LMFDB - Embedded newform 966.4.a.m.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:	$5$
Coefficient field:	$\mathbb{Q}[x]/(x^{5} - \cdots)$
Defining polynomial:	$ x^{5} - x^{4} - 351x^{3} - 663x^{2} + 18451x - 19243 $ x^5 - x^4 - 351x^3 - 663x^2 + 18451*x - 19243
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$-13.0148$ of defining polynomial
Character	$\chi$	$=$	966.1

$q$-expansion

$f(q)$	$=$	$q-2.00000 q^{2} -3.00000 q^{3} +4.00000 q^{4} -12.7819 q^{5} +6.00000 q^{6} -7.00000 q^{7} -8.00000 q^{8} +9.00000 q^{9} +O(q^{10})$	\(q-2.00000 q^{2} -3.00000 q^{3} +4.00000 q^{4} -12.7819 q^{5} +6.00000 q^{6} -7.00000 q^{7} -8.00000 q^{8} +9.00000 q^{9} +25.5638 q^{10} -4.56319 q^{11} -12.0000 q^{12} -70.6646 q^{13} +14.0000 q^{14} +38.3456 q^{15} +16.0000 q^{16} -78.3781 q^{17} -18.0000 q^{18} -43.1688 q^{19} -51.1275 q^{20} +21.0000 q^{21} +9.12638 q^{22} -23.0000 q^{23} +24.0000 q^{24} +38.3765 q^{25} +141.329 q^{26} -27.0000 q^{27} -28.0000 q^{28} +166.607 q^{29} -76.6913 q^{30} -147.257 q^{31} -32.0000 q^{32} +13.6896 q^{33} +156.756 q^{34} +89.4732 q^{35} +36.0000 q^{36} -363.445 q^{37} +86.3375 q^{38} +211.994 q^{39} +102.255 q^{40} -295.204 q^{41} -42.0000 q^{42} -456.253 q^{43} -18.2528 q^{44} -115.037 q^{45} +46.0000 q^{46} -117.941 q^{47} -48.0000 q^{48} +49.0000 q^{49} -76.7529 q^{50} +235.134 q^{51} -282.658 q^{52} -221.354 q^{53} +54.0000 q^{54} +58.3262 q^{55} +56.0000 q^{56} +129.506 q^{57} -333.215 q^{58} -22.7176 q^{59} +153.383 q^{60} -399.012 q^{61} +294.514 q^{62} -63.0000 q^{63} +64.0000 q^{64} +903.226 q^{65} -27.3791 q^{66} +446.717 q^{67} -313.512 q^{68} +69.0000 q^{69} -178.946 q^{70} +321.137 q^{71} -72.0000 q^{72} -519.488 q^{73} +726.889 q^{74} -115.129 q^{75} -172.675 q^{76} +31.9423 q^{77} -423.988 q^{78} +85.1065 q^{79} -204.510 q^{80} +81.0000 q^{81} +590.408 q^{82} -163.878 q^{83} +84.0000 q^{84} +1001.82 q^{85} +912.506 q^{86} -499.822 q^{87} +36.5055 q^{88} -955.704 q^{89} +230.074 q^{90} +494.652 q^{91} -92.0000 q^{92} +441.772 q^{93} +235.882 q^{94} +551.778 q^{95} +96.0000 q^{96} -476.957 q^{97} -98.0000 q^{98} -41.0687 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 5 q - 10 q^{2} - 15 q^{3} + 20 q^{4} + 10 q^{5} + 30 q^{6} - 35 q^{7} - 40 q^{8} + 45 q^{9}+O(q^{10}) $ 5 * q - 10 * q^2 - 15 * q^3 + 20 * q^4 + 10 * q^5 + 30 * q^6 - 35 * q^7 - 40 * q^8 + 45 * q^9	\( 5 q - 10 q^{2} - 15 q^{3} + 20 q^{4} + 10 q^{5} + 30 q^{6} - 35 q^{7} - 40 q^{8} + 45 q^{9} - 20 q^{10} + 4 q^{11} - 60 q^{12} + 24 q^{13} + 70 q^{14} - 30 q^{15} + 80 q^{16} + 28 q^{17} - 90 q^{18} - 160 q^{19} + 40 q^{20} + 105 q^{21} - 8 q^{22} - 115 q^{23} + 120 q^{24} + 219 q^{25} - 48 q^{26} - 135 q^{27} - 140 q^{28} + 79 q^{29} + 60 q^{30} - 162 q^{31} - 160 q^{32} - 12 q^{33} - 56 q^{34} - 70 q^{35} + 180 q^{36} + 301 q^{37} + 320 q^{38} - 72 q^{39} - 80 q^{40} + 251 q^{41} - 210 q^{42} - 380 q^{43} + 16 q^{44} + 90 q^{45} + 230 q^{46} - 505 q^{47} - 240 q^{48} + 245 q^{49} - 438 q^{50} - 84 q^{51} + 96 q^{52} + 93 q^{53} + 270 q^{54} - 503 q^{55} + 280 q^{56} + 480 q^{57} - 158 q^{58} + 637 q^{59} - 120 q^{60} - 679 q^{61} + 324 q^{62} - 315 q^{63} + 320 q^{64} + 961 q^{65} + 24 q^{66} - 1483 q^{67} + 112 q^{68} + 345 q^{69} + 140 q^{70} + 95 q^{71} - 360 q^{72} - 1310 q^{73} - 602 q^{74} - 657 q^{75} - 640 q^{76} - 28 q^{77} + 144 q^{78} + 494 q^{79} + 160 q^{80} + 405 q^{81} - 502 q^{82} - 482 q^{83} + 420 q^{84} - 291 q^{85} + 760 q^{86} - 237 q^{87} - 32 q^{88} + 661 q^{89} - 180 q^{90} - 168 q^{91} - 460 q^{92} + 486 q^{93} + 1010 q^{94} - 629 q^{95} + 480 q^{96} - 1905 q^{97} - 490 q^{98} + 36 q^{99}+O(q^{100}) \) 5 * q - 10 * q^2 - 15 * q^3 + 20 * q^4 + 10 * q^5 + 30 * q^6 - 35 * q^7 - 40 * q^8 + 45 * q^9 - 20 * q^10 + 4 * q^11 - 60 * q^12 + 24 * q^13 + 70 * q^14 - 30 * q^15 + 80 * q^16 + 28 * q^17 - 90 * q^18 - 160 * q^19 + 40 * q^20 + 105 * q^21 - 8 * q^22 - 115 * q^23 + 120 * q^24 + 219 * q^25 - 48 * q^26 - 135 * q^27 - 140 * q^28 + 79 * q^29 + 60 * q^30 - 162 * q^31 - 160 * q^32 - 12 * q^33 - 56 * q^34 - 70 * q^35 + 180 * q^36 + 301 * q^37 + 320 * q^38 - 72 * q^39 - 80 * q^40 + 251 * q^41 - 210 * q^42 - 380 * q^43 + 16 * q^44 + 90 * q^45 + 230 * q^46 - 505 * q^47 - 240 * q^48 + 245 * q^49 - 438 * q^50 - 84 * q^51 + 96 * q^52 + 93 * q^53 + 270 * q^54 - 503 * q^55 + 280 * q^56 + 480 * q^57 - 158 * q^58 + 637 * q^59 - 120 * q^60 - 679 * q^61 + 324 * q^62 - 315 * q^63 + 320 * q^64 + 961 * q^65 + 24 * q^66 - 1483 * q^67 + 112 * q^68 + 345 * q^69 + 140 * q^70 + 95 * q^71 - 360 * q^72 - 1310 * q^73 - 602 * q^74 - 657 * q^75 - 640 * q^76 - 28 * q^77 + 144 * q^78 + 494 * q^79 + 160 * q^80 + 405 * q^81 - 502 * q^82 - 482 * q^83 + 420 * q^84 - 291 * q^85 + 760 * q^86 - 237 * q^87 - 32 * q^88 + 661 * q^89 - 180 * q^90 - 168 * q^91 - 460 * q^92 + 486 * q^93 + 1010 * q^94 - 629 * q^95 + 480 * q^96 - 1905 * q^97 - 490 * q^98 + 36 * 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
$5$	−12.7819	−1.14325	−0.571623	−	0.820516i	$-0.693686\pi$
$5$	−12.7819	−1.14325	−0.571623	+	0.820516i	$0.693686\pi$
$6$	6.00000	0.408248
$7$	−7.00000	−0.377964
$7$	−7.00000	−0.377964
$8$	−8.00000	−0.353553
$9$	9.00000	0.333333
$10$	25.5638	0.808397
$11$	−4.56319	−0.125078	−0.0625388	−	0.998043i	$-0.519920\pi$
$11$	−4.56319	−0.125078	−0.0625388	+	0.998043i	$0.519920\pi$
$12$	−12.0000	−0.288675
$13$	−70.6646	−1.50760	−0.753801	−	0.657102i	$-0.771782\pi$
$13$	−70.6646	−1.50760	−0.753801	+	0.657102i	$0.771782\pi$
$14$	14.0000	0.267261
$15$	38.3456	0.660053
$16$	16.0000	0.250000
$17$	−78.3781	−1.11820	−0.559102	−	0.829099i	$-0.688854\pi$
$17$	−78.3781	−1.11820	−0.559102	+	0.829099i	$0.688854\pi$
$18$	−18.0000	−0.235702
$19$	−43.1688	−0.521242	−0.260621	−	0.965441i	$-0.583927\pi$
$19$	−43.1688	−0.521242	−0.260621	+	0.965441i	$0.583927\pi$
$20$	−51.1275	−0.571623
$21$	21.0000	0.218218
$22$	9.12638	0.0884432
$23$	−23.0000	−0.208514
$23$	−23.0000	−0.208514
$24$	24.0000	0.204124
$25$	38.3765	0.307012
$26$	141.329	1.06604
$27$	−27.0000	−0.192450
$28$	−28.0000	−0.188982
$29$	166.607	1.06684	0.533418	−	0.845852i	$-0.320907\pi$
$29$	166.607	1.06684	0.533418	+	0.845852i	$0.320907\pi$
$30$	−76.6913	−0.466728
$31$	−147.257	−0.853167	−0.426584	−	0.904448i	$-0.640283\pi$
