LMFDB - Embedded newform 405.4.e.t.271.2

Newspace parameters

Level:	$ N $	$=$	$ 405 = 3^{4} \cdot 5 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	405.e (of order $3$, degree $2$, not minimal)

Newform invariants

Self dual:	no
Analytic conductor:	$23.8957735523$
Analytic rank:	$0$
Dimension:	$6$
Relative dimension:	$3$ over $\Q(\zeta_{3})$
Coefficient field:	6.0.95327307.1
Defining polynomial:	$ x^{6} - 3x^{5} + 20x^{4} - 35x^{3} + 85x^{2} - 68x + 16 $ x^6 - 3x^5 + 20x^4 - 35x^3 + 85x^2 - 68*x + 16
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 3^{3} $
Twist minimal:	no (minimal twist has level 135)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			271.2
Root			$0.500000 - 3.26212i$ of defining polynomial
Character	$\chi$	$=$	405.271
Dual form			405.4.e.t.136.2

$q$-expansion

$f(q)$	$=$	$q+(0.129356 + 0.224051i) q^{2} +(3.96653 - 6.87024i) q^{4} +(-2.50000 + 4.33013i) q^{5} +(-7.25871 - 12.5725i) q^{7} +4.12208 q^{8} +O(q^{10})$	\(q+(0.129356 + 0.224051i) q^{2} +(3.96653 - 6.87024i) q^{4} +(-2.50000 + 4.33013i) q^{5} +(-7.25871 - 12.5725i) q^{7} +4.12208 q^{8} -1.29356 q^{10} +(24.6423 + 42.6817i) q^{11} +(-36.0900 + 62.5097i) q^{13} +(1.87792 - 3.25265i) q^{14} +(-31.1991 - 54.0383i) q^{16} +118.017 q^{17} +123.389 q^{19} +(19.8327 + 34.3512i) q^{20} +(-6.37526 + 11.0423i) q^{22} +(45.7442 - 79.2312i) q^{23} +(-12.5000 - 21.6506i) q^{25} -18.6739 q^{26} -115.168 q^{28} +(-87.2001 - 151.035i) q^{29} +(23.1478 - 40.0932i) q^{31} +(24.5599 - 42.5390i) q^{32} +(15.2662 + 26.4418i) q^{34} +72.5871 q^{35} +154.977 q^{37} +(15.9611 + 27.6455i) q^{38} +(-10.3052 + 17.8491i) q^{40} +(182.101 - 315.409i) q^{41} +(-62.8569 - 108.871i) q^{43} +390.978 q^{44} +23.6692 q^{46} +(110.762 + 191.845i) q^{47} +(66.1222 - 114.527i) q^{49} +(3.23390 - 5.60129i) q^{50} +(286.304 + 495.894i) q^{52} -13.6794 q^{53} -246.423 q^{55} +(-29.9210 - 51.8247i) q^{56} +(22.5597 - 39.0746i) q^{58} +(-119.543 + 207.055i) q^{59} +(27.2729 + 47.2380i) q^{61} +11.9772 q^{62} -486.477 q^{64} +(-180.450 - 312.549i) q^{65} +(38.0279 - 65.8662i) q^{67} +(468.118 - 810.804i) q^{68} +(9.38959 + 16.2633i) q^{70} +728.303 q^{71} -501.815 q^{73} +(20.0472 + 34.7227i) q^{74} +(489.427 - 847.712i) q^{76} +(357.742 - 619.628i) q^{77} +(-198.805 - 344.340i) q^{79} +311.991 q^{80} +94.2237 q^{82} +(684.731 + 1185.99i) q^{83} +(-295.042 + 511.028i) q^{85} +(16.2619 - 28.1664i) q^{86} +(101.577 + 175.937i) q^{88} +1468.13 q^{89} +1047.87 q^{91} +(-362.892 - 628.547i) q^{92} +(-28.6554 + 49.6326i) q^{94} +(-308.473 + 534.290i) q^{95} +(-167.512 - 290.139i) q^{97} +34.2133 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q + q^{2} - 23 q^{4} - 15 q^{5} - 44 q^{7} - 72 q^{8}+O(q^{10}) $ 6 * q + q^2 - 23 * q^4 - 15 * q^5 - 44 * q^7 - 72 * q^8	$ 6 q + q^{2} - 23 q^{4} - 15 q^{5} - 44 q^{7} - 72 q^{8} - 10 q^{10} - 38 q^{11} - 28 q^{13} + 108 q^{14} - 191 q^{16} - 38 q^{17} + 374 q^{19} - 115 q^{20} - 122 q^{22} + 81 q^{23} - 75 q^{25} + 832 q^{26} + 820 q^{28} - 160 q^{29} - 227 q^{31} + 569 q^{32} - 17 q^{34} + 440 q^{35} + 156 q^{37} + 757 q^{38} + 180 q^{40} + 338 q^{41} - 22 q^{43} + 3272 q^{44} - 2850 q^{46} + 472 q^{47} + 197 q^{49} + 25 q^{50} + 1566 q^{52} + 1042 q^{53} + 380 q^{55} + 1254 q^{56} + 2096 q^{58} - 140 q^{59} - 595 q^{61} + 2814 q^{62} - 1836 q^{64} - 140 q^{65} - 878 q^{67} + 3053 q^{68} + 540 q^{70} - 1204 q^{71} + 2588 q^{73} - 2878 q^{74} - 525 q^{76} - 288 q^{77} - 629 q^{79} + 1910 q^{80} - 3364 q^{82} + 1287 q^{83} + 95 q^{85} + 3730 q^{86} + 858 q^{88} + 4308 q^{89} - 880 q^{91} - 1959 q^{92} + 1108 q^{94} - 935 q^{95} - 1392 q^{97} - 5386 q^{98}+O(q^{100}) $ 6 * q + q^2 - 23 * q^4 - 15 * q^5 - 44 * q^7 - 72 * q^8 - 10 * q^10 - 38 * q^11 - 28 * q^13 + 108 * q^14 - 191 * q^16 - 38 * q^17 + 374 * q^19 - 115 * q^20 - 122 * q^22 + 81 * q^23 - 75 * q^25 + 832 * q^26 + 820 * q^28 - 160 * q^29 - 227 * q^31 + 569 * q^32 - 17 * q^34 + 440 * q^35 + 156 * q^37 + 757 * q^38 + 180 * q^40 + 338 * q^41 - 22 * q^43 + 3272 * q^44 - 2850 * q^46 + 472 * q^47 + 197 * q^49 + 25 * q^50 + 1566 * q^52 + 1042 * q^53 + 380 * q^55 + 1254 * q^56 + 2096 * q^58 - 140 * q^59 - 595 * q^61 + 2814 * q^62 - 1836 * q^64 - 140 * q^65 - 878 * q^67 + 3053 * q^68 + 540 * q^70 - 1204 * q^71 + 2588 * q^73 - 2878 * q^74 - 525 * q^76 - 288 * q^77 - 629 * q^79 + 1910 * q^80 - 3364 * q^82 + 1287 * q^83 + 95 * q^85 + 3730 * q^86 + 858 * q^88 + 4308 * q^89 - 880 * q^91 - 1959 * q^92 + 1108 * q^94 - 935 * q^95 - 1392 * q^97 - 5386 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/405\mathbb{Z}\right)^\times$.

