LMFDB - Embedded newform 966.4.a.p.1.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [966,4,Mod(1,966)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(966, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 4, names="a")

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

chi := DirichletCharacter("966.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

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

Newform invariants

comment: select newform

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

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

Self dual:	yes
Analytic conductor:	$56.9958450655$
Analytic rank:	$0$
Dimension:	$5$
Coefficient field:	$\mathbb{Q}[x]/(x^{5} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{5} - 456x^{3} - 1295x^{2} + 36752x + 117404 $ x^5 - 456x^3 - 1295x^2 + 36752*x + 117404
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.4
Root			$9.99241$ of defining polynomial
Character	$\chi$	$=$	966.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+2.00000 q^{2} -3.00000 q^{3} +4.00000 q^{4} +7.99241 q^{5} -6.00000 q^{6} -7.00000 q^{7} +8.00000 q^{8} +9.00000 q^{9} +O(q^{10})$	\(q+2.00000 q^{2} -3.00000 q^{3} +4.00000 q^{4} +7.99241 q^{5} -6.00000 q^{6} -7.00000 q^{7} +8.00000 q^{8} +9.00000 q^{9} +15.9848 q^{10} +20.6690 q^{11} -12.0000 q^{12} +62.1816 q^{13} -14.0000 q^{14} -23.9772 q^{15} +16.0000 q^{16} +28.8812 q^{17} +18.0000 q^{18} -41.8226 q^{19} +31.9696 q^{20} +21.0000 q^{21} +41.3379 q^{22} +23.0000 q^{23} -24.0000 q^{24} -61.1213 q^{25} +124.363 q^{26} -27.0000 q^{27} -28.0000 q^{28} -131.889 q^{29} -47.9545 q^{30} +96.6740 q^{31} +32.0000 q^{32} -62.0069 q^{33} +57.7624 q^{34} -55.9469 q^{35} +36.0000 q^{36} +67.7473 q^{37} -83.6452 q^{38} -186.545 q^{39} +63.9393 q^{40} -87.7072 q^{41} +42.0000 q^{42} +280.843 q^{43} +82.6759 q^{44} +71.9317 q^{45} +46.0000 q^{46} +523.297 q^{47} -48.0000 q^{48} +49.0000 q^{49} -122.243 q^{50} -86.6436 q^{51} +248.726 q^{52} +116.647 q^{53} -54.0000 q^{54} +165.195 q^{55} -56.0000 q^{56} +125.468 q^{57} -263.778 q^{58} -36.8665 q^{59} -95.9089 q^{60} -861.080 q^{61} +193.348 q^{62} -63.0000 q^{63} +64.0000 q^{64} +496.981 q^{65} -124.014 q^{66} +318.473 q^{67} +115.525 q^{68} -69.0000 q^{69} -111.894 q^{70} +160.040 q^{71} +72.0000 q^{72} +1098.57 q^{73} +135.495 q^{74} +183.364 q^{75} -167.290 q^{76} -144.683 q^{77} -373.090 q^{78} +1272.37 q^{79} +127.879 q^{80} +81.0000 q^{81} -175.414 q^{82} +914.695 q^{83} +84.0000 q^{84} +230.830 q^{85} +561.687 q^{86} +395.667 q^{87} +165.352 q^{88} -1361.88 q^{89} +143.863 q^{90} -435.271 q^{91} +92.0000 q^{92} -290.022 q^{93} +1046.59 q^{94} -334.264 q^{95} -96.0000 q^{96} -759.573 q^{97} +98.0000 q^{98} +186.021 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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	\( 5 q + 10 q^{2} - 15 q^{3} + 20 q^{4} - 10 q^{5} - 30 q^{6} - 35 q^{7} + 40 q^{8} + 45 q^{9} - 20 q^{10} + 9 q^{11} - 60 q^{12} - 102 q^{13} - 70 q^{14} + 30 q^{15} + 80 q^{16} - 30 q^{17} + 90 q^{18} - 27 q^{19} - 40 q^{20} + 105 q^{21} + 18 q^{22} + 115 q^{23} - 120 q^{24} + 307 q^{25} - 204 q^{26} - 135 q^{27} - 140 q^{28} + 135 q^{29} + 60 q^{30} + 160 q^{31} + 160 q^{32} - 27 q^{33} - 60 q^{34} + 70 q^{35} + 180 q^{36} + 153 q^{37} - 54 q^{38} + 306 q^{39} - 80 q^{40} + 76 q^{41} + 210 q^{42} + 980 q^{43} + 36 q^{44} - 90 q^{45} + 230 q^{46} - 8 q^{47} - 240 q^{48} + 245 q^{49} + 614 q^{50} + 90 q^{51} - 408 q^{52} + 676 q^{53} - 270 q^{54} + 1403 q^{55} - 280 q^{56} + 81 q^{57} + 270 q^{58} - 208 q^{59} + 120 q^{60} + 204 q^{61} + 320 q^{62} - 315 q^{63} + 320 q^{64} + 971 q^{65} - 54 q^{66} + 767 q^{67} - 120 q^{68} - 345 q^{69} + 140 q^{70} + 1353 q^{71} + 360 q^{72} + 92 q^{73} + 306 q^{74} - 921 q^{75} - 108 q^{76} - 63 q^{77} + 612 q^{78} + 2958 q^{79} - 160 q^{80} + 405 q^{81} + 152 q^{82} + 1370 q^{83} + 420 q^{84} + 1725 q^{85} + 1960 q^{86} - 405 q^{87} + 72 q^{88} + 1207 q^{89} - 180 q^{90} + 714 q^{91} + 460 q^{92} - 480 q^{93} - 16 q^{94} + 2995 q^{95} - 480 q^{96} + 1633 q^{97} + 490 q^{98} + 81 q^{99}+O(q^{100}) \) 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 + 9 * q^11 - 60 * q^12 - 102 * q^13 - 70 * q^14 + 30 * q^15 + 80 * q^16 - 30 * q^17 + 90 * q^18 - 27 * q^19 - 40 * q^20 + 105 * q^21 + 18 * q^22 + 115 * q^23 - 120 * q^24 + 307 * q^25 - 204 * q^26 - 135 * q^27 - 140 * q^28 + 135 * q^29 + 60 * q^30 + 160 * q^31 + 160 * q^32 - 27 * q^33 - 60 * q^34 + 70 * q^35 + 180 * q^36 + 153 * q^37 - 54 * q^38 + 306 * q^39 - 80 * q^40 + 76 * q^41 + 210 * q^42 + 980 * q^43 + 36 * q^44 - 90 * q^45 + 230 * q^46 - 8 * q^47 - 240 * q^48 + 245 * q^49 + 614 * q^50 + 90 * q^51 - 408 * q^52 + 676 * q^53 - 270 * q^54 + 1403 * q^55 - 280 * q^56 + 81 * q^57 + 270 * q^58 - 208 * q^59 + 120 * q^60 + 204 * q^61 + 320 * q^62 - 315 * q^63 + 320 * q^64 + 971 * q^65 - 54 * q^66 + 767 * q^67 - 120 * q^68 - 345 * q^69 + 140 * q^70 + 1353 * q^71 + 360 * q^72 + 92 * q^73 + 306 * q^74 - 921 * q^75 - 108 * q^76 - 63 * q^77 + 612 * q^78 + 2958 * q^79 - 160 * q^80 + 405 * q^81 + 152 * q^82 + 1370 * q^83 + 420 * q^84 + 1725 * q^85 + 1960 * q^86 - 405 * q^87 + 72 * q^88 + 1207 * q^89 - 180 * q^90 + 714 * q^91 + 460 * q^92 - 480 * q^93 - 16 * q^94 + 2995 * q^95 - 480 * q^96 + 1633 * q^97 + 490 * q^98 + 81 * 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
$5$	7.99241	0.714863	0.357432	−	0.933939i	$-0.383653\pi$
$5$	7.99241	0.714863	0.357432	+	0.933939i	$0.383653\pi$
$6$	−6.00000	−0.408248
$7$	−7.00000	−0.377964
$7$	−7.00000	−0.377964
$8$	8.00000	0.353553
$9$	9.00000	0.333333
$10$	15.9848	0.505485
$11$	20.6690	0.566539	0.283269	−	0.959040i	$-0.408581\pi$
$11$	20.6690	0.566539	0.283269	+	0.959040i	$0.408581\pi$
$12$	−12.0000	−0.288675
$13$	62.1816	1.32662	0.663311	−	0.748344i	$-0.269151\pi$
$13$	62.1816	1.32662	0.663311	+	0.748344i	$0.269151\pi$
$14$	−14.0000	−0.267261
$15$	−23.9772	−0.412726
$16$	16.0000	0.250000
$17$	28.8812	0.412042	0.206021	−	0.978548i	$-0.433948\pi$
$17$	28.8812	0.412042	0.206021	+	0.978548i	$0.433948\pi$
$18$	18.0000	0.235702
$19$	−41.8226	−0.504988	−0.252494	−	0.967598i	$-0.581251\pi$
$19$	−41.8226	−0.504988	−0.252494	+	0.967598i	$0.581251\pi$
$20$	31.9696	0.357432
$21$	21.0000	0.218218
