LMFDB - Embedded newform 81.10.c.h.55.2

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			55.2
Root			$0.577142 - 0.999640i$ of defining polynomial
Character	$\chi$	$=$	81.55
Dual form			81.10.c.h.28.2

$q$-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 $\left(\mathbb{Z}/81\mathbb{Z}\right)^\times$.

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

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	1.73143	−	2.99892i	0.0765190	−	0.132535i	−0.825227	−	0.564801i	$-0.808953\pi$
$2$	1.73143	−	2.99892i	0.0765190	−	0.132535i	0.901746	+	0.432267i	$0.142286\pi$
$3$		0			0
$3$		0			0
$4$	250.004	+	433.020i	0.488290	+	0.845743i
$5$	702.004	+	1215.91i	0.502313	+	0.870032i	0.999996	+	0.00267343i	$0.000850982\pi$
$5$	702.004	+	1215.91i	0.502313	+	0.870032i	−0.497683	+	0.867359i	$0.665816\pi$
$6$		0			0
$7$	−832.785	+	1442.43i	−0.131097	+	0.227066i	−0.924100	−	0.382152i	$-0.875183\pi$
$7$	−832.785	+	1442.43i	−0.131097	+	0.227066i	0.793003	+	0.609218i	$0.208516\pi$
$8$	3504.44			0.302492
$9$		0			0
$10$	4861.88			0.153746
$11$	−31809.3	+	55095.3i	−0.655069	+	1.13461i	0.326808	+	0.945091i	$0.394027\pi$
$11$	−31809.3	+	55095.3i	−0.655069	+	1.13461i	−0.981877	+	0.189521i	$0.939306\pi$
$12$		0			0
$13$	55604.8	+	96310.3i	0.539967	+	0.935250i	0.998905	+	0.0467819i	$0.0148966\pi$
$13$	55604.8	+	96310.3i	0.539967	+	0.935250i	−0.458938	+	0.888468i	$0.651770\pi$
$14$	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	$-0.311864\pi$
$17$	383783.			1.11446			0.557231	+	0.830358i	$0.311864\pi$
$18$		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	−0.679713	−	0.733478i	$-0.737896\pi$
$23$	−1.30861e6	−	2.26658e6i	−0.975067	−	1.68887i	−0.295354	−	0.955388i	$-0.595438\pi$
$24$		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	$-0.809112\pi$
$29$	289545.	−	501507.i	0.0760196	−	0.131670i	0.901529	+	0.432718i	$0.142446\pi$
$30$		0			0
$31$	−1.75915e6	−	3.04695e6i	−0.342118	−	0.592566i	0.642708	−	0.766112i	$-0.277811\pi$
$31$	−1.75915e6	−	3.04695e6i	−0.342118	−	0.592566i	−0.984826	+	0.173545i	$0.944478\pi$
$32$	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	$-0.00321759\pi$
$41$	8.88800e6	+	1.53945e7i	0.491221	+	0.850819i	−0.508728	+	0.860927i	$0.669884\pi$
$42$		0			0
$43$	−1.95649e7	+	3.38874e7i	−0.872709	+	1.51158i	−0.0135261	+	0.999909i	$0.504306\pi$
$43$	−1.95649e7	+	3.38874e7i	−0.872709	+	1.51158i	−0.859183	+	0.511668i	$0.829028\pi$
$44$	−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	$-0.702219\pi$
$47$	1.33934e7	−	2.31980e7i	0.400359	−	0.693442i	0.993769	+	0.111458i	$0.0355521\pi$
$48$		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	$-0.323651\pi$
$53$	6.04430e7			1.05222			0.526108	+	0.850418i	$0.323651\pi$
$54$		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	−0.959287	−	0.282432i	$-0.908859\pi$
$59$	−6.74085e7	−	1.16755e8i	−0.724237	−	1.25441i	0.235051	−	0.971983i	$-0.424474\pi$
$60$		0			0
$61$	−7.03846e7	+	1.21910e8i	−0.650869	+	1.12734i	0.332043	+	0.943264i	$0.392262\pi$
$61$	−7.03846e7	+	1.21910e8i	−0.650869	+	1.12734i	−0.982912	+	0.184074i	$0.941071\pi$
$62$	−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	0.733629	−	0.679551i	$-0.237825\pi$
