LMFDB - Embedded newform 180.9.c.a.91.2

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [180,9,Mod(91,180)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(180, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([1, 0, 0])) N = Newforms(chi, 9, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("180.91"); S:= CuspForms(chi, 9); N := Newforms(S);

Level:	$ N $	$=$	$ 180 = 2^{2} \cdot 3^{2} \cdot 5 $
Weight:	$ k $	$=$	$ 9 $
Character orbit:	$[\chi]$	$=$	180.c (of order $2$, degree $1$, minimal)

Newform invariants

comment:select newform

sage:traces = [16,-6] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(2)] == traces)

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

Self dual:	no
Analytic conductor:	$73.3281498110$
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} + 15630052 x^{14} + 100431843210026 x^{12} + \cdots + 41\!\cdots\!25 $ x^16 + 15630052x^14 + 100431843210026x^12 + 340815019972466359600x^10 + 649371842679456980126645875x^8 + 673266389314517670870339888950000x^6 + 325232066696204458027621996847496406250x^4 + 40989992790937256917294995464570014826562500*x^2 + 414509653712510017117723543124903397237712890625
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{58}\cdot 3^{4}\cdot 5^{16} $
Twist minimal:	no (minimal twist has level 20)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			91.2
Root			$1313.48i$ of defining polynomial
Character	$\chi$	$=$	180.91
Dual form			180.9.c.a.91.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-14.5274 + 6.70489i) q^{2} +(166.089 - 194.809i) q^{4} -279.508 q^{5} +2626.96i q^{7} +(-1106.66 + 3943.67i) q^{8} +(4060.52 - 1874.07i) q^{10} -2300.68i q^{11} +47058.2 q^{13} +(-17613.5 - 38162.8i) q^{14} +(-10365.0 - 64711.2i) q^{16} +51967.0 q^{17} -59554.7i q^{19} +(-46423.2 + 54450.7i) q^{20} +(15425.8 + 33422.9i) q^{22} -77570.5i q^{23} +78125.0 q^{25} +(-683632. + 315520. i) q^{26} +(511754. + 436308. i) q^{28} -902211. q^{29} +340014. i q^{31} +(584457. + 870587. i) q^{32} +(-754943. + 348433. i) q^{34} -734257. i q^{35} -584324. q^{37} +(399308. + 865173. i) q^{38} +(309321. - 1.10229e6i) q^{40} -293985. q^{41} -2.95292e6i q^{43} +(-448194. - 382118. i) q^{44} +(520102. + 1.12689e6i) q^{46} -5.03746e6i q^{47} -1.13610e6 q^{49} +(-1.13495e6 + 523820. i) q^{50} +(7.81585e6 - 9.16736e6i) q^{52} +7.54985e6 q^{53} +643061. i q^{55} +(-1.03598e7 - 2.90715e6i) q^{56} +(1.31068e7 - 6.04923e6i) q^{58} -8.82594e6i q^{59} +1.08173e7 q^{61} +(-2.27976e6 - 4.93951e6i) q^{62} +(-1.43278e7 - 8.72861e6i) q^{64} -1.31532e7 q^{65} +1.44347e7i q^{67} +(8.63113e6 - 1.01236e7i) q^{68} +(4.92311e6 + 1.06668e7i) q^{70} +3.71149e6i q^{71} -3.62775e7 q^{73} +(8.48869e6 - 3.91783e6i) q^{74} +(-1.16018e7 - 9.89137e6i) q^{76} +6.04380e6 q^{77} +4.88562e7i q^{79} +(2.89710e6 + 1.80873e7i) q^{80} +(4.27083e6 - 1.97114e6i) q^{82} -6.93862e7i q^{83} -1.45252e7 q^{85} +(1.97990e7 + 4.28982e7i) q^{86} +(9.07314e6 + 2.54608e6i) q^{88} +1.05906e8 q^{89} +1.23620e8i q^{91} +(-1.51114e7 - 1.28836e7i) q^{92} +(3.37756e7 + 7.31810e7i) q^{94} +1.66460e7i q^{95} +1.33519e8 q^{97} +(1.65045e7 - 7.61742e6i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 6 q^{2} - 52 q^{4} + 14184 q^{8} + 8750 q^{10} + 51392 q^{13} - 68472 q^{14} - 81424 q^{16} - 27552 q^{17} - 172500 q^{20} - 389120 q^{22} + 1250000 q^{25} - 1037124 q^{26} + 1288520 q^{28} - 2764896 q^{29}+ \cdots + 285387714 q^{98}+O(q^{100}) $ 16 * q - 6 * q^2 - 52 * q^4 + 14184 * q^8 + 8750 * q^10 + 51392 * q^13 - 68472 * q^14 - 81424 * q^16 - 27552 * q^17 - 172500 * q^20 - 389120 * q^22 + 1250000 * q^25 - 1037124 * q^26 + 1288520 * q^28 - 2764896 * q^29 + 4379904 * q^32 + 3793964 * q^34 + 9009472 * q^37 + 3087360 * q^38 + 385000 * q^40 + 8576448 * q^41 - 16921200 * q^44 - 7974152 * q^46 - 32803600 * q^49 - 468750 * q^50 + 6679352 * q^52 - 2452032 * q^53 - 34134768 * q^56 + 52156572 * q^58 + 8371712 * q^61 - 1290000 * q^62 - 47543872 * q^64 - 9060000 * q^65 - 16095192 * q^68 + 10500000 * q^70 + 61907232 * q^73 + 138210876 * q^74 + 2570400 * q^76 + 156997440 * q^77 - 37590000 * q^80 + 83921012 * q^82 - 106960000 * q^85 + 101724672 * q^86 + 44728480 * q^88 - 106647456 * q^89 + 13876200 * q^92 + 55264632 * q^94 + 171851232 * q^97 + 285387714 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/180\mathbb{Z}\right)^\times$.

