LMFDB - Embedded newform 841.4.a.a.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [841,4,Mod(1,841)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(841, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("841.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 841 = 29^{2} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	841.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:	$49.6206063148$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(\zeta_{8})^+$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - 2 $ x^2 - 2
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 29)
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$1.41421$ of defining polynomial
Character	$\chi$	$=$	841.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+2.41421 q^{2} +0.757359 q^{3} -2.17157 q^{4} -10.6569 q^{5} +1.82843 q^{6} -22.1421 q^{7} -24.5563 q^{8} -26.4264 q^{9} +O(q^{10})$	\(q+2.41421 q^{2} +0.757359 q^{3} -2.17157 q^{4} -10.6569 q^{5} +1.82843 q^{6} -22.1421 q^{7} -24.5563 q^{8} -26.4264 q^{9} -25.7279 q^{10} -39.3259 q^{11} -1.64466 q^{12} +23.7696 q^{13} -53.4558 q^{14} -8.07107 q^{15} -41.9117 q^{16} -4.54416 q^{17} -63.7990 q^{18} +155.255 q^{19} +23.1421 q^{20} -16.7696 q^{21} -94.9411 q^{22} -41.8823 q^{23} -18.5980 q^{24} -11.4315 q^{25} +57.3848 q^{26} -40.4630 q^{27} +48.0833 q^{28} -19.4853 q^{30} +57.9045 q^{31} +95.2670 q^{32} -29.7838 q^{33} -10.9706 q^{34} +235.966 q^{35} +57.3869 q^{36} -235.196 q^{37} +374.818 q^{38} +18.0021 q^{39} +261.693 q^{40} +175.161 q^{41} -40.4853 q^{42} +402.831 q^{43} +85.3991 q^{44} +281.622 q^{45} -101.113 q^{46} -227.742 q^{47} -31.7422 q^{48} +147.274 q^{49} -27.5980 q^{50} -3.44156 q^{51} -51.6173 q^{52} +673.534 q^{53} -97.6863 q^{54} +419.090 q^{55} +543.730 q^{56} +117.584 q^{57} -800.725 q^{59} +17.5269 q^{60} +222.270 q^{61} +139.794 q^{62} +585.137 q^{63} +565.288 q^{64} -253.309 q^{65} -71.9045 q^{66} -524.479 q^{67} +9.86797 q^{68} -31.7199 q^{69} +569.671 q^{70} -281.917 q^{71} +648.936 q^{72} -1229.10 q^{73} -567.813 q^{74} -8.65772 q^{75} -337.147 q^{76} +870.759 q^{77} +43.4609 q^{78} -611.247 q^{79} +446.647 q^{80} +682.868 q^{81} +422.877 q^{82} +515.490 q^{83} +36.4163 q^{84} +48.4264 q^{85} +972.519 q^{86} +965.701 q^{88} +358.219 q^{89} +679.897 q^{90} -526.309 q^{91} +90.9504 q^{92} +43.8545 q^{93} -549.818 q^{94} -1654.53 q^{95} +72.1514 q^{96} -829.415 q^{97} +355.551 q^{98} +1039.24 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + 2 q^{2} + 10 q^{3} - 10 q^{4} - 10 q^{5} - 2 q^{6} - 16 q^{7} - 18 q^{8} + 32 q^{9}+O(q^{10}) $ 2 * q + 2 * q^2 + 10 * q^3 - 10 * q^4 - 10 * q^5 - 2 * q^6 - 16 * q^7 - 18 * q^8 + 32 * q^9	\( 2 q + 2 q^{2} + 10 q^{3} - 10 q^{4} - 10 q^{5} - 2 q^{6} - 16 q^{7} - 18 q^{8} + 32 q^{9} - 26 q^{10} + 26 q^{11} - 74 q^{12} - 26 q^{13} - 56 q^{14} - 2 q^{15} + 18 q^{16} - 60 q^{17} - 88 q^{18} + 220 q^{19} + 18 q^{20} + 40 q^{21} - 122 q^{22} + 52 q^{23} + 42 q^{24} - 136 q^{25} + 78 q^{26} + 250 q^{27} - 22 q^{30} + 294 q^{31} + 18 q^{32} + 574 q^{33} + 12 q^{34} + 240 q^{35} - 400 q^{36} - 312 q^{37} + 348 q^{38} - 442 q^{39} + 266 q^{40} - 40 q^{41} - 64 q^{42} + 322 q^{43} - 426 q^{44} + 320 q^{45} - 140 q^{46} + 130 q^{47} + 522 q^{48} - 158 q^{49} + 24 q^{50} - 516 q^{51} + 338 q^{52} + 1002 q^{53} - 218 q^{54} + 462 q^{55} + 584 q^{56} + 716 q^{57} - 900 q^{59} - 30 q^{60} + 948 q^{61} + 42 q^{62} + 944 q^{63} + 118 q^{64} - 286 q^{65} - 322 q^{66} + 320 q^{67} + 444 q^{68} + 836 q^{69} + 568 q^{70} - 660 q^{71} + 1032 q^{72} - 648 q^{73} - 536 q^{74} - 1160 q^{75} - 844 