LMFDB - Embedded newform 81.10.c.h.55.3

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			55.3
Root			$5.38886 - 9.33377i$ of defining polynomial
Character	$\chi$	$=$	81.55
Dual form			81.10.c.h.28.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(16.1666 - 28.0013i) q^{2} +(-266.716 - 461.965i) q^{4} +(-1035.81 - 1794.08i) q^{5} +(5258.56 - 9108.09i) q^{7} -692.954 q^{8} -66982.2 q^{10} +(15810.3 - 27384.2i) q^{11} +(-23811.1 - 41242.0i) q^{13} +(-170026. - 294493. i) q^{14} +(125356. - 217123. i) q^{16} +34440.3 q^{17} +763166. q^{19} +(-552535. + 957020. i) q^{20} +(-511196. - 885417. i) q^{22} +(-742671. - 1.28634e6i) q^{23} +(-1.16925e6 + 2.02521e6i) q^{25} -1.53977e6 q^{26} -5.61016e6 q^{28} +(-2.40253e6 + 4.16130e6i) q^{29} +(3.91152e6 + 6.77496e6i) q^{31} +(-4.23054e6 - 7.32752e6i) q^{32} +(556781. - 964373. i) q^{34} -2.17875e7 q^{35} +9.43456e6 q^{37} +(1.23378e7 - 2.13696e7i) q^{38} +(717771. + 1.24322e6i) q^{40} +(-6.14495e6 - 1.06434e7i) q^{41} +(-1.87211e7 + 3.24260e7i) q^{43} -1.68674e7 q^{44} -4.80258e7 q^{46} +(-9.91171e6 + 1.71676e7i) q^{47} +(-3.51280e7 - 6.08435e7i) q^{49} +(3.78057e7 + 6.54813e7i) q^{50} +(-1.27016e7 + 2.19998e7i) q^{52} +5.78978e7 q^{53} -6.55059e7 q^{55} +(-3.64394e6 + 6.31149e6i) q^{56} +(7.76813e7 + 1.34548e8i) q^{58} +(1.42494e7 + 2.46807e7i) q^{59} +(-2.22571e7 + 3.85504e7i) q^{61} +2.52944e8 q^{62} -1.45209e8 q^{64} +(-4.93277e7 + 8.54380e7i) q^{65} +(9.09671e7 + 1.57560e8i) q^{67} +(-9.18576e6 - 1.59102e7i) q^{68} +(-3.52229e8 + 6.10079e8i) q^{70} +1.53722e8 q^{71} +1.55706e7 q^{73} +(1.52524e8 - 2.64180e8i) q^{74} +(-2.03548e8 - 3.52556e8i) q^{76} +(-1.66278e8 - 2.88003e8i) q^{77} +(1.63085e8 - 2.82471e8i) q^{79} -5.19381e8 q^{80} -3.97371e8 q^{82} +(-2.50591e7 + 4.34036e7i) q^{83} +(-3.56737e7 - 6.17886e7i) q^{85} +(6.05313e8 + 1.04843e9i) q^{86} +(-1.09558e7 + 1.89760e7i) q^{88} -1.59066e8 q^{89} -5.00848e8 q^{91} +(-3.96164e8 + 6.86177e8i) q^{92} +(3.20477e8 + 5.55082e8i) q^{94} +(-7.90497e8 - 1.36918e9i) q^{95} +(7.46865e7 - 1.29361e8i) q^{97} -2.27160e9 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	16.1666	−	28.0013i	0.714468	−	1.23750i	−0.248696	−	0.968582i	$-0.580002\pi$
$2$	16.1666	−	28.0013i	0.714468	−	1.23750i	0.963164	−	0.268914i	$-0.0866646\pi$
$3$		0			0
$3$		0			0
$4$	−266.716	−	461.965i	−0.520929	−	0.902276i
$5$	−1035.81	−	1794.08i	−0.741167	−	1.28374i	−0.951964	−	0.306210i	$-0.900939\pi$
$5$	−1035.81	−	1794.08i	−0.741167	−	1.28374i	0.210797	−	0.977530i	$-0.432394\pi$
$6$		0			0
$7$	5258.56	−	9108.09i	0.827800	−	1.43379i	−0.0719610	−	0.997407i	$-0.522926\pi$
$7$	5258.56	−	9108.09i	0.827800	−	1.43379i	0.899761	−	0.436384i	$-0.143741\pi$
$8$	−692.954			−0.0598136
$9$		0			0
$10$	−66982.2			−2.11816
$11$	15810.3	−	27384.2i	0.325591	−	0.563940i	−0.656041	−	0.754725i	$-0.727770\pi$
$11$	15810.3	−	27384.2i	0.325591	−	0.563940i	0.981632	+	0.190785i	$0.0611035\pi$
$12$		0			0
$13$	−23811.1	−	41242.0i	−0.231225	−	0.400493i	0.726944	−	0.686697i	$-0.240940\pi$
$13$	−23811.1	−	41242.0i	−0.231225	−	0.400493i	−0.958169	+	0.286204i	$0.907607\pi$
$14$	−170026.	−	294493.i	−1.18287	−	2.04880i
$15$		0			0
$16$	125356.	−	217123.i	0.478195	−	0.828257i
$17$	34440.3			0.100011			0.0500053	−	0.998749i	$-0.484076\pi$
$17$	34440.3			0.100011			0.0500053	+	0.998749i	$0.484076\pi$
$18$		0			0
$19$	763166.			1.34347			0.671735	−	0.740792i	$-0.265550\pi$
$19$	763166.			1.34347			0.671735	+	0.740792i	$0.265550\pi$
$20$	−552535.	+	957020.i	−0.772192	+	1.33748i
$21$		0			0
$22$	−511196.	−	885417.i	−0.465249	−	0.805834i
$23$	−742671.	−	1.28634e6i	−0.553377	−	0.958477i	−0.998028	−	0.0627734i	$-0.980005\pi$
$23$	−742671.	−	1.28634e6i	−0.553377	−	0.958477i	0.444651	−	0.895704i	$-0.353328\pi$
$24$		0			0
$25$	−1.16925e6	+	2.02521e6i	−0.598658	+	1.03691i
$26$	−1.53977e6			−0.660811
$27$		0			0
$28$	−5.61016e6			−1.72490
$29$	−2.40253e6	+	4.16130e6i	−0.630780	+	1.09254i	0.356613	+	0.934252i	$0.383931\pi$
$29$	−2.40253e6	+	4.16130e6i	−0.630780	+	1.09254i	−0.987393	+	0.158290i	$0.949402\pi$
$30$		0			0
$31$	3.91152e6	+	6.77496e6i	0.760708	+	1.31759i	0.942486	+	0.334246i	$0.108482\pi$
$31$	3.91152e6	+	6.77496e6i	0.760708	+	1.31759i	−0.181777	+	0.983340i	$0.558185\pi$
$32$	−4.23054e6	−	7.32752e6i	−0.713216	−	1.23533i
$33$		0			0
$34$	556781.	−	964373.i	0.0714544	−	0.123763i
$35$	−2.17875e7			−2.45415
$36$		0			0
$37$	9.43456e6			0.827587			0.413794	−	0.910371i	$-0.364204\pi$
$37$	9.43456e6			0.827587			0.413794	+	0.910371i	$0.364204\pi$
$38$	1.23378e7	−	2.13696e7i	0.959866	−	1.66254i
$39$		0			0
$40$	717771.	+	1.24322e6i	0.0443319	+	0.0767850i
$41$	−6.14495e6	−	1.06434e7i	−0.339618	−	0.588236i	0.644743	−	0.764400i	$-0.276965\pi$
$41$	−6.14495e6	−	1.06434e7i	−0.339618	−	0.588236i	−0.984361	+	0.176164i	$0.943631\pi$
$42$		0			0
$43$	−1.87211e7	+	3.24260e7i	−0.835072	+	1.44639i	0.0588992	+	0.998264i	$0.481241\pi$
$43$	−1.87211e7	+	3.24260e7i	−0.835072	+	1.44639i	−0.893972	+	0.448124i	$0.852092\pi$
$44$	−1.68674e7			−0.678439
$45$		0			0
$46$	−4.80258e7			−1.58148
$47$	−9.91171e6	+	1.71676e7i	−0.296284	+	0.513179i	−0.975283	−	0.220960i	$-0.929081\pi$
$47$	−9.91171e6	+	1.71676e7i	−0.296284	+	0.513179i	0.678999	+	0.734139i	$0.262414\pi$
$48$		0			0
$49$	−3.51280e7	−	6.08435e7i	−0.870505	−	1.50776i
$50$	3.78057e7	+	6.54813e7i	0.855444	+	1.48167i
$51$		0			0
$52$	−1.27016e7	+	2.19998e7i	−0.240903	+	0.417257i
$53$	5.78978e7			1.00791			0.503953	−	0.863731i	$-0.331878\pi$
$53$	5.78978e7			1.00791			0.503953	+	0.863731i	$0.331878\pi$
$54$		0			0
$55$	−6.55059e7			−0.965269
$56$	−3.64394e6	+	6.31149e6i	−0.0495136	+	0.0857602i
$57$		0			0
$58$	7.76813e7	+	1.34548e8i	0.901344	+	1.56117i
$59$	1.42494e7	+	2.46807e7i	0.153095	+	0.265169i	0.932364	−	0.361521i	$-0.117742\pi$
$59$	1.42494e7	+	2.46807e7i	0.153095	+	0.265169i	−0.779268	+	0.626690i	$0.784409\pi$
$60$		0			0
$61$	−2.22571e7	+	3.85504e7i	−0.205818	+	0.356487i	−0.950393	−	0.311051i	$-0.899319\pi$
$61$	−2.22571e7	+	3.85504e7i	−0.205818	+	0.356487i	0.744575	+	0.667539i	$0.232652\pi$
$62$	2.52944e8			2.17401
$63$		0			0
$64$	−1.45209e8			−1.08189
$65$	−4.93277e7	+	8.54380e7i	−0.342752	+	0.593665i
$66$		0			0
$67$	9.09671e7	+	1.57560e8i	0.551503	+	0.955231i	0.998166	+	0.0605292i	$0.0192788\pi$
$67$	9.09671e7	+	1.57560e8i	0.551503	+	0.955231i	−0.446663	+	0.894702i	$0.647388\pi$
$68$	−9.18576e6	−	1.59102e7i	−0.0520985	−	0.0902372i
$69$		0			0
$70$	−3.52229e8	+	6.10079e8i	−1.75341	+	3.03700i
$71$	1.53722e8			0.717915			0.358958	−	0.933354i	$-0.383132\pi$
$71$	1.53722e8			0.717915			0.358958	+	0.933354i	$0.383132\pi$
$72$		0			0
$73$	1.55706e7			0.0641729			0.0320864	−	0.999485i	$-0.489785\pi$
$73$	1.55706e7			0.0641729			0.0320864	+	0.999485i	$0.489785\pi$
$74$	1.52524e8	−	2.64180e8i	0.591285	−	1.02414i
$75$		0			0
$76$	−2.03548e8	−	3.52556e8i	−0.699853	−	1.21218i
$77$	−1.66278e8	−	2.88003e8i	−0.539048	−	0.933659i
$78$		0			0
$79$	1.63085e8	−	2.82471e8i	0.471077	−	0.815929i	−0.528376	−	0.849011i	$-0.677199\pi$
$79$	1.63085e8	−	2.82471e8i	0.471077	−	0.815929i	0.999453	+	0.0330816i	$0.0105321\pi$
$80$	−5.19381e8			−1.41769
$81$		0			0
$82$	−3.97371e8			−0.970586
$83$	−2.50591e7	+	4.34036e7i	−0.0579580	+	0.100386i	−0.893549	−	0.448966i	$-0.851792\pi$
$83$	−2.50591e7	+	4.34036e7i	−0.0579580	+	0.100386i	0.835591	+	0.549353i	$0.185126\pi$
$84$		0			0