$22$	41.3379	0.400603
$23$	23.0000	0.208514
$23$	23.0000	0.208514
$24$	−24.0000	−0.204124
$25$	−61.1213	−0.488971
$26$	124.363	0.938063
$27$	−27.0000	−0.192450
$28$	−28.0000	−0.188982
$29$	−131.889	−0.844524	−0.422262	−	0.906474i	$-0.638764\pi$
$29$	−131.889	−0.844524	−0.422262	+	0.906474i	$0.638764\pi$
$30$	−47.9545	−0.291842
$31$	96.6740	0.560102	0.280051	−	0.959985i	$-0.409649\pi$
$31$	96.6740	0.560102	0.280051	+	0.959985i	$0.409649\pi$
$32$	32.0000	0.176777
$33$	−62.0069	−0.327091
$34$	57.7624	0.291358
$35$	−55.9469	−0.270193
$36$	36.0000	0.166667
$37$	67.7473	0.301016	0.150508	−	0.988609i	$-0.451909\pi$
$37$	67.7473	0.301016	0.150508	+	0.988609i	$0.451909\pi$
$38$	−83.6452	−0.357080
$39$	−186.545	−0.765925
$40$	63.9393	0.252742
$41$	−87.7072	−0.334087	−0.167044	−	0.985950i	$-0.553422\pi$
$41$	−87.7072	−0.334087	−0.167044	+	0.985950i	$0.553422\pi$
$42$	42.0000	0.154303
$43$	280.843	0.996005	0.498002	−	0.867176i	$-0.334067\pi$
$43$	280.843	0.996005	0.498002	+	0.867176i	$0.334067\pi$
$44$	82.6759	0.283269
$45$	71.9317	0.238288
$46$	46.0000	0.147442
$47$	523.297	1.62406	0.812029	−	0.583618i	$-0.198363\pi$
$47$	523.297	1.62406	0.812029	+	0.583618i	$0.198363\pi$
$48$	−48.0000	−0.144338
$49$	49.0000	0.142857
$50$	−122.243	−0.345755
$51$	−86.6436	−0.237893
$52$	248.726	0.663311
$53$	116.647	0.302316	0.151158	−	0.988510i	$-0.451700\pi$
$53$	116.647	0.302316	0.151158	+	0.988510i	$0.451700\pi$
$54$	−54.0000	−0.136083
$55$	165.195	0.404998
$56$	−56.0000	−0.133631
$57$	125.468	0.291555
$58$	−263.778	−0.597169
$59$	−36.8665	−0.0813493	−0.0406747	−	0.999172i	$-0.512951\pi$
$59$	−36.8665	−0.0813493	−0.0406747	+	0.999172i	$0.512951\pi$
$60$	−95.9089	−0.206363
$61$	−861.080	−1.80738	−0.903688	−	0.428191i	$-0.859151\pi$
$61$	−861.080	−1.80738	−0.903688	+	0.428191i	$0.859151\pi$
$62$	193.348	0.396052
$63$	−63.0000	−0.125988
$64$	64.0000	0.125000
$65$	496.981	0.948353
$66$	−124.014	−0.231289
$67$	318.473	0.580712	0.290356	−	0.956919i	$-0.406226\pi$
$67$	318.473	0.580712	0.290356	+	0.956919i	$0.406226\pi$
$68$	115.525	0.206021
$69$	−69.0000	−0.120386
$70$	−111.894	−0.191055
$71$	160.040	0.267510	0.133755	−	0.991014i	$-0.457297\pi$
$71$	160.040	0.267510	0.133755	+	0.991014i	$0.457297\pi$
$72$	72.0000	0.117851
$73$	1098.57	1.76134	0.880671	−	0.473729i	$-0.157092\pi$
$73$	1098.57	1.76134	0.880671	+	0.473729i	$0.157092\pi$
$74$	135.495	0.212851
$75$	183.364	0.282307
$76$	−167.290	−0.252494
$77$	−144.683	−0.214132
$78$	−373.090	−0.541591
$79$	1272.37	1.81205	0.906027	−	0.423220i	$-0.139100\pi$
$79$	1272.37	1.81205	0.906027	+	0.423220i	$0.139100\pi$
$80$	127.879	0.178716
$81$	81.0000	0.111111
$82$	−175.414	−0.236235
$83$	914.695	1.20965	0.604824	−	0.796359i	$-0.293243\pi$
$83$	914.695	1.20965	0.604824	+	0.796359i	$0.293243\pi$
$84$	84.0000	0.109109
$85$	230.830	0.294554
$86$	561.687	0.704282
$87$	395.667	0.487586
$88$	165.352	0.200302
$89$	−1361.88	−1.62202	−0.811008	−	0.585036i	$-0.801081\pi$
$89$	−1361.88	−1.62202	−0.811008	+	0.585036i	$0.801081\pi$
$90$	143.863	0.168495
$91$	−435.271	−0.501416
$92$	92.0000	0.104257
$93$	−290.022	−0.323375
$94$	1046.59	1.14838
$95$	−334.264	−0.360997
$96$	−96.0000	−0.102062
$97$	−759.573	−0.795082	−0.397541	−	0.917584i	$-0.630136\pi$
$97$	−759.573	−0.795082	−0.397541	+	0.917584i	$0.630136\pi$
$98$	98.0000	0.101015
$99$	186.021	0.188846
$100$	−244.485	−0.244485
$101$	−885.099	−0.871986	−0.435993	−	0.899950i	$-0.643603\pi$
$101$	−885.099	−0.871986	−0.435993	+	0.899950i	$0.643603\pi$
$102$	−173.287	−0.168216
$103$	1093.96	1.04651	0.523256	−	0.852175i	$-0.324717\pi$
$103$	1093.96	1.04651	0.523256	+	0.852175i	$0.324717\pi$
$104$	497.453	0.469032
$105$	167.841	0.155996
$106$	233.295	0.213770
$107$	−613.969	−0.554716	−0.277358	−	0.960767i	$-0.589459\pi$
$107$	−613.969	−0.554716	−0.277358	+	0.960767i	$0.589459\pi$
$108$	−108.000	−0.0962250
$109$	1791.70	1.57444	0.787219	−	0.616673i	$-0.211520\pi$
$109$	1791.70	1.57444	0.787219	+	0.616673i	$0.211520\pi$
$110$	330.390	0.286377
$111$	−203.242	−0.173792
$112$	−112.000	−0.0944911
$113$	1350.21	1.12405	0.562024	−	0.827121i	$-0.310023\pi$
$113$	1350.21	1.12405	0.562024	+	0.827121i	$0.310023\pi$
$114$	250.936	0.206160
$115$	183.825	0.149059
$116$	−527.557	−0.422262
$117$	559.635	0.442207
$118$	−73.7330	−0.0575227
$119$	−202.168	−0.155737
$120$	−191.818	−0.145921
$121$	−903.794	−0.679034
$122$	−1722.16	−1.27801
$123$	263.122	0.192885
$124$	386.696	0.280051
$125$	−1487.56	−1.06441
$126$	−126.000	−0.0890871
$127$	1605.04	1.12145	0.560724	−	0.828003i	$-0.310523\pi$
$127$	1605.04	1.12145	0.560724	+	0.828003i	$0.310523\pi$
$128$	128.000	0.0883883
$129$	−842.530	−0.575043
$130$	993.962	0.670587
$131$	2729.21	1.82025	0.910124	−	0.414336i	$-0.135986\pi$
$131$	2729.21	1.82025	0.910124	+	0.414336i	$0.135986\pi$
$132$	−248.028	−0.163546
$133$	292.758	0.190867
$134$	636.946	0.410625
$135$	−215.795	−0.137575
$136$	231.050	0.145679
$137$	−647.806	−0.403984	−0.201992	−	0.979387i	$-0.564741\pi$
$137$	−647.806	−0.403984	−0.201992	+	0.979387i	$0.564741\pi$
$138$	−138.000	−0.0851257
$139$	−1132.95	−0.691335	−0.345667	−	0.938357i	$-0.612347\pi$
$139$	−1132.95	−0.691335	−0.345667	+	0.938357i	$0.612347\pi$
$140$	−223.788	−0.135096
$141$	−1569.89	−0.937650
$142$	320.079	0.189158
$143$	1285.23	0.751583
$144$	144.000	0.0833333
$145$	−1054.11	−0.603719
$146$	2197.14	1.24546
$147$	−147.000	−0.0824786
$148$	270.989	0.150508
$149$	1469.24	0.807818	0.403909	−	0.914799i	$-0.367651\pi$
$149$	1469.24	0.807818	0.403909	+	0.914799i	$0.367651\pi$
$150$	366.728	0.199621
$151$	−2293.34	−1.23596	−0.617978	−	0.786195i	$-0.712048\pi$
$151$	−2293.34	−1.23596	−0.617978	+	0.786195i	$0.712048\pi$
$152$	−334.581	−0.178540
$153$	259.931	0.137347
$154$	−289.365	−0.151414
$155$	772.658	0.400396
$156$	−746.179	−0.382963
$157$	−697.543	−0.354586	−0.177293	−	0.984158i	$-0.556734\pi$
$157$	−697.543	−0.354586	−0.177293	+	0.984158i	$0.556734\pi$
$158$	2544.73	1.28132
$159$	−349.942	−0.174542
$160$	255.757	0.126371
$161$	−161.000	−0.0788110
$162$	162.000	0.0785674
$163$	944.491	0.453854	0.226927	−	0.973912i	$-0.427132\pi$
$163$	944.491	0.453854	0.226927	+	0.973912i	$0.427132\pi$
$164$	−350.829	−0.167044
$165$	−495.585	−0.233826
$166$	1829.39	0.855350
