LMFDB - Embedded newform 966.4.a.f.1.1

Newspace parameters

Level:	$ N $	$=$	$ 966 = 2 \cdot 3 \cdot 7 \cdot 23 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	966.a (trivial)

Newform invariants

Self dual:	yes
Analytic conductor:	$56.9958450655$
Analytic rank:	$0$
Dimension:	$3$
Coefficient field:	3.3.12197.1
Defining polynomial:	$ x^{3} - x^{2} - 15x - 4 $ x^3 - x^2 - 15*x - 4
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$4.51691$ of defining polynomial
Character	$\chi$	$=$	966.1

$q$-expansion

$f(q)$	$=$	$q+2.00000 q^{2} -3.00000 q^{3} +4.00000 q^{4} -9.55073 q^{5} -6.00000 q^{6} +7.00000 q^{7} +8.00000 q^{8} +9.00000 q^{9} +O(q^{10})$	\(q+2.00000 q^{2} -3.00000 q^{3} +4.00000 q^{4} -9.55073 q^{5} -6.00000 q^{6} +7.00000 q^{7} +8.00000 q^{8} +9.00000 q^{9} -19.1015 q^{10} -35.9402 q^{11} -12.0000 q^{12} +6.86023 q^{13} +14.0000 q^{14} +28.6522 q^{15} +16.0000 q^{16} -16.4786 q^{17} +18.0000 q^{18} -27.6437 q^{19} -38.2029 q^{20} -21.0000 q^{21} -71.8804 q^{22} -23.0000 q^{23} -24.0000 q^{24} -33.7836 q^{25} +13.7205 q^{26} -27.0000 q^{27} +28.0000 q^{28} +307.579 q^{29} +57.3044 q^{30} +278.757 q^{31} +32.0000 q^{32} +107.821 q^{33} -32.9572 q^{34} -66.8551 q^{35} +36.0000 q^{36} -225.756 q^{37} -55.2874 q^{38} -20.5807 q^{39} -76.4058 q^{40} +151.015 q^{41} -42.0000 q^{42} -434.639 q^{43} -143.761 q^{44} -85.9566 q^{45} -46.0000 q^{46} +281.123 q^{47} -48.0000 q^{48} +49.0000 q^{49} -67.5672 q^{50} +49.4358 q^{51} +27.4409 q^{52} -337.199 q^{53} -54.0000 q^{54} +343.255 q^{55} +56.0000 q^{56} +82.9311 q^{57} +615.158 q^{58} +744.753 q^{59} +114.609 q^{60} -345.004 q^{61} +557.514 q^{62} +63.0000 q^{63} +64.0000 q^{64} -65.5202 q^{65} +215.641 q^{66} +465.795 q^{67} -65.9144 q^{68} +69.0000 q^{69} -133.710 q^{70} +956.929 q^{71} +72.0000 q^{72} +536.007 q^{73} -451.512 q^{74} +101.351 q^{75} -110.575 q^{76} -251.582 q^{77} -41.1614 q^{78} -541.100 q^{79} -152.812 q^{80} +81.0000 q^{81} +302.030 q^{82} +352.599 q^{83} -84.0000 q^{84} +157.383 q^{85} -869.278 q^{86} -922.736 q^{87} -287.522 q^{88} +1532.67 q^{89} -171.913 q^{90} +48.0216 q^{91} -92.0000 q^{92} -836.271 q^{93} +562.246 q^{94} +264.017 q^{95} -96.0000 q^{96} -226.807 q^{97} +98.0000 q^{98} -323.462 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 3 q + 6 q^{2} - 9 q^{3} + 12 q^{4} + 9 q^{5} - 18 q^{6} + 21 q^{7} + 24 q^{8} + 27 q^{9}+O(q^{10}) $ 3 * q + 6 * q^2 - 9 * q^3 + 12 * q^4 + 9 * q^5 - 18 * q^6 + 21 * q^7 + 24 * q^8 + 27 * q^9	\( 3 q + 6 q^{2} - 9 q^{3} + 12 q^{4} + 9 q^{5} - 18 q^{6} + 21 q^{7} + 24 q^{8} + 27 q^{9} + 18 q^{10} + 53 q^{11} - 36 q^{12} + 61 q^{13} + 42 q^{14} - 27 q^{15} + 48 q^{16} - 2 q^{17} + 54 q^{18} + 63 q^{19} + 36 q^{20} - 63 q^{21} + 106 q^{22} - 69 q^{23} - 72 q^{24} - 72 q^{25} + 122 q^{26} - 81 q^{27} + 84 q^{28} + 312 q^{29} - 54 q^{30} + 220 q^{31} + 96 q^{32} - 159 q^{33} - 4 q^{34} + 63 q^{35} + 108 q^{36} - 44 q^{37} + 126 q^{38} - 183 q^{39} + 72 q^{40} + 171 q^{41} - 126 q^{42} - 627 q^{43} + 212 q^{44} + 81 q^{45} - 138 q^{46} + 353 q^{47} - 144 q^{48} + 147 q^{49} - 144 q^{50} + 6 q^{51} + 244 q^{52} - 504 q^{53} - 162 q^{54} + 1181 q^{55} + 168 q^{56} - 189 q^{57} + 624 q^{58} + 538 q^{59} - 108 q^{60} + 256 q^{61} + 440 q^{62} + 189 q^{63} + 192 q^{64} + 244 q^{65} - 318 q^{66} + 1113 q^{67} - 8 q^{68} + 207 q^{69} + 126 q^{70} + 53 q^{71} + 216 q^{72} + 360 q^{73} - 88 q^{74} + 216 q^{75} + 252 q^{76} + 371 q^{77} - 366 q^{78} + 134 q^{79} + 144 q^{80} + 243 q^{81} + 342 q^{82} + 1506 q^{83} - 252 q^{84} + 577 q^{85} - 1254 q^{86} - 936 q^{87} + 424 q^{88} + 2381 q^{89} + 162 q^{90} + 427 q^{91} - 276 q^{92} - 660 q^{93} + 706 q^{94} + 945 q^{95} - 288 q^{96} - 88 q^{97} + 294 q^{98} + 477 q^{99}+O(q^{100}) \) 3 * q + 6 * q^2 - 9 * q^3 + 12 * q^4 + 9 * q^5 - 18 * q^6 + 21 * q^7 + 24 * q^8 + 27 * q^9 + 18 * q^10 + 53 * q^11 - 36 * q^12 + 61 * q^13 + 42 * q^14 - 27 * q^15 + 48 * q^16 - 2 * q^17 + 54 * q^18 + 63 * q^19 + 36 * q^20 - 63 * q^21 + 106 * q^22 - 69 * q^23 - 72 * q^24 - 72 * q^25 + 122 * q^26 - 81 * q^27 + 84 * q^28 + 312 * q^29 - 54 * q^30 + 220 * q^31 + 96 * q^32 - 159 * q^33 - 4 * q^34 + 63 * q^35 + 108 * q^36 - 44 * q^37 + 126 * q^38 - 183 * q^39 + 72 * q^40 + 171 * q^41 - 126 * q^42 - 627 * q^43 + 212 * q^44 + 81 * q^45 - 138 * q^46 + 353 * q^47 - 144 * q^48 + 147 * q^49 - 144 * q^50 + 6 * q^51 + 244 * q^52 - 504 * q^53 - 162 * q^54 + 1181 * q^55 + 168 * q^56 - 189 * q^57 + 624 * q^58 + 538 * q^59 - 108 * q^60 + 256 * q^61 + 440 * q^62 + 189 * q^63 + 192 * q^64 + 244 * q^65 - 318 * q^66 + 1113 * q^67 - 8 * q^68 + 207 * q^69 + 126 * q^70 + 53 * q^71 + 216 * q^72 + 360 * q^73 - 88 * q^74 + 216 * q^75 + 252 * q^76 + 371 * q^77 - 366 * q^78 + 134 * q^79 + 144 * q^80 + 243 * q^81 + 342 * q^82 + 1506 * q^83 - 252 * q^84 + 577 * q^85 - 1254 * q^86 - 936 * q^87 + 424 * q^88 + 2381 * q^89 + 162 * q^90 + 427 * q^91 - 276 * q^92 - 660 * q^93 + 706 * q^94 + 945 * q^95 - 288 * q^96 - 88 * q^97 + 294 * q^98 + 477 * q^99

Display 100 coefficients 10 coefficients

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 $

$2$	2.00000	0.707107
$2$	2.00000	0.707107
$3$	−3.00000	−0.577350
$3$	−3.00000	−0.577350
$4$	4.00000	0.500000
$5$	−9.55073	−0.854243	−0.427122	−	0.904194i	$-0.640472\pi$
$5$	−9.55073	−0.854243	−0.427122	+	0.904194i	$0.640472\pi$
$6$	−6.00000	−0.408248
$7$	7.00000	0.377964
$7$	7.00000	0.377964
$8$	8.00000	0.353553
$9$	9.00000	0.333333
$10$	−19.1015	−0.604041
$11$	−35.9402	−0.985126	−0.492563	−	0.870277i	$-0.663940\pi$
$11$	−35.9402	−0.985126	−0.492563	+	0.870277i	$0.663940\pi$
$12$	−12.0000	−0.288675
$13$	6.86023	0.146360	0.0731802	−	0.997319i	$-0.476685\pi$
$13$	6.86023	0.146360	0.0731802	+	0.997319i	$0.476685\pi$
$14$	14.0000	0.267261
$15$	28.6522	0.493197
$16$	16.0000	0.250000
$17$	−16.4786	−0.235097	−0.117548	−	0.993067i	$-0.537504\pi$
$17$	−16.4786	−0.235097	−0.117548	+	0.993067i	$0.537504\pi$
$18$	18.0000	0.235702
$19$	−27.6437	−0.333784	−0.166892	−	0.985975i	$-0.553373\pi$
$19$	−27.6437	−0.333784	−0.166892	+	0.985975i	$0.553373\pi$
$20$	−38.2029	−0.427122
$21$	−21.0000	−0.218218
$22$	−71.8804	−0.696589
$23$	−23.0000	−0.208514
$23$	−23.0000	−0.208514
$24$	−24.0000	−0.204124
$25$	−33.7836	−0.270269
$26$	13.7205	0.103492