$67$	−3.65671e7	−	6.33360e7i	−0.221694	−	0.383985i	−0.955322	+	0.295566i	$0.904492\pi$
$68$	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	$-0.280061\pi$
$71$	2.72910e8			1.27455			0.637276	+	0.770636i	$0.280061\pi$
$72$		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	0.141376	+	0.989956i	$0.454847\pi$
$79$	−2.72331e8	+	4.71691e8i	−0.786639	+	1.36250i	−0.928015	+	0.372542i	$0.878486\pi$
$80$	−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	$-0.768848\pi$
$83$	8.69938e7	−	1.50678e8i	0.201204	−	0.348496i	0.948917	+	0.315527i	$0.102181\pi$
$84$		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	$-0.659662\pi$
$89$	−5.69208e8			−0.961647			−0.480823	+	0.876817i	$0.659662\pi$
$90$		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	−0.647400	−	0.762150i	$-0.724144\pi$
$97$	2.93260e8	−	5.07941e8i	0.336341	−	0.582560i	0.983742	+	0.179590i	$0.0574772\pi$
$98$	1.30132e8			0.142517
$99$		0			0
$100$	−9.05808e6			−0.00905808
$101$	−8.12194e8	+	1.40676e9i	−0.776629	+	1.34516i	0.157246	+	0.987559i	$0.449738\pi$
$101$	−8.12194e8	+	1.40676e9i	−0.776629	+	1.34516i	−0.933875	+	0.357601i	$0.883595\pi$
$102$		0			0
$103$	−2.96352e8	−	5.13297e8i	−0.259442	−	0.449367i	0.706650	−	0.707563i	$-0.250205\pi$
$103$	−2.96352e8	−	5.13297e8i	−0.259442	−	0.449367i	−0.966093	+	0.258196i	$0.916872\pi$
$104$	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	$-0.444622\pi$
$107$	4.69405e8			0.346195			0.173098	+	0.984905i	$0.444622\pi$
$108$		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	$-0.284445\pi$
$113$	−6.26779e8	−	1.08561e9i	−0.361628	−	0.626357i	−0.988229	+	0.152983i	$0.951112\pi$
$114$		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	$-0.259569\pi$
$131$	−9.69871e8	−	1.67987e9i	−0.287735	−	0.498372i	−0.973269	+	0.229669i	$0.926236\pi$
$132$		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	−0.240130	−	0.970741i	$-0.577190\pi$
$137$	2.97132e9	−	5.14648e9i	0.720621	−	1.24815i	0.960751	−	0.277412i	$-0.0894766\pi$
$138$		0			0
$139$	2.77575e9	+	4.80774e9i	0.630687	+	1.09238i	0.987412	+	0.158172i	$0.0505600\pi$
$139$	2.77575e9	+	4.80774e9i	0.630687	+	1.09238i	−0.356725	+	0.934209i	$0.616107\pi$
$140$	−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	0.914163	+	0.405347i	$0.132849\pi$
$149$	4.86200e9	+	8.42124e9i	0.808122	+	1.39971i	−0.106040	+	0.994362i	$0.533817\pi$
$150$		0			0
$151$	1.60926e9	−	2.78732e9i	0.251901	−	0.436305i	−0.712148	−	0.702029i	$-0.752278\pi$
$151$	1.60926e9	−	2.78732e9i	0.251901	−	0.436305i	0.964049	+	0.265724i	$0.0856110\pi$
$152$	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	0.820709	−	0.571347i	$-0.193579\pi$
$157$	−6.42880e8	−	1.11350e9i	−0.0844465	−	0.146266i	−0.905155	+	0.425081i	$0.860246\pi$
$158$	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	$-0.142332\pi$
$167$	7.67671e8	+	1.32965e9i	0.0763750	+	0.132285i	−0.825308	+	0.564682i	$0.808999\pi$
$168$		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	$-0.843577\pi$
$173$	−3.79098e8	+	6.56618e8i	−0.0321769	+	0.0557321i	0.849489	+	0.527607i	$0.176911\pi$
$174$		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	$-0.640350\pi$
$179$	−1.17238e10			−0.853549			−0.426774	+	0.904358i	$0.640350\pi$