$n$	$82$	$326$
$\chi(n)$	$1$	$e\left(\frac{1}{3}\right)$

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 $

$2$	0.129356	+	0.224051i	0.0457343	+	0.0792142i	0.887986	−	0.459870i	$-0.152104\pi$
$2$	0.129356	+	0.224051i	0.0457343	+	0.0792142i	−0.842252	+	0.539084i	$0.818771\pi$
$3$		0			0
$3$		0			0
$4$	3.96653	−	6.87024i	0.495817	−	0.858780i
$5$	−2.50000	+	4.33013i	−0.223607	+	0.387298i
$5$	−2.50000	+	4.33013i	−0.223607	+	0.387298i
$6$		0			0
$7$	−7.25871	−	12.5725i	−0.391934	−	0.678849i	0.600771	−	0.799421i	$-0.294860\pi$
$7$	−7.25871	−	12.5725i	−0.391934	−	0.678849i	−0.992705	+	0.120572i	$0.961527\pi$
$8$	4.12208			0.182172
$9$		0			0
$10$	−1.29356			−0.0409060
$11$	24.6423	+	42.6817i	0.675448	+	1.16991i	0.976338	+	0.216251i	$0.0693829\pi$
$11$	24.6423	+	42.6817i	0.675448	+	1.16991i	−0.300890	+	0.953659i	$0.597284\pi$
$12$		0			0
$13$	−36.0900	+	62.5097i	−0.769967	+	1.33362i	0.167614	+	0.985853i	$0.446394\pi$
$13$	−36.0900	+	62.5097i	−0.769967	+	1.33362i	−0.937580	+	0.347768i	$0.886940\pi$
$14$	1.87792	−	3.25265i	0.0358496	−	0.0620934i
$15$		0			0
$16$	−31.1991	−	54.0383i	−0.487485	−	0.844349i
$17$	118.017			1.68372			0.841861	−	0.539694i	$-0.181460\pi$
$17$	118.017			1.68372			0.841861	+	0.539694i	$0.181460\pi$
$18$		0			0
$19$	123.389			1.48986			0.744932	−	0.667141i	$-0.232482\pi$
$19$	123.389			1.48986			0.744932	+	0.667141i	$0.232482\pi$
$20$	19.8327	+	34.3512i	0.221736	+	0.384058i
$21$		0			0
$22$	−6.37526	+	11.0423i	−0.0617823	+	0.107010i
$23$	45.7442	−	79.2312i	0.414709	−	0.718298i	−0.580688	−	0.814126i	$-0.697217\pi$
$23$	45.7442	−	79.2312i	0.414709	−	0.718298i	0.995398	+	0.0958280i	$0.0305499\pi$
$24$		0			0
$25$	−12.5000	−	21.6506i	−0.100000	−	0.173205i
$26$	−18.6739			−0.140856
$27$		0			0
$28$	−115.168			−0.777309
$29$	−87.2001	−	151.035i	−0.558367	−	0.967120i	−0.997633	−	0.0687632i	$-0.978095\pi$
$29$	−87.2001	−	151.035i	−0.558367	−	0.967120i	0.439266	−	0.898357i	$-0.355239\pi$
$30$		0			0
$31$	23.1478	−	40.0932i	0.134112	−	0.232289i	−0.791146	−	0.611627i	$-0.790515\pi$
$31$	23.1478	−	40.0932i	0.134112	−	0.232289i	0.925258	+	0.379339i	$0.123849\pi$
$32$	24.5599	−	42.5390i	0.135676	−	0.234997i
$33$		0			0
$34$	15.2662	+	26.4418i	0.0770039	+	0.133375i
$35$	72.5871			0.350556
$36$		0			0
$37$	154.977			0.688595			0.344297	−	0.938861i	$-0.388117\pi$
$37$	154.977			0.688595			0.344297	+	0.938861i	$0.388117\pi$
$38$	15.9611	+	27.6455i	0.0681379	+	0.118018i
$39$		0			0
$40$	−10.3052	+	17.8491i	−0.0407349	+	0.0705549i
$41$	182.101	−	315.409i	0.693645	−	1.20143i	−0.276990	−	0.960873i	$-0.589337\pi$
$41$	182.101	−	315.409i	0.693645	−	1.20143i	0.970635	−	0.240556i	$-0.0773296\pi$
$42$		0			0
$43$	−62.8569	−	108.871i	−0.222921	−	0.386110i	0.732773	−	0.680473i	$-0.238226\pi$
$43$	−62.8569	−	108.871i	−0.222921	−	0.386110i	−0.955694	+	0.294363i	$0.904892\pi$
$44$	390.978			1.33959
$45$		0			0
$46$	23.6692			0.0758658
$47$	110.762	+	191.845i	0.343750	+	0.595392i	0.985126	−	0.171835i	$-0.0549695\pi$
$47$	110.762	+	191.845i	0.343750	+	0.595392i	−0.641376	+	0.767227i	$0.721636\pi$
$48$		0			0
$49$	66.1222	−	114.527i	0.192776	−	0.333898i
$50$	3.23390	−	5.60129i	0.00914686	−	0.0158428i
$51$		0			0
$52$	286.304	+	495.894i	0.763525	+	1.32246i
$53$	−13.6794			−0.0354530			−0.0177265	−	0.999843i	$-0.505643\pi$
$53$	−13.6794			−0.0354530			−0.0177265	+	0.999843i	$0.505643\pi$
$54$		0			0
$55$	−246.423			−0.604139
$56$	−29.9210	−	51.8247i	−0.0713993	−	0.123667i
$57$		0			0
$58$	22.5597	−	39.0746i	0.0510731	−	0.0884612i
$59$	−119.543	+	207.055i	−0.263784	+	0.456887i	−0.967244	−	0.253848i	$-0.918304\pi$
$59$	−119.543	+	207.055i	−0.263784	+	0.456887i	0.703461	+	0.710734i	$0.251637\pi$
$60$		0			0
$61$	27.2729	+	47.2380i	0.0572448	+	0.0991509i	0.893228	−	0.449605i	$-0.148435\pi$
$61$	27.2729	+	47.2380i	0.0572448	+	0.0991509i	−0.835983	+	0.548756i	$0.815102\pi$
$62$	11.9772			0.0245341
$63$		0			0
$64$	−486.477			−0.950150
$65$	−180.450	−	312.549i	−0.344339	−	0.596413i
$66$		0			0
$67$	38.0279	−	65.8662i	0.0693410	−	0.120102i	−0.829270	−	0.558848i	$-0.811244\pi$
$67$	38.0279	−	65.8662i	0.0693410	−	0.120102i	0.898611	+	0.438745i	$0.144577\pi$
$68$	468.118	−	810.804i	0.834818	−	1.44595i
$69$		0			0
$70$	9.38959	+	16.2633i	0.0160324	+	0.0277690i
$71$	728.303			1.21738			0.608688	−	0.793410i	$-0.291696\pi$
$71$	728.303			1.21738			0.608688	+	0.793410i	$0.291696\pi$
$72$		0			0
$73$	−501.815			−0.804562			−0.402281	−	0.915516i	$-0.631782\pi$
$73$	−501.815			−0.804562			−0.402281	+	0.915516i	$0.631782\pi$
$74$	20.0472	+	34.7227i	0.0314924	+	0.0545464i
$75$		0			0
$76$	489.427	−	847.712i	0.738699	−	1.27946i
$77$	357.742	−	619.628i	0.529461	−	0.917054i
$78$		0			0
$79$	−198.805	−	344.340i	−0.283130	−	0.490396i	0.689024	−	0.724739i	$-0.258040\pi$
$79$	−198.805	−	344.340i	−0.283130	−	0.490396i	−0.972154	+	0.234343i	$0.924706\pi$
$80$	311.991			0.436020
$81$		0			0
$82$	94.2237			0.126894
$83$	684.731	+	1185.99i	0.905530	+	1.56842i	0.820205	+	0.572070i	$0.193859\pi$
$83$	684.731	+	1185.99i	0.905530	+	1.56842i	0.0853248	+	0.996353i	$0.472807\pi$
$84$		0			0
$85$	−295.042	+	511.028i	−0.376492	+	0.652103i
$86$	16.2619	−	28.1664i	0.0203902	−	0.0353169i
$87$		0			0
$88$	101.577	+	175.937i	0.123048	+	0.213125i
$89$	1468.13			1.74856			0.874278	−	0.485425i	$-0.161335\pi$
$89$	1468.13			1.74856			0.874278	+	0.485425i	$0.161335\pi$
$90$		0			0
$91$	1047.87			1.20710
$92$	−362.892	−	628.547i	−0.411240	−	0.712288i
$93$		0			0
$94$	−28.6554	+	49.6326i	−0.0314423	+	0.0544597i
$95$	−308.473	+	534.290i	−0.333144	+	0.577022i
$96$		0			0
$97$	−167.512	−	290.139i	−0.175343	−	0.303702i	0.764937	−	0.644105i	$-0.222770\pi$
$97$	−167.512	−	290.139i	−0.175343	−	0.303702i	−0.940280	+	0.340403i	$0.889437\pi$
$98$	34.2133			0.0352659
$99$		0			0
$100$	−198.327			−0.198327
$101$	603.043	+	1044.50i	0.594109	+	1.02903i	0.993672	+	0.112321i	$0.0358286\pi$
$101$	603.043	+	1044.50i	0.594109	+	1.02903i	−0.399563	+	0.916706i	$0.630838\pi$
$102$		0			0
$103$	−530.555	+	918.948i	−0.507545	+	0.879093i	0.492417	+	0.870359i	$0.336113\pi$
$103$	−530.555	+	918.948i	−0.507545	+	0.879093i	−0.999962	+	0.00873396i	$0.997220\pi$
$104$	−148.766	+	257.670i	−0.140266	+	0.242948i
$105$		0			0
$106$	−1.76951	−	3.06489i	−0.00162142	−	0.00280838i
$107$	−475.578			−0.429681			−0.214841	−	0.976649i	$-0.568923\pi$
