LMFDB - Embedded newform 1045.4.a.g.1.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1045,4,Mod(1,1045)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1045, 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("1045.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 1045 = 5 \cdot 11 \cdot 19 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	1045.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:	$61.6569959560$
Analytic rank:	$0$
Dimension:	$23$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Character	$\chi$	$=$	1045.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-4.38057 q^{2} +7.64668 q^{3} +11.1894 q^{4} -5.00000 q^{5} -33.4968 q^{6} +9.94553 q^{7} -13.9715 q^{8} +31.4717 q^{9} +O(q^{10})$	\(q-4.38057 q^{2} +7.64668 q^{3} +11.1894 q^{4} -5.00000 q^{5} -33.4968 q^{6} +9.94553 q^{7} -13.9715 q^{8} +31.4717 q^{9} +21.9029 q^{10} -11.0000 q^{11} +85.5619 q^{12} -33.3297 q^{13} -43.5671 q^{14} -38.2334 q^{15} -28.3123 q^{16} -16.7436 q^{17} -137.864 q^{18} -19.0000 q^{19} -55.9471 q^{20} +76.0503 q^{21} +48.1863 q^{22} +190.389 q^{23} -106.835 q^{24} +25.0000 q^{25} +146.003 q^{26} +34.1939 q^{27} +111.285 q^{28} -198.174 q^{29} +167.484 q^{30} +96.4083 q^{31} +235.796 q^{32} -84.1135 q^{33} +73.3466 q^{34} -49.7277 q^{35} +352.150 q^{36} +20.1082 q^{37} +83.2309 q^{38} -254.862 q^{39} +69.8573 q^{40} +212.679 q^{41} -333.144 q^{42} +189.014 q^{43} -123.084 q^{44} -157.359 q^{45} -834.013 q^{46} -135.263 q^{47} -216.495 q^{48} -244.086 q^{49} -109.514 q^{50} -128.033 q^{51} -372.940 q^{52} +440.409 q^{53} -149.789 q^{54} +55.0000 q^{55} -138.954 q^{56} -145.287 q^{57} +868.114 q^{58} +537.721 q^{59} -427.809 q^{60} +830.724 q^{61} -422.323 q^{62} +313.003 q^{63} -806.422 q^{64} +166.648 q^{65} +368.465 q^{66} +264.540 q^{67} -187.351 q^{68} +1455.84 q^{69} +217.836 q^{70} +410.187 q^{71} -439.706 q^{72} +511.777 q^{73} -88.0853 q^{74} +191.167 q^{75} -212.599 q^{76} -109.401 q^{77} +1116.44 q^{78} +38.9454 q^{79} +141.562 q^{80} -588.267 q^{81} -931.654 q^{82} -50.2607 q^{83} +850.958 q^{84} +83.7180 q^{85} -827.990 q^{86} -1515.37 q^{87} +153.686 q^{88} +646.569 q^{89} +689.321 q^{90} -331.482 q^{91} +2130.34 q^{92} +737.203 q^{93} +592.531 q^{94} +95.0000 q^{95} +1803.06 q^{96} -706.026 q^{97} +1069.24 q^{98} -346.189 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 23 q + 6 q^{2} + 9 q^{3} + 92 q^{4} - 115 q^{5} - 25 q^{6} - 37 q^{7} + 42 q^{8} + 170 q^{9}+O(q^{10}) $ 23 * q + 6 * q^2 + 9 * q^3 + 92 * q^4 - 115 * q^5 - 25 * q^6 - 37 * q^7 + 42 * q^8 + 170 * q^9	\( 23 q + 6 q^{2} + 9 q^{3} + 92 q^{4} - 115 q^{5} - 25 q^{6} - 37 q^{7} + 42 q^{8} + 170 q^{9} - 30 q^{10} - 253 q^{11} + 44 q^{12} - 37 q^{13} + 61 q^{14} - 45 q^{15} + 588 q^{16} - 73 q^{17} + 391 q^{18} - 437 q^{19} - 460 q^{20} - 127 q^{21} - 66 q^{22} - 175 q^{23} + 16 q^{24} + 575 q^{25} + 719 q^{26} + 21 q^{27} + 253 q^{28} + 71 q^{29} + 125 q^{30} + 302 q^{31} + 1107 q^{32} - 99 q^{33} + 1267 q^{34} + 185 q^{35} + 703 q^{36} - 500 q^{37} - 114 q^{38} + 457 q^{39} - 210 q^{40} + 770 q^{41} + 2596 q^{42} - 902 q^{43} - 1012 q^{44} - 850 q^{45} - 1101 q^{46} + 356 q^{47} + 1221 q^{48} + 908 q^{49} + 150 q^{50} - 451 q^{51} - 358 q^{52} + 1327 q^{53} + 2534 q^{54} + 1265 q^{55} + 3135 q^{56} - 171 q^{57} + 1014 q^{58} + 3619 q^{59} - 220 q^{60} - 1432 q^{61} + 1826 q^{62} + 1658 q^{63} + 4006 q^{64} + 185 q^{65} + 275 q^{66} - 605 q^{67} + 5128 q^{68} + 3099 q^{69} - 305 q^{70} + 3230 q^{71} + 2152 q^{72} - 637 q^{73} + 5063 q^{74} + 225 q^{75} - 1748 q^{76} + 407 q^{77} + 7230 q^{78} + 2074 q^{79} - 2940 q^{80} + 2291 q^{81} + 530 q^{82} + 3882 q^{83} + 5096 q^{84} + 365 q^{85} + 2262 q^{86} - 27 q^{87} - 462 q^{88} - 210 q^{89} - 1955 q^{90} + 4133 q^{91} - 6064 q^{92} + 824 q^{93} - 392 q^{94} + 2185 q^{95} + 2462 q^{96} + 2032 q^{97} + 7896 q^{98} - 1870 q^{99}+O(q^{100}) \) 23 * q + 6 * q^2 + 9 * q^3 + 92 * q^4 - 115 * q^5 - 25 * q^6 - 37 * q^7 + 42 * q^8 + 170 * q^9 - 30 * q^10 - 253 * q^11 + 44 * q^12 - 37 * q^13 + 61 * q^14 - 45 * q^15 + 588 * q^16 - 73 * q^17 + 391 * q^18 - 437 * q^19 - 460 * q^20 - 127 * q^21 - 66 * q^22 - 175 * q^23 + 16 * q^24 + 575 * q^25 + 719 * q^26 + 21 * q^27 + 253 * q^28 + 71 * q^29 + 125 * q^30 + 302 * q^31 + 1107 * q^32 - 99 * q^33 + 1267 * q^34 + 185 * q^35 + 703 * q^36 - 500 * q^37 - 114 * q^38 + 457 * q^39 - 210 * q^40 + 770 * q^41 + 2596 * q^42 - 902 * q^43 - 1012 * q^44 - 850 * q^45 - 1101 * q^46 + 356 * q^47 + 1221 * q^48 + 908 * q^49 + 150 * q^50 - 451 * q^51 - 358 * q^52 + 1327 * q^53 + 2534 * q^54 + 1265 * q^55 + 3135 * q^56 - 171 * q^57 + 1014 * q^58 + 3619 * q^59 - 220 * q^60 - 1432 * q^61 + 1826 * q^62 + 1658 * q^63 + 4006 * q^64 + 185 * q^65 + 275 * q^66 - 605 * q^67 + 5128 * q^68 + 3099 * q^69 - 305 * q^70 + 3230 * q^71 + 2152 * q^72 - 637 * q^73 + 5063 * q^74 + 225 * q^75 - 1748 * q^76 + 407 * q^77 + 7230 * q^78 + 2074 * q^79 - 2940 * q^80 + 2291 * q^81 + 530 * q^82 + 3882 * q^83 + 5096 * q^84 + 365 * q^85 + 2262 * q^86 - 27 * q^87 - 462 * q^88 - 210 * q^89 - 1955 * q^90 + 4133 * q^91 - 6064 * q^92 + 824 * q^93 - 392 * q^94 + 2185 * q^95 + 2462 * q^96 + 2032 * q^97 + 7896 * q^98 - 1870 * 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 $

$2$	−4.38057	−1.54877	−0.774383	−	0.632717i	$-0.781940\pi$
$2$	−4.38057	−1.54877	−0.774383	+	0.632717i	$0.781940\pi$
$3$	7.64668	1.47160	0.735802	−	0.677196i	$-0.236805\pi$
$3$	7.64668	1.47160	0.735802	+	0.677196i	$0.236805\pi$
$4$	11.1894	1.39868
$5$	−5.00000	−0.447214
$5$	−5.00000	−0.447214
$6$	−33.4968	−2.27917
$7$	9.94553	0.537008	0.268504	−	0.963279i	$-0.413471\pi$
$7$	9.94553	0.537008	0.268504	+	0.963279i	$0.413471\pi$
$8$	−13.9715	−0.617457
$9$	31.4717	1.16562
$10$	21.9029	0.692629
$11$	−11.0000	−0.301511
$11$	−11.0000	−0.301511
$12$	85.5619	2.05830
$13$	−33.3297	−0.711077	−0.355538	−	0.934662i	$-0.615702\pi$
$13$	−33.3297	−0.711077	−0.355538	+	0.934662i	$0.615702\pi$
$14$	−43.5671	−0.831700
$15$	−38.2334	−0.658122
$16$	−28.3123	−0.442380
$17$	−16.7436	−0.238878	−0.119439	−	0.992842i	$-0.538110\pi$
$17$	−16.7436	−0.238878	−0.119439	+	0.992842i	$0.538110\pi$
$18$	−137.864	−1.80527
$19$	−19.0000	−0.229416
$19$	−19.0000	−0.229416
$20$	−55.9471	−0.625507
$21$	76.0503	0.790264
$22$	48.1863	0.466971
