LMFDB - Embedded newform 180.5.f.g.19.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [180,5,Mod(19,180)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(180, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 5, names="a")

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

chi := DirichletCharacter("180.19");

S:= CuspForms(chi, 5);

N := Newforms(S);

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

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$18.6065933551$
Analytic rank:	$0$
Dimension:	$8$
Coefficient field:	8.0.1816805376000000.2
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} + 6x^{6} + 31x^{4} + 96x^{2} + 256 $ x^8 + 6x^6 + 31x^4 + 96*x^2 + 256
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{14} $
Twist minimal:	no (minimal twist has level 20)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			19.2
Root			$1.42849 + 1.39980i$ of defining polynomial
Character	$\chi$	$=$	180.19
Dual form			180.5.f.g.19.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-2.85697 + 2.79959i) q^{2} +(0.324555 - 15.9967i) q^{4} +(17.6491 - 17.7062i) q^{5} +39.0703 q^{7} +(43.8570 + 46.6107i) q^{8} +(-0.852871 + 99.9964i) q^{10} -138.357i q^{11} +124.999i q^{13} +(-111.623 + 109.381i) q^{14} +(-255.789 - 10.3836i) q^{16} +160.412i q^{17} -650.252i q^{19} +(-277.513 - 288.074i) q^{20} +(387.344 + 395.283i) q^{22} -416.491 q^{23} +(-2.01779 - 624.997i) q^{25} +(-349.947 - 357.119i) q^{26} +(12.6805 - 624.997i) q^{28} -236.807 q^{29} -41.5345i q^{31} +(759.852 - 686.440i) q^{32} +(-449.088 - 458.291i) q^{34} +(689.557 - 691.786i) q^{35} +206.138i q^{37} +(1820.44 + 1857.75i) q^{38} +(1599.34 + 46.0975i) q^{40} +1816.56 q^{41} +3162.64 q^{43} +(-2213.26 - 44.9046i) q^{44} +(1189.90 - 1166.01i) q^{46} -823.584 q^{47} -874.509 q^{49} +(1755.50 + 1779.95i) q^{50} +(1999.58 + 40.5692i) q^{52} -4866.53i q^{53} +(-2449.78 - 2441.88i) q^{55} +(1713.51 + 1821.10i) q^{56} +(676.551 - 662.964i) q^{58} -3638.55i q^{59} +4136.07 q^{61} +(116.280 + 118.663i) q^{62} +(-249.122 + 4088.42i) q^{64} +(2213.26 + 2206.13i) q^{65} -3208.70 q^{67} +(2566.06 + 52.0625i) q^{68} +(-33.3220 + 3906.89i) q^{70} +456.333i q^{71} -5905.66i q^{73} +(-577.102 - 588.929i) q^{74} +(-10401.9 - 211.043i) q^{76} -5405.67i q^{77} -2808.68i q^{79} +(-4698.31 + 4345.79i) q^{80} +(-5189.86 + 5085.63i) q^{82} -3048.15 q^{83} +(2840.28 + 2831.12i) q^{85} +(-9035.57 + 8854.10i) q^{86} +(6448.94 - 6067.94i) q^{88} +5143.40 q^{89} +4883.77i q^{91} +(-135.174 + 6662.49i) q^{92} +(2352.96 - 2305.70i) q^{94} +(-11513.5 - 11476.4i) q^{95} +4506.56i q^{97} +(2498.45 - 2448.27i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 48 q^{4} + 40 q^{5} - 160 q^{10} - 640 q^{14} - 832 q^{16} + 400 q^{20} - 2040 q^{25} - 2496 q^{26} - 2704 q^{29} - 2176 q^{34} + 6400 q^{40} - 1456 q^{41} - 1920 q^{44} + 7040 q^{46} - 8008 q^{49}+ \cdots + 10880 q^{94}+O(q^{100}) $ 8 * q - 48 * q^4 + 40 * q^5 - 160 * q^10 - 640 * q^14 - 832 * q^16 + 400 * q^20 - 2040 * q^25 - 2496 * q^26 - 2704 * q^29 - 2176 * q^34 + 6400 * q^40 - 1456 * q^41 - 1920 * q^44 + 7040 * q^46 - 8008 * q^49 + 12480 * q^50 + 14720 * q^56 + 6576 * q^61 + 6912 * q^64 + 1920 * q^65 - 6400 * q^70 + 23616 * q^74 - 48000 * q^76 - 19520 * q^80 + 8960 * q^85 - 37120 * q^86 - 27664 * q^89 + 10880 * q^94