q^{76} + 1272 q^{77} + 234 q^{78} - 258 q^{79} + 486 q^{80} + 1790 q^{81} + 512 q^{82} + 1212 q^{83} - 408 q^{84} + 12 q^{85} + 1006 q^{86} + 1394 q^{88} - 760 q^{89} + 664 q^{90} - 832 q^{91} - 644 q^{92} + 2226 q^{93} - 698 q^{94} - 1612 q^{95} - 642 q^{96} - 24 q^{97} + 482 q^{98} + 4856 q^{99}+O(q^{100}) \) 2 * q + 2 * q^2 + 10 * q^3 - 10 * q^4 - 10 * q^5 - 2 * q^6 - 16 * q^7 - 18 * q^8 + 32 * q^9 - 26 * q^10 + 26 * q^11 - 74 * q^12 - 26 * q^13 - 56 * q^14 - 2 * q^15 + 18 * q^16 - 60 * q^17 - 88 * q^18 + 220 * q^19 + 18 * q^20 + 40 * q^21 - 122 * q^22 + 52 * q^23 + 42 * q^24 - 136 * q^25 + 78 * q^26 + 250 * q^27 - 22 * q^30 + 294 * q^31 + 18 * q^32 + 574 * q^33 + 12 * q^34 + 240 * q^35 - 400 * q^36 - 312 * q^37 + 348 * q^38 - 442 * q^39 + 266 * q^40 - 40 * q^41 - 64 * q^42 + 322 * q^43 - 426 * q^44 + 320 * q^45 - 140 * q^46 + 130 * q^47 + 522 * q^48 - 158 * q^49 + 24 * q^50 - 516 * q^51 + 338 * q^52 + 1002 * q^53 - 218 * q^54 + 462 * q^55 + 584 * q^56 + 716 * q^57 - 900 * q^59 - 30 * q^60 + 948 * q^61 + 42 * q^62 + 944 * q^63 + 118 * q^64 - 286 * q^65 - 322 * q^66 + 320 * q^67 + 444 * q^68 + 836 * q^69 + 568 * q^70 - 660 * q^71 + 1032 * q^72 - 648 * q^73 - 536 * q^74 - 1160 * q^75 - 844 * q^76 + 1272 * q^77 + 234 * q^78 - 258 * q^79 + 486 * q^80 + 1790 * q^81 + 512 * q^82 + 1212 * q^83 - 408 * q^84 + 12 * q^85 + 1006 * q^86 + 1394 * q^88 - 760 * q^89 + 664 * q^90 - 832 * q^91 - 644 * q^92 + 2226 * q^93 - 698 * q^94 - 1612 * q^95 - 642 * q^96 - 24 * q^97 + 482 * q^98 + 4856 * 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 $

$2$	2.41421	0.853553	0.426777	−	0.904357i	$-0.359649\pi$
$2$	2.41421	0.853553	0.426777	+	0.904357i	$0.359649\pi$
$3$	0.757359	0.145754	0.0728769	−	0.997341i	$-0.476782\pi$
$3$	0.757359	0.145754	0.0728769	+	0.997341i	$0.476782\pi$
$4$	−2.17157	−0.271447
$5$	−10.6569	−0.953178	−0.476589	−	0.879126i	$-0.658127\pi$
$5$	−10.6569	−0.953178	−0.476589	+	0.879126i	$0.658127\pi$
$6$	1.82843	0.124409
$7$	−22.1421	−1.19556	−0.597781	−	0.801659i	$-0.703951\pi$
$7$	−22.1421	−1.19556	−0.597781	+	0.801659i	$0.703951\pi$
$8$	−24.5563	−1.08525
$9$	−26.4264	−0.978756
$10$	−25.7279	−0.813588
$11$	−39.3259	−1.07793	−0.538964	−	0.842329i	$-0.681184\pi$
$11$	−39.3259	−1.07793	−0.538964	+	0.842329i	$0.681184\pi$
$12$	−1.64466	−0.0395644
$13$	23.7696	0.507114	0.253557	−	0.967320i	$-0.418399\pi$
$13$	23.7696	0.507114	0.253557	+	0.967320i	$0.418399\pi$
$14$	−53.4558	−1.02048
$15$	−8.07107	−0.138929
$16$	−41.9117	−0.654870
$17$	−4.54416	−0.0648306	−0.0324153	−	0.999474i	$-0.510320\pi$
$17$	−4.54416	−0.0648306	−0.0324153	+	0.999474i	$0.510320\pi$
$18$	−63.7990	−0.835420
$19$	155.255	1.87463	0.937313	−	0.348488i	$-0.113305\pi$
$19$	155.255	1.87463	0.937313	+	0.348488i	$0.113305\pi$
$20$	23.1421	0.258737
$21$	−16.7696	−0.174258
$22$	−94.9411	−0.920069
$23$	−41.8823	−0.379698	−0.189849	−	0.981813i	$-0.560800\pi$
$23$	−41.8823	−0.379698	−0.189849	+	0.981813i	$0.560800\pi$
$24$	−18.5980	−0.158179
$25$	−11.4315	−0.0914517
$26$	57.3848	0.432849
$27$	−40.4630	−0.288411
$28$	48.0833	0.324532
$29$	0	0
$29$	0	0
$30$	−19.4853	−0.118584
$31$	57.9045	0.335483	0.167741	−	0.985831i	$-0.446353\pi$
$31$	57.9045	0.335483	0.167741	+	0.985831i	$0.446353\pi$
$32$	95.2670	0.526281
$33$	−29.7838	−0.157112
$34$	−10.9706	−0.0553364
$35$	235.966	1.13958
$36$	57.3869	0.265680
$37$	−235.196	−1.04503	−0.522513	−	0.852631i	$-0.675005\pi$
$37$	−235.196	−1.04503	−0.522513	+	0.852631i	$0.675005\pi$
$38$	374.818	1.60009
$39$	18.0021	0.0739139
$40$	261.693	1.03443
$41$	175.161	0.667210	0.333605	−	0.942713i	$-0.391735\pi$