$180$		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	$-0.860539\pi$
$191$	−1.57008e9	+	2.71947e9i	−0.0853636	+	0.147854i	0.820182	+	0.572102i	$0.193872\pi$
$192$		0			0
$193$	1.53175e10	+	2.65307e10i	0.794658	+	1.37639i	0.923056	+	0.384665i	$0.125683\pi$
$193$	1.53175e10	+	2.65307e10i	0.794658	+	1.37639i	−0.128398	+	0.991723i	$0.540984\pi$
$194$	−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	$-0.328927\pi$
$197$	2.16444e10			1.02388			0.511939	+	0.859022i	$0.328927\pi$
$198$		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	0.950431	−	0.310935i	$-0.100642\pi$
$211$	5.92937e9	+	1.02700e10i	0.205938	+	0.356696i	−0.744493	+	0.667630i	$0.767309\pi$
$212$	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	−0.709484	−	0.704722i	$-0.751072\pi$
$223$	9.43784e9	−	1.63468e10i	0.255565	−	0.442651i	0.965049	+	0.262070i	$0.0844053\pi$
$224$	−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	$-0.841481\pi$
$227$	−1.02386e9	+	1.77337e9i	−0.0255931	+	0.0443285i	0.852945	+	0.522000i	$0.174814\pi$
$228$		0			0
$229$	−1.06967e9	−	1.85272e9i	−0.0257034	−	0.0445196i	0.852888	−	0.522095i	$-0.174849\pi$
$229$	−1.06967e9	−	1.85272e9i	−0.0257034	−	0.0445196i	−0.878591	+	0.477575i	$0.841516\pi$
$230$	−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	$-0.352321\pi$
$233$	4.02632e10			0.894966			0.447483	+	0.894292i	$0.352321\pi$
$234$		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	$-0.195936\pi$
$239$	−4.63163e9	−	8.02222e9i	−0.0918213	−	0.159039i	−0.908278	+	0.418368i	$0.862602\pi$
$240$		0			0
$241$	3.90476e10	−	6.76324e10i	0.745620	−	1.29145i	−0.204285	−	0.978912i	$-0.565487\pi$
$241$	3.90476e10	−	6.76324e10i	0.745620	−	1.29145i	0.949905	−	0.312540i	$-0.101180\pi$
$242$	−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	$-0.460738\pi$
$251$	1.54732e10			0.246064			0.123032	+	0.992403i	$0.460738\pi$
$252$		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	−0.978377	−	0.206829i	$-0.933686\pi$
$257$	−4.67386e10	−	8.09536e10i	−0.668308	−	1.15754i	0.310069	−	0.950714i	$-0.399648\pi$
$258$		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	$-0.849565\pi$
$263$	−3.95489e9	+	6.85008e9i	−0.0509723	+	0.0882866i	0.839413	+	0.543493i	$0.182899\pi$
$264$		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	$-0.187853\pi$
$269$	1.42705e11			1.66171			0.830853	+	0.556492i	$0.187853\pi$
$270$		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	−0.735162	−	0.677892i	$-0.762894\pi$
$277$	2.15068e10	−	3.72508e10i	0.219491	−	0.380169i	0.954652	+	0.297723i	$0.0962271\pi$
$278$	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	$-0.993907\pi$
$281$	−5.05155e10	+	8.74954e10i	−0.483333	+	0.837157i	0.516484	+	0.856297i	$0.327240\pi$
$282$		0			0
$283$	4.08977e10	+	7.08368e10i	0.379018	+	0.656478i	0.990920	−	0.134456i	$-0.0429286\pi$
$283$	4.08977e10	+	7.08368e10i	0.379018	+	0.656478i	−0.611902	+	0.790934i	$0.709595\pi$
$284$	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	$-0.270578\pi$
$293$	−4.04552e10	−	7.00704e10i	−0.320678	−	0.555431i	−0.980628	+	0.195879i	$0.937244\pi$
$294$		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	0.998990	+	0.0449400i	$0.0143097\pi$
