LMFDB - Embedded newform 180.9.c.a.91.8

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			91.8
Root			$-105.172i$ of defining polynomial
Character	$\chi$	$=$	180.91
Dual form			180.9.c.a.91.7

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-4.64016 + 15.3124i) q^{2} +(-212.938 - 142.104i) q^{4} +279.508 q^{5} -210.345i q^{7} +(3164.01 - 2601.20i) q^{8} +(-1296.96 + 4279.94i) q^{10} +141.724i q^{11} -17655.5 q^{13} +(3220.88 + 976.035i) q^{14} +(25149.0 + 60518.5i) q^{16} +102231. q^{17} -107088. i q^{19} +(-59517.9 - 39719.2i) q^{20} +(-2170.13 - 657.620i) q^{22} +455526. i q^{23} +78125.0 q^{25} +(81924.3 - 270348. i) q^{26} +(-29890.8 + 44790.4i) q^{28} -865184. q^{29} -429788. i q^{31} +(-1.04338e6 + 104276. i) q^{32} +(-474366. + 1.56539e6i) q^{34} -58793.2i q^{35} -2.51809e6 q^{37} +(1.63978e6 + 496908. i) q^{38} +(884368. - 727057. i) q^{40} +2.98042e6 q^{41} -2.22228e6i q^{43} +(20139.5 - 30178.3i) q^{44} +(-6.97518e6 - 2.11371e6i) q^{46} -7.63886e6i q^{47} +5.72056e6 q^{49} +(-362513. + 1.19628e6i) q^{50} +(3.75952e6 + 2.50891e6i) q^{52} -1.55615e7 q^{53} +39613.0i q^{55} +(-547149. - 665534. i) q^{56} +(4.01459e6 - 1.32480e7i) q^{58} +6.38433e6i q^{59} +2.03289e6 q^{61} +(6.58108e6 + 1.99429e6i) q^{62} +(3.24473e6 - 1.64605e7i) q^{64} -4.93486e6 q^{65} -2.03503e7i q^{67} +(-2.17688e7 - 1.45274e7i) q^{68} +(900264. + 272810. i) q^{70} -4.44463e7i q^{71} +1.79865e7 q^{73} +(1.16843e7 - 3.85579e7i) q^{74} +(-1.52177e7 + 2.28032e7i) q^{76} +29810.9 q^{77} -2.03988e7i q^{79} +(7.02937e6 + 1.69154e7i) q^{80} +(-1.38296e7 + 4.56374e7i) q^{82} +5.09090e7i q^{83} +2.85743e7 q^{85} +(3.40284e7 + 1.03117e7i) q^{86} +(368651. + 448415. i) q^{88} +2.68313e7 q^{89} +3.71375e6i q^{91} +(6.47319e7 - 9.69986e7i) q^{92} +(1.16969e8 + 3.54456e7i) q^{94} -2.99321e7i q^{95} +3.38260e7 q^{97} +(-2.65443e7 + 8.75953e7i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−4.64016	+	15.3124i	−0.290010	+	0.957024i
$2$	−4.64016	+	15.3124i	−0.290010	+	0.957024i
$3$		0			0
$3$		0			0
$4$	−212.938	−	142.104i	−0.831788	−	0.555093i
$5$	279.508			0.447214
$5$	279.508			0.447214
$6$		0			0
$7$		−	210.345i		−	0.0876072i	−0.999040	−	0.0438036i	$-0.986052\pi$
$7$		−	210.345i		−	0.0876072i	0.999040	−	0.0438036i	$-0.0139476\pi$
$8$	3164.01	−	2601.20i	0.772464	−	0.635059i
$9$		0			0
$10$	−1296.96	+	4279.94i	−0.129696	+	0.427994i
$11$			141.724i			0.00967991i	0.999988	+	0.00483996i	$0.00154061\pi$
$11$			141.724i			0.00967991i	−0.999988	+	0.00483996i	$0.998459\pi$
$12$		0			0
$13$	−17655.5			−0.618168			−0.309084	−	0.951035i	$-0.600022\pi$
$13$	−17655.5			−0.618168			−0.309084	+	0.951035i	$0.600022\pi$
$14$	3220.88	+	976.035i	0.0838422	+	0.0254070i
$15$		0			0
$16$	25149.0	+	60518.5i	0.383744	+	0.923440i
$17$	102231.			1.22401			0.612005	−	0.790854i	$-0.290363\pi$
$17$	102231.			1.22401			0.612005	+	0.790854i	$0.290363\pi$
$18$		0			0
$19$		−	107088.i		−	0.821728i	−0.911697	−	0.410864i	$-0.865227\pi$
$19$		−	107088.i		−	0.821728i	0.911697	−	0.410864i	$-0.134773\pi$
$20$	−59517.9	−	39719.2i	−0.371987	−	0.248245i
$21$		0			0
$22$	−2170.13	−	657.620i	−0.00926391	−	0.00280727i
$23$			455526.i			1.62780i	0.581004	+	0.813901i	$0.302660\pi$
$23$			455526.i			1.62780i	−0.581004	+	0.813901i	$0.697340\pi$
$24$		0			0
$25$	78125.0			0.200000
$26$	81924.3	−	270348.i	0.179275	−	0.591601i
$27$		0			0
$28$	−29890.8	+	44790.4i	−0.0486302	+	0.0728707i
$29$	−865184.			−1.22325			−0.611627	−	0.791146i	$-0.709485\pi$
$29$	−865184.			−1.22325			−0.611627	+	0.791146i	$0.709485\pi$
$30$		0			0
$31$		−	429788.i		−	0.465380i	−0.972551	−	0.232690i	$-0.925247\pi$
$31$		−	429788.i		−	0.465380i	0.972551	−	0.232690i	$-0.0747528\pi$
$32$	−1.04338e6	+	104276.i	−0.995043	+	0.0994450i
$33$		0			0
$34$	−474366.	+	1.56539e6i	−0.354975	+	1.17141i
$35$		−	58793.2i		−	0.0391792i
$36$		0			0
$37$	−2.51809e6			−1.34358			−0.671791	−	0.740741i	$-0.734475\pi$
$37$	−2.51809e6			−1.34358			−0.671791	+	0.740741i	$0.734475\pi$
$38$	1.63978e6	+	496908.i	0.786414	+	0.238310i
$39$		0			0
$40$	884368.	−	727057.i	0.345456	−	0.284007i
$41$	2.98042e6			1.05473			0.527366	−	0.849638i	$-0.323180\pi$
$41$	2.98042e6			1.05473			0.527366	+	0.849638i	$0.323180\pi$
$42$		0			0
$43$		−	2.22228e6i		−	0.650018i	−0.945711	−	0.325009i	$-0.894633\pi$
$43$		−	2.22228e6i		−	0.650018i	0.945711	−	0.325009i	$-0.105367\pi$
$44$	20139.5	−	30178.3i	0.00537325	−	0.00805164i
$45$		0			0
$46$	−6.97518e6	−	2.11371e6i	−1.55784	−	0.472079i
$47$		−	7.63886e6i		−	1.56544i	−0.622372	−	0.782722i	$-0.713831\pi$
$47$		−	7.63886e6i		−	1.56544i	0.622372	−	0.782722i	$-0.286169\pi$
$48$		0			0
$49$	5.72056e6			0.992325
$50$	−362513.	+	1.19628e6i	−0.0580020	+	0.191405i
$51$		0			0
$52$	3.75952e6	+	2.50891e6i	0.514185	+	0.343141i
$53$	−1.55615e7			−1.97219			−0.986094	−	0.166186i	$-0.946855\pi$
$53$	−1.55615e7			−1.97219			−0.986094	+	0.166186i	$0.946855\pi$
$54$		0			0
$55$			39613.0i			0.00432899i
$56$	−547149.	−	665534.i	−0.0556357	−	0.0676734i
$57$		0			0
$58$	4.01459e6	−	1.32480e7i	0.354756	−	1.17068i
$59$			6.38433e6i			0.526874i	0.964677	+	0.263437i	$0.0848562\pi$
$59$			6.38433e6i			0.526874i	−0.964677	+	0.263437i	$0.915144\pi$
$60$		0			0
$61$	2.03289e6			0.146823			0.0734116	−	0.997302i	$-0.476611\pi$
$61$	2.03289e6			0.146823			0.0734116	+	0.997302i	$0.476611\pi$
$62$	6.58108e6	+	1.99429e6i	0.445380	+	0.134965i
$63$		0			0
$64$	3.24473e6	−	1.64605e7i	0.193401	−	0.981120i
$65$	−4.93486e6			−0.276453
$66$		0			0
$67$		−	2.03503e7i		−	1.00988i	−0.863154	−	0.504941i	$-0.831514\pi$
$67$		−	2.03503e7i		−	1.00988i	0.863154	−	0.504941i	$-0.168486\pi$
$68$	−2.17688e7	−	1.45274e7i	−1.01812	−	0.679439i
$69$		0			0
$70$	900264.	+	272810.i	0.0374954	+	0.0113623i
$71$		−	4.44463e7i		−	1.74905i	−0.484979	−	0.874526i	$-0.661173\pi$
$71$		−	4.44463e7i		−	1.74905i	0.484979	−	0.874526i	$-0.338827\pi$
$72$		0			0
$73$	1.79865e7			0.633366			0.316683	−	0.948531i	$-0.397431\pi$
$73$	1.79865e7			0.633366			0.316683	+	0.948531i	$0.397431\pi$
$74$	1.16843e7	−	3.85579e7i	0.389652	−	1.28584i
$75$		0			0
$76$	−1.52177e7	+	2.28032e7i	−0.456136	+	0.683504i
$77$	29810.9			0.000848031
$78$		0			0
$79$		−	2.03988e7i		−	0.523716i	−0.965106	−	0.261858i	$-0.915665\pi$
$79$		−	2.03988e7i		−	0.523716i	0.965106	−	0.261858i	$-0.0843352\pi$
$80$	7.02937e6	+	1.69154e7i	0.171615	+	0.412975i
$81$		0			0
$82$	−1.38296e7	+	4.56374e7i	−0.305883	+	1.00940i
$83$			5.09090e7i			1.07271i	0.843992	+	0.536355i	$0.180199\pi$
$83$			5.09090e7i			1.07271i	−0.843992	+	0.536355i	$0.819801\pi$
$84$		0			0
$85$	2.85743e7			0.547394
$86$	3.40284e7	+	1.03117e7i	0.622082	+	0.188512i
$87$		0			0
$88$	368651.	+	448415.i	0.00614731	+	0.00747738i
$89$	2.68313e7			0.427644			0.213822	−	0.976873i	$-0.431409\pi$
$89$	2.68313e7			0.427644			0.213822	+	0.976873i	$0.431409\pi$
$90$		0			0
