LMFDB - Embedded newform 144.5.m.a.19.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [144,5,Mod(19,144)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(144, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 3, 0]))

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

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

chi := DirichletCharacter("144.19");

S:= CuspForms(chi, 5);

N := Newforms(S);

Level:	$ N $	$=$	$ 144 = 2^{4} \cdot 3^{2} $
Weight:	$ k $	$=$	$ 5 $
Character orbit:	$[\chi]$	$=$	144.m (of order $4$, degree $2$, 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:	$14.8852746841$
Analytic rank:	$0$
Dimension:	$14$
Relative dimension:	$7$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{14} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{14} - 4 x^{13} + 15 x^{12} - 34 x^{11} + 62 x^{10} - 312 x^{9} + 1432 x^{8} - 4960 x^{7} + \cdots + 2097152 $ x^14 - 4x^13 + 15x^12 - 34x^11 + 62x^10 - 312x^9 + 1432x^8 - 4960x^7 + 11456x^6 - 19968x^5 + 31744x^4 - 139264x^3 + 491520x^2 - 1048576*x + 2097152
Coefficient ring:	$\Z[a_1, \ldots, a_{25}]$
Coefficient ring index:	$ 2^{21} $
Twist minimal:	no (minimal twist has level 16)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			19.5
Root			$2.79265 + 0.448449i$ of defining polynomial
Character	$\chi$	$=$	144.19
Dual form			144.5.m.a.91.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(2.34420 - 3.24110i) q^{2} +(-5.00945 - 15.1956i) q^{4} +(29.2002 - 29.2002i) q^{5} +59.6196 q^{7} +(-60.9935 - 19.3854i) q^{8} +O(q^{10})$	\(q+(2.34420 - 3.24110i) q^{2} +(-5.00945 - 15.1956i) q^{4} +(29.2002 - 29.2002i) q^{5} +59.6196 q^{7} +(-60.9935 - 19.3854i) q^{8} +(-26.1896 - 163.092i) q^{10} +(18.0837 + 18.0837i) q^{11} +(50.7721 + 50.7721i) q^{13} +(139.760 - 193.233i) q^{14} +(-205.811 + 152.243i) q^{16} +223.769 q^{17} +(14.7360 - 14.7360i) q^{19} +(-589.990 - 297.436i) q^{20} +(101.003 - 16.2192i) q^{22} -739.082 q^{23} -1080.30i q^{25} +(283.577 - 45.5374i) q^{26} +(-298.661 - 905.954i) q^{28} +(-938.904 - 938.904i) q^{29} +938.741i q^{31} +(10.9723 + 1023.94i) q^{32} +(524.560 - 725.259i) q^{34} +(1740.90 - 1740.90i) q^{35} +(263.837 - 263.837i) q^{37} +(-13.2167 - 82.3049i) q^{38} +(-2347.08 + 1214.96i) q^{40} +248.841i q^{41} +(1035.00 + 1035.00i) q^{43} +(184.203 - 365.381i) q^{44} +(-1732.56 + 2395.44i) q^{46} +2018.46i q^{47} +1153.50 q^{49} +(-3501.35 - 2532.44i) q^{50} +(517.171 - 1025.85i) q^{52} +(-833.240 + 833.240i) q^{53} +1056.09 q^{55} +(-3636.41 - 1155.75i) q^{56} +(-5244.06 + 842.101i) q^{58} +(2223.17 + 2223.17i) q^{59} +(-341.374 - 341.374i) q^{61} +(3042.55 + 2200.60i) q^{62} +(3344.42 + 2364.76i) q^{64} +2965.11 q^{65} +(4845.43 - 4845.43i) q^{67} +(-1120.96 - 3400.30i) q^{68} +(-1561.41 - 9723.46i) q^{70} +4180.93 q^{71} +9071.36i q^{73} +(-236.635 - 1473.61i) q^{74} +(-297.741 - 150.103i) q^{76} +(1078.14 + 1078.14i) q^{77} -735.536i q^{79} +(-1564.19 + 10455.2i) q^{80} +(806.518 + 583.333i) q^{82} +(-1441.90 + 1441.90i) q^{83} +(6534.10 - 6534.10i) q^{85} +(5780.81 - 928.294i) q^{86} +(-752.429 - 1453.55i) q^{88} -5071.77i q^{89} +(3027.01 + 3027.01i) q^{91} +(3702.39 + 11230.8i) q^{92} +(6542.05 + 4731.69i) q^{94} -860.586i q^{95} -2523.85 q^{97} +(2704.03 - 3738.60i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 14 q + 2 q^{2} - 8 q^{4} + 2 q^{5} - 4 q^{7} + 92 q^{8}+O(q^{10}) $ 14 * q + 2 * q^2 - 8 * q^4 + 2 * q^5 - 4 * q^7 + 92 * q^8	$ 14 q + 2 q^{2} - 8 q^{4} + 2 q^{5} - 4 q^{7} + 92 q^{8} - 100 q^{10} - 94 q^{11} - 2 q^{13} - 44 q^{14} - 168 q^{16} + 4 q^{17} - 706 q^{19} - 1900 q^{20} + 900 q^{22} - 1148 q^{23} + 3416 q^{26} - 3784 q^{28} - 862 q^{29} - 3208 q^{32} + 7508 q^{34} - 1340 q^{35} - 1826 q^{37} - 3568 q^{38} - 5144 q^{40} + 1694 q^{43} + 14636 q^{44} - 5316 q^{46} + 682 q^{49} - 20070 q^{50} + 20452 q^{52} + 482 q^{53} - 11780 q^{55} + 6952 q^{56} - 20456 q^{58} + 2786 q^{59} - 3778 q^{61} + 11472 q^{62} + 15808 q^{64} + 2020 q^{65} + 7998 q^{67} - 18032 q^{68} + 15296 q^{70} - 19964 q^{71} + 23780 q^{74} - 23996 q^{76} + 9508 q^{77} - 1384 q^{80} + 16016 q^{82} + 17282 q^{83} + 9948 q^{85} + 4796 q^{86} + 7288 q^{88} - 28036 q^{91} + 14632 q^{92} + 432 q^{94} - 4 q^{97} + 12246 q^{98}+O(q^{100}) $ 14 * q + 2 * q^2 - 8 * q^4 + 2 * q^5 - 4 * q^7 + 92 * q^8 - 100 * q^10 - 94 * q^11 - 2 * q^13 - 44 * q^14 - 168 * q^16 + 4 * q^17 - 706 * q^19 - 1900 * q^20 + 900 * q^22 - 1148 * q^23 + 3416 * q^26 - 3784 * q^28 - 862 * q^29 - 3208 * q^32 + 7508 * q^34 - 1340 * q^35 - 1826 * q^37 - 3568 * q^38 - 5144 * q^40 + 1694 * q^43 + 14636 * q^44 - 5316 * q^46 + 682 * q^49 - 20070 * q^50 + 20452 * q^52 + 482 * q^53 - 11780 * q^55 + 6952 * q^56 - 20456 * q^58 + 2786 * q^59 - 3778 * q^61 + 11472 * q^62 + 15808 * q^64 + 2020 * q^65 + 7998 * q^67 - 18032 * q^68 + 15296 * q^70 - 19964 * q^71 + 23780 * q^74 - 23996 * q^76 + 9508 * q^77 - 1384 * q^80 + 16016 * q^82 + 17282 * q^83 + 9948 * q^85 + 4796 * q^86 + 7288 * q^88 - 28036 * q^91 + 14632 * q^92 + 432 * q^94 - 4 * q^97 + 12246 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/144\mathbb{Z}\right)^\times$.

$n$	$37$	$65$	$127$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$1$	$-1$

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 $

$2$	2.34420	−	3.24110i	0.586050	−	0.810275i
$2$	2.34420	−	3.24110i	0.586050	−	0.810275i
$3$		0			0
$3$		0			0
$4$	−5.00945	−	15.1956i	−0.313090	−	0.949723i
$5$	29.2002	−	29.2002i	1.16801	−	1.16801i	0.185330	−	0.982676i	$-0.440665\pi$
$5$	29.2002	−	29.2002i	1.16801	−	1.16801i	0.982676	−	0.185330i	$-0.0593353\pi$
$6$		0			0
$7$	59.6196			1.21673			0.608363	−	0.793659i	$-0.291826\pi$
$7$	59.6196			1.21673			0.608363	+	0.793659i	$0.291826\pi$
$8$	−60.9935	−	19.3854i	−0.953024	−	0.302896i
$9$		0			0
$10$	−26.1896	−	163.092i	−0.261896	−	1.63092i
$11$	18.0837	+	18.0837i	0.149452	+	0.149452i	0.777873	−	0.628421i	$-0.216299\pi$
$11$	18.0837	+	18.0837i	0.149452	+	0.149452i	−0.628421	+	0.777873i	$0.716299\pi$
$12$		0			0
$13$	50.7721	+	50.7721i	0.300427	+	0.300427i	0.841181	−	0.540754i	$-0.181861\pi$
$13$	50.7721	+	50.7721i	0.300427	+	0.300427i	−0.540754	+	0.841181i	$0.681861\pi$
$14$	139.760	−	193.233i	0.713063	−	0.985883i
$15$		0			0
$16$	−205.811	+	152.243i	−0.803949	+	0.594699i
$17$	223.769			0.774289			0.387144	−	0.922019i	$-0.373462\pi$
$17$	223.769			0.774289			0.387144	+	0.922019i	$0.373462\pi$
$18$		0			0
$19$	14.7360	−	14.7360i	0.0408199	−	0.0408199i	−0.686402	−	0.727222i	$-0.740811\pi$
$19$	14.7360	−	14.7360i	0.0408199	−	0.0408199i	0.727222	+	0.686402i	$0.240811\pi$
$20$	−589.990	−	297.436i	−1.47497	−	0.743591i
$21$		0			0
$22$	101.003	−	16.2192i	0.208684	−	0.0335108i
$23$	−739.082			−1.39713			−0.698565	−	0.715547i	$-0.746178\pi$
$23$	−739.082			−1.39713			−0.698565	+	0.715547i	$0.746178\pi$
$24$		0			0
$25$		−	1080.30i		−	1.72848i
$26$	283.577	−	45.5374i	0.419493	−	0.0673631i
$27$		0			0
$28$	−298.661	−	905.954i	−0.380946	−	1.15555i
$29$	−938.904	−	938.904i	−1.11641	−	1.11641i	−0.992263	−	0.124150i	$-0.960380\pi$
$29$	−938.904	−	938.904i	−1.11641	−	1.11641i	−0.124150	−	0.992263i	$-0.539620\pi$
$30$		0			0
$31$			938.741i			0.976838i	0.872609	+	0.488419i	$0.162426\pi$
$31$			938.741i			0.976838i	−0.872609	+	0.488419i	$0.837574\pi$
$32$	10.9723	+	1023.94i	0.0107151	+	0.999943i
$33$		0			0
$34$	524.560	−	725.259i	0.453772	−	0.627387i
$35$	1740.90	−	1740.90i	1.42114	−	1.42114i
$36$		0			0
$37$	263.837	−	263.837i	0.192722	−	0.192722i	−0.604149	−	0.796871i	$-0.706487\pi$
$37$	263.837	−	263.837i	0.192722	−	0.192722i	0.796871	+	0.604149i	$0.206487\pi$
$38$	−13.2167	−	82.3049i	−0.00915283	−	0.0569979i
$39$		0			0
$40$	−2347.08	+	1214.96i	−1.46692	+	0.759353i
