LMFDB - Embedded newform 27.12.c.a.10.7

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [27,12,Mod(10,27)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("27.10"); S:= CuspForms(chi, 12); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(27, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([2])) N = Newforms(chi, 12, names="a")

Level:	$ N $	$=$	$ 27 = 3^{3} $
Weight:	$ k $	$=$	$ 12 $
Character orbit:	$[\chi]$	$=$	27.c (of order $3$, degree $2$, not minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$20.7452658751$
Analytic rank:	$0$
Dimension:	$20$
Relative dimension:	$10$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} + \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} + 9863 x^{18} + 40416552 x^{16} + 89424581388 x^{14} + 116167273852206 x^{12} + \cdots + 59\!\cdots\!24 $ x^20 + 9863x^18 + 40416552x^16 + 89424581388x^14 + 116167273852206x^12 + 90155066123992770x^10 + 40615438428348034476x^8 + 9750032167348768665084x^6 + 1016547159346572680888121x^4 + 22772285013675084656406191*x^2 + 59348899944549565171293124
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{24}\cdot 3^{65} $
Twist minimal:	no (minimal twist has level 9)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			10.7
Root			$-20.7390i$ of defining polynomial
Character	$\chi$	$=$	27.10
Dual form			27.12.c.a.19.7

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(19.4605 + 33.7066i) q^{2} +(266.578 - 461.726i) q^{4} +(-1691.47 + 2929.71i) q^{5} +(-16014.5 - 27738.0i) q^{7} +100461. q^{8} -131667. q^{10} +(336053. + 582060. i) q^{11} +(847942. - 1.46868e6i) q^{13} +(623302. - 1.07959e6i) q^{14} +(1.40907e6 + 2.44059e6i) q^{16} +5.41320e6 q^{17} +8.84256e6 q^{19} +(901815. + 1.56199e6i) q^{20} +(-1.30795e7 + 2.26544e7i) q^{22} +(-2.61299e6 + 4.52583e6i) q^{23} +(1.86919e7 + 3.23754e7i) q^{25} +6.60055e7 q^{26} -1.70765e7 q^{28} +(3.61628e7 + 6.26357e7i) q^{29} +(-1.03012e8 + 1.78423e8i) q^{31} +(4.80297e7 - 8.31898e7i) q^{32} +(1.05344e8 + 1.82461e8i) q^{34} +1.08352e8 q^{35} +7.22103e8 q^{37} +(1.72081e8 + 2.98053e8i) q^{38} +(-1.69927e8 + 2.94322e8i) q^{40} +(2.14524e8 - 3.71567e8i) q^{41} +(-6.85488e8 - 1.18730e9i) q^{43} +3.58337e8 q^{44} -2.03400e8 q^{46} +(-3.70158e7 - 6.41133e7i) q^{47} +(4.75733e8 - 8.23993e8i) q^{49} +(-7.27509e8 + 1.26008e9i) q^{50} +(-4.52085e8 - 7.83034e8i) q^{52} -5.54718e9 q^{53} -2.27369e9 q^{55} +(-1.60884e9 - 2.78659e9i) q^{56} +(-1.40749e9 + 2.43785e9i) q^{58} +(1.80632e9 - 3.12864e9i) q^{59} +(-3.08036e9 - 5.33534e9i) q^{61} -8.01870e9 q^{62} +9.51029e9 q^{64} +(2.86853e9 + 4.96845e9i) q^{65} +(3.11581e9 - 5.39674e9i) q^{67} +(1.44304e9 - 2.49942e9i) q^{68} +(2.10859e9 + 3.65218e9i) q^{70} +1.73266e10 q^{71} -1.89972e10 q^{73} +(1.40525e10 + 2.43396e10i) q^{74} +(2.35723e9 - 4.08284e9i) q^{76} +(1.07635e10 - 1.86428e10i) q^{77} +(1.79243e10 + 3.10458e10i) q^{79} -9.53361e9 q^{80} +1.66990e10 q^{82} +(1.24856e10 + 2.16257e10i) q^{83} +(-9.15626e9 + 1.58591e10i) q^{85} +(2.66799e10 - 4.62109e10i) q^{86} +(3.37602e10 + 5.84744e10i) q^{88} -7.94245e10 q^{89} -5.43176e10 q^{91} +(1.39313e9 + 2.41297e9i) q^{92} +(1.44069e9 - 2.49536e9i) q^{94} +(-1.49569e10 + 2.59061e10i) q^{95} +(-3.32985e10 - 5.76747e10i) q^{97} +3.70320e10 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q + 33 q^{2} - 9217 q^{4} + 7230 q^{5} + 8512 q^{7} + 29118 q^{8} + 4092 q^{10} + 112776 q^{11} + 279706 q^{13} + 3901584 q^{14} - 7342081 q^{16} - 27765792 q^{17} + 7029400 q^{19} + 34163508 q^{20}+ \cdots - 1310123604078 q^{98}+O(q^{100}) $ 20 * q + 33 * q^2 - 9217 * q^4 + 7230 * q^5 + 8512 * q^7 + 29118 * q^8 + 4092 * q^10 + 112776 * q^11 + 279706 * q^13 + 3901584 * q^14 - 7342081 * q^16 - 27765792 * q^17 + 7029400 * q^19 + 34163508 * q^20 + 2274591 * q^22 + 69371616 * q^23 - 45286204 * q^25 - 481929144 * q^26 - 61345796 * q^28 + 25437246 * q^29 + 114575368 * q^31 - 80396559 * q^32 - 243855063 * q^34 + 178147464 * q^35 - 134218328 * q^37 - 489799995 * q^38 + 107425416 * q^40 - 331873026 * q^41 - 1118847584 * q^43 - 278477274 * q^44 + 2882537592 * q^46 + 1469650704 * q^47 - 3553434720 * q^49 + 6643771701 * q^50 + 3632448874 * q^52 - 14914261944 * q^53 + 4981449984 * q^55 + 27669139026 * q^56 - 1387480560 * q^58 + 26505032592 * q^59 + 990409066 * q^61 - 91044996180 * q^62 - 7516709566 * q^64 + 39045315390 * q^65 + 6557215720 * q^67 + 77299152993 * q^68 - 785437278 * q^70 - 122053719744 * q^71 - 12612893936 * q^73 + 109519086216 * q^74 + 14574055597 * q^76 + 88616208018 * q^77 - 7621233248 * q^79 - 399166683072 * q^80 - 59168477334 * q^82 + 99007044180 * q^83 + 12911595156 * q^85 + 214357830519 * q^86 - 54423523605 * q^88 - 476597704824 * q^89 + 138211652216 * q^91 + 461776423998 * q^92 + 13393667064 * q^94 + 418952909328 * q^95 + 123483551938 * q^97 - 1310123604078 * q^98

Character values

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

$n$	$2$
$\chi(n)$	$e\left(\frac{1}{3}\right)$

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 $

$2$	19.4605	+	33.7066i	0.430020	+	0.744817i	0.996875	−	0.0790010i	$-0.0251730\pi$
$2$	19.4605	+	33.7066i	0.430020	+	0.744817i	−0.566854	+	0.823818i	$0.691840\pi$
$3$		0			0
$3$		0			0
$4$	266.578	−	461.726i	0.130165	−	0.225452i
$5$	−1691.47	+	2929.71i	−0.242063	+	0.419266i	−0.961302	−	0.275497i	$-0.911157\pi$
$5$	−1691.47	+	2929.71i	−0.242063	+	0.419266i	0.719239	+	0.694763i	$0.244491\pi$
$6$		0			0
$7$	−16014.5	−	27738.0i	−0.360143	−	0.623786i	0.627841	−	0.778342i	$-0.283939\pi$
$7$	−16014.5	−	27738.0i	−0.360143	−	0.623786i	−0.987984	+	0.154556i	$0.950605\pi$
$8$	100461.			1.08394
$9$		0			0
$10$	−131667.			−0.416368
$11$	336053.	+	582060.i	0.629140	+	1.08970i	0.987725	+	0.156206i	$0.0499263\pi$
$11$	336053.	+	582060.i	0.629140	+	1.08970i	−0.358584	+	0.933497i	$0.616740\pi$
$12$		0			0
$13$	847942.	−	1.46868e6i	0.633400	−	1.09708i	−0.353452	−	0.935453i	$-0.614992\pi$
$13$	847942.	−	1.46868e6i	0.633400	−	1.09708i	0.986852	−	0.161628i	$-0.0516744\pi$
$14$	623302.	−	1.07959e6i	0.309738	−	0.536481i
$15$		0			0
$16$	1.40907e6	+	2.44059e6i	0.335949	+	0.581881i
$17$	5.41320e6			0.924667			0.462333	−	0.886706i	$-0.347012\pi$
$17$	5.41320e6			0.924667			0.462333	+	0.886706i	$0.347012\pi$
$18$		0			0
$19$	8.84256e6			0.819282			0.409641	−	0.912247i	$-0.365654\pi$
$19$	8.84256e6			0.819282			0.409641	+	0.912247i	$0.365654\pi$
$20$	901815.	+	1.56199e6i	0.0630163	+	0.109147i
$21$		0			0
$22$	−1.30795e7	+	2.26544e7i	−0.541086	+	0.937189i
$23$	−2.61299e6	+	4.52583e6i	−0.0846515	+	0.146621i	−0.905243	−	0.424895i	$-0.860311\pi$
$23$	−2.61299e6	+	4.52583e6i	−0.0846515	+	0.146621i	0.820591	+	0.571516i	$0.193644\pi$
$24$		0			0
$25$	1.86919e7	+	3.23754e7i	0.382811	+	0.663048i
$26$	6.60055e7			1.08950
$27$		0			0
$28$	−1.70765e7			−0.187512
$29$	3.61628e7	+	6.26357e7i	0.327395	+	0.567065i	0.981994	−	0.188911i	$-0.0604958\pi$
$29$	3.61628e7	+	6.26357e7i	0.327395	+	0.567065i	−0.654599	+	0.755976i	$0.727162\pi$
$30$		0			0
$31$	−1.03012e8	+	1.78423e8i	−0.646250	+	1.11934i	0.337762	+	0.941232i	$0.390330\pi$
$31$	−1.03012e8	+	1.78423e8i	−0.646250	+	1.11934i	−0.984011	+	0.178106i	$0.943003\pi$
$32$	4.80297e7	−	8.31898e7i	0.253037	−	0.438274i
$33$		0			0
$34$	1.05344e8	+	1.82461e8i	0.397626	+	0.688708i
$35$	1.08352e8			0.348709
$36$		0			0
$37$	7.22103e8			1.71194			0.855972	−	0.517021i	$-0.172959\pi$
$37$	7.22103e8			1.71194			0.855972	+	0.517021i	$0.172959\pi$
$38$	1.72081e8	+	2.98053e8i	0.352308	+	0.610215i
$39$		0			0
$40$	−1.69927e8	+	2.94322e8i	−0.262381	+	0.454457i
$41$	2.14524e8	−	3.71567e8i	0.289178	−	0.500871i	−0.684436	−	0.729073i	$-0.739951\pi$
$41$	2.14524e8	−	3.71567e8i	0.289178	−	0.500871i	0.973614	+	0.228202i	$0.0732848\pi$
$42$		0			0
$43$	−6.85488e8	−	1.18730e9i	−0.711088	−	1.23164i	−0.964449	−	0.264269i	$-0.914869\pi$
$43$	−6.85488e8	−	1.18730e9i	−0.711088	−	1.23164i	0.253361	−	0.967372i	$-0.418464\pi$
$44$	3.58337e8			0.327568
$45$		0			0
$46$	−2.03400e8			−0.145608