$23$	190.389	1.72604	0.863019	−	0.505172i	$-0.168571\pi$
$23$	190.389	1.72604	0.863019	+	0.505172i	$0.168571\pi$
$24$	−106.835	−0.908653
$25$	25.0000	0.200000
$26$	146.003	1.10129
$27$	34.1939	0.243727
$28$	111.285	0.751101
$29$	−198.174	−1.26896	−0.634482	−	0.772938i	$-0.718786\pi$
$29$	−198.174	−1.26896	−0.634482	+	0.772938i	$0.718786\pi$
$30$	167.484	1.01928
$31$	96.4083	0.558562	0.279281	−	0.960209i	$-0.409904\pi$
$31$	96.4083	0.558562	0.279281	+	0.960209i	$0.409904\pi$
$32$	235.796	1.30260
$33$	−84.1135	−0.443705
$34$	73.3466	0.369966
$35$	−49.7277	−0.240157
$36$	352.150	1.63033
$37$	20.1082	0.0893449	0.0446725	−	0.999002i	$-0.485776\pi$
$37$	20.1082	0.0893449	0.0446725	+	0.999002i	$0.485776\pi$
$38$	83.2309	0.355311
$39$	−254.862	−1.04642
$40$	69.8573	0.276135
$41$	212.679	0.810118	0.405059	−	0.914291i	$-0.367251\pi$
$41$	212.679	0.810118	0.405059	+	0.914291i	$0.367251\pi$
$42$	−333.144	−1.22393
$43$	189.014	0.670335	0.335167	−	0.942159i	$-0.391207\pi$
$43$	189.014	0.670335	0.335167	+	0.942159i	$0.391207\pi$
$44$	−123.084	−0.421717
$45$	−157.359	−0.521281
$46$	−834.013	−2.67323
$47$	−135.263	−0.419791	−0.209895	−	0.977724i	$-0.567312\pi$
$47$	−135.263	−0.419791	−0.209895	+	0.977724i	$0.567312\pi$
$48$	−216.495	−0.651008
$49$	−244.086	−0.711622
$50$	−109.514	−0.309753
$51$	−128.033	−0.351533
$52$	−372.940	−0.994566
$53$	440.409	1.14141	0.570706	−	0.821154i	$-0.306669\pi$
$53$	440.409	1.14141	0.570706	+	0.821154i	$0.306669\pi$
$54$	−149.789	−0.377476
$55$	55.0000	0.134840
$56$	−138.954	−0.331580
$57$	−145.287	−0.337609
$58$	868.114	1.96533
$59$	537.721	1.18653	0.593266	−	0.805007i	$-0.297838\pi$
$59$	537.721	1.18653	0.593266	+	0.805007i	$0.297838\pi$
$60$	−427.809	−0.920499
$61$	830.724	1.74366	0.871830	−	0.489809i	$-0.162933\pi$
$61$	830.724	1.74366	0.871830	+	0.489809i	$0.162933\pi$
$62$	−422.323	−0.865083
$63$	313.003	0.625947
$64$	−806.422	−1.57504
$65$	166.648	0.318003
$66$	368.465	0.687196
$67$	264.540	0.482369	0.241185	−	0.970479i	$-0.422464\pi$
$67$	264.540	0.482369	0.241185	+	0.970479i	$0.422464\pi$
$68$	−187.351	−0.334113
$69$	1455.84	2.54004
$70$	217.836	0.371948
$71$	410.187	0.685637	0.342819	−	0.939402i	$-0.388618\pi$
$71$	410.187	0.685637	0.342819	+	0.939402i	$0.388618\pi$
$72$	−439.706	−0.719720
$73$	511.777	0.820533	0.410267	−	0.911966i	$-0.365436\pi$
$73$	511.777	0.820533	0.410267	+	0.911966i	$0.365436\pi$
$74$	−88.0853	−0.138374
$75$	191.167	0.294321
$76$	−212.599	−0.320878
$77$	−109.401	−0.161914
$78$	1116.44	1.62067
$79$	38.9454	0.0554646	0.0277323	−	0.999615i	$-0.491171\pi$
$79$	38.9454	0.0554646	0.0277323	+	0.999615i	$0.491171\pi$
$80$	141.562	0.197838
$81$	−588.267	−0.806950
$82$	−931.654	−1.25468
$83$	−50.2607	−0.0664678	−0.0332339	−	0.999448i	$-0.510581\pi$
$83$	−50.2607	−0.0664678	−0.0332339	+	0.999448i	$0.510581\pi$
$84$	850.958	1.10532
$85$	83.7180	0.106829
$86$	−827.990	−1.03819
$87$	−1515.37	−1.86741
$88$	153.686	0.186170
$89$	646.569	0.770070	0.385035	−	0.922902i	$-0.374189\pi$
$89$	646.569	0.770070	0.385035	+	0.922902i	$0.374189\pi$
$90$	689.321	0.807342
$91$	−331.482	−0.381854
$92$	2130.34	2.41417
$93$	737.203	0.821983
$94$	592.531	0.650158
$95$	95.0000	0.102598
$96$	1803.06	1.91691
$97$	−706.026	−0.739032	−0.369516	−	0.929224i	$-0.620476\pi$
$97$	−706.026	−0.739032	−0.369516	+	0.929224i	$0.620476\pi$
$98$	1069.24	1.10214
$99$	−346.189	−0.351448
$100$	279.735	0.279735
$101$	−1156.54	−1.13940	−0.569702	−	0.821851i	$-0.692941\pi$
$101$	−1156.54	−1.13940	−0.569702	+	0.821851i	$0.692941\pi$
$102$	560.858	0.544443
$103$	1214.39	1.16172	0.580860	−	0.814003i	$-0.302716\pi$
$103$	1214.39	1.16172	0.580860	+	0.814003i	$0.302716\pi$
$104$	465.665	0.439059
$105$	−380.252	−0.353417
$106$	−1929.25	−1.76778
$107$	604.906	0.546527	0.273264	−	0.961939i	$-0.411897\pi$
$107$	604.906	0.546527	0.273264	+	0.961939i	$0.411897\pi$
$108$	382.610	0.340895
$109$	−1708.65	−1.50146	−0.750731	−	0.660608i	$-0.770299\pi$
$109$	−1708.65	−1.50146	−0.750731	+	0.660608i	$0.770299\pi$
$110$	−240.931	−0.208836
$111$	153.761	0.131480
$112$	−281.581	−0.237562
$113$	1757.05	1.46274	0.731368	−	0.681983i	$-0.238882\pi$
$113$	1757.05	1.46274	0.731368	+	0.681983i	$0.238882\pi$
$114$	636.440	0.522878
$115$	−951.945	−0.771907
$116$	−2217.45	−1.77487
$117$	−1048.94	−0.828845
$118$	−2355.53	−1.83766
$119$	−166.524	−0.128279
$120$	534.177	0.406362
$121$	121.000	0.0909091
$122$	−3639.04	−2.70052
$123$	1626.29	1.19217
$124$	1078.75	0.781248
$125$	−125.000	−0.0894427
$126$	−1371.13	−0.969446
$127$	−1666.71	−1.16454	−0.582269	−	0.812996i	$-0.697835\pi$
$127$	−1666.71	−1.16454	−0.582269	+	0.812996i	$0.697835\pi$
$128$	1646.22	1.13677
$129$	1445.33	0.986468
$130$	−730.016	−0.492512
$131$	1547.13	1.03186	0.515928	−	0.856632i	$-0.327447\pi$
$131$	1547.13	1.03186	0.515928	+	0.856632i	$0.327447\pi$
$132$	−941.181	−0.620601
$133$	−188.965	−0.123198
$134$	−1158.84	−0.747077
$135$	−170.970	−0.108998
$136$	233.933	0.147497
$137$	959.377	0.598286	0.299143	−	0.954208i	$-0.403299\pi$
$137$	959.377	0.598286	0.299143	+	0.954208i	$0.403299\pi$
$138$	−6377.43	−3.93394
$139$	−2858.10	−1.74404	−0.872018	−	0.489474i	$-0.837189\pi$
$139$	−2858.10	−1.74404	−0.872018	+	0.489474i	$0.837189\pi$
$140$	−556.423	−0.335903
$141$	−1034.32	−0.617766
$142$	−1796.85	−1.06189
$143$	366.627	0.214398
$144$	−891.037	−0.515647
$145$	990.868	0.567498
$146$	−2241.87	−1.27081
$147$	−1866.45	−1.04723
$148$	224.999	0.124965
$149$	1947.45	1.07075	0.535374	−	0.844615i	$-0.320171\pi$
$149$	1947.45	1.07075	0.535374	+	0.844615i	$0.320171\pi$
$150$	−837.421	−0.455834
$151$	−1665.61	−0.897651	−0.448826	−	0.893619i	$-0.648158\pi$
$151$	−1665.61	−0.897651	−0.448826	+	0.893619i	$0.648158\pi$
$152$	265.458	0.141654
$153$	−526.950	−0.278440
$154$	479.238	0.250767
$155$	−482.041	−0.249797
$156$	−2851.75	−1.46361
$157$	3116.93	1.58445	0.792223	−	0.610231i	$-0.208924\pi$
$157$	3116.93	1.58445	0.792223	+	0.610231i	$0.208924\pi$
$158$	−170.603	−0.0859017
$159$	3367.67	1.67971
$160$	−1178.98	−0.582541
$161$	1893.52	0.926896
$162$	2576.95	1.24978
$163$	−926.037	−0.444987	−0.222493	−	0.974934i	$-0.571420\pi$
$163$	−926.037	−0.444987	−0.222493	+	0.974934i	$0.571420\pi$
$164$	2379.75	1.13309
$165$	420.567	0.198431
$166$	220.170	0.102943
