LMFDB - Embedded newform 100.9.b.d.51.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [100,9,Mod(51,100)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(100, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 0]))

N = Newforms(chi, 9, names="a")

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

chi := DirichletCharacter("100.51");

S:= CuspForms(chi, 9);

N := Newforms(S);

Level:	$ N $	$=$	$ 100 = 2^{2} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 9 $
Character orbit:	$[\chi]$	$=$	100.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:	$40.7378610061$
Analytic rank:	$0$
Dimension:	$16$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 5 x^{15} + 26 x^{14} - 834 x^{13} + 4390 x^{12} - 61783 x^{11} + 466168 x^{10} + \cdots + 206161212459445 $ x^16 - 5x^15 + 26x^14 - 834x^13 + 4390x^12 - 61783x^11 + 466168x^10 - 1105435x^9 + 46850799x^8 - 116275535x^7 + 626274432x^6 - 8558999923x^5 + 34408048994x^4 - 448299413930x^3 + 1712647133330x^2 + 15986651928135*x + 206161212459445
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{61}\cdot 5^{16} $
Twist minimal:	no (minimal twist has level 20)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			51.2
Root			$-5.64565 - 3.35245i$ of defining polynomial
Character	$\chi$	$=$	100.51
Dual form			100.9.b.d.51.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-14.5274 + 6.70489i) q^{2} +150.211i q^{3} +(166.089 - 194.809i) q^{4} +(-1007.15 - 2182.17i) q^{6} -2626.96i q^{7} +(-1106.66 + 3943.67i) q^{8} -16002.3 q^{9} +O(q^{10})$	\(q+(-14.5274 + 6.70489i) q^{2} +150.211i q^{3} +(166.089 - 194.809i) q^{4} +(-1007.15 - 2182.17i) q^{6} -2626.96i q^{7} +(-1106.66 + 3943.67i) q^{8} -16002.3 q^{9} +2300.68i q^{11} +(29262.4 + 24948.4i) q^{12} -47058.2 q^{13} +(17613.5 + 38162.8i) q^{14} +(-10365.0 - 64711.2i) q^{16} +51967.0 q^{17} +(232472. - 107294. i) q^{18} -59554.7i q^{19} +394598. q^{21} +(-15425.8 - 33422.9i) q^{22} -77570.5i q^{23} +(-592382. - 166233. i) q^{24} +(683632. - 315520. i) q^{26} -1.41819e6i q^{27} +(-511754. - 436308. i) q^{28} +902211. q^{29} +340014. i q^{31} +(584457. + 870587. i) q^{32} -345588. q^{33} +(-754943. + 348433. i) q^{34} +(-2.65781e6 + 3.11740e6i) q^{36} +584324. q^{37} +(399308. + 865173. i) q^{38} -7.06866e6i q^{39} +293985. q^{41} +(-5.73247e6 + 2.64573e6i) q^{42} +2.95292e6i q^{43} +(448194. + 382118. i) q^{44} +(520102. + 1.12689e6i) q^{46} -5.03746e6i q^{47} +(9.72033e6 - 1.55693e6i) q^{48} -1.13610e6 q^{49} +7.80601e6i q^{51} +(-7.81585e6 + 9.16736e6i) q^{52} +7.54985e6 q^{53} +(9.50883e6 + 2.06026e7i) q^{54} +(1.03598e7 + 2.90715e6i) q^{56} +8.94577e6 q^{57} +(-1.31068e7 + 6.04923e6i) q^{58} +8.82594e6i q^{59} +1.08173e7 q^{61} +(-2.27976e6 - 4.93951e6i) q^{62} +4.20375e7i q^{63} +(-1.43278e7 - 8.72861e6i) q^{64} +(5.02049e6 - 2.31713e6i) q^{66} -1.44347e7i q^{67} +(8.63113e6 - 1.01236e7i) q^{68} +1.16519e7 q^{69} -3.71149e6i q^{71} +(1.77092e7 - 6.31079e7i) q^{72} +3.62775e7 q^{73} +(-8.48869e6 + 3.91783e6i) q^{74} +(-1.16018e7 - 9.89137e6i) q^{76} +6.04380e6 q^{77} +(4.73946e7 + 1.02689e8i) q^{78} +4.88562e7i q^{79} +1.08037e8 q^{81} +(-4.27083e6 + 1.97114e6i) q^{82} -6.93862e7i q^{83} +(6.55383e7 - 7.68711e7i) q^{84} +(-1.97990e7 - 4.28982e7i) q^{86} +1.35522e8i q^{87} +(-9.07314e6 - 2.54608e6i) q^{88} -1.05906e8 q^{89} +1.23620e8i q^{91} +(-1.51114e7 - 1.28836e7i) q^{92} -5.10738e7 q^{93} +(3.37756e7 + 7.31810e7i) q^{94} +(-1.30772e8 + 8.77919e7i) q^{96} -1.33519e8 q^{97} +(1.65045e7 - 7.61742e6i) q^{98} -3.68163e7i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 6 q^{2} - 52 q^{4} + 4368 q^{6} + 14184 q^{8} - 38800 q^{9}+O(q^{10}) $ 16 * q - 6 * q^2 - 52 * q^4 + 4368 * q^6 + 14184 * q^8 - 38800 * q^9	$ 16 q - 6 q^{2} - 52 q^{4} + 4368 q^{6} + 14184 q^{8} - 38800 q^{9} + 64040 q^{12} - 51392 q^{13} + 68472 q^{14} - 81424 q^{16} - 27552 q^{17} + 616994 q^{18} + 414496 q^{21} + 389120 q^{22} + 163792 q^{24} + 1037124 q^{26} - 1288520 q^{28} + 2764896 q^{29} + 4379904 q^{32} + 5521600 q^{33} + 3793964 q^{34} - 5468916 q^{36} - 9009472 q^{37} + 3087360 q^{38} - 8576448 q^{41} + 4067400 q^{42} + 16921200 q^{44} - 7974152 q^{46} + 2696640 q^{48} - 32803600 q^{49} - 6679352 q^{52} - 2452032 q^{53} + 8898704 q^{54} + 34134768 q^{56} - 11957760 q^{57} - 52156572 q^{58} + 8371712 q^{61} - 1290000 q^{62} - 47543872 q^{64} + 19358000 q^{66} - 16095192 q^{68} + 7527264 q^{69} + 42242664 q^{72} - 61907232 q^{73} - 138210876 q^{74} + 2570400 q^{76} + 156997440 q^{77} + 104032400 q^{78} + 140586672 q^{81} - 83921012 q^{82} + 69761824 q^{84} - 101724672 q^{86} - 44728480 q^{88} + 106647456 q^{89} + 13876200 q^{92} - 105563840 q^{93} + 55264632 q^{94} - 453389952 q^{96} - 171851232 q^{97} + 285387714 q^{98}+O(q^{100}) $ 16 * q - 6 * q^2 - 52 * q^4 + 4368 * q^6 + 14184 * q^8 - 38800 * q^9 + 64040 * q^12 - 51392 * q^13 + 68472 * q^14 - 81424 * q^16 - 27552 * q^17 + 616994 * q^18 + 414496 * q^21 + 389120 * q^22 + 163792 * q^24 + 1037124 * q^26 - 1288520 * q^28 + 2764896 * q^29 + 4379904 * q^32 + 5521600 * q^33 + 3793964 * q^34 - 5468916 * q^36 - 9009472 * q^37 + 3087360 * q^38 - 8576448 * q^41 + 4067400 * q^42 + 16921200 * q^44 - 7974152 * q^46 + 2696640 * q^48 - 32803600 * q^49 - 6679352 * q^52 - 2452032 * q^53 + 8898704 * q^54 + 34134768 * q^56 - 11957760 * q^57 - 52156572 * q^58 + 8371712 * q^61 - 1290000 * q^62 - 47543872 * q^64 + 19358000 * q^66 - 16095192 * q^68 + 7527264 * q^69 + 42242664 * q^72 - 61907232 * q^73 - 138210876 * q^74 + 2570400 * q^76 + 156997440 * q^77 + 104032400 * q^78 + 140586672 * q^81 - 83921012 * q^82 + 69761824 * q^84 - 101724672 * q^86 - 44728480 * q^88 + 106647456 * q^89 + 13876200 * q^92 - 105563840 * q^93 + 55264632 * q^94 - 453389952 * q^96 - 171851232 * q^97 + 285387714 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/100\mathbb{Z}\right)^\times$.

$n$	$51$	$77$
$\chi(n)$	$-1$	$1$

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 $

$2$	−14.5274	+	6.70489i	−0.907961	+	0.419056i
$2$	−14.5274	+	6.70489i	−0.907961	+	0.419056i
$3$			150.211i			1.85446i	0.374496	+	0.927228i	$0.377816\pi$
$3$			150.211i			1.85446i	−0.374496	+	0.927228i	$0.622184\pi$
$4$	166.089	−	194.809i	0.648785	−	0.760972i
$5$		0			0
$5$		0			0
$6$	−1007.15	−	2182.17i	−0.777121	−	1.68377i
$7$		−	2626.96i		−	1.09411i	−0.837097	−	0.547055i	$-0.815749\pi$
$7$		−	2626.96i		−	1.09411i	0.837097	−	0.547055i	$-0.184251\pi$
$8$	−1106.66	+	3943.67i	−0.270181	+	0.962810i
$9$	−16002.3			−2.43901
$10$		0			0
$11$			2300.68i			0.157140i	0.996909	+	0.0785699i	$0.0250354\pi$
$11$			2300.68i			0.157140i	−0.996909	+	0.0785699i	$0.974965\pi$
$12$	29262.4	+	24948.4i	1.41119	+	1.20314i
$13$	−47058.2			−1.64764			−0.823820	−	0.566852i	$-0.808161\pi$
$13$	−47058.2			−1.64764			−0.823820	+	0.566852i	$0.808161\pi$
$14$	17613.5	+	38162.8i	0.458493	+	0.993408i
$15$		0			0
$16$	−10365.0	−	64711.2i	−0.158157	−	0.987414i
$17$	51967.0			0.622202			0.311101	−	0.950377i	$-0.399302\pi$
$17$	51967.0			0.622202			0.311101	+	0.950377i	$0.399302\pi$
$18$	232472.	−	107294.i	2.21452	−	1.02208i
$19$		−	59554.7i		−	0.456985i	−0.973546	−	0.228492i	$-0.926620\pi$
$19$		−	59554.7i		−	0.456985i	0.973546	−	0.228492i	$-0.0733796\pi$
$20$		0			0
$21$	394598.			2.02898
$22$	−15425.8	−	33422.9i	−0.0658503	−	0.142677i
$23$		−	77570.5i		−	0.277195i	−0.990349	−	0.138597i	$-0.955741\pi$
$23$		−	77570.5i		−	0.277195i	0.990349	−	0.138597i	$-0.0442594\pi$
$24$	−592382.	−	166233.i	−1.78549	−	0.501039i
$25$		0			0
$26$	683632.	−	315520.i	1.49599	−	0.690453i
$27$		−	1.41819e6i		−	2.66858i
$28$	−511754.	−	436308.i	−0.832587	−	0.709841i
$29$	902211.			1.27561			0.637803	−	0.770200i	$-0.279844\pi$
$29$	902211.			1.27561			0.637803	+	0.770200i	$0.279844\pi$
$30$		0			0
$31$			340014.i			0.368171i	0.982910	+	0.184086i	$0.0589324\pi$
$31$			340014.i			0.368171i	−0.982910	+	0.184086i	$0.941068\pi$
$32$	584457.	+	870587.i	0.557382	+	0.830256i
$33$	−345588.			−0.291409
$34$	−754943.	+	348433.i	−0.564935	+	0.260737i
$35$		0			0
$36$	−2.65781e6	+	3.11740e6i	−1.58239	+	1.85602i
$37$	584324.			0.311779			0.155890	−	0.987774i	$-0.450176\pi$