$n$	$37$	$91$	$101$
$\chi(n)$	$1$	$-1$	$1$

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
$3$		0			0
$3$		0			0
$4$	166.089	−	194.809i	0.648785	−	0.760972i
$5$	−279.508			−0.447214
$5$	−279.508			−0.447214
$6$		0			0
$7$			2626.96i			1.09411i	0.837097	+	0.547055i	$0.184251\pi$
$7$			2626.96i			1.09411i	−0.837097	+	0.547055i	$0.815749\pi$
$8$	−1106.66	+	3943.67i	−0.270181	+	0.962810i
$9$		0			0
$10$	4060.52	−	1874.07i	0.406052	−	0.187407i
$11$		−	2300.68i		−	0.157140i	−0.996909	−	0.0785699i	$-0.974965\pi$
$11$		−	2300.68i		−	0.157140i	0.996909	−	0.0785699i	$-0.0250354\pi$
$12$		0			0
$13$	47058.2			1.64764			0.823820	−	0.566852i	$-0.191839\pi$
$13$	47058.2			1.64764			0.823820	+	0.566852i	$0.191839\pi$
$14$	−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	$0.399302\pi$
$18$		0			0
$19$		−	59554.7i		−	0.456985i	−0.973546	−	0.228492i	$-0.926620\pi$
$19$		−	59554.7i		−	0.456985i	0.973546	−	0.228492i	$-0.0733796\pi$
$20$	−46423.2	+	54450.7i	−0.290145	+	0.340317i
$21$		0			0
$22$	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	$-0.0442594\pi$
$24$		0			0
$25$	78125.0			0.200000
$26$	−683632.	+	315520.i	−1.49599	+	0.690453i
$27$		0			0
$28$	511754.	+	436308.i	0.832587	+	0.709841i
$29$	−902211.			−1.27561			−0.637803	−	0.770200i	$-0.720156\pi$
$29$	−902211.			−1.27561			−0.637803	+	0.770200i	$0.720156\pi$
$30$		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
$33$		0			0
$34$	−754943.	+	348433.i	−0.564935	+	0.260737i
$35$		−	734257.i		−	0.489301i
$36$		0			0
$37$	−584324.			−0.311779			−0.155890	−	0.987774i	$-0.549824\pi$
$37$	−584324.			−0.311779			−0.155890	+	0.987774i	$0.549824\pi$
$38$	399308.	+	865173.i	0.191502	+	0.414924i
$39$		0			0
$40$	309321.	−	1.10229e6i	0.120829	−	0.430582i
$41$	−293985.			−0.104037			−0.0520187	−	0.998646i	$-0.516566\pi$
$41$	−293985.			−0.104037			−0.0520187	+	0.998646i	$0.516566\pi$
$42$		0			0
$43$		−	2.95292e6i		−	0.863731i	−0.901938	−	0.431866i	$-0.857856\pi$
$43$		−	2.95292e6i		−	0.863731i	0.901938	−	0.431866i	$-0.142144\pi$
$44$	−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	$-0.172642\pi$
$48$		0			0
$49$	−1.13610e6			−0.197075
$50$	−1.13495e6	+	523820.i	−0.181592	+	0.0838111i
$51$		0			0
$52$	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	$0.341211\pi$
$54$		0			0
$55$			643061.i			0.0702751i
$56$	−1.03598e7	−	2.90715e6i	−1.05342	−	0.295608i
$57$		0			0
$58$	1.31068e7	−	6.04923e6i	1.15820	−	0.534550i
$59$		−	8.82594e6i		−	0.728372i	−0.931326	−	0.364186i	$-0.881347\pi$
$59$		−	8.82594e6i		−	0.728372i	0.931326	−	0.364186i	$-0.118653\pi$
$60$		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
$63$		0			0
$64$	−1.43278e7	−	8.72861e6i	−0.854004	−	0.520266i
$65$	−1.31532e7			−0.736847
$66$		0			0
$67$			1.44347e7i			0.716324i	0.933659	+	0.358162i	$0.116596\pi$
$67$			1.44347e7i			0.716324i	−0.933659	+	0.358162i	$0.883404\pi$
$68$	8.63113e6	−	1.01236e7i	0.403675	−	0.473479i
$69$		0			0
$70$	4.92311e6	+	1.06668e7i	0.205044	+	0.444266i
$71$			3.71149e6i			0.146054i	0.997330	+	0.0730272i	$0.0232660\pi$
$71$			3.71149e6i			0.146054i	−0.997330	+	0.0730272i	$0.976734\pi$
$72$		0			0
$73$	−3.62775e7			−1.27746			−0.638728	−	0.769433i	$-0.720539\pi$
$73$	−3.62775e7			−1.27746			−0.638728	+	0.769433i	$0.720539\pi$
$74$	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
$78$		0			0
$79$			4.88562e7i			1.25433i	0.778887	+	0.627164i	$0.215785\pi$
$79$			4.88562e7i			1.25433i	−0.778887	+	0.627164i	$0.784215\pi$
$80$	2.89710e6	+	1.80873e7i	0.0707300	+	0.441585i
$81$		0			0
$82$	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	$-0.260957\pi$
$84$		0			0
$85$	−1.45252e7			−0.278257
$86$	1.97990e7	+	4.28982e7i	0.361951	+	0.784234i
$87$		0			0
$88$	9.07314e6	+	2.54608e6i	0.151296	+	0.0424562i
$89$	1.05906e8			1.68796			0.843979	−	0.536377i	$-0.180207\pi$
$89$	1.05906e8			1.68796			0.843979	+	0.536377i	$0.180207\pi$
$90$		0			0
$91$			1.23620e8i			1.80270i
$92$	−1.51114e7	−	1.28836e7i	−0.210938	−	0.179840i
$93$		0			0
$94$	3.37756e7	+	7.31810e7i	0.432605	+	0.937319i
$95$			1.66460e7i			0.204370i
$96$		0			0
$97$	1.33519e8			1.50819			0.754093	−	0.656768i	$-0.228077\pi$
$97$	1.33519e8			1.50819			0.754093	+	0.656768i	$0.228077\pi$
$98$	1.65045e7	−	7.61742e6i	0.178936	−	0.0825854i
$99$		0			0
$100$	1.29757e7	−	1.52194e7i	0.129757	−	0.152194i
$101$	6.08853e7			0.585096			0.292548	−	0.956251i	$-0.405497\pi$
$101$	6.08853e7			0.585096			0.292548	+	0.956251i	$0.405497\pi$
$102$		0			0
$103$			2.63324e7i			0.233960i	0.993134	+	0.116980i	$0.0373214\pi$
$103$			2.63324e7i			0.233960i	−0.993134	+	0.116980i	$0.962679\pi$
$104$	−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	$0.839891\pi$
$108$		0			0
$109$	7.75869e7			0.549645			0.274822	−	0.961495i	$-0.411381\pi$
$109$	7.75869e7			0.549645			0.274822	+	0.961495i	$0.411381\pi$
$110$	−4.31165e6	−	9.34198e6i	−0.0294492	−	0.0638070i
$111$		0			0
$112$	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	$0.410253\pi$
$114$		0			0
$115$			2.16816e7i			0.123965i
$116$	−1.49847e8	+	1.75759e8i	−0.827593	+	0.970700i
$117$		0			0
$118$	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
$123$		0			0
$124$	6.62377e7	+	5.64725e7i	0.280168	+	0.238864i
$125$	−2.18366e7			−0.0894427
$126$		0			0
$127$			3.10844e8i			1.19489i	0.801910	+	0.597445i	$0.203817\pi$
$127$			3.10844e8i			1.19489i	−0.801910	+	0.597445i	$0.796183\pi$
$128$	2.66670e8	+	3.07374e7i	0.993423	+	0.114506i
$129$		0			0
$130$	1.91081e8	−	8.81906e7i	0.669028	−	0.308780i
$131$			5.44781e8i			1.84985i	0.380150	+	0.924925i	$0.375872\pi$
$131$			5.44781e8i			1.84985i	−0.380150	+	0.924925i	$0.624128\pi$
$132$		0			0
$133$	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	$0.443997\pi$
$138$		0			0
$139$		−	6.72621e8i		−	1.80182i	−0.434008	−	0.900909i	$-0.642901\pi$
$139$		−	6.72621e8i		−	1.80182i	0.434008	−	0.900909i	$-0.357099\pi$
$140$	−1.43040e8	−	1.21952e8i	−0.372344	−	0.317451i
$141$		0			0
$142$	−2.48851e7	−	5.39181e7i	−0.0612049	−	0.132612i
