LMFDB - Embedded newform 81.10.c.g.28.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [81,10,Mod(28,81)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(81, base_ring=CyclotomicField(6))

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

N = Newforms(chi, 10, names="a")

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

chi := DirichletCharacter("81.28");

S:= CuspForms(chi, 10);

N := Newforms(S);

Level:	$ N $	$=$	$ 81 = 3^{4} $
Weight:	$ k $	$=$	$ 10 $
Character orbit:	$[\chi]$	$=$	81.c (of order $3$, degree $2$, not minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$41.7179027293$
Analytic rank:	$0$
Dimension:	$6$
Relative dimension:	$3$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{6} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - x^{5} + 119x^{4} - 154x^{3} + 14060x^{2} - 16048x + 18496 $ x^6 - x^5 + 119x^4 - 154x^3 + 14060x^2 - 16048x + 18496
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{2}\cdot 3^{8} $
Twist minimal:	no (minimal twist has level 27)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			28.2
Root			$0.577142 + 0.999640i$ of defining polynomial
Character	$\chi$	$=$	81.28
Dual form			81.10.c.g.55.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.73143 - 2.99892i) q^{2} +(250.004 - 433.020i) q^{4} +(-702.004 + 1215.91i) q^{5} +(-832.785 - 1442.43i) q^{7} -3504.44 q^{8} +4861.88 q^{10} +(31809.3 + 55095.3i) q^{11} +(55604.8 - 96310.3i) q^{13} +(-2883.81 + 4994.91i) q^{14} +(-121935. - 211197. i) q^{16} -383783. q^{17} +7441.82 q^{19} +(351008. + 607964. i) q^{20} +(110151. - 190787. i) q^{22} +(1.30861e6 - 2.26658e6i) q^{23} +(-9057.92 - 15688.8i) q^{25} -385102. q^{26} -832799. q^{28} +(-289545. - 501507. i) q^{29} +(-1.75915e6 + 3.04695e6i) q^{31} +(-1.31938e6 + 2.28523e6i) q^{32} +(664492. + 1.15093e6i) q^{34} +2.33847e6 q^{35} -9.82783e6 q^{37} +(-12885.0 - 22317.4i) q^{38} +(2.46013e6 - 4.26107e6i) q^{40} +(-8.88800e6 + 1.53945e7i) q^{41} +(-1.95649e7 - 3.38874e7i) q^{43} +3.18098e7 q^{44} -9.06304e6 q^{46} +(-1.33934e7 - 2.31980e7i) q^{47} +(1.87897e7 - 3.25448e7i) q^{49} +(-31366.3 + 54327.9i) q^{50} +(-2.78029e7 - 4.81560e7i) q^{52} -6.04430e7 q^{53} -8.93210e7 q^{55} +(2.91844e6 + 5.05489e6i) q^{56} +(-1.00265e6 + 1.73665e6i) q^{58} +(6.74085e7 - 1.16755e8i) q^{59} +(-7.03846e7 - 1.21910e8i) q^{61} +1.21834e7 q^{62} -1.15723e8 q^{64} +(7.80696e7 + 1.35221e8i) q^{65} +(-3.65671e7 + 6.33360e7i) q^{67} +(-9.59473e7 + 1.66186e8i) q^{68} +(-4.04890e6 - 7.01290e6i) q^{70} -2.72910e8 q^{71} -2.64531e8 q^{73} +(1.70162e7 + 2.94729e7i) q^{74} +(1.86049e6 - 3.22246e6i) q^{76} +(5.29806e7 - 9.17651e7i) q^{77} +(-2.72331e8 - 4.71691e8i) q^{79} +3.42394e8 q^{80} +6.15557e7 q^{82} +(-8.69938e7 - 1.50678e8i) q^{83} +(2.69417e8 - 4.66644e8i) q^{85} +(-6.77504e7 + 1.17347e8i) q^{86} +(-1.11474e8 - 1.93078e8i) q^{88} +5.69208e8 q^{89} -1.85227e8 q^{91} +(-6.54316e8 - 1.13331e9i) q^{92} +(-4.63793e7 + 8.03313e7i) q^{94} +(-5.22419e6 + 9.04856e6i) q^{95} +(2.93260e8 + 5.07941e8i) q^{97} -1.30132e8 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 3 q^{2} - 597 q^{4} + 1983 q^{5} + 3693 q^{7} - 9006 q^{8} - 37962 q^{10} + 16863 q^{11} - 116916 q^{13} + 503463 q^{14} + 239919 q^{16} - 2028096 q^{17} - 30444 q^{19} + 2548407 q^{20} - 305721 q^{22}+ \cdots + 5184364572 q^{98}+O(q^{100}) $ 6 * q - 3 * q^2 - 597 * q^4 + 1983 * q^5 + 3693 * q^7 - 9006 * q^8 - 37962 * q^10 + 16863 * q^11 - 116916 * q^13 + 503463 * q^14 + 239919 * q^16 - 2028096 * q^17 - 30444 * q^19 + 2548407 * q^20 - 305721 * q^22 + 2927118 * q^23 - 2133732 * q^25 - 9530232 * q^26 - 7071450 * q^28 + 5768790 * q^29 + 6575223 * q^31 - 2687697 * q^32 - 17098128 * q^34 + 34681074 * q^35 - 23372052 * q^37 - 50473374 * q^38 + 4130811 * q^40 - 22213518 * q^41 - 45384414 * q^43 + 114413982 * q^44 - 191277180 * q^46 + 12392034 * q^47 - 18933462 * q^49 - 82984044 * q^50 - 182736492 * q^52 - 161159274 * q^53 - 349470666 * q^55 + 21850521 * q^56 + 102758922 * q^58 + 244026660 * q^59 - 369729960 * q^61 - 332594682 * q^62 - 841384254 * q^64 + 492225684 * q^65 + 252614586 * q^67 + 162270144 * q^68 - 935092377 * q^70 - 806386176 * q^71 - 813253434 * q^73 - 641373558 * q^74 + 39499590 * q^76 + 360443199 * q^77 - 265451856 * q^79 + 2336719674 * q^80 - 1768816332 * q^82 + 121625871 * q^83 - 316251216 * q^85 - 2368956570 * q^86 - 219257739 * q^88 - 755808012 * q^89 + 490118280 * q^91 - 1178754558 * q^92 - 86583438 * q^94 + 536878770 * q^95 + 438907539 * q^97 + 5184364572 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/81\mathbb{Z}\right)^\times$.

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

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 $

$2$	−1.73143	−	2.99892i	−0.0765190	−	0.132535i	0.825227	−	0.564801i	$-0.191047\pi$
$2$	−1.73143	−	2.99892i	−0.0765190	−	0.132535i	−0.901746	+	0.432267i	$0.857714\pi$
$3$		0			0
$3$		0			0
$4$	250.004	−	433.020i	0.488290	−	0.845743i
$5$	−702.004	+	1215.91i	−0.502313	+	0.870032i	0.497683	+	0.867359i	$0.334184\pi$
$5$	−702.004	+	1215.91i	−0.502313	+	0.870032i	−0.999996	+	0.00267343i	$0.999149\pi$
$6$		0			0
$7$	−832.785	−	1442.43i	−0.131097	−	0.227066i	0.793003	−	0.609218i	$-0.208516\pi$
$7$	−832.785	−	1442.43i	−0.131097	−	0.227066i	−0.924100	+	0.382152i	$0.875183\pi$
$8$	−3504.44			−0.302492
$9$		0			0
$10$	4861.88			0.153746
$11$	31809.3	+	55095.3i	0.655069	+	1.13461i	0.981877	+	0.189521i	$0.0606937\pi$
$11$	31809.3	+	55095.3i	0.655069	+	1.13461i	−0.326808	+	0.945091i	$0.605973\pi$
$12$		0			0
$13$	55604.8	−	96310.3i	0.539967	−	0.935250i	−0.458938	−	0.888468i	$-0.651770\pi$
$13$	55604.8	−	96310.3i	0.539967	−	0.935250i	0.998905	−	0.0467819i	$-0.0148966\pi$
$14$	−2883.81	+	4994.91i	−0.0200628	+	0.0347497i
$15$		0			0
$16$	−121935.	−	211197.i	−0.465143	−	0.805652i
$17$	−383783.			−1.11446			−0.557231	−	0.830358i	$-0.688136\pi$
$17$	−383783.			−1.11446			−0.557231	+	0.830358i	$0.688136\pi$
$18$		0			0
$19$	7441.82			0.0131005			0.00655025	−	0.999979i	$-0.497915\pi$
$19$	7441.82			0.0131005			0.00655025	+	0.999979i	$0.497915\pi$
$20$	351008.	+	607964.i	0.490549	+	0.849656i
$21$		0			0
$22$	110151.	−	190787.i	0.100250	−	0.173639i
$23$	1.30861e6	−	2.26658e6i	0.975067	−	1.68887i	0.295354	−	0.955388i	$-0.404562\pi$
$23$	1.30861e6	−	2.26658e6i	0.975067	−	1.68887i	0.679713	−	0.733478i	$-0.262104\pi$
$24$		0			0
$25$	−9057.92	−	15688.8i	−0.00463766	−	0.00803266i
$26$	−385102.			−0.165271
$27$		0			0
$28$	−832799.			−0.256053
$29$	−289545.	−	501507.i	−0.0760196	−	0.131670i	0.825510	−	0.564388i	$-0.190888\pi$
$29$	−289545.	−	501507.i	−0.0760196	−	0.131670i	−0.901529	+	0.432718i	$0.857554\pi$
$30$		0			0
$31$	−1.75915e6	+	3.04695e6i	−0.342118	+	0.592566i	−0.984826	−	0.173545i	$-0.944478\pi$
$31$	−1.75915e6	+	3.04695e6i	−0.342118	+	0.592566i	0.642708	+	0.766112i	$0.277811\pi$
$32$	−1.31938e6	+	2.28523e6i	−0.222430	+	0.385261i
$33$		0			0
$34$	664492.	+	1.15093e6i	0.0852775	+	0.147705i
$35$	2.33847e6			0.263407
$36$		0			0
$37$	−9.82783e6			−0.862084			−0.431042	−	0.902332i	$-0.641854\pi$
$37$	−9.82783e6			−0.862084			−0.431042	+	0.902332i	$0.641854\pi$
$38$	−12885.0	−	22317.4i	−0.00100244	−	0.00173627i
$39$		0			0
$40$	2.46013e6	−	4.26107e6i	0.151946	−	0.263178i
$41$	−8.88800e6	+	1.53945e7i	−0.491221	+	0.850819i	−0.999949	−	0.0101082i	$-0.996782\pi$
$41$	−8.88800e6	+	1.53945e7i	−0.491221	+	0.850819i	0.508728	+	0.860927i	$0.330116\pi$
$42$		0			0
$43$	−1.95649e7	−	3.38874e7i	−0.872709	−	1.51158i	−0.859183	−	0.511668i	$-0.829028\pi$
$43$	−1.95649e7	−	3.38874e7i	−0.872709	−	1.51158i	−0.0135261	−	0.999909i	$-0.504306\pi$
$44$	3.18098e7			1.27945
$45$		0			0
$46$	−9.06304e6			−0.298445
$47$	−1.33934e7	−	2.31980e7i	−0.400359	−	0.693442i	0.593410	−	0.804900i	$-0.297781\pi$
$47$	−1.33934e7	−	2.31980e7i	−0.400359	−	0.693442i	−0.993769	+	0.111458i	$0.964448\pi$
$48$		0			0
$49$	1.87897e7	−	3.25448e7i	0.465627	−	0.806490i