$41$	175.161	0.667210	0.333605	+	0.942713i	$0.391735\pi$
$42$	−40.4853	−0.148738
$43$	402.831	1.42863	0.714315	−	0.699824i	$-0.246738\pi$
$43$	402.831	1.42863	0.714315	+	0.699824i	$0.246738\pi$
$44$	85.3991	0.292600
$45$	281.622	0.932929
$46$	−101.113	−0.324092
$47$	−227.742	−0.706800	−0.353400	−	0.935472i	$-0.614975\pi$
$47$	−227.742	−0.706800	−0.353400	+	0.935472i	$0.614975\pi$
$48$	−31.7422	−0.0954499
$49$	147.274	0.429371
$50$	−27.5980	−0.0780589
$51$	−3.44156	−0.00944931
$52$	−51.6173	−0.137654
$53$	673.534	1.74560	0.872802	−	0.488074i	$-0.162301\pi$
$53$	673.534	1.74560	0.872802	+	0.488074i	$0.162301\pi$
$54$	−97.6863	−0.246174
$55$	419.090	1.02746
$56$	543.730	1.29748
$57$	117.584	0.273234
$58$	0	0
$59$	−800.725	−1.76687	−0.883437	−	0.468551i	$-0.844776\pi$
$59$	−800.725	−1.76687	−0.883437	+	0.468551i	$0.844776\pi$
$60$	17.5269	0.0377119
$61$	222.270	0.466537	0.233268	−	0.972412i	$-0.425058\pi$
$61$	222.270	0.466537	0.233268	+	0.972412i	$0.425058\pi$
$62$	139.794	0.286352
$63$	585.137	1.17016
$64$	565.288	1.10408
$65$	−253.309	−0.483370
$66$	−71.9045	−0.134104
$67$	−524.479	−0.956349	−0.478174	−	0.878265i	$-0.658701\pi$
$67$	−524.479	−0.956349	−0.478174	+	0.878265i	$0.658701\pi$
$68$	9.86797	0.0175980
$69$	−31.7199	−0.0553424
$70$	569.671	0.972696
$71$	−281.917	−0.471230	−0.235615	−	0.971846i	$-0.575711\pi$
$71$	−281.917	−0.471230	−0.235615	+	0.971846i	$0.575711\pi$
$72$	648.936	1.06219
$73$	−1229.10	−1.97061	−0.985307	−	0.170790i	$-0.945368\pi$
$73$	−1229.10	−1.97061	−0.985307	+	0.170790i	$0.945368\pi$
$74$	−567.813	−0.891986
$75$	−8.65772	−0.0133294
$76$	−337.147	−0.508861
$77$	870.759	1.28873
$78$	43.4609	0.0630895
$79$	−611.247	−0.870514	−0.435257	−	0.900306i	$-0.643343\pi$
$79$	−611.247	−0.870514	−0.435257	+	0.900306i	$0.643343\pi$
$80$	446.647	0.624208
$81$	682.868	0.936719
$82$	422.877	0.569500
$83$	515.490	0.681716	0.340858	−	0.940115i	$-0.389282\pi$
$83$	515.490	0.681716	0.340858	+	0.940115i	$0.389282\pi$
$84$	36.4163	0.0473017
$85$	48.4264	0.0617951
$86$	972.519	1.21941
$87$	0	0
$88$	965.701	1.16982
$89$	358.219	0.426643	0.213321	−	0.976982i	$-0.431572\pi$
$89$	358.219	0.426643	0.213321	+	0.976982i	$0.431572\pi$
$90$	679.897	0.796304
$91$	−526.309	−0.606287
$92$	90.9504	0.103068
$93$	43.8545	0.0488979
$94$	−549.818	−0.603292
$95$	−1654.53	−1.78685
$96$	72.1514	0.0767075
$97$	−829.415	−0.868189	−0.434095	−	0.900867i	$-0.642932\pi$
$97$	−829.415	−0.868189	−0.434095	+	0.900867i	$0.642932\pi$
$98$	355.551	0.366491
$99$	1039.24	1.05503
$100$	24.8242	0.0248242
$101$	978.010	0.963521	0.481761	−	0.876303i	$-0.339997\pi$
$101$	978.010	0.963521	0.481761	+	0.876303i	$0.339997\pi$
$102$	−8.30866	−0.00806549
$103$	−1217.33	−1.16453	−0.582266	−	0.812998i	$-0.697834\pi$
$103$	−1217.33	−1.16453	−0.582266	+	0.812998i	$0.697834\pi$
$104$	−583.693	−0.550345
$105$	178.711	0.166099
$106$	1626.06	1.48997
$107$	−707.044	−0.638808	−0.319404	−	0.947619i	$-0.603483\pi$
$107$	−707.044	−0.638808	−0.319404	+	0.947619i	$0.603483\pi$
$108$	87.8683	0.0782883
$109$	−1496.14	−1.31471	−0.657357	−	0.753580i	$-0.728326\pi$
$109$	−1496.14	−1.31471	−0.657357	+	0.753580i	$0.728326\pi$
$110$	1011.77	0.876989
$111$	−178.128	−0.152317
$112$	928.014	0.782938
$113$	1067.23	0.888469	0.444234	−	0.895911i	$-0.353476\pi$
$113$	1067.23	0.888469	0.444234	+	0.895911i	$0.353476\pi$
$114$	283.872	0.233220
$115$	446.333	0.361920
$116$	0	0
$117$	−628.144	−0.496341
$118$	−1933.12	−1.50812
$119$	100.617	0.0775090
$120$	198.196	0.150773
$121$	215.527	0.161928
$122$	536.607	0.398214
$123$	132.660	0.0972485
$124$	−125.744	−0.0910656