$41$			248.841i			0.148031i	0.997257	+	0.0740157i	$0.0235815\pi$
$41$			248.841i			0.148031i	−0.997257	+	0.0740157i	$0.976418\pi$
$42$		0			0
$43$	1035.00	+	1035.00i	0.559765	+	0.559765i	0.929240	−	0.369476i	$-0.120463\pi$
$43$	1035.00	+	1035.00i	0.559765	+	0.559765i	−0.369476	+	0.929240i	$0.620463\pi$
$44$	184.203	−	365.381i	0.0951461	−	0.188730i
$45$		0			0
$46$	−1732.56	+	2395.44i	−0.818788	+	1.13206i
$47$			2018.46i			0.913746i	0.889532	+	0.456873i	$0.151031\pi$
$47$			2018.46i			0.913746i	−0.889532	+	0.456873i	$0.848969\pi$
$48$		0			0
$49$	1153.50			0.480424
$50$	−3501.35	−	2532.44i	−1.40054	−	1.01297i
$51$		0			0
$52$	517.171	−	1025.85i	0.191261	−	0.379383i
$53$	−833.240	+	833.240i	−0.296632	+	0.296632i	−0.839693	−	0.543061i	$-0.817265\pi$
$53$	−833.240	+	833.240i	−0.296632	+	0.296632i	0.543061	+	0.839693i	$0.317265\pi$
$54$		0			0
$55$	1056.09			0.349122
$56$	−3636.41	−	1155.75i	−1.15957	−	0.368542i
$57$		0			0
$58$	−5244.06	+	842.101i	−1.55888	+	0.250327i
$59$	2223.17	+	2223.17i	0.638660	+	0.638660i	0.950225	−	0.311565i	$-0.100853\pi$
$59$	2223.17	+	2223.17i	0.638660	+	0.638660i	−0.311565	+	0.950225i	$0.600853\pi$
$60$		0			0
$61$	−341.374	−	341.374i	−0.0917425	−	0.0917425i	0.659746	−	0.751489i	$-0.270664\pi$
$61$	−341.374	−	341.374i	−0.0917425	−	0.0917425i	−0.751489	+	0.659746i	$0.770664\pi$
$62$	3042.55	+	2200.60i	0.791507	+	0.572476i
$63$		0			0
$64$	3344.42	+	2364.76i	0.816508	+	0.577334i
$65$	2965.11			0.701800
$66$		0			0
$67$	4845.43	−	4845.43i	1.07940	−	1.07940i	0.0828379	−	0.996563i	$-0.473602\pi$
$67$	4845.43	−	4845.43i	1.07940	−	1.07940i	0.996563	−	0.0828379i	$-0.0263984\pi$
$68$	−1120.96	−	3400.30i	−0.242422	−	0.735360i
$69$		0			0
$70$	−1561.41	−	9723.46i	−0.318656	−	1.98438i
$71$	4180.93			0.829386			0.414693	−	0.909961i	$-0.363889\pi$
$71$	4180.93			0.829386			0.414693	+	0.909961i	$0.363889\pi$
$72$		0			0
$73$			9071.36i			1.70226i	0.524953	+	0.851131i	$0.324083\pi$
$73$			9071.36i			1.70226i	−0.524953	+	0.851131i	$0.675917\pi$
$74$	−236.635	−	1473.61i	−0.0432131	−	0.269103i
$75$		0			0
$76$	−297.741	−	150.103i	−0.0515479	−	0.0259873i
$77$	1078.14	+	1078.14i	0.181842	+	0.181842i
$78$		0			0
$79$		−	735.536i		−	0.117855i	−0.998262	−	0.0589277i	$-0.981232\pi$
$79$		−	735.536i		−	0.117855i	0.998262	−	0.0589277i	$-0.0187682\pi$
$80$	−1564.19	+	10455.2i	−0.244405	+	1.63363i
$81$		0			0
$82$	806.518	+	583.333i	0.119946	+	0.0867539i
$83$	−1441.90	+	1441.90i	−0.209305	+	0.209305i	−0.803972	−	0.594667i	$-0.797284\pi$
$83$	−1441.90	+	1441.90i	−0.209305	+	0.209305i	0.594667	+	0.803972i	$0.297284\pi$
$84$		0			0
$85$	6534.10	−	6534.10i	0.904374	−	0.904374i
$86$	5780.81	−	928.294i	0.781613	−	0.125513i
$87$		0			0
$88$	−752.429	−	1453.55i	−0.0971628	−	0.187700i
$89$		−	5071.77i		−	0.640294i	−0.947368	−	0.320147i	$-0.896268\pi$
$89$		−	5071.77i		−	0.640294i	0.947368	−	0.320147i	$-0.103732\pi$
$90$		0			0
$91$	3027.01	+	3027.01i	0.365537	+	0.365537i
$92$	3702.39	+	11230.8i	0.437428	+	1.32689i
$93$		0			0
$94$	6542.05	+	4731.69i	0.740385	+	0.535501i
$95$		−	860.586i		−	0.0953558i
$96$		0			0
$97$	−2523.85			−0.268238			−0.134119	−	0.990965i	$-0.542820\pi$
$97$	−2523.85			−0.268238			−0.134119	+	0.990965i	$0.542820\pi$
$98$	2704.03	−	3738.60i	0.281552	−	0.389275i
$99$		0			0
$100$	−16415.7	+	5411.70i	−1.64157	+	0.541170i
$101$	−425.990	+	425.990i	−0.0417596	+	0.0417596i	−0.727678	−	0.685919i	$-0.759401\pi$
$101$	−425.990	+	425.990i	−0.0417596	+	0.0417596i	0.685919	+	0.727678i	$0.259401\pi$
$102$		0			0
$103$	13178.6			1.24221			0.621103	−	0.783729i	$-0.286685\pi$
$103$	13178.6			1.24221			0.621103	+	0.783729i	$0.286685\pi$
$104$	−2112.53	−	4081.00i	−0.195316	−	0.377312i
$105$		0			0
$106$	747.332	+	4653.90i	0.0665123	+	0.414195i
$107$	10821.5	+	10821.5i	0.945190	+	0.945190i	0.998574	−	0.0533845i	$-0.0170009\pi$
$107$	10821.5	+	10821.5i	0.945190	+	0.945190i	−0.0533845	+	0.998574i	$0.517001\pi$
$108$		0			0
$109$	−1428.57	−	1428.57i	−0.120240	−	0.120240i	0.644426	−	0.764666i	$-0.277096\pi$
$109$	−1428.57	−	1428.57i	−0.120240	−	0.120240i	−0.764666	+	0.644426i	$0.777096\pi$
$110$	2475.69	−	3422.90i	0.204603	−	0.282885i
$111$		0			0
$112$	−12270.4	+	9076.66i	−0.978186	+	0.723586i
$113$	−20121.5			−1.57581			−0.787904	−	0.615798i	$-0.788834\pi$
$113$	−20121.5			−1.57581			−0.787904	+	0.615798i	$0.788834\pi$
$114$		0			0
$115$	−21581.3	+	21581.3i	−1.63186	+	1.63186i
$116$	−9563.79	+	18970.6i	−0.710745	+	1.40982i
$117$		0			0
$118$	12417.1	−	1993.96i	0.891776	−	0.143203i
$119$	13341.0			0.942098
$120$		0			0
$121$		−	13987.0i		−	0.955328i
$122$	−1906.68	+	306.178i	−0.128102	+	0.0205709i
$123$		0			0
$124$	14264.7	−	4702.57i	0.927725	−	0.305839i
$125$	−13294.8	−	13294.8i	−0.850865	−	0.850865i
$126$		0			0
$127$		−	2630.54i		−	0.163094i	−0.996669	−	0.0815470i	$-0.974014\pi$
$127$		−	2630.54i		−	0.163094i	0.996669	−	0.0815470i	$-0.0259861\pi$
$128$	15504.4	−	5296.11i	0.946314	−	0.323249i
$129$		0			0
$130$	6950.80	−	9610.20i	0.411290	−	0.568651i
$131$	−12437.0	+	12437.0i	−0.724722	+	0.724722i	−0.969563	−	0.244841i	$-0.921264\pi$
$131$	−12437.0	+	12437.0i	−0.724722	+	0.724722i	0.244841	+	0.969563i	$0.421264\pi$
$132$		0			0
$133$	878.554	−	878.554i	0.0496667	−	0.0496667i
$134$	−4345.86	−	27063.2i	−0.242028	−	1.50719i
$135$		0			0
$136$	−13648.5	−	4337.85i	−0.737915	−	0.234529i
$137$		−	15392.0i		−	0.820078i	−0.912068	−	0.410039i	$-0.865515\pi$
$137$		−	15392.0i		−	0.820078i	0.912068	−	0.410039i	$-0.134485\pi$
$138$		0			0
$139$	12151.3	+	12151.3i	0.628915	+	0.628915i	0.947795	−	0.318880i	$-0.103307\pi$
$139$	12151.3	+	12151.3i	0.628915	+	0.628915i	−0.318880	+	0.947795i	$0.603307\pi$
$140$	−35175.0	−	17733.0i	−1.79464	−	0.904747i
$141$		0			0
$142$	9800.95	−	13550.8i	0.486062	−	0.672030i
$143$			1836.29i			0.0897987i
$144$		0			0
$145$	−54832.3			−2.60796
$146$	29401.2	+	21265.1i	1.37930	+	0.997611i
$147$		0			0
$148$	−5330.83	−	2687.48i	−0.243373	−	0.122693i
$149$	20803.7	−	20803.7i	0.937062	−	0.937062i	−0.0610710	−	0.998133i	$-0.519452\pi$
$149$	20803.7	−	20803.7i	0.937062	−	0.937062i	0.998133	+	0.0610710i	$0.0194516\pi$
$150$		0			0
$151$	−7756.67			−0.340190			−0.170095	−	0.985428i	$-0.554407\pi$
$151$	−7756.67			−0.340190			−0.170095	+	0.985428i	$0.554407\pi$
$152$	−1184.46	+	613.137i	−0.0512665	+	0.0265381i
$153$		0			0
$154$	6021.75	−	966.985i	0.253911	−	0.0407735i
$155$	27411.4	+	27411.4i	1.14095	+	1.14095i
$156$		0			0
$157$	7040.20	+	7040.20i	0.285618	+	0.285618i	0.835345	−	0.549727i	$-0.185268\pi$
$157$	7040.20	+	7040.20i	0.285618	+	0.285618i	−0.549727	+	0.835345i	$0.685268\pi$
$158$	−2383.95	−	1724.24i	−0.0954953	−	0.0690692i
$159$		0			0
$160$	30219.6	+	29578.8i	1.18045	+	1.15542i
$161$	−44063.8			−1.69993
$162$		0			0
$163$	7273.43	−	7273.43i	0.273756	−	0.273756i	−0.556854	−	0.830610i	$-0.687992\pi$
$163$	7273.43	−	7273.43i	0.273756	−	0.273756i	0.830610	+	0.556854i	$0.187992\pi$
$164$	3781.28	−	1246.56i	0.140589	−	0.0463472i
$165$		0			0
$166$	1293.24	+	8053.46i	0.0469313	+	0.292258i
$167$	−30069.6			−1.07819			−0.539095	−	0.842245i	$-0.681234\pi$
$167$	−30069.6			−1.07819			−0.539095	+	0.842245i	$0.681234\pi$
$168$		0			0
$169$		−	23405.4i		−	0.819488i
$170$	−5860.43	−	36494.9i	−0.202783	−	1.26280i
$171$		0			0
$172$	10542.7	−	20912.3i	0.356365	−	0.706878i
$173$	8329.72	+	8329.72i	0.278316	+	0.278316i	0.832436	−	0.554121i	$-0.186945\pi$
$173$	8329.72	+	8329.72i	0.278316	+	0.278316i	−0.554121	+	0.832436i	$0.686945\pi$
$174$		0			0
$175$		−	64406.9i		−	2.10308i
$176$	−6474.93	−	968.707i	−0.209031	−	0.0312728i
$177$		0			0
$178$	−16438.1	−	11889.2i	−0.518814	−	0.375244i
$179$	7537.56	−	7537.56i	0.235247	−	0.235247i	−0.579632	−	0.814879i	$-0.696803\pi$