$167$	−1091.71	−0.505862	−0.252931	−	0.967484i	$-0.581395\pi$
$167$	−1091.71	−0.505862	−0.252931	+	0.967484i	$0.581395\pi$
$168$	−1062.53	−0.487954
$169$	−1086.13	−0.494370
$170$	−366.733	−0.165454
$171$	−597.963	−0.267412
$172$	2114.96	0.937582
$173$	304.506	0.133822	0.0669110	−	0.997759i	$-0.478686\pi$
$173$	304.506	0.133822	0.0669110	+	0.997759i	$0.478686\pi$
$174$	6638.19	2.89218
$175$	248.638	0.107402
$176$	311.435	0.133383
$177$	4111.78	1.74610
$178$	−2832.34	−1.19266
$179$	2570.68	1.07342	0.536709	−	0.843767i	$-0.319667\pi$
$179$	2570.68	1.07342	0.536709	+	0.843767i	$0.319667\pi$
$180$	−1760.75	−0.729104
$181$	−1271.13	−0.522001	−0.261000	−	0.965339i	$-0.584052\pi$
$181$	−1271.13	−0.522001	−0.261000	+	0.965339i	$0.584052\pi$
$182$	1452.08	0.591402
$183$	6352.28	2.56598
$184$	−2660.01	−1.06575
$185$	−100.541	−0.0399563
$186$	−3229.37	−1.27306
$187$	184.180	0.0720243
$188$	−1513.52	−0.587152
$189$	340.077	0.130883
$190$	−416.154	−0.158900
$191$	3121.51	1.18254	0.591268	−	0.806475i	$-0.298628\pi$
$191$	3121.51	1.18254	0.591268	+	0.806475i	$0.298628\pi$
$192$	−6166.45	−2.31784
$193$	1191.13	0.444245	0.222122	−	0.975019i	$-0.428702\pi$
$193$	1191.13	0.444245	0.222122	+	0.975019i	$0.428702\pi$
$194$	3092.80	1.14459
$195$	1274.31	0.467975
$196$	−2731.18	−0.995330
$197$	−2997.31	−1.08401	−0.542003	−	0.840376i	$-0.682334\pi$
$197$	−2997.31	−1.08401	−0.542003	+	0.840376i	$0.682334\pi$
$198$	1516.51	0.544310
$199$	5097.41	1.81581	0.907903	−	0.419180i	$-0.137682\pi$
$199$	5097.41	1.81581	0.907903	+	0.419180i	$0.137682\pi$
$200$	−349.287	−0.123491
$201$	2022.85	0.709857
$202$	5066.30	1.76467
$203$	−1970.94	−0.681444
$204$	−1432.61	−0.491682
$205$	−1063.39	−0.362296
$206$	−5319.71	−1.79923
$207$	5991.87	2.01190
$208$	943.641	0.314566
$209$	209.000	0.0691714
$210$	1665.72	0.547360
$211$	2932.92	0.956921	0.478461	−	0.878109i	$-0.341195\pi$
$211$	2932.92	0.956921	0.478461	+	0.878109i	$0.341195\pi$
$212$	4927.92	1.59647
$213$	3136.57	1.00899
$214$	−2649.83	−0.846443
$215$	−945.071	−0.299783
$216$	−477.739	−0.150491
$217$	958.831	0.299953
$218$	7484.89	2.32541
$219$	3913.39	1.20750
$220$	615.418	0.188598
$221$	558.059	0.169860
$222$	−673.560	−0.203632
$223$	−3882.80	−1.16597	−0.582986	−	0.812482i	$-0.698116\pi$
$223$	−3882.80	−1.16597	−0.582986	+	0.812482i	$0.698116\pi$
$224$	2345.11	0.699507
$225$	786.793	0.233124
$226$	−7696.87	−2.26544
$227$	313.570	0.0916843	0.0458422	−	0.998949i	$-0.485403\pi$
$227$	313.570	0.0916843	0.0458422	+	0.998949i	$0.485403\pi$
$228$	−1625.68	−0.472206
$229$	5506.93	1.58912	0.794560	−	0.607186i	$-0.207702\pi$
$229$	5506.93	1.58912	0.794560	+	0.607186i	$0.207702\pi$
$230$	4170.07	1.19550
$231$	−836.553	−0.238273
$232$	2768.78	0.783531
$233$	−597.717	−0.168059	−0.0840295	−	0.996463i	$-0.526779\pi$
$233$	−597.717	−0.168059	−0.0840295	+	0.996463i	$0.526779\pi$
$234$	4594.97	1.28369
$235$	676.316	0.187736
$236$	6016.79	1.65957
$237$	297.803	0.0816219
$238$	729.470	0.198675
$239$	4645.92	1.25740	0.628702	−	0.777646i	$-0.283586\pi$
$239$	4645.92	1.25740	0.628702	+	0.777646i	$0.283586\pi$
$240$	1082.48	0.291140
$241$	2153.63	0.575633	0.287816	−	0.957686i	$-0.407071\pi$
$241$	2153.63	0.575633	0.287816	+	0.957686i	$0.407071\pi$
$242$	−530.049	−0.140797
$243$	−5421.52	−1.43124
$244$	9295.31	2.43882
$245$	1220.43	0.318247
$246$	−7124.06	−1.84640
$247$	633.264	0.163132
$248$	−1346.96	−0.344888
$249$	−384.327	−0.0978142
$250$	547.572	0.138526
$251$	6033.88	1.51735	0.758676	−	0.651468i	$-0.225847\pi$
$251$	6033.88	1.51735	0.758676	+	0.651468i	$0.225847\pi$
$252$	3502.32	0.875498
$253$	−2094.28	−0.520420
$254$	7301.14	1.80360
$255$	640.165	0.157211
$256$	−760.027	−0.185554
$257$	−5445.66	−1.32175	−0.660877	−	0.750494i	$-0.729815\pi$
$257$	−5445.66	−1.32175	−0.660877	+	0.750494i	$0.729815\pi$
$258$	−6331.38	−1.52781
$259$	199.986	0.0479789
$260$	1864.70	0.444784
$261$	−6236.87	−1.47913
$262$	−6777.30	−1.59810
$263$	3049.91	0.715079	0.357540	−	0.933898i	$-0.383616\pi$
$263$	3049.91	0.715079	0.357540	+	0.933898i	$0.383616\pi$
$264$	1175.19	0.273969
$265$	−2202.05	−0.510455
$266$	827.775	0.190805
$267$	4944.11	1.13324
$268$	2960.05	0.674679
$269$	3984.51	0.903123	0.451561	−	0.892240i	$-0.350867\pi$
$269$	3984.51	0.903123	0.451561	+	0.892240i	$0.350867\pi$
$270$	748.945	0.168812
$271$	2717.85	0.609217	0.304608	−	0.952478i	$-0.401474\pi$
$271$	2717.85	0.609217	0.304608	+	0.952478i	$0.401474\pi$
$272$	474.050	0.105675
$273$	−2534.73	−0.561938
$274$	−4202.62	−0.926605
$275$	−275.000	−0.0603023
$276$	16290.0	3.55270
$277$	−2299.91	−0.498875	−0.249438	−	0.968391i	$-0.580246\pi$
$277$	−2299.91	−0.498875	−0.249438	+	0.968391i	$0.580246\pi$
$278$	12520.1	2.70110
$279$	3034.14	0.651071
$280$	694.768	0.148287
$281$	3082.85	0.654474	0.327237	−	0.944942i	$-0.393882\pi$
$281$	3082.85	0.654474	0.327237	+	0.944942i	$0.393882\pi$
$282$	4530.89	0.956776
$283$	−6299.01	−1.32310	−0.661550	−	0.749901i	$-0.730101\pi$
$283$	−6299.01	−1.32310	−0.661550	+	0.749901i	$0.730101\pi$
$284$	4589.75	0.958985
$285$	726.435	0.150983
$286$	−1606.03	−0.332052
$287$	2115.20	0.435040
$288$	7420.90	1.51834
$289$	−4632.65	−0.942937
$290$	−4340.57	−0.878921
$291$	−5398.76	−1.08756
$292$	5726.48	1.14766
$293$	4522.93	0.901817	0.450908	−	0.892570i	$-0.351100\pi$
$293$	4522.93	0.901817	0.450908	+	0.892570i	$0.351100\pi$
$294$	8176.12	1.62191
$295$	−2688.61	−0.530633
$296$	−280.940	−0.0551667
$297$	−376.133	−0.0734864
$298$	−8530.96	−1.65834
$299$	−6345.61	−1.22734
$300$	2139.05	0.411660
$301$	1879.85	0.359975
$302$	7296.32	1.39025
$303$	−8843.68	−1.67675
$304$	537.934	0.101489
$305$	−4153.62	−0.779788
$306$	2308.34	0.431239
$307$	5455.02	1.01412	0.507060	−	0.861911i	$-0.330732\pi$
$307$	5455.02	1.01412	0.507060	+	0.861911i	$0.330732\pi$
$308$	−1224.13	−0.226465
$309$	9286.04	1.70959
$310$	2111.62	0.386877
$311$	−916.121	−0.167037	−0.0835184	−	0.996506i	$-0.526616\pi$
$311$	−916.121	−0.167037	−0.0835184	+	0.996506i	$0.526616\pi$
$312$	3560.79	0.646122
$313$	−7300.31	−1.31833	−0.659166	−	0.751997i	$-0.729091\pi$
$313$	−7300.31	−1.31833	−0.659166	+	0.751997i	$0.729091\pi$
$314$	−13653.9	−2.45394
$315$	−1565.02	−0.279932
$316$	435.776	0.0775770
$317$	9226.45	1.63473	0.817364	−	0.576121i	$-0.195434\pi$
$317$	9226.45	1.63473	0.817364	+	0.576121i	$0.195434\pi$