$125$	1453.93	1.04035
$126$	1412.65	0.998798
$127$	1179.58	0.824177	0.412088	−	0.911144i	$-0.364799\pi$
$127$	1179.58	0.824177	0.412088	+	0.911144i	$0.364799\pi$
$128$	602.591	0.416109
$129$	305.087	0.208228
$130$	−611.541	−0.412582
$131$	2357.47	1.57231	0.786156	−	0.618028i	$-0.212068\pi$
$131$	2357.47	1.57231	0.786156	+	0.618028i	$0.212068\pi$
$132$	64.6778	0.0426476
$133$	−3437.67	−2.24123
$134$	−1266.21	−0.816295
$135$	431.208	0.274907
$136$	111.588	0.0703572
$137$	−722.489	−0.450558	−0.225279	−	0.974294i	$-0.572329\pi$
$137$	−722.489	−0.450558	−0.225279	+	0.974294i	$0.572329\pi$
$138$	−76.5786	−0.0472377
$139$	1398.24	0.853219	0.426610	−	0.904436i	$-0.359708\pi$
$139$	1398.24	0.853219	0.426610	+	0.904436i	$0.359708\pi$
$140$	−512.416	−0.309336
$141$	−172.483	−0.103019
$142$	−680.607	−0.402220
$143$	−934.759	−0.546633
$144$	1107.58	0.640958
$145$	0	0
$146$	−2967.30	−1.68203
$147$	111.539	0.0625824
$148$	510.745	0.283669
$149$	2830.63	1.55634	0.778168	−	0.628056i	$-0.216149\pi$
$149$	2830.63	1.55634	0.778168	+	0.628056i	$0.216149\pi$
$150$	−20.9016	−0.0113774
$151$	1705.58	0.919194	0.459597	−	0.888128i	$-0.347994\pi$
$151$	1705.58	0.919194	0.459597	+	0.888128i	$0.347994\pi$
$152$	−3812.49	−2.03443
$153$	120.086	0.0634533
$154$	2102.20	1.10000
$155$	−617.080	−0.319775
$156$	−39.0929	−0.0200637
$157$	2670.84	1.35768	0.678841	−	0.734286i	$-0.262483\pi$
$157$	2670.84	1.35768	0.678841	+	0.734286i	$0.262483\pi$
$158$	−1475.68	−0.743031
$159$	510.107	0.254429
$160$	−1015.25	−0.501639
$161$	927.362	0.453953
$162$	1648.59	0.799539
$163$	2151.92	1.03406	0.517028	−	0.855968i	$-0.327038\pi$
$163$	2151.92	1.03406	0.517028	+	0.855968i	$0.327038\pi$
$164$	−380.376	−0.181112
$165$	317.402	0.149756
$166$	1244.50	0.581881
$167$	999.387	0.463083	0.231542	−	0.972825i	$-0.425623\pi$
$167$	999.387	0.463083	0.231542	+	0.972825i	$0.425623\pi$
$168$	411.799	0.189113
$169$	−1632.01	−0.742835
$170$	116.912	0.0527454
$171$	−4102.83	−1.83480
$172$	−874.776	−0.387797
$173$	−2534.30	−1.11375	−0.556877	−	0.830595i	$-0.688001\pi$
$173$	−2534.30	−1.11375	−0.556877	+	0.830595i	$0.688001\pi$
$174$	0	0
$175$	253.117	0.109336
$176$	1648.21	0.705903
$177$	−606.437	−0.257529
$178$	864.818	0.364162
$179$	3550.27	1.48245	0.741227	−	0.671254i	$-0.234244\pi$
$179$	3550.27	1.48245	0.741227	+	0.671254i	$0.234244\pi$
$180$	−611.563	−0.253240
$181$	−3034.68	−1.24622	−0.623110	−	0.782135i	$-0.714131\pi$
$181$	−3034.68	−1.24622	−0.623110	+	0.782135i	$0.714131\pi$
$182$	−1270.62	−0.517499
$183$	168.338	0.0679996
$184$	1028.48	0.412066
$185$	2506.45	0.996096
$186$	105.874	0.0417370
$187$	178.703	0.0698827
$188$	494.559	0.191859
$189$	895.937	0.344814
$190$	−3994.38	−1.52517
$191$	−2224.00	−0.842529	−0.421265	−	0.906938i	$-0.638414\pi$
$191$	−2224.00	−0.842529	−0.421265	+	0.906938i	$0.638414\pi$
$192$	428.126	0.160924
$193$	632.830	0.236021	0.118011	−	0.993012i	$-0.462348\pi$
$193$	632.830	0.236021	0.118011	+	0.993012i	$0.462348\pi$
$194$	−2002.39	−0.741046
$195$	−191.846	−0.0704531
$196$	−319.817	−0.116551
$197$	1369.80	0.495404	0.247702	−	0.968836i	$-0.420325\pi$
$197$	1369.80	0.495404	0.247702	+	0.968836i	$0.420325\pi$
$198$	2508.95	0.900523
$199$	1416.38	0.504544	0.252272	−	0.967656i	$-0.418822\pi$
$199$	1416.38	0.504544	0.252272	+	0.967656i	$0.418822\pi$
$200$	280.715	0.0992477
$201$	−397.219	−0.139391
$202$	2361.13	0.822417
$203$	0	0
$204$	7.47360	0.00256498
$205$	−1866.67	−0.635970
$206$	−2938.89	−0.993991
$207$	1106.80	0.371632
$208$	−996.222	−0.332094
$209$	−6105.54	−2.02071
$210$	431.446	0.141774
$211$	896.432	0.292478	0.146239	−	0.989249i	$-0.453283\pi$