$50$	−31366.3	+	54327.9i	−0.000709737	+	0.00122930i
$51$		0			0
$52$	−2.78029e7	−	4.81560e7i	−0.527321	−	0.913346i
$53$	−6.04430e7			−1.05222			−0.526108	−	0.850418i	$-0.676349\pi$
$53$	−6.04430e7			−1.05222			−0.526108	+	0.850418i	$0.676349\pi$
$54$		0			0
$55$	−8.93210e7			−1.31620
$56$	2.91844e6	+	5.05489e6i	0.0396556	+	0.0686856i
$57$		0			0
$58$	−1.00265e6	+	1.73665e6i	−0.0116339	+	0.0201505i
$59$	6.74085e7	−	1.16755e8i	0.724237	−	1.25441i	−0.235051	−	0.971983i	$-0.575526\pi$
$59$	6.74085e7	−	1.16755e8i	0.724237	−	1.25441i	0.959287	−	0.282432i	$-0.0911411\pi$
$60$		0			0
$61$	−7.03846e7	−	1.21910e8i	−0.650869	−	1.12734i	−0.982912	−	0.184074i	$-0.941071\pi$
$61$	−7.03846e7	−	1.21910e8i	−0.650869	−	1.12734i	0.332043	−	0.943264i	$-0.392262\pi$
$62$	1.21834e7			0.104714
$63$		0			0
$64$	−1.15723e8			−0.862206
$65$	7.80696e7	+	1.35221e8i	0.542465	+	0.939577i
$66$		0			0
$67$	−3.65671e7	+	6.33360e7i	−0.221694	+	0.383985i	−0.955322	−	0.295566i	$-0.904492\pi$
$67$	−3.65671e7	+	6.33360e7i	−0.221694	+	0.383985i	0.733629	+	0.679551i	$0.237825\pi$
$68$	−9.59473e7	+	1.66186e8i	−0.544180	+	0.942548i
$69$		0			0
$70$	−4.04890e6	−	7.01290e6i	−0.0201556	−	0.0349105i
$71$	−2.72910e8			−1.27455			−0.637276	−	0.770636i	$-0.719939\pi$
$71$	−2.72910e8			−1.27455			−0.637276	+	0.770636i	$0.719939\pi$
$72$		0			0
$73$	−2.64531e8			−1.09025			−0.545123	−	0.838356i	$-0.683517\pi$
$73$	−2.64531e8			−1.09025			−0.545123	+	0.838356i	$0.683517\pi$
$74$	1.70162e7	+	2.94729e7i	0.0659658	+	0.114256i
$75$		0			0
$76$	1.86049e6	−	3.22246e6i	0.00639684	−	0.0110797i
$77$	5.29806e7	−	9.17651e7i	0.171755	−	0.297488i
$78$		0			0
$79$	−2.72331e8	−	4.71691e8i	−0.786639	−	1.36250i	−0.928015	−	0.372542i	$-0.878486\pi$
$79$	−2.72331e8	−	4.71691e8i	−0.786639	−	1.36250i	0.141376	−	0.989956i	$-0.454847\pi$
$80$	3.42394e8			0.934591
$81$		0			0
$82$	6.15557e7			0.150351
$83$	−8.69938e7	−	1.50678e8i	−0.201204	−	0.348496i	0.747713	−	0.664023i	$-0.231152\pi$
$83$	−8.69938e7	−	1.50678e8i	−0.201204	−	0.348496i	−0.948917	+	0.315527i	$0.897819\pi$
$84$		0			0
$85$	2.69417e8	−	4.66644e8i	0.559809	−	0.969618i
$86$	−6.77504e7	+	1.17347e8i	−0.133558	+	0.231329i
$87$		0			0
$88$	−1.11474e8	−	1.93078e8i	−0.198153	−	0.343211i
$89$	5.69208e8			0.961647			0.480823	−	0.876817i	$-0.340338\pi$
$89$	5.69208e8			0.961647			0.480823	+	0.876817i	$0.340338\pi$
$90$		0			0
$91$	−1.85227e8			−0.283151
$92$	−6.54316e8	−	1.13331e9i	−0.952231	−	1.64931i
$93$		0			0
$94$	−4.63793e7	+	8.03313e7i	−0.0612701	+	0.106123i
$95$	−5.22419e6	+	9.04856e6i	−0.00658056	+	0.0113979i
$96$		0			0
$97$	2.93260e8	+	5.07941e8i	0.336341	+	0.582560i	0.983742	−	0.179590i	$-0.0574772\pi$
$97$	2.93260e8	+	5.07941e8i	0.336341	+	0.582560i	−0.647400	+	0.762150i	$0.724144\pi$
$98$	−1.30132e8			−0.142517
$99$		0			0
$100$	−9.05808e6			−0.00905808
$101$	8.12194e8	+	1.40676e9i	0.776629	+	1.34516i	0.933875	+	0.357601i	$0.116405\pi$
$101$	8.12194e8	+	1.40676e9i	0.776629	+	1.34516i	−0.157246	+	0.987559i	$0.550262\pi$
$102$		0			0
$103$	−2.96352e8	+	5.13297e8i	−0.259442	+	0.449367i	−0.966093	−	0.258196i	$-0.916872\pi$
$103$	−2.96352e8	+	5.13297e8i	−0.259442	+	0.449367i	0.706650	+	0.707563i	$0.250205\pi$
$104$	−1.94864e8	+	3.37514e8i	−0.163335	+	0.282905i
$105$		0			0
$106$	1.04653e8	+	1.81264e8i	0.0805144	+	0.139455i
$107$	−4.69405e8			−0.346195			−0.173098	−	0.984905i	$-0.555378\pi$
$107$	−4.69405e8			−0.346195			−0.173098	+	0.984905i	$0.555378\pi$
$108$		0			0
$109$	2.10211e9			1.42639			0.713193	−	0.700968i	$-0.247248\pi$
$109$	2.10211e9			1.42639			0.713193	+	0.700968i	$0.247248\pi$
$110$	1.54653e8	+	2.67867e8i	0.100714	+	0.174442i
$111$		0			0
$112$	−2.03090e8	+	3.51763e8i	−0.121957	+	0.211237i
$113$	6.26779e8	−	1.08561e9i	0.361628	−	0.626357i	−0.626601	−	0.779340i	$-0.715555\pi$
$113$	6.26779e8	−	1.08561e9i	0.361628	−	0.626357i	0.988229	+	0.152983i	$0.0488879\pi$
$114$		0			0
$115$	1.83730e9	+	3.18229e9i	0.979579	+	1.69668i
$116$	−2.89550e8			−0.148478
$117$		0			0
$118$	−4.66851e8			−0.221671
$119$	3.19608e8	+	5.53578e8i	0.146102	+	0.253057i
$120$		0			0
$121$	−8.44688e8	+	1.46304e9i	−0.358230	+	0.620473i
$122$	−2.43732e8	+	4.22156e8i	−0.0996077	+	0.172526i
$123$		0			0
$124$	8.79593e8	+	1.52350e9i	0.334106	+	0.578688i
$125$	−2.71677e9			−0.995309
$126$		0			0
$127$	3.81433e9			1.30107			0.650536	−	0.759476i	$-0.274544\pi$
$127$	3.81433e9			1.30107			0.650536	+	0.759476i	$0.274544\pi$
$128$	8.75888e8	+	1.51708e9i	0.288406	+	0.499533i
$129$		0			0
$130$	2.70344e8	−	4.68249e8i	0.0830178	−	0.143791i
$131$	9.69871e8	−	1.67987e9i	0.287735	−	0.498372i	−0.685533	−	0.728041i	$-0.740431\pi$
$131$	9.69871e8	−	1.67987e9i	0.287735	−	0.498372i	0.973269	+	0.229669i	$0.0737643\pi$
$132$		0			0
$133$	−6.19743e6	−	1.07343e7i	−0.00171743	−	0.00297468i
$134$	2.53253e8			0.0678551
$135$		0			0
$136$	1.34494e9			0.337115
$137$	−2.97132e9	−	5.14648e9i	−0.720621	−	1.24815i	−0.960751	−	0.277412i	$-0.910523\pi$
$137$	−2.97132e9	−	5.14648e9i	−0.720621	−	1.24815i	0.240130	−	0.970741i	$-0.422810\pi$
$138$		0			0
$139$	2.77575e9	−	4.80774e9i	0.630687	−	1.09238i	−0.356725	−	0.934209i	$-0.616107\pi$
$139$	2.77575e9	−	4.80774e9i	0.630687	−	1.09238i	0.987412	−	0.158172i	$-0.0505600\pi$
$140$	5.84629e8	−	1.01261e9i	0.128619	−	0.222774i
$141$		0			0
$142$	4.72524e8	+	8.18436e8i	0.0975274	+	0.168922i
$143$	7.07500e9			1.41486
$144$		0			0
$145$	8.13049e8			0.152743
$146$	4.58017e8	+	7.93308e8i	0.0834245	+	0.144495i
$147$		0			0
$148$	−2.45700e9	+	4.25565e9i	−0.420947	+	0.729102i
$149$	−4.86200e9	+	8.42124e9i	−0.808122	+	1.39971i	0.106040	+	0.994362i	$0.466183\pi$
$149$	−4.86200e9	+	8.42124e9i	−0.808122	+	1.39971i	−0.914163	+	0.405347i	$0.867151\pi$
$150$		0			0
$151$	1.60926e9	+	2.78732e9i	0.251901	+	0.436305i	0.964049	−	0.265724i	$-0.0856110\pi$
$151$	1.60926e9	+	2.78732e9i	0.251901	+	0.436305i	−0.712148	+	0.702029i	$0.752278\pi$
$152$	−2.60794e7			−0.00396279
$153$		0			0
$154$	−3.66928e8			−0.0525700
$155$	−2.46987e9	−	4.27794e9i	−0.343701	−	0.595308i
$156$		0			0
$157$	−6.42880e8	+	1.11350e9i	−0.0844465	+	0.146266i	−0.905155	−	0.425081i	$-0.860246\pi$
$157$	−6.42880e8	+	1.11350e9i	−0.0844465	+	0.146266i	0.820709	+	0.571347i	$0.193579\pi$
$158$	−9.43043e8	+	1.63340e9i	−0.120386	+	0.208514i
$159$		0			0
$160$	−1.85242e9	−	3.20848e9i	−0.223460	−	0.387043i
$161$	−4.35916e9			−0.511312
$162$		0			0
$163$	4.38269e9			0.486291			0.243146	−	0.969990i	$-0.421821\pi$
$163$	4.38269e9			0.486291			0.243146	+	0.969990i	$0.421821\pi$
$164$	4.44407e9	+	7.69736e9i	0.479716	+	0.830892i
$165$		0			0
$166$	−3.01247e8	+	5.21775e8i	−0.0307919	+	0.0533331i
$167$	−7.67671e8	+	1.32965e9i	−0.0763750	+	0.132285i	−0.901683	−	0.432397i	$-0.857668\pi$
$167$	−7.67671e8	+	1.32965e9i	−0.0763750	+	0.132285i	0.825308	+	0.564682i	$0.191001\pi$
$168$		0			0
$169$	−8.81536e8	−	1.52687e9i	−0.0831285	−	0.143983i
$170$	−1.86590e9			−0.171344
$171$		0			0
$172$	−1.95652e10			−1.70454
$173$	3.79098e8	+	6.56618e8i	0.0321769	+	0.0557321i	0.881665	−	0.471875i	$-0.156423\pi$
$173$	3.79098e8	+	6.56618e8i	0.0321769	+	0.0557321i	−0.849489	+	0.527607i	$0.823089\pi$
$174$		0			0
$175$	−1.50866e7	+	2.61308e7i	−0.00121596	+	0.00210611i
$176$	7.75730e9	−	1.34360e10i	0.609402	−	1.05551i
$177$		0			0
$178$	−9.85541e8	−	1.70701e9i	−0.0735842	−	0.127452i
$179$	1.17238e10			0.853549			0.426774	−	0.904358i	$-0.359650\pi$
$179$	1.17238e10			0.853549			0.426774	+	0.904358i	$0.359650\pi$
$180$		0			0
$181$	−8.83265e9			−0.611698			−0.305849	−	0.952080i	$-0.598940\pi$
$181$	−8.83265e9			−0.611698			−0.305849	+	0.952080i	$0.598940\pi$
$182$	3.20708e8	+	5.55482e8i	0.0216665	+	0.0375274i
$183$		0			0
$184$	−4.58594e9	+	7.94308e9i	−0.294950	+	0.510868i
$185$	6.89918e9	−	1.19497e10i	0.433037	−	0.750041i
$186$		0			0
$187$	−1.22079e10	−	2.11446e10i	−0.730049	−	1.26448i
$188$	−1.33936e10			−0.781965
$189$		0			0
$190$	3.61812e7			0.00201415