$37$	584324.			0.311779			0.155890	+	0.987774i	$0.450176\pi$
$38$	399308.	+	865173.i	0.191502	+	0.414924i
$39$		−	7.06866e6i		−	3.05548i
$40$		0			0
$41$	293985.			0.104037			0.0520187	−	0.998646i	$-0.483434\pi$
$41$	293985.			0.104037			0.0520187	+	0.998646i	$0.483434\pi$
$42$	−5.73247e6	+	2.64573e6i	−1.84223	+	0.850255i
$43$			2.95292e6i			0.863731i	0.901938	+	0.431866i	$0.142144\pi$
$43$			2.95292e6i			0.863731i	−0.901938	+	0.431866i	$0.857856\pi$
$44$	448194.	+	382118.i	0.119579	+	0.101950i
$45$		0			0
$46$	520102.	+	1.12689e6i	0.116160	+	0.251682i
$47$		−	5.03746e6i		−	1.03233i	−0.856488	−	0.516167i	$-0.827358\pi$
$47$		−	5.03746e6i		−	1.03233i	0.856488	−	0.516167i	$-0.172642\pi$
$48$	9.72033e6	−	1.55693e6i	1.83112	−	0.293295i
$49$	−1.13610e6			−0.197075
$50$		0			0
$51$			7.80601e6i			1.15385i
$52$	−7.81585e6	+	9.16736e6i	−1.06896	+	1.25381i
$53$	7.54985e6			0.956830			0.478415	−	0.878134i	$-0.341211\pi$
$53$	7.54985e6			0.956830			0.478415	+	0.878134i	$0.341211\pi$
$54$	9.50883e6	+	2.06026e7i	1.11828	+	2.42297i
$55$		0			0
$56$	1.03598e7	+	2.90715e6i	1.05342	+	0.295608i
$57$	8.94577e6			0.847458
$58$	−1.31068e7	+	6.04923e6i	−1.15820	+	0.534550i
$59$			8.82594e6i			0.728372i	0.931326	+	0.364186i	$0.118653\pi$
$59$			8.82594e6i			0.728372i	−0.931326	+	0.364186i	$0.881347\pi$
$60$		0			0
$61$	1.08173e7			0.781269			0.390634	−	0.920546i	$-0.372256\pi$
$61$	1.08173e7			0.781269			0.390634	+	0.920546i	$0.372256\pi$
$62$	−2.27976e6	−	4.93951e6i	−0.154284	−	0.334285i
$63$			4.20375e7i			2.66854i
$64$	−1.43278e7	−	8.72861e6i	−0.854004	−	0.520266i
$65$		0			0
$66$	5.02049e6	−	2.31713e6i	0.264588	−	0.122117i
$67$		−	1.44347e7i		−	0.716324i	−0.933659	−	0.358162i	$-0.883404\pi$
$67$		−	1.44347e7i		−	0.716324i	0.933659	−	0.358162i	$-0.116596\pi$
$68$	8.63113e6	−	1.01236e7i	0.403675	−	0.473479i
$69$	1.16519e7			0.514046
$70$		0			0
$71$		−	3.71149e6i		−	0.146054i	−0.997330	−	0.0730272i	$-0.976734\pi$
$71$		−	3.71149e6i		−	0.146054i	0.997330	−	0.0730272i	$-0.0232660\pi$
$72$	1.77092e7	−	6.31079e7i	0.658975	−	2.34830i
$73$	3.62775e7			1.27746			0.638728	−	0.769433i	$-0.279461\pi$
$73$	3.62775e7			1.27746			0.638728	+	0.769433i	$0.279461\pi$
$74$	−8.48869e6	+	3.91783e6i	−0.283083	+	0.130653i
$75$		0			0
$76$	−1.16018e7	−	9.89137e6i	−0.347752	−	0.296485i
$77$	6.04380e6			0.171928
$78$	4.73946e7	+	1.02689e8i	1.28041	+	2.77425i
$79$			4.88562e7i			1.25433i	0.778887	+	0.627164i	$0.215785\pi$
$79$			4.88562e7i			1.25433i	−0.778887	+	0.627164i	$0.784215\pi$
$80$		0			0
$81$	1.08037e8			2.50976
$82$	−4.27083e6	+	1.97114e6i	−0.0944619	+	0.0435975i
$83$		−	6.93862e7i		−	1.46205i	−0.682353	−	0.731023i	$-0.739043\pi$
$83$		−	6.93862e7i		−	1.46205i	0.682353	−	0.731023i	$-0.260957\pi$
$84$	6.55383e7	−	7.68711e7i	1.31637	−	1.54400i
$85$		0			0
$86$	−1.97990e7	−	4.28982e7i	−0.361951	−	0.784234i
$87$			1.35522e8i			2.36555i
$88$	−9.07314e6	−	2.54608e6i	−0.151296	−	0.0424562i
$89$	−1.05906e8			−1.68796			−0.843979	−	0.536377i	$-0.819793\pi$
$89$	−1.05906e8			−1.68796			−0.843979	+	0.536377i	$0.819793\pi$
$90$		0			0
$91$			1.23620e8i			1.80270i
$92$	−1.51114e7	−	1.28836e7i	−0.210938	−	0.179840i
$93$	−5.10738e7			−0.682758
$94$	3.37756e7	+	7.31810e7i	0.432605	+	0.937319i
$95$		0			0
$96$	−1.30772e8	+	8.77919e7i	−1.53967	+	1.03364i
$97$	−1.33519e8			−1.50819			−0.754093	−	0.656768i	$-0.771923\pi$
$97$	−1.33519e8			−1.50819			−0.754093	+	0.656768i	$0.771923\pi$
$98$	1.65045e7	−	7.61742e6i	0.178936	−	0.0825854i
$99$		−	3.68163e7i		−	0.383266i
$100$		0			0
$101$	−6.08853e7			−0.585096			−0.292548	−	0.956251i	$-0.594503\pi$
$101$	−6.08853e7			−0.585096			−0.292548	+	0.956251i	$0.594503\pi$
$102$	−5.23384e7	−	1.13401e8i	−0.483526	−	1.04765i
$103$		−	2.63324e7i		−	0.233960i	−0.993134	−	0.116980i	$-0.962679\pi$
$103$		−	2.63324e7i		−	0.233960i	0.993134	−	0.116980i	$-0.0373214\pi$
$104$	5.20776e7	−	1.85582e8i	0.445161	−	1.58636i
$105$		0			0
$106$	−1.09679e8	+	5.06209e7i	−0.868764	+	0.400965i
$107$			1.26375e8i			0.964108i	0.876141	+	0.482054i	$0.160109\pi$
$107$			1.26375e8i			0.964108i	−0.876141	+	0.482054i	$0.839891\pi$
$108$	−2.76277e8	−	2.35546e8i	−2.03072	−	1.73133i
$109$	7.75869e7			0.549645			0.274822	−	0.961495i	$-0.411381\pi$
$109$	7.75869e7			0.549645			0.274822	+	0.961495i	$0.411381\pi$
$110$		0			0
$111$			8.77719e7i			0.578181i
$112$	−1.69993e8	+	2.72283e7i	−1.08034	+	0.173041i
$113$	9.07281e7			0.556453			0.278226	−	0.960516i	$-0.410253\pi$
$113$	9.07281e7			0.556453			0.278226	+	0.960516i	$0.410253\pi$
$114$	−1.29958e8	+	5.99804e7i	−0.769459	+	0.355132i
$115$		0			0
$116$	1.49847e8	−	1.75759e8i	0.827593	−	0.970700i
$117$	7.53042e8			4.01861
$118$	−5.91770e7	−	1.28218e8i	−0.305228	−	0.661333i
$119$		−	1.36515e8i		−	0.680757i
$120$		0			0
$121$	2.09066e8			0.975307
$122$	−1.57147e8	+	7.25290e7i	−0.709361	+	0.327395i
$123$			4.41598e7i			0.192933i
$124$	6.62377e7	+	5.64725e7i	0.280168	+	0.238864i
$125$		0			0
$126$	−2.81857e8	−	6.10694e8i	−1.11827	−	2.42293i
$127$		−	3.10844e8i		−	1.19489i	−0.801910	−	0.597445i	$-0.796183\pi$
$127$		−	3.10844e8i		−	1.19489i	0.801910	−	0.597445i	$-0.203817\pi$
$128$	2.66670e8	+	3.07374e7i	0.993423	+	0.114506i
$129$	−4.43562e8			−1.60175
$130$		0			0
$131$		−	5.44781e8i		−	1.84985i	−0.380150	−	0.924925i	$-0.624128\pi$
$131$		−	5.44781e8i		−	1.84985i	0.380150	−	0.924925i	$-0.375872\pi$
$132$	−5.73983e7	+	6.73236e7i	−0.189062	+	0.221754i
$133$	−1.56448e8			−0.499991
$134$	9.67833e7	+	2.09699e8i	0.300180	+	0.650394i
$135$		0			0
$136$	−5.75099e7	+	2.04940e8i	−0.168107	+	0.599062i
$137$	1.23319e8			0.350065			0.175033	−	0.984563i	$-0.443997\pi$
$137$	1.23319e8			0.350065			0.175033	+	0.984563i	$0.443997\pi$
$138$	−1.69272e8	+	7.81250e7i	−0.466733	+	0.215414i
$139$		−	6.72621e8i		−	1.80182i	−0.434008	−	0.900909i	$-0.642901\pi$
$139$		−	6.72621e8i		−	1.80182i	0.434008	−	0.900909i	$-0.357099\pi$
$140$		0			0
$141$	7.56682e8			1.91442
$142$	2.48851e7	+	5.39181e7i	0.0612049	+	0.132612i
$143$		−	1.08266e8i		−	0.258910i
$144$	1.65864e8	+	1.03553e9i	0.385746	+	2.40831i
$145$		0			0
$146$	−5.27017e8	+	2.43237e8i	−1.15988	+	0.535325i
$147$		−	1.70655e8i		−	0.365467i
$148$	9.70497e7	−	1.13832e8i	0.202277	−	0.237255i
$149$	2.47048e8			0.501229			0.250615	−	0.968087i	$-0.419367\pi$
$149$	2.47048e8			0.501229			0.250615	+	0.968087i	$0.419367\pi$
$150$		0			0
$151$			4.00056e8i			0.769508i	0.923019	+	0.384754i	$0.125714\pi$
$151$			4.00056e8i			0.769508i	−0.923019	+	0.384754i	$0.874286\pi$
$152$	2.34864e8	+	6.59069e7i	0.439989	+	0.123469i
$153$	−8.31593e8			−1.51756
$154$	−8.78005e7	+	4.05230e7i	−0.156104	+	0.0720475i
$155$		0			0
$156$	−1.37704e9	−	1.17403e9i	−2.32513	−	1.98235i
$157$	7.00538e8			1.15301			0.576505	−	0.817094i	$-0.304416\pi$
$157$	7.00538e8			1.15301			0.576505	+	0.817094i	$0.304416\pi$
$158$	−3.27575e8	−	7.09752e8i	−0.525634	−	1.13888i
$159$			1.13407e9i			1.77440i
$160$		0			0
$161$	−2.03774e8			−0.303281
$162$	−1.56949e9	+	7.24376e8i	−2.27876	+	1.05173i
$163$		−	2.24412e8i		−	0.317903i	−0.987286	−	0.158952i	$-0.949189\pi$
$163$		−	2.24412e8i		−	0.317903i	0.987286	−	0.158952i	$-0.0508114\pi$
$164$	4.88277e7	−	5.72709e7i	0.0674979	−	0.0791696i
$165$		0			0
$166$	4.65227e8	+	1.00800e9i	0.612678	+	1.32748i
$167$			1.11919e9i			1.43893i	0.694530	+	0.719464i	$0.255613\pi$
$167$			1.11919e9i			1.43893i	−0.694530	+	0.719464i	$0.744387\pi$
$168$	−4.36686e8	+	1.55616e9i	−0.548192	+	1.95352i
$169$	1.39875e9			1.71472
$170$		0			0
$171$			9.53015e8i			1.11459i
$172$	5.75256e8	+	4.90448e8i	0.657275	+	0.560375i
$173$	1.58033e9			1.76426			0.882130	−	0.471005i	$-0.156109\pi$
$173$	1.58033e9			1.76426			0.882130	+	0.471005i	$0.156109\pi$
$174$	−9.08661e8	−	1.96878e9i	−0.991299	−	2.14783i
$175$		0			0
$176$	1.48880e8	−	2.38465e7i	0.155162	−	0.0248528i
$177$	−1.32575e9			−1.35073
$178$	1.53854e9	−	7.10090e8i	1.53260	−	0.707348i
$179$		−	4.43340e8i		−	0.431841i	−0.976411	−	0.215921i	$-0.930725\pi$
$179$		−	4.43340e8i		−	0.431841i	0.976411	−	0.215921i	$-0.0692753\pi$
$180$		0			0
$181$	−1.87230e8			−0.174446			−0.0872232	−	0.996189i	$-0.527799\pi$