$211$	896.432	0.292478	0.146239	+	0.989249i	$0.453283\pi$
$212$	−1462.63	−0.473838
$213$	−213.512	−0.0686837
$214$	−1706.95	−0.545257
$215$	−4292.91	−1.36174
$216$	993.623	0.312998
$217$	−1282.13	−0.401091
$218$	−3611.99	−1.12218
$219$	−930.868	−0.287225
$220$	−910.085	−0.278900
$221$	−108.013	−0.0328765
$222$	−430.039	−0.130010
$223$	−2268.94	−0.681344	−0.340672	−	0.940182i	$-0.610655\pi$
$223$	−2268.94	−0.681344	−0.340672	+	0.940182i	$0.610655\pi$
$224$	−2109.42	−0.629202
$225$	302.092	0.0895088
$226$	2576.53	0.758356
$227$	−2078.09	−0.607610	−0.303805	−	0.952734i	$-0.598257\pi$
$227$	−2078.09	−0.607610	−0.303805	+	0.952734i	$0.598257\pi$
$228$	−255.342	−0.0741685
$229$	3715.05	1.07204	0.536020	−	0.844205i	$-0.319927\pi$
$229$	3715.05	1.07204	0.536020	+	0.844205i	$0.319927\pi$
$230$	1077.54	0.308918
$231$	659.478	0.187837
$232$	0	0
$233$	2521.35	0.708923	0.354461	−	0.935071i	$-0.384664\pi$
$233$	2521.35	0.708923	0.354461	+	0.935071i	$0.384664\pi$
$234$	−1516.47	−0.423654
$235$	2427.02	0.673707
$236$	1738.83	0.479612
$237$	−462.933	−0.126881
$238$	242.912	0.0661581
$239$	3940.04	1.06636	0.533179	−	0.846002i	$-0.320997\pi$
$239$	3940.04	1.06636	0.533179	+	0.846002i	$0.320997\pi$
$240$	338.272	0.0909807
$241$	−1973.06	−0.527369	−0.263684	−	0.964609i	$-0.584938\pi$
$241$	−1973.06	−0.527369	−0.263684	+	0.964609i	$0.584938\pi$
$242$	520.327	0.138214
$243$	1609.68	0.424942
$244$	−482.675	−0.126640
$245$	−1569.48	−0.409267
$246$	320.270	0.0830068
$247$	3690.34	0.950650
$248$	−1421.92	−0.364082
$249$	390.411	0.0993627
$250$	3510.10	0.887992
$251$	1236.65	0.310982	0.155491	−	0.987837i	$-0.450304\pi$
$251$	1236.65	0.310982	0.155491	+	0.987837i	$0.450304\pi$
$252$	−1270.67	−0.317637
$253$	1647.06	0.409287
$254$	2847.75	0.703479
$255$	36.6762	0.00900687
$256$	−3067.52	−0.748907
$257$	2918.10	0.708272	0.354136	−	0.935194i	$-0.384775\pi$
$257$	2918.10	0.708272	0.354136	+	0.935194i	$0.384775\pi$
$258$	736.546	0.177734
$259$	5207.74	1.24939
$260$	550.078	0.131209
$261$	0	0
$262$	5691.43	1.34205
$263$	310.789	0.0728673	0.0364336	−	0.999336i	$-0.488400\pi$
$263$	310.789	0.0728673	0.0364336	+	0.999336i	$0.488400\pi$
$264$	731.382	0.170506
$265$	−7177.75	−1.66387
$266$	−8299.28	−1.91301
$267$	271.301	0.0621848
$268$	1138.95	0.259598
$269$	1839.98	0.417047	0.208523	−	0.978017i	$-0.433134\pi$
$269$	1839.98	0.417047	0.208523	+	0.978017i	$0.433134\pi$
$270$	1041.03	0.234648
$271$	−5187.35	−1.16277	−0.581383	−	0.813630i	$-0.697488\pi$
$271$	−5187.35	−1.16277	−0.581383	+	0.813630i	$0.697488\pi$
$272$	190.453	0.0424556
$273$	−398.605	−0.0883687
$274$	−1744.24	−0.384575
$275$	449.552	0.0985783
$276$	68.8821	0.0150225
$277$	8666.41	1.87983	0.939917	−	0.341403i	$-0.110902\pi$
$277$	8666.41	1.87983	0.939917	+	0.341403i	$0.110902\pi$
$278$	3375.66	0.728268
$279$	−1530.21	−0.328356
$280$	−5794.45	−1.23673
$281$	7856.96	1.66800	0.833998	−	0.551767i	$-0.186046\pi$
$281$	7856.96	1.66800	0.833998	+	0.551767i	$0.186046\pi$
$282$	−416.410	−0.0879321
$283$	−3054.71	−0.641638	−0.320819	−	0.947141i	$-0.603958\pi$
$283$	−3054.71	−0.641638	−0.320819	+	0.947141i	$0.603958\pi$
$284$	612.203	0.127914
$285$	−1253.07	−0.260441
$286$	−2256.71	−0.466580
$287$	−3878.45	−0.797692
$288$	−2517.57	−0.515101
$289$	−4892.35	−0.995797
$290$	0	0
$291$	−628.166	−0.126542
$292$	2669.07	0.534917
$293$	−2847.83	−0.567822	−0.283911	−	0.958851i	$-0.591632\pi$
$293$	−2847.83	−0.567822	−0.283911	+	0.958851i	$0.591632\pi$
$294$	269.280	0.0534175
$295$	8533.21	1.68414
$296$	5775.55	1.13411
$297$	1591.24	0.310887
$298$	6833.74	1.32842
