LMFDB - Embedded newform 5.10.b.a.4.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [5,10,Mod(4,5)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(5, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1]))

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

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

chi := DirichletCharacter("5.4");

S:= CuspForms(chi, 10);

N := Newforms(S);

Level:	$ N $	$=$	$ 5 $
Weight:	$ k $	$=$	$ 10 $
Character orbit:	$[\chi]$	$=$	5.b (of order $2$, degree $1$, 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:	$2.57517918082$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	4.0.49740556.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} + 45x^{2} + 304 $ x^4 + 45*x^2 + 304
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2^{5}\cdot 3^{2}\cdot 5^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			4.2
Root			$-6.05982i$ of defining polynomial
Character	$\chi$	$=$	5.4
Dual form			5.10.b.a.4.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-0.843944i q^{2} -179.263i q^{3} +511.288 q^{4} +(-568.288 - 1276.78i) q^{5} -151.288 q^{6} +8712.99i q^{7} -863.597i q^{8} -12452.2 q^{9} +O(q^{10})$	\(q-0.843944i q^{2} -179.263i q^{3} +511.288 q^{4} +(-568.288 - 1276.78i) q^{5} -151.288 q^{6} +8712.99i q^{7} -863.597i q^{8} -12452.2 q^{9} +(-1077.53 + 479.603i) q^{10} +44557.8 q^{11} -91654.9i q^{12} +21430.4i q^{13} +7353.27 q^{14} +(-228880. + 101873. i) q^{15} +261051. q^{16} +300220. i q^{17} +10508.9i q^{18} -565385. q^{19} +(-290559. - 652803. i) q^{20} +1.56192e6 q^{21} -37604.2i q^{22} -950727. i q^{23} -154811. q^{24} +(-1.30722e6 + 1.45116e6i) q^{25} +18086.1 q^{26} -1.29622e6i q^{27} +4.45485e6i q^{28} +803167. q^{29} +(85975.0 + 193162. i) q^{30} -1.99843e6 q^{31} -662474. i q^{32} -7.98755e6i q^{33} +253369. q^{34} +(1.11246e7 - 4.95149e6i) q^{35} -6.36665e6 q^{36} +9.53656e6i q^{37} +477153. i q^{38} +3.84168e6 q^{39} +(-1.10263e6 + 490772. i) q^{40} -2.54355e7 q^{41} -1.31817e6i q^{42} +2.32830e7i q^{43} +2.27818e7 q^{44} +(7.07642e6 + 1.58987e7i) q^{45} -802360. q^{46} -3.77353e7i q^{47} -4.67967e7i q^{48} -3.55626e7 q^{49} +(1.22470e6 + 1.10322e6i) q^{50} +5.38183e7 q^{51} +1.09571e7i q^{52} +4.79297e7i q^{53} -1.09393e6 q^{54} +(-2.53216e7 - 5.68906e7i) q^{55} +7.52451e6 q^{56} +1.01353e8i q^{57} -677827. i q^{58} -7.00069e7 q^{59} +(-1.17023e8 + 5.20864e7i) q^{60} +1.26942e8 q^{61} +1.68656e6i q^{62} -1.08496e8i q^{63} +1.33099e8 q^{64} +(2.73620e7 - 1.21787e7i) q^{65} -6.74104e6 q^{66} -2.66595e8i q^{67} +1.53499e8i q^{68} -1.70430e8 q^{69} +(-4.17877e6 - 9.38853e6i) q^{70} +6.59169e7 q^{71} +1.07537e7i q^{72} -1.47516e7i q^{73} +8.04832e6 q^{74} +(2.60139e8 + 2.34337e8i) q^{75} -2.89074e8 q^{76} +3.88231e8i q^{77} -3.24216e6i q^{78} +4.66498e7 q^{79} +(-1.48352e8 - 3.33305e8i) q^{80} -4.77460e8 q^{81} +2.14661e7i q^{82} -2.01840e8i q^{83} +7.98588e8 q^{84} +(3.83316e8 - 1.70611e8i) q^{85} +1.96495e7 q^{86} -1.43978e8i q^{87} -3.84800e7i q^{88} -5.54039e8 q^{89} +(1.34176e7 - 5.97210e6i) q^{90} -1.86723e8 q^{91} -4.86095e8i q^{92} +3.58244e8i q^{93} -3.18465e7 q^{94} +(3.21301e8 + 7.21874e8i) q^{95} -1.18757e8 q^{96} +3.39489e8i q^{97} +3.00128e7i q^{98} -5.54841e8 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 1368 q^{4} + 1140 q^{5} + 2808 q^{6} + 11628 q^{9}+O(q^{10}) $ 4 * q - 1368 * q^4 + 1140 * q^5 + 2808 * q^6 + 11628 * q^9	\( 4 q - 1368 q^{4} + 1140 q^{5} + 2808 q^{6} + 11628 q^{9} - 69160 q^{10} + 109968 q^{11} - 424536 q^{14} - 396720 q^{15} + 1631264 q^{16} - 636880 q^{19} - 3302280 q^{20} + 3523968 q^{21} - 2435040 q^{24} - 1337900 q^{25} + 6618768 q^{26} - 3531720 q^{29} + 3712680 q^{30} - 10587712 q^{31} + 26434624 q^{34} + 13629840 q^{35} - 56399976 q^{36} + 1686816 q^{39} + 43578400 q^{40} - 16788552 q^{41} + 20638944 q^{44} + 55737180 q^{45} - 61250072 q^{46} - 46921028 q^{49} - 150092400 q^{50} + 84017088 q^{51} + 115855920 q^{54} - 26907120 q^{55} + 315178080 q^{56} - 460829040 q^{59} - 307006560 q^{60} + 360490568 q^{61} + 134995072 q^{64} + 183895680 q^{65} + 18949536 q^{66} - 286524864 q^{69} - 508341960 q^{70} - 47611872 q^{71} + 1176861744 q^{74} + 659239200 q^{75} - 1168489440 q^{76} - 728043520 q^{79} + 965843040 q^{80} - 343387836 q^{81} + 1118898144 q^{84} + 1275419840 q^{85} - 2375904552 q^{86} - 1582700760 q^{89} - 1197088920 q^{90} + 473322528 q^{91} + 3327101704 q^{94} + 1204791600 q^{95} + 399339648 q^{96} - 728787024 q^{99}+O(q^{100}) \) 4 * q - 1368 * q^4 + 1140 * q^5 + 2808 * q^6 + 11628 * q^9 - 69160 * q^10 + 109968 * q^11 - 424536 * q^14 - 396720 * q^15 + 1631264 * q^16 - 636880 * q^19 - 3302280 * q^20 + 3523968 * q^21 - 2435040 * q^24 - 1337900 * q^25 + 6618768 * q^26 - 3531720 * q^29 + 3712680 * q^30 - 10587712 * q^31 + 26434624 * q^34 + 13629840 * q^35 - 56399976 * q^36 + 1686816 * q^39 + 43578400 * q^40 - 16788552 * q^41 + 20638944 * q^44 + 55737180 * q^45 - 61250072 * q^46 - 46921028 * q^49 - 150092400 * q^50 + 84017088 * q^51 + 115855920 * q^54 - 26907120 * q^55 + 315178080 * q^56 - 460829040 * q^59 - 307006560 * q^60 + 360490568 * q^61 + 134995072 * q^64 + 183895680 * q^65 + 18949536 * q^66 - 286524864 * q^69 - 508341960 * q^70 - 47611872 * q^71 + 1176861744 * q^74 + 659239200 * q^75 - 1168489440 * q^76 - 728043520 * q^79 + 965843040 * q^80 - 343387836 * q^81 + 1118898144 * q^84 + 1275419840 * q^85 - 2375904552 * q^86 - 1582700760 * q^89 - 1197088920 * q^90 + 473322528 * q^91 + 3327101704 * q^94 + 1204791600 * q^95 + 399339648 * q^96 - 728787024 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/5\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$-1$

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 $

$2$		−	0.843944i		−	0.0372974i	−0.999826	−	0.0186487i	$-0.994064\pi$
$2$		−	0.843944i		−	0.0372974i	0.999826	−	0.0186487i	$-0.00593641\pi$
$3$		−	179.263i		−	1.27775i	−0.769312	−	0.638873i	$-0.779401\pi$
$3$		−	179.263i		−	1.27775i	0.769312	−	0.638873i	$-0.220599\pi$
$4$	511.288			0.998609
$5$	−568.288	−	1276.78i	−0.406634	−	0.913591i
$5$	−568.288	−	1276.78i	−0.406634	−	0.913591i
$6$	−151.288			−0.0476566
$7$			8712.99i			1.37160i	0.727792	+	0.685798i	$0.240547\pi$
$7$			8712.99i			1.37160i	−0.727792	+	0.685798i	$0.759453\pi$
$8$		−	863.597i		−	0.0745429i
$9$	−12452.2			−0.632636
$10$	−1077.53	+	479.603i	−0.0340746	+	0.0151664i
$11$	44557.8			0.917606			0.458803	−	0.888538i	$-0.348278\pi$
$11$	44557.8			0.917606			0.458803	+	0.888538i	$0.348278\pi$
$12$		−	91654.9i		−	1.27597i
$13$			21430.4i			0.208107i	0.994572	+	0.104053i	$0.0331813\pi$
$13$			21430.4i			0.208107i	−0.994572	+	0.104053i	$0.966819\pi$
$14$	7353.27			0.0511569
$15$	−228880.	+	101873.i	−1.16734	+	0.519575i
$16$	261051.			0.995829
$17$			300220.i			0.871805i	0.899994	+	0.435903i	$0.143571\pi$
$17$			300220.i			0.871805i	−0.899994	+	0.435903i	$0.856429\pi$
$18$			10508.9i			0.0235957i
$19$	−565385.			−0.995298			−0.497649	−	0.867379i	$-0.665803\pi$
$19$	−565385.			−0.995298			−0.497649	+	0.867379i	$0.665803\pi$
$20$	−290559.	−	652803.i	−0.406068	−	0.912320i
$21$	1.56192e6			1.75255
$22$		−	37604.2i		−	0.0342243i
$23$		−	950727.i		−	0.708403i	−0.935169	−	0.354202i	$-0.884753\pi$
$23$		−	950727.i		−	0.708403i	0.935169	−	0.354202i	$-0.115247\pi$
$24$	−154811.			−0.0952469
$25$	−1.30722e6	+	1.45116e6i	−0.669298	+	0.742994i
$26$	18086.1			0.00776183
$27$		−	1.29622e6i		−	0.469398i
$28$			4.45485e6i			1.36969i
$29$	803167.			0.210870			0.105435	−	0.994426i	$-0.466377\pi$
$29$	803167.			0.210870			0.105435	+	0.994426i	$0.466377\pi$
$30$	85975.0	+	193162.i	0.0193788	+	0.0435387i
$31$	−1.99843e6			−0.388652			−0.194326	−	0.980937i	$-0.562252\pi$
$31$	−1.99843e6			−0.388652			−0.194326	+	0.980937i	$0.562252\pi$
$32$		−	662474.i		−	0.111685i
$33$		−	7.98755e6i		−	1.17247i
$34$	253369.			0.0325161
$35$	1.11246e7	−	4.95149e6i	1.25308	−	0.557737i
$36$	−6.36665e6			−0.631756
$37$			9.53656e6i			0.836535i	0.908324	+	0.418267i	$0.137363\pi$
$37$			9.53656e6i			0.836535i	−0.908324	+	0.418267i	$0.862637\pi$
$38$			477153.i			0.0371220i