$31$	−147.257	−0.853167	−0.426584	+	0.904448i	$0.640283\pi$
$32$	−32.0000	−0.176777
$33$	13.6896	0.0722136
$34$	156.756	0.790690
$35$	89.4732	0.432106
$36$	36.0000	0.166667
$37$	−363.445	−1.61486	−0.807432	−	0.589961i	$-0.799143\pi$
$37$	−363.445	−1.61486	−0.807432	+	0.589961i	$0.799143\pi$
$38$	86.3375	0.368574
$39$	211.994	0.870415
$40$	102.255	0.404199
$41$	−295.204	−1.12447	−0.562233	−	0.826979i	$-0.690058\pi$
$41$	−295.204	−1.12447	−0.562233	+	0.826979i	$0.690058\pi$
$42$	−42.0000	−0.154303
$43$	−456.253	−1.61809	−0.809046	−	0.587746i	$-0.800015\pi$
$43$	−456.253	−1.61809	−0.809046	+	0.587746i	$0.800015\pi$
$44$	−18.2528	−0.0625388
$45$	−115.037	−0.381082
$46$	46.0000	0.147442
$47$	−117.941	−0.366031	−0.183016	−	0.983110i	$-0.558586\pi$
$47$	−117.941	−0.366031	−0.183016	+	0.983110i	$0.558586\pi$
$48$	−48.0000	−0.144338
$49$	49.0000	0.142857
$50$	−76.7529	−0.217090
$51$	235.134	0.645596
$52$	−282.658	−0.753801
$53$	−221.354	−0.573685	−0.286842	−	0.957978i	$-0.592606\pi$
$53$	−221.354	−0.573685	−0.286842	+	0.957978i	$0.592606\pi$
$54$	54.0000	0.136083
$55$	58.3262	0.142994
$56$	56.0000	0.133631
$57$	129.506	0.300939
$58$	−333.215	−0.754367
$59$	−22.7176	−0.0501284	−0.0250642	−	0.999686i	$-0.507979\pi$
$59$	−22.7176	−0.0501284	−0.0250642	+	0.999686i	$0.507979\pi$
$60$	153.383	0.330027
$61$	−399.012	−0.837512	−0.418756	−	0.908099i	$-0.637534\pi$
$61$	−399.012	−0.837512	−0.418756	+	0.908099i	$0.637534\pi$
$62$	294.514	0.603280
$63$	−63.0000	−0.125988
$64$	64.0000	0.125000
$65$	903.226	1.72356
$66$	−27.3791	−0.0510627
$67$	446.717	0.814555	0.407278	−	0.913304i	$-0.366478\pi$
$67$	446.717	0.814555	0.407278	+	0.913304i	$0.366478\pi$
$68$	−313.512	−0.559102
$69$	69.0000	0.120386
$70$	−178.946	−0.305545
$71$	321.137	0.536788	0.268394	−	0.963309i	$-0.413507\pi$
$71$	321.137	0.536788	0.268394	+	0.963309i	$0.413507\pi$
$72$	−72.0000	−0.117851
$73$	−519.488	−0.832897	−0.416449	−	0.909159i	$-0.636725\pi$
$73$	−519.488	−0.832897	−0.416449	+	0.909159i	$0.636725\pi$
$74$	726.889	1.14188
$75$	−115.129	−0.177253
$76$	−172.675	−0.260621
$77$	31.9423	0.0472749
$78$	−423.988	−0.615476
$79$	85.1065	0.121205	0.0606027	−	0.998162i	$-0.480698\pi$
$79$	85.1065	0.121205	0.0606027	+	0.998162i	$0.480698\pi$
$80$	−204.510	−0.285812
$81$	81.0000	0.111111
$82$	590.408	0.795118
$83$	−163.878	−0.216723	−0.108361	−	0.994112i	$-0.534560\pi$
$83$	−163.878	−0.216723	−0.108361	+	0.994112i	$0.534560\pi$
$84$	84.0000	0.109109
$85$	1001.82	1.27838
$86$	912.506	1.14416
$87$	−499.822	−0.615938
$88$	36.5055	0.0442216
$89$	−955.704	−1.13825	−0.569126	−	0.822251i	$-0.692718\pi$
$89$	−955.704	−1.13825	−0.569126	+	0.822251i	$0.692718\pi$
$90$	230.074	0.269466
$91$	494.652	0.569820
$92$	−92.0000	−0.104257
$93$	441.772	0.492576
$94$	235.882	0.258823
$95$	551.778	0.595908
$96$	96.0000	0.102062
$97$	−476.957	−0.499255	−0.249627	−	0.968342i	$-0.580308\pi$
$97$	−476.957	−0.499255	−0.249627	+	0.968342i	$0.580308\pi$
$98$	−98.0000	−0.101015
$99$	−41.0687	−0.0416925
$100$	153.506	0.153506
$101$	1340.97	1.32110	0.660552	−	0.750780i	$-0.270322\pi$
$101$	1340.97	1.32110	0.660552	+	0.750780i	$0.270322\pi$
$102$	−470.268	−0.456505
$103$	−1349.60	−1.29107	−0.645536	−	0.763730i	$-0.723366\pi$
$103$	−1349.60	−1.29107	−0.645536	+	0.763730i	$0.723366\pi$
$104$	565.317	0.533018
$105$	−268.419	−0.249477
$106$	442.708	0.405656
$107$	816.118	0.737356	0.368678	−	0.929557i	$-0.379810\pi$
$107$	816.118	0.737356	0.368678	+	0.929557i	$0.379810\pi$
$108$	−108.000	−0.0962250
$109$	−793.928	−0.697656	−0.348828	−	0.937187i	$-0.613420\pi$
$109$	−793.928	−0.697656	−0.348828	+	0.937187i	$0.613420\pi$
$110$	−116.652	−0.101112
$111$	1090.33	0.932342
$112$	−112.000	−0.0944911
$113$	−756.248	−0.629574	−0.314787	−	0.949162i	$-0.601933\pi$
$113$	−756.248	−0.629574	−0.314787	+	0.949162i	$0.601933\pi$
$114$	−259.013	−0.212796
$115$	293.983	0.238383
$116$	666.430	0.533418
$117$	−635.981	−0.502534
$118$	45.4351	0.0354461
$119$	548.647	0.422642
$120$	−306.765	−0.233364
$121$	−1310.18	−0.984356
$122$	798.024	0.592211
$123$	885.612	0.649211
$124$	−589.029	−0.426584
$125$	1107.21	0.792256
$126$	126.000	0.0890871
$127$	250.192	0.174811	0.0874053	−	0.996173i	$-0.472142\pi$
$127$	250.192	0.174811	0.0874053	+	0.996173i	$0.472142\pi$
$128$	−128.000	−0.0883883
$129$	1368.76	0.934205
$130$	−1806.45	−1.21874
$131$	1623.93	1.08308	0.541541	−	0.840675i	$-0.317841\pi$
$131$	1623.93	1.08308	0.541541	+	0.840675i	$0.317841\pi$
$132$	54.7583	0.0361068
$133$	302.181	0.197011
$134$	−893.434	−0.575977
$135$	345.111	0.220018
$136$	627.025	0.395345
$137$	1110.52	0.692539	0.346270	−	0.938135i	$-0.387448\pi$
$137$	1110.52	0.692539	0.346270	+	0.938135i	$0.387448\pi$
$138$	−138.000	−0.0851257
$139$	−352.003	−0.214795	−0.107398	−	0.994216i	$-0.534252\pi$
$139$	−352.003	−0.214795	−0.107398	+	0.994216i	$0.534252\pi$
$140$	357.893	0.216053
$141$	353.823	0.211328
$142$	−642.274	−0.379566
$143$	322.456	0.188567
$144$	144.000	0.0833333
$145$	−2129.56	−1.21966
$146$	1038.98	0.588947
$147$	−147.000	−0.0824786
$148$	−1453.78	−0.807432
$149$	552.442	0.303744	0.151872	−	0.988400i	$-0.451470\pi$
$149$	552.442	0.303744	0.151872	+	0.988400i	$0.451470\pi$
$150$	230.259	0.125337
$151$	2159.00	1.16356	0.581779	−	0.813347i	$-0.302357\pi$
$151$	2159.00	1.16356	0.581779	+	0.813347i	$0.302357\pi$
$152$	345.350	0.184287
$153$	−705.403	−0.372735
$154$	−63.8847	−0.0334284
$155$	1882.22	0.975380
$156$	847.975	0.435207
$157$	1335.03	0.678643	0.339321	−	0.940670i	$-0.389803\pi$
$157$	1335.03	0.678643	0.339321	+	0.940670i	$0.389803\pi$
$158$	−170.213	−0.0857052
$159$	664.062	0.331217
$160$	409.020	0.202099
$161$	161.000	0.0788110
$162$	−162.000	−0.0785674
$163$	1555.57	0.747493	0.373747	−	0.927531i	$-0.378073\pi$
$163$	1555.57	0.747493	0.373747	+	0.927531i	$0.378073\pi$
$164$	−1180.82	−0.562233
$165$	−174.978	−0.0825579
$166$	327.757	0.153246
$167$	−2422.61	−1.12256	−0.561279	−	0.827627i	$-0.689690\pi$
$167$	−2422.61	−1.12256	−0.561279	+	0.827627i	$0.689690\pi$
$168$	−168.000	−0.0771517
$169$	2796.49	1.27287
$170$	−2003.64	−0.903953
$171$	−388.519	−0.173747
$172$	−1825.01	−0.809046
$173$	1552.30	0.682193	0.341096	−	0.940028i	$-0.389202\pi$
$173$	1552.30	0.682193	0.341096	+	0.940028i	$0.389202\pi$