$179$	7537.56	−	7537.56i	0.235247	−	0.235247i	0.814879	+	0.579632i	$0.196803\pi$
$180$		0			0
$181$	3802.64	−	3802.64i	0.116072	−	0.116072i	−0.646685	−	0.762757i	$-0.723845\pi$
$181$	3802.64	−	3802.64i	0.116072	−	0.116072i	0.762757	+	0.646685i	$0.223845\pi$
$182$	16906.8	−	2714.92i	0.510409	−	0.0819624i
$183$		0			0
$184$	45079.2	+	14327.4i	1.33150	+	0.423185i
$185$		−	15408.2i		−	0.450202i
$186$		0			0
$187$	4046.58	+	4046.58i	0.115719	+	0.115719i
$188$	30671.7	−	10111.4i	0.867806	−	0.286085i
$189$		0			0
$190$	−2789.25	−	2017.39i	−0.0772644	−	0.0558833i
$191$		−	52248.1i		−	1.43220i	−0.697997	−	0.716100i	$-0.745925\pi$
$191$		−	52248.1i		−	1.43220i	0.697997	−	0.716100i	$-0.254075\pi$
$192$		0			0
$193$	−24380.0			−0.654514			−0.327257	−	0.944935i	$-0.606124\pi$
$193$	−24380.0			−0.654514			−0.327257	+	0.944935i	$0.606124\pi$
$194$	−5916.41	+	8180.04i	−0.157201	+	0.217346i
$195$		0			0
$196$	−5778.38	−	17528.0i	−0.150416	−	0.456269i
$197$	−31537.9	+	31537.9i	−0.812644	+	0.812644i	−0.985030	−	0.172386i	$-0.944852\pi$
$197$	−31537.9	+	31537.9i	−0.812644	+	0.812644i	0.172386	+	0.985030i	$0.444852\pi$
$198$		0			0
$199$	−71129.4			−1.79615			−0.898076	−	0.439841i	$-0.855035\pi$
$199$	−71129.4			−1.79615			−0.898076	+	0.439841i	$0.855035\pi$
$200$	−20942.0	+	65891.2i	−0.523549	+	1.64728i
$201$		0			0
$202$	382.069	+	2379.28i	0.00936353	+	0.0583099i
$203$	−55977.1	−	55977.1i	−1.35837	−	1.35837i
$204$		0			0
$205$	7266.19	+	7266.19i	0.172902	+	0.172902i
$206$	30893.2	−	42713.0i	0.727995	−	1.00653i
$207$		0			0
$208$	−18179.1	−	2719.76i	−0.420191	−	0.0628643i
$209$	532.962			0.0122012
$210$		0			0
$211$	−13393.4	+	13393.4i	−0.300833	+	0.300833i	−0.841340	−	0.540507i	$-0.818233\pi$
$211$	−13393.4	+	13393.4i	−0.300833	+	0.300833i	0.540507	+	0.841340i	$0.318233\pi$
$212$	16835.6	+	8487.49i	0.374591	+	0.188846i
$213$		0			0
$214$	60441.2	−	9705.77i	1.31979	−	0.211935i
$215$	60444.6			1.30762
$216$		0			0
$217$			55967.4i			1.18854i
$218$	−7978.99	+	1281.28i	−0.167894	+	0.0269607i
$219$		0			0
$220$	−5290.44	−	16047.9i	−0.109307	−	0.331569i
$221$	11361.2	+	11361.2i	0.232617	+	0.232617i
$222$		0			0
$223$			54266.9i			1.09125i	0.838029	+	0.545626i	$0.183708\pi$
$223$			54266.9i			1.09125i	−0.838029	+	0.545626i	$0.816292\pi$
$224$	654.161	+	61047.0i	0.0130373	+	1.21666i
$225$		0			0
$226$	−47168.8	+	65215.7i	−0.923502	+	1.27684i
$227$	−14529.0	+	14529.0i	−0.281957	+	0.281957i	−0.833889	−	0.551932i	$-0.813891\pi$
$227$	−14529.0	+	14529.0i	−0.281957	+	0.281957i	0.551932	+	0.833889i	$0.313891\pi$
$228$		0			0
$229$	21618.1	−	21618.1i	0.412237	−	0.412237i	−0.470280	−	0.882517i	$-0.655847\pi$
$229$	21618.1	−	21618.1i	0.412237	−	0.412237i	0.882517	+	0.470280i	$0.155847\pi$
$230$	19356.2	+	120538.i	0.365902	+	2.27860i
$231$		0			0
$232$	39066.0	+	75468.0i	0.725811	+	1.40213i
$233$			92103.6i			1.69654i	0.529562	+	0.848271i	$0.322356\pi$
$233$			92103.6i			1.69654i	−0.529562	+	0.848271i	$0.677644\pi$
$234$		0			0
$235$	58939.5	+	58939.5i	1.06726	+	1.06726i
$236$	22645.5	−	44919.3i	0.406592	−	0.806508i
$237$		0			0
$238$	31274.1	−	43239.6i	0.552116	−	0.763358i
$239$			70411.0i			1.23266i	0.787487	+	0.616332i	$0.211382\pi$
$239$			70411.0i			1.23266i	−0.787487	+	0.616332i	$0.788618\pi$
$240$		0			0
$241$	22402.6			0.385714			0.192857	−	0.981227i	$-0.438225\pi$
$241$	22402.6			0.385714			0.192857	+	0.981227i	$0.438225\pi$
$242$	−45333.1	−	32788.2i	−0.774078	−	0.559870i
$243$		0			0
$244$	−3477.28	+	6897.47i	−0.0584063	+	0.115854i
$245$	33682.3	−	33682.3i	0.561138	−	0.561138i
$246$		0			0
$247$	1496.35			0.0245268
$248$	18197.8	−	57257.1i	0.295880	−	0.930949i
$249$		0			0
$250$	−74255.3	+	11924.1i	−1.18808	+	0.190785i
$251$	72407.6	+	72407.6i	1.14931	+	1.14931i	0.986689	+	0.162621i	$0.0519947\pi$
$251$	72407.6	+	72407.6i	1.14931	+	1.14931i	0.162621	+	0.986689i	$0.448005\pi$
$252$		0			0
$253$	−13365.3	−	13365.3i	−0.208804	−	0.208804i
$254$	−8525.85	−	6166.52i	−0.132151	−	0.0955813i
$255$		0			0
$256$	19180.2	−	62666.5i	0.292667	−	0.956214i
$257$	56466.3			0.854916			0.427458	−	0.904035i	$-0.359409\pi$
$257$	56466.3			0.854916			0.427458	+	0.904035i	$0.359409\pi$
$258$		0			0
$259$	15729.9	−	15729.9i	0.234490	−	0.234490i
$260$	−14853.5	−	45056.5i	−0.219727	−	0.666516i
$261$		0			0
$262$	11154.7	+	69464.1i	0.162501	+	1.01195i
$263$	−76515.5			−1.10621			−0.553105	−	0.833111i	$-0.686557\pi$
$263$	−76515.5			−1.10621			−0.553105	+	0.833111i	$0.686557\pi$
$264$		0			0
$265$			48661.5i			0.692937i
$266$	−787.974	−	4906.99i	−0.0111365	−	0.0693508i
$267$		0			0
$268$	−97902.0	−	49356.2i	−1.36308	−	0.687182i
$269$	−1928.97	−	1928.97i	−0.0266576	−	0.0266576i	0.693652	−	0.720310i	$-0.256000\pi$
$269$	−1928.97	−	1928.97i	−0.0266576	−	0.0266576i	−0.720310	+	0.693652i	$0.756000\pi$
$270$		0			0
$271$		−	128685.i		−	1.75222i	−0.482109	−	0.876111i	$-0.660129\pi$
$271$		−	128685.i		−	1.75222i	0.482109	−	0.876111i	$-0.339871\pi$
$272$	−46054.2	+	34067.3i	−0.622488	+	0.460468i
$273$		0			0
$274$	−49887.1	−	36082.0i	−0.664488	−	0.480607i
$275$	19535.8	−	19535.8i	0.258324	−	0.258324i
$276$		0			0
$277$	56674.5	−	56674.5i	0.738632	−	0.738632i	−0.233681	−	0.972313i	$-0.575077\pi$
$277$	56674.5	−	56674.5i	0.738632	−	0.738632i	0.972313	+	0.233681i	$0.0750772\pi$
$278$	67868.5	−	10898.5i	0.878170	−	0.141018i
$279$		0			0
$280$	−139932.	+	72435.7i	−1.78484	+	0.923925i
$281$		−	10599.7i		−	0.134240i	−0.997745	−	0.0671200i	$-0.978619\pi$
$281$		−	10599.7i		−	0.134240i	0.997745	−	0.0671200i	$-0.0213810\pi$
$282$		0			0
$283$	63293.6	+	63293.6i	0.790291	+	0.790291i	0.981541	−	0.191251i	$-0.0612543\pi$
$283$	63293.6	+	63293.6i	0.790291	+	0.790291i	−0.191251	+	0.981541i	$0.561254\pi$
$284$	−20944.2	−	63531.7i	−0.259673	−	0.787687i
$285$		0			0
$286$	5951.61	+	4304.64i	0.0727617	+	0.0526266i
$287$			14835.8i			0.180114i
$288$		0			0
$289$	−33448.2			−0.400477
$290$	−128538.	+	177717.i	−1.52839	+	2.11316i
$291$		0			0
$292$	137844.	−	45442.5i	1.61668	−	0.532962i
$293$	89072.9	−	89072.9i	1.03755	−	1.03755i	0.0382867	−	0.999267i	$-0.487810\pi$
$293$	89072.9	−	89072.9i	1.03755	−	1.03755i	0.999267	−	0.0382867i	$-0.0121900\pi$
$294$		0			0
$295$	129834.			1.49192
$296$	−21206.9	+	10977.8i	−0.242044	+	0.125294i
$297$		0			0
$298$	−18658.8	−	116195.i	−0.210113	−	1.30844i
$299$	−37524.7	−	37524.7i	−0.419735	−	0.419735i
$300$		0			0
$301$	61706.6	+	61706.6i	0.681080	+	0.681080i
$302$	−18183.2	+	25140.1i	−0.199368	+	0.275647i
$303$		0			0
$304$	−789.377	+	5276.27i	−0.00854157	+	0.0570927i
$305$	−19936.3			−0.214312
$306$		0			0
$307$	−124227.	+	124227.i	−1.31807	+	1.31807i	−0.402769	+	0.915302i	$0.631952\pi$
$307$	−124227.	+	124227.i	−1.31807	+	1.31807i	−0.915302	+	0.402769i	$0.868048\pi$
$308$	10982.1	−	21783.9i	0.115767	−	0.229633i
$309$		0			0
$310$	153101.	−	24585.2i	1.59314	−	0.255830i
$311$	−15733.9			−0.162673			−0.0813364	−	0.996687i	$-0.525919\pi$
$311$	−15733.9			−0.162673			−0.0813364	+	0.996687i	$0.525919\pi$
$312$		0			0
$313$		−	104554.i		−	1.06721i	−0.845733	−	0.533606i	$-0.820837\pi$
$313$		−	104554.i		−	1.06721i	0.845733	−	0.533606i	$-0.179163\pi$
$314$	39321.6	−	6314.34i	0.398816	−	0.0640426i
$315$		0			0
$316$	−11176.9	+	3684.63i	−0.111930	+	0.0368994i
$317$	−45847.9	−	45847.9i	−0.456248	−	0.456248i	0.441174	−	0.897422i	$-0.354562\pi$
$317$	−45847.9	−	45847.9i	−0.456248	−	0.456248i	−0.897422	+	0.441174i	$0.854562\pi$
$318$		0			0
$319$		−	33957.7i		−	0.333700i
$320$	166709.	−	28606.1i	1.62802	−	0.279356i
$321$		0			0
$322$	−103294.	+	142815.i	−0.996241	+	1.37741i
$323$	3297.46	−	3297.46i	0.0316064	−	0.0316064i
$324$		0			0
$325$	54849.0	−	54849.0i	0.519281	−	0.519281i
$326$	−6523.53	−	40624.3i	−0.0613829	−	0.382253i