$85$	−3.56737e7	−	6.17886e7i	−0.0741246	−	0.128388i
$86$	6.05313e8	+	1.04843e9i	1.19327	+	2.06680i
$87$		0			0
$88$	−1.09558e7	+	1.89760e7i	−0.0194747	+	0.0337313i
$89$	−1.59066e8			−0.268735			−0.134367	−	0.990932i	$-0.542900\pi$
$89$	−1.59066e8			−0.268735			−0.134367	+	0.990932i	$0.542900\pi$
$90$		0			0
$91$	−5.00848e8			−0.765631
$92$	−3.96164e8	+	6.86177e8i	−0.576541	+	0.998598i
$93$		0			0
$94$	3.20477e8	+	5.55082e8i	0.423371	+	0.733300i
$95$	−7.90497e8	−	1.36918e9i	−0.995736	−	1.72466i
$96$		0			0
$97$	7.46865e7	−	1.29361e8i	0.0856583	−	0.148365i	−0.820013	−	0.572345i	$-0.806034\pi$
$97$	7.46865e7	−	1.29361e8i	0.0856583	−	0.148365i	0.905672	+	0.423980i	$0.139367\pi$
$98$	−2.27160e9			−2.48779
$99$		0			0
$100$	1.24743e9			1.24743
$101$	9.21325e8	−	1.59578e9i	0.880981	−	1.52590i	0.0307293	−	0.999528i	$-0.490217\pi$
$101$	9.21325e8	−	1.59578e9i	0.880981	−	1.52590i	0.850252	−	0.526376i	$-0.176450\pi$
$102$		0			0
$103$	1.75215e8	+	3.03481e8i	0.153392	+	0.265683i	0.932472	−	0.361241i	$-0.117647\pi$
$103$	1.75215e8	+	3.03481e8i	0.153392	+	0.265683i	−0.779080	+	0.626924i	$0.784314\pi$
$104$	1.65000e7	+	2.85788e7i	0.0138304	+	0.0239549i
$105$		0			0
$106$	9.36008e8	−	1.62121e9i	0.720117	−	1.24728i
$107$	7.93460e8			0.585192			0.292596	−	0.956236i	$-0.405481\pi$
$107$	7.93460e8			0.585192			0.292596	+	0.956236i	$0.405481\pi$
$108$		0			0
$109$	1.09944e9			0.746020			0.373010	−	0.927827i	$-0.378326\pi$
$109$	1.09944e9			0.746020			0.373010	+	0.927827i	$0.378326\pi$
$110$	−1.05901e9	+	1.83425e9i	−0.689654	+	1.19452i
$111$		0			0
$112$	−1.31838e9	−	2.28350e9i	−0.791699	−	1.37126i
$113$	−1.45685e9	−	2.52334e9i	−0.840547	−	1.45587i	−0.889433	−	0.457065i	$-0.848901\pi$
$113$	−1.45685e9	−	2.52334e9i	−0.840547	−	1.45587i	0.0488867	−	0.998804i	$-0.484433\pi$
$114$		0			0
$115$	−1.53854e9	+	2.66482e9i	−0.820290	+	1.42078i
$116$	2.56317e9			1.31437
$117$		0			0
$118$	9.21455e8			0.437527
$119$	1.81106e8	−	3.13685e8i	0.0827888	−	0.143394i
$120$		0			0
$121$	6.79045e8	+	1.17614e9i	0.287981	+	0.498798i
$122$	7.19640e8	+	1.24645e9i	0.294101	+	0.509398i
$123$		0			0
$124$	2.08653e9	−	3.61398e9i	0.792551	−	1.37274i
$125$	7.98371e8			0.292489
$126$		0			0
$127$	1.58765e9			0.541551			0.270776	−	0.962643i	$-0.412720\pi$
$127$	1.58765e9			0.541551			0.270776	+	0.962643i	$0.412720\pi$
$128$	−1.81495e8	+	3.14358e8i	−0.0597612	+	0.103509i
$129$		0			0
$130$	1.59492e9	+	2.76248e9i	0.489771	+	0.848309i
$131$	1.88000e9	+	3.25625e9i	0.557745	+	0.966043i	0.997684	+	0.0680156i	$0.0216668\pi$
$131$	1.88000e9	+	3.25625e9i	0.557745	+	0.966043i	−0.439939	+	0.898028i	$0.645000\pi$
$132$		0			0
$133$	4.01315e9	−	6.95098e9i	1.11212	−	1.92625i
$134$	5.88251e9			1.57613
$135$		0			0
$136$	−2.38655e7			−0.00598199
$137$	−4.94173e8	+	8.55933e8i	−0.119850	+	0.207586i	−0.919708	−	0.392603i	$-0.871575\pi$
$137$	−4.94173e8	+	8.55933e8i	−0.119850	+	0.207586i	0.799858	+	0.600189i	$0.204908\pi$
$138$		0			0
$139$	−2.35800e9	−	4.08418e9i	−0.535769	−	0.927979i	−0.999126	−	0.0418075i	$-0.986688\pi$
$139$	−2.35800e9	−	4.08418e9i	−0.535769	−	0.927979i	0.463356	−	0.886172i	$-0.346645\pi$
$140$	5.81108e9	+	1.00651e10i	1.27844	+	2.21432i
$141$		0			0
$142$	2.48515e9	−	4.30441e9i	0.512927	−	0.888416i
$143$	−1.50584e9			−0.301139
$144$		0			0
$145$	9.95428e9			1.87005
$146$	2.51723e8	−	4.35996e8i	0.0458495	−	0.0794136i
$147$		0			0
$148$	−2.51635e9	−	4.35844e9i	−0.431115	−	0.746712i
$149$	−2.18439e9	−	3.78347e9i	−0.363071	−	0.628858i	0.625393	−	0.780310i	$-0.284939\pi$
$149$	−2.18439e9	−	3.78347e9i	−0.363071	−	0.628858i	−0.988465	+	0.151452i	$0.951605\pi$
$150$		0			0
$151$	−3.23754e9	+	5.60758e9i	−0.506779	+	0.877767i	0.493190	+	0.869922i	$0.335831\pi$
$151$	−3.23754e9	+	5.60758e9i	−0.506779	+	0.877767i	−0.999969	+	0.00784581i	$0.997503\pi$
$152$	−5.28839e8			−0.0803577
$153$		0			0
$154$	−1.07526e10			−1.54053
$155$	8.10321e9	−	1.40352e10i	1.12762	−	1.95310i
$156$		0			0
$157$	4.25430e8	+	7.36866e8i	0.0558830	+	0.0967922i	0.892614	−	0.450823i	$-0.148869\pi$
$157$	4.25430e8	+	7.36866e8i	0.0558830	+	0.0967922i	−0.836731	+	0.547615i	$0.815536\pi$
$158$	−5.27305e9	−	9.13318e9i	−0.673139	−	1.16591i
$159$		0			0
$160$	−8.76410e9	+	1.51799e10i	−1.05723	+	1.83117i
$161$	−1.56215e10			−1.83234
$162$		0			0
$163$	−8.54283e9			−0.947889			−0.473945	−	0.880555i	$-0.657170\pi$
$163$	−8.54283e9			−0.947889			−0.473945	+	0.880555i	$0.657170\pi$
$164$	−3.27791e9	+	5.67751e9i	−0.353834	+	0.612859i
$165$		0			0
$166$	8.10238e8	+	1.40337e9i	0.0828183	+	0.143445i
$167$	−2.28606e8	−	3.95957e8i	−0.0227438	−	0.0393934i	0.854429	−	0.519567i	$-0.173907\pi$
$167$	−2.28606e8	−	3.95957e8i	−0.0227438	−	0.0393934i	−0.877173	+	0.480174i	$0.840574\pi$
$168$		0			0
$169$	4.16831e9	−	7.21973e9i	0.393070	−	0.680818i
$170$	−2.30688e9			−0.211839
$171$		0			0
$172$	1.99729e10			1.74005
$173$	−4.56554e9	+	7.90775e9i	−0.387511	+	0.671190i	−0.992114	−	0.125338i	$-0.959999\pi$
$173$	−4.56554e9	+	7.90775e9i	−0.387511	+	0.671190i	0.604603	+	0.796527i	$0.293332\pi$
$174$		0			0
$175$	1.22972e10	+	2.12993e10i	0.991138	+	1.71670i
$176$	−3.96382e9	−	6.86554e9i	−0.311392	−	0.539346i
$177$		0			0
$178$	−2.57156e9	+	4.45407e9i	−0.192002	+	0.332558i
$179$	1.84541e9			0.134355			0.0671777	−	0.997741i	$-0.478601\pi$
$179$	1.84541e9			0.134355			0.0671777	+	0.997741i	$0.478601\pi$
$180$		0			0
$181$	−1.02105e10			−0.707123			−0.353562	−	0.935411i	$-0.615030\pi$
$181$	−1.02105e10			−0.707123			−0.353562	+	0.935411i	$0.615030\pi$
$182$	−8.09699e9	+	1.40244e10i	−0.547019	+	0.947464i
$183$		0			0
$184$	5.14637e8	+	8.91378e8i	0.0330995	+	0.0573300i
$185$	−9.77244e9	−	1.69264e10i	−0.613381	−	1.06241i
$186$		0			0
$187$	5.44510e8	−	9.43119e8i	0.0325626	−	0.0564000i
$188$	1.05744e10			0.617372
$189$		0			0
$190$	−5.11185e10			−2.84569
$191$	−5.01150e9	+	8.68017e9i	−0.272469	+	0.471931i	−0.969494	−	0.245117i	$-0.921174\pi$
$191$	−5.01150e9	+	8.68017e9i	−0.272469	+	0.471931i	0.697024	+	0.717048i	$0.254507\pi$
$192$		0			0
$193$	−2.93622e9	−	5.08568e9i	−0.152328	−	0.263840i	0.779755	−	0.626085i	$-0.215344\pi$
$193$	−2.93622e9	−	5.08568e9i	−0.152328	−	0.263840i	−0.932083	+	0.362245i	$0.882010\pi$
$194$	−2.41485e9	−	4.18264e9i	−0.122400	−	0.212003i
$195$		0			0
$196$	−1.87384e10	+	3.24558e10i	−0.906943	+	1.57087i
$197$	−2.73628e10			−1.29438			−0.647191	−	0.762328i	$-0.724056\pi$
$197$	−2.73628e10			−1.29438			−0.647191	+	0.762328i	$0.724056\pi$
$198$		0			0
$199$	2.21639e9			0.100186			0.0500930	−	0.998745i	$-0.484048\pi$
$199$	2.21639e9			0.100186			0.0500930	+	0.998745i	$0.484048\pi$
$200$	8.10240e8	−	1.40338e9i	0.0358079	−	0.0620211i
$201$		0			0
$202$	−2.97893e10	−	5.15966e10i	−1.25887	−	2.18042i
$203$	2.52677e10	+	4.37649e10i	1.04432	+	1.80881i
$204$		0			0
$205$	−1.27300e10	+	2.20491e10i	−0.503428	+	0.871963i
$206$	1.13305e10			0.438376
$207$		0			0
$208$	−1.19394e10			−0.442281
$209$	1.20659e10	−	2.08987e10i	0.437421	−	0.757636i
$210$		0			0
$211$	6.76033e9	+	1.17092e10i	0.234799	+	0.406685i	0.959214	−	0.282680i	$-0.0912233\pi$
$211$	6.76033e9	+	1.17092e10i	0.234799	+	0.406685i	−0.724415	+	0.689364i	$0.757890\pi$
$212$	−1.54423e10	−	2.67468e10i	−0.525048	−	0.909410i
$213$		0			0
$214$	1.28275e10	−	2.22179e10i	0.418101	−	0.724172i
$215$	7.75664e10			2.47571
$216$		0			0
$217$	8.22758e10			2.51886
$218$	1.77741e10	−	3.07856e10i	0.533007	−	0.923196i
$219$		0			0