$174$	999.645	0.435534
$175$	−268.635	−0.116039
$176$	−73.0110	−0.0312694
$177$	68.1527	0.0289416
$178$	1911.41	0.804865
$179$	3121.09	1.30325	0.651624	−	0.758542i	$-0.274088\pi$
$179$	3121.09	1.30325	0.651624	+	0.758542i	$0.274088\pi$
$180$	−460.148	−0.190541
$181$	−808.858	−0.332166	−0.166083	−	0.986112i	$-0.553112\pi$
$181$	−808.858	−0.332166	−0.166083	+	0.986112i	$0.553112\pi$
$182$	−989.304	−0.402924
$183$	1197.04	0.483538
$184$	184.000	0.0737210
$185$	4645.51	1.84619
$186$	−883.543	−0.348304
$187$	357.654	0.139862
$188$	−471.764	−0.183016
$189$	189.000	0.0727393
$190$	−1103.56	−0.421370
$191$	−2975.03	−1.12705	−0.563523	−	0.826100i	$-0.690555\pi$
$191$	−2975.03	−1.12705	−0.563523	+	0.826100i	$0.690555\pi$
$192$	−192.000	−0.0721688
$193$	950.504	0.354501	0.177251	−	0.984166i	$-0.443280\pi$
$193$	950.504	0.354501	0.177251	+	0.984166i	$0.443280\pi$
$194$	953.915	0.353026
$195$	−2709.68	−0.995098
$196$	196.000	0.0714286
$197$	−1721.87	−0.622731	−0.311366	−	0.950290i	$-0.600786\pi$
$197$	−1721.87	−0.622731	−0.311366	+	0.950290i	$0.600786\pi$
$198$	82.1374	0.0294811
$199$	2116.67	0.754004	0.377002	−	0.926212i	$-0.376955\pi$
$199$	2116.67	0.754004	0.377002	+	0.926212i	$0.376955\pi$
$200$	−307.012	−0.108545
$201$	−1340.15	−0.470284
$202$	−2681.94	−0.934161
$203$	−1166.25	−0.403226
$204$	940.537	0.322798
$205$	3773.26	1.28554
$206$	2699.21	0.912926
$207$	−207.000	−0.0695048
$208$	−1130.63	−0.376901
$209$	196.987	0.0651957
$210$	536.839	0.176407
$211$	−872.114	−0.284544	−0.142272	−	0.989828i	$-0.545441\pi$
$211$	−872.114	−0.284544	−0.142272	+	0.989828i	$0.545441\pi$
$212$	−885.415	−0.286842
$213$	−963.411	−0.309915
$214$	−1632.24	−0.521390
$215$	5831.77	1.84988
$216$	216.000	0.0680414
$217$	1030.80	0.322467
$218$	1587.86	0.493317
$219$	1558.46	0.480874
$220$	233.305	0.0714972
$221$	5538.56	1.68581
$222$	−2180.67	−0.659265
$223$	2471.17	0.742070	0.371035	−	0.928619i	$-0.379003\pi$
$223$	2471.17	0.742070	0.371035	+	0.928619i	$0.379003\pi$
$224$	224.000	0.0668153
$225$	345.388	0.102337
$226$	1512.50	0.445176
$227$	2923.30	0.854742	0.427371	−	0.904076i	$-0.359440\pi$
$227$	2923.30	0.854742	0.427371	+	0.904076i	$0.359440\pi$
$228$	518.025	0.150470
$229$	5006.00	1.44457	0.722284	−	0.691597i	$-0.243092\pi$
$229$	5006.00	1.44457	0.722284	+	0.691597i	$0.243092\pi$
$230$	−587.966	−0.168562
$231$	−95.8270	−0.0272942
$232$	−1332.86	−0.377183
$233$	2162.09	0.607910	0.303955	−	0.952686i	$-0.401693\pi$
$233$	2162.09	0.607910	0.303955	+	0.952686i	$0.401693\pi$
$234$	1271.96	0.355345
$235$	1507.51	0.418464
$236$	−90.8702	−0.0250642
$237$	−255.319	−0.0699780
$238$	−1097.29	−0.298853
$239$	−2815.63	−0.762041	−0.381021	−	0.924567i	$-0.624427\pi$
$239$	−2815.63	−0.762041	−0.381021	+	0.924567i	$0.624427\pi$
$240$	613.530	0.165013
$241$	5516.45	1.47446	0.737231	−	0.675640i	$-0.236133\pi$
$241$	5516.45	1.47446	0.737231	+	0.675640i	$0.236133\pi$
$242$	2620.35	0.696045
$243$	−243.000	−0.0641500
$244$	−1596.05	−0.418756
$245$	−626.312	−0.163321
$246$	−1771.22	−0.459062
$247$	3050.50	0.785825
$248$	1178.06	0.301640
$249$	491.635	0.125125
$250$	−2214.42	−0.560210
$251$	−5526.99	−1.38988	−0.694941	−	0.719067i	$-0.744570\pi$
$251$	−5526.99	−1.38988	−0.694941	+	0.719067i	$0.744570\pi$
$252$	−252.000	−0.0629941
$253$	104.953	0.0260805
$254$	−500.384	−0.123610
$255$	−3005.46	−0.738075
$256$	256.000	0.0625000
$257$	3872.51	0.939925	0.469962	−	0.882686i	$-0.344267\pi$
$257$	3872.51	0.939925	0.469962	+	0.882686i	$0.344267\pi$
$258$	−2737.52	−0.660583
$259$	2544.11	0.610361
$260$	3612.91	0.861780
$261$	1499.47	0.355612
$262$	−3247.86	−0.765854
$263$	−2293.87	−0.537817	−0.268908	−	0.963166i	$-0.586663\pi$
$263$	−2293.87	−0.537817	−0.268908	+	0.963166i	$0.586663\pi$
$264$	−109.517	−0.0255314
$265$	2829.32	0.655863
$266$	−604.363	−0.139308
$267$	2867.11	0.657170
$268$	1786.87	0.407278
$269$	−1112.28	−0.252108	−0.126054	−	0.992023i	$-0.540231\pi$
$269$	−1112.28	−0.252108	−0.126054	+	0.992023i	$0.540231\pi$
$270$	−690.222	−0.155576
$271$	−6593.76	−1.47802	−0.739009	−	0.673696i	$-0.764706\pi$
$271$	−6593.76	−1.47802	−0.739009	+	0.673696i	$0.764706\pi$
$272$	−1254.05	−0.279551
$273$	−1483.96	−0.328986
$274$	−2221.03	−0.489699
$275$	−175.119	−0.0384003
$276$	276.000	0.0601929
$277$	−7047.11	−1.52859	−0.764296	−	0.644865i	$-0.776913\pi$
$277$	−7047.11	−1.52859	−0.764296	+	0.644865i	$0.776913\pi$
$278$	704.006	0.151883
$279$	−1325.32	−0.284389
$280$	−715.785	−0.152773
$281$	−1606.77	−0.341110	−0.170555	−	0.985348i	$-0.554556\pi$
$281$	−1606.77	−0.341110	−0.170555	+	0.985348i	$0.554556\pi$
$282$	−707.647	−0.149432
$283$	−7435.54	−1.56183	−0.780913	−	0.624640i	$-0.785246\pi$
$283$	−7435.54	−1.56183	−0.780913	+	0.624640i	$0.785246\pi$
$284$	1284.55	0.268394
$285$	−1655.33	−0.344047
$286$	−644.912	−0.133337
$287$	2066.43	0.425008
$288$	−288.000	−0.0589256
$289$	1230.12	0.250381
$290$	4259.11	0.862427
$291$	1430.87	0.288245
$292$	−2077.95	−0.416449
$293$	−984.078	−0.196213	−0.0981066	−	0.995176i	$-0.531279\pi$
$293$	−984.078	−0.196213	−0.0981066	+	0.995176i	$0.531279\pi$
$294$	294.000	0.0583212
$295$	290.373	0.0573091
$296$	2907.56	0.570940
$297$	123.206	0.0240712
$298$	−1104.88	−0.214779
$299$	1625.29	0.314357
$300$	−460.517	−0.0886266
$301$	3193.77	0.611581
$302$	−4318.01	−0.822760
$303$	−4022.91	−0.762740
$304$	−690.700	−0.130310
$305$	5100.12	0.957483
$306$	1410.81	0.263563
$307$	−7577.17	−1.40864	−0.704319	−	0.709883i	$-0.748748\pi$
$307$	−7577.17	−1.40864	−0.704319	+	0.709883i	$0.748748\pi$
$308$	127.769	0.0236374
$309$	4048.81	0.745401
$310$	−3764.45	−0.689698
$311$	−2223.18	−0.405353	−0.202677	−	0.979246i	$-0.564964\pi$
$311$	−2223.18	−0.405353	−0.202677	+	0.979246i	$0.564964\pi$
$312$	−1695.95	−0.307738
$313$	−3421.67	−0.617904	−0.308952	−	0.951078i	$-0.599978\pi$
$313$	−3421.67	−0.617904	−0.308952	+	0.951078i	$0.599978\pi$
$314$	−2670.06	−0.479873
$315$	805.258	0.144035
$316$	340.426	0.0606027
$317$	−1190.22	−0.210882	−0.105441	−	0.994426i	$-0.533625\pi$
$317$	−1190.22	−0.210882	−0.105441	+	0.994426i	$0.533625\pi$
$318$	−1328.12	−0.234206
$319$	−760.262	−0.133437
$320$	−818.040	−0.142906
$321$	−2448.35	−0.425713
$322$	−322.000	−0.0557278
$323$	3383.48	0.582855
$324$	324.000	0.0555556