$27$	−27.0000	−0.192450
$28$	28.0000	0.188982
$29$	307.579	1.96952	0.984758	−	0.173932i	$-0.0556472\pi$
$29$	307.579	1.96952	0.984758	+	0.173932i	$0.0556472\pi$
$30$	57.3044	0.348743
$31$	278.757	1.61504	0.807520	−	0.589841i	$-0.200809\pi$
$31$	278.757	1.61504	0.807520	+	0.589841i	$0.200809\pi$
$32$	32.0000	0.176777
$33$	107.821	0.568763
$34$	−32.9572	−0.166239
$35$	−66.8551	−0.322874
$36$	36.0000	0.166667
$37$	−225.756	−1.00308	−0.501541	−	0.865134i	$-0.667233\pi$
$37$	−225.756	−1.00308	−0.501541	+	0.865134i	$0.667233\pi$
$38$	−55.2874	−0.236021
$39$	−20.5807	−0.0845012
$40$	−76.4058	−0.302021
$41$	151.015	0.575233	0.287617	−	0.957746i	$-0.407137\pi$
$41$	151.015	0.575233	0.287617	+	0.957746i	$0.407137\pi$
$42$	−42.0000	−0.154303
$43$	−434.639	−1.54144	−0.770719	−	0.637176i	$-0.780103\pi$
$43$	−434.639	−1.54144	−0.770719	+	0.637176i	$0.780103\pi$
$44$	−143.761	−0.492563
$45$	−85.9566	−0.284748
$46$	−46.0000	−0.147442
$47$	281.123	0.872468	0.436234	−	0.899833i	$-0.356312\pi$
$47$	281.123	0.872468	0.436234	+	0.899833i	$0.356312\pi$
$48$	−48.0000	−0.144338
$49$	49.0000	0.142857
$50$	−67.5672	−0.191109
$51$	49.4358	0.135733
$52$	27.4409	0.0731802
$53$	−337.199	−0.873922	−0.436961	−	0.899480i	$-0.643945\pi$
$53$	−337.199	−0.873922	−0.436961	+	0.899480i	$0.643945\pi$
$54$	−54.0000	−0.136083
$55$	343.255	0.841537
$56$	56.0000	0.133631
$57$	82.9311	0.192710
$58$	615.158	1.39266
$59$	744.753	1.64337	0.821683	−	0.569945i	$-0.193036\pi$
$59$	744.753	1.64337	0.821683	+	0.569945i	$0.193036\pi$
$60$	114.609	0.246599
$61$	−345.004	−0.724151	−0.362076	−	0.932149i	$-0.617932\pi$
$61$	−345.004	−0.724151	−0.362076	+	0.932149i	$0.617932\pi$
$62$	557.514	1.14201
$63$	63.0000	0.125988
$64$	64.0000	0.125000
$65$	−65.5202	−0.125027
$66$	215.641	0.402176
$67$	465.795	0.849341	0.424671	−	0.905348i	$-0.360390\pi$
$67$	465.795	0.849341	0.424671	+	0.905348i	$0.360390\pi$
$68$	−65.9144	−0.117548
$69$	69.0000	0.120386
$70$	−133.710	−0.228306
$71$	956.929	1.59953	0.799765	−	0.600313i	$-0.204957\pi$
$71$	956.929	1.59953	0.799765	+	0.600313i	$0.204957\pi$
$72$	72.0000	0.117851
$73$	536.007	0.859383	0.429691	−	0.902976i	$-0.358622\pi$
$73$	536.007	0.859383	0.429691	+	0.902976i	$0.358622\pi$
$74$	−451.512	−0.709286
$75$	101.351	0.156040
$76$	−110.575	−0.166892
$77$	−251.582	−0.372343
$78$	−41.1614	−0.0597514
$79$	−541.100	−0.770614	−0.385307	−	0.922789i	$-0.625904\pi$
$79$	−541.100	−0.770614	−0.385307	+	0.922789i	$0.625904\pi$
$80$	−152.812	−0.213561
$81$	81.0000	0.111111
$82$	302.030	0.406751
$83$	352.599	0.466299	0.233149	−	0.972441i	$-0.425097\pi$
$83$	352.599	0.466299	0.233149	+	0.972441i	$0.425097\pi$
$84$	−84.0000	−0.109109
$85$	157.383	0.200830
$86$	−869.278	−1.08996
$87$	−922.736	−1.13710
$88$	−287.522	−0.348295
$89$	1532.67	1.82542	0.912709	−	0.408609i	$-0.133986\pi$
$89$	1532.67	1.82542	0.912709	+	0.408609i	$0.133986\pi$
$90$	−171.913	−0.201347
$91$	48.0216	0.0553190
$92$	−92.0000	−0.104257
$93$	−836.271	−0.932443
$94$	562.246	0.616928
$95$	264.017	0.285133
$96$	−96.0000	−0.102062
$97$	−226.807	−0.237410	−0.118705	−	0.992930i	$-0.537874\pi$
$97$	−226.807	−0.237410	−0.118705	+	0.992930i	$0.537874\pi$
$98$	98.0000	0.101015
$99$	−323.462	−0.328375
$100$	−135.134	−0.135134
$101$	1469.57	1.44780	0.723898	−	0.689907i	$-0.242348\pi$
$101$	1469.57	1.44780	0.723898	+	0.689907i	$0.242348\pi$
$102$	98.8715	0.0959779
$103$	385.377	0.368664	0.184332	−	0.982864i	$-0.440988\pi$
$103$	385.377	0.368664	0.184332	+	0.982864i	$0.440988\pi$
$104$	54.8818	0.0517462
$105$	200.565	0.186411
$106$	−674.398	−0.617956
$107$	−800.857	−0.723568	−0.361784	−	0.932262i	$-0.617832\pi$
$107$	−800.857	−0.723568	−0.361784	+	0.932262i	$0.617832\pi$
$108$	−108.000	−0.0962250
$109$	1223.90	1.07549	0.537746	−	0.843107i	$-0.319276\pi$
$109$	1223.90	1.07549	0.537746	+	0.843107i	$0.319276\pi$
$110$	686.510	0.595056
$111$	677.268	0.579130
$112$	112.000	0.0944911
$113$	1282.72	1.06786	0.533929	−	0.845529i	$-0.320715\pi$
$113$	1282.72	1.06786	0.533929	+	0.845529i	$0.320715\pi$
$114$	165.862	0.136267
$115$	219.667	0.178122
$116$	1230.32	0.984758
$117$	61.7420	0.0487868
$118$	1489.51	1.16204
$119$	−115.350	−0.0888582
$120$	229.217	0.174372
$121$	−39.3008	−0.0295273
$122$	−690.008	−0.512052
$123$	−453.045	−0.332111
$124$	1115.03	0.807520
$125$	1516.50	1.08512
$126$	126.000	0.0890871
$127$	2271.45	1.58708	0.793538	−	0.608521i	$-0.208237\pi$
$127$	2271.45	1.58708	0.793538	+	0.608521i	$0.208237\pi$
$128$	128.000	0.0883883
$129$	1303.92	0.889949
$130$	−131.040	−0.0884077
$131$	564.729	0.376646	0.188323	−	0.982107i	$-0.439695\pi$
$131$	564.729	0.376646	0.188323	+	0.982107i	$0.439695\pi$
$132$	431.283	0.284381
$133$	−193.506	−0.126159
$134$	931.589	0.600575
$135$	257.870	0.164399
$136$	−131.829	−0.0831193
$137$	328.883	0.205097	0.102549	−	0.994728i	$-0.467300\pi$
$137$	328.883	0.205097	0.102549	+	0.994728i	$0.467300\pi$
$138$	138.000	0.0851257
$139$	−2044.79	−1.24775	−0.623874	−	0.781525i	$-0.714442\pi$
$139$	−2044.79	−1.24775	−0.623874	+	0.781525i	$0.714442\pi$
$140$	−267.420	−0.161437
$141$	−843.369	−0.503720
$142$	1913.86	1.13104
$143$	−246.558	−0.144183
$144$	144.000	0.0833333
$145$	−2937.60	−1.68244
$146$	1072.01	0.607675
$147$	−147.000	−0.0824786
$148$	−903.024	−0.501541
$149$	579.529	0.318637	0.159318	−	0.987227i	$-0.449070\pi$
$149$	579.529	0.318637	0.159318	+	0.987227i	$0.449070\pi$
$150$	202.702	0.110337
$151$	3304.67	1.78100	0.890498	−	0.454988i	$-0.150357\pi$
$151$	3304.67	1.78100	0.890498	+	0.454988i	$0.150357\pi$
$152$	−221.150	−0.118011
$153$	−148.307	−0.0783656
$154$	−503.163	−0.263286
$155$	−2662.33	−1.37964
$156$	−82.3227	−0.0422506
$157$	−1808.40	−0.919272	−0.459636	−	0.888107i	$-0.652020\pi$
$157$	−1808.40	−0.919272	−0.459636	+	0.888107i	$0.652020\pi$
$158$	−1082.20	−0.544906
$159$	1011.60	0.504559
$160$	−305.623	−0.151010
$161$	−161.000	−0.0788110
$162$	162.000	0.0785674
$163$	−66.5723	−0.0319898	−0.0159949	−	0.999872i	$-0.505092\pi$
$163$	−66.5723	−0.0319898	−0.0159949	+	0.999872i	$0.505092\pi$
$164$	604.060	0.287617
$165$	−1029.77	−0.485862
$166$	705.198	0.329723
$167$	−336.954	−0.156133	−0.0780667	−	0.996948i	$-0.524875\pi$
$167$	−336.954	−0.156133	−0.0780667	+	0.996948i	$0.524875\pi$
$168$	−168.000	−0.0771517
$169$	−2149.94	−0.978579