$318$	−14752.3	−2.60148
$319$	2179.91	0.382607
$320$	4032.11	0.704381
$321$	4625.52	0.804272
$322$	−8294.70	−1.43555
$323$	318.128	0.0548023
$324$	−6582.36	−1.12866
$325$	−833.242	−0.142215
$326$	4056.57	0.689180
$327$	−13065.5	−2.20956
$328$	−2971.43	−0.500213
$329$	−1345.26	−0.225431
$330$	−1842.33	−0.307323
$331$	9726.10	1.61509	0.807545	−	0.589806i	$-0.200796\pi$
$331$	9726.10	1.61509	0.807545	+	0.589806i	$0.200796\pi$
$332$	−562.387	−0.0929669
$333$	632.839	0.104142
$334$	4782.31	0.783462
$335$	−1322.70	−0.215722
$336$	−2153.16	−0.349597
$337$	5525.57	0.893166	0.446583	−	0.894742i	$-0.352641\pi$
$337$	5525.57	0.893166	0.446583	+	0.894742i	$0.352641\pi$
$338$	4757.88	0.765664
$339$	13435.6	2.15257
$340$	936.756	0.149420
$341$	−1060.49	−0.168413
$342$	2619.42	0.414158
$343$	−5838.89	−0.919155
$344$	−2640.80	−0.413903
$345$	−7279.22	−1.13594
$346$	−1333.91	−0.207259
$347$	−7968.44	−1.23276	−0.616381	−	0.787448i	$-0.711402\pi$
$347$	−7968.44	−1.23276	−0.616381	+	0.787448i	$0.711402\pi$
$348$	−16956.1	−2.61191
$349$	2268.68	0.347965	0.173983	−	0.984749i	$-0.444336\pi$
$349$	2268.68	0.347965	0.173983	+	0.984749i	$0.444336\pi$
$350$	−1089.18	−0.166340
$351$	−1139.67	−0.173308
$352$	−2593.75	−0.392749
$353$	8082.15	1.21861	0.609305	−	0.792936i	$-0.291448\pi$
$353$	8082.15	1.21861	0.609305	+	0.792936i	$0.291448\pi$
$354$	−18012.0	−2.70431
$355$	−2050.93	−0.306626
$356$	7234.73	1.07708
$357$	−1273.36	−0.188776
$358$	−11261.1	−1.66247
$359$	−952.986	−0.140102	−0.0700511	−	0.997543i	$-0.522316\pi$
$359$	−952.986	−0.140102	−0.0700511	+	0.997543i	$0.522316\pi$
$360$	2198.53	0.321869
$361$	361.000	0.0526316
$362$	5568.27	0.808457
$363$	925.248	0.133782
$364$	−3709.08	−0.534090
$365$	−2558.88	−0.366954
$366$	−27826.6	−3.97410
$367$	−2951.54	−0.419807	−0.209904	−	0.977722i	$-0.567315\pi$
$367$	−2951.54	−0.419807	−0.209904	+	0.977722i	$0.567315\pi$
$368$	−5390.35	−0.763564
$369$	6693.36	0.944289
$370$	440.426	0.0618829
$371$	4380.10	0.612948
$372$	8248.87	1.14969
$373$	−1336.46	−0.185521	−0.0927607	−	0.995688i	$-0.529569\pi$
$373$	−1336.46	−0.185521	−0.0927607	+	0.995688i	$0.529569\pi$
$374$	−806.812	−0.111549
$375$	−955.835	−0.131624
$376$	1889.83	0.259203
$377$	6605.07	0.902330
$378$	−1489.73	−0.202708
$379$	−2813.57	−0.381328	−0.190664	−	0.981655i	$-0.561064\pi$
$379$	−2813.57	−0.381328	−0.190664	+	0.981655i	$0.561064\pi$
$380$	1062.99	0.143501
$381$	−12744.8	−1.71374
$382$	−13674.0	−1.83147
$383$	−1222.18	−0.163055	−0.0815277	−	0.996671i	$-0.525980\pi$
$383$	−1222.18	−0.163055	−0.0815277	+	0.996671i	$0.525980\pi$
$384$	12588.2	1.67288
$385$	547.004	0.0724102
$386$	−5217.82	−0.688032
$387$	5948.60	0.781355
$388$	−7900.02	−1.03367
$389$	2576.99	0.335883	0.167941	−	0.985797i	$-0.446288\pi$
$389$	2576.99	0.335883	0.167941	+	0.985797i	$0.446288\pi$
$390$	−5582.20	−0.724784
$391$	−3187.80	−0.412312
$392$	3410.24	0.439396
$393$	11830.4	1.51848
$394$	13129.9	1.67887
$395$	−194.727	−0.0248045
$396$	−3873.65	−0.491562
$397$	5182.66	0.655189	0.327595	−	0.944818i	$-0.393762\pi$
$397$	5182.66	0.655189	0.327595	+	0.944818i	$0.393762\pi$
$398$	−22329.6	−2.81226
$399$	−1444.96	−0.181299
$400$	−707.808	−0.0884760
$401$	−5750.98	−0.716185	−0.358092	−	0.933686i	$-0.616573\pi$
$401$	−5750.98	−0.716185	−0.358092	+	0.933686i	$0.616573\pi$
$402$	−8861.26	−1.09940
$403$	−3213.26	−0.397181
$404$	−12941.0	−1.59366
$405$	2941.33	0.360879
$406$	8633.86	1.05540
$407$	−221.190	−0.0269385
$408$	1788.81	0.217057
$409$	1277.53	0.154450	0.0772250	−	0.997014i	$-0.475394\pi$
$409$	1277.53	0.154450	0.0772250	+	0.997014i	$0.475394\pi$
$410$	4658.27	0.561111
$411$	7336.05	0.880440
$412$	13588.3	1.62487
$413$	5347.92	0.637177
$414$	−26247.8	−3.11597
$415$	251.303	0.0297253
$416$	−7859.00	−0.926248
$417$	−21855.0	−2.56653
$418$	−915.540	−0.107130
$419$	7463.43	0.870196	0.435098	−	0.900383i	$-0.356714\pi$
$419$	7463.43	0.870196	0.435098	+	0.900383i	$0.356714\pi$
$420$	−4254.79	−0.494316
$421$	60.1072	0.00695830	0.00347915	−	0.999994i	$-0.498893\pi$
$421$	60.1072	0.00695830	0.00347915	+	0.999994i	$0.498893\pi$
$422$	−12847.9	−1.48205
$423$	−4256.97	−0.489317
$424$	−6153.16	−0.704774
$425$	−418.590	−0.0477755
$426$	−13740.0	−1.56268
$427$	8261.99	0.936360
$428$	6768.54	0.764415
$429$	2803.48	0.315509
$430$	4139.95	0.464293
$431$	−9189.17	−1.02698	−0.513488	−	0.858097i	$-0.671647\pi$
$431$	−9189.17	−1.02698	−0.513488	+	0.858097i	$0.671647\pi$
$432$	−968.109	−0.107820
$433$	−769.069	−0.0853559	−0.0426780	−	0.999089i	$-0.513589\pi$
$433$	−769.069	−0.0853559	−0.0426780	+	0.999089i	$0.513589\pi$
$434$	−4200.23	−0.464556
$435$	7576.86	0.835132
$436$	−19118.8	−2.10006
$437$	−3617.39	−0.395980
$438$	−17142.9	−1.87014
$439$	−11673.3	−1.26910	−0.634549	−	0.772883i	$-0.718814\pi$
$439$	−11673.3	−1.26910	−0.634549	+	0.772883i	$0.718814\pi$
$440$	−768.430	−0.0832579
$441$	−7681.82	−0.829481
$442$	−2444.62	−0.263074
$443$	7255.70	0.778169	0.389084	−	0.921202i	$-0.372791\pi$
$443$	7255.70	0.778169	0.389084	+	0.921202i	$0.372791\pi$
$444$	1720.49	0.183899
$445$	−3232.85	−0.344386
$446$	17008.9	1.80582
$447$	14891.5	1.57572
$448$	−8020.30	−0.845811
$449$	11867.6	1.24737	0.623684	−	0.781677i	$-0.285635\pi$
$449$	11867.6	1.24737	0.623684	+	0.781677i	$0.285635\pi$
$450$	−3446.61	−0.361054
$451$	−2339.46	−0.244260
$452$	19660.3	2.04589
$453$	−12736.4	−1.32099
$454$	−1373.61	−0.141998
$455$	1657.41	0.170770
$456$	2029.87	0.208459
$457$	3798.04	0.388764	0.194382	−	0.980926i	$-0.437730\pi$
$457$	3798.04	0.388764	0.194382	+	0.980926i	$0.437730\pi$
$458$	−24123.5	−2.46118
$459$	−572.529	−0.0582209
$460$	−10651.7	−1.07965
$461$	−583.597	−0.0589605	−0.0294803	−	0.999565i	$-0.509385\pi$
$461$	−583.597	−0.0589605	−0.0294803	+	0.999565i	$0.509385\pi$
$462$	3664.58	0.369030
$463$	−7229.62	−0.725678	−0.362839	−	0.931852i	$-0.618193\pi$
$463$	−7229.62	−0.725678	−0.362839	+	0.931852i	$0.618193\pi$
$464$	5610.76	0.561364
$465$	−3686.02	−0.367602
$466$	2618.34	0.260284
$467$	−8308.28	−0.823257	−0.411629	−	0.911352i	$-0.635040\pi$
$467$	−8308.28	−0.823257	−0.411629	+	0.911352i	$0.635040\pi$
$468$	−11737.1	−1.15929
$469$	2630.99	0.259036
$470$	−2962.65	−0.290760
$471$	23834.2	2.33168
$472$	−7512.75	−0.732632
$473$	−2079.16	−0.202114
$474$	−1304.55	−0.126413