$181$	−1.87230e8			−0.174446			−0.0872232	+	0.996189i	$0.527799\pi$
$182$	−8.28858e8	−	1.79587e9i	−0.755431	−	1.63678i
$183$			1.62488e9i			1.44883i
$184$	3.05912e8	+	8.58443e7i	0.266886	+	0.0748928i
$185$		0			0
$186$	7.41968e8	−	3.42444e8i	0.619917	−	0.286114i
$187$			1.19560e8i			0.0977728i
$188$	−9.81342e8	−	8.36666e8i	−0.785577	−	0.669762i
$189$	−3.72553e9			−2.91972
$190$		0			0
$191$			5.22344e8i			0.392485i	0.980555	+	0.196242i	$0.0628740\pi$
$191$			5.22344e8i			0.392485i	−0.980555	+	0.196242i	$0.937126\pi$
$192$	1.31113e9	−	2.15220e9i	0.964811	−	1.58371i
$193$	−5.01793e7			−0.0361655			−0.0180828	−	0.999836i	$-0.505756\pi$
$193$	−5.01793e7			−0.0361655			−0.0180828	+	0.999836i	$0.505756\pi$
$194$	1.93967e9	−	8.95227e8i	1.36937	−	0.632014i
$195$		0			0
$196$	−1.88693e8	+	2.21322e8i	−0.127859	+	0.149969i
$197$	2.63629e8			0.175036			0.0875181	−	0.996163i	$-0.472106\pi$
$197$	2.63629e8			0.175036			0.0875181	+	0.996163i	$0.472106\pi$
$198$	2.46850e8	+	5.34845e8i	0.160610	+	0.347990i
$199$		−	1.26573e9i		−	0.807105i	−0.914956	−	0.403553i	$-0.867775\pi$
$199$		−	1.26573e9i		−	0.807105i	0.914956	−	0.403553i	$-0.132225\pi$
$200$		0			0
$201$	2.16826e9			1.32839
$202$	8.84503e8	−	4.08229e8i	0.531244	−	0.245188i
$203$		−	2.37007e9i		−	1.39565i
$204$	1.52068e9	+	1.29649e9i	0.878046	+	0.748598i
$205$		0			0
$206$	1.76556e8	+	3.82541e8i	0.0980423	+	0.212427i
$207$			1.24131e9i			0.676081i
$208$	4.87757e8	+	3.04519e9i	0.260586	+	1.62690i
$209$	1.37017e8			0.0718105
$210$		0			0
$211$		−	9.34053e8i		−	0.471240i	−0.971845	−	0.235620i	$-0.924288\pi$
$211$		−	9.34053e8i		−	0.471240i	0.971845	−	0.235620i	$-0.0757120\pi$
$212$	1.25395e9	−	1.47078e9i	0.620777	−	0.728121i
$213$	5.57506e8			0.270852
$214$	−8.47330e8	−	1.83590e9i	−0.404015	−	0.875372i
$215$		0			0
$216$	5.59288e9	+	1.56946e9i	2.56934	+	0.721000i
$217$	8.93202e8			0.402820
$218$	−1.12713e9	+	5.20212e8i	−0.499056	+	0.230332i
$219$			5.44928e9i			2.36899i
$220$		0			0
$221$	−2.44547e9			−1.02517
$222$	−5.88501e8	−	1.27509e9i	−0.242290	−	0.524965i
$223$		−	5.22225e8i		−	0.211173i	−0.994410	−	0.105586i	$-0.966328\pi$
$223$		−	5.22225e8i		−	0.211173i	0.994410	−	0.105586i	$-0.0336720\pi$
$224$	2.28699e9	−	1.53534e9i	0.908391	−	0.609837i
$225$		0			0
$226$	−1.31804e9	+	6.08322e8i	−0.505237	+	0.233185i
$227$		−	3.46698e9i		−	1.30571i	−0.757482	−	0.652856i	$-0.773570\pi$
$227$		−	3.46698e9i		−	1.30571i	0.757482	−	0.652856i	$-0.226430\pi$
$228$	1.48579e9	−	1.74271e9i	0.549818	−	0.644892i
$229$	1.31243e9			0.477239			0.238619	−	0.971113i	$-0.423305\pi$
$229$	1.31243e9			0.477239			0.238619	+	0.971113i	$0.423305\pi$
$230$		0			0
$231$			9.07845e8i			0.318833i
$232$	−9.98443e8	+	3.55802e9i	−0.344644	+	1.22816i
$233$	2.43802e9			0.827207			0.413604	−	0.910457i	$-0.364270\pi$
$233$	2.43802e9			0.827207			0.413604	+	0.910457i	$0.364270\pi$
$234$	−1.09397e10	+	5.04906e9i	−3.64874	+	1.68402i
$235$		0			0
$236$	1.71937e9	+	1.46589e9i	0.554271	+	0.472556i
$237$	−7.33874e9			−2.32610
$238$	9.15318e8	+	1.98320e9i	0.285275	+	0.618101i
$239$		−	2.78783e9i		−	0.854427i	−0.904151	−	0.427214i	$-0.859495\pi$
$239$		−	2.78783e9i		−	0.854427i	0.904151	−	0.427214i	$-0.140505\pi$
$240$		0			0
$241$	1.16299e9			0.344753			0.172376	−	0.985031i	$-0.444856\pi$
$241$	1.16299e9			0.344753			0.172376	+	0.985031i	$0.444856\pi$
$242$	−3.03717e9	+	1.40176e9i	−0.885540	+	0.408708i
$243$			6.92356e9i			1.98566i
$244$	1.79664e9	−	2.10731e9i	0.506875	−	0.594524i
$245$		0			0
$246$	−2.96087e8	−	6.41526e8i	−0.0808497	−	0.175176i
$247$			2.80254e9i			0.752946i
$248$	−1.34090e9	−	3.76281e8i	−0.354479	−	0.0994729i
$249$	1.04226e10			2.71130
$250$		0			0
$251$		−	6.20014e9i		−	1.56209i	−0.624474	−	0.781046i	$-0.714687\pi$
$251$		−	6.20014e9i		−	1.56209i	0.624474	−	0.781046i	$-0.285313\pi$
$252$	8.18927e9	+	6.98195e9i	2.03069	+	1.73131i
$253$	1.78465e8			0.0435584
$254$	2.08418e9	+	4.51575e9i	0.500725	+	1.08491i
$255$		0			0
$256$	−4.08010e9	+	1.34146e9i	−0.949973	+	0.312333i
$257$	1.12108e9			0.256983			0.128491	−	0.991711i	$-0.458987\pi$
$257$	1.12108e9			0.256983			0.128491	+	0.991711i	$0.458987\pi$
$258$	6.44378e9	−	2.97403e9i	1.45433	−	0.671223i
$259$		−	1.53499e9i		−	0.341120i
$260$		0			0
$261$	−1.44375e10			−3.11121
$262$	3.65269e9	+	7.91423e9i	0.775190	+	1.67959i
$263$			1.51480e9i			0.316616i	0.987390	+	0.158308i	$0.0506038\pi$
$263$			1.51480e9i			0.316616i	−0.987390	+	0.158308i	$0.949396\pi$
$264$	3.82449e8	−	1.36288e9i	0.0787332	−	0.280571i
$265$		0			0
$266$	2.27277e9	−	1.04896e9i	0.453972	−	0.209524i
$267$		−	1.59083e10i		−	3.13024i
$268$	−2.81201e9	−	2.39745e9i	−0.545102	−	0.464740i
$269$	−2.73389e9			−0.522121			−0.261060	−	0.965322i	$-0.584072\pi$
$269$	−2.73389e9			−0.522121			−0.261060	+	0.965322i	$0.584072\pi$
$270$		0			0
$271$			9.38092e9i			1.73927i	0.493691	+	0.869637i	$0.335647\pi$
$271$			9.38092e9i			1.73927i	−0.493691	+	0.869637i	$0.664353\pi$
$272$	−5.38636e8	−	3.36284e9i	−0.0984056	−	0.614371i
$273$	−1.85691e10			−3.34302
$274$	−1.79151e9	+	8.26843e8i	−0.317845	+	0.146697i
$275$		0			0
$276$	1.93526e9	−	2.26990e9i	0.333505	−	0.391174i
$277$	−1.88891e9			−0.320842			−0.160421	−	0.987049i	$-0.551285\pi$
$277$	−1.88891e9			−0.320842			−0.160421	+	0.987049i	$0.551285\pi$
$278$	4.50985e9	+	9.77141e9i	0.755062	+	1.63598i
$279$		−	5.44102e9i		−	0.897973i
$280$		0			0
$281$	−1.65526e9			−0.265485			−0.132743	−	0.991151i	$-0.542378\pi$
$281$	−1.65526e9			−0.265485			−0.132743	+	0.991151i	$0.542378\pi$
$282$	−1.09926e10	+	5.07347e9i	−1.73822	+	0.802248i
$283$		−	8.61833e9i		−	1.34362i	−0.740722	−	0.671811i	$-0.765517\pi$
$283$		−	8.61833e9i		−	1.34362i	0.740722	−	0.671811i	$-0.234483\pi$
$284$	−7.23031e8	−	6.16437e8i	−0.111143	−	0.0947578i
$285$		0			0
$286$	7.25913e8	+	1.57282e9i	0.108498	+	0.235080i
$287$		−	7.72286e8i		−	0.113828i
$288$	−9.35268e9	−	1.39314e10i	−1.35946	−	2.02500i
$289$	−4.27519e9			−0.612864
$290$		0			0
$291$		−	2.00560e10i		−	2.79686i
$292$	6.02529e9	−	7.06718e9i	0.828794	−	0.972108i
$293$	5.51315e9			0.748048			0.374024	−	0.927419i	$-0.377978\pi$
$293$	5.51315e9			0.748048			0.374024	+	0.927419i	$0.377978\pi$
$294$	1.14422e9	+	2.47916e9i	0.153151	+	0.331830i
$295$		0			0
$296$	−6.46649e8	+	2.30438e9i	−0.0842368	+	0.300184i
$297$	3.26282e9			0.419341
$298$	−3.58896e9	+	1.65643e9i	−0.455096	+	0.210043i
$299$			3.65033e9i			0.456717i
$300$		0			0
$301$	7.75720e9			0.945016
$302$	−2.68233e9	−	5.81177e9i	−0.322467	−	0.698683i
$303$		−	9.14564e9i		−	1.08504i
$304$	−3.85385e9	+	6.17283e8i	−0.451233	+	0.0722753i
$305$		0			0
$306$	1.20809e10	−	5.57574e9i	1.37788	−	0.635941i
$307$			1.53502e10i			1.72806i	0.503437	+	0.864032i	$0.332069\pi$
$307$			1.53502e10i			1.72806i	−0.503437	+	0.864032i	$0.667931\pi$
$308$	1.00381e9	−	1.17739e9i	0.111544	−	0.130833i
$309$	3.95542e9			0.433869
$310$		0			0
$311$		−	5.55831e9i		−	0.594157i	−0.954853	−	0.297079i	$-0.903988\pi$
$311$		−	5.55831e9i		−	0.594157i	0.954853	−	0.297079i	$-0.0960123\pi$
$312$	2.78765e10	+	7.82262e9i	2.94184	+	0.825532i
$313$	1.76829e10			1.84237			0.921183	−	0.389131i	$-0.127225\pi$
$313$	1.76829e10			1.84237			0.921183	+	0.389131i	$0.127225\pi$
$314$	−1.01770e10	+	4.69703e9i	−1.04689	+	0.483176i
$315$		0			0
$316$	9.51762e9	+	8.11447e9i	0.954509	+	0.813789i
$317$	2.84291e9			0.281531			0.140766	−	0.990043i	$-0.455044\pi$
$317$	2.84291e9			0.281531			0.140766	+	0.990043i	$0.455044\pi$
$318$	−7.60382e9	−	1.64751e10i	−0.743572	−	1.61109i
$319$			2.07570e9i			0.200448i
$320$		0			0
$321$	−1.89829e10			−1.78790
$322$	2.96030e9	−	1.36628e9i	0.275368	−	0.127092i
$323$		−	3.09488e9i		−	0.284337i
$324$	1.79437e10	−	2.10465e10i	1.62829	−	1.90986i
$325$		0			0
$326$	1.50466e9	+	3.26011e9i	0.133219	+	0.288643i
$327$			1.16544e10i			1.01929i
$328$	−3.25342e8	+	1.15938e9i	−0.0281090	+	0.100168i
$329$	−1.32332e10			−1.12949
$330$		0			0
$331$		−	1.16323e10i		−	0.969068i	−0.874773	−	0.484534i	$-0.838989\pi$
$331$		−	1.16323e10i		−	0.969068i	0.874773	−	0.484534i	$-0.161011\pi$
$332$	−1.35171e10	−	1.15243e10i	−1.11258	−	0.948553i
$333$	−9.35056e9			−0.760432