$143$		−	1.08266e8i		−	0.258910i
$144$		0			0
$145$	2.52176e8			0.570468
$146$	5.27017e8	−	2.43237e8i	1.15988	−	0.535325i
$147$		0			0
$148$	−9.70497e7	+	1.13832e8i	−0.202277	+	0.237255i
$149$	−2.47048e8			−0.501229			−0.250615	−	0.968087i	$-0.580633\pi$
$149$	−2.47048e8			−0.501229			−0.250615	+	0.968087i	$0.580633\pi$
$150$		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
$153$		0			0
$154$	−8.78005e7	+	4.05230e7i	−0.156104	+	0.0720475i
$155$		−	9.50368e7i		−	0.164651i
$156$		0			0
$157$	−7.00538e8			−1.15301			−0.576505	−	0.817094i	$-0.695584\pi$
$157$	−7.00538e8			−1.15301			−0.576505	+	0.817094i	$0.695584\pi$
$158$	−3.27575e8	−	7.09752e8i	−0.525634	−	1.13888i
$159$		0			0
$160$	−1.63361e8	−	2.43336e8i	−0.249269	−	0.371302i
$161$	2.03774e8			0.303281
$162$		0			0
$163$			2.24412e8i			0.317903i	0.987286	+	0.158952i	$0.0508114\pi$
$163$			2.24412e8i			0.317903i	−0.987286	+	0.158952i	$0.949189\pi$
$164$	−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	$0.744387\pi$
$168$		0			0
$169$	1.39875e9			1.71472
$170$	2.11013e8	−	9.73899e7i	0.252647	−	0.116605i
$171$		0			0
$172$	−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	$0.156109\pi$
$174$		0			0
$175$			2.05231e8i			0.218822i
$176$	−1.48880e8	+	2.38465e7i	−0.155162	+	0.0248528i
$177$		0			0
$178$	−1.53854e9	+	7.10090e8i	−1.53260	+	0.707348i
$179$			4.43340e8i			0.431841i	0.976411	+	0.215921i	$0.0692753\pi$
$179$			4.43340e8i			0.431841i	−0.976411	+	0.215921i	$0.930725\pi$
$180$		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
$183$		0			0
$184$	3.05912e8	+	8.58443e7i	0.266886	+	0.0748928i
$185$	1.63324e8			0.139432
$186$		0			0
$187$		−	1.19560e8i		−	0.0977728i
$188$	−9.81342e8	−	8.36666e8i	−0.785577	−	0.669762i
$189$		0			0
$190$	−1.11610e8	−	2.41823e8i	−0.0856423	−	0.185560i
$191$		−	5.22344e8i		−	0.392485i	−0.980555	−	0.196242i	$-0.937126\pi$
$191$		−	5.22344e8i		−	0.392485i	0.980555	−	0.196242i	$-0.0628740\pi$
$192$		0			0
$193$	5.01793e7			0.0361655			0.0180828	−	0.999836i	$-0.494244\pi$
$193$	5.01793e7			0.0361655			0.0180828	+	0.999836i	$0.494244\pi$
$194$	−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	$0.472106\pi$
$198$		0			0
$199$		−	1.26573e9i		−	0.807105i	−0.914956	−	0.403553i	$-0.867775\pi$
$199$		−	1.26573e9i		−	0.807105i	0.914956	−	0.403553i	$-0.132225\pi$
$200$	−8.64580e7	+	3.08099e8i	−0.0540362	+	0.192562i
$201$		0			0
$202$	−8.84503e8	+	4.08229e8i	−0.531244	+	0.245188i
$203$		−	2.37007e9i		−	1.39565i
$204$		0			0
$205$	8.21713e7			0.0465270
$206$	−1.76556e8	−	3.82541e8i	−0.0980423	−	0.212427i
$207$		0			0
$208$	−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
$213$		0			0
$214$	−8.47330e8	−	1.83590e9i	−0.404015	−	0.875372i
$215$			8.25367e8i			0.386272i
$216$		0			0
$217$	−8.93202e8			−0.402820
$218$	−1.12713e9	+	5.20212e8i	−0.499056	+	0.230332i
$219$		0			0
$220$	1.25274e8	+	1.06805e8i	0.0534774	+	0.0455934i
$221$	2.44547e9			1.02517
$222$		0			0
$223$			5.22225e8i			0.211173i	0.994410	+	0.105586i	$0.0336720\pi$
$223$			5.22225e8i			0.211173i	−0.994410	+	0.105586i	$0.966328\pi$
$224$	−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	$-0.226430\pi$
$228$		0			0
$229$	1.31243e9			0.477239			0.238619	−	0.971113i	$-0.423305\pi$
$229$	1.31243e9			0.477239			0.238619	+	0.971113i	$0.423305\pi$
$230$	−1.45373e8	−	3.14977e8i	−0.0519484	−	0.112556i
$231$		0			0
$232$	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	$0.364270\pi$
$234$		0			0
$235$			1.40801e9i			0.461674i
$236$	−1.71937e9	−	1.46589e9i	−0.554271	−	0.472556i
$237$		0			0
$238$	−9.15318e8	−	1.98320e9i	−0.285275	−	0.618101i
$239$			2.78783e9i			0.854427i	0.904151	+	0.427214i	$0.140505\pi$
$239$			2.78783e9i			0.854427i	−0.904151	+	0.427214i	$0.859495\pi$
$240$		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
$243$		0			0
$244$	1.79664e9	−	2.10731e9i	0.506875	−	0.594524i
$245$	3.17549e8			0.0881347
$246$		0			0
$247$		−	2.80254e9i		−	0.752946i
$248$	−1.34090e9	−	3.76281e8i	−0.354479	−	0.0994729i
$249$		0			0
$250$	3.17228e8	−	1.46412e8i	0.0812105	−	0.0374815i
$251$			6.20014e9i			1.56209i	0.624474	+	0.781046i	$0.285313\pi$
$251$			6.20014e9i			1.56209i	−0.624474	+	0.781046i	$0.714687\pi$
$252$		0			0
$253$	−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	$0.458987\pi$
$258$		0			0
$259$		−	1.53499e9i		−	0.341120i
$260$	−2.18460e9	+	2.56235e9i	−0.478055	+	0.560720i
$261$		0			0
$262$	−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	$0.949396\pi$
$264$		0			0
$265$	−2.11025e9			−0.427907
$266$	−2.27277e9	+	1.04896e9i	−0.453972	+	0.209524i
$267$		0			0
$268$	2.81201e9	+	2.39745e9i	0.545102	+	0.464740i
$269$	2.73389e9			0.522121			0.261060	−	0.965322i	$-0.415928\pi$
$269$	2.73389e9			0.522121			0.261060	+	0.965322i	$0.415928\pi$
$270$		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
$273$		0			0
$274$	−1.79151e9	+	8.26843e8i	−0.317845	+	0.146697i
$275$		−	1.79741e8i		−	0.0314280i
$276$		0			0
$277$	1.88891e9			0.320842			0.160421	−	0.987049i	$-0.448715\pi$
$277$	1.88891e9			0.320842			0.160421	+	0.987049i	$0.448715\pi$
$278$	4.50985e9	+	9.77141e9i	0.755062	+	1.63598i
$279$		0			0
$280$	2.89566e9	+	8.12574e8i	0.471103	+	0.132200i
$281$	1.65526e9			0.265485			0.132743	−	0.991151i	$-0.457622\pi$
$281$	1.65526e9			0.265485			0.132743	+	0.991151i	$0.457622\pi$
$282$		0			0
$283$			8.61833e9i			1.34362i	0.740722	+	0.671811i	$0.234483\pi$
$283$			8.61833e9i			1.34362i	−0.740722	+	0.671811i	$0.765517\pi$
$284$	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
$288$		0			0
$289$	−4.27519e9			−0.612864
$290$	−3.66345e9	+	1.69081e9i	−0.517962	+	0.239058i
$291$		0			0
$292$	−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	$0.377978\pi$
$294$		0			0
$295$			2.46693e9i			0.325738i
$296$	6.46649e8	−	2.30438e9i	0.0842368	−	0.300184i
$297$		0			0
$298$	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
$303$		0			0
$304$	−3.85385e9	+	6.17283e8i	−0.451233	+	0.0722753i
$305$	−3.02353e9			−0.349394
$306$		0			0
$307$		−	1.53502e10i		−	1.72806i	−0.503437	−	0.864032i	$-0.667931\pi$