$475$	−475.000	−0.0458831
$476$	−1863.31	−0.179421
$477$	13860.4	1.33045
$478$	−20351.8	−1.94743
$479$	−6815.52	−0.650123	−0.325062	−	0.945693i	$-0.605385\pi$
$479$	−6815.52	−0.650123	−0.325062	+	0.945693i	$0.605385\pi$
$480$	−9015.28	−0.857269
$481$	−670.199	−0.0635311
$482$	−9434.13	−0.891520
$483$	14479.1	1.36402
$484$	1353.92	0.127152
$485$	3530.13	0.330505
$486$	23749.4	2.21665
$487$	−11584.9	−1.07795	−0.538975	−	0.842322i	$-0.681188\pi$
$487$	−11584.9	−1.07795	−0.538975	+	0.842322i	$0.681188\pi$
$488$	−11606.4	−1.07664
$489$	−7081.11	−0.654844
$490$	−5346.19	−0.492890
$491$	−19180.5	−1.76294	−0.881471	−	0.472238i	$-0.843446\pi$
$491$	−19180.5	−1.76294	−0.881471	+	0.472238i	$0.843446\pi$
$492$	18197.2	1.66746
$493$	3318.14	0.303127
$494$	−2774.06	−0.252654
$495$	1730.95	0.157172
$496$	−2729.54	−0.247097
$497$	4079.53	0.368193
$498$	1683.57	0.151491
$499$	−3992.85	−0.358206	−0.179103	−	0.983830i	$-0.557319\pi$
$499$	−3992.85	−0.358206	−0.179103	+	0.983830i	$0.557319\pi$
$500$	−1398.68	−0.125101
$501$	−8347.95	−0.744429
$502$	−26431.9	−2.35002
$503$	−16018.0	−1.41990	−0.709949	−	0.704253i	$-0.751282\pi$
$503$	−16018.0	−1.41990	−0.709949	+	0.704253i	$0.751282\pi$
$504$	−4373.11	−0.386496
$505$	5782.69	0.509557
$506$	9174.14	0.806009
$507$	−8305.30	−0.727517
$508$	−18649.5	−1.62881
$509$	10605.5	0.923541	0.461770	−	0.886999i	$-0.347214\pi$
$509$	10605.5	0.923541	0.461770	+	0.886999i	$0.347214\pi$
$510$	−2804.29	−0.243482
$511$	5089.89	0.440633
$512$	−9840.44	−0.849395
$513$	−649.684	−0.0559147
$514$	23855.1	2.04709
$515$	−6071.94	−0.519537
$516$	16172.4	1.37975
$517$	1487.90	0.126572
$518$	−876.055	−0.0743082
$519$	2328.46	0.196933
$520$	−2328.32	−0.196353
$521$	−10575.7	−0.889312	−0.444656	−	0.895701i	$-0.646674\pi$
$521$	−10575.7	−0.889312	−0.444656	+	0.895701i	$0.646674\pi$
$522$	27321.1	2.29082
$523$	708.353	0.0592239	0.0296120	−	0.999561i	$-0.490573\pi$
$523$	708.353	0.0592239	0.0296120	+	0.999561i	$0.490573\pi$
$524$	17311.5	1.44323
$525$	1901.26	0.158053
$526$	−13360.4	−1.10749
$527$	−1614.22	−0.133428
$528$	2381.45	0.196286
$529$	24081.0	1.97921
$530$	9646.23	0.790576
$531$	16923.0	1.38304
$532$	−2114.41	−0.172314
$533$	−7088.51	−0.576056
$534$	−21658.0	−1.75512
$535$	−3024.53	−0.244415
$536$	−3696.01	−0.297842
$537$	19657.2	1.57965
$538$	−17454.4	−1.39873
$539$	2684.95	0.214562
$540$	−1913.05	−0.152453
$541$	18460.7	1.46708	0.733539	−	0.679648i	$-0.237867\pi$
$541$	18460.7	1.46708	0.733539	+	0.679648i	$0.237867\pi$
$542$	−11905.7	−0.943534
$543$	−9719.91	−0.768179
$544$	−3948.07	−0.311162
$545$	8543.27	0.671475
$546$	11103.6	0.870310
$547$	−11513.7	−0.899985	−0.449993	−	0.893032i	$-0.648573\pi$
$547$	−11513.7	−0.899985	−0.449993	+	0.893032i	$0.648573\pi$
$548$	10734.9	0.836808
$549$	26144.3	2.03244
$550$	1204.66	0.0933941
$551$	3765.30	0.291120
$552$	−20340.3	−1.56837
$553$	387.333	0.0297849
$554$	10074.9	0.772641
$555$	−768.804	−0.0587998
$556$	−31980.5	−2.43934
$557$	15473.4	1.17707	0.588535	−	0.808472i	$-0.299705\pi$
$557$	15473.4	1.17707	0.588535	+	0.808472i	$0.299705\pi$
$558$	−13291.2	−1.00836
$559$	−6299.79	−0.476659
$560$	1407.90	0.106241
$561$	1408.36	0.105991
$562$	−13504.6	−1.01363
$563$	−11476.6	−0.859112	−0.429556	−	0.903040i	$-0.641330\pi$
$563$	−11476.6	−0.859112	−0.429556	+	0.903040i	$0.641330\pi$
$564$	−11573.4	−0.864055
$565$	−8785.24	−0.654155
$566$	27593.3	2.04917
$567$	−5850.63	−0.433339
$568$	−5730.91	−0.423352
$569$	23742.8	1.74930	0.874649	−	0.484757i	$-0.161092\pi$
$569$	23742.8	1.74930	0.874649	+	0.484757i	$0.161092\pi$
$570$	−3182.20	−0.233838
$571$	16624.1	1.21838	0.609191	−	0.793023i	$-0.291494\pi$
$571$	16624.1	1.21838	0.609191	+	0.793023i	$0.291494\pi$
$572$	4102.34	0.299873
$573$	23869.2	1.74022
$574$	−9265.79	−0.673775
$575$	4759.73	0.345208
$576$	−25379.5	−1.83590
$577$	−8409.71	−0.606761	−0.303380	−	0.952870i	$-0.598115\pi$
$577$	−8409.71	−0.606761	−0.303380	+	0.952870i	$0.598115\pi$
$578$	20293.7	1.46039
$579$	9108.18	0.653753
$580$	11087.2	0.793746
$581$	−499.869	−0.0356937
$582$	23649.6	1.68438
$583$	−4844.50	−0.344149
$584$	−7150.27	−0.506644
$585$	5244.72	0.370671
$586$	−19813.0	−1.39670
$587$	965.789	0.0679086	0.0339543	−	0.999423i	$-0.489190\pi$
$587$	965.789	0.0679086	0.0339543	+	0.999423i	$0.489190\pi$
$588$	−20884.5	−1.46473
$589$	−1831.76	−0.128143
$590$	11777.6	0.821826
$591$	−22919.5	−1.59523
$592$	−569.309	−0.0395244
$593$	−11473.1	−0.794509	−0.397255	−	0.917708i	$-0.630037\pi$
$593$	−11473.1	−0.794509	−0.397255	+	0.917708i	$0.630037\pi$
$594$	1647.68	0.113813
$595$	832.620	0.0573682
$596$	21790.9	1.49763
$597$	38978.2	2.67215
$598$	27797.4	1.90087
$599$	−23706.2	−1.61704	−0.808521	−	0.588467i	$-0.799732\pi$
$599$	−23706.2	−1.61704	−0.808521	+	0.588467i	$0.799732\pi$
$600$	−2670.88	−0.181731
$601$	6573.58	0.446159	0.223080	−	0.974800i	$-0.428389\pi$
$601$	6573.58	0.446159	0.223080	+	0.974800i	$0.428389\pi$
$602$	−8234.80	−0.557517
$603$	8325.54	0.562259
$604$	−18637.2	−1.25552
$605$	−605.000	−0.0406558
$606$	38740.4	2.59690
$607$	−24566.4	−1.64270	−0.821352	−	0.570422i	$-0.806780\pi$
$607$	−24566.4	−1.64270	−0.821352	+	0.570422i	$0.806780\pi$
$608$	−4480.12	−0.298837
$609$	−15071.2	−1.00282
$610$	18195.2	1.20771
$611$	4508.28	0.298503
$612$	−5896.26	−0.389448
$613$	−16573.4	−1.09199	−0.545996	−	0.837788i	$-0.683849\pi$
$613$	−16573.4	−1.09199	−0.545996	+	0.837788i	$0.683849\pi$
$614$	−23896.1	−1.57063
$615$	−8131.43	−0.533156
$616$	1528.49	0.0999750
$617$	−20542.8	−1.34039	−0.670195	−	0.742185i	$-0.733790\pi$
$617$	−20542.8	−1.34039	−0.670195	+	0.742185i	$0.733790\pi$
$618$	−40678.2	−2.64776
$619$	16603.5	1.07811	0.539056	−	0.842270i	$-0.318781\pi$
$619$	16603.5	1.07811	0.539056	+	0.842270i	$0.318781\pi$
$620$	−5393.76	−0.349385
$621$	6510.15	0.420681
$622$	4013.13	0.258701
$623$	6430.47	0.413534
$624$	7215.72	0.462917
$625$	625.000	0.0400000
$626$	31979.6	2.04179
$627$	1598.16	0.101793
$628$	34876.6	2.21613
$629$	−336.683	−0.0213425
$630$	6855.66	0.433549
$631$	−747.368	−0.0471509	−0.0235755	−	0.999722i	$-0.507505\pi$
$631$	−747.368	−0.0471509	−0.0235755	+	0.999722i	$0.507505\pi$
$632$	−544.124	−0.0342470
$633$	22427.1	1.40821
$634$	−40417.1	−2.53181
$635$	8333.54	0.520798
$636$	37682.3	2.34937
$637$	8135.33	0.506018
$638$	−9549.26	−0.592568