$167$	−574.916	−0.266397	−0.133199	−	0.991089i	$-0.542525\pi$
$167$	−574.916	−0.266397	−0.133199	+	0.991089i	$0.542525\pi$
$168$	168.000	0.0771517
$169$	1669.55	0.759924
$170$	461.661	0.208281
$171$	−376.404	−0.168329
$172$	1123.37	0.498002
$173$	451.266	0.198319	0.0991593	−	0.995072i	$-0.468385\pi$
$173$	451.266	0.198319	0.0991593	+	0.995072i	$0.468385\pi$
$174$	791.335	0.344775
$175$	427.849	0.184814
$176$	330.703	0.141635
$177$	110.600	0.0469671
$178$	−2723.77	−1.14694
$179$	2632.68	1.09931	0.549653	−	0.835393i	$-0.314760\pi$
$179$	2632.68	1.09931	0.549653	+	0.835393i	$0.314760\pi$
$180$	287.727	0.119144
$181$	4775.31	1.96103	0.980514	−	0.196451i	$-0.0629415\pi$
$181$	4775.31	1.96103	0.980514	+	0.196451i	$0.0629415\pi$
$182$	−870.543	−0.354554
$183$	2583.24	1.04349
$184$	184.000	0.0737210
$185$	541.465	0.215185
$186$	−580.044	−0.228661
$187$	596.944	0.233438
$188$	2093.19	0.812029
$189$	189.000	0.0727393
$190$	−668.527	−0.255264
$191$	1977.90	0.749298	0.374649	−	0.927167i	$-0.377763\pi$
$191$	1977.90	0.749298	0.374649	+	0.927167i	$0.377763\pi$
$192$	−192.000	−0.0721688
$193$	−2676.99	−0.998414	−0.499207	−	0.866483i	$-0.666375\pi$
$193$	−2676.99	−0.998414	−0.499207	+	0.866483i	$0.666375\pi$
$194$	−1519.15	−0.562208
$195$	−1490.94	−0.547532
$196$	196.000	0.0714286
$197$	1663.53	0.601632	0.300816	−	0.953682i	$-0.402741\pi$
$197$	1663.53	0.601632	0.300816	+	0.953682i	$0.402741\pi$
$198$	372.041	0.133534
$199$	−3270.71	−1.16510	−0.582550	−	0.812795i	$-0.697945\pi$
$199$	−3270.71	−1.16510	−0.582550	+	0.812795i	$0.697945\pi$
$200$	−488.971	−0.172877
$201$	−955.419	−0.335274
$202$	−1770.20	−0.616587
$203$	923.224	0.319200
$204$	−346.574	−0.118946
$205$	−700.992	−0.238827
$206$	2187.91	0.739996
$207$	207.000	0.0695048
$208$	994.906	0.331655
$209$	−864.430	−0.286095
$210$	335.681	0.110306
$211$	1883.05	0.614381	0.307190	−	0.951648i	$-0.400611\pi$
$211$	1883.05	0.614381	0.307190	+	0.951648i	$0.400611\pi$
$212$	466.589	0.151158
$213$	−480.119	−0.154447
$214$	−1227.94	−0.392244
$215$	2244.62	0.712007
$216$	−216.000	−0.0680414
$217$	−676.718	−0.211699
$218$	3583.40	1.11330
$219$	−3295.71	−1.01691
$220$	660.779	0.202499
$221$	1795.88	0.546624
$222$	−406.484	−0.122889
$223$	−2312.46	−0.694412	−0.347206	−	0.937789i	$-0.612870\pi$
$223$	−2312.46	−0.694412	−0.347206	+	0.937789i	$0.612870\pi$
$224$	−224.000	−0.0668153
$225$	−550.092	−0.162990
$226$	2700.43	0.794822
$227$	−5757.74	−1.68350	−0.841750	−	0.539867i	$-0.818474\pi$
$227$	−5757.74	−1.68350	−0.841750	+	0.539867i	$0.818474\pi$
$228$	501.871	0.145777
$229$	5414.97	1.56258	0.781291	−	0.624167i	$-0.214562\pi$
$229$	5414.97	1.56258	0.781291	+	0.624167i	$0.214562\pi$
$230$	367.651	0.105401
$231$	434.048	0.123629
$232$	−1055.11	−0.298584
$233$	−1192.68	−0.335344	−0.167672	−	0.985843i	$-0.553625\pi$
$233$	−1192.68	−0.335344	−0.167672	+	0.985843i	$0.553625\pi$
$234$	1119.27	0.312688
$235$	4182.40	1.16098
$236$	−147.466	−0.0406747
$237$	−3817.10	−1.04619
$238$	−404.337	−0.110123
$239$	324.141	0.0877278	0.0438639	−	0.999038i	$-0.486033\pi$
$239$	324.141	0.0877278	0.0438639	+	0.999038i	$0.486033\pi$
$240$	−383.636	−0.103182
$241$	−2085.31	−0.557372	−0.278686	−	0.960382i	$-0.589899\pi$
$241$	−2085.31	−0.557372	−0.278686	+	0.960382i	$0.589899\pi$
$242$	−1807.59	−0.480149
$243$	−243.000	−0.0641500
$244$	−3444.32	−0.903688
$245$	391.628	0.102123
$246$	526.243	0.136390
$247$	−2600.60	−0.669928
$248$	773.392	0.198026
$249$	−2744.08	−0.698391
$250$	−2975.12	−0.752652
$251$	959.320	0.241242	0.120621	−	0.992699i	$-0.461511\pi$
$251$	959.320	0.241242	0.120621	+	0.992699i	$0.461511\pi$
$252$	−252.000	−0.0629941
$253$	475.386	0.118132
$254$	3210.07	0.792984
$255$	−692.491	−0.170061
$256$	256.000	0.0625000
$257$	1158.43	0.281172	0.140586	−	0.990069i	$-0.455101\pi$
$257$	1158.43	0.281172	0.140586	+	0.990069i	$0.455101\pi$
$258$	−1685.06	−0.406617
$259$	−474.231	−0.113773
$260$	1987.92	0.474176
$261$	−1187.00	−0.281508
$262$	5458.43	1.28711
$263$	13.2329	0.00310257	0.00155128	−	0.999999i	$-0.499506\pi$
$263$	13.2329	0.00310257	0.00155128	+	0.999999i	$0.499506\pi$
$264$	−496.055	−0.115644
$265$	932.294	0.216115
$266$	585.517	0.134964
$267$	4085.65	0.936471
$268$	1273.89	0.290356
$269$	−6027.46	−1.36617	−0.683087	−	0.730337i	$-0.739363\pi$
$269$	−6027.46	−1.36617	−0.683087	+	0.730337i	$0.739363\pi$
$270$	−431.590	−0.0972805
$271$	−1621.50	−0.363464	−0.181732	−	0.983348i	$-0.558170\pi$
$271$	−1621.50	−0.363464	−0.181732	+	0.983348i	$0.558170\pi$
$272$	462.099	0.103011
$273$	1305.81	0.289493
$274$	−1295.61	−0.285660
$275$	−1263.31	−0.277021
$276$	−276.000	−0.0601929
$277$	−4545.47	−0.985960	−0.492980	−	0.870041i	$-0.664092\pi$
$277$	−4545.47	−0.985960	−0.492980	+	0.870041i	$0.664092\pi$
$278$	−2265.90	−0.488848
$279$	870.066	0.186701
$280$	−447.575	−0.0955276
$281$	−6518.61	−1.38387	−0.691935	−	0.721960i	$-0.743242\pi$
$281$	−6518.61	−1.38387	−0.691935	+	0.721960i	$0.743242\pi$
$282$	−3139.78	−0.663019
$283$	−4195.96	−0.881358	−0.440679	−	0.897665i	$-0.645262\pi$
$283$	−4195.96	−0.881358	−0.440679	+	0.897665i	$0.645262\pi$
$284$	640.158	0.133755
$285$	1002.79	0.208422
$286$	2570.46	0.531449
$287$	613.951	0.126273
$288$	288.000	0.0589256
$289$	−4078.88	−0.830221
$290$	−2108.22	−0.426894
$291$	2278.72	0.459041
$292$	4394.28	0.880671
$293$	−3719.32	−0.741587	−0.370793	−	0.928715i	$-0.620914\pi$
$293$	−3719.32	−0.741587	−0.370793	+	0.928715i	$0.620914\pi$
$294$	−294.000	−0.0583212
$295$	−294.652	−0.0581536
$296$	541.979	0.106425
$297$	−558.062	−0.109030
$298$	2938.48	0.571214
$299$	1430.18	0.276620
$300$	733.456	0.141154
$301$	−1965.90	−0.376454
$302$	−4586.68	−0.873953
$303$	2655.30	0.503442
$304$	−669.162	−0.126247
$305$	−6882.11	−1.29203
$306$	519.862	0.0971193
$307$	−5960.55	−1.10810	−0.554050	−	0.832483i	$-0.686918\pi$
$307$	−5960.55	−1.10810	−0.554050	+	0.832483i	$0.686918\pi$
$308$	−578.731	−0.107066
$309$	−3281.87	−0.604204
$310$	1545.32	0.283123
$311$	−6445.76	−1.17526	−0.587630	−	0.809130i	$-0.699939\pi$
$311$	−6445.76	−1.17526	−0.587630	+	0.809130i	$0.699939\pi$
$312$	−1492.36	−0.270795
$313$	−4755.73	−0.858818	−0.429409	−	0.903110i	$-0.641278\pi$
$313$	−4755.73	−0.858818	−0.429409	+	0.903110i	$0.641278\pi$
$314$	−1395.09	−0.250730
$315$	−503.522	−0.0900643
$316$	5089.46	0.906027