$47$	−3.70158e7	−	6.41133e7i	−0.0235423	−	0.0407765i	0.854014	−	0.520250i	$-0.174161\pi$
$47$	−3.70158e7	−	6.41133e7i	−0.0235423	−	0.0407765i	−0.877557	+	0.479473i	$0.840828\pi$
$48$		0			0
$49$	4.75733e8	−	8.23993e8i	0.240594	−	0.416721i
$50$	−7.27509e8	+	1.26008e9i	−0.329233	+	0.570248i
$51$		0			0
$52$	−4.52085e8	−	7.83034e8i	−0.164893	−	0.285603i
$53$	−5.54718e9			−1.82203			−0.911014	−	0.412377i	$-0.864699\pi$
$53$	−5.54718e9			−1.82203			−0.911014	+	0.412377i	$0.864699\pi$
$54$		0			0
$55$	−2.27369e9			−0.609167
$56$	−1.60884e9	−	2.78659e9i	−0.390372	−	0.676144i
$57$		0			0
$58$	−1.40749e9	+	2.43785e9i	−0.281573	+	0.487699i
$59$	1.80632e9	−	3.12864e9i	0.328934	−	0.569731i	−0.653367	−	0.757042i	$-0.726644\pi$
$59$	1.80632e9	−	3.12864e9i	0.328934	−	0.569731i	0.982301	+	0.187311i	$0.0599773\pi$
$60$		0			0
$61$	−3.08036e9	−	5.33534e9i	−0.466968	−	0.808813i	0.532320	−	0.846543i	$-0.321320\pi$
$61$	−3.08036e9	−	5.33534e9i	−0.466968	−	0.808813i	−0.999288	+	0.0377307i	$0.987987\pi$
$62$	−8.01870e9			−1.11160
$63$		0			0
$64$	9.51029e9			1.10714
$65$	2.86853e9	+	4.96845e9i	0.306645	+	0.531126i
$66$		0			0
$67$	3.11581e9	−	5.39674e9i	0.281942	−	0.488337i	−0.689921	−	0.723884i	$-0.742355\pi$
$67$	3.11581e9	−	5.39674e9i	0.281942	−	0.488337i	0.971863	+	0.235547i	$0.0756882\pi$
$68$	1.44304e9	−	2.49942e9i	0.120359	−	0.208468i
$69$		0			0
$70$	2.10859e9	+	3.65218e9i	0.149952	+	0.259725i
$71$	1.73266e10			1.13970			0.569852	−	0.821747i	$-0.307001\pi$
$71$	1.73266e10			1.13970			0.569852	+	0.821747i	$0.307001\pi$
$72$		0			0
$73$	−1.89972e10			−1.07254			−0.536270	−	0.844046i	$-0.680167\pi$
$73$	−1.89972e10			−1.07254			−0.536270	+	0.844046i	$0.680167\pi$
$74$	1.40525e10	+	2.43396e10i	0.736171	+	1.27509i
$75$		0			0
$76$	2.35723e9	−	4.08284e9i	0.106642	−	0.184709i
$77$	1.07635e10	−	1.86428e10i	0.453161	−	0.784898i
$78$		0			0
$79$	1.79243e10	+	3.10458e10i	0.655379	+	1.13515i	0.981799	+	0.189925i	$0.0608245\pi$
$79$	1.79243e10	+	3.10458e10i	0.655379	+	1.13515i	−0.326420	+	0.945225i	$0.605842\pi$
$80$	−9.53361e9			−0.325284
$81$		0			0
$82$	1.66990e10			0.497410
$83$	1.24856e10	+	2.16257e10i	0.347921	+	0.602617i	0.985880	−	0.167454i	$-0.0535544\pi$
$83$	1.24856e10	+	2.16257e10i	0.347921	+	0.602617i	−0.637959	+	0.770070i	$0.720221\pi$
$84$		0			0
$85$	−9.15626e9	+	1.58591e10i	−0.223828	+	0.387681i
$86$	2.66799e10	−	4.62109e10i	0.611565	−	1.05926i
$87$		0			0
$88$	3.37602e10	+	5.84744e10i	0.681947	+	1.18117i
$89$	−7.94245e10			−1.50768			−0.753841	−	0.657057i	$-0.771801\pi$
$89$	−7.94245e10			−1.50768			−0.753841	+	0.657057i	$0.771801\pi$
$90$		0			0
$91$	−5.43176e10			−0.912458
$92$	1.39313e9	+	2.41297e9i	0.0220373	+	0.0381698i
$93$		0			0
$94$	1.44069e9	−	2.49536e9i	0.0202474	−	0.0350695i
$95$	−1.49569e10	+	2.59061e10i	−0.198318	+	0.343497i
$96$		0			0
$97$	−3.32985e10	−	5.76747e10i	−0.393713	−	0.681932i	0.599223	−	0.800582i	$-0.295476\pi$
$97$	−3.32985e10	−	5.76747e10i	−0.393713	−	0.681932i	−0.992936	+	0.118651i	$0.962143\pi$
$98$	3.70320e10			0.413841
$99$		0			0
$100$	1.99314e10			0.199314
$101$	6.60489e10	+	1.14400e11i	0.625314	+	1.08308i	0.988480	+	0.151351i	$0.0483624\pi$
$101$	6.60489e10	+	1.14400e11i	0.625314	+	1.08308i	−0.363166	+	0.931724i	$0.618304\pi$
$102$		0			0
$103$	2.87869e10	−	4.98604e10i	0.244675	−	0.423790i	−0.717365	−	0.696698i	$-0.754652\pi$
$103$	2.87869e10	−	4.98604e10i	0.244675	−	0.423790i	0.962040	+	0.272908i	$0.0879853\pi$
$104$	8.51853e10	−	1.47545e11i	0.686564	−	1.18916i
$105$		0			0
$106$	−1.07951e11	−	1.86976e11i	−0.783509	−	1.35708i
$107$	−2.21267e11			−1.52513			−0.762563	−	0.646914i	$-0.776059\pi$
$107$	−2.21267e11			−1.52513			−0.762563	+	0.646914i	$0.776059\pi$
$108$		0			0
$109$	5.26853e10			0.327977			0.163989	−	0.986462i	$-0.447564\pi$
$109$	5.26853e10			0.327977			0.163989	+	0.986462i	$0.447564\pi$
$110$	−4.42471e10	−	7.66383e10i	−0.261954	−	0.453718i
$111$		0			0
$112$	4.51313e10	−	7.81697e10i	0.241980	−	0.419121i
$113$	−1.07929e11	+	1.86938e11i	−0.551070	+	0.954480i	0.447128	+	0.894470i	$0.352447\pi$
$113$	−1.07929e11	+	1.86938e11i	−0.551070	+	0.954480i	−0.998198	+	0.0600105i	$0.980887\pi$
$114$		0			0
$115$	−8.83958e9	−	1.53106e10i	−0.0409820	−	0.0709830i
$116$	3.85607e10			0.170462
$117$		0			0
$118$	1.40608e11			0.565794
$119$	−8.66899e10	−	1.50151e11i	−0.333012	−	0.576794i
$120$		0			0
$121$	−8.32069e10	+	1.44119e11i	−0.291635	+	0.505127i
$122$	1.19891e11	−	2.07657e11i	0.401612	−	0.695612i
$123$		0			0
$124$	5.49216e10	+	9.51271e10i	0.168238	+	0.291397i
$125$	−2.91650e11			−0.854784
$126$		0			0
$127$	−3.30771e11			−0.888398			−0.444199	−	0.895928i	$-0.646512\pi$
$127$	−3.30771e11			−0.888398			−0.444199	+	0.895928i	$0.646512\pi$
$128$	8.67103e10	+	1.50187e11i	0.223057	+	0.386346i
$129$		0			0
$130$	−1.11646e11	+	1.93377e11i	−0.263728	+	0.456790i
$131$	−5.74247e10	+	9.94625e10i	−0.130049	+	0.225251i	−0.923695	−	0.383128i	$-0.874847\pi$
$131$	−5.74247e10	+	9.94625e10i	−0.130049	+	0.225251i	0.793646	+	0.608379i	$0.208180\pi$
$132$		0			0
$133$	−1.41610e11	−	2.45275e11i	−0.295059	−	0.511057i
$134$	2.42541e11			0.484963
$135$		0			0
$136$	5.43817e11			1.00228
$137$	3.02550e11	+	5.24032e11i	0.535592	+	0.927673i	0.999134	+	0.0415983i	$0.0132450\pi$
$137$	3.02550e11	+	5.24032e11i	0.535592	+	0.927673i	−0.463542	+	0.886075i	$0.653422\pi$
$138$		0			0
$139$	−2.69249e11	+	4.66353e11i	−0.440121	+	0.762313i	−0.997698	−	0.0678128i	$-0.978398\pi$
$139$	−2.69249e11	+	4.66353e11i	−0.440121	+	0.762313i	0.557577	+	0.830125i	$0.311731\pi$
$140$	2.88843e10	−	5.00291e10i	0.0453897	−	0.0786173i
$141$		0			0
$142$	3.37184e11	+	5.84020e11i	0.490096	+	0.848871i
$143$	1.13981e12			1.59399
$144$		0			0
$145$	−2.44673e11			−0.317001
$146$	−3.69695e11	−	6.40330e11i	−0.461214	−	0.798846i
$147$		0			0
$148$	1.92497e11	−	3.33414e11i	0.222835	−	0.385962i
$149$	−8.09634e10	+	1.40233e11i	−0.0903159	+	0.156432i	−0.907644	−	0.419741i	$-0.862121\pi$
$149$	−8.09634e10	+	1.40233e11i	−0.0903159	+	0.156432i	0.817328	+	0.576172i	$0.195454\pi$
$150$		0			0
$151$	3.23356e11	+	5.60069e11i	0.335203	+	0.580589i	0.983524	−	0.180779i	$-0.0578618\pi$
$151$	3.23356e11	+	5.60069e11i	0.335203	+	0.580589i	−0.648321	+	0.761367i	$0.724528\pi$
$152$	8.88334e11			0.888048
$153$		0			0
$154$	8.37849e11			0.779474
$155$	−3.48484e11	−	6.03593e11i	−0.312867	−	0.541901i
$156$		0			0
$157$	7.20572e11	−	1.24807e12i	0.602878	−	1.04422i	−0.389505	−	0.921024i	$-0.627354\pi$
$157$	7.20572e11	−	1.24807e12i	0.602878	−	1.04422i	0.992383	−	0.123191i	$-0.0393127\pi$
$158$	−6.97631e11	+	1.20833e12i	−0.563653	+	0.976275i
$159$		0			0
$160$	1.62481e11	+	2.81426e11i	0.122502	+	0.212180i
$161$	1.67383e11			0.121947
$162$		0			0
$163$	−1.78980e12			−1.21835			−0.609175	−	0.793035i	$-0.708499\pi$
$163$	−1.78980e12			−1.21835			−0.609175	+	0.793035i	$0.708499\pi$
$164$	−1.14375e11	−	1.98103e11i	−0.0752816	−	0.130392i
$165$		0			0
$166$	−4.85953e11	+	8.41695e11i	−0.299226	+	0.518275i
$167$	1.42085e11	−	2.46098e11i	0.0846461	−	0.146611i	−0.820594	−	0.571511i	$-0.806357\pi$
$167$	1.42085e11	−	2.46098e11i	0.0846461	−	0.146611i	0.905240	+	0.424900i	$0.139691\pi$
$168$		0			0
$169$	−5.41932e11	−	9.38654e11i	−0.302390	−	0.523756i
$170$	−7.12742e11			−0.385002
$171$		0			0
$172$	−7.30943e11			−0.370235
$173$	−7.53686e11	−	1.30542e12i	−0.369775	−	0.640468i	0.619756	−	0.784795i	$-0.287232\pi$
$173$	−7.53686e11	−	1.30542e12i	−0.369775	−	0.640468i	−0.989530	+	0.144327i	$0.953898\pi$
$174$		0			0
$175$	5.98685e11	−	1.03695e12i	0.275733	−	0.477584i
$176$	−9.47046e11	+	1.64033e12i	−0.422719	+	0.732170i
$177$		0			0
$178$	−1.54564e12	−	2.67713e12i	−0.648334	−	1.12295i
$179$	−1.54494e12			−0.628377			−0.314189	−	0.949361i	$-0.601732\pi$
$179$	−1.54494e12			−0.628377			−0.314189	+	0.949361i	$0.601732\pi$
$180$		0			0
$181$	−3.80037e11			−0.145410			−0.0727048	−	0.997354i	$-0.523163\pi$
$181$	−3.80037e11			−0.145410			−0.0727048	+	0.997354i	$0.523163\pi$