$327$		0			0
$328$	4823.87	−	15177.7i	0.0448382	−	0.141077i
$329$			120340.i			1.11178i
$330$		0			0
$331$	−137545.	−	137545.i	−1.25542	−	1.25542i	−0.953258	−	0.302159i	$-0.902293\pi$
$331$	−137545.	−	137545.i	−1.25542	−	1.25542i	−0.302159	−	0.953258i	$-0.597707\pi$
$332$	29133.7	+	14687.4i	0.264313	+	0.133250i
$333$		0			0
$334$	−70489.2	+	97458.6i	−0.631873	+	0.873630i
$335$		−	282975.i		−	2.52149i
$336$		0			0
$337$	−40849.6			−0.359690			−0.179845	−	0.983695i	$-0.557560\pi$
$337$	−40849.6			−0.359690			−0.179845	+	0.983695i	$0.557560\pi$
$338$	−75859.2	−	54866.9i	−0.664010	−	0.480261i
$339$		0			0
$340$	−132022.	−	66557.2i	−1.14206	−	0.575754i
$341$	−16975.9	+	16975.9i	−0.145990	+	0.145990i
$342$		0			0
$343$	−74375.6			−0.632182
$344$	−43064.6	−	83192.5i	−0.363918	−	0.703019i
$345$		0			0
$346$	46524.0	−	7470.91i	0.388619	−	0.0624053i
$347$	−21361.1	−	21361.1i	−0.177404	−	0.177404i	0.612819	−	0.790223i	$-0.290035\pi$
$347$	−21361.1	−	21361.1i	−0.177404	−	0.177404i	−0.790223	+	0.612819i	$0.790035\pi$
$348$		0			0
$349$	139275.	+	139275.i	1.14347	+	1.14347i	0.987812	+	0.155654i	$0.0497484\pi$
$349$	139275.	+	139275.i	1.14347	+	1.14347i	0.155654	+	0.987812i	$0.450252\pi$
$350$	−208749.	−	150983.i	−1.70408	−	1.23251i
$351$		0			0
$352$	−18318.2	+	18715.1i	−0.147842	+	0.151045i
$353$	100461.			0.806209			0.403105	−	0.915154i	$-0.367931\pi$
$353$	100461.			0.806209			0.403105	+	0.915154i	$0.367931\pi$
$354$		0			0
$355$	122084.	−	122084.i	0.968728	−	0.968728i
$356$	−77068.4	+	25406.7i	−0.608102	+	0.200470i
$357$		0			0
$358$	−6760.42	−	42099.5i	−0.0527482	−	0.328482i
$359$	−96352.7			−0.747609			−0.373805	−	0.927507i	$-0.621947\pi$
$359$	−96352.7			−0.747609			−0.373805	+	0.927507i	$0.621947\pi$
$360$		0			0
$361$			129887.i			0.996667i
$362$	−3410.58	−	21238.9i	−0.0260262	−	0.162074i
$363$		0			0
$364$	30833.5	−	61160.9i	0.232713	−	0.461605i
$365$	264885.	+	264885.i	1.98825	+	1.98825i
$366$		0			0
$367$		−	190661.i		−	1.41557i	−0.706429	−	0.707784i	$-0.749695\pi$
$367$		−	190661.i		−	1.41557i	0.706429	−	0.707784i	$-0.250305\pi$
$368$	152111.	−	112520.i	1.12322	−	0.830871i
$369$		0			0
$370$	−49939.4	−	36119.8i	−0.364787	−	0.263841i
$371$	−49677.5	+	49677.5i	−0.360920	+	0.360920i
$372$		0			0
$373$	51771.9	−	51771.9i	0.372114	−	0.372114i	−0.496133	−	0.868247i	$-0.665247\pi$
$373$	51771.9	−	51771.9i	0.372114	−	0.372114i	0.868247	+	0.496133i	$0.165247\pi$
$374$	22601.3	−	3629.37i	0.161581	−	0.0259471i
$375$		0			0
$376$	39128.7	−	123113.i	0.276770	−	0.870821i
$377$		−	95340.2i		−	0.670801i
$378$		0			0
$379$	121232.	+	121232.i	0.843990	+	0.843990i	0.989375	−	0.145385i	$-0.0464420\pi$
$379$	121232.	+	121232.i	0.843990	+	0.843990i	−0.145385	+	0.989375i	$0.546442\pi$
$380$	−13077.1	+	4311.06i	−0.0905616	+	0.0298550i
$381$		0			0
$382$	−169341.	−	122480.i	−1.16048	−	0.839341i
$383$		−	8262.20i		−	0.0563246i	−0.999603	−	0.0281623i	$-0.991034\pi$
$383$		−	8262.20i		−	0.0563246i	0.999603	−	0.0281623i	$-0.00896552\pi$
$384$		0			0
$385$	62963.9			0.424786
$386$	−57151.6	+	79018.0i	−0.383578	+	0.530336i
$387$		0			0
$388$	12643.1	+	38351.3i	0.0839826	+	0.254752i
$389$	−43964.9	+	43964.9i	−0.290541	+	0.290541i	−0.837294	−	0.546753i	$-0.815864\pi$
$389$	−43964.9	+	43964.9i	−0.290541	+	0.290541i	0.546753	+	0.837294i	$0.315864\pi$
$390$		0			0
$391$	−165384.			−1.08178
$392$	−70355.8	−	22360.9i	−0.457855	−	0.145518i
$393$		0			0
$394$	28286.3	+	176149.i	0.182215	+	1.13471i
$395$	−21477.8	−	21477.8i	−0.137656	−	0.137656i
$396$		0			0
$397$	72864.3	+	72864.3i	0.462311	+	0.462311i	0.899412	−	0.437101i	$-0.143995\pi$
$397$	72864.3	+	72864.3i	0.462311	+	0.462311i	−0.437101	+	0.899412i	$0.643995\pi$
$398$	−166742.	+	230537.i	−1.05263	+	1.45538i
$399$		0			0
$400$	164468.	+	222337.i	1.02792	+	1.38961i
$401$	−237249.			−1.47542			−0.737711	−	0.675116i	$-0.764093\pi$
$401$	−237249.			−1.47542			−0.737711	+	0.675116i	$0.764093\pi$
$402$		0			0
$403$	−47661.9	+	47661.9i	−0.293468	+	0.293468i
$404$	8607.13	+	4339.18i	0.0527346	+	0.0265855i
$405$		0			0
$406$	−312649.	+	50205.8i	−1.89673	+	0.304580i
$407$	9542.29			0.0576055
$408$		0			0
$409$			150042.i			0.896945i	0.893797	+	0.448473i	$0.148032\pi$
$409$			150042.i			0.896945i	−0.893797	+	0.448473i	$0.851968\pi$
$410$	40583.9	−	6517.04i	0.241427	−	0.0387688i
$411$		0			0
$412$	−66017.3	−	200256.i	−0.388923	−	1.17975i
$413$	132545.	+	132545.i	0.777074	+	0.777074i
$414$		0			0
$415$			84207.5i			0.488939i
$416$	−51430.6	+	52544.7i	−0.297190	+	0.303629i
$417$		0			0
$418$	1249.37	−	1727.38i	0.00715053	−	0.00988635i
$419$	−71760.1	+	71760.1i	−0.408747	+	0.408747i	−0.881302	−	0.472554i	$-0.843332\pi$
$419$	−71760.1	+	71760.1i	−0.408747	+	0.408747i	0.472554	+	0.881302i	$0.343332\pi$
$420$		0			0
$421$	−209821.	+	209821.i	−1.18382	+	1.18382i	−0.205070	+	0.978747i	$0.565742\pi$
$421$	−209821.	+	209821.i	−1.18382	+	1.18382i	−0.978747	+	0.205070i	$0.934258\pi$
$422$	12012.5	+	74806.1i	0.0674542	+	0.420061i
$423$		0			0
$424$	66974.9	−	34669.6i	0.372546	−	0.192849i
$425$		−	241738.i		−	1.33834i
$426$		0			0
$427$	−20352.6	−	20352.6i	−0.111626	−	0.111626i
$428$	110229.	−	218648.i	0.601739	−	1.19360i
$429$		0			0
$430$	141694.	−	195907.i	0.766329	−	1.05953i
$431$		−	123853.i		−	0.666731i	−0.942798	−	0.333366i	$-0.891816\pi$
$431$		−	123853.i		−	0.666731i	0.942798	−	0.333366i	$-0.108184\pi$
$432$		0			0
$433$	−265114.			−1.41402			−0.707012	−	0.707202i	$-0.749957\pi$
$433$	−265114.			−1.41402			−0.707012	+	0.707202i	$0.749957\pi$
$434$	181396.	+	131199.i	0.963047	+	0.696547i
$435$		0			0
$436$	−14551.6	+	28864.3i	−0.0765486	+	0.151841i
$437$	−10891.1	+	10891.1i	−0.0570307	+	0.0570307i
$438$		0			0
$439$	186089.			0.965590			0.482795	−	0.875734i	$-0.339622\pi$
$439$	186089.			0.965590			0.482795	+	0.875734i	$0.339622\pi$
$440$	−64414.8	−	20472.7i	−0.332721	−	0.105748i
$441$		0			0
$442$	63456.0	−	10189.9i	0.324809	−	0.0521585i
$443$	−25618.8	−	25618.8i	−0.130542	−	0.130542i	0.638817	−	0.769359i	$-0.279424\pi$
$443$	−25618.8	−	25618.8i	−0.130542	−	0.130542i	−0.769359	+	0.638817i	$0.779424\pi$
$444$		0			0
$445$	−148096.	−	148096.i	−0.747867	−	0.747867i
$446$	175884.	+	127212.i	0.884214	+	0.639529i
$447$		0			0
$448$	199393.	+	140986.i	0.993467	+	0.702458i
$449$	2307.59			0.0114463			0.00572316	−	0.999984i	$-0.498178\pi$
$449$	2307.59			0.0114463			0.00572316	+	0.999984i	$0.498178\pi$
$450$		0			0
$451$	−4499.96	+	4499.96i	−0.0221236	+	0.0221236i
$452$	100798.	+	305758.i	0.493370	+	1.49658i
$453$		0			0
$454$	13031.0	+	81148.6i	0.0632217	+	0.393704i
$455$	176778.			0.853899
$456$		0			0
$457$		−	262378.i		−	1.25631i	−0.778090	−	0.628153i	$-0.783811\pi$
$457$		−	262378.i		−	1.25631i	0.778090	−	0.628153i	$-0.216189\pi$
$458$	−19389.3	−	120744.i	−0.0924338	−	0.575617i
$459$		0			0
$460$	436051.	+	219830.i	2.06073	+	1.03889i
$461$	−136771.	−	136771.i	−0.643564	−	0.643564i	0.307866	−	0.951430i	$-0.400385\pi$
$461$	−136771.	−	136771.i	−0.643564	−	0.643564i	−0.951430	+	0.307866i	$0.900385\pi$
$462$		0			0
$463$		−	22250.8i		−	0.103797i	−0.998652	−	0.0518983i	$-0.983473\pi$
$463$		−	22250.8i		−	0.103797i	0.998652	−	0.0518983i	$-0.0165272\pi$
$464$	336178.	+	50295.2i	1.56147	+	0.233610i
$465$		0			0
$466$	298517.	+	215909.i	1.37467	+	0.994259i
$467$	−175541.	+	175541.i	−0.804906	+	0.804906i	−0.983858	−	0.178952i	$-0.942729\pi$
$467$	−175541.	+	175541.i	−0.804906	+	0.804906i	0.178952	+	0.983858i	$0.442729\pi$
$468$		0			0
$469$	288883.	−	288883.i	1.31334	−	1.31334i
$470$	329195.	−	52862.7i	1.49024	−	0.239306i
$471$		0			0
$472$	−92502.2	−	178696.i	−0.415210	−	0.802105i
$473$			37433.4i			0.167316i
$474$		0			0
$475$	−15919.3	−	15919.3i	−0.0705563	−	0.0705563i