$317$	10844.4	1.92139	0.960695	−	0.277608i	$-0.0895415\pi$
$317$	10844.4	1.92139	0.960695	+	0.277608i	$0.0895415\pi$
$318$	−699.884	−0.123420
$319$	−2726.01	−0.478456
$320$	511.514	0.0893579
$321$	1841.91	0.320265
$322$	−322.000	−0.0557278
$323$	−1207.89	−0.208076
$324$	324.000	0.0555556
$325$	−3800.62	−0.648679
$326$	1888.98	0.320923
$327$	−5375.10	−0.909002
$328$	−701.658	−0.118118
$329$	−3663.08	−0.613836
$330$	−991.169	−0.165340
$331$	−5878.11	−0.976103	−0.488052	−	0.872815i	$-0.662292\pi$
$331$	−5878.11	−0.976103	−0.488052	+	0.872815i	$0.662292\pi$
$332$	3658.78	0.604824
$333$	609.726	0.100339
$334$	−1149.83	−0.188371
$335$	2545.37	0.415129
$336$	336.000	0.0545545
$337$	8273.93	1.33742	0.668709	−	0.743524i	$-0.266847\pi$
$337$	8273.93	1.33742	0.668709	+	0.743524i	$0.266847\pi$
$338$	3339.11	0.537348
$339$	−4050.64	−0.648970
$340$	923.322	0.147277
$341$	1998.15	0.317319
$342$	−752.807	−0.119027
$343$	−343.000	−0.0539949
$344$	2246.75	0.352141
$345$	−551.476	−0.0860594
$346$	902.532	0.140232
$347$	−1869.94	−0.289289	−0.144645	−	0.989484i	$-0.546204\pi$
$347$	−1869.94	−0.289289	−0.144645	+	0.989484i	$0.546204\pi$
$348$	1582.67	0.243793
$349$	−6645.17	−1.01922	−0.509610	−	0.860405i	$-0.670210\pi$
$349$	−6645.17	−1.01922	−0.509610	+	0.860405i	$0.670210\pi$
$350$	855.699	0.130683
$351$	−1678.90	−0.255308
$352$	661.407	0.100151
$353$	−3977.94	−0.599786	−0.299893	−	0.953973i	$-0.596951\pi$
$353$	−3977.94	−0.599786	−0.299893	+	0.953973i	$0.596951\pi$
$354$	221.199	0.0332107
$355$	1279.10	0.191233
$356$	−5447.53	−0.811008
$357$	606.505	0.0899150
$358$	5265.36	0.777327
$359$	3222.94	0.473817	0.236908	−	0.971532i	$-0.423866\pi$
$359$	3222.94	0.473817	0.236908	+	0.971532i	$0.423866\pi$
$360$	575.454	0.0842474
$361$	−5109.87	−0.744987
$362$	9550.62	1.38666
$363$	2711.38	0.392040
$364$	−1741.09	−0.250708
$365$	8780.23	1.25912
$366$	5166.48	0.737858
$367$	−85.2070	−0.0121193	−0.00605963	−	0.999982i	$-0.501929\pi$
$367$	−85.2070	−0.0121193	−0.00605963	+	0.999982i	$0.501929\pi$
$368$	368.000	0.0521286
$369$	−789.365	−0.111362
$370$	1082.93	0.152159
$371$	−816.532	−0.114265
$372$	−1160.09	−0.161687
$373$	−5209.85	−0.723206	−0.361603	−	0.932332i	$-0.617770\pi$
$373$	−5209.85	−0.723206	−0.361603	+	0.932332i	$0.617770\pi$
$374$	1193.89	0.165066
$375$	4462.68	0.614538
$376$	4186.37	0.574191
$377$	−8201.08	−1.12036
$378$	378.000	0.0514344
$379$	−4940.50	−0.669595	−0.334798	−	0.942290i	$-0.608668\pi$
$379$	−4940.50	−0.669595	−0.334798	+	0.942290i	$0.608668\pi$
$380$	−1337.05	−0.180499
$381$	−4815.11	−0.647468
$382$	3955.80	0.529833
$383$	−11729.7	−1.56491	−0.782455	−	0.622707i	$-0.786033\pi$
$383$	−11729.7	−1.56491	−0.782455	+	0.622707i	$0.786033\pi$
$384$	−384.000	−0.0510310
$385$	−1156.36	−0.153075
$386$	−5353.98	−0.705986
$387$	2527.59	0.332002
$388$	−3038.29	−0.397541
$389$	−7283.50	−0.949327	−0.474664	−	0.880167i	$-0.657430\pi$
$389$	−7283.50	−0.949327	−0.474664	+	0.880167i	$0.657430\pi$
$390$	−2981.89	−0.387163
$391$	664.268	0.0859168
$392$	392.000	0.0505076
$393$	−8187.64	−1.05092
$394$	3327.05	0.425418
$395$	10169.3	1.29537
$396$	744.083	0.0944231
$397$	−8062.85	−1.01930	−0.509651	−	0.860381i	$-0.670226\pi$
$397$	−8062.85	−1.01930	−0.509651	+	0.860381i	$0.670226\pi$
$398$	−6541.43	−0.823850
$399$	−878.275	−0.110197
$400$	−977.942	−0.122243
$401$	8841.18	1.10102	0.550508	−	0.834830i	$-0.314434\pi$
$401$	8841.18	1.10102	0.550508	+	0.834830i	$0.314434\pi$
$402$	−1910.84	−0.237074
$403$	6011.34	0.743043
$404$	−3540.39	−0.435993
$405$	647.385	0.0794292
$406$	1846.45	0.225709
$407$	1400.27	0.170537
$408$	−693.149	−0.0841078
$409$	12541.8	1.51626	0.758130	−	0.652103i	$-0.226113\pi$
$409$	12541.8	1.51626	0.758130	+	0.652103i	$0.226113\pi$
$410$	−1401.98	−0.168876
$411$	1943.42	0.233240
$412$	4375.83	0.523256
$413$	258.066	0.0307472
$414$	414.000	0.0491473
$415$	7310.62	0.864733
$416$	1989.81	0.234516
$417$	3398.85	0.399142
$418$	−1728.86	−0.202300
$419$	9883.80	1.15240	0.576200	−	0.817309i	$-0.304535\pi$
$419$	9883.80	1.15240	0.576200	+	0.817309i	$0.304535\pi$
$420$	671.363	0.0779980
$421$	−16000.0	−1.85224	−0.926122	−	0.377225i	$-0.876878\pi$
$421$	−16000.0	−1.85224	−0.926122	+	0.377225i	$0.876878\pi$
$422$	3766.10	0.434433
$423$	4709.67	0.541352
$424$	933.179	0.106885
$425$	−1765.26	−0.201477
$426$	−960.237	−0.109210
$427$	6027.56	0.683124
$428$	−2455.88	−0.277358
$429$	−3855.69	−0.433926
$430$	4489.23	0.503465
$431$	11511.0	1.28646	0.643231	−	0.765673i	$-0.277594\pi$
$431$	11511.0	1.28646	0.643231	+	0.765673i	$0.277594\pi$
$432$	−432.000	−0.0481125
$433$	−3802.72	−0.422049	−0.211024	−	0.977481i	$-0.567680\pi$
$433$	−3802.72	−0.422049	−0.211024	+	0.977481i	$0.567680\pi$
$434$	−1353.44	−0.149693
$435$	3162.34	0.348557
$436$	7166.80	0.787219
$437$	−961.920	−0.105297
$438$	−6591.42	−0.719065
$439$	−4841.70	−0.526383	−0.263191	−	0.964744i	$-0.584775\pi$
$439$	−4841.70	−0.526383	−0.263191	+	0.964744i	$0.584775\pi$
$440$	1321.56	0.143188
$441$	441.000	0.0476190
$442$	3591.76	0.386522
$443$	12479.2	1.33839	0.669195	−	0.743087i	$-0.266639\pi$
$443$	12479.2	1.33839	0.669195	+	0.743087i	$0.266639\pi$
$444$	−812.968	−0.0868959
$445$	−10884.7	−1.15952
$446$	−4624.92	−0.491023
$447$	−4407.72	−0.466394
$448$	−448.000	−0.0472456
$449$	5888.14	0.618883	0.309442	−	0.950918i	$-0.399858\pi$
$449$	5888.14	0.618883	0.309442	+	0.950918i	$0.399858\pi$
$450$	−1100.18	−0.115252
$451$	−1812.82	−0.189273
$452$	5400.86	0.562024
$453$	6880.02	0.713580
$454$	−11515.5	−1.19041
$455$	−3478.87	−0.358444
$456$	1003.74	0.103080
$457$	−2154.17	−0.220498	−0.110249	−	0.993904i	$-0.535165\pi$
$457$	−2154.17	−0.220498	−0.110249	+	0.993904i	$0.535165\pi$
$458$	10829.9	1.10491
$459$	−779.792	−0.0792976
$460$	735.302	0.0745296
$461$	279.193	0.0282067	0.0141034	−	0.999901i	$-0.495511\pi$
$461$	279.193	0.0282067	0.0141034	+	0.999901i	$0.495511\pi$
$462$	868.096	0.0874188
$463$	654.077	0.0656534	0.0328267	−	0.999461i	$-0.489549\pi$
$463$	654.077	0.0656534	0.0328267	+	0.999461i	$0.489549\pi$
$464$	−2110.23	−0.211131
$465$	−2317.97	−0.231169
$466$	−2385.37	−0.237124
$467$	6632.74	0.657230	0.328615	−	0.944464i	$-0.393418\pi$
$467$	6632.74	0.657230	0.328615	+	0.944464i	$0.393418\pi$
$468$	2238.54	0.221104
$469$	−2229.31	−0.219488
$470$	8364.81	0.820936