$39$	3.84168e6			0.265908
$40$	−1.10263e6	+	490772.i	−0.0681017	+	0.0303116i
$41$	−2.54355e7			−1.40576			−0.702882	−	0.711306i	$-0.748104\pi$
$41$	−2.54355e7			−1.40576			−0.702882	+	0.711306i	$0.748104\pi$
$42$		−	1.31817e6i		−	0.0653656i
$43$			2.32830e7i			1.03856i	0.854605	+	0.519279i	$0.173800\pi$
$43$			2.32830e7i			1.03856i	−0.854605	+	0.519279i	$0.826200\pi$
$44$	2.27818e7			0.916329
$45$	7.07642e6	+	1.58987e7i	0.257251	+	0.577971i
$46$	−802360.			−0.0264216
$47$		−	3.77353e7i		−	1.12800i	−0.825776	−	0.563998i	$-0.809262\pi$
$47$		−	3.77353e7i		−	1.12800i	0.825776	−	0.563998i	$-0.190738\pi$
$48$		−	4.67967e7i		−	1.27242i
$49$	−3.55626e7			−0.881274
$50$	1.22470e6	+	1.10322e6i	0.0277117	+	0.0249631i
$51$	5.38183e7			1.11395
$52$			1.09571e7i			0.207817i
$53$			4.79297e7i			0.834379i	0.908819	+	0.417190i	$0.136985\pi$
$53$			4.79297e7i			0.834379i	−0.908819	+	0.417190i	$0.863015\pi$
$54$	−1.09393e6			−0.0175073
$55$	−2.53216e7	−	5.68906e7i	−0.373129	−	0.838317i
$56$	7.52451e6			0.102243
$57$			1.01353e8i			1.27174i
$58$		−	677827.i		−	0.00786490i
$59$	−7.00069e7			−0.752154			−0.376077	−	0.926588i	$-0.622727\pi$
$59$	−7.00069e7			−0.752154			−0.376077	+	0.926588i	$0.622727\pi$
$60$	−1.17023e8	+	5.20864e7i	−1.16571	+	0.518852i
$61$	1.26942e8			1.17387			0.586936	−	0.809633i	$-0.300334\pi$
$61$	1.26942e8			1.17387			0.586936	+	0.809633i	$0.300334\pi$
$62$			1.68656e6i			0.0144957i
$63$		−	1.08496e8i		−	0.867721i
$64$	1.33099e8			0.991663
$65$	2.73620e7	−	1.21787e7i	0.190124	−	0.0846231i
$66$	−6.74104e6			−0.0437300
$67$		−	2.66595e8i		−	1.61628i	−0.588993	−	0.808138i	$-0.700475\pi$
$67$		−	2.66595e8i		−	1.61628i	0.588993	−	0.808138i	$-0.299525\pi$
$68$			1.53499e8i			0.870593i
$69$	−1.70430e8			−0.905160
$70$	−4.17877e6	−	9.38853e6i	−0.0208021	−	0.0467365i
$71$	6.59169e7			0.307846			0.153923	−	0.988083i	$-0.450809\pi$
$71$	6.59169e7			0.307846			0.153923	+	0.988083i	$0.450809\pi$
$72$			1.07537e7i			0.0471585i
$73$		−	1.47516e7i		−	0.0607977i	−0.999538	−	0.0303989i	$-0.990322\pi$
$73$		−	1.47516e7i		−	0.0607977i	0.999538	−	0.0303989i	$-0.00967775\pi$
$74$	8.04832e6			0.0312006
$75$	2.60139e8	+	2.34337e8i	0.949358	+	0.855193i
$76$	−2.89074e8			−0.993913
$77$			3.88231e8i			1.25858i
$78$		−	3.24216e6i		−	0.00991766i
$79$	4.66498e7			0.134750			0.0673748	−	0.997728i	$-0.478538\pi$
$79$	4.66498e7			0.134750			0.0673748	+	0.997728i	$0.478538\pi$
$80$	−1.48352e8	−	3.33305e8i	−0.404937	−	0.909780i
$81$	−4.77460e8			−1.23241
$82$			2.14661e7i			0.0524313i
$83$		−	2.01840e8i		−	0.466826i	−0.972378	−	0.233413i	$-0.925011\pi$
$83$		−	2.01840e8i		−	0.466826i	0.972378	−	0.233413i	$-0.0749895\pi$
$84$	7.98588e8			1.75011
$85$	3.83316e8	−	1.70611e8i	0.796474	−	0.354505i
$86$	1.96495e7			0.0387355
$87$		−	1.43978e8i		−	0.269438i
$88$		−	3.84800e7i		−	0.0684010i
$89$	−5.54039e8			−0.936020			−0.468010	−	0.883723i	$-0.655029\pi$
$89$	−5.54039e8			−0.936020			−0.468010	+	0.883723i	$0.655029\pi$
$90$	1.34176e7	−	5.97210e6i	0.0215568	−	0.00959480i
$91$	−1.86723e8			−0.285438
$92$		−	4.86095e8i		−	0.707418i
$93$			3.58244e8i			0.496599i
$94$	−3.18465e7			−0.0420713
$95$	3.21301e8	+	7.21874e8i	0.404722	+	0.909295i
$96$	−1.18757e8			−0.142705
$97$			3.39489e8i			0.389361i	0.980867	+	0.194681i	$0.0623670\pi$
$97$			3.39489e8i			0.389361i	−0.980867	+	0.194681i	$0.937633\pi$
$98$			3.00128e7i			0.0328692i
$99$	−5.54841e8			−0.580511
$100$	−6.68367e8	+	7.41960e8i	−0.668367	+	0.741960i
$101$	1.33921e9			1.28056			0.640282	−	0.768140i	$-0.278817\pi$
$101$	1.33921e9			1.28056			0.640282	+	0.768140i	$0.278817\pi$
$102$		−	4.54196e7i		−	0.0415473i
$103$			3.84306e8i			0.336442i	0.985749	+	0.168221i	$0.0538022\pi$
$103$			3.84306e8i			0.336442i	−0.985749	+	0.168221i	$0.946198\pi$
$104$	1.85073e7			0.0155129
$105$	−8.87618e8	−	1.99423e9i	−0.712646	−	1.60112i
$106$	4.04500e7			0.0311202
$107$		−	7.97379e8i		−	0.588082i	−0.955793	−	0.294041i	$-0.905000\pi$
$107$		−	7.97379e8i		−	0.588082i	0.955793	−	0.294041i	$-0.0950002\pi$
$108$		−	6.62740e8i		−	0.468745i
$109$	6.63230e8			0.450034			0.225017	−	0.974355i	$-0.427756\pi$
$109$	6.63230e8			0.450034			0.225017	+	0.974355i	$0.427756\pi$
$110$	−4.80124e7	+	2.13700e7i	−0.0312670	+	0.0139168i
$111$	1.70955e9			1.06888
$112$			2.27453e9i			1.36587i
$113$		−	1.48164e9i		−	0.854847i	−0.904051	−	0.427424i	$-0.859421\pi$
$113$		−	1.48164e9i		−	0.854847i	0.904051	−	0.427424i	$-0.140579\pi$
$114$	8.55358e7			0.0474325
$115$	−1.21387e9	+	5.40286e8i	−0.647191	+	0.288060i
$116$	4.10649e8			0.210577
$117$		−	2.66856e8i		−	0.131656i
$118$			5.90819e7i			0.0280534i
$119$	−2.61581e9			−1.19576
$120$	8.79771e7	+	1.97660e8i	0.0387306	+	0.0870168i
$121$	−3.72554e8			−0.157999
$122$		−	1.07132e8i		−	0.0437824i
$123$			4.55964e9i			1.79621i
$124$	−1.02177e9			−0.388112
$125$	2.59569e9	+	8.44363e8i	0.950952	+	0.309339i
$126$	−9.15643e7			−0.0323637
$127$		−	2.28772e9i		−	0.780344i	−0.920742	−	0.390172i	$-0.872416\pi$
$127$		−	2.28772e9i		−	0.780344i	0.920742	−	0.390172i	$-0.127584\pi$
$128$		−	4.51514e8i		−	0.148671i
$129$	4.17378e9			1.32701
$130$	−1.02781e7	−	2.30920e7i	−0.00315622	−	0.00709114i
$131$	−3.83999e9			−1.13922			−0.569612	−	0.821914i	$-0.692906\pi$
$131$	−3.83999e9			−1.13922			−0.569612	+	0.821914i	$0.692906\pi$
$132$		−	4.08394e9i		−	1.17084i
$133$		−	4.92619e9i		−	1.36515i
$134$	−2.24991e8			−0.0602829
$135$	−1.65499e9	+	7.36625e8i	−0.428838	+	0.190873i
$136$	2.59269e8			0.0649869
$137$			5.82666e9i			1.41311i	0.707657	+	0.706556i	$0.249752\pi$
$137$			5.82666e9i			1.41311i	−0.707657	+	0.706556i	$0.750248\pi$
$138$			1.43833e8i			0.0337601i
$139$	5.89895e9			1.34032			0.670159	−	0.742217i	$-0.266226\pi$
$139$	5.89895e9			1.34032			0.670159	+	0.742217i	$0.266226\pi$
$140$	5.68787e9	−	2.53163e9i	1.25133	−	0.556961i
$141$	−6.76455e9			−1.44129
$142$		−	5.56301e7i		−	0.0114819i
$143$			9.54892e8i			0.190960i
$144$	−3.25065e9			−0.629997
$145$	−4.56430e8	−	1.02547e9i	−0.0857468	−	0.192649i
$146$	−1.24495e7			−0.00226760
$147$			6.37505e9i			1.12604i
$148$			4.87593e9i			0.835371i
$149$	−5.39333e9			−0.896436			−0.448218	−	0.893924i	$-0.647941\pi$
$149$	−5.39333e9			−0.896436			−0.448218	+	0.893924i	$0.647941\pi$
$150$	1.97767e8	−	2.19543e8i	0.0318965	−	0.0354086i
$151$	7.92204e8			0.124005			0.0620027	−	0.998076i	$-0.480251\pi$
$151$	7.92204e8			0.124005			0.0620027	+	0.998076i	$0.480251\pi$
$152$			4.88265e8i			0.0741924i
$153$		−	3.73839e9i		−	0.551536i
$154$	3.27645e8			0.0469419
$155$	1.13568e9	+	2.55156e9i	0.158039	+	0.355069i
$156$	1.96420e9			0.265538
$157$		−	1.18606e10i		−	1.55797i	−0.627042	−	0.778985i	$-0.715735\pi$
$157$		−	1.18606e10i		−	1.55797i	0.627042	−	0.778985i	$-0.284265\pi$
$158$		−	3.93698e7i		−	0.00502581i
$159$	8.59202e9			1.06613
$160$	−8.45835e8	+	3.76476e8i	−0.102034	+	0.0454148i
$161$	8.28367e9			0.971642
$162$			4.02949e8i			0.0459656i
$163$		−	3.99906e9i		−	0.443724i	−0.975078	−	0.221862i	$-0.928787\pi$
$163$		−	3.99906e9i		−	0.443724i	0.975078	−	0.221862i	$-0.0712135\pi$
$164$	−1.30048e10			−1.40381
$165$	−1.01984e10	+	4.53923e9i	−1.07116	+	0.476765i
$166$	−1.70341e8			−0.0174114
$167$		−	1.09118e10i		−	1.08560i	−0.839861	−	0.542802i	$-0.817363\pi$
$167$		−	1.09118e10i		−	1.08560i	0.839861	−	0.542802i	$-0.182637\pi$
$168$		−	1.34887e9i		−	0.130640i
$169$	1.01452e10			0.956692
$170$	−1.43986e8	−	3.23497e8i	−0.0132221	−	0.0297064i
$171$	7.04028e9			0.629662
$172$			1.19043e10i			1.03711i
$173$			1.89328e10i			1.60696i	0.595329	+	0.803482i	$0.297022\pi$
$173$			1.89328e10i			1.60696i	−0.595329	+	0.803482i	$0.702978\pi$
$174$	−1.21509e8			−0.0100493
$175$	−1.26439e10	−	1.13898e10i	−1.01909	−	0.918006i
$176$	1.16318e10			0.913778
$177$			1.25496e10i			0.961062i
$178$			4.67577e8i			0.0349111i
$179$	−2.09763e10			−1.52718			−0.763592	−	0.645699i	$-0.776566\pi$
$179$	−2.09763e10			−1.52718			−0.763592	+	0.645699i	$0.776566\pi$
$180$	3.61809e9	+	8.12882e9i	0.256893	+	0.577167i
$181$	−7.16950e9			−0.496518			−0.248259	−	0.968694i	$-0.579858\pi$
$181$	−7.16950e9			−0.496518			−0.248259	+	0.968694i	$0.579858\pi$