$334$	−7.50407e9	−	1.62589e10i	−0.602991	−	1.30649i
$335$		0			0
$336$	−4.09000e9	−	2.55349e10i	−0.320897	−	2.00344i
$337$	−2.09960e10			−1.62786			−0.813930	−	0.580963i	$-0.802676\pi$
$337$	−2.09960e10			−1.62786			−0.813930	+	0.580963i	$0.802676\pi$
$338$	−2.03201e10	+	9.37844e9i	−1.55689	+	0.718561i
$339$			1.36284e10i			1.03192i
$340$		0			0
$341$	−7.82265e8			−0.0578544
$342$	−6.38986e9	−	1.38448e10i	−0.467075	−	1.01200i
$343$		−	1.21594e10i		−	0.878488i
$344$	−1.16454e10	−	3.26789e9i	−0.831608	−	0.233364i
$345$		0			0
$346$	−2.29580e10	+	1.05959e10i	−1.60188	+	0.739324i
$347$		−	7.43114e9i		−	0.512552i	−0.966604	−	0.256276i	$-0.917504\pi$
$347$		−	7.43114e9i		−	0.512552i	0.966604	−	0.256276i	$-0.0824955\pi$
$348$	2.64009e10	+	2.25087e10i	1.80012	+	1.53474i
$349$	5.43305e9			0.366220			0.183110	−	0.983092i	$-0.441384\pi$
$349$	5.43305e9			0.366220			0.183110	+	0.983092i	$0.441384\pi$
$350$		0			0
$351$			6.67377e10i			4.39686i
$352$	−2.00295e9	+	1.34465e9i	−0.130466	+	0.0875869i
$353$	−7.17687e9			−0.462207			−0.231103	−	0.972929i	$-0.574234\pi$
$353$	−7.17687e9			−0.462207			−0.231103	+	0.972929i	$0.574234\pi$
$354$	1.92597e10	−	8.88904e9i	1.22641	−	0.566033i
$355$		0			0
$356$	−1.75898e10	+	2.06315e10i	−1.09512	+	1.28449i
$357$	2.05060e10			1.26244
$358$	2.97254e9	+	6.44056e9i	0.180966	+	0.392095i
$359$		−	1.10278e10i		−	0.663913i	−0.943295	−	0.331957i	$-0.892291\pi$
$359$		−	1.10278e10i		−	0.663913i	0.943295	−	0.331957i	$-0.107709\pi$
$360$		0			0
$361$	1.34368e10			0.791165
$362$	2.71996e9	−	1.25536e9i	0.158390	−	0.0731027i
$363$			3.14040e10i			1.80866i
$364$	2.40823e10	+	2.05319e10i	1.37180	+	1.16956i
$365$		0			0
$366$	−1.08947e10	−	2.36052e10i	−0.607140	−	1.31548i
$367$			3.39042e10i			1.86891i	0.356076	+	0.934457i	$0.384114\pi$
$367$			3.39042e10i			1.86891i	−0.356076	+	0.934457i	$0.615886\pi$
$368$	−5.01968e9	+	8.04016e8i	−0.273706	+	0.0438403i
$369$	−4.70445e9			−0.253748
$370$		0			0
$371$		−	1.98331e10i		−	1.04688i
$372$	−8.48279e9	+	9.94963e9i	−0.442963	+	0.519560i
$373$	−3.19254e10			−1.64930			−0.824651	−	0.565641i	$-0.808629\pi$
$373$	−3.19254e10			−1.64930			−0.824651	+	0.565641i	$0.808629\pi$
$374$	−8.01634e8	−	1.73689e9i	−0.0409722	−	0.0887738i
$375$		0			0
$376$	1.98661e10	+	5.57477e9i	0.993941	+	0.278917i
$377$	−4.24565e10			−2.10174
$378$	5.41222e10	−	2.49793e10i	2.65099	−	1.22353i
$379$			2.66340e10i			1.29086i	0.763819	+	0.645430i	$0.223322\pi$
$379$			2.66340e10i			1.29086i	−0.763819	+	0.645430i	$0.776678\pi$
$380$		0			0
$381$	4.66922e10			2.21587
$382$	−3.50226e9	−	7.58828e9i	−0.164473	−	0.356361i
$383$			1.61064e10i			0.748518i	0.927324	+	0.374259i	$0.122103\pi$
$383$			1.61064e10i			0.748518i	−0.927324	+	0.374259i	$0.877897\pi$
$384$	−4.61709e9	+	4.00567e10i	−0.212346	+	1.84226i
$385$		0			0
$386$	7.28973e8	−	3.36446e8i	0.0328369	−	0.0151554i
$387$		−	4.72537e10i		−	2.10665i
$388$	−2.21759e10	+	2.60106e10i	−0.978487	+	1.14769i
$389$	1.81674e10			0.793405			0.396702	−	0.917947i	$-0.370154\pi$
$389$	1.81674e10			0.793405			0.396702	+	0.917947i	$0.370154\pi$
$390$		0			0
$391$		−	4.03110e9i		−	0.172471i
$392$	1.25728e9	−	4.48040e9i	0.0532460	−	0.189746i
$393$	8.18320e10			3.43047
$394$	−3.82983e9	+	1.76760e9i	−0.158926	+	0.0733499i
$395$		0			0
$396$	−7.17215e9	−	6.11479e9i	−0.291654	−	0.248657i
$397$	4.03325e10			1.62365			0.811827	−	0.583898i	$-0.198473\pi$
$397$	4.03325e10			1.62365			0.811827	+	0.583898i	$0.198473\pi$
$398$	8.48661e9	+	1.83878e10i	0.338222	+	0.732820i
$399$		−	2.35001e10i		−	0.927212i
$400$		0			0
$401$	1.86384e10			0.720826			0.360413	−	0.932793i	$-0.382636\pi$
$401$	1.86384e10			0.720826			0.360413	+	0.932793i	$0.382636\pi$
$402$	−3.14990e10	+	1.45379e10i	−1.20613	+	0.556670i
$403$		−	1.60005e10i		−	0.606614i
$404$	−1.01124e10	+	1.18610e10i	−0.379601	+	0.445242i
$405$		0			0
$406$	1.58911e10	+	3.44309e10i	0.584856	+	1.26720i
$407$			1.34435e9i			0.0489929i
$408$	−3.07843e10	−	8.63861e9i	−1.11094	−	0.311748i
$409$	−1.95383e10			−0.698222			−0.349111	−	0.937081i	$-0.613516\pi$
$409$	−1.95383e10			−0.698222			−0.349111	+	0.937081i	$0.613516\pi$
$410$		0			0
$411$			1.85239e10i			0.649181i
$412$	−5.12979e9	−	4.37352e9i	−0.178037	−	0.151790i
$413$	2.31854e10			0.796918
$414$	−8.32284e9	−	1.80330e10i	−0.283316	−	0.613855i
$415$		0			0
$416$	−2.75035e10	−	4.09683e10i	−0.918364	−	1.36796i
$417$	1.01035e11			3.34139
$418$	−1.99049e9	+	9.18681e8i	−0.0652011	+	0.0300926i
$419$		−	1.60399e10i		−	0.520410i	−0.965553	−	0.260205i	$-0.916210\pi$
$419$		−	1.60399e10i		−	0.520410i	0.965553	−	0.260205i	$-0.0837901\pi$
$420$		0			0
$421$	8.80074e9			0.280150			0.140075	−	0.990141i	$-0.455266\pi$
$421$	8.80074e9			0.280150			0.140075	+	0.990141i	$0.455266\pi$
$422$	6.26273e9	+	1.35693e10i	0.197476	+	0.427867i
$423$			8.06112e10i			2.51787i
$424$	−8.35513e9	+	2.97741e10i	−0.258517	+	0.921245i
$425$		0			0
$426$	−8.09910e9	+	3.73802e9i	−0.245922	+	0.113502i
$427$		−	2.84166e10i		−	0.854794i
$428$	2.46190e10	+	2.09895e10i	0.733659	+	0.625499i
$429$	1.62628e10			0.480137
$430$		0			0
$431$		−	2.17255e10i		−	0.629593i	−0.949159	−	0.314797i	$-0.898064\pi$
$431$		−	2.17255e10i		−	0.629593i	0.949159	−	0.314797i	$-0.101936\pi$
$432$	−9.17730e10	+	1.46995e10i	−2.63499	+	0.422055i
$433$	−2.50658e10			−0.713066			−0.356533	−	0.934283i	$-0.616041\pi$
$433$	−2.50658e10			−0.713066			−0.356533	+	0.934283i	$0.616041\pi$
$434$	−1.29759e10	+	5.98882e9i	−0.365744	+	0.168804i
$435$		0			0
$436$	1.28863e10	−	1.51146e10i	0.356601	−	0.418264i
$437$	−4.61969e9			−0.126674
$438$	−3.65368e10	−	7.91637e10i	−0.992738	−	2.15095i
$439$		−	2.69059e10i		−	0.724419i	−0.932097	−	0.362210i	$-0.882022\pi$
$439$		−	2.69059e10i		−	0.724419i	0.932097	−	0.362210i	$-0.117978\pi$
$440$		0			0
$441$	1.81802e10			0.480668
$442$	3.55263e10	−	1.63966e10i	0.930809	−	0.429601i
$443$		−	5.16514e10i		−	1.34112i	−0.741856	−	0.670560i	$-0.766054\pi$
$443$		−	5.16514e10i		−	1.34112i	0.741856	−	0.670560i	$-0.233946\pi$
$444$	1.70987e10	+	1.45779e10i	0.439979	+	0.375115i
$445$		0			0
$446$	3.50146e9	+	7.58655e9i	0.0884932	+	0.191737i
$447$			3.71093e10i			0.929508i
$448$	−2.29297e10	+	3.76385e10i	−0.569228	+	0.934374i
$449$	−4.61561e10			−1.13565			−0.567825	−	0.823150i	$-0.692215\pi$
$449$	−4.61561e10			−1.13565			−0.567825	+	0.823150i	$0.692215\pi$
$450$		0			0
$451$			6.76367e8i			0.0163484i
$452$	1.50689e10	−	1.76746e10i	0.361018	−	0.423445i
$453$	−6.00929e10			−1.42702
$454$	2.32457e10	+	5.03661e10i	0.547166	+	1.18554i
$455$		0			0
$456$	−9.89994e9	+	3.52791e10i	−0.228967	+	0.815941i
$457$	3.11288e10			0.713669			0.356835	−	0.934168i	$-0.383856\pi$
$457$	3.11288e10			0.713669			0.356835	+	0.934168i	$0.383856\pi$
$458$	−1.90662e10	+	8.79973e9i	−0.433314	+	0.199990i
$459$		−	7.36992e10i		−	1.66040i
$460$		0			0
$461$	4.68016e10			1.03623			0.518116	−	0.855310i	$-0.326634\pi$
$461$	4.68016e10			1.03623			0.518116	+	0.855310i	$0.326634\pi$
$462$	−6.08700e9	−	1.31886e10i	−0.133609	−	0.289488i
$463$		−	2.03332e10i		−	0.442468i	−0.975221	−	0.221234i	$-0.928992\pi$
$463$		−	2.03332e10i		−	0.442468i	0.975221	−	0.221234i	$-0.0710085\pi$
$464$	−9.35140e9	−	5.83831e10i	−0.201746	−	1.25955i
$465$		0			0
$466$	−3.54181e10	+	1.63467e10i	−0.751072	+	0.346646i
$467$		−	5.89675e10i		−	1.23978i	−0.784688	−	0.619891i	$-0.787177\pi$
$467$		−	5.89675e10i		−	1.23978i	0.784688	−	0.619891i	$-0.212823\pi$
$468$	1.25072e11	−	1.46699e11i	2.60721	−	3.05805i
$469$	−3.79194e10			−0.783737
$470$		0			0
$471$			1.05229e11i			2.13821i
$472$	−3.48066e10	−	9.76734e9i	−0.701283	−	0.196792i
$473$	−6.79375e9			−0.135727
$474$	1.06613e11	−	4.92054e10i	2.11201	−	0.974765i
$475$		0			0
$476$	−2.65943e10	−	2.26736e10i	−0.518037	−	0.441665i
$477$	−1.20815e11			−2.33372
$478$	1.86921e10	+	4.04999e10i	0.358053	+	0.775786i
$479$			1.20229e10i			0.228384i	0.993459	+	0.114192i	$0.0364279\pi$
$479$			1.20229e10i			0.228384i	−0.993459	+	0.114192i	$0.963572\pi$
$480$		0			0
$481$	−2.74973e10			−0.513699
$482$	−1.68952e10	+	7.79772e9i	−0.313022	+	0.144471i
$483$		−	3.06091e10i		−	0.562422i
$484$	3.47235e10	−	4.07279e10i	0.632764	−	0.742181i