$107$	−475.578			−0.429681			−0.214841	+	0.976649i	$0.568923\pi$
$108$		0			0
$109$	1320.42			1.16030			0.580152	−	0.814508i	$-0.302993\pi$
$109$	1320.42			1.16030			0.580152	+	0.814508i	$0.302993\pi$
$110$	−31.8763	−	55.2114i	−0.0276299	−	0.0478563i
$111$		0			0
$112$	−452.930	+	784.498i	−0.382124	+	0.661858i
$113$	34.0875	−	59.0413i	0.0283777	−	0.0491517i	−0.851488	−	0.524374i	$-0.824299\pi$
$113$	34.0875	−	59.0413i	0.0283777	−	0.0491517i	0.879865	+	0.475223i	$0.157633\pi$
$114$		0			0
$115$	228.721	+	396.156i	0.185464	+	0.321233i
$116$	−1383.53			−1.10739
$117$		0			0
$118$	−61.8547			−0.0482559
$119$	−856.650	−	1483.76i	−0.659907	−	1.14299i
$120$		0			0
$121$	−548.983	+	950.867i	−0.412459	+	0.714400i
$122$	−7.05583	+	12.2211i	−0.00523610	+	0.00906920i
$123$		0			0
$124$	−183.633	−	318.062i	−0.132990	−	0.230345i
$125$	125.000			0.0894427
$126$		0			0
$127$	−593.009			−0.414339			−0.207170	−	0.978305i	$-0.566425\pi$
$127$	−593.009			−0.414339			−0.207170	+	0.978305i	$0.566425\pi$
$128$	−259.408	−	449.308i	−0.179130	−	0.310262i
$129$		0			0
$130$	46.6846	−	80.8602i	0.0314963	−	0.0545531i
$131$	−169.469	+	293.528i	−0.113027	+	0.195769i	−0.916989	−	0.398912i	$-0.869388\pi$
$131$	−169.469	+	293.528i	−0.113027	+	0.195769i	0.803962	+	0.594680i	$0.202721\pi$
$132$		0			0
$133$	−895.646	−	1551.30i	−0.583927	−	1.01139i
$134$	19.6766			0.0126850
$135$		0			0
$136$	486.475			0.306727
$137$	405.721	+	702.729i	0.253015	+	0.438235i	0.964354	−	0.264614i	$-0.0852444\pi$
$137$	405.721	+	702.729i	0.253015	+	0.438235i	−0.711339	+	0.702849i	$0.751911\pi$
$138$		0			0
$139$	1553.06	−	2689.98i	0.947691	−	1.64145i	0.197420	−	0.980319i	$-0.436744\pi$
$139$	1553.06	−	2689.98i	0.947691	−	1.64145i	0.750271	−	0.661130i	$-0.229923\pi$
$140$	287.919	−	498.691i	0.173812	−	0.301050i
$141$		0			0
$142$	94.2105	+	163.177i	0.0556758	+	0.0964334i
$143$	−3557.36			−2.08029
$144$		0			0
$145$	872.001			0.499419
$146$	−64.9129	−	112.432i	−0.0367961	−	0.0637327i
$147$		0			0
$148$	614.720	−	1064.73i	0.341417	−	0.591351i
$149$	−1270.51	+	2200.58i	−0.698550	+	1.20992i	0.270419	+	0.962743i	$0.412838\pi$
$149$	−1270.51	+	2200.58i	−0.698550	+	1.20992i	−0.968969	+	0.247181i	$0.920496\pi$
$150$		0			0
$151$	562.685	+	974.599i	0.303249	+	0.525243i	0.976870	−	0.213834i	$-0.0685952\pi$
$151$	562.685	+	974.599i	0.303249	+	0.525243i	−0.673621	+	0.739077i	$0.735262\pi$
$152$	508.620			0.271411
$153$		0			0
$154$	185.105			0.0968582
$155$	115.739	+	200.466i	0.0599767	+	0.103883i
$156$		0			0
$157$	−1615.03	+	2797.31i	−0.820975	+	1.42197i	0.0839811	+	0.996467i	$0.473236\pi$
$157$	−1615.03	+	2797.31i	−0.820975	+	1.42197i	−0.904957	+	0.425504i	$0.860097\pi$
$158$	51.4333	−	89.0850i	0.0258975	−	0.0448559i
$159$		0			0
$160$	122.800	+	212.695i	0.0606760	+	0.105094i
$161$	−1328.17			−0.650154
$162$		0			0
$163$	−694.054			−0.333512			−0.166756	−	0.985998i	$-0.553329\pi$
$163$	−694.054			−0.333512			−0.166756	+	0.985998i	$0.553329\pi$
$164$	−1444.62	−	2502.16i	−0.687842	−	1.19138i
$165$		0			0
$166$	−177.148	+	306.830i	−0.0828275	+	0.143462i
$167$	−1608.02	+	2785.17i	−0.745103	+	1.29056i	0.205044	+	0.978753i	$0.434266\pi$
$167$	−1608.02	+	2785.17i	−0.745103	+	1.29056i	−0.950147	+	0.311803i	$0.899067\pi$
$168$		0			0
$169$	−1506.48	−	2609.29i	−0.685697	−	1.18766i
$170$	−152.662			−0.0688744
$171$		0			0
$172$	−997.296			−0.442111
$173$	−148.773	−	257.683i	−0.0653816	−	0.113244i	0.831482	−	0.555552i	$-0.187493\pi$
$173$	−148.773	−	257.683i	−0.0653816	−	0.113244i	−0.896863	+	0.442308i	$0.854160\pi$
$174$		0			0
$175$	−181.468	+	314.311i	−0.0783867	+	0.135770i
$176$	1537.63	−	2663.26i	0.658542	−	1.14063i
$177$		0			0
$178$	189.912	+	328.937i	0.0799690	+	0.138510i
$179$	−3450.12			−1.44064			−0.720320	−	0.693642i	$-0.756005\pi$
$179$	−3450.12			−1.44064			−0.720320	+	0.693642i	$0.756005\pi$
$180$		0			0
$181$	−3089.75			−1.26883			−0.634417	−	0.772991i	$-0.718760\pi$
$181$	−3089.75			−1.26883			−0.634417	+	0.772991i	$0.718760\pi$
$182$	135.548	+	234.776i	0.0552060	+	0.0956197i
$183$		0			0
$184$	188.561	−	326.598i	0.0755484	−	0.130854i
$185$	−387.442	+	671.069i	−0.153974	+	0.266692i
$186$		0			0
$187$	2908.20	+	5037.15i	1.13727	+	1.96980i
$188$	1757.36			0.681748
$189$		0			0
$190$	−159.611			−0.0609444
$191$	−766.057	−	1326.85i	−0.290209	−	0.502657i	0.683650	−	0.729810i	$-0.260392\pi$
$191$	−766.057	−	1326.85i	−0.290209	−	0.502657i	−0.973859	+	0.227153i	$0.927058\pi$
$192$		0			0
$193$	2597.21	−	4498.50i	0.968660	−	1.67777i	0.269219	−	0.963079i	$-0.413235\pi$
$193$	2597.21	−	4498.50i	0.968660	−	1.67777i	0.699442	−	0.714690i	$-0.253432\pi$
$194$	43.3373	−	75.0625i	0.0160383	−	0.0277792i
$195$		0			0
$196$	−524.552	−	908.550i	−0.191163	−	0.331104i
$197$	−2005.61			−0.725349			−0.362674	−	0.931916i	$-0.618136\pi$
$197$	−2005.61			−0.725349			−0.362674	+	0.931916i	$0.618136\pi$
$198$		0			0
$199$	−2874.68			−1.02402			−0.512011	−	0.858979i	$-0.671099\pi$
$199$	−2874.68			−1.02402			−0.512011	+	0.858979i	$0.671099\pi$
$200$	−51.5260	−	89.2457i	−0.0182172	−	0.0315531i
$201$		0			0
$202$	−156.015	+	270.225i	−0.0543424	+	0.0941237i
$203$	−1265.92	+	2192.64i	−0.437686	+	0.758094i
$204$		0			0
$205$	910.506	+	1577.04i	0.310207	+	0.537295i
$206$	−274.522			−0.0928488
$207$		0			0
$208$	4503.90			1.50139
$209$	3040.59	+	5266.45i	1.00632	+	1.74301i
$210$		0			0
$211$	1374.97	−	2381.52i	0.448610	−	0.777016i	−0.549686	−	0.835372i	$-0.685253\pi$
$211$	1374.97	−	2381.52i	0.448610	−	0.777016i	0.998296	+	0.0583560i	$0.0185858\pi$
$212$	−54.2598	+	93.9807i	−0.0175782	+	0.0304463i
$213$		0			0
$214$	−61.5190	−	106.554i	−0.0196512	−	0.0340368i
$215$	628.569			0.199386
$216$		0			0
$217$	−672.093			−0.210252
$218$	170.804	+	295.842i	0.0530657	+	0.0919125i
$219$		0			0
$220$	−977.444	+	1692.98i	−0.299542	+	0.518822i
$221$	−4259.23	+	7377.20i	−1.29641	+	2.24545i
$222$		0			0
$223$	391.864	+	678.728i	0.117673	+	0.203816i	0.918845	−	0.394618i	$-0.129123\pi$
$223$	391.864	+	678.728i	0.117673	+	0.203816i	−0.801172	+	0.598434i	$0.795790\pi$
$224$	−713.093			−0.212703
$225$		0			0
$226$	17.6377			0.00519134
$227$	72.8326	+	126.150i	0.0212955	+	0.0368848i	0.876477	−	0.481444i	$-0.159888\pi$
$227$	72.8326	+	126.150i	0.0212955	+	0.0368848i	−0.855181	+	0.518329i	$0.826554\pi$
$228$		0			0
$229$	1705.91	−	2954.72i	0.492270	−	0.852636i	−0.507691	−	0.861539i	$-0.669501\pi$