$191$	1.57008e9	+	2.71947e9i	0.0853636	+	0.147854i	0.905546	−	0.424248i	$-0.139461\pi$
$191$	1.57008e9	+	2.71947e9i	0.0853636	+	0.147854i	−0.820182	+	0.572102i	$0.806128\pi$
$192$		0			0
$193$	1.53175e10	−	2.65307e10i	0.794658	−	1.37639i	−0.128398	−	0.991723i	$-0.540984\pi$
$193$	1.53175e10	−	2.65307e10i	0.794658	−	1.37639i	0.923056	−	0.384665i	$-0.125683\pi$
$194$	1.01552e9	−	1.75893e9i	0.0514729	−	0.0891538i
$195$		0			0
$196$	−9.39503e9	−	1.62727e10i	−0.454722	−	0.787602i
$197$	−2.16444e10			−1.02388			−0.511939	−	0.859022i	$-0.671073\pi$
$197$	−2.16444e10			−1.02388			−0.511939	+	0.859022i	$0.671073\pi$
$198$		0			0
$199$	−3.61495e9			−0.163404			−0.0817021	−	0.996657i	$-0.526036\pi$
$199$	−3.61495e9			−0.163404			−0.0817021	+	0.996657i	$0.526036\pi$
$200$	3.17429e7	+	5.49803e7i	0.00140285	+	0.00242981i
$201$		0			0
$202$	2.81251e9	−	4.87141e9i	0.118854	−	0.205861i
$203$	−4.82258e8	+	8.35296e8i	−0.0199318	+	0.0345230i
$204$		0			0
$205$	−1.24788e10	−	2.16140e10i	−0.493493	−	0.854756i
$206$	2.05245e9			0.0794091
$207$		0			0
$208$	−2.71206e10			−1.00465
$209$	2.36719e8	+	4.10009e8i	0.00858173	+	0.0148640i
$210$		0			0
$211$	5.92937e9	−	1.02700e10i	0.205938	−	0.356696i	−0.744493	−	0.667630i	$-0.767309\pi$
$211$	5.92937e9	−	1.02700e10i	0.205938	−	0.356696i	0.950431	+	0.310935i	$0.100642\pi$
$212$	−1.51110e10	+	2.61730e10i	−0.513786	+	0.889903i
$213$		0			0
$214$	8.12740e8	+	1.40771e9i	0.0264905	+	0.0458829i
$215$	5.49386e10			1.75349
$216$		0			0
$217$	5.85999e9			0.179402
$218$	−3.63966e9	−	6.30407e9i	−0.109146	−	0.189046i
$219$		0			0
$220$	−2.23306e10	+	3.86778e10i	−0.642687	+	1.11317i
$221$	−2.13402e10	+	3.69622e10i	−0.601773	+	1.04230i
$222$		0			0
$223$	9.43784e9	+	1.63468e10i	0.255565	+	0.442651i	0.965049	−	0.262070i	$-0.0844053\pi$
$223$	9.43784e9	+	1.63468e10i	0.255565	+	0.442651i	−0.709484	+	0.704722i	$0.751072\pi$
$224$	4.39503e9			0.116640
$225$		0			0
$226$	−4.34089e9			−0.110685
$227$	1.02386e9	+	1.77337e9i	0.0255931	+	0.0443285i	0.878538	−	0.477672i	$-0.158519\pi$
$227$	1.02386e9	+	1.77337e9i	0.0255931	+	0.0443285i	−0.852945	+	0.522000i	$0.825186\pi$
$228$		0			0
$229$	−1.06967e9	+	1.85272e9i	−0.0257034	+	0.0445196i	−0.878591	−	0.477575i	$-0.841516\pi$
$229$	−1.06967e9	+	1.85272e9i	−0.0257034	+	0.0445196i	0.852888	+	0.522095i	$0.174849\pi$
$230$	6.36229e9	−	1.10198e10i	0.149913	−	0.259656i
$231$		0			0
$232$	1.01469e9	+	1.75750e9i	0.0229953	+	0.0398290i
$233$	−4.02632e10			−0.894966			−0.447483	−	0.894292i	$-0.647679\pi$
$233$	−4.02632e10			−0.894966			−0.447483	+	0.894292i	$0.647679\pi$
$234$		0			0
$235$	3.76088e10			0.804423
$236$	−3.37048e10	−	5.83785e10i	−0.707275	−	1.22504i
$237$		0			0
$238$	1.10676e9	−	1.91696e9i	0.0223592	−	0.0387272i
$239$	4.63163e9	−	8.02222e9i	0.0918213	−	0.159039i	−0.816456	−	0.577407i	$-0.804064\pi$
$239$	4.63163e9	−	8.02222e9i	0.0918213	−	0.159039i	0.908278	+	0.418368i	$0.137398\pi$
$240$		0			0
$241$	3.90476e10	+	6.76324e10i	0.745620	+	1.29145i	0.949905	+	0.312540i	$0.101180\pi$
$241$	3.90476e10	+	6.76324e10i	0.745620	+	1.29145i	−0.204285	+	0.978912i	$0.565487\pi$
$242$	5.85006e9			0.109646
$243$		0			0
$244$	−7.03859e10			−1.27125
$245$	2.63810e10	+	4.56932e10i	0.467782	+	0.810222i
$246$		0			0
$247$	4.13801e8	−	7.16724e8i	0.00707384	−	0.0122522i
$248$	6.16485e9	−	1.06778e10i	0.103488	−	0.179246i
$249$		0			0
$250$	4.70389e9	+	8.14737e9i	0.0761600	+	0.131913i
$251$	−1.54732e10			−0.246064			−0.123032	−	0.992403i	$-0.539262\pi$
$251$	−1.54732e10			−0.246064			−0.123032	+	0.992403i	$0.539262\pi$
$252$		0			0
$253$	1.66504e11			2.55494
$254$	−6.60423e9	−	1.14389e10i	−0.0995567	−	0.172437i
$255$		0			0
$256$	−2.65921e10	+	4.60589e10i	−0.386966	+	0.670245i
$257$	4.67386e10	−	8.09536e10i	0.668308	−	1.15754i	−0.310069	−	0.950714i	$-0.600352\pi$
$257$	4.67386e10	−	8.09536e10i	0.668308	−	1.15754i	0.978377	−	0.206829i	$-0.0663143\pi$
$258$		0			0
$259$	8.18447e9	+	1.41759e10i	0.113016	+	0.195750i
$260$	7.80710e10			1.05952
$261$		0			0
$262$	−6.71704e9			−0.0880689
$263$	3.95489e9	+	6.85008e9i	0.0509723	+	0.0882866i	0.890386	−	0.455207i	$-0.150435\pi$
$263$	3.95489e9	+	6.85008e9i	0.0509723	+	0.0882866i	−0.839413	+	0.543493i	$0.817101\pi$
$264$		0			0
$265$	4.24313e10	−	7.34931e10i	0.528542	−	0.915461i
$266$	−2.14608e7	+	3.71712e7i	−0.000262832	+	0.000455239i
$267$		0			0
$268$	1.82838e10	+	3.16686e10i	0.216502	+	0.374992i
$269$	−1.42705e11			−1.66171			−0.830853	−	0.556492i	$-0.812147\pi$
$269$	−1.42705e11			−1.66171			−0.830853	+	0.556492i	$0.812147\pi$
$270$		0			0
$271$	6.60775e10			0.744203			0.372102	−	0.928192i	$-0.378637\pi$
$271$	6.60775e10			0.744203			0.372102	+	0.928192i	$0.378637\pi$
$272$	4.67964e10	+	8.10537e10i	0.518385	+	0.897868i
$273$		0			0
$274$	−1.02892e10	+	1.78215e10i	−0.110282	+	0.191015i
$275$	5.76252e8	−	9.98098e8i	0.00607597	−	0.0105239i
$276$		0			0
$277$	2.15068e10	+	3.72508e10i	0.219491	+	0.380169i	0.954652	−	0.297723i	$-0.0962271\pi$
$277$	2.15068e10	+	3.72508e10i	0.219491	+	0.380169i	−0.735162	+	0.677892i	$0.762894\pi$
$278$	−1.92240e10			−0.193038
$279$		0			0
$280$	−8.19504e9			−0.0796783
$281$	5.05155e10	+	8.74954e10i	0.483333	+	0.837157i	0.999817	−	0.0191402i	$-0.00609287\pi$
$281$	5.05155e10	+	8.74954e10i	0.483333	+	0.837157i	−0.516484	+	0.856297i	$0.672760\pi$
$282$		0			0
$283$	4.08977e10	−	7.08368e10i	0.379018	−	0.656478i	−0.611902	−	0.790934i	$-0.709595\pi$
$283$	4.08977e10	−	7.08368e10i	0.379018	−	0.656478i	0.990920	+	0.134456i	$0.0429286\pi$
$284$	−6.82288e10	+	1.18176e11i	−0.622351	+	1.07794i
$285$		0			0
$286$	−1.22498e10	−	2.12173e10i	−0.108264	−	0.187518i
$287$	2.96072e10			0.257590
$288$		0			0
$289$	2.87013e10			0.242025
$290$	−1.40773e9	−	2.43827e9i	−0.0116877	−	0.0202437i
$291$		0			0
$292$	−6.61340e10	+	1.14547e11i	−0.532356	+	0.922067i
$293$	4.04552e10	−	7.00704e10i	0.320678	−	0.555431i	−0.659950	−	0.751310i	$-0.729422\pi$
$293$	4.04552e10	−	7.00704e10i	0.320678	−	0.555431i	0.980628	+	0.195879i	$0.0627558\pi$
$294$		0			0
$295$	9.46421e10	+	1.63925e11i	0.727588	+	1.26022i
$296$	3.44410e10			0.260773
$297$		0			0
$298$	3.36728e10			0.247347
$299$	−1.45530e11	−	2.52065e11i	−1.05301	−	1.82386i
$300$		0			0
$301$	−3.25867e10	+	5.64418e10i	−0.228819	+	0.396325i
$302$	5.57263e9	−	9.65207e9i	0.0385504	−	0.0667712i
$303$		0			0
$304$	−9.07415e8	−	1.57169e9i	−0.00609361	−	0.0105544i
$305$	1.97641e11			1.30776
$306$		0			0
$307$	7.58062e10			0.487060			0.243530	−	0.969893i	$-0.421695\pi$
$307$	7.58062e10			0.487060			0.243530	+	0.969893i	$0.421695\pi$
$308$	−2.64908e10	−	4.58833e10i	−0.167732	−	0.290520i
$309$		0			0
$310$	−8.55279e9	+	1.48139e10i	−0.0525994	+	0.0911047i
$311$	−8.88256e10	+	1.53850e11i	−0.538414	+	0.932560i	0.460576	+	0.887620i	$0.347643\pi$
$311$	−8.88256e10	+	1.53850e11i	−0.538414	+	0.932560i	−0.998990	+	0.0449400i	$0.985690\pi$
$312$		0			0
$313$	−4.18712e10	−	7.25231e10i	−0.246585	−	0.427097i	0.715991	−	0.698109i	$-0.245975\pi$
$313$	−4.18712e10	−	7.25231e10i	−0.246585	−	0.427097i	−0.962576	+	0.271012i	$0.912642\pi$
$314$	4.45240e9			0.0258470
$315$		0			0
$316$	−2.72336e11			−1.53643
$317$	2.65016e10	+	4.59021e10i	0.147403	+	0.255309i	0.930267	−	0.366884i	$-0.119575\pi$
$317$	2.65016e10	+	4.59021e10i	0.147403	+	0.255309i	−0.782864	+	0.622193i	$0.786242\pi$
$318$		0			0
$319$	1.84205e10	−	3.19052e10i	0.0995962	−	0.172506i
$320$	8.12383e10	−	1.40709e11i	0.433098	−	0.750147i
$321$		0			0
$322$	7.54756e9	+	1.30728e10i	0.0391251	+	0.0677666i
$323$	−2.85604e9			−0.0146000
$324$		0			0
$325$	−2.01466e9			−0.0100167
$326$	−7.58831e9	−	1.31433e10i	−0.0372105	−	0.0644505i
$327$		0			0
$328$	3.11474e10	−	5.39489e10i	0.148590	−	0.257366i
$329$	−2.23076e10	+	3.86379e10i	−0.104971	+	0.181816i
$330$		0			0
$331$	−1.10989e11	−	1.92239e11i	−0.508225	−	0.880271i	−0.999955	−	0.00952305i	$-0.996969\pi$
$331$	−1.10989e11	−	1.92239e11i	−0.508225	−	0.880271i	0.491730	−	0.870748i	$-0.336365\pi$