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 $

$2$	−2.85697	+	2.79959i	−0.714243	+	0.699898i
$2$	−2.85697	+	2.79959i	−0.714243	+	0.699898i
$3$		0			0
$3$		0			0
$4$	0.324555	−	15.9967i	0.0202847	−	0.999794i
$5$	17.6491	−	17.7062i	0.705964	−	0.708247i
$5$	17.6491	−	17.7062i	0.705964	−	0.708247i
$6$		0			0
$7$	39.0703			0.797354			0.398677	−	0.917091i	$-0.369469\pi$
$7$	39.0703			0.797354			0.398677	+	0.917091i	$0.369469\pi$
$8$	43.8570	+	46.6107i	0.685266	+	0.728293i
$9$		0			0
$10$	−0.852871	+	99.9964i	−0.00852871	+	0.999964i
$11$		−	138.357i		−	1.14345i	−0.820446	−	0.571724i	$-0.806275\pi$
$11$		−	138.357i		−	1.14345i	0.820446	−	0.571724i	$-0.193725\pi$
$12$		0			0
$13$			124.999i			0.739641i	0.929103	+	0.369821i	$0.120581\pi$
$13$			124.999i			0.739641i	−0.929103	+	0.369821i	$0.879419\pi$
$14$	−111.623	+	109.381i	−0.569504	+	0.558067i
$15$		0			0
$16$	−255.789	−	10.3836i	−0.999177	−	0.0405611i
$17$			160.412i			0.555058i	0.960717	+	0.277529i	$0.0895154\pi$
$17$			160.412i			0.555058i	−0.960717	+	0.277529i	$0.910485\pi$
$18$		0			0
$19$		−	650.252i		−	1.80125i	−0.434595	−	0.900626i	$-0.643108\pi$
$19$		−	650.252i		−	1.80125i	0.434595	−	0.900626i	$-0.356892\pi$
$20$	−277.513	−	288.074i	−0.693781	−	0.720186i
$21$		0			0
$22$	387.344	+	395.283i	0.800298	+	0.816700i
$23$	−416.491			−0.787318			−0.393659	−	0.919257i	$-0.628791\pi$
$23$	−416.491			−0.787318			−0.393659	+	0.919257i	$0.628791\pi$
$24$		0			0
$25$	−2.01779	−	624.997i	−0.00322846	−	0.999995i
$26$	−349.947	−	357.119i	−0.517674	−	0.528283i
$27$		0			0
$28$	12.6805	−	624.997i	0.0161741	−	0.797190i
$29$	−236.807			−0.281578			−0.140789	−	0.990040i	$-0.544964\pi$
$29$	−236.807			−0.281578			−0.140789	+	0.990040i	$0.544964\pi$
$30$		0			0
$31$		−	41.5345i		−	0.0432201i	−0.999766	−	0.0216101i	$-0.993121\pi$
$31$		−	41.5345i		−	0.0432201i	0.999766	−	0.0216101i	$-0.00687923\pi$
$32$	759.852	−	686.440i	0.742043	−	0.670352i
$33$		0			0
$34$	−449.088	−	458.291i	−0.388484	−	0.396446i
$35$	689.557	−	691.786i	0.562903	−	0.564724i
$36$		0			0
$37$			206.138i			0.150575i	0.997162	+	0.0752877i	$0.0239875\pi$
$37$			206.138i			0.150575i	−0.997162	+	0.0752877i	$0.976012\pi$
$38$	1820.44	+	1857.75i	1.26069	+	1.28653i
$39$		0			0
$40$	1599.34	+	46.0975i	0.999585	+	0.0288109i
$41$	1816.56			1.08064			0.540321	−	0.841459i	$-0.318303\pi$
$41$	1816.56			1.08064			0.540321	+	0.841459i	$0.318303\pi$
$42$		0			0
$43$	3162.64			1.71046			0.855230	−	0.518249i	$-0.173416\pi$
$43$	3162.64			1.71046			0.855230	+	0.518249i	$0.173416\pi$
$44$	−2213.26	−	44.9046i	−1.14321	−	0.0231945i
$45$		0			0
$46$	1189.90	−	1166.01i	0.562336	−	0.551043i
$47$	−823.584			−0.372831			−0.186416	−	0.982471i	$-0.559687\pi$
$47$	−823.584			−0.372831			−0.186416	+	0.982471i	$0.559687\pi$
$48$		0			0
$49$	−874.509			−0.364227
$50$	1755.50	+	1779.95i	0.702201	+	0.711979i
$51$		0			0
$52$	1999.58	+	40.5692i	0.739489	+	0.0150034i
$53$		−	4866.53i		−	1.73248i	−0.499631	−	0.866238i	$-0.666531\pi$
$53$		−	4866.53i		−	1.73248i	0.499631	−	0.866238i	$-0.333469\pi$
$54$		0			0
$55$	−2449.78	−	2441.88i	−0.809844	−	0.807234i
$56$	1713.51	+	1821.10i	0.546400	+	0.580707i
$57$		0			0
$58$	676.551	−	662.964i	0.201115	−	0.197076i
$59$		−	3638.55i		−	1.04526i	−0.852560	−	0.522630i	$-0.824951\pi$
$59$		−	3638.55i		−	1.04526i	0.852560	−	0.522630i	$-0.175049\pi$
$60$		0			0
$61$	4136.07			1.11155			0.555774	−	0.831334i	$-0.312422\pi$
$61$	4136.07			1.11155			0.555774	+	0.831334i	$0.312422\pi$
$62$	116.280	+	118.663i	0.0302497	+	0.0308696i
$63$		0			0
$64$	−249.122	+	4088.42i	−0.0608207	+	0.998149i
$65$	2213.26	+	2206.13i	0.523849	+	0.522160i
$66$		0			0
$67$	−3208.70			−0.714792			−0.357396	−	0.933953i	$-0.616335\pi$
$67$	−3208.70			−0.714792			−0.357396	+	0.933953i	$0.616335\pi$
$68$	2566.06	+	52.0625i	0.554944	+	0.0112592i
$69$		0			0
$70$	−33.3220	+	3906.89i	−0.00680040	+	0.797325i
$71$			456.333i			0.0905243i	0.998975	+	0.0452621i	$0.0144123\pi$
$71$			456.333i			0.0905243i	−0.998975	+	0.0452621i	$0.985588\pi$
$72$		0			0
$73$		−	5905.66i		−	1.10821i	−0.832446	−	0.554106i	$-0.813060\pi$
$73$		−	5905.66i		−	1.10821i	0.832446	−	0.554106i	$-0.186940\pi$
$74$	−577.102	−	588.929i	−0.105387	−	0.107547i
$75$		0			0
$76$	−10401.9	−	211.043i	−1.80088	−	0.0365379i
$77$		−	5405.67i		−	0.911733i
$78$		0			0
$79$		−	2808.68i		−	0.450037i	−0.974354	−	0.225018i	$-0.927756\pi$
$79$		−	2808.68i		−	0.450037i	0.974354	−	0.225018i	$-0.0722442\pi$
$80$	−4698.31	+	4345.79i	−0.734111	+	0.679030i
$81$		0			0
$82$	−5189.86	+	5085.63i	−0.771841	+	0.756340i
$83$	−3048.15			−0.442466			−0.221233	−	0.975221i	$-0.571008\pi$
$83$	−3048.15			−0.442466			−0.221233	+	0.975221i	$0.571008\pi$
$84$		0			0
$85$	2840.28	+	2831.12i	0.393118	+	0.391851i
$86$	−9035.57	+	8854.10i	−1.22168	+	1.19715i
$87$		0			0
$88$	6448.94	−	6067.94i	0.832765	−	0.783567i
$89$	5143.40			0.649337			0.324668	−	0.945828i	$-0.394747\pi$
$89$	5143.40			0.649337			0.324668	+	0.945828i	$0.394747\pi$
$90$		0			0
$91$			4883.77i			0.589756i
$92$	−135.174	+	6662.49i	−0.0159705	+	0.787156i
$93$		0			0
$94$	2352.96	−	2305.70i	0.266292	−	0.260944i
$95$	−11513.5	−	11476.4i	−1.27573	−	1.27162i
$96$		0			0
$97$			4506.56i			0.478963i	0.970901	+	0.239481i	$0.0769774\pi$
$97$			4506.56i			0.478963i	−0.970901	+	0.239481i	$0.923023\pi$
$98$	2498.45	−	2448.27i	0.260146	−	0.254922i
$99$		0			0
$100$	−9998.55	−	170.568i	−0.999855	−	0.0170568i
$101$	1737.92			0.170368			0.0851840	−	0.996365i	$-0.472852\pi$
$101$	1737.92			0.170368			0.0851840	+	0.996365i	$0.472852\pi$
$102$		0			0
$103$	−12672.6			−1.19452			−0.597258	−	0.802049i	$-0.703743\pi$
$103$	−12672.6			−1.19452			−0.597258	+	0.802049i	$0.703743\pi$
$104$	−5826.31	+	5482.10i	−0.538675	+	0.506851i
$105$		0			0
$106$	13624.3	+	13903.5i	1.21256	+	1.23741i
$107$	−6987.88			−0.610349			−0.305174	−	0.952297i	$-0.598715\pi$
$107$	−6987.88			−0.610349			−0.305174	+	0.952297i	$0.598715\pi$
$108$		0			0
$109$	−811.156			−0.0682734			−0.0341367	−	0.999417i	$-0.510868\pi$
$109$	−811.156			−0.0682734			−0.0341367	+	0.999417i	$0.510868\pi$
$110$	13835.2	+	118.001i	1.14341	+	0.00975215i
$111$		0			0
$112$	−9993.77	−	405.692i	−0.796698	−	0.0323415i
$113$			6342.41i			0.496704i	0.968670	+	0.248352i	$0.0798889\pi$
$113$			6342.41i			0.496704i	−0.968670	+	0.248352i	$0.920111\pi$
$114$		0			0
$115$	−7350.70	+	7374.47i	−0.555819	+	0.557616i
$116$	−76.8570	+	3788.13i	−0.00571173	+	0.281520i
$117$		0			0
$118$	10186.5	+	10395.2i	0.731576	+	0.746569i
$119$			6267.34i			0.442577i
$120$		0			0
$121$	−4501.74			−0.307475
$122$	−11816.6	+	11579.3i	−0.793914	+	0.777970i
$123$		0			0
$124$	−664.416	−	13.4803i	−0.0432112	−	0.000876707i
$125$	−11101.9	−	10994.9i	−0.710523	−	0.703674i
$126$		0			0
$127$	7702.06			0.477529			0.238764	−	0.971078i	$-0.423258\pi$
$127$	7702.06			0.477529			0.238764	+	0.971078i	$0.423258\pi$
$128$	−10734.2	−	12377.9i	−0.655162	−	0.755489i
$129$		0			0
$130$	−12499.5	−	106.608i	−0.739614	−	0.00630819i
$131$			15619.8i			0.910192i	0.890442	+	0.455096i	$0.150395\pi$
$131$			15619.8i			0.910192i	−0.890442	+	0.455096i	$0.849605\pi$
$132$		0			0
$133$		−	25405.6i		−	1.43624i
$134$	9167.16	−	8983.06i	0.510535	−	0.500282i
$135$		0			0
$136$	−7476.91	+	7035.18i	−0.404245	+	0.380362i
$137$			3770.61i			0.200896i	0.994942	+	0.100448i	$0.0320275\pi$
$137$			3770.61i			0.200896i	−0.994942	+	0.100448i	$0.967972\pi$
$138$		0			0
$139$		−	7001.21i		−	0.362363i	−0.983450	−	0.181181i	$-0.942008\pi$
$139$		−	7001.21i		−	0.362363i	0.983450	−	0.181181i	$-0.0579921\pi$
$140$	−10842.5	−	11255.2i	−0.553189	−	0.574243i
$141$		0			0
$142$	−1277.55	−	1303.73i	−0.0633578	−	0.0646563i
$143$	17294.6			0.845742
$144$		0			0
$145$	−4179.43	+	4192.95i	−0.198784	+	0.199427i
$146$	16533.5	+	16872.3i	0.775636	+	0.791532i
$147$		0			0
$148$	3297.53	+	66.9031i	0.150544	+	0.00305438i
$149$	29966.7			1.34979			0.674894	−	0.737914i	$-0.264189\pi$
$149$	29966.7			1.34979			0.674894	+	0.737914i	$0.264189\pi$
$150$		0			0
$151$			12397.1i			0.543710i	0.962338	+	0.271855i	$0.0876372\pi$
$151$			12397.1i			0.543710i	−0.962338	+	0.271855i	$0.912363\pi$
$152$	30308.7	−	28518.1i	1.31184	−	1.23434i
$153$		0			0
$154$	15133.7	+	15443.8i	0.638121	+	0.651199i