$91$			3.71375e6i			0.0541560i
$92$	6.47319e7	−	9.69986e7i	0.903581	−	1.35399i
$93$		0			0
$94$	1.16969e8	+	3.54456e7i	1.49817	+	0.453994i
$95$		−	2.99321e7i		−	0.367488i
$96$		0			0
$97$	3.38260e7			0.382089			0.191044	−	0.981581i	$-0.438813\pi$
$97$	3.38260e7			0.382089			0.191044	+	0.981581i	$0.438813\pi$
$98$	−2.65443e7	+	8.75953e7i	−0.287784	+	0.949678i
$99$		0			0
$100$	−1.66358e7	−	1.11019e7i	−0.166358	−	0.111019i
$101$	−5.46440e7			−0.525118			−0.262559	−	0.964916i	$-0.584566\pi$
$101$	−5.46440e7			−0.525118			−0.262559	+	0.964916i	$0.584566\pi$
$102$		0			0
$103$		−	5.49350e6i		−	0.0488090i	−0.999702	−	0.0244045i	$-0.992231\pi$
$103$		−	5.49350e6i		−	0.0488090i	0.999702	−	0.0244045i	$-0.00776897\pi$
$104$	−5.58622e7	+	4.59255e7i	−0.477513	+	0.392573i
$105$		0			0
$106$	7.22080e7	−	2.38284e8i	0.571955	−	1.88743i
$107$			4.58185e7i			0.349547i	0.984609	+	0.174773i	$0.0559193\pi$
$107$			4.58185e7i			0.349547i	−0.984609	+	0.174773i	$0.944081\pi$
$108$		0			0
$109$	1.34989e8			0.956295			0.478147	−	0.878280i	$-0.341308\pi$
$109$	1.34989e8			0.956295			0.478147	+	0.878280i	$0.341308\pi$
$110$	−606569.	−	183810.i	−0.00414294	−	0.00125545i
$111$		0			0
$112$	1.27298e7	−	5.28997e6i	0.0809000	−	0.0336187i
$113$	1.52579e8			0.935796			0.467898	−	0.883783i	$-0.345011\pi$
$113$	1.52579e8			0.935796			0.467898	+	0.883783i	$0.345011\pi$
$114$		0			0
$115$			1.27323e8i			0.727975i
$116$	1.84230e8	+	1.22946e8i	1.01749	+	0.679020i
$117$		0			0
$118$	−9.77592e7	−	2.96243e7i	−0.504231	−	0.152799i
$119$		−	2.15037e7i		−	0.107232i
$120$		0			0
$121$	2.14339e8			0.999906
$122$	−9.43293e6	+	3.11284e7i	−0.0425802	+	0.140513i
$123$		0			0
$124$	−6.10746e7	+	9.15182e7i	−0.258329	+	0.387098i
$125$	2.18366e7			0.0894427
$126$		0			0
$127$		−	3.88910e8i		−	1.49498i	−0.664275	−	0.747488i	$-0.731260\pi$
$127$		−	3.88910e8i		−	1.49498i	0.664275	−	0.747488i	$-0.268740\pi$
$128$	2.36993e8	+	1.26064e8i	0.882866	+	0.469624i
$129$		0			0
$130$	2.28985e7	−	7.55645e7i	0.0801742	−	0.264572i
$131$		−	5.32310e8i		−	1.80750i	−0.428056	−	0.903752i	$-0.640801\pi$
$131$		−	5.32310e8i		−	1.80750i	0.428056	−	0.903752i	$-0.359199\pi$
$132$		0			0
$133$	−2.25255e7			−0.0719894
$134$	3.11611e8	+	9.44285e7i	0.966482	+	0.292876i
$135$		0			0
$136$	3.23459e8	−	2.65922e8i	0.945504	−	0.777318i
$137$	5.11356e8			1.45158			0.725790	−	0.687916i	$-0.241474\pi$
$137$	5.11356e8			1.45158			0.725790	+	0.687916i	$0.241474\pi$
$138$		0			0
$139$		−	4.03705e8i		−	1.08145i	−0.841201	−	0.540723i	$-0.818151\pi$
$139$		−	4.03705e8i		−	1.08145i	0.841201	−	0.540723i	$-0.181849\pi$
$140$	−8.35474e6	+	1.25193e7i	−0.0217481	+	0.0325888i
$141$		0			0
$142$	6.80579e8	+	2.06238e8i	1.67388	+	0.507243i
$143$		−	2.50220e6i		−	0.00598381i
$144$		0			0
$145$	−2.41826e8			−0.547056
$146$	−8.34602e7	+	2.75416e8i	−0.183683	+	0.606146i
$147$		0			0
$148$	5.36196e8	+	3.57830e8i	1.11758	+	0.745813i
$149$	−2.52732e8			−0.512761			−0.256381	−	0.966576i	$-0.582530\pi$
$149$	−2.52732e8			−0.512761			−0.256381	+	0.966576i	$0.582530\pi$
$150$		0			0
$151$		−	1.14787e8i		−	0.220792i	−0.993888	−	0.110396i	$-0.964788\pi$
$151$		−	1.14787e8i		−	0.220792i	0.993888	−	0.110396i	$-0.0352119\pi$
$152$	−2.78559e8	−	3.38829e8i	−0.521846	−	0.634756i
$153$		0			0
$154$	−138327.	+	456475.i	−0.000245937	+	0.000811585i
$155$		−	1.20130e8i		−	0.208124i
$156$		0			0
$157$	3.48763e8			0.574026			0.287013	−	0.957927i	$-0.407338\pi$
$157$	3.48763e8			0.574026			0.287013	+	0.957927i	$0.407338\pi$
$158$	3.12354e8	+	9.46536e7i	0.501209	+	0.151883i
$159$		0			0
$160$	−2.91633e8	+	2.91459e7i	−0.444997	+	0.0444732i
$161$	9.58175e7			0.142607
$162$		0			0
$163$		−	2.96216e8i		−	0.419622i	−0.977742	−	0.209811i	$-0.932715\pi$
$163$		−	2.96216e8i		−	0.419622i	0.977742	−	0.209811i	$-0.0672848\pi$
$164$	−6.34645e8	−	4.23529e8i	−0.877314	−	0.585475i
$165$		0			0
$166$	−7.79538e8	−	2.36226e8i	−1.02661	−	0.311097i
$167$			1.56004e8i			0.200572i	0.994959	+	0.100286i	$0.0319757\pi$
$167$			1.56004e8i			0.200572i	−0.994959	+	0.100286i	$0.968024\pi$
$168$		0			0
$169$	−5.04014e8			−0.617868
$170$	−1.32589e8	+	4.37541e8i	−0.158750	+	0.523869i
$171$		0			0
$172$	−3.15795e8	+	4.73208e8i	−0.360820	+	0.540677i
$173$	−4.66034e8			−0.520276			−0.260138	−	0.965572i	$-0.583768\pi$
$173$	−4.66034e8			−0.520276			−0.260138	+	0.965572i	$0.583768\pi$
$174$		0			0
$175$		−	1.64332e7i		−	0.0175214i
$176$	−8.57691e6	+	3.56421e6i	−0.00893882	+	0.00371461i
$177$		0			0
$178$	−1.24502e8	+	4.10851e8i	−0.124021	+	0.409265i
$179$		−	1.44673e9i		−	1.40921i	−0.709600	−	0.704605i	$-0.751124\pi$
$179$		−	1.44673e9i		−	1.40921i	0.709600	−	0.704605i	$-0.248876\pi$
$180$		0			0
$181$	−5.80491e8			−0.540855			−0.270428	−	0.962740i	$-0.587165\pi$
$181$	−5.80491e8			−0.540855			−0.270428	+	0.962740i	$0.587165\pi$
$182$	−5.68663e7	−	1.72324e7i	−0.0518286	−	0.0157058i
$183$		0			0
$184$	1.18491e9	+	1.44129e9i	1.03375	+	1.25742i
$185$	−7.03827e8			−0.600868
$186$		0			0
$187$			1.44885e7i			0.0118483i
$188$	−1.08551e9	+	1.62660e9i	−0.868966	+	1.30212i
$189$		0			0
$190$	4.58332e8	+	1.38890e8i	0.351695	+	0.106575i
$191$		−	2.29528e9i		−	1.72465i	−0.506351	−	0.862327i	$-0.669006\pi$
$191$		−	2.29528e9i		−	1.72465i	0.506351	−	0.862327i	$-0.330994\pi$
$192$		0			0
$193$	−1.42541e9			−1.02733			−0.513665	−	0.857991i	$-0.671713\pi$
$193$	−1.42541e9			−1.02733			−0.513665	+	0.857991i	$0.671713\pi$
$194$	−1.56958e8	+	5.17957e8i	−0.110810	+	0.365668i
$195$		0			0
$196$	−1.21812e9	−	8.12913e8i	−0.825404	−	0.550833i
$197$	−1.42075e9			−0.943305			−0.471652	−	0.881785i	$-0.656342\pi$
$197$	−1.42075e9			−0.943305			−0.471652	+	0.881785i	$0.656342\pi$
$198$		0			0
$199$			1.90032e9i			1.21176i	0.795557	+	0.605878i	$0.207178\pi$
$199$			1.90032e9i			1.21176i	−0.795557	+	0.605878i	$0.792822\pi$
$200$	2.47188e8	−	2.03219e8i	0.154493	−	0.127012i
$201$		0			0
$202$	2.53557e8	−	8.36729e8i	0.152289	−	0.502550i
$203$			1.81987e8i			0.107166i
$204$		0			0
$205$	8.33053e8			0.471691
$206$	8.41185e7	+	2.54907e7i	0.0467114	+	0.0141551i
$207$		0			0
$208$	−4.44019e8	−	1.06848e9i	−0.237218	−	0.570841i
$209$	1.51770e7			0.00795426
$210$		0			0
$211$		−	1.67947e9i		−	0.847311i	−0.905823	−	0.423655i	$-0.860747\pi$
$211$		−	1.67947e9i		−	0.847311i	0.905823	−	0.423655i	$-0.139253\pi$
$212$	3.31364e9	+	2.21135e9i	1.64044	+	1.09475i
$213$		0			0
$214$	−7.01590e8	−	2.12605e8i	−0.334525	−	0.101372i
$215$		−	6.21146e8i		−	0.290697i
$216$		0			0
$217$	−9.04039e7			−0.0407707
$218$	−6.26370e8	+	2.06700e9i	−0.277335	+	0.915197i
$219$		0			0
$220$	5.62915e6	−	8.43510e6i	0.00240299	−	0.00360080i
$221$	−1.80493e9			−0.756644
$222$		0			0
$223$		−	1.10738e9i		−	0.447795i	−0.974613	−	0.223897i	$-0.928122\pi$
$223$		−	1.10738e9i		−	0.447795i	0.974613	−	0.223897i	$-0.0718780\pi$
$224$	2.19339e7	+	2.19469e8i	0.00871210	+	0.0871730i