$639$	12909.3	0.799192
$640$	−8231.12	−0.508381
$641$	−13240.5	−0.815864	−0.407932	−	0.913012i	$-0.633750\pi$
$641$	−13240.5	−0.815864	−0.407932	+	0.913012i	$0.633750\pi$
$642$	−20262.4	−1.24563
$643$	3227.13	0.197925	0.0989623	−	0.995091i	$-0.468448\pi$
$643$	3227.13	0.197925	0.0989623	+	0.995091i	$0.468448\pi$
$644$	21187.4	1.29643
$645$	−7226.66	−0.441162
$646$	−1393.58	−0.0848759
$647$	−4518.96	−0.274588	−0.137294	−	0.990530i	$-0.543841\pi$
$647$	−4518.96	−0.274588	−0.137294	+	0.990530i	$0.543841\pi$
$648$	8218.95	0.498257
$649$	−5914.93	−0.357753
$650$	3650.08	0.220258
$651$	7331.88	0.441412
$652$	−10361.8	−0.622392
$653$	−133.161	−0.00798008	−0.00399004	−	0.999992i	$-0.501270\pi$
$653$	−133.161	−0.00798008	−0.00399004	+	0.999992i	$0.501270\pi$
$654$	57234.5	3.42209
$655$	−7735.64	−0.461460
$656$	−6021.42	−0.358380
$657$	16106.5	0.956430
$658$	5893.03	0.349140
$659$	13733.0	0.811776	0.405888	−	0.913923i	$-0.366962\pi$
$659$	13733.0	0.811776	0.405888	+	0.913923i	$0.366962\pi$
$660$	4705.90	0.277541
$661$	−17445.8	−1.02657	−0.513284	−	0.858219i	$-0.671571\pi$
$661$	−17445.8	−1.02657	−0.513284	+	0.858219i	$0.671571\pi$
$662$	−42605.9	−2.50140
$663$	4267.30	0.249967
$664$	702.215	0.0410410
$665$	944.825	0.0550959
$666$	−2772.20	−0.161292
$667$	−37730.1	−2.19028
$668$	−12215.6	−0.707538
$669$	−29690.6	−1.71585
$670$	5794.19	0.334103
$671$	−9137.96	−0.525733
$672$	17932.3	1.02940
$673$	−1251.21	−0.0716653	−0.0358327	−	0.999358i	$-0.511408\pi$
$673$	−1251.21	−0.0716653	−0.0358327	+	0.999358i	$0.511408\pi$
$674$	−24205.1	−1.38330
$675$	854.848	0.0487453
$676$	−12153.2	−0.691464
$677$	−29234.3	−1.65962	−0.829812	−	0.558043i	$-0.811552\pi$
$677$	−29234.3	−1.65962	−0.829812	+	0.558043i	$0.811552\pi$
$678$	−58855.5	−3.33382
$679$	−7021.81	−0.396866
$680$	−1169.66	−0.0659625
$681$	2397.77	0.134923
$682$	4645.56	0.260832
$683$	−3211.90	−0.179941	−0.0899706	−	0.995944i	$-0.528677\pi$
$683$	−3211.90	−0.179941	−0.0899706	+	0.995944i	$0.528677\pi$
$684$	−6690.86	−0.374022
$685$	−4796.89	−0.267561
$686$	25577.7	1.42356
$687$	42109.8	2.33856
$688$	−5351.43	−0.296543
$689$	−14678.7	−0.811632
$690$	31887.2	1.75931
$691$	−31274.1	−1.72174	−0.860869	−	0.508826i	$-0.830080\pi$
$691$	−31274.1	−1.72174	−0.860869	+	0.508826i	$0.830080\pi$
$692$	3407.25	0.187174
$693$	−3443.03	−0.188730
$694$	34906.3	1.90926
$695$	14290.5	0.779956
$696$	21172.0	1.15305
$697$	−3561.01	−0.193519
$698$	−9938.14	−0.538917
$699$	−4570.55	−0.247316
$700$	2782.12	0.150220
$701$	8291.33	0.446732	0.223366	−	0.974735i	$-0.428295\pi$
$701$	8291.33	0.446732	0.223366	+	0.974735i	$0.428295\pi$
$702$	4992.42	0.268414
$703$	−382.055	−0.0204971
$704$	8870.65	0.474893
$705$	5171.58	0.276273
$706$	−35404.5	−1.88734
$707$	−11502.4	−0.611870
$708$	46008.4	2.44224
$709$	−28125.1	−1.48979	−0.744895	−	0.667181i	$-0.767501\pi$
$709$	−28125.1	−1.48979	−0.744895	+	0.667181i	$0.767501\pi$
$710$	8984.27	0.474892
$711$	1225.68	0.0646506
$712$	−9033.52	−0.475485
$713$	18355.1	0.964100
$714$	5578.03	0.292370
$715$	−1833.13	−0.0958815
$716$	28764.4	1.50136
$717$	35525.9	1.85040
$718$	4174.63	0.216986
$719$	−16888.3	−0.875979	−0.437989	−	0.898980i	$-0.644309\pi$
$719$	−16888.3	−0.875979	−0.437989	+	0.898980i	$0.644309\pi$
$720$	4455.19	0.230604
$721$	12077.7	0.623853
$722$	−1581.39	−0.0815140
$723$	16468.1	0.847103
$724$	−14223.2	−0.730111
$725$	−4954.34	−0.253793
$726$	−4053.12	−0.207197
$727$	−31239.2	−1.59367	−0.796835	−	0.604196i	$-0.793494\pi$
$727$	−31239.2	−1.59367	−0.796835	+	0.604196i	$0.793494\pi$
$728$	4631.28	0.235778
$729$	−25573.5	−1.29927
$730$	11209.4	0.568325
$731$	−3164.78	−0.160128
$732$	71078.3	3.58897
$733$	20043.9	1.01001	0.505007	−	0.863115i	$-0.331490\pi$
$733$	20043.9	1.01001	0.505007	+	0.863115i	$0.331490\pi$
$734$	12929.4	0.650183
$735$	9332.26	0.468334
$736$	44893.0	2.24834
$737$	−2909.94	−0.145440
$738$	−29320.8	−1.46248
$739$	31481.7	1.56708	0.783541	−	0.621340i	$-0.213411\pi$
$739$	31481.7	1.56708	0.783541	+	0.621340i	$0.213411\pi$
$740$	−1124.99	−0.0558859
$741$	4842.37	0.240066
$742$	−19187.4	−0.949313
$743$	10820.2	0.534259	0.267129	−	0.963661i	$-0.413925\pi$
$743$	10820.2	0.534259	0.267129	+	0.963661i	$0.413925\pi$
$744$	−10299.8	−0.507539
$745$	−9737.26	−0.478853
$746$	5854.47	0.287329
$747$	−1581.79	−0.0774761
$748$	2060.86	0.100739
$749$	6016.11	0.293490
$750$	4187.11	0.203855
$751$	14559.3	0.707425	0.353712	−	0.935354i	$-0.384919\pi$
$751$	14559.3	0.707425	0.353712	+	0.935354i	$0.384919\pi$
$752$	3829.62	0.185707
$753$	46139.2	2.23294
$754$	−28934.0	−1.39750
$755$	8328.04	0.401442
$756$	3805.26	0.183063
$757$	12939.6	0.621264	0.310632	−	0.950530i	$-0.399459\pi$
$757$	12939.6	0.621264	0.310632	+	0.950530i	$0.399459\pi$
$758$	12325.1	0.590589
$759$	−16014.3	−0.765852
$760$	−1327.29	−0.0633498
$761$	−1592.60	−0.0758629	−0.0379314	−	0.999280i	$-0.512077\pi$
$761$	−1592.60	−0.0758629	−0.0379314	+	0.999280i	$0.512077\pi$
$762$	55829.5	2.65418
$763$	−16993.5	−0.806298
$764$	34927.8	1.65398
$765$	2634.75	0.124522
$766$	5353.83	0.252535
$767$	−17922.1	−0.843715
$768$	−5811.69	−0.273061
$769$	17663.5	0.828297	0.414149	−	0.910209i	$-0.364079\pi$
$769$	17663.5	0.828297	0.414149	+	0.910209i	$0.364079\pi$
$770$	−2396.19	−0.112146
$771$	−41641.2	−1.94510
$772$	13328.0	0.621355
$773$	4390.93	0.204309	0.102154	−	0.994769i	$-0.467426\pi$
$773$	4390.93	0.204309	0.102154	+	0.994769i	$0.467426\pi$
$774$	−26058.3	−1.21014
$775$	2410.21	0.111712
$776$	9864.22	0.456321
$777$	1529.23	0.0706060
$778$	−11288.7	−0.520204
$779$	−4040.89	−0.185854
$780$	14258.8	0.654545
$781$	−4512.06	−0.206727
$782$	13964.4	0.638575
$783$	−6776.33	−0.309280
$784$	6910.65	0.314807
$785$	−15584.6	−0.708586
$786$	−51823.9	−2.35178
$787$	25145.4	1.13893	0.569465	−	0.822016i	$-0.307150\pi$
$787$	25145.4	1.13893	0.569465	+	0.822016i	$0.307150\pi$
$788$	−33538.1	−1.51617
$789$	23321.7	1.05231
$790$	853.016	0.0384164
$791$	17474.8	0.785501
$792$	4836.77	0.217004
$793$	−27687.8	−1.23988
$794$	−22703.0	−1.01473
$795$	−16838.3	−0.751188
$796$	57037.0	2.53973
$797$	34987.1	1.55497	0.777483	−	0.628905i	$-0.216496\pi$
$797$	34987.1	1.55497	0.777483	+	0.628905i	$0.216496\pi$
$798$	6329.73	0.280790
$799$	2264.79	0.100279
$800$	5894.90	0.260520
$801$	20348.7	0.897608