$307$		−	1.53502e10i		−	1.72806i	0.503437	−	0.864032i	$-0.332069\pi$
$308$	1.00381e9	−	1.17739e9i	0.111544	−	0.130833i
$309$		0			0
$310$	6.37211e8	+	1.38063e9i	0.0689980	+	0.149497i
$311$			5.55831e9i			0.594157i	0.954853	+	0.297079i	$0.0960123\pi$
$311$			5.55831e9i			0.594157i	−0.954853	+	0.297079i	$0.903988\pi$
$312$		0			0
$313$	−1.76829e10			−1.84237			−0.921183	−	0.389131i	$-0.872775\pi$
$313$	−1.76829e10			−1.84237			−0.921183	+	0.389131i	$0.872775\pi$
$314$	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	$0.455044\pi$
$318$		0			0
$319$			2.07570e9i			0.200448i
$320$	4.00475e9	+	2.43972e9i	0.381922	+	0.232670i
$321$		0			0
$322$	−2.96030e9	+	1.36628e9i	−0.275368	+	0.127092i
$323$		−	3.09488e9i		−	0.284337i
$324$		0			0
$325$	3.67642e9			0.329528
$326$	−1.50466e9	−	3.26011e9i	−0.133219	−	0.288643i
$327$		0			0
$328$	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
$333$		0			0
$334$	−7.50407e9	−	1.62589e10i	−0.602991	−	1.30649i
$335$		−	4.03463e9i		−	0.320350i
$336$		0			0
$337$	2.09960e10			1.62786			0.813930	−	0.580963i	$-0.197324\pi$
$337$	2.09960e10			1.62786			0.813930	+	0.580963i	$0.197324\pi$
$338$	−2.03201e10	+	9.37844e9i	−1.55689	+	0.718561i
$339$		0			0
$340$	−2.41248e9	+	2.82964e9i	−0.180529	+	0.211746i
$341$	7.82265e8			0.0578544
$342$		0			0
$343$			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	$-0.0824955\pi$
$348$		0			0
$349$	5.43305e9			0.366220			0.183110	−	0.983092i	$-0.441384\pi$
$349$	5.43305e9			0.366220			0.183110	+	0.983092i	$0.441384\pi$
$350$	−1.37605e9	−	2.98147e9i	−0.0916985	−	0.198682i
$351$		0			0
$352$	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	$0.574234\pi$
$354$		0			0
$355$		−	1.03739e9i		−	0.0653175i
$356$	1.75898e10	−	2.06315e10i	1.09512	−	1.28449i
$357$		0			0
$358$	−2.97254e9	−	6.44056e9i	−0.180966	−	0.392095i
$359$			1.10278e10i			0.663913i	0.943295	+	0.331957i	$0.107709\pi$
$359$			1.10278e10i			0.663913i	−0.943295	+	0.331957i	$0.892291\pi$
$360$		0			0
$361$	1.34368e10			0.791165
$362$	2.71996e9	−	1.25536e9i	0.158390	−	0.0731027i
$363$		0			0
$364$	2.40823e10	+	2.05319e10i	1.37180	+	1.16956i
$365$	1.01399e10			0.571296
$366$		0			0
$367$		−	3.39042e10i		−	1.86891i	−0.356076	−	0.934457i	$-0.615886\pi$
$367$		−	3.39042e10i		−	1.86891i	0.356076	−	0.934457i	$-0.384114\pi$
$368$	−5.01968e9	+	8.04016e8i	−0.273706	+	0.0438403i
$369$		0			0
$370$	−2.37266e9	+	1.09507e9i	−0.126599	+	0.0584297i
$371$			1.98331e10i			1.04688i
$372$		0			0
$373$	3.19254e10			1.64930			0.824651	−	0.565641i	$-0.191371\pi$
$373$	3.19254e10			1.64930			0.824651	+	0.565641i	$0.191371\pi$
$374$	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
$378$		0			0
$379$			2.66340e10i			1.29086i	0.763819	+	0.645430i	$0.223322\pi$
$379$			2.66340e10i			1.29086i	−0.763819	+	0.645430i	$0.776678\pi$
$380$	3.24280e9	+	2.76472e9i	0.155520	+	0.132592i
$381$		0			0
$382$	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	$0.877897\pi$
$384$		0			0
$385$	−1.68929e9			−0.0768886
$386$	−7.28973e8	+	3.36446e8i	−0.0328369	+	0.0151554i
$387$		0			0
$388$	2.21759e10	−	2.60106e10i	0.978487	−	1.14769i
$389$	−1.81674e10			−0.793405			−0.396702	−	0.917947i	$-0.629846\pi$
$389$	−1.81674e10			−0.793405			−0.396702	+	0.917947i	$0.629846\pi$
$390$		0			0
$391$		−	4.03110e9i		−	0.172471i
$392$	1.25728e9	−	4.48040e9i	0.0532460	−	0.189746i
$393$		0			0
$394$	−3.82983e9	+	1.76760e9i	−0.158926	+	0.0733499i
$395$		−	1.36557e10i		−	0.560953i
$396$		0			0
$397$	−4.03325e10			−1.62365			−0.811827	−	0.583898i	$-0.801527\pi$
$397$	−4.03325e10			−1.62365			−0.811827	+	0.583898i	$0.801527\pi$
$398$	8.48661e9	+	1.83878e10i	0.338222	+	0.732820i
$399$		0			0
$400$	−8.09764e8	−	5.05556e9i	−0.0316314	−	0.197483i
$401$	−1.86384e10			−0.720826			−0.360413	−	0.932793i	$-0.617364\pi$
$401$	−1.86384e10			−0.720826			−0.360413	+	0.932793i	$0.617364\pi$
$402$		0			0
$403$			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
$408$		0			0
$409$	−1.95383e10			−0.698222			−0.349111	−	0.937081i	$-0.613516\pi$
$409$	−1.95383e10			−0.698222			−0.349111	+	0.937081i	$0.613516\pi$
$410$	−1.19373e9	+	5.50950e8i	−0.0422447	+	0.0194974i
$411$		0			0
$412$	5.12979e9	+	4.37352e9i	0.178037	+	0.151790i
$413$	2.31854e10			0.796918
$414$		0			0
$415$			1.93940e10i			0.653847i
$416$	2.75035e10	+	4.09683e10i	0.918364	+	1.36796i
$417$		0			0
$418$	1.99049e9	−	9.18681e8i	0.0652011	−	0.0300926i
$419$			1.60399e10i			0.520410i	0.965553	+	0.260205i	$0.0837901\pi$
$419$			1.60399e10i			0.520410i	−0.965553	+	0.260205i	$0.916210\pi$
$420$		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
$423$		0			0
$424$	−8.35513e9	+	2.97741e10i	−0.258517	+	0.921245i
$425$	4.05992e9			0.124440
$426$		0			0
$427$			2.84166e10i			0.854794i
$428$	2.46190e10	+	2.09895e10i	0.733659	+	0.625499i
$429$		0			0
$430$	−5.53400e9	−	1.19904e10i	−0.161870	−	0.350720i
$431$			2.17255e10i			0.629593i	0.949159	+	0.314797i	$0.101936\pi$
$431$			2.17255e10i			0.629593i	−0.949159	+	0.314797i	$0.898064\pi$
$432$		0			0
$433$	2.50658e10			0.713066			0.356533	−	0.934283i	$-0.383959\pi$
$433$	2.50658e10			0.713066			0.356533	+	0.934283i	$0.383959\pi$
$434$	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
$438$		0			0
$439$		−	2.69059e10i		−	0.724419i	−0.932097	−	0.362210i	$-0.882022\pi$
$439$		−	2.69059e10i		−	0.724419i	0.932097	−	0.362210i	$-0.117978\pi$
$440$	−2.53602e9	−	7.11651e8i	−0.0676615	−	0.0189870i
$441$		0			0
$442$	−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	$-0.233946\pi$
$444$		0			0
$445$	−2.96017e10			−0.754878
$446$	−3.50146e9	−	7.58655e9i	−0.0884932	−	0.191737i
$447$		0			0
$448$	2.29297e10	−	3.76385e10i	0.569228	−	0.934374i
$449$	4.61561e10			1.13565			0.567825	−	0.823150i	$-0.307785\pi$
$449$	4.61561e10			1.13565			0.567825	+	0.823150i	$0.307785\pi$
$450$		0			0
$451$			6.76367e8i			0.0163484i
$452$	1.50689e10	−	1.76746e10i	0.361018	−	0.423445i
$453$		0			0
$454$	2.32457e10	+	5.03661e10i	0.547166	+	1.18554i