$471$	2092.63	0.204720
$472$	−294.932	−0.0287613
$473$	5804.74	0.564275
$474$	−7634.19	−0.739768
$475$	2556.26	0.246924
$476$	−808.674	−0.0778687
$477$	1049.83	0.100772
$478$	648.282	0.0620329
$479$	16280.5	1.55297	0.776486	−	0.630134i	$-0.217000\pi$
$479$	16280.5	1.55297	0.776486	+	0.630134i	$0.217000\pi$
$480$	−767.272	−0.0729604
$481$	4212.64	0.399334
$482$	−4170.62	−0.394122
$483$	483.000	0.0455016
$484$	−3615.18	−0.339517
$485$	−6070.82	−0.568375
$486$	−486.000	−0.0453609
$487$	−8538.70	−0.794508	−0.397254	−	0.917709i	$-0.630037\pi$
$487$	−8538.70	−0.794508	−0.397254	+	0.917709i	$0.630037\pi$
$488$	−6888.64	−0.639004
$489$	−2833.47	−0.262033
$490$	783.256	0.0722121
$491$	1540.24	0.141568	0.0707840	−	0.997492i	$-0.477450\pi$
$491$	1540.24	0.141568	0.0707840	+	0.997492i	$0.477450\pi$
$492$	1052.49	0.0964426
$493$	−3809.12	−0.347980
$494$	−5201.20	−0.473710
$495$	1486.75	0.134999
$496$	1546.78	0.140025
$497$	−1120.28	−0.101109
$498$	−5488.17	−0.493837
$499$	−4821.41	−0.432537	−0.216268	−	0.976334i	$-0.569389\pi$
$499$	−4821.41	−0.432537	−0.216268	+	0.976334i	$0.569389\pi$
$500$	−5950.23	−0.532205
$501$	1724.75	0.153805
$502$	1918.64	0.170584
$503$	−9434.57	−0.836316	−0.418158	−	0.908374i	$-0.637324\pi$
$503$	−9434.57	−0.836316	−0.418158	+	0.908374i	$0.637324\pi$
$504$	−504.000	−0.0445435
$505$	−7074.07	−0.623351
$506$	950.772	0.0835316
$507$	−5008.66	−0.438743
$508$	6420.14	0.560724
$509$	17217.4	1.49931	0.749655	−	0.661828i	$-0.230219\pi$
$509$	17217.4	1.49931	0.749655	+	0.661828i	$0.230219\pi$
$510$	−1384.98	−0.120251
$511$	−7689.99	−0.665725
$512$	512.000	0.0441942
$513$	1129.21	0.0971849
$514$	2316.87	0.198818
$515$	8743.36	0.748113
$516$	−3370.12	−0.287522
$517$	10816.0	0.920091
$518$	−948.463	−0.0804499
$519$	−1353.80	−0.114499
$520$	3975.85	0.335293
$521$	580.062	0.0487773	0.0243886	−	0.999703i	$-0.492236\pi$
$521$	580.062	0.0487773	0.0243886	+	0.999703i	$0.492236\pi$
$522$	−2374.00	−0.199056
$523$	−21316.9	−1.78226	−0.891132	−	0.453744i	$-0.850088\pi$
$523$	−21316.9	−1.78226	−0.891132	+	0.453744i	$0.850088\pi$
$524$	10916.9	0.910124
$525$	−1283.55	−0.106702
$526$	26.4658	0.00219385
$527$	2792.06	0.230786
$528$	−992.110	−0.0817728
$529$	529.000	0.0434783
$530$	1864.59	0.152816
$531$	−331.799	−0.0271164
$532$	1171.03	0.0954337
$533$	−5453.78	−0.443207
$534$	8171.30	0.662185
$535$	−4907.09	−0.396546
$536$	2547.78	0.205313
$537$	−7898.04	−0.634685
$538$	−12054.9	−0.966031
$539$	1012.78	0.0809341
$540$	−863.181	−0.0687877
$541$	16587.0	1.31817	0.659084	−	0.752069i	$-0.270944\pi$
$541$	16587.0	1.31817	0.659084	+	0.752069i	$0.270944\pi$
$542$	−3242.99	−0.257008
$543$	−14325.9	−1.13220
$544$	924.198	0.0728395
$545$	14320.0	1.12551
$546$	2611.63	0.204702
$547$	12537.0	0.979967	0.489984	−	0.871732i	$-0.337003\pi$
$547$	12537.0	0.979967	0.489984	+	0.871732i	$0.337003\pi$
$548$	−2591.22	−0.201992
$549$	−7749.72	−0.602459
$550$	−2526.63	−0.195883
$551$	5515.95	0.426474
$552$	−552.000	−0.0425628
$553$	−8906.56	−0.684892
$554$	−9090.94	−0.697179
$555$	−1624.39	−0.124237
$556$	−4531.80	−0.345667
$557$	7770.29	0.591091	0.295545	−	0.955329i	$-0.404499\pi$
$557$	7770.29	0.591091	0.295545	+	0.955329i	$0.404499\pi$
$558$	1740.13	0.132017
$559$	17463.3	1.32132
$560$	−895.150	−0.0675482
$561$	−1790.83	−0.134775
$562$	−13037.2	−0.978544
$563$	−13777.8	−1.03137	−0.515687	−	0.856777i	$-0.672463\pi$
$563$	−13777.8	−1.03137	−0.515687	+	0.856777i	$0.672463\pi$
$564$	−6279.56	−0.468825
$565$	10791.5	0.803541
$566$	−8391.93	−0.623214
$567$	−567.000	−0.0419961
$568$	1280.32	0.0945790
$569$	−25757.0	−1.89769	−0.948847	−	0.315737i	$-0.897748\pi$
$569$	−25757.0	−1.89769	−0.948847	+	0.315737i	$0.897748\pi$
$570$	2005.58	0.147376
$571$	−8861.16	−0.649436	−0.324718	−	0.945811i	$-0.605269\pi$
$571$	−8861.16	−0.649436	−0.324718	+	0.945811i	$0.605269\pi$
$572$	5140.92	0.375791
$573$	−5933.70	−0.432607
$574$	1227.90	0.0892885
$575$	−1405.79	−0.101957
$576$	576.000	0.0416667
$577$	−17320.5	−1.24967	−0.624836	−	0.780756i	$-0.714834\pi$
$577$	−17320.5	−1.24967	−0.624836	+	0.780756i	$0.714834\pi$
$578$	−8157.75	−0.587055
$579$	8030.97	0.576435
$580$	−4216.45	−0.301860
$581$	−6402.86	−0.457204
$582$	4557.44	0.324591
$583$	2410.98	0.171274
$584$	8788.56	0.622728
$585$	4472.83	0.316118
$586$	−7438.64	−0.524381
$587$	−11863.9	−0.834199	−0.417099	−	0.908861i	$-0.636953\pi$
$587$	−11863.9	−0.834199	−0.417099	+	0.908861i	$0.636953\pi$
$588$	−588.000	−0.0412393
$589$	−4043.16	−0.282845
$590$	−589.305	−0.0411208
$591$	−4990.58	−0.347352
$592$	1083.96	0.0752540
$593$	22011.4	1.52428	0.762142	−	0.647409i	$-0.224148\pi$
$593$	22011.4	1.52428	0.762142	+	0.647409i	$0.224148\pi$
$594$	−1116.12	−0.0770962
$595$	−1615.81	−0.111331
$596$	5876.96	0.403909
$597$	9812.14	0.672670
$598$	2860.35	0.195600
$599$	3904.56	0.266337	0.133169	−	0.991093i	$-0.457485\pi$
$599$	3904.56	0.266337	0.133169	+	0.991093i	$0.457485\pi$
$600$	1466.91	0.0998107
$601$	−13326.3	−0.904479	−0.452240	−	0.891896i	$-0.649375\pi$
$601$	−13326.3	−0.904479	−0.452240	+	0.891896i	$0.649375\pi$
$602$	−3931.81	−0.266193
$603$	2866.26	0.193571
$604$	−9173.36	−0.617978
$605$	−7223.49	−0.485416
$606$	5310.59	0.355987
$607$	−15667.0	−1.04762	−0.523809	−	0.851836i	$-0.675489\pi$
$607$	−15667.0	−1.04762	−0.523809	+	0.851836i	$0.675489\pi$
$608$	−1338.32	−0.0892701
$609$	−2769.67	−0.184290
$610$	−13764.2	−0.913601
$611$	32539.4	2.15451
$612$	1039.72	0.0686737
$613$	12695.8	0.836508	0.418254	−	0.908330i	$-0.362642\pi$
$613$	12695.8	0.836508	0.418254	+	0.908330i	$0.362642\pi$
$614$	−11921.1	−0.783545
$615$	2102.98	0.137887
$616$	−1157.46	−0.0757069
$617$	−17810.5	−1.16211	−0.581055	−	0.813864i	$-0.697360\pi$
$617$	−17810.5	−1.16211	−0.581055	+	0.813864i	$0.697360\pi$
$618$	−6563.74	−0.427237
$619$	−24158.7	−1.56869	−0.784347	−	0.620322i	$-0.787002\pi$
$619$	−24158.7	−1.56869	−0.784347	+	0.620322i	$0.787002\pi$
$620$	3090.63	0.200198
$621$	−621.000	−0.0401286
$622$	−12891.5	−0.831034
$623$	9533.18	0.613064
$624$	−2984.72	−0.191481
$625$	−4249.01	−0.271937
$626$	−9511.47	−0.607276
$627$	2593.29	0.165177
$628$	−2790.17	−0.177293
$629$	1956.62	0.124031
$630$	−1007.04	−0.0636851
$631$	17158.6	1.08253	0.541263	−	0.840853i	$-0.317946\pi$
$631$	17158.6	1.08253	0.541263	+	0.840853i	$0.317946\pi$