$802$	25192.6	1.10920
$803$	−5629.54	−0.247400
$804$	22634.6	0.992860
$805$	−9467.60	−0.414521
$806$	14075.9	0.615140
$807$	30468.3	1.32904
$808$	16158.5	0.703534
$809$	−12785.3	−0.555632	−0.277816	−	0.960634i	$-0.589611\pi$
$809$	−12785.3	−0.555632	−0.277816	+	0.960634i	$0.589611\pi$
$810$	−12884.7	−0.558918
$811$	−4873.59	−0.211017	−0.105509	−	0.994418i	$-0.533647\pi$
$811$	−4873.59	−0.211017	−0.105509	+	0.994418i	$0.533647\pi$
$812$	−22053.7	−0.953119
$813$	20782.5	0.896526
$814$	968.938	0.0417214
$815$	4630.18	0.199004
$816$	3624.91	0.155511
$817$	−3591.27	−0.153785
$818$	−5596.33	−0.239207
$819$	−10432.3	−0.445096
$820$	−11898.7	−0.506734
$821$	−32748.1	−1.39210	−0.696050	−	0.717993i	$-0.745061\pi$
$821$	−32748.1	−1.39210	−0.696050	+	0.717993i	$0.745061\pi$
$822$	−32136.1	−1.36360
$823$	−31545.2	−1.33608	−0.668042	−	0.744124i	$-0.732867\pi$
$823$	−31545.2	−1.33608	−0.668042	+	0.744124i	$0.732867\pi$
$824$	−16966.8	−0.717313
$825$	−2102.84	−0.0887411
$826$	−23427.0	−0.986838
$827$	17041.8	0.716570	0.358285	−	0.933612i	$-0.383362\pi$
$827$	17041.8	0.716570	0.358285	+	0.933612i	$0.383362\pi$
$828$	67045.6	2.81400
$829$	−22891.8	−0.959067	−0.479533	−	0.877524i	$-0.659194\pi$
$829$	−22891.8	−0.959067	−0.479533	+	0.877524i	$0.659194\pi$
$830$	−1100.85	−0.0460375
$831$	−17586.7	−0.734147
$832$	26877.8	1.11998
$833$	4086.89	0.169991
$834$	95737.3	3.97496
$835$	5458.55	0.226228
$836$	2338.59	0.0967485
$837$	3296.58	0.136137
$838$	−32694.1	−1.34773
$839$	18230.5	0.750161	0.375081	−	0.926992i	$-0.377615\pi$
$839$	18230.5	0.750161	0.375081	+	0.926992i	$0.377615\pi$
$840$	5312.67	0.218220
$841$	14883.8	0.610267
$842$	−263.304	−0.0107768
$843$	23573.6	0.963127
$844$	32817.6	1.33842
$845$	5430.66	0.221089
$846$	18648.0	0.757837
$847$	1203.41	0.0488189
$848$	−12469.0	−0.504938
$849$	−48166.5	−1.94708
$850$	1833.66	0.0739931
$851$	3828.37	0.154213
$852$	35096.4	1.41125
$853$	16189.4	0.649840	0.324920	−	0.945742i	$-0.394663\pi$
$853$	16189.4	0.649840	0.324920	+	0.945742i	$0.394663\pi$
$854$	−36192.2	−1.45020
$855$	2989.81	0.119590
$856$	−8451.42	−0.337457
$857$	−19759.1	−0.787582	−0.393791	−	0.919200i	$-0.628837\pi$
$857$	−19759.1	−0.787582	−0.393791	+	0.919200i	$0.628837\pi$
$858$	−12280.8	−0.488649
$859$	−27664.4	−1.09883	−0.549415	−	0.835549i	$-0.685149\pi$
$859$	−27664.4	−1.09883	−0.549415	+	0.835549i	$0.685149\pi$
$860$	−10574.8	−0.419299
$861$	16174.3	0.640206
$862$	40253.8	1.59055
$863$	34842.1	1.37432	0.687160	−	0.726506i	$-0.258857\pi$
$863$	34842.1	1.37432	0.687160	+	0.726506i	$0.258857\pi$
$864$	8062.78	0.317478
$865$	−1522.53	−0.0598470
$866$	3368.96	0.132196
$867$	−35424.4	−1.38763
$868$	10728.8	0.419537
$869$	−428.400	−0.0167232
$870$	−33191.0	−1.29342
$871$	−8817.05	−0.343001
$872$	23872.4	0.927089
$873$	−22219.9	−0.861430
$874$	15846.2	0.613281
$875$	−1243.19	−0.0480315
$876$	43788.6	1.68890
$877$	−5628.05	−0.216700	−0.108350	−	0.994113i	$-0.534557\pi$
$877$	−5628.05	−0.216700	−0.108350	+	0.994113i	$0.534557\pi$
$878$	51135.5	1.96554
$879$	34585.4	1.32712
$880$	−1557.18	−0.0596505
$881$	−40489.0	−1.54836	−0.774182	−	0.632963i	$-0.781839\pi$
$881$	−40489.0	−1.54836	−0.774182	+	0.632963i	$0.781839\pi$
$882$	33650.8	1.28467
$883$	46650.7	1.77794	0.888971	−	0.457964i	$-0.151421\pi$
$883$	46650.7	1.77794	0.888971	+	0.457964i	$0.151421\pi$
$884$	6244.36	0.237580
$885$	−20558.9	−0.780882
$886$	−31784.1	−1.20520
$887$	−22381.0	−0.847215	−0.423607	−	0.905846i	$-0.639236\pi$
$887$	−22381.0	−0.847215	−0.423607	+	0.905846i	$0.639236\pi$
$888$	−2148.26	−0.0811835
$889$	−16576.3	−0.625367
$890$	14161.7	0.533373
$891$	6470.94	0.243305
$892$	−43446.3	−1.63082
$893$	2570.00	0.0963066
$894$	−65233.5	−2.44042
$895$	−12853.4	−0.480047
$896$	16372.6	0.610457
$897$	−48522.9	−1.80617
$898$	−51987.0	−1.93188
$899$	−19105.6	−0.708795
$900$	8803.76	0.326065
$901$	−7374.04	−0.272658
$902$	10248.2	0.378301
$903$	14374.6	0.529741
$904$	−24548.5	−0.903177
$905$	6355.64	0.233446
$906$	55792.6	2.04590
$907$	−7682.96	−0.281266	−0.140633	−	0.990062i	$-0.544914\pi$
$907$	−7682.96	−0.281266	−0.140633	+	0.990062i	$0.544914\pi$
$908$	3508.66	0.128237
$909$	−36398.3	−1.32811
$910$	−7260.39	−0.264483
$911$	6295.36	0.228951	0.114476	−	0.993426i	$-0.463481\pi$
$911$	6295.36	0.228951	0.114476	+	0.993426i	$0.463481\pi$
$912$	4113.41	0.149352
$913$	552.867	0.0200408
$914$	−16637.6	−0.602104
$915$	−31761.4	−1.14754
$916$	61619.4	2.22267
$917$	15387.0	0.554115
$918$	2508.01	0.0901705
$919$	−31995.5	−1.14846	−0.574230	−	0.818694i	$-0.694699\pi$
$919$	−31995.5	−1.14846	−0.574230	+	0.818694i	$0.694699\pi$
$920$	13300.1	0.476620
$921$	41712.8	1.49238
$922$	2556.49	0.0913161
$923$	−13671.4	−0.487540
$924$	−9360.54	−0.333268
$925$	502.704	0.0178690
$926$	31669.9	1.12391
$927$	38218.9	1.35412
$928$	−46728.5	−1.65295
$929$	47836.5	1.68941	0.844707	−	0.535229i	$-0.179775\pi$
$929$	47836.5	1.68941	0.844707	+	0.535229i	$0.179775\pi$
$930$	16146.9	0.569330
$931$	4637.64	0.163257
$932$	−6688.11	−0.235060
$933$	−7005.28	−0.245812
$934$	36395.0	1.27503
$935$	−920.898	−0.0322103
$936$	14655.3	0.511776
$937$	−10177.3	−0.354832	−0.177416	−	0.984136i	$-0.556774\pi$
$937$	−10177.3	−0.354832	−0.177416	+	0.984136i	$0.556774\pi$
$938$	−11525.3	−0.401187
$939$	−55823.2	−1.94006
$940$	7567.58	0.262582
$941$	35515.8	1.23037	0.615186	−	0.788382i	$-0.289081\pi$
$941$	35515.8	1.23037	0.615186	+	0.788382i	$0.289081\pi$
$942$	−104407.	−3.61122
$943$	40491.7	1.39829
$944$	−15224.1	−0.524898
$945$	−1700.38	−0.0585328
$946$	9107.89	0.313027
$947$	593.936	0.0203805	0.0101902	−	0.999948i	$-0.496756\pi$
$947$	593.936	0.0203805	0.0101902	+	0.999948i	$0.496756\pi$
$948$	3332.24	0.114163
$949$	−17057.4	−0.583462
$950$	2080.77	0.0710623
$951$	70551.7	2.40567
$952$	2326.58	0.0792070
$953$	40356.7	1.37175	0.685877	−	0.727718i	$-0.259419\pi$
$953$	40356.7	1.37175	0.685877	+	0.727718i	$0.259419\pi$
$954$	−60716.7	−2.06056
$955$	−15607.5	−0.528846
$956$	51985.2	1.75870
$957$	16669.1	0.563046
$958$	29855.9	1.00689
$959$	9541.52	0.321284
$960$	30832.3	1.03657
$961$	−20496.4	−0.688008
$962$	2935.86	0.0983948
$963$	19037.4	0.637043
$964$	24097.9	0.805124
$965$	−5955.64	−0.198672
$966$	−63426.9	−2.11256
$967$	−57517.7	−1.91277	−0.956383	−	0.292114i	$-0.905641\pi$