$332$	−8.69953e10			−0.392984
$333$		0			0
$334$	5.31667e9			0.0233765
$335$	−5.13405e10	−	8.89243e10i	−0.222720	−	0.385762i
$336$		0			0
$337$	1.56720e8	−	2.71446e8i	0.000661895	−	0.00114644i	−0.865694	−	0.500573i	$-0.833123\pi$
$337$	1.56720e8	−	2.71446e8i	0.000661895	−	0.00114644i	0.866356	+	0.499427i	$0.166456\pi$
$338$	−3.05263e9	+	5.28731e9i	−0.0127218	+	0.0220348i
$339$		0			0
$340$	−1.34711e11	−	2.33326e11i	−0.546698	−	0.946909i
$341$	−2.23830e11			−0.896444
$342$		0			0
$343$	−1.29803e11			−0.506362
$344$	6.85640e10	+	1.18756e11i	0.263987	+	0.457239i
$345$		0			0
$346$	1.31276e9	−	2.27377e9i	0.00492429	−	0.00852912i
$347$	−1.48136e11	+	2.56579e11i	−0.548502	+	0.950034i	0.449875	+	0.893091i	$0.351468\pi$
$347$	−1.48136e11	+	2.56579e11i	−0.548502	+	0.950034i	−0.998377	+	0.0569424i	$0.981865\pi$
$348$		0			0
$349$	−1.10780e11	−	1.91877e11i	−0.399712	−	0.692322i	0.593978	−	0.804481i	$-0.297557\pi$
$349$	−1.10780e11	−	1.91877e11i	−0.399712	−	0.692322i	−0.993690	+	0.112160i	$0.964223\pi$
$350$	1.04485e8			0.000372177
$351$		0			0
$352$	−1.67874e11			−0.582829
$353$	1.90537e11	+	3.30019e11i	0.653119	+	1.13124i	0.982362	+	0.186990i	$0.0598731\pi$
$353$	1.90537e11	+	3.30019e11i	0.653119	+	1.13124i	−0.329243	+	0.944245i	$0.606794\pi$
$354$		0			0
$355$	1.91584e11	−	3.31834e11i	0.640225	−	1.10890i
$356$	1.42304e11	−	2.46478e11i	0.469562	−	0.813306i
$357$		0			0
$358$	−2.02988e10	−	3.51586e10i	−0.0653127	−	0.113125i
$359$	3.34181e11			1.06183			0.530917	−	0.847424i	$-0.321847\pi$
$359$	3.34181e11			1.06183			0.530917	+	0.847424i	$0.321847\pi$
$360$		0			0
$361$	−3.22632e11			−0.999828
$362$	1.52931e10	+	2.64884e10i	0.0468065	+	0.0810713i
$363$		0			0
$364$	−4.63076e10	+	8.02072e10i	−0.138260	+	0.239473i
$365$	1.85702e11	−	3.21646e11i	0.547645	−	0.948549i
$366$		0			0
$367$	−2.31386e11	−	4.00773e11i	−0.665795	−	1.15319i	−0.979069	−	0.203528i	$-0.934759\pi$
$367$	−2.31386e11	−	4.00773e11i	−0.665795	−	1.15319i	0.313274	−	0.949663i	$-0.398574\pi$
$368$	−6.38258e11			−1.81418
$369$		0			0
$370$	−4.77817e10			−0.132542
$371$	5.03360e10	+	8.71845e10i	0.137942	+	0.238922i
$372$		0			0
$373$	1.16370e11	−	2.01558e11i	0.311280	−	0.539152i	−0.667360	−	0.744735i	$-0.732576\pi$
$373$	1.16370e11	−	2.01558e11i	0.311280	−	0.539152i	0.978640	+	0.205583i	$0.0659091\pi$
$374$	−4.22740e10	+	7.32207e10i	−0.111725	+	0.193514i
$375$		0			0
$376$	4.69362e10	+	8.12960e10i	0.121105	+	0.209760i
$377$	−6.44005e10			−0.164192
$378$		0			0
$379$	5.92570e10			0.147524			0.0737621	−	0.997276i	$-0.476499\pi$
$379$	5.92570e10			0.147524			0.0737621	+	0.997276i	$0.476499\pi$
$380$	2.61214e9	+	4.52436e9i	0.00642644	+	0.0111309i
$381$		0			0
$382$	5.43697e9	−	9.41711e9i	0.0130639	−	0.0226273i
$383$	−5.52900e10	+	9.57651e10i	−0.131296	+	0.227412i	−0.924177	−	0.381966i	$-0.875247\pi$
$383$	−5.52900e10	+	9.57651e10i	−0.131296	+	0.227412i	0.792880	+	0.609377i	$0.208581\pi$
$384$		0			0
$385$	7.43852e10	+	1.28839e11i	0.172549	+	0.298864i
$386$	−1.06085e11			−0.243226
$387$		0			0
$388$	2.93265e11			0.656928
$389$	−2.59862e11	−	4.50094e11i	−0.575400	−	0.996622i	−0.995998	−	0.0893747i	$-0.971513\pi$
$389$	−2.59862e11	−	4.50094e11i	−0.575400	−	0.996622i	0.420598	−	0.907247i	$-0.361820\pi$
$390$		0			0
$391$	−5.02221e11	+	8.69873e11i	−1.08668	+	1.88218i
$392$	−6.58475e10	+	1.14051e11i	−0.140848	+	0.243957i
$393$		0			0
$394$	3.74758e10	+	6.49099e10i	0.0783461	+	0.135699i
$395$	7.64711e11			1.58056
$396$		0			0
$397$	−4.49123e11			−0.907420			−0.453710	−	0.891149i	$-0.649900\pi$
$397$	−4.49123e11			−0.907420			−0.453710	+	0.891149i	$0.649900\pi$
$398$	6.25902e9	+	1.08409e10i	0.0125035	+	0.0216567i
$399$		0			0
$400$	−2.20895e9	+	3.82601e9i	−0.00431435	+	0.00747267i
$401$	2.37645e11	−	4.11613e11i	0.458964	−	0.794950i	−0.539942	−	0.841702i	$-0.681554\pi$
$401$	2.37645e11	−	4.11613e11i	0.458964	−	0.794950i	0.998907	+	0.0467526i	$0.0148872\pi$
$402$		0			0
$403$	1.95635e11	+	3.38850e11i	0.369465	+	0.639933i
$404$	8.12208e11			1.51688
$405$		0			0
$406$	3.33998e9			0.00610066
$407$	−3.12616e11	−	5.41467e11i	−0.564725	−	0.978132i
$408$		0			0
$409$	2.15970e11	−	3.74070e11i	0.381626	−	0.660995i	−0.609669	−	0.792656i	$-0.708698\pi$
$409$	2.15970e11	−	3.74070e11i	0.381626	−	0.660995i	0.991295	+	0.131661i	$0.0420310\pi$
$410$	−4.32123e10	+	7.48460e10i	−0.0755232	+	0.130810i
$411$		0			0
$412$	1.48179e11	+	2.56653e11i	0.253366	+	0.438843i
$413$	−2.24547e11			−0.379780
$414$		0			0
$415$	2.44280e11			0.404270
$416$	1.46727e11	+	2.54139e11i	0.240210	+	0.416056i
$417$		0			0
$418$	8.19723e8	−	1.41980e9i	0.00131333	−	0.00227475i
$419$	−4.52231e11	+	7.83288e11i	−0.716799	+	1.24153i	0.245462	+	0.969406i	$0.421060\pi$
$419$	−4.52231e11	+	7.83288e11i	−0.716799	+	1.24153i	−0.962261	+	0.272126i	$0.912273\pi$
$420$		0			0
$421$	−7.67841e10	−	1.32994e11i	−0.119125	−	0.206330i	0.800296	−	0.599605i	$-0.204676\pi$
$421$	−7.67841e10	−	1.32994e11i	−0.119125	−	0.206330i	−0.919421	+	0.393275i	$0.871342\pi$
$422$	−4.10651e10			−0.0630328
$423$		0			0
$424$	2.11819e11			0.318286
$425$	3.47627e9	+	6.02108e9i	0.00516849	+	0.00895209i
$426$		0			0
$427$	−1.17231e11	+	2.03049e11i	−0.170654	+	0.295581i
$428$	−1.17353e11	+	2.03262e11i	−0.169043	+	0.292792i
$429$		0			0
$430$	−9.51221e10	−	1.64756e11i	−0.134176	−	0.232399i
$431$	−1.01001e12			−1.40987			−0.704933	−	0.709274i	$-0.749023\pi$
$431$	−1.01001e12			−1.40987			−0.704933	+	0.709274i	$0.749023\pi$
$432$		0			0
$433$	1.38892e12			1.89881			0.949407	−	0.314048i	$-0.101685\pi$
$433$	1.38892e12			1.89881			0.949407	+	0.314048i	$0.101685\pi$
$434$	−1.01461e10	−	1.75736e10i	−0.0137277	−	0.0237770i
$435$		0			0
$436$	5.25537e11	−	9.10258e11i	0.696489	−	1.20635i
$437$	9.73843e9	−	1.68675e10i	0.0127739	−	0.0221250i
$438$		0			0
$439$	5.68209e11	+	9.84166e11i	0.730159	+	1.26467i	0.956815	+	0.290698i	$0.0938874\pi$
$439$	5.68209e11	+	9.84166e11i	0.730159	+	1.26467i	−0.226656	+	0.973975i	$0.572779\pi$
$440$	3.13020e11			0.398139
$441$		0			0
$442$	1.47796e11			0.184188
$443$	4.51021e11	+	7.81192e11i	0.556391	+	0.963698i	0.997794	+	0.0663886i	$0.0211477\pi$
$443$	4.51021e11	+	7.81192e11i	0.556391	+	0.963698i	−0.441403	+	0.897309i	$0.645519\pi$
$444$		0			0
$445$	−3.99586e11	+	6.92104e11i	−0.483048	+	0.836664i
$446$	3.26819e10	−	5.66067e10i	0.0391111	−	0.0677424i
$447$		0			0
$448$	9.63727e10	+	1.66922e11i	0.113032	+	0.195778i
$449$	4.28311e11			0.497337			0.248668	−	0.968589i	$-0.420007\pi$
$449$	4.28311e11			0.497337			0.248668	+	0.968589i	$0.420007\pi$
$450$		0			0
$451$	−1.13088e12			−1.28713
$452$	−3.13395e11	−	5.42816e11i	−0.353158	−	0.611688i
$453$		0			0
$454$	3.54546e9	−	6.14092e9i	0.00391671	−	0.00678395i
$455$	1.30030e11	−	2.25219e11i	0.142231	−	0.246351i
$456$		0			0
$457$	2.87623e11	+	4.98178e11i	0.308461	+	0.534271i	0.978026	−	0.208483i	$-0.0668527\pi$
$457$	2.87623e11	+	4.98178e11i	0.308461	+	0.534271i	−0.669565	+	0.742754i	$0.733519\pi$
$458$	7.40822e9			0.00786719
$459$		0			0
$460$	1.83733e12			1.91327
$461$	5.32572e11	+	9.22441e11i	0.549192	+	0.951228i	0.998330	+	0.0577655i	$0.0183976\pi$
$461$	5.32572e11	+	9.22441e11i	0.549192	+	0.951228i	−0.449139	+	0.893462i	$0.648269\pi$
$462$		0			0
$463$	3.45830e11	−	5.98996e11i	0.349743	−	0.605772i	−0.636461	−	0.771309i	$-0.719602\pi$
$463$	3.45830e11	−	5.98996e11i	0.349743	−	0.605772i	0.986204	+	0.165537i	$0.0529356\pi$
$464$	−7.06112e10	+	1.22302e11i	−0.0707200	+	0.122491i
$465$		0			0
$466$	6.97128e10	+	1.20746e11i	0.0684819	+	0.118614i
$467$	−1.39973e12			−1.36181			−0.680907	−	0.732370i	$-0.738414\pi$
$467$	−1.39973e12			−1.36181			−0.680907	+	0.732370i	$0.738414\pi$
$468$		0			0
$469$	1.21810e11			0.116253
$470$	−6.51169e10	−	1.12786e11i	−0.0615536	−	0.106614i
$471$		0			0
$472$	−2.36229e11	+	4.09160e11i	−0.219076	+	0.379450i
$473$	1.24469e12	−	2.15587e12i	1.14337	−	1.98037i
$474$		0			0