$632$	10178.9	0.640658
$633$	−5649.14	−0.354713
$634$	21688.7	1.35863
$635$	12828.1	0.801682
$636$	−1399.77	−0.0872711
$637$	3046.90	0.189517
$638$	−5452.02	−0.338319
$639$	1440.36	0.0891699
$640$	1023.03	0.0631856
$641$	15674.3	0.965830	0.482915	−	0.875667i	$-0.339578\pi$
$641$	15674.3	0.965830	0.482915	+	0.875667i	$0.339578\pi$
$642$	3683.81	0.226462
$643$	−7140.72	−0.437951	−0.218975	−	0.975730i	$-0.570271\pi$
$643$	−7140.72	−0.437951	−0.218975	+	0.975730i	$0.570271\pi$
$644$	−644.000	−0.0394055
$645$	−6733.85	−0.411077
$646$	−2415.78	−0.147132
$647$	−21173.8	−1.28659	−0.643297	−	0.765617i	$-0.722434\pi$
$647$	−21173.8	−1.28659	−0.643297	+	0.765617i	$0.722434\pi$
$648$	648.000	0.0392837
$649$	−761.993	−0.0460876
$650$	−7601.25	−0.458685
$651$	2030.15	0.122224
$652$	3777.96	0.226927
$653$	31794.5	1.90538	0.952691	−	0.303942i	$-0.0983029\pi$
$653$	31794.5	1.90538	0.952691	+	0.303942i	$0.0983029\pi$
$654$	−10750.2	−0.642762
$655$	21813.0	1.30123
$656$	−1403.32	−0.0835218
$657$	9887.13	0.587114
$658$	−7326.16	−0.434048
$659$	−3794.06	−0.224273	−0.112136	−	0.993693i	$-0.535769\pi$
$659$	−3794.06	−0.224273	−0.112136	+	0.993693i	$0.535769\pi$
$660$	−1982.34	−0.116913
$661$	−13846.5	−0.814777	−0.407388	−	0.913255i	$-0.633560\pi$
$661$	−13846.5	−0.814777	−0.407388	+	0.913255i	$0.633560\pi$
$662$	−11756.2	−0.690209
$663$	−5387.64	−0.315594
$664$	7317.56	0.427675
$665$	2339.85	0.136444
$666$	1219.45	0.0709502
$667$	−3033.45	−0.176095
$668$	−2299.67	−0.133199
$669$	6937.38	0.400919
$670$	5090.74	0.293541
$671$	−17797.6	−1.02395
$672$	672.000	0.0385758
$673$	−31621.7	−1.81118	−0.905592	−	0.424150i	$-0.860573\pi$
$673$	−31621.7	−1.81118	−0.905592	+	0.424150i	$0.860573\pi$
$674$	16547.9	0.945697
$675$	1650.28	0.0941025
$676$	6678.22	0.379962
$677$	3083.55	0.175052	0.0875262	−	0.996162i	$-0.472104\pi$
$677$	3083.55	0.175052	0.0875262	+	0.996162i	$0.472104\pi$
$678$	−8101.28	−0.458891
$679$	5317.01	0.300513
$680$	1846.64	0.104141
$681$	17273.2	0.971969
$682$	3996.30	0.224379
$683$	20249.4	1.13444	0.567218	−	0.823568i	$-0.308020\pi$
$683$	20249.4	1.13444	0.567218	+	0.823568i	$0.308020\pi$
$684$	−1505.61	−0.0841646
$685$	−5177.53	−0.288793
$686$	−686.000	−0.0381802
$687$	−16244.9	−0.902157
$688$	4493.49	0.249001
$689$	7253.32	0.401059
$690$	−1102.95	−0.0608532
$691$	−26143.5	−1.43928	−0.719642	−	0.694346i	$-0.755694\pi$
$691$	−26143.5	−1.43928	−0.719642	+	0.694346i	$0.755694\pi$
$692$	1805.06	0.0991593
$693$	−1302.14	−0.0713772
$694$	−3739.87	−0.204559
$695$	−9055.00	−0.494210
$696$	3165.34	0.172388
$697$	−2533.09	−0.137658
$698$	−13290.3	−0.720698
$699$	3578.05	0.193611
$700$	1711.40	0.0924068
$701$	−18427.4	−0.992856	−0.496428	−	0.868078i	$-0.665355\pi$
$701$	−18427.4	−0.992856	−0.496428	+	0.868078i	$0.665355\pi$
$702$	−3357.81	−0.180530
$703$	−2833.37	−0.152009
$704$	1322.81	0.0708174
$705$	−12547.2	−0.670291
$706$	−7955.88	−0.424113
$707$	6195.69	0.329580
$708$	442.398	0.0234835
$709$	28025.3	1.48450	0.742251	−	0.670122i	$-0.233758\pi$
$709$	28025.3	1.48450	0.742251	+	0.670122i	$0.233758\pi$
$710$	2558.20	0.135222
$711$	11451.3	0.604018
$712$	−10895.1	−0.573469
$713$	2223.50	0.116789
$714$	1213.01	0.0635795
$715$	10272.1	0.537279
$716$	10530.7	0.549653
$717$	−972.424	−0.0506497
$718$	6445.88	0.335039
$719$	9834.57	0.510108	0.255054	−	0.966927i	$-0.417907\pi$
$719$	9834.57	0.510108	0.255054	+	0.966927i	$0.417907\pi$
$720$	1150.91	0.0595719
$721$	−7657.70	−0.395545
$722$	−10219.7	−0.526786
$723$	6255.93	0.321799
$724$	19101.2	0.980514
$725$	8061.24	0.412948
$726$	5422.76	0.277214
$727$	6490.28	0.331102	0.165551	−	0.986201i	$-0.447060\pi$
$727$	6490.28	0.331102	0.165551	+	0.986201i	$0.447060\pi$
$728$	−3482.17	−0.177277
$729$	729.000	0.0370370
$730$	17560.5	0.890331
$731$	8111.09	0.410396
$732$	10333.0	0.521745
$733$	−4243.44	−0.213827	−0.106913	−	0.994268i	$-0.534097\pi$
$733$	−4243.44	−0.213827	−0.106913	+	0.994268i	$0.534097\pi$
$734$	−170.414	−0.00856961
$735$	−1174.88	−0.0589609
$736$	736.000	0.0368605
$737$	6582.51	0.328996
$738$	−1578.73	−0.0787451
$739$	14759.8	0.734708	0.367354	−	0.930081i	$-0.380264\pi$
$739$	14759.8	0.734708	0.367354	+	0.930081i	$0.380264\pi$
$740$	2165.86	0.107593
$741$	7801.80	0.386783
$742$	−1633.06	−0.0807974
$743$	−9737.02	−0.480776	−0.240388	−	0.970677i	$-0.577275\pi$
$743$	−9737.02	−0.480776	−0.240388	+	0.970677i	$0.577275\pi$
$744$	−2320.17	−0.114330
$745$	11742.8	0.577479
$746$	−10419.7	−0.511384
$747$	8232.25	0.403216
$748$	2387.78	0.116719
$749$	4297.78	0.209663
$750$	8925.35	0.434544
$751$	8050.13	0.391150	0.195575	−	0.980689i	$-0.437343\pi$
$751$	8050.13	0.391150	0.195575	+	0.980689i	$0.437343\pi$
$752$	8372.75	0.406014
$753$	−2877.96	−0.139281
$754$	−16402.2	−0.792217
$755$	−18329.3	−0.883540
$756$	756.000	0.0363696
$757$	−4043.21	−0.194125	−0.0970627	−	0.995278i	$-0.530945\pi$
$757$	−4043.21	−0.194125	−0.0970627	+	0.995278i	$0.530945\pi$
$758$	−9881.00	−0.473475
$759$	−1426.16	−0.0682033
$760$	−2674.11	−0.127632
$761$	25144.0	1.19773	0.598864	−	0.800851i	$-0.295619\pi$
$761$	25144.0	1.19773	0.598864	+	0.800851i	$0.295619\pi$
$762$	−9630.22	−0.457829
$763$	−12541.9	−0.595082
$764$	7911.60	0.374649
$765$	2077.47	0.0981846
$766$	−23459.4	−1.10656
$767$	−2292.42	−0.107920
$768$	−768.000	−0.0360844
$769$	14531.7	0.681439	0.340719	−	0.940165i	$-0.389329\pi$
$769$	14531.7	0.681439	0.340719	+	0.940165i	$0.389329\pi$
$770$	−2312.73	−0.108240
$771$	−3475.30	−0.162334
$772$	−10708.0	−0.499207
$773$	11270.6	0.524416	0.262208	−	0.965011i	$-0.415549\pi$
$773$	11270.6	0.524416	0.262208	+	0.965011i	$0.415549\pi$
$774$	5055.18	0.234761
$775$	−5908.84	−0.273873
$776$	−6076.58	−0.281104
$777$	1422.69	0.0656871
$778$	−14567.0	−0.671276
$779$	3668.15	0.168710
$780$	−5963.77	−0.273766
$781$	3307.85	0.151555
$782$	1328.54	0.0607523
$783$	3561.01	0.162529
$784$	784.000	0.0357143
$785$	−5575.05	−0.253480
$786$	−16375.3	−0.743113
$787$	−14040.1	−0.635928	−0.317964	−	0.948103i	$-0.602999\pi$
$787$	−14040.1	−0.635928	−0.317964	+	0.948103i	$0.602999\pi$
$788$	6654.11	0.300816
$789$	−39.6987	−0.00179127
$790$	20338.5	0.915965
$791$	−9451.50	−0.424850
$792$	1488.17	0.0667672
$793$	−53543.3	−2.39770
$794$	−16125.7	−0.720756
$795$	−2796.88	−0.124774