$485$		0			0
$486$	−4.64217e10	−	1.00581e11i	−0.832102	−	1.80290i
$487$			4.85939e10i			0.863905i	0.901896	+	0.431953i	$0.142175\pi$
$487$			4.85939e10i			0.863905i	−0.901896	+	0.431953i	$0.857825\pi$
$488$	−1.19711e10	+	4.26599e10i	−0.211084	+	0.752213i
$489$	3.37091e10			0.589538
$490$		0			0
$491$		−	1.71586e9i		−	0.0295226i	−0.999891	−	0.0147613i	$-0.995301\pi$
$491$		−	1.71586e9i		−	0.0295226i	0.999891	−	0.0147613i	$-0.00469884\pi$
$492$	8.60272e9	+	7.33445e9i	0.146817	+	0.125172i
$493$	4.68852e10			0.793685
$494$	−1.87907e10	−	4.07135e10i	−0.315526	−	0.683645i
$495$		0			0
$496$	2.20027e10	−	3.52424e9i	0.363537	−	0.0582289i
$497$	−9.74991e9			−0.159799
$498$	−1.51413e11	+	6.98822e10i	−2.46175	+	1.13619i
$499$			6.25565e10i			1.00895i	0.863426	+	0.504476i	$0.168314\pi$
$499$			6.25565e10i			1.00895i	−0.863426	+	0.504476i	$0.831686\pi$
$500$		0			0
$501$	−1.68115e11			−2.66843
$502$	4.15712e10	+	9.00717e10i	0.654603	+	1.41832i
$503$		−	8.60985e10i		−	1.34500i	−0.740095	−	0.672502i	$-0.765220\pi$
$503$		−	8.60985e10i		−	1.34500i	0.740095	−	0.672502i	$-0.234780\pi$
$504$	−1.65782e11	−	4.65213e10i	−2.56930	−	0.720990i
$505$		0			0
$506$	−2.59263e9	+	1.19659e9i	−0.0395493	+	0.0182534i
$507$			2.10107e11i			3.17987i
$508$	−6.05552e10	−	5.16277e10i	−0.909278	−	0.775226i
$509$	5.17187e10			0.770506			0.385253	−	0.922811i	$-0.374114\pi$
$509$	5.17187e10			0.770506			0.385253	+	0.922811i	$0.374114\pi$
$510$		0			0
$511$		−	9.52994e10i		−	1.39768i
$512$	5.02788e10	−	4.68445e10i	0.731653	−	0.681677i
$513$	−8.44601e10			−1.21950
$514$	−1.62863e10	+	7.51672e9i	−0.233330	+	0.107690i
$515$		0			0
$516$	−7.36707e10	+	8.64098e10i	−1.03919	+	1.21889i
$517$	1.15896e10			0.162221
$518$	1.02920e10	+	2.22994e10i	0.142948	+	0.309724i
$519$			2.37383e11i			3.27175i
$520$		0			0
$521$	6.36828e10			0.864313			0.432157	−	0.901799i	$-0.357753\pi$
$521$	6.36828e10			0.864313			0.432157	+	0.901799i	$0.357753\pi$
$522$	2.09739e11	−	9.68018e10i	2.82486	−	1.30377i
$523$			3.05582e10i			0.408434i	0.978926	+	0.204217i	$0.0654648\pi$
$523$			3.05582e10i			0.408434i	−0.978926	+	0.204217i	$0.934535\pi$
$524$	−1.06128e11	−	9.04820e10i	−1.40768	−	1.20015i
$525$		0			0
$526$	−1.01566e10	−	2.20061e10i	−0.132680	−	0.287474i
$527$			1.76695e10i			0.229077i
$528$	3.58201e9	+	2.23634e10i	0.0460884	+	0.287741i
$529$	7.22938e10			0.923163
$530$		0			0
$531$		−	1.41236e11i		−	1.77651i
$532$	−2.59842e10	+	3.04774e10i	−0.324387	+	0.380479i
$533$	−1.38344e10			−0.171416
$534$	1.06663e11	+	2.31105e11i	1.31175	+	2.84214i
$535$		0			0
$536$	5.69258e10	+	1.59744e10i	0.689683	+	0.193537i
$537$	6.65945e10			0.800831
$538$	3.97162e10	−	1.83304e10i	0.474065	−	0.218798i
$539$		−	2.61380e9i		−	0.0309683i
$540$		0			0
$541$	2.53545e10			0.295982			0.147991	−	0.988989i	$-0.452719\pi$
$541$	2.53545e10			0.295982			0.147991	+	0.988989i	$0.452719\pi$
$542$	−6.28980e10	−	1.36280e11i	−0.728853	−	1.57919i
$543$		−	2.81240e10i		−	0.323503i
$544$	3.03725e10	+	4.52418e10i	0.346804	+	0.516587i
$545$		0			0
$546$	2.69760e11	−	1.24504e11i	3.03533	−	1.40091i
$547$		−	5.79915e10i		−	0.647762i	−0.946098	−	0.323881i	$-0.895012\pi$
$547$		−	5.79915e10i		−	0.647762i	0.946098	−	0.323881i	$-0.104988\pi$
$548$	2.04820e10	−	2.40237e10i	0.227117	−	0.266390i
$549$	−1.73103e11			−1.90552
$550$		0			0
$551$		−	5.37309e10i		−	0.582932i
$552$	−1.28948e10	+	4.59514e10i	−0.138885	+	0.494928i
$553$	1.28343e11			1.37237
$554$	2.74408e10	−	1.26649e10i	0.291312	−	0.134451i
$555$		0			0
$556$	−1.31032e11	−	1.11715e11i	−1.37113	−	1.16899i
$557$	−1.71554e11			−1.78230			−0.891149	−	0.453710i	$-0.850100\pi$
$557$	−1.71554e11			−1.78230			−0.891149	+	0.453710i	$0.850100\pi$
$558$	3.64814e10	+	7.90437e10i	0.376301	+	0.815324i
$559$		−	1.38959e11i		−	1.42312i
$560$		0			0
$561$	−1.79592e10			−0.181315
$562$	2.40465e10	−	1.10983e10i	0.241050	−	0.111253i
$563$		−	5.49966e8i		−	0.00547397i	−0.999996	−	0.00273698i	$-0.999129\pi$
$563$		−	5.49966e8i		−	0.00547397i	0.999996	−	0.00273698i	$-0.000871210\pi$
$564$	1.25676e11	−	1.47408e11i	1.24205	−	1.45682i
$565$		0			0
$566$	5.77850e10	+	1.25202e11i	0.563053	+	1.21996i
$567$		−	2.83808e11i		−	2.74595i
$568$	1.46369e10	+	4.10736e9i	0.140623	+	0.0394611i
$569$	−1.48683e10			−0.141845			−0.0709223	−	0.997482i	$-0.522594\pi$
$569$	−1.48683e10			−0.141845			−0.0709223	+	0.997482i	$0.522594\pi$
$570$		0			0
$571$			3.55169e10i			0.334111i	0.985947	+	0.167056i	$0.0534259\pi$
$571$			3.55169e10i			0.334111i	−0.985947	+	0.167056i	$0.946574\pi$
$572$	−2.10912e10	−	1.79818e10i	−0.197023	−	0.167977i
$573$	−7.84618e10			−0.727846
$574$	5.17809e9	+	1.12193e10i	0.0477004	+	0.103352i
$575$		0			0
$576$	2.29279e11	+	1.39678e11i	2.08292	+	1.26893i
$577$	−4.14670e10			−0.374110			−0.187055	−	0.982349i	$-0.559894\pi$
$577$	−4.14670e10			−0.374110			−0.187055	+	0.982349i	$0.559894\pi$
$578$	6.21073e10	−	2.86647e10i	0.556457	−	0.256824i
$579$		−	7.53748e9i		−	0.0670674i
$580$		0			0
$581$	−1.82275e11			−1.59964
$582$	1.34473e11	+	2.91360e11i	1.17204	+	2.53944i
$583$			1.73698e10i			0.150356i
$584$	−4.01469e10	+	1.43066e11i	−0.345145	+	1.22995i
$585$		0			0
$586$	−8.00916e10	+	3.69651e10i	−0.679198	+	0.313474i
$587$		−	2.88322e10i		−	0.242843i	−0.992601	−	0.121421i	$-0.961255\pi$
$587$		−	2.88322e10i		−	0.242843i	0.992601	−	0.121421i	$-0.0387453\pi$
$588$	−3.32450e10	−	2.83438e10i	−0.278110	−	0.237110i
$589$	2.02494e10			0.168249
$590$		0			0
$591$			3.95999e10i			0.324597i
$592$	−6.05651e9	−	3.78123e10i	−0.0493100	−	0.307855i
$593$	4.33851e10			0.350850			0.175425	−	0.984493i	$-0.443870\pi$
$593$	4.33851e10			0.350850			0.175425	+	0.984493i	$0.443870\pi$
$594$	−4.74001e10	+	2.18768e10i	−0.380745	+	0.175727i
$595$		0			0
$596$	4.10319e10	−	4.81272e10i	0.325190	−	0.381422i
$597$	1.90127e11			1.49674
$598$	−2.44751e10	−	5.30297e10i	−0.191390	−	0.414681i
$599$		−	1.41612e11i		−	1.10000i	−0.835164	−	0.550000i	$-0.814628\pi$
$599$		−	1.41612e11i		−	1.10000i	0.835164	−	0.550000i	$-0.185372\pi$
$600$		0			0
$601$	−1.16789e11			−0.895170			−0.447585	−	0.894241i	$-0.647716\pi$
$601$	−1.16789e11			−0.895170			−0.447585	+	0.894241i	$0.647716\pi$
$602$	−1.12692e11	+	5.20112e10i	−0.858037	+	0.396014i
$603$			2.30989e11i			1.74712i
$604$	7.79345e10	+	6.64449e10i	0.585574	+	0.499245i
$605$		0			0
$606$	6.13205e10	+	1.32862e11i	0.454690	+	0.985169i
$607$		−	4.19809e10i		−	0.309241i	−0.987974	−	0.154620i	$-0.950585\pi$
$607$		−	4.19809e10i		−	0.309241i	0.987974	−	0.154620i	$-0.0494155\pi$
$608$	5.18475e10	−	3.48072e10i	0.379414	−	0.254715i
$609$	3.56011e11			2.58818
$610$		0			0
$611$			2.37054e11i			1.70091i
$612$	−1.38118e11	+	1.62002e11i	−0.984568	+	1.15482i
$613$	−1.73299e11			−1.22731			−0.613655	−	0.789575i	$-0.710301\pi$
$613$	−1.73299e11			−1.22731			−0.613655	+	0.789575i	$0.710301\pi$
$614$	−1.02921e11	−	2.22998e11i	−0.724155	−	1.56901i
$615$		0			0
$616$	−6.68844e9	+	2.38347e10i	−0.0464518	+	0.165534i
$617$	−2.09205e11			−1.44355			−0.721773	−	0.692130i	$-0.756672\pi$
$617$	−2.09205e11			−1.44355			−0.721773	+	0.692130i	$0.756672\pi$
$618$	−5.74618e10	+	2.65206e10i	−0.393936	+	0.181815i
$619$		−	1.25079e11i		−	0.851965i	−0.904731	−	0.425983i	$-0.859928\pi$
$619$		−	1.25079e11i		−	0.851965i	0.904731	−	0.425983i	$-0.140072\pi$
$620$		0			0
$621$	−1.10010e11			−0.739717
$622$	3.72679e10	+	8.07476e10i	0.248985	+	0.539471i
$623$			2.78211e11i			1.84681i
$624$	−4.57421e11	+	7.32665e10i	−3.01702	+	0.483245i
$625$		0			0
$626$	−2.56886e11	+	1.18562e11i	−1.67279	+	0.772054i
$627$			2.05814e10i			0.133169i
$628$	1.16352e11	−	1.36471e11i	0.748055	−	0.877409i
$629$	3.03656e10			0.193990
$630$		0			0
$631$		−	2.63720e11i		−	1.66351i	−0.555143	−	0.831755i	$-0.687337\pi$
$631$		−	2.63720e11i		−	1.66351i	0.555143	−	0.831755i	$-0.312663\pi$
$632$	−1.92673e11	−	5.40673e10i	−1.20768	−	0.338896i
$633$	1.40305e11			0.873894
$634$	−4.13001e10	+	1.90614e10i	−0.255619	+	0.117977i
$635$		0			0
$636$	2.20927e11	+	1.88356e11i	1.35027	+	1.15120i
$637$	5.34628e10			0.324709
$638$	−1.39174e10	−	3.01545e10i	−0.0839990	−	0.181999i
$639$			5.93925e10i			0.356228i