$311$	8.88256e10	+	1.53850e11i	0.538414	+	0.932560i	−0.460576	+	0.887620i	$0.652357\pi$
$312$		0			0
$313$	−4.18712e10	+	7.25231e10i	−0.246585	+	0.427097i	−0.962576	−	0.271012i	$-0.912642\pi$
$313$	−4.18712e10	+	7.25231e10i	−0.246585	+	0.427097i	0.715991	+	0.698109i	$0.245975\pi$
$314$	−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	$-0.880425\pi$
$317$	−2.65016e10	+	4.59021e10i	−0.147403	+	0.255309i	0.782864	+	0.622193i	$0.213758\pi$
$318$		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	0.491730	+	0.870748i	$0.336365\pi$
$331$	−1.10989e11	+	1.92239e11i	−0.508225	+	0.880271i	−0.999955	+	0.00952305i	$0.996969\pi$
$332$	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	0.866356	−	0.499427i	$-0.166456\pi$
$337$	1.56720e8	+	2.71446e8i	0.000661895	+	0.00114644i	−0.865694	+	0.500573i	$0.833123\pi$
$338$	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	0.998377	+	0.0569424i	$0.0181351\pi$
$347$	1.48136e11	+	2.56579e11i	0.548502	+	0.950034i	−0.449875	+	0.893091i	$0.648532\pi$
$348$		0			0
$349$	−1.10780e11	+	1.91877e11i	−0.399712	+	0.692322i	−0.993690	−	0.112160i	$-0.964223\pi$
$349$	−1.10780e11	+	1.91877e11i	−0.399712	+	0.692322i	0.593978	+	0.804481i	$0.297557\pi$
$350$	−1.04485e8			−0.000372177
$351$		0			0
$352$	−1.67874e11			−0.582829
$353$	−1.90537e11	+	3.30019e11i	−0.653119	+	1.13124i	0.329243	+	0.944245i	$0.393206\pi$
$353$	−1.90537e11	+	3.30019e11i	−0.653119	+	1.13124i	−0.982362	+	0.186990i	$0.940127\pi$
$354$		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	$-0.678153\pi$
$359$	−3.34181e11			−1.06183			−0.530917	+	0.847424i	$0.678153\pi$
$360$		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	0.313274	+	0.949663i	$0.398574\pi$
$367$	−2.31386e11	+	4.00773e11i	−0.665795	+	1.15319i	−0.979069	+	0.203528i	$0.934759\pi$
$368$	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	0.978640	−	0.205583i	$-0.0659091\pi$
$373$	1.16370e11	+	2.01558e11i	0.311280	+	0.539152i	−0.667360	+	0.744735i	$0.732576\pi$
$374$	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	$-0.124753\pi$
$383$	5.52900e10	+	9.57651e10i	0.131296	+	0.227412i	−0.792880	+	0.609377i	$0.791419\pi$
$384$		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	−0.420598	−	0.907247i	$-0.638180\pi$
$389$	2.59862e11	−	4.50094e11i	0.575400	−	0.996622i	0.995998	−	0.0893747i	$-0.0284869\pi$
$390$		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	$-0.318446\pi$
$401$	−2.37645e11	−	4.11613e11i	−0.458964	−	0.794950i	−0.998907	+	0.0467526i	$0.985113\pi$
$402$		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	0.991295	−	0.131661i	$-0.0420310\pi$
$409$	2.15970e11	+	3.74070e11i	0.381626	+	0.660995i	−0.609669	+	0.792656i	$0.708698\pi$
$410$	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	0.962261	+	0.272126i	$0.0877269\pi$
$419$	4.52231e11	+	7.83288e11i	0.716799	+	1.24153i	−0.245462	+	0.969406i	$0.578940\pi$
$420$		0			0
$421$	−7.67841e10	+	1.32994e11i	−0.119125	+	0.206330i	−0.919421	−	0.393275i	$-0.871342\pi$
$421$	−7.67841e10	+	1.32994e11i	−0.119125	+	0.206330i	0.800296	+	0.599605i	$0.204676\pi$
$422$	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	$-0.250977\pi$
$431$	1.01001e12			1.40987			0.704933	+	0.709274i	$0.250977\pi$