$170$	314.765	0.142008
$171$	−248.793	−0.111261
$172$	−1738.56	−0.770719
$173$	−318.130	−0.139809	−0.0699045	−	0.997554i	$-0.522269\pi$
$173$	−318.130	−0.139809	−0.0699045	+	0.997554i	$0.522269\pi$
$174$	−1845.47	−0.804051
$175$	−236.485	−0.102152
$176$	−575.043	−0.246281
$177$	−2234.26	−0.948798
$178$	3065.33	1.29077
$179$	−1968.94	−0.822152	−0.411076	−	0.911601i	$-0.634847\pi$
$179$	−1968.94	−0.822152	−0.411076	+	0.911601i	$0.634847\pi$
$180$	−343.826	−0.142374
$181$	3805.14	1.56262	0.781308	−	0.624146i	$-0.214553\pi$
$181$	3805.14	1.56262	0.781308	+	0.624146i	$0.214553\pi$
$182$	96.0432	0.0391164
$183$	1035.01	0.418089
$184$	−184.000	−0.0737210
$185$	2156.13	0.856876
$186$	−1672.54	−0.659337
$187$	592.244	0.231600
$188$	1124.49	0.436234
$189$	−189.000	−0.0727393
$190$	528.035	0.201619
$191$	1563.67	0.592374	0.296187	−	0.955130i	$-0.404285\pi$
$191$	1563.67	0.592374	0.296187	+	0.955130i	$0.404285\pi$
$192$	−192.000	−0.0721688
$193$	−4114.00	−1.53436	−0.767182	−	0.641430i	$-0.778342\pi$
$193$	−4114.00	−1.53436	−0.767182	+	0.641430i	$0.778342\pi$
$194$	−453.614	−0.167874
$195$	196.560	0.0721845
$196$	196.000	0.0714286
$197$	1143.47	0.413548	0.206774	−	0.978389i	$-0.433703\pi$
$197$	1143.47	0.413548	0.206774	+	0.978389i	$0.433703\pi$
$198$	−646.924	−0.232196
$199$	−4.64969	−0.00165632	−0.000828161	−	1.00000i	$-0.500264\pi$
$199$	−4.64969	−0.00165632	−0.000828161		1.00000i	$0.500264\pi$
$200$	−270.269	−0.0955544
$201$	−1397.38	−0.490367
$202$	2939.14	1.02375
$203$	2153.05	0.744407
$204$	197.743	0.0678666
$205$	−1442.30	−0.491389
$206$	770.754	0.260685
$207$	−207.000	−0.0695048
$208$	109.764	0.0365901
$209$	993.521	0.328819
$210$	401.131	0.131813
$211$	−164.636	−0.0537157	−0.0268579	−	0.999639i	$-0.508550\pi$
$211$	−164.636	−0.0537157	−0.0268579	+	0.999639i	$0.508550\pi$
$212$	−1348.80	−0.436961
$213$	−2870.79	−0.923489
$214$	−1601.71	−0.511640
$215$	4151.12	1.31676
$216$	−216.000	−0.0680414
$217$	1951.30	0.610427
$218$	2447.81	0.760488
$219$	−1608.02	−0.496165
$220$	1373.02	0.420768
$221$	−113.047	−0.0344088
$222$	1354.54	0.409507
$223$	−4061.56	−1.21965	−0.609826	−	0.792536i	$-0.708761\pi$
$223$	−4061.56	−1.21965	−0.609826	+	0.792536i	$0.708761\pi$
$224$	224.000	0.0668153
$225$	−304.052	−0.0900896
$226$	2565.44	0.755090
$227$	−3183.98	−0.930961	−0.465481	−	0.885058i	$-0.654118\pi$
$227$	−3183.98	−0.930961	−0.465481	+	0.885058i	$0.654118\pi$
$228$	331.724	0.0963552
$229$	1190.00	0.343395	0.171697	−	0.985150i	$-0.445075\pi$
$229$	1190.00	0.343395	0.171697	+	0.985150i	$0.445075\pi$
$230$	439.333	0.125951
$231$	754.745	0.214972
$232$	2460.63	0.696329
$233$	−6794.69	−1.91045	−0.955225	−	0.295880i	$-0.904387\pi$
$233$	−6794.69	−1.91045	−0.955225	+	0.295880i	$0.904387\pi$
$234$	123.484	0.0344975
$235$	−2684.93	−0.745300
$236$	2979.01	0.821683
$237$	1623.30	0.444914
$238$	−230.700	−0.0628323
$239$	−4026.00	−1.08962	−0.544812	−	0.838558i	$-0.683399\pi$
$239$	−4026.00	−1.08962	−0.544812	+	0.838558i	$0.683399\pi$
$240$	458.435	0.123299
$241$	4787.52	1.27963	0.639816	−	0.768528i	$-0.279011\pi$
$241$	4787.52	1.27963	0.639816	+	0.768528i	$0.279011\pi$
$242$	−78.6016	−0.0208789
$243$	−243.000	−0.0641500
$244$	−1380.02	−0.362076
$245$	−467.986	−0.122035
$246$	−906.089	−0.234838
$247$	−189.642	−0.0488528
$248$	2230.06	0.571003
$249$	−1057.80	−0.269218
$250$	3033.00	0.767295
$251$	−5233.59	−1.31610	−0.658050	−	0.752974i	$-0.728618\pi$
$251$	−5233.59	−1.31610	−0.658050	+	0.752974i	$0.728618\pi$
$252$	252.000	0.0629941
$253$	826.625	0.205413
$254$	4542.90	1.12223
$255$	−472.148	−0.115949
$256$	256.000	0.0625000
$257$	3160.14	0.767020	0.383510	−	0.923537i	$-0.374715\pi$
$257$	3160.14	0.767020	0.383510	+	0.923537i	$0.374715\pi$
$258$	2607.83	0.629289
$259$	−1580.29	−0.379130
$260$	−262.081	−0.0625137
$261$	2768.21	0.656505
$262$	1129.46	0.266329
$263$	5199.28	1.21902	0.609509	−	0.792779i	$-0.291367\pi$
$263$	5199.28	1.21902	0.609509	+	0.792779i	$0.291367\pi$
$264$	862.565	0.201088
$265$	3220.50	0.746542
$266$	−387.012	−0.0892076
$267$	−4598.00	−1.05391
$268$	1863.18	0.424671
$269$	−4909.49	−1.11278	−0.556389	−	0.830922i	$-0.687813\pi$
$269$	−4909.49	−1.11278	−0.556389	+	0.830922i	$0.687813\pi$
$270$	515.739	0.116248
$271$	4007.30	0.898252	0.449126	−	0.893468i	$-0.351735\pi$
$271$	4007.30	0.898252	0.449126	+	0.893468i	$0.351735\pi$
$272$	−263.657	−0.0587742
$273$	−144.065	−0.0319384
$274$	657.766	0.145026
$275$	1214.19	0.266249
$276$	276.000	0.0601929
$277$	2529.96	0.548775	0.274388	−	0.961619i	$-0.411525\pi$
$277$	2529.96	0.548775	0.274388	+	0.961619i	$0.411525\pi$
$278$	−4089.59	−0.882292
$279$	2508.81	0.538346
$280$	−534.841	−0.114153
$281$	−8234.37	−1.74812	−0.874059	−	0.485820i	$-0.838521\pi$
$281$	−8234.37	−1.74812	−0.874059	+	0.485820i	$0.838521\pi$
$282$	−1686.74	−0.356184
$283$	6374.51	1.33896	0.669479	−	0.742831i	$-0.266517\pi$
$283$	6374.51	1.33896	0.669479	+	0.742831i	$0.266517\pi$
$284$	3827.72	0.799765
$285$	−792.052	−0.164622
$286$	−493.116	−0.101953
$287$	1057.10	0.217418
$288$	288.000	0.0589256
$289$	−4641.46	−0.944729
$290$	−5875.20	−1.18967
$291$	680.420	0.137069
$292$	2144.03	0.429691
$293$	3946.21	0.786825	0.393413	−	0.919362i	$-0.371294\pi$
$293$	3946.21	0.786825	0.393413	+	0.919362i	$0.371294\pi$
$294$	−294.000	−0.0583212
$295$	−7112.93	−1.40383
$296$	−1806.05	−0.354643
$297$	970.386	0.189588
$298$	1159.06	0.225310
$299$	−157.785	−0.0305182
$300$	405.403	0.0780199
$301$	−3042.47	−0.582609
$302$	6609.34	1.25935
$303$	−4408.70	−0.835886
$304$	−442.299	−0.0834461
$305$	3295.04	0.618601
$306$	−296.615	−0.0554128
$307$	−251.364	−0.0467300	−0.0233650	−	0.999727i	$-0.507438\pi$
$307$	−251.364	−0.0467300	−0.0233650	+	0.999727i	$0.507438\pi$
$308$	−1006.33	−0.186171
$309$	−1156.13	−0.212848
$310$	−5324.66	−0.975550
$311$	−2787.66	−0.508276	−0.254138	−	0.967168i	$-0.581792\pi$
$311$	−2787.66	−0.508276	−0.254138	+	0.967168i	$0.581792\pi$
$312$	−164.645	−0.0298757
$313$	−585.191	−0.105677	−0.0528386	−	0.998603i	$-0.516827\pi$
$313$	−585.191	−0.105677	−0.0528386	+	0.998603i	$0.516827\pi$
$314$	−3616.79	−0.650024
$315$	−601.696	−0.107625
$316$	−2164.40	−0.385307
$317$	2421.83	0.429096	0.214548	−	0.976713i	$-0.431172\pi$
$317$	2421.83	0.429096	0.214548	+	0.976713i	$0.431172\pi$