$155$	−735.418	−	733.048i	−0.0306105	−	0.0305119i
$156$		0			0
$157$			18293.8i			0.742171i	0.928599	+	0.371085i	$0.121014\pi$
$157$			18293.8i			0.742171i	−0.928599	+	0.371085i	$0.878986\pi$
$158$	7863.16	+	8024.32i	0.314980	+	0.321436i
$159$		0			0
$160$	1256.48	−	25569.1i	0.0490813	−	0.998795i
$161$	−16272.5			−0.627771
$162$		0			0
$163$	26437.3			0.995043			0.497522	−	0.867452i	$-0.334244\pi$
$163$	26437.3			0.995043			0.497522	+	0.867452i	$0.334244\pi$
$164$	589.574	−	29059.0i	0.0219205	−	1.08042i
$165$		0			0
$166$	8708.47	−	8533.58i	0.316028	−	0.309681i
$167$	16417.6			0.588677			0.294339	−	0.955701i	$-0.404901\pi$
$167$	16417.6			0.588677			0.294339	+	0.955701i	$0.404901\pi$
$168$		0			0
$169$	12936.2			0.452931
$170$	−16040.6	−	136.811i	−0.555038	−	0.00473393i
$171$		0			0
$172$	1026.45	−	50591.8i	0.0346962	−	1.71011i
$173$		−	14503.0i		−	0.484581i	−0.970204	−	0.242291i	$-0.922101\pi$
$173$		−	14503.0i		−	0.484581i	0.970204	−	0.242291i	$-0.0778987\pi$
$174$		0			0
$175$	−78.8356	−	24418.8i	−0.00257422	−	0.797350i
$176$	−1436.65	+	35390.3i	−0.0463795	+	1.14251i
$177$		0			0
$178$	−14694.5	+	14399.4i	−0.463784	+	0.454470i
$179$		−	29882.7i		−	0.932640i	−0.884616	−	0.466320i	$-0.845580\pi$
$179$		−	29882.7i		−	0.932640i	0.884616	−	0.466320i	$-0.154420\pi$
$180$		0			0
$181$	−13028.0			−0.397669			−0.198834	−	0.980033i	$-0.563716\pi$
$181$	−13028.0			−0.397669			−0.198834	+	0.980033i	$0.563716\pi$
$182$	−13672.6	−	13952.8i	−0.412769	−	0.421229i
$183$		0			0
$184$	−18266.1	−	19413.0i	−0.539522	−	0.573398i
$185$	3649.91	+	3638.15i	0.106645	+	0.106301i
$186$		0			0
$187$	22194.1			0.634680
$188$	−267.299	+	13174.6i	−0.00756277	+	0.372754i
$189$		0			0
$190$	65022.8	+	554.581i	1.80119	+	0.0153624i
$191$			53818.5i			1.47525i	0.675212	+	0.737624i	$0.264052\pi$
$191$			53818.5i			1.47525i	−0.675212	+	0.737624i	$0.735948\pi$
$192$		0			0
$193$			48440.5i			1.30045i	0.759741	+	0.650225i	$0.225326\pi$
$193$			48440.5i			1.30045i	−0.759741	+	0.650225i	$0.774674\pi$
$194$	−12616.5	−	12875.1i	−0.335225	−	0.342096i
$195$		0			0
$196$	−283.827	+	13989.3i	−0.00738824	+	0.364152i
$197$			74216.3i			1.91235i	0.292798	+	0.956174i	$0.405414\pi$
$197$			74216.3i			1.91235i	−0.292798	+	0.956174i	$0.594586\pi$
$198$		0			0
$199$		−	13240.2i		−	0.334341i	−0.985928	−	0.167170i	$-0.946537\pi$
$199$		−	13240.2i		−	0.334341i	0.985928	−	0.167170i	$-0.0534630\pi$
$200$	29043.1	−	27504.6i	0.726077	−	0.687614i
$201$		0			0
$202$	−4965.19	+	4865.48i	−0.121684	+	0.119240i
$203$	−9252.13			−0.224517
$204$		0			0
$205$	32060.7	−	32164.3i	0.762895	−	0.765362i
$206$	36205.3	−	35478.2i	0.853174	−	0.836040i
$207$		0			0
$208$	1297.95	−	31973.5i	0.0300006	−	0.739032i
$209$	−89967.1			−2.05964
$210$		0			0
$211$			4466.51i			0.100324i	0.998741	+	0.0501618i	$0.0159737\pi$
$211$			4466.51i			0.100324i	−0.998741	+	0.0501618i	$0.984026\pi$
$212$	−77848.4	−	1579.46i	−1.73212	−	0.0351428i
$213$		0			0
$214$	19964.2	−	19563.2i	0.435937	−	0.427182i
$215$	55817.8	−	55998.3i	1.20752	−	1.21143i
$216$		0			0
$217$		−	1622.77i		−	0.0344617i
$218$	2317.45	−	2270.91i	0.0487637	−	0.0477844i
$219$		0			0
$220$	−39857.2	+	38395.9i	−0.823495	+	0.793303i
$221$	−20051.4			−0.410544
$222$		0			0
$223$	−4344.79			−0.0873694			−0.0436847	−	0.999045i	$-0.513910\pi$
$223$	−4344.79			−0.0873694			−0.0436847	+	0.999045i	$0.513910\pi$
$224$	29687.7	−	26819.5i	0.591671	−	0.534508i
$225$		0			0
$226$	−17756.2	−	18120.1i	−0.347642	−	0.354767i
$227$	62311.6			1.20925			0.604626	−	0.796509i	$-0.293323\pi$
$227$	62311.6			1.20925			0.604626	+	0.796509i	$0.293323\pi$
$228$		0			0
$229$	−78625.5			−1.49931			−0.749657	−	0.661827i	$-0.769781\pi$
$229$	−78625.5			−1.49931			−0.749657	+	0.661827i	$0.769781\pi$
$230$	355.214	−	41647.6i	0.00671481	−	0.787290i
$231$		0			0
$232$	−10385.7	−	11037.8i	−0.192956	−	0.205071i
$233$		−	2464.06i		−	0.0453878i	−0.999742	−	0.0226939i	$-0.992776\pi$
$233$		−	2464.06i		−	0.0453878i	0.999742	−	0.0226939i	$-0.00722431\pi$
$234$		0			0
$235$	−14535.5	+	14582.5i	−0.263206	+	0.264057i
$236$	−58204.8	−	1180.91i	−1.04505	−	0.0212028i
$237$		0			0
$238$	−17546.0	−	17905.6i	−0.309759	−	0.316108i
$239$			54386.5i			0.952128i	0.879411	+	0.476064i	$0.157937\pi$
$239$			54386.5i			0.952128i	−0.879411	+	0.476064i	$0.842063\pi$
$240$		0			0
$241$	4097.25			0.0705437			0.0352718	−	0.999378i	$-0.488770\pi$
$241$	4097.25			0.0705437			0.0352718	+	0.999378i	$0.488770\pi$
$242$	12861.3	−	12603.0i	0.219612	−	0.215201i
$243$		0			0
$244$	1342.38	−	66163.5i	0.0225474	−	1.11132i
$245$	−15434.3	+	15484.2i	−0.257131	+	0.257963i
$246$		0			0
$247$	81281.1			1.33228
$248$	1935.96	−	1821.58i	0.0314769	−	0.0296173i
$249$		0			0
$250$	62499.1	+	331.270i	0.999986	+	0.00530033i
$251$			48310.9i			0.766828i	0.923577	+	0.383414i	$0.125252\pi$
$251$			48310.9i			0.766828i	−0.923577	+	0.383414i	$0.874748\pi$
$252$		0			0
$253$			57624.6i			0.900258i
$254$	−22004.6	+	21562.6i	−0.341071	+	0.334222i
$255$		0			0
$256$	65320.4	+	5312.05i	0.996710	+	0.0810554i
$257$		−	24560.5i		−	0.371853i	−0.982564	−	0.185927i	$-0.940471\pi$
$257$		−	24560.5i		−	0.371853i	0.982564	−	0.185927i	$-0.0595287\pi$
$258$		0			0
$259$			8053.87i			0.120062i
$260$	36009.1	−	34688.9i	0.532679	−	0.513149i
$261$		0			0
$262$	−43729.1	−	44625.3i	−0.637042	−	0.650098i
$263$	−83305.2			−1.20437			−0.602186	−	0.798356i	$-0.705703\pi$
$263$	−83305.2			−1.20437			−0.602186	+	0.798356i	$0.705703\pi$
$264$		0			0
$265$	−86167.6	−	85889.9i	−1.22702	−	1.22307i
$266$	71125.2	+	72582.9i	1.00522	+	1.02582i
$267$		0			0
$268$	−1041.40	+	51328.6i	−0.0144993	+	0.714645i
$269$	26533.4			0.366681			0.183341	−	0.983049i	$-0.441309\pi$
$269$	26533.4			0.366681			0.183341	+	0.983049i	$0.441309\pi$
$270$		0			0
$271$			110062.i			1.49864i	0.662207	+	0.749321i	$0.269620\pi$
$271$			110062.i			1.49864i	−0.662207	+	0.749321i	$0.730380\pi$
$272$	1665.66	−	41031.6i	0.0225137	−	0.554601i
$273$		0			0
$274$	−10556.2	−	10772.5i	−0.140606	−	0.143488i
$275$	−86472.9	+	279.176i	−1.14344	+	0.00369158i
$276$		0			0
$277$			111083.i			1.44773i	0.689942	+	0.723864i	$0.257636\pi$
$277$			111083.i			1.44773i	−0.689942	+	0.723864i	$0.742364\pi$
$278$	19600.5	+	20002.2i	0.253617	+	0.258815i
$279$		0			0
$280$	62486.6	+	1801.04i	0.797023	+	0.0229725i
$281$	66386.2			0.840747			0.420374	−	0.907351i	$-0.361899\pi$
$281$	66386.2			0.840747			0.420374	+	0.907351i	$0.361899\pi$
$282$		0			0
$283$	−123904.			−1.54708			−0.773540	−	0.633747i	$-0.781516\pi$
$283$	−123904.			−1.54708			−0.773540	+	0.633747i	$0.781516\pi$
$284$	7299.83	+	148.105i	0.0905057	+	0.00183626i
$285$		0			0
$286$	−49410.1	+	48417.8i	−0.604065	+	0.591933i
$287$	70973.6			0.861654
$288$		0			0
$289$	57789.1			0.691911
$290$	201.966	−	23679.9i	0.00240150	−	0.281568i
$291$		0			0
$292$	−94471.2	−	1916.71i	−1.10798	−	0.0224798i
$293$			79770.8i			0.929199i	0.885521	+	0.464600i	$0.153802\pi$
$293$			79770.8i			0.929199i	−0.885521	+	0.464600i	$0.846198\pi$
$294$		0			0
$295$	−64424.8	−	64217.2i	−0.740303	−	0.737917i
$296$	−9608.23	+	9040.59i	−0.109663	+	0.103184i
$297$		0			0
$298$	−85613.9	+	83894.5i	−0.964077	+	0.944715i
$299$		−	52061.1i		−	0.582333i
$300$		0			0
$301$	123565.			1.36384
$302$	−34707.0	−	35418.3i	−0.380542	−	0.388341i
$303$		0			0
$304$	−6751.98	+	166328.i	−0.0730607	+	1.79977i
$305$	72997.9	−	73234.0i	0.784713	−	0.787250i
$306$		0			0
$307$	102607.			1.08868			0.544340	−	0.838865i	$-0.316780\pi$
$307$	102607.			1.08868			0.544340	+	0.838865i	$0.316780\pi$
$308$	−86472.9	−	1754.44i	−0.911546	−	0.0184942i
$309$		0			0
$310$	4153.30	+	35.4236i	0.0432185	+	0.000368612i
$311$			113118.i			1.16953i	0.811203	+	0.584764i	$0.198813\pi$
$311$			113118.i			1.16953i	−0.811203	+	0.584764i	$0.801187\pi$
$312$		0			0
$313$		−	180078.i		−	1.83811i	−0.394128	−	0.919055i	$-0.628953\pi$
$313$		−	180078.i		−	1.83811i	0.394128	−	0.919055i	$-0.371047\pi$
$314$	−51215.1	−	52264.7i	−0.519444	−	0.530090i
$315$		0			0
$316$	−44929.6	−	911.572i	−0.449944	−	0.00912887i
$317$		−	19461.2i		−	0.193665i	−0.995301	−	0.0968324i	$-0.969129\pi$
$317$		−	19461.2i		−	0.193665i	0.995301	−	0.0968324i	$-0.0308711\pi$
$318$		0			0
$319$			32764.0i			0.321970i
$320$	67993.5	+	76567.9i	0.663999	+	0.747734i