$299$	−995.522	−0.192550
$300$	18.8009	0.00361823
$301$	−8919.53	−1.70802
$302$	4117.64	0.784581
$303$	740.705	0.140437
$304$	−6506.99	−1.22764
$305$	−2368.70	−0.444693
$306$	289.913	0.0541608
$307$	2470.79	0.459334	0.229667	−	0.973269i	$-0.426236\pi$
$307$	2470.79	0.459334	0.229667	+	0.973269i	$0.426236\pi$
$308$	−1890.92	−0.349822
$309$	−921.955	−0.169735
$310$	−1489.76	−0.272945
$311$	5653.29	1.03077	0.515384	−	0.856959i	$-0.327649\pi$
$311$	5653.29	1.03077	0.515384	+	0.856959i	$0.327649\pi$
$312$	−442.066	−0.0802149
$313$	−8289.72	−1.49701	−0.748503	−	0.663132i	$-0.769227\pi$
$313$	−8289.72	−1.49701	−0.748503	+	0.663132i	$0.769227\pi$
$314$	6447.97	1.15885
$315$	−6235.72	−1.11537
$316$	1327.37	0.236298
$317$	−2577.06	−0.456600	−0.228300	−	0.973591i	$-0.573317\pi$
$317$	−2577.06	−0.456600	−0.228300	+	0.973591i	$0.573317\pi$
$318$	1231.51	0.217168
$319$	0	0
$320$	−6024.20	−1.05238
$321$	−535.486	−0.0931088
$322$	2238.85	0.387473
$323$	−705.502	−0.121533
$324$	−1482.90	−0.254269
$325$	−271.721	−0.0463765
$326$	5195.19	0.882622
$327$	−1133.11	−0.191625
$328$	−4301.33	−0.724088
$329$	5042.70	0.845024
$330$	766.276	0.127825
$331$	−7672.12	−1.27401	−0.637006	−	0.770859i	$-0.719827\pi$
$331$	−7672.12	−1.27401	−0.637006	+	0.770859i	$0.719827\pi$
$332$	−1119.42	−0.185049
$333$	6215.38	1.02283
$334$	2412.73	0.395266
$335$	5589.30	0.911570
$336$	702.840	0.114116
$337$	−3650.77	−0.590120	−0.295060	−	0.955479i	$-0.595340\pi$
$337$	−3650.77	−0.590120	−0.295060	+	0.955479i	$0.595340\pi$
$338$	−3940.02	−0.634049
$339$	808.280	0.129498
$340$	−105.161	−0.0167741
$341$	−2277.15	−0.361626
$342$	−9905.10	−1.56610
$343$	4333.79	0.682223
$344$	−9892.05	−1.55042
$345$	338.034	0.0527512
$346$	−6118.35	−0.950649
$347$	−8737.06	−1.35167	−0.675835	−	0.737053i	$-0.736217\pi$
$347$	−8737.06	−1.35167	−0.675835	+	0.737053i	$0.736217\pi$
$348$	0	0
$349$	−2143.83	−0.328816	−0.164408	−	0.986392i	$-0.552571\pi$
$349$	−2143.83	−0.328816	−0.164408	+	0.986392i	$0.552571\pi$
$350$	611.078	0.0933243
$351$	−961.787	−0.146258
$352$	−3746.46	−0.567293
$353$	−5111.17	−0.770651	−0.385326	−	0.922781i	$-0.625911\pi$
$353$	−5111.17	−0.770651	−0.385326	+	0.922781i	$0.625911\pi$
$354$	−1464.07	−0.219814
$355$	3004.35	0.449167
$356$	−777.900	−0.115811
$357$	76.2035	0.0112972
$358$	8571.10	1.26535
$359$	−4520.87	−0.664630	−0.332315	−	0.943168i	$-0.607830\pi$
$359$	−4520.87	−0.664630	−0.332315	+	0.943168i	$0.607830\pi$
$360$	−6915.62	−1.01246
$361$	17245.1	2.51422
$362$	−7326.35	−1.06371
$363$	163.231	0.0236017
$364$	1142.92	0.164575
$365$	13098.3	1.87835
$366$	406.404	0.0580413
$367$	486.272	0.0691641	0.0345820	−	0.999402i	$-0.488990\pi$
$367$	486.272	0.0691641	0.0345820	+	0.999402i	$0.488990\pi$
$368$	1755.36	0.248653
$369$	−4628.89	−0.653036
$370$	6051.10	0.850221
$371$	−14913.5	−2.08698
$372$	−95.2333	−0.0132732
$373$	10053.1	1.39552	0.697758	−	0.716333i	$-0.254181\pi$
$373$	10053.1	1.39552	0.697758	+	0.716333i	$0.254181\pi$
$374$	431.427	0.0596486
$375$	1101.15	0.151635
$376$	5592.52	0.767053
$377$	0	0
$378$	2162.98	0.294317
$379$	11602.8	1.57255	0.786273	−	0.617879i	$-0.212008\pi$
$379$	11602.8	1.57255	0.786273	+	0.617879i	$0.212008\pi$
$380$	3592.93	0.485035
$381$	893.363	0.120127
$382$	−5369.22	−0.719144
$383$	−4161.38	−0.555187	−0.277593	−	0.960699i	$-0.589537\pi$
$383$	−4161.38	−0.555187	−0.277593	+	0.960699i	$0.589537\pi$
$384$	456.378	0.0606496
$385$	−9279.56	−1.22839
$386$	1527.79	0.201457
$387$	−10645.4	−1.39828
$388$	1801.14	0.235667
$389$	6843.95	0.892036	0.446018	−	0.895024i	$-0.352842\pi$
$389$	6843.95	0.892036	0.446018	+	0.895024i	$0.352842\pi$