$475$	−6.74074e7	−	1.16753e8i	−6.07556e−5	−	0.000105232i
$476$	3.19614e11			0.285361
$477$		0			0
$478$	−3.20773e10			−0.0281043
$479$	−4.78401e11	−	8.28615e11i	−0.415224	−	0.719189i	0.580228	−	0.814454i	$-0.302964\pi$
$479$	−4.78401e11	−	8.28615e11i	−0.415224	−	0.719189i	−0.995452	+	0.0952650i	$0.969630\pi$
$480$		0			0
$481$	−5.46474e11	+	9.46521e11i	−0.465497	+	0.806265i
$482$	1.35216e11	−	2.34201e11i	0.114108	−	0.197641i
$483$		0			0
$484$	4.22351e11	+	7.31534e11i	0.349840	+	0.605941i
$485$	−8.23479e11			−0.675795
$486$		0			0
$487$	−2.88361e11			−0.232303			−0.116152	−	0.993231i	$-0.537056\pi$
$487$	−2.88361e11			−0.232303			−0.116152	+	0.993231i	$0.537056\pi$
$488$	2.46659e11	+	4.27225e11i	0.196882	+	0.341010i
$489$		0			0
$490$	9.13534e10	−	1.58229e11i	0.0715884	−	0.123995i
$491$	−1.17312e11	+	2.03190e11i	−0.0910910	+	0.157774i	−0.907970	−	0.419034i	$-0.862369\pi$
$491$	−1.17312e11	+	2.03190e11i	−0.0910910	+	0.157774i	0.816879	+	0.576808i	$0.195702\pi$
$492$		0			0
$493$	1.11123e11	+	1.92470e11i	0.0847210	+	0.146741i
$494$	−2.86586e9			−0.00216513
$495$		0			0
$496$	8.58007e11			0.636536
$497$	2.27276e11	+	3.93653e11i	0.167090	+	0.289408i
$498$		0			0
$499$	−1.26477e12	+	2.19065e12i	−0.913189	+	1.58169i	−0.103658	+	0.994613i	$0.533055\pi$
$499$	−1.26477e12	+	2.19065e12i	−0.913189	+	1.58169i	−0.809531	+	0.587077i	$0.800279\pi$
$500$	−6.79204e11	+	1.17642e12i	−0.485999	+	0.841775i
$501$		0			0
$502$	2.67907e10	+	4.64028e10i	0.0188286	+	0.0326120i
$503$	3.09347e11			0.215471			0.107736	−	0.994180i	$-0.465640\pi$
$503$	3.09347e11			0.215471			0.107736	+	0.994180i	$0.465640\pi$
$504$		0			0
$505$	−2.28065e12			−1.56044
$506$	−2.88289e11	−	4.99331e11i	−0.195502	−	0.338619i
$507$		0			0
$508$	9.53598e11	−	1.65168e12i	0.635300	−	1.10037i
$509$	−1.27179e12	+	2.20280e12i	−0.839816	+	1.45460i	0.0502320	+	0.998738i	$0.484004\pi$
$509$	−1.27179e12	+	2.20280e12i	−0.839816	+	1.45460i	−0.890048	+	0.455867i	$0.849329\pi$
$510$		0			0
$511$	2.20298e11	+	3.81567e11i	0.142928	+	0.247558i
$512$	1.08108e12			0.695252
$513$		0			0
$514$	−3.23698e11			−0.204553
$515$	−4.16081e11	−	7.20674e11i	−0.260643	−	0.451447i
$516$		0			0
$517$	8.52067e11	−	1.47582e12i	0.524525	−	0.908504i
$518$	2.83416e10	−	4.90891e10i	0.0172958	−	0.0299572i
$519$		0			0
$520$	−2.73590e11	−	4.73872e11i	−0.164091	−	0.284214i
$521$	1.75471e12			1.04336			0.521682	−	0.853140i	$-0.325305\pi$
$521$	1.75471e12			1.04336			0.521682	+	0.853140i	$0.325305\pi$
$522$		0			0
$523$	9.65849e11			0.564484			0.282242	−	0.959343i	$-0.408922\pi$
$523$	9.65849e11			0.564484			0.282242	+	0.959343i	$0.408922\pi$
$524$	−4.84944e11	−	8.39948e11i	−0.280996	−	0.486700i
$525$		0			0
$526$	1.36952e10	−	2.37208e10i	0.00780069	−	0.0135112i
$527$	6.75133e11	−	1.16936e12i	0.381278	−	0.660393i
$528$		0			0
$529$	−2.52434e12	−	4.37228e12i	−1.40151	−	2.42749i
$530$	−2.93866e11			−0.161774
$531$		0			0
$532$	−6.19754e9			−0.00335442
$533$	9.88430e11	+	1.71201e12i	0.530486	+	0.918828i
$534$		0			0
$535$	3.29524e11	−	5.70753e11i	0.173898	−	0.301201i
$536$	1.28147e11	−	2.21957e11i	0.0670605	−	0.116152i
$537$		0			0
$538$	2.47083e11	+	4.27961e11i	0.127152	+	0.220234i
$539$	2.39075e12			1.22007
$540$		0			0
$541$	−2.09700e12			−1.05247			−0.526235	−	0.850339i	$-0.676397\pi$
$541$	−2.09700e12			−1.05247			−0.526235	+	0.850339i	$0.676397\pi$
$542$	−1.14408e11	−	1.98161e11i	−0.0569457	−	0.0986328i
$543$		0			0
$544$	5.06354e11	−	8.77031e11i	0.247890	−	0.429358i
$545$	−1.47569e12	+	2.55598e12i	−0.716493	+	1.24100i
$546$		0			0
$547$	−7.51610e11	−	1.30183e12i	−0.358963	−	0.621742i	0.628825	−	0.777547i	$-0.283536\pi$
$547$	−7.51610e11	−	1.30183e12i	−0.358963	−	0.621742i	−0.987788	+	0.155805i	$0.950203\pi$
$548$	−2.97137e12			−1.40749
$549$		0			0
$550$	−3.99095e9			−0.00185971
$551$	−2.15474e9	−	3.73213e9i	−0.000995895	−	0.00172494i
$552$		0			0
$553$	−4.53587e11	+	7.85635e11i	−0.206251	+	0.357238i
$554$	7.44747e10	−	1.28994e11i	0.0335904	−	0.0581803i
$555$		0			0
$556$	−1.38790e12	−	2.40391e12i	−0.615916	−	1.06680i
$557$	−4.83664e11			−0.212910			−0.106455	−	0.994318i	$-0.533950\pi$
$557$	−4.83664e11			−0.212910			−0.106455	+	0.994318i	$0.533950\pi$
$558$		0			0
$559$	−4.35161e12			−1.88494
$560$	−2.85141e11	−	4.93878e11i	−0.122522	−	0.212214i
$561$		0			0
$562$	1.74928e11	−	3.02984e11i	0.0739682	−	0.128117i
$563$	1.23877e12	−	2.14562e12i	0.519641	−	0.900045i	−0.480098	−	0.877215i	$-0.659399\pi$
$563$	1.23877e12	−	2.14562e12i	0.519641	−	0.900045i	0.999739	−	0.0228302i	$-0.00726772\pi$
$564$		0			0
$565$	8.80003e11	+	1.52421e12i	0.363301	+	0.629255i
$566$	−2.83245e11			−0.116008
$567$		0			0
$568$	9.56398e11			0.385541
$569$	−1.75498e12	−	3.03971e12i	−0.701886	−	1.21570i	−0.967804	−	0.251706i	$-0.919008\pi$
$569$	−1.75498e12	−	3.03971e12i	−0.701886	−	1.21570i	0.265918	−	0.963996i	$-0.414325\pi$
$570$		0			0
$571$	−1.28628e11	+	2.22790e11i	−0.0506375	+	0.0877066i	−0.890233	−	0.455505i	$-0.849459\pi$
$571$	−1.28628e11	+	2.22790e11i	−0.0506375	+	0.0877066i	0.839596	+	0.543212i	$0.182792\pi$
$572$	1.76878e12	−	3.06362e12i	0.690862	−	1.19661i
$573$		0			0
$574$	−5.12626e10	−	8.87895e10i	−0.0197105	−	0.0341396i
$575$	−4.74131e10			−0.0180881
$576$		0			0
$577$	7.55281e11			0.283673			0.141836	−	0.989890i	$-0.454699\pi$
$577$	7.55281e11			0.283673			0.141836	+	0.989890i	$0.454699\pi$
$578$	−4.96941e10	−	8.60728e10i	−0.0185195	−	0.0320768i
$579$		0			0
$580$	2.03266e11	−	3.52066e11i	0.0745827	−	0.129181i
$581$	−1.44894e11	+	2.50964e11i	−0.0527544	+	0.0913733i
$582$		0			0
$583$	−1.92265e12	−	3.33013e12i	−0.689273	−	1.19386i
$584$	9.27034e11			0.329790
$585$		0			0
$586$	−2.80181e11			−0.0981519
$587$	2.56556e12	+	4.44367e12i	0.891888	+	1.54479i	0.837610	+	0.546269i	$0.183952\pi$
$587$	2.56556e12	+	4.44367e12i	0.891888	+	1.54479i	0.0542776	+	0.998526i	$0.482714\pi$
$588$		0			0
$589$	−1.30913e10	+	2.26748e10i	−0.00448192	+	0.00776292i
$590$	3.27732e11	−	5.67648e11i	0.111349	−	0.192861i
$591$		0			0
$592$	1.19835e12	+	2.07561e12i	0.400993	+	0.694540i
$593$	−1.98175e12			−0.658116			−0.329058	−	0.944310i	$-0.606731\pi$
$593$	−1.98175e12			−0.658116			−0.329058	+	0.944310i	$0.606731\pi$
$594$		0			0
$595$	−8.97466e11			−0.293557
$596$	2.43104e12	+	4.21069e12i	0.789196	+	1.36693i
$597$		0			0
$598$	−5.03948e11	+	8.72864e11i	−0.161150	+	0.279120i
$599$	5.16257e11	−	8.94184e11i	0.163850	−	0.283796i	−0.772397	−	0.635141i	$-0.780942\pi$
$599$	5.16257e11	−	8.94184e11i	0.163850	−	0.283796i	0.936246	+	0.351345i	$0.114275\pi$
$600$		0			0
$601$	5.34090e11	+	9.25071e11i	0.166986	+	0.289228i	0.937359	−	0.348366i	$-0.113263\pi$
$601$	5.34090e11	+	9.25071e11i	0.166986	+	0.289228i	−0.770373	+	0.637594i	$0.779930\pi$
$602$	2.25686e11			0.0700358
$603$		0			0
$604$	1.60929e12			0.492002
$605$	−1.18595e12	−	2.05412e12i	−0.359888	−	0.623343i
$606$		0			0
$607$	−1.66935e12	+	2.89140e12i	−0.499112	+	0.864488i	−0.999999	−	0.00102472i	$-0.999674\pi$
$607$	−1.66935e12	+	2.89140e12i	−0.499112	+	0.864488i	0.500887	+	0.865513i	$0.333007\pi$
$608$	−9.81857e9	+	1.70063e10i	−0.00291395	+	0.00504711i
$609$		0			0
$610$	−3.42201e11	−	5.92710e11i	−0.100069	−	0.173324i
$611$	−2.97894e12			−0.864722
$612$		0			0
$613$	−4.12503e12			−1.17993			−0.589964	−	0.807430i	$-0.700858\pi$
$613$	−4.12503e12			−1.17993			−0.589964	+	0.807430i	$0.700858\pi$
$614$	−1.31253e11	−	2.27337e11i	−0.0372693	−	0.0645523i
$615$		0			0
$616$	−1.85667e11	+	3.21585e11i	−0.0519543	+	0.0899876i
$617$	−2.16264e12	+	3.74580e12i	−0.600759	+	1.04055i	0.391947	+	0.919988i	$0.371802\pi$
$617$	−2.16264e12	+	3.74580e12i	−0.600759	+	1.04055i	−0.992706	+	0.120558i	$0.961532\pi$
$618$		0			0
$619$	3.15688e12	+	5.46787e12i	0.864271	+	1.49696i	0.867770	+	0.496967i	$0.165553\pi$
$619$	3.15688e12	+	5.46787e12i	0.864271	+	1.49696i	−0.00349896	+	0.999994i	$0.501114\pi$
$620$	−2.46991e12			−0.671303
$621$		0			0
$622$	6.15180e11			0.164796