$640$		0			0
$641$	1.68400e10			0.0997495			0.0498748	−	0.998755i	$-0.484118\pi$
$641$	1.68400e10			0.0997495			0.0498748	+	0.998755i	$0.484118\pi$
$642$	2.75772e11	−	1.27278e11i	1.62334	−	0.749228i
$643$		−	2.84422e11i		−	1.66387i	−0.554871	−	0.831936i	$-0.687233\pi$
$643$		−	2.84422e11i		−	1.66387i	0.554871	−	0.831936i	$-0.312767\pi$
$644$	−3.38446e10	+	3.96970e10i	−0.196764	+	0.230789i
$645$		0			0
$646$	2.07508e10	+	4.49604e10i	0.119153	+	0.258167i
$647$		−	2.11657e11i		−	1.20785i	−0.797040	−	0.603927i	$-0.793602\pi$
$647$		−	2.11657e11i		−	1.20785i	0.797040	−	0.603927i	$-0.206398\pi$
$648$	−1.19560e11	+	4.26062e11i	−0.678090	+	2.41642i
$649$	−2.03057e10			−0.114456
$650$		0			0
$651$			1.34169e11i			0.747012i
$652$	−4.37174e10	−	3.72723e10i	−0.241915	−	0.206251i
$653$	2.94426e11			1.61929			0.809644	−	0.586922i	$-0.199660\pi$
$653$	2.94426e11			1.61929			0.809644	+	0.586922i	$0.199660\pi$
$654$	−7.81415e10	−	1.69308e11i	−0.427140	−	0.925478i
$655$		0			0
$656$	−3.04715e9	−	1.90241e10i	−0.0164543	−	0.102728i
$657$	−5.80525e11			−3.11573
$658$	1.92243e11	−	8.87271e10i	1.02553	−	0.473318i
$659$		−	1.18352e11i		−	0.627529i	−0.949501	−	0.313765i	$-0.898410\pi$
$659$		−	1.18352e11i		−	0.627529i	0.949501	−	0.313765i	$-0.101590\pi$
$660$		0			0
$661$	2.01300e11			1.05448			0.527239	−	0.849717i	$-0.323227\pi$
$661$	2.01300e11			1.05448			0.527239	+	0.849717i	$0.323227\pi$
$662$	7.79934e10	+	1.68987e11i	0.406093	+	0.879875i
$663$		−	3.67337e11i		−	1.90112i
$664$	2.73636e11	+	7.67871e10i	1.40767	+	0.395017i
$665$		0			0
$666$	1.35839e11	−	6.26945e10i	0.690442	−	0.318663i
$667$		−	6.99850e10i		−	0.353591i
$668$	2.18029e11	+	1.85886e11i	1.09498	+	0.933555i
$669$	7.84439e10			0.391611
$670$		0			0
$671$			2.48873e10i			0.122768i
$672$	2.30625e11	+	3.43532e11i	1.13092	+	1.68457i
$673$	−2.21745e11			−1.08092			−0.540461	−	0.841369i	$-0.681750\pi$
$673$	−2.21745e11			−1.08092			−0.540461	+	0.841369i	$0.681750\pi$
$674$	3.05017e11	−	1.40776e11i	1.47803	−	0.682164i
$675$		0			0
$676$	2.32316e11	−	2.72488e11i	1.11248	−	1.30485i
$677$	3.56145e11			1.69540			0.847701	−	0.530475i	$-0.177986\pi$
$677$	3.56145e11			1.69540			0.847701	+	0.530475i	$0.177986\pi$
$678$	−9.13767e10	−	1.97984e11i	−0.432431	−	0.936940i
$679$			3.50747e11i			1.65012i
$680$		0			0
$681$	5.20778e11			2.42139
$682$	1.13642e10	−	5.24500e9i	0.0525295	−	0.0242442i
$683$			2.15409e11i			0.989878i	0.868928	+	0.494939i	$0.164810\pi$
$683$			2.15409e11i			0.989878i	−0.868928	+	0.494939i	$0.835190\pi$
$684$	1.85656e11	+	1.58285e11i	0.848172	+	0.723129i
$685$		0			0
$686$	8.15274e10	+	1.76644e11i	0.368135	+	0.797632i
$687$			1.97142e11i			0.885018i
$688$	1.91087e11	−	3.06070e10i	0.852860	−	0.136605i
$689$	−3.55283e11			−1.57651
$690$		0			0
$691$			2.64031e11i			1.15809i	0.815296	+	0.579045i	$0.196574\pi$
$691$			2.64031e11i			1.15809i	−0.815296	+	0.579045i	$0.803426\pi$
$692$	2.62475e11	−	3.07862e11i	1.14463	−	1.34255i
$693$	−9.67149e10			−0.419334
$694$	4.98250e10	+	1.07955e11i	0.214788	+	0.465377i
$695$		0			0
$696$	−5.34454e11	−	1.49977e11i	−2.27758	−	0.639128i
$697$	1.52775e10			0.0647324
$698$	−7.89280e10	+	3.64280e10i	−0.332514	+	0.153467i
$699$			3.66218e11i			1.53402i
$700$		0			0
$701$	−1.98676e11			−0.822758			−0.411379	−	0.911464i	$-0.634953\pi$
$701$	−1.98676e11			−0.822758			−0.411379	+	0.911464i	$0.634953\pi$
$702$	−4.47469e11	−	9.69523e11i	−1.84253	−	3.99218i
$703$		−	3.47992e10i		−	0.142478i
$704$	2.00818e10	−	3.29638e10i	0.0817545	−	0.134198i
$705$		0			0
$706$	1.04261e11	−	4.81201e10i	0.419666	−	0.193690i
$707$			1.59943e11i			0.640159i
$708$	−2.20193e11	+	2.58269e11i	−0.876335	+	1.02787i
$709$	−1.08511e11			−0.429427			−0.214713	−	0.976677i	$-0.568882\pi$
$709$	−1.08511e11			−0.429427			−0.214713	+	0.976677i	$0.568882\pi$
$710$		0			0
$711$		−	7.81814e11i		−	3.05932i
$712$	1.17202e11	−	4.17659e11i	0.456054	−	1.62518i
$713$	2.63750e10			0.102055
$714$	−2.97899e11	+	1.37491e11i	−1.14624	+	0.529031i
$715$		0			0
$716$	−8.63665e10	−	7.36338e10i	−0.328619	−	0.280172i
$717$	4.18763e11			1.58450
$718$	7.39403e10	+	1.60205e11i	0.278217	+	0.602807i
$719$		−	3.56644e11i		−	1.33450i	−0.744832	−	0.667252i	$-0.767471\pi$
$719$		−	3.56644e11i		−	1.33450i	0.744832	−	0.667252i	$-0.232529\pi$
$720$		0			0
$721$	−6.91741e10			−0.255978
$722$	−1.95201e11	+	9.00923e10i	−0.718347	+	0.331542i
$723$			1.74694e11i			0.639329i
$724$	−3.10969e10	+	3.64741e10i	−0.113178	+	0.132749i
$725$		0			0
$726$	−2.10560e11	−	4.56217e11i	−0.757931	−	1.64220i
$727$			8.05781e10i			0.288456i	0.989544	+	0.144228i	$0.0460699\pi$
$727$			8.05781e10i			0.288456i	−0.989544	+	0.144228i	$0.953930\pi$
$728$	−4.87516e11	−	1.36805e11i	−1.73565	−	0.487055i
$729$	−3.31165e11			−1.17256
$730$		0			0
$731$			1.53455e11i			0.537415i
$732$	3.16541e11	+	2.69875e11i	1.10252	+	0.939978i
$733$	−3.80343e11			−1.31753			−0.658763	−	0.752351i	$-0.728920\pi$
$733$	−3.80343e11			−1.31753			−0.658763	+	0.752351i	$0.728920\pi$
$734$	−2.27324e11	−	4.92539e11i	−0.783179	−	1.69690i
$735$		0			0
$736$	6.75318e10	−	4.53366e10i	0.230143	−	0.154503i
$737$	3.32098e10			0.112563
$738$	6.83433e10	−	3.15428e10i	0.230394	−	0.106335i
$739$			4.01614e11i			1.34658i	0.739381	+	0.673288i	$0.235118\pi$
$739$			4.01614e11i			1.34658i	−0.739381	+	0.673288i	$0.764882\pi$
$740$		0			0
$741$	−4.20972e11			−1.39631
$742$	1.32979e11	+	2.88123e11i	0.438700	+	0.950523i
$743$			3.54474e11i			1.16313i	0.813499	+	0.581566i	$0.197560\pi$
$743$			3.54474e11i			1.16313i	−0.813499	+	0.581566i	$0.802440\pi$
$744$	5.65215e10	−	2.01418e11i	0.184468	−	0.657366i
$745$		0			0
$746$	4.63791e11	−	2.14056e11i	1.49750	−	0.691150i
$747$			1.11034e12i			3.56594i
$748$	2.32913e10	+	1.98575e10i	0.0744024	+	0.0634335i
$749$	3.31981e11			1.05484
$750$		0			0
$751$			4.84888e11i			1.52434i	0.647378	+	0.762169i	$0.275866\pi$
$751$			4.84888e11i			1.52434i	−0.647378	+	0.762169i	$0.724134\pi$
$752$	−3.25980e11	+	5.22132e10i	−1.01934	+	0.163271i
$753$	9.31329e11			2.89683
$754$	6.16781e11	−	2.84666e11i	1.90829	−	0.880745i
$755$		0			0
$756$	−6.18770e11	+	7.25767e11i	−1.89427	+	2.22183i
$757$	−1.22819e11			−0.374009			−0.187004	−	0.982359i	$-0.559878\pi$
$757$	−1.22819e11			−0.374009			−0.187004	+	0.982359i	$0.559878\pi$
$758$	−1.78578e11	−	3.86922e11i	−0.540942	−	1.17205i
$759$			2.68074e10i			0.0807771i
$760$		0			0
$761$	−1.93019e11			−0.575521			−0.287761	−	0.957702i	$-0.592911\pi$
$761$	−1.93019e11			−0.575521			−0.287761	+	0.957702i	$0.592911\pi$
$762$	−6.78315e11	+	3.13066e11i	−2.01192	+	0.928573i
$763$		−	2.03817e11i		−	0.601372i
$764$	1.01757e11	+	8.67555e10i	0.298670	+	0.254638i
$765$		0			0
$766$	−1.07991e11	−	2.33983e11i	−0.313671	−	0.679625i
$767$		−	4.15333e11i		−	1.20009i
$768$	−2.01502e11	−	6.12876e11i	−0.579208	−	1.76168i
$769$	1.34359e11			0.384202			0.192101	−	0.981375i	$-0.438470\pi$
$769$	1.34359e11			0.384202			0.192101	+	0.981375i	$0.438470\pi$
$770$		0			0
$771$			1.68399e11i			0.476564i
$772$	−8.33422e9	+	9.77536e9i	−0.0234636	+	0.0275210i
$773$	1.97017e11			0.551804			0.275902	−	0.961186i	$-0.411024\pi$
$773$	1.97017e11			0.551804			0.275902	+	0.961186i	$0.411024\pi$
$774$	3.16831e11	+	6.86472e11i	0.882803	+	1.91275i
$775$		0			0
$776$	1.47760e11	−	5.26553e11i	0.407483	−	1.45210i
$777$	2.30573e11			0.632593
$778$	−2.63925e11	+	1.21811e11i	−0.720380	+	0.332481i
$779$		−	1.75082e10i		−	0.0475435i
$780$		0			0
$781$	8.53896e9			0.0229510
$782$	2.70281e10	+	5.85613e10i	0.0722751	+	0.156597i
$783$		−	1.27951e12i		−	3.40406i
$784$	1.17756e10	+	7.35183e10i	0.0311688	+	0.194595i
$785$		0			0
$786$	−1.18880e12	+	5.48675e11i	−3.11473	+	1.43756i
$787$			3.63175e11i			0.946711i	0.880871	+	0.473356i	$0.156957\pi$
$787$			3.63175e11i			0.946711i	−0.880871	+	0.473356i	$0.843043\pi$
$788$	4.37858e10	−	5.13572e10i	0.113561	−	0.133198i
$789$	−2.27540e11			−0.587150
$790$		0			0
$791$		−	2.38339e11i		−	0.608820i
$792$	1.45191e11	+	4.07433e10i	0.369012	+	0.103551i
$793$	−5.09044e11			−1.28725
$794$	−5.85926e11	+	2.70425e11i	−1.47421	+	0.680402i
$795$		0			0
$796$	−2.46576e11	−	2.10224e11i	−0.614184	−	0.523637i