$796$	−13082.9	−0.582550
$797$	20993.0	0.933013	0.466506	−	0.884518i	$-0.345512\pi$
$797$	20993.0	0.933013	0.466506	+	0.884518i	$0.345512\pi$
$798$	−1756.55	−0.0779213
$799$	15113.4	0.669180
$800$	−1955.88	−0.0864386
$801$	−12257.0	−0.540672
$802$	17682.4	0.778536
$803$	22706.3	0.997868
$804$	−3821.68	−0.167637
$805$	−1286.78	−0.0563391
$806$	12022.7	0.525411
$807$	18082.4	0.788761
$808$	−7080.79	−0.308294
$809$	8942.24	0.388619	0.194309	−	0.980940i	$-0.437753\pi$
$809$	8942.24	0.388619	0.194309	+	0.980940i	$0.437753\pi$
$810$	1294.77	0.0561649
$811$	16345.9	0.707746	0.353873	−	0.935293i	$-0.384864\pi$
$811$	16345.9	0.707746	0.353873	+	0.935293i	$0.384864\pi$
$812$	3692.90	0.159600
$813$	4864.49	0.209846
$814$	2800.53	0.120588
$815$	7548.76	0.324444
$816$	−1386.30	−0.0594732
$817$	−11745.6	−0.502970
$818$	25083.5	1.07216
$819$	−3917.44	−0.167139
$820$	−2803.97	−0.119413
$821$	−22316.2	−0.948650	−0.474325	−	0.880350i	$-0.657308\pi$
$821$	−22316.2	−0.948650	−0.474325	+	0.880350i	$0.657308\pi$
$822$	3886.84	0.164926
$823$	19914.7	0.843479	0.421739	−	0.906717i	$-0.361420\pi$
$823$	19914.7	0.843479	0.421739	+	0.906717i	$0.361420\pi$
$824$	8751.66	0.369998
$825$	3789.94	0.159938
$826$	516.131	0.0217415
$827$	25144.1	1.05725	0.528624	−	0.848856i	$-0.322708\pi$
$827$	25144.1	1.05725	0.528624	+	0.848856i	$0.322708\pi$
$828$	828.000	0.0347524
$829$	−45808.3	−1.91917	−0.959583	−	0.281425i	$-0.909193\pi$
$829$	−45808.3	−1.91917	−0.959583	+	0.281425i	$0.909193\pi$
$830$	14621.2	0.611458
$831$	13636.4	0.569244
$832$	3979.62	0.165828
$833$	1415.18	0.0588632
$834$	6797.70	0.282236
$835$	−4594.97	−0.190438
$836$	−3457.72	−0.143048
$837$	−2610.20	−0.107792
$838$	19767.6	0.814870
$839$	1594.69	0.0656195	0.0328097	−	0.999462i	$-0.489554\pi$
$839$	1594.69	0.0656195	0.0328097	+	0.999462i	$0.489554\pi$
$840$	1342.73	0.0551529
$841$	−6994.26	−0.286779
$842$	−32000.1	−1.30973
$843$	19555.8	0.798978
$844$	7532.19	0.307190
$845$	13343.8	0.543242
$846$	9419.34	0.382794
$847$	6326.56	0.256651
$848$	1866.36	0.0755790
$849$	12587.9	0.508852
$850$	−3530.52	−0.142466
$851$	1558.19	0.0627662
$852$	−1920.47	−0.0772234
$853$	−41131.1	−1.65100	−0.825499	−	0.564403i	$-0.809106\pi$
$853$	−41131.1	−1.65100	−0.825499	+	0.564403i	$0.809106\pi$
$854$	12055.1	0.483042
$855$	−3008.37	−0.120332
$856$	−4911.75	−0.196122
$857$	12175.8	0.485316	0.242658	−	0.970112i	$-0.421981\pi$
$857$	12175.8	0.485316	0.242658	+	0.970112i	$0.421981\pi$
$858$	−7711.38	−0.306832
$859$	8324.41	0.330646	0.165323	−	0.986239i	$-0.447133\pi$
$859$	8324.41	0.330646	0.165323	+	0.986239i	$0.447133\pi$
$860$	8978.46	0.356003
$861$	−1841.85	−0.0729038
$862$	23022.0	0.909665
$863$	−24489.3	−0.965960	−0.482980	−	0.875631i	$-0.660446\pi$
$863$	−24489.3	−0.965960	−0.482980	+	0.875631i	$0.660446\pi$
$864$	−864.000	−0.0340207
$865$	3606.71	0.141771
$866$	−7605.44	−0.298434
$867$	12236.6	0.479328
$868$	−2706.87	−0.105849
$869$	26298.5	1.02660
$870$	6324.67	0.246467
$871$	19803.2	0.770384
$872$	14333.6	0.556648
$873$	−6836.16	−0.265027
$874$	−1923.84	−0.0744564
$875$	10412.9	0.402309
$876$	−13182.8	−0.508456
$877$	33294.2	1.28194	0.640972	−	0.767564i	$-0.278531\pi$
$877$	33294.2	1.28194	0.640972	+	0.767564i	$0.278531\pi$
$878$	−9683.41	−0.372209
$879$	11158.0	0.428155
$880$	2643.12	0.101249
$881$	20716.7	0.792242	0.396121	−	0.918198i	$-0.370356\pi$
$881$	20716.7	0.792242	0.396121	+	0.918198i	$0.370356\pi$
$882$	882.000	0.0336718
$883$	−26512.1	−1.01042	−0.505211	−	0.862996i	$-0.668585\pi$
$883$	−26512.1	−1.01042	−0.505211	+	0.862996i	$0.668585\pi$
$884$	7183.52	0.273312
$885$	883.957	0.0335750
$886$	24958.5	0.946384
$887$	32208.7	1.21923	0.609617	−	0.792696i	$-0.291323\pi$
$887$	32208.7	1.21923	0.609617	+	0.792696i	$0.291323\pi$
$888$	−1625.94	−0.0614447
$889$	−11235.3	−0.423868
$890$	−21769.5	−0.819904
$891$	1674.19	0.0629488
$892$	−9249.84	−0.347206
$893$	−21885.6	−0.820129
$894$	−8815.45	−0.329790
$895$	21041.5	0.785853
$896$	−896.000	−0.0334077
$897$	−4290.53	−0.159706
$898$	11776.3	0.437616
$899$	−12750.2	−0.473019
$900$	−2200.37	−0.0814951
$901$	3368.92	0.124567
$902$	−3625.64	−0.133836
$903$	5897.71	0.217346
$904$	10801.7	0.397411
$905$	38166.2	1.40187
$906$	13760.0	0.504577
$907$	14535.0	0.532113	0.266056	−	0.963957i	$-0.414279\pi$
$907$	14535.0	0.532113	0.266056	+	0.963957i	$0.414279\pi$
$908$	−23031.0	−0.841750
$909$	−7965.89	−0.290662
$910$	−6957.74	−0.253458
$911$	−5369.26	−0.195271	−0.0976354	−	0.995222i	$-0.531128\pi$
$911$	−5369.26	−0.195271	−0.0976354	+	0.995222i	$0.531128\pi$
$912$	2007.49	0.0728887
$913$	18905.8	0.685313
$914$	−4308.33	−0.155916
$915$	20646.3	0.745952
$916$	21659.9	0.781291
$917$	−19104.5	−0.687989
$918$	−1559.58	−0.0560719
$919$	11806.1	0.423772	0.211886	−	0.977294i	$-0.432039\pi$
$919$	11806.1	0.423772	0.211886	+	0.977294i	$0.432039\pi$
$920$	1470.60	0.0527004
$921$	17881.7	0.639762
$922$	558.385	0.0199452
$923$	9951.52	0.354884
$924$	1736.19	0.0618145
$925$	−4140.81	−0.147188
$926$	1308.15	0.0464240
$927$	9845.62	0.348838
$928$	−4220.45	−0.149292
$929$	39491.5	1.39470	0.697349	−	0.716732i	$-0.254363\pi$
$929$	39491.5	1.39470	0.697349	+	0.716732i	$0.254363\pi$
$930$	−4635.95	−0.163461
$931$	−2049.31	−0.0721411
$932$	−4770.73	−0.167672
$933$	19337.3	0.678536
$934$	13265.5	0.464732
$935$	4771.03	0.166876
$936$	4477.08	0.156344
$937$	18648.9	0.650195	0.325097	−	0.945681i	$-0.394603\pi$
$937$	18648.9	0.650195	0.325097	+	0.945681i	$0.394603\pi$
$938$	−4458.62	−0.155202
$939$	14267.2	0.495839
$940$	16729.6	0.580489
$941$	−32442.0	−1.12389	−0.561945	−	0.827175i	$-0.689947\pi$
$941$	−32442.0	−1.12389	−0.561945	+	0.827175i	$0.689947\pi$
$942$	4185.26	0.144759
$943$	−2017.27	−0.0696620
$944$	−589.864	−0.0203373
$945$	1510.57	0.0519986
$946$	11609.5	0.399003
$947$	−26949.0	−0.924735	−0.462368	−	0.886688i	$-0.653000\pi$
$947$	−26949.0	−0.924735	−0.462368	+	0.886688i	$0.653000\pi$
$948$	−15268.4	−0.523095
$949$	68310.9	2.33663
$950$	5112.51	0.174602
$951$	−32533.1	−1.10931
$952$	−1617.35	−0.0550615
$953$	−21431.1	−0.728460	−0.364230	−	0.931309i	$-0.618668\pi$
$953$	−21431.1	−0.728460	−0.364230	+	0.931309i	$0.618668\pi$
$954$	2099.65	0.0712566
$955$	15808.2	0.535645
$956$	1296.56	0.0438639
$957$	8178.03	0.276236
$958$	32561.0	1.09812