$182$			1.57584e8i			0.0106461i
$183$		−	2.27560e10i		−	1.49991i
$184$	−8.21045e8			−0.0528064
$185$	1.21761e10	−	5.41951e9i	0.764251	−	0.340163i
$186$	3.02338e8			0.0185218
$187$			1.33771e10i			0.799974i
$188$		−	1.92936e10i		−	1.12643i
$189$	1.12939e10			0.643824
$190$	6.09221e8	−	2.71160e8i	0.0339143	−	0.0150951i
$191$	1.75301e10			0.953091			0.476545	−	0.879150i	$-0.341889\pi$
$191$	1.75301e10			0.953091			0.476545	+	0.879150i	$0.341889\pi$
$192$		−	2.38597e10i		−	1.26709i
$193$			3.13528e10i			1.62655i	0.581877	+	0.813277i	$0.302319\pi$
$193$			3.13528e10i			1.62655i	−0.581877	+	0.813277i	$0.697681\pi$
$194$	2.86509e8			0.0145222
$195$	−2.18318e9	−	4.90499e9i	−0.108127	−	0.242931i
$196$	−1.81827e10			−0.880048
$197$		−	1.85971e10i		−	0.879725i	−0.898065	−	0.439862i	$-0.855027\pi$
$197$		−	1.85971e10i		−	0.879725i	0.898065	−	0.439862i	$-0.144973\pi$
$198$			4.68255e8i			0.0216515i
$199$	1.26662e10			0.572544			0.286272	−	0.958148i	$-0.407584\pi$
$199$	1.26662e10			0.572544			0.286272	+	0.958148i	$0.407584\pi$
$200$	1.25322e9	+	1.12891e9i	0.0553849	+	0.0498914i
$201$	−4.77906e10			−2.06519
$202$		−	1.13021e9i		−	0.0477617i
$203$			6.99798e9i			0.289228i
$204$	2.75166e10			1.11240
$205$	1.44547e10	+	3.24756e10i	0.571631	+	1.28429i
$206$	3.24333e8			0.0125484
$207$			1.18386e10i			0.448161i
$208$			5.59443e9i			0.207239i
$209$	−2.51923e10			−0.913291
$210$	−1.68301e9	+	7.49099e8i	−0.0597174	+	0.0265798i
$211$	−6.20579e9			−0.215539			−0.107770	−	0.994176i	$-0.534371\pi$
$211$	−6.20579e9			−0.215539			−0.107770	+	0.994176i	$0.534371\pi$
$212$			2.45059e10i			0.833218i
$213$		−	1.18164e10i		−	0.393350i
$214$	−6.72943e8			−0.0219339
$215$	2.97273e10	−	1.32314e10i	0.948818	−	0.422313i
$216$	−1.11941e9			−0.0349903
$217$		−	1.74123e10i		−	0.533074i
$218$		−	5.59729e8i		−	0.0167851i
$219$	−2.64442e9			−0.0776841
$220$	−1.29466e10	−	2.90875e10i	−0.372610	−	0.837151i
$221$	−6.43385e9			−0.181428
$222$		−	1.44277e9i		−	0.0398664i
$223$		−	4.30855e10i		−	1.16670i	−0.812221	−	0.583350i	$-0.801742\pi$
$223$		−	4.30855e10i		−	1.16670i	0.812221	−	0.583350i	$-0.198258\pi$
$224$	5.77213e9			0.153186
$225$	1.62778e10	−	1.80701e10i	0.423422	−	0.470045i
$226$	−1.25042e9			−0.0318836
$227$			2.28857e10i			0.572068i	0.958219	+	0.286034i	$0.0923371\pi$
$227$			2.28857e10i			0.572068i	−0.958219	+	0.286034i	$0.907663\pi$
$228$			5.18203e10i			1.26997i
$229$	5.26747e9			0.126573			0.0632867	−	0.997995i	$-0.479842\pi$
$229$	5.26747e9			0.126573			0.0632867	+	0.997995i	$0.479842\pi$
$230$	4.55971e8	+	1.02444e9i	0.0107439	+	0.0241385i
$231$	6.95955e10			1.60815
$232$		−	6.93612e8i		−	0.0157189i
$233$		−	3.55179e10i		−	0.789488i	−0.918791	−	0.394744i	$-0.870833\pi$
$233$		−	3.55179e10i		−	0.789488i	0.918791	−	0.394744i	$-0.129167\pi$
$234$	−2.25211e8			−0.00491042
$235$	−4.81798e10	+	2.14445e10i	−1.03053	+	0.458681i
$236$	−3.57937e10			−0.751108
$237$		−	8.36257e9i		−	0.172176i
$238$			2.20760e9i			0.0445989i
$239$	−5.72471e10			−1.13491			−0.567457	−	0.823403i	$-0.692073\pi$
$239$	−5.72471e10			−1.13491			−0.567457	+	0.823403i	$0.692073\pi$
$240$	−5.97492e10	+	2.65940e10i	−1.16247	+	0.517407i
$241$	3.89830e10			0.744386			0.372193	−	0.928155i	$-0.378606\pi$
$241$	3.89830e10			0.744386			0.372193	+	0.928155i	$0.378606\pi$
$242$			3.14415e8i			0.00589296i
$243$			6.00774e10i			1.10531i
$244$	6.49039e10			1.17224
$245$	2.02098e10	+	4.54057e10i	0.358356	+	0.805124i
$246$	3.84808e9			0.0669939
$247$		−	1.21164e10i		−	0.207128i
$248$			1.72584e9i			0.0289713i
$249$	−3.61824e10			−0.596486
$250$	7.12595e8	−	2.19062e9i	0.0115375	−	0.0354680i
$251$	4.56895e10			0.726581			0.363291	−	0.931676i	$-0.381653\pi$
$251$	4.56895e10			0.726581			0.363291	+	0.931676i	$0.381653\pi$
$252$		−	5.54725e10i		−	0.866514i
$253$		−	4.23622e10i		−	0.650035i
$254$	−1.93071e9			−0.0291048
$255$	−3.05843e10	−	6.87143e10i	−0.452968	−	1.01769i
$256$	6.77655e10			0.986118
$257$		−	1.29955e10i		−	0.185821i	−0.995674	−	0.0929104i	$-0.970383\pi$
$257$		−	1.29955e10i		−	0.185821i	0.995674	−	0.0929104i	$-0.0296170\pi$
$258$		−	3.52243e9i		−	0.0494942i
$259$	−8.30920e10			−1.14739
$260$	1.39899e10	−	6.22680e9i	0.189860	−	0.0845054i
$261$	−1.00012e10			−0.133404
$262$			3.24073e9i			0.0424901i
$263$			4.80103e10i			0.618776i	0.950936	+	0.309388i	$0.100124\pi$
$263$			4.80103e10i			0.618776i	−0.950936	+	0.309388i	$0.899876\pi$
$264$	−6.89803e9			−0.0873991
$265$	6.11958e10	−	2.72379e10i	0.762282	−	0.339287i
$266$	−4.15743e9			−0.0509164
$267$			9.93185e10i			1.19600i
$268$		−	1.36307e11i		−	1.61403i
$269$	9.98823e10			1.16306			0.581531	−	0.813524i	$-0.302454\pi$
$269$	9.98823e10			1.16306			0.581531	+	0.813524i	$0.302454\pi$
$270$	6.21670e8	+	1.39672e9i	0.00711906	+	0.0159945i
$271$	−4.80217e10			−0.540849			−0.270424	−	0.962741i	$-0.587164\pi$
$271$	−4.80217e10			−0.540849			−0.270424	+	0.962741i	$0.587164\pi$
$272$			7.83726e10i			0.868169i
$273$			3.34725e10i			0.364718i
$274$	4.91737e9			0.0527054
$275$	−5.82469e10	+	6.46604e10i	−0.614152	+	0.681776i
$276$	−8.71388e10			−0.903900
$277$			1.77838e10i			0.181495i	0.995874	+	0.0907477i	$0.0289257\pi$
$277$			1.77838e10i			0.181495i	−0.995874	+	0.0907477i	$0.971074\pi$
$278$		−	4.97838e9i		−	0.0499904i
$279$	2.48848e10			0.245875
$280$	−4.27609e9	−	9.60717e9i	−0.0415753	−	0.0934080i
$281$	−1.52044e11			−1.45476			−0.727379	−	0.686236i	$-0.759262\pi$
$281$	−1.52044e11			−1.45476			−0.727379	+	0.686236i	$0.759262\pi$
$282$			5.70890e9i			0.0537565i
$283$			1.86733e11i			1.73055i	0.501301	+	0.865273i	$0.332855\pi$
$283$			1.86733e11i			1.73055i	−0.501301	+	0.865273i	$0.667145\pi$
$284$	3.37025e10			0.307418
$285$	1.29405e11	−	5.75974e10i	1.16185	−	0.517132i
$286$	8.05875e8			0.00712230
$287$		−	2.21619e11i		−	1.92814i
$288$			8.24924e9i			0.0706558i
$289$	2.84558e10			0.239955
$290$	−8.65438e8	+	3.85201e8i	−0.00718530	+	0.00319813i
$291$	6.08577e10			0.497505
$292$		−	7.54233e9i		−	0.0607132i
$293$		−	1.28928e11i		−	1.02198i	−0.859586	−	0.510991i	$-0.829278\pi$
$293$		−	1.28928e11i		−	1.02198i	0.859586	−	0.510991i	$-0.170722\pi$
$294$	5.38018e9			0.0419985
$295$	3.97841e10	+	8.93836e10i	0.305851	+	0.687161i
$296$	8.23575e9			0.0623577
$297$		−	5.77565e10i		−	0.430722i
$298$			4.55167e9i			0.0334347i
$299$	2.03745e10			0.147423
$300$	1.33006e11	+	1.19813e11i	0.948037	+	0.854004i
$301$	−2.02865e11			−1.42448
$302$		−	6.68575e8i		−	0.00462508i
$303$		−	2.40070e11i		−	1.63624i
$304$	−1.47594e11			−0.991146
$305$	−7.21396e10	−	1.62077e11i	−0.477336	−	1.07244i
$306$	−3.15499e9			−0.0205708
$307$			8.78331e10i			0.564333i	0.959365	+	0.282167i	$0.0910531\pi$
$307$			8.78331e10i			0.564333i	−0.959365	+	0.282167i	$0.908947\pi$
$308$			1.98498e11i			1.25683i
$309$	6.88919e10			0.429887
$310$	2.15337e9	−	9.58452e8i	0.0132432	−	0.00589444i
$311$	2.76204e11			1.67420			0.837101	−	0.547049i	$-0.184249\pi$
$311$	2.76204e11			1.67420			0.837101	+	0.547049i	$0.184249\pi$
$312$		−	3.31767e9i		−	0.0198215i
$313$			1.84107e11i			1.08423i	0.840304	+	0.542115i	$0.182376\pi$
$313$			1.84107e11i			1.08423i	−0.840304	+	0.542115i	$0.817624\pi$
$314$	−1.00097e10			−0.0581082
$315$	−1.38525e11	+	6.16568e10i	−0.792742	+	0.352845i
$316$	2.38515e10			0.134562
$317$			3.48865e11i			1.94040i	0.242313	+	0.970198i	$0.422094\pi$
$317$			3.48865e11i			1.94040i	−0.242313	+	0.970198i	$0.577906\pi$
$318$		−	7.25118e9i		−	0.0397637i
$319$	3.57873e10			0.193496
$320$	−7.56384e10	−	1.69938e11i	−0.403244	−	0.905975i
$321$	−1.42940e11			−0.751419
$322$		−	6.99095e9i		−	0.0362397i
$323$		−	1.69740e11i		−	0.867706i
$324$	−2.44119e11			−1.23069
$325$	−3.10990e10	−	2.80144e10i	−0.154622	−	0.139285i
$326$	−3.37498e9			−0.0165498
$327$		−	1.18893e11i		−	0.575029i
$328$			2.19660e10i			0.104790i
$329$	3.28788e11			1.54716
$330$	3.83085e9	+	8.60685e9i	0.0177821	+	0.0399513i
$331$	2.88744e11			1.32217			0.661084	−	0.750312i	$-0.270097\pi$
$331$	2.88744e11			1.32217			0.661084	+	0.750312i	$0.270097\pi$
$332$		−	1.03198e11i		−	0.466177i
$333$		−	1.18751e11i		−	0.529222i
$334$	−9.20892e9			−0.0404902