$455$		−	3.45528e10i		−	0.806191i
$456$		0			0
$457$	−3.11288e10			−0.713669			−0.356835	−	0.934168i	$-0.616144\pi$
$457$	−3.11288e10			−0.713669			−0.356835	+	0.934168i	$0.616144\pi$
$458$	−1.90662e10	+	8.79973e9i	−0.433314	+	0.199990i
$459$		0			0
$460$	4.22377e9	+	3.60107e9i	0.0943341	+	0.0804268i
$461$	−4.68016e10			−1.03623			−0.518116	−	0.855310i	$-0.673366\pi$
$461$	−4.68016e10			−1.03623			−0.518116	+	0.855310i	$0.673366\pi$
$462$		0			0
$463$			2.03332e10i			0.442468i	0.975221	+	0.221234i	$0.0710085\pi$
$463$			2.03332e10i			0.442468i	−0.975221	+	0.221234i	$0.928992\pi$
$464$	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	$-0.212823\pi$
$468$		0			0
$469$	−3.79194e10			−0.783737
$470$	−9.44057e9	−	2.04547e10i	−0.193467	−	0.419182i
$471$		0			0
$472$	3.48066e10	+	9.76734e9i	0.701283	+	0.196792i
$473$	−6.79375e9			−0.135727
$474$		0			0
$475$		−	4.65271e9i		−	0.0913969i
$476$	2.65943e10	+	2.26736e10i	0.518037	+	0.441665i
$477$		0			0
$478$	−1.86921e10	−	4.04999e10i	−0.358053	−	0.775786i
$479$		−	1.20229e10i		−	0.228384i	−0.993459	−	0.114192i	$-0.963572\pi$
$479$		−	1.20229e10i		−	0.228384i	0.993459	−	0.114192i	$-0.0364279\pi$
$480$		0			0
$481$	−2.74973e10			−0.513699
$482$	−1.68952e10	+	7.79772e9i	−0.313022	+	0.144471i
$483$		0			0
$484$	3.47235e10	−	4.07279e10i	0.632764	−	0.742181i
$485$	−3.73196e10			−0.674481
$486$		0			0
$487$		−	4.85939e10i		−	0.863905i	−0.901896	−	0.431953i	$-0.857825\pi$
$487$		−	4.85939e10i		−	0.863905i	0.901896	−	0.431953i	$-0.142175\pi$
$488$	−1.19711e10	+	4.26599e10i	−0.211084	+	0.752213i
$489$		0			0
$490$	−4.61315e9	+	2.12913e9i	−0.0800228	+	0.0369333i
$491$			1.71586e9i			0.0295226i	0.999891	+	0.0147613i	$0.00469884\pi$
$491$			1.71586e9i			0.0295226i	−0.999891	+	0.0147613i	$0.995301\pi$
$492$		0			0
$493$	−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
$498$		0			0
$499$			6.25565e10i			1.00895i	0.863426	+	0.504476i	$0.168314\pi$
$499$			6.25565e10i			1.00895i	−0.863426	+	0.504476i	$0.831686\pi$
$500$	−3.62682e9	+	4.25396e9i	−0.0580291	+	0.0680634i
$501$		0			0
$502$	−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	$-0.234780\pi$
$504$		0			0
$505$	−1.70180e10			−0.261663
$506$	2.59263e9	−	1.19659e9i	0.0395493	−	0.0182534i
$507$		0			0
$508$	6.05552e10	+	5.16277e10i	0.909278	+	0.775226i
$509$	−5.17187e10			−0.770506			−0.385253	−	0.922811i	$-0.625886\pi$
$509$	−5.17187e10			−0.770506			−0.385253	+	0.922811i	$0.625886\pi$
$510$		0			0
$511$		−	9.52994e10i		−	1.39768i
$512$	5.02788e10	−	4.68445e10i	0.731653	−	0.681677i
$513$		0			0
$514$	−1.62863e10	+	7.51672e9i	−0.233330	+	0.107690i
$515$		−	7.36013e9i		−	0.104630i
$516$		0			0
$517$	−1.15896e10			−0.162221
$518$	1.02920e10	+	2.22994e10i	0.142948	+	0.309724i
$519$		0			0
$520$	1.45561e10	−	5.18717e10i	0.199082	−	0.709443i
$521$	−6.36828e10			−0.864313			−0.432157	−	0.901799i	$-0.642247\pi$
$521$	−6.36828e10			−0.864313			−0.432157	+	0.901799i	$0.642247\pi$
$522$		0			0
$523$		−	3.05582e10i		−	0.408434i	−0.978926	−	0.204217i	$-0.934535\pi$
$523$		−	3.05582e10i		−	0.408434i	0.978926	−	0.204217i	$-0.0654648\pi$
$524$	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
$528$		0			0
$529$	7.22938e10			0.923163
$530$	3.06563e10	−	1.41490e10i	0.388523	−	0.179317i
$531$		0			0
$532$	2.59842e10	−	3.04774e10i	0.324387	−	0.380479i
$533$	−1.38344e10			−0.171416
$534$		0			0
$535$		−	3.53229e10i		−	0.431162i
$536$	−5.69258e10	−	1.59744e10i	−0.689683	−	0.193537i
$537$		0			0
$538$	−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
$543$		0			0
$544$	3.03725e10	+	4.52418e10i	0.346804	+	0.516587i
$545$	−2.16862e10			−0.245809
$546$		0			0
$547$			5.79915e10i			0.647762i	0.946098	+	0.323881i	$0.104988\pi$
$547$			5.79915e10i			0.647762i	−0.946098	+	0.323881i	$0.895012\pi$
$548$	2.04820e10	−	2.40237e10i	0.227117	−	0.266390i
$549$		0			0
$550$	1.20514e9	+	2.61116e9i	0.0131701	+	0.0285354i
$551$			5.37309e10i			0.582932i
$552$		0			0
$553$	−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	$0.850100\pi$
$558$		0			0
$559$		−	1.38959e11i		−	1.42312i
$560$	−4.75146e10	+	7.61055e9i	−0.483142	+	0.0773863i
$561$		0			0
$562$	−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	$-0.000871210\pi$
$564$		0			0
$565$	−2.53593e10			−0.248853
$566$	−5.77850e10	−	1.25202e11i	−0.563053	−	1.21996i
$567$		0			0
$568$	−1.46369e10	−	4.10736e9i	−0.140623	−	0.0394611i
$569$	1.48683e10			0.141845			0.0709223	−	0.997482i	$-0.477406\pi$
$569$	1.48683e10			0.141845			0.0709223	+	0.997482i	$0.477406\pi$
$570$		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
$573$		0			0
$574$	5.17809e9	+	1.12193e10i	0.0477004	+	0.103352i
$575$		−	6.06019e9i		−	0.0554390i
$576$		0			0
$577$	4.14670e10			0.374110			0.187055	−	0.982349i	$-0.440106\pi$
$577$	4.14670e10			0.374110			0.187055	+	0.982349i	$0.440106\pi$
$578$	6.21073e10	−	2.86647e10i	0.556457	−	0.256824i
$579$		0			0
$580$	4.18836e10	−	4.91261e10i	0.370111	−	0.434110i
$581$	1.82275e11			1.59964
$582$		0			0
$583$		−	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	$-0.0387453\pi$
$588$		0			0
$589$	2.02494e10			0.168249
$590$	−1.65405e10	−	3.58379e10i	−0.136502	−	0.295757i
$591$		0			0
$592$	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	$0.443870\pi$
$594$		0			0
$595$		−	3.81571e10i		−	0.304444i
$596$	−4.10319e10	+	4.81272e10i	−0.325190	+	0.381422i
$597$		0			0
$598$	2.44751e10	+	5.30297e10i	0.191390	+	0.414681i
$599$			1.41612e11i			1.10000i	0.835164	+	0.550000i	$0.185372\pi$
$599$			1.41612e11i			1.10000i	−0.835164	+	0.550000i	$0.814628\pi$
$600$		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
$603$		0			0
$604$	7.79345e10	+	6.64449e10i	0.585574	+	0.499245i
$605$	−5.84356e10			−0.436171
$606$		0			0
$607$			4.19809e10i			0.309241i	0.987974	+	0.154620i	$0.0494155\pi$
$607$			4.19809e10i			0.309241i	−0.987974	+	0.154620i	$0.950585\pi$
$608$	5.18475e10	−	3.48072e10i	0.379414	−	0.254715i
$609$		0			0
$610$	4.39240e10	−	2.02725e10i	0.317236	−	0.146416i
$611$		−	2.37054e11i		−	1.70091i