$220$	1.74715e10	+	3.02615e10i	0.502837	+	0.870940i
$221$	−8.20060e8	−	1.42039e9i	−0.0231249	−	0.0400536i
$222$		0			0
$223$	1.48641e9	−	2.57454e9i	0.0402502	−	0.0697154i	−0.845199	−	0.534452i	$-0.820518\pi$
$223$	1.48641e9	−	2.57454e9i	0.0402502	−	0.0697154i	0.885449	+	0.464737i	$0.153851\pi$
$224$	−8.89862e10			−2.36160
$225$		0			0
$226$	−9.42090e10			−2.40218
$227$	1.67299e10	−	2.89771e10i	0.418194	−	0.724333i	−0.577564	−	0.816345i	$-0.695997\pi$
$227$	1.67299e10	−	2.89771e10i	0.418194	−	0.724333i	0.995758	+	0.0920123i	$0.0293299\pi$
$228$		0			0
$229$	3.80393e10	+	6.58859e10i	0.914055	+	1.58319i	0.808279	+	0.588800i	$0.200399\pi$
$229$	3.80393e10	+	6.58859e10i	0.914055	+	1.58319i	0.105776	+	0.994390i	$0.466267\pi$
$230$	4.97457e10	+	8.61621e10i	1.17214	+	2.03021i
$231$		0			0
$232$	1.66484e9	−	2.88359e9i	0.0377292	−	0.0653489i
$233$	6.49552e10			1.44382			0.721909	−	0.691988i	$-0.243265\pi$
$233$	6.49552e10			1.44382			0.721909	+	0.691988i	$0.243265\pi$
$234$		0			0
$235$	4.10667e10			0.878384
$236$	7.60108e9	−	1.31655e10i	0.159504	−	0.276269i
$237$		0			0
$238$	−5.85573e9	−	1.01424e10i	−0.118300	−	0.204901i
$239$	1.99236e10	+	3.45086e10i	0.394981	+	0.684128i	0.993099	−	0.117281i	$-0.0374177\pi$
$239$	1.99236e10	+	3.45086e10i	0.394981	+	0.684128i	−0.598117	+	0.801408i	$0.704084\pi$
$240$		0			0
$241$	−5.93072e9	+	1.02723e10i	−0.113248	+	0.196151i	−0.917078	−	0.398708i	$-0.869459\pi$
$241$	−5.93072e9	+	1.02723e10i	−0.113248	+	0.196151i	0.803830	+	0.594859i	$0.202792\pi$
$242$	4.39113e10			0.823014
$243$		0			0
$244$	2.37452e10			0.428867
$245$	−7.27721e10	+	1.26045e11i	−1.29038	+	2.23500i
$246$		0			0
$247$	−1.81718e10	−	3.14745e10i	−0.310643	−	0.538050i
$248$	−2.71051e9	−	4.69474e9i	−0.0455007	−	0.0788095i
$249$		0			0
$250$	1.29069e10	−	2.23554e10i	0.208974	−	0.361954i
$251$	−6.51966e10			−1.03680			−0.518398	−	0.855139i	$-0.673471\pi$
$251$	−6.51966e10			−1.03680			−0.518398	+	0.855139i	$0.673471\pi$
$252$		0			0
$253$	−4.69673e10			−0.720698
$254$	2.56669e10	−	4.44564e10i	0.386921	−	0.670167i
$255$		0			0
$256$	−3.13052e10	−	5.42223e10i	−0.455551	−	0.789038i
$257$	−1.90082e10	−	3.29232e10i	−0.271796	−	0.470764i	0.697526	−	0.716559i	$-0.254284\pi$
$257$	−1.90082e10	−	3.29232e10i	−0.271796	−	0.470764i	−0.969322	+	0.245796i	$0.920951\pi$
$258$		0			0
$259$	4.96121e10	−	8.59307e10i	0.685076	−	1.18659i
$260$	5.26259e10			0.714199
$261$		0			0
$262$	1.21572e11			1.59397
$263$	−1.76962e10	+	3.06508e10i	−0.228076	+	0.395039i	−0.957238	−	0.289302i	$-0.906577\pi$
$263$	−1.76962e10	+	3.06508e10i	−0.228076	+	0.395039i	0.729162	+	0.684341i	$0.239910\pi$
$264$		0			0
$265$	−5.99713e10	−	1.03873e11i	−0.747028	−	1.29389i
$266$	−1.29758e11	−	2.24747e11i	−1.58915	−	2.75249i
$267$		0			0
$268$	4.85248e10	−	8.40473e10i	0.574588	−	0.995216i
$269$	−6.44475e9			−0.0750448			−0.0375224	−	0.999296i	$-0.511947\pi$
$269$	−6.44475e9			−0.0750448			−0.0375224	+	0.999296i	$0.511947\pi$
$270$		0			0
$271$	1.68603e11			1.89890			0.949452	−	0.313912i	$-0.101640\pi$
$271$	1.68603e11			1.89890			0.949452	+	0.313912i	$0.101640\pi$
$272$	4.31729e9	−	7.47776e9i	0.0478246	−	0.0828346i
$273$		0			0
$274$	1.59782e10	+	2.76750e10i	0.171257	+	0.296627i
$275$	3.69725e10	+	6.40382e10i	0.389835	+	0.675215i
$276$		0			0
$277$	2.43561e10	−	4.21860e10i	0.248570	−	0.430536i	−0.714559	−	0.699575i	$-0.753373\pi$
$277$	2.43561e10	−	4.21860e10i	0.248570	−	0.430536i	0.963129	+	0.269039i	$0.0867060\pi$
$278$	−1.52483e11			−1.53116
$279$		0			0
$280$	1.50978e10			0.146792
$281$	−7.56804e10	+	1.31082e11i	−0.724110	+	1.25420i	0.235229	+	0.971940i	$0.424416\pi$
$281$	−7.56804e10	+	1.31082e11i	−0.724110	+	1.25420i	−0.959339	+	0.282256i	$0.908917\pi$
$282$		0			0
$283$	3.57141e10	+	6.18586e10i	0.330979	+	0.573273i	0.982704	−	0.185183i	$-0.0592876\pi$
$283$	3.57141e10	+	6.18586e10i	0.330979	+	0.573273i	−0.651725	+	0.758455i	$0.725954\pi$
$284$	−4.10001e10	−	7.10142e10i	−0.373983	−	0.647758i
$285$		0			0
$286$	−2.43442e10	+	4.21655e10i	−0.215154	+	0.372657i
$287$	−1.29254e11			−1.12454
$288$		0			0
$289$	−1.17402e11			−0.989998
$290$	1.60927e11	−	2.78733e11i	1.33609	−	2.31418i
$291$		0			0
$292$	−4.15292e9	−	7.19306e9i	−0.0334295	−	0.0579017i
$293$	−1.11136e11	−	1.92493e11i	−0.880945	−	1.52584i	−0.850291	−	0.526312i	$-0.823574\pi$
$293$	−1.11136e11	−	1.92493e11i	−0.880945	−	1.52584i	−0.0306540	−	0.999530i	$-0.509759\pi$
$294$		0			0
$295$	2.95194e10	−	5.11291e10i	0.226939	−	0.393069i
$296$	−6.53772e9			−0.0495009
$297$		0			0
$298$	−1.41256e11			−1.03761
$299$	−3.53676e10	+	6.12585e10i	−0.255909	+	0.443247i
$300$		0			0
$301$	1.96892e11	+	3.41027e11i	1.38255	+	2.39464i
$302$	1.04680e11	+	1.81311e11i	0.724155	+	1.25427i
$303$		0			0
$304$	9.56673e10	−	1.65701e11i	0.642440	−	1.11274i
$305$	9.22166e10			0.610183
$306$		0			0
$307$	2.24657e11			1.44343			0.721717	−	0.692188i	$-0.243353\pi$
$307$	2.24657e11			1.44343			0.721717	+	0.692188i	$0.243353\pi$
$308$	−8.86981e10	+	1.53630e11i	−0.561612	+	0.972740i
$309$		0			0
$310$	−2.62002e11	−	4.53801e11i	−1.61130	−	2.79086i
$311$	1.49945e11	+	2.59712e11i	0.908886	+	1.57424i	0.815615	+	0.578595i	$0.196399\pi$
$311$	1.49945e11	+	2.59712e11i	0.908886	+	1.57424i	0.0932707	+	0.995641i	$0.470268\pi$
$312$		0			0
$313$	−7.52510e10	+	1.30339e11i	−0.443162	+	0.767580i	−0.997922	−	0.0644309i	$-0.979477\pi$
$313$	−7.52510e10	+	1.30339e11i	−0.443162	+	0.767580i	0.554760	+	0.832011i	$0.312810\pi$
$314$	2.75110e10			0.159706
$315$		0			0
$316$	−1.73989e11			−0.981591
$317$	1.24948e11	−	2.16417e11i	0.694966	−	1.20372i	−0.275227	−	0.961379i	$-0.588753\pi$
$317$	1.24948e11	−	2.16417e11i	0.694966	−	1.20372i	0.970192	−	0.242336i	$-0.0779137\pi$
$318$		0			0
$319$	7.59693e10	+	1.31583e11i	0.410752	+	0.711444i
$320$	1.50409e11	+	2.60517e11i	0.801863	+	1.38887i
$321$		0			0
$322$	−2.52546e11	+	4.37423e11i	−1.30915	+	2.26751i
$323$	2.62836e10			0.134361
$324$		0			0
$325$	1.11365e11			0.553698
$326$	−1.38108e11	+	2.39211e11i	−0.677237	+	1.17301i
$327$		0			0
$328$	4.25817e9	+	7.37537e9i	0.0203138	+	0.0351845i
$329$	1.04243e11	+	1.80553e11i	0.490528	+	0.849619i
$330$		0			0
$331$	−2.66225e10	+	4.61115e10i	−0.121905	+	0.211146i	−0.920519	−	0.390698i	$-0.872234\pi$
$331$	−2.66225e10	+	4.61115e10i	−0.121905	+	0.211146i	0.798614	+	0.601844i	$0.205567\pi$
$332$	2.67346e10			0.120768
$333$		0			0
$334$	−1.47831e10			−0.0649989
$335$	1.88450e11	−	3.26405e11i	0.817512	−	1.41597i
$336$		0			0
$337$	−1.77381e10	−	3.07233e10i	−0.0749156	−	0.129758i	0.826134	−	0.563474i	$-0.190535\pi$
$337$	−1.77381e10	−	3.07233e10i	−0.0749156	−	0.129758i	−0.901050	+	0.433716i	$0.857202\pi$
$338$	−1.34775e11	−	2.33437e11i	−0.561672	−	0.972845i
$339$		0			0
$340$	−1.90295e10	+	3.29600e10i	−0.0772274	+	0.133762i
$341$	2.47369e11			0.990719
$342$		0			0
$343$	−3.14487e11			−1.22681
$344$	1.29729e10	−	2.24697e10i	0.0499486	−	0.0865136i
$345$		0			0
$346$	1.47618e11	+	2.55682e11i	0.553729	+	0.959087i
$347$	−1.96079e11	−	3.39618e11i	−0.726019	−	1.25750i	−0.958553	−	0.284914i	$-0.908035\pi$
$347$	−1.96079e11	−	3.39618e11i	−0.726019	−	1.25750i	0.232534	−	0.972588i	$-0.425298\pi$
$348$		0			0
$349$	4.15073e10	−	7.18927e10i	0.149765	−	0.259400i	−0.781376	−	0.624061i	$-0.785482\pi$
$349$	4.15073e10	−	7.18927e10i	0.149765	−	0.259400i	0.931140	+	0.364661i	$0.118815\pi$
$350$	7.95213e11			2.83255
$351$		0			0
$352$	−2.67544e11			−0.928867