$321$		0			0
$322$	46489.9	−	45556.3i	0.448381	−	0.439376i
$323$	104308.			0.999799
$324$		0			0
$325$	78124.2	−	252.222i	0.739637	−	0.00238790i
$326$	−75530.6	+	74013.7i	−0.710702	+	0.696429i
$327$		0			0
$328$	79668.9	+	84671.2i	0.740527	+	0.787024i
$329$	−32177.7			−0.297278
$330$		0			0
$331$		−	62028.6i		−	0.566156i	−0.959097	−	0.283078i	$-0.908644\pi$
$331$		−	62028.6i		−	0.566156i	0.959097	−	0.283078i	$-0.0913555\pi$
$332$	−989.293	+	48760.4i	−0.00897530	+	0.442375i
$333$		0			0
$334$	−46904.6	+	45962.6i	−0.420458	+	0.412014i
$335$	−56630.7	+	56813.8i	−0.504618	+	0.506249i
$336$		0			0
$337$			26723.7i			0.235308i	0.993055	+	0.117654i	$0.0375374\pi$
$337$			26723.7i			0.235308i	−0.993055	+	0.117654i	$0.962463\pi$
$338$	−36958.2	+	36216.0i	−0.323503	+	0.317006i
$339$		0			0
$340$	46210.5	−	44516.3i	0.399745	−	0.385089i
$341$	−5746.61			−0.0494200
$342$		0			0
$343$	−127975.			−1.08777
$344$	138704.	+	147413.i	1.17212	+	1.24572i
$345$		0			0
$346$	40602.6	+	41434.7i	0.339157	+	0.346108i
$347$	−138874.			−1.15335			−0.576675	−	0.816974i	$-0.695650\pi$
$347$	−138874.			−1.15335			−0.576675	+	0.816974i	$0.695650\pi$
$348$		0			0
$349$	74063.7			0.608072			0.304036	−	0.952661i	$-0.401666\pi$
$349$	74063.7			0.608072			0.304036	+	0.952661i	$0.401666\pi$
$350$	68588.0	+	69543.2i	0.559902	+	0.567699i
$351$		0			0
$352$	−94974.0	−	105131.i	−0.766513	−	0.848489i
$353$		−	22898.3i		−	0.183761i	−0.995770	−	0.0918805i	$-0.970712\pi$
$353$		−	22898.3i		−	0.183761i	0.995770	−	0.0918805i	$-0.0292878\pi$
$354$		0			0
$355$	8079.91	+	8053.87i	0.0641136	+	0.0639069i
$356$	1669.32	−	82277.4i	0.0131716	−	0.649203i
$357$		0			0
$358$	83659.4	+	85374.0i	0.652753	+	0.666131i
$359$		−	216833.i		−	1.68242i	−0.540705	−	0.841212i	$-0.681842\pi$
$359$		−	216833.i		−	1.68242i	0.540705	−	0.841212i	$-0.318158\pi$
$360$		0			0
$361$	−292507.			−2.24451
$362$	37220.7	−	36473.2i	0.284032	−	0.278328i
$363$		0			0
$364$	78124.2	+	1585.05i	0.589634	+	0.0119630i
$365$	−104567.	−	104230.i	−0.784888	−	0.782358i
$366$		0			0
$367$	−17075.9			−0.126780			−0.0633900	−	0.997989i	$-0.520191\pi$
$367$	−17075.9			−0.126780			−0.0633900	+	0.997989i	$0.520191\pi$
$368$	106534.	+	4324.69i	0.786670	+	0.0319345i
$369$		0			0
$370$	−20613.0	−	175.809i	−0.150570	−	0.00128421i
$371$		−	190137.i		−	1.38140i
$372$		0			0
$373$			8495.42i			0.0610615i	0.999534	+	0.0305307i	$0.00971975\pi$
$373$			8495.42i			0.0610615i	−0.999534	+	0.0305307i	$0.990280\pi$
$374$	−63408.0	+	62134.5i	−0.453316	+	0.444212i
$375$		0			0
$376$	−36120.0	−	38387.9i	−0.255489	−	0.271530i
$377$		−	29600.7i		−	0.208267i
$378$		0			0
$379$			59878.5i			0.416862i	0.978037	+	0.208431i	$0.0668357\pi$
$379$			59878.5i			0.416862i	−0.978037	+	0.208431i	$0.933164\pi$
$380$	−187321.	+	180453.i	−1.29724	+	1.24967i
$381$		0			0
$382$	−150670.	−	153758.i	−1.03252	−	1.05368i
$383$	−144186.			−0.982935			−0.491467	−	0.870896i	$-0.663539\pi$
$383$	−144186.			−0.982935			−0.491467	+	0.870896i	$0.663539\pi$
$384$		0			0
$385$	−95713.7	−	95405.2i	−0.645733	−	0.643651i
$386$	−135614.	−	138393.i	−0.910183	−	0.928837i
$387$		0			0
$388$	72090.1	+	1462.63i	0.478864	+	0.00971562i
$389$	237951.			1.57249			0.786247	−	0.617913i	$-0.212021\pi$
$389$	237951.			1.57249			0.786247	+	0.617913i	$0.212021\pi$
$390$		0			0
$391$		−	66810.1i		−	0.437007i
$392$	−38353.4	−	40761.5i	−0.249592	−	0.265264i
$393$		0			0
$394$	−207776.	−	212034.i	−1.33845	−	1.36588i
$395$	−49731.0	−	49570.7i	−0.318737	−	0.317710i
$396$		0			0
$397$			267251.i			1.69566i	0.530271	+	0.847828i	$0.322090\pi$
$397$			267251.i			1.69566i	−0.530271	+	0.847828i	$0.677910\pi$
$398$	37067.2	+	37826.9i	0.234004	+	0.238800i
$399$		0			0
$400$	−5973.61	+	159888.i	−0.0373351	+	0.999303i
$401$	−17276.0			−0.107437			−0.0537185	−	0.998556i	$-0.517107\pi$
$401$	−17276.0			−0.107437			−0.0537185	+	0.998556i	$0.517107\pi$
$402$		0			0
$403$	5191.79			0.0319674
$404$	564.052	−	27801.1i	0.00345586	−	0.170333i
$405$		0			0
$406$	26433.1	−	25902.2i	0.160360	−	0.157139i
$407$	28520.7			0.172175
$408$		0			0
$409$	126218.			0.754530			0.377265	−	0.926105i	$-0.376865\pi$
$409$	126218.			0.754530			0.377265	+	0.926105i	$0.376865\pi$
$410$	−1549.29	+	181649.i	−0.00921649	+	1.08060i
$411$		0			0
$412$	−4112.97	+	202720.i	−0.0242304	+	1.19427i
$413$		−	142159.i		−	0.833442i
$414$		0			0
$415$	−53797.1	+	53971.1i	−0.312365	+	0.313375i
$416$	85804.6	+	94981.1i	0.495820	+	0.548846i
$417$		0			0
$418$	257033.	−	251871.i	1.47108	−	1.44154i
$419$			270580.i			1.54123i	0.637299	+	0.770617i	$0.280052\pi$
$419$			270580.i			1.54123i	−0.637299	+	0.770617i	$0.719948\pi$
$420$		0			0
$421$	260404.			1.46921			0.734605	−	0.678495i	$-0.237368\pi$
$421$	260404.			1.46921			0.734605	+	0.678495i	$0.237368\pi$
$422$	−12504.4	−	12760.7i	−0.0702163	−	0.0716554i
$423$		0			0
$424$	226832.	−	213431.i	1.26175	−	1.18721i
$425$	100257.	−	323.677i	0.555055	−	0.00179198i
$426$		0			0
$427$	161598.			0.886296
$428$	−2267.95	+	111783.i	−0.0123807	+	0.610223i
$429$		0			0
$430$	−2697.32	+	316252.i	−0.0145880	+	1.71040i
$431$		−	326771.i		−	1.75909i	−0.475814	−	0.879546i	$-0.657847\pi$
$431$		−	326771.i		−	1.75909i	0.475814	−	0.879546i	$-0.342153\pi$
$432$		0			0
$433$		−	164821.i		−	0.879099i	−0.898218	−	0.439549i	$-0.855138\pi$
$433$		−	164821.i		−	0.879099i	0.898218	−	0.439549i	$-0.144862\pi$
$434$	4543.09	+	4636.20i	0.0241197	+	0.0246140i
$435$		0			0
$436$	−263.265	+	12975.8i	−0.00138491	+	0.0682593i
$437$			270824.i			1.41816i
$438$		0			0
$439$		−	273776.i		−	1.42058i	−0.703907	−	0.710292i	$-0.748563\pi$
$439$		−	273776.i		−	1.42058i	0.703907	−	0.710292i	$-0.251437\pi$
$440$	6377.92	−	221280.i	0.0329438	−	1.14297i
$441$		0			0
$442$	57286.1	−	56135.7i	0.293228	−	0.287339i
$443$	−10446.4			−0.0532305			−0.0266153	−	0.999646i	$-0.508473\pi$
$443$	−10446.4			−0.0532305			−0.0266153	+	0.999646i	$0.508473\pi$
$444$		0			0
$445$	90776.4	−	91069.9i	0.458409	−	0.459891i
$446$	12412.9	−	12163.7i	0.0624029	−	0.0611497i
$447$		0			0
$448$	−9733.27	+	159736.i	−0.0484956	+	0.795878i
$449$	−193840.			−0.961502			−0.480751	−	0.876857i	$-0.659636\pi$
$449$	−193840.			−0.961502			−0.480751	+	0.876857i	$0.659636\pi$
$450$		0			0
$451$		−	251334.i		−	1.23566i
$452$	101458.	+	2058.46i	0.496601	+	0.0100755i
$453$		0			0
$454$	−178022.	+	174447.i	−0.863699	+	0.846354i
$455$	86472.9	+	86194.1i	0.417693	+	0.416347i
$456$		0			0
$457$		−	31679.4i		−	0.151686i	−0.997120	−	0.0758428i	$-0.975835\pi$
$457$		−	31679.4i		−	0.151686i	0.997120	−	0.0758428i	$-0.0241647\pi$
$458$	224631.	−	220119.i	1.07087	−	1.04937i
$459$		0			0
$460$	115582.	+	119980.i	0.546227	+	0.567015i
$461$	92279.5			0.434213			0.217107	−	0.976148i	$-0.430338\pi$
$461$	92279.5			0.434213			0.217107	+	0.976148i	$0.430338\pi$
$462$		0			0
$463$	196264.			0.915542			0.457771	−	0.889070i	$-0.348648\pi$
$463$	196264.			0.915542			0.457771	+	0.889070i	$0.348648\pi$
$464$	60572.7	+	2458.92i	0.281346	+	0.0114211i
$465$		0			0
$466$	6898.35	+	7039.73i	0.0317668	+	0.0324179i
$467$	261041.			1.19695			0.598475	−	0.801142i	$-0.295774\pi$
$467$	261041.			1.19695			0.598475	+	0.801142i	$0.295774\pi$
$468$		0			0
$469$	−125365.			−0.569942
$470$	702.411	−	82355.4i	0.00317977	−	0.372818i
$471$		0			0
$472$	169596.	−	159576.i	0.761255	−	0.716281i
$473$		−	437574.i		−	1.95582i
$474$		0			0
$475$	−406405.	+	1312.07i	−1.80124	+	0.00581527i
$476$	100257.	+	2034.10i	0.442486	+	0.00897755i
$477$		0			0
$478$	−152260.	−	155381.i	−0.666393	−	0.680051i
$479$		−	105637.i		−	0.460410i	−0.973142	−	0.230205i	$-0.926060\pi$
$479$		−	105637.i		−	0.460410i	0.973142	−	0.230205i	$-0.0739396\pi$
$480$		0			0
$481$	−25767.1			−0.111372
$482$	−11705.7	+	11470.6i	−0.0503853	+	0.0493734i
$483$		0			0
$484$	−1461.06	+	72013.0i	−0.00623704	+	0.307412i
$485$	79794.0	+	79536.8i	0.339224	+	0.338131i
$486$		0			0
$487$	332629.			1.40250			0.701249	−	0.712916i	$-0.252626\pi$
$487$	332629.			1.40250			0.701249	+	0.712916i	$0.252626\pi$
$488$	181396.	+	192785.i	0.761706	+	0.809532i
$489$		0			0
$490$	745.844	−	87447.7i	0.00310639	−	0.364214i
$491$		−	94449.4i		−	0.391775i	−0.980626	−	0.195887i	$-0.937241\pi$
$491$		−	94449.4i		−	0.391775i	0.980626	−	0.195887i	$-0.0627587\pi$