$612$		0			0
$613$	1.73299e11			1.22731			0.613655	−	0.789575i	$-0.289699\pi$
$613$	1.73299e11			1.22731			0.613655	+	0.789575i	$0.289699\pi$
$614$	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	$0.756672\pi$
$618$		0			0
$619$		−	1.25079e11i		−	0.851965i	−0.904731	−	0.425983i	$-0.859928\pi$
$619$		−	1.25079e11i		−	0.851965i	0.904731	−	0.425983i	$-0.140072\pi$
$620$	−1.85140e10	−	1.57846e10i	−0.125295	−	0.106823i
$621$		0			0
$622$	−3.72679e10	−	8.07476e10i	−0.248985	−	0.539471i
$623$			2.78211e11i			1.84681i
$624$		0			0
$625$	6.10352e9			0.0400000
$626$	2.56886e11	−	1.18562e11i	1.67279	−	0.772054i
$627$		0			0
$628$	−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
$633$		0			0
$634$	−4.13001e10	+	1.90614e10i	−0.255619	+	0.117977i
$635$		−	8.68836e10i		−	0.534371i
$636$		0			0
$637$	−5.34628e10			−0.324709
$638$	−1.39174e10	−	3.01545e10i	−0.0839990	−	0.181999i
$639$		0			0
$640$	−7.45365e10	−	8.59135e9i	−0.444272	−	0.0512085i
$641$	−1.68400e10			−0.0997495			−0.0498748	−	0.998755i	$-0.515882\pi$
$641$	−1.68400e10			−0.0997495			−0.0498748	+	0.998755i	$0.515882\pi$
$642$		0			0
$643$			2.84422e11i			1.66387i	0.554871	+	0.831936i	$0.312767\pi$
$643$			2.84422e11i			1.66387i	−0.554871	+	0.831936i	$0.687233\pi$
$644$	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	$-0.206398\pi$
$648$		0			0
$649$	−2.03057e10			−0.114456
$650$	−5.34088e10	+	2.46500e10i	−0.299198	+	0.138091i
$651$		0			0
$652$	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	$0.199660\pi$
$654$		0			0
$655$		−	1.52271e11i		−	0.827278i
$656$	3.04715e9	+	1.90241e10i	0.0164543	+	0.102728i
$657$		0			0
$658$	−1.92243e11	+	8.87271e10i	−1.02553	+	0.473318i
$659$			1.18352e11i			0.627529i	0.949501	+	0.313765i	$0.101590\pi$
$659$			1.18352e11i			0.627529i	−0.949501	+	0.313765i	$0.898410\pi$
$660$		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
$663$		0			0
$664$	2.73636e11	+	7.67871e10i	1.40767	+	0.395017i
$665$	−4.37284e10			−0.223603
$666$		0			0
$667$			6.99850e10i			0.353591i
$668$	2.18029e11	+	1.85886e11i	1.09498	+	0.933555i
$669$		0			0
$670$	2.70518e10	+	5.86125e10i	0.134244	+	0.290865i
$671$		−	2.48873e10i		−	0.122768i
$672$		0			0
$673$	2.21745e11			1.08092			0.540461	−	0.841369i	$-0.318250\pi$
$673$	2.21745e11			1.08092			0.540461	+	0.841369i	$0.318250\pi$
$674$	−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	$0.177986\pi$
$678$		0			0
$679$			3.50747e11i			1.65012i
$680$	1.60745e10	−	5.72826e10i	0.0751799	−	0.267909i
$681$		0			0
$682$	−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	$0.835190\pi$
$684$		0			0
$685$	−3.44688e10			−0.156554
$686$	−8.15274e10	−	1.76644e11i	−0.368135	−	0.797632i
$687$		0			0
$688$	−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
$693$		0			0
$694$	4.98250e10	+	1.07955e11i	0.214788	+	0.465377i
$695$			1.88003e11i			0.805797i
$696$		0			0
$697$	−1.52775e10			−0.0647324
$698$	−7.89280e10	+	3.64280e10i	−0.332514	+	0.153467i
$699$		0			0
$700$	3.99808e10	+	3.40866e10i	0.166517	+	0.141968i
$701$	1.98676e11			0.822758			0.411379	−	0.911464i	$-0.365047\pi$
$701$	1.98676e11			0.822758			0.411379	+	0.911464i	$0.365047\pi$
$702$		0			0
$703$			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
$708$		0			0
$709$	−1.08511e11			−0.429427			−0.214713	−	0.976677i	$-0.568882\pi$
$709$	−1.08511e11			−0.429427			−0.214713	+	0.976677i	$0.568882\pi$
$710$	6.95560e9	+	1.50706e10i	0.0273717	+	0.0593057i
$711$		0			0
$712$	−1.17202e11	+	4.17659e11i	−0.456054	+	1.62518i
$713$	2.63750e10			0.102055
$714$		0			0
$715$			3.02613e10i			0.115788i
$716$	8.63665e10	+	7.36338e10i	0.328619	+	0.280172i
$717$		0			0
$718$	−7.39403e10	−	1.60205e11i	−0.278217	−	0.602807i
$719$			3.56644e11i			1.33450i	0.744832	+	0.667252i	$0.232529\pi$
$719$			3.56644e11i			1.33450i	−0.744832	+	0.667252i	$0.767471\pi$
$720$		0			0
$721$	−6.91741e10			−0.255978
$722$	−1.95201e11	+	9.00923e10i	−0.718347	+	0.331542i
$723$		0			0
$724$	−3.10969e10	+	3.64741e10i	−0.113178	+	0.132749i
$725$	−7.04853e10			−0.255121
$726$		0			0
$727$		−	8.05781e10i		−	0.288456i	−0.989544	−	0.144228i	$-0.953930\pi$
$727$		−	8.05781e10i		−	0.288456i	0.989544	−	0.144228i	$-0.0460699\pi$
$728$	−4.87516e11	−	1.36805e11i	−1.73565	−	0.487055i
$729$		0			0
$730$	−1.47306e11	+	6.79867e10i	−0.518714	+	0.239405i
$731$		−	1.53455e11i		−	0.537415i
$732$		0			0
$733$	3.80343e11			1.31753			0.658763	−	0.752351i	$-0.271080\pi$
$733$	3.80343e11			1.31753			0.658763	+	0.752351i	$0.271080\pi$
$734$	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
$738$		0			0
$739$			4.01614e11i			1.34658i	0.739381	+	0.673288i	$0.235118\pi$
$739$			4.01614e11i			1.34658i	−0.739381	+	0.673288i	$0.764882\pi$
$740$	2.71262e10	−	3.18169e10i	0.0904612	−	0.106104i
$741$		0			0
$742$	−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	$0.802440\pi$
$744$		0			0
$745$	6.90521e10			0.224157
$746$	−4.63791e11	+	2.14056e11i	−1.49750	+	0.691150i
$747$		0			0
$748$	−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
$753$		0			0
$754$	6.16781e11	−	2.84666e11i	1.90829	−	0.880745i
$755$		−	1.11819e11i		−	0.344135i
$756$		0			0
$757$	1.22819e11			0.374009			0.187004	−	0.982359i	$-0.440122\pi$
$757$	1.22819e11			0.374009			0.187004	+	0.982359i	$0.440122\pi$
$758$	−1.78578e11	−	3.86922e11i	−0.540942	−	1.17205i
$759$		0			0
$760$	−6.56465e10	−	1.84215e10i	−0.196769	−	0.0552168i
$761$	1.93019e11			0.575521			0.287761	−	0.957702i	$-0.407089\pi$
$761$	1.93019e11			0.575521			0.287761	+	0.957702i	$0.407089\pi$
$762$		0			0
$763$			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
$768$		0			0
$769$	1.34359e11			0.384202			0.192101	−	0.981375i	$-0.438470\pi$
$769$	1.34359e11			0.384202			0.192101	+	0.981375i	$0.438470\pi$
$770$	2.45410e10	−	1.13265e10i	0.0698118	−	0.0322206i
$771$		0			0
$772$	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	$0.411024\pi$
$774$		0			0
$775$			2.65636e10i			0.0736343i
$776$	−1.47760e11	+	5.26553e11i	−0.407483	+	1.45210i
$777$		0			0