$318$	2023.19	0.356777
$319$	−11054.4	−1.94022
$320$	−611.247	−0.106780
$321$	2402.57	0.417752
$322$	−322.000	−0.0557278
$323$	455.529	0.0784716
$324$	324.000	0.0555556
$325$	−231.763	−0.0395566
$326$	−133.145	−0.0226202
$327$	−3671.71	−0.620936
$328$	1208.12	0.203376
$329$	1967.86	0.329762
$330$	−2059.53	−0.343556
$331$	1910.61	0.317270	0.158635	−	0.987337i	$-0.449291\pi$
$331$	1910.61	0.317270	0.158635	+	0.987337i	$0.449291\pi$
$332$	1410.40	0.233149
$333$	−2031.80	−0.334361
$334$	−673.908	−0.110403
$335$	−4448.68	−0.725544
$336$	−336.000	−0.0545545
$337$	−1119.18	−0.180907	−0.0904533	−	0.995901i	$-0.528832\pi$
$337$	−1119.18	−0.180907	−0.0904533	+	0.995901i	$0.528832\pi$
$338$	−4299.87	−0.691960
$339$	−3848.15	−0.616528
$340$	629.530	0.100415
$341$	−10018.6	−1.59102
$342$	−497.587	−0.0786737
$343$	343.000	0.0539949
$344$	−3477.11	−0.544980
$345$	−659.000	−0.102839
$346$	−636.260	−0.0988599
$347$	11398.3	1.76338	0.881688	−	0.471833i	$-0.156407\pi$
$347$	11398.3	1.76338	0.881688	+	0.471833i	$0.156407\pi$
$348$	−3690.95	−0.568550
$349$	1577.30	0.241922	0.120961	−	0.992657i	$-0.461402\pi$
$349$	1577.30	0.241922	0.120961	+	0.992657i	$0.461402\pi$
$350$	−472.970	−0.0722324
$351$	−185.226	−0.0281671
$352$	−1150.09	−0.174147
$353$	−4929.64	−0.743282	−0.371641	−	0.928377i	$-0.621205\pi$
$353$	−4929.64	−0.743282	−0.371641	+	0.928377i	$0.621205\pi$
$354$	−4468.52	−0.670901
$355$	−9139.37	−1.36639
$356$	6130.66	0.912709
$357$	346.050	0.0513023
$358$	−3937.87	−0.581349
$359$	5323.22	0.782588	0.391294	−	0.920266i	$-0.372028\pi$
$359$	5323.22	0.782588	0.391294	+	0.920266i	$0.372028\pi$
$360$	−687.652	−0.100674
$361$	−6094.83	−0.888588
$362$	7610.27	1.10494
$363$	117.902	0.0170476
$364$	192.086	0.0276595
$365$	−5119.26	−0.734122
$366$	2070.02	0.295633
$367$	−3760.29	−0.534839	−0.267419	−	0.963580i	$-0.586171\pi$
$367$	−3760.29	−0.534839	−0.267419	+	0.963580i	$0.586171\pi$
$368$	−368.000	−0.0521286
$369$	1359.13	0.191744
$370$	4312.27	0.605903
$371$	−2360.39	−0.330311
$372$	−3345.08	−0.466222
$373$	−9210.62	−1.27857	−0.639287	−	0.768969i	$-0.720770\pi$
$373$	−9210.62	−1.27857	−0.639287	+	0.768969i	$0.720770\pi$
$374$	1184.49	0.163766
$375$	−4549.50	−0.626493
$376$	2248.98	0.308464
$377$	2110.06	0.288259
$378$	−378.000	−0.0514344
$379$	6305.61	0.854611	0.427305	−	0.904107i	$-0.359463\pi$
$379$	6305.61	0.854611	0.427305	+	0.904107i	$0.359463\pi$
$380$	1056.07	0.142566
$381$	−6814.35	−0.916299
$382$	3127.35	0.418872
$383$	13571.9	1.81069	0.905344	−	0.424679i	$-0.139613\pi$
$383$	13571.9	1.81069	0.905344	+	0.424679i	$0.139613\pi$
$384$	−384.000	−0.0510310
$385$	2402.79	0.318071
$386$	−8228.00	−1.08496
$387$	−3911.75	−0.513812
$388$	−907.227	−0.118705
$389$	−7448.01	−0.970769	−0.485384	−	0.874301i	$-0.661320\pi$
$389$	−7448.01	−0.970769	−0.485384	+	0.874301i	$0.661320\pi$
$390$	393.121	0.0510422
$391$	379.008	0.0490211
$392$	392.000	0.0505076
$393$	−1694.19	−0.217456
$394$	2286.94	0.292423
$395$	5167.90	0.658291
$396$	−1293.85	−0.164188
$397$	9795.19	1.23830	0.619152	−	0.785271i	$-0.287477\pi$
$397$	9795.19	1.23830	0.619152	+	0.785271i	$0.287477\pi$
$398$	−9.29939	−0.00117120
$399$	580.518	0.0728377
$400$	−540.537	−0.0675672
$401$	−7996.68	−0.995848	−0.497924	−	0.867221i	$-0.665904\pi$
$401$	−7996.68	−0.995848	−0.497924	+	0.867221i	$0.665904\pi$
$402$	−2794.77	−0.346742
$403$	1912.34	0.236378
$404$	5878.27	0.723898
$405$	−773.609	−0.0949159
$406$	4306.10	0.526375
$407$	8113.72	0.988162
$408$	395.486	0.0479889
$409$	5516.67	0.666948	0.333474	−	0.942759i	$-0.391779\pi$
$409$	5516.67	0.666948	0.333474	+	0.942759i	$0.391779\pi$
$410$	−2884.60	−0.347465
$411$	−986.648	−0.118413
$412$	1541.51	0.184332
$413$	5213.27	0.621134
$414$	−414.000	−0.0491473
$415$	−3367.58	−0.398332
$416$	219.527	0.0258731
$417$	6134.38	0.720388
$418$	1987.04	0.232510
$419$	4037.28	0.470726	0.235363	−	0.971908i	$-0.424372\pi$
$419$	4037.28	0.470726	0.235363	+	0.971908i	$0.424372\pi$
$420$	802.261	0.0932056
$421$	6466.80	0.748629	0.374314	−	0.927302i	$-0.377878\pi$
$421$	6466.80	0.748629	0.374314	+	0.927302i	$0.377878\pi$
$422$	−329.272	−0.0379828
$423$	2530.11	0.290823
$424$	−2697.59	−0.308978
$425$	556.706	0.0635393
$426$	−5741.58	−0.653005
$427$	−2415.03	−0.273703
$428$	−3203.43	−0.361784
$429$	739.674	0.0832443
$430$	8302.24	0.931091
$431$	−7418.83	−0.829124	−0.414562	−	0.910021i	$-0.636065\pi$
$431$	−7418.83	−0.829124	−0.414562	+	0.910021i	$0.636065\pi$
$432$	−432.000	−0.0481125
$433$	−16487.7	−1.82990	−0.914952	−	0.403563i	$-0.867772\pi$
$433$	−16487.7	−1.82990	−0.914952	+	0.403563i	$0.867772\pi$
$434$	3902.60	0.431637
$435$	8812.80	0.971360
$436$	4895.61	0.537746
$437$	635.805	0.0695988
$438$	−3216.04	−0.350841
$439$	−15767.2	−1.71418	−0.857091	−	0.515165i	$-0.827731\pi$
$439$	−15767.2	−1.71418	−0.857091	+	0.515165i	$0.827731\pi$
$440$	2746.04	0.297528
$441$	441.000	0.0476190
$442$	−226.094	−0.0243307
$443$	−17663.7	−1.89442	−0.947208	−	0.320619i	$-0.896109\pi$
$443$	−17663.7	−1.89442	−0.947208	+	0.320619i	$0.896109\pi$
$444$	2709.07	0.289565
$445$	−14638.1	−1.55935
$446$	−8123.12	−0.862424
$447$	−1738.59	−0.183965
$448$	448.000	0.0472456
$449$	11973.0	1.25844	0.629222	−	0.777226i	$-0.283374\pi$
$449$	11973.0	1.25844	0.629222	+	0.777226i	$0.283374\pi$
$450$	−608.105	−0.0637029
$451$	−5427.51	−0.566677
$452$	5130.87	0.533929
$453$	−9914.01	−1.02826
$454$	−6367.96	−0.658289
$455$	−458.641	−0.0472559
$456$	663.449	0.0681334
$457$	−1742.13	−0.178323	−0.0891614	−	0.996017i	$-0.528419\pi$
$457$	−1742.13	−0.178323	−0.0891614	+	0.996017i	$0.528419\pi$
$458$	2380.00	0.242817
$459$	444.922	0.0452444
$460$	878.667	0.0890610
$461$	12085.2	1.22097	0.610483	−	0.792030i	$-0.290975\pi$
$461$	12085.2	1.22097	0.610483	+	0.792030i	$0.290975\pi$
$462$	1509.49	0.152008
$463$	13460.5	1.35110	0.675551	−	0.737313i	$-0.263906\pi$
$463$	13460.5	1.35110	0.675551	+	0.737313i	$0.263906\pi$
$464$	4921.26	0.492379
$465$	7986.99	0.796533
$466$	−13589.4	−1.35089
$467$	−3956.79	−0.392074	−0.196037	−	0.980597i	$-0.562807\pi$
$467$	−3956.79	−0.392074	−0.196037	+	0.980597i	$0.562807\pi$
$468$	246.968	0.0243934
$469$	3260.56	0.321021
$470$	−5369.86	−0.527007
$471$	5425.19	0.530742
$472$	5958.02	0.581018
$473$	15621.0	1.51851
$474$	3246.60	0.314602
$475$	933.903	0.0902114