$229$	1705.91	−	2954.72i	0.492270	−	0.852636i	0.999960	+	0.00890324i	$0.00283403\pi$
$230$	−59.1729	+	102.490i	−0.0169641	+	0.0293827i
$231$		0			0
$232$	−359.446	−	622.578i	−0.101719	−	0.176182i
$233$	134.977			0.0379511			0.0189756	−	0.999820i	$-0.493960\pi$
$233$	134.977			0.0379511			0.0189756	+	0.999820i	$0.493960\pi$
$234$		0			0
$235$	−1107.62			−0.307459
$236$	948.347	+	1642.58i	0.261577	+	0.453064i
$237$		0			0
$238$	221.626	−	383.867i	0.0603608	−	0.104548i
$239$	1122.66	−	1944.51i	0.303845	−	0.526275i	−0.673159	−	0.739498i	$-0.735063\pi$
$239$	1122.66	−	1944.51i	0.303845	−	0.526275i	0.977003	+	0.213223i	$0.0683962\pi$
$240$		0			0
$241$	−2079.27	−	3601.40i	−0.555757	−	0.962600i	−0.997844	−	0.0656276i	$-0.979095\pi$
$241$	−2079.27	−	3601.40i	−0.555757	−	0.962600i	0.442087	−	0.896972i	$-0.354238\pi$
$242$	−284.057			−0.0754542
$243$		0			0
$244$	432.715			0.113532
$245$	330.611	+	572.635i	0.0862121	+	0.149324i
$246$		0			0
$247$	−4453.11	+	7713.02i	−1.14714	+	1.98691i
$248$	95.4171	−	165.267i	0.0244314	−	0.0423165i
$249$		0			0
$250$	16.1695	+	28.0064i	0.00409060	+	0.00708513i
$251$	3946.14			0.992343			0.496171	−	0.868225i	$-0.334739\pi$
$251$	3946.14			0.992343			0.496171	+	0.868225i	$0.334739\pi$
$252$		0			0
$253$	4508.96			1.12046
$254$	−76.7094	−	132.865i	−0.0189495	−	0.0328215i
$255$		0			0
$256$	−1878.80	+	3254.17i	−0.458690	+	0.794475i
$257$	2847.92	−	4932.74i	0.691239	−	1.19726i	−0.280193	−	0.959944i	$-0.590399\pi$
$257$	2847.92	−	4932.74i	0.691239	−	1.19726i	0.971432	−	0.237317i	$-0.0762681\pi$
$258$		0			0
$259$	−1124.93	−	1948.44i	−0.269883	−	0.467452i
$260$	−2863.04			−0.682917
$261$		0			0
$262$	−87.6873			−0.0206769
$263$	−1407.03	−	2437.05i	−0.329891	−	0.571387i	0.652599	−	0.757703i	$-0.273679\pi$
$263$	−1407.03	−	2437.05i	−0.329891	−	0.571387i	−0.982490	+	0.186316i	$0.940345\pi$
$264$		0			0
$265$	34.1985	−	59.2335i	0.00792753	−	0.0137309i
$266$	231.715	−	401.342i	0.0534110	−	0.0925106i
$267$		0			0
$268$	−301.678	−	522.521i	−0.0687608	−	0.119097i
$269$	200.985			0.0455548			0.0227774	−	0.999741i	$-0.492749\pi$
$269$	200.985			0.0455548			0.0227774	+	0.999741i	$0.492749\pi$
$270$		0			0
$271$	−2406.05			−0.539326			−0.269663	−	0.962955i	$-0.586912\pi$
$271$	−2406.05			−0.539326			−0.269663	+	0.962955i	$0.586912\pi$
$272$	−3682.01	−	6377.43i	−0.820790	−	1.42165i
$273$		0			0
$274$	−104.965	+	181.805i	−0.0231429	+	0.0400847i
$275$	616.057	−	1067.04i	0.135090	−	0.233982i
$276$		0			0
$277$	4214.67	+	7300.02i	0.914205	+	1.58345i	0.808061	+	0.589098i	$0.200517\pi$
$277$	4214.67	+	7300.02i	0.914205	+	1.58345i	0.106143	+	0.994351i	$0.466150\pi$
$278$	803.593			0.173368
$279$		0			0
$280$	299.210			0.0638615
$281$	−1987.13	−	3441.81i	−0.421859	−	0.730681i	0.574263	−	0.818671i	$-0.305289\pi$
$281$	−1987.13	−	3441.81i	−0.421859	−	0.730681i	−0.996121	+	0.0879906i	$0.971955\pi$
$282$		0			0
$283$	1536.20	−	2660.78i	0.322678	−	0.558895i	−0.658362	−	0.752702i	$-0.728750\pi$
$283$	1536.20	−	2660.78i	0.322678	−	0.558895i	0.981040	+	0.193807i	$0.0620836\pi$
$284$	2888.84	−	5003.62i	0.603595	−	1.04546i
$285$		0			0
$286$	−460.166	−	797.031i	−0.0951406	−	0.164788i
$287$	−5287.28			−1.08745
$288$		0			0
$289$	9014.97			1.83492
$290$	112.799	+	195.373i	0.0228406	+	0.0395610i
$291$		0			0
$292$	−1990.47	+	3447.59i	−0.398915	+	0.690942i
$293$	−1991.11	+	3448.70i	−0.397002	+	0.687628i	−0.993355	−	0.115095i	$-0.963283\pi$
$293$	−1991.11	+	3448.70i	−0.397002	+	0.687628i	0.596352	+	0.802723i	$0.296616\pi$
$294$		0			0
$295$	−597.717	−	1035.28i	−0.117968	−	0.204326i
$296$	638.826			0.125443
$297$		0			0
$298$	−657.391			−0.127791
$299$	3301.81	+	5718.91i	0.638625	+	1.10613i
$300$		0			0
$301$	−912.520	+	1580.53i	−0.174740	+	0.302659i
$302$	−145.574	+	252.141i	−0.0277378	+	0.0480433i
$303$		0			0
$304$	−3849.62	−	6667.74i	−0.726286	−	1.25796i
$305$	−272.729			−0.0512013
$306$		0			0
$307$	−2996.06			−0.556984			−0.278492	−	0.960439i	$-0.589835\pi$
$307$	−2996.06			−0.556984			−0.278492	+	0.960439i	$0.589835\pi$
$308$	−2837.99	−	4915.55i	−0.525032	−	0.909381i
$309$		0			0
$310$	−29.9431	+	51.8630i	−0.00548598	+	0.00950200i
$311$	1539.97	−	2667.30i	0.280783	−	0.486331i	−0.690795	−	0.723051i	$-0.742739\pi$
$311$	1539.97	−	2667.30i	0.280783	−	0.486331i	0.971578	+	0.236720i	$0.0760724\pi$
$312$		0			0
$313$	−3976.82	−	6888.06i	−0.718158	−	1.24389i	−0.961729	−	0.274003i	$-0.911652\pi$
$313$	−3976.82	−	6888.06i	−0.718158	−	1.24389i	0.243571	−	0.969883i	$-0.421681\pi$
$314$	−835.655			−0.150187
$315$		0			0
$316$	−3154.26			−0.561523
$317$	3416.49	+	5917.53i	0.605328	+	1.04846i	0.991999	+	0.126242i	$0.0402915\pi$
$317$	3416.49	+	5917.53i	0.605328	+	1.04846i	−0.386671	+	0.922218i	$0.626375\pi$
$318$		0			0
$319$	4297.62	−	7443.69i	0.754296	−	1.30648i
$320$	1216.19	−	2106.51i	0.212460	−	0.367992i
$321$		0			0
$322$	−171.808	−	297.580i	−0.0297344	−	0.0515014i
$323$	14562.0			2.50852
$324$		0			0
$325$	1804.50			0.307987
$326$	−89.7802	−	155.504i	−0.0152530	−	0.0264189i
$327$		0			0
$328$	750.636	−	1300.14i	0.126363	−	0.218867i
$329$	1607.97	−	2785.09i	0.269454	−	0.466708i
$330$		0			0
$331$	1148.29	+	1988.89i	0.190682	+	0.330270i	0.945476	−	0.325691i	$-0.105597\pi$
$331$	1148.29	+	1988.89i	0.190682	+	0.330270i	−0.754795	+	0.655961i	$0.772264\pi$
$332$	10864.0			1.79591
$333$		0			0
$334$	−832.028			−0.136307
$335$	190.139	+	329.331i	0.0310102	+	0.0537113i
$336$		0			0
$337$	−3630.74	+	6288.63i	−0.586881	+	1.01651i	0.407757	+	0.913091i	$0.366311\pi$
$337$	−3630.74	+	6288.63i	−0.586881	+	1.01651i	−0.994638	+	0.103418i	$0.967022\pi$
$338$	389.744	−	675.056i	0.0627198	−	0.108634i
$339$		0			0
$340$	2340.59	+	4054.02i	0.373342	+	0.646647i
$341$	2281.66			0.362342
$342$		0			0
$343$	−6899.32			−1.08609
$344$	−259.101	−	448.777i	−0.0406099	−	0.0703384i
$345$		0			0
$346$	38.4894	−	66.6657i	0.00598036	−	0.0103583i
$347$	−3712.61	+	6430.43i	−0.574361	+	0.994822i	0.421750	+	0.906712i	$0.361416\pi$
$347$	−3712.61	+	6430.43i	−0.574361	+	0.994822i	−0.996111	+	0.0881101i	$0.971917\pi$
$348$		0			0
$349$	239.080	+	414.098i	0.0366695	+	0.0635134i	0.883778	−	0.467907i	$-0.154992\pi$
$349$	239.080	+	414.098i	0.0366695	+	0.0635134i	−0.847108	+	0.531420i	$0.821658\pi$
$350$	−93.8959			−0.0143399
$351$		0			0
$352$	2420.85			0.366567