$492$		0			0
$493$		−	37986.6i		−	0.156292i
$494$	−232218.	+	227554.i	−0.951571	+	0.932461i
$495$		0			0
$496$	−431.279	+	10624.1i	−0.00175305	+	0.0431846i
$497$			17829.1i			0.0721799i
$498$		0			0
$499$			301032.i			1.20896i	0.796621	+	0.604479i	$0.206619\pi$
$499$			301032.i			1.20896i	−0.796621	+	0.604479i	$0.793381\pi$
$500$	−179486.	+	174026.i	−0.717942	+	0.696103i
$501$		0			0
$502$	−135251.	−	138023.i	−0.536702	−	0.547701i
$503$	−3184.75			−0.0125875			−0.00629374	−	0.999980i	$-0.502003\pi$
$503$	−3184.75			−0.0125875			−0.00629374	+	0.999980i	$0.502003\pi$
$504$		0			0
$505$	30672.8	−	30772.0i	0.120274	−	0.120663i
$506$	−161325.	−	164632.i	−0.630089	−	0.643003i
$507$		0			0
$508$	2499.75	−	123208.i	0.00968653	−	0.477431i
$509$	159009.			0.613741			0.306871	−	0.951751i	$-0.400718\pi$
$509$	159009.			0.613741			0.306871	+	0.951751i	$0.400718\pi$
$510$		0			0
$511$		−	230736.i		−	0.883637i
$512$	−201490.	+	167694.i	−0.768623	+	0.639702i
$513$		0			0
$514$	68759.5	+	70168.7i	0.260260	+	0.265593i
$515$	−223660.	+	224384.i	−0.843286	+	0.846013i
$516$		0			0
$517$			113949.i			0.426313i
$518$	−22547.6	−	23009.7i	−0.0840311	−	0.0857533i
$519$		0			0
$520$	−5762.16	+	199916.i	−0.0213097	+	0.739334i
$521$	−36476.2			−0.134380			−0.0671899	−	0.997740i	$-0.521403\pi$
$521$	−36476.2			−0.134380			−0.0671899	+	0.997740i	$0.521403\pi$
$522$		0			0
$523$	449988.			1.64512			0.822559	−	0.568679i	$-0.192546\pi$
$523$	449988.			1.64512			0.822559	+	0.568679i	$0.192546\pi$
$524$	249865.	+	5069.49i	0.910004	+	0.0184630i
$525$		0			0
$526$	238000.	−	233221.i	0.860214	−	0.842938i
$527$	6662.63			0.0239897
$528$		0			0
$529$	−106376.			−0.380130
$530$	486635.	+	4150.52i	1.73241	+	0.0147758i
$531$		0			0
$532$	−406405.	−	8245.51i	−1.43594	−	0.0291336i
$533$			227069.i			0.799287i
$534$		0			0
$535$	−123330.	+	123729.i	−0.430884	+	0.432278i
$536$	−140724.	−	149560.i	−0.489823	−	0.520578i
$537$		0			0
$538$	−75805.2	+	74282.8i	−0.261899	+	0.256640i
$539$			120995.i			0.416475i
$540$		0			0
$541$	−247407.			−0.845314			−0.422657	−	0.906290i	$-0.638903\pi$
$541$	−247407.			−0.845314			−0.422657	+	0.906290i	$0.638903\pi$
$542$	−308128.	−	314443.i	−1.04890	−	1.07039i
$543$		0			0
$544$	110113.	+	121889.i	0.372084	+	0.411877i
$545$	−14316.2	+	14362.5i	−0.0481986	+	0.0483544i
$546$		0			0
$547$	−313468.			−1.04765			−0.523827	−	0.851824i	$-0.675496\pi$
$547$	−313468.			−1.04765			−0.523827	+	0.851824i	$0.675496\pi$
$548$	60317.3	+	1223.77i	0.200854	+	0.00407511i
$549$		0			0
$550$	246269.	−	242886.i	0.814112	−	0.802930i
$551$			153984.i			0.507193i
$552$		0			0
$553$		−	109736.i		−	0.358839i
$554$	−310987.	−	317360.i	−1.01326	−	1.03403i
$555$		0			0
$556$	−111996.	−	2272.28i	−0.362288	−	0.00735042i
$557$			123970.i			0.399581i	0.979839	+	0.199790i	$0.0640261\pi$
$557$			123970.i			0.399581i	−0.979839	+	0.199790i	$0.935974\pi$
$558$		0			0
$559$			395328.i			1.26513i
$560$	−183564.	+	169791.i	−0.585346	+	0.541427i
$561$		0			0
$562$	−189663.	+	185854.i	−0.600497	+	0.588437i
$563$	−81897.7			−0.258378			−0.129189	−	0.991620i	$-0.541237\pi$
$563$	−81897.7			−0.258378			−0.129189	+	0.991620i	$0.541237\pi$
$564$		0			0
$565$	112300.	+	111938.i	0.351789	+	0.350655i
$566$	353990.	−	346881.i	1.10499	−	1.08280i
$567$		0			0
$568$	−21270.0	+	20013.4i	−0.0659282	+	0.0620332i
$569$	−479808.			−1.48198			−0.740990	−	0.671516i	$-0.765644\pi$
$569$	−479808.			−1.48198			−0.740990	+	0.671516i	$0.765644\pi$
$570$		0			0
$571$			314368.i			0.964199i	0.876116	+	0.482100i	$0.160126\pi$
$571$			314368.i			0.964199i	−0.876116	+	0.482100i	$0.839874\pi$
$572$	5613.05	−	276656.i	0.0171556	−	0.845568i
$573$		0			0
$574$	−202769.	+	198697.i	−0.615430	+	0.603070i
$575$	840.391	+	260306.i	0.00254182	+	0.787314i
$576$		0			0
$577$			229486.i			0.689294i	0.938732	+	0.344647i	$0.112001\pi$
$577$			229486.i			0.689294i	−0.938732	+	0.344647i	$0.887999\pi$
$578$	−165102.	+	161786.i	−0.494192	+	0.484267i
$579$		0			0
$580$	65716.9	+	68218.0i	0.195354	+	0.202788i
$581$	−119092.			−0.352802
$582$		0			0
$583$	−673319.			−1.98100
$584$	275267.	−	259005.i	0.807103	−	0.759420i
$585$		0			0
$586$	−223326.	−	227903.i	−0.650345	−	0.663674i
$587$	308124.			0.894230			0.447115	−	0.894476i	$-0.352451\pi$
$587$	308124.			0.894230			0.447115	+	0.894476i	$0.352451\pi$
$588$		0			0
$589$	−27007.9			−0.0778503
$590$	363842.	+	3103.22i	1.04522	+	0.00891472i
$591$		0			0
$592$	2140.46	−	52727.8i	0.00610750	−	0.150452i
$593$			379121.i			1.07812i	0.842266	+	0.539062i	$0.181221\pi$
$593$			379121.i			1.07812i	−0.842266	+	0.539062i	$0.818779\pi$
$594$		0			0
$595$	110971.	+	110613.i	0.313454	+	0.312444i
$596$	9725.84	−	479368.i	0.0273801	−	1.34951i
$597$		0			0
$598$	145750.	+	148737.i	0.407574	+	0.415927i
$599$			415907.i			1.15916i	0.814916	+	0.579579i	$0.196783\pi$
$599$			415907.i			1.15916i	−0.814916	+	0.579579i	$0.803217\pi$
$600$		0			0
$601$	95042.6			0.263130			0.131565	−	0.991308i	$-0.458000\pi$
$601$	95042.6			0.263130			0.131565	+	0.991308i	$0.458000\pi$
$602$	−353023.	+	345933.i	−0.974113	+	0.954550i
$603$		0			0
$604$	198313.	+	4023.56i	0.543599	+	0.0110290i
$605$	−79451.7	+	79708.7i	−0.217066	+	0.217768i
$606$		0			0
$607$	253259.			0.687364			0.343682	−	0.939086i	$-0.388326\pi$
$607$	253259.			0.687364			0.343682	+	0.939086i	$0.388326\pi$
$608$	−446359.	−	494095.i	−1.20747	−	1.33661i
$609$		0			0
$610$	−3527.53	+	413592.i	−0.00948007	+	1.11151i
$611$		−	102947.i		−	0.275761i
$612$		0			0
$613$			427719.i			1.13825i	0.822251	+	0.569125i	$0.192718\pi$
$613$			427719.i			1.13825i	−0.822251	+	0.569125i	$0.807282\pi$
$614$	−293145.	+	287258.i	−0.777581	+	0.761965i
$615$		0			0
$616$	251962.	−	237076.i	0.664009	−	0.624780i
$617$			283218.i			0.743962i	0.928240	+	0.371981i	$0.121321\pi$
$617$			283218.i			0.743962i	−0.928240	+	0.371981i	$0.878679\pi$
$618$		0			0
$619$		−	647178.i		−	1.68905i	−0.535517	−	0.844525i	$-0.679883\pi$
$619$		−	647178.i		−	1.68905i	0.535517	−	0.844525i	$-0.320117\pi$
$620$	−11965.0	+	11526.4i	−0.0311265	+	0.0299853i
$621$		0			0
$622$	−316684.	−	323175.i	−0.818551	−	0.835327i
$623$	200954.			0.517751
$624$		0			0
$625$	−390617.	+	2522.22i	−0.999979	+	0.00645689i
$626$	504145.	+	514477.i	1.28649	+	1.31286i
$627$		0			0
$628$	292640.	+	5937.34i	0.742018	+	0.0150547i
$629$	−33066.9			−0.0835781
$630$		0			0
$631$			552250.i			1.38700i	0.720455	+	0.693501i	$0.243933\pi$
$631$			552250.i			1.38700i	−0.720455	+	0.693501i	$0.756067\pi$
$632$	130915.	−	123180.i	0.327759	−	0.308395i
$633$		0			0
$634$	54483.4	+	55600.0i	0.135546	+	0.138324i
$635$	135935.	−	136374.i	0.337118	−	0.338208i
$636$		0			0
$637$		−	109313.i		−	0.269397i
$638$	−91725.9	−	93605.7i	−0.225346	−	0.229965i
$639$		0			0
$640$	−408614.	−	28398.2i	−0.997594	−	0.0693314i
$641$	−394430.			−0.959962			−0.479981	−	0.877279i	$-0.659356\pi$
$641$	−394430.			−0.959962			−0.479981	+	0.877279i	$0.659356\pi$
$642$		0			0
$643$	−320916.			−0.776192			−0.388096	−	0.921619i	$-0.626867\pi$
$643$	−320916.			−0.776192			−0.388096	+	0.921619i	$0.626867\pi$
$644$	−5281.31	+	260306.i	−0.0127342	+	0.627642i
$645$		0			0
$646$	−298005.	+	292020.i	−0.714099	+	0.699758i
$647$	−378985.			−0.905344			−0.452672	−	0.891677i	$-0.649529\pi$
$647$	−378985.			−0.905344			−0.452672	+	0.891677i	$0.649529\pi$
$648$		0			0
$649$	−503420.			−1.19520
$650$	−222492.	+	219437.i	−0.526609	+	0.519376i
$651$		0			0
$652$	8580.37	−	422910.i	0.0201842	−	0.994838i
$653$			205104.i			0.481003i	0.970649	+	0.240501i	$0.0773119\pi$
$653$			205104.i			0.481003i	−0.970649	+	0.240501i	$0.922688\pi$
$654$		0			0
$655$	276567.	+	275676.i	0.644641	+	0.642563i
$656$	−464657.	−	18862.5i	−1.07975	−	0.0438320i
$657$		0			0
$658$	91930.7	−	90084.5i	0.212329	−	0.208065i
$659$			204237.i			0.470288i	0.971961	+	0.235144i	$0.0755562\pi$
$659$			204237.i			0.470288i	−0.971961	+	0.235144i	$0.924444\pi$
$660$		0			0
$661$	549151.			1.25687			0.628433	−	0.777864i	$-0.283697\pi$
$661$	549151.			1.25687			0.628433	+	0.777864i	$0.283697\pi$
$662$	173655.	+	177214.i	0.396252	+	0.404373i
$663$		0			0
$664$	−133683.	−	142076.i	−0.303207	−	0.322245i
$665$	−449836.	−	448386.i	−1.01721	−	1.01393i
$666$		0			0
$667$	98628.1			0.221691