$182$	−1.05705e12	−	1.83086e12i	−0.392376	−	0.679614i
$183$		0			0
$184$	−2.62504e11	+	4.54670e11i	−0.0917568	+	0.158927i
$185$	−1.22141e12	+	2.11555e12i	−0.414399	+	0.717760i
$186$		0			0
$187$	1.81912e12	+	3.15081e12i	0.581745	+	1.00761i
$188$	−3.94704e10			−0.0122575
$189$		0			0
$190$	−1.16428e12			−0.341123
$191$	−1.16514e12	−	2.01808e12i	−0.331661	−	0.574453i	0.651177	−	0.758926i	$-0.274276\pi$
$191$	−1.16514e12	−	2.01808e12i	−0.331661	−	0.574453i	−0.982838	+	0.184473i	$0.940942\pi$
$192$		0			0
$193$	2.49630e12	−	4.32372e12i	0.671015	−	1.16223i	−0.306602	−	0.951838i	$-0.599192\pi$
$193$	2.49630e12	−	4.32372e12i	0.671015	−	1.16223i	0.977617	−	0.210394i	$-0.0674747\pi$
$194$	1.29601e12	−	2.24476e12i	0.338610	−	0.586489i
$195$		0			0
$196$	−2.53640e11	−	4.39317e11i	−0.0626338	−	0.108485i
$197$	2.51169e12			0.603117			0.301559	−	0.953448i	$-0.402493\pi$
$197$	2.51169e12			0.603117			0.301559	+	0.953448i	$0.402493\pi$
$198$		0			0
$199$	2.69518e12			0.612204			0.306102	−	0.951999i	$-0.400975\pi$
$199$	2.69518e12			0.612204			0.306102	+	0.951999i	$0.400975\pi$
$200$	1.87781e12	+	3.25247e12i	0.414942	+	0.718701i
$201$		0			0
$202$	−2.57069e12	+	4.45257e12i	−0.537796	+	0.931489i
$203$	1.15826e12	−	2.00616e12i	0.235818	−	0.408449i
$204$		0			0
$205$	7.25722e11	+	1.25699e12i	0.139999	+	0.242485i
$206$	2.24083e12			0.420861
$207$		0			0
$208$	4.77925e12			0.851161
$209$	2.97157e12	+	5.14690e12i	0.515443	+	0.892774i
$210$		0			0
$211$	−3.03292e12	+	5.25317e12i	−0.499238	+	0.864705i	−1.00000		0.000880164i	$-0.999720\pi$
$211$	−3.03292e12	+	5.25317e12i	−0.499238	+	0.864705i	0.500762	+	0.865585i	$0.333053\pi$
$212$	−1.47875e12	+	2.56128e12i	−0.237164	+	0.410780i
$213$		0			0
$214$	−4.30597e12	−	7.45815e12i	−0.655835	−	1.13594i
$215$	4.63792e12			0.688513
$216$		0			0
$217$	6.59878e12			0.930969
$218$	1.02528e12	+	1.77584e12i	0.141037	+	0.244283i
$219$		0			0
$220$	−6.06115e11	+	1.04982e12i	−0.0792921	+	0.137338i
$221$	4.59008e12	−	7.95026e12i	0.585684	−	1.01443i
$222$		0			0
$223$	2.78833e12	+	4.82953e12i	0.338585	+	0.586446i	0.984167	−	0.177245i	$-0.0567184\pi$
$223$	2.78833e12	+	4.82953e12i	0.338585	+	0.586446i	−0.645582	+	0.763691i	$0.723385\pi$
$224$	−3.07669e12			−0.364519
$225$		0			0
$226$	−8.40140e12			−0.947885
$227$	2.00720e12	+	3.47657e12i	0.221028	+	0.382832i	0.955120	−	0.296218i	$-0.0957253\pi$
$227$	2.00720e12	+	3.47657e12i	0.221028	+	0.382832i	−0.734092	+	0.679050i	$0.762392\pi$
$228$		0			0
$229$	−5.12105e12	+	8.86992e12i	−0.537358	+	0.930731i	0.461687	+	0.887043i	$0.347244\pi$
$229$	−5.12105e12	+	8.86992e12i	−0.537358	+	0.930731i	−0.999045	+	0.0436886i	$0.986089\pi$
$230$	3.44045e11	−	5.95904e11i	0.0352462	−	0.0610482i
$231$		0			0
$232$	3.63295e12	+	6.29246e12i	0.354875	+	0.614662i
$233$	−1.36342e13			−1.30069			−0.650343	−	0.759641i	$-0.725375\pi$
$233$	−1.36342e13			−1.30069			−0.650343	+	0.759641i	$0.725375\pi$
$234$		0			0
$235$	2.50444e11			0.0227949
$236$	−9.63050e11	−	1.66805e12i	−0.0856314	−	0.148318i
$237$		0			0
$238$	3.37406e12	−	5.84404e12i	0.286404	−	0.496067i
$239$	4.75673e12	−	8.23891e12i	0.394567	−	0.683410i	−0.598479	−	0.801138i	$-0.704228\pi$
$239$	4.75673e12	−	8.23891e12i	0.394567	−	0.683410i	0.993046	+	0.117729i	$0.0375614\pi$
$240$		0			0
$241$	3.60961e12	+	6.25202e12i	0.286000	+	0.495366i	0.972851	−	0.231432i	$-0.0743409\pi$
$241$	3.60961e12	+	6.25202e12i	0.286000	+	0.495366i	−0.686851	+	0.726798i	$0.741008\pi$
$242$	−6.47699e12			−0.501636
$243$		0			0
$244$	−3.28462e12			−0.243131
$245$	1.60937e12	+	2.78752e12i	0.116478	+	0.201746i
$246$		0			0
$247$	7.49798e12	−	1.29869e13i	0.518933	−	0.898818i
$248$	−1.03488e13	+	1.79246e13i	−0.700493	+	1.21329i
$249$		0			0
$250$	−5.67565e12	−	9.83051e12i	−0.367575	−	0.636658i
$251$	−7.98786e12			−0.506087			−0.253043	−	0.967455i	$-0.581432\pi$
$251$	−7.98786e12			−0.506087			−0.253043	+	0.967455i	$0.581432\pi$
$252$		0			0
$253$	−3.51241e12			−0.213031
$254$	−6.43698e12	−	1.11492e13i	−0.382029	−	0.661694i
$255$		0			0
$256$	6.36369e12	−	1.10222e13i	0.361734	−	0.626541i
$257$	1.37682e13	−	2.38473e13i	0.766030	−	1.32680i	−0.173670	−	0.984804i	$-0.555563\pi$
$257$	1.37682e13	−	2.38473e13i	0.766030	−	1.32680i	0.939700	−	0.341999i	$-0.111104\pi$
$258$		0			0
$259$	−1.15641e13	−	2.00297e13i	−0.616545	−	1.06789i
$260$	3.05875e12			0.159658
$261$		0			0
$262$	−4.47006e12			−0.223695
$263$	1.49440e13	+	2.58838e13i	0.732337	+	1.26845i	0.955882	+	0.293752i	$0.0949039\pi$
$263$	1.49440e13	+	2.58838e13i	0.732337	+	1.26845i	−0.223544	+	0.974694i	$0.571763\pi$
$264$		0			0
$265$	9.38287e12	−	1.62516e13i	0.441046	−	0.763913i
$266$	5.51158e12	−	9.54634e12i	0.253763	−	0.439530i
$267$		0			0
$268$	−1.66121e12	−	2.87730e12i	−0.0733978	−	0.127129i
$269$	−9.80257e12			−0.424329			−0.212164	−	0.977234i	$-0.568051\pi$
$269$	−9.80257e12			−0.424329			−0.212164	+	0.977234i	$0.568051\pi$
$270$		0			0
$271$	−1.00339e13			−0.417003			−0.208501	−	0.978022i	$-0.566859\pi$
$271$	−1.00339e13			−0.417003			−0.208501	+	0.978022i	$0.566859\pi$
$272$	7.62760e12	+	1.32114e13i	0.310641	+	0.538046i
$273$		0			0
$274$	−1.17756e13	+	2.03959e13i	−0.460631	+	0.797837i
$275$	−1.25629e13	+	2.17597e13i	−0.481684	+	0.834300i
$276$		0			0
$277$	4.26434e12	+	7.38606e12i	0.157113	+	0.272128i	0.933827	−	0.357726i	$-0.116448\pi$
$277$	4.26434e12	+	7.38606e12i	0.157113	+	0.272128i	−0.776713	+	0.629855i	$0.783115\pi$
$278$	−2.09589e13			−0.757045
$279$		0			0
$280$	1.08852e13			0.377978
$281$	−1.89458e13	−	3.28151e13i	−0.645103	−	1.11735i	−0.984278	−	0.176627i	$-0.943481\pi$
$281$	−1.89458e13	−	3.28151e13i	−0.645103	−	1.11735i	0.339175	−	0.940723i	$-0.389852\pi$
$282$		0			0
$283$	2.05667e12	−	3.56225e12i	0.0673502	−	0.116654i	−0.830384	−	0.557192i	$-0.811879\pi$
$283$	2.05667e12	−	3.56225e12i	0.0673502	−	0.116654i	0.897734	+	0.440538i	$0.145212\pi$
$284$	4.61888e12	−	8.00014e12i	0.148349	−	0.256949i
$285$		0			0
$286$	2.21813e13	+	3.84192e13i	0.685448	+	1.18723i
$287$	−1.37420e13			−0.416582
$288$		0			0
$289$	−4.96913e12			−0.144991
$290$	−4.76145e12	−	8.24707e12i	−0.136317	−	0.236108i
$291$		0			0
$292$	−5.06423e12	+	8.77150e12i	−0.139607	+	0.241807i
$293$	4.49380e12	−	7.78349e12i	0.121574	−	0.210573i	−0.798814	−	0.601578i	$-0.794539\pi$
$293$	4.49380e12	−	7.78349e12i	0.121574	−	0.210573i	0.920389	+	0.391005i	$0.127872\pi$
$294$		0			0
$295$	6.11067e12	+	1.05840e13i	0.159246	+	0.275822i
$296$	7.25433e13			1.85564
$297$		0			0
$298$	−6.30235e12			−0.155351
$299$	4.43133e12	+	7.67529e12i	0.107237	+	0.185739i
$300$		0			0
$301$	−2.19555e13	+	3.80281e13i	−0.512187	+	0.887134i
$302$	−1.25853e13	+	2.17985e13i	−0.288288	+	0.499330i
$303$		0			0
$304$	1.24598e13	+	2.15810e13i	0.275237	+	0.476725i
$305$	2.08413e13			0.452143
$306$		0			0
$307$	1.27887e13			0.267649			0.133825	−	0.991005i	$-0.457274\pi$
$307$	1.27887e13			0.267649			0.133825	+	0.991005i	$0.457274\pi$
$308$	−5.73859e12	−	9.93953e12i	−0.117971	−	0.204332i
$309$		0			0
$310$	1.35634e13	−	2.34924e13i	0.269078	−	0.466057i
$311$	−6.93395e12	+	1.20100e13i	−0.135145	+	0.234077i	−0.925653	−	0.378374i	$-0.876483\pi$
$311$	−6.93395e12	+	1.20100e13i	−0.135145	+	0.234077i	0.790508	+	0.612452i	$0.209817\pi$
$312$		0			0
$313$	−3.21105e13	−	5.56170e13i	−0.604162	−	1.04644i	−0.992183	−	0.124789i	$-0.960175\pi$
$313$	−3.21105e13	−	5.56170e13i	−0.604162	−	1.04644i	0.388021	−	0.921650i	$-0.373159\pi$
$314$	5.60908e13			1.03700
$315$		0			0
$316$	1.91128e13			0.341229
$317$	2.74494e13	+	4.75438e13i	0.481623	+	0.834195i	0.999778	−	0.0210916i	$-0.00671416\pi$
$317$	2.74494e13	+	4.75438e13i	0.481623	+	0.834195i	−0.518155	+	0.855287i	$0.673381\pi$
$318$		0			0
$319$	−2.43052e13	+	4.20978e13i	−0.411955	+	0.713528i
$320$	−1.60864e13	+	2.78624e13i	−0.267999	+	0.464187i
$321$		0			0
$322$	3.25736e12	+	5.64192e12i	0.0524395	+	0.0908280i
$323$	4.78666e13			0.757563
$324$		0			0
$325$	6.33987e13			0.969889
$326$	−3.48304e13	−	6.03280e13i	−0.523916	−	0.907449i