$778$	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
$783$		0			0
$784$	1.17756e10	+	7.35183e10i	0.0311688	+	0.194595i
$785$	1.95806e11			0.515642
$786$		0			0
$787$		−	3.63175e11i		−	0.946711i	−0.880871	−	0.473356i	$-0.843043\pi$
$787$		−	3.63175e11i		−	0.946711i	0.880871	−	0.473356i	$-0.156957\pi$
$788$	4.37858e10	−	5.13572e10i	0.113561	−	0.133198i
$789$		0			0
$790$	9.15601e10	+	1.98382e11i	0.235070	+	0.509323i
$791$			2.38339e11i			0.608820i
$792$		0			0
$793$	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	$0.477171\pi$
$798$		0			0
$799$		−	2.61782e11i		−	0.642321i
$800$	4.56607e10	+	6.80146e10i	0.111476	+	0.166051i
$801$		0			0
$802$	2.70766e11	−	1.24968e11i	0.654481	−	0.302066i
$803$			8.34631e10i			0.200739i
$804$		0			0
$805$	−5.69566e10			−0.135632
$806$	−1.07281e11	−	2.32444e11i	−0.254205	−	0.550781i
$807$		0			0
$808$	−6.73795e10	+	2.40111e11i	−0.158082	+	0.563336i
$809$	1.75206e11			0.409031			0.204515	−	0.978863i	$-0.434438\pi$
$809$	1.75206e11			0.409031			0.204515	+	0.978863i	$0.434438\pi$
$810$		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
$813$		0			0
$814$	−9.01369e9	−	1.95298e10i	−0.0205308	−	0.0444836i
$815$		−	6.27249e10i		−	0.142171i
$816$		0			0
$817$	−1.75860e11			−0.394712
$818$	2.83840e11	−	1.31002e11i	0.633958	−	0.292594i
$819$		0			0
$820$	1.36477e10	−	1.60077e10i	0.0301860	−	0.0354057i
$821$	3.12544e11			0.687922			0.343961	−	0.938984i	$-0.388231\pi$
$821$	3.12544e11			0.687922			0.343961	+	0.938984i	$0.388231\pi$
$822$		0			0
$823$		−	6.75905e11i		−	1.47328i	−0.676283	−	0.736641i	$-0.736411\pi$
$823$		−	6.75905e11i		−	1.47328i	0.676283	−	0.736641i	$-0.263589\pi$
$824$	−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	$-0.295620\pi$
$828$		0			0
$829$	−6.27639e11			−1.32890			−0.664449	−	0.747333i	$-0.731334\pi$
$829$	−6.27639e11			−1.32890			−0.664449	+	0.747333i	$0.731334\pi$
$830$	−1.30035e11	−	2.81744e11i	−0.273998	−	0.593667i
$831$		0			0
$832$	−6.74242e11	−	4.10753e11i	−1.40709	−	0.857211i
$833$	−5.90396e10			−0.122621
$834$		0			0
$835$		−	3.12824e11i		−	0.643508i
$836$	−2.27569e10	+	2.66920e10i	−0.0465895	+	0.0546458i
$837$		0			0
$838$	−1.07546e11	−	2.33018e11i	−0.218081	−	0.472512i
$839$		−	8.86257e11i		−	1.78860i	−0.447473	−	0.894298i	$-0.647676\pi$
$839$		−	8.86257e11i		−	1.78860i	0.447473	−	0.894298i	$-0.352324\pi$
$840$		0			0
$841$	3.13739e11			0.627168
$842$	−1.27852e11	+	5.90080e10i	−0.254365	+	0.117398i
$843$		0			0
$844$	−1.81962e11	−	1.55136e11i	−0.358600	−	0.305733i
$845$	−3.90961e11			−0.766844
$846$		0			0
$847$			5.49207e11i			1.06709i
$848$	−7.82540e10	−	4.88560e11i	−0.151329	−	0.944787i
$849$		0			0
$850$	−5.89799e10	+	2.72213e10i	−0.112987	+	0.0521475i
$851$			4.53263e10i			0.0864235i
$852$		0			0
$853$	−4.42385e10			−0.0835611			−0.0417805	−	0.999127i	$-0.513303\pi$
$853$	−4.42385e10			−0.0835611			−0.0417805	+	0.999127i	$0.513303\pi$
$854$	−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	$0.0873463\pi$
$858$		0			0
$859$		−	5.28066e11i		−	0.969874i	−0.874549	−	0.484937i	$-0.838842\pi$
$859$		−	5.28066e11i		−	0.969874i	0.874549	−	0.484937i	$-0.161158\pi$
$860$	1.60789e11	+	1.37084e11i	0.293942	+	0.250608i
$861$		0			0
$862$	−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	$0.944965\pi$
$864$		0			0
$865$	−4.41715e11			−0.789001
$866$	−3.64140e11	+	1.68063e11i	−0.647436	+	0.298814i
$867$		0			0
$868$	−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
$873$		0			0
$874$	6.71119e10	−	3.09745e10i	0.115015	−	0.0530834i
$875$		−	5.73638e10i		−	0.0978601i
$876$		0			0
$877$	2.36707e11			0.400140			0.200070	−	0.979782i	$-0.435883\pi$
$877$	2.36707e11			0.400140			0.200070	+	0.979782i	$0.435883\pi$
$878$	1.80401e11	+	3.90872e11i	0.303572	+	0.657744i
$879$		0			0
$880$	4.16132e10	−	6.66531e9i	0.0693906	−	0.0111145i
$881$	−3.49205e11			−0.579665			−0.289832	−	0.957077i	$-0.593600\pi$
$881$	−3.49205e11			−0.579665			−0.289832	+	0.957077i	$0.593600\pi$
$882$		0			0
$883$		−	5.98818e11i		−	0.985035i	−0.870302	−	0.492518i	$-0.836077\pi$
$883$		−	5.98818e11i		−	0.985035i	0.870302	−	0.492518i	$-0.163923\pi$
$884$	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	$0.845980\pi$
$888$		0			0
$889$	−8.16574e11			−1.30734
$890$	4.30035e11	−	1.98476e11i	0.685399	−	0.316336i
$891$		0			0
$892$	1.01734e11	+	8.67357e10i	0.160697	+	0.137006i
$893$	−3.00004e11			−0.471761
$894$		0			0
$895$		−	1.23917e11i		−	0.193125i
$896$	−8.07457e10	+	7.00530e11i	−0.125282	+	1.08691i
$897$		0			0
$898$	−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
$903$		0			0
$904$	−1.00405e11	+	3.57802e11i	−0.150343	+	0.535758i
$905$	5.23325e10			0.0780148
$906$		0			0
$907$		−	4.04494e11i		−	0.597699i	−0.954300	−	0.298849i	$-0.903397\pi$
$907$		−	4.04494e11i		−	0.597699i	0.954300	−	0.298849i	$-0.0966029\pi$
$908$	−6.75398e11	−	5.75827e11i	−0.993611	−	0.847126i
$909$		0			0
$910$	2.31673e11	+	5.01961e11i	0.337839	+	0.731989i
$911$			6.18016e11i			0.897276i	0.893714	+	0.448638i	$0.148091\pi$
$911$			6.18016e11i			0.897276i	−0.893714	+	0.448638i	$0.851909\pi$
$912$		0			0
$913$	−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
$918$		0			0
$919$		−	5.11050e11i		−	0.716476i	−0.933630	−	0.358238i	$-0.883378\pi$
$919$		−	5.11050e11i		−	0.716476i	0.933630	−	0.358238i	$-0.116622\pi$
$920$	−8.55051e10	−	2.39942e10i	−0.119355	−	0.0334931i
$921$		0			0
$922$	6.79904e11	−	3.13800e11i	0.940858	−	0.434239i
$923$			1.74656e11i			0.240645i
$924$		0			0
$925$	−4.56503e10			−0.0623558
$926$	−1.36332e11	−	2.95388e11i	−0.185419	−	0.401744i
$927$		0			0
$928$	−5.27304e11	−	7.85453e11i	−0.710999	−	1.05908i
$929$	−3.49578e11			−0.469333			−0.234666	−	0.972076i	$-0.575400\pi$
$929$	−3.49578e11			−0.469333			−0.234666	+	0.972076i	$0.575400\pi$
$930$		0			0
$931$			6.76600e10i			0.0900603i
$932$	4.04929e11	−	4.74949e11i	0.536680	−	0.629482i
$933$		0			0
$934$	3.95371e11	+	8.56642e11i	0.519537	+	1.12567i
$935$			3.34179e10i			0.0437253i
$936$		0			0
$937$	−1.37124e11			−0.177891			−0.0889457	−	0.996036i	$-0.528350\pi$