$476$	−66831.3	−	202725.i	−0.294962	−	0.894732i
$477$		0			0
$478$	228209.	+	165057.i	0.998796	+	0.722403i
$479$			117920.i			0.513945i	0.966419	+	0.256973i	$0.0827250\pi$
$479$			117920.i			0.513945i	−0.966419	+	0.256973i	$0.917275\pi$
$480$		0			0
$481$	26791.1			0.115798
$482$	52516.3	−	72609.2i	0.226048	−	0.312534i
$483$		0			0
$484$	−212540.	+	70066.9i	−0.907297	+	0.299104i
$485$	−73696.7	+	73696.7i	−0.313303	+	0.313303i
$486$		0			0
$487$	−449942.			−1.89714			−0.948568	−	0.316574i	$-0.897467\pi$
$487$	−449942.			−1.89714			−0.948568	+	0.316574i	$0.897467\pi$
$488$	14203.9	+	27439.2i	0.0596443	+	0.115221i
$489$		0			0
$490$	−30209.6	−	188126.i	−0.125821	−	0.783531i
$491$	122509.	+	122509.i	0.508166	+	0.508166i	0.913963	−	0.405797i	$-0.133006\pi$
$491$	122509.	+	122509.i	0.508166	+	0.508166i	−0.405797	+	0.913963i	$0.633006\pi$
$492$		0			0
$493$	−210098.	−	210098.i	−0.864426	−	0.864426i
$494$	3507.75	−	4849.83i	0.0143739	−	0.0198734i
$495$		0			0
$496$	−142917.	−	193203.i	−0.580924	−	0.785327i
$497$	249266.			1.00914
$498$		0			0
$499$	−44886.9	+	44886.9i	−0.180268	+	0.180268i	−0.791473	−	0.611205i	$-0.790685\pi$
$499$	−44886.9	+	44886.9i	−0.180268	+	0.180268i	0.611205	+	0.791473i	$0.290685\pi$
$500$	−135422.	+	268621.i	−0.541689	+	1.07448i
$501$		0			0
$502$	404418.	−	64942.3i	1.60481	−	0.257704i
$503$	−235778.			−0.931896			−0.465948	−	0.884812i	$-0.654287\pi$
$503$	−235778.			−0.931896			−0.465948	+	0.884812i	$0.654287\pi$
$504$		0			0
$505$			24877.9i			0.0975509i
$506$	−74649.4	+	11987.3i	−0.291558	+	0.0468190i
$507$		0			0
$508$	−39972.6	+	13177.6i	−0.154894	+	0.0510632i
$509$	−227812.	−	227812.i	−0.879308	−	0.879308i	0.114155	−	0.993463i	$-0.463584\pi$
$509$	−227812.	−	227812.i	−0.879308	−	0.879308i	−0.993463	+	0.114155i	$0.963584\pi$
$510$		0			0
$511$			540831.i			2.07119i
$512$	−158146.	−	209068.i	−0.603279	−	0.797530i
$513$		0			0
$514$	132368.	−	183013.i	0.501024	−	0.692717i
$515$	384816.	−	384816.i	1.45090	−	1.45090i
$516$		0			0
$517$	−36501.3	+	36501.3i	−0.136561	+	0.136561i
$518$	−14108.1	−	87856.0i	−0.0525785	−	0.327425i
$519$		0			0
$520$	−180852.	−	57479.6i	−0.668832	−	0.212573i
$521$			539683.i			1.98822i	0.108395	+	0.994108i	$0.465429\pi$
$521$			539683.i			1.98822i	−0.108395	+	0.994108i	$0.534571\pi$
$522$		0			0
$523$	−175071.	−	175071.i	−0.640044	−	0.640044i	0.310522	−	0.950566i	$-0.399496\pi$
$523$	−175071.	−	175071.i	−0.640044	−	0.640044i	−0.950566	+	0.310522i	$0.899496\pi$
$524$	251289.	+	126684.i	0.915189	+	0.461382i
$525$		0			0
$526$	−179368.	+	247994.i	−0.648295	+	0.896334i
$527$			210062.i			0.756354i
$528$		0			0
$529$	266401.			0.951972
$530$	157717.	+	114072.i	0.561469	+	0.406096i
$531$		0			0
$532$	−17751.2	−	8949.06i	−0.0627198	−	0.0316194i
$533$	−12634.2	+	12634.2i	−0.0444726	+	0.0444726i
$534$		0			0
$535$	631977.			2.20797
$536$	−389470.	+	201609.i	−1.35564	+	0.701748i
$537$		0			0
$538$	−10773.9	+	1730.09i	−0.0372227	+	0.00597729i
$539$	20859.5	+	20859.5i	0.0718003	+	0.0718003i
$540$		0			0
$541$	−142203.	−	142203.i	−0.485863	−	0.485863i	0.421135	−	0.906998i	$-0.361632\pi$
$541$	−142203.	−	142203.i	−0.485863	−	0.485863i	−0.906998	+	0.421135i	$0.861632\pi$
$542$	−417081.	−	301663.i	−1.41978	−	1.02689i
$543$		0			0
$544$	2455.25	+	229127.i	0.00829657	+	0.774244i
$545$	−83428.9			−0.280882
$546$		0			0
$547$	−265412.	+	265412.i	−0.887045	+	0.887045i	−0.994238	−	0.107193i	$-0.965814\pi$
$547$	−265412.	+	265412.i	−0.887045	+	0.887045i	0.107193	+	0.994238i	$0.465814\pi$
$548$	−233891.	+	77105.6i	−0.778847	+	0.256758i
$549$		0			0
$550$	−17521.6	−	109113.i	−0.0579227	−	0.360705i
$551$	−27671.3			−0.0911438
$552$		0			0
$553$		−	43852.4i		−	0.143398i
$554$	−50831.3	−	316544.i	−0.165620	−	1.03137i
$555$		0			0
$556$	123774.	−	245517.i	0.400388	−	0.794203i
$557$	−168105.	−	168105.i	−0.541837	−	0.541837i	0.382230	−	0.924067i	$-0.375156\pi$
$557$	−168105.	−	168105.i	−0.541837	−	0.541837i	−0.924067	+	0.382230i	$0.875156\pi$
$558$		0			0
$559$			105099.i			0.336336i
$560$	−93256.6	+	623336.i	−0.297374	+	1.98768i
$561$		0			0
$562$	−34354.8	−	24847.9i	−0.108771	−	0.0786714i
$563$	181113.	−	181113.i	0.571389	−	0.571389i	−0.361127	−	0.932517i	$-0.617608\pi$
$563$	181113.	−	181113.i	0.571389	−	0.571389i	0.932517	+	0.361127i	$0.117608\pi$
$564$		0			0
$565$	−587551.	+	587551.i	−1.84055	+	1.84055i
$566$	353514.	−	56767.9i	1.10350	−	0.177203i
$567$		0			0
$568$	−255010.	−	81048.9i	−0.790424	−	0.251218i
$569$		−	124083.i		−	0.383254i	−0.981468	−	0.191627i	$-0.938624\pi$
$569$		−	124083.i		−	0.383254i	0.981468	−	0.191627i	$-0.0613765\pi$
$570$		0			0
$571$	−92801.0	−	92801.0i	−0.284630	−	0.284630i	0.550322	−	0.834952i	$-0.314505\pi$
$571$	−92801.0	−	92801.0i	−0.284630	−	0.284630i	−0.834952	+	0.550322i	$0.814505\pi$
$572$	27903.5	−	9198.82i	0.0852840	−	0.0281151i
$573$		0			0
$574$	48084.3	+	34778.1i	0.145942	+	0.105556i
$575$			798429.i			2.41491i
$576$		0			0
$577$	182478.			0.548098			0.274049	−	0.961716i	$-0.411637\pi$
$577$	182478.			0.548098			0.274049	+	0.961716i	$0.411637\pi$
$578$	−78409.4	+	108409.i	−0.234700	+	0.324496i
$579$		0			0
$580$	274679.	+	833208.i	0.816526	+	2.47684i
$581$	−85965.6	+	85965.6i	−0.254667	+	0.254667i
$582$		0			0
$583$	−30136.1			−0.0886646
$584$	175851.	−	553294.i	0.515609	−	1.62230i
$585$		0			0
$586$	−79889.4	−	497499.i	−0.232645	−	1.44876i
$587$	−197015.	−	197015.i	−0.571772	−	0.571772i	0.360851	−	0.932623i	$-0.382486\pi$
$587$	−197015.	−	197015.i	−0.571772	−	0.571772i	−0.932623	+	0.360851i	$0.882486\pi$
$588$		0			0
$589$	13833.3	+	13833.3i	0.0398744	+	0.0398744i
$590$	304357.	−	420805.i	0.874338	−	1.20886i
$591$		0			0
$592$	−14133.2	+	94467.8i	−0.0403272	+	0.269551i
$593$	478257.			1.36004			0.680020	−	0.733194i	$-0.261971\pi$
$593$	478257.			1.36004			0.680020	+	0.733194i	$0.261971\pi$
$594$		0			0
$595$	389561.	−	389561.i	1.10038	−	1.10038i
$596$	−420340.	−	211909.i	−1.18334	−	0.596565i
$597$		0			0
$598$	−209587.	+	33655.9i	−0.586087	+	0.0941150i
$599$	141800.			0.395206			0.197603	−	0.980282i	$-0.436684\pi$
$599$	141800.			0.395206			0.197603	+	0.980282i	$0.436684\pi$
$600$		0			0
$601$		−	50813.1i		−	0.140678i	−0.997523	−	0.0703391i	$-0.977592\pi$
$601$		−	50813.1i		−	0.140678i	0.997523	−	0.0703391i	$-0.0224081\pi$
$602$	344650.	−	55344.5i	0.951010	−	0.152715i
$603$		0			0
$604$	38856.6	+	117867.i	0.106510	+	0.323086i
$605$	−408421.	−	408421.i	−1.11583	−	1.11583i
$606$		0			0
$607$		−	448023.i		−	1.21597i	−0.793948	−	0.607985i	$-0.791978\pi$
$607$		−	448023.i		−	1.21597i	0.793948	−	0.607985i	$-0.208022\pi$
$608$	15250.5	+	14927.1i	0.0412550	+	0.0403802i
$609$		0			0
$610$	−46734.8	+	64615.7i	−0.125597	+	0.173651i
$611$	−102482.	+	102482.i	−0.274514	+	0.274514i
$612$		0			0
$613$	8742.04	−	8742.04i	0.0232644	−	0.0232644i	−0.695379	−	0.718643i	$-0.744763\pi$
$613$	8742.04	−	8742.04i	0.0232644	−	0.0232644i	0.718643	+	0.695379i	$0.244763\pi$
$614$	111419.	+	693844.i	0.295544	+	1.84045i
$615$		0			0
$616$	−44859.5	−	86659.9i	−0.118221	−	0.228379i
$617$		−	488336.i		−	1.28277i	−0.767220	−	0.641384i	$-0.778361\pi$
$617$		−	488336.i		−	1.28277i	0.767220	−	0.641384i	$-0.221639\pi$
$618$		0			0
$619$	−416206.	−	416206.i	−1.08624	−	1.08624i	−0.995912	−	0.0903309i	$-0.971208\pi$
$619$	−416206.	−	416206.i	−1.08624	−	1.08624i	−0.0903309	−	0.995912i	$-0.528792\pi$
$620$	279216.	−	553847.i	0.726368	−	1.44081i
$621$		0			0
$622$	−36883.4	+	50995.1i	−0.0953344	+	0.131810i
$623$		−	302377.i		−	0.779062i
$624$		0			0
$625$	−101233.			−0.259155
$626$	−338869.	−	245095.i	−0.864734	−	0.625439i
$627$		0			0
$628$	71712.3	−	142247.i	0.181834	−	0.360682i
$629$	59038.6	−	59038.6i	0.149223	−	0.149223i