$225$		0			0
$226$	−7.07991e8	+	2.33635e9i	−0.271390	+	0.895579i
$227$		−	4.15603e9i		−	1.56522i	−0.622512	−	0.782610i	$-0.713888\pi$
$227$		−	4.15603e9i		−	1.56522i	0.622512	−	0.782610i	$-0.286112\pi$
$228$		0			0
$229$	1.34641e9			0.489594			0.244797	−	0.969574i	$-0.421279\pi$
$229$	1.34641e9			0.489594			0.244797	+	0.969574i	$0.421279\pi$
$230$	−1.94962e9	−	5.90800e8i	−0.696689	−	0.211120i
$231$		0			0
$232$	−2.73745e9	+	2.25052e9i	−0.944920	+	0.776838i
$233$	−2.57794e8			−0.0874681			−0.0437341	−	0.999043i	$-0.513925\pi$
$233$	−2.57794e8			−0.0874681			−0.0437341	+	0.999043i	$0.513925\pi$
$234$		0			0
$235$		−	2.13513e9i		−	0.700087i
$236$	9.07237e8	−	1.35946e9i	0.292464	−	0.438248i
$237$		0			0
$238$	3.29273e8	+	9.97806e7i	0.102624	+	0.0310984i
$239$			3.82549e8i			0.117245i	0.998280	+	0.0586227i	$0.0186709\pi$
$239$			3.82549e8i			0.117245i	−0.998280	+	0.0586227i	$0.981329\pi$
$240$		0			0
$241$	−5.49743e9			−1.62964			−0.814820	−	0.579714i	$-0.803164\pi$
$241$	−5.49743e9			−1.62964			−0.814820	+	0.579714i	$0.803164\pi$
$242$	−9.94566e8	+	3.28204e9i	−0.289983	+	0.956934i
$243$		0			0
$244$	−4.32879e8	−	2.88881e8i	−0.122126	−	0.0815005i
$245$	1.59894e9			0.443781
$246$		0			0
$247$			1.89070e9i			0.507966i
$248$	−1.11797e9	−	1.35986e9i	−0.295544	−	0.359490i
$249$		0			0
$250$	−1.01325e8	+	3.34370e8i	−0.0259393	+	0.0855988i
$251$			7.22250e9i			1.81967i	0.414971	+	0.909835i	$0.363792\pi$
$251$			7.22250e9i			1.81967i	−0.414971	+	0.909835i	$0.636208\pi$
$252$		0			0
$253$	−6.45587e7			−0.0157570
$254$	5.95514e9	+	1.80460e9i	1.43073	+	0.433558i
$255$		0			0
$256$	−3.03002e9	+	3.04396e9i	−0.705482	+	0.708728i
$257$	1.49317e9			0.342277			0.171138	−	0.985247i	$-0.445256\pi$
$257$	1.49317e9			0.342277			0.171138	+	0.985247i	$0.445256\pi$
$258$		0			0
$259$			5.29667e8i			0.117707i
$260$	1.05082e9	+	7.01262e8i	0.229950	+	0.153457i
$261$		0			0
$262$	8.15093e9	+	2.47000e9i	1.72982	+	0.524195i
$263$		−	4.58536e9i		−	0.958409i	−0.877703	−	0.479205i	$-0.840925\pi$
$263$		−	4.58536e9i		−	0.958409i	0.877703	−	0.479205i	$-0.159075\pi$
$264$		0			0
$265$	−4.34958e9			−0.881990
$266$	1.04522e8	−	3.44919e8i	0.0208776	−	0.0688955i
$267$		0			0
$268$	−2.89185e9	+	4.33334e9i	−0.560579	+	0.840009i
$269$	−5.70969e9			−1.09044			−0.545222	−	0.838292i	$-0.683555\pi$
$269$	−5.70969e9			−1.09044			−0.545222	+	0.838292i	$0.683555\pi$
$270$		0			0
$271$		−	8.61657e9i		−	1.59756i	−0.601623	−	0.798780i	$-0.705479\pi$
$271$		−	8.61657e9i		−	1.59756i	0.601623	−	0.798780i	$-0.294521\pi$
$272$	2.57100e9	+	6.18684e9i	0.469706	+	1.13030i
$273$		0			0
$274$	−2.37277e9	+	7.83008e9i	−0.420973	+	1.38920i
$275$			1.10722e7i			0.00193598i
$276$		0			0
$277$	5.74438e9			0.975717			0.487858	−	0.872923i	$-0.337778\pi$
$277$	5.74438e9			0.975717			0.487858	+	0.872923i	$0.337778\pi$
$278$	6.18168e9	+	1.87326e9i	1.03497	+	0.313630i
$279$		0			0
$280$	−1.52933e8	−	1.86022e8i	−0.0248811	−	0.0302645i
$281$	−7.75176e9			−1.24330			−0.621648	−	0.783296i	$-0.713537\pi$
$281$	−7.75176e9			−1.24330			−0.621648	+	0.783296i	$0.713537\pi$
$282$		0			0
$283$			3.56052e9i			0.555096i	0.960712	+	0.277548i	$0.0895217\pi$
$283$			3.56052e9i			0.555096i	−0.960712	+	0.277548i	$0.910478\pi$
$284$	−6.31599e9	+	9.46431e9i	−0.970886	+	1.45484i
$285$		0			0
$286$	3.83146e7	+	1.16106e7i	0.00572665	+	0.00173537i
$287$		−	6.26917e8i		−	0.0924022i
$288$		0			0
$289$	3.47533e9			0.498201
$290$	1.12211e9	−	3.70294e9i	0.158652	−	0.523545i
$291$		0			0
$292$	−3.83000e9	−	2.55595e9i	−0.526826	−	0.351577i
$293$	5.61859e9			0.762355			0.381177	−	0.924502i	$-0.375519\pi$
$293$	5.61859e9			0.762355			0.381177	+	0.924502i	$0.375519\pi$
$294$		0			0
$295$			1.78447e9i			0.235625i
$296$	−7.96726e9	+	6.55005e9i	−1.03787	+	0.853253i
$297$		0			0
$298$	1.17272e9	−	3.86993e9i	0.148706	−	0.490725i
$299$		−	8.04253e9i		−	1.00625i
$300$		0			0
$301$	−4.67446e8			−0.0569463
$302$	1.75766e9	+	5.32628e8i	0.211303	+	0.0640319i
$303$		0			0
$304$	6.48084e9	−	2.69317e9i	0.758817	−	0.315333i
$305$	5.68210e8			0.0656613
$306$		0			0
$307$			1.17341e10i			1.32099i	0.750832	+	0.660493i	$0.229653\pi$
$307$			1.17341e10i			1.32099i	−0.750832	+	0.660493i	$0.770347\pi$
$308$	−6.34786e6	−	4.23623e6i	−0.000705382	−	0.000470736i
$309$		0			0
$310$	1.83947e9	+	5.57420e8i	0.199180	+	0.0603582i
$311$		−	8.30766e9i		−	0.888050i	−0.896014	−	0.444025i	$-0.853550\pi$
$311$		−	8.30766e9i		−	0.888050i	0.896014	−	0.444025i	$-0.146450\pi$
$312$		0			0
$313$	−8.58561e9			−0.894528			−0.447264	−	0.894402i	$-0.647601\pi$
$313$	−8.58561e9			−0.894528			−0.447264	+	0.894402i	$0.647601\pi$
$314$	−1.61831e9	+	5.34038e9i	−0.166473	+	0.549356i
$315$		0			0
$316$	−2.89874e9	+	4.34367e9i	−0.290711	+	0.435621i
$317$	2.51112e9			0.248674			0.124337	−	0.992240i	$-0.460320\pi$
$317$	2.51112e9			0.248674			0.124337	+	0.992240i	$0.460320\pi$
$318$		0			0
$319$		−	1.22617e8i		−	0.0118410i
$320$	9.06931e8	−	4.60084e9i	0.0864917	−	0.438770i
$321$		0			0
$322$	−4.44609e8	+	1.46719e9i	−0.0413575	+	0.136478i
$323$		−	1.09477e10i		−	1.00580i
$324$		0			0
$325$	−1.37934e9			−0.123634
$326$	4.53577e9	+	1.37449e9i	0.401588	+	0.121694i
$327$		0			0
$328$	9.43009e9	−	7.75267e9i	0.814743	−	0.669817i
$329$	−1.60680e9			−0.137144
$330$		0			0
$331$		−	1.38910e10i		−	1.15724i	−0.815599	−	0.578618i	$-0.803592\pi$
$331$		−	1.38910e10i		−	1.15724i	0.815599	−	0.578618i	$-0.196408\pi$
$332$	7.23437e9	−	1.08405e10i	0.595454	−	0.892268i
$333$		0			0
$334$	−2.38879e9	−	7.23883e8i	−0.191952	−	0.0581678i
$335$		−	5.68807e9i		−	0.451633i
$336$		0			0
$337$	1.74804e10			1.35529			0.677643	−	0.735391i	$-0.263001\pi$
$337$	1.74804e10			1.35529			0.677643	+	0.735391i	$0.263001\pi$
$338$	2.33871e9	−	7.71766e9i	0.179188	−	0.591315i
$339$		0			0
$340$	−6.08455e9	−	4.06052e9i	−0.455316	−	0.303855i
$341$	6.09112e7			0.00450484
$342$		0			0
$343$		−	2.41589e9i		−	0.174542i
$344$	−5.78060e9	−	7.03133e9i	−0.412799	−	0.502115i
$345$		0			0
$346$	2.16247e9	−	7.13609e9i	0.150885	−	0.497916i
$347$			4.08751e8i			0.0281930i	0.999901	+	0.0140965i	$0.00448720\pi$
$347$			4.08751e8i			0.0281930i	−0.999901	+	0.0140965i	$0.995513\pi$
$348$		0			0
$349$	−1.52539e10			−1.02820			−0.514102	−	0.857729i	$-0.671875\pi$
$349$	−1.52539e10			−1.02820			−0.514102	+	0.857729i	$0.671875\pi$
$350$	2.51631e8	+	7.62527e7i	0.0167684	+	0.00508140i
$351$		0			0
$352$	−1.47783e7	−	1.47871e8i	−0.000962619	−	0.00963193i
$353$	2.36311e9			0.152190			0.0760950	−	0.997101i	$-0.475755\pi$
$353$	2.36311e9			0.152190			0.0760950	+	0.997101i	$0.475755\pi$
$354$		0			0
$355$		−	1.24231e10i		−	0.782200i
$356$	−5.71340e9	−	3.81283e9i	−0.355709	−	0.237382i
$357$		0			0
$358$	2.21529e10	+	6.71306e9i	1.34865	+	0.408685i
$359$			1.95665e10i			1.17797i	0.808143	+	0.588987i	$0.200473\pi$