$353$	−9.28123e10	+	1.60756e11i	−0.318141	+	0.551036i	−0.980100	−	0.198504i	$-0.936392\pi$
$353$	−9.28123e10	+	1.60756e11i	−0.318141	+	0.551036i	0.661959	+	0.749540i	$0.269725\pi$
$354$		0			0
$355$	−1.59227e11	−	2.75789e11i	−0.532095	−	0.921616i
$356$	4.24256e10	+	7.34832e10i	0.139992	+	0.242473i
$357$		0			0
$358$	2.98340e10	−	5.16740e10i	0.0959926	−	0.166264i
$359$	−3.92754e11			−1.24794			−0.623972	−	0.781447i	$-0.714482\pi$
$359$	−3.92754e11			−1.24794			−0.623972	+	0.781447i	$0.714482\pi$
$360$		0			0
$361$	2.59734e11			0.804909
$362$	−1.65069e11	+	2.85908e11i	−0.505217	+	0.875061i
$363$		0			0
$364$	1.33584e11	+	2.31374e11i	0.398840	+	0.690810i
$365$	−1.61282e10	−	2.79349e10i	−0.0475629	−	0.0823813i
$366$		0			0
$367$	−2.48729e10	+	4.30812e10i	−0.0715698	+	0.123963i	−0.899589	−	0.436737i	$-0.856134\pi$
$367$	−2.48729e10	+	4.30812e10i	−0.0715698	+	0.123963i	0.828020	+	0.560699i	$0.189468\pi$
$368$	−3.72393e11			−1.05849
$369$		0			0
$370$	−6.31947e11			−1.75296
$371$	3.04459e11	−	5.27338e11i	0.834345	−	1.44513i
$372$		0			0
$373$	−2.01578e11	−	3.49143e11i	−0.539204	−	0.933929i	−0.998947	−	0.0458766i	$-0.985392\pi$
$373$	−2.01578e11	−	3.49143e11i	−0.539204	−	0.933929i	0.459743	−	0.888052i	$-0.347941\pi$
$374$	−1.76057e10	−	3.04940e10i	−0.0465298	−	0.0805920i
$375$		0			0
$376$	6.86836e9	−	1.18964e10i	0.0177218	−	0.0306951i
$377$	2.28827e11			0.583407
$378$		0			0
$379$	−3.41222e11			−0.849494			−0.424747	−	0.905312i	$-0.639637\pi$
$379$	−3.41222e11			−0.849494			−0.424747	+	0.905312i	$0.639637\pi$
$380$	−4.21676e11	+	7.30365e11i	−1.03742	+	1.79686i
$381$		0			0
$382$	1.62037e11	+	2.80657e11i	0.389341	+	0.674359i
$383$	−1.58499e11	−	2.74529e11i	−0.376385	−	0.651918i	0.614148	−	0.789191i	$-0.289500\pi$
$383$	−1.58499e11	−	2.74529e11i	−0.376385	−	0.651918i	−0.990533	+	0.137273i	$0.956166\pi$
$384$		0			0
$385$	−3.44467e11	+	5.96634e11i	−0.799050	+	1.38399i
$386$	−1.89874e11			−0.435335
$387$		0			0
$388$	−7.96803e10			−0.178488
$389$	5.59546e10	−	9.69163e10i	0.123898	−	0.214597i	−0.797404	−	0.603446i	$-0.793794\pi$
$389$	5.59546e10	−	9.69163e10i	0.123898	−	0.214597i	0.921301	+	0.388849i	$0.127127\pi$
$390$		0			0
$391$	−2.55778e10	−	4.43020e10i	−0.0553436	−	0.0958580i
$392$	2.43421e10	+	4.21618e10i	0.0520680	+	0.0901844i
$393$		0			0
$394$	−4.42362e11	+	7.66194e11i	−0.924794	+	1.60179i
$395$	−6.75702e11			−1.39659
$396$		0			0
$397$	3.48788e11			0.704700			0.352350	−	0.935868i	$-0.385383\pi$
$397$	3.48788e11			0.704700			0.352350	+	0.935868i	$0.385383\pi$
$398$	3.58314e10	−	6.20617e10i	0.0715796	−	0.123980i
$399$		0			0
$400$	2.93146e11	+	5.07743e11i	0.572550	+	0.991686i
$401$	−1.27488e11	−	2.20816e11i	−0.246218	−	0.426463i	0.716255	−	0.697839i	$-0.245855\pi$
$401$	−1.27488e11	−	2.20816e11i	−0.246218	−	0.426463i	−0.962473	+	0.271376i	$0.912521\pi$
$402$		0			0
$403$	1.86275e11	−	3.22638e11i	0.351789	−	0.609317i
$404$	−9.82928e11			−1.83572
$405$		0			0
$406$	1.63397e12			2.98453
$407$	1.49163e11	−	2.58358e11i	0.269455	−	0.466709i
$408$		0			0
$409$	−1.34167e10	−	2.32384e10i	−0.0237078	−	0.0410631i	0.853928	−	0.520391i	$-0.174214\pi$
$409$	−1.34167e10	−	2.32384e10i	−0.0237078	−	0.0410631i	−0.877636	+	0.479328i	$0.840880\pi$
$410$	4.11602e11	+	7.12916e11i	0.719367	+	1.24598i
$411$		0			0
$412$	9.34652e10	−	1.61886e11i	0.159813	−	0.276804i
$413$	2.99725e11			0.506930
$414$		0			0
$415$	1.03826e11			0.171826
$416$	−2.01468e11	+	3.48952e11i	−0.329826	+	0.571276i
$417$		0			0
$418$	−3.90127e11	−	6.75720e11i	−0.625047	−	1.08261i
$419$	4.33610e9	+	7.51035e9i	0.00687284	+	0.0119041i	0.869441	−	0.494036i	$-0.164479\pi$
$419$	4.33610e9	+	7.51035e9i	0.00687284	+	0.0119041i	−0.862569	+	0.505940i	$0.831146\pi$
$420$		0			0
$421$	4.84053e11	−	8.38404e11i	0.750971	−	1.30072i	−0.196382	−	0.980528i	$-0.562919\pi$
$421$	4.84053e11	−	8.38404e11i	0.750971	−	1.30072i	0.947353	−	0.320192i	$-0.103747\pi$
$422$	4.37166e11			0.671027
$423$		0			0
$424$	−4.01205e10			−0.0602865
$425$	−4.02694e10	+	6.97487e10i	−0.0598722	+	0.103702i
$426$		0			0
$427$	2.34080e11	+	4.05438e11i	0.340752	+	0.590200i
$428$	−2.11628e11	−	3.66551e11i	−0.304844	−	0.528004i
$429$		0			0
$430$	1.25398e12	−	2.17196e12i	1.76882	−	3.06368i
$431$	−1.38264e12			−1.93001			−0.965006	−	0.262227i	$-0.915543\pi$
$431$	−1.38264e12			−1.93001			−0.965006	+	0.262227i	$0.915543\pi$
$432$		0			0
$433$	−1.26247e12			−1.72594			−0.862971	−	0.505254i	$-0.831399\pi$
$433$	−1.26247e12			−1.72594			−0.862971	+	0.505254i	$0.831399\pi$
$434$	1.33012e12	−	2.30383e12i	1.79964	−	3.11707i
$435$		0			0
$436$	−2.93237e11	−	5.07901e11i	−0.388624	−	0.673116i
$437$	−5.66781e11	−	9.81694e11i	−0.743445	−	1.28768i
$438$		0			0
$439$	−2.18121e11	+	3.77796e11i	−0.280290	+	0.485476i	−0.971456	−	0.237220i	$-0.923764\pi$
$439$	−2.18121e11	+	3.77796e11i	−0.280290	+	0.485476i	0.691166	+	0.722696i	$0.257097\pi$
$440$	4.53926e10			0.0577362
$441$		0			0
$442$	−5.30302e10			−0.0660881
$443$	−2.53997e11	+	4.39936e11i	−0.313337	+	0.542716i	−0.979083	−	0.203463i	$-0.934780\pi$
$443$	−2.53997e11	+	4.39936e11i	−0.313337	+	0.542716i	0.665745	+	0.746179i	$0.268114\pi$
$444$		0			0
$445$	1.64763e11	+	2.85378e11i	0.199177	+	0.344985i
$446$	−4.80604e10	−	8.32431e10i	−0.0575149	−	0.0996188i
$447$		0			0
$448$	−7.63590e11	+	1.32258e12i	−0.895590	+	1.55121i
$449$	1.47077e12			1.70780			0.853899	−	0.520439i	$-0.174232\pi$
$449$	1.47077e12			1.70780			0.853899	+	0.520439i	$0.174232\pi$
$450$		0			0
$451$	−3.88613e11			−0.442307
$452$	−7.77130e11	+	1.34603e12i	−0.875731	+	1.51681i
$453$		0			0
$454$	−5.40931e11	−	9.36920e11i	−0.597573	−	1.03503i
$455$	5.18785e11	+	8.98561e11i	0.567461	+	0.982871i
$456$		0			0
$457$	5.59957e11	−	9.69874e11i	0.600526	−	1.04014i	−0.392215	−	0.919874i	$-0.628291\pi$
$457$	5.59957e11	−	9.69874e11i	0.600526	−	1.04014i	0.992741	−	0.120268i	$-0.0383755\pi$
$458$	2.45986e12			2.61225
$459$		0			0
$460$	1.64141e12			1.70925
$461$	−8.63344e11	+	1.49535e12i	−0.890286	+	1.54202i	−0.0507531	+	0.998711i	$0.516162\pi$
$461$	−8.63344e11	+	1.49535e12i	−0.890286	+	1.54202i	−0.839533	+	0.543309i	$0.817171\pi$
$462$		0			0
$463$	−1.37336e11	−	2.37874e11i	−0.138890	−	0.240565i	0.788187	−	0.615436i	$-0.211020\pi$
$463$	−1.37336e11	−	2.37874e11i	−0.138890	−	0.240565i	−0.927077	+	0.374871i	$0.877687\pi$
$464$	6.02342e11	+	1.04329e12i	0.603271	+	1.04490i
$465$		0			0
$466$	1.05010e12	−	1.81883e12i	1.03156	−	1.78672i
$467$	1.14495e12			1.11394			0.556971	−	0.830532i	$-0.311964\pi$
$467$	1.14495e12			1.11394			0.556971	+	0.830532i	$0.311964\pi$
$468$		0			0
$469$	1.91342e12			1.82614
$470$	6.63908e11	−	1.14992e12i	0.627578	−	1.08700i
$471$		0			0
$472$	−9.87418e9	−	1.71026e10i	−0.00915719	−	0.0158607i
$473$	5.91972e11	+	1.02533e12i	0.543784	+	0.941861i
$474$		0			0
$475$	−8.92335e11	+	1.54557e12i	−0.804279	+	1.39305i
$476$	−1.93215e11			−0.172508
$477$		0			0
$478$	1.28838e12			1.12881
$479$	−4.66326e11	+	8.07701e11i	−0.404744	+	0.701036i	−0.994292	−	0.106697i	$-0.965973\pi$
$479$	−4.66326e11	+	8.07701e11i	−0.404744	+	0.701036i	0.589548	+	0.807733i	$0.299306\pi$
$480$		0			0
$481$	−2.24647e11	−	3.89100e11i	−0.191359	−	0.331443i
$482$	1.91759e11	+	3.32136e11i	0.161824	+	0.280288i
$483$		0			0
$484$	3.62224e11	−	6.27390e11i	0.300036	−	0.519677i
$485$	−3.09445e11			−0.253949
$486$		0			0
$487$	−1.02912e12			−0.829059			−0.414530	−	0.910036i	$-0.636054\pi$