$335$	−3.40384e11	+	1.51503e11i	−1.47662	+	0.657232i
$336$	4.07739e11			1.74524
$337$		−	1.25882e11i		−	0.531654i	−0.964021	−	0.265827i	$-0.914355\pi$
$337$		−	1.25882e11i		−	0.531654i	0.964021	−	0.265827i	$-0.0856450\pi$
$338$		−	8.56201e9i		−	0.0356821i
$339$	−2.65602e11			−1.09228
$340$	1.95985e11	−	8.72315e10i	0.795366	−	0.354012i
$341$	−8.90455e10			−0.356630
$342$		−	5.94160e9i		−	0.0234847i
$343$			4.17441e10i			0.162844i
$344$	2.01071e10			0.0774172
$345$	9.68533e10	+	2.17602e11i	0.368068	+	0.826946i
$346$	1.59782e10			0.0599356
$347$		−	2.95822e11i		−	1.09534i	−0.836695	−	0.547669i	$-0.815515\pi$
$347$		−	2.95822e11i		−	1.09534i	0.836695	−	0.547669i	$-0.184485\pi$
$348$		−	7.36142e10i		−	0.269064i
$349$	−3.73474e11			−1.34755			−0.673777	−	0.738934i	$-0.735329\pi$
$349$	−3.73474e11			−1.34755			−0.673777	+	0.738934i	$0.735329\pi$
$350$	−9.61237e9	+	1.06708e10i	−0.0342392	+	0.0380093i
$351$	2.77785e10			0.0976848
$352$		−	2.95183e10i		−	0.102483i
$353$			4.89872e11i			1.67918i	0.543223	+	0.839589i	$0.317204\pi$
$353$			4.89872e11i			1.67918i	−0.543223	+	0.839589i	$0.682796\pi$
$354$	1.05912e10			0.0358451
$355$	−3.74598e10	−	8.41615e10i	−0.125181	−	0.281246i
$356$	−2.83273e11			−0.934718
$357$			4.68918e11i			1.52788i
$358$			1.77029e10i			0.0569600i
$359$	4.27559e11			1.35854			0.679268	−	0.733891i	$-0.262298\pi$
$359$	4.27559e11			1.35854			0.679268	+	0.733891i	$0.262298\pi$
$360$	1.37301e10	−	6.11118e9i	0.0430836	−	0.0191762i
$361$	−3.02753e9			−0.00938223
$362$			6.05065e9i			0.0185188i
$363$			6.67851e10i			0.201883i
$364$	−9.54693e10			−0.285041
$365$	−1.88346e10	+	8.38317e9i	−0.0555443	+	0.0247224i
$366$	−1.92048e10			−0.0559428
$367$			2.54403e10i			0.0732023i	0.999330	+	0.0366012i	$0.0116531\pi$
$367$			2.54403e10i			0.0732023i	−0.999330	+	0.0366012i	$0.988347\pi$
$368$		−	2.48188e11i		−	0.705448i
$369$	3.16727e11			0.889337
$370$	−4.57376e9	−	1.02760e10i	−0.0126872	−	0.0285046i
$371$	−4.17611e11			−1.14443
$372$			1.83166e11i			0.495908i
$373$		−	7.26003e11i		−	1.94200i	−0.239087	−	0.970998i	$-0.576848\pi$
$373$		−	7.26003e11i		−	1.94200i	0.239087	−	0.970998i	$-0.423152\pi$
$374$	1.12895e10			0.0298369
$375$	1.51363e11	−	4.65312e11i	0.395256	−	1.21508i
$376$	−3.25881e10			−0.0840842
$377$			1.72122e10i			0.0438834i
$378$		−	9.53144e9i		−	0.0240129i
$379$	2.76699e11			0.688859			0.344430	−	0.938812i	$-0.388072\pi$
$379$	2.76699e11			0.688859			0.344430	+	0.938812i	$0.388072\pi$
$380$	1.64277e11	+	3.69085e11i	0.404159	+	0.908031i
$381$	−4.10103e11			−0.997082
$382$		−	1.47944e10i		−	0.0355478i
$383$			1.71143e11i			0.406410i	0.979136	+	0.203205i	$0.0651358\pi$
$383$			1.71143e11i			0.406410i	−0.979136	+	0.203205i	$0.934864\pi$
$384$	−8.09398e10			−0.189964
$385$	4.95687e11	−	2.20627e11i	1.14983	−	0.511783i
$386$	2.64600e10			0.0606662
$387$		−	2.89924e11i		−	0.657030i
$388$			1.73576e11i			0.388819i
$389$	−3.92384e10			−0.0868837			−0.0434419	−	0.999056i	$-0.513832\pi$
$389$	−3.92384e10			−0.0868837			−0.0434419	+	0.999056i	$0.513832\pi$
$390$	−4.13954e9	+	1.84248e9i	−0.00906068	+	0.00403285i
$391$	2.85427e11			0.617590
$392$			3.07117e10i			0.0656927i
$393$			6.88367e11i			1.45564i
$394$	−1.56949e10			−0.0328114
$395$	−2.65105e10	−	5.95616e10i	−0.0547937	−	0.123106i
$396$	−2.83684e11			−0.579703
$397$		−	3.91381e11i		−	0.790756i	−0.918519	−	0.395378i	$-0.870614\pi$
$397$		−	3.91381e11i		−	0.790756i	0.918519	−	0.395378i	$-0.129386\pi$
$398$		−	1.06896e10i		−	0.0213544i
$399$	−8.83084e11			−1.74431
$400$	−3.41251e11	+	3.78826e11i	−0.666506	+	0.739895i
$401$	−5.04969e11			−0.975248			−0.487624	−	0.873054i	$-0.662136\pi$
$401$	−5.04969e11			−0.975248			−0.487624	+	0.873054i	$0.662136\pi$
$402$			4.03326e10i			0.0770263i
$403$		−	4.28272e10i		−	0.0808811i
$404$	6.84720e11			1.27878
$405$	2.71335e11	+	6.09613e11i	0.501138	+	1.12592i
$406$	5.90590e9			0.0107875
$407$			4.24928e11i			0.767609i
$408$		−	4.64773e10i		−	0.0830368i
$409$	−9.44998e9			−0.0166985			−0.00834923	−	0.999965i	$-0.502658\pi$
$409$	−9.44998e9			−0.0166985			−0.00834923	+	0.999965i	$0.502658\pi$
$410$	2.74075e10	−	1.21989e10i	0.0479008	−	0.0213203i
$411$	1.04450e12			1.80560
$412$			1.96491e11i			0.335974i
$413$		−	6.09969e11i		−	1.03165i
$414$	9.99113e9			0.0167153
$415$	−2.57706e11	+	1.14703e11i	−0.426488	+	0.189827i
$416$	1.41971e10			0.0232423
$417$		−	1.05746e12i		−	1.71259i
$418$			2.12609e10i			0.0340634i
$419$	5.77328e10			0.0915081			0.0457541	−	0.998953i	$-0.485431\pi$
$419$	5.77328e10			0.0915081			0.0457541	+	0.998953i	$0.485431\pi$
$420$	−4.53828e11	−	1.01962e12i	−0.711655	−	1.59889i
$421$	4.38976e9			0.00681038			0.00340519	−	0.999994i	$-0.498916\pi$
$421$	4.38976e9			0.00681038			0.00340519	+	0.999994i	$0.498916\pi$
$422$			5.23734e9i			0.00803905i
$423$			4.69887e11i			0.713612i
$424$	4.13920e10			0.0621970
$425$	−4.35667e11	−	3.92455e11i	−0.647746	−	0.583498i
$426$	−9.97242e9			−0.0146709
$427$			1.10604e12i			1.61008i
$428$		−	4.07690e11i		−	0.587264i
$429$	1.71177e11			0.243998
$430$	−1.11666e10	−	2.50882e10i	−0.0157512	−	0.0353884i
$431$	9.94476e11			1.38818			0.694091	−	0.719887i	$-0.255807\pi$
$431$	9.94476e11			1.38818			0.694091	+	0.719887i	$0.255807\pi$
$432$		−	3.38378e11i		−	0.467440i
$433$		−	1.91618e11i		−	0.261963i	−0.991385	−	0.130982i	$-0.958187\pi$
$433$		−	1.91618e11i		−	0.261963i	0.991385	−	0.130982i	$-0.0418129\pi$
$434$	−1.46950e10			−0.0198823
$435$	−1.83829e11	+	8.18209e10i	−0.246157	+	0.109563i
$436$	3.39101e11			0.449407
$437$			5.37527e11i			0.705072i
$438$			2.23174e9i			0.00289741i
$439$	−1.38202e12			−1.77592			−0.887962	−	0.459917i	$-0.847879\pi$
$439$	−1.38202e12			−1.77592			−0.887962	+	0.459917i	$0.847879\pi$
$440$	−4.91305e10	+	2.18677e10i	−0.0624906	+	0.0278141i
$441$	4.42832e11			0.557526
$442$			5.42980e9i			0.00676681i
$443$		−	3.05660e11i		−	0.377070i	−0.982066	−	0.188535i	$-0.939626\pi$
$443$		−	3.05660e11i		−	0.377070i	0.982066	−	0.188535i	$-0.0603740\pi$
$444$	8.74073e11			1.06739
$445$	3.14853e11	+	7.07387e11i	0.380617	+	0.855139i
$446$	−3.63617e10			−0.0435148
$447$			9.66825e11i			1.14542i
$448$			1.15969e12i			1.36016i
$449$	−1.49518e12			−1.73614			−0.868069	−	0.496444i	$-0.834639\pi$
$449$	−1.49518e12			−1.73614			−0.868069	+	0.496444i	$0.834639\pi$
$450$	−1.52501e10	−	1.37375e10i	−0.0175314	−	0.0157925i
$451$	−1.13335e12			−1.28994
$452$		−	7.57542e11i		−	0.853658i
$453$		−	1.42013e11i		−	0.158447i
$454$	1.93142e10			0.0213367
$455$	1.06112e11	+	2.38405e11i	0.116069	+	0.260774i
$456$	8.75278e10			0.0947991
$457$		−	1.17977e12i		−	1.26525i	−0.774459	−	0.632624i	$-0.781978\pi$
$457$		−	1.17977e12i		−	1.26525i	0.774459	−	0.632624i	$-0.218022\pi$
$458$		−	4.44545e9i		−	0.00472086i
$459$	3.89151e11			0.409223
$460$	−6.20638e11	+	2.76242e11i	−0.646291	+	0.287660i
$461$	1.54415e12			1.59234			0.796170	−	0.605074i	$-0.206856\pi$
$461$	1.54415e12			1.59234			0.796170	+	0.605074i	$0.206856\pi$
$462$		−	5.87346e10i		−	0.0599799i
$463$		−	4.55769e11i		−	0.460926i	−0.973081	−	0.230463i	$-0.925976\pi$
$463$		−	4.55769e11i		−	0.460926i	0.973081	−	0.230463i	$-0.0740240\pi$
$464$	2.09667e11			0.209990
$465$	4.57400e11	−	2.03586e11i	0.453689	−	0.201934i
$466$	−2.99751e10			−0.0294458
$467$		−	6.97342e11i		−	0.678454i	−0.940705	−	0.339227i	$-0.889835\pi$
$467$		−	6.97342e11i		−	0.678454i	0.940705	−	0.339227i	$-0.110165\pi$
$468$		−	1.36440e11i		−	0.131473i
$469$	2.32284e12			2.21688
$470$	1.80980e10	+	4.06611e10i	0.0171076	+	0.0384360i
$471$	−2.12617e12			−1.99069
$472$			6.04578e10i			0.0560677i
$473$			1.03744e12i			0.952987i
$474$	−7.05754e9			−0.00642171
$475$	7.39084e11	−	8.20464e11i	0.666151	−	0.739500i
$476$	−1.33743e12			−1.19410
$477$		−	5.96829e11i		−	0.527858i
$478$			4.83134e10i			0.0423294i
$479$	−2.43471e11			−0.211318			−0.105659	−	0.994402i	$-0.533695\pi$
$479$	−2.43471e11			−0.211318			−0.105659	+	0.994402i	$0.533695\pi$
$480$	6.74881e10	+	1.51627e11i	0.0580285	+	0.130374i
$481$	−2.04373e11			−0.174088
$482$		−	3.28994e10i		−	0.0277637i
$483$		−	1.48495e12i		−	1.24151i
$484$	−1.90482e11			−0.157780