$353$	2496.54	+	4324.14i	0.376424	+	0.651985i	0.990539	−	0.137231i	$-0.0438204\pi$
$353$	2496.54	+	4324.14i	0.376424	+	0.651985i	−0.614115	+	0.789216i	$0.710487\pi$
$354$		0			0
$355$	−1820.76	+	3153.64i	−0.272213	+	0.471488i
$356$	5823.39	−	10086.4i	0.866964	−	1.50162i
$357$		0			0
$358$	−446.295	−	773.006i	−0.0658867	−	0.114119i
$359$	−6873.09			−1.01044			−0.505219	−	0.862991i	$-0.668588\pi$
$359$	−6873.09			−1.01044			−0.505219	+	0.862991i	$0.668588\pi$
$360$		0			0
$361$	8365.87			1.21969
$362$	−399.678	−	692.262i	−0.0580293	−	0.100510i
$363$		0			0
$364$	4156.40	−	7199.10i	0.598502	−	1.03664i
$365$	1254.54	−	2172.92i	0.179906	−	0.311605i
$366$		0			0
$367$	4344.36	+	7524.65i	0.617912	+	1.07025i	0.989866	+	0.142004i	$0.0453545\pi$
$367$	4344.36	+	7524.65i	0.617912	+	1.07025i	−0.371954	+	0.928251i	$0.621312\pi$
$368$	−5708.70			−0.808659
$369$		0			0
$370$	−200.472			−0.0281677
$371$	99.2948	+	171.984i	0.0138952	+	0.0240672i
$372$		0			0
$373$	−1747.27	+	3026.36i	−0.242548	+	0.420105i	−0.961439	−	0.275017i	$-0.911316\pi$
$373$	−1747.27	+	3026.36i	−0.242548	+	0.420105i	0.718892	+	0.695122i	$0.244650\pi$
$374$	−752.388	+	1303.17i	−0.104024	+	0.180175i
$375$		0			0
$376$	456.568	+	790.799i	0.0626216	+	0.108464i
$377$	12588.2			1.71970
$378$		0			0
$379$	−5802.83			−0.786468			−0.393234	−	0.919438i	$-0.628644\pi$
$379$	−5802.83			−0.786468			−0.393234	+	0.919438i	$0.628644\pi$
$380$	2447.14	+	4238.56i	0.330356	+	0.572194i
$381$		0			0
$382$	198.189	−	343.273i	0.0265450	−	0.0459774i
$383$	1679.28	−	2908.60i	0.224040	−	0.388049i	−0.731991	−	0.681314i	$-0.761409\pi$
$383$	1679.28	−	2908.60i	0.224040	−	0.388049i	0.956031	+	0.293266i	$0.0947420\pi$
$384$		0			0
$385$	1788.71	+	3098.14i	0.236782	+	0.410119i
$386$	1343.86			0.177204
$387$		0			0
$388$	−2657.76			−0.347751
$389$	−9.56850	−	16.5731i	−0.00124715	−	0.00216013i	0.865401	−	0.501080i	$-0.167064\pi$
$389$	−9.56850	−	16.5731i	−0.00124715	−	0.00216013i	−0.866648	+	0.498920i	$0.833730\pi$
$390$		0			0
$391$	5398.58	−	9350.62i	0.698256	−	1.20941i
$392$	272.561	−	472.090i	0.0351184	−	0.0608268i
$393$		0			0
$394$	−259.438	−	449.360i	−0.0331733	−	0.0574579i
$395$	1988.05			0.253239
$396$		0			0
$397$	−4348.59			−0.549747			−0.274873	−	0.961480i	$-0.588636\pi$
$397$	−4348.59			−0.549747			−0.274873	+	0.961480i	$0.588636\pi$
$398$	−371.857	−	644.076i	−0.0468330	−	0.0811171i
$399$		0			0
$400$	−779.976	+	1350.96i	−0.0974970	+	0.168870i
$401$	−4250.81	+	7362.61i	−0.529364	+	0.916886i	0.470049	+	0.882640i	$0.344236\pi$
$401$	−4250.81	+	7362.61i	−0.529364	+	0.916886i	−0.999413	+	0.0342457i	$0.989097\pi$
$402$		0			0
$403$	1670.81	+	2893.93i	0.206523	+	0.357709i
$404$	9567.96			1.17828
$405$		0			0
$406$	−655.019			−0.0800690
$407$	3818.98	+	6614.66i	0.465110	+	0.805594i
$408$		0			0
$409$	1405.33	−	2434.11i	0.169900	−	0.294276i	−0.768484	−	0.639869i	$-0.778989\pi$
$409$	1405.33	−	2434.11i	0.169900	−	0.294276i	0.938385	+	0.345593i	$0.112322\pi$
$410$	−235.559	+	408.001i	−0.0283742	+	0.0491456i
$411$		0			0
$412$	4208.93	+	7290.07i	0.503298	+	0.871738i
$413$	3470.93			0.413543
$414$		0			0
$415$	−6847.31			−0.809930
$416$	1772.73	+	3070.47i	0.208931	+	0.361880i
$417$		0			0
$418$	−786.638	+	1362.50i	−0.0920471	+	0.159430i
$419$	8177.71	−	14164.2i	0.953478	−	1.65147i	0.215666	−	0.976467i	$-0.430808\pi$
$419$	8177.71	−	14164.2i	0.953478	−	1.65147i	0.737812	−	0.675006i	$-0.235859\pi$
$420$		0			0
$421$	2255.45	+	3906.55i	0.261102	+	0.452242i	0.966535	−	0.256535i	$-0.0825808\pi$
$421$	2255.45	+	3906.55i	0.261102	+	0.452242i	−0.705433	+	0.708776i	$0.749248\pi$
$422$	711.443			0.0820675
$423$		0			0
$424$	−56.3876			−0.00645854
$425$	−1475.21	−	2555.14i	−0.168372	−	0.291629i
$426$		0			0
$427$	395.932	−	685.774i	0.0448723	−	0.0777212i
$428$	−1886.40	+	3267.33i	−0.213043	+	0.369001i
$429$		0			0
$430$	81.3093	+	140.832i	0.00911880	+	0.0157942i
$431$	5850.47			0.653845			0.326923	−	0.945051i	$-0.393988\pi$
$431$	5850.47			0.653845			0.326923	+	0.945051i	$0.393988\pi$
$432$		0			0
$433$	−3836.82			−0.425833			−0.212916	−	0.977070i	$-0.568296\pi$
$433$	−3836.82			−0.425833			−0.212916	+	0.977070i	$0.568296\pi$
$434$	−86.9394	−	150.583i	−0.00961572	−	0.0166549i
$435$		0			0
$436$	5237.48	−	9071.59i	0.575298	−	0.996446i
$437$	5644.33	−	9776.27i	0.617860	−	1.07017i
$438$		0			0
$439$	−8113.67	−	14053.3i	−0.882106	−	1.52785i	−0.848995	−	0.528400i	$-0.822792\pi$
$439$	−8113.67	−	14053.3i	−0.882106	−	1.52785i	−0.0331103	−	0.999452i	$-0.510541\pi$
$440$	−1015.77			−0.110057
$441$		0			0
$442$	−2203.83			−0.237162
$443$	−3352.56	−	5806.81i	−0.359560	−	0.622776i	0.628327	−	0.777949i	$-0.283740\pi$
$443$	−3352.56	−	5806.81i	−0.359560	−	0.622776i	−0.987887	+	0.155173i	$0.950407\pi$
$444$		0			0
$445$	−3670.33	+	6357.19i	−0.390989	+	0.677213i
$446$	−101.380	+	175.595i	−0.0107634	+	0.0186428i
$447$		0			0
$448$	3531.20	+	6116.21i	0.372396	+	0.645009i
$449$	213.100			0.0223982			0.0111991	−	0.999937i	$-0.496435\pi$
$449$	213.100			0.0223982			0.0111991	+	0.999937i	$0.496435\pi$
$450$		0			0
$451$	17949.6			1.87408
$452$	−270.419	−	468.379i	−0.0281403	−	0.0487404i
$453$		0			0
$454$	−18.8427	+	32.6365i	−0.00194787	+	0.00337381i
$455$	−2619.67	+	4537.40i	−0.269916	+	0.467509i
$456$		0			0
$457$	−8231.03	−	14256.6i	−0.842520	−	1.45929i	−0.887758	−	0.460311i	$-0.847738\pi$
$457$	−8231.03	−	14256.6i	−0.842520	−	1.45929i	0.0452381	−	0.998976i	$-0.485595\pi$
$458$	882.680			0.0900545
$459$		0			0
$460$	3628.92			0.367824
$461$	−781.029	−	1352.78i	−0.0789071	−	0.136671i	0.823872	−	0.566777i	$-0.191810\pi$
$461$	−781.029	−	1352.78i	−0.0789071	−	0.136671i	−0.902779	+	0.430105i	$0.858476\pi$
$462$		0			0
$463$	2962.14	−	5130.57i	0.297326	−	0.514984i	−0.678197	−	0.734880i	$-0.737238\pi$
$463$	2962.14	−	5130.57i	0.297326	−	0.514984i	0.975523	+	0.219896i	$0.0705717\pi$
$464$	−5441.12	+	9424.30i	−0.544392	+	0.942914i
$465$		0			0
$466$	17.4601	+	30.2417i	0.00173567	+	0.00300627i
$467$	−17905.1			−1.77420			−0.887098	−	0.461582i	$-0.847282\pi$
$467$	−17905.1			−1.77420			−0.887098	+	0.461582i	$0.847282\pi$
$468$		0			0
$469$	−1104.13			−0.108708
$470$	−143.277	−	248.163i	−0.0140614	−	0.0243551i
$471$		0			0
$472$	−492.768	+	853.499i	−0.0480540	+	0.0832320i
$473$	3097.87	−	5365.67i	0.301142	−	0.521594i
$474$		0			0
$475$	−1542.36	−	2671.45i	−0.148986	−	0.258052i