$623$	−4.74028e11	−	8.21040e11i	−0.126069	−	0.218357i
$624$		0			0
$625$	1.92488e12	−	3.33398e12i	0.504595	−	0.873984i
$626$	−1.44994e11	+	2.51137e11i	−0.0377368	+	0.0653621i
$627$		0			0
$628$	3.21446e11	+	5.56760e11i	0.0824687	+	0.142840i
$629$	3.77175e12			0.960760
$630$		0			0
$631$	6.69921e12			1.68225			0.841127	−	0.540838i	$-0.181893\pi$
$631$	6.69921e12			1.68225			0.841127	+	0.540838i	$0.181893\pi$
$632$	9.54367e11	+	1.65301e12i	0.237952	+	0.412144i
$633$		0			0
$634$	9.17711e10	−	1.58952e11i	0.0225582	−	0.0390719i
$635$	−2.67767e12	+	4.63787e12i	−0.653546	+	1.13197i
$636$		0			0
$637$	−2.08960e12	−	3.61929e12i	−0.502847	−	0.870956i
$638$	−1.27575e11			−0.0304840
$639$		0			0
$640$	−2.45951e12			−0.579480
$641$	−3.53417e12	−	6.12136e12i	−0.826849	−	1.43214i	−0.900498	−	0.434860i	$-0.856798\pi$
$641$	−3.53417e12	−	6.12136e12i	−0.826849	−	1.43214i	0.0736498	−	0.997284i	$-0.476535\pi$
$642$		0			0
$643$	−8.53171e11	+	1.47774e12i	−0.196828	+	0.340916i	−0.947498	−	0.319761i	$-0.896397\pi$
$643$	−8.53171e11	+	1.47774e12i	−0.196828	+	0.340916i	0.750670	+	0.660677i	$0.229731\pi$
$644$	−1.08981e12	+	1.88760e12i	−0.249669	+	0.432439i
$645$		0			0
$646$	4.94503e9	+	8.56504e9i	0.00111718	+	0.00193501i
$647$	3.85704e12			0.865336			0.432668	−	0.901553i	$-0.357572\pi$
$647$	3.85704e12			0.865336			0.432668	+	0.901553i	$0.357572\pi$
$648$		0			0
$649$	8.57687e12			1.89770
$650$	3.48823e9	+	6.04179e9i	0.000766469	+	0.00132756i
$651$		0			0
$652$	1.09569e12	−	1.89779e12i	0.237451	−	0.411277i
$653$	2.31206e12	−	4.00460e12i	0.497610	−	0.861886i	−0.502386	−	0.864644i	$-0.667544\pi$
$653$	2.31206e12	−	4.00460e12i	0.497610	−	0.861886i	0.999996	+	0.00275722i	$0.000877652\pi$
$654$		0			0
$655$	1.36171e12	+	2.35855e12i	0.289067	+	0.500678i
$656$	4.33501e12			0.913952
$657$		0			0
$658$	1.54496e11			0.0321292
$659$	−4.08401e11	−	7.07371e11i	−0.0843533	−	0.146104i	0.820762	−	0.571270i	$-0.193549\pi$
$659$	−4.08401e11	−	7.07371e11i	−0.0843533	−	0.146104i	−0.905115	+	0.425166i	$0.860216\pi$
$660$		0			0
$661$	5.73853e11	−	9.93942e11i	0.116921	−	0.202514i	−0.801625	−	0.597827i	$-0.796031\pi$
$661$	5.73853e11	−	9.93942e11i	0.116921	−	0.202514i	0.918546	+	0.395314i	$0.129364\pi$
$662$	−3.84340e11	+	6.65697e11i	−0.0777776	+	0.134715i
$663$		0			0
$664$	3.04864e11	+	5.28041e11i	0.0608626	+	0.105417i
$665$	1.74025e10			0.00345076
$666$		0			0
$667$	−1.51561e12			−0.296497
$668$	3.83842e11	+	6.64834e11i	0.0745862	+	0.129187i
$669$		0			0
$670$	−1.77785e11	+	3.07932e11i	−0.0340845	+	0.0590361i
$671$	4.47777e12	−	7.75573e12i	0.852728	−	1.47697i
$672$		0			0
$673$	3.58758e12	+	6.21386e12i	0.674114	+	1.16760i	0.976727	+	0.214486i	$0.0688077\pi$
$673$	3.58758e12	+	6.21386e12i	0.674114	+	1.16760i	−0.302613	+	0.953114i	$0.597859\pi$
$674$	−1.08539e9			−0.000202590
$675$		0			0
$676$	−8.81552e11			−0.162363
$677$	−2.60502e12	−	4.51203e12i	−0.476609	−	0.825510i	0.523032	−	0.852313i	$-0.324801\pi$
$677$	−2.60502e12	−	4.51203e12i	−0.476609	−	0.825510i	−0.999641	+	0.0268026i	$0.991467\pi$
$678$		0			0
$679$	4.88445e11	−	8.46011e11i	0.0881864	−	0.152743i
$680$	−9.44156e11	+	1.63533e12i	−0.169338	+	0.293301i
$681$		0			0
$682$	3.87545e11	+	6.71248e11i	0.0685950	+	0.118810i
$683$	−2.81291e12			−0.494611			−0.247305	−	0.968938i	$-0.579545\pi$
$683$	−2.81291e12			−0.494611			−0.247305	+	0.968938i	$0.579545\pi$
$684$		0			0
$685$	8.34352e12			1.44791
$686$	2.24744e11	+	3.89269e11i	0.0387463	+	0.0671106i
$687$		0			0
$688$	−4.77127e12	+	8.26409e12i	−0.811870	+	1.40620i
$689$	−3.36092e12	+	5.82128e12i	−0.568161	+	0.984084i
$690$		0			0
$691$	3.87496e12	+	6.71162e12i	0.646570	+	1.11989i	0.983937	+	0.178519i	$0.0571305\pi$
$691$	3.87496e12	+	6.71162e12i	0.646570	+	1.11989i	−0.337366	+	0.941373i	$0.609536\pi$
$692$	3.79105e11			0.0628466
$693$		0			0
$694$	1.02595e12			0.167883
$695$	3.89718e12	+	6.75011e12i	0.633605	+	1.09744i
$696$		0			0
$697$	3.41106e12	−	5.90813e12i	0.547447	−	0.948205i
$698$	−3.83615e11	+	6.64441e11i	−0.0611711	+	0.105951i
$699$		0			0
$700$	7.54343e9	+	1.30656e10i	0.00118748	+	0.00205678i
$701$	−1.86576e12			−0.291826			−0.145913	−	0.989297i	$-0.546612\pi$
$701$	−1.86576e12			−0.291826			−0.145913	+	0.989297i	$0.546612\pi$
$702$		0			0
$703$	−7.31369e10			−0.0112937
$704$	−3.68108e12	−	6.37581e12i	−0.564804	−	0.978270i
$705$		0			0
$706$	6.59800e11	−	1.14281e12i	0.0999520	−	0.173122i
$707$	1.35277e12	−	2.34306e12i	0.203627	−	0.352692i
$708$		0			0
$709$	−1.13808e11	−	1.97122e11i	−0.0169148	−	0.0292972i	0.857444	−	0.514577i	$-0.172051\pi$
$709$	−1.13808e11	−	1.97122e11i	−0.0169148	−	0.0292972i	−0.874359	+	0.485280i	$0.838718\pi$
$710$	−1.32686e12			−0.195957
$711$		0			0
$712$	−1.99475e12			−0.290890
$713$	4.60409e12	+	7.97452e12i	0.667177	+	1.15558i
$714$		0			0
$715$	−4.96668e12	+	8.60254e12i	−0.710704	+	1.23098i
$716$	2.93099e12	−	5.07662e12i	0.416779	−	0.721882i
$717$		0			0
$718$	−5.78610e11	−	1.00218e12i	−0.0812505	−	0.140730i
$719$	−2.12785e12			−0.296934			−0.148467	−	0.988917i	$-0.547434\pi$
$719$	−2.12785e12			−0.296934			−0.148467	+	0.988917i	$0.547434\pi$
$720$		0			0
$721$	9.87191e11			0.136048
$722$	5.58614e11	+	9.67548e11i	0.0765058	+	0.132512i
$723$		0			0
$724$	−2.20820e12	+	3.82471e12i	−0.298686	+	0.517339i
$725$	−5.24536e9	+	9.08523e9i	−0.000705106	+	0.00122128i
$726$		0			0
$727$	7.88780e11	+	1.36621e12i	0.104725	+	0.181389i	0.913626	−	0.406556i	$-0.133270\pi$
$727$	7.88780e11	+	1.36621e12i	0.104725	+	0.181389i	−0.808901	+	0.587945i	$0.799937\pi$
$728$	6.49118e11			0.0856510
$729$		0			0
$730$	−1.28612e12			−0.167621
$731$	7.50867e12	+	1.30054e13i	0.972601	+	1.68459i
$732$		0			0
$733$	2.30042e12	−	3.98444e12i	0.294333	−	0.509799i	−0.680497	−	0.732751i	$-0.738236\pi$
$733$	2.30042e12	−	3.98444e12i	0.294333	−	0.509799i	0.974829	+	0.222952i	$0.0715693\pi$
$734$	−8.01257e11	+	1.38782e12i	−0.101892	+	0.176482i
$735$		0			0
$736$	3.45310e12	+	5.98094e12i	0.433769	+	0.751310i
$737$	−4.65269e12			−0.580899
$738$		0			0
$739$	−2.25557e12			−0.278199			−0.139099	−	0.990278i	$-0.544421\pi$
$739$	−2.25557e12			−0.278199			−0.139099	+	0.990278i	$0.544421\pi$
$740$	−3.44965e12	−	5.97497e12i	−0.422895	−	0.732475i
$741$		0			0
$742$	1.74306e11	−	3.01907e11i	0.0211103	−	0.0365642i
$743$	5.38723e12	−	9.33095e12i	0.648508	−	1.12325i	−0.334971	−	0.942228i	$-0.608727\pi$
$743$	5.38723e12	−	9.33095e12i	0.648508	−	1.12325i	0.983479	−	0.181021i	$-0.0579401\pi$
$744$		0			0
$745$	−6.82630e12	−	1.18235e13i	−0.811862	−	1.40619i
$746$	−8.05943e11			−0.0952752
$747$		0			0
$748$	−1.22081e13			−1.42590
$749$	3.90913e11	+	6.77082e11i	0.0453850	+	0.0786092i
$750$		0			0
$751$	2.66024e12	−	4.60766e12i	0.305169	−	0.528568i	−0.672130	−	0.740433i	$-0.734620\pi$
$751$	2.66024e12	−	4.60766e12i	0.305169	−	0.528568i	0.977299	+	0.211865i	$0.0679537\pi$
$752$	−3.26623e12	+	5.65728e12i	−0.372449	+	0.645100i
$753$		0			0
$754$	1.11505e11	+	1.93132e11i	0.0125638	+	0.0217612i
$755$	−4.51883e12			−0.506133
$756$		0			0
$757$	8.65829e12			0.958298			0.479149	−	0.877734i	$-0.340945\pi$
$757$	8.65829e12			0.958298			0.479149	+	0.877734i	$0.340945\pi$
$758$	−1.02599e11	−	1.77707e11i	−0.0112884	−	0.0195521i
$759$		0			0
$760$	1.83078e10	−	3.17101e10i	0.00199056	−	0.00344776i
$761$	−3.52267e12	+	6.10144e12i	−0.380751	+	0.659480i	−0.991170	−	0.132599i	$-0.957668\pi$
$761$	−3.52267e12	+	6.10144e12i	−0.380751	+	0.659480i	0.610419	+	0.792079i	$0.291001\pi$
$762$		0			0
$763$	−1.75061e12	−	3.03214e12i	−0.186994	−	0.323884i
$764$	1.57011e12			0.166729
$765$		0			0
$766$	3.82923e11			0.0401866
$767$	−7.49647e12	−	1.29843e13i	−0.782128	−	1.35469i
$768$		0			0
$769$	3.29135e12	−	5.70079e12i	0.339395	−	0.587850i	−0.644924	−	0.764247i	$-0.723111\pi$
$769$	3.29135e12	−	5.70079e12i	0.339395	−	0.587850i	0.984319	+	0.176397i	$0.0564442\pi$
$770$	2.57585e11	−	4.46150e11i	0.0264066	−	0.0457376i
$771$		0			0