$390$	−463.156	−0.0601355
$391$	190.319	0.0246160
$392$	−3616.52	−0.465974
$393$	1785.45	0.229171
$394$	3307.00	0.422854
$395$	6513.97	0.829755
$396$	−2256.79	−0.286384
$397$	5474.73	0.692112	0.346056	−	0.938214i	$-0.387521\pi$
$397$	5474.73	0.692112	0.346056	+	0.938214i	$0.387521\pi$
$398$	3419.43	0.430655
$399$	−2603.55	−0.326669
$400$	479.112	0.0598890
$401$	890.013	0.110836	0.0554178	−	0.998463i	$-0.482351\pi$
$401$	890.013	0.110836	0.0554178	+	0.998463i	$0.482351\pi$
$402$	−958.972	−0.118978
$403$	1376.37	0.170128
$404$	−2123.82	−0.261545
$405$	−7277.22	−0.892860
$406$	0	0
$407$	9249.29	1.12646
$408$	84.5121	0.0102548
$409$	−8107.81	−0.980209	−0.490104	−	0.871664i	$-0.663041\pi$
$409$	−8107.81	−0.980209	−0.490104	+	0.871664i	$0.663041\pi$
$410$	−4506.54	−0.542835
$411$	−547.184	−0.0656706
$412$	2643.52	0.316109
$413$	17729.8	2.11241
$414$	2672.05	0.317207
$415$	−5493.51	−0.649797
$416$	2264.45	0.266885
$417$	1058.97	0.124360
$418$	−14740.1	−1.72479
$419$	4237.59	0.494080	0.247040	−	0.969005i	$-0.420542\pi$
$419$	4237.59	0.494080	0.247040	+	0.969005i	$0.420542\pi$
$420$	−388.083	−0.0450870
$421$	953.634	0.110397	0.0551987	−	0.998475i	$-0.482421\pi$
$421$	953.634	0.110397	0.0551987	+	0.998475i	$0.482421\pi$
$422$	2164.18	0.249646
$423$	6018.41	0.691785
$424$	−16539.5	−1.89441
$425$	51.9463	0.00592886
$426$	−515.464	−0.0586252
$427$	−4921.53	−0.557774
$428$	1535.40	0.173402
$429$	−707.949	−0.0796738
$430$	−10364.0	−1.16232
$431$	−10098.8	−1.12864	−0.564318	−	0.825557i	$-0.690861\pi$
$431$	−10098.8	−1.12864	−0.564318	+	0.825557i	$0.690861\pi$
$432$	1695.87	0.188872
$433$	12833.1	1.42430	0.712148	−	0.702029i	$-0.247722\pi$
$433$	12833.1	1.42430	0.712148	+	0.702029i	$0.247722\pi$
$434$	−3095.34	−0.342352
$435$	0	0
$436$	3248.97	0.356875
$437$	−6502.42	−0.711792
$438$	−2247.31	−0.245162
$439$	−14434.8	−1.56932	−0.784662	−	0.619924i	$-0.787164\pi$
$439$	−14434.8	−1.56932	−0.784662	+	0.619924i	$0.787164\pi$
$440$	−10291.3	−1.11505
$441$	−3891.93	−0.420249
$442$	−260.765	−0.0280619
$443$	7020.65	0.752959	0.376480	−	0.926425i	$-0.377134\pi$
$443$	7020.65	0.752959	0.376480	+	0.926425i	$0.377134\pi$
$444$	386.818	0.0413458
$445$	−3817.49	−0.406666
$446$	−5477.71	−0.581563
$447$	2143.80	0.226842
$448$	−12516.7	−1.32000
$449$	−13210.5	−1.38851	−0.694254	−	0.719730i	$-0.744265\pi$
$449$	−13210.5	−1.38851	−0.694254	+	0.719730i	$0.744265\pi$
$450$	729.315	0.0764006
$451$	−6888.38	−0.719205
$452$	−2317.58	−0.241172
$453$	1291.74	0.133976
$454$	−5016.95	−0.518628
$455$	5608.79	0.577900
$456$	−2887.43	−0.296527
$457$	−2811.18	−0.287749	−0.143875	−	0.989596i	$-0.545956\pi$
$457$	−2811.18	−0.287749	−0.143875	+	0.989596i	$0.545956\pi$
$458$	8968.92	0.915044
$459$	183.870	0.0186979
$460$	−969.245	−0.0982419
$461$	9645.10	0.974441	0.487220	−	0.873279i	$-0.338011\pi$
$461$	9645.10	0.974441	0.487220	+	0.873279i	$0.338011\pi$
$462$	1592.12	0.160329
$463$	6923.23	0.694924	0.347462	−	0.937694i	$-0.387044\pi$
$463$	6923.23	0.694924	0.347462	+	0.937694i	$0.387044\pi$
$464$	0	0
$465$	−467.352	−0.0466084
$466$	6087.07	0.605103
$467$	124.351	0.0123218	0.00616089	−	0.999981i	$-0.498039\pi$
$467$	124.351	0.0123218	0.00616089	+	0.999981i	$0.498039\pi$
$468$	1364.06	0.134730
$469$	11613.1	1.14337
$470$	5859.33	0.575044
$471$	2022.78	0.197887
$472$	19662.9	1.91749
$473$	−15841.7	−1.53996
$474$	−1117.62	−0.108300
$475$	−1774.79	−0.171438
$476$	−218.498	−0.0210396
$477$	−17799.1	−1.70852
$478$	9512.09	0.910194
$479$	4461.48	0.425575	0.212788	−	0.977098i	$-0.431746\pi$
$479$	4461.48	0.425575	0.212788	+	0.977098i	$0.431746\pi$