$359$			1.95665e10i			1.17797i	−0.808143	+	0.588987i	$0.799527\pi$
$360$		0			0
$361$	5.51562e9			0.324762
$362$	2.69357e9	−	8.88870e9i	0.156854	−	0.517611i
$363$		0			0
$364$	5.27737e8	−	7.90797e8i	0.0300616	−	0.0450463i
$365$	5.02737e9			0.283250
$366$		0			0
$367$		−	2.40655e10i		−	1.32657i	−0.748367	−	0.663285i	$-0.769162\pi$
$367$		−	2.40655e10i		−	1.32657i	0.748367	−	0.663285i	$-0.230838\pi$
$368$	−2.75677e10	+	1.14560e10i	−1.50318	+	0.624659i
$369$		0			0
$370$	3.26587e9	−	1.07773e10i	0.174258	−	0.575045i
$371$			3.27329e9i			0.172778i
$372$		0			0
$373$	1.70488e10			0.880760			0.440380	−	0.897811i	$-0.354844\pi$
$373$	1.70488e10			0.880760			0.440380	+	0.897811i	$0.354844\pi$
$374$	−2.21853e8	−	6.72289e7i	−0.0113391	−	0.00343613i
$375$		0			0
$376$	−1.98702e10	−	2.41695e10i	−0.994148	−	1.20925i
$377$	1.52753e10			0.756176
$378$		0			0
$379$		−	1.60429e10i		−	0.777545i	−0.921334	−	0.388772i	$-0.872899\pi$
$379$		−	1.60429e10i		−	0.777545i	0.921334	−	0.388772i	$-0.127101\pi$
$380$	−4.25347e9	+	6.37368e9i	−0.203990	+	0.305672i
$381$		0			0
$382$	3.51462e10	+	1.06505e10i	1.65054	+	0.500167i
$383$			1.23891e10i			0.575765i	0.957666	+	0.287883i	$0.0929513\pi$
$383$			1.23891e10i			0.575765i	−0.957666	+	0.287883i	$0.907049\pi$
$384$		0			0
$385$	8.33239e6			0.000379251
$386$	6.61413e9	−	2.18264e10i	0.297936	−	0.983180i
$387$		0			0
$388$	−7.20284e9	−	4.80681e9i	−0.317817	−	0.212095i
$389$	1.27527e10			0.556935			0.278467	−	0.960446i	$-0.410174\pi$
$389$	1.27527e10			0.556935			0.278467	+	0.960446i	$0.410174\pi$
$390$		0			0
$391$			4.65686e10i			1.99245i
$392$	1.80999e10	−	1.48803e10i	0.766535	−	0.630184i
$393$		0			0
$394$	6.59250e9	−	2.17550e10i	0.273568	−	0.902765i
$395$		−	5.70163e9i		−	0.234213i
$396$		0			0
$397$	−1.95226e10			−0.785914			−0.392957	−	0.919557i	$-0.628548\pi$
$397$	−1.95226e10			−0.785914			−0.392957	+	0.919557i	$0.628548\pi$
$398$	−2.90985e10	−	8.81781e9i	−1.15968	−	0.351422i
$399$		0			0
$400$	1.96477e9	+	4.72801e9i	0.0767487	+	0.184688i
$401$	−2.44896e10			−0.947119			−0.473559	−	0.880762i	$-0.657031\pi$
$401$	−2.44896e10			−0.947119			−0.473559	+	0.880762i	$0.657031\pi$
$402$		0			0
$403$			7.58813e9i			0.287683i
$404$	1.16358e10	+	7.76512e9i	0.436787	+	0.291489i
$405$		0			0
$406$	−2.78666e9	−	8.44450e8i	−0.102560	−	0.0310792i
$407$		−	3.56873e8i		−	0.0130058i
$408$		0			0
$409$	1.79748e10			0.642350			0.321175	−	0.947020i	$-0.395922\pi$
$409$	1.79748e10			0.642350			0.321175	+	0.947020i	$0.395922\pi$
$410$	−3.86550e9	+	1.27560e10i	−0.136795	+	0.451419i
$411$		0			0
$412$	−7.80647e8	+	1.16977e9i	−0.0270935	+	0.0405988i
$413$	1.34291e9			0.0461580
$414$		0			0
$415$			1.42295e10i			0.479731i
$416$	1.84214e10	−	1.84104e9i	0.615104	−	0.0614737i
$417$		0			0
$418$	−7.04236e7	+	2.32395e8i	−0.00230682	+	0.00761241i
$419$			3.49871e10i			1.13515i	0.823323	+	0.567573i	$0.192117\pi$
$419$			3.49871e10i			1.13515i	−0.823323	+	0.567573i	$0.807883\pi$
$420$		0			0
$421$	1.17473e10			0.373947			0.186973	−	0.982365i	$-0.440132\pi$
$421$	1.17473e10			0.373947			0.186973	+	0.982365i	$0.440132\pi$
$422$	2.57167e10	+	7.79302e9i	0.810896	+	0.245729i
$423$		0			0
$424$	−4.92368e10	+	4.04786e10i	−1.52344	+	1.25246i
$425$	7.98676e9			0.244802
$426$		0			0
$427$		−	4.27608e8i		−	0.0128628i
$428$	6.51098e9	−	9.75649e9i	0.194031	−	0.290749i
$429$		0			0
$430$	9.51123e9	+	2.88222e9i	0.278204	+	0.0843050i
$431$		−	4.11908e10i		−	1.19369i	−0.802357	−	0.596845i	$-0.796421\pi$
$431$		−	4.11908e10i		−	1.19369i	0.802357	−	0.596845i	$-0.203579\pi$
$432$		0			0
$433$	−1.38879e10			−0.395079			−0.197540	−	0.980295i	$-0.563295\pi$
$433$	−1.38879e10			−0.395079			−0.197540	+	0.980295i	$0.563295\pi$
$434$	4.19488e8	−	1.38430e9i	0.0118239	−	0.0390185i
$435$		0			0
$436$	−2.87442e10	−	1.91824e10i	−0.795435	−	0.530833i
$437$	4.87815e10			1.33761
$438$		0			0
$439$			2.26777e10i			0.610577i	0.952260	+	0.305289i	$0.0987530\pi$
$439$			2.26777e10i			0.610577i	−0.952260	+	0.305289i	$0.901247\pi$
$440$	1.03041e8	+	1.25336e8i	0.00274916	+	0.00334399i
$441$		0			0
$442$	8.37517e9	−	2.76378e10i	0.219434	−	0.724126i
$443$			4.08182e10i			1.05984i	0.848049	+	0.529919i	$0.177778\pi$
$443$			4.08182e10i			1.05984i	−0.848049	+	0.529919i	$0.822222\pi$
$444$		0			0
$445$	7.49958e9			0.191248
$446$	1.69567e10	+	5.13844e9i	0.428550	+	0.129865i
$447$		0			0
$448$	−3.46237e9	−	6.82514e8i	−0.0859532	−	0.0169434i
$449$	−4.15880e10			−1.02325			−0.511626	−	0.859208i	$-0.670957\pi$
$449$	−4.15880e10			−1.02325			−0.511626	+	0.859208i	$0.670957\pi$
$450$		0			0
$451$			4.22396e8i			0.0102097i
$452$	−3.24898e10	−	2.16821e10i	−0.778384	−	0.519454i
$453$		0			0
$454$	6.36387e10	+	1.92847e10i	1.49795	+	0.453929i
$455$			1.03802e9i			0.0242193i
$456$		0			0
$457$	7.96321e10			1.82567			0.912837	−	0.408324i	$-0.133887\pi$
$457$	7.96321e10			1.82567			0.912837	+	0.408324i	$0.133887\pi$
$458$	−6.24756e9	+	2.06168e10i	−0.141987	+	0.468553i
$459$		0			0
$460$	1.80931e10	−	2.71119e10i	0.404094	−	0.605521i
$461$	2.32904e10			0.515671			0.257836	−	0.966189i	$-0.416991\pi$
$461$	2.32904e10			0.515671			0.257836	+	0.966189i	$0.416991\pi$
$462$		0			0
$463$			3.77433e10i			0.821327i	0.911787	+	0.410664i	$0.134703\pi$
$463$			3.77433e10i			0.821327i	−0.911787	+	0.410664i	$0.865297\pi$
$464$	−2.17585e10	−	5.23597e10i	−0.469416	−	1.12960i
$465$		0			0
$466$	1.19621e9	−	3.94745e9i	0.0253666	−	0.0837091i
$467$			3.59265e10i			0.755349i	0.925938	+	0.377674i	$0.123276\pi$
$467$			3.59265e10i			0.755349i	−0.925938	+	0.377674i	$0.876724\pi$
$468$		0			0
$469$	−4.28058e9			−0.0884731
$470$	3.26939e10	+	9.90733e9i	0.670000	+	0.203032i
$471$		0			0
$472$	1.66069e10	+	2.02001e10i	0.334596	+	0.406991i
$473$	3.14950e8			0.00629212
$474$		0			0
$475$		−	8.36629e9i		−	0.164346i
$476$	−3.05576e9	+	4.57895e9i	−0.0595238	+	0.0891945i
$477$		0			0
$478$	−5.85774e9	−	1.77509e9i	−0.112207	−	0.0340024i
$479$			4.40663e10i			0.837076i	0.908199	+	0.418538i	$0.137457\pi$
$479$			4.40663e10i			0.837076i	−0.908199	+	0.418538i	$0.862543\pi$
$480$		0			0
$481$	4.44581e10			0.830559
$482$	2.55090e10	−	8.41787e10i	0.472612	−	1.55960i
$483$		0			0
$484$	−4.56408e10	−	3.04584e10i	−0.831710	−	0.555041i
$485$	9.45466e9			0.170875
$486$		0			0
$487$		−	3.99322e10i		−	0.709916i	−0.934882	−	0.354958i	$-0.884495\pi$
$487$		−	3.99322e10i		−	0.709916i	0.934882	−	0.354958i	$-0.115505\pi$
$488$	6.43209e9	−	5.28795e9i	0.113416	−	0.0932413i
$489$		0			0
$490$	−7.41936e9	+	2.44836e10i	−0.128701	+	0.424709i
$491$			7.96737e10i			1.37085i	0.728145	+	0.685423i	$0.240383\pi$
$491$			7.96737e10i			1.37085i	−0.728145	+	0.685423i	$0.759617\pi$
$492$		0			0
$493$	−8.84483e10			−1.49728
$494$	−2.89511e10	−	8.77315e9i	−0.486136	−	0.147315i
$495$		0			0
$496$	2.60102e10	−	1.08088e10i	0.429751	−	0.178587i
$497$	−9.34907e9			−0.153230
$498$		0			0