$630$		0			0
$631$	77166.0			0.193806			0.0969030	−	0.995294i	$-0.469106\pi$
$631$	77166.0			0.193806			0.0969030	+	0.995294i	$0.469106\pi$
$632$	−14258.6	+	44862.9i	−0.0356980	+	0.112319i
$633$		0			0
$634$	−256074.	+	41120.9i	−0.637070	+	0.102302i
$635$	−76812.3	−	76812.3i	−0.190495	−	0.190495i
$636$		0			0
$637$	58565.5	+	58565.5i	0.144332	+	0.144332i
$638$	−110060.	−	79603.6i	−0.270389	−	0.195565i
$639$		0			0
$640$	298084.	−	607378.i	0.727744	−	1.48286i
$641$	−692532.			−1.68548			−0.842740	−	0.538321i	$-0.819059\pi$
$641$	−692532.			−1.68548			−0.842740	+	0.538321i	$0.819059\pi$
$642$		0			0
$643$	515879.	−	515879.i	1.24774	−	1.24774i	0.291031	−	0.956714i	$-0.406002\pi$
$643$	515879.	−	515879.i	1.24774	−	1.24774i	0.956714	−	0.291031i	$-0.0939984\pi$
$644$	220735.	+	669574.i	0.532230	+	1.61446i
$645$		0			0
$646$	−2957.49	−	18417.3i	−0.00708693	−	0.0441328i
$647$	187947.			0.448980			0.224490	−	0.974476i	$-0.427928\pi$
$647$	187947.			0.448980			0.224490	+	0.974476i	$0.427928\pi$
$648$		0			0
$649$			80406.4i			0.190898i
$650$	−49194.0	−	306348.i	−0.116435	−	0.725084i
$651$		0			0
$652$	−146960.	−	74088.1i	−0.345703	−	0.174282i
$653$	−363478.	−	363478.i	−0.852415	−	0.852415i	0.138015	−	0.990430i	$-0.455928\pi$
$653$	−363478.	−	363478.i	−0.852415	−	0.852415i	−0.990430	+	0.138015i	$0.955928\pi$
$654$		0			0
$655$			726322.i			1.69296i
$656$	−37884.2	−	51214.2i	−0.0880341	−	0.119010i
$657$		0			0
$658$	390034.	+	282101.i	0.900847	+	0.651558i
$659$	59401.3	−	59401.3i	0.136781	−	0.136781i	−0.635401	−	0.772182i	$-0.719165\pi$
$659$	59401.3	−	59401.3i	0.136781	−	0.136781i	0.772182	+	0.635401i	$0.219165\pi$
$660$		0			0
$661$	−352242.	+	352242.i	−0.806191	+	0.806191i	−0.984055	−	0.177864i	$-0.943081\pi$
$661$	−352242.	+	352242.i	−0.806191	+	0.806191i	0.177864	+	0.984055i	$0.443081\pi$
$662$	−768228.	+	123364.i	−1.75297	+	0.281495i
$663$		0			0
$664$	115898.	−	59994.9i	0.262870	−	0.136075i
$665$		−	51307.8i		−	0.116022i
$666$		0			0
$667$	693927.	+	693927.i	1.55977	+	1.55977i
$668$	150632.	+	456925.i	0.337571	+	1.02398i
$669$		0			0
$670$	−917149.	−	663349.i	−2.04310	−	1.47772i
$671$		−	12346.6i		−	0.0274222i
$672$		0			0
$673$	678354.			1.49771			0.748853	−	0.662736i	$-0.230605\pi$
$673$	678354.			1.49771			0.748853	+	0.662736i	$0.230605\pi$
$674$	−95759.7	+	132398.i	−0.210796	+	0.291448i
$675$		0			0
$676$	−355658.	+	117248.i	−0.778287	+	0.256574i
$677$	348304.	−	348304.i	0.759943	−	0.759943i	−0.216369	−	0.976312i	$-0.569421\pi$
$677$	348304.	−	348304.i	0.759943	−	0.759943i	0.976312	+	0.216369i	$0.0694214\pi$
$678$		0			0
$679$	−150471.			−0.326372
$680$	−525204.	+	271872.i	−1.13582	+	0.587958i
$681$		0			0
$682$	15225.7	+	94815.5i	0.0327346	+	0.203850i
$683$	218970.	+	218970.i	0.469401	+	0.469401i	0.901721	−	0.432319i	$-0.142305\pi$
$683$	218970.	+	218970.i	0.469401	+	0.469401i	−0.432319	+	0.901721i	$0.642305\pi$
$684$		0			0
$685$	−449450.	−	449450.i	−0.957856	−	0.957856i
$686$	−174351.	+	241059.i	−0.370491	+	0.512241i
$687$		0			0
$688$	−370587.	−	55443.1i	−0.782913	−	0.117131i
$689$	−84610.7			−0.178233
$690$		0			0
$691$	166441.	−	166441.i	0.348581	−	0.348581i	−0.511000	−	0.859581i	$-0.670725\pi$
$691$	166441.	−	166441.i	0.348581	−	0.348581i	0.859581	+	0.511000i	$0.170725\pi$
$692$	84847.5	−	168302.i	0.177185	−	0.351461i
$693$		0			0
$694$	−119308.	+	19158.7i	−0.247714	+	0.0397784i
$695$	709638.			1.46915
$696$		0			0
$697$			55683.0i			0.114619i
$698$	777894.	−	124916.i	1.59665	−	0.256393i
$699$		0			0
$700$	−978700.	+	322643.i	−1.99735	+	0.658455i
$701$	606601.	+	606601.i	1.23443	+	1.23443i	0.962244	+	0.272188i	$0.0877473\pi$
$701$	606601.	+	606601.i	1.23443	+	1.23443i	0.272188	+	0.962244i	$0.412253\pi$
$702$		0			0
$703$		−	7775.80i		−	0.0157338i
$704$	17715.8	+	103243.i	0.0357450	+	0.208313i
$705$		0			0
$706$	235501.	−	325604.i	0.472479	−	0.653251i
$707$	−25397.3	+	25397.3i	−0.0508100	+	0.0508100i
$708$		0			0
$709$	590171.	−	590171.i	1.17405	−	1.17405i	0.192811	−	0.981236i	$-0.438240\pi$
$709$	590171.	−	590171.i	1.17405	−	1.17405i	0.981236	−	0.192811i	$-0.0617603\pi$
$710$	−109497.	−	681875.i	−0.217213	−	1.35266i
$711$		0			0
$712$	−98318.0	+	309345.i	−0.193942	+	0.610215i
$713$		−	693806.i		−	1.36477i
$714$		0			0
$715$	53620.1	+	53620.1i	0.104885	+	0.104885i
$716$	−152296.	−	76778.5i	−0.297073	−	0.149766i
$717$		0			0
$718$	−225870.	+	312289.i	−0.438137	+	0.605769i
$719$			319294.i			0.617637i	0.951121	+	0.308819i	$0.0999336\pi$
$719$			319294.i			0.617637i	−0.951121	+	0.308819i	$0.900066\pi$
$720$		0			0
$721$	785701.			1.51143
$722$	420976.	+	304480.i	0.807575	+	0.584097i
$723$		0			0
$724$	−76832.4	−	38734.2i	−0.146578	−	0.0738954i
$725$	−1.01430e6	+	1.01430e6i	−1.92969	+	1.92969i
$726$		0			0
$727$	−295780.			−0.559628			−0.279814	−	0.960054i	$-0.590273\pi$
$727$	−295780.			−0.559628			−0.279814	+	0.960054i	$0.590273\pi$
$728$	−125948.	−	243308.i	−0.237646	−	0.459085i
$729$		0			0
$730$	1.47946e6	−	237575.i	2.77625	−	0.445815i
$731$	231602.	+	231602.i	0.433419	+	0.433419i
$732$		0			0
$733$	353645.	+	353645.i	0.658203	+	0.658203i	0.954955	−	0.296752i	$-0.0959033\pi$
$733$	353645.	+	353645.i	0.658203	+	0.658203i	−0.296752	+	0.954955i	$0.595903\pi$
$734$	−617953.	−	446949.i	−1.14700	−	0.829594i
$735$		0			0
$736$	−8109.39	−	756776.i	−0.0149704	−	1.39705i
$737$	175247.			0.322637
$738$		0			0
$739$	−23782.9	+	23782.9i	−0.0435488	+	0.0435488i	−0.728546	−	0.684997i	$-0.759803\pi$
$739$	−23782.9	+	23782.9i	−0.0435488	+	0.0435488i	0.684997	+	0.728546i	$0.259803\pi$
$740$	−234136.	+	77186.4i	−0.427567	+	0.140954i
$741$		0			0
$742$	44555.6	+	277463.i	0.0809273	+	0.503962i
$743$	912931.			1.65371			0.826857	−	0.562412i	$-0.190127\pi$
$743$	912931.			1.65371			0.826857	+	0.562412i	$0.190127\pi$
$744$		0			0
$745$		−	1.21494e6i		−	2.18899i
$746$	−46434.1	−	289161.i	−0.0834372	−	0.519592i
$747$		0			0
$748$	41218.9	−	81761.2i	0.0736705	−	0.146132i
$749$	645172.	+	645172.i	1.15004	+	1.15004i
$750$		0			0
$751$			799005.i			1.41667i	0.705875	+	0.708336i	$0.250554\pi$
$751$			799005.i			1.41667i	−0.705875	+	0.708336i	$0.749446\pi$
$752$	−307297.	−	415422.i	−0.543404	−	0.734605i
$753$		0			0
$754$	−309007.	−	223497.i	−0.543533	−	0.393123i
$755$	−226496.	+	226496.i	−0.397344	+	0.397344i
$756$		0			0
$757$	−24122.0	+	24122.0i	−0.0420940	+	0.0420940i	−0.727841	−	0.685746i	$-0.759476\pi$
$757$	−24122.0	+	24122.0i	−0.0420940	+	0.0420940i	0.685746	+	0.727841i	$0.259476\pi$
$758$	677115.	−	108732.i	1.17848	−	0.189243i
$759$		0			0
$760$	−16682.8	+	52490.2i	−0.0288829	+	0.0908763i
$761$			97444.6i			0.168263i	0.996455	+	0.0841315i	$0.0268116\pi$
$761$			97444.6i			0.168263i	−0.996455	+	0.0841315i	$0.973188\pi$
$762$		0			0
$763$	−85170.8	−	85170.8i	−0.146299	−	0.146299i
$764$	−793940.	+	261734.i	−1.36019	+	0.448408i
$765$		0			0
$766$	−26778.6	−	19368.3i	−0.0456384	−	0.0330090i
$767$			225750.i			0.383741i
$768$		0			0
$769$	−747937.			−1.26477			−0.632386	−	0.774653i	$-0.717924\pi$
$769$	−747937.			−1.26477			−0.632386	+	0.774653i	$0.717924\pi$
$770$	147600.	−	204072.i	0.248946	−	0.344193i
$771$		0			0
$772$	122130.	+	370468.i	0.204922	+	0.621607i
$773$	328529.	−	328529.i	0.549813	−	0.549813i	−0.376574	−	0.926387i	$-0.622898\pi$
$773$	328529.	−	328529.i	0.549813	−	0.549813i	0.926387	+	0.376574i	$0.122898\pi$
$774$		0			0
$775$	1.01412e6			1.68844
$776$	153938.	+	48925.7i	0.255637	+	0.0812481i
$777$		0			0
$778$	39432.1	+	245557.i	0.0651464	+	0.405689i
$779$	3666.92	+	3666.92i	0.00604263	+	0.00604263i
$780$		0			0
$781$	75606.7	+	75606.7i	0.123953	+	0.123953i
$782$	−387693.	+	536026.i	−0.633978	+	0.876541i
$783$		0			0
$784$	−237402.	+	175612.i	−0.386236	+	0.285707i