$432$		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	−0.226656	−	0.973975i	$-0.572779\pi$
$439$	5.68209e11	−	9.84166e11i	0.730159	−	1.26467i	0.956815	−	0.290698i	$-0.0938874\pi$
$440$	−3.13020e11			−0.398139
$441$		0			0
$442$	1.47796e11			0.184188
$443$	−4.51021e11	+	7.81192e11i	−0.556391	+	0.963698i	0.441403	+	0.897309i	$0.354481\pi$
$443$	−4.51021e11	+	7.81192e11i	−0.556391	+	0.963698i	−0.997794	+	0.0663886i	$0.978852\pi$
$444$		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	$-0.579993\pi$
$449$	−4.28311e11			−0.497337			−0.248668	+	0.968589i	$0.579993\pi$
$450$		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	−0.669565	−	0.742754i	$-0.733519\pi$
$457$	2.87623e11	−	4.98178e11i	0.308461	−	0.534271i	0.978026	+	0.208483i	$0.0668527\pi$
$458$	−7.40822e9			−0.00786719
$459$		0			0
$460$	1.83733e12			1.91327
$461$	−5.32572e11	+	9.22441e11i	−0.549192	+	0.951228i	0.449139	+	0.893462i	$0.351731\pi$
$461$	−5.32572e11	+	9.22441e11i	−0.549192	+	0.951228i	−0.998330	+	0.0577655i	$0.981602\pi$
$462$		0			0
$463$	3.45830e11	+	5.98996e11i	0.349743	+	0.605772i	0.986204	−	0.165537i	$-0.0529356\pi$
$463$	3.45830e11	+	5.98996e11i	0.349743	+	0.605772i	−0.636461	+	0.771309i	$0.719602\pi$
$464$	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	$-0.261586\pi$
$467$	1.39973e12			1.36181			0.680907	+	0.732370i	$0.261586\pi$
$468$		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	$-0.697036\pi$
$479$	4.78401e11	−	8.28615e11i	0.415224	−	0.719189i	0.995452	+	0.0952650i	$0.0303698\pi$
$480$		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	$-0.137631\pi$
$491$	1.17312e11	+	2.03190e11i	0.0910910	+	0.157774i	−0.816879	+	0.576808i	$0.804298\pi$
$492$		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	−0.809531	−	0.587077i	$-0.800279\pi$
$499$	−1.26477e12	−	2.19065e12i	−0.913189	−	1.58169i	−0.103658	−	0.994613i	$-0.533055\pi$
$500$	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	$-0.534360\pi$
$503$	−3.09347e11			−0.215471			−0.107736	+	0.994180i	$0.534360\pi$
$504$		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	0.890048	+	0.455867i	$0.150671\pi$
$509$	1.27179e12	+	2.20280e12i	0.839816	+	1.45460i	−0.0502320	+	0.998738i	$0.515996\pi$
$510$		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	$-0.674695\pi$
$521$	−1.75471e12			−1.04336			−0.521682	+	0.853140i	$0.674695\pi$
$522$		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	−0.987788	−	0.155805i	$-0.950203\pi$
$547$	−7.51610e11	+	1.30183e12i	−0.358963	+	0.621742i	0.628825	+	0.777547i	$0.283536\pi$
$548$	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	$-0.466050\pi$
$557$	4.83664e11			0.212910			0.106455	+	0.994318i	$0.466050\pi$
$558$		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	−0.999739	−	0.0228302i	$-0.992732\pi$
$563$	−1.23877e12	−	2.14562e12i	−0.519641	−	0.900045i	0.480098	−	0.877215i	$-0.340601\pi$
$564$		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	−0.265918	−	0.963996i	$-0.585675\pi$
$569$	1.75498e12	−	3.03971e12i	0.701886	−	1.21570i	0.967804	−	0.251706i	$-0.0809917\pi$
$570$		0			0
$571$	−1.28628e11	−	2.22790e11i	−0.0506375	−	0.0877066i	0.839596	−	0.543212i	$-0.182792\pi$