$499$		−	1.56191e10i		−	0.251915i	−0.992036	−	0.125957i	$-0.959800\pi$
$499$		−	1.56191e10i		−	0.251915i	0.992036	−	0.125957i	$-0.0402002\pi$
$500$	−4.64984e9	−	3.10306e9i	−0.0743974	−	0.0496490i
$501$		0			0
$502$	−1.10594e11	−	3.35136e10i	−1.74147	−	0.527722i
$503$			6.13884e10i			0.958990i	0.877544	+	0.479495i	$0.159180\pi$
$503$			6.13884e10i			0.958990i	−0.877544	+	0.479495i	$0.840820\pi$
$504$		0			0
$505$	−1.52735e10			−0.234840
$506$	2.99563e8	−	9.88548e8i	0.00456968	−	0.0150798i
$507$		0			0
$508$	−5.52656e10	+	8.28136e10i	−0.829850	+	1.24350i
$509$	1.27845e10			0.190464			0.0952322	−	0.995455i	$-0.469641\pi$
$509$	1.27845e10			0.190464			0.0952322	+	0.995455i	$0.469641\pi$
$510$		0			0
$511$		−	3.78337e9i		−	0.0554875i
$512$	−3.25506e10	−	6.05213e10i	−0.473673	−	0.880701i
$513$		0			0
$514$	−6.92856e9	+	2.28640e10i	−0.0992637	+	0.327567i
$515$		−	1.53548e9i		−	0.0218280i
$516$		0			0
$517$	1.08261e9			0.0151534
$518$	−8.11047e9	−	2.45774e9i	−0.112649	−	0.0341364i
$519$		0			0
$520$	−1.56140e10	+	1.28366e10i	−0.213550	+	0.175564i
$521$	−2.70385e10			−0.366971			−0.183486	−	0.983022i	$-0.558738\pi$
$521$	−2.70385e10			−0.366971			−0.183486	+	0.983022i	$0.558738\pi$
$522$		0			0
$523$			1.26822e11i			1.69508i	0.530734	+	0.847538i	$0.321916\pi$
$523$			1.26822e11i			1.69508i	−0.530734	+	0.847538i	$0.678084\pi$
$524$	−7.56433e10	+	1.13349e11i	−1.00333	+	1.50346i
$525$		0			0
$526$	7.02128e10	+	2.12768e10i	0.917220	+	0.277948i
$527$		−	4.39375e10i		−	0.569630i
$528$		0			0
$529$	−1.29193e11			−1.64974
$530$	2.01827e10	−	6.66024e10i	0.255786	−	0.844085i
$531$		0			0
$532$	4.79654e9	+	3.20096e9i	0.0598799	+	0.0399608i
$533$	−5.26208e10			−0.652002
$534$		0			0
$535$			1.28067e10i			0.156322i
$536$	−5.29351e10	−	6.43885e10i	−0.641335	−	0.780098i
$537$		0			0
$538$	2.64939e10	−	8.74289e10i	0.316240	−	1.04358i
$539$			8.10738e8i			0.00960562i
$540$		0			0
$541$	1.86619e10			0.217854			0.108927	−	0.994050i	$-0.465259\pi$
$541$	1.86619e10			0.217854			0.108927	+	0.994050i	$0.465259\pi$
$542$	1.31940e11	+	3.99823e10i	1.52890	+	0.463308i
$543$		0			0
$544$	−1.06665e11	+	1.06602e10i	−1.21794	+	0.121722i
$545$	3.77305e10			0.427668
$546$		0			0
$547$		−	2.19453e9i		−	0.0245128i	−0.999925	−	0.0122564i	$-0.996099\pi$
$547$		−	2.19453e9i		−	0.0245128i	0.999925	−	0.0122564i	$-0.00390143\pi$
$548$	−1.08887e11	−	7.26656e10i	−1.20741	−	0.805762i
$549$		0			0
$550$	−1.69541e8	−	5.13766e7i	−0.00185278	−	0.000561454i
$551$			9.26513e10i			1.00518i
$552$		0			0
$553$	−4.29078e9			−0.0458813
$554$	−2.66548e10	+	8.79601e10i	−0.282968	+	0.933784i
$555$		0			0
$556$	−5.73680e10	+	8.59640e10i	−0.600303	+	0.899534i
$557$	1.97889e10			0.205590			0.102795	−	0.994703i	$-0.467221\pi$
$557$	1.97889e10			0.205590			0.102795	+	0.994703i	$0.467221\pi$
$558$		0			0
$559$			3.92355e10i			0.401820i
$560$	3.55808e9	−	1.47859e9i	0.0361796	−	0.0150348i
$561$		0			0
$562$	3.59694e10	−	1.18698e11i	0.360569	−	1.18986i
$563$			3.05862e10i			0.304433i	0.988347	+	0.152216i	$0.0486411\pi$
$563$			3.05862e10i			0.304433i	−0.988347	+	0.152216i	$0.951359\pi$
$564$		0			0
$565$	4.26471e10			0.418501
$566$	−5.45200e10	−	1.65214e10i	−0.531240	−	0.160983i
$567$		0			0
$568$	−1.15614e11	−	1.40629e11i	−1.11075	−	1.35108i
$569$	−1.99299e11			−1.90132			−0.950661	−	0.310230i	$-0.899594\pi$
$569$	−1.99299e11			−1.90132			−0.950661	+	0.310230i	$0.899594\pi$
$570$		0			0
$571$			8.63094e10i			0.811921i	0.913891	+	0.405960i	$0.133063\pi$
$571$			8.63094e10i			0.811921i	−0.913891	+	0.405960i	$0.866937\pi$
$572$	−3.55572e8	+	5.32813e8i	−0.00332157	+	0.00497727i
$573$		0			0
$574$	9.59959e9	+	2.90900e9i	0.0884311	+	0.0267976i
$575$			3.55879e10i			0.325560i
$576$		0			0
$577$	−8.87088e10			−0.800320			−0.400160	−	0.916445i	$-0.631045\pi$
$577$	−8.87088e10			−0.800320			−0.400160	+	0.916445i	$0.631045\pi$
$578$	−1.61261e10	+	5.32156e10i	−0.144483	+	0.476791i
$579$		0			0
$580$	5.14940e10	+	3.43644e10i	0.455035	+	0.303667i
$581$	1.07085e10			0.0939772
$582$		0			0
$583$		−	2.20543e9i		−	0.0190906i
$584$	5.69095e10	−	4.67864e10i	0.489252	−	0.402225i
$585$		0			0
$586$	−2.60712e10	+	8.60340e10i	−0.221091	+	0.729591i
$587$		−	1.67947e11i		−	1.41456i	−0.706936	−	0.707278i	$-0.749923\pi$
$587$		−	1.67947e11i		−	1.41456i	0.706936	−	0.707278i	$-0.250077\pi$
$588$		0			0
$589$	−4.60254e10			−0.382416
$590$	−2.73245e10	−	8.28024e9i	−0.225499	−	0.0683337i
$591$		0			0
$592$	−6.33275e10	−	1.52391e11i	−0.515591	−	1.24072i
$593$	1.04027e11			0.841252			0.420626	−	0.907234i	$-0.361810\pi$
$593$	1.04027e11			0.841252			0.420626	+	0.907234i	$0.361810\pi$
$594$		0			0
$595$		−	6.01046e9i		−	0.0479557i
$596$	5.38162e10	+	3.59142e10i	0.426509	+	0.284630i
$597$		0			0
$598$	1.23150e11	+	3.73186e10i	0.963009	+	0.291824i
$599$		−	1.28089e11i		−	0.994960i	−0.867475	−	0.497480i	$-0.834259\pi$
$599$		−	1.28089e11i		−	0.994960i	0.867475	−	0.497480i	$-0.165741\pi$
$600$		0			0
$601$	−6.55306e10			−0.502281			−0.251140	−	0.967951i	$-0.580806\pi$
$601$	−6.55306e10			−0.502281			−0.251140	+	0.967951i	$0.580806\pi$
$602$	2.16902e9	−	7.15771e9i	0.0165150	−	0.0544989i
$603$		0			0
$604$	−1.63116e10	+	2.44424e10i	−0.122560	+	0.183652i
$605$	5.99095e10			0.447172
$606$		0			0
$607$			2.09475e11i			1.54304i	0.636204	+	0.771521i	$0.280504\pi$
$607$			2.09475e11i			1.54304i	−0.636204	+	0.771521i	$0.719496\pi$
$608$	1.11667e10	+	1.11734e11i	0.0817168	+	0.817655i
$609$		0			0
$610$	−2.63659e9	+	8.70064e9i	−0.0190424	+	0.0628394i
$611$			1.34868e11i			0.967707i
$612$		0			0
$613$	1.26502e11			0.895894			0.447947	−	0.894060i	$-0.352155\pi$
$613$	1.26502e11			0.895894			0.447947	+	0.894060i	$0.352155\pi$
$614$	−1.79678e11	−	5.44483e10i	−1.26421	−	0.383099i
$615$		0			0
$616$	9.43219e7	−	7.75440e7i	0.000655073	−	0.000538549i
$617$	2.25072e11			1.55303			0.776517	−	0.630096i	$-0.216984\pi$
$617$	2.25072e11			1.55303			0.776517	+	0.630096i	$0.216984\pi$
$618$		0			0
$619$		−	6.03060e10i		−	0.410769i	−0.978681	−	0.205385i	$-0.934155\pi$
$619$		−	6.03060e10i		−	0.410769i	0.978681	−	0.205385i	$-0.0658445\pi$
$620$	−1.70709e10	+	2.55801e10i	−0.115528	+	0.173115i
$621$		0			0
$622$	1.27210e11	+	3.85489e10i	0.849884	+	0.257543i
$623$		−	5.64383e9i		−	0.0374647i
$624$		0			0
$625$	6.10352e9			0.0400000
$626$	3.98386e10	−	1.31466e11i	0.259422	−	0.856084i
$627$		0			0
$628$	−7.42647e10	−	4.95605e10i	−0.477468	−	0.318638i
$629$	−2.57426e11			−1.64456
$630$		0			0
$631$		−	1.40158e11i		−	0.884097i	−0.896991	−	0.442049i	$-0.854252\pi$
$631$		−	1.40158e11i		−	0.884097i	0.896991	−	0.442049i	$-0.145748\pi$
$632$	−5.30613e10	−	6.45420e10i	−0.332590	−	0.404552i
$633$		0			0
$634$	−1.16520e10	+	3.84512e10i	−0.0721179	+	0.237987i
$635$		−	1.08704e11i		−	0.668573i
$636$		0			0
$637$	−1.00999e11			−0.613424
$638$	1.87756e9	+	5.68963e8i	0.0113321	+	0.00343401i