$785$	411150.			0.667207
$786$		0			0
$787$	−76254.3	+	76254.3i	−0.123116	+	0.123116i	−0.765980	−	0.642864i	$-0.777746\pi$
$787$	−76254.3	+	76254.3i	−0.123116	+	0.123116i	0.642864	+	0.765980i	$0.277746\pi$
$788$	637224.	+	321249.i	1.02622	+	0.517356i
$789$		0			0
$790$	−119960.	+	19263.4i	−0.192212	+	0.0308659i
$791$	−1.19964e6			−1.91733
$792$		0			0
$793$		−	34664.5i		−	0.0551238i
$794$	406969.	−	65351.9i	0.645536	−	0.103661i
$795$		0			0
$796$	356319.	+	1.08085e6i	0.562358	+	1.70585i
$797$	−10472.2	−	10472.2i	−0.0164862	−	0.0164862i	0.698816	−	0.715302i	$-0.253711\pi$
$797$	−10472.2	−	10472.2i	−0.0164862	−	0.0164862i	−0.715302	+	0.698816i	$0.753711\pi$
$798$		0			0
$799$			451671.i			0.707503i
$800$	1.10616e6	−	11853.3i	1.72838	−	0.0185208i
$801$		0			0
$802$	−556160.	+	768949.i	−0.864671	+	1.19550i
$803$	−164044.	+	164044.i	−0.254407	+	0.254407i
$804$		0			0
$805$	−1.28667e6	+	1.28667e6i	−1.98552	+	1.98552i
$806$	42747.9	+	266206.i	0.0658028	+	0.409777i
$807$		0			0
$808$	34240.6	−	17724.6i	0.0524467	−	0.0271491i
$809$			569939.i			0.870826i	0.900231	+	0.435413i	$0.143398\pi$
$809$			569939.i			0.870826i	−0.900231	+	0.435413i	$0.856602\pi$
$810$		0			0
$811$	−207525.	−	207525.i	−0.315521	−	0.315521i	0.531523	−	0.847044i	$-0.321620\pi$
$811$	−207525.	−	207525.i	−0.315521	−	0.315521i	−0.847044	+	0.531523i	$0.821620\pi$
$812$	−570189.	+	1.13102e6i	−0.864783	+	1.71537i
$813$		0			0
$814$	22369.0	−	30927.5i	0.0337597	−	0.0466763i
$815$		−	424771.i		−	0.639498i
$816$		0			0
$817$	30503.6			0.0456991
$818$	486301.	+	351728.i	0.726772	+	0.525655i
$819$		0			0
$820$	74014.3	−	146814.i	0.110075	−	0.218343i
$821$	597985.	−	597985.i	0.887163	−	0.887163i	−0.107086	−	0.994250i	$-0.534152\pi$
$821$	597985.	−	597985.i	0.887163	−	0.887163i	0.994250	+	0.107086i	$0.0341521\pi$
$822$		0			0
$823$	−17487.0			−0.0258176			−0.0129088	−	0.999917i	$-0.504109\pi$
$823$	−17487.0			−0.0258176			−0.0129088	+	0.999917i	$0.504109\pi$
$824$	−803807.	−	255471.i	−1.18385	−	0.376260i
$825$		0			0
$826$	740302.	−	118879.i	1.08505	−	0.174239i
$827$	−108277.	−	108277.i	−0.158316	−	0.158316i	0.623504	−	0.781820i	$-0.285709\pi$
$827$	−108277.	−	108277.i	−0.158316	−	0.158316i	−0.781820	+	0.623504i	$0.785709\pi$
$828$		0			0
$829$	368289.	+	368289.i	0.535895	+	0.535895i	0.922321	−	0.386426i	$-0.126290\pi$
$829$	368289.	+	368289.i	0.535895	+	0.535895i	−0.386426	+	0.922321i	$0.626290\pi$
$830$	272925.	+	197399.i	0.396175	+	0.286543i
$831$		0			0
$832$	49739.1	+	289867.i	0.0718541	+	0.418747i
$833$	258117.			0.371987
$834$		0			0
$835$	−878038.	+	878038.i	−1.25933	+	1.25933i
$836$	−2669.85	−	8098.66i	−0.00382009	−	0.0115878i
$837$		0			0
$838$	64361.5	+	400802.i	0.0916512	+	0.570744i
$839$	105615.			0.150038			0.0750188	−	0.997182i	$-0.476098\pi$
$839$	105615.			0.150038			0.0750188	+	0.997182i	$0.476098\pi$
$840$		0			0
$841$			1.05580e6i			1.49276i
$842$	188188.	+	1.17191e6i	0.265441	+	1.65299i
$843$		0			0
$844$	270614.	+	136427.i	0.379896	+	0.191520i
$845$	−683441.	−	683441.i	−0.957167	−	0.957167i
$846$		0			0
$847$		−	833897.i		−	1.16237i
$848$	44635.0	−	298345.i	0.0620703	−	0.414884i
$849$		0			0
$850$	−783496.	−	566682.i	−1.08442	−	0.784334i
$851$	−194997.	+	194997.i	−0.269258	+	0.269258i
$852$		0			0
$853$	1.00366e6	−	1.00366e6i	1.37939	−	1.37939i	0.533742	−	0.845647i	$-0.320785\pi$
$853$	1.00366e6	−	1.00366e6i	1.37939	−	1.37939i	0.845647	−	0.533742i	$-0.179215\pi$
$854$	−113675.	+	18254.2i	−0.155866	+	0.0250292i
$855$		0			0
$856$	−450262.	−	869818.i	−0.614494	−	1.18708i
$857$			677179.i			0.922024i	0.887394	+	0.461012i	$0.152513\pi$
$857$			677179.i			0.922024i	−0.887394	+	0.461012i	$0.847487\pi$
$858$		0			0
$859$	−750520.	−	750520.i	−1.01713	−	1.01713i	−0.999851	−	0.0172783i	$-0.994500\pi$
$859$	−750520.	−	750520.i	−1.01713	−	1.01713i	−0.0172783	−	0.999851i	$-0.505500\pi$
$860$	−302794.	−	918490.i	−0.409402	−	1.24187i
$861$		0			0
$862$	−401419.	−	290335.i	−0.540236	−	0.390738i
$863$		−	61525.8i		−	0.0826106i	−0.999147	−	0.0413053i	$-0.986848\pi$
$863$		−	61525.8i		−	0.0826106i	0.999147	−	0.0413053i	$-0.0131516\pi$
$864$		0			0
$865$	486458.			0.650149
$866$	−621480.	+	859260.i	−0.828688	+	1.14575i
$867$		0			0
$868$	850456.	−	280366.i	1.12879	−	0.372122i
$869$	13301.2	−	13301.2i	0.0176137	−	0.0176137i
$870$		0			0
$871$	492025.			0.648562
$872$	59440.2	+	114827.i	0.0781712	+	0.151012i
$873$		0			0
$874$	9768.21	+	60830.1i	0.0127877	+	0.0796334i
$875$	−792629.	−	792629.i	−1.03527	−	1.03527i
$876$		0			0
$877$	−818941.	−	818941.i	−1.06476	−	1.06476i	−0.997752	−	0.0670114i	$-0.978654\pi$
$877$	−818941.	−	818941.i	−1.06476	−	1.06476i	−0.0670114	−	0.997752i	$-0.521346\pi$
$878$	436231.	−	603134.i	0.565884	−	0.782393i
$879$		0			0
$880$	−217355.	+	160783.i	−0.280676	+	0.207622i
$881$	−349159.			−0.449853			−0.224927	−	0.974376i	$-0.572214\pi$
$881$	−349159.			−0.449853			−0.224927	+	0.974376i	$0.572214\pi$
$882$		0			0
$883$	353886.	−	353886.i	0.453881	−	0.453881i	−0.442760	−	0.896640i	$-0.646001\pi$
$883$	353886.	−	353886.i	0.453881	−	0.453881i	0.896640	+	0.442760i	$0.146001\pi$
$884$	115727.	−	229554.i	0.148092	−	0.293752i
$885$		0			0
$886$	−143089.	+	22977.4i	−0.182279	+	0.0292708i
$887$	−1.16958e6			−1.48656			−0.743282	−	0.668978i	$-0.766732\pi$
$887$	−1.16958e6			−1.48656			−0.743282	+	0.668978i	$0.766732\pi$
$888$		0			0
$889$		−	156832.i		−	0.198441i
$890$	−827163.	+	132827.i	−1.04427	+	0.167690i
$891$		0			0
$892$	824617.	−	271847.i	1.03639	−	0.341661i
$893$	29744.1	+	29744.1i	0.0372990	+	0.0372990i
$894$		0			0
$895$		−	440196.i		−	0.549540i
$896$	924367.	−	315752.i	1.15141	−	0.393306i
$897$		0			0
$898$	5409.45	−	7479.13i	0.00670812	−	0.00927466i
$899$	881387.	−	881387.i	1.09055	−	1.09055i
$900$		0			0
$901$	−186454.	+	186454.i	−0.229679	+	0.229679i
$902$	4036.01	+	25133.6i	0.00496066	+	0.0308917i
$903$		0			0
$904$	1.22728e6	+	390062.i	1.50178	+	0.477306i
$905$		−	222075.i		−	0.271146i
$906$		0			0
$907$	110870.	+	110870.i	0.134772	+	0.134772i	0.771274	−	0.636503i	$-0.219620\pi$
$907$	110870.	+	110870.i	0.134772	+	0.134772i	−0.636503	+	0.771274i	$0.719620\pi$
$908$	293558.	+	147994.i	0.356059	+	0.179503i
$909$		0			0
$910$	414404.	−	572957.i	0.500428	−	0.691893i
$911$		−	162563.i		−	0.195877i	−0.995192	−	0.0979387i	$-0.968775\pi$
$911$		−	162563.i		−	0.195877i	0.995192	−	0.0979387i	$-0.0312249\pi$
$912$		0			0
$913$	−52149.8			−0.0625621
$914$	−850394.	−	615068.i	−1.01795	−	0.736259i
$915$		0			0
$916$	−436795.	−	220205.i	−0.520579	−	0.262444i
$917$	−741487.	+	741487.i	−0.881789	+	0.881789i
$918$		0			0
$919$	−615695.			−0.729012			−0.364506	−	0.931201i	$-0.618762\pi$
$919$	−615695.			−0.729012			−0.364506	+	0.931201i	$0.618762\pi$
$920$	1.73468e6	−	897958.i	2.04948	−	1.06091i
$921$		0			0
$922$	−763906.	+	122670.i	−0.898624	+	0.144303i
$923$	212275.	+	212275.i	0.249170	+	0.249170i
$924$		0			0
$925$	−285023.	−	285023.i	−0.333116	−	0.333116i
$926$	−72117.0	−	52160.3i	−0.0841038	−	0.0608301i
$927$		0			0
$928$	951080.	−	971684.i	1.10439	−	1.12831i
$929$	−228015.			−0.264199			−0.132099	−	0.991236i	$-0.542172\pi$
$929$	−228015.			−0.264199			−0.132099	+	0.991236i	$0.542172\pi$
$930$		0			0
$931$	16997.9	−	16997.9i	0.0196108	−	0.0196108i
$932$	1.39957e6	−	461388.i	1.61125	−	0.531171i
$933$		0			0
$934$	157443.	+	980449.i	0.180480	+	1.12391i
$935$	236321.			0.270321
$936$		0			0
$937$		−	431768.i		−	0.491781i	−0.969298	−	0.245890i	$-0.920920\pi$
$937$		−	431768.i		−	0.491781i	0.969298	−	0.245890i	$-0.0790803\pi$
$938$	−259098.	−	1.61350e6i	−0.294482	−	1.83384i
$939$		0			0
$940$	600365.	−	1.19087e6i	0.679453	−	1.34775i
$941$	532946.	+	532946.i	0.601871	+	0.601871i	0.940809	−	0.338938i	$-0.110068\pi$