$476$	−461.401	−0.0444291
$477$	−3034.79	−0.291307
$478$	−8052.00	−0.770481
$479$	16387.3	1.56316	0.781579	−	0.623806i	$-0.214414\pi$
$479$	16387.3	1.56316	0.781579	+	0.623806i	$0.214414\pi$
$480$	916.870	0.0871858
$481$	−1548.74	−0.146811
$482$	9575.04	0.904836
$483$	483.000	0.0455016
$484$	−157.203	−0.0147636
$485$	2166.17	0.202806
$486$	−486.000	−0.0453609
$487$	8974.92	0.835097	0.417549	−	0.908655i	$-0.362889\pi$
$487$	8974.92	0.835097	0.417549	+	0.908655i	$0.362889\pi$
$488$	−2760.03	−0.256026
$489$	199.717	0.0184693
$490$	−935.971	−0.0862916
$491$	14046.8	1.29109	0.645544	−	0.763723i	$-0.276631\pi$
$491$	14046.8	1.29109	0.645544	+	0.763723i	$0.276631\pi$
$492$	−1812.18	−0.166056
$493$	−5068.47	−0.463027
$494$	−379.284	−0.0345441
$495$	3089.30	0.280512
$496$	4460.11	0.403760
$497$	6698.51	0.604565
$498$	−2115.60	−0.190366
$499$	−15952.7	−1.43114	−0.715570	−	0.698541i	$-0.753833\pi$
$499$	−15952.7	−1.43114	−0.715570	+	0.698541i	$0.753833\pi$
$500$	6066.00	0.542559
$501$	1010.86	0.0901436
$502$	−10467.2	−0.930623
$503$	16375.1	1.45155	0.725776	−	0.687931i	$-0.241481\pi$
$503$	16375.1	1.45155	0.725776	+	0.687931i	$0.241481\pi$
$504$	504.000	0.0445435
$505$	−14035.4	−1.23677
$506$	1653.25	0.145249
$507$	6449.81	0.564983
$508$	9085.80	0.793538
$509$	−22768.3	−1.98269	−0.991345	−	0.131283i	$-0.958090\pi$
$509$	−22768.3	−1.98269	−0.991345	+	0.131283i	$0.958090\pi$
$510$	−944.295	−0.0819884
$511$	3752.05	0.324816
$512$	512.000	0.0441942
$513$	746.380	0.0642368
$514$	6320.28	0.542365
$515$	−3680.63	−0.314928
$516$	5215.67	0.444975
$517$	−10103.6	−0.859491
$518$	−3160.58	−0.268085
$519$	954.389	0.0807188
$520$	−524.161	−0.0442038
$521$	528.725	0.0444604	0.0222302	−	0.999753i	$-0.492923\pi$
$521$	528.725	0.0444604	0.0222302	+	0.999753i	$0.492923\pi$
$522$	5536.42	0.464219
$523$	−13524.7	−1.13078	−0.565388	−	0.824825i	$-0.691273\pi$
$523$	−13524.7	−1.13078	−0.565388	+	0.824825i	$0.691273\pi$
$524$	2258.91	0.188323
$525$	709.455	0.0589775
$526$	10398.6	0.861975
$527$	−4593.52	−0.379691
$528$	1725.13	0.142191
$529$	529.000	0.0434783
$530$	6440.99	0.527885
$531$	6702.78	0.547789
$532$	−774.024	−0.0630793
$533$	1036.00	0.0841913
$534$	−9196.00	−0.745224
$535$	7648.77	0.618103
$536$	3726.36	0.300287
$537$	5906.81	0.474670
$538$	−9818.99	−0.786852
$539$	−1761.07	−0.140732
$540$	1031.48	0.0821996
$541$	−10436.3	−0.829371	−0.414686	−	0.909965i	$-0.636108\pi$
$541$	−10436.3	−0.829371	−0.414686	+	0.909965i	$0.636108\pi$
$542$	8014.60	0.635160
$543$	−11415.4	−0.902177
$544$	−527.315	−0.0415596
$545$	−11689.2	−0.918732
$546$	−288.129	−0.0225839
$547$	−17369.1	−1.35768	−0.678838	−	0.734288i	$-0.737516\pi$
$547$	−17369.1	−1.35768	−0.678838	+	0.734288i	$0.737516\pi$
$548$	1315.53	0.102549
$549$	−3105.04	−0.241384
$550$	2428.38	0.188266
$551$	−8502.62	−0.657393
$552$	552.000	0.0425628
$553$	−3787.70	−0.291265
$554$	5059.92	0.388043
$555$	−6468.40	−0.494718
$556$	−8179.17	−0.623874
$557$	−13555.3	−1.03116	−0.515579	−	0.856842i	$-0.672423\pi$
$557$	−13555.3	−1.03116	−0.515579	+	0.856842i	$0.672423\pi$
$558$	5017.62	0.380668
$559$	−2981.72	−0.225605
$560$	−1069.68	−0.0807184
$561$	−1776.73	−0.133714
$562$	−16468.7	−1.23611
$563$	−5311.89	−0.397636	−0.198818	−	0.980036i	$-0.563710\pi$
$563$	−5311.89	−0.397636	−0.198818	+	0.980036i	$0.563710\pi$
$564$	−3373.48	−0.251860
$565$	−12250.9	−0.912210
$566$	12749.0	0.946786
$567$	567.000	0.0419961
$568$	7655.43	0.565519
$569$	17501.8	1.28948	0.644738	−	0.764403i	$-0.276966\pi$
$569$	17501.8	1.28948	0.644738	+	0.764403i	$0.276966\pi$
$570$	−1584.10	−0.116405
$571$	16321.0	1.19617	0.598083	−	0.801434i	$-0.295929\pi$
$571$	16321.0	1.19617	0.598083	+	0.801434i	$0.295929\pi$
$572$	−986.232	−0.0720917
$573$	−4691.02	−0.342007
$574$	2114.21	0.153738
$575$	777.023	0.0563549
$576$	576.000	0.0416667
$577$	5414.53	0.390659	0.195329	−	0.980738i	$-0.437422\pi$
$577$	5414.53	0.390659	0.195329	+	0.980738i	$0.437422\pi$
$578$	−9282.91	−0.668025
$579$	12342.0	0.885865
$580$	−11750.4	−0.841222
$581$	2468.19	0.176244
$582$	1360.84	0.0969221
$583$	12119.0	0.860923
$584$	4288.06	0.303838
$585$	−589.681	−0.0416758
$586$	7892.41	0.556369
$587$	20409.5	1.43507	0.717537	−	0.696520i	$-0.245269\pi$
$587$	20409.5	1.43507	0.717537	+	0.696520i	$0.245269\pi$
$588$	−588.000	−0.0412393
$589$	−7705.87	−0.539075
$590$	−14225.9	−0.992660
$591$	−3430.42	−0.238762
$592$	−3612.10	−0.250771
$593$	3585.23	0.248276	0.124138	−	0.992265i	$-0.460383\pi$
$593$	3585.23	0.248276	0.124138	+	0.992265i	$0.460383\pi$
$594$	1940.77	0.134059
$595$	1101.68	0.0759065
$596$	2318.12	0.159318
$597$	13.9491	0.000956278 0
$598$	−315.570	−0.0215797
$599$	19228.3	1.31159	0.655797	−	0.754937i	$-0.272333\pi$
$599$	19228.3	1.31159	0.655797	+	0.754937i	$0.272333\pi$
$600$	810.806	0.0551684
$601$	−27989.7	−1.89971	−0.949853	−	0.312698i	$-0.898767\pi$
$601$	−27989.7	−1.89971	−0.949853	+	0.312698i	$0.898767\pi$
$602$	−6084.94	−0.411966
$603$	4192.15	0.283114
$604$	13218.7	0.890498
$605$	375.351	0.0252235
$606$	−8817.41	−0.591061
$607$	−13757.2	−0.919915	−0.459958	−	0.887941i	$-0.652135\pi$
$607$	−13757.2	−0.919915	−0.459958	+	0.887941i	$0.652135\pi$
$608$	−884.598	−0.0590053
$609$	−6459.15	−0.429784
$610$	6590.08	0.437417
$611$	1928.57	0.127695
$612$	−593.229	−0.0391828
$613$	10360.3	0.682626	0.341313	−	0.939950i	$-0.389128\pi$
$613$	10360.3	0.682626	0.341313	+	0.939950i	$0.389128\pi$
$614$	−502.729	−0.0330431
$615$	4326.91	0.283704
$616$	−2012.65	−0.131643
$617$	−2143.45	−0.139858	−0.0699288	−	0.997552i	$-0.522277\pi$
$617$	−2143.45	−0.139858	−0.0699288	+	0.997552i	$0.522277\pi$
$618$	−2312.26	−0.150506
$619$	23282.7	1.51181	0.755906	−	0.654680i	$-0.227197\pi$
$619$	23282.7	1.51181	0.755906	+	0.654680i	$0.227197\pi$
$620$	−10649.3	−0.689818
$621$	621.000	0.0401286
$622$	−5575.33	−0.359406
$623$	10728.7	0.689944
$624$	−329.291	−0.0211253
$625$	−10260.7	−0.656686
$626$	−1170.38	−0.0747250
$627$	−2980.56	−0.189844
$628$	−7233.59	−0.459636
$629$	3720.14	0.235821
$630$	−1203.39	−0.0761020
$631$	10965.6	0.691813	0.345906	−	0.938269i	$-0.387571\pi$
$631$	10965.6	0.691813	0.345906	+	0.938269i	$0.387571\pi$
$632$	−4328.80	−0.272453
$633$	493.909	0.0310128
$634$	4843.65	0.303416
$635$	−21694.0	−1.35575
$636$	4046.39	0.252280