$485$	4.33453e11	−	1.92927e11i	0.355717	−	0.158327i
$486$	5.07019e10			0.0412251
$487$			1.56961e12i			1.26448i	0.774773	+	0.632239i	$0.217864\pi$
$487$			1.56961e12i			1.26448i	−0.774773	+	0.632239i	$0.782136\pi$
$488$		−	1.09627e11i		−	0.0875039i
$489$	−7.16882e11			−0.566967
$490$	3.83198e10	−	1.70559e10i	0.0300290	−	0.0133657i
$491$	6.52870e11			0.506944			0.253472	−	0.967343i	$-0.418427\pi$
$491$	6.52870e11			0.506944			0.253472	+	0.967343i	$0.418427\pi$
$492$			2.33129e12i			1.79371i
$493$			2.41127e11i			0.183838i
$494$	−1.02256e10			−0.00772534
$495$	3.15309e11	+	7.08412e11i	0.236055	+	0.530350i
$496$	−5.21691e11			−0.387031
$497$			5.74333e11i			0.422241i
$498$			3.05359e10i			0.0222474i
$499$	7.51465e11			0.542571			0.271285	−	0.962499i	$-0.412551\pi$
$499$	7.51465e11			0.542571			0.271285	+	0.962499i	$0.412551\pi$
$500$	1.32715e12	+	4.31713e11i	0.949629	+	0.308908i
$501$	−1.95608e12			−1.38713
$502$		−	3.85593e10i		−	0.0270996i
$503$			1.31120e12i			0.913299i	0.889647	+	0.456649i	$0.150951\pi$
$503$			1.31120e12i			0.913299i	−0.889647	+	0.456649i	$0.849049\pi$
$504$	−9.36966e10			−0.0646824
$505$	−7.61055e11	−	1.70988e12i	−0.520721	−	1.16991i
$506$	−3.57513e10			−0.0242446
$507$		−	1.81866e12i		−	1.22241i
$508$		−	1.16968e12i		−	0.779259i
$509$	−1.78629e12			−1.17957			−0.589783	−	0.807561i	$-0.700787\pi$
$509$	−1.78629e12			−1.17957			−0.589783	+	0.807561i	$0.700787\pi$
$510$	−5.79910e10	+	2.58114e10i	−0.0379572	+	0.0168945i
$511$	1.28531e11			0.0833899
$512$		−	2.88366e11i		−	0.185451i
$513$			7.32862e11i			0.467191i
$514$	−1.09675e10			−0.00693063
$515$	4.90676e11	−	2.18397e11i	0.307370	−	0.136809i
$516$	2.13400e12			1.32517
$517$		−	1.68140e12i		−	1.03506i
$518$			7.01249e10i			0.0427946i
$519$	3.39394e12			2.05329
$520$	−1.05175e10	−	2.36298e10i	−0.00630805	−	0.0141724i
$521$	5.88627e11			0.350002			0.175001	−	0.984568i	$-0.444007\pi$
$521$	5.88627e11			0.350002			0.175001	+	0.984568i	$0.444007\pi$
$522$			8.44043e9i			0.00497562i
$523$			6.01202e11i			0.351369i	0.984447	+	0.175684i	$0.0562138\pi$
$523$			6.01202e11i			0.351369i	−0.984447	+	0.175684i	$0.943786\pi$
$524$	−1.96334e12			−1.13764
$525$	−2.04177e12	+	2.26659e12i	−1.17298	+	1.30213i
$526$	4.05180e10			0.0230787
$527$		−	5.99968e11i		−	0.338829i
$528$		−	2.08515e12i		−	1.16758i
$529$	8.97272e11			0.498165
$530$	−2.29872e10	−	5.16458e10i	−0.0126545	−	0.0284311i
$531$	8.71739e11			0.475840
$532$		−	2.51870e12i		−	1.36325i
$533$		−	5.45093e11i		−	0.292549i
$534$	8.38193e10			0.0446075
$535$	−1.01808e12	+	4.53141e11i	−0.537266	+	0.239134i
$536$	−2.30231e11			−0.120482
$537$			3.76028e12i			1.95135i
$538$		−	8.42950e10i		−	0.0433792i
$539$	−1.58459e12			−0.808662
$540$	−8.46175e11	+	3.76627e11i	−0.428241	+	0.190607i
$541$	1.40863e12			0.706982			0.353491	−	0.935438i	$-0.384995\pi$
$541$	1.40863e12			0.706982			0.353491	+	0.935438i	$0.384995\pi$
$542$			4.05276e10i			0.0201723i
$543$			1.28522e12i			0.634424i
$544$	1.98888e11			0.0973673
$545$	−3.76905e11	−	8.46800e11i	−0.182999	−	0.411147i
$546$	2.82489e10			0.0136030
$547$			8.05933e10i			0.0384907i	0.999815	+	0.0192454i	$0.00612636\pi$
$547$			8.05933e10i			0.0384907i	−0.999815	+	0.0192454i	$0.993874\pi$
$548$			2.97910e12i			1.41115i
$549$	−1.58070e12			−0.742635
$550$	5.45698e10	+	4.91571e10i	0.0254285	+	0.0229063i
$551$	−4.54098e11			−0.209878
$552$			1.47183e11i			0.0674732i
$553$			4.06459e11i			0.184822i
$554$	1.50085e10			0.00676930
$555$	−9.71517e11	−	2.18273e12i	−0.434642	−	0.976519i
$556$	3.01606e12			1.33845
$557$			3.92066e12i			1.72588i	0.505305	+	0.862941i	$0.331380\pi$
$557$			3.92066e12i			1.72588i	−0.505305	+	0.862941i	$0.668620\pi$
$558$		−	2.10014e10i		−	0.00917051i
$559$	−4.98965e11			−0.216131
$560$	2.90408e12	−	1.29259e12i	1.24785	−	0.555410i
$561$	2.39802e12			1.02216
$562$			1.28317e11i			0.0542587i
$563$		−	3.86627e12i		−	1.62182i	−0.585168	−	0.810912i	$-0.698971\pi$
$563$		−	3.86627e12i		−	1.62182i	0.585168	−	0.810912i	$-0.301029\pi$
$564$	−3.45863e12			−1.43929
$565$	−1.89173e12	+	8.41996e11i	−0.780981	+	0.347610i
$566$	1.57592e11			0.0645448
$567$		−	4.16010e12i		−	1.69036i
$568$		−	5.69256e10i		−	0.0229478i
$569$	1.87990e12			0.751849			0.375924	−	0.926650i	$-0.377325\pi$
$569$	1.87990e12			0.751849			0.375924	+	0.926650i	$0.377325\pi$
$570$	−4.86090e10	−	1.09211e11i	−0.0192877	−	0.0433339i
$571$	−3.44726e12			−1.35710			−0.678550	−	0.734554i	$-0.737391\pi$
$571$	−3.44726e12			−1.35710			−0.678550	+	0.734554i	$0.737391\pi$
$572$			4.88225e11i			0.190694i
$573$		−	3.14250e12i		−	1.21781i
$574$	−1.87034e11			−0.0719146
$575$	1.37966e12	+	1.24281e12i	0.526339	+	0.474133i
$576$	−1.65737e12			−0.627362
$577$			1.68433e12i			0.632608i	0.948658	+	0.316304i	$0.102442\pi$
$577$			1.68433e12i			0.632608i	−0.948658	+	0.316304i	$0.897558\pi$
$578$		−	2.40151e10i		−	0.00894971i
$579$	5.62039e12			2.07832
$580$	−2.33367e11	−	5.24310e11i	−0.0856275	−	0.192381i
$581$	1.75863e12			0.640297
$582$		−	5.13605e10i		−	0.0185556i
$583$			2.13564e12i			0.765631i
$584$	−1.27395e10			−0.00453204
$585$	−3.40717e11	+	1.51651e11i	−0.120280	+	0.0535357i
$586$	−1.08808e11			−0.0381173
$587$		−	5.04715e12i		−	1.75458i	−0.479956	−	0.877292i	$-0.659348\pi$
$587$		−	5.04715e12i		−	1.75458i	0.479956	−	0.877292i	$-0.340652\pi$
$588$			3.25949e12i			1.12448i
$589$	1.12988e12			0.386825
$590$	7.54347e10	−	3.35755e10i	0.0256293	−	0.0114074i
$591$	−3.33377e12			−1.12407
$592$			2.48952e12i			0.833045i
$593$		−	6.66924e11i		−	0.221478i	−0.993850	−	0.110739i	$-0.964678\pi$
$593$		−	6.66924e11i		−	0.221478i	0.993850	−	0.110739i	$-0.0353217\pi$
$594$	−4.87433e10			−0.0160648
$595$	1.48654e12	+	3.33983e12i	0.486238	+	1.09244i
$596$	−2.75755e12			−0.895189
$597$		−	2.27059e12i		−	0.731566i
$598$		−	1.71949e10i		−	0.00549851i
$599$	−3.36479e12			−1.06792			−0.533958	−	0.845511i	$-0.679296\pi$
$599$	−3.36479e12			−1.06792			−0.533958	+	0.845511i	$0.679296\pi$
$600$	2.02372e11	−	2.24655e11i	0.0637486	−	0.0707679i
$601$	−2.79891e12			−0.875092			−0.437546	−	0.899196i	$-0.644152\pi$
$601$	−2.79891e12			−0.875092			−0.437546	+	0.899196i	$0.644152\pi$
$602$			1.71206e11i			0.0531295i
$603$			3.31969e12i			1.02251i
$604$	4.05044e11			0.123833
$605$	2.11718e11	+	4.75671e11i	0.0642478	+	0.144347i
$606$	−2.02606e11			−0.0610274
$607$			3.38683e12i			1.01261i	0.862353	+	0.506307i	$0.168990\pi$
$607$			3.38683e12i			1.01261i	−0.862353	+	0.506307i	$0.831010\pi$
$608$			3.74553e11i			0.111160i
$609$	1.25448e12			0.369560
$610$	−1.36784e11	+	6.08817e10i	−0.0399992	+	0.0178034i
$611$	8.08685e11			0.234744
$612$		−	1.91139e12i		−	0.550768i
$613$		−	7.53866e11i		−	0.215636i	−0.994171	−	0.107818i	$-0.965614\pi$
$613$		−	7.53866e11i		−	0.215636i	0.994171	−	0.107818i	$-0.0343864\pi$
$614$	7.41262e10			0.0210482
$615$	5.82166e12	−	2.59119e12i	1.64100	−	0.730399i
$616$	3.35275e11			0.0938185
$617$		−	1.42132e11i		−	0.0394827i	−0.999805	−	0.0197414i	$-0.993716\pi$
$617$		−	1.42132e11i		−	0.0394827i	0.999805	−	0.0197414i	$-0.00628428\pi$
$618$		−	5.81408e10i		−	0.0160337i
$619$	1.03073e12			0.282186			0.141093	−	0.989996i	$-0.454938\pi$
$619$	1.03073e12			0.282186			0.141093	+	0.989996i	$0.454938\pi$
$620$	5.80661e11	+	1.30458e12i	0.157819	+	0.354575i
$621$	−1.23235e12			−0.332523
$622$		−	2.33100e11i		−	0.0624433i
$623$		−	4.82733e12i		−	1.28384i
$624$	1.00287e12			0.264798
$625$	−3.97033e11	−	3.79398e12i	−0.104080	−	0.994569i
$626$	1.55376e11			0.0404390
$627$			4.51604e12i			1.16695i
$628$		−	6.06419e12i		−	1.55580i
$629$	−2.86307e12			−0.729296
$630$	5.20349e10	+	1.16908e11i	0.0131602	+	0.0295672i
$631$	−4.61780e12			−1.15959			−0.579793	−	0.814764i	$-0.696867\pi$
$631$	−4.61780e12			−1.15959			−0.579793	+	0.814764i	$0.696867\pi$
$632$		−	4.02866e10i		−	0.0100446i
$633$			1.11247e12i			0.275404i
$634$	2.94422e11			0.0723717
$635$	−2.92092e12	+	1.30008e12i	−0.712916	+	0.317314i
$636$	4.39299e12			1.06464
$637$		−	7.62122e11i		−	0.183399i
$638$		−	3.02025e10i		−	0.00721688i
$639$	−8.20809e11			−0.194755
$640$	−5.76486e11	+	2.56590e11i	−0.135825	+	0.0604547i