$797$	5.78264e10			0.143316			0.0716578	−	0.997429i	$-0.477171\pi$
$797$	5.78264e10			0.143316			0.0716578	+	0.997429i	$0.477171\pi$
$798$	1.57566e11	+	3.41395e11i	0.388553	+	0.841872i
$799$		−	2.61782e11i		−	0.642321i
$800$		0			0
$801$	1.69475e12			4.11694
$802$	−2.70766e11	+	1.24968e11i	−0.654481	+	0.302066i
$803$			8.34631e10i			0.200739i
$804$	3.60123e11	−	4.22395e11i	0.861840	−	1.01087i
$805$		0			0
$806$	1.07281e11	+	2.32444e11i	0.254205	+	0.550781i
$807$		−	4.10660e11i		−	0.968251i
$808$	6.73795e10	−	2.40111e11i	0.158082	−	0.563336i
$809$	−1.75206e11			−0.409031			−0.204515	−	0.978863i	$-0.565562\pi$
$809$	−1.75206e11			−0.409031			−0.204515	+	0.978863i	$0.565562\pi$
$810$		0			0
$811$			1.53398e11i			0.354599i	0.984157	+	0.177299i	$0.0567361\pi$
$811$			1.53398e11i			0.354599i	−0.984157	+	0.177299i	$0.943264\pi$
$812$	−4.61711e11	−	3.93642e11i	−1.06205	−	0.905477i
$813$	−1.40912e12			−3.22541
$814$	−9.01369e9	−	1.95298e10i	−0.0205308	−	0.0444836i
$815$		0			0
$816$	5.05136e11	−	8.09091e10i	1.13932	−	0.182489i
$817$	1.75860e11			0.394712
$818$	2.83840e11	−	1.31002e11i	0.633958	−	0.292594i
$819$		−	1.97821e12i		−	4.39680i
$820$		0			0
$821$	−3.12544e11			−0.687922			−0.343961	−	0.938984i	$-0.611769\pi$
$821$	−3.12544e11			−0.687922			−0.343961	+	0.938984i	$0.611769\pi$
$822$	−1.24201e11	−	2.69104e11i	−0.272043	−	0.589431i
$823$			6.75905e11i			1.47328i	0.676283	+	0.736641i	$0.263589\pi$
$823$			6.75905e11i			1.47328i	−0.676283	+	0.736641i	$0.736411\pi$
$824$	1.03846e11	+	2.91411e10i	0.225259	+	0.0632116i
$825$		0			0
$826$	−3.36822e11	+	1.55455e11i	−0.723570	+	0.333953i
$827$		−	7.49212e11i		−	1.60171i	−0.598861	−	0.800853i	$-0.704380\pi$
$827$		−	7.49212e11i		−	1.60171i	0.598861	−	0.800853i	$-0.295620\pi$
$828$	2.41818e11	+	2.06168e11i	0.514479	+	0.438631i
$829$	−6.27639e11			−1.32890			−0.664449	−	0.747333i	$-0.731334\pi$
$829$	−6.27639e11			−1.32890			−0.664449	+	0.747333i	$0.731334\pi$
$830$		0			0
$831$		−	2.83735e11i		−	0.594988i
$832$	6.74242e11	+	4.10753e11i	1.40709	+	0.857211i
$833$	−5.90396e10			−0.122621
$834$	−1.46777e12	+	6.77429e11i	−3.03385	+	1.40023i
$835$		0			0
$836$	2.27569e10	−	2.66920e10i	0.0465895	−	0.0546458i
$837$	4.82206e11			0.982495
$838$	1.07546e11	+	2.33018e11i	0.218081	+	0.472512i
$839$			8.86257e11i			1.78860i	0.447473	+	0.894298i	$0.352324\pi$
$839$			8.86257e11i			1.78860i	−0.447473	+	0.894298i	$0.647676\pi$
$840$		0			0
$841$	3.13739e11			0.627168
$842$	−1.27852e11	+	5.90080e10i	−0.254365	+	0.117398i
$843$		−	2.48638e11i		−	0.492331i
$844$	−1.81962e11	−	1.55136e11i	−0.358600	−	0.305733i
$845$		0			0
$846$	−5.40489e11	−	1.17107e12i	−1.05513	−	2.28613i
$847$		−	5.49207e11i		−	1.06709i
$848$	−7.82540e10	−	4.88560e11i	−0.151329	−	0.944787i
$849$	1.29457e12			2.49169
$850$		0			0
$851$		−	4.53263e10i		−	0.0864235i
$852$	9.25956e10	−	1.08607e11i	0.175724	−	0.206110i
$853$	4.42385e10			0.0835611			0.0417805	−	0.999127i	$-0.486697\pi$
$853$	4.42385e10			0.0835611			0.0417805	+	0.999127i	$0.486697\pi$
$854$	1.90530e11	+	4.12819e11i	0.358206	+	0.776119i
$855$		0			0
$856$	−4.98381e11	−	1.39854e11i	−0.928253	−	0.260484i
$857$	1.03847e12			1.92517			0.962586	−	0.270976i	$-0.0873463\pi$
$857$	1.03847e12			1.92517			0.962586	+	0.270976i	$0.0873463\pi$
$858$	−2.36255e11	+	1.09040e11i	−0.435945	+	0.201204i
$859$		−	5.28066e11i		−	0.969874i	−0.874549	−	0.484937i	$-0.838842\pi$
$859$		−	5.28066e11i		−	0.969874i	0.874549	−	0.484937i	$-0.161158\pi$
$860$		0			0
$861$	1.16006e11			0.211090
$862$	1.45667e11	+	3.15614e11i	0.263835	+	0.571646i
$863$			1.90850e11i			0.344072i	0.985091	+	0.172036i	$0.0550346\pi$
$863$			1.90850e11i			0.344072i	−0.985091	+	0.172036i	$0.944965\pi$
$864$	1.23466e12	−	8.28873e11i	2.21561	−	1.48742i
$865$		0			0
$866$	3.64140e11	−	1.68063e11i	0.647436	−	0.298814i
$867$		−	6.42181e11i		−	1.13653i
$868$	1.48351e11	−	1.74004e11i	0.261343	−	0.306534i
$869$	−1.12403e11			−0.197105
$870$		0			0
$871$			6.79273e11i			1.18024i
$872$	−8.58624e10	+	3.05977e11i	−0.148504	+	0.529203i
$873$	2.13661e12			3.67848
$874$	6.71119e10	−	3.09745e10i	0.115015	−	0.0530834i
$875$		0			0
$876$	1.06157e12	+	9.05065e11i	1.80273	+	1.53696i
$877$	−2.36707e11			−0.400140			−0.200070	−	0.979782i	$-0.564117\pi$
$877$	−2.36707e11			−0.400140			−0.200070	+	0.979782i	$0.564117\pi$
$878$	1.80401e11	+	3.90872e11i	0.303572	+	0.657744i
$879$			8.28136e11i			1.38722i
$880$		0			0
$881$	3.49205e11			0.579665			0.289832	−	0.957077i	$-0.406400\pi$
$881$	3.49205e11			0.579665			0.289832	+	0.957077i	$0.406400\pi$
$882$	−2.64111e11	+	1.21897e11i	−0.436428	+	0.201427i
$883$			5.98818e11i			0.985035i	0.870302	+	0.492518i	$0.163923\pi$
$883$			5.98818e11i			0.985035i	−0.870302	+	0.492518i	$0.836077\pi$
$884$	−4.06166e11	+	4.76400e11i	−0.665111	+	0.780122i
$885$		0			0
$886$	3.46317e11	+	7.50359e11i	0.562004	+	1.21768i
$887$			5.75931e11i			0.930413i	0.885202	+	0.465207i	$0.154020\pi$
$887$			5.75931e11i			0.930413i	−0.885202	+	0.465207i	$0.845980\pi$
$888$	−3.46143e11	−	9.71338e10i	−0.556678	−	0.156214i
$889$	−8.16574e11			−1.30734
$890$		0			0
$891$			2.48559e11i			0.394383i
$892$	−1.01734e11	−	8.67357e10i	−0.160697	−	0.137006i
$893$	−3.00004e11			−0.471761
$894$	−2.48814e11	−	5.39101e11i	−0.389516	−	0.843957i
$895$		0			0
$896$	8.07457e10	−	7.00530e11i	0.125282	−	1.08691i
$897$	−5.48320e11			−0.846962
$898$	6.70527e11	−	3.09472e11i	1.03112	−	0.475900i
$899$			3.06764e11i			0.469641i
$900$		0			0
$901$	3.92343e11			0.595342
$902$	−4.53497e9	−	9.82583e9i	−0.00685091	−	0.0148437i
$903$			1.16522e12i			1.75249i
$904$	−1.00405e11	+	3.57802e11i	−0.150343	+	0.535758i
$905$		0			0
$906$	8.72991e11	−	4.02916e11i	1.29568	−	0.598001i
$907$			4.04494e11i			0.597699i	0.954300	+	0.298849i	$0.0966029\pi$
$907$			4.04494e11i			0.597699i	−0.954300	+	0.298849i	$0.903397\pi$
$908$	−6.75398e11	−	5.75827e11i	−0.993611	−	0.847126i
$909$	9.74308e11			1.42705
$910$		0			0
$911$		−	6.18016e11i		−	0.897276i	−0.893714	−	0.448638i	$-0.851909\pi$
$911$		−	6.18016e11i		−	0.897276i	0.893714	−	0.448638i	$-0.148091\pi$
$912$	−9.27227e10	−	5.78891e11i	−0.134031	−	0.836792i
$913$	1.59636e11			0.229746
$914$	−4.52219e11	+	2.08715e11i	−0.647984	+	0.299067i
$915$		0			0
$916$	2.17981e11	−	2.55674e11i	0.309625	−	0.363165i
$917$	−1.43111e12			−2.02394
$918$	4.94145e11	+	1.07066e12i	0.695799	+	1.50758i
$919$		−	5.11050e11i		−	0.716476i	−0.933630	−	0.358238i	$-0.883378\pi$
$919$		−	5.11050e11i		−	0.716476i	0.933630	−	0.358238i	$-0.116622\pi$
$920$		0			0
$921$	−2.30577e12			−3.20462
$922$	−6.79904e11	+	3.13800e11i	−0.940858	+	0.434239i
$923$			1.74656e11i			0.240645i
$924$	1.76856e11	+	1.50783e11i	0.242623	+	0.206854i
$925$		0			0
$926$	1.36332e11	+	2.95388e11i	0.185419	+	0.401744i
$927$			4.21380e11i			0.570631i
$928$	5.27304e11	+	7.85453e11i	0.710999	+	1.05908i
$929$	3.49578e11			0.469333			0.234666	−	0.972076i	$-0.424600\pi$
$929$	3.49578e11			0.469333			0.234666	+	0.972076i	$0.424600\pi$
$930$		0			0
$931$			6.76600e10i			0.0900603i
$932$	4.04929e11	−	4.74949e11i	0.536680	−	0.629482i
$933$	8.34919e11			1.10184
$934$	3.95371e11	+	8.56642e11i	0.519537	+	1.12567i
$935$		0			0
$936$	−8.33363e11	+	2.96975e12i	−1.08575	+	3.86915i
$937$	1.37124e11			0.177891			0.0889457	−	0.996036i	$-0.471650\pi$
$937$	1.37124e11			0.177891			0.0889457	+	0.996036i	$0.471650\pi$
$938$	5.50869e11	−	2.54245e11i	0.711602	−	0.328429i
$939$			2.65616e12i			3.41659i
$940$		0			0
$941$	−4.32170e10			−0.0551183			−0.0275592	−	0.999620i	$-0.508773\pi$
$941$	−4.32170e10			−0.0551183			−0.0275592	+	0.999620i	$0.508773\pi$
$942$	−7.05546e11	−	1.52869e12i	−0.896028	−	1.94141i
$943$		−	2.28046e10i		−	0.0288387i
$944$	5.71137e11	−	9.14807e10i	0.719204	−	0.115197i
$945$		0			0
$946$	9.86953e10	−	4.55513e10i	0.123234	−	0.0568770i
$947$			1.24527e12i			1.54832i	0.632987	+	0.774162i	$0.281829\pi$
$947$			1.24527e12i			1.54832i	−0.632987	+	0.774162i	$0.718171\pi$
$948$	−1.21888e12	+	1.42965e12i	−1.50914	+	1.77010i
$949$	−1.70716e12			−2.10479
$950$		0			0
$951$			4.27037e11i			0.522088i
$952$	5.38370e11	+	1.51076e11i	0.655440	+	0.183928i