$571$	−1.28628e11	−	2.22790e11i	−0.0506375	−	0.0877066i	−0.890233	+	0.455505i	$0.849459\pi$
$572$	−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	−0.0542776	+	0.998526i	$0.517286\pi$
$587$	−2.56556e12	+	4.44367e12i	−0.891888	+	1.54479i	−0.837610	+	0.546269i	$0.816048\pi$
$588$		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	$-0.393269\pi$
$593$	1.98175e12			0.658116			0.329058	+	0.944310i	$0.393269\pi$
$594$		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	$-0.219058\pi$
$599$	−5.16257e11	−	8.94184e11i	−0.163850	−	0.283796i	−0.936246	+	0.351345i	$0.885725\pi$
$600$		0			0
$601$	5.34090e11	−	9.25071e11i	0.166986	−	0.289228i	−0.770373	−	0.637594i	$-0.779930\pi$
$601$	5.34090e11	−	9.25071e11i	0.166986	−	0.289228i	0.937359	+	0.348366i	$0.113263\pi$
$602$	−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	0.500887	−	0.865513i	$-0.333007\pi$
$607$	−1.66935e12	−	2.89140e12i	−0.499112	−	0.864488i	−0.999999	+	0.00102472i	$0.999674\pi$
$608$	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	0.992706	+	0.120558i	$0.0384684\pi$
$617$	2.16264e12	+	3.74580e12i	0.600759	+	1.04055i	−0.391947	+	0.919988i	$0.628198\pi$
$618$		0			0
$619$	3.15688e12	−	5.46787e12i	0.864271	−	1.49696i	−0.00349896	−	0.999994i	$-0.501114\pi$
$619$	3.15688e12	−	5.46787e12i	0.864271	−	1.49696i	0.867770	−	0.496967i	$-0.165553\pi$
$620$	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	−0.0736498	−	0.997284i	$-0.523465\pi$
$641$	3.53417e12	−	6.12136e12i	0.826849	−	1.43214i	0.900498	−	0.434860i	$-0.143202\pi$
$642$		0			0
$643$	−8.53171e11	−	1.47774e12i	−0.196828	−	0.340916i	0.750670	−	0.660677i	$-0.229731\pi$
$643$	−8.53171e11	−	1.47774e12i	−0.196828	−	0.340916i	−0.947498	+	0.319761i	$0.896397\pi$
$644$	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	$-0.642428\pi$
$647$	−3.85704e12			−0.865336			−0.432668	+	0.901553i	$0.642428\pi$
$648$		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	$-0.332456\pi$
$653$	−2.31206e12	−	4.00460e12i	−0.497610	−	0.861886i	−0.999996	+	0.00275722i	$0.999122\pi$
$654$		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	$-0.806451\pi$
$659$	4.08401e11	−	7.07371e11i	0.0843533	−	0.146104i	0.905115	+	0.425166i	$0.139784\pi$
$660$		0			0
$661$	5.73853e11	+	9.93942e11i	0.116921	+	0.202514i	0.918546	−	0.395314i	$-0.129364\pi$
$661$	5.73853e11	+	9.93942e11i	0.116921	+	0.202514i	−0.801625	+	0.597827i	$0.796031\pi$
$662$	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	−0.302613	−	0.953114i	$-0.597859\pi$
$673$	3.58758e12	−	6.21386e12i	0.674114	−	1.16760i	0.976727	−	0.214486i	$-0.0688077\pi$
$674$	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	$-0.675199\pi$
$677$	2.60502e12	−	4.51203e12i	0.476609	−	0.825510i	0.999641	+	0.0268026i	$0.00853256\pi$
$678$		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	$-0.420455\pi$
$683$	2.81291e12			0.494611			0.247305	+	0.968938i	$0.420455\pi$
$684$		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	−0.337366	−	0.941373i	$-0.609536\pi$
$691$	3.87496e12	−	6.71162e12i	0.646570	−	1.11989i	0.983937	−	0.178519i	$-0.0571305\pi$
$692$	−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	$-0.453388\pi$