$637$	336.151	0.0209086
$638$	−22108.9	−1.37194
$639$	8612.36	0.533177
$640$	−1222.49	−0.0755051
$641$	13655.3	0.841425	0.420712	−	0.907194i	$-0.361780\pi$
$641$	13655.3	0.841425	0.420712	+	0.907194i	$0.361780\pi$
$642$	4805.14	0.295395
$643$	4110.59	0.252109	0.126054	−	0.992023i	$-0.459769\pi$
$643$	4110.59	0.252109	0.126054	+	0.992023i	$0.459769\pi$
$644$	−644.000	−0.0394055
$645$	−12453.4	−0.760233
$646$	911.059	0.0554878
$647$	18237.5	1.10818	0.554088	−	0.832458i	$-0.313067\pi$
$647$	18237.5	1.10818	0.554088	+	0.832458i	$0.313067\pi$
$648$	648.000	0.0392837
$649$	−26766.6	−1.61892
$650$	−463.526	−0.0279708
$651$	−5853.89	−0.352430
$652$	−266.289	−0.0159949
$653$	−28056.9	−1.68140	−0.840699	−	0.541503i	$-0.817855\pi$
$653$	−28056.9	−1.68140	−0.840699	+	0.541503i	$0.817855\pi$
$654$	−7343.42	−0.439068
$655$	−5393.57	−0.321747
$656$	2416.24	0.143808
$657$	4824.07	0.286461
$658$	3935.72	0.233177
$659$	10838.1	0.640655	0.320328	−	0.947307i	$-0.396207\pi$
$659$	10838.1	0.640655	0.320328	+	0.947307i	$0.396207\pi$
$660$	−4119.06	−0.242931
$661$	−21151.8	−1.24464	−0.622321	−	0.782762i	$-0.713810\pi$
$661$	−21151.8	−1.24464	−0.622321	+	0.782762i	$0.713810\pi$
$662$	3821.22	0.224344
$663$	339.141	0.0198660
$664$	2820.79	0.164861
$665$	1848.12	0.107770
$666$	−4063.61	−0.236429
$667$	−7074.31	−0.410672
$668$	−1347.82	−0.0780667
$669$	12184.7	0.704166
$670$	−8897.35	−0.513037
$671$	12399.5	0.713380
$672$	−672.000	−0.0385758
$673$	5933.06	0.339826	0.169913	−	0.985459i	$-0.445651\pi$
$673$	5933.06	0.339826	0.169913	+	0.985459i	$0.445651\pi$
$674$	−2238.36	−0.127920
$675$	912.157	0.0520132
$676$	−8599.75	−0.489289
$677$	22207.5	1.26071	0.630357	−	0.776305i	$-0.282908\pi$
$677$	22207.5	1.26071	0.630357	+	0.776305i	$0.282908\pi$
$678$	−7696.31	−0.435951
$679$	−1587.65	−0.0897324
$680$	1259.06	0.0710041
$681$	9551.94	0.537491
$682$	−20037.2	−1.12502
$683$	7323.69	0.410298	0.205149	−	0.978731i	$-0.434232\pi$
$683$	7323.69	0.410298	0.205149	+	0.978731i	$0.434232\pi$
$684$	−995.173	−0.0556307
$685$	−3141.07	−0.175203
$686$	686.000	0.0381802
$687$	−3570.00	−0.198259
$688$	−6954.22	−0.385359
$689$	−2313.26	−0.127907
$690$	−1318.00	−0.0727180
$691$	−9596.05	−0.528294	−0.264147	−	0.964482i	$-0.585090\pi$
$691$	−9596.05	−0.528294	−0.264147	+	0.964482i	$0.585090\pi$
$692$	−1272.52	−0.0699045
$693$	−2264.23	−0.124114
$694$	22796.5	1.24690
$695$	19529.3	1.06588
$696$	−7381.89	−0.402026
$697$	−2488.51	−0.135236
$698$	3154.60	0.171065
$699$	20384.1	1.10300
$700$	−945.941	−0.0510760
$701$	−28684.1	−1.54548	−0.772740	−	0.634722i	$-0.781115\pi$
$701$	−28684.1	−1.54548	−0.772740	+	0.634722i	$0.781115\pi$
$702$	−370.452	−0.0199171
$703$	6240.73	0.334813
$704$	−2300.17	−0.123141
$705$	8054.79	0.430299
$706$	−9859.29	−0.525580
$707$	10287.0	0.547216
$708$	−8937.04	−0.474399
$709$	−10857.3	−0.575111	−0.287555	−	0.957764i	$-0.592843\pi$
$709$	−10857.3	−0.575111	−0.287555	+	0.957764i	$0.592843\pi$
$710$	−18278.7	−0.966182
$711$	−4869.90	−0.256871
$712$	12261.3	0.645383
$713$	−6411.41	−0.336759
$714$	692.101	0.0362762
$715$	2354.81	0.123168
$716$	−7875.74	−0.411076
$717$	12078.0	0.629095
$718$	10646.4	0.553373
$719$	−19066.6	−0.988962	−0.494481	−	0.869188i	$-0.664642\pi$
$719$	−19066.6	−0.988962	−0.494481	+	0.869188i	$0.664642\pi$
$720$	−1375.30	−0.0711869
$721$	2697.64	0.139342
$722$	−12189.7	−0.628327
$723$	−14362.6	−0.738796
$724$	15220.5	0.781308
$725$	−10391.1	−0.532298
$726$	235.805	0.0120545
$727$	23234.8	1.18533	0.592663	−	0.805451i	$-0.298077\pi$
$727$	23234.8	1.18533	0.592663	+	0.805451i	$0.298077\pi$
$728$	384.173	0.0195582
$729$	729.000	0.0370370
$730$	−10238.5	−0.519102
$731$	7162.24	0.362387
$732$	4140.05	0.209044
$733$	−10581.8	−0.533218	−0.266609	−	0.963805i	$-0.585903\pi$
$733$	−10581.8	−0.533218	−0.266609	+	0.963805i	$0.585903\pi$
$734$	−7520.59	−0.378188
$735$	1403.96	0.0704568
$736$	−736.000	−0.0368605
$737$	−16740.8	−0.836708
$738$	2718.27	0.135584
$739$	−33930.6	−1.68898	−0.844491	−	0.535570i	$-0.820097\pi$
$739$	−33930.6	−1.68898	−0.844491	+	0.535570i	$0.820097\pi$
$740$	8624.54	0.428438
$741$	568.926	0.0282052
$742$	−4720.79	−0.233565
$743$	35816.7	1.76849	0.884245	−	0.467023i	$-0.154673\pi$
$743$	35816.7	1.76849	0.884245	+	0.467023i	$0.154673\pi$
$744$	−6690.17	−0.329668
$745$	−5534.92	−0.272193
$746$	−18421.2	−0.904088
$747$	3173.39	0.155433
$748$	2368.98	0.115800
$749$	−5606.00	−0.273483
$750$	−9098.99	−0.442998
$751$	36266.5	1.76216	0.881081	−	0.472966i	$-0.156817\pi$
$751$	36266.5	1.76216	0.881081	+	0.472966i	$0.156817\pi$
$752$	4497.97	0.218117
$753$	15700.8	0.759851
$754$	4220.12	0.203830
$755$	−31562.0	−1.52140
$756$	−756.000	−0.0363696
$757$	10970.6	0.526727	0.263363	−	0.964697i	$-0.415168\pi$
$757$	10970.6	0.526727	0.263363	+	0.964697i	$0.415168\pi$
$758$	12611.2	0.604301
$759$	−2479.87	−0.118595
$760$	2112.14	0.100810
$761$	12254.8	0.583752	0.291876	−	0.956456i	$-0.405721\pi$
$761$	12254.8	0.583752	0.291876	+	0.956456i	$0.405721\pi$
$762$	−13628.7	−0.647921
$763$	8567.32	0.406498
$764$	6254.69	0.296187
$765$	1416.44	0.0669433
$766$	27143.9	1.28035
$767$	5109.17	0.240524
$768$	−768.000	−0.0360844
$769$	9003.57	0.422207	0.211103	−	0.977464i	$-0.432294\pi$
$769$	9003.57	0.422207	0.211103	+	0.977464i	$0.432294\pi$
$770$	4805.57	0.224910
$771$	−9480.42	−0.442839
$772$	−16456.0	−0.767182
$773$	8783.80	0.408708	0.204354	−	0.978897i	$-0.434491\pi$
$773$	8783.80	0.408708	0.204354	+	0.978897i	$0.434491\pi$
$774$	−7823.50	−0.363320
$775$	−9417.41	−0.436495
$776$	−1814.45	−0.0839370
$777$	4740.88	0.218891
$778$	−14896.0	−0.686437
$779$	−4174.61	−0.192004
$780$	786.242	0.0360923
$781$	−34392.2	−1.57574
$782$	758.015	0.0346631
$783$	−8304.63	−0.379033
$784$	784.000	0.0357143
$785$	17271.5	0.785282
$786$	−3388.37	−0.153765
$787$	28920.9	1.30994	0.654968	−	0.755656i	$-0.272682\pi$
$787$	28920.9	1.30994	0.654968	+	0.755656i	$0.272682\pi$
$788$	4573.89	0.206774
$789$	−15597.9	−0.703800
$790$	10335.8	0.465482
$791$	8979.02	0.403612
$792$	−2587.70	−0.116098
$793$	−2366.80	−0.105987
$794$	19590.4	0.875613
$795$	−9661.49	−0.431016
$796$	−18.5988	−0.000828161 0
$797$	−18091.1	−0.804039	−0.402019	−	0.915631i	$-0.631692\pi$
$797$	−18091.1	−0.804039	−0.402019	+	0.915631i	$0.631692\pi$
$798$	1161.04	0.0515040