$953$	−9.35275e11			−1.13388			−0.566941	−	0.823759i	$-0.691873\pi$
$953$	−9.35275e11			−1.13388			−0.566941	+	0.823759i	$0.691873\pi$
$954$	1.75513e12	−	8.10053e11i	2.11892	−	0.977958i
$955$		0			0
$956$	−5.43095e11	−	4.63028e11i	−0.650195	−	0.554339i
$957$	−3.11793e11			−0.371723
$958$	−8.06120e10	−	1.74661e11i	−0.0957057	−	0.207364i
$959$		−	3.23955e11i		−	0.383010i
$960$		0			0
$961$	7.37282e11			0.864450
$962$	3.99463e11	−	1.84366e11i	0.466419	−	0.215269i
$963$		−	2.02229e12i		−	2.35147i
$964$	1.93160e11	−	2.26561e11i	0.223670	−	0.262347i
$965$		0			0
$966$	2.05231e11	+	4.44670e11i	0.235686	+	0.510657i
$967$			1.52906e12i			1.74871i	0.485286	+	0.874355i	$0.338715\pi$
$967$			1.52906e12i			1.74871i	−0.485286	+	0.874355i	$0.661285\pi$
$968$	−2.31365e11	+	8.24486e11i	−0.263510	+	0.939035i
$969$	4.64884e11			0.527290
$970$		0			0
$971$			5.95468e11i			0.669856i	0.942244	+	0.334928i	$0.108712\pi$
$971$			5.95468e11i			0.669856i	−0.942244	+	0.334928i	$0.891288\pi$
$972$	1.34877e12	+	1.14993e12i	1.51103	+	1.28826i
$973$	−1.76694e12			−1.97139
$974$	−3.25817e11	−	7.05942e11i	−0.362024	−	0.784392i
$975$		0			0
$976$	−1.12121e11	−	7.00002e11i	−0.123563	−	0.771436i
$977$	−1.10548e12			−1.21332			−0.606659	−	0.794962i	$-0.707491\pi$
$977$	−1.10548e12			−1.21332			−0.606659	+	0.794962i	$0.707491\pi$
$978$	−4.89704e11	+	2.26016e11i	−0.535277	+	0.247049i
$979$		−	2.43657e11i		−	0.265245i
$980$		0			0
$981$	−1.24157e12			−1.34059
$982$	1.15046e10	+	2.49269e10i	0.0123716	+	0.0268054i
$983$		−	1.26644e10i		−	0.0135634i	−0.999977	−	0.00678172i	$-0.997841\pi$
$983$		−	1.26644e10i		−	0.0135634i	0.999977	−	0.00678172i	$-0.00215871\pi$
$984$	−1.74152e11	−	4.88700e10i	−0.185758	−	0.0521269i
$985$		0			0
$986$	−6.81118e11	+	3.14360e11i	−0.720634	+	0.332598i
$987$		−	1.98777e12i		−	2.09458i
$988$	5.45959e11	+	4.65470e11i	0.572971	+	0.488500i
$989$	2.29060e11			0.239422
$990$		0			0
$991$			7.11883e11i			0.738098i	0.929410	+	0.369049i	$0.120317\pi$
$991$			7.11883e11i			0.738098i	−0.929410	+	0.369049i	$0.879683\pi$
$992$	−2.96012e11	+	1.98724e11i	−0.305677	+	0.205212i
$993$	1.74730e12			1.79709
$994$	1.41641e11	−	6.53721e10i	0.145092	−	0.0669649i
$995$		0			0
$996$	1.73107e12	−	2.03041e12i	1.75905	−	2.06322i
$997$	−2.60515e11			−0.263665			−0.131832	−	0.991272i	$-0.542086\pi$
$997$	−2.60515e11			−0.263665			−0.131832	+	0.991272i	$0.542086\pi$
$998$	−4.19435e11	−	9.08782e11i	−0.422807	−	0.916089i
$999$		−	8.28685e11i		−	0.832008i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	100.9.b.d.51.2		16
4.3	odd	2	inner	100.9.b.d.51.1		16
5.2	odd	4		100.9.d.c.99.11		32
5.3	odd	4		100.9.d.c.99.22		32
5.4	even	2		20.9.b.a.11.15	✓	16
15.14	odd	2		180.9.c.a.91.2		16
20.3	even	4		100.9.d.c.99.12		32
20.7	even	4		100.9.d.c.99.21		32
20.19	odd	2		20.9.b.a.11.16	yes	16
40.19	odd	2		320.9.b.d.191.1		16
40.29	even	2		320.9.b.d.191.16		16
60.59	even	2		180.9.c.a.91.1		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
20.9.b.a.11.15	✓	16	5.4	even	2
20.9.b.a.11.16	yes	16	20.19	odd	2
100.9.b.d.51.1		16	4.3	odd	2	inner
100.9.b.d.51.2		16	1.1	even	1	trivial
100.9.d.c.99.11		32	5.2	odd	4
100.9.d.c.99.12		32	20.3	even	4
100.9.d.c.99.21		32	20.7	even	4
100.9.d.c.99.22		32	5.3	odd	4
180.9.c.a.91.1		16	60.59	even	2
180.9.c.a.91.2		16	15.14	odd	2
320.9.b.d.191.1		16	40.19	odd	2
320.9.b.d.191.16		16	40.29	even	2

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:	\( N \)	\(=\)	\( 100 = 2^{2} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 9 \)
Character orbit:	\([\chi]\)	\(=\)	100.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-14.5274 + 6.70489i) q^{2} +150.211i q^{3} +(166.089 - 194.809i) q^{4} +(-1007.15 - 2182.17i) q^{6} -2626.96i q^{7} +(-1106.66 + 3943.67i) q^{8} -16002.3 q^{9} +O(q^{10})\)	\(q+(-14.5274 + 6.70489i) q^{2} +150.211i q^{3} +(166.089 - 194.809i) q^{4} +(-1007.15 - 2182.17i) q^{6} -2626.96i q^{7} +(-1106.66 + 3943.67i) q^{8} -16002.3 q^{9} +2300.68i q^{11} +(29262.4 + 24948.4i) q^{12} -47058.2 q^{13} +(17613.5 + 38162.8i) q^{14} +(-10365.0 - 64711.2i) q^{16} +51967.0 q^{17} +(232472. - 107294. i) q^{18} -59554.7i q^{19} +394598. q^{21} +(-15425.8 - 33422.9i) q^{22} -77570.5i q^{23} +(-592382. - 166233. i) q^{24} +(683632. - 315520. i) q^{26} -1.41819e6i q^{27} +(-511754. - 436308. i) q^{28} +902211. q^{29} +340014. i q^{31} +(584457. + 870587. i) q^{32} -345588. q^{33} +(-754943. + 348433. i) q^{34} +(-2.65781e6 + 3.11740e6i) q^{36} +584324. q^{37} +(399308. + 865173. i) q^{38} -7.06866e6i q^{39} +293985. q^{41} +(-5.73247e6 + 2.64573e6i) q^{42} +2.95292e6i q^{43} +(448194. + 382118. i) q^{44} +(520102. + 1.12689e6i) q^{46} -5.03746e6i q^{47} +(9.72033e6 - 1.55693e6i) q^{48} -1.13610e6 q^{49} +7.80601e6i q^{51} +(-7.81585e6 + 9.16736e6i) q^{52} +7.54985e6 q^{53} +(9.50883e6 + 2.06026e7i) q^{54} +(1.03598e7 + 2.90715e6i) q^{56} +8.94577e6 q^{57} +(-1.31068e7 + 6.04923e6i) q^{58} +8.82594e6i q^{59} +1.08173e7 q^{61} +(-2.27976e6 - 4.93951e6i) q^{62} +4.20375e7i q^{63} +(-1.43278e7 - 8.72861e6i) q^{64} +(5.02049e6 - 2.31713e6i) q^{66} -1.44347e7i q^{67} +(8.63113e6 - 1.01236e7i) q^{68} +1.16519e7 q^{69} -3.71149e6i q^{71} +(1.77092e7 - 6.31079e7i) q^{72} +3.62775e7 q^{73} +(-8.48869e6 + 3.91783e6i) q^{74} +(-1.16018e7 - 9.89137e6i) q^{76} +6.04380e6 q^{77} +(4.73946e7 + 1.02689e8i) q^{78} +4.88562e7i q^{79} +1.08037e8 q^{81} +(-4.27083e6 + 1.97114e6i) q^{82} -6.93862e7i q^{83} +(6.55383e7 - 7.68711e7i) q^{84} +(-1.97990e7 - 4.28982e7i) q^{86} +1.35522e8i q^{87} +(-9.07314e6 - 2.54608e6i) q^{88} -1.05906e8 q^{89} +1.23620e8i q^{91} +(-1.51114e7 - 1.28836e7i) q^{92} -5.10738e7 q^{93} +(3.37756e7 + 7.31810e7i) q^{94} +(-1.30772e8 + 8.77919e7i) q^{96} -1.33519e8 q^{97} +(1.65045e7 - 7.61742e6i) q^{98} -3.68163e7i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 6 q^{2} - 52 q^{4} + 4368 q^{6} + 14184 q^{8} - 38800 q^{9}+O(q^{10}) \) 16 * q - 6 * q^2 - 52 * q^4 + 4368 * q^6 + 14184 * q^8 - 38800 * q^9	\( 16 q - 6 q^{2} - 52 q^{4} + 4368 q^{6} + 14184 q^{8} - 38800 q^{9} + 64040 q^{12} - 51392 q^{13} + 68472 q^{14} - 81424 q^{16} - 27552 q^{17} + 616994 q^{18} + 414496 q^{21} + 389120 q^{22} + 163792 q^{24} + 1037124 q^{26} - 1288520 q^{28} + 2764896 q^{29} + 4379904 q^{32} + 5521600 q^{33} + 3793964 q^{34} - 5468916 q^{36} - 9009472 q^{37} + 3087360 q^{38} - 8576448 q^{41} + 4067400 q^{42} + 16921200 q^{44} - 7974152 q^{46} + 2696640 q^{48} - 32803600 q^{49} - 6679352 q^{52} - 2452032 q^{53} + 8898704 q^{54} + 34134768 q^{56} - 11957760 q^{57} - 52156572 q^{58} + 8371712 q^{61} - 1290000 q^{62} - 47543872 q^{64} + 19358000 q^{66} - 16095192 q^{68} + 7527264 q^{69} + 42242664 q^{72} - 61907232 q^{73} - 138210876 q^{74} + 2570400 q^{76} + 156997440 q^{77} + 104032400 q^{78} + 140586672 q^{81} - 83921012 q^{82} + 69761824 q^{84} - 101724672 q^{86} - 44728480 q^{88} + 106647456 q^{89} + 13876200 q^{92} - 105563840 q^{93} + 55264632 q^{94} - 453389952 q^{96} - 171851232 q^{97} + 285387714 q^{98}+O(q^{100}) \) 16 * q - 6 * q^2 - 52 * q^4 + 4368 * q^6 + 14184 * q^8 - 38800 * q^9 + 64040 * q^12 - 51392 * q^13 + 68472 * q^14 - 81424 * q^16 - 27552 * q^17 + 616994 * q^18 + 414496 * q^21 + 389120 * q^22 + 163792 * q^24 + 1037124 * q^26 - 1288520 * q^28 + 2764896 * q^29 + 4379904 * q^32 + 5521600 * q^33 + 3793964 * q^34 - 5468916 * q^36 - 9009472 * q^37 + 3087360 * q^38 - 8576448 * q^41 + 4067400 * q^42 + 16921200 * q^44 - 7974152 * q^46 + 2696640 * q^48 - 32803600 * q^49 - 6679352 * q^52 - 2452032 * q^53 + 8898704 * q^54 + 34134768 * q^56 - 11957760 * q^57 - 52156572 * q^58 + 8371712 * q^61 - 1290000 * q^62 - 47543872 * q^64 + 19358000 * q^66 - 16095192 * q^68 + 7527264 * q^69 + 42242664 * q^72 - 61907232 * q^73 - 138210876 * q^74 + 2570400 * q^76 + 156997440 * q^77 + 104032400 * q^78 + 140586672 * q^81 - 83921012 * q^82 + 69761824 * q^84 - 101724672 * q^86 - 44728480 * q^88 + 106647456 * q^89 + 13876200 * q^92 - 105563840 * q^93 + 55264632 * q^94 - 453389952 * q^96 - 171851232 * q^97 + 285387714 * q^98

Introduction

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