$639$		0			0
$640$	6.62415e10	+	3.52359e10i	0.394830	+	0.210022i
$641$	1.84845e11			1.09490			0.547452	−	0.836837i	$-0.315598\pi$
$641$	1.84845e11			1.09490			0.547452	+	0.836837i	$0.315598\pi$
$642$		0			0
$643$		−	2.62671e11i		−	1.53662i	−0.640076	−	0.768312i	$-0.721097\pi$
$643$		−	2.62671e11i		−	1.53662i	0.640076	−	0.768312i	$-0.278903\pi$
$644$	−2.04032e10	−	1.36160e10i	−0.118619	−	0.0791602i
$645$		0			0
$646$	1.67636e11	+	5.07992e10i	0.962578	+	0.291693i
$647$		−	2.14765e11i		−	1.22560i	−0.790240	−	0.612798i	$-0.790044\pi$
$647$		−	2.14765e11i		−	1.22560i	0.790240	−	0.612798i	$-0.209956\pi$
$648$		0			0
$649$	−9.04810e8			−0.00510010
$650$	6.40034e9	−	2.11209e10i	0.0358550	−	0.118320i
$651$		0			0
$652$	−4.20934e10	+	6.30755e10i	−0.232929	+	0.349036i
$653$	−2.41679e11			−1.32919			−0.664593	−	0.747206i	$-0.731395\pi$
$653$	−2.41679e11			−1.32919			−0.664593	+	0.747206i	$0.731395\pi$
$654$		0			0
$655$		−	1.48785e11i		−	0.808341i
$656$	7.49547e10	+	1.80371e11i	0.404747	+	0.973982i
$657$		0			0
$658$	7.45579e9	−	2.46039e10i	0.0397732	−	0.131250i
$659$			1.45001e11i			0.768828i	0.923161	+	0.384414i	$0.125597\pi$
$659$			1.45001e11i			0.768828i	−0.923161	+	0.384414i	$0.874403\pi$
$660$		0			0
$661$	9.94275e10			0.520836			0.260418	−	0.965496i	$-0.416140\pi$
$661$	9.94275e10			0.520836			0.260418	+	0.965496i	$0.416140\pi$
$662$	2.12705e11	+	6.44566e10i	1.10750	+	0.335610i
$663$		0			0
$664$	1.32425e11	+	1.61077e11i	0.681234	+	0.828630i
$665$	−6.29608e9			−0.0321946
$666$		0			0
$667$		−	3.94114e11i		−	1.99121i
$668$	2.21687e10	−	3.32191e10i	0.111336	−	0.166833i
$669$		0			0
$670$	8.70979e10	+	2.63936e10i	0.432224	+	0.130978i
$671$			2.88108e8i			0.00142123i
$672$		0			0
$673$	2.01911e10			0.0984239			0.0492120	−	0.998788i	$-0.484329\pi$
$673$	2.01911e10			0.0984239			0.0492120	+	0.998788i	$0.484329\pi$
$674$	−8.11117e10	+	2.67666e11i	−0.393047	+	1.29704i
$675$		0			0
$676$	1.07324e11	+	7.16223e10i	0.513936	+	0.342974i
$677$	−3.25587e10			−0.154993			−0.0774966	−	0.996993i	$-0.524693\pi$
$677$	−3.25587e10			−0.154993			−0.0774966	+	0.996993i	$0.524693\pi$
$678$		0			0
$679$		−	7.11514e9i		−	0.0334737i
$680$	9.04095e10	−	7.43275e10i	0.422842	−	0.347627i
$681$		0			0
$682$	−2.82638e8	+	9.32695e8i	−0.00130645	+	0.00431124i
$683$			2.46509e10i			0.113279i	0.998395	+	0.0566396i	$0.0180386\pi$
$683$			2.46509e10i			0.113279i	−0.998395	+	0.0566396i	$0.981961\pi$
$684$		0			0
$685$	1.42928e11			0.649166
$686$	3.69930e10	+	1.12101e10i	0.167041	+	0.0506190i
$687$		0			0
$688$	1.34489e11	−	5.58882e10i	0.600252	−	0.249440i
$689$	2.74746e11			1.21914
$690$		0			0
$691$			3.02518e11i			1.32690i	0.748220	+	0.663451i	$0.230909\pi$
$691$			3.02518e11i			1.32690i	−0.748220	+	0.663451i	$0.769091\pi$
$692$	9.92363e10	+	6.62252e10i	0.432759	+	0.288801i
$693$		0			0
$694$	−6.25894e9	−	1.89667e9i	−0.0269813	−	0.00817624i
$695$		−	1.12839e11i		−	0.483637i
$696$		0			0
$697$	3.04690e11			1.29100
$698$	7.07805e10	−	2.33573e11i	0.298189	−	0.984015i
$699$		0			0
$700$	−2.33522e9	+	3.49925e9i	−0.00972603	+	0.0145741i
$701$	1.07716e11			0.446076			0.223038	−	0.974810i	$-0.428403\pi$
$701$	1.07716e11			0.446076			0.223038	+	0.974810i	$0.428403\pi$
$702$		0			0
$703$			2.69658e11i			1.10406i
$704$	2.33284e9	+	4.59856e8i	0.00949715	+	0.00187211i
$705$		0			0
$706$	−1.09652e10	+	3.61849e10i	−0.0441366	+	0.145649i
$707$			1.14941e10i			0.0460041i
$708$		0			0
$709$	−2.10543e10			−0.0833213			−0.0416606	−	0.999132i	$-0.513265\pi$
$709$	−2.10543e10			−0.0833213			−0.0416606	+	0.999132i	$0.513265\pi$
$710$	1.90228e11	+	5.76453e10i	0.748584	+	0.226846i
$711$		0			0
$712$	8.48946e10	−	6.97936e10i	0.330339	−	0.271579i
$713$	1.95780e11			0.757547
$714$		0			0
$715$		−	6.99386e8i		−	0.00267604i
$716$	−2.05586e11	+	3.08064e11i	−0.782242	+	1.17216i
$717$		0			0
$718$	−2.99610e11	−	9.07918e10i	−1.12735	−	0.341624i
$719$		−	1.84186e11i		−	0.689193i	−0.938751	−	0.344597i	$-0.888016\pi$
$719$		−	1.84186e11i		−	0.689193i	0.938751	−	0.344597i	$-0.111984\pi$
$720$		0			0
$721$	−1.15553e9			−0.00427602
$722$	−2.55934e10	+	8.44573e10i	−0.0941843	+	0.310805i
$723$		0			0
$724$	1.23608e11	+	8.24900e10i	0.449877	+	0.300225i
$725$	−6.75925e10			−0.244651
$726$		0			0
$727$		−	1.34820e11i		−	0.482632i	−0.970447	−	0.241316i	$-0.922421\pi$
$727$		−	1.34820e11i		−	0.482632i	0.970447	−	0.241316i	$-0.0775791\pi$
$728$	9.66019e9	+	1.17503e10i	0.0343922	+	0.0418336i
$729$		0			0
$730$	−2.33278e10	+	7.69811e10i	−0.0821453	+	0.271077i
$731$		−	2.27185e11i		−	0.795628i
$732$		0			0
$733$	−5.46288e10			−0.189237			−0.0946184	−	0.995514i	$-0.530163\pi$
$733$	−5.46288e10			−0.189237			−0.0946184	+	0.995514i	$0.530163\pi$
$734$	3.68500e11	+	1.11668e11i	1.26956	+	0.384719i
$735$		0			0
$736$	−4.75002e10	−	4.75285e11i	−0.161877	−	1.61973i
$737$	2.88411e9			0.00977558
$738$		0			0
$739$		−	2.87010e11i		−	0.962320i	−0.876633	−	0.481160i	$-0.840216\pi$
$739$		−	2.87010e11i		−	0.962320i	0.876633	−	0.481160i	$-0.159784\pi$
$740$	1.49871e11	+	1.00016e11i	0.499795	+	0.333538i
$741$		0			0
$742$	−5.01218e10	−	1.51886e10i	−0.165353	−	0.0501074i
$743$		−	1.72722e11i		−	0.566750i	−0.959009	−	0.283375i	$-0.908546\pi$
$743$		−	1.72722e11i		−	0.566750i	0.959009	−	0.283375i	$-0.0914541\pi$
$744$		0			0
$745$	−7.06407e10			−0.229314
$746$	−7.91090e10	+	2.61057e11i	−0.255429	+	0.842908i
$747$		0			0
$748$	2.05887e9	−	3.08515e9i	0.00657692	−	0.00985529i
$749$	9.63769e9			0.0306228
$750$		0			0
$751$			1.75776e11i			0.552586i	0.961073	+	0.276293i	$0.0891060\pi$
$751$			1.75776e11i			0.552586i	−0.961073	+	0.276293i	$0.910894\pi$
$752$	4.62293e11	−	1.92110e11i	1.44559	−	0.600729i
$753$		0			0
$754$	−7.08796e10	+	2.33901e11i	−0.219299	+	0.723679i
$755$		−	3.20838e10i		−	0.0987412i
$756$		0			0
$757$	2.40268e11			0.731665			0.365833	−	0.930681i	$-0.380784\pi$
$757$	2.40268e11			0.731665			0.365833	+	0.930681i	$0.380784\pi$
$758$	2.45655e11	+	7.44415e10i	0.744129	+	0.225496i
$759$		0			0
$760$	−7.78595e10	−	9.47057e10i	−0.233376	−	0.283871i
$761$	−5.00466e11			−1.49223			−0.746115	−	0.665817i	$-0.768083\pi$
$761$	−5.00466e11			−1.49223			−0.746115	+	0.665817i	$0.768083\pi$
$762$		0			0
$763$		−	2.83942e10i		−	0.0837784i
$764$	−3.26168e11	+	4.88752e11i	−0.957344	+	1.43455i
$765$		0			0
$766$	−1.89707e11	−	5.74875e10i	−0.551021	−	0.166978i
$767$		−	1.12718e11i		−	0.325697i
$768$		0			0
$769$	1.02605e11			0.293402			0.146701	−	0.989181i	$-0.453135\pi$
$769$	1.02605e11			0.293402			0.146701	+	0.989181i	$0.453135\pi$
$770$	−3.86636e7	+	1.27589e8i	−0.000109987	+	0.000362952i
$771$		0			0
$772$	3.03523e11	+	2.02556e11i	0.854522	+	0.570264i
$773$	−5.93175e11			−1.66136			−0.830682	−	0.556747i	$-0.812049\pi$
$773$	−5.93175e11			−1.66136			−0.830682	+	0.556747i	$0.812049\pi$
$774$		0			0