$799$	−4632.51	−0.205114
$800$	−1081.07	−0.0477772
$801$	13794.0	0.608473
$802$	−15993.4	−0.704171
$803$	−19264.2	−0.846600
$804$	−5589.53	−0.245184
$805$	1537.67	0.0673238
$806$	3824.67	0.167144
$807$	14728.5	0.642462
$808$	11756.5	0.511873
$809$	−31525.0	−1.37004	−0.685018	−	0.728526i	$-0.740206\pi$
$809$	−31525.0	−1.37004	−0.685018	+	0.728526i	$0.740206\pi$
$810$	−1547.22	−0.0671157
$811$	1459.50	0.0631936	0.0315968	−	0.999501i	$-0.489941\pi$
$811$	1459.50	0.0631936	0.0315968	+	0.999501i	$0.489941\pi$
$812$	8612.21	0.372203
$813$	−12021.9	−0.518606
$814$	16227.4	0.698736
$815$	635.814	0.0273271
$816$	790.972	0.0339333
$817$	12015.0	0.514507
$818$	11033.3	0.471604
$819$	432.194	0.0184397
$820$	−5769.21	−0.245695
$821$	34470.9	1.46534	0.732669	−	0.680585i	$-0.238274\pi$
$821$	34470.9	1.46534	0.732669	+	0.680585i	$0.238274\pi$
$822$	−1973.30	−0.0837307
$823$	−12245.1	−0.518635	−0.259317	−	0.965792i	$-0.583498\pi$
$823$	−12245.1	−0.518635	−0.259317	+	0.965792i	$0.583498\pi$
$824$	3083.02	0.130342
$825$	−3642.57	−0.153719
$826$	10426.5	0.439208
$827$	21699.6	0.912418	0.456209	−	0.889873i	$-0.349207\pi$
$827$	21699.6	0.912418	0.456209	+	0.889873i	$0.349207\pi$
$828$	−828.000	−0.0347524
$829$	9666.34	0.404977	0.202489	−	0.979285i	$-0.435097\pi$
$829$	9666.34	0.404977	0.202489	+	0.979285i	$0.435097\pi$
$830$	−6735.16	−0.281664
$831$	−7589.89	−0.316835
$832$	439.054	0.0182950
$833$	−807.451	−0.0335853
$834$	12268.8	0.509391
$835$	3218.15	0.133376
$836$	3974.08	0.164410
$837$	−7526.44	−0.310814
$838$	8074.56	0.332853
$839$	6492.29	0.267150	0.133575	−	0.991039i	$-0.457354\pi$
$839$	6492.29	0.267150	0.133575	+	0.991039i	$0.457354\pi$
$840$	1604.52	0.0659063
$841$	70215.7	2.87899
$842$	12933.6	0.529360
$843$	24703.1	1.00928
$844$	−658.545	−0.0268579
$845$	20533.5	0.835944
$846$	5060.21	0.205643
$847$	−275.106	−0.0111603
$848$	−5395.19	−0.218480
$849$	−19123.5	−0.773048
$850$	1113.41	0.0449291
$851$	5192.39	0.209157
$852$	−11483.2	−0.461744
$853$	−273.587	−0.0109818	−0.00549088	−	0.999985i	$-0.501748\pi$
$853$	−273.587	−0.0109818	−0.00549088	+	0.999985i	$0.501748\pi$
$854$	−4830.05	−0.193538
$855$	2376.16	0.0950443
$856$	−6406.85	−0.255820
$857$	20910.7	0.833483	0.416741	−	0.909025i	$-0.363172\pi$
$857$	20910.7	0.833483	0.416741	+	0.909025i	$0.363172\pi$
$858$	1479.35	0.0588626
$859$	43191.5	1.71557	0.857785	−	0.514009i	$-0.171840\pi$
$859$	43191.5	1.71557	0.857785	+	0.514009i	$0.171840\pi$
$860$	16604.5	0.658381
$861$	−3171.31	−0.125526
$862$	−14837.7	−0.586279
$863$	15061.2	0.594077	0.297038	−	0.954866i	$-0.404001\pi$
$863$	15061.2	0.594077	0.297038	+	0.954866i	$0.404001\pi$
$864$	−864.000	−0.0340207
$865$	3038.37	0.119431
$866$	−32975.4	−1.29394
$867$	13924.4	0.545440
$868$	7805.19	0.305214
$869$	19447.2	0.759151
$870$	17625.6	0.686855
$871$	3195.46	0.124310
$872$	9791.22	0.380244
$873$	−2041.26	−0.0791366
$874$	1271.61	0.0492138
$875$	10615.5	0.410136
$876$	−6432.09	−0.248082
$877$	−11979.5	−0.461252	−0.230626	−	0.973042i	$-0.574077\pi$
$877$	−11979.5	−0.461252	−0.230626	+	0.973042i	$0.574077\pi$
$878$	−31534.3	−1.21211
$879$	−11838.6	−0.454274
$880$	5492.08	0.210384
$881$	1497.59	0.0572703	0.0286352	−	0.999590i	$-0.490884\pi$
$881$	1497.59	0.0572703	0.0286352	+	0.999590i	$0.490884\pi$
$882$	882.000	0.0336718
$883$	−3415.01	−0.130152	−0.0650761	−	0.997880i	$-0.520729\pi$
$883$	−3415.01	−0.130152	−0.0650761	+	0.997880i	$0.520729\pi$
$884$	−452.187	−0.0172044
$885$	21338.8	0.810504
$886$	−35327.3	−1.33955
$887$	−36693.1	−1.38899	−0.694495	−	0.719498i	$-0.744372\pi$
$887$	−36693.1	−1.38899	−0.694495	+	0.719498i	$0.744372\pi$
$888$	5418.14	0.204753
$889$	15900.2	0.599858
$890$	−29276.2	−1.10263
$891$	−2911.16	−0.109458
$892$	−16246.2	−0.609826
$893$	−7771.28	−0.291216
$894$	−3477.17	−0.130083
$895$	18804.8	0.702318
$896$	896.000	0.0334077
$897$	473.356	0.0176197
$898$	23946.0	0.889854
$899$	85739.7	3.18084
$900$	−1216.21	−0.0450448
$901$	5556.57	0.205456
$902$	−10855.0	−0.400701
$903$	9127.42	0.336369
$904$	10261.7	0.377545
$905$	−36341.8	−1.33485
$906$	−19828.0	−0.727088
$907$	−2621.57	−0.0959733	−0.0479866	−	0.998848i	$-0.515280\pi$
$907$	−2621.57	−0.0959733	−0.0479866	+	0.998848i	$0.515280\pi$
$908$	−12735.9	−0.465481
$909$	13226.1	0.482599
$910$	−917.282	−0.0334150
$911$	18982.7	0.690368	0.345184	−	0.938535i	$-0.387817\pi$
$911$	18982.7	0.690368	0.345184	+	0.938535i	$0.387817\pi$
$912$	1326.90	0.0481776
$913$	−12672.5	−0.459363
$914$	−3484.26	−0.126093
$915$	−9885.12	−0.357150
$916$	4760.00	0.171697
$917$	3953.10	0.142359
$918$	889.844	0.0319926
$919$	−10192.2	−0.365845	−0.182922	−	0.983127i	$-0.558556\pi$
$919$	−10192.2	−0.365845	−0.182922	+	0.983127i	$0.558556\pi$
$920$	1757.33	0.0629756
$921$	754.093	0.0269796
$922$	24170.5	0.863353
$923$	6564.75	0.234108
$924$	3018.98	0.107486
$925$	7626.85	0.271102
$926$	26920.9	0.955373
$927$	3468.40	0.122888
$928$	9842.52	0.348164
$929$	53333.7	1.88355	0.941777	−	0.336238i	$-0.109155\pi$
$929$	53333.7	1.88355	0.941777	+	0.336238i	$0.109155\pi$
$930$	15974.0	0.563234
$931$	−1354.54	−0.0476835
$932$	−27178.8	−0.955225
$933$	8362.99	0.293453
$934$	−7913.58	−0.277238
$935$	−5656.36	−0.197843
$936$	493.936	0.0172487
$937$	40735.5	1.42025	0.710124	−	0.704077i	$-0.248639\pi$
$937$	40735.5	1.42025	0.710124	+	0.704077i	$0.248639\pi$
$938$	6521.12	0.226996
$939$	1755.57	0.0610127
$940$	−10739.7	−0.372650
$941$	−10130.8	−0.350963	−0.175481	−	0.984483i	$-0.556148\pi$
$941$	−10130.8	−0.350963	−0.175481	+	0.984483i	$0.556148\pi$
$942$	10850.4	0.375291
$943$	−3473.34	−0.119944
$944$	11916.0	0.410841
$945$	1805.09	0.0621370
$946$	31242.0	1.07375
$947$	−3536.91	−0.121367	−0.0606833	−	0.998157i	$-0.519328\pi$
$947$	−3536.91	−0.121367	−0.0606833	+	0.998157i	$0.519328\pi$
$948$	6493.20	0.222457
$949$	3677.13	0.125780
$950$	1867.81	0.0637891
$951$	−7265.48	−0.247739
$952$	−922.801	−0.0314161
$953$	−30525.8	−1.03759	−0.518797	−	0.854897i	$-0.673620\pi$
$953$	−30525.8	−1.03759	−0.518797	+	0.854897i	$0.673620\pi$
$954$	−6069.58	−0.205985
$955$	−14934.2	−0.506031
$956$	−16104.0	−0.544812
$957$	33163.3	1.12019
$958$	32774.5	1.10532
$959$	2302.18	0.0775196
$960$	1833.74	0.0616497
$961$	47914.4	1.60835
$962$	−3097.47	−0.103811
$963$	−7207.71	−0.241189
$964$	19150.1	0.639816