$641$	7.51099e12			1.75726			0.878630	−	0.477503i	$-0.158458\pi$
$641$	7.51099e12			1.75726			0.878630	+	0.477503i	$0.158458\pi$
$642$			1.20634e11i			0.0280260i
$643$			4.42841e12i			1.02164i	0.859687	+	0.510821i	$0.170659\pi$
$643$			4.42841e12i			1.02164i	−0.859687	+	0.510821i	$0.829341\pi$
$644$	4.23534e12			0.970291
$645$	−2.37191e12	−	5.32901e12i	−0.539609	−	1.21235i
$646$	−1.43251e11			−0.0323632
$647$			1.09396e12i			0.245432i	0.992442	+	0.122716i	$0.0391604\pi$
$647$			1.09396e12i			0.245432i	−0.992442	+	0.122716i	$0.960840\pi$
$648$			4.12333e11i			0.0918672i
$649$	−3.11935e12			−0.690181
$650$	−2.36425e10	+	2.62458e10i	−0.00519498	+	0.00576699i
$651$	−3.12138e12			−0.681133
$652$		−	2.04467e12i		−	0.443107i
$653$			8.24881e12i			1.77534i	0.460477	+	0.887671i	$0.347678\pi$
$653$			8.24881e12i			1.77534i	−0.460477	+	0.887671i	$0.652322\pi$
$654$	−1.00339e11			−0.0214471
$655$	2.18222e12	+	4.90283e12i	0.463247	+	1.04078i
$656$	−6.63994e12			−1.39990
$657$			1.83690e11i			0.0384628i
$658$		−	2.77478e11i		−	0.0577049i
$659$	2.64086e12			0.545458			0.272729	−	0.962091i	$-0.412074\pi$
$659$	2.64086e12			0.545458			0.272729	+	0.962091i	$0.412074\pi$
$660$	−5.21430e12	+	2.32085e12i	−1.06967	+	0.476102i
$661$	8.94654e12			1.82284			0.911420	−	0.411478i	$-0.134987\pi$
$661$	8.94654e12			1.82284			0.911420	+	0.411478i	$0.134987\pi$
$662$		−	2.43683e11i		−	0.0493134i
$663$			1.15335e12i			0.231820i
$664$	−1.74308e11			−0.0347986
$665$	−6.28968e12	+	2.79950e12i	−1.24719	+	0.555114i
$666$	−1.00219e11			−0.0197386
$667$		−	7.63592e11i		−	0.149381i
$668$		−	5.57906e12i		−	1.08409i
$669$	−7.72362e12			−1.49075
$670$	1.27860e11	+	2.87265e11i	0.0245130	+	0.0550739i
$671$	5.65625e12			1.07715
$672$		−	1.03473e12i		−	0.195733i
$673$		−	6.40541e12i		−	1.20359i	−0.798650	−	0.601796i	$-0.794452\pi$
$673$		−	6.40541e12i		−	1.20359i	0.798650	−	0.601796i	$-0.205548\pi$
$674$	−1.06237e11			−0.0198293
$675$	1.88102e12	+	1.69445e12i	0.348760	+	0.314167i
$676$	5.18713e12			0.955361
$677$		−	6.41491e12i		−	1.17366i	−0.809711	−	0.586829i	$-0.800376\pi$
$677$		−	6.41491e12i		−	1.17366i	0.809711	−	0.586829i	$-0.199624\pi$
$678$			2.24153e11i			0.0407391i
$679$	−2.95796e12			−0.534046
$680$	−1.47339e11	−	3.31030e11i	−0.0264259	−	0.0593715i
$681$	4.10256e12			0.730958
$682$			7.51494e10i			0.0133014i
$683$			2.15592e12i			0.379088i	0.981872	+	0.189544i	$0.0607009\pi$
$683$			2.15592e12i			0.379088i	−0.981872	+	0.189544i	$0.939299\pi$
$684$	3.59961e12			0.628786
$685$	7.43937e12	−	3.31122e12i	1.29101	−	0.574619i
$686$	3.52297e10			0.00607366
$687$		−	9.44262e11i		−	0.161729i
$688$			6.07804e12i			1.03423i
$689$	−1.02715e12			−0.173640
$690$	1.83644e11	−	8.17387e10i	0.0308429	−	0.0137280i
$691$	−4.58074e12			−0.764336			−0.382168	−	0.924093i	$-0.624822\pi$
$691$	−4.58074e12			−0.764336			−0.382168	+	0.924093i	$0.624822\pi$
$692$			9.68009e12i			1.60473i
$693$		−	4.83433e12i		−	0.796226i
$694$	−2.49657e11			−0.0408533
$695$	−3.35230e12	−	7.53168e12i	−0.545019	−	1.22450i
$696$	−1.24339e11			−0.0200847
$697$		−	7.63624e12i		−	1.22555i
$698$			3.15191e11i			0.0502603i
$699$	−6.36704e12			−1.00877
$700$	−6.46469e12	−	5.82348e12i	−1.01767	−	0.916729i
$701$	−1.22474e12			−0.191564			−0.0957819	−	0.995402i	$-0.530535\pi$
$701$	−1.22474e12			−0.191564			−0.0957819	+	0.995402i	$0.530535\pi$
$702$		−	2.34435e10i		−	0.00364339i
$703$		−	5.39183e12i		−	0.832601i
$704$	5.93058e12			0.909956
$705$	3.84421e12	+	8.63686e12i	0.586079	+	1.31675i
$706$	4.13424e11			0.0626289
$707$			1.16685e13i			1.75642i
$708$			6.41648e12i			0.959725i
$709$	5.65887e12			0.841049			0.420525	−	0.907281i	$-0.361846\pi$
$709$	5.65887e12			0.841049			0.420525	+	0.907281i	$0.361846\pi$
$710$	−7.10276e10	+	3.16139e10i	−0.0104897	+	0.00466891i
$711$	−5.80891e11			−0.0852475
$712$			4.78466e11i			0.0697736i
$713$			1.89996e12i			0.275322i
$714$	3.95741e11			0.0569861
$715$	1.21919e12	−	5.42653e11i	0.174459	−	0.0776507i
$716$	−1.07250e13			−1.52506
$717$			1.02623e13i			1.45013i
$718$		−	3.60836e11i		−	0.0506698i
$719$	6.02904e12			0.841333			0.420667	−	0.907215i	$-0.361796\pi$
$719$	6.02904e12			0.841333			0.420667	+	0.907215i	$0.361796\pi$
$720$	1.84730e12	+	4.15037e12i	0.256178	+	0.575560i
$721$	−3.34846e12			−0.461462
$722$			2.55506e9i			0.000349933i
$723$		−	6.98820e12i		−	0.951137i
$724$	−3.66568e12			−0.495827
$725$	−1.04992e12	+	1.16552e12i	−0.141135	+	0.156675i
$726$	5.63629e10			0.00752971
$727$		−	2.63469e12i		−	0.349805i	−0.984586	−	0.174902i	$-0.944039\pi$
$727$		−	2.63469e12i		−	0.349805i	0.984586	−	0.174902i	$-0.0559609\pi$
$728$			1.61254e11i			0.0212774i
$729$	1.37180e12			0.179894
$730$	7.07493e9	+	1.58954e10i	0.000922081	+	0.00207166i
$731$	−6.99002e12			−0.905421
$732$		−	1.16349e13i		−	1.49783i
$733$			5.28609e12i			0.676343i	0.941085	+	0.338171i	$0.109808\pi$
$733$			5.28609e12i			0.676343i	−0.941085	+	0.338171i	$0.890192\pi$
$734$	2.14702e10			0.00273026
$735$	8.13955e12	−	3.62286e12i	1.02874	−	0.457888i
$736$	−6.29831e11			−0.0791178
$737$		−	1.18789e13i		−	1.48310i
$738$		−	2.67300e11i		−	0.0331700i
$739$	−2.51810e12			−0.310580			−0.155290	−	0.987869i	$-0.549631\pi$
$739$	−2.51810e12			−0.310580			−0.155290	+	0.987869i	$0.549631\pi$
$740$	6.22550e12	−	2.77093e12i	0.763188	−	0.339690i
$741$	−2.17203e12			−0.264657
$742$			3.52440e11i			0.0426843i
$743$			7.02537e11i			0.0845706i	0.999106	+	0.0422853i	$0.0134638\pi$
$743$			7.02537e11i			0.0845706i	−0.999106	+	0.0422853i	$0.986536\pi$
$744$	3.09379e11			0.0370179
$745$	3.06497e12	+	6.88612e12i	0.364521	+	0.818976i
$746$	−6.12705e11			−0.0724314
$747$			2.51335e12i			0.295331i
$748$			6.83956e12i			0.798861i
$749$	6.94755e12			0.806610
$750$	−3.92697e11	−	1.27742e11i	−0.0453191	−	0.0147420i
$751$	4.60108e12			0.527813			0.263907	−	0.964548i	$-0.414989\pi$
$751$	4.60108e12			0.527813			0.263907	+	0.964548i	$0.414989\pi$
$752$		−	9.85083e12i		−	1.12329i
$753$		−	8.19042e12i		−	0.928387i
$754$	1.45261e10			0.00163674
$755$	−4.50200e11	−	1.01147e12i	−0.0504248	−	0.113290i
$756$	5.77445e12			0.642928
$757$			3.05764e12i			0.338419i	0.985580	+	0.169210i	$0.0541215\pi$
$757$			3.05764e12i			0.338419i	−0.985580	+	0.169210i	$0.945878\pi$
$758$		−	2.33518e11i		−	0.0256927i
$759$	−7.59398e12			−0.830580
$760$	6.23408e11	−	2.77475e11i	0.0677815	−	0.0301691i
$761$	−9.86753e12			−1.06654			−0.533270	−	0.845945i	$-0.679037\pi$
$761$	−9.86753e12			−1.06654			−0.533270	+	0.845945i	$0.679037\pi$
$762$			3.46104e11i			0.0371886i
$763$			5.77872e12i			0.617264i
$764$	8.96293e12			0.951765
$765$	−4.77312e12	+	2.12448e12i	−0.503878	+	0.224273i
$766$	1.44435e11			0.0151580
$767$		−	1.50028e12i		−	0.156528i
$768$		−	1.21478e13i		−	1.26001i
$769$	−1.65694e13			−1.70859			−0.854294	−	0.519790i	$-0.826010\pi$
$769$	−1.65694e13			−1.70859			−0.854294	+	0.519790i	$0.826010\pi$
$770$	−1.86197e11	−	4.18332e11i	−0.0190882	−	0.0428857i
$771$	−2.32961e12			−0.237432
$772$			1.60303e13i			1.62429i
$773$			1.10674e13i			1.11490i	0.830210	+	0.557451i	$0.188221\pi$
$773$			1.10674e13i			1.11490i	−0.830210	+	0.557451i	$0.811779\pi$
$774$	−2.44680e11			−0.0245055
$775$	2.61239e12	−	2.90004e12i	0.260124	−	0.288766i
$776$	2.93181e11			0.0290241
$777$			1.48953e13i			1.46607i
$778$			3.31150e10i			0.00324054i
$779$	1.43808e13			1.39915
$780$	−1.11623e12	−	2.50786e12i	−0.107977	−	0.242593i
$781$	2.93711e12			0.282482
$782$		−	2.40884e11i		−	0.0230345i
$783$		−	1.04108e12i		−	0.0989819i
$784$	−9.28363e12			−0.877598
$785$	−1.51434e13	+	6.74025e12i	−1.42335	+	0.633523i
$786$	5.80943e11			0.0542915
$787$			1.67201e12i			0.155365i	0.996978	+	0.0776825i	$0.0247520\pi$
$787$			1.67201e12i			0.155365i	−0.996978	+	0.0776825i	$0.975248\pi$
$788$		−	9.50846e12i		−	0.878501i
$789$	8.60646e12			0.790638
$790$	−5.02666e10	+	2.23734e10i	−0.00459154	+	0.00204366i
$791$	1.29095e13			1.17250
$792$			4.79159e11i			0.0432730i
$793$			2.72042e12i			0.244291i
$794$	−3.30303e11			−0.0294931
$795$	−4.88274e12	−	1.09701e13i	−0.433522	−	0.974003i
$796$	6.47609e12			0.571748