$325$	−2711.86	−0.462852
$326$	−3111.13	−0.528557
$327$	2381.78	0.402792
$328$	2361.63	0.397559
$329$	825.588	0.138347
$330$	349.957	0.0583773
$331$	−7499.16	−1.24529	−0.622645	−	0.782504i	$-0.713942\pi$
$331$	−7499.16	−1.24529	−0.622645	+	0.782504i	$0.713942\pi$
$332$	−655.513	−0.108361
$333$	−3271.00	−0.538288
$334$	4845.22	0.793768
$335$	−5709.89	−0.931237
$336$	336.000	0.0545545
$337$	3476.33	0.561922	0.280961	−	0.959719i	$-0.409347\pi$
$337$	3476.33	0.561922	0.280961	+	0.959719i	$0.409347\pi$
$338$	−5592.97	−0.900052
$339$	2268.74	0.363485
$340$	4007.28	0.639191
$341$	671.963	0.106712
$342$	777.038	0.122858
$343$	−343.000	−0.0539949
$344$	3650.02	0.572082
$345$	−881.950	−0.137631
$346$	−3104.60	−0.482383
$347$	7365.59	1.13950	0.569749	−	0.821819i	$-0.307041\pi$
$347$	7365.59	1.13950	0.569749	+	0.821819i	$0.307041\pi$
$348$	−1999.29	−0.307969
$349$	−4338.06	−0.665361	−0.332680	−	0.943040i	$-0.607953\pi$
$349$	−4338.06	−0.665361	−0.332680	+	0.943040i	$0.607953\pi$
$350$	537.270	0.0820523
$351$	1907.94	0.290138
$352$	146.022	0.0221108
$353$	1473.91	0.222233	0.111117	−	0.993807i	$-0.464557\pi$
$353$	1473.91	0.222233	0.111117	+	0.993807i	$0.464557\pi$
$354$	−136.305	−0.0204648
$355$	−4104.73	−0.613681
$356$	−3822.81	−0.569126
$357$	−1645.94	−0.244012
$358$	−6242.18	−0.921535
$359$	1733.26	0.254813	0.127406	−	0.991851i	$-0.459335\pi$
$359$	1733.26	0.254813	0.127406	+	0.991851i	$0.459335\pi$
$360$	920.295	0.134733
$361$	−4995.46	−0.728307
$362$	1617.72	0.234876
$363$	3930.53	0.568318
$364$	1978.61	0.284910
$365$	6640.04	0.952207
$366$	−2394.07	−0.341913
$367$	3146.54	0.447543	0.223771	−	0.974642i	$-0.428163\pi$
$367$	3146.54	0.447543	0.223771	+	0.974642i	$0.428163\pi$
$368$	−368.000	−0.0521286
$369$	−2656.84	−0.374822
$370$	−9291.01	−1.30545
$371$	1549.48	0.216832
$372$	1767.09	0.246288
$373$	10403.0	1.44409	0.722043	−	0.691848i	$-0.243203\pi$
$373$	10403.0	1.44409	0.722043	+	0.691848i	$0.243203\pi$
$374$	−715.308	−0.0988976
$375$	−3321.64	−0.457409
$376$	943.529	0.129412
$377$	−11773.2	−1.60836
$378$	−378.000	−0.0514344
$379$	−5985.36	−0.811207	−0.405604	−	0.914049i	$-0.632939\pi$
$379$	−5985.36	−0.811207	−0.405604	+	0.914049i	$0.632939\pi$
$380$	2207.11	0.297954
$381$	−750.576	−0.100927
$382$	5950.07	0.796942
$383$	−2885.03	−0.384904	−0.192452	−	0.981306i	$-0.561644\pi$
$383$	−2885.03	−0.384904	−0.192452	+	0.981306i	$0.561644\pi$
$384$	384.000	0.0510310
$385$	−408.283	−0.0540468
$386$	−1901.01	−0.250670
$387$	−4106.28	−0.539364
$388$	−1907.83	−0.249627
$389$	11285.6	1.47095	0.735476	−	0.677551i	$-0.236959\pi$
$389$	11285.6	1.47095	0.735476	+	0.677551i	$0.236959\pi$
$390$	5419.36	0.703641
$391$	1802.70	0.233162
$392$	−392.000	−0.0505076
$393$	−4871.80	−0.625317
$394$	3443.74	0.440338
$395$	−1087.82	−0.138568
$396$	−164.275	−0.0208463
$397$	−2475.74	−0.312982	−0.156491	−	0.987679i	$-0.550018\pi$
$397$	−2475.74	−0.312982	−0.156491	+	0.987679i	$0.550018\pi$
$398$	−4233.34	−0.533161
$399$	−906.544	−0.113744
$400$	614.023	0.0767529
$401$	−7899.41	−0.983734	−0.491867	−	0.870670i	$-0.663685\pi$
$401$	−7899.41	−0.983734	−0.491867	+	0.870670i	$0.663685\pi$
$402$	2680.30	0.332541
$403$	10405.9	1.28624
$404$	5363.88	0.660552
$405$	−1035.33	−0.127027
$406$	2332.50	0.285124
$407$	1658.47	0.201983
$408$	−1881.07	−0.228253
$409$	−11771.3	−1.42311	−0.711554	−	0.702631i	$-0.752008\pi$
$409$	−11771.3	−1.42311	−0.711554	+	0.702631i	$0.752008\pi$
$410$	−7546.53	−0.909016
$411$	−3331.55	−0.399838
$412$	−5398.42	−0.645536
$413$	159.023	0.0189467
$414$	414.000	0.0491473
$415$	2094.67	0.247767
$416$	2261.27	0.266509
$417$	1056.01	0.124012
$418$	−393.975	−0.0461003
$419$	−1052.14	−0.122674	−0.0613370	−	0.998117i	$-0.519536\pi$
$419$	−1052.14	−0.122674	−0.0613370	+	0.998117i	$0.519536\pi$
$420$	−1073.68	−0.124738
$421$	−10346.9	−1.19780	−0.598902	−	0.800823i	$-0.704396\pi$
$421$	−10346.9	−1.19780	−0.598902	+	0.800823i	$0.704396\pi$
$422$	1744.23	0.201203
$423$	−1061.47	−0.122010
$424$	1770.83	0.202828
$425$	−3007.87	−0.343302
$426$	1926.82	0.219143
$427$	2793.08	0.316550
$428$	3264.47	0.368678
$429$	−967.368	−0.108869
$430$	−11663.5	−1.30806
$431$	5904.08	0.659836	0.329918	−	0.944010i	$-0.392979\pi$
$431$	5904.08	0.659836	0.329918	+	0.944010i	$0.392979\pi$
$432$	−432.000	−0.0481125
$433$	−8543.55	−0.948214	−0.474107	−	0.880467i	$-0.657229\pi$
$433$	−8543.55	−0.948214	−0.474107	+	0.880467i	$0.657229\pi$
$434$	−2061.60	−0.228019
$435$	6388.67	0.704168
$436$	−3175.71	−0.348828
$437$	992.881	0.108686
$438$	−3116.93	−0.340029
$439$	17210.9	1.87114	0.935572	−	0.353135i	$-0.114884\pi$
$439$	17210.9	1.87114	0.935572	+	0.353135i	$0.114884\pi$
$440$	−466.609	−0.0505562
$441$	441.000	0.0476190
$442$	−11077.1	−1.19205
$443$	−11853.5	−1.27128	−0.635642	−	0.771984i	$-0.719265\pi$
$443$	−11853.5	−1.27128	−0.635642	+	0.771984i	$0.719265\pi$
$444$	4361.34	0.466171
$445$	12215.7	1.30130
$446$	−4942.34	−0.524723
$447$	−1657.33	−0.175367
$448$	−448.000	−0.0472456
$449$	−13335.0	−1.40160	−0.700799	−	0.713359i	$-0.747173\pi$
$449$	−13335.0	−1.40160	−0.700799	+	0.713359i	$0.747173\pi$
$450$	−690.776	−0.0723633
$451$	1347.07	0.140646
$452$	−3024.99	−0.314787
$453$	−6477.01	−0.671781
$454$	−5846.61	−0.604394
$455$	−6322.58	−0.651445
$456$	−1036.05	−0.106398
$457$	−16084.7	−1.64642	−0.823208	−	0.567740i	$-0.807818\pi$
$457$	−16084.7	−1.64642	−0.823208	+	0.567740i	$0.807818\pi$
$458$	−10012.0	−1.02146
$459$	2116.21	0.215199
$460$	1175.93	0.119192
$461$	4358.86	0.440374	0.220187	−	0.975458i	$-0.429333\pi$
$461$	4358.86	0.440374	0.220187	+	0.975458i	$0.429333\pi$
$462$	191.654	0.0192999
$463$	521.026	0.0522984	0.0261492	−	0.999658i	$-0.491676\pi$
$463$	521.026	0.0522984	0.0261492	+	0.999658i	$0.491676\pi$
$464$	2665.72	0.266709
$465$	−5646.67	−0.563136
$466$	−4324.18	−0.429857
$467$	76.1495	0.00754556	0.00377278	−	0.999993i	$-0.498799\pi$
$467$	76.1495	0.00754556	0.00377278	+	0.999993i	$0.498799\pi$
$468$	−2543.93	−0.251267
$469$	−3127.02	−0.307873
$470$	−3015.02	−0.295899
$471$	−4005.09	−0.391815
$472$	181.740	0.0177231
$473$	2081.97	0.202387
$474$	510.639	0.0494819
$475$	−1656.66	−0.160027
$476$	2194.59	0.211321
$477$	−1992.18	−0.191228
$478$	5631.26	0.538845
$479$	−16679.8	−1.59106	−0.795532	−	0.605911i	$-0.792809\pi$