$959$	4534.64	0.152692
$960$	−1534.54	−0.0515908
$961$	−20445.1	−0.686286
$962$	8425.28	0.282372
$963$	−5525.72	−0.184905
$964$	−8341.24	−0.278686
$965$	−21395.6	−0.713730
$966$	966.000	0.0321745
$967$	5832.84	0.193973	0.0969864	−	0.995286i	$-0.469080\pi$
$967$	5832.84	0.193973	0.0969864	+	0.995286i	$0.469080\pi$
$968$	−7230.35	−0.240075
$969$	3623.66	0.120133
$970$	−12141.6	−0.401902
$971$	32145.7	1.06242	0.531208	−	0.847242i	$-0.321738\pi$
$971$	32145.7	1.06242	0.531208	+	0.847242i	$0.321738\pi$
$972$	−972.000	−0.0320750
$973$	7930.65	0.261300
$974$	−17077.4	−0.561802
$975$	11401.9	0.374515
$976$	−13777.3	−0.451844
$977$	−36929.4	−1.20929	−0.604645	−	0.796495i	$-0.706685\pi$
$977$	−36929.4	−1.20929	−0.604645	+	0.796495i	$0.706685\pi$
$978$	−5666.95	−0.185285
$979$	−28148.7	−0.918935
$980$	1566.51	0.0510616
$981$	16125.3	0.524813
$982$	3080.47	0.100104
$983$	12220.5	0.396515	0.198258	−	0.980150i	$-0.436472\pi$
$983$	12220.5	0.396515	0.198258	+	0.980150i	$0.436472\pi$
$984$	2104.97	0.0681952
$985$	13295.6	0.430084
$986$	−7618.23	−0.246059
$987$	10989.2	0.354398
$988$	−10402.4	−0.334964
$989$	6459.40	0.207681
$990$	2973.51	0.0954589
$991$	5076.06	0.162711	0.0813554	−	0.996685i	$-0.474075\pi$
$991$	5076.06	0.162711	0.0813554	+	0.996685i	$0.474075\pi$
$992$	3093.57	0.0990129
$993$	17634.3	0.563553
$994$	−2240.55	−0.0714950
$995$	−26140.9	−0.832886
$996$	−10976.3	−0.349195
$997$	−51803.1	−1.64556	−0.822778	−	0.568362i	$-0.807577\pi$
$997$	−51803.1	−1.64556	−0.822778	+	0.568362i	$0.807577\pi$
$998$	−9642.81	−0.305850
$999$	−1829.18	−0.0579306

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	966.4.a.p.1.4	✓	5

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
966.4.a.p.1.4	✓	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)

\(f(q)\)	\(=\)	\(q+2.00000 q^{2} -3.00000 q^{3} +4.00000 q^{4} +7.99241 q^{5} -6.00000 q^{6} -7.00000 q^{7} +8.00000 q^{8} +9.00000 q^{9} +O(q^{10})\)	\(q+2.00000 q^{2} -3.00000 q^{3} +4.00000 q^{4} +7.99241 q^{5} -6.00000 q^{6} -7.00000 q^{7} +8.00000 q^{8} +9.00000 q^{9} +15.9848 q^{10} +20.6690 q^{11} -12.0000 q^{12} +62.1816 q^{13} -14.0000 q^{14} -23.9772 q^{15} +16.0000 q^{16} +28.8812 q^{17} +18.0000 q^{18} -41.8226 q^{19} +31.9696 q^{20} +21.0000 q^{21} +41.3379 q^{22} +23.0000 q^{23} -24.0000 q^{24} -61.1213 q^{25} +124.363 q^{26} -27.0000 q^{27} -28.0000 q^{28} -131.889 q^{29} -47.9545 q^{30} +96.6740 q^{31} +32.0000 q^{32} -62.0069 q^{33} +57.7624 q^{34} -55.9469 q^{35} +36.0000 q^{36} +67.7473 q^{37} -83.6452 q^{38} -186.545 q^{39} +63.9393 q^{40} -87.7072 q^{41} +42.0000 q^{42} +280.843 q^{43} +82.6759 q^{44} +71.9317 q^{45} +46.0000 q^{46} +523.297 q^{47} -48.0000 q^{48} +49.0000 q^{49} -122.243 q^{50} -86.6436 q^{51} +248.726 q^{52} +116.647 q^{53} -54.0000 q^{54} +165.195 q^{55} -56.0000 q^{56} +125.468 q^{57} -263.778 q^{58} -36.8665 q^{59} -95.9089 q^{60} -861.080 q^{61} +193.348 q^{62} -63.0000 q^{63} +64.0000 q^{64} +496.981 q^{65} -124.014 q^{66} +318.473 q^{67} +115.525 q^{68} -69.0000 q^{69} -111.894 q^{70} +160.040 q^{71} +72.0000 q^{72} +1098.57 q^{73} +135.495 q^{74} +183.364 q^{75} -167.290 q^{76} -144.683 q^{77} -373.090 q^{78} +1272.37 q^{79} +127.879 q^{80} +81.0000 q^{81} -175.414 q^{82} +914.695 q^{83} +84.0000 q^{84} +230.830 q^{85} +561.687 q^{86} +395.667 q^{87} +165.352 q^{88} -1361.88 q^{89} +143.863 q^{90} -435.271 q^{91} +92.0000 q^{92} -290.022 q^{93} +1046.59 q^{94} -334.264 q^{95} -96.0000 q^{96} -759.573 q^{97} +98.0000 q^{98} +186.021 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 5 q + 10 q^{2} - 15 q^{3} + 20 q^{4} - 10 q^{5} - 30 q^{6} - 35 q^{7} + 40 q^{8} + 45 q^{9}+O(q^{10}) \) 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	\( 5 q + 10 q^{2} - 15 q^{3} + 20 q^{4} - 10 q^{5} - 30 q^{6} - 35 q^{7} + 40 q^{8} + 45 q^{9} - 20 q^{10} + 9 q^{11} - 60 q^{12} - 102 q^{13} - 70 q^{14} + 30 q^{15} + 80 q^{16} - 30 q^{17} + 90 q^{18} - 27 q^{19} - 40 q^{20} + 105 q^{21} + 18 q^{22} + 115 q^{23} - 120 q^{24} + 307 q^{25} - 204 q^{26} - 135 q^{27} - 140 q^{28} + 135 q^{29} + 60 q^{30} + 160 q^{31} + 160 q^{32} - 27 q^{33} - 60 q^{34} + 70 q^{35} + 180 q^{36} + 153 q^{37} - 54 q^{38} + 306 q^{39} - 80 q^{40} + 76 q^{41} + 210 q^{42} + 980 q^{43} + 36 q^{44} - 90 q^{45} + 230 q^{46} - 8 q^{47} - 240 q^{48} + 245 q^{49} + 614 q^{50} + 90 q^{51} - 408 q^{52} + 676 q^{53} - 270 q^{54} + 1403 q^{55} - 280 q^{56} + 81 q^{57} + 270 q^{58} - 208 q^{59} + 120 q^{60} + 204 q^{61} + 320 q^{62} - 315 q^{63} + 320 q^{64} + 971 q^{65} - 54 q^{66} + 767 q^{67} - 120 q^{68} - 345 q^{69} + 140 q^{70} + 1353 q^{71} + 360 q^{72} + 92 q^{73} + 306 q^{74} - 921 q^{75} - 108 q^{76} - 63 q^{77} + 612 q^{78} + 2958 q^{79} - 160 q^{80} + 405 q^{81} + 152 q^{82} + 1370 q^{83} + 420 q^{84} + 1725 q^{85} + 1960 q^{86} - 405 q^{87} + 72 q^{88} + 1207 q^{89} - 180 q^{90} + 714 q^{91} + 460 q^{92} - 480 q^{93} - 16 q^{94} + 2995 q^{95} - 480 q^{96} + 1633 q^{97} + 490 q^{98} + 81 q^{99}+O(q^{100}) \) 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 + 9 * q^11 - 60 * q^12 - 102 * q^13 - 70 * q^14 + 30 * q^15 + 80 * q^16 - 30 * q^17 + 90 * q^18 - 27 * q^19 - 40 * q^20 + 105 * q^21 + 18 * q^22 + 115 * q^23 - 120 * q^24 + 307 * q^25 - 204 * q^26 - 135 * q^27 - 140 * q^28 + 135 * q^29 + 60 * q^30 + 160 * q^31 + 160 * q^32 - 27 * q^33 - 60 * q^34 + 70 * q^35 + 180 * q^36 + 153 * q^37 - 54 * q^38 + 306 * q^39 - 80 * q^40 + 76 * q^41 + 210 * q^42 + 980 * q^43 + 36 * q^44 - 90 * q^45 + 230 * q^46 - 8 * q^47 - 240 * q^48 + 245 * q^49 + 614 * q^50 + 90 * q^51 - 408 * q^52 + 676 * q^53 - 270 * q^54 + 1403 * q^55 - 280 * q^56 + 81 * q^57 + 270 * q^58 - 208 * q^59 + 120 * q^60 + 204 * q^61 + 320 * q^62 - 315 * q^63 + 320 * q^64 + 971 * q^65 - 54 * q^66 + 767 * q^67 - 120 * q^68 - 345 * q^69 + 140 * q^70 + 1353 * q^71 + 360 * q^72 + 92 * q^73 + 306 * q^74 - 921 * q^75 - 108 * q^76 - 63 * q^77 + 612 * q^78 + 2958 * q^79 - 160 * q^80 + 405 * q^81 + 152 * q^82 + 1370 * q^83 + 420 * q^84 + 1725 * q^85 + 1960 * q^86 - 405 * q^87 + 72 * q^88 + 1207 * q^89 - 180 * q^90 + 714 * q^91 + 460 * q^92 - 480 * q^93 - 16 * q^94 + 2995 * q^95 - 480 * q^96 + 1633 * q^97 + 490 * q^98 + 81 * q^99

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