$701$	1.86576e12			0.291826			0.145913	+	0.989297i	$0.453388\pi$
$702$		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	−0.874359	−	0.485280i	$-0.838718\pi$
$709$	−1.13808e11	+	1.97122e11i	−0.0169148	+	0.0292972i	0.857444	+	0.514577i	$0.172051\pi$
$710$	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	$-0.452566\pi$
$719$	2.12785e12			0.296934			0.148467	+	0.988917i	$0.452566\pi$
$720$		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	−0.808901	−	0.587945i	$-0.799937\pi$
$727$	7.88780e11	−	1.36621e12i	0.104725	−	0.181389i	0.913626	+	0.406556i	$0.133270\pi$
$728$	−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	0.974829	−	0.222952i	$-0.0715693\pi$
$733$	2.30042e12	+	3.98444e12i	0.294333	+	0.509799i	−0.680497	+	0.732751i	$0.738236\pi$
$734$	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	−0.983479	−	0.181021i	$-0.942060\pi$
$743$	−5.38723e12	−	9.33095e12i	−0.648508	−	1.12325i	0.334971	−	0.942228i	$-0.391273\pi$
$744$		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	0.977299	−	0.211865i	$-0.0679537\pi$
$751$	2.66024e12	+	4.60766e12i	0.305169	+	0.528568i	−0.672130	+	0.740433i	$0.734620\pi$
$752$	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	$-0.0423323\pi$
$761$	3.52267e12	+	6.10144e12i	0.380751	+	0.659480i	−0.610419	+	0.792079i	$0.708999\pi$
$762$		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	0.984319	−	0.176397i	$-0.0564442\pi$
$769$	3.29135e12	+	5.70079e12i	0.339395	+	0.587850i	−0.644924	+	0.764247i	$0.723111\pi$
$770$	−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	$-0.737742\pi$
$773$	−1.34877e13			−1.35872			−0.679360	+	0.733805i	$0.737742\pi$
$774$		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	0.996362	+	0.0852254i	$0.0271610\pi$
$787$	6.15564e12	+	1.06619e13i	0.571988	+	0.990713i	−0.424374	+	0.905487i	$0.639506\pi$
$788$	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	$-0.333288\pi$
$797$	−5.69410e12	−	9.86247e12i	−0.499877	−	0.865812i	−1.00000		0.000142537i	$0.999955\pi$
$798$		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	$-0.625987\pi$
$809$	−9.39455e12			−0.771095			−0.385547	+	0.922688i	$0.625987\pi$
$810$		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	0.485419	+	0.874282i	$0.338667\pi$
$821$	−6.69699e12	+	1.15995e13i	−0.514441	+	0.891037i	−0.999860	+	0.0167556i	$0.994666\pi$
$822$		0			0
$823$	−9.32974e12	−	1.61596e13i	−0.708876	−	1.22781i	−0.965274	−	0.261238i	$-0.915869\pi$
$823$	−9.32974e12	−	1.61596e13i	−0.708876	−	1.22781i	0.256399	−	0.966571i	$-0.417464\pi$
$824$	−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	$-0.342447\pi$
$827$	1.27791e13			0.950006			0.475003	+	0.879984i	$0.342447\pi$
$828$		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	$-0.967876\pi$
$839$	−5.88748e12	+	1.01974e13i	−0.410205	+	0.710495i	0.584707	+	0.811244i	$0.301209\pi$
$840$		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	−0.876876	−	0.480716i	$-0.840377\pi$
$853$	−3.42110e11	+	5.92552e11i	−0.0221256	+	0.0383227i	0.854751	+	0.519039i	$0.173710\pi$
$854$	−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	$-0.714003\pi$
$857$	5.78222e12	−	1.00151e13i	0.366168	−	0.634222i	0.988963	+	0.148163i	$0.0473361\pi$