$479$	−16679.8	−1.59106	−0.795532	+	0.605911i	$0.792809\pi$
$480$	−1227.06	−0.116682
$481$	25682.7	2.43457
$482$	−11032.9	−1.04260
$483$	−483.000	−0.0455016
$484$	−5240.71	−0.492178
$485$	6096.41	0.570771
$486$	486.000	0.0453609
$487$	−12398.8	−1.15368	−0.576839	−	0.816858i	$-0.695714\pi$
$487$	−12398.8	−1.15368	−0.576839	+	0.816858i	$0.695714\pi$
$488$	3192.10	0.296105
$489$	−4666.70	−0.431565
$490$	1252.62	0.115485
$491$	14269.3	1.31154	0.655770	−	0.754960i	$-0.272344\pi$
$491$	14269.3	1.31154	0.655770	+	0.754960i	$0.272344\pi$
$492$	3542.45	0.324606
$493$	−13058.4	−1.19294
$494$	−6101.01	−0.555662
$495$	524.935	0.0476648
$496$	−2356.12	−0.213292
$497$	−2247.96	−0.202887
$498$	−983.270	−0.0884767
$499$	−11324.5	−1.01594	−0.507970	−	0.861375i	$-0.669604\pi$
$499$	−11324.5	−1.01594	−0.507970	+	0.861375i	$0.669604\pi$
$500$	4428.85	0.396128
$501$	7267.83	0.648109
$502$	11054.0	0.982795
$503$	−16241.4	−1.43970	−0.719850	−	0.694130i	$-0.755789\pi$
$503$	−16241.4	−1.43970	−0.719850	+	0.694130i	$0.755789\pi$
$504$	504.000	0.0445435
$505$	−17140.1	−1.51035
$506$	−209.907	−0.0184417
$507$	−8389.46	−0.734889
$508$	1000.77	0.0874053
$509$	22052.4	1.92035	0.960173	−	0.279405i	$-0.0901373\pi$
$509$	22052.4	1.92035	0.960173	+	0.279405i	$0.0901373\pi$
$510$	6010.91	0.521898
$511$	3636.42	0.314806
$512$	−512.000	−0.0441942
$513$	1165.56	0.100313
$514$	−7745.02	−0.664627
$515$	17250.5	1.47601
$516$	5475.04	0.467103
$517$	538.188	0.0457823
$518$	−5088.23	−0.431590
$519$	−4656.91	−0.393864
$520$	−7225.81	−0.609371
$521$	6126.02	0.515136	0.257568	−	0.966260i	$-0.417079\pi$
$521$	6126.02	0.515136	0.257568	+	0.966260i	$0.417079\pi$
$522$	−2998.93	−0.251456
$523$	−11267.8	−0.942081	−0.471040	−	0.882112i	$-0.656121\pi$
$523$	−11267.8	−0.942081	−0.471040	+	0.882112i	$0.656121\pi$
$524$	6495.73	0.541541
$525$	805.906	0.0669954
$526$	4587.73	0.380294
$527$	11541.7	0.954015
$528$	219.033	0.0180534
$529$	529.000	0.0434783
$530$	−5658.64	−0.463765
$531$	−204.458	−0.0167095
$532$	1208.73	0.0985054
$533$	20860.5	1.69525
$534$	−5734.22	−0.464689
$535$	−10431.5	−0.842980
$536$	−3573.74	−0.287989
$537$	−9363.27	−0.752430
$538$	2224.57	0.178267
$539$	−223.596	−0.0178682
$540$	1380.44	0.110009
$541$	−2051.38	−0.163023	−0.0815117	−	0.996672i	$-0.525975\pi$
$541$	−2051.38	−0.163023	−0.0815117	+	0.996672i	$0.525975\pi$
$542$	13187.5	1.04512
$543$	2426.57	0.191776
$544$	2508.10	0.197672
$545$	10147.9	0.797592
$546$	2967.91	0.232628
$547$	8692.02	0.679422	0.339711	−	0.940530i	$-0.389671\pi$
$547$	8692.02	0.679422	0.339711	+	0.940530i	$0.389671\pi$
$548$	4442.07	0.346270
$549$	−3591.11	−0.279171
$550$	350.238	0.0271531
$551$	−7192.24	−0.556079
$552$	−552.000	−0.0425628
$553$	−595.745	−0.0458113
$554$	14094.2	1.08088
$555$	−13936.5	−1.06590
$556$	−1408.01	−0.107398
$557$	6835.31	0.519967	0.259983	−	0.965613i	$-0.416283\pi$
$557$	6835.31	0.519967	0.259983	+	0.965613i	$0.416283\pi$
$558$	2650.63	0.201093
$559$	32240.9	2.43944
$560$	1431.57	0.108027
$561$	−1072.96	−0.0807496
$562$	3213.54	0.241201
$563$	−5526.23	−0.413682	−0.206841	−	0.978375i	$-0.566318\pi$
$563$	−5526.23	−0.413682	−0.206841	+	0.978375i	$0.566318\pi$
$564$	1415.29	0.105664
$565$	9666.27	0.719758
$566$	14871.1	1.10438
$567$	−567.000	−0.0419961
$568$	−2569.10	−0.189783
$569$	−17664.7	−1.30148	−0.650741	−	0.759300i	$-0.725542\pi$
$569$	−17664.7	−1.30148	−0.650741	+	0.759300i	$0.725542\pi$
$570$	3310.67	0.243278
$571$	14924.4	1.09381	0.546907	−	0.837194i	$-0.315805\pi$
$571$	14924.4	1.09381	0.546907	+	0.837194i	$0.315805\pi$
$572$	1289.82	0.0942837
$573$	8925.10	0.650701
$574$	−4132.86	−0.300526
$575$	−882.658	−0.0640164
$576$	576.000	0.0416667
$577$	16922.4	1.22095	0.610474	−	0.792036i	$-0.290979\pi$
$577$	16922.4	1.22095	0.610474	+	0.792036i	$0.290979\pi$
$578$	−2460.25	−0.177046
$579$	−2851.51	−0.204671
$580$	−8518.23	−0.609828
$581$	1147.15	0.0819135
$582$	−2861.74	−0.203820
$583$	1010.08	0.0717551
$584$	4155.91	0.294474
$585$	8129.04	0.574520
$586$	1968.16	0.138744
$587$	9803.68	0.689338	0.344669	−	0.938724i	$-0.387991\pi$
$587$	9803.68	0.689338	0.344669	+	0.938724i	$0.387991\pi$
$588$	−588.000	−0.0412393
$589$	6356.91	0.444706
$590$	−580.746	−0.0405236
$591$	5165.61	0.359534
$592$	−5815.12	−0.403716
$593$	8747.09	0.605734	0.302867	−	0.953033i	$-0.402056\pi$
$593$	8747.09	0.605734	0.302867	+	0.953033i	$0.402056\pi$
$594$	−246.412	−0.0170209
$595$	−7012.73	−0.483183
$596$	2209.77	0.151872
$597$	−6350.01	−0.435324
$598$	−3250.57	−0.222284
$599$	−20587.5	−1.40431	−0.702157	−	0.712022i	$-0.747779\pi$
$599$	−20587.5	−1.40431	−0.702157	+	0.712022i	$0.747779\pi$
$600$	921.035	0.0626685
$601$	−1385.33	−0.0940244	−0.0470122	−	0.998894i	$-0.514970\pi$
$601$	−1385.33	−0.0940244	−0.0470122	+	0.998894i	$0.514970\pi$
$602$	−6387.54	−0.432453
$603$	4020.46	0.271518
$604$	8636.02	0.581779
$605$	16746.5	1.12536
$606$	8045.82	0.539338
$607$	−6297.96	−0.421131	−0.210565	−	0.977580i	$-0.567530\pi$
$607$	−6297.96	−0.421131	−0.210565	+	0.977580i	$0.567530\pi$
$608$	1381.40	0.0921434
$609$	3498.76	0.232803
$610$	−10200.2	−0.677042
$611$	8334.26	0.551830
$612$	−2821.61	−0.186367
$613$	20987.9	1.38286	0.691430	−	0.722444i	$-0.256981\pi$
$613$	20987.9	1.38286	0.691430	+	0.722444i	$0.256981\pi$
$614$	15154.3	0.996058
$615$	−11319.8	−0.742208
$616$	−255.539	−0.0167142
$617$	−88.3741	−0.00576630	−0.00288315	−	0.999996i	$-0.500918\pi$
$617$	−88.3741	−0.00576630	−0.00288315	+	0.999996i	$0.500918\pi$
$618$	−8097.63	−0.527078
$619$	−16529.3	−1.07330	−0.536648	−	0.843806i	$-0.680310\pi$
$619$	−16529.3	−1.07330	−0.536648	+	0.843806i	$0.680310\pi$
$620$	7528.90	0.487690
$621$	621.000	0.0401286
$622$	4446.36	0.286628
$623$	6689.93	0.430219
$624$	3391.90	0.217604
$625$	−18949.3	−1.21276
$626$	6843.33	0.436924
$627$	−590.962	−0.0376407
$628$	5340.12	0.339321
$629$	28486.1	1.80575
$630$	−1610.52	−0.101848
$631$	−5525.99	−0.348631	−0.174316	−	0.984690i	$-0.555771\pi$
$631$	−5525.99	−0.348631	−0.174316	+	0.984690i	$0.555771\pi$
$632$	−680.852	−0.0428526
$633$	2616.34	0.164282
$634$	2380.44	0.149116
$635$	−3197.92	−0.199852
$636$	2656.25	0.165609
$637$	−3462.57	−0.215372
$638$	1520.52	0.0943544
$639$	2890.23	0.178929
$640$	1636.08	0.101050