$327$		0			0
$328$	2.15514e13	−	3.73280e13i	0.313450	−	0.542911i
$329$	−1.18558e12	+	2.05349e12i	−0.0169572	+	0.0293708i
$330$		0			0
$331$	−1.76867e13	−	3.06343e13i	−0.244677	−	0.423793i	0.717364	−	0.696699i	$-0.245349\pi$
$331$	−1.76867e13	−	3.06343e13i	−0.244677	−	0.423793i	−0.962041	+	0.272906i	$0.912015\pi$
$332$	1.33136e13			0.181148
$333$		0			0
$334$	1.10602e13			0.145598
$335$	1.05406e13	+	1.82568e13i	0.136495	+	0.236417i
$336$		0			0
$337$	−1.08224e13	+	1.87450e13i	−0.135631	+	0.234920i	−0.925838	−	0.377919i	$-0.876640\pi$
$337$	−1.08224e13	+	1.87450e13i	−0.135631	+	0.234920i	0.790207	+	0.612840i	$0.209973\pi$
$338$	2.10925e13	−	3.65334e13i	0.260068	−	0.450451i
$339$		0			0
$340$	4.88171e12	+	8.45537e12i	0.0582690	+	0.100925i
$341$	−1.38470e14			−1.62633
$342$		0			0
$343$	−9.38065e13			−1.06688
$344$	−6.88649e13	−	1.19278e14i	−0.770773	−	1.33502i
$345$		0			0
$346$	2.93342e13	−	5.08084e13i	0.318021	−	0.550829i
$347$	−6.35777e13	+	1.10120e14i	−0.678411	+	1.17504i	0.297049	+	0.954862i	$0.403998\pi$
$347$	−6.35777e13	+	1.10120e14i	−0.678411	+	1.17504i	−0.975459	+	0.220179i	$0.929336\pi$
$348$		0			0
$349$	−3.80647e13	−	6.59299e13i	−0.393534	−	0.681621i	0.599379	−	0.800465i	$-0.295414\pi$
$349$	−3.80647e13	−	6.59299e13i	−0.393534	−	0.681621i	−0.992913	+	0.118845i	$0.962081\pi$
$350$	4.66029e13			0.474284
$351$		0			0
$352$	6.45620e13			0.636784
$353$	−5.05553e13	−	8.75644e13i	−0.490915	−	0.850290i	0.509030	−	0.860749i	$-0.330004\pi$
$353$	−5.05553e13	−	8.75644e13i	−0.490915	−	0.850290i	−0.999945	+	0.0104590i	$0.996671\pi$
$354$		0			0
$355$	−2.93074e13	+	5.07618e13i	−0.275880	+	0.477839i
$356$	−2.11728e13	+	3.66724e13i	−0.196247	+	0.339910i
$357$		0			0
$358$	−3.00653e13	−	5.20747e13i	−0.270215	−	0.468026i
$359$	−1.24969e14			−1.10607			−0.553034	−	0.833159i	$-0.686530\pi$
$359$	−1.24969e14			−1.10607			−0.553034	+	0.833159i	$0.686530\pi$
$360$		0			0
$361$	−3.82993e13			−0.328777
$362$	−7.39570e12	−	1.28097e13i	−0.0625291	−	0.108304i
$363$		0			0
$364$	−1.44799e13	+	2.50799e13i	−0.118770	+	0.205716i
$365$	3.21331e13	−	5.56562e13i	0.259622	−	0.449679i
$366$		0			0
$367$	3.50638e13	+	6.07323e13i	0.274913	+	0.476163i	0.970113	−	0.242653i	$-0.0780176\pi$
$367$	3.50638e13	+	6.07323e13i	0.274913	+	0.476163i	−0.695200	+	0.718816i	$0.744684\pi$
$368$	−1.47276e13			−0.113754
$369$		0			0
$370$	−9.50773e13			−0.712800
$371$	8.88355e13	+	1.53868e14i	0.656190	+	1.13656i
$372$		0			0
$373$	6.99358e13	−	1.21132e14i	0.501535	−	0.868684i	−0.498464	−	0.866911i	$-0.666102\pi$
$373$	6.99358e13	−	1.21132e14i	0.501535	−	0.868684i	0.999998	−	0.00177306i	$-0.000564381\pi$
$374$	−7.08020e13	+	1.22633e14i	−0.500325	+	0.866588i
$375$		0			0
$376$	−3.71866e12	−	6.44090e12i	−0.0255184	−	0.0441991i
$377$	1.22656e14			0.829489
$378$		0			0
$379$	−1.23834e14			−0.813435			−0.406717	−	0.913554i	$-0.633327\pi$
$379$	−1.23834e14			−0.813435			−0.406717	+	0.913554i	$0.633327\pi$
$380$	7.97436e12	+	1.38120e13i	0.0516281	+	0.0894225i
$381$		0			0
$382$	4.53484e13	−	7.85457e13i	0.285242	−	0.494053i
$383$	7.23117e13	−	1.25248e14i	0.448348	−	0.776562i	−0.549930	−	0.835210i	$-0.685346\pi$
$383$	7.23117e13	−	1.25248e14i	0.448348	−	0.776562i	0.998279	+	0.0586484i	$0.0186791\pi$
$384$		0			0
$385$	3.64121e13	+	6.30675e13i	0.219387	+	0.379990i
$386$	1.94317e14			1.15420
$387$		0			0
$388$	−3.55066e13			−0.204991
$389$	−6.35282e13	−	1.10034e14i	−0.361613	−	0.626331i	0.626614	−	0.779330i	$-0.284440\pi$
$389$	−6.35282e13	−	1.10034e14i	−0.361613	−	0.626331i	−0.988226	+	0.152999i	$0.951107\pi$
$390$		0			0
$391$	−1.41447e13	+	2.44993e13i	−0.0782745	+	0.135575i
$392$	4.77927e13	−	8.27793e13i	0.260788	−	0.451698i
$393$		0			0
$394$	4.88788e13	+	8.46605e13i	0.259353	+	0.449212i
$395$	−1.21273e14			−0.634573
$396$		0			0
$397$	3.66597e14			1.86570			0.932850	−	0.360266i	$-0.117314\pi$
$397$	3.66597e14			1.86570			0.932850	+	0.360266i	$0.117314\pi$
$398$	5.24496e13	+	9.08454e13i	0.263260	+	0.455980i
$399$		0			0
$400$	−5.26766e13	+	9.12386e13i	−0.257210	+	0.445501i
$401$	5.46435e13	−	9.46453e13i	0.263175	−	0.455832i	−0.703909	−	0.710290i	$-0.748564\pi$
$401$	5.46435e13	−	9.46453e13i	0.263175	−	0.455832i	0.967084	+	0.254458i	$0.0818970\pi$
$402$		0			0
$403$	1.74697e14	+	3.02584e14i	0.818669	+	1.41798i
$404$	7.04287e13			0.325576
$405$		0			0
$406$	9.01612e13			0.405627
$407$	2.42665e14	+	4.20308e14i	1.07705	+	1.86551i
$408$		0			0
$409$	7.46658e13	−	1.29325e14i	0.322584	−	0.558733i	−0.658436	−	0.752637i	$-0.728782\pi$
$409$	7.46658e13	−	1.29325e14i	0.322584	−	0.558733i	0.981021	+	0.193904i	$0.0621150\pi$
$410$	−2.82458e13	+	4.89232e13i	−0.120405	+	0.208547i
$411$		0			0
$412$	−1.53479e13	−	2.65833e13i	−0.0636963	−	0.110325i
$413$	−1.15710e14			−0.473853
$414$		0			0
$415$	−8.44761e13			−0.336875
$416$	−8.14528e13	−	1.41080e14i	−0.320548	−	0.555205i
$417$		0			0
$418$	−1.15656e14	+	2.00323e14i	−0.443302	+	0.767822i
$419$	2.31670e14	−	4.01263e14i	0.876379	−	1.51793i	0.0210919	−	0.999778i	$-0.493286\pi$
$419$	2.31670e14	−	4.01263e14i	0.876379	−	1.51793i	0.855287	−	0.518155i	$-0.173381\pi$
$420$		0			0
$421$	−9.64810e13	−	1.67110e14i	−0.355541	−	0.615816i	0.631669	−	0.775238i	$-0.282370\pi$
$421$	−9.64810e13	−	1.67110e14i	−0.355541	−	0.615816i	−0.987210	+	0.159422i	$0.949037\pi$
$422$	−2.36088e14			−0.858729
$423$		0			0
$424$	−5.57276e14			−1.97496
$425$	1.01183e14	+	1.75255e14i	0.353972	+	0.613098i
$426$		0			0
$427$	−9.86610e13	+	1.70886e14i	−0.336351	+	0.582576i
$428$	−5.89848e13	+	1.02165e14i	−0.198518	+	0.343843i
$429$		0			0
$430$	9.02563e13	+	1.56329e14i	0.296075	+	0.512816i
$431$	1.26743e14			0.410485			0.205243	−	0.978711i	$-0.434202\pi$
$431$	1.26743e14			0.410485			0.205243	+	0.978711i	$0.434202\pi$
$432$		0			0
$433$	1.11003e14			0.350471			0.175235	−	0.984527i	$-0.443931\pi$
$433$	1.11003e14			0.350471			0.175235	+	0.984527i	$0.443931\pi$
$434$	1.28416e14	+	2.22422e14i	0.400336	+	0.693402i
$435$		0			0
$436$	1.40447e13	−	2.43262e13i	0.0426911	−	0.0739432i
$437$	−2.31055e13	+	4.00200e13i	−0.0693535	+	0.120124i
$438$		0			0
$439$	−1.89807e14	−	3.28756e14i	−0.555594	−	0.962317i	−0.997857	−	0.0654319i	$-0.979157\pi$
$439$	−1.89807e14	−	3.28756e14i	−0.555594	−	0.962317i	0.442263	−	0.896886i	$-0.354176\pi$
$440$	−2.28417e14			−0.660297
$441$		0			0
$442$	3.57301e14			1.00742
$443$	−2.75292e14	−	4.76819e14i	−0.766607	−	1.32780i	−0.939393	−	0.342843i	$-0.888610\pi$
$443$	−2.75292e14	−	4.76819e14i	−0.766607	−	1.32780i	0.172786	−	0.984959i	$-0.444723\pi$
$444$		0			0
$445$	1.34344e14	−	2.32691e14i	0.364954	−	0.632119i
$446$	−1.08525e14	+	1.87970e14i	−0.291197	+	0.504368i
$447$		0			0
$448$	−1.52303e14	−	2.63796e14i	−0.398730	−	0.690621i
$449$	−2.83340e14			−0.732744			−0.366372	−	0.930468i	$-0.619400\pi$
$449$	−2.83340e14			−0.732744			−0.366372	+	0.930468i	$0.619400\pi$
$450$		0			0
$451$	2.88366e14			0.727734
$452$	5.75429e13	+	9.96672e13i	0.143460	+	0.248480i
$453$		0			0
$454$	−7.81221e13	+	1.35312e14i	−0.190093	+	0.329251i
$455$	9.18765e13	−	1.59135e14i	0.220872	−	0.382562i
$456$		0			0
$457$	−6.37486e13	−	1.10416e14i	−0.149600	−	0.259115i	0.781480	−	0.623931i	$-0.214465\pi$
$457$	−6.37486e13	−	1.10416e14i	−0.149600	−	0.259115i	−0.931080	+	0.364816i	$0.881132\pi$
$458$	−3.98633e14			−0.924300
$459$		0			0
$460$	−9.42574e12			−0.0213377
$461$	−1.53674e14	−	2.66171e14i	−0.343752	−	0.595396i	0.641374	−	0.767228i	$-0.278365\pi$
$461$	−1.53674e14	−	2.66171e14i	−0.343752	−	0.595396i	−0.985126	+	0.171832i	$0.945031\pi$
$462$		0			0
$463$	−2.18470e14	+	3.78401e14i	−0.477195	+	0.826526i	−0.999658	−	0.0261358i	$-0.991680\pi$
$463$	−2.18470e14	+	3.78401e14i	−0.477195	+	0.826526i	0.522463	+	0.852662i	$0.325013\pi$
$464$	−1.01912e14	+	1.76517e14i	−0.219976	+	0.381010i
$465$		0			0
$466$	−2.65328e14	−	4.59562e14i	−0.559321	−	0.968773i
$467$	6.49256e13			0.135261			0.0676306	−	0.997710i	$-0.478456\pi$
$467$	6.49256e13			0.135261			0.0676306	+	0.997710i	$0.478456\pi$