$772$	−7.65889e12	−	1.32656e13i	−0.776047	−	1.34415i
$773$	1.34877e13			1.35872			0.679360	−	0.733805i	$-0.262258\pi$
$773$	1.34877e13			1.35872			0.679360	+	0.733805i	$0.262258\pi$
$774$		0			0
$775$	6.37371e10			0.00634651
$776$	−1.02771e12	−	1.78005e12i	−0.101740	−	0.176219i
$777$		0			0
$778$	−8.99864e11	+	1.55861e12i	−0.0880580	+	0.152521i
$779$	−6.61429e10	+	1.14563e11i	−0.00643523	+	0.0111462i
$780$		0			0
$781$	−8.68109e12	−	1.50361e13i	−0.834919	−	1.44612i
$782$	3.47824e12			0.332605
$783$		0			0
$784$	−9.16447e12			−0.866334
$785$	−9.02609e11	−	1.56337e12i	−0.0848372	−	0.146942i
$786$		0			0
$787$	6.15564e12	−	1.06619e13i	0.571988	−	0.990713i	−0.424374	−	0.905487i	$-0.639506\pi$
$787$	6.15564e12	−	1.06619e13i	0.571988	−	0.990713i	0.996362	−	0.0852254i	$-0.0271610\pi$
$788$	−5.41120e12	+	9.37248e12i	−0.499949	+	0.865938i
$789$		0			0
$790$	−1.32404e12	−	2.29331e12i	−0.120943	−	0.209479i
$791$	−2.08789e12			−0.189633
$792$		0			0
$793$	−1.56549e13			−1.40579
$794$	7.77624e11	+	1.34688e12i	0.0694349	+	0.120265i
$795$		0			0
$796$	−9.03753e11	+	1.56535e12i	−0.0797886	+	0.138198i
$797$	5.69410e12	−	9.86247e12i	0.499877	−	0.865812i	−0.500123	−	0.865954i	$-0.666712\pi$
$797$	5.69410e12	−	9.86247e12i	0.499877	−	0.865812i	1.00000		0.000142537i	$4.53711e-5\pi$
$798$		0			0
$799$	5.14014e12	+	8.90299e12i	0.446185	+	0.772815i
$800$	4.78033e10			0.00412622
$801$		0			0
$802$	−1.64586e12			−0.140478
$803$	−8.41455e12	−	1.45744e13i	−0.714186	−	1.23701i
$804$		0			0
$805$	3.06015e12	−	5.30033e12i	0.256839	−	0.444858i
$806$	6.77455e11	−	1.17339e12i	0.0565422	−	0.0979340i
$807$		0			0
$808$	−2.84628e12	−	4.92990e12i	−0.234924	−	0.406900i
$809$	9.39455e12			0.771095			0.385547	−	0.922688i	$-0.374013\pi$
$809$	9.39455e12			0.771095			0.385547	+	0.922688i	$0.374013\pi$
$810$		0			0
$811$	8.85202e12			0.718536			0.359268	−	0.933234i	$-0.383026\pi$
$811$	8.85202e12			0.718536			0.359268	+	0.933234i	$0.383026\pi$
$812$	2.41133e11	+	4.17655e11i	0.0194650	+	0.0337144i
$813$		0			0
$814$	−1.08254e12	+	1.87502e12i	−0.0864243	+	0.149691i
$815$	−3.07667e12	+	5.32894e12i	−0.244271	+	0.423089i
$816$		0			0
$817$	−1.45598e11	−	2.52184e11i	−0.0114329	−	0.0198024i
$818$	−1.49574e12			−0.116806
$819$		0			0
$820$	−1.24790e13			−0.963871
$821$	6.69699e12	+	1.15995e13i	0.514441	+	0.891037i	0.999860	+	0.0167556i	$0.00533373\pi$
$821$	6.69699e12	+	1.15995e13i	0.514441	+	0.891037i	−0.485419	+	0.874282i	$0.661333\pi$
$822$		0			0
$823$	−9.32974e12	+	1.61596e13i	−0.708876	+	1.22781i	0.256399	+	0.966571i	$0.417464\pi$
$823$	−9.32974e12	+	1.61596e13i	−0.708876	+	1.22781i	−0.965274	+	0.261238i	$0.915869\pi$
$824$	1.03855e12	−	1.79882e12i	0.0784792	−	0.135930i
$825$		0			0
$826$	3.88787e11	+	6.73399e11i	0.0290604	+	0.0503341i
$827$	−1.27791e13			−0.950006			−0.475003	−	0.879984i	$-0.657553\pi$
$827$	−1.27791e13			−0.950006			−0.475003	+	0.879984i	$0.657553\pi$
$828$		0			0
$829$	−8.09935e12			−0.595600			−0.297800	−	0.954628i	$-0.596253\pi$
$829$	−8.09935e12			−0.595600			−0.297800	+	0.954628i	$0.596253\pi$
$830$	−4.22953e11	−	7.32576e11i	−0.0309343	−	0.0535798i
$831$		0			0
$832$	−6.43477e12	+	1.11454e13i	−0.465563	+	0.806378i
$833$	−7.21118e12	+	1.24901e13i	−0.518924	+	0.898803i
$834$		0			0
$835$	−1.07782e12	−	1.86683e12i	−0.0767284	−	0.132897i
$836$	2.36723e11			0.0167615
$837$		0			0
$838$	3.13202e12			0.219395
$839$	5.88748e12	+	1.01974e13i	0.410205	+	0.710495i	0.994912	−	0.100749i	$-0.0321240\pi$
$839$	5.88748e12	+	1.01974e13i	0.410205	+	0.710495i	−0.584707	+	0.811244i	$0.698791\pi$
$840$		0			0
$841$	7.08590e12	−	1.22731e13i	0.488442	−	0.846006i
$842$	−2.65892e11	+	4.60539e11i	−0.0182306	+	0.0315763i
$843$		0			0
$844$	−2.96474e12	−	5.13507e12i	−0.201115	−	0.348342i
$845$	2.47537e12			0.167026
$846$		0			0
$847$	2.81377e12			0.187851
$848$	7.37009e12	+	1.27654e13i	0.489431	+	0.847719i
$849$		0			0
$850$	1.20378e10	−	2.08501e10i	0.000790975	−	0.00137001i
$851$	−1.28608e13	+	2.22755e13i	−0.840590	+	1.45595i
$852$		0			0
$853$	−3.42110e11	−	5.92552e11i	−0.0221256	−	0.0383227i	0.854751	−	0.519039i	$-0.173710\pi$
$853$	−3.42110e11	−	5.92552e11i	−0.0221256	−	0.0383227i	−0.876876	+	0.480716i	$0.840377\pi$
$854$	8.11904e11			0.0522329
$855$		0			0
$856$	1.64500e12			0.104721
$857$	−5.78222e12	−	1.00151e13i	−0.366168	−	0.634222i	0.622795	−	0.782385i	$-0.285997\pi$
$857$	−5.78222e12	−	1.00151e13i	−0.366168	−	0.634222i	−0.988963	+	0.148163i	$0.952664\pi$
$858$		0			0
$859$	−7.51305e12	+	1.30130e13i	−0.470812	+	0.815470i	−0.999443	−	0.0333820i	$-0.989372\pi$
$859$	−7.51305e12	+	1.30130e13i	−0.470812	+	0.815470i	0.528631	+	0.848852i	$0.322706\pi$
$860$	1.37349e13	−	2.37895e13i	0.856213	−	1.48300i
$861$		0			0
$862$	1.74876e12	+	3.02894e12i	0.107882	+	0.186856i
$863$	−1.54066e13			−0.945490			−0.472745	−	0.881199i	$-0.656737\pi$
$863$	−1.54066e13			−0.945490			−0.472745	+	0.881199i	$0.656737\pi$
$864$		0			0
$865$	−1.06451e12			−0.0646516
$866$	−2.40482e12	−	4.16527e12i	−0.145295	−	0.251659i
$867$		0			0
$868$	1.46502e12	−	2.53749e12i	0.0876003	−	0.151728i
$869$	1.73253e13	−	3.00083e13i	1.03060	−	1.78506i
$870$		0			0
$871$	4.06661e12	+	7.04357e12i	0.239415	+	0.414678i
$872$	−7.36673e12			−0.431470
$873$		0			0
$874$	−6.74455e10			−0.00390977
$875$	2.26249e12	+	3.91874e12i	0.130482	+	0.226001i
$876$		0			0
$877$	1.28821e13	−	2.23124e13i	0.735338	−	1.27364i	−0.219236	−	0.975672i	$-0.570357\pi$
$877$	1.28821e13	−	2.23124e13i	0.735338	−	1.27364i	0.954575	−	0.297972i	$-0.0963101\pi$
$878$	1.96762e12	−	3.40802e12i	0.111742	−	0.193543i
$879$		0			0
$880$	1.08913e13	+	1.88643e13i	0.612221	+	1.06040i
$881$	8.67327e12			0.485055			0.242528	−	0.970144i	$-0.422023\pi$
$881$	8.67327e12			0.485055			0.242528	+	0.970144i	$0.422023\pi$
$882$		0			0
$883$	1.27283e13			0.704607			0.352304	−	0.935886i	$-0.385398\pi$
$883$	1.27283e13			0.704607			0.352304	+	0.935886i	$0.385398\pi$
$884$	1.06703e13	+	1.84814e13i	0.587679	+	1.01789i
$885$		0			0
$886$	1.56182e12	−	2.70515e12i	0.0851490	−	0.147482i
$887$	1.99661e12	−	3.45824e12i	0.108302	−	0.187585i	−0.806780	−	0.590852i	$-0.798792\pi$
$887$	1.99661e12	−	3.45824e12i	0.108302	−	0.187585i	0.915083	+	0.403266i	$0.132125\pi$
$888$		0			0
$889$	−3.17651e12	−	5.50188e12i	−0.170566	−	0.295429i
$890$	2.76742e12			0.147849
$891$		0			0
$892$	9.43801e12			0.499159
$893$	−9.96711e10	−	1.72635e11i	−0.00524490	−	0.00908444i
$894$		0			0
$895$	−8.23013e12	+	1.42550e13i	−0.428749	+	0.742615i
$896$	1.45885e12	−	2.52681e12i	0.0756180	−	0.130974i
$897$		0			0
$898$	−7.41589e11	−	1.28447e12i	−0.0380557	−	0.0659144i
$899$	2.03742e12			0.104031
$900$		0			0
$901$	2.31970e13			1.17265
$902$	1.95804e12	+	3.39143e12i	0.0984901	+	0.170590i
$903$		0			0
$904$	−2.19651e12	+	3.80446e12i	−0.109389	+	0.189468i
$905$	6.20056e12	−	1.07397e13i	0.307264	−	0.532197i
$906$		0			0
$907$	4.39889e12	+	7.61910e12i	0.215829	+	0.373827i	0.953529	−	0.301302i	$-0.0974212\pi$
$907$	4.39889e12	+	7.61910e12i	0.215829	+	0.373827i	−0.737699	+	0.675129i	$0.764088\pi$
$908$	1.02387e12			0.0499874
$909$		0			0
$910$	−9.00552e11			−0.0435334
$911$	−1.47806e13	−	2.56007e13i	−0.710983	−	1.23146i	−0.964489	−	0.264125i	$-0.914917\pi$
$911$	−1.47806e13	−	2.56007e13i	−0.710983	−	1.23146i	0.253506	−	0.967334i	$-0.418416\pi$
$912$		0			0
$913$	5.53442e12	−	9.58590e12i	0.263605	−	0.456577i
$914$	9.95996e11	−	1.72512e12i	0.0472063	−	0.0817637i
$915$		0			0
$916$	5.34844e11	+	9.26378e11i	0.0251014	+	0.0434769i
$917$	−3.23078e12			−0.150885
$918$		0			0
$919$	−1.05646e13			−0.488577			−0.244288	−	0.969703i	$-0.578554\pi$
$919$	−1.05646e13			−0.488577			−0.244288	+	0.969703i	$0.578554\pi$
$920$	−6.43870e12	−	1.11522e13i	−0.296314	−	0.513232i
$921$		0			0
$922$	1.84422e12	−	3.19428e12i	0.0840471	−	0.145574i
$923$	−1.51751e13	+	2.62841e13i	−0.688216	+	1.19203i
$924$		0			0
$925$	8.90197e10	+	1.54187e11i	0.00399805	+	0.00692483i