$668$	5328.42	−	262628.i	0.0119411	−	0.588556i
$669$		0			0
$670$	2736.61	−	320858.i	0.00609626	−	0.714766i
$671$		−	572255.i		−	1.27100i
$672$		0			0
$673$		−	506727.i		−	1.11878i	−0.828905	−	0.559389i	$-0.811036\pi$
$673$		−	506727.i		−	1.11878i	0.828905	−	0.559389i	$-0.188964\pi$
$674$	−74815.5	−	76348.8i	−0.164692	−	0.168067i
$675$		0			0
$676$	4198.50	−	206936.i	0.00918757	−	0.452838i
$677$		−	548346.i		−	1.19640i	−0.801346	−	0.598202i	$-0.795882\pi$
$677$		−	548346.i		−	1.19640i	0.801346	−	0.598202i	$-0.204118\pi$
$678$		0			0
$679$			176073.i			0.381903i
$680$	−7394.58	+	256552.i	−0.0159917	+	0.554827i
$681$		0			0
$682$	16417.9	−	16088.2i	0.0352979	−	0.0345890i
$683$	537201.			1.15158			0.575792	−	0.817596i	$-0.304694\pi$
$683$	537201.			1.15158			0.575792	+	0.817596i	$0.304694\pi$
$684$		0			0
$685$	66763.1	+	66547.9i	0.142284	+	0.141825i
$686$	365621.	−	358279.i	0.776933	−	0.761329i
$687$		0			0
$688$	−808969.	−	32839.7i	−1.70905	−	0.0693781i
$689$	608313.			1.28141
$690$		0			0
$691$		−	197108.i		−	0.412808i	−0.978467	−	0.206404i	$-0.933824\pi$
$691$		−	197108.i		−	0.412808i	0.978467	−	0.206404i	$-0.0661760\pi$
$692$	−232001.	−	4707.03i	−0.484481	−	0.00982958i
$693$		0			0
$694$	396758.	−	388790.i	0.823771	−	0.807227i
$695$	−123965.	−	123565.i	−0.256642	−	0.255815i
$696$		0			0
$697$			291397.i			0.599819i
$698$	−211598.	+	207348.i	−0.434311	+	0.425588i
$699$		0			0
$700$	−390647.	−	6664.15i	−0.797238	−	0.0136003i
$701$	555586.			1.13062			0.565308	−	0.824880i	$-0.308757\pi$
$701$	555586.			1.13062			0.565308	+	0.824880i	$0.308757\pi$
$702$		0			0
$703$	134041.			0.271224
$704$	565662.	+	34467.8i	1.14133	+	0.0695454i
$705$		0			0
$706$	64105.9	+	65419.7i	0.128614	+	0.131250i
$707$	67901.2			0.135844
$708$		0			0
$709$	833981.			1.65907			0.829533	−	0.558458i	$-0.188607\pi$
$709$	833981.			1.65907			0.829533	+	0.558458i	$0.188607\pi$
$710$	−45631.6	−	389.193i	−0.0905210	−	0.000772056i
$711$		0			0
$712$	225574.	+	239737.i	0.444968	+	0.472907i
$713$			17298.8i			0.0340280i
$714$		0			0
$715$	305234.	−	306221.i	0.597064	−	0.598994i
$716$	−478025.	−	9698.59i	−0.932448	−	0.0189183i
$717$		0			0
$718$	607043.	+	619484.i	1.17753	+	1.20166i
$719$			450137.i			0.870737i	0.900252	+	0.435368i	$0.143382\pi$
$719$			450137.i			0.870737i	−0.900252	+	0.435368i	$0.856618\pi$
$720$		0			0
$721$	−495124.			−0.952452
$722$	835683.	−	818899.i	1.60312	−	1.57093i
$723$		0			0
$724$	−4228.31	+	208406.i	−0.00806659	+	0.397587i
$725$	477.826	+	148004.i	0.000909063	+	0.281577i
$726$		0			0
$727$	281881.			0.533331			0.266666	−	0.963789i	$-0.414078\pi$
$727$	281881.			0.533331			0.266666	+	0.963789i	$0.414078\pi$
$728$	−227636.	+	214187.i	−0.429515	+	0.404140i
$729$		0			0
$730$	590545.	+	5036.77i	1.10817	+	0.00945163i
$731$			507324.i			0.949404i
$732$		0			0
$733$		−	59324.7i		−	0.110415i	−0.998475	−	0.0552074i	$-0.982418\pi$
$733$		−	59324.7i		−	0.110415i	0.998475	−	0.0552074i	$-0.0175820\pi$
$734$	48785.2	−	47805.5i	0.0905516	−	0.0887331i
$735$		0			0
$736$	−316472.	+	285896.i	−0.584224	+	0.527780i
$737$			443947.i			0.817328i
$738$		0			0
$739$		−	11842.3i		−	0.0216845i	−0.999941	−	0.0108422i	$-0.996549\pi$
$739$		−	11842.3i		−	0.0216845i	0.999941	−	0.0108422i	$-0.00345126\pi$
$740$	59383.0	−	57205.8i	0.108442	−	0.104466i
$741$		0			0
$742$	532306.	+	543215.i	0.966837	+	0.986652i
$743$	8652.18			0.0156728			0.00783642	−	0.999969i	$-0.497506\pi$
$743$	8652.18			0.0156728			0.00783642	+	0.999969i	$0.497506\pi$
$744$		0			0
$745$	528885.	−	530595.i	0.952903	−	0.955984i
$746$	−23783.7	−	24271.2i	−0.0427368	−	0.0436127i
$747$		0			0
$748$	7203.22	−	355033.i	0.0128743	−	0.634550i
$749$	−273019.			−0.486664
$750$		0			0
$751$		−	952787.i		−	1.68934i	−0.535291	−	0.844668i	$-0.679798\pi$
$751$		−	952787.i		−	1.68934i	0.535291	−	0.844668i	$-0.320202\pi$
$752$	210664.	+	8551.80i	0.372524	+	0.0151224i
$753$		0			0
$754$	82870.0	+	84568.4i	0.145765	+	0.148753i
$755$	219506.	+	218799.i	0.385081	+	0.383840i
$756$		0			0
$757$			605031.i			1.05581i	0.849303	+	0.527905i	$0.177022\pi$
$757$			605031.i			1.05581i	−0.849303	+	0.527905i	$0.822978\pi$
$758$	−167635.	−	171071.i	−0.291761	−	0.297741i
$759$		0			0
$760$	29975.0	−	1.03997e6i	0.0518957	−	1.80050i
$761$	−229134.			−0.395659			−0.197830	−	0.980236i	$-0.563389\pi$
$761$	−229134.			−0.395659			−0.197830	+	0.980236i	$0.563389\pi$
$762$		0			0
$763$	−31692.1			−0.0544380
$764$	860919.	+	17467.1i	1.47494	+	0.0299250i
$765$		0			0
$766$	411934.	−	403661.i	0.702054	−	0.687954i
$767$	454816.			0.773117
$768$		0			0
$769$	−802587.			−1.35719			−0.678593	−	0.734515i	$-0.737410\pi$
$769$	−802587.			−1.35719			−0.678593	+	0.734515i	$0.737410\pi$
$770$	540547.	+	4610.34i	0.911700	+	0.00777591i
$771$		0			0
$772$	774888.	+	15721.6i	1.30018	+	0.0263793i
$773$		−	285645.i		−	0.478045i	−0.971014	−	0.239022i	$-0.923173\pi$
$773$		−	285645.i		−	0.478045i	0.971014	−	0.239022i	$-0.0768269\pi$
$774$		0			0
$775$	−25958.9	+	83.8078i	−0.0432199	+	0.000139534i
$776$	−210054.	+	197644.i	−0.348825	+	0.328217i
$777$		0			0
$778$	−679820.	+	666167.i	−1.12314	+	1.10059i
$779$		−	1.18122e6i		−	1.94651i
$780$		0			0
$781$	63137.0			0.103510
$782$	187041.	+	190874.i	0.305861	+	0.312129i
$783$		0			0
$784$	223690.	+	9080.58i	0.363927	+	0.0147734i
$785$	323913.	+	322869.i	0.525640	+	0.523946i
$786$		0			0
$787$	−369344.			−0.596324			−0.298162	−	0.954515i	$-0.596373\pi$
$787$	−369344.			−0.596324			−0.298162	+	0.954515i	$0.596373\pi$
$788$	1.18722e6	+	24087.3i	1.91196	+	0.0387914i
$789$		0			0
$790$	280858.	+	2395.44i	0.450021	+	0.00383824i
$791$			247800.i			0.396048i
$792$		0			0
$793$			517006.i			0.822146i
$794$	−748193.	−	763527.i	−1.18679	−	1.21111i
$795$		0			0
$796$	−211800.	−	4297.18i	−0.334272	−	0.00678200i
$797$		−	282731.i		−	0.445100i	−0.974921	−	0.222550i	$-0.928562\pi$
$797$		−	282731.i		−	0.445100i	0.974921	−	0.222550i	$-0.0714380\pi$
$798$		0			0
$799$		−	132113.i		−	0.206943i
$800$	−430556.	−	473520.i	−0.672744	−	0.739875i
$801$		0			0
$802$	49357.0	−	48365.7i	0.0767361	−	0.0751950i
$803$	−817092.			−1.26718
$804$		0			0
$805$	−287194.	+	288123.i	−0.443184	+	0.444617i
$806$	−14832.8	+	14534.9i	−0.0228325	+	0.0223739i
$807$		0			0
$808$	76220.2	+	81005.9i	0.116747	+	0.124078i
$809$	866021.			1.32322			0.661609	−	0.749849i	$-0.269874\pi$
$809$	866021.			1.32322			0.661609	+	0.749849i	$0.269874\pi$
$810$		0			0
$811$			550380.i			0.836798i	0.908263	+	0.418399i	$0.137409\pi$
$811$			550380.i			0.836798i	−0.908263	+	0.418399i	$0.862591\pi$
$812$	−3002.83	+	148004.i	−0.00455427	+	0.224471i
$813$		0			0
$814$	−81482.7	+	79846.3i	−0.122975	+	0.120505i
$815$	466595.	−	468104.i	0.702465	−	0.704737i
$816$		0			0
$817$		−	2.05651e6i		−	3.08097i
$818$	−360602.	+	353360.i	−0.538917	+	0.528094i
$819$		0			0
$820$	−504118.	−	523304.i	−0.749729	−	0.778263i
$821$	−60251.5			−0.0893884			−0.0446942	−	0.999001i	$-0.514231\pi$
$821$	−60251.5			−0.0893884			−0.0446942	+	0.999001i	$0.514231\pi$
$822$		0			0
$823$	760386.			1.12262			0.561312	−	0.827604i	$-0.310297\pi$
$823$	760386.			1.12262			0.561312	+	0.827604i	$0.310297\pi$
$824$	−555784.	−	590680.i	−0.818561	−	0.869957i
$825$		0			0
$826$	397988.	+	406145.i	0.583325	+	0.595280i
$827$	−1.18336e6			−1.73024			−0.865118	−	0.501568i	$-0.832757\pi$
$827$	−1.18336e6			−1.73024			−0.865118	+	0.501568i	$0.832757\pi$
$828$		0			0
$829$	518356.			0.754257			0.377129	−	0.926161i	$-0.376911\pi$
$829$	518356.			0.754257			0.377129	+	0.926161i	$0.376911\pi$
$830$	2599.68	−	304804.i	0.00377367	−	0.442450i
$831$		0			0
$832$	−511049.	−	31140.1i	−0.738272	−	0.0449855i
$833$		−	140281.i		−	0.202167i
$834$		0			0
$835$	289756.	−	290693.i	0.415585	−	0.416929i
$836$	−29199.3	+	1.43918e6i	−0.0417792	+	2.05922i
$837$		0			0
$838$	−757515.	−	773040.i	−1.07871	−	1.10081i
$839$		−	519063.i		−	0.737388i	−0.929551	−	0.368694i	$-0.879805\pi$
$839$		−	519063.i		−	0.737388i	0.929551	−	0.368694i	$-0.120195\pi$
$840$		0			0
$841$	−651203.			−0.920714
$842$	−743967.	+	729026.i	−1.04937	+	1.02830i
$843$		0			0
$844$	71449.4	+	1449.63i	0.100303	+	0.00203503i
$845$	228312.	−	229050.i	0.319753	−	0.320787i
$846$		0			0
$847$	−175885.			−0.245166
$848$	−50532.2	+	1.24481e6i	−0.0702711	+	1.73105i