$468$		0			0
$469$	−1.99593e14			−0.406157
$470$	4.87377e12	+	8.44163e12i	0.00980228	+	0.0169781i
$471$		0			0
$472$	1.81465e14	−	3.14307e14i	0.356543	−	0.617551i
$473$	4.60720e14	−	7.97991e14i	0.894748	−	1.54975i
$474$		0			0
$475$	1.65285e14	+	2.86281e14i	0.313630	+	0.543223i
$476$	−9.24384e13			−0.173386
$477$		0			0
$478$	3.70274e14			0.678687
$479$	5.05849e14	+	8.76156e14i	0.916590	+	1.58758i	0.804556	+	0.593877i	$0.202403\pi$
$479$	5.05849e14	+	8.76156e14i	0.916590	+	1.58758i	0.112034	+	0.993704i	$0.464263\pi$
$480$		0			0
$481$	6.12302e14	−	1.06054e15i	1.08435	−	1.87814i
$482$	−1.40489e14	+	2.43335e14i	−0.245972	+	0.426035i
$483$		0			0
$484$	4.43622e13	+	7.68376e13i	0.0759213	+	0.131500i
$485$	2.25293e14			0.381214
$486$		0			0
$487$	−3.00339e14			−0.496824			−0.248412	−	0.968654i	$-0.579909\pi$
$487$	−3.00339e14			−0.496824			−0.248412	+	0.968654i	$0.579909\pi$
$488$	−3.09456e14	−	5.35994e14i	−0.506163	−	0.876700i
$489$		0			0
$490$	−6.26384e13	+	1.08493e14i	−0.100176	+	0.173509i
$491$	−4.58229e14	+	7.93676e14i	−0.724661	+	1.25515i	0.234453	+	0.972127i	$0.424670\pi$
$491$	−4.58229e14	+	7.93676e14i	−0.724661	+	1.25515i	−0.959114	+	0.283021i	$0.908663\pi$
$492$		0			0
$493$	1.95756e14	+	3.39060e14i	0.302732	+	0.524347i
$494$	5.83658e14			0.892607
$495$		0			0
$496$	−5.80608e14			−0.868429
$497$	−2.77477e14	−	4.80605e14i	−0.410456	−	0.710931i
$498$		0			0
$499$	−5.91285e14	+	1.02414e15i	−0.855547	+	1.48185i	0.0205902	+	0.999788i	$0.493445\pi$
$499$	−5.91285e14	+	1.02414e15i	−0.855547	+	1.48185i	−0.876137	+	0.482062i	$0.839888\pi$
$500$	−7.77473e13	+	1.34662e14i	−0.111263	+	0.192713i
$501$		0			0
$502$	−1.55448e14	−	2.69243e14i	−0.217628	−	0.376942i
$503$	5.42478e14			0.751205			0.375603	−	0.926781i	$-0.377436\pi$
$503$	5.42478e14			0.751205			0.375603	+	0.926781i	$0.377436\pi$
$504$		0			0
$505$	−4.46878e14			−0.605462
$506$	−6.83533e13	−	1.18391e14i	−0.0916076	−	0.158669i
$507$		0			0
$508$	−8.81763e13	+	1.52726e14i	−0.115638	+	0.200291i
$509$	−1.86946e14	+	3.23799e14i	−0.242531	+	0.420076i	−0.961435	−	0.275034i	$-0.911311\pi$
$509$	−1.86946e14	+	3.23799e14i	−0.242531	+	0.420076i	0.718903	+	0.695110i	$0.244644\pi$
$510$		0			0
$511$	3.04231e14	+	5.26944e14i	0.386268	+	0.669036i
$512$	8.50527e14			1.06833
$513$		0			0
$514$	1.07175e15			1.31763
$515$	9.73842e13	+	1.68674e14i	0.118454	+	0.205168i
$516$		0			0
$517$	2.48785e13	−	4.30909e13i	0.0296229	−	0.0513083i
$518$	4.50088e14	−	7.79576e14i	0.530254	−	0.918427i
$519$		0			0
$520$	2.88176e14	+	4.99136e14i	0.332384	+	0.575706i
$521$	−9.41376e14			−1.07437			−0.537187	−	0.843463i	$-0.680513\pi$
$521$	−9.41376e14			−1.07437			−0.537187	+	0.843463i	$0.680513\pi$
$522$		0			0
$523$	6.38561e13			0.0713581			0.0356791	−	0.999363i	$-0.488641\pi$
$523$	6.38561e13			0.0713581			0.0356791	+	0.999363i	$0.488641\pi$
$524$	3.06163e13	+	5.30290e13i	0.0338556	+	0.0586396i
$525$		0			0
$526$	−5.81637e14	+	1.00742e15i	−0.629840	+	1.09091i
$527$	−5.57627e14	+	9.65839e14i	−0.597566	+	1.03501i
$528$		0			0
$529$	4.62749e14	+	8.01506e14i	0.485668	+	0.841202i
$530$	7.30382e14			0.758634
$531$		0			0
$532$	−1.51000e14			−0.153625
$533$	−3.63808e14	−	6.30134e14i	−0.366330	−	0.634503i
$534$		0			0
$535$	3.74266e14	−	6.48248e14i	0.369177	−	0.639433i
$536$	3.13018e14	−	5.42163e14i	0.305607	−	0.529326i
$537$		0			0
$538$	−1.90763e14	−	3.30411e14i	−0.182470	−	0.316047i
$539$	6.39485e14			0.605469
$540$		0			0
$541$	7.25322e14			0.672893			0.336447	−	0.941703i	$-0.390775\pi$
$541$	7.25322e14			0.672893			0.336447	+	0.941703i	$0.390775\pi$
$542$	−1.95265e14	−	3.38208e14i	−0.179320	−	0.310591i
$543$		0			0
$544$	2.59994e14	−	4.50323e14i	0.233975	−	0.405257i
$545$	−8.91154e13	+	1.54352e14i	−0.0793912	+	0.137510i
$546$		0			0
$547$	5.57468e13	+	9.65563e13i	0.0486732	+	0.0843044i	0.889336	−	0.457255i	$-0.151167\pi$
$547$	5.57468e13	+	9.65563e13i	0.0486732	+	0.0843044i	−0.840662	+	0.541560i	$0.817834\pi$
$548$	3.22613e14			0.278861
$549$		0			0
$550$	−9.77925e14			−0.828535
$551$	3.19771e14	+	5.53860e14i	0.268229	+	0.464586i
$552$		0			0
$553$	5.74098e14	−	9.94366e14i	0.472060	−	0.817633i
$554$	−1.65972e14	+	2.87473e14i	−0.135124	+	0.234042i
$555$		0			0
$556$	1.43552e14	+	2.48639e14i	0.114577	+	0.198453i
$557$	2.27003e14			0.179402			0.0897012	−	0.995969i	$-0.471409\pi$
$557$	2.27003e14			0.179402			0.0897012	+	0.995969i	$0.471409\pi$
$558$		0			0
$559$	−2.32502e15			−1.80161
$560$	1.52676e14	+	2.64443e14i	0.117149	+	0.202908i
$561$		0			0
$562$	7.37391e14	−	1.27720e15i	0.554815	−	0.960967i
$563$	−7.04849e14	+	1.22083e15i	−0.525170	+	0.909621i	0.474401	+	0.880309i	$0.342665\pi$
$563$	−7.04849e14	+	1.22083e15i	−0.525170	+	0.909621i	−0.999570	+	0.0293116i	$0.990668\pi$
$564$		0			0
$565$	−3.65117e14	−	6.32400e14i	−0.266787	−	0.462089i
$566$	1.60095e14			0.115848
$567$		0			0
$568$	1.74065e15			1.23537
$569$	−2.01731e14	−	3.49408e14i	−0.141793	−	0.245593i	0.786379	−	0.617745i	$-0.211953\pi$
$569$	−2.01731e14	−	3.49408e14i	−0.141793	−	0.245593i	−0.928172	+	0.372152i	$0.878620\pi$
$570$		0			0
$571$	−6.94825e13	+	1.20347e14i	−0.0479046	+	0.0829731i	−0.888983	−	0.457939i	$-0.848588\pi$
$571$	−6.94825e13	+	1.20347e14i	−0.0479046	+	0.0829731i	0.841079	+	0.540913i	$0.181921\pi$
$572$	3.03849e14	−	5.26281e14i	0.207481	−	0.359368i
$573$		0			0
$574$	−2.67427e14	−	4.63196e14i	−0.179139	−	0.310277i
$575$	−1.95367e14			−0.129622
$576$		0			0
$577$	−1.49055e14			−0.0970240			−0.0485120	−	0.998823i	$-0.515448\pi$
$577$	−1.49055e14			−0.0970240			−0.0485120	+	0.998823i	$0.515448\pi$
$578$	−9.67017e13	−	1.67492e14i	−0.0623492	−	0.107992i
$579$		0			0
$580$	−6.52243e13	+	1.12972e14i	−0.0412625	+	0.0714687i
$581$	3.99903e14	−	6.92652e14i	0.250603	−	0.434056i
$582$		0			0
$583$	−1.86414e15	−	3.22879e15i	−1.14631	−	1.98547i
$584$	−1.90848e15			−1.16256
$585$		0			0
$586$	3.49806e14			0.209118
$587$	−1.26588e15	−	2.19256e15i	−0.749690	−	1.29850i	−0.947971	−	0.318356i	$-0.896869\pi$
$587$	−1.26588e15	−	2.19256e15i	−0.749690	−	1.29850i	0.198281	−	0.980145i	$-0.436464\pi$
$588$		0			0
$589$	−9.10894e14	+	1.57771e15i	−0.529461	+	0.917053i
$590$	−2.37833e14	+	4.11939e14i	−0.136958	+	0.237218i
$591$		0			0
$592$	1.01750e15	+	1.76236e15i	0.575127	+	0.996149i
$593$	−7.38349e14			−0.413486			−0.206743	−	0.978395i	$-0.566286\pi$
$593$	−7.38349e14			−0.413486			−0.206743	+	0.978395i	$0.566286\pi$
$594$		0			0
$595$	5.86533e14			0.322440
$596$	4.31661e13	+	7.47658e13i	0.0235119	+	0.0407238i
$597$		0			0
$598$	−1.72472e14	+	2.98730e14i	−0.0922278	+	0.159743i
$599$	−1.23555e15	+	2.14004e15i	−0.654656	+	1.13390i	0.327324	+	0.944912i	$0.393853\pi$
$599$	−1.23555e15	+	2.14004e15i	−0.654656	+	1.13390i	−0.981980	+	0.188985i	$0.939480\pi$
$600$		0			0
$601$	−1.05481e15	−	1.82698e15i	−0.548735	−	0.950437i	−0.998362	−	0.0572204i	$-0.981776\pi$
$601$	−1.05481e15	−	1.82698e15i	−0.548735	−	0.950437i	0.449626	−	0.893217i	$-0.351557\pi$
$602$	−1.70906e15			−0.881003
$603$		0			0
$604$	3.44798e14			0.174527
$605$	−2.81484e14	−	4.87544e14i	−0.141188	−	0.244545i
$606$		0			0
$607$	−1.43917e15	+	2.49272e15i	−0.708883	+	1.22782i	0.256389	+	0.966574i	$0.417467\pi$
$607$	−1.43917e15	+	2.49272e15i	−0.708883	+	1.22782i	−0.965272	+	0.261247i	$0.915866\pi$
$608$	4.24705e14	−	7.35611e14i	0.207309	−	0.359070i
$609$		0			0
$610$	4.05582e14	+	7.02489e14i	0.194431	+	0.336764i
$611$	−1.25549e14			−0.0596468
$612$		0			0
$613$	1.06157e15			0.495352			0.247676	−	0.968843i	$-0.420333\pi$
$613$	1.06157e15			0.495352			0.247676	+	0.968843i	$0.420333\pi$
$614$	2.48875e14	+	4.31064e14i	0.115095	+	0.199350i
$615$		0			0
$616$	1.08131e15	−	1.87288e15i	0.491197	−	0.850778i
$617$	9.37838e14	−	1.62438e15i	0.422240	−	0.731342i	−0.573918	−	0.818913i	$-0.694577\pi$
$617$	9.37838e14	−	1.62438e15i	0.422240	−	0.731342i	0.996158	+	0.0875712i	$0.0279105\pi$
$618$		0			0
$619$	1.39839e15	+	2.42208e15i	0.618485	+	1.07125i	0.989762	+	0.142725i	$0.0455865\pi$