$797$		−	6.97864e12i		−	0.612644i	−0.951928	−	0.306322i	$-0.900902\pi$
$797$		−	6.97864e12i		−	0.612644i	0.951928	−	0.306322i	$-0.0990985\pi$
$798$			7.45273e11i			0.0650582i
$799$	1.13289e13			0.983394
$800$	9.61355e11	+	8.66001e11i	0.0829811	+	0.0747504i
$801$	6.89899e12			0.592160
$802$			4.26165e11i			0.0363742i
$803$		−	6.57300e11i		−	0.0557884i
$804$	−2.44348e13			−2.06232
$805$	−4.70751e12	−	1.05764e13i	−0.395102	−	0.887684i
$806$	−3.61437e10			−0.00301665
$807$		−	1.79052e13i		−	1.48610i
$808$		−	1.15654e12i		−	0.0954570i
$809$	−5.27673e12			−0.433108			−0.216554	−	0.976271i	$-0.569482\pi$
$809$	−5.27673e12			−0.433108			−0.216554	+	0.976271i	$0.569482\pi$
$810$	5.14479e11	−	2.28991e11i	0.0419938	−	0.0186912i
$811$	−1.43675e12			−0.116624			−0.0583118	−	0.998298i	$-0.518572\pi$
$811$	−1.43675e12			−0.116624			−0.0583118	+	0.998298i	$0.518572\pi$
$812$			3.57798e12i			0.288826i
$813$			8.60851e12i			0.691068i
$814$	3.58615e11			0.0286298
$815$	−5.10592e12	+	2.27261e12i	−0.405383	+	0.180433i
$816$	1.40493e13			1.10930
$817$		−	1.31639e13i		−	1.03367i
$818$			7.97525e9i			0.000622809i
$819$	2.32511e12			0.180578
$820$	7.39049e12	+	1.66044e13i	0.570836	+	1.28251i
$821$	9.44899e12			0.725840			0.362920	−	0.931820i	$-0.381780\pi$
$821$	9.44899e12			0.725840			0.362920	+	0.931820i	$0.381780\pi$
$822$		−	8.81502e11i		−	0.0673442i
$823$		−	1.20237e13i		−	0.913562i	−0.889579	−	0.456781i	$-0.849002\pi$
$823$		−	1.20237e13i		−	0.913562i	0.889579	−	0.456781i	$-0.150998\pi$
$824$	3.31886e11			0.0250794
$825$	1.15912e13	+	1.04415e13i	0.871136	+	0.784731i
$826$	−5.14780e11			−0.0384779
$827$			7.86848e12i			0.584947i	0.956274	+	0.292473i	$0.0944782\pi$
$827$			7.86848e12i			0.584947i	−0.956274	+	0.292473i	$0.905522\pi$
$828$			6.05294e12i			0.447538i
$829$	−4.86184e12			−0.357524			−0.178762	−	0.983892i	$-0.557209\pi$
$829$	−4.86184e12			−0.357524			−0.178762	+	0.983892i	$0.557209\pi$
$830$	9.68029e10	+	2.17489e11i	0.00708006	+	0.0159069i
$831$	3.18798e12			0.231905
$832$			2.85236e12i			0.206372i
$833$		−	1.06766e13i		−	0.768299i
$834$	−8.92439e11			−0.0638750
$835$	−1.39320e13	+	6.20103e12i	−0.991798	+	0.441443i
$836$	−1.28805e13			−0.912021
$837$			2.59040e12i			0.182432i
$838$		−	4.87232e10i		−	0.00341301i
$839$	−1.76025e13			−1.22644			−0.613218	−	0.789914i	$-0.710125\pi$
$839$	−1.76025e13			−1.22644			−0.613218	+	0.789914i	$0.710125\pi$
$840$	−1.72221e12	+	7.66544e11i	−0.119352	+	0.0531227i
$841$	−1.38621e13			−0.955534
$842$		−	3.70471e9i		−	0.000254009i
$843$			2.72559e13i			1.85881i
$844$	−3.17294e12			−0.215239
$845$	−5.76541e12	−	1.29533e13i	−0.389023	−	0.874025i
$846$	3.96558e11			0.0266159
$847$		−	3.24606e12i		−	0.216711i
$848$			1.25121e13i			0.830899i
$849$	3.34744e13			2.21120
$850$	−3.31209e11	+	3.67679e11i	−0.0217629	+	0.0241592i
$851$	9.06666e12			0.592604
$852$		−	6.04161e12i		−	0.392802i
$853$			9.20458e11i			0.0595296i	0.999557	+	0.0297648i	$0.00947584\pi$
$853$			9.20458e11i			0.0595296i	−0.999557	+	0.0297648i	$0.990524\pi$
$854$	9.33439e11			0.0600517
$855$	−4.00090e12	−	8.98890e12i	−0.256042	−	0.575253i
$856$	−6.88614e11			−0.0438373
$857$			2.35047e13i			1.48847i	0.667915	+	0.744237i	$0.267187\pi$
$857$			2.35047e13i			1.48847i	−0.667915	+	0.744237i	$0.732813\pi$
$858$		−	1.44463e11i		−	0.00910050i
$859$	2.02385e13			1.26826			0.634132	−	0.773225i	$-0.281357\pi$
$859$	2.02385e13			1.26826			0.634132	+	0.773225i	$0.281357\pi$
$860$	1.51992e13	−	6.76508e12i	0.947498	−	0.421725i
$861$	−3.97281e13			−2.46367
$862$		−	8.39281e11i		−	0.0517756i
$863$		−	3.07364e13i		−	1.88627i	−0.332406	−	0.943136i	$-0.607860\pi$
$863$		−	3.07364e13i		−	1.88627i	0.332406	−	0.943136i	$-0.392140\pi$
$864$	−8.58710e11			−0.0524245
$865$	2.41730e13	−	1.07593e13i	1.46811	−	0.653446i
$866$	−1.61715e11			−0.00977055
$867$		−	5.10107e12i		−	0.306602i
$868$		−	8.90269e12i		−	0.532332i
$869$	2.07861e12			0.123647
$870$	6.90522e10	+	1.55141e11i	0.00408640	+	0.00918100i
$871$	5.71325e12			0.336358
$872$		−	5.72763e11i		−	0.0335468i
$873$		−	4.22737e12i		−	0.246324i
$874$	4.53642e11			0.0262973
$875$	−7.35693e12	+	2.26163e13i	−0.424288	+	1.30432i
$876$	−1.35206e12			−0.0775760
$877$			6.65840e12i			0.380077i	0.981777	+	0.190039i	$0.0608613\pi$
$877$			6.65840e12i			0.380077i	−0.981777	+	0.190039i	$0.939139\pi$
$878$			1.16635e12i			0.0662373i
$879$	−2.31120e13			−1.30584
$880$	−6.61022e12	−	1.48513e13i	−0.371573	−	0.834820i
$881$	3.41842e12			0.191176			0.0955882	−	0.995421i	$-0.469527\pi$
$881$	3.41842e12			0.191176			0.0955882	+	0.995421i	$0.469527\pi$
$882$		−	3.73725e11i		−	0.0207943i
$883$		−	1.92500e13i		−	1.06563i	−0.846231	−	0.532815i	$-0.821134\pi$
$883$		−	1.92500e13i		−	1.06563i	0.846231	−	0.532815i	$-0.178866\pi$
$884$	−3.28955e12			−0.181176
$885$	1.60232e13	−	7.13181e12i	0.878018	−	0.390800i
$886$	−2.57960e11			−0.0140637
$887$			1.48977e13i			0.808095i	0.914738	+	0.404048i	$0.132397\pi$
$887$			1.48977e13i			0.808095i	−0.914738	+	0.404048i	$0.867603\pi$
$888$		−	1.47636e12i		−	0.0796774i
$889$	1.99329e13			1.07032
$890$	5.96995e11	−	2.65718e11i	0.0318945	−	0.0141960i
$891$	−2.12745e13			−1.13086
$892$		−	2.20291e13i		−	1.16508i
$893$			2.13350e13i			1.12269i
$894$	8.15946e11			0.0427211
$895$	1.19206e13	+	2.67822e13i	0.621004	+	1.39522i
$896$	3.93404e12			0.203917
$897$		−	3.65239e12i		−	0.188370i
$898$			1.26185e12i			0.0647534i
$899$	−1.60507e12			−0.0819551
$900$	8.32263e12	−	9.23902e12i	0.422833	−	0.469391i
$901$	−1.43895e13			−0.727416
$902$			9.56481e11i			0.0481113i
$903$			3.63661e13i			1.82013i
$904$	−1.27954e12			−0.0637228
$905$	4.07434e12	+	9.15389e12i	0.201901	+	0.453615i
$906$	−1.19851e11			−0.00590968
$907$		−	1.11529e13i		−	0.547210i	−0.961842	−	0.273605i	$-0.911784\pi$
$907$		−	1.11529e13i		−	0.547210i	0.961842	−	0.273605i	$-0.0882162\pi$
$908$			1.17012e13i			0.571273i
$909$	−1.66760e13			−0.810132
$910$	2.01200e11	−	8.95530e10i	0.00972618	−	0.00432906i
$911$	−2.25248e12			−0.108350			−0.0541750	−	0.998531i	$-0.517253\pi$
$911$	−2.25248e12			−0.108350			−0.0541750	+	0.998531i	$0.517253\pi$
$912$			2.64581e13i			1.26643i
$913$		−	8.99353e12i		−	0.428363i
$914$	−9.95663e11			−0.0471905
$915$	−2.90545e13	+	1.29320e13i	−1.37031	+	0.609915i
$916$	2.69319e12			0.126397
$917$		−	3.34578e13i		−	1.56255i
$918$		−	3.28421e11i		−	0.0152630i
$919$	−1.40633e13			−0.650380			−0.325190	−	0.945649i	$-0.605428\pi$
$919$	−1.40633e13			−0.650380			−0.325190	+	0.945649i	$0.605428\pi$
$920$	4.66590e11	+	1.04830e12i	0.0214729	+	0.0482435i
$921$	1.57452e13			0.721075
$922$		−	1.30318e12i		−	0.0593901i
$923$			1.41263e12i			0.0640649i
$924$	3.55833e13			1.60591
$925$	−1.38391e13	−	1.24664e13i	−0.621540	−	0.559891i
$926$	−3.84644e11			−0.0171913
$927$		−	4.78545e12i		−	0.212845i
$928$		−	5.32077e11i		−	0.0235509i
$929$	−1.04912e13			−0.462118			−0.231059	−	0.972940i	$-0.574219\pi$
$929$	−1.04912e13			−0.462118			−0.231059	+	0.972940i	$0.574219\pi$
$930$	−1.71815e11	−	3.86020e11i	−0.00753161	−	0.0169214i
$931$	2.01066e13			0.877130
$932$		−	1.81599e13i		−	0.788389i
$933$		−	4.95131e13i		−	2.13920i
$934$	−5.88518e11			−0.0253045
$935$	1.70797e13	−	7.60206e12i	0.730849	−	0.325296i
$936$	−2.30456e11			−0.00981400
$937$			3.77841e13i			1.60133i	0.599111	+	0.800666i	$0.295521\pi$
$937$			3.77841e13i			1.60133i	−0.599111	+	0.800666i	$0.704479\pi$
$938$		−	1.96035e12i		−	0.0826837i
$939$	3.30036e13			1.38537
$940$	−2.46338e13	+	1.09643e13i	−1.02909	+	0.458043i
$941$	1.11142e13			0.462088			0.231044	−	0.972943i	$-0.425786\pi$
$941$	1.11142e13			0.462088			0.231044	+	0.972943i	$0.425786\pi$
$942$			1.79437e12i			0.0742476i
$943$			2.41822e13i			0.995847i
$944$	−1.82753e13			−0.749017
$945$	−6.41820e12	−	1.44199e13i	−0.261800	−	0.588192i
$946$	8.75539e11			0.0355439
$947$			4.96563e12i			0.200631i	0.994956	+	0.100316i	$0.0319853\pi$
$947$			4.96563e12i			0.200631i	−0.994956	+	0.100316i	$0.968015\pi$
$948$		−	4.27568e12i		−	0.171936i
$949$	3.16134e11			0.0126524
$950$	−6.92425e11	−	6.23745e11i	−0.0275814	−	0.0248457i
$951$	6.25385e13			2.47933