$849$		0			0
$850$	−285525.	+	281603.i	−0.395190	+	0.389762i
$851$		−	85854.6i		−	0.118551i
$852$		0			0
$853$			1.08704e6i			1.49398i	0.664834	+	0.746992i	$0.268502\pi$
$853$			1.08704e6i			1.49398i	−0.664834	+	0.746992i	$0.731498\pi$
$854$	−461679.	+	452407.i	−0.633031	+	0.620317i
$855$		0			0
$856$	−306468.	−	325710.i	−0.418251	−	0.444512i
$857$		−	1.32143e6i		−	1.79921i	−0.436705	−	0.899605i	$-0.643854\pi$
$857$		−	1.32143e6i		−	1.79921i	0.436705	−	0.899605i	$-0.356146\pi$
$858$		0			0
$859$			54795.2i			0.0742602i	0.999310	+	0.0371301i	$0.0118216\pi$
$859$			54795.2i			0.0742602i	−0.999310	+	0.0371301i	$0.988178\pi$
$860$	−877672.	−	911075.i	−1.18668	−	1.23185i
$861$		0			0
$862$	914825.	+	933574.i	1.23119	+	1.25642i
$863$	−1.00023e6			−1.34300			−0.671502	−	0.741002i	$-0.734351\pi$
$863$	−1.00023e6			−1.34300			−0.671502	+	0.741002i	$0.734351\pi$
$864$		0			0
$865$	−256793.	−	255965.i	−0.343203	−	0.342097i
$866$	461433.	+	470890.i	0.615280	+	0.627890i
$867$		0			0
$868$	−25958.9	−	526.678i	−0.0344546	−	0.000699046i
$869$	−388601.			−0.514594
$870$		0			0
$871$		−	401085.i		−	0.528689i
$872$	−35574.9	−	37808.6i	−0.0467854	−	0.0497230i
$873$		0			0
$874$	−758198.	−	773737.i	−0.992567	−	1.01291i
$875$	−433756.	−	429575.i	−0.566538	−	0.561077i
$876$		0			0
$877$		−	403840.i		−	0.525061i	−0.964924	−	0.262531i	$-0.915443\pi$
$877$		−	403840.i		−	0.525061i	0.964924	−	0.262531i	$-0.0845571\pi$
$878$	766463.	+	782171.i	0.994264	+	1.01464i
$879$		0			0
$880$	601272.	+	650045.i	0.776436	+	0.839418i
$881$	−642029.			−0.827185			−0.413593	−	0.910462i	$-0.635726\pi$
$881$	−642029.			−0.827185			−0.413593	+	0.910462i	$0.635726\pi$
$882$		0			0
$883$	−238590.			−0.306006			−0.153003	−	0.988226i	$-0.548894\pi$
$883$	−238590.			−0.306006			−0.153003	+	0.988226i	$0.548894\pi$
$884$	−6507.78	+	320756.i	−0.00832776	+	0.410459i
$885$		0			0
$886$	29845.2	−	29245.8i	0.0380195	−	0.0372560i
$887$	439336.			0.558406			0.279203	−	0.960232i	$-0.409930\pi$
$887$	439336.			0.558406			0.279203	+	0.960232i	$0.409930\pi$
$888$		0			0
$889$	300922.			0.380759
$890$	−4386.65	+	514321.i	−0.00553801	+	0.649313i
$891$		0			0
$892$	−1410.13	+	69502.4i	−0.00177226	+	0.0873514i
$893$			535537.i			0.671563i
$894$		0			0
$895$	−529109.	−	527403.i	−0.660540	−	0.658411i
$896$	−419388.	−	483610.i	−0.522396	−	0.602392i
$897$		0			0
$898$	553795.	−	542673.i	0.686746	−	0.672954i
$899$			9835.67i			0.0121698i
$900$		0			0
$901$	780648.			0.961625
$902$	703634.	+	718054.i	0.864836	+	0.882560i
$903$		0			0
$904$	−295624.	+	278159.i	−0.361746	+	0.340374i
$905$	−229933.	+	230677.i	−0.280740	+	0.281648i
$906$		0			0
$907$	−1.10959e6			−1.34880			−0.674398	−	0.738368i	$-0.735597\pi$
$907$	−1.10959e6			−1.34880			−0.674398	+	0.738368i	$0.735597\pi$
$908$	20223.6	−	996780.i	0.0245293	−	1.20900i
$909$		0			0
$910$	−488359.	−	4165.22i	−0.589734	−	0.00502986i
$911$		−	249223.i		−	0.300297i	−0.988663	−	0.150148i	$-0.952025\pi$
$911$		−	249223.i		−	0.300297i	0.988663	−	0.150148i	$-0.0479752\pi$
$912$		0			0
$913$			421734.i			0.505937i
$914$	88689.4	+	90507.0i	0.106164	+	0.108340i
$915$		0			0
$916$	−25518.3	+	1.25775e6i	−0.0304131	+	1.49900i
$917$			610271.i			0.725745i
$918$		0			0
$919$		−	385756.i		−	0.456753i	−0.973573	−	0.228376i	$-0.926658\pi$
$919$		−	385756.i		−	0.456753i	0.973573	−	0.228376i	$-0.0733417\pi$
$920$	−666109.	−	19199.2i	−0.786991	−	0.0226834i
$921$		0			0
$922$	−263640.	+	258345.i	−0.310134	+	0.303905i
$923$	−57041.3			−0.0669555
$924$		0			0
$925$	128835.	−	415.942i	0.150575	−	0.000486127i
$926$	−560720.	+	549459.i	−0.653919	+	0.640786i
$927$		0			0
$928$	−179938.	+	162554.i	−0.208943	+	0.188756i
$929$	297906.			0.345182			0.172591	−	0.984994i	$-0.444786\pi$
$929$	297906.			0.345182			0.172591	+	0.984994i	$0.444786\pi$
$930$		0			0
$931$			568651.i			0.656064i
$932$	−39416.8	−	799.722i	−0.0453784	−	0.000920677i
$933$		0			0
$934$	−745788.	+	730810.i	−0.854912	+	0.837743i
$935$	391707.	−	392973.i	0.448062	−	0.449511i
$936$		0			0
$937$		−	661095.i		−	0.752982i	−0.926420	−	0.376491i	$-0.877131\pi$
$937$		−	661095.i		−	0.752982i	0.926420	−	0.376491i	$-0.122869\pi$
$938$	358164.	−	350971.i	0.407077	−	0.398901i
$939$		0			0
$940$	228555.	+	237253.i	0.258663	+	0.268508i
$941$	1.71686e6			1.93890			0.969448	−	0.245298i	$-0.0788858\pi$
$941$	1.71686e6			1.93890			0.969448	+	0.245298i	$0.0788858\pi$
$942$		0			0
$943$	−756581.			−0.850809
$944$	−37781.4	+	930702.i	−0.0423969	+	1.04440i
$945$		0			0
$946$	1.22503e6	+	1.25014e6i	1.36888	+	1.39693i
$947$	659116.			0.734957			0.367478	−	0.930032i	$-0.380221\pi$
$947$	659116.			0.734957			0.367478	+	0.930032i	$0.380221\pi$
$948$		0			0
$949$	738204.			0.819679
$950$	1.15741e6	−	1.14152e6i	1.28245	−	1.26484i
$951$		0			0
$952$	−292125.	+	274867.i	−0.322326	+	0.303283i
$953$		−	870368.i		−	0.958335i	−0.877724	−	0.479167i	$-0.840939\pi$
$953$		−	870368.i		−	0.958335i	0.877724	−	0.479167i	$-0.159061\pi$
$954$		0			0
$955$	952921.	+	949849.i	1.04484	+	1.04147i
$956$	870005.	+	17651.4i	0.951933	+	0.0193136i
$957$		0			0
$958$	295740.	+	301801.i	0.322240	+	0.328844i
$959$			147319.i			0.160185i
$960$		0			0
$961$	921796.			0.998132
$962$	73615.8	−	72137.4i	0.0795465	−	0.0779489i
$963$		0			0
$964$	1329.78	−	65542.4i	0.00143096	−	0.0705291i
$965$	857696.	+	854932.i	0.921041	+	0.918072i
$966$		0			0
$967$	−1.50355e6			−1.60792			−0.803961	−	0.594682i	$-0.797278\pi$
$967$	−1.50355e6			−1.60792			−0.803961	+	0.594682i	$0.797278\pi$
$968$	−197433.	−	209829.i	−0.210702	−	0.223932i
$969$		0			0
$970$	−450640.	−	3843.52i	−0.478945	−	0.00408494i
$971$			1.39973e6i			1.48459i	0.670074	+	0.742295i	$0.266262\pi$
$971$			1.39973e6i			1.48459i	−0.670074	+	0.742295i	$0.733738\pi$
$972$		0			0
$973$		−	273540.i		−	0.288931i
$974$	−950311.	+	931226.i	−1.00172	+	0.981606i
$975$		0			0
$976$	−1.05796e6	−	42947.4i	−1.11063	−	0.0450855i
$977$		−	1.27509e6i		−	1.33583i	−0.744236	−	0.667917i	$-0.767186\pi$
$977$		−	1.27509e6i		−	1.33583i	0.744236	−	0.667917i	$-0.232814\pi$
$978$		0			0
$979$		−	711626.i		−	0.742483i
$980$	242687.	+	251924.i	0.252694	+	0.262311i
$981$		0			0
$982$	264420.	+	269839.i	0.274202	+	0.279822i
$983$	652901.			0.675679			0.337839	−	0.941204i	$-0.390304\pi$
$983$	652901.			0.675679			0.337839	+	0.941204i	$0.390304\pi$
$984$		0			0
$985$	1.31409e6	+	1.30985e6i	1.35442	+	1.35005i
$986$	106347.	+	108527.i	0.109389	+	0.111630i
$987$		0			0
$988$	26380.2	−	1.30023e6i	0.0270249	−	1.33201i
$989$	−1.31721e6			−1.34668
$990$		0			0
$991$			817175.i			0.832086i	0.909345	+	0.416043i	$0.136583\pi$
$991$			817175.i			0.832086i	−0.909345	+	0.416043i	$0.863417\pi$
$992$	−28511.0	−	31560.1i	−0.0289727	−	0.0320712i
$993$		0			0
$994$	−49914.2	−	50937.2i	−0.0505186	−	0.0515539i
$995$	−234434.	−	233678.i	−0.236796	−	0.236033i
$996$		0			0
$997$		−	295553.i		−	0.297335i	−0.988887	−	0.148667i	$-0.952502\pi$
$997$		−	295553.i		−	0.297335i	0.988887	−	0.148667i	$-0.0474984\pi$
$998$	−842766.	−	860038.i	−0.846147	−	0.863489i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	180.5.f.g.19.2		8
3.2	odd	2		20.5.d.c.19.7	yes	8
4.3	odd	2	inner	180.5.f.g.19.8		8
5.4	even	2	inner	180.5.f.g.19.7		8
12.11	even	2		20.5.d.c.19.1	✓	8
15.2	even	4		100.5.b.e.51.6		8
15.8	even	4		100.5.b.e.51.3		8
15.14	odd	2		20.5.d.c.19.2	yes	8
20.19	odd	2	inner	180.5.f.g.19.1		8
24.5	odd	2		320.5.h.f.319.3		8
24.11	even	2		320.5.h.f.319.5		8
60.23	odd	4		100.5.b.e.51.4		8
60.47	odd	4		100.5.b.e.51.5		8
60.59	even	2		20.5.d.c.19.8	yes	8
120.29	odd	2		320.5.h.f.319.6		8
120.59	even	2		320.5.h.f.319.4		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
20.5.d.c.19.1	✓	8	12.11	even	2
20.5.d.c.19.2	yes	8	15.14	odd	2
20.5.d.c.19.7	yes	8	3.2	odd	2
20.5.d.c.19.8	yes	8	60.59	even	2
100.5.b.e.51.3		8	15.8	even	4
100.5.b.e.51.4		8	60.23	odd	4
100.5.b.e.51.5		8	60.47	odd	4
100.5.b.e.51.6		8	15.2	even	4
180.5.f.g.19.1		8	20.19	odd	2	inner
180.5.f.g.19.2		8	1.1	even	1	trivial
180.5.f.g.19.7		8	5.4	even	2	inner
180.5.f.g.19.8		8	4.3	odd	2	inner
320.5.h.f.319.3		8	24.5	odd	2
320.5.h.f.319.4		8	120.59	even	2
320.5.h.f.319.5		8	24.11	even	2
320.5.h.f.319.6		8	120.29	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 $\F_{q}$