$937$	−1.37124e11			−0.177891			−0.0889457	+	0.996036i	$0.528350\pi$
$938$	5.50869e11	−	2.54245e11i	0.711602	−	0.328429i
$939$		0			0
$940$	2.74293e11	+	2.33855e11i	0.351321	+	0.299527i
$941$	4.32170e10			0.0551183			0.0275592	−	0.999620i	$-0.491227\pi$
$941$	4.32170e10			0.0551183			0.0275592	+	0.999620i	$0.491227\pi$
$942$		0			0
$943$			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	$0.718171\pi$
$948$		0			0
$949$	−1.70716e12			−2.10479
$950$	3.11959e10	+	6.75916e10i	0.0383004	+	0.0829848i
$951$		0			0
$952$	−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	$0.691873\pi$
$954$		0			0
$955$			1.46000e11i			0.175525i
$956$	5.43095e11	+	4.63028e11i	0.650195	+	0.554339i
$957$		0			0
$958$	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
$963$		0			0
$964$	1.93160e11	−	2.26561e11i	0.223670	−	0.262347i
$965$	−1.40255e10			−0.0161737
$966$		0			0
$967$		−	1.52906e12i		−	1.74871i	−0.485286	−	0.874355i	$-0.661285\pi$
$967$		−	1.52906e12i		−	1.74871i	0.485286	−	0.874355i	$-0.338715\pi$
$968$	−2.31365e11	+	8.24486e11i	−0.263510	+	0.939035i
$969$		0			0
$970$	5.42155e11	−	2.50224e11i	0.612402	−	0.282645i
$971$		−	5.95468e11i		−	0.669856i	−0.942244	−	0.334928i	$-0.891288\pi$
$971$		−	5.95468e11i		−	0.669856i	0.942244	−	0.334928i	$-0.108712\pi$
$972$		0			0
$973$	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	$0.707491\pi$
$978$		0			0
$979$		−	2.43657e11i		−	0.265245i
$980$	5.27414e10	−	6.18614e10i	0.0571804	−	0.0670680i
$981$		0			0
$982$	−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	$-0.00215871\pi$
$984$		0			0
$985$	−7.36865e10			−0.0782786
$986$	6.81118e11	−	3.14360e11i	0.720634	−	0.332598i
$987$		0			0
$988$	−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
$993$		0			0
$994$	1.41641e11	−	6.53721e10i	0.145092	−	0.0669649i
$995$			3.53783e11i			0.360948i
$996$		0			0
$997$	2.60515e11			0.263665			0.131832	−	0.991272i	$-0.457914\pi$
$997$	2.60515e11			0.263665			0.131832	+	0.991272i	$0.457914\pi$
$998$	−4.19435e11	−	9.08782e11i	−0.422807	−	0.916089i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	180.9.c.a.91.2		16
3.2	odd	2		20.9.b.a.11.15	✓	16
4.3	odd	2	inner	180.9.c.a.91.1		16
12.11	even	2		20.9.b.a.11.16	yes	16
15.2	even	4		100.9.d.c.99.22		32
15.8	even	4		100.9.d.c.99.11		32
15.14	odd	2		100.9.b.d.51.2		16
24.5	odd	2		320.9.b.d.191.16		16
24.11	even	2		320.9.b.d.191.1		16
60.23	odd	4		100.9.d.c.99.21		32
60.47	odd	4		100.9.d.c.99.12		32
60.59	even	2		100.9.b.d.51.1		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
20.9.b.a.11.15	✓	16	3.2	odd	2
20.9.b.a.11.16	yes	16	12.11	even	2
100.9.b.d.51.1		16	60.59	even	2
100.9.b.d.51.2		16	15.14	odd	2
100.9.d.c.99.11		32	15.8	even	4
100.9.d.c.99.12		32	60.47	odd	4
100.9.d.c.99.21		32	60.23	odd	4
100.9.d.c.99.22		32	15.2	even	4
180.9.c.a.91.1		16	4.3	odd	2	inner
180.9.c.a.91.2		16	1.1	even	1	trivial
320.9.b.d.191.1		16	24.11	even	2
320.9.b.d.191.16		16	24.5	odd	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 180 = 2^{2} \cdot 3^{2} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 9 \)
Character orbit:	\([\chi]\)	\(=\)	180.c (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-14.5274 + 6.70489i) q^{2} +(166.089 - 194.809i) q^{4} -279.508 q^{5} +2626.96i q^{7} +(-1106.66 + 3943.67i) q^{8} +(4060.52 - 1874.07i) q^{10} -2300.68i q^{11} +47058.2 q^{13} +(-17613.5 - 38162.8i) q^{14} +(-10365.0 - 64711.2i) q^{16} +51967.0 q^{17} -59554.7i q^{19} +(-46423.2 + 54450.7i) q^{20} +(15425.8 + 33422.9i) q^{22} -77570.5i q^{23} +78125.0 q^{25} +(-683632. + 315520. i) q^{26} +(511754. + 436308. i) q^{28} -902211. q^{29} +340014. i q^{31} +(584457. + 870587. i) q^{32} +(-754943. + 348433. i) q^{34} -734257. i q^{35} -584324. q^{37} +(399308. + 865173. i) q^{38} +(309321. - 1.10229e6i) q^{40} -293985. q^{41} -2.95292e6i q^{43} +(-448194. - 382118. i) q^{44} +(520102. + 1.12689e6i) q^{46} -5.03746e6i q^{47} -1.13610e6 q^{49} +(-1.13495e6 + 523820. i) q^{50} +(7.81585e6 - 9.16736e6i) q^{52} +7.54985e6 q^{53} +643061. i q^{55} +(-1.03598e7 - 2.90715e6i) q^{56} +(1.31068e7 - 6.04923e6i) q^{58} -8.82594e6i q^{59} +1.08173e7 q^{61} +(-2.27976e6 - 4.93951e6i) q^{62} +(-1.43278e7 - 8.72861e6i) q^{64} -1.31532e7 q^{65} +1.44347e7i q^{67} +(8.63113e6 - 1.01236e7i) q^{68} +(4.92311e6 + 1.06668e7i) q^{70} +3.71149e6i q^{71} -3.62775e7 q^{73} +(8.48869e6 - 3.91783e6i) q^{74} +(-1.16018e7 - 9.89137e6i) q^{76} +6.04380e6 q^{77} +4.88562e7i q^{79} +(2.89710e6 + 1.80873e7i) q^{80} +(4.27083e6 - 1.97114e6i) q^{82} -6.93862e7i q^{83} -1.45252e7 q^{85} +(1.97990e7 + 4.28982e7i) q^{86} +(9.07314e6 + 2.54608e6i) q^{88} +1.05906e8 q^{89} +1.23620e8i q^{91} +(-1.51114e7 - 1.28836e7i) q^{92} +(3.37756e7 + 7.31810e7i) q^{94} +1.66460e7i q^{95} +1.33519e8 q^{97} +(1.65045e7 - 7.61742e6i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 6 q^{2} - 52 q^{4} + 14184 q^{8} + 8750 q^{10} + 51392 q^{13} - 68472 q^{14} - 81424 q^{16} - 27552 q^{17} - 172500 q^{20} - 389120 q^{22} + 1250000 q^{25} - 1037124 q^{26} + 1288520 q^{28} - 2764896 q^{29}+ \cdots + 285387714 q^{98}+O(q^{100}) \) 16 * q - 6 * q^2 - 52 * q^4 + 14184 * q^8 + 8750 * q^10 + 51392 * q^13 - 68472 * q^14 - 81424 * q^16 - 27552 * q^17 - 172500 * q^20 - 389120 * q^22 + 1250000 * q^25 - 1037124 * q^26 + 1288520 * q^28 - 2764896 * q^29 + 4379904 * q^32 + 3793964 * q^34 + 9009472 * q^37 + 3087360 * q^38 + 385000 * q^40 + 8576448 * q^41 - 16921200 * q^44 - 7974152 * q^46 - 32803600 * q^49 - 468750 * q^50 + 6679352 * q^52 - 2452032 * q^53 - 34134768 * q^56 + 52156572 * q^58 + 8371712 * q^61 - 1290000 * q^62 - 47543872 * q^64 - 9060000 * q^65 - 16095192 * q^68 + 10500000 * q^70 + 61907232 * q^73 + 138210876 * q^74 + 2570400 * q^76 + 156997440 * q^77 - 37590000 * q^80 + 83921012 * q^82 - 106960000 * q^85 + 101724672 * q^86 + 44728480 * q^88 - 106647456 * q^89 + 13876200 * q^92 + 55264632 * q^94 + 171851232 * q^97 + 285387714 * q^98

Introduction

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