$619$	1.39839e15	+	2.42208e15i	0.618485	+	1.07125i	−0.371278	+	0.928522i	$0.621080\pi$
$620$	−3.71593e14			−0.162897
$621$		0			0
$622$	−5.39752e14			−0.232460
$623$	1.27195e15	+	2.20308e15i	0.542981	+	0.940471i
$624$		0			0
$625$	−4.19376e14	+	7.26381e14i	−0.175899	+	0.304666i
$626$	1.24977e15	−	2.16467e15i	0.519604	−	0.899981i
$627$		0			0
$628$	−3.84177e14	−	6.65414e14i	−0.156947	−	0.271840i
$629$	3.90889e15			1.58298
$630$		0			0
$631$	−1.21754e14			−0.0484530			−0.0242265	−	0.999706i	$-0.507712\pi$
$631$	−1.21754e14			−0.0484530			−0.0242265	+	0.999706i	$0.507712\pi$
$632$	1.80069e15	+	3.11889e15i	0.710388	+	1.23043i
$633$		0			0
$634$	−1.06836e15	+	1.85045e15i	−0.414215	+	0.717442i
$635$	5.59489e14	−	9.69064e14i	0.215048	−	0.372475i
$636$		0			0
$637$	−8.06788e14	−	1.39740e15i	−0.304784	−	0.527902i
$638$	−1.89196e15			−0.708597
$639$		0			0
$640$	−5.86671e14			−0.215975
$641$	1.26661e14	+	2.19383e14i	0.0462300	+	0.0800727i	0.888214	−	0.459429i	$-0.151946\pi$
$641$	1.26661e14	+	2.19383e14i	0.0462300	+	0.0800727i	−0.841984	+	0.539502i	$0.818613\pi$
$642$		0			0
$643$	2.56414e15	−	4.44122e15i	0.919986	−	1.59346i	0.120553	−	0.992707i	$-0.461533\pi$
$643$	2.56414e15	−	4.44122e15i	0.919986	−	1.59346i	0.799433	−	0.600756i	$-0.205134\pi$
$644$	4.46207e13	−	7.72853e13i	0.0158732	−	0.0274931i
$645$		0			0
$646$	9.31508e14	+	1.61342e15i	0.325767	+	0.564246i
$647$	1.76264e14			0.0611210			0.0305605	−	0.999533i	$-0.490271\pi$
$647$	1.76264e14			0.0611210			0.0305605	+	0.999533i	$0.490271\pi$
$648$		0			0
$649$	2.42808e15			0.827783
$650$	1.23377e15	+	2.13695e15i	0.417072	+	0.722390i
$651$		0			0
$652$	−4.77120e14	+	8.26397e14i	−0.158587	+	0.274680i
$653$	6.43823e14	−	1.11513e15i	0.212199	−	0.367540i	−0.740203	−	0.672383i	$-0.765271\pi$
$653$	6.43823e14	−	1.11513e15i	0.212199	−	0.367540i	0.952403	+	0.304843i	$0.0986041\pi$
$654$		0			0
$655$	−1.94264e14	−	3.36475e14i	−0.0629601	−	0.109050i
$656$	1.20912e15			0.388596
$657$		0			0
$658$	−9.22882e13			−0.0291678
$659$	2.69693e15	+	4.67122e15i	0.845279	+	1.46407i	0.885378	+	0.464871i	$0.153899\pi$
$659$	2.69693e15	+	4.67122e15i	0.845279	+	1.46407i	−0.0400991	+	0.999196i	$0.512767\pi$
$660$		0			0
$661$	−8.10649e14	+	1.40409e15i	−0.249876	+	0.432798i	−0.963491	−	0.267740i	$-0.913723\pi$
$661$	−8.10649e14	+	1.40409e15i	−0.249876	+	0.432798i	0.713615	+	0.700538i	$0.247057\pi$
$662$	6.88385e14	−	1.19232e15i	0.210432	−	0.364479i
$663$		0			0
$664$	1.25432e15	+	2.17255e15i	0.377124	+	0.653197i
$665$	9.58112e14			0.285691
$666$		0			0
$667$	−3.77972e14			−0.110858
$668$	−7.57533e13	−	1.31208e14i	−0.0220359	−	0.0381673i
$669$		0			0
$670$	−4.10250e14	+	7.10574e14i	−0.117392	+	0.203328i
$671$	2.07033e15	−	3.58591e15i	0.587577	−	1.01771i
$672$		0			0
$673$	2.96587e15	+	5.13703e15i	0.828073	+	1.43426i	0.899548	+	0.436822i	$0.143896\pi$
$673$	2.96587e15	+	5.13703e15i	0.828073	+	1.43426i	−0.0714748	+	0.997442i	$0.522771\pi$
$674$	−8.42439e14			−0.233297
$675$		0			0
$676$	−5.77868e14			−0.157443
$677$	−3.37554e15	−	5.84661e15i	−0.912234	−	1.58003i	−0.810902	−	0.585182i	$-0.801023\pi$
$677$	−3.37554e15	−	5.84661e15i	−0.912234	−	1.58003i	−0.101332	−	0.994853i	$-0.532310\pi$
$678$		0			0
$679$	−1.06652e15	+	1.84727e15i	−0.283586	+	0.491186i
$680$	−9.19848e14	+	1.59322e15i	−0.242615	+	0.420221i
$681$		0			0
$682$	−2.69470e15	−	4.66736e15i	−0.699354	−	1.21132i
$683$	−4.47959e15			−1.15325			−0.576626	−	0.817008i	$-0.695631\pi$
$683$	−4.47959e15			−1.15325			−0.576626	+	0.817008i	$0.695631\pi$
$684$		0			0
$685$	−2.04702e15			−0.518589
$686$	−1.82552e15	−	3.16190e15i	−0.458780	−	0.794630i
$687$		0			0
$688$	1.93181e15	−	3.34599e15i	0.477779	−	0.827538i
$689$	−4.70369e15	+	8.14702e15i	−1.15407	+	1.99891i
$690$		0			0
$691$	1.88090e15	+	3.25782e15i	0.454189	+	0.786679i	0.998641	−	0.0521131i	$-0.0165956\pi$
$691$	1.88090e15	+	3.25782e15i	0.454189	+	0.786679i	−0.544452	+	0.838792i	$0.683262\pi$
$692$	−8.03664e14			−0.192527
$693$		0			0
$694$	−4.94902e15			−1.16692
$695$	−9.10852e14	−	1.57764e15i	−0.213074	−	0.369056i
$696$		0			0
$697$	1.16126e15	−	2.01137e15i	0.267393	−	0.463139i
$698$	1.48151e15	−	2.56606e15i	0.338455	−	0.586221i
$699$		0			0
$700$	−3.19192e14	−	5.52857e14i	−0.0717816	−	0.124329i
$701$	−5.60965e15			−1.25166			−0.625831	−	0.779959i	$-0.715240\pi$
$701$	−5.60965e15			−1.25166			−0.625831	+	0.779959i	$0.715240\pi$
$702$		0			0
$703$	6.38524e15			1.40257
$704$	3.19596e15	+	5.53556e15i	0.696549	+	1.20646i
$705$		0			0
$706$	1.96766e15	−	3.40810e15i	0.422207	−	0.731284i
$707$	2.11548e15	−	3.66413e15i	0.450405	−	0.780124i
$708$		0			0
$709$	−2.46228e15	−	4.26479e15i	−0.516159	−	0.894013i	−0.999824	−	0.0187600i	$-0.994028\pi$
$709$	−2.46228e15	−	4.26479e15i	−0.516159	−	0.894013i	0.483665	−	0.875253i	$-0.339305\pi$
$710$	−2.28134e15			−0.474537
$711$		0			0
$712$	−7.97908e15			−1.63423
$713$	−5.38341e14	−	9.32434e14i	−0.109412	−	0.189507i
$714$		0			0
$715$	−1.92796e15	+	3.33932e15i	−0.385846	+	0.668305i
$716$	−4.11847e14	+	7.13340e14i	−0.0817926	+	0.141669i
$717$		0			0
$718$	−2.43195e15	−	4.21226e15i	−0.475631	−	0.823818i
$719$	9.38020e15			1.82055			0.910276	−	0.414002i	$-0.135869\pi$
$719$	9.38020e15			1.82055			0.910276	+	0.414002i	$0.135869\pi$
$720$		0			0
$721$	−1.84403e15			−0.352472
$722$	−7.45324e14	−	1.29094e15i	−0.141381	−	0.244879i
$723$		0			0
$724$	−1.01309e14	+	1.75473e14i	−0.0189272	+	0.0327829i
$725$	−1.35190e15	+	2.34157e15i	−0.250661	+	0.434158i
$726$		0			0
$727$	−7.34653e14	−	1.27246e15i	−0.134166	−	0.232383i	0.791112	−	0.611671i	$-0.209502\pi$
$727$	−7.34653e14	−	1.27246e15i	−0.134166	−	0.232383i	−0.925279	+	0.379288i	$0.876169\pi$
$728$	−5.45681e15			−0.989045
$729$		0			0
$730$	2.50131e15			0.446572
$731$	−3.71069e15	−	6.42710e15i	−0.657519	−	1.13886i
$732$		0			0
$733$	4.32056e15	−	7.48343e15i	0.754169	−	1.30626i	−0.191618	−	0.981470i	$-0.561373\pi$
$733$	4.32056e15	−	7.48343e15i	0.754169	−	1.30626i	0.945787	−	0.324789i	$-0.105293\pi$
$734$	−1.36472e15	+	2.36376e15i	−0.236437	+	0.409520i
$735$		0			0
$736$	2.51002e14	+	4.34749e14i	0.0428400	+	0.0742011i
$737$	4.18830e15			0.709524
$738$		0			0
$739$	1.31994e15			0.220298			0.110149	−	0.993915i	$-0.464867\pi$
$739$	1.31994e15			0.220298			0.110149	+	0.993915i	$0.464867\pi$
$740$	6.51204e14	+	1.12792e15i	0.107880	+	0.186854i
$741$		0			0
$742$	−3.45757e15	+	5.98868e15i	−0.564351	+	0.977484i
$743$	−2.13155e15	+	3.69195e15i	−0.345348	+	0.598160i	−0.985417	−	0.170158i	$-0.945572\pi$
$743$	−2.13155e15	+	3.69195e15i	−0.345348	+	0.598160i	0.640069	+	0.768317i	$0.278906\pi$
$744$		0			0
$745$	−2.73894e14	−	4.74398e14i	−0.0437243	−	0.0757327i
$746$	5.44394e15			0.862681
$747$		0			0
$748$	1.93975e15			0.302891
$749$	3.54349e15	+	6.13750e15i	0.549264	+	0.951352i
$750$		0			0
$751$	3.05553e15	−	5.29233e15i	0.466731	−	0.808402i	−0.532547	−	0.846401i	$-0.678765\pi$
$751$	3.05553e15	−	5.29233e15i	0.466731	−	0.808402i	0.999278	+	0.0379988i	$0.0120983\pi$
$752$	1.04316e14	−	1.80681e14i	0.0158181	−	0.0273977i
$753$		0			0
$754$	2.38694e15	+	4.13431e15i	0.356697	+	0.617817i
$755$	−2.18779e15			−0.324561
$756$		0			0
$757$	9.63454e15			1.40865			0.704326	−	0.709877i	$-0.251250\pi$
$757$	9.63454e15			1.40865			0.704326	+	0.709877i	$0.251250\pi$
$758$	−2.40986e15	−	4.17400e15i	−0.349793	−	0.605860i
$759$		0			0
$760$	−1.50259e15	+	2.60256e15i	−0.214964	+	0.372328i
$761$	1.42240e15	−	2.46367e15i	0.202026	−	0.349919i	−0.747155	−	0.664650i	$-0.768581\pi$
$761$	1.42240e15	−	2.46367e15i	0.202026	−	0.349919i	0.949181	+	0.314731i	$0.101914\pi$
$762$		0			0
$763$	−8.43730e14	−	1.46138e15i	−0.118119	−	0.204588i
$764$	−1.24240e15			−0.172682
$765$		0			0
$766$	5.62889e15			0.771196
$767$	−3.06331e15	−	5.30581e15i	−0.416694	−	0.721734i
$768$		0			0
$769$	−7.00344e15	+	1.21303e16i	−0.939110	+	1.62659i	−0.171975	+	0.985101i	$0.555015\pi$
$769$	−7.00344e15	+	1.21303e16i	−0.939110	+	1.62659i	−0.767135	+	0.641485i	$0.778319\pi$