$775$		−	3.35772e10i		−	0.0930761i
$776$	1.07026e11	−	8.79883e10i	0.295150	−	0.242649i
$777$		0			0
$778$	−5.91747e10	+	1.95274e11i	−0.161517	+	0.533000i
$779$		−	3.19169e11i		−	0.866704i
$780$		0			0
$781$	6.29910e9			0.0169307
$782$	−7.13077e11	−	2.16086e11i	−1.90682	−	0.577829i
$783$		0			0
$784$	1.43866e11	+	3.46200e11i	0.380798	+	0.916352i
$785$	9.74821e10			0.256712
$786$		0			0
$787$		−	1.93252e11i		−	0.503761i	−0.967758	−	0.251880i	$-0.918951\pi$
$787$		−	1.93252e11i		−	0.503761i	0.967758	−	0.251880i	$-0.0810489\pi$
$788$	3.02531e11	+	2.01894e11i	0.784630	+	0.523622i
$789$		0			0
$790$	8.73055e10	+	2.64565e10i	0.224147	+	0.0679241i
$791$		−	3.20942e10i		−	0.0819825i
$792$		0			0
$793$	−3.58917e10			−0.0907613
$794$	9.05879e10	−	2.98937e11i	0.227923	−	0.752139i
$795$		0			0
$796$	2.70043e11	−	4.04651e11i	0.672638	−	1.00793i
$797$	4.34328e11			1.07643			0.538213	−	0.842809i	$-0.319099\pi$
$797$	4.34328e11			1.07643			0.538213	+	0.842809i	$0.319099\pi$
$798$		0			0
$799$		−	7.80925e11i		−	1.91612i
$800$	−8.15139e10	+	8.14654e9i	−0.199009	+	0.0198890i
$801$		0			0
$802$	1.13636e11	−	3.74994e11i	0.274674	−	0.906415i
$803$			2.54911e9i			0.00613093i
$804$		0			0
$805$	2.67818e10			0.0637759
$806$	−1.16192e11	−	3.52101e10i	−0.275320	−	0.0834310i
$807$		0			0
$808$	−1.72894e11	+	1.42140e11i	−0.405635	+	0.333481i
$809$	−7.57515e11			−1.76847			−0.884234	−	0.467044i	$-0.845319\pi$
$809$	−7.57515e11			−1.76847			−0.884234	+	0.467044i	$0.845319\pi$
$810$		0			0
$811$		−	1.15001e11i		−	0.265838i	−0.991127	−	0.132919i	$-0.957565\pi$
$811$		−	1.15001e11i		−	0.265838i	0.991127	−	0.132919i	$-0.0424350\pi$
$812$	2.58611e10	−	3.87520e10i	0.0594870	−	0.0891394i
$813$		0			0
$814$	5.46457e9	+	1.65595e9i	0.0124468	+	0.00377180i
$815$		−	8.27948e10i		−	0.187660i
$816$		0			0
$817$	−2.37981e11			−0.534138
$818$	−8.34061e10	+	2.75238e11i	−0.186288	+	0.614744i
$819$		0			0
$820$	−1.77389e11	−	1.18380e11i	−0.392347	−	0.261832i
$821$	2.18337e11			0.480568			0.240284	−	0.970703i	$-0.422760\pi$
$821$	2.18337e11			0.480568			0.240284	+	0.970703i	$0.422760\pi$
$822$		0			0
$823$			2.44330e11i			0.532572i	0.963894	+	0.266286i	$0.0857965\pi$
$823$			2.44330e11i			0.532572i	−0.963894	+	0.266286i	$0.914203\pi$
$824$	−1.42897e10	−	1.73815e10i	−0.0309966	−	0.0377032i
$825$		0			0
$826$	−6.23132e9	+	2.05632e10i	−0.0133863	+	0.0441743i
$827$			6.25569e11i			1.33738i	0.743543	+	0.668688i	$0.233144\pi$
$827$			6.25569e11i			1.33738i	−0.743543	+	0.668688i	$0.766856\pi$
$828$		0			0
$829$	−7.91341e11			−1.67550			−0.837752	−	0.546051i	$-0.816131\pi$
$829$	−7.91341e11			−1.67550			−0.837752	+	0.546051i	$0.816131\pi$
$830$	−2.17888e11	−	6.60272e10i	−0.459114	−	0.139127i
$831$		0			0
$832$	−5.72874e10	+	2.90618e11i	−0.119554	+	0.606497i
$833$	5.84816e11			1.21462
$834$		0			0
$835$			4.36044e10i			0.0896984i
$836$	−3.23175e9	−	2.15670e9i	−0.00661626	−	0.00441535i
$837$		0			0
$838$	−5.35735e11	−	1.62346e11i	−1.08636	−	0.329204i
$839$		−	1.97673e11i		−	0.398933i	−0.979905	−	0.199466i	$-0.936079\pi$
$839$		−	1.97673e11i		−	0.398933i	0.979905	−	0.199466i	$-0.0639209\pi$
$840$		0			0
$841$	2.48297e11			0.496350
$842$	−5.45094e10	+	1.79879e11i	−0.108448	+	0.357876i
$843$		0			0
$844$	−2.38659e11	+	3.57623e11i	−0.470336	+	0.704783i
$845$	−1.40876e11			−0.276319
$846$		0			0
$847$		−	4.50851e10i		−	0.0875990i
$848$	−3.91357e11	−	9.41760e11i	−0.756815	−	1.82120i
$849$		0			0
$850$	−3.70599e10	+	1.22296e11i	−0.0709951	+	0.234281i
$851$		−	1.14705e12i		−	2.18708i
$852$		0			0
$853$	9.60505e11			1.81428			0.907138	−	0.420833i	$-0.138262\pi$
$853$	9.60505e11			1.81428			0.907138	+	0.420833i	$0.138262\pi$
$854$	6.54770e9	+	1.98417e9i	0.0123100	+	0.00373033i
$855$		0			0
$856$	1.19183e11	+	1.44970e11i	0.221983	+	0.270012i
$857$	−1.83889e10			−0.0340904			−0.0170452	−	0.999855i	$-0.505426\pi$
$857$	−1.83889e10			−0.0340904			−0.0170452	+	0.999855i	$0.505426\pi$
$858$		0			0
$859$		−	2.58648e11i		−	0.475048i	−0.971382	−	0.237524i	$-0.923664\pi$
$859$		−	2.58648e11i		−	0.475048i	0.971382	−	0.237524i	$-0.0763358\pi$
$860$	−8.82673e10	+	1.32266e11i	−0.161364	+	0.241798i
$861$		0			0
$862$	6.30729e11	+	1.91132e11i	1.14239	+	0.346182i
$863$			4.58083e11i			0.825849i	0.910765	+	0.412925i	$0.135493\pi$
$863$			4.58083e11i			0.825849i	−0.910765	+	0.412925i	$0.864507\pi$
$864$		0			0
$865$	−1.30261e11			−0.232674
$866$	6.44420e10	−	2.12656e11i	0.114577	−	0.378100i
$867$		0			0
$868$	1.92504e10	+	1.28467e10i	0.0339126	+	0.0226315i
$869$	2.89099e9			0.00506953
$870$		0			0
$871$			3.59294e11i			0.624277i
$872$	4.27106e11	−	3.51133e11i	0.738703	−	0.607303i
$873$		0			0
$874$	−2.26354e11	+	7.46961e11i	−0.387921	+	1.28012i
$875$		−	4.59322e9i		−	0.00783583i
$876$		0			0
$877$	−9.94220e11			−1.68068			−0.840338	−	0.542062i	$-0.817644\pi$
$877$	−9.94220e11			−1.68068			−0.840338	+	0.542062i	$0.817644\pi$
$878$	−3.47249e11	−	1.05228e11i	−0.584337	−	0.177074i
$879$		0			0
$880$	−2.39732e9	+	9.96227e8i	−0.00399756	+	0.00166122i
$881$	−4.02463e11			−0.668071			−0.334036	−	0.942560i	$-0.608411\pi$
$881$	−4.02463e11			−0.668071			−0.334036	+	0.942560i	$0.608411\pi$
$882$		0			0
$883$			7.19682e11i			1.18385i	0.805992	+	0.591926i	$0.201632\pi$
$883$			7.19682e11i			1.18385i	−0.805992	+	0.591926i	$0.798368\pi$
$884$	3.84338e11	+	2.56488e11i	0.629368	+	0.420008i
$885$		0			0
$886$	−6.25024e11	−	1.89403e11i	−1.01429	−	0.307363i
$887$		−	4.82885e11i		−	0.780097i	−0.920794	−	0.390049i	$-0.872458\pi$
$887$		−	4.82885e11i		−	0.780097i	0.920794	−	0.390049i	$-0.127542\pi$
$888$		0			0
$889$	−8.18053e10			−0.130971
$890$	−3.47993e10	+	1.14836e11i	−0.0554639	+	0.183029i
$891$		0			0
$892$	−1.57364e11	+	2.35804e11i	−0.248568	+	0.372470i
$893$	−8.18034e11			−1.28637
$894$		0			0
$895$		−	4.04373e11i		−	0.630218i
$896$	2.65169e10	−	4.98502e10i	0.0411425	−	0.0773455i
$897$		0			0
$898$	1.92975e11	−	6.36811e11i	0.296753	−	0.979277i
$899$			3.71846e11i			0.569278i
$900$		0			0
$901$	−1.59086e12			−2.41398
$902$	−6.46789e9	−	1.95999e9i	−0.00977094	−	0.00296092i
$903$		0			0
$904$	4.82762e11	−	3.96889e11i	0.722869	−	0.594285i
$905$	−1.62252e11			−0.241878
$906$		0			0
$907$			1.11961e12i			1.65439i	0.561917	+	0.827194i	$0.310064\pi$
$907$			1.11961e12i			1.65439i	−0.561917	+	0.827194i	$0.689936\pi$
$908$	−5.90588e11	+	8.84976e11i	−0.868842	+	1.30193i
$909$		0			0
$910$	−1.58946e10	−	4.81660e9i	−0.0231784	−	0.00702384i
$911$			1.90411e10i			0.0276451i	0.999904	+	0.0138225i	$0.00439999\pi$
$911$			1.90411e10i			0.0276451i	−0.999904	+	0.0138225i	$0.995600\pi$
$912$		0			0
$913$	−7.21501e9			−0.0103837
$914$	−3.69506e11	+	1.21936e12i	−0.529464	+	1.74721i
$915$		0			0
$916$	−2.86702e11	−	1.91330e11i	−0.407238	−	0.271770i
$917$	−1.11969e11			−0.158351
$918$		0			0
$919$		−	1.16760e11i		−	0.163694i	−0.996645	−	0.0818470i	$-0.973918\pi$