$641$	2098.71	0.129320	0.0646601	−	0.997907i	$-0.479404\pi$
$641$	2098.71	0.129320	0.0646601	+	0.997907i	$0.479404\pi$
$642$	4896.71	0.301024
$643$	−13772.3	−0.844677	−0.422338	−	0.906438i	$-0.638791\pi$
$643$	−13772.3	−0.844677	−0.422338	+	0.906438i	$0.638791\pi$
$644$	644.000	0.0394055
$645$	−17495.3	−1.06803
$646$	−6766.97	−0.412141
$647$	−22099.9	−1.34287	−0.671436	−	0.741063i	$-0.734322\pi$
$647$	−22099.9	−1.34287	−0.671436	+	0.741063i	$0.734322\pi$
$648$	−648.000	−0.0392837
$649$	103.665	0.00626994
$650$	5423.71	0.327285
$651$	−3092.40	−0.186176
$652$	6222.27	0.373747
$653$	−10236.7	−0.613467	−0.306734	−	0.951795i	$-0.599236\pi$
$653$	−10236.7	−0.613467	−0.306734	+	0.951795i	$0.599236\pi$
$654$	−4763.57	−0.284817
$655$	−20756.9	−1.23823
$656$	−4723.27	−0.281117
$657$	−4675.39	−0.277632
$658$	−1651.18	−0.0978260
$659$	−4648.69	−0.274791	−0.137396	−	0.990516i	$-0.543873\pi$
$659$	−4648.69	−0.274791	−0.137396	+	0.990516i	$0.543873\pi$
$660$	−699.914	−0.0412790
$661$	1656.45	0.0974713	0.0487356	−	0.998812i	$-0.484481\pi$
$661$	1656.45	0.0974713	0.0487356	+	0.998812i	$0.484481\pi$
$662$	14998.3	0.880553
$663$	−16615.7	−0.973302
$664$	1311.03	0.0766230
$665$	−3862.44	−0.225232
$666$	6542.00	0.380627
$667$	−3831.97	−0.222451
$668$	−9690.43	−0.561279
$669$	−7413.50	−0.428434
$670$	11419.8	0.658484
$671$	1820.77	0.104754
$672$	−672.000	−0.0385758
$673$	1740.37	0.0996826	0.0498413	−	0.998757i	$-0.484128\pi$
$673$	1740.37	0.0996826	0.0498413	+	0.998757i	$0.484128\pi$
$674$	−6952.66	−0.397339
$675$	−1036.16	−0.0590844
$676$	11185.9	0.636433
$677$	12725.2	0.722406	0.361203	−	0.932487i	$-0.382366\pi$
$677$	12725.2	0.722406	0.361203	+	0.932487i	$0.382366\pi$
$678$	−4537.49	−0.257022
$679$	3338.70	0.188700
$680$	−8014.55	−0.451977
$681$	−8769.91	−0.493485
$682$	−1343.93	−0.0754569
$683$	−19212.1	−1.07632	−0.538162	−	0.842841i	$-0.680881\pi$
$683$	−19212.1	−1.07632	−0.538162	+	0.842841i	$0.680881\pi$
$684$	−1554.08	−0.0868736
$685$	−14194.5	−0.791743
$686$	686.000	0.0381802
$687$	−15018.0	−0.834022
$688$	−7300.05	−0.404523
$689$	15641.9	0.864888
$690$	1763.90	0.0973196
$691$	−24225.5	−1.33369	−0.666846	−	0.745195i	$-0.732356\pi$
$691$	−24225.5	−1.33369	−0.666846	+	0.745195i	$0.732356\pi$
$692$	6209.21	0.341096
$693$	287.481	0.0157583
$694$	−14731.2	−0.805746
$695$	4499.26	0.245564
$696$	3998.58	0.217767
$697$	23137.5	1.25738
$698$	8676.12	0.470481
$699$	−6486.26	−0.350977
$700$	−1074.54	−0.0580197
$701$	−3628.45	−0.195499	−0.0977494	−	0.995211i	$-0.531164\pi$
$701$	−3628.45	−0.195499	−0.0977494	+	0.995211i	$0.531164\pi$
$702$	−3815.89	−0.205159
$703$	15689.5	0.841734
$704$	−292.044	−0.0156347
$705$	−4522.53	−0.241600
$706$	−2947.82	−0.157143
$707$	−9386.79	−0.499330
$708$	272.611	0.0144708
$709$	20542.5	1.08814	0.544069	−	0.839041i	$-0.316883\pi$
$709$	20542.5	1.08814	0.544069	+	0.839041i	$0.316883\pi$
$710$	8209.47	0.433938
$711$	765.958	0.0404018
$712$	7645.63	0.402433
$713$	3386.92	0.177898
$714$	3291.88	0.172543
$715$	−4121.59	−0.215579
$716$	12484.4	0.651624
$717$	8446.89	0.439965
$718$	−3466.52	−0.180180
$719$	615.398	0.0319200	0.0159600	−	0.999873i	$-0.494920\pi$
$719$	615.398	0.0319200	0.0159600	+	0.999873i	$0.494920\pi$
$720$	−1840.59	−0.0952705
$721$	9447.23	0.487980
$722$	9990.92	0.514991
$723$	−16549.3	−0.851281
$724$	−3235.43	−0.166083
$725$	6393.80	0.327531
$726$	−7861.06	−0.401861
$727$	13930.0	0.710638	0.355319	−	0.934745i	$-0.384372\pi$
$727$	13930.0	0.710638	0.355319	+	0.934745i	$0.384372\pi$
$728$	−3957.22	−0.201462
$729$	729.000	0.0370370
$730$	−13280.1	−0.673312
$731$	35760.2	1.80936
$732$	4788.14	0.241769
$733$	38591.7	1.94463	0.972316	−	0.233668i	$-0.0750728\pi$
$733$	38591.7	1.94463	0.972316	+	0.233668i	$0.0750728\pi$
$734$	−6293.08	−0.316460
$735$	1878.94	0.0942933
$736$	736.000	0.0368605
$737$	−2038.46	−0.101883
$738$	5313.67	0.265039
$739$	−3312.27	−0.164877	−0.0824383	−	0.996596i	$-0.526271\pi$
$739$	−3312.27	−0.164877	−0.0824383	+	0.996596i	$0.526271\pi$
$740$	18582.0	0.923093
$741$	−9151.51	−0.453696
$742$	−3098.95	−0.153324
$743$	−31981.0	−1.57910	−0.789550	−	0.613687i	$-0.789686\pi$
$743$	−31981.0	−1.57910	−0.789550	+	0.613687i	$0.789686\pi$
$744$	−3534.17	−0.174152
$745$	−7061.25	−0.347254
$746$	−20805.9	−1.02112
$747$	−1474.90	−0.0722409
$748$	1430.62	0.0699312
$749$	−5712.83	−0.278694
$750$	6643.27	0.323437
$751$	18460.9	0.897001	0.448500	−	0.893783i	$-0.351958\pi$
$751$	18460.9	0.897001	0.448500	+	0.893783i	$0.351958\pi$
$752$	−1887.06	−0.0915079
$753$	16581.0	0.802449
$754$	23546.5	1.13728
$755$	−27596.1	−1.33023
$756$	756.000	0.0363696
$757$	568.470	0.0272938	0.0136469	−	0.999907i	$-0.495656\pi$
$757$	568.470	0.0272938	0.0136469	+	0.999907i	$0.495656\pi$
$758$	11970.7	0.573610
$759$	−314.860	−0.0150576
$760$	−4414.22	−0.210685
$761$	29609.3	1.41043	0.705215	−	0.708994i	$-0.250851\pi$
$761$	29609.3	1.41043	0.705215	+	0.708994i	$0.250851\pi$
$762$	1501.15	0.0713662
$763$	5557.49	0.263689
$764$	−11900.1	−0.563523
$765$	9016.37	0.426128
$766$	5770.07	0.272169
$767$	1605.33	0.0755737
$768$	−768.000	−0.0360844
$769$	−31575.5	−1.48068	−0.740339	−	0.672234i	$-0.765335\pi$
$769$	−31575.5	−1.48068	−0.740339	+	0.672234i	$0.765335\pi$
$770$	816.566	0.0382169
$771$	−11617.5	−0.542666
$772$	3802.01	0.177251
$773$	−33899.2	−1.57732	−0.788660	−	0.614830i	$-0.789225\pi$
$773$	−33899.2	−1.57732	−0.788660	+	0.614830i	$0.789225\pi$
$774$	8212.55	0.381388
$775$	−5651.21	−0.261932
$776$	3815.66	0.176513
$777$	−7632.34	−0.352392
$778$	−22571.1	−1.04012
$779$	12743.6	0.586119
$780$	−10838.7	−0.497549
$781$	−1465.41	−0.0671402
$782$	−3605.39	−0.164870
$783$	−4498.40	−0.205313
$784$	784.000	0.0357143
$785$	−17064.2	−0.775856
$786$	9743.59	0.442166
$787$	−6835.67	−0.309613	−0.154807	−	0.987945i	$-0.549475\pi$
$787$	−6835.67	−0.309613	−0.154807	+	0.987945i	$0.549475\pi$
$788$	−6887.47	−0.311366
$789$	6881.60	0.310509
$790$	2175.64	0.0979821
$791$	5293.74	0.237956
$792$	328.550	0.0147405
$793$	28196.0	1.26264
$794$	4951.48	0.221312
$795$	−8487.95	−0.378663
$796$	8466.68	0.377002
$797$	567.471	0.0252206	0.0126103	−	0.999920i	$-0.495986\pi$
$797$	567.471	0.0252206	0.0126103	+	0.999920i	$0.495986\pi$
$798$	1813.09	0.0804293
$799$	9244.00	0.409298
$800$	−1228.05	−0.0542725