$926$	−2.39512e12			−0.107048
$927$		0			0
$928$	1.52808e12			0.0676363
$929$	−9.99756e12	−	1.73163e13i	−0.440376	−	0.762753i	0.557341	−	0.830283i	$-0.311821\pi$
$929$	−9.99756e12	−	1.73163e13i	−0.440376	−	0.762753i	−0.997717	+	0.0675301i	$0.978488\pi$
$930$		0			0
$931$	1.39830e11	−	2.42192e11i	0.00609995	−	0.0105654i
$932$	−1.00660e13	+	1.74348e13i	−0.437003	+	0.756911i
$933$		0			0
$934$	2.42353e12	+	4.19767e12i	0.104205	+	0.180488i
$935$	3.42799e13			1.46685
$936$		0			0
$937$	3.60094e13			1.52612			0.763058	−	0.646330i	$-0.223697\pi$
$937$	3.60094e13			1.52612			0.763058	+	0.646330i	$0.223697\pi$
$938$	−2.10905e11	−	3.65298e11i	−0.00889558	−	0.0154076i
$939$		0			0
$940$	9.40237e12	−	1.62854e13i	0.392791	−	0.680335i
$941$	−1.10042e13	+	1.90598e13i	−0.457514	+	0.792438i	−0.998829	−	0.0483823i	$-0.984593\pi$
$941$	−1.10042e13	+	1.90598e13i	−0.457514	+	0.792438i	0.541315	+	0.840820i	$0.317927\pi$
$942$		0			0
$943$	2.32618e13	+	4.02907e13i	0.957946	+	1.65921i
$944$	−3.28777e13			−1.34750
$945$		0			0
$946$	−8.62036e12			−0.349958
$947$	1.13571e13	+	1.96711e13i	0.458873	+	0.794791i	0.998902	−	0.0468555i	$-0.0149200\pi$
$947$	1.13571e13	+	1.96711e13i	0.458873	+	0.794791i	−0.540029	+	0.841646i	$0.681587\pi$
$948$		0			0
$949$	−1.47092e13	+	2.54771e13i	−0.588697	+	1.01965i
$950$	−2.33422e8	+	4.04299e8i	−9.29791e−6	+	1.61045e-5i
$951$		0			0
$952$	−1.12005e12	−	1.93998e12i	−0.0441947	−	0.0765475i
$953$	1.64449e13			0.645824			0.322912	−	0.946429i	$-0.395338\pi$
$953$	1.64449e13			0.645824			0.322912	+	0.946429i	$0.395338\pi$
$954$		0			0
$955$	−4.40882e12			−0.171517
$956$	−2.31585e12	−	4.01118e12i	−0.0896708	−	0.155314i
$957$		0			0
$958$	−1.65663e12	+	2.86937e12i	−0.0635450	+	0.110063i
$959$	−4.94894e12	+	8.57182e12i	−0.188942	+	0.327257i
$960$		0			0
$961$	7.03056e12	+	1.21773e13i	0.265910	+	0.460570i
$962$	3.78472e12			0.142477
$963$		0			0
$964$	3.90483e13			1.45631
$965$	2.15059e13	+	3.72493e13i	0.798335	+	1.38276i
$966$		0			0
$967$	−1.24653e13	+	2.15906e13i	−0.458442	+	0.794044i	−0.998879	−	0.0473402i	$-0.984926\pi$
$967$	−1.24653e13	+	2.15906e13i	−0.458442	+	0.794044i	0.540437	+	0.841384i	$0.318259\pi$
$968$	2.96015e12	−	5.12714e12i	0.108362	−	0.187688i
$969$		0			0
$970$	1.42579e12	+	2.46955e12i	0.0517111	+	0.0895663i
$971$	4.38342e13			1.58244			0.791218	−	0.611534i	$-0.209447\pi$
$971$	4.38342e13			1.58244			0.791218	+	0.611534i	$0.209447\pi$
$972$		0			0
$973$	−9.24641e12			−0.330724
$974$	4.99275e11	+	8.64770e11i	0.0177756	+	0.0307883i
$975$		0			0
$976$	−1.71646e13	+	2.97300e13i	−0.605495	+	1.04875i
$977$	2.28679e12	−	3.96084e12i	0.0802973	−	0.139079i	−0.823080	−	0.567925i	$-0.807746\pi$
$977$	2.28679e12	−	3.96084e12i	0.0802973	−	0.139079i	0.903378	+	0.428846i	$0.141080\pi$
$978$		0			0
$979$	1.81061e13	+	3.13607e13i	0.629945	+	1.09110i
$980$	2.63814e13			0.913652
$981$		0			0
$982$	8.12468e11			0.0278808
$983$	−2.39203e13	−	4.14312e13i	−0.817101	−	1.41526i	−0.907809	−	0.419383i	$-0.862246\pi$
$983$	−2.39203e13	−	4.14312e13i	−0.817101	−	1.41526i	0.0907080	−	0.995878i	$-0.471087\pi$
$984$		0			0
$985$	1.51945e13	−	2.63176e13i	0.514308	−	0.890807i
$986$	3.84801e11	−	6.66495e11i	0.0129655	−	0.0224569i
$987$		0			0
$988$	−2.06904e11	−	3.58368e11i	−0.00690816	−	0.0119653i
$989$	−1.02411e14			−3.40380
$990$		0			0
$991$	−1.94011e13			−0.638993			−0.319496	−	0.947588i	$-0.603514\pi$
$991$	−1.94011e13			−0.638993			−0.319496	+	0.947588i	$0.603514\pi$
$992$	−4.64198e12	−	8.04014e12i	−0.152195	−	0.263610i
$993$		0			0
$994$	7.87023e11	−	1.36316e12i	0.0255710	−	0.0442903i
$995$	2.53771e12	−	4.39544e12i	0.0820802	−	0.142167i
$996$		0			0
$997$	−2.36927e13	−	4.10370e13i	−0.759429	−	1.31537i	−0.943142	−	0.332389i	$-0.892145\pi$
$997$	−2.36927e13	−	4.10370e13i	−0.759429	−	1.31537i	0.183714	−	0.982980i	$-0.441188\pi$
$998$	8.75946e12			0.279505
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	81.10.c.g.28.2		6
3.2	odd	2		81.10.c.h.28.2		6
9.2	odd	6		81.10.c.h.55.2		6
9.4	even	3		27.10.a.c.1.2	yes	3
9.5	odd	6		27.10.a.b.1.2	✓	3
9.7	even	3	inner	81.10.c.g.55.2		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
27.10.a.b.1.2	✓	3	9.5	odd	6
27.10.a.c.1.2	yes	3	9.4	even	3
81.10.c.g.28.2		6	1.1	even	1	trivial
81.10.c.g.55.2		6	9.7	even	3	inner
81.10.c.h.28.2		6	3.2	odd	2
81.10.c.h.55.2		6	9.2	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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 81 = 3^{4} \)
Weight:	\( k \)	\(=\)	\( 10 \)
Character orbit:	\([\chi]\)	\(=\)	81.c (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.73143 - 2.99892i) q^{2} +(250.004 - 433.020i) q^{4} +(-702.004 + 1215.91i) q^{5} +(-832.785 - 1442.43i) q^{7} -3504.44 q^{8} +4861.88 q^{10} +(31809.3 + 55095.3i) q^{11} +(55604.8 - 96310.3i) q^{13} +(-2883.81 + 4994.91i) q^{14} +(-121935. - 211197. i) q^{16} -383783. q^{17} +7441.82 q^{19} +(351008. + 607964. i) q^{20} +(110151. - 190787. i) q^{22} +(1.30861e6 - 2.26658e6i) q^{23} +(-9057.92 - 15688.8i) q^{25} -385102. q^{26} -832799. q^{28} +(-289545. - 501507. i) q^{29} +(-1.75915e6 + 3.04695e6i) q^{31} +(-1.31938e6 + 2.28523e6i) q^{32} +(664492. + 1.15093e6i) q^{34} +2.33847e6 q^{35} -9.82783e6 q^{37} +(-12885.0 - 22317.4i) q^{38} +(2.46013e6 - 4.26107e6i) q^{40} +(-8.88800e6 + 1.53945e7i) q^{41} +(-1.95649e7 - 3.38874e7i) q^{43} +3.18098e7 q^{44} -9.06304e6 q^{46} +(-1.33934e7 - 2.31980e7i) q^{47} +(1.87897e7 - 3.25448e7i) q^{49} +(-31366.3 + 54327.9i) q^{50} +(-2.78029e7 - 4.81560e7i) q^{52} -6.04430e7 q^{53} -8.93210e7 q^{55} +(2.91844e6 + 5.05489e6i) q^{56} +(-1.00265e6 + 1.73665e6i) q^{58} +(6.74085e7 - 1.16755e8i) q^{59} +(-7.03846e7 - 1.21910e8i) q^{61} +1.21834e7 q^{62} -1.15723e8 q^{64} +(7.80696e7 + 1.35221e8i) q^{65} +(-3.65671e7 + 6.33360e7i) q^{67} +(-9.59473e7 + 1.66186e8i) q^{68} +(-4.04890e6 - 7.01290e6i) q^{70} -2.72910e8 q^{71} -2.64531e8 q^{73} +(1.70162e7 + 2.94729e7i) q^{74} +(1.86049e6 - 3.22246e6i) q^{76} +(5.29806e7 - 9.17651e7i) q^{77} +(-2.72331e8 - 4.71691e8i) q^{79} +3.42394e8 q^{80} +6.15557e7 q^{82} +(-8.69938e7 - 1.50678e8i) q^{83} +(2.69417e8 - 4.66644e8i) q^{85} +(-6.77504e7 + 1.17347e8i) q^{86} +(-1.11474e8 - 1.93078e8i) q^{88} +5.69208e8 q^{89} -1.85227e8 q^{91} +(-6.54316e8 - 1.13331e9i) q^{92} +(-4.63793e7 + 8.03313e7i) q^{94} +(-5.22419e6 + 9.04856e6i) q^{95} +(2.93260e8 + 5.07941e8i) q^{97} -1.30132e8 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 3 q^{2} - 597 q^{4} + 1983 q^{5} + 3693 q^{7} - 9006 q^{8} - 37962 q^{10} + 16863 q^{11} - 116916 q^{13} + 503463 q^{14} + 239919 q^{16} - 2028096 q^{17} - 30444 q^{19} + 2548407 q^{20} - 305721 q^{22}+ \cdots + 5184364572 q^{98}+O(q^{100}) \) 6 * q - 3 * q^2 - 597 * q^4 + 1983 * q^5 + 3693 * q^7 - 9006 * q^8 - 37962 * q^10 + 16863 * q^11 - 116916 * q^13 + 503463 * q^14 + 239919 * q^16 - 2028096 * q^17 - 30444 * q^19 + 2548407 * q^20 - 305721 * q^22 + 2927118 * q^23 - 2133732 * q^25 - 9530232 * q^26 - 7071450 * q^28 + 5768790 * q^29 + 6575223 * q^31 - 2687697 * q^32 - 17098128 * q^34 + 34681074 * q^35 - 23372052 * q^37 - 50473374 * q^38 + 4130811 * q^40 - 22213518 * q^41 - 45384414 * q^43 + 114413982 * q^44 - 191277180 * q^46 + 12392034 * q^47 - 18933462 * q^49 - 82984044 * q^50 - 182736492 * q^52 - 161159274 * q^53 - 349470666 * q^55 + 21850521 * q^56 + 102758922 * q^58 + 244026660 * q^59 - 369729960 * q^61 - 332594682 * q^62 - 841384254 * q^64 + 492225684 * q^65 + 252614586 * q^67 + 162270144 * q^68 - 935092377 * q^70 - 806386176 * q^71 - 813253434 * q^73 - 641373558 * q^74 + 39499590 * q^76 + 360443199 * q^77 - 265451856 * q^79 + 2336719674 * q^80 - 1768816332 * q^82 + 121625871 * q^83 - 316251216 * q^85 - 2368956570 * q^86 - 219257739 * q^88 - 755808012 * q^89 + 490118280 * q^91 - 1178754558 * q^92 - 86583438 * q^94 + 536878770 * q^95 + 438907539 * q^97 + 5184364572 * q^98

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