$858$		0			0
$859$	−7.51305e12	−	1.30130e13i	−0.470812	−	0.815470i	0.528631	−	0.848852i	$-0.322706\pi$
$859$	−7.51305e12	−	1.30130e13i	−0.470812	−	0.815470i	−0.999443	+	0.0333820i	$0.989372\pi$
$860$	−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	$-0.343263\pi$
$863$	1.54066e13			0.945490			0.472745	+	0.881199i	$0.343263\pi$
$864$		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	0.954575	+	0.297972i	$0.0963101\pi$
$877$	1.28821e13	+	2.23124e13i	0.735338	+	1.27364i	−0.219236	+	0.975672i	$0.570357\pi$
$878$	−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	$-0.577977\pi$
$881$	−8.67327e12			−0.485055			−0.242528	+	0.970144i	$0.577977\pi$
$882$		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	$-0.201208\pi$
$887$	−1.99661e12	−	3.45824e12i	−0.108302	−	0.187585i	−0.915083	+	0.403266i	$0.867875\pi$
$888$		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	−0.737699	−	0.675129i	$-0.764088\pi$
$907$	4.39889e12	−	7.61910e12i	0.215829	−	0.373827i	0.953529	+	0.301302i	$0.0974212\pi$
$908$	−1.02387e12			−0.0499874
$909$		0			0
$910$	−9.00552e11			−0.0435334
$911$	1.47806e13	−	2.56007e13i	0.710983	−	1.23146i	−0.253506	−	0.967334i	$-0.581584\pi$
$911$	1.47806e13	−	2.56007e13i	0.710983	−	1.23146i	0.964489	−	0.264125i	$-0.0850830\pi$
$912$		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	$-0.688179\pi$
$929$	9.99756e12	−	1.73163e13i	0.440376	−	0.762753i	0.997717	+	0.0675301i	$0.0215119\pi$
$930$		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	$-0.0154066\pi$
$941$	1.10042e13	+	1.90598e13i	0.457514	+	0.792438i	−0.541315	+	0.840820i	$0.682073\pi$
$942$		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	$-0.985080\pi$
$947$	−1.13571e13	+	1.96711e13i	−0.458873	+	0.794791i	0.540029	+	0.841646i	$0.318413\pi$
$948$		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	$-0.604662\pi$
$953$	−1.64449e13			−0.645824			−0.322912	+	0.946429i	$0.604662\pi$
$954$		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	0.540437	−	0.841384i	$-0.318259\pi$
$967$	−1.24653e13	−	2.15906e13i	−0.458442	−	0.794044i	−0.998879	+	0.0473402i	$0.984926\pi$
$968$	−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	$-0.790553\pi$
$971$	−4.38342e13			−1.58244			−0.791218	+	0.611534i	$0.790553\pi$
$972$		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	$-0.192254\pi$
$977$	−2.28679e12	−	3.96084e12i	−0.0802973	−	0.139079i	−0.903378	+	0.428846i	$0.858920\pi$
$978$		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	−0.0907080	−	0.995878i	$-0.528913\pi$
$983$	2.39203e13	−	4.14312e13i	0.817101	−	1.41526i	0.907809	−	0.419383i	$-0.137754\pi$
$984$		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	0.183714	+	0.982980i	$0.441188\pi$
$997$	−2.36927e13	+	4.10370e13i	−0.759429	+	1.31537i	−0.943142	+	0.332389i	$0.892145\pi$
$998$	−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.h.55.2		6
3.2	odd	2		81.10.c.g.55.2		6
9.2	odd	6		27.10.a.c.1.2	yes	3
9.4	even	3	inner	81.10.c.h.28.2		6
9.5	odd	6		81.10.c.g.28.2		6
9.7	even	3		27.10.a.b.1.2	✓	3

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

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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