$476$	−13591.7			−1.30877
$477$		0			0
$478$	580.893			0.0555846
$479$	−4957.72	−	8587.02i	−0.472910	−	0.819104i	0.526609	−	0.850107i	$-0.323463\pi$
$479$	−4957.72	−	8587.02i	−0.472910	−	0.819104i	−0.999519	+	0.0310033i	$0.990130\pi$
$480$		0			0
$481$	−5593.11	+	9687.55i	−0.530195	+	0.918324i
$482$	537.933	−	931.727i	0.0508344	−	0.0880477i
$483$		0			0
$484$	4355.12	+	7543.29i	0.409008	+	0.708423i
$485$	1675.12			0.156831
$486$		0			0
$487$	11910.8			1.10828			0.554138	−	0.832425i	$-0.313048\pi$
$487$	11910.8			1.10828			0.554138	+	0.832425i	$0.313048\pi$
$488$	112.421	+	194.719i	0.0104284	+	0.0180625i
$489$		0			0
$490$	−85.5331	+	148.148i	−0.00788570	+	0.0136584i
$491$	−5531.88	+	9581.50i	−0.508453	+	0.880666i	0.491499	+	0.870878i	$0.336449\pi$
$491$	−5531.88	+	9581.50i	−0.508453	+	0.880666i	−0.999952	+	0.00978823i	$0.996884\pi$
$492$		0			0
$493$	−10291.1	−	17824.7i	−0.940135	−	1.62836i
$494$	−2304.15			−0.209856
$495$		0			0
$496$	−2888.76			−0.261510
$497$	−5286.54	−	9156.56i	−0.477130	−	0.826414i
$498$		0			0
$499$	−4673.62	+	8094.95i	−0.419279	+	0.726212i	−0.995867	−	0.0908227i	$-0.971050\pi$
$499$	−4673.62	+	8094.95i	−0.419279	+	0.726212i	0.576588	+	0.817035i	$0.304384\pi$
$500$	495.817	−	858.780i	0.0443472	−	0.0768116i
$501$		0			0
$502$	510.457	+	884.138i	0.0453841	+	0.0786076i
$503$	−19474.2			−1.72627			−0.863135	−	0.504973i	$-0.831502\pi$
$503$	−19474.2			−1.72627			−0.863135	+	0.504973i	$0.831502\pi$
$504$		0			0
$505$	−6030.43			−0.531387
$506$	583.262	+	1010.24i	0.0512434	+	0.0887562i
$507$		0			0
$508$	−2352.19	+	4074.12i	−0.205436	+	0.355826i
$509$	−11082.0	+	19194.7i	−0.965035	+	1.67149i	−0.255514	+	0.966805i	$0.582245\pi$
$509$	−11082.0	+	19194.7i	−0.965035	+	1.67149i	−0.709521	+	0.704684i	$0.751089\pi$
$510$		0			0
$511$	3642.53	+	6309.05i	0.315335	+	0.546176i
$512$	−5122.66			−0.442172
$513$		0			0
$514$	1473.58			0.126453
$515$	−2652.77	−	4594.74i	−0.226981	−	0.393142i
$516$		0			0
$517$	−5458.83	+	9454.98i	−0.464370	+	0.804312i
$518$	291.034	−	504.085i	0.0246859	−	0.0427572i
$519$		0			0
$520$	−743.830	−	1288.35i	−0.0627290	−	0.108650i
$521$	−254.564			−0.0214062			−0.0107031	−	0.999943i	$-0.503407\pi$
$521$	−254.564			−0.0214062			−0.0107031	+	0.999943i	$0.503407\pi$
$522$		0			0
$523$	4049.92			0.338606			0.169303	−	0.985564i	$-0.445848\pi$
$523$	4049.92			0.338606			0.169303	+	0.985564i	$0.445848\pi$
$524$	1344.41	+	2328.58i	0.112081	+	0.194131i
$525$		0			0
$526$	364.016	−	630.495i	0.0301747	−	0.0522640i
$527$	2731.83	−	4731.67i	0.225807	−	0.391110i
$528$		0			0
$529$	1898.44	+	3288.20i	0.156032	+	0.270256i
$530$	17.6951			0.00145024
$531$		0			0
$532$	−14210.4			−1.15808
$533$	13144.1	+	22766.2i	1.06817	+	1.85012i
$534$		0			0
$535$	1188.95	−	2059.31i	0.0960796	−	0.166415i
$536$	156.754	−	271.506i	0.0126320	−	0.0218792i
$537$		0			0
$538$	25.9986	+	45.0309i	0.00208342	+	0.00360859i
$539$	6517.60			0.520841
$540$		0			0
$541$	−4085.88			−0.324705			−0.162353	−	0.986733i	$-0.551908\pi$
$541$	−4085.88			−0.324705			−0.162353	+	0.986733i	$0.551908\pi$
$542$	−311.238	−	539.079i	−0.0246657	−	0.0427222i
$543$		0			0
$544$	2898.48	−	5020.32i	0.228440	−	0.395670i
$545$	−3301.05	+	5717.58i	−0.259452	+	0.449384i
$546$		0			0
$547$	7696.10	+	13330.0i	0.601575	+	1.04196i	0.992583	+	0.121571i	$0.0387932\pi$
$547$	7696.10	+	13330.0i	0.601575	+	1.04196i	−0.391008	+	0.920387i	$0.627873\pi$
$548$	6437.22			0.501796
$549$		0			0
$550$	318.763			0.0247129
$551$	−10759.5	−	18636.1i	−0.831891	−	1.44088i
$552$		0			0
$553$	−2886.13	+	4998.93i	−0.221937	+	0.384405i
$554$	−1090.39	+	1888.60i	−0.0836211	+	0.144836i
$555$		0			0
$556$	−12320.6	−	21339.8i	−0.939762	−	1.62772i
$557$	−10897.6			−0.828987			−0.414493	−	0.910052i	$-0.636041\pi$
$557$	−10897.6			−0.828987			−0.414493	+	0.910052i	$0.636041\pi$
$558$		0			0
$559$	9074.02			0.686566
$560$	−2264.65	−	3922.49i	−0.170891	−	0.295992i
$561$		0			0
$562$	514.095	−	890.439i	0.0385868	−	0.0668343i
$563$	775.845	−	1343.80i	0.0580781	−	0.100594i	−0.835525	−	0.549453i	$-0.814836\pi$
$563$	775.845	−	1343.80i	0.0580781	−	0.100594i	0.893603	+	0.448859i	$0.148169\pi$
$564$		0			0
$565$	170.438	+	295.207i	0.0126909	+	0.0219813i
$566$	794.870			0.0590298
$567$		0			0
$568$	3002.12			0.221772
$569$	623.475	+	1079.89i	0.0459357	+	0.0795630i	0.888079	−	0.459691i	$-0.152040\pi$
$569$	623.475	+	1079.89i	0.0459357	+	0.0795630i	−0.842143	+	0.539254i	$0.818706\pi$
$570$		0			0
$571$	−2098.29	+	3634.34i	−0.153784	+	0.266362i	−0.932616	−	0.360871i	$-0.882479\pi$
$571$	−2098.29	+	3634.34i	−0.153784	+	0.266362i	0.778832	+	0.627233i	$0.215813\pi$
$572$	−14110.4	+	24439.9i	−1.03144	+	1.78651i
$573$		0			0
$574$	−683.943	−	1184.62i	−0.0497338	−	0.0861415i
$575$	−2287.21			−0.165884
$576$		0			0
$577$	20585.1			1.48521			0.742607	−	0.669728i	$-0.233589\pi$
$577$	20585.1			1.48521			0.742607	+	0.669728i	$0.233589\pi$
$578$	1166.14	+	2019.82i	0.0839189	+	0.145352i
$579$		0			0
$580$	3458.82	−	5990.85i	0.247620	−	0.428891i
$581$	9940.53	−	17217.5i	0.709815	−	1.22944i
$582$		0			0
$583$	−337.091	−	583.859i	−0.0239466	−	0.0414768i
$584$	−2068.52			−0.146569
$585$		0			0
$586$	−1030.25			−0.0726265
$587$	2427.89	+	4205.23i	0.170715	+	0.295687i	0.938670	−	0.344817i	$-0.112059\pi$
$587$	2427.89	+	4205.23i	0.170715	+	0.295687i	−0.767955	+	0.640504i	$0.778726\pi$
$588$		0			0
$589$	2856.19	−	4947.06i	0.199808	−	0.346078i
$590$	154.637	−	267.839i	0.0107903	−	0.0186894i
$591$		0			0
$592$	−4835.13	−	8374.68i	−0.335680	−	0.581414i
$593$	−23965.6			−1.65961			−0.829804	−	0.558055i	$-0.811548\pi$
$593$	−23965.6			−1.65961			−0.829804	+	0.558055i	$0.811548\pi$
$594$		0			0
$595$	8566.50			0.590239
$596$	10079.0	+	17457.4i	0.692706	+	1.19980i
$597$		0			0
$598$	−854.220	+	1479.55i	−0.0584141	+	0.101176i
$599$	−7114.56	+	12322.8i	−0.485297	+	0.840560i	−0.999857	−	0.0168947i	$-0.994622\pi$
$599$	−7114.56	+	12322.8i	−0.485297	+	0.840560i	0.514560	+	0.857454i	$0.327955\pi$
$600$		0			0
$601$	4438.98	+	7688.55i	0.301281	+	0.521834i	0.976426	−	0.215851i	$-0.0692524\pi$
$601$	4438.98	+	7688.55i	0.301281	+	0.521834i	−0.675145	+	0.737685i	$0.735919\pi$
$602$	−472.161			−0.0319665
$603$		0			0
$604$	8927.64			0.601424
$605$	−2744.92	−	4754.33i	−0.184457	−	0.319490i
$606$		0			0
$607$	5438.36	−	9419.51i	0.363651	−	0.629862i	−0.624908	−	0.780699i	$-0.714863\pi$