$941$	532946.	+	532946.i	0.601871	+	0.601871i	−0.338938	+	0.940809i	$0.610068\pi$
$942$		0			0
$943$		−	183914.i		−	0.206819i
$944$	−796016.	−	119091.i	−0.893260	−	0.133640i
$945$		0			0
$946$	121325.	+	87751.4i	0.135572	+	0.0980555i
$947$	1.02432e6	−	1.02432e6i	1.14218	−	1.14218i	0.154128	−	0.988051i	$-0.450743\pi$
$947$	1.02432e6	−	1.02432e6i	1.14218	−	1.14218i	0.988051	−	0.154128i	$-0.0492569\pi$
$948$		0			0
$949$	−460572.	+	460572.i	−0.511405	+	0.511405i
$950$	−88913.8	+	14278.0i	−0.0985195	+	0.0158205i
$951$		0			0
$952$	−813717.	−	258621.i	−0.897841	−	0.285358i
$953$			264733.i			0.291490i	0.989322	+	0.145745i	$0.0465578\pi$
$953$			264733.i			0.291490i	−0.989322	+	0.145745i	$0.953442\pi$
$954$		0			0
$955$	−1.52565e6	−	1.52565e6i	−1.67282	−	1.67282i
$956$	1.06994e6	−	352720.i	1.17069	−	0.385935i
$957$		0			0
$958$	382191.	+	276428.i	0.416437	+	0.301198i
$959$		−	917667.i		−	0.997810i
$960$		0			0
$961$	42286.5			0.0457883
$962$	62803.8	−	86832.7i	0.0678634	−	0.0938281i
$963$		0			0
$964$	−112225.	−	340421.i	−0.120763	−	0.366321i
$965$	−711899.	+	711899.i	−0.764476	+	0.764476i
$966$		0			0
$967$	61058.3			0.0652967			0.0326484	−	0.999467i	$-0.489606\pi$
$967$	61058.3			0.0652967			0.0326484	+	0.999467i	$0.489606\pi$
$968$	−271142.	+	853114.i	−0.289365	+	0.910450i
$969$		0			0
$970$	66098.5	+	411618.i	0.0702503	+	0.437473i
$971$	−404297.	−	404297.i	−0.428807	−	0.428807i	0.459415	−	0.888222i	$-0.348059\pi$
$971$	−404297.	−	404297.i	−0.428807	−	0.428807i	−0.888222	+	0.459415i	$0.848059\pi$
$972$		0			0
$973$	724454.	+	724454.i	0.765218	+	0.765218i
$974$	−1.05475e6	+	1.45831e6i	−1.11182	+	1.53720i
$975$		0			0
$976$	122230.	+	18286.7i	0.128315	+	0.0191971i
$977$	1.83431e6			1.92169			0.960845	−	0.277086i	$-0.0893687\pi$
$977$	1.83431e6			1.92169			0.960845	+	0.277086i	$0.0893687\pi$
$978$		0			0
$979$	91716.3	−	91716.3i	0.0956932	−	0.0956932i
$980$	−680551.	−	343092.i	−0.708612	−	0.357239i
$981$		0			0
$982$	684251.	−	109878.i	0.709565	−	0.113943i
$983$	−586823.			−0.607296			−0.303648	−	0.952784i	$-0.598205\pi$
$983$	−586823.			−0.607296			−0.303648	+	0.952784i	$0.598205\pi$
$984$		0			0
$985$			1.84182e6i			1.89835i
$986$	−1.17346e6	+	188437.i	−1.20702	+	0.193826i
$987$		0			0
$988$	−7495.91	−	22738.0i	−0.00767910	−	0.0232937i
$989$	−764953.	−	764953.i	−0.782064	−	0.782064i
$990$		0			0
$991$			1.20757e6i			1.22961i	0.788680	+	0.614804i	$0.210765\pi$
$991$			1.20757e6i			1.22961i	−0.788680	+	0.614804i	$0.789235\pi$
$992$	−961216.	+	10300.1i	−0.976782	+	0.0104669i
$993$		0			0
$994$	584329.	−	807894.i	0.591404	−	0.817677i
$995$	−2.07699e6	+	2.07699e6i	−2.09792	+	2.09792i
$996$		0			0
$997$	833662.	−	833662.i	0.838686	−	0.838686i	−0.150000	−	0.988686i	$-0.547927\pi$
$997$	833662.	−	833662.i	0.838686	−	0.838686i	0.988686	+	0.150000i	$0.0479272\pi$
$998$	40259.0	+	250707.i	0.0404206	+	0.251713i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	144.5.m.a.19.5		14
3.2	odd	2		16.5.f.a.3.3	✓	14
4.3	odd	2		576.5.m.a.559.7		14
12.11	even	2		64.5.f.a.47.5		14
16.5	even	4		576.5.m.a.271.7		14
16.11	odd	4	inner	144.5.m.a.91.5		14
24.5	odd	2		128.5.f.b.95.5		14
24.11	even	2		128.5.f.a.95.3		14
48.5	odd	4		64.5.f.a.15.5		14
48.11	even	4		16.5.f.a.11.3	yes	14
48.29	odd	4		128.5.f.a.31.3		14
48.35	even	4		128.5.f.b.31.5		14

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
16.5.f.a.3.3	✓	14	3.2	odd	2
16.5.f.a.11.3	yes	14	48.11	even	4
64.5.f.a.15.5		14	48.5	odd	4
64.5.f.a.47.5		14	12.11	even	2
128.5.f.a.31.3		14	48.29	odd	4
128.5.f.a.95.3		14	24.11	even	2
128.5.f.b.31.5		14	48.35	even	4
128.5.f.b.95.5		14	24.5	odd	2
144.5.m.a.19.5		14	1.1	even	1	trivial
144.5.m.a.91.5		14	16.11	odd	4	inner
576.5.m.a.271.7		14	16.5	even	4
576.5.m.a.559.7		14	4.3	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:	\( N \)	\(=\)	\( 144 = 2^{4} \cdot 3^{2} \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	144.m (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(2.34420 - 3.24110i) q^{2} +(-5.00945 - 15.1956i) q^{4} +(29.2002 - 29.2002i) q^{5} +59.6196 q^{7} +(-60.9935 - 19.3854i) q^{8} +O(q^{10})\)	\(q+(2.34420 - 3.24110i) q^{2} +(-5.00945 - 15.1956i) q^{4} +(29.2002 - 29.2002i) q^{5} +59.6196 q^{7} +(-60.9935 - 19.3854i) q^{8} +(-26.1896 - 163.092i) q^{10} +(18.0837 + 18.0837i) q^{11} +(50.7721 + 50.7721i) q^{13} +(139.760 - 193.233i) q^{14} +(-205.811 + 152.243i) q^{16} +223.769 q^{17} +(14.7360 - 14.7360i) q^{19} +(-589.990 - 297.436i) q^{20} +(101.003 - 16.2192i) q^{22} -739.082 q^{23} -1080.30i q^{25} +(283.577 - 45.5374i) q^{26} +(-298.661 - 905.954i) q^{28} +(-938.904 - 938.904i) q^{29} +938.741i q^{31} +(10.9723 + 1023.94i) q^{32} +(524.560 - 725.259i) q^{34} +(1740.90 - 1740.90i) q^{35} +(263.837 - 263.837i) q^{37} +(-13.2167 - 82.3049i) q^{38} +(-2347.08 + 1214.96i) q^{40} +248.841i q^{41} +(1035.00 + 1035.00i) q^{43} +(184.203 - 365.381i) q^{44} +(-1732.56 + 2395.44i) q^{46} +2018.46i q^{47} +1153.50 q^{49} +(-3501.35 - 2532.44i) q^{50} +(517.171 - 1025.85i) q^{52} +(-833.240 + 833.240i) q^{53} +1056.09 q^{55} +(-3636.41 - 1155.75i) q^{56} +(-5244.06 + 842.101i) q^{58} +(2223.17 + 2223.17i) q^{59} +(-341.374 - 341.374i) q^{61} +(3042.55 + 2200.60i) q^{62} +(3344.42 + 2364.76i) q^{64} +2965.11 q^{65} +(4845.43 - 4845.43i) q^{67} +(-1120.96 - 3400.30i) q^{68} +(-1561.41 - 9723.46i) q^{70} +4180.93 q^{71} +9071.36i q^{73} +(-236.635 - 1473.61i) q^{74} +(-297.741 - 150.103i) q^{76} +(1078.14 + 1078.14i) q^{77} -735.536i q^{79} +(-1564.19 + 10455.2i) q^{80} +(806.518 + 583.333i) q^{82} +(-1441.90 + 1441.90i) q^{83} +(6534.10 - 6534.10i) q^{85} +(5780.81 - 928.294i) q^{86} +(-752.429 - 1453.55i) q^{88} -5071.77i q^{89} +(3027.01 + 3027.01i) q^{91} +(3702.39 + 11230.8i) q^{92} +(6542.05 + 4731.69i) q^{94} -860.586i q^{95} -2523.85 q^{97} +(2704.03 - 3738.60i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 14 q + 2 q^{2} - 8 q^{4} + 2 q^{5} - 4 q^{7} + 92 q^{8}+O(q^{10}) \) 14 * q + 2 * q^2 - 8 * q^4 + 2 * q^5 - 4 * q^7 + 92 * q^8	\( 14 q + 2 q^{2} - 8 q^{4} + 2 q^{5} - 4 q^{7} + 92 q^{8} - 100 q^{10} - 94 q^{11} - 2 q^{13} - 44 q^{14} - 168 q^{16} + 4 q^{17} - 706 q^{19} - 1900 q^{20} + 900 q^{22} - 1148 q^{23} + 3416 q^{26} - 3784 q^{28} - 862 q^{29} - 3208 q^{32} + 7508 q^{34} - 1340 q^{35} - 1826 q^{37} - 3568 q^{38} - 5144 q^{40} + 1694 q^{43} + 14636 q^{44} - 5316 q^{46} + 682 q^{49} - 20070 q^{50} + 20452 q^{52} + 482 q^{53} - 11780 q^{55} + 6952 q^{56} - 20456 q^{58} + 2786 q^{59} - 3778 q^{61} + 11472 q^{62} + 15808 q^{64} + 2020 q^{65} + 7998 q^{67} - 18032 q^{68} + 15296 q^{70} - 19964 q^{71} + 23780 q^{74} - 23996 q^{76} + 9508 q^{77} - 1384 q^{80} + 16016 q^{82} + 17282 q^{83} + 9948 q^{85} + 4796 q^{86} + 7288 q^{88} - 28036 q^{91} + 14632 q^{92} + 432 q^{94} - 4 q^{97} + 12246 q^{98}+O(q^{100}) \) 14 * q + 2 * q^2 - 8 * q^4 + 2 * q^5 - 4 * q^7 + 92 * q^8 - 100 * q^10 - 94 * q^11 - 2 * q^13 - 44 * q^14 - 168 * q^16 + 4 * q^17 - 706 * q^19 - 1900 * q^20 + 900 * q^22 - 1148 * q^23 + 3416 * q^26 - 3784 * q^28 - 862 * q^29 - 3208 * q^32 + 7508 * q^34 - 1340 * q^35 - 1826 * q^37 - 3568 * q^38 - 5144 * q^40 + 1694 * q^43 + 14636 * q^44 - 5316 * q^46 + 682 * q^49 - 20070 * q^50 + 20452 * q^52 + 482 * q^53 - 11780 * q^55 + 6952 * q^56 - 20456 * q^58 + 2786 * q^59 - 3778 * q^61 + 11472 * q^62 + 15808 * q^64 + 2020 * q^65 + 7998 * q^67 - 18032 * q^68 + 15296 * q^70 - 19964 * q^71 + 23780 * q^74 - 23996 * q^76 + 9508 * q^77 - 1384 * q^80 + 16016 * q^82 + 17282 * q^83 + 9948 * q^85 + 4796 * q^86 + 7288 * q^88 - 28036 * q^91 + 14632 * q^92 + 432 * q^94 - 4 * q^97 + 12246 * q^98

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