76i) q^{20} +(10564.9 + 18298.9i) q^{22} +(-3657.39 + 2111.59i) q^{23} +(8737.93 - 15134.5i) q^{25} +6862.31i q^{26} +14522.9 q^{28} +(2799.35 + 1616.21i) q^{29} +(-22229.2 - 38502.0i) q^{31} +(-37917.4 + 21891.6i) q^{32} +(-32696.9 + 56632.7i) q^{34} -30330.3i q^{35} +6453.68 q^{37} +(15009.9 + 8665.95i) q^{38} +(-25849.5 - 44772.6i) q^{40} +(53284.9 - 30764.1i) q^{41} +(-11382.6 + 19715.3i) q^{43} -149739. i q^{44} +51915.3 q^{46} +(38957.3 + 22492.0i) q^{47} +(44928.7 + 77818.8i) q^{49} +(-186048. + 107415. i) q^{50} +(24315.4 - 42115.6i) q^{52} +72344.4i q^{53} -312722. q^{55} +(-41025.1 - 23685.9i) q^{56} +(-19867.9 - 34412.2i) q^{58} +(175718. - 101451. i) q^{59} +(181034. - 313560. i) q^{61} +546522. i q^{62} +404959. q^{64} +(-87956.1 - 50781.5i) q^{65} +(244451. + 423401. i) q^{67} +(401337. - 231712. i) q^{68} +(-186424. + 322895. i) q^{70} -152912. i q^{71} +17880.2 q^{73} +(-68705.7 - 39667.3i) q^{74} +(-61412.6 - 106370. i) q^{76} +(-248157. + 143274. i) q^{77} +(146033. - 252936. i) q^{79} -378839. i q^{80} -756360. q^{82} +(-356275. - 205696. i) q^{83} +(-483917. - 838170. i) q^{85} +(242359. - 139926. i) q^{86} +(-244215. + 422992. i) q^{88} +758118. i q^{89} -93062.0 q^{91} +(-318616. - 183953. i) q^{92} +(-276492. - 478899. i) q^{94} +(-222148. + 128257. i) q^{95} +(-477655. + 827322. i) q^{97} -1.10461e6i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q + 3 q^{2} + 127 q^{4} + 219 q^{5} - 121 q^{7}+O(q^{10}) \) 10 * q + 3 * q^2 + 127 * q^4 + 219 * q^5 - 121 * q^7	\( 10 q + 3 q^{2} + 127 q^{4} + 219 q^{5} - 121 q^{7} - 132 q^{10} - 483 q^{11} - 841 q^{13} - 12174 q^{14} - 1985 q^{16} + 6176 q^{19} + 63186 q^{20} + 3471 q^{22} - 53565 q^{23} + 8452 q^{25} - 22660 q^{28} + 80679 q^{29} - 24601 q^{31} - 218295 q^{32} + 7425 q^{34} + 12764 q^{37} + 371877 q^{38} + 54150 q^{40} - 232251 q^{41} - 93271 q^{43} + 112512 q^{46} + 142887 q^{47} + 86238 q^{49} - 318459 q^{50} + 186920 q^{52} - 419982 q^{55} - 342546 q^{56} - 380658 q^{58} + 995061 q^{59} - 59305 q^{61} + 403066 q^{64} - 1642029 q^{65} + 158513 q^{67} + 1693791 q^{68} - 304788 q^{70} + 933896 q^{73} - 595182 q^{74} + 666641 q^{76} + 2198883 q^{77} + 468707 q^{79} - 2038470 q^{82} - 3008337 q^{83} - 1189944 q^{85} - 1905549 q^{86} - 349773 q^{88} - 211778 q^{91} + 973788 q^{92} + 809124 q^{94} + 2562954 q^{95} + 336029 q^{97}+O(q^{100}) \) 10 * q + 3 * q^2 + 127 * q^4 + 219 * q^5 - 121 * q^7 - 132 * q^10 - 483 * q^11 - 841 * q^13 - 12174 * q^14 - 1985 * q^16 + 6176 * q^19 + 63186 * q^20 + 3471 * q^22 - 53565 * q^23 + 8452 * q^25 - 22660 * q^28 + 80679 * q^29 - 24601 * q^31 - 218295 * q^32 + 7425 * q^34 + 12764 * q^37 + 371877 * q^38 + 54150 * q^40 - 232251 * q^41 - 93271 * q^43 + 112512 * q^46 + 142887 * q^47 + 86238 * q^49 - 318459 * q^50 + 186920 * q^52 - 419982 * q^55 - 342546 * q^56 - 380658 * q^58 + 995061 * q^59 - 59305 * q^61 + 403066 * q^64 - 1642029 * q^65 + 158513 * q^67 + 1693791 * q^68 - 304788 * q^70 + 933896 * q^73 - 595182 * q^74 + 666641 * q^76 + 2198883 * q^77 + 468707 * q^79 - 2038470 * q^82 - 3008337 * q^83 - 1189944 * q^85 - 1905549 * q^86 - 349773 * q^88 - 211778 * q^91 + 973788 * q^92 + 809124 * q^94 + 2562954 * q^95 + 336029 * q^97

Introduction

L-functions

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