$607$	5438.36	−	9419.51i	0.363651	−	0.629862i	0.988559	+	0.150837i	$0.0481968\pi$
$608$	3030.42	−	5248.85i	0.202138	−	0.350113i
$609$		0			0
$610$	−35.2791	−	61.1053i	−0.00234166	−	0.00405587i
$611$	−15989.5			−1.05870
$612$		0			0
$613$	−19544.8			−1.28778			−0.643890	−	0.765118i	$-0.722680\pi$
$613$	−19544.8			−1.28778			−0.643890	+	0.765118i	$0.722680\pi$
$614$	−387.559	−	671.272i	−0.0254733	−	0.0441210i
$615$		0			0
$616$	1474.64	−	2554.16i	0.0964530	−	0.167062i
$617$	−2520.88	+	4366.29i	−0.164484	+	0.284895i	−0.936472	−	0.350742i	$-0.885929\pi$
$617$	−2520.88	+	4366.29i	−0.164484	+	0.284895i	0.771988	+	0.635637i	$0.219263\pi$
$618$		0			0
$619$	2604.03	+	4510.31i	0.169087	+	0.292867i	0.938099	−	0.346367i	$-0.112585\pi$
$619$	2604.03	+	4510.31i	0.169087	+	0.292867i	−0.769012	+	0.639234i	$0.779252\pi$
$620$	1836.33			0.118950
$621$		0			0
$622$	796.818			0.0513657
$623$	−10656.7	−	18458.0i	−0.685318	−	1.18701i
$624$		0			0
$625$	−312.500	+	541.266i	−0.0200000	+	0.0346410i
$626$	1028.85	−	1782.03i	0.0656889	−	0.113777i
$627$		0			0
$628$	12812.1	+	22191.2i	0.814107	+	1.41007i
$629$	18289.9			1.15940
$630$		0			0
$631$	−20284.6			−1.27974			−0.639872	−	0.768482i	$-0.721013\pi$
$631$	−20284.6			−1.27974			−0.639872	+	0.768482i	$0.721013\pi$
$632$	−819.490	−	1419.40i	−0.0515784	−	0.0893364i
$633$		0			0
$634$	−883.888	+	1530.94i	−0.0553686	+	0.0959012i
$635$	1482.52	−	2567.81i	0.0926491	−	0.160473i
$636$		0			0
$637$	4772.70	+	8266.56i	0.296862	+	0.514180i
$638$	2223.69			0.137989
$639$		0			0
$640$	2594.08			0.160219
$641$	10426.2	+	18058.7i	0.642449	+	1.11275i	0.984885	+	0.173212i	$0.0554147\pi$
$641$	10426.2	+	18058.7i	0.642449	+	1.11275i	−0.342436	+	0.939541i	$0.611252\pi$
$642$		0			0
$643$	1093.61	−	1894.19i	0.0670729	−	0.116174i	−0.830539	−	0.556961i	$-0.811967\pi$
$643$	1093.61	−	1894.19i	0.0670729	−	0.116174i	0.897612	+	0.440787i	$0.145301\pi$
$644$	−5268.25	+	9124.88i	−0.322357	+	0.558339i
$645$		0			0
$646$	1883.68	+	3262.63i	0.114725	+	0.198710i
$647$	17044.1			1.03566			0.517831	−	0.855483i	$-0.326740\pi$
$647$	17044.1			1.03566			0.517831	+	0.855483i	$0.326740\pi$
$648$		0			0
$649$	−11783.3			−0.712688
$650$	233.423	+	404.301i	0.0140856	+	0.0243969i
$651$		0			0
$652$	−2752.99	+	4768.32i	−0.165361	+	0.286414i
$653$	−4237.13	+	7338.93i	−0.253923	+	0.439808i	−0.964602	−	0.263708i	$-0.915054\pi$
$653$	−4237.13	+	7338.93i	−0.253923	+	0.439808i	0.710679	+	0.703516i	$0.248388\pi$
$654$		0			0
$655$	−847.343	−	1467.64i	−0.0505472	−	0.0875504i
$656$	−22725.6			−1.35257
$657$		0			0
$658$	832.005			0.0492932
$659$	−12780.1	−	22135.7i	−0.755450	−	1.30848i	−0.945151	−	0.326635i	$-0.894085\pi$
$659$	−12780.1	−	22135.7i	−0.755450	−	1.30848i	0.189701	−	0.981842i	$-0.439248\pi$
$660$		0			0
$661$	−604.797	+	1047.54i	−0.0355883	+	0.0616407i	−0.883271	−	0.468863i	$-0.844664\pi$
$661$	−604.797	+	1047.54i	−0.0355883	+	0.0616407i	0.847683	+	0.530504i	$0.177997\pi$
$662$	−297.076	+	514.551i	−0.0174414	+	0.0302093i
$663$		0			0
$664$	2822.52	+	4888.74i	0.164962	+	0.285723i
$665$	8956.46			0.522281
$666$		0			0
$667$	−15955.6			−0.926241
$668$	12756.5	+	22094.9i	0.738869	+	1.27976i
$669$		0			0
$670$	−49.1914	+	85.2020i	−0.00283646	+	0.00491290i
$671$	−1344.13	+	2328.10i	−0.0773318	+	0.133943i
$672$		0			0
$673$	4349.11	+	7532.87i	0.249102	+	0.431457i	0.963277	−	0.268510i	$-0.0865312\pi$
$673$	4349.11	+	7532.87i	0.249102	+	0.431457i	−0.714175	+	0.699967i	$0.753198\pi$
$674$	−1878.64			−0.107362
$675$		0			0
$676$	−23902.0			−1.35992
$677$	4212.24	+	7295.82i	0.239128	+	0.414182i	0.960464	−	0.278403i	$-0.0898051\pi$
$677$	4212.24	+	7295.82i	0.239128	+	0.414182i	−0.721336	+	0.692585i	$0.756472\pi$
$678$		0			0
$679$	−2431.84	+	4212.07i	−0.137445	+	0.238062i
$680$	−1216.19	+	2106.50i	−0.0685863	+	0.118795i
$681$		0			0
$682$	295.147	+	511.209i	0.0165715	+	0.0287026i
$683$	−17828.6			−0.998817			−0.499408	−	0.866367i	$-0.666449\pi$
$683$	−17828.6			−0.998817			−0.499408	+	0.866367i	$0.666449\pi$
$684$		0			0
$685$	−4057.21			−0.226304
$686$	−892.470	−	1545.80i	−0.0496715	−	0.0860336i
$687$		0			0
$688$	−3922.15	+	6793.37i	−0.217341	+	0.376446i
$689$	493.689	−	855.095i	0.0272976	−	0.0472809i
$690$		0			0
$691$	−7262.54	−	12579.1i	−0.399826	−	0.692519i	0.593878	−	0.804555i	$-0.297596\pi$
$691$	−7262.54	−	12579.1i	−0.399826	−	0.692519i	−0.993704	+	0.112036i	$0.964263\pi$
$692$	−2360.45			−0.129669
$693$		0			0
$694$	−1921.00			−0.105072
$695$	7765.31	+	13449.9i	0.423820	+	0.734078i
$696$		0			0
$697$	21491.0	−	37223.5i	1.16791	−	2.02287i
$698$	−61.8529	+	107.132i	−0.00335411	+	0.00580949i
$699$		0			0
$700$	1439.60	+	2493.45i	0.0777309	+	0.134634i
$701$	18815.5			1.01377			0.506883	−	0.862015i	$-0.330798\pi$
$701$	18815.5			1.01377			0.506883	+	0.862015i	$0.330798\pi$
$702$		0			0
$703$	19122.4			1.02591
$704$	−11987.9	−	20763.6i	−0.641777	−	1.11159i
$705$		0			0
$706$	−645.886	+	1118.71i	−0.0344310	+	0.0596362i
$707$	8754.63	−	15163.5i	0.465703	−	0.806621i
$708$		0			0
$709$	6467.21	+	11201.5i	0.342569	+	0.593346i	0.984909	−	0.173073i	$-0.0553697\pi$
$709$	6467.21	+	11201.5i	0.342569	+	0.593346i	−0.642340	+	0.766420i	$0.722036\pi$
$710$	−942.105			−0.0497980
$711$		0			0
$712$	6051.75			0.318538
$713$	−2117.75	−	3668.06i	−0.111235	−	0.192665i
$714$		0			0
$715$	8893.40	−	15403.8i	0.465167	−	0.805692i
$716$	−13685.0	+	23703.2i	−0.714293	+	1.23719i
$717$		0			0
$718$	−889.076	−	1539.92i	−0.0462117	−	0.0800411i
$719$	−8471.10			−0.439386			−0.219693	−	0.975569i	$-0.570506\pi$
$719$	−8471.10			−0.439386			−0.219693	+	0.975569i	$0.570506\pi$
$720$		0			0
$721$	15404.6			0.795695
$722$	1082.18	+	1874.39i	0.0557818	+	0.0966169i
$723$		0			0
$724$	−12255.6	+	21227.3i	−0.629109	+	1.08965i
$725$	−2180.00	+	3775.87i	−0.111673	+	0.193424i
$726$		0			0
$727$	−12184.7	−	21104.6i	−0.621605	−	1.07665i	−0.989187	−	0.146660i	$-0.953148\pi$
$727$	−12184.7	−	21104.6i	−0.621605	−	1.07665i	0.367582	−	0.929991i	$-0.380186\pi$
$728$	4319.40			0.219900
$729$		0			0
$730$	649.129			0.0329114
$731$	−7418.17	−	12848.7i	−0.375337	−	0.650102i
$732$		0			0
$733$	17705.9	−	30667.5i	0.892199	−	1.54533i	0.0549659	−	0.998488i	$-0.482495\pi$
$733$	17705.9	−	30667.5i	0.892199	−	1.54533i	0.837233	−	0.546846i	$-0.184172\pi$
$734$	−1123.94	+	1946.72i	−0.0565196	+	0.0978947i