$965$	39291.7	1.31072
$966$	966.000	0.0321745
$967$	33897.9	1.12728	0.563642	−	0.826019i	$-0.309400\pi$
$967$	33897.9	1.12728	0.563642	+	0.826019i	$0.309400\pi$
$968$	−314.407	−0.0104395
$969$	−1366.59	−0.0453056
$970$	4332.34	0.143405
$971$	−15613.9	−0.516040	−0.258020	−	0.966140i	$-0.583070\pi$
$971$	−15613.9	−0.516040	−0.258020	+	0.966140i	$0.583070\pi$
$972$	−972.000	−0.0320750
$973$	−14313.6	−0.471605
$974$	17949.8	0.590503
$975$	695.289	0.0228380
$976$	−5520.06	−0.181038
$977$	−30489.2	−0.998399	−0.499199	−	0.866487i	$-0.666372\pi$
$977$	−30489.2	−0.998399	−0.499199	+	0.866487i	$0.666372\pi$
$978$	399.434	0.0130598
$979$	−55084.4	−1.79827
$980$	−1871.94	−0.0610174
$981$	11015.1	0.358497
$982$	28093.7	0.912938
$983$	35753.1	1.16007	0.580034	−	0.814593i	$-0.303039\pi$
$983$	35753.1	1.16007	0.580034	+	0.814593i	$0.303039\pi$
$984$	−3624.36	−0.117419
$985$	−10921.0	−0.353271
$986$	−10136.9	−0.327409
$987$	−5903.58	−0.190388
$988$	−758.568	−0.0244264
$989$	9996.69	0.321412
$990$	6178.59	0.198352
$991$	13696.3	0.439030	0.219515	−	0.975609i	$-0.429553\pi$
$991$	13696.3	0.439030	0.219515	+	0.975609i	$0.429553\pi$
$992$	8920.22	0.285501
$993$	−5731.82	−0.183176
$994$	13397.0	0.427492
$995$	44.4080	0.00141490
$996$	−4231.19	−0.134609
$997$	40838.4	1.29726	0.648628	−	0.761106i	$-0.275343\pi$
$997$	40838.4	1.29726	0.648628	+	0.761106i	$0.275343\pi$
$998$	−31905.3	−1.01197
$999$	6095.41	0.193043

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	966.4.a.f.1.1	✓	3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
966.4.a.f.1.1	✓	3	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 966 = 2 \cdot 3 \cdot 7 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	966.a (trivial)

\(f(q)\)	\(=\)	\(q+2.00000 q^{2} -3.00000 q^{3} +4.00000 q^{4} -9.55073 q^{5} -6.00000 q^{6} +7.00000 q^{7} +8.00000 q^{8} +9.00000 q^{9} +O(q^{10})\)	\(q+2.00000 q^{2} -3.00000 q^{3} +4.00000 q^{4} -9.55073 q^{5} -6.00000 q^{6} +7.00000 q^{7} +8.00000 q^{8} +9.00000 q^{9} -19.1015 q^{10} -35.9402 q^{11} -12.0000 q^{12} +6.86023 q^{13} +14.0000 q^{14} +28.6522 q^{15} +16.0000 q^{16} -16.4786 q^{17} +18.0000 q^{18} -27.6437 q^{19} -38.2029 q^{20} -21.0000 q^{21} -71.8804 q^{22} -23.0000 q^{23} -24.0000 q^{24} -33.7836 q^{25} +13.7205 q^{26} -27.0000 q^{27} +28.0000 q^{28} +307.579 q^{29} +57.3044 q^{30} +278.757 q^{31} +32.0000 q^{32} +107.821 q^{33} -32.9572 q^{34} -66.8551 q^{35} +36.0000 q^{36} -225.756 q^{37} -55.2874 q^{38} -20.5807 q^{39} -76.4058 q^{40} +151.015 q^{41} -42.0000 q^{42} -434.639 q^{43} -143.761 q^{44} -85.9566 q^{45} -46.0000 q^{46} +281.123 q^{47} -48.0000 q^{48} +49.0000 q^{49} -67.5672 q^{50} +49.4358 q^{51} +27.4409 q^{52} -337.199 q^{53} -54.0000 q^{54} +343.255 q^{55} +56.0000 q^{56} +82.9311 q^{57} +615.158 q^{58} +744.753 q^{59} +114.609 q^{60} -345.004 q^{61} +557.514 q^{62} +63.0000 q^{63} +64.0000 q^{64} -65.5202 q^{65} +215.641 q^{66} +465.795 q^{67} -65.9144 q^{68} +69.0000 q^{69} -133.710 q^{70} +956.929 q^{71} +72.0000 q^{72} +536.007 q^{73} -451.512 q^{74} +101.351 q^{75} -110.575 q^{76} -251.582 q^{77} -41.1614 q^{78} -541.100 q^{79} -152.812 q^{80} +81.0000 q^{81} +302.030 q^{82} +352.599 q^{83} -84.0000 q^{84} +157.383 q^{85} -869.278 q^{86} -922.736 q^{87} -287.522 q^{88} +1532.67 q^{89} -171.913 q^{90} +48.0216 q^{91} -92.0000 q^{92} -836.271 q^{93} +562.246 q^{94} +264.017 q^{95} -96.0000 q^{96} -226.807 q^{97} +98.0000 q^{98} -323.462 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 3 q + 6 q^{2} - 9 q^{3} + 12 q^{4} + 9 q^{5} - 18 q^{6} + 21 q^{7} + 24 q^{8} + 27 q^{9}+O(q^{10}) \) 3 * q + 6 * q^2 - 9 * q^3 + 12 * q^4 + 9 * q^5 - 18 * q^6 + 21 * q^7 + 24 * q^8 + 27 * q^9	\( 3 q + 6 q^{2} - 9 q^{3} + 12 q^{4} + 9 q^{5} - 18 q^{6} + 21 q^{7} + 24 q^{8} + 27 q^{9} + 18 q^{10} + 53 q^{11} - 36 q^{12} + 61 q^{13} + 42 q^{14} - 27 q^{15} + 48 q^{16} - 2 q^{17} + 54 q^{18} + 63 q^{19} + 36 q^{20} - 63 q^{21} + 106 q^{22} - 69 q^{23} - 72 q^{24} - 72 q^{25} + 122 q^{26} - 81 q^{27} + 84 q^{28} + 312 q^{29} - 54 q^{30} + 220 q^{31} + 96 q^{32} - 159 q^{33} - 4 q^{34} + 63 q^{35} + 108 q^{36} - 44 q^{37} + 126 q^{38} - 183 q^{39} + 72 q^{40} + 171 q^{41} - 126 q^{42} - 627 q^{43} + 212 q^{44} + 81 q^{45} - 138 q^{46} + 353 q^{47} - 144 q^{48} + 147 q^{49} - 144 q^{50} + 6 q^{51} + 244 q^{52} - 504 q^{53} - 162 q^{54} + 1181 q^{55} + 168 q^{56} - 189 q^{57} + 624 q^{58} + 538 q^{59} - 108 q^{60} + 256 q^{61} + 440 q^{62} + 189 q^{63} + 192 q^{64} + 244 q^{65} - 318 q^{66} + 1113 q^{67} - 8 q^{68} + 207 q^{69} + 126 q^{70} + 53 q^{71} + 216 q^{72} + 360 q^{73} - 88 q^{74} + 216 q^{75} + 252 q^{76} + 371 q^{77} - 366 q^{78} + 134 q^{79} + 144 q^{80} + 243 q^{81} + 342 q^{82} + 1506 q^{83} - 252 q^{84} + 577 q^{85} - 1254 q^{86} - 936 q^{87} + 424 q^{88} + 2381 q^{89} + 162 q^{90} + 427 q^{91} - 276 q^{92} - 660 q^{93} + 706 q^{94} + 945 q^{95} - 288 q^{96} - 88 q^{97} + 294 q^{98} + 477 q^{99}+O(q^{100}) \) 3 * q + 6 * q^2 - 9 * q^3 + 12 * q^4 + 9 * q^5 - 18 * q^6 + 21 * q^7 + 24 * q^8 + 27 * q^9 + 18 * q^10 + 53 * q^11 - 36 * q^12 + 61 * q^13 + 42 * q^14 - 27 * q^15 + 48 * q^16 - 2 * q^17 + 54 * q^18 + 63 * q^19 + 36 * q^20 - 63 * q^21 + 106 * q^22 - 69 * q^23 - 72 * q^24 - 72 * q^25 + 122 * q^26 - 81 * q^27 + 84 * q^28 + 312 * q^29 - 54 * q^30 + 220 * q^31 + 96 * q^32 - 159 * q^33 - 4 * q^34 + 63 * q^35 + 108 * q^36 - 44 * q^37 + 126 * q^38 - 183 * q^39 + 72 * q^40 + 171 * q^41 - 126 * q^42 - 627 * q^43 + 212 * q^44 + 81 * q^45 - 138 * q^46 + 353 * q^47 - 144 * q^48 + 147 * q^49 - 144 * q^50 + 6 * q^51 + 244 * q^52 - 504 * q^53 - 162 * q^54 + 1181 * q^55 + 168 * q^56 - 189 * q^57 + 624 * q^58 + 538 * q^59 - 108 * q^60 + 256 * q^61 + 440 * q^62 + 189 * q^63 + 192 * q^64 + 244 * q^65 - 318 * q^66 + 1113 * q^67 - 8 * q^68 + 207 * q^69 + 126 * q^70 + 53 * q^71 + 216 * q^72 + 360 * q^73 - 88 * q^74 + 216 * q^75 + 252 * q^76 + 371 * q^77 - 366 * q^78 + 134 * q^79 + 144 * q^80 + 243 * q^81 + 342 * q^82 + 1506 * q^83 - 252 * q^84 + 577 * q^85 - 1254 * q^86 - 936 * q^87 + 424 * q^88 + 2381 * q^89 + 162 * q^90 + 427 * q^91 - 276 * q^92 - 660 * q^93 + 706 * q^94 + 945 * q^95 - 288 * q^96 - 88 * q^97 + 294 * q^98 + 477 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more