$487$	−1.02912e12			−0.829059			−0.414530	+	0.910036i	$0.636054\pi$
$488$	1.54231e10	−	2.67136e10i	0.0123107	−	0.0213228i
$489$		0			0
$490$	2.35295e12	+	4.07543e12i	1.84387	+	3.19368i
$491$	−8.64444e11	−	1.49726e12i	−0.671228	−	1.16260i	−0.977556	−	0.210675i	$-0.932434\pi$
$491$	−8.64444e11	−	1.49726e12i	−0.671228	−	1.16260i	0.306328	−	0.951926i	$-0.400900\pi$
$492$		0			0
$493$	−8.27437e10	+	1.43316e11i	−0.0630847	+	0.109266i
$494$	−1.17510e12			−0.887779
$495$		0			0
$496$	1.96133e12			1.45507
$497$	8.08355e11	−	1.40011e12i	0.594290	−	1.02934i
$498$		0			0
$499$	−1.19988e12	−	2.07826e12i	−0.866336	−	1.50054i	−0.865715	−	0.500538i	$-0.833136\pi$
$499$	−1.19988e12	−	2.07826e12i	−0.866336	−	1.50054i	−0.000620882	−	1.00000i	$-0.500198\pi$
$500$	−2.12938e11	−	3.68820e11i	−0.152366	−	0.263906i
$501$		0			0
$502$	−1.05401e12	+	1.82559e12i	−0.740758	+	1.28303i
$503$	1.98201e12			1.38054			0.690271	−	0.723551i	$-0.257491\pi$
$503$	1.98201e12			1.38054			0.690271	+	0.723551i	$0.257491\pi$
$504$		0			0
$505$	−3.81728e12			−2.61182
$506$	−7.59300e11	+	1.31515e12i	−0.514916	+	0.891861i
$507$		0			0
$508$	−4.23453e11	−	7.33442e11i	−0.282110	−	0.488629i
$509$	1.12779e12	+	1.95340e12i	0.744731	+	1.28991i	0.950320	+	0.311274i	$0.100756\pi$
$509$	1.12779e12	+	1.95340e12i	0.744731	+	1.28991i	−0.205589	+	0.978638i	$0.565911\pi$
$510$		0			0
$511$	8.18787e10	−	1.41818e11i	0.0531223	−	0.0920105i
$512$	−2.21024e12			−1.42143
$513$		0			0
$514$	−1.22919e12			−0.776757
$515$	3.62980e11	−	6.28699e11i	0.227379	−	0.393831i
$516$		0			0
$517$	3.13414e11	+	5.42848e11i	0.192935	+	0.334173i
$518$	−1.60412e12	−	2.77841e12i	−0.978931	−	1.69556i
$519$		0			0
$520$	3.41818e10	−	5.92046e10i	0.0205012	−	0.0355092i
$521$	−7.71315e11			−0.458630			−0.229315	−	0.973352i	$-0.573649\pi$
$521$	−7.71315e11			−0.458630			−0.229315	+	0.973352i	$0.573649\pi$
$522$		0			0
$523$	−1.54315e12			−0.901886			−0.450943	−	0.892553i	$-0.648912\pi$
$523$	−1.54315e12			−0.901886			−0.450943	+	0.892553i	$0.648912\pi$
$524$	1.00285e12	−	1.73699e12i	0.581092	−	1.00648i
$525$		0			0
$526$	5.72174e11	+	9.91035e11i	0.325906	+	0.564486i
$527$	1.34714e11	+	2.33331e11i	0.0760790	+	0.131773i
$528$		0			0
$529$	−2.02545e11	+	3.50817e11i	−0.112453	+	0.194774i
$530$	−3.87812e12			−2.13491
$531$		0			0
$532$	−4.28148e12			−2.31735
$533$	−2.92636e11	+	5.06860e11i	−0.157056	+	0.272029i
$534$		0			0
$535$	−8.21876e11	−	1.42353e12i	−0.433725	−	0.751234i
$536$	−6.30361e10	−	1.09182e11i	−0.0329874	−	0.0571358i
$537$		0			0
$538$	−1.04189e11	+	1.80461e11i	−0.0536171	+	0.0928676i
$539$	−2.22153e12			−1.13371
$540$		0			0
$541$	3.58683e12			1.80021			0.900105	−	0.435674i	$-0.143490\pi$
$541$	3.58683e12			1.80021			0.900105	+	0.435674i	$0.143490\pi$
$542$	2.72573e12	−	4.72110e12i	1.35671	−	2.34988i
$543$		0			0
$544$	−1.45701e11	−	2.52362e11i	−0.0713292	−	0.123546i
$545$	−1.13881e12	−	1.97248e12i	−0.552926	−	0.957695i
$546$		0			0
$547$	1.30505e12	−	2.26042e12i	0.623282	−	1.07956i	−0.365588	−	0.930777i	$-0.619132\pi$
$547$	1.30505e12	−	2.26042e12i	0.623282	−	1.07956i	0.988870	−	0.148780i	$-0.0475346\pi$
$548$	5.27215e11			0.249733
$549$		0			0
$550$	2.39087e12			1.11410
$551$	−1.83353e12	+	3.17576e12i	−0.847433	+	1.46780i
$552$		0			0
$553$	−1.71518e12	−	2.97078e12i	−0.779915	−	1.35085i
$554$	−7.87509e11	−	1.36401e12i	−0.355191	−	0.615209i
$555$		0			0
$556$	−1.25783e12	+	2.17863e12i	−0.558196	+	0.966824i
$557$	−1.44707e12			−0.637002			−0.318501	−	0.947923i	$-0.603179\pi$
$557$	−1.44707e12			−0.637002			−0.318501	+	0.947923i	$0.603179\pi$
$558$		0			0
$559$	1.78308e12			0.772357
$560$	−2.73119e12	+	4.73056e12i	−1.17356	+	2.03267i
$561$		0			0
$562$	2.44698e12	+	4.23830e12i	1.03471	+	1.79217i
$563$	1.51468e12	+	2.62351e12i	0.635380	+	1.10051i	0.986435	+	0.164155i	$0.0524898\pi$
$563$	1.51468e12	+	2.62351e12i	0.635380	+	1.10051i	−0.351055	+	0.936355i	$0.614177\pi$
$564$		0			0
$565$	−3.01805e12	+	5.22741e12i	−1.24597	+	2.15809i
$566$	2.30950e12			0.945897
$567$		0			0
$568$	−1.06522e11			−0.0429411
$569$	4.11797e11	−	7.13253e11i	0.164694	−	0.285258i	−0.771853	−	0.635802i	$-0.780670\pi$
$569$	4.11797e11	−	7.13253e11i	0.164694	−	0.285258i	0.936547	+	0.350543i	$0.114003\pi$
$570$		0			0
$571$	3.77466e11	+	6.53791e11i	0.148599	+	0.257381i	0.930710	−	0.365758i	$-0.119190\pi$
$571$	3.77466e11	+	6.53791e11i	0.148599	+	0.257381i	−0.782111	+	0.623139i	$0.785857\pi$
$572$	4.01631e11	+	6.95646e11i	0.156872	+	0.271710i
$573$		0			0
$574$	−2.08960e12	+	3.61929e12i	−0.803451	+	1.39162i
$575$	3.47349e12			1.32514
$576$		0			0
$577$	−4.22193e12			−1.58569			−0.792847	−	0.609420i	$-0.791402\pi$
$577$	−4.22193e12			−1.58569			−0.792847	+	0.609420i	$0.791402\pi$
$578$	−1.89798e12	+	3.28740e12i	−0.707322	+	1.22512i
$579$		0			0
$580$	−2.65497e12	−	4.59853e12i	−0.974166	−	1.68730i
$581$	2.63549e11	+	4.56480e11i	0.0959552	+	0.166199i
$582$		0			0
$583$	9.15379e11	−	1.58548e12i	0.328165	−	0.568399i
$584$	−1.07897e10			−0.00383841
$585$		0			0
$586$	−7.18673e12			−2.51763
$587$	1.26363e12	−	2.18868e12i	0.439289	−	0.760870i	−0.558346	−	0.829608i	$-0.688564\pi$
$587$	1.26363e12	−	2.18868e12i	0.439289	−	0.760870i	0.997635	+	0.0687377i	$0.0218972\pi$
$588$		0			0
$589$	2.98514e12	+	5.17041e12i	1.02199	+	1.77014i
$590$	−9.54455e11	−	1.65317e12i	−0.324281	−	0.561671i
$591$		0			0
$592$	1.18268e12	−	2.04846e12i	0.395748	−	0.685455i
$593$	−2.59659e12			−0.862299			−0.431150	−	0.902280i	$-0.641892\pi$
$593$	−2.59659e12			−0.862299			−0.431150	+	0.902280i	$0.641892\pi$
$594$		0			0
$595$	−7.50368e11			−0.245441
$596$	−1.16522e12	+	2.01823e12i	−0.378269	+	0.655181i
$597$		0			0
$598$	1.14355e12	+	1.98068e12i	0.365678	+	0.633372i
$599$	1.78002e12	+	3.08309e12i	0.564944	+	0.978511i	0.997055	+	0.0766909i	$0.0244355\pi$
$599$	1.78002e12	+	3.08309e12i	0.564944	+	0.978511i	−0.432111	+	0.901820i	$0.642231\pi$
$600$		0			0
$601$	−9.66732e11	+	1.67443e12i	−0.302253	+	0.523518i	−0.976646	−	0.214855i	$-0.931072\pi$
$601$	−9.66732e11	+	1.67443e12i	−0.302253	+	0.523518i	0.674393	+	0.738373i	$0.264405\pi$
$602$	1.27323e13			3.95114
$603$		0			0
$604$	3.45401e12			1.05598
$605$	1.40673e12	−	2.43652e12i	0.426885	−	0.739386i
$606$		0			0
$607$	−6.61448e11	−	1.14566e12i	−0.197764	−	0.342537i	0.750039	−	0.661393i	$-0.230035\pi$
$607$	−6.61448e11	−	1.14566e12i	−0.197764	−	0.342537i	−0.947803	+	0.318856i	$0.896701\pi$
$608$	−3.22861e12	−	5.59211e12i	−0.958184	−	1.65962i
$609$		0			0
$610$	1.49083e12	−	2.58219e12i	0.435956	−	0.755098i
$611$	9.44034e11			0.274033
$612$		0			0
$613$	−9.74984e11			−0.278885			−0.139443	−	0.990230i	$-0.544531\pi$
$613$	−9.74984e11			−0.278885			−0.139443	+	0.990230i	$0.544531\pi$
$614$	3.63193e12	−	6.29069e12i	1.03129	−	1.78624i
$615$		0			0
$616$	1.15223e11	+	1.99573e11i	0.0322424	+	0.0558454i
$617$	1.43614e12	+	2.48746e12i	0.398945	+	0.690993i	0.993596	−	0.112991i	$-0.0360431\pi$
$617$	1.43614e12	+	2.48746e12i	0.398945	+	0.690993i	−0.594651	+	0.803984i	$0.702710\pi$
$618$		0			0
$619$	2.08071e12	−	3.60390e12i	0.569645	−	0.986655i	−0.426956	−	0.904273i	$-0.640414\pi$
$619$	2.08071e12	−	3.60390e12i	0.569645	−	0.986655i	0.996601	−	0.0823820i	$-0.0262528\pi$
$620$	−8.64502e12			−2.34965
$621$		0			0
$622$	9.69636e12			2.59748
$623$	−8.36460e11	+	1.44879e12i	−0.222458	+	0.385309i
$624$		0			0
$625$	1.45674e12	+	2.52314e12i	0.381875	+	0.661427i