$801$	−8601.33	−0.379417
$802$	15798.8	0.695605
$803$	2370.52	0.104177
$804$	−5360.61	−0.235142
$805$	−2057.88	−0.0901004
$806$	−20811.7	−0.909507
$807$	3336.85	0.145555
$808$	−10727.8	−0.467081
$809$	−453.037	−0.0196884	−0.00984421	−	0.999952i	$-0.503134\pi$
$809$	−453.037	−0.0196884	−0.00984421	+	0.999952i	$0.503134\pi$
$810$	2070.66	0.0898219
$811$	−4837.90	−0.209472	−0.104736	−	0.994500i	$-0.533400\pi$
$811$	−4837.90	−0.209472	−0.104736	+	0.994500i	$0.533400\pi$
$812$	−4665.01	−0.201613
$813$	19781.3	0.853334
$814$	−3316.93	−0.142824
$815$	−19883.1	−0.854568
$816$	3762.15	0.161399
$817$	19695.9	0.843417
$818$	23542.5	1.00629
$819$	4451.87	0.189940
$820$	15093.1	0.642771
$821$	−16163.9	−0.687117	−0.343558	−	0.939131i	$-0.611632\pi$
$821$	−16163.9	−0.687117	−0.343558	+	0.939131i	$0.611632\pi$
$822$	6663.10	0.282728
$823$	36866.5	1.56146	0.780732	−	0.624866i	$-0.214847\pi$
$823$	36866.5	1.56146	0.780732	+	0.624866i	$0.214847\pi$
$824$	10796.8	0.456463
$825$	525.357	0.0221704
$826$	−318.046	−0.0133974
$827$	7053.95	0.296602	0.148301	−	0.988942i	$-0.452620\pi$
$827$	7053.95	0.296602	0.148301	+	0.988942i	$0.452620\pi$
$828$	−828.000	−0.0347524
$829$	25899.6	1.08508	0.542540	−	0.840030i	$-0.317463\pi$
$829$	25899.6	1.08508	0.542540	+	0.840030i	$0.317463\pi$
$830$	−4189.35	−0.175198
$831$	21141.3	0.882533
$832$	−4522.53	−0.188450
$833$	−3840.53	−0.159743
$834$	−2112.02	−0.0876897
$835$	30965.5	1.28336
$836$	787.949	0.0325978
$837$	3975.95	0.164192
$838$	2104.28	0.0867436
$839$	−28305.1	−1.16472	−0.582359	−	0.812932i	$-0.697870\pi$
$839$	−28305.1	−1.16472	−0.582359	+	0.812932i	$0.697870\pi$
$840$	2147.36	0.0882034
$841$	3369.04	0.138138
$842$	20693.7	0.846975
$843$	4820.32	0.196940
$844$	−3488.46	−0.142272
$845$	−35744.3	−1.45520
$846$	2122.94	0.0862744
$847$	9171.24	0.372051
$848$	−3541.66	−0.143421
$849$	22306.6	0.901721
$850$	6015.75	0.242751
$851$	8359.23	0.336722
$852$	−3853.64	−0.154957
$853$	24137.4	0.968874	0.484437	−	0.874826i	$-0.339024\pi$
$853$	24137.4	0.968874	0.484437	+	0.874826i	$0.339024\pi$
$854$	−5586.17	−0.223835
$855$	4966.00	0.198636
$856$	−6528.95	−0.260695
$857$	45567.7	1.81629	0.908146	−	0.418653i	$-0.137498\pi$
$857$	45567.7	1.81629	0.908146	+	0.418653i	$0.137498\pi$
$858$	1934.74	0.0769823
$859$	12381.3	0.491788	0.245894	−	0.969297i	$-0.420919\pi$
$859$	12381.3	0.491788	0.245894	+	0.969297i	$0.420919\pi$
$860$	23327.1	0.924938
$861$	−6199.29	−0.245379
$862$	−11808.2	−0.466574
$863$	−12015.9	−0.473958	−0.236979	−	0.971515i	$-0.576157\pi$
$863$	−12015.9	−0.473958	−0.236979	+	0.971515i	$0.576157\pi$
$864$	864.000	0.0340207
$865$	−19841.3	−0.779914
$866$	17087.1	0.670488
$867$	−3690.37	−0.144558
$868$	4123.20	0.161233
$869$	−388.357	−0.0151601
$870$	−12777.3	−0.497922
$871$	−31567.1	−1.22803
$872$	6351.42	0.246659
$873$	−4292.62	−0.166418
$874$	−1985.76	−0.0768529
$875$	−7750.48	−0.299445
$876$	6233.86	0.240437
$877$	29870.9	1.15014	0.575069	−	0.818105i	$-0.304975\pi$
$877$	29870.9	1.15014	0.575069	+	0.818105i	$0.304975\pi$
$878$	−34421.8	−1.32310
$879$	2952.23	0.113284
$880$	933.218	0.0357486
$881$	−18857.5	−0.721143	−0.360571	−	0.932732i	$-0.617418\pi$
$881$	−18857.5	−0.721143	−0.360571	+	0.932732i	$0.617418\pi$
$882$	−882.000	−0.0336718
$883$	43540.2	1.65939	0.829697	−	0.558213i	$-0.188513\pi$
$883$	43540.2	1.65939	0.829697	+	0.558213i	$0.188513\pi$
$884$	22154.2	0.842904
$885$	−871.119	−0.0330874
$886$	23707.1	0.898934
$887$	−26111.3	−0.988422	−0.494211	−	0.869342i	$-0.664543\pi$
$887$	−26111.3	−0.988422	−0.494211	+	0.869342i	$0.664543\pi$
$888$	−8722.67	−0.329633
$889$	−1751.34	−0.0660722
$890$	−24431.4	−0.920159
$891$	−369.618	−0.0138975
$892$	9884.67	0.371035
$893$	5091.37	0.190791
$894$	3314.65	0.124003
$895$	−39893.4	−1.48993
$896$	896.000	0.0334077
$897$	−4875.86	−0.181494
$898$	26670.0	0.991079
$899$	−24534.2	−0.910189
$900$	1381.55	0.0511686
$901$	17349.3	0.641497
$902$	−2694.15	−0.0994515
$903$	−9581.31	−0.353096
$904$	6049.98	0.222588
$905$	10338.7	0.379747
$906$	12954.0	0.475021
$907$	−3966.29	−0.145202	−0.0726012	−	0.997361i	$-0.523130\pi$
$907$	−3966.29	−0.145202	−0.0726012	+	0.997361i	$0.523130\pi$
$908$	11693.2	0.427371
$909$	12068.7	0.440368
$910$	12645.2	0.460641
$911$	−17533.1	−0.637649	−0.318824	−	0.947814i	$-0.603288\pi$
$911$	−17533.1	−0.637649	−0.318824	+	0.947814i	$0.603288\pi$
$912$	2072.10	0.0752348
$913$	747.808	0.0271072
$914$	32169.5	1.16419
$915$	−15300.4	−0.552803
$916$	20024.0	0.722284
$917$	−11367.5	−0.409366
$918$	−4232.42	−0.152168
$919$	47649.9	1.71036	0.855182	−	0.518328i	$-0.173445\pi$
$919$	47649.9	1.71036	0.855182	+	0.518328i	$0.173445\pi$
$920$	−2351.87	−0.0842812
$921$	22731.5	0.813278
$922$	−8717.72	−0.311391
$923$	−22693.0	−0.809263
$924$	−383.308	−0.0136471
$925$	−13947.7	−0.495782
$926$	−1042.05	−0.0369805
$927$	−12146.4	−0.430358
$928$	−5331.44	−0.188592
$929$	3997.24	0.141168	0.0705841	−	0.997506i	$-0.477514\pi$
$929$	3997.24	0.141168	0.0705841	+	0.997506i	$0.477514\pi$
$930$	11293.3	0.398197
$931$	−2115.27	−0.0744631
$932$	8648.35	0.303955
$933$	6669.53	0.234031
$934$	−152.299	−0.00533552
$935$	−4571.49	−0.159897
$936$	5087.85	0.177673
$937$	−56435.2	−1.96762	−0.983808	−	0.179225i	$-0.942641\pi$
$937$	−56435.2	−1.96762	−0.983808	+	0.179225i	$0.942641\pi$
$938$	6254.04	0.217699
$939$	10265.0	0.356747
$940$	6030.04	0.209232
$941$	42259.7	1.46400	0.732002	−	0.681302i	$-0.238586\pi$
$941$	42259.7	1.46400	0.732002	+	0.681302i	$0.238586\pi$
$942$	8010.18	0.277055
$943$	6789.69	0.234468
$944$	−363.481	−0.0125321
$945$	−2415.78	−0.0831589
$946$	−4163.94	−0.143109
$947$	−51670.3	−1.77303	−0.886514	−	0.462701i	$-0.846880\pi$
$947$	−51670.3	−1.77303	−0.886514	+	0.462701i	$0.846880\pi$
$948$	−1021.28	−0.0349890
$949$	36709.4	1.25568
$950$	3313.33	0.113156
$951$	3570.66	0.121753
$952$	−4389.17	−0.149426
$953$	50516.5	1.71709	0.858546	−	0.512736i	$-0.171368\pi$
$953$	50516.5	1.71709	0.858546	+	0.512736i	$0.171368\pi$
$954$	3984.37	0.135219
$955$	38026.5	1.28849
$956$	−11262.5	−0.381021
$957$	2280.78	0.0770400
$958$	33359.6	1.12505
$959$	−7773.62	−0.261755
$960$	2454.12	0.0825067
$961$	−8106.30	−0.272106
$962$	−51365.3	−1.72150
$963$	7345.06	0.245785
$964$	22065.8	0.737231
$965$	−12149.2	−0.405282