$967$	−57517.7	−1.91277	−0.956383	+	0.292114i	$0.905641\pi$
$968$	−1690.55	−0.0561325
$969$	2432.63	0.0806473
$970$	−15464.0	−0.511875
$971$	7946.07	0.262617	0.131309	−	0.991342i	$-0.458082\pi$
$971$	7946.07	0.262617	0.131309	+	0.991342i	$0.458082\pi$
$972$	−60663.7	−2.00184
$973$	−28425.3	−0.936561
$974$	50748.4	1.66949
$975$	−6371.54	−0.209285
$976$	−23519.7	−0.771360
$977$	6098.76	0.199710	0.0998550	−	0.995002i	$-0.468162\pi$
$977$	6098.76	0.199710	0.0998550	+	0.995002i	$0.468162\pi$
$978$	31019.3	1.01420
$979$	−7112.26	−0.232185
$980$	13655.9	0.445125
$981$	−53774.3	−1.75013
$982$	84021.7	2.73039
$983$	45371.9	1.47217	0.736083	−	0.676891i	$-0.236673\pi$
$983$	45371.9	1.47217	0.736083	+	0.676891i	$0.236673\pi$
$984$	−22721.6	−0.736116
$985$	14986.5	0.484782
$986$	−14535.4	−0.469473
$987$	−10286.8	−0.331746
$988$	7085.86	0.228169
$989$	35986.2	1.15702
$990$	−7582.53	−0.243423
$991$	−39397.5	−1.26287	−0.631435	−	0.775429i	$-0.717534\pi$
$991$	−39397.5	−1.26287	−0.631435	+	0.775429i	$0.717534\pi$
$992$	22732.7	0.727584
$993$	74372.4	2.37677
$994$	−17870.7	−0.570244
$995$	−25487.0	−0.812053
$996$	−4300.40	−0.136811
$997$	−26893.1	−0.854276	−0.427138	−	0.904186i	$-0.640478\pi$
$997$	−26893.1	−0.854276	−0.427138	+	0.904186i	$0.640478\pi$
$998$	17491.0	0.554777
$999$	687.577	0.0217757

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1045.4.a.g.1.3	✓	23

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1045.4.a.g.1.3	✓	23	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:	\( N \)	\(=\)	\( 1045 = 5 \cdot 11 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	1045.a (trivial)

\(f(q)\)	\(=\)	\(q-4.38057 q^{2} +7.64668 q^{3} +11.1894 q^{4} -5.00000 q^{5} -33.4968 q^{6} +9.94553 q^{7} -13.9715 q^{8} +31.4717 q^{9} +O(q^{10})\)	\(q-4.38057 q^{2} +7.64668 q^{3} +11.1894 q^{4} -5.00000 q^{5} -33.4968 q^{6} +9.94553 q^{7} -13.9715 q^{8} +31.4717 q^{9} +21.9029 q^{10} -11.0000 q^{11} +85.5619 q^{12} -33.3297 q^{13} -43.5671 q^{14} -38.2334 q^{15} -28.3123 q^{16} -16.7436 q^{17} -137.864 q^{18} -19.0000 q^{19} -55.9471 q^{20} +76.0503 q^{21} +48.1863 q^{22} +190.389 q^{23} -106.835 q^{24} +25.0000 q^{25} +146.003 q^{26} +34.1939 q^{27} +111.285 q^{28} -198.174 q^{29} +167.484 q^{30} +96.4083 q^{31} +235.796 q^{32} -84.1135 q^{33} +73.3466 q^{34} -49.7277 q^{35} +352.150 q^{36} +20.1082 q^{37} +83.2309 q^{38} -254.862 q^{39} +69.8573 q^{40} +212.679 q^{41} -333.144 q^{42} +189.014 q^{43} -123.084 q^{44} -157.359 q^{45} -834.013 q^{46} -135.263 q^{47} -216.495 q^{48} -244.086 q^{49} -109.514 q^{50} -128.033 q^{51} -372.940 q^{52} +440.409 q^{53} -149.789 q^{54} +55.0000 q^{55} -138.954 q^{56} -145.287 q^{57} +868.114 q^{58} +537.721 q^{59} -427.809 q^{60} +830.724 q^{61} -422.323 q^{62} +313.003 q^{63} -806.422 q^{64} +166.648 q^{65} +368.465 q^{66} +264.540 q^{67} -187.351 q^{68} +1455.84 q^{69} +217.836 q^{70} +410.187 q^{71} -439.706 q^{72} +511.777 q^{73} -88.0853 q^{74} +191.167 q^{75} -212.599 q^{76} -109.401 q^{77} +1116.44 q^{78} +38.9454 q^{79} +141.562 q^{80} -588.267 q^{81} -931.654 q^{82} -50.2607 q^{83} +850.958 q^{84} +83.7180 q^{85} -827.990 q^{86} -1515.37 q^{87} +153.686 q^{88} +646.569 q^{89} +689.321 q^{90} -331.482 q^{91} +2130.34 q^{92} +737.203 q^{93} +592.531 q^{94} +95.0000 q^{95} +1803.06 q^{96} -706.026 q^{97} +1069.24 q^{98} -346.189 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 23 q + 6 q^{2} + 9 q^{3} + 92 q^{4} - 115 q^{5} - 25 q^{6} - 37 q^{7} + 42 q^{8} + 170 q^{9}+O(q^{10}) \) 23 * q + 6 * q^2 + 9 * q^3 + 92 * q^4 - 115 * q^5 - 25 * q^6 - 37 * q^7 + 42 * q^8 + 170 * q^9	\( 23 q + 6 q^{2} + 9 q^{3} + 92 q^{4} - 115 q^{5} - 25 q^{6} - 37 q^{7} + 42 q^{8} + 170 q^{9} - 30 q^{10} - 253 q^{11} + 44 q^{12} - 37 q^{13} + 61 q^{14} - 45 q^{15} + 588 q^{16} - 73 q^{17} + 391 q^{18} - 437 q^{19} - 460 q^{20} - 127 q^{21} - 66 q^{22} - 175 q^{23} + 16 q^{24} + 575 q^{25} + 719 q^{26} + 21 q^{27} + 253 q^{28} + 71 q^{29} + 125 q^{30} + 302 q^{31} + 1107 q^{32} - 99 q^{33} + 1267 q^{34} + 185 q^{35} + 703 q^{36} - 500 q^{37} - 114 q^{38} + 457 q^{39} - 210 q^{40} + 770 q^{41} + 2596 q^{42} - 902 q^{43} - 1012 q^{44} - 850 q^{45} - 1101 q^{46} + 356 q^{47} + 1221 q^{48} + 908 q^{49} + 150 q^{50} - 451 q^{51} - 358 q^{52} + 1327 q^{53} + 2534 q^{54} + 1265 q^{55} + 3135 q^{56} - 171 q^{57} + 1014 q^{58} + 3619 q^{59} - 220 q^{60} - 1432 q^{61} + 1826 q^{62} + 1658 q^{63} + 4006 q^{64} + 185 q^{65} + 275 q^{66} - 605 q^{67} + 5128 q^{68} + 3099 q^{69} - 305 q^{70} + 3230 q^{71} + 2152 q^{72} - 637 q^{73} + 5063 q^{74} + 225 q^{75} - 1748 q^{76} + 407 q^{77} + 7230 q^{78} + 2074 q^{79} - 2940 q^{80} + 2291 q^{81} + 530 q^{82} + 3882 q^{83} + 5096 q^{84} + 365 q^{85} + 2262 q^{86} - 27 q^{87} - 462 q^{88} - 210 q^{89} - 1955 q^{90} + 4133 q^{91} - 6064 q^{92} + 824 q^{93} - 392 q^{94} + 2185 q^{95} + 2462 q^{96} + 2032 q^{97} + 7896 q^{98} - 1870 q^{99}+O(q^{100}) \) 23 * q + 6 * q^2 + 9 * q^3 + 92 * q^4 - 115 * q^5 - 25 * q^6 - 37 * q^7 + 42 * q^8 + 170 * q^9 - 30 * q^10 - 253 * q^11 + 44 * q^12 - 37 * q^13 + 61 * q^14 - 45 * q^15 + 588 * q^16 - 73 * q^17 + 391 * q^18 - 437 * q^19 - 460 * q^20 - 127 * q^21 - 66 * q^22 - 175 * q^23 + 16 * q^24 + 575 * q^25 + 719 * q^26 + 21 * q^27 + 253 * q^28 + 71 * q^29 + 125 * q^30 + 302 * q^31 + 1107 * q^32 - 99 * q^33 + 1267 * q^34 + 185 * q^35 + 703 * q^36 - 500 * q^37 - 114 * q^38 + 457 * q^39 - 210 * q^40 + 770 * q^41 + 2596 * q^42 - 902 * q^43 - 1012 * q^44 - 850 * q^45 - 1101 * q^46 + 356 * q^47 + 1221 * q^48 + 908 * q^49 + 150 * q^50 - 451 * q^51 - 358 * q^52 + 1327 * q^53 + 2534 * q^54 + 1265 * q^55 + 3135 * q^56 - 171 * q^57 + 1014 * q^58 + 3619 * q^59 - 220 * q^60 - 1432 * q^61 + 1826 * q^62 + 1658 * q^63 + 4006 * q^64 + 185 * q^65 + 275 * q^66 - 605 * q^67 + 5128 * q^68 + 3099 * q^69 - 305 * q^70 + 3230 * q^71 + 2152 * q^72 - 637 * q^73 + 5063 * q^74 + 225 * q^75 - 1748 * q^76 + 407 * q^77 + 7230 * q^78 + 2074 * q^79 - 2940 * q^80 + 2291 * q^81 + 530 * q^82 + 3882 * q^83 + 5096 * q^84 + 365 * q^85 + 2262 * q^86 - 27 * q^87 - 462 * q^88 - 210 * q^89 - 1955 * q^90 + 4133 * q^91 - 6064 * q^92 + 824 * q^93 - 392 * q^94 + 2185 * q^95 + 2462 * q^96 + 2032 * q^97 + 7896 * q^98 - 1870 * q^99

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