$626$	2.43310e12	+	4.21425e12i	0.633251	+	1.09682i
$627$		0			0
$628$	2.26938e11	−	3.93068e11i	0.0582222	−	0.100844i
$629$	3.24929e11			0.0827675
$630$		0			0
$631$	−3.22906e12			−0.810855			−0.405428	−	0.914127i	$-0.632877\pi$
$631$	−3.22906e12			−0.810855			−0.405428	+	0.914127i	$0.632877\pi$
$632$	−1.13010e11	+	1.95740e11i	−0.0281768	+	0.0488036i
$633$		0			0
$634$	−4.03997e12	−	6.99743e12i	−0.993061	−	1.72003i
$635$	−1.64451e12	−	2.84838e12i	−0.401380	−	0.695210i
$636$		0			0
$637$	−1.67287e12	+	2.89750e12i	−0.402564	+	0.697262i
$638$	4.91265e12			1.17388
$639$		0			0
$640$	7.51978e11			0.177172
$641$	−2.45653e12	+	4.25484e12i	−0.574727	+	0.995456i	0.421345	+	0.906901i	$0.361558\pi$
$641$	−2.45653e12	+	4.25484e12i	−0.574727	+	0.995456i	−0.996071	+	0.0885551i	$0.971775\pi$
$642$		0			0
$643$	−5.92873e11	−	1.02689e12i	−0.136777	−	0.236904i	0.789498	−	0.613753i	$-0.210341\pi$
$643$	−5.92873e11	−	1.02689e12i	−0.136777	−	0.236904i	−0.926275	+	0.376849i	$0.877008\pi$
$644$	4.16650e12	+	7.21660e12i	0.954521	+	1.65328i
$645$		0			0
$646$	4.24916e11	−	7.35976e11i	0.0959968	−	0.166271i
$647$	6.72898e12			1.50966			0.754832	−	0.655919i	$-0.227719\pi$
$647$	6.72898e12			1.50966			0.754832	+	0.655919i	$0.227719\pi$
$648$		0			0
$649$	9.01147e11			0.199386
$650$	1.80039e12	−	3.11836e12i	0.395600	−	0.685199i
$651$		0			0
$652$	2.27851e12	+	3.94649e12i	0.493783	+	0.855258i
$653$	−3.62463e11	−	6.27804e11i	−0.0780107	−	0.135119i	0.824381	−	0.566036i	$-0.191524\pi$
$653$	−3.62463e11	−	6.27804e11i	−0.0780107	−	0.135119i	−0.902392	+	0.430917i	$0.858190\pi$
$654$		0			0
$655$	3.89465e12	−	6.74573e12i	0.826765	−	1.43200i
$656$	−3.08122e12			−0.649615
$657$		0			0
$658$	6.74098e12			1.40187
$659$	3.01262e12	−	5.21801e12i	0.622242	−	1.07776i	−0.366825	−	0.930290i	$-0.619555\pi$
$659$	3.01262e12	−	5.21801e12i	0.622242	−	1.07776i	0.989067	−	0.147465i	$-0.0471115\pi$
$660$		0			0
$661$	−8.74869e11	−	1.51532e12i	−0.178253	−	0.308743i	0.763029	−	0.646364i	$-0.223711\pi$
$661$	−8.74869e11	−	1.51532e12i	−0.178253	−	0.308743i	−0.941282	+	0.337621i	$0.890378\pi$
$662$	8.60788e11	+	1.49093e12i	0.174195	+	0.301714i
$663$		0			0
$664$	1.73648e10	−	3.00767e10i	0.00346667	−	0.00600446i
$665$	−1.66275e13			−3.29708
$666$		0			0
$667$	7.13716e12			1.39624
$668$	−1.21946e11	+	2.11216e11i	−0.0236958	+	0.0410424i
$669$		0			0
$670$	−6.09318e12	−	1.05537e13i	−1.16817	−	2.02333i
$671$	7.03780e11	+	1.21898e12i	0.134025	+	0.232138i
$672$		0			0
$673$	1.79733e12	−	3.11307e12i	0.337722	−	0.584952i	−0.646282	−	0.763099i	$-0.723677\pi$
$673$	1.79733e12	−	3.11307e12i	0.337722	−	0.584952i	0.984004	+	0.178147i	$0.0570102\pi$
$674$	−1.14706e12			−0.214099
$675$		0			0
$676$	−4.44702e12			−0.819048
$677$	1.16956e12	−	2.02573e12i	0.213980	−	0.370624i	−0.738977	−	0.673731i	$-0.764691\pi$
$677$	1.16956e12	−	2.02573e12i	0.213980	−	0.370624i	0.952957	+	0.303107i	$0.0980240\pi$
$678$		0			0
$679$	−7.85487e11	−	1.36050e12i	−0.141816	−	0.245632i
$680$	2.47202e10	+	4.28167e10i	0.00443366	+	0.00767932i
$681$		0			0
$682$	3.99911e12	−	6.92666e12i	0.707837	−	1.22601i
$683$	4.03165e11			0.0708907			0.0354453	−	0.999372i	$-0.488715\pi$
$683$	4.03165e11			0.0708907			0.0354453	+	0.999372i	$0.488715\pi$
$684$		0			0
$685$	2.04748e12			0.355315
$686$	−5.08417e12	+	8.80605e12i	−0.876520	+	1.51818i
$687$		0			0
$688$	4.69361e12	+	8.12956e12i	0.798654	+	1.38331i
$689$	−1.37861e12	−	2.38782e12i	−0.233053	−	0.403660i
$690$		0			0
$691$	−3.89736e12	+	6.75043e12i	−0.650308	+	1.12637i	0.332740	+	0.943019i	$0.392027\pi$
$691$	−3.89736e12	+	6.75043e12i	−0.650308	+	1.12637i	−0.983048	+	0.183348i	$0.941306\pi$
$692$	4.87081e12			0.807465
$693$		0			0
$694$	−1.26797e13			−2.07487
$695$	−4.88490e12	+	8.46089e12i	−0.794189	+	1.37558i
$696$		0			0
$697$	−2.11634e11	−	3.66560e11i	−0.0339655	−	0.0588299i
$698$	−1.34206e12	−	2.32452e12i	−0.214004	−	0.370666i
$699$		0			0
$700$	6.55970e12	−	1.13617e13i	1.03263	−	1.78856i
$701$	−2.40116e12			−0.375569			−0.187784	−	0.982210i	$-0.560131\pi$
$701$	−2.40116e12			−0.375569			−0.187784	+	0.982210i	$0.560131\pi$
$702$		0			0
$703$	7.20013e12			1.11184
$704$	−2.29580e12	+	3.97643e12i	−0.352254	+	0.610122i
$705$		0			0
$706$	3.00091e12	+	5.19773e12i	0.454603	+	0.787395i
$707$	−9.68967e12	−	1.67830e13i	−1.45855	−	2.52629i
$708$		0			0
$709$	2.68067e12	−	4.64306e12i	0.398415	−	0.690075i	−0.595115	−	0.803640i	$-0.702894\pi$
$709$	2.68067e12	−	4.64306e12i	0.398415	−	0.690075i	0.993531	+	0.113565i	$0.0362270\pi$
$710$	−1.02966e13			−1.52066
$711$		0			0
$712$	1.10226e11			0.0160740
$713$	5.80995e12	−	1.00631e13i	0.841917	−	1.45824i
$714$		0			0
$715$	1.55977e12	+	2.70160e12i	0.223194	+	0.386583i
$716$	−4.92201e11	−	8.52517e11i	−0.0699897	−	0.121226i
$717$		0			0
$718$	−6.34948e12	+	1.09976e13i	−0.891617	+	1.54433i
$719$	5.40289e12			0.753956			0.376978	−	0.926222i	$-0.376963\pi$
$719$	5.40289e12			0.753956			0.376978	+	0.926222i	$0.376963\pi$
$720$		0			0
$721$	3.68551e12			0.507912
$722$	4.19901e12	−	7.27290e12i	0.575082	−	0.996071i
$723$		0			0
$724$	2.72331e12	+	4.71692e12i	0.368361	+	0.638020i
$725$	−5.61834e12	−	9.73124e12i	−0.755243	−	1.30812i
$726$		0			0
$727$	−1.57786e12	+	2.73293e12i	−0.209490	+	0.362847i	−0.951554	−	0.307482i	$-0.900514\pi$
$727$	−1.57786e12	+	2.73293e12i	−0.209490	+	0.362847i	0.742064	+	0.670329i	$0.233847\pi$
$728$	3.47065e11			0.0457951
$729$		0			0
$730$	−1.04295e12			−0.135929
$731$	−6.44761e11	+	1.11676e12i	−0.0835161	+	0.144654i
$732$		0			0
$733$	6.03203e12	+	1.04478e13i	0.771784	+	1.33677i	0.936584	+	0.350442i	$0.113969\pi$
$733$	6.03203e12	+	1.04478e13i	0.771784	+	1.33677i	−0.164800	+	0.986327i	$0.552698\pi$
$734$	8.04220e11	+	1.39295e12i	0.102269	+	0.177135i
$735$		0			0
$736$	−6.28380e12	+	1.08839e13i	−0.789355	+	1.36720i
$737$	5.75286e12			0.718257
$738$		0			0
$739$	8.39060e12			1.03489			0.517444	−	0.855717i	$-0.326884\pi$
$739$	8.39060e12			1.03489			0.517444	+	0.855717i	$0.326884\pi$
$740$	−5.21293e12	+	9.02906e12i	−0.639056	+	1.10688i
$741$		0			0
$742$	−9.84410e12	−	1.70505e13i	−1.19223	−	2.06500i
$743$	−3.70497e11	−	6.41720e11i	−0.0446001	−	0.0772496i	0.842864	−	0.538127i	$-0.180868\pi$
$743$	−3.70497e11	−	6.41720e11i	−0.0446001	−	0.0772496i	−0.887464	+	0.460878i	$0.847535\pi$
$744$		0			0
$745$	−4.52524e12	+	7.83794e12i	−0.538193	+	0.932178i
$746$	−1.30353e13			−1.54098
$747$		0			0
$748$	−5.80918e11			−0.0678512
$749$	4.17245e12	−	7.22690e12i	0.484421	−	0.839043i
$750$		0			0
$751$	−7.05624e12	−	1.22218e13i	−0.809457	−	1.40202i	−0.913241	−	0.407420i	$-0.866428\pi$
$751$	−7.05624e12	−	1.22218e13i	−0.809457	−	1.40202i	0.103784	−	0.994600i	$-0.466905\pi$
$752$	2.48498e12	+	4.30411e12i	0.283363	+	0.490799i
$753$		0			0
$754$	3.69935e12	−	6.40747e12i	0.416826	−	0.721964i
$755$	1.34139e13			1.50243
$756$		0			0
$757$	5.66623e12			0.627138			0.313569	−	0.949565i	$-0.398475\pi$
$757$	5.66623e12			0.627138			0.313569	+	0.949565i	$0.398475\pi$
$758$	−5.51639e12	+	9.55466e12i	−0.606936	+	1.05124i
$759$		0			0
$760$	5.47778e11	+	9.48780e11i	0.0595585	+	0.103158i
$761$	6.70655e12	+	1.16161e13i	0.724883	+	1.25553i	0.959022	+	0.283332i	$0.0914397\pi$
$761$	6.70655e12	+	1.16161e13i	0.724883	+	1.25553i	−0.234139	+	0.972203i	$0.575227\pi$
$762$		0			0
$763$	5.78144e12	−	1.00137e13i	0.617555	−	1.06964i
$764$	5.34658e12			0.567749
$765$		0			0
$766$	−1.02495e13			−1.07566