$919$		−	1.16760e11i		−	0.163694i	0.996645	−	0.0818470i	$-0.0260819\pi$
$920$	3.31193e11	+	4.02852e11i	0.462307	+	0.562334i
$921$		0			0
$922$	−1.08071e11	+	3.56631e11i	−0.149550	+	0.493509i
$923$			7.84722e11i			1.08121i
$924$		0			0
$925$	−1.96726e11			−0.268716
$926$	−5.77940e11	−	1.75135e11i	−0.786030	−	0.238193i
$927$		0			0
$928$	9.02714e11	−	9.02177e10i	1.21719	−	0.121647i
$929$	8.06361e11			1.08260			0.541298	−	0.840831i	$-0.317933\pi$
$929$	8.06361e11			1.08260			0.541298	+	0.840831i	$0.317933\pi$
$930$		0			0
$931$		−	6.12606e11i		−	0.815422i
$932$	5.48942e10	+	3.66336e10i	0.0727550	+	0.0485529i
$933$		0			0
$934$	−5.50120e11	−	1.66705e11i	−0.722887	−	0.219059i
$935$			4.04965e9i			0.00529873i
$936$		0			0
$937$	1.43350e12			1.85968			0.929842	−	0.367959i	$-0.119943\pi$
$937$	1.43350e12			1.85968			0.929842	+	0.367959i	$0.119943\pi$
$938$	1.98626e10	−	6.55458e10i	0.0256581	−	0.0846708i
$939$		0			0
$940$	−3.03410e11	+	4.54649e11i	−0.388614	+	0.582325i
$941$	1.41766e12			1.80806			0.904029	−	0.427472i	$-0.140596\pi$
$941$	1.41766e12			1.80806			0.904029	+	0.427472i	$0.140596\pi$
$942$		0			0
$943$			1.35766e12i			1.71690i
$944$	−3.86370e11	+	1.60560e11i	−0.486537	+	0.202185i
$945$		0			0
$946$	−1.46142e9	+	4.82263e9i	−0.00182478	+	0.00602170i
$947$		−	7.59493e11i		−	0.944331i	−0.881510	−	0.472165i	$-0.843473\pi$
$947$		−	7.59493e11i		−	0.944331i	0.881510	−	0.472165i	$-0.156527\pi$
$948$		0			0
$949$	−3.17560e11			−0.391527
$950$	1.28108e11	+	3.88209e10i	0.157283	+	0.0476619i
$951$		0			0
$952$	−5.59354e10	−	6.80379e10i	−0.0680987	−	0.0828330i
$953$	−3.72618e11			−0.451743			−0.225872	−	0.974157i	$-0.572523\pi$
$953$	−3.72618e11			−0.451743			−0.225872	+	0.974157i	$0.572523\pi$
$954$		0			0
$955$		−	6.41550e11i		−	0.771289i
$956$	5.43617e10	−	8.14592e10i	0.0650821	−	0.0975234i
$957$		0			0
$958$	−6.74760e11	−	2.04475e11i	−0.801101	−	0.242760i
$959$		−	1.07561e11i		−	0.127169i
$960$		0			0
$961$	6.68173e11			0.783421
$962$	−2.06293e11	+	6.80759e11i	−0.240870	+	0.794865i
$963$		0			0
$964$	1.17061e12	+	7.81206e11i	1.35552	+	0.904601i
$965$	−3.98414e11			−0.459436
$966$		0			0
$967$			7.07203e11i			0.808794i	0.914584	+	0.404397i	$0.132519\pi$
$967$			7.07203e11i			0.808794i	−0.914584	+	0.404397i	$0.867481\pi$
$968$	6.78171e11	−	5.57538e11i	0.772392	−	0.634999i
$969$		0			0
$970$	−4.38712e10	+	1.44773e11i	−0.0495555	+	0.163532i
$971$			1.48456e12i			1.67001i	0.550240	+	0.835007i	$0.314536\pi$
$971$			1.48456e12i			1.67001i	−0.550240	+	0.835007i	$0.685464\pi$
$972$		0			0
$973$	−8.49173e10			−0.0947425
$974$	6.11457e11	+	1.85292e11i	0.679407	+	0.205883i
$975$		0			0
$976$	5.11252e10	+	1.23027e11i	0.0563424	+	0.135582i
$977$	4.31329e10			0.0473402			0.0236701	−	0.999720i	$-0.492465\pi$
$977$	4.31329e10			0.0473402			0.0236701	+	0.999720i	$0.492465\pi$
$978$		0			0
$979$			3.80263e9i			0.00413955i
$980$	−3.40476e11	−	2.27216e11i	−0.369132	−	0.246340i
$981$		0			0
$982$	−1.21999e12	−	3.69699e11i	−1.31193	−	0.397559i
$983$			1.13842e12i			1.21923i	0.792696	+	0.609617i	$0.208677\pi$
$983$			1.13842e12i			1.21923i	−0.792696	+	0.609617i	$0.791323\pi$
$984$		0			0
$985$	−3.97111e11			−0.421859
$986$	4.10414e11	−	1.35435e12i	0.434225	−	1.43293i
$987$		0			0
$988$	2.68676e11	−	4.02602e11i	0.281968	−	0.422520i
$989$	1.01231e12			1.05810
$990$		0			0
$991$			6.27241e11i			0.650339i	0.945656	+	0.325170i	$0.105421\pi$
$991$			6.27241e11i			0.650339i	−0.945656	+	0.325170i	$0.894579\pi$
$992$	4.48165e10	+	4.48432e11i	0.0462797	+	0.463073i
$993$		0			0
$994$	4.33812e10	−	1.43156e11i	0.0444381	−	0.146644i
$995$			5.31157e11i			0.541914i
$996$		0			0
$997$	2.64260e11			0.267455			0.133728	−	0.991018i	$-0.457305\pi$
$997$	2.64260e11			0.267455			0.133728	+	0.991018i	$0.457305\pi$
$998$	2.39165e11	+	7.24750e10i	0.241088	+	0.0730578i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	180.9.c.a.91.8		16
3.2	odd	2		20.9.b.a.11.9	✓	16
4.3	odd	2	inner	180.9.c.a.91.7		16
12.11	even	2		20.9.b.a.11.10	yes	16
15.2	even	4		100.9.d.c.99.30		32
15.8	even	4		100.9.d.c.99.3		32
15.14	odd	2		100.9.b.d.51.8		16
24.5	odd	2		320.9.b.d.191.12		16
24.11	even	2		320.9.b.d.191.5		16
60.23	odd	4		100.9.d.c.99.29		32
60.47	odd	4		100.9.d.c.99.4		32
60.59	even	2		100.9.b.d.51.7		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
20.9.b.a.11.9	✓	16	3.2	odd	2
20.9.b.a.11.10	yes	16	12.11	even	2
100.9.b.d.51.7		16	60.59	even	2
100.9.b.d.51.8		16	15.14	odd	2
100.9.d.c.99.3		32	15.8	even	4
100.9.d.c.99.4		32	60.47	odd	4
100.9.d.c.99.29		32	60.23	odd	4
100.9.d.c.99.30		32	15.2	even	4
180.9.c.a.91.7		16	4.3	odd	2	inner
180.9.c.a.91.8		16	1.1	even	1	trivial
320.9.b.d.191.5		16	24.11	even	2
320.9.b.d.191.12		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)

\(f(q)\)	\(=\)	\(q+(-4.64016 + 15.3124i) q^{2} +(-212.938 - 142.104i) q^{4} +279.508 q^{5} -210.345i q^{7} +(3164.01 - 2601.20i) q^{8} +(-1296.96 + 4279.94i) q^{10} +141.724i q^{11} -17655.5 q^{13} +(3220.88 + 976.035i) q^{14} +(25149.0 + 60518.5i) q^{16} +102231. q^{17} -107088. i q^{19} +(-59517.9 - 39719.2i) q^{20} +(-2170.13 - 657.620i) q^{22} +455526. i q^{23} +78125.0 q^{25} +(81924.3 - 270348. i) q^{26} +(-29890.8 + 44790.4i) q^{28} -865184. q^{29} -429788. i q^{31} +(-1.04338e6 + 104276. i) q^{32} +(-474366. + 1.56539e6i) q^{34} -58793.2i q^{35} -2.51809e6 q^{37} +(1.63978e6 + 496908. i) q^{38} +(884368. - 727057. i) q^{40} +2.98042e6 q^{41} -2.22228e6i q^{43} +(20139.5 - 30178.3i) q^{44} +(-6.97518e6 - 2.11371e6i) q^{46} -7.63886e6i q^{47} +5.72056e6 q^{49} +(-362513. + 1.19628e6i) q^{50} +(3.75952e6 + 2.50891e6i) q^{52} -1.55615e7 q^{53} +39613.0i q^{55} +(-547149. - 665534. i) q^{56} +(4.01459e6 - 1.32480e7i) q^{58} +6.38433e6i q^{59} +2.03289e6 q^{61} +(6.58108e6 + 1.99429e6i) q^{62} +(3.24473e6 - 1.64605e7i) q^{64} -4.93486e6 q^{65} -2.03503e7i q^{67} +(-2.17688e7 - 1.45274e7i) q^{68} +(900264. + 272810. i) q^{70} -4.44463e7i q^{71} +1.79865e7 q^{73} +(1.16843e7 - 3.85579e7i) q^{74} +(-1.52177e7 + 2.28032e7i) q^{76} +29810.9 q^{77} -2.03988e7i q^{79} +(7.02937e6 + 1.69154e7i) q^{80} +(-1.38296e7 + 4.56374e7i) q^{82} +5.09090e7i q^{83} +2.85743e7 q^{85} +(3.40284e7 + 1.03117e7i) q^{86} +(368651. + 448415. i) q^{88} +2.68313e7 q^{89} +3.71375e6i q^{91} +(6.47319e7 - 9.69986e7i) q^{92} +(1.16969e8 + 3.54456e7i) q^{94} -2.99321e7i q^{95} +3.38260e7 q^{97} +(-2.65443e7 + 8.75953e7i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 6 q^{2} - 52 q^{4} + 14184 q^{8} + 8750 q^{10} + 51392 q^{13} - 68472 q^{14} - 81424 q^{16} - 27552 q^{17} - 172500 q^{20} - 389120 q^{22} + 1250000 q^{25} - 1037124 q^{26} + 1288520 q^{28} - 2764896 q^{29}+ \cdots + 285387714 q^{98}+O(q^{100}) \) 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

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more