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

\(f(q)\)	\(=\)	\(q+(-2.85697 + 2.79959i) q^{2} +(0.324555 - 15.9967i) q^{4} +(17.6491 - 17.7062i) q^{5} +39.0703 q^{7} +(43.8570 + 46.6107i) q^{8} +(-0.852871 + 99.9964i) q^{10} -138.357i q^{11} +124.999i q^{13} +(-111.623 + 109.381i) q^{14} +(-255.789 - 10.3836i) q^{16} +160.412i q^{17} -650.252i q^{19} +(-277.513 - 288.074i) q^{20} +(387.344 + 395.283i) q^{22} -416.491 q^{23} +(-2.01779 - 624.997i) q^{25} +(-349.947 - 357.119i) q^{26} +(12.6805 - 624.997i) q^{28} -236.807 q^{29} -41.5345i q^{31} +(759.852 - 686.440i) q^{32} +(-449.088 - 458.291i) q^{34} +(689.557 - 691.786i) q^{35} +206.138i q^{37} +(1820.44 + 1857.75i) q^{38} +(1599.34 + 46.0975i) q^{40} +1816.56 q^{41} +3162.64 q^{43} +(-2213.26 - 44.9046i) q^{44} +(1189.90 - 1166.01i) q^{46} -823.584 q^{47} -874.509 q^{49} +(1755.50 + 1779.95i) q^{50} +(1999.58 + 40.5692i) q^{52} -4866.53i q^{53} +(-2449.78 - 2441.88i) q^{55} +(1713.51 + 1821.10i) q^{56} +(676.551 - 662.964i) q^{58} -3638.55i q^{59} +4136.07 q^{61} +(116.280 + 118.663i) q^{62} +(-249.122 + 4088.42i) q^{64} +(2213.26 + 2206.13i) q^{65} -3208.70 q^{67} +(2566.06 + 52.0625i) q^{68} +(-33.3220 + 3906.89i) q^{70} +456.333i q^{71} -5905.66i q^{73} +(-577.102 - 588.929i) q^{74} +(-10401.9 - 211.043i) q^{76} -5405.67i q^{77} -2808.68i q^{79} +(-4698.31 + 4345.79i) q^{80} +(-5189.86 + 5085.63i) q^{82} -3048.15 q^{83} +(2840.28 + 2831.12i) q^{85} +(-9035.57 + 8854.10i) q^{86} +(6448.94 - 6067.94i) q^{88} +5143.40 q^{89} +4883.77i q^{91} +(-135.174 + 6662.49i) q^{92} +(2352.96 - 2305.70i) q^{94} +(-11513.5 - 11476.4i) q^{95} +4506.56i q^{97} +(2498.45 - 2448.27i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 48 q^{4} + 40 q^{5} - 160 q^{10} - 640 q^{14} - 832 q^{16} + 400 q^{20} - 2040 q^{25} - 2496 q^{26} - 2704 q^{29} - 2176 q^{34} + 6400 q^{40} - 1456 q^{41} - 1920 q^{44} + 7040 q^{46} - 8008 q^{49}+ \cdots + 10880 q^{94}+O(q^{100}) \) 8 * q - 48 * q^4 + 40 * q^5 - 160 * q^10 - 640 * q^14 - 832 * q^16 + 400 * q^20 - 2040 * q^25 - 2496 * q^26 - 2704 * q^29 - 2176 * q^34 + 6400 * q^40 - 1456 * q^41 - 1920 * q^44 + 7040 * q^46 - 8008 * q^49 + 12480 * q^50 + 14720 * q^56 + 6576 * q^61 + 6912 * q^64 + 1920 * q^65 - 6400 * q^70 + 23616 * q^74 - 48000 * q^76 - 19520 * q^80 + 8960 * q^85 - 37120 * q^86 - 27664 * q^89 + 10880 * q^94

Introduction

L-functions

Modular forms

Varieties

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Representations

Groups

Database

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