$966$	966.000	0.0321745
$967$	−87.5748	−0.00291232	−0.00145616	−	0.999999i	$-0.500464\pi$
$967$	−87.5748	−0.00291232	−0.00145616	+	0.999999i	$0.500464\pi$
$968$	10481.4	0.348022
$969$	−10150.5	−0.336511
$970$	−12192.8	−0.403596
$971$	−45984.9	−1.51980	−0.759900	−	0.650040i	$-0.774752\pi$
$971$	−45984.9	−1.51980	−0.759900	+	0.650040i	$0.774752\pi$
$972$	−972.000	−0.0320750
$973$	2464.02	0.0811849
$974$	24797.5	0.815774
$975$	8135.57	0.267227
$976$	−6384.19	−0.209378
$977$	−26575.8	−0.870249	−0.435125	−	0.900370i	$-0.643296\pi$
$977$	−26575.8	−0.870249	−0.435125	+	0.900370i	$0.643296\pi$
$978$	9333.40	0.305163
$979$	4361.06	0.142370
$980$	−2505.25	−0.0816604
$981$	−7145.35	−0.232552
$982$	−28538.7	−0.927399
$983$	7451.37	0.241772	0.120886	−	0.992666i	$-0.461426\pi$
$983$	7451.37	0.241772	0.120886	+	0.992666i	$0.461426\pi$
$984$	−7084.90	−0.229531
$985$	22008.7	0.711935
$986$	26116.7	0.843536
$987$	−2476.76	−0.0798746
$988$	12202.0	0.392913
$989$	10493.8	0.337395
$990$	−1049.87	−0.0337041
$991$	50945.4	1.63303	0.816515	−	0.577324i	$-0.195903\pi$
$991$	50945.4	1.63303	0.816515	+	0.577324i	$0.195903\pi$
$992$	4712.23	0.150820
$993$	22497.5	0.718968
$994$	4495.92	0.143463
$995$	−27055.0	−0.862012
$996$	1966.54	0.0625624
$997$	−16659.1	−0.529187	−0.264593	−	0.964360i	$-0.585238\pi$
$997$	−16659.1	−0.529187	−0.264593	+	0.964360i	$0.585238\pi$
$998$	22649.0	0.718378
$999$	9813.01	0.310781

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	966.4.a.m.1.1	✓	5

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
966.4.a.m.1.1	✓	5	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)

\(f(q)\)	\(=\)	\(q-2.00000 q^{2} -3.00000 q^{3} +4.00000 q^{4} -12.7819 q^{5} +6.00000 q^{6} -7.00000 q^{7} -8.00000 q^{8} +9.00000 q^{9} +O(q^{10})\)	\(q-2.00000 q^{2} -3.00000 q^{3} +4.00000 q^{4} -12.7819 q^{5} +6.00000 q^{6} -7.00000 q^{7} -8.00000 q^{8} +9.00000 q^{9} +25.5638 q^{10} -4.56319 q^{11} -12.0000 q^{12} -70.6646 q^{13} +14.0000 q^{14} +38.3456 q^{15} +16.0000 q^{16} -78.3781 q^{17} -18.0000 q^{18} -43.1688 q^{19} -51.1275 q^{20} +21.0000 q^{21} +9.12638 q^{22} -23.0000 q^{23} +24.0000 q^{24} +38.3765 q^{25} +141.329 q^{26} -27.0000 q^{27} -28.0000 q^{28} +166.607 q^{29} -76.6913 q^{30} -147.257 q^{31} -32.0000 q^{32} +13.6896 q^{33} +156.756 q^{34} +89.4732 q^{35} +36.0000 q^{36} -363.445 q^{37} +86.3375 q^{38} +211.994 q^{39} +102.255 q^{40} -295.204 q^{41} -42.0000 q^{42} -456.253 q^{43} -18.2528 q^{44} -115.037 q^{45} +46.0000 q^{46} -117.941 q^{47} -48.0000 q^{48} +49.0000 q^{49} -76.7529 q^{50} +235.134 q^{51} -282.658 q^{52} -221.354 q^{53} +54.0000 q^{54} +58.3262 q^{55} +56.0000 q^{56} +129.506 q^{57} -333.215 q^{58} -22.7176 q^{59} +153.383 q^{60} -399.012 q^{61} +294.514 q^{62} -63.0000 q^{63} +64.0000 q^{64} +903.226 q^{65} -27.3791 q^{66} +446.717 q^{67} -313.512 q^{68} +69.0000 q^{69} -178.946 q^{70} +321.137 q^{71} -72.0000 q^{72} -519.488 q^{73} +726.889 q^{74} -115.129 q^{75} -172.675 q^{76} +31.9423 q^{77} -423.988 q^{78} +85.1065 q^{79} -204.510 q^{80} +81.0000 q^{81} +590.408 q^{82} -163.878 q^{83} +84.0000 q^{84} +1001.82 q^{85} +912.506 q^{86} -499.822 q^{87} +36.5055 q^{88} -955.704 q^{89} +230.074 q^{90} +494.652 q^{91} -92.0000 q^{92} +441.772 q^{93} +235.882 q^{94} +551.778 q^{95} +96.0000 q^{96} -476.957 q^{97} -98.0000 q^{98} -41.0687 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 5 q - 10 q^{2} - 15 q^{3} + 20 q^{4} + 10 q^{5} + 30 q^{6} - 35 q^{7} - 40 q^{8} + 45 q^{9}+O(q^{10}) \) 5 * q - 10 * q^2 - 15 * q^3 + 20 * q^4 + 10 * q^5 + 30 * q^6 - 35 * q^7 - 40 * q^8 + 45 * q^9	\( 5 q - 10 q^{2} - 15 q^{3} + 20 q^{4} + 10 q^{5} + 30 q^{6} - 35 q^{7} - 40 q^{8} + 45 q^{9} - 20 q^{10} + 4 q^{11} - 60 q^{12} + 24 q^{13} + 70 q^{14} - 30 q^{15} + 80 q^{16} + 28 q^{17} - 90 q^{18} - 160 q^{19} + 40 q^{20} + 105 q^{21} - 8 q^{22} - 115 q^{23} + 120 q^{24} + 219 q^{25} - 48 q^{26} - 135 q^{27} - 140 q^{28} + 79 q^{29} + 60 q^{30} - 162 q^{31} - 160 q^{32} - 12 q^{33} - 56 q^{34} - 70 q^{35} + 180 q^{36} + 301 q^{37} + 320 q^{38} - 72 q^{39} - 80 q^{40} + 251 q^{41} - 210 q^{42} - 380 q^{43} + 16 q^{44} + 90 q^{45} + 230 q^{46} - 505 q^{47} - 240 q^{48} + 245 q^{49} - 438 q^{50} - 84 q^{51} + 96 q^{52} + 93 q^{53} + 270 q^{54} - 503 q^{55} + 280 q^{56} + 480 q^{57} - 158 q^{58} + 637 q^{59} - 120 q^{60} - 679 q^{61} + 324 q^{62} - 315 q^{63} + 320 q^{64} + 961 q^{65} + 24 q^{66} - 1483 q^{67} + 112 q^{68} + 345 q^{69} + 140 q^{70} + 95 q^{71} - 360 q^{72} - 1310 q^{73} - 602 q^{74} - 657 q^{75} - 640 q^{76} - 28 q^{77} + 144 q^{78} + 494 q^{79} + 160 q^{80} + 405 q^{81} - 502 q^{82} - 482 q^{83} + 420 q^{84} - 291 q^{85} + 760 q^{86} - 237 q^{87} - 32 q^{88} + 661 q^{89} - 180 q^{90} - 168 q^{91} - 460 q^{92} + 486 q^{93} + 1010 q^{94} - 629 q^{95} + 480 q^{96} - 1905 q^{97} - 490 q^{98} + 36 q^{99}+O(q^{100}) \) 5 * q - 10 * q^2 - 15 * q^3 + 20 * q^4 + 10 * q^5 + 30 * q^6 - 35 * q^7 - 40 * q^8 + 45 * q^9 - 20 * q^10 + 4 * q^11 - 60 * q^12 + 24 * q^13 + 70 * q^14 - 30 * q^15 + 80 * q^16 + 28 * q^17 - 90 * q^18 - 160 * q^19 + 40 * q^20 + 105 * q^21 - 8 * q^22 - 115 * q^23 + 120 * q^24 + 219 * q^25 - 48 * q^26 - 135 * q^27 - 140 * q^28 + 79 * q^29 + 60 * q^30 - 162 * q^31 - 160 * q^32 - 12 * q^33 - 56 * q^34 - 70 * q^35 + 180 * q^36 + 301 * q^37 + 320 * q^38 - 72 * q^39 - 80 * q^40 + 251 * q^41 - 210 * q^42 - 380 * q^43 + 16 * q^44 + 90 * q^45 + 230 * q^46 - 505 * q^47 - 240 * q^48 + 245 * q^49 - 438 * q^50 - 84 * q^51 + 96 * q^52 + 93 * q^53 + 270 * q^54 - 503 * q^55 + 280 * q^56 + 480 * q^57 - 158 * q^58 + 637 * q^59 - 120 * q^60 - 679 * q^61 + 324 * q^62 - 315 * q^63 + 320 * q^64 + 961 * q^65 + 24 * q^66 - 1483 * q^67 + 112 * q^68 + 345 * q^69 + 140 * q^70 + 95 * q^71 - 360 * q^72 - 1310 * q^73 - 602 * q^74 - 657 * q^75 - 640 * q^76 - 28 * q^77 + 144 * q^78 + 494 * q^79 + 160 * q^80 + 405 * q^81 - 502 * q^82 - 482 * q^83 + 420 * q^84 - 291 * q^85 + 760 * q^86 - 237 * q^87 - 32 * q^88 + 661 * q^89 - 180 * q^90 - 168 * q^91 - 460 * q^92 + 486 * q^93 + 1010 * q^94 - 629 * q^95 + 480 * q^96 - 1905 * q^97 - 490 * q^98 + 36 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

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