$767$	6.78587e11	−	1.17535e12i	0.0707989	−	0.122627i
$768$		0			0
$769$	3.32364e12	+	5.75672e12i	0.342725	+	0.593617i	0.984938	−	0.172909i	$-0.0553167\pi$
$769$	3.32364e12	+	5.75672e12i	0.342725	+	0.593617i	−0.642213	+	0.766527i	$0.721983\pi$
$770$	1.11377e13	+	1.92910e13i	1.14179	+	1.97764i
$771$		0			0
$772$	−1.56627e12	+	2.71286e12i	−0.158705	+	0.274884i
$773$	1.79549e13			1.80874			0.904369	−	0.426752i	$-0.140342\pi$
$773$	1.79549e13			1.80874			0.904369	+	0.426752i	$0.140342\pi$
$774$		0			0
$775$	−1.82943e13			−1.82162
$776$	−5.17544e10	+	8.96412e10i	−0.00512353	+	0.00887421i
$777$		0			0
$778$	−1.80919e12	−	3.13361e12i	−0.177042	−	0.306645i
$779$	−4.68962e12	−	8.12266e12i	−0.456267	−	0.790277i
$780$		0			0
$781$	2.43038e12	−	4.20955e12i	0.233747	−	0.404861i
$782$	−1.65402e12			−0.158165
$783$		0			0
$784$	−1.76140e13			−1.66508
$785$	8.81332e11	−	1.52651e12i	0.0828373	−	0.143478i
$786$		0			0
$787$	−4.68003e12	−	8.10604e12i	−0.434873	−	0.753221i	0.562413	−	0.826857i	$-0.309873\pi$
$787$	−4.68003e12	−	8.10604e12i	−0.434873	−	0.753221i	−0.997285	+	0.0736353i	$0.976540\pi$
$788$	7.29809e12	+	1.26407e13i	0.674281	+	1.16789i
$789$		0			0
$790$	−1.09238e13	+	1.89205e13i	−0.997817	+	1.72827i
$791$	−3.06437e13			−2.78322
$792$		0			0
$793$	2.11986e12			0.190361
$794$	5.63871e12	−	9.76652e12i	0.503486	−	0.872063i
$795$		0			0
$796$	−5.91145e11	−	1.02389e12i	−0.0521898	−	0.0903954i
$797$	8.00565e12	+	1.38662e13i	0.702803	+	1.21729i	0.967478	+	0.252954i	$0.0814020\pi$
$797$	8.00565e12	+	1.38662e13i	0.702803	+	1.21729i	−0.264675	+	0.964338i	$0.585265\pi$
$798$		0			0
$799$	−3.41362e11	+	5.91256e11i	−0.0296316	+	0.0513234i
$800$	1.97863e13			1.70789
$801$		0			0
$802$	−8.24419e12			−0.703661
$803$	2.46175e11	−	4.26387e11i	0.0208941	−	0.0361897i
$804$		0			0
$805$	1.61810e13	+	2.80262e13i	1.35807	+	2.35225i
$806$	−6.02286e12	−	1.04319e13i	−0.502684	−	0.870675i
$807$		0			0
$808$	−6.38436e11	+	1.10580e12i	−0.0526946	+	0.0912697i
$809$	1.53912e13			1.26329			0.631645	−	0.775258i	$-0.282380\pi$
$809$	1.53912e13			1.26329			0.631645	+	0.775258i	$0.282380\pi$
$810$		0			0
$811$	−1.81531e13			−1.47352			−0.736760	−	0.676154i	$-0.763645\pi$
$811$	−1.81531e13			−1.47352			−0.736760	+	0.676154i	$0.763645\pi$
$812$	1.34786e13	−	2.33456e13i	1.08803	−	1.88453i
$813$		0			0
$814$	−4.82290e12	−	8.35352e12i	−0.385034	−	0.666898i
$815$	8.84877e12	+	1.53265e13i	0.702545	+	1.21684i
$816$		0			0
$817$	−1.42873e13	+	2.47464e13i	−1.12189	+	1.94318i
$818$	−8.67609e11			−0.0677539
$819$		0			0
$820$	1.35812e13			1.04900
$821$	−1.10104e13	+	1.90706e13i	−0.845786	+	1.46494i	0.0391513	+	0.999233i	$0.487535\pi$
$821$	−1.10104e13	+	1.90706e13i	−0.845786	+	1.46494i	−0.884937	+	0.465711i	$0.845799\pi$
$822$		0			0
$823$	8.62069e12	+	1.49315e13i	0.655002	+	1.13450i	0.981893	+	0.189435i	$0.0606657\pi$
$823$	8.62069e12	+	1.49315e13i	0.655002	+	1.13450i	−0.326891	+	0.945062i	$0.606001\pi$
$824$	−1.21416e11	−	2.10299e11i	−0.00917494	−	0.0158915i
$825$		0			0
$826$	4.84552e12	−	8.39269e12i	0.362185	−	0.627323i
$827$	−3.54008e12			−0.263171			−0.131585	−	0.991305i	$-0.542007\pi$
$827$	−3.54008e12			−0.263171			−0.131585	+	0.991305i	$0.542007\pi$
$828$		0			0
$829$	1.85206e13			1.36194			0.680971	−	0.732310i	$-0.261558\pi$
$829$	1.85206e13			1.36194			0.680971	+	0.732310i	$0.261558\pi$
$830$	1.67851e12	−	2.90727e12i	0.122764	−	0.212634i
$831$		0			0
$832$	3.45759e12	+	5.98872e12i	0.250160	+	0.433290i
$833$	−1.20982e12	−	2.09547e12i	−0.0870598	−	0.150792i
$834$		0			0
$835$	−4.73586e11	+	8.20274e11i	−0.0337139	+	0.0583942i
$836$	−1.28726e13			−0.911462
$837$		0			0
$838$	2.80399e11			0.0196417
$839$	−5.50126e12	+	9.52847e12i	−0.383295	+	0.663887i	−0.991531	−	0.129869i	$-0.958544\pi$
$839$	−5.50126e12	+	9.52847e12i	−0.383295	+	0.663887i	0.608236	+	0.793756i	$0.291878\pi$
$840$		0			0
$841$	−4.29072e12	−	7.43175e12i	−0.295766	−	0.512282i
$842$	−1.56509e13	−	2.71082e13i	−1.07309	−	1.85865i
$843$		0			0
$844$	3.60618e12	−	6.24608e12i	0.244628	−	0.423708i
$845$	−1.72704e13			−1.16532
$846$		0			0
$847$	1.42832e13			0.953563
$848$	7.25782e12	−	1.25709e13i	0.481976	−	0.834806i
$849$		0			0
$850$	1.30204e12	+	2.25519e12i	0.0855536	+	0.148183i
$851$	−7.00677e12	−	1.21361e13i	−0.457968	−	0.793224i
$852$		0			0
$853$	7.41174e12	−	1.28375e13i	0.479347	−	0.830253i	−0.520373	−	0.853939i	$-0.674207\pi$
$853$	7.41174e12	−	1.28375e13i	0.479347	−	0.830253i	0.999719	+	0.0236864i	$0.00754032\pi$
$854$	1.51371e13			0.973826
$855$		0			0
$856$	−5.49832e11			−0.0350024
$857$	3.84200e12	−	6.65453e12i	0.243301	−	0.421409i	−0.718352	−	0.695680i	$-0.755103\pi$
$857$	3.84200e12	−	6.65453e12i	0.243301	−	0.421409i	0.961652	+	0.274271i	$0.0884365\pi$
$858$		0			0
$859$	9.52142e11	+	1.64916e12i	0.0596667	+	0.103346i	0.894316	−	0.447436i	$-0.147663\pi$
$859$	9.52142e11	+	1.64916e12i	0.0596667	+	0.103346i	−0.834649	+	0.550782i	$0.814330\pi$
$860$	−2.06882e13	−	3.58330e13i	−1.28967	−	2.23378i
$861$		0			0
$862$	−2.23525e13	+	3.87156e13i	−1.37893	+	2.38838i
$863$	3.09626e12			0.190015			0.0950077	−	0.995477i	$-0.469712\pi$
$863$	3.09626e12			0.190015			0.0950077	+	0.995477i	$0.469712\pi$
$864$		0			0
$865$	1.89162e13			1.14884
$866$	−2.04098e13	+	3.53509e13i	−1.23313	+	2.13584i
$867$		0			0
$868$	−2.19443e13	−	3.80086e13i	−1.31215	−	2.27270i
$869$	−5.15683e12	−	8.93189e12i	−0.306757	−	0.531318i
$870$		0			0
$871$	4.33205e12	−	7.50334e12i	0.255042	−	0.441746i
$872$	−7.61858e11			−0.0446221
$873$		0			0
$874$	−3.66516e13			−2.12467
$875$	4.19828e12	−	7.27163e12i	0.242122	−	0.419368i
$876$		0			0
$877$	−2.07463e12	−	3.59336e12i	−0.118425	−	0.205117i	0.800719	−	0.599040i	$-0.204451\pi$
$877$	−2.07463e12	−	3.59336e12i	−0.118425	−	0.205117i	−0.919144	+	0.393923i	$0.871118\pi$
$878$	7.05253e12	+	1.22153e13i	0.400516	+	0.693714i
$879$		0			0
$880$	−8.21155e12	+	1.42228e13i	−0.461586	+	0.799491i
$881$	−1.36244e13			−0.761948			−0.380974	−	0.924586i	$-0.624411\pi$
$881$	−1.36244e13			−0.761948			−0.380974	+	0.924586i	$0.624411\pi$
$882$		0			0
$883$	−1.83775e13			−1.01734			−0.508668	−	0.860963i	$-0.669862\pi$
$883$	−1.83775e13			−1.01734			−0.508668	+	0.860963i	$0.669862\pi$
$884$	−4.37446e11	+	7.57679e11i	−0.0240929	+	0.0417302i
$885$		0			0
$886$	8.21253e12	+	1.42245e13i	0.447739	+	0.775507i
$887$	1.48912e13	+	2.57922e13i	0.807741	+	1.39905i	0.914425	+	0.404755i	$0.132643\pi$
$887$	1.48912e13	+	2.57922e13i	0.807741	+	1.39905i	−0.106684	+	0.994293i	$0.534023\pi$
$888$		0			0
$889$	8.34877e12	−	1.44605e13i	0.448296	−	0.776471i
$890$	1.06546e13			0.569223
$891$		0			0
$892$	−1.58580e12			−0.0838700
$893$	−7.56428e12	+	1.31017e13i	−0.398048	+	0.689440i
$894$		0			0
$895$	−1.91150e12	−	3.31082e12i	−0.0995798	−	0.172477i
$896$	1.90880e12	+	3.30614e12i	0.0989405	+	0.171370i
$897$		0			0
$898$	2.37773e13	−	4.11835e13i	1.22017	−	2.11339i
$899$	−3.75902e13			−1.91936
$900$		0			0
$901$	1.99401e12			0.100801
$902$	−6.28255e12	+	1.08817e13i	−0.316014	+	0.547352i
$903$		0			0
$904$	1.00953e12	+	1.74856e12i	0.0502761	+	0.0870807i
$905$	1.05762e13	+	1.83185e13i	0.524097	+	0.907762i
$906$		0			0
$907$	1.74771e13	−	3.02712e13i	0.857504	−	1.48524i	−0.0167986	−	0.999859i	$-0.505347\pi$
$907$	1.74771e13	−	3.02712e13i	0.857504	−	1.48524i	0.874303	−	0.485381i	$-0.161319\pi$
$908$	−1.78486e13			−0.871398
$909$		0			0
$910$	3.35479e13			1.62173