$770$	−1.41719e15	+	2.45465e15i	−0.188682	+	0.326807i
$771$		0			0
$772$	−1.33092e15	−	2.30522e15i	−0.174685	−	0.302564i
$773$	1.33026e16			1.73360			0.866798	−	0.498659i	$-0.166174\pi$
$773$	1.33026e16			1.73360			0.866798	+	0.498659i	$0.166174\pi$
$774$		0			0
$775$	−7.70201e15			−0.989566
$776$	−3.34521e15	−	5.79407e15i	−0.426760	−	0.739170i
$777$		0			0
$778$	2.47258e15	−	4.28263e15i	0.311002	−	0.538670i
$779$	1.89694e15	−	3.28560e15i	0.236918	−	0.410354i
$780$		0			0
$781$	5.82264e15	+	1.00851e16i	0.717034	+	1.24194i
$782$	−1.10105e15			−0.134638
$783$		0			0
$784$	2.68137e15			0.323309
$785$	2.43765e15	+	4.22213e15i	0.291869	+	0.505532i
$786$		0			0
$787$	−4.20146e15	+	7.27714e15i	−0.496065	+	0.859211i	−0.999990	−	0.00453730i	$-0.998556\pi$
$787$	−4.20146e15	+	7.27714e15i	−0.496065	+	0.859211i	0.503924	+	0.863748i	$0.331889\pi$
$788$	6.69561e14	−	1.15971e15i	0.0785047	−	0.135974i
$789$		0			0
$790$	−2.36004e15	−	4.08771e15i	−0.272879	−	0.472641i
$791$	6.91372e15			0.793855
$792$		0			0
$793$	−1.04479e16			−1.18311
$794$	7.13417e15	+	1.23567e16i	0.802289	+	1.38961i
$795$		0			0
$796$	7.18476e14	−	1.24444e15i	0.0796875	−	0.138023i
$797$	−5.06866e15	+	8.77918e15i	−0.558306	+	0.967015i	0.439332	+	0.898325i	$0.355215\pi$
$797$	−5.06866e15	+	8.77918e15i	−0.558306	+	0.967015i	−0.997638	+	0.0686902i	$0.978118\pi$
$798$		0			0
$799$	−2.00374e14	−	3.47058e14i	−0.0217688	−	0.0377047i
$800$	3.59107e15			0.387462
$801$		0			0
$802$	4.25356e15			0.452682
$803$	−6.38405e15	−	1.10575e16i	−0.674778	−	1.16875i
$804$		0			0
$805$	−2.83123e14	+	4.90384e14i	−0.0295188	+	0.0511280i
$806$	−6.79939e15	+	1.17769e16i	−0.704089	+	1.21952i
$807$		0			0
$808$	6.63535e15	+	1.14928e16i	0.677800	+	1.17398i
$809$	1.09699e14			0.0111297			0.00556487	−	0.999985i	$-0.498229\pi$
$809$	1.09699e14			0.0111297			0.00556487	+	0.999985i	$0.498229\pi$
$810$		0			0
$811$	5.29565e15			0.530035			0.265018	−	0.964244i	$-0.414622\pi$
$811$	5.29565e15			0.530035			0.265018	+	0.964244i	$0.414622\pi$
$812$	−6.17532e14	−	1.06960e15i	−0.0613905	−	0.106332i
$813$		0			0
$814$	−9.44475e15	+	1.63588e16i	−0.926310	+	1.60442i
$815$	3.02739e15	−	5.24359e15i	0.294918	−	0.510813i
$816$		0			0
$817$	−6.06147e15	−	1.04988e16i	−0.582582	−	1.00906i
$818$	5.81214e15			0.554872
$819$		0			0
$820$	7.73845e14			0.0728916
$821$	2.22133e15	+	3.84745e15i	0.207838	+	0.359986i	0.951033	−	0.309088i	$-0.100024\pi$
$821$	2.22133e15	+	3.84745e15i	0.207838	+	0.359986i	−0.743195	+	0.669075i	$0.766691\pi$
$822$		0			0
$823$	5.57068e15	−	9.64870e15i	0.514291	−	0.890779i	−0.485571	−	0.874197i	$-0.661388\pi$
$823$	5.57068e15	−	9.64870e15i	0.514291	−	0.890779i	0.999863	−	0.0165815i	$-0.00527830\pi$
$824$	2.89197e15	−	5.00903e15i	0.265212	−	0.459361i
$825$		0			0
$826$	−2.25177e15	−	3.90017e15i	−0.203767	−	0.352934i
$827$	−1.64160e16			−1.47567			−0.737833	−	0.674983i	$-0.764151\pi$
$827$	−1.64160e16			−1.47567			−0.737833	+	0.674983i	$0.764151\pi$
$828$		0			0
$829$	−1.29613e16			−1.14973			−0.574867	−	0.818247i	$-0.694946\pi$
$829$	−1.29613e16			−1.14973			−0.574867	+	0.818247i	$0.694946\pi$
$830$	−1.64395e15	−	2.84740e15i	−0.144863	−	0.250911i
$831$		0			0
$832$	8.06418e15	−	1.39676e16i	0.701264	−	1.21463i
$833$	2.57524e15	−	4.46044e15i	0.222469	−	0.385328i
$834$		0			0
$835$	4.80664e14	+	8.32534e14i	0.0409794	+	0.0709784i
$836$	3.16861e15			0.268371
$837$		0			0
$838$	1.80336e16			1.50744
$839$	2.44690e15	+	4.23815e15i	0.203201	+	0.351954i	0.949558	−	0.313592i	$-0.101532\pi$
$839$	2.44690e15	+	4.23815e15i	0.203201	+	0.351954i	−0.746357	+	0.665545i	$0.768199\pi$
$840$		0			0
$841$	3.48476e15	−	6.03579e15i	0.285625	−	0.494716i
$842$	3.75514e15	−	6.50409e15i	0.305780	−	0.529627i
$843$		0			0
$844$	1.61702e15	+	2.80076e15i	0.129966	+	0.225108i
$845$	3.66664e15			0.292790
$846$		0			0
$847$	5.33008e15			0.420122
$848$	−7.81638e15	−	1.35384e16i	−0.612109	−	1.06020i
$849$		0			0
$850$	−3.93815e15	+	6.82108e15i	−0.304431	+	0.527290i
$851$	−1.88685e15	+	3.26812e15i	−0.144919	+	0.251007i
$852$		0			0
$853$	−3.53915e15	−	6.13000e15i	−0.268337	−	0.464773i	0.700096	−	0.714049i	$-0.253141\pi$
$853$	−3.53915e15	−	6.13000e15i	−0.268337	−	0.464773i	−0.968432	+	0.249276i	$0.919807\pi$
$854$	−7.67997e15			−0.578551
$855$		0			0
$856$	−2.22287e16			−1.65314
$857$	1.15585e15	+	2.00199e15i	0.0854095	+	0.147934i	0.905566	−	0.424206i	$-0.139447\pi$
$857$	1.15585e15	+	2.00199e15i	0.0854095	+	0.147934i	−0.820156	+	0.572140i	$0.806113\pi$
$858$		0			0
$859$	9.89075e15	−	1.71313e16i	0.721551	−	1.24976i	−0.238827	−	0.971062i	$-0.576763\pi$
$859$	9.89075e15	−	1.71313e16i	0.721551	−	1.24976i	0.960378	−	0.278701i	$-0.0899038\pi$
$860$	1.23637e15	−	2.14145e15i	0.0896202	−	0.155227i
$861$		0			0
$862$	2.46648e15	+	4.27206e15i	0.176517	+	0.305737i
$863$	−1.59925e16			−1.13725			−0.568627	−	0.822595i	$-0.692525\pi$
$863$	−1.59925e16			−1.13725			−0.568627	+	0.822595i	$0.692525\pi$
$864$		0			0
$865$	5.09934e15			0.358035
$866$	2.16018e15	+	3.74154e15i	0.150710	+	0.261037i
$867$		0			0
$868$	1.75909e15	−	3.04683e15i	0.121180	−	0.209889i
$869$	−1.20470e16	+	2.08660e16i	−0.824651	+	1.42834i
$870$		0			0
$871$	−5.28405e15	−	9.15225e15i	−0.357164	−	0.618626i
$872$	5.29282e15			0.355506
$873$		0			0
$874$	−1.79858e15			−0.119294
$875$	4.67063e15	+	8.08977e15i	0.307845	+	0.533202i
$876$		0			0
$877$	−7.04123e15	+	1.21958e16i	−0.458301	+	0.793801i	−0.998871	−	0.0474981i	$-0.984875\pi$
$877$	−7.04123e15	+	1.21958e16i	−0.458301	+	0.793801i	0.540570	+	0.841299i	$0.318209\pi$
$878$	7.38749e15	−	1.27955e16i	0.477834	−	0.827632i
$879$		0			0
$880$	−3.20379e15	−	5.54914e15i	−0.204649	−	0.354463i
$881$	−2.05758e16			−1.30614			−0.653068	−	0.757299i	$-0.726519\pi$
$881$	−2.05758e16			−1.30614			−0.653068	+	0.757299i	$0.726519\pi$
$882$		0			0
$883$	−1.09044e16			−0.683627			−0.341814	−	0.939768i	$-0.611041\pi$
$883$	−1.09044e16			−0.683627			−0.341814	+	0.939768i	$0.611041\pi$
$884$	−2.44723e15	−	4.23872e15i	−0.152471	−	0.264087i
$885$		0			0
$886$	1.07146e16	−	1.85583e16i	0.659313	−	1.14196i
$887$	3.04486e15	−	5.27385e15i	0.186203	−	0.322513i	−0.757778	−	0.652512i	$-0.773715\pi$
$887$	3.04486e15	−	5.27385e15i	0.186203	−	0.322513i	0.943981	+	0.329999i	$0.107048\pi$
$888$		0			0
$889$	5.29715e15	+	9.17493e15i	0.319950	+	0.554170i
$890$	1.04576e16			0.627751
$891$		0			0
$892$	2.97323e15			0.176287
$893$	−3.27315e14	−	5.66926e14i	−0.0192878	−	0.0334075i
$894$		0			0
$895$	2.61322e15	−	4.52623e15i	0.152107	−	0.263457i
$896$	2.77725e15	−	4.81034e15i	0.160665	−	0.278280i
$897$		0			0
$898$	−5.51393e15	−	9.55041e15i	−0.315095	−	0.545761i
$899$	−1.49009e16			−0.846317
$900$		0			0
$901$	−3.00280e16			−1.68477
$902$	5.61174e15	+	9.71982e15i	0.312940	+	0.542029i
$903$		0			0
$904$	−1.08427e16	+	1.87800e16i	−0.597324	+	1.03459i
$905$	6.42820e14	−	1.11340e15i	0.0351983	−	0.0609653i
$906$		0			0
$907$	9.12148e15	+	1.57989e16i	0.493429	+	0.854645i	0.999971	−	0.00757046i	$-0.00240977\pi$
$907$	9.12148e15	+	1.57989e16i	0.493429	+	0.854645i	−0.506542	+	0.862215i	$0.669076\pi$
$908$	2.14030e15			0.115081
$909$		0			0
$910$	7.15185e15			0.379919
$911$	6.17535e15	+	1.06960e16i	0.326070	+	0.564769i	0.981728	−	0.190288i	$-0.0609422\pi$
$911$	6.17535e15	+	1.06960e16i	0.326070	+	0.564769i	−0.655658	+	0.755058i	$0.727609\pi$
$912$		0			0
$913$	−8.39165e15	+	1.45348e16i	−0.437782	+	0.758261i
$914$	2.48116e15	−	4.29750e15i	0.128662	−	0.222849i
$915$		0			0
$916$	2.73031e15	+	4.72904e15i	0.139890	+	0.242297i
$917$	3.67852e15			0.187345
$918$		0			0
$919$	−8.70126e14			−0.0437871			−0.0218936	−	0.999760i	$-0.506969\pi$
$919$	−8.70126e14			−0.0437871			−0.0218936	+	0.999760i	$0.506969\pi$
$920$	−8.88034e14	−	1.53812e15i	−0.0444219	−	0.0769409i
$921$		0			0
$922$	5.98115e15	−	1.03597e16i	0.295641	−	0.512065i
$923$	1.46919e16	−	2.54472e16i	0.721888	−	1.25035i
$924$		0			0
$925$	1.34975e16	+	2.33784e16i	0.655351	+	1.13510i
$926$	−1.70061e16			−0.820814