$735$		0			0
$736$	−2246.94	−	3891.82i	−0.112532	−	0.194911i
$737$	3748.37			0.187345
$738$		0			0
$739$	−24447.0			−1.21691			−0.608456	−	0.793588i	$-0.708211\pi$
$739$	−24447.0			−1.21691			−0.608456	+	0.793588i	$0.708211\pi$
$740$	3073.60	+	5323.63i	0.152686	+	0.264460i
$741$		0			0
$742$	−25.6888	+	44.4943i	−0.00127098	+	0.00220140i
$743$	12063.0	−	20893.7i	0.595623	−	1.03165i	−0.397836	−	0.917457i	$-0.630239\pi$
$743$	12063.0	−	20893.7i	0.595623	−	1.03165i	0.993459	−	0.114192i	$-0.0364280\pi$
$744$		0			0
$745$	−6352.53	−	11002.9i	−0.312401	−	0.541094i
$746$	−904.081			−0.0443710
$747$		0			0
$748$	46141.9			2.25550
$749$	3452.08	+	5979.19i	0.168406	+	0.291689i
$750$		0			0
$751$	−5941.19	+	10290.4i	−0.288678	+	0.500005i	−0.973494	−	0.228711i	$-0.926549\pi$
$751$	−5941.19	+	10290.4i	−0.288678	+	0.500005i	0.684816	+	0.728716i	$0.259882\pi$
$752$	6911.31	−	11970.7i	0.335146	−	0.580490i
$753$		0			0
$754$	1628.36	+	2820.41i	0.0786491	+	0.136224i
$755$	−5626.85			−0.271234
$756$		0			0
$757$	−14601.3			−0.701049			−0.350525	−	0.936554i	$-0.613997\pi$
$757$	−14601.3			−0.701049			−0.350525	+	0.936554i	$0.613997\pi$
$758$	−750.632	−	1300.13i	−0.0359686	−	0.0622994i
$759$		0			0
$760$	−1271.55	+	2202.39i	−0.0606894	+	0.105117i
$761$	10148.2	−	17577.1i	0.483404	−	0.837281i	−0.516414	−	0.856339i	$-0.672733\pi$
$761$	10148.2	−	17577.1i	0.483404	−	0.837281i	0.999818	+	0.0190580i	$0.00606673\pi$
$762$		0			0
$763$	−9584.54	−	16600.9i	−0.454762	−	0.787671i
$764$	−12154.4			−0.575562
$765$		0			0
$766$	868.902			0.0409853
$767$	−8628.65	−	14945.3i	−0.406209	−	0.703575i
$768$		0			0
$769$	−18161.0	+	31455.8i	−0.851629	+	1.47506i	0.0281090	+	0.999605i	$0.491051\pi$
$769$	−18161.0	+	31455.8i	−0.851629	+	1.47506i	−0.879738	+	0.475459i	$0.842282\pi$
$770$	−462.762	+	801.527i	−0.0216582	+	0.0375130i
$771$		0			0
$772$	−20603.9	−	35686.9i	−0.960556	−	1.66373i
$773$	28930.9			1.34615			0.673073	−	0.739576i	$-0.264974\pi$
$773$	28930.9			1.34615			0.673073	+	0.739576i	$0.264974\pi$
$774$		0			0
$775$	−1157.39			−0.0536448
$776$	−690.497	−	1195.98i	−0.0319425	−	0.0553261i
$777$		0			0
$778$	2.47549	−	4.28767i	0.000114075	−	0.000197584i
$779$	22469.3	−	38918.0i	1.03344	−	1.78996i
$780$		0			0
$781$	17947.0	+	31085.2i	0.822274	+	1.42422i
$782$	2793.36			0.127737
$783$		0			0
$784$	−8251.80			−0.375902
$785$	−8075.13	−	13986.5i

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:	\( N \)	\(=\)	\( 405 = 3^{4} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	405.e (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.129356 + 0.224051i) q^{2} +(3.96653 - 6.87024i) q^{4} +(-2.50000 + 4.33013i) q^{5} +(-7.25871 - 12.5725i) q^{7} +4.12208 q^{8} +O(q^{10})\)	\(q+(0.129356 + 0.224051i) q^{2} +(3.96653 - 6.87024i) q^{4} +(-2.50000 + 4.33013i) q^{5} +(-7.25871 - 12.5725i) q^{7} +4.12208 q^{8} -1.29356 q^{10} +(24.6423 + 42.6817i) q^{11} +(-36.0900 + 62.5097i) q^{13} +(1.87792 - 3.25265i) q^{14} +(-31.1991 - 54.0383i) q^{16} +118.017 q^{17} +123.389 q^{19} +(19.8327 + 34.3512i) q^{20} +(-6.37526 + 11.0423i) q^{22} +(45.7442 - 79.2312i) q^{23} +(-12.5000 - 21.6506i) q^{25} -18.6739 q^{26} -115.168 q^{28} +(-87.2001 - 151.035i) q^{29} +(23.1478 - 40.0932i) q^{31} +(24.5599 - 42.5390i) q^{32} +(15.2662 + 26.4418i) q^{34} +72.5871 q^{35} +154.977 q^{37} +(15.9611 + 27.6455i) q^{38} +(-10.3052 + 17.8491i) q^{40} +(182.101 - 315.409i) q^{41} +(-62.8569 - 108.871i) q^{43} +390.978 q^{44} +23.6692 q^{46} +(110.762 + 191.845i) q^{47} +(66.1222 - 114.527i) q^{49} +(3.23390 - 5.60129i) q^{50} +(286.304 + 495.894i) q^{52} -13.6794 q^{53} -246.423 q^{55} +(-29.9210 - 51.8247i) q^{56} +(22.5597 - 39.0746i) q^{58} +(-119.543 + 207.055i) q^{59} +(27.2729 + 47.2380i) q^{61} +11.9772 q^{62} -486.477 q^{64} +(-180.450 - 312.549i) q^{65} +(38.0279 - 65.8662i) q^{67} +(468.118 - 810.804i) q^{68} +(9.38959 + 16.2633i) q^{70} +728.303 q^{71} -501.815 q^{73} +(20.0472 + 34.7227i) q^{74} +(489.427 - 847.712i) q^{76} +(357.742 - 619.628i) q^{77} +(-198.805 - 344.340i) q^{79} +311.991 q^{80} +94.2237 q^{82} +(684.731 + 1185.99i) q^{83} +(-295.042 + 511.028i) q^{85} +(16.2619 - 28.1664i) q^{86} +(101.577 + 175.937i) q^{88} +1468.13 q^{89} +1047.87 q^{91} +(-362.892 - 628.547i) q^{92} +(-28.6554 + 49.6326i) q^{94} +(-308.473 + 534.290i) q^{95} +(-167.512 - 290.139i) q^{97} +34.2133 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + q^{2} - 23 q^{4} - 15 q^{5} - 44 q^{7} - 72 q^{8}+O(q^{10}) \) 6 * q + q^2 - 23 * q^4 - 15 * q^5 - 44 * q^7 - 72 * q^8	\( 6 q + q^{2} - 23 q^{4} - 15 q^{5} - 44 q^{7} - 72 q^{8} - 10 q^{10} - 38 q^{11} - 28 q^{13} + 108 q^{14} - 191 q^{16} - 38 q^{17} + 374 q^{19} - 115 q^{20} - 122 q^{22} + 81 q^{23} - 75 q^{25} + 832 q^{26} + 820 q^{28} - 160 q^{29} - 227 q^{31} + 569 q^{32} - 17 q^{34} + 440 q^{35} + 156 q^{37} + 757 q^{38} + 180 q^{40} + 338 q^{41} - 22 q^{43} + 3272 q^{44} - 2850 q^{46} + 472 q^{47} + 197 q^{49} + 25 q^{50} + 1566 q^{52} + 1042 q^{53} + 380 q^{55} + 1254 q^{56} + 2096 q^{58} - 140 q^{59} - 595 q^{61} + 2814 q^{62} - 1836 q^{64} - 140 q^{65} - 878 q^{67} + 3053 q^{68} + 540 q^{70} - 1204 q^{71} + 2588 q^{73} - 2878 q^{74} - 525 q^{76} - 288 q^{77} - 629 q^{79} + 1910 q^{80} - 3364 q^{82} + 1287 q^{83} + 95 q^{85} + 3730 q^{86} + 858 q^{88} + 4308 q^{89} - 880 q^{91} - 1959 q^{92} + 1108 q^{94} - 935 q^{95} - 1392 q^{97} - 5386 q^{98}+O(q^{100}) \) 6 * q + q^2 - 23 * q^4 - 15 * q^5 - 44 * q^7 - 72 * q^8 - 10 * q^10 - 38 * q^11 - 28 * q^13 + 108 * q^14 - 191 * q^16 - 38 * q^17 + 374 * q^19 - 115 * q^20 - 122 * q^22 + 81 * q^23 - 75 * q^25 + 832 * q^26 + 820 * q^28 - 160 * q^29 - 227 * q^31 + 569 * q^32 - 17 * q^34 + 440 * q^35 + 156 * q^37 + 757 * q^38 + 180 * q^40 + 338 * q^41 - 22 * q^43 + 3272 * q^44 - 2850 * q^46 + 472 * q^47 + 197 * q^49 + 25 * q^50 + 1566 * q^52 + 1042 * q^53 + 380 * q^55 + 1254 * q^56 + 2096 * q^58 - 140 * q^59 - 595 * q^61 + 2814 * q^62 - 1836 * q^64 - 140 * q^65 - 878 * q^67 + 3053 * q^68 + 540 * q^70 - 1204 * q^71 + 2588 * q^73 - 2878 * q^74 - 525 * q^76 - 288 * q^77 - 629 * q^79 + 1910 * q^80 - 3364 * q^82 + 1287 * q^83 + 95 * q^85 + 3730 * q^86 + 858 * q^88 + 4308 * q^89 - 880 * q^91 - 1959 * q^92 + 1108 * q^94 - 935 * q^95 - 1392 * q^97 - 5386 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more