$911$	−1.01137e13	+	1.75175e13i	−0.486494	+	0.842633i	−0.999879	−	0.0155252i	$-0.995058\pi$
$911$	−1.01137e13	+	1.75175e13i	−0.486494	+	0.842633i	0.513385	+	0.858158i	$0.328391\pi$
$912$		0			0
$913$	7.92381e11	+	1.37244e12i	0.0377412	+	0.0653697i
$914$	−1.81052e13	−	3.13591e13i	−0.858114	−	1.48630i
$915$		0			0
$916$	2.02913e13	−	3.51456e13i	0.952316	−	1.64946i
$917$	3.95442e13			1.84681
$918$		0			0
$919$	4.43929e12			0.205302			0.102651	−	0.994717i	$-0.467268\pi$
$919$	4.43929e12			0.205302			0.102651	+	0.994717i	$0.467268\pi$
$920$	1.06614e12	−	1.84660e12i	0.0490645	−	0.0849822i
$921$		0			0
$922$	2.79146e13	+	4.83495e13i	1.27216	+	2.20345i
$923$	−3.66028e12	−	6.33980e12i	−0.166000	−	0.287520i
$924$		0			0
$925$	−1.10314e13	+	1.91069e13i	−0.495442	+	0.858131i
$926$	−8.88104e12			−0.396930
$927$		0			0
$928$	4.06560e13			1.79953
$929$	5.82256e12	−	1.00850e13i	0.256474	−	0.444226i	−0.708821	−	0.705388i	$-0.750773\pi$
$929$	5.82256e12	−	1.00850e13i	0.256474	−	0.444226i	0.965295	+	0.261163i	$0.0841059\pi$
$930$		0			0
$931$	−2.68085e13	−	4.64337e13i	−1.16950	−	2.02563i
$932$	−1.73246e13	−	3.00071e13i	−0.752127	−	1.30272i
$933$		0			0
$934$	1.85100e13	−	3.20602e13i	0.795876	−	1.37850i
$935$	−2.25604e12			−0.0965372
$936$		0			0
$937$	−6.68375e12			−0.283265			−0.141632	−	0.989919i	$-0.545235\pi$
$937$	−6.68375e12			−0.283265			−0.141632	+	0.989919i	$0.545235\pi$
$938$	3.09335e13	−	5.35784e13i	1.30472	−	2.25983i
$939$		0			0
$940$	−1.09531e13	−	1.89714e13i	−0.457576	−	0.792545i
$941$	1.38922e13	+	2.40619e13i	0.577586	+	1.00041i	0.995755	+	0.0920387i	$0.0293383\pi$
$941$	1.38922e13	+	2.40619e13i	0.577586	+	1.00041i	−0.418170	+	0.908369i	$0.637328\pi$
$942$		0			0
$943$	−9.12736e12	+	1.58090e13i	−0.375874	+	0.651033i
$944$	7.14498e12			0.292838
$945$		0			0
$946$	3.82806e13			1.55406
$947$	1.01127e13	−	1.75157e13i	0.408595	−	0.707707i	−0.586138	−	0.810211i	$-0.699352\pi$
$947$	1.01127e13	−	1.75157e13i	0.408595	−	0.707707i	0.994733	+	0.102505i	$0.0326857\pi$
$948$		0			0
$949$	−3.70752e11	−	6.42162e11i	−0.0148384	−	0.0257008i
$950$	2.88520e13	+	4.99731e13i	1.14926	+	1.99058i
$951$		0			0
$952$	−1.25498e11	+	2.17369e11i	−0.00495189	+	0.00857693i
$953$	−1.95165e13			−0.766450			−0.383225	−	0.923655i	$-0.625187\pi$
$953$	−1.95165e13			−0.766450			−0.383225	+	0.923655i	$0.625187\pi$
$954$		0			0
$955$	2.07639e13			0.807781
$956$	1.06279e13	−	1.84080e13i	0.411515	−	0.712765i
$957$		0			0
$958$	1.50778e13	+	2.61155e13i	0.578353	+	1.00174i
$959$	5.19728e12	+	9.00195e12i	0.198423	+	0.343679i
$960$		0			0
$961$	−1.73802e13	+	3.01034e13i	−0.657355	+	1.13857i
$962$	−1.45271e13			−0.546878
$963$		0			0
$964$	6.32727e12			0.235977
$965$	−6.08275e12	+	1.05356e13i	−0.225802	+	0.391100i
$966$		0			0
$967$	−2.10162e13	−	3.64011e13i	−0.772919	−	1.33874i	−0.935956	−	0.352116i	$-0.885462\pi$
$967$	−2.10162e13	−	3.64011e13i	−0.772919	−	1.33874i	0.163037	−	0.986620i	$-0.447871\pi$
$968$	−4.70547e11	−	8.15011e11i	−0.0172252	−	0.0298349i
$969$		0			0
$970$	−5.00267e12	+	8.66487e12i	−0.181438	+	0.314260i
$971$	8.15237e12			0.294305			0.147152	−	0.989114i	$-0.452989\pi$
$971$	8.15237e12			0.294305			0.147152	+	0.989114i	$0.452989\pi$
$972$		0			0
$973$	−4.95988e13			−1.77404
$974$	−1.66373e13	+	2.88167e13i	−0.592336	+	1.02596i
$975$		0			0
$976$	5.58010e12	+	9.66502e12i	0.196842	+	0.340941i
$977$	7.42874e12	+	1.28670e13i	0.260849	+	0.451804i	0.966468	−	0.256788i	$-0.0826641\pi$
$977$	7.42874e12	+	1.28670e13i	0.260849	+	0.451804i	−0.705618	+	0.708592i	$0.749331\pi$
$978$		0			0
$979$	−2.51488e12	+	4.35591e12i	−0.0874975	+	0.151550i
$980$	7.76379e13			2.68879
$981$		0			0
$982$	−5.59004e13			−1.91828
$983$	4.19117e12	−	7.25931e12i	0.143167	−	0.247973i	−0.785520	−	0.618836i	$-0.787605\pi$
$983$	4.19117e12	−	7.25931e12i	0.143167	−	0.247973i	0.928688	+	0.370863i	$0.120938\pi$
$984$		0			0
$985$	2.83427e13	+	4.90910e13i	0.959353	+	1.66165i
$986$	2.67536e12	+	4.63387e12i	0.0901440	+	0.156134i
$987$		0			0
$988$	−9.69342e12	+	1.67895e13i	−0.323646	+	0.560572i
$989$	5.56146e13			1.84844
$990$		0			0
$991$	3.54621e13			1.16797			0.583986	−	0.811763i	$-0.301492\pi$
$991$	3.54621e13			1.16797			0.583986	+	0.811763i	$0.301492\pi$
$992$	3.30957e13	−	5.73235e13i	1.08510	−	1.87945i
$993$		0			0
$994$	−2.61366e13	−	4.52700e13i	−0.849202	−	1.47086i
$995$	−2.29576e12	−	3.97638e12i	−0.0742545	−	0.128613i
$996$		0			0
$997$	−2.08978e13	+	3.61960e13i	−0.669841	+	1.16020i	0.308108	+	0.951351i	$0.400304\pi$
$997$	−2.08978e13	+	3.61960e13i	−0.669841	+	1.16020i	−0.977948	+	0.208846i	$0.933029\pi$
$998$	−7.75919e13			−2.47588
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	81.10.c.h.55.3		6
3.2	odd	2		81.10.c.g.55.1		6
9.2	odd	6		27.10.a.c.1.3	yes	3
9.4	even	3	inner	81.10.c.h.28.3		6
9.5	odd	6		81.10.c.g.28.1		6
9.7	even	3		27.10.a.b.1.1	✓	3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
27.10.a.b.1.1	✓	3	9.7	even	3
27.10.a.c.1.3	yes	3	9.2	odd	6
81.10.c.g.28.1		6	9.5	odd	6
81.10.c.g.55.1		6	3.2	odd	2
81.10.c.h.28.3		6	9.4	even	3	inner
81.10.c.h.55.3		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)

\(f(q)\)	\(=\)	\(q+(16.1666 - 28.0013i) q^{2} +(-266.716 - 461.965i) q^{4} +(-1035.81 - 1794.08i) q^{5} +(5258.56 - 9108.09i) q^{7} -692.954 q^{8} -66982.2 q^{10} +(15810.3 - 27384.2i) q^{11} +(-23811.1 - 41242.0i) q^{13} +(-170026. - 294493. i) q^{14} +(125356. - 217123. i) q^{16} +34440.3 q^{17} +763166. q^{19} +(-552535. + 957020. i) q^{20} +(-511196. - 885417. i) q^{22} +(-742671. - 1.28634e6i) q^{23} +(-1.16925e6 + 2.02521e6i) q^{25} -1.53977e6 q^{26} -5.61016e6 q^{28} +(-2.40253e6 + 4.16130e6i) q^{29} +(3.91152e6 + 6.77496e6i) q^{31} +(-4.23054e6 - 7.32752e6i) q^{32} +(556781. - 964373. i) q^{34} -2.17875e7 q^{35} +9.43456e6 q^{37} +(1.23378e7 - 2.13696e7i) q^{38} +(717771. + 1.24322e6i) q^{40} +(-6.14495e6 - 1.06434e7i) q^{41} +(-1.87211e7 + 3.24260e7i) q^{43} -1.68674e7 q^{44} -4.80258e7 q^{46} +(-9.91171e6 + 1.71676e7i) q^{47} +(-3.51280e7 - 6.08435e7i) q^{49} +(3.78057e7 + 6.54813e7i) q^{50} +(-1.27016e7 + 2.19998e7i) q^{52} +5.78978e7 q^{53} -6.55059e7 q^{55} +(-3.64394e6 + 6.31149e6i) q^{56} +(7.76813e7 + 1.34548e8i) q^{58} +(1.42494e7 + 2.46807e7i) q^{59} +(-2.22571e7 + 3.85504e7i) q^{61} +2.52944e8 q^{62} -1.45209e8 q^{64} +(-4.93277e7 + 8.54380e7i) q^{65} +(9.09671e7 + 1.57560e8i) q^{67} +(-9.18576e6 - 1.59102e7i) q^{68} +(-3.52229e8 + 6.10079e8i) q^{70} +1.53722e8 q^{71} +1.55706e7 q^{73} +(1.52524e8 - 2.64180e8i) q^{74} +(-2.03548e8 - 3.52556e8i) q^{76} +(-1.66278e8 - 2.88003e8i) q^{77} +(1.63085e8 - 2.82471e8i) q^{79} -5.19381e8 q^{80} -3.97371e8 q^{82} +(-2.50591e7 + 4.34036e7i) q^{83} +(-3.56737e7 - 6.17886e7i) q^{85} +(6.05313e8 + 1.04843e9i) q^{86} +(-1.09558e7 + 1.89760e7i) q^{88} -1.59066e8 q^{89} -5.00848e8 q^{91} +(-3.96164e8 + 6.86177e8i) q^{92} +(3.20477e8 + 5.55082e8i) q^{94} +(-7.90497e8 - 1.36918e9i) q^{95} +(7.46865e7 - 1.29361e8i) q^{97} -2.27160e9 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + 3 q^{2} - 597 q^{4} - 1983 q^{5} + 3693 q^{7} + 9006 q^{8} - 37962 q^{10} - 16863 q^{11} - 116916 q^{13} - 503463 q^{14} + 239919 q^{16} + 2028096 q^{17} - 30444 q^{19} - 2548407 q^{20} - 305721 q^{22}+ \cdots - 5184364572 q^{98}+O(q^{100}) \) 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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