$927$		0			0
$928$	6.94754e15			0.331373
$929$	9.92079e15	+	1.71833e16i	0.470392	+	0.814743i	0.999427	−	0.0338573i	$-0.0107792\pi$
$929$	9.92079e15	+	1.71833e16i	0.470392	+	0.814743i	−0.529035	+	0.848600i	$0.677446\pi$
$930$		0			0
$931$	4.20670e15	−	7.28621e15i	0.197114	−	0.341412i
$932$	−3.63457e15	+	6.29527e15i	−0.169304	+	0.293242i
$933$		0			0
$934$	1.26349e15	+	2.18842e15i	0.0581651	+	0.100745i
$935$	−1.23079e16			−0.563276
$936$		0			0
$937$	2.15194e16			0.973336			0.486668	−	0.873587i	$-0.338212\pi$
$937$	2.15194e16			0.973336			0.486668	+	0.873587i	$0.338212\pi$
$938$	−3.88418e15	−	6.72759e15i	−0.174656	−	0.302513i
$939$		0			0
$940$	6.67629e13	−	1.15637e14i	0.00296710	−	0.00513917i
$941$	1.00976e16	−	1.74895e16i	0.446142	−	0.772741i	−0.551989	−	0.833852i	$-0.686131\pi$
$941$	1.00976e16	−	1.74895e16i	0.446142	−	0.772741i	0.998131	+	0.0611104i	$0.0194642\pi$
$942$		0			0
$943$	1.12110e15	+	1.94180e15i	0.0489587	+	0.0847990i
$944$	1.01810e16			0.442021
$945$		0			0
$946$	3.58634e16			1.53904
$947$	1.28829e16	+	2.23139e16i	0.549654	+	0.952028i	0.998298	+	0.0583180i	$0.0185737\pi$
$947$	1.28829e16	+	2.23139e16i	0.549654	+	0.952028i	−0.448644	+	0.893710i	$0.648093\pi$
$948$		0			0
$949$	−1.61085e16	+	2.79008e16i	−0.679347	+	1.17666i
$950$	−6.43304e15	+	1.11424e16i	−0.269735	+	0.467194i
$951$		0			0
$952$	−8.70897e15	−	1.50844e16i	−0.360964	−	0.625208i
$953$	5.27859e15			0.217524			0.108762	−	0.994068i	$-0.465311\pi$
$953$	5.27859e15			0.217524			0.108762	+	0.994068i	$0.465311\pi$
$954$		0			0
$955$	7.88318e15			0.321131
$956$	−2.53608e15	−	4.39262e15i	−0.102717	−	0.177912i
$957$		0			0
$958$	−1.96881e16	+	3.41009e16i	−0.788305	+	1.36538i
$959$	9.69040e15	−	1.67843e16i	0.385780	−	0.668190i
$960$		0			0
$961$	−8.51889e15	−	1.47552e16i	−0.335278	−	0.580718i
$962$	4.76628e16			1.86516
$963$		0			0
$964$	3.84896e15			0.148909
$965$	8.44483e15	+	1.46269e16i	0.324856	+	0.562667i
$966$		0			0
$967$	5.58416e15	−	9.67205e15i	0.212379	−	0.367852i	−0.740079	−	0.672520i	$-0.765212\pi$
$967$	5.58416e15	−	9.67205e15i	0.212379	−	0.367852i	0.952459	+	0.304668i	$0.0985454\pi$
$968$	−8.35906e15	+	1.44783e16i	−0.316114	+	0.547525i
$969$		0			0
$970$	4.38432e15	+	7.59387e15i	0.163930	+	0.283935i
$971$	3.16576e16			1.17699			0.588494	−	0.808502i	$-0.299721\pi$
$971$	3.16576e16			1.17699			0.588494	+	0.808502i	$0.299721\pi$
$972$		0			0
$973$	1.72476e16			0.634027
$974$	−5.84475e15	−	1.01234e16i	−0.213645	−	0.370043i
$975$		0			0
$976$	8.68091e15	−	1.50358e16i	0.313755	−	0.543440i
$977$	−5.99405e15	+	1.03820e16i	−0.215427	+	0.373131i	−0.953405	−	0.301695i	$-0.902448\pi$
$977$	−5.99405e15	+	1.03820e16i	−0.215427	+	0.373131i	0.737977	+	0.674825i	$0.235781\pi$
$978$		0			0
$979$	−2.66908e16	−	4.62299e16i	−0.948543	−	1.64293i
$980$	1.71609e15			0.0606453
$981$		0			0
$982$	−3.56695e16			−1.24648
$983$	−8.60000e15	−	1.48956e16i	−0.298850	−	0.517624i	0.677023	−	0.735962i	$-0.263270\pi$
$983$	−8.60000e15	−	1.48956e16i	−0.298850	−	0.517624i	−0.975873	+	0.218338i	$0.929937\pi$
$984$		0			0
$985$	−4.24844e15	+	7.35852e15i	−0.145992	+	0.252866i
$986$	−7.61903e15	+	1.31966e16i	−0.260362	+	0.450959i
$987$		0			0
$988$	−3.99759e15	−	6.92403e15i	−0.135094	−	0.233989i
$989$	7.16470e15			0.240779
$990$		0			0
$991$	5.83721e15			0.193999			0.0969996	−	0.995284i	$-0.469075\pi$
$991$	5.83721e15			0.193999			0.0969996	+	0.995284i	$0.469075\pi$
$992$	9.89531e15	+	1.71392e16i	0.327051	+	0.566469i
$993$		0			0
$994$	1.07997e16	−	1.87056e16i	0.353009	−	0.611430i
$995$	−4.55881e15	+	7.89610e15i	−0.148192	+	0.256676i
$996$		0			0
$997$	1.46620e16	+	2.53953e16i	0.471378	+	0.816451i	0.999464	−	0.0327400i	$-0.0104233\pi$
$997$	1.46620e16	+	2.53953e16i	0.471378	+	0.816451i	−0.528086	+	0.849191i	$0.677090\pi$
$998$	−4.60268e16			−1.47161
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	27.12.c.a.10.7		20
3.2	odd	2		9.12.c.a.4.4	✓	20
9.2	odd	6		9.12.c.a.7.4	yes	20
9.4	even	3		81.12.a.c.1.4		10
9.5	odd	6		81.12.a.e.1.7		10
9.7	even	3	inner	27.12.c.a.19.7		20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
9.12.c.a.4.4	✓	20	3.2	odd	2
9.12.c.a.7.4	yes	20	9.2	odd	6
27.12.c.a.10.7		20	1.1	even	1	trivial
27.12.c.a.19.7		20	9.7	even	3	inner
81.12.a.c.1.4		10	9.4	even	3
81.12.a.e.1.7		10	9.5	odd	6

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 27 = 3^{3} \)
Weight:	\( k \)	\(=\)	\( 12 \)
Character orbit:	\([\chi]\)	\(=\)	27.c (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(19.4605 + 33.7066i) q^{2} +(266.578 - 461.726i) q^{4} +(-1691.47 + 2929.71i) q^{5} +(-16014.5 - 27738.0i) q^{7} +100461. q^{8} -131667. q^{10} +(336053. + 582060. i) q^{11} +(847942. - 1.46868e6i) q^{13} +(623302. - 1.07959e6i) q^{14} +(1.40907e6 + 2.44059e6i) q^{16} +5.41320e6 q^{17} +8.84256e6 q^{19} +(901815. + 1.56199e6i) q^{20} +(-1.30795e7 + 2.26544e7i) q^{22} +(-2.61299e6 + 4.52583e6i) q^{23} +(1.86919e7 + 3.23754e7i) q^{25} +6.60055e7 q^{26} -1.70765e7 q^{28} +(3.61628e7 + 6.26357e7i) q^{29} +(-1.03012e8 + 1.78423e8i) q^{31} +(4.80297e7 - 8.31898e7i) q^{32} +(1.05344e8 + 1.82461e8i) q^{34} +1.08352e8 q^{35} +7.22103e8 q^{37} +(1.72081e8 + 2.98053e8i) q^{38} +(-1.69927e8 + 2.94322e8i) q^{40} +(2.14524e8 - 3.71567e8i) q^{41} +(-6.85488e8 - 1.18730e9i) q^{43} +3.58337e8 q^{44} -2.03400e8 q^{46} +(-3.70158e7 - 6.41133e7i) q^{47} +(4.75733e8 - 8.23993e8i) q^{49} +(-7.27509e8 + 1.26008e9i) q^{50} +(-4.52085e8 - 7.83034e8i) q^{52} -5.54718e9 q^{53} -2.27369e9 q^{55} +(-1.60884e9 - 2.78659e9i) q^{56} +(-1.40749e9 + 2.43785e9i) q^{58} +(1.80632e9 - 3.12864e9i) q^{59} +(-3.08036e9 - 5.33534e9i) q^{61} -8.01870e9 q^{62} +9.51029e9 q^{64} +(2.86853e9 + 4.96845e9i) q^{65} +(3.11581e9 - 5.39674e9i) q^{67} +(1.44304e9 - 2.49942e9i) q^{68} +(2.10859e9 + 3.65218e9i) q^{70} +1.73266e10 q^{71} -1.89972e10 q^{73} +(1.40525e10 + 2.43396e10i) q^{74} +(2.35723e9 - 4.08284e9i) q^{76} +(1.07635e10 - 1.86428e10i) q^{77} +(1.79243e10 + 3.10458e10i) q^{79} -9.53361e9 q^{80} +1.66990e10 q^{82} +(1.24856e10 + 2.16257e10i) q^{83} +(-9.15626e9 + 1.58591e10i) q^{85} +(2.66799e10 - 4.62109e10i) q^{86} +(3.37602e10 + 5.84744e10i) q^{88} -7.94245e10 q^{89} -5.43176e10 q^{91} +(1.39313e9 + 2.41297e9i) q^{92} +(1.44069e9 - 2.49536e9i) q^{94} +(-1.49569e10 + 2.59061e10i) q^{95} +(-3.32985e10 - 5.76747e10i) q^{97} +3.70320e10 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q + 33 q^{2} - 9217 q^{4} + 7230 q^{5} + 8512 q^{7} + 29118 q^{8} + 4092 q^{10} + 112776 q^{11} + 279706 q^{13} + 3901584 q^{14} - 7342081 q^{16} - 27765792 q^{17} + 7029400 q^{19} + 34163508 q^{20}+ \cdots - 1310123604078 q^{98}+O(q^{100}) \) 20 * q + 33 * q^2 - 9217 * q^4 + 7230 * q^5 + 8512 * q^7 + 29118 * q^8 + 4092 * q^10 + 112776 * q^11 + 279706 * q^13 + 3901584 * q^14 - 7342081 * q^16 - 27765792 * q^17 + 7029400 * q^19 + 34163508 * q^20 + 2274591 * q^22 + 69371616 * q^23 - 45286204 * q^25 - 481929144 * q^26 - 61345796 * q^28 + 25437246 * q^29 + 114575368 * q^31 - 80396559 * q^32 - 243855063 * q^34 + 178147464 * q^35 - 134218328 * q^37 - 489799995 * q^38 + 107425416 * q^40 - 331873026 * q^41 - 1118847584 * q^43 - 278477274 * q^44 + 2882537592 * q^46 + 1469650704 * q^47 - 3553434720 * q^49 + 6643771701 * q^50 + 3632448874 * q^52 - 14914261944 * q^53 + 4981449984 * q^55 + 27669139026 * q^56 - 1387480560 * q^58 + 26505032592 * q^59 + 990409066 * q^61 - 91044996180 * q^62 - 7516709566 * q^64 + 39045315390 * q^65 + 6557215720 * q^67 + 77299152993 * q^68 - 785437278 * q^70 - 122053719744 * q^71 - 12612893936 * q^73 + 109519086216 * q^74 + 14574055597 * q^76 + 88616208018 * q^77 - 7621233248 * q^79 - 399166683072 * q^80 - 59168477334 * q^82 + 99007044180 * q^83 + 12911595156 * q^85 + 214357830519 * q^86 - 54423523605 * q^88 - 476597704824 * q^89 + 138211652216 * q^91 + 461776423998 * q^92 + 13393667064 * q^94 + 418952909328 * q^95 + 123483551938 * q^97 - 1310123604078 * q^98

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