$952$			2.25901e12i			0.0891357i
$953$		−	3.02750e13i		−	1.18896i	−0.804111	−	0.594479i	$-0.797358\pi$
$953$		−	3.02750e13i		−	1.18896i	0.804111	−	0.594479i	$-0.202642\pi$
$954$	−5.03690e11			−0.0196877
$955$	−9.96214e12	−	2.23821e13i	−0.387559	−	0.870736i
$956$	−2.92698e13			−1.13334
$957$		−	6.41533e12i		−	0.247238i
$958$			2.05476e11i			0.00788162i
$959$	−5.07676e13			−1.93822
$960$	−3.04636e13	+	1.35592e13i	−1.15761	+	0.515243i
$961$	−2.24459e13			−0.848949
$962$			1.72479e11i			0.00649304i
$963$			9.92910e12i			0.372042i
$964$	1.99315e13			0.743351
$965$	4.00307e13	−	1.78174e13i	1.48601	−	0.661412i
$966$	−1.25322e12			−0.0463052
$967$			2.48487e13i			0.913869i	0.889500	+	0.456934i	$0.151053\pi$
$967$			2.48487e13i			0.913869i	−0.889500	+	0.456934i	$0.848947\pi$
$968$			3.21737e11i			0.0117777i
$969$	−3.04281e13			−1.10871
$970$	−1.62820e11	−	3.65810e11i	−0.00590519	−	0.0132673i
$971$	4.43278e13			1.60026			0.800128	−	0.599829i	$-0.204765\pi$
$971$	4.43278e13			1.60026			0.800128	+	0.599829i	$0.204765\pi$
$972$			3.07168e13i			1.10377i
$973$			5.13975e13i			1.83837i
$974$	1.32466e12			0.0471618
$975$	−5.02193e12	+	5.57489e12i	−0.177971	+	0.197568i
$976$	3.31383e13			1.16898
$977$		−	9.73746e11i		−	0.0341917i	−0.999854	−	0.0170958i	$-0.994558\pi$
$977$		−	9.73746e11i		−	0.0341917i	0.999854	−	0.0170958i	$-0.00544204\pi$
$978$			6.05008e11i			0.0211464i
$979$	−2.46867e13			−0.858897
$980$	1.03330e13	+	2.32154e13i	0.357857	+	0.804004i
$981$	−8.25866e12			−0.284708
$982$		−	5.50985e11i		−	0.0189077i
$983$			2.85792e13i			0.976247i	0.872775	+	0.488123i	$0.162318\pi$
$983$			2.85792e13i			0.976247i	−0.872775	+	0.488123i	$0.837682\pi$
$984$	3.93769e12			0.133895
$985$	−2.37444e13	+	1.05685e13i	−0.803709	+	0.357726i
$986$	2.03497e11			0.00685666
$987$		−	5.89394e13i		−	1.97687i
$988$		−	6.19499e12i		−	0.206840i
$989$	2.21358e13			0.735718
$990$	5.97859e11	−	2.66103e11i	0.0197807	−	0.00880424i
$991$	−3.49036e13			−1.14958			−0.574789	−	0.818302i	$-0.694916\pi$
$991$	−3.49036e13			−1.14958			−0.574789	+	0.818302i	$0.694916\pi$
$992$			1.32391e12i			0.0434065i
$993$		−	5.17610e13i		−	1.68940i
$994$	4.84705e11			0.0157485
$995$	−7.19807e12	−	1.61720e13i	−0.232816	−	0.523071i
$996$	−1.84996e13			−0.595656
$997$		−	8.78834e12i		−	0.281695i	−0.990031	−	0.140847i	$-0.955017\pi$
$997$		−	8.78834e12i		−	0.281695i	0.990031	−	0.140847i	$-0.0449827\pi$
$998$		−	6.34194e11i		−	0.0202365i
$999$	1.23615e13			0.392668

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	5.10.b.a.4.2	✓	4
3.2	odd	2		45.10.b.b.19.3		4
4.3	odd	2		80.10.c.c.49.4		4
5.2	odd	4		25.10.a.e.1.3		4
5.3	odd	4		25.10.a.e.1.2		4
5.4	even	2	inner	5.10.b.a.4.3	yes	4
15.2	even	4		225.10.a.s.1.2		4
15.8	even	4		225.10.a.s.1.3		4
15.14	odd	2		45.10.b.b.19.2		4
20.3	even	4		400.10.a.ba.1.1		4
20.7	even	4		400.10.a.ba.1.4		4
20.19	odd	2		80.10.c.c.49.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
5.10.b.a.4.2	✓	4	1.1	even	1	trivial
5.10.b.a.4.3	yes	4	5.4	even	2	inner
25.10.a.e.1.2		4	5.3	odd	4
25.10.a.e.1.3		4	5.2	odd	4
45.10.b.b.19.2		4	15.14	odd	2
45.10.b.b.19.3		4	3.2	odd	2
80.10.c.c.49.1		4	20.19	odd	2
80.10.c.c.49.4		4	4.3	odd	2
225.10.a.s.1.2		4	15.2	even	4
225.10.a.s.1.3		4	15.8	even	4
400.10.a.ba.1.1		4	20.3	even	4
400.10.a.ba.1.4		4	20.7	even	4

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:	\( N \)	\(=\)	\( 5 \)
Weight:	\( k \)	\(=\)	\( 10 \)
Character orbit:	\([\chi]\)	\(=\)	5.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-0.843944i q^{2} -179.263i q^{3} +511.288 q^{4} +(-568.288 - 1276.78i) q^{5} -151.288 q^{6} +8712.99i q^{7} -863.597i q^{8} -12452.2 q^{9} +O(q^{10})\)	\(q-0.843944i q^{2} -179.263i q^{3} +511.288 q^{4} +(-568.288 - 1276.78i) q^{5} -151.288 q^{6} +8712.99i q^{7} -863.597i q^{8} -12452.2 q^{9} +(-1077.53 + 479.603i) q^{10} +44557.8 q^{11} -91654.9i q^{12} +21430.4i q^{13} +7353.27 q^{14} +(-228880. + 101873. i) q^{15} +261051. q^{16} +300220. i q^{17} +10508.9i q^{18} -565385. q^{19} +(-290559. - 652803. i) q^{20} +1.56192e6 q^{21} -37604.2i q^{22} -950727. i q^{23} -154811. q^{24} +(-1.30722e6 + 1.45116e6i) q^{25} +18086.1 q^{26} -1.29622e6i q^{27} +4.45485e6i q^{28} +803167. q^{29} +(85975.0 + 193162. i) q^{30} -1.99843e6 q^{31} -662474. i q^{32} -7.98755e6i q^{33} +253369. q^{34} +(1.11246e7 - 4.95149e6i) q^{35} -6.36665e6 q^{36} +9.53656e6i q^{37} +477153. i q^{38} +3.84168e6 q^{39} +(-1.10263e6 + 490772. i) q^{40} -2.54355e7 q^{41} -1.31817e6i q^{42} +2.32830e7i q^{43} +2.27818e7 q^{44} +(7.07642e6 + 1.58987e7i) q^{45} -802360. q^{46} -3.77353e7i q^{47} -4.67967e7i q^{48} -3.55626e7 q^{49} +(1.22470e6 + 1.10322e6i) q^{50} +5.38183e7 q^{51} +1.09571e7i q^{52} +4.79297e7i q^{53} -1.09393e6 q^{54} +(-2.53216e7 - 5.68906e7i) q^{55} +7.52451e6 q^{56} +1.01353e8i q^{57} -677827. i q^{58} -7.00069e7 q^{59} +(-1.17023e8 + 5.20864e7i) q^{60} +1.26942e8 q^{61} +1.68656e6i q^{62} -1.08496e8i q^{63} +1.33099e8 q^{64} +(2.73620e7 - 1.21787e7i) q^{65} -6.74104e6 q^{66} -2.66595e8i q^{67} +1.53499e8i q^{68} -1.70430e8 q^{69} +(-4.17877e6 - 9.38853e6i) q^{70} +6.59169e7 q^{71} +1.07537e7i q^{72} -1.47516e7i q^{73} +8.04832e6 q^{74} +(2.60139e8 + 2.34337e8i) q^{75} -2.89074e8 q^{76} +3.88231e8i q^{77} -3.24216e6i q^{78} +4.66498e7 q^{79} +(-1.48352e8 - 3.33305e8i) q^{80} -4.77460e8 q^{81} +2.14661e7i q^{82} -2.01840e8i q^{83} +7.98588e8 q^{84} +(3.83316e8 - 1.70611e8i) q^{85} +1.96495e7 q^{86} -1.43978e8i q^{87} -3.84800e7i q^{88} -5.54039e8 q^{89} +(1.34176e7 - 5.97210e6i) q^{90} -1.86723e8 q^{91} -4.86095e8i q^{92} +3.58244e8i q^{93} -3.18465e7 q^{94} +(3.21301e8 + 7.21874e8i) q^{95} -1.18757e8 q^{96} +3.39489e8i q^{97} +3.00128e7i q^{98} -5.54841e8 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 1368 q^{4} + 1140 q^{5} + 2808 q^{6} + 11628 q^{9}+O(q^{10}) \) 4 * q - 1368 * q^4 + 1140 * q^5 + 2808 * q^6 + 11628 * q^9	\( 4 q - 1368 q^{4} + 1140 q^{5} + 2808 q^{6} + 11628 q^{9} - 69160 q^{10} + 109968 q^{11} - 424536 q^{14} - 396720 q^{15} + 1631264 q^{16} - 636880 q^{19} - 3302280 q^{20} + 3523968 q^{21} - 2435040 q^{24} - 1337900 q^{25} + 6618768 q^{26} - 3531720 q^{29} + 3712680 q^{30} - 10587712 q^{31} + 26434624 q^{34} + 13629840 q^{35} - 56399976 q^{36} + 1686816 q^{39} + 43578400 q^{40} - 16788552 q^{41} + 20638944 q^{44} + 55737180 q^{45} - 61250072 q^{46} - 46921028 q^{49} - 150092400 q^{50} + 84017088 q^{51} + 115855920 q^{54} - 26907120 q^{55} + 315178080 q^{56} - 460829040 q^{59} - 307006560 q^{60} + 360490568 q^{61} + 134995072 q^{64} + 183895680 q^{65} + 18949536 q^{66} - 286524864 q^{69} - 508341960 q^{70} - 47611872 q^{71} + 1176861744 q^{74} + 659239200 q^{75} - 1168489440 q^{76} - 728043520 q^{79} + 965843040 q^{80} - 343387836 q^{81} + 1118898144 q^{84} + 1275419840 q^{85} - 2375904552 q^{86} - 1582700760 q^{89} - 1197088920 q^{90} + 473322528 q^{91} + 3327101704 q^{94} + 1204791600 q^{95} + 399339648 q^{96} - 728787024 q^{99}+O(q^{100}) \) 4 * q - 1368 * q^4 + 1140 * q^5 + 2808 * q^6 + 11628 * q^9 - 69160 * q^10 + 109968 * q^11 - 424536 * q^14 - 396720 * q^15 + 1631264 * q^16 - 636880 * q^19 - 3302280 * q^20 + 3523968 * q^21 - 2435040 * q^24 - 1337900 * q^25 + 6618768 * q^26 - 3531720 * q^29 + 3712680 * q^30 - 10587712 * q^31 + 26434624 * q^34 + 13629840 * q^35 - 56399976 * q^36 + 1686816 * q^39 + 43578400 * q^40 - 16788552 * q^41 + 20638944 * q^44 + 55737180 * q^45 - 61250072 * q^46 - 46921028 * q^49 - 150092400 * q^50 + 84017088 * q^51 + 115855920 * q^54 - 26907120 * q^55 + 315178080 * q^56 - 460829040 * q^59 - 307006560 * q^60 + 360490568 * q^61 + 134995072 * q^64 + 183895680 * q^65 + 18949536 * q^66 - 286524864 * q^69 - 508341960 * q^70 - 47611872 * q^71 + 1176861744 * q^74 + 659239200 * q^75 - 1168489440 * q^76 - 728043520 * q^79 + 965843040 * q^80 - 343387836 * q^81 + 1118898144 * q^84 + 1275419840 * q^85 - 2375904552 * q^86 - 1582700760 * q^89 - 1197088920 * q^90 + 473322528 * q^91 + 3327101704 * q^94 + 1204791600 * q^95 + 399339648 * q^96 - 728787024 * q^99

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