$480$	−768.907	−0.0731159
$481$	−5590.50	−0.529948
$482$	−4763.39	−0.450137
$483$	702.347	0.0661654
$484$	−468.032	−0.0439549
$485$	8838.96	0.827539
$486$	3886.10	0.362710
$487$	−5660.72	−0.526718	−0.263359	−	0.964698i	$-0.584830\pi$
$487$	−5660.72	−0.526718	−0.263359	+	0.964698i	$0.584830\pi$
$488$	−5458.14	−0.506308
$489$	1629.77	0.150718
$490$	−3789.06	−0.349331
$491$	−5587.50	−0.513565	−0.256782	−	0.966469i	$-0.582662\pi$
$491$	−5587.50	−0.513565	−0.256782	+	0.966469i	$0.582662\pi$
$492$	−288.081	−0.0263978
$493$	0	0
$494$	8909.26	0.811431
$495$	−11075.1	−1.00563
$496$	−2426.88	−0.219698
$497$	6242.24	0.563386
$498$	942.537	0.0848114
$499$	−4210.19	−0.377703	−0.188851	−	0.982006i	$-0.560476\pi$
$499$	−4210.19	−0.377703	−0.188851	+	0.982006i	$0.560476\pi$
$500$	−3157.32	−0.282399
$501$	756.895	0.0674962
$502$	2985.53	0.265440
$503$	−10796.7	−0.957063	−0.478532	−	0.878070i	$-0.658831\pi$
$503$	−10796.7	−0.957063	−0.478532	+	0.878070i	$0.658831\pi$
$504$	−14368.8	−1.26992
$505$	−10422.5	−0.918407
$506$	3976.35	0.349348
$507$	−1236.02	−0.108271
$508$	−2561.54	−0.223720
$509$	14983.6	1.30479	0.652395	−	0.757879i	$-0.273764\pi$
$509$	14983.6	1.30479	0.652395	+	0.757879i	$0.273764\pi$
$510$	88.5442	0.00768785
$511$	27214.8	2.35599
$512$	−12226.4	−1.05534
$513$	−6282.07	−0.540663
$514$	7044.91	0.604548
$515$	12972.9	1.11001
$516$	−662.520	−0.0565229
$517$	8956.17	0.761880
$518$	12572.6	1.06643
$519$	−1919.38	−0.162334
$520$	6220.34	0.524576
$521$	−10770.3	−0.905671	−0.452836	−	0.891594i	$-0.649588\pi$
$521$	−10770.3	−0.905671	−0.452836	+	0.891594i	$0.649588\pi$
$522$	0	0
$523$	−7538.93	−0.630314	−0.315157	−	0.949040i	$-0.602057\pi$
$523$	−7538.93	−0.630314	−0.315157	+	0.949040i	$0.602057\pi$
$524$	−5119.41	−0.426799
$525$	191.700	0.0159362
$526$	750.312	0.0621961
$527$	−263.127	−0.0217495
$528$	1248.29	0.102888
$529$	−10412.9	−0.855829
$530$	−17328.6	−1.42020
$531$	21160.3	1.72934
$532$	7465.16	0.608375
$533$	4163.51	0.338352
$534$	654.978	0.0530781
$535$	7534.86	0.608898
$536$	12879.3	1.03787
$537$	2688.83	0.216073
$538$	4442.11	0.355972
$539$	−5791.69	−0.462831
$540$	−936.400	−0.0746227
$541$	−595.816	−0.0473496	−0.0236748	−	0.999720i	$-0.507537\pi$
$541$	−595.816	−0.0473496	−0.0236748	+	0.999720i	$0.507537\pi$
$542$	−12523.4	−0.992482
$543$	−2298.34	−0.181641
$544$	−432.908	−0.0341191
$545$	15944.1	1.25316
$546$	−962.317	−0.0754274
$547$	12703.4	0.992978	0.496489	−	0.868043i	$-0.334622\pi$
$547$	12703.4	0.992978	0.496489	+	0.868043i	$0.334622\pi$
$548$	1568.94	0.122302
$549$	−5873.80	−0.456626
$550$	1085.32	0.0841418
$551$	0	0
$552$	778.925	0.0600603
$553$	13534.3	1.04075
$554$	20922.6	1.60454
$555$	1898.28	0.145185
$556$	−3036.39	−0.231604
$557$	−14973.0	−1.13901	−0.569503	−	0.821990i	$-0.692864\pi$
$557$	−14973.0	−1.13901	−0.569503	+	0.821990i	$0.692864\pi$
$558$	−3694.25	−0.280269
$559$	9575.10	0.724479
$560$	−9889.71	−0.746280
$561$	135.342	0.0101857
$562$	18968.4	1.42372
$563$	10439.3	0.781466	0.390733	−	0.920504i	$-0.372222\pi$
$563$	10439.3	0.781466	0.390733	+	0.920504i	$0.372222\pi$
$564$	374.559	0.0279641
$565$	−11373.4	−0.846869
$566$	−7374.71	−0.547672
$567$	−15120.2	−1.11991
$568$	6922.85	0.511402
$569$	8859.72	0.652757	0.326379	−	0.945239i	$-0.394172\pi$
$569$	8859.72	0.652757	0.326379	+	0.945239i	$0.394172\pi$
$570$	−3025.18	−0.222300
$571$	−5078.17	−0.372180	−0.186090	−	0.982533i	$-0.559582\pi$
$571$	−5078.17	−0.372180	−0.186090	+	0.982533i	$0.559582\pi$
$572$	2029.90	0.148382
$573$	−1684.37	−0.122802
$574$	−9363.40	−0.680873
$575$	478.775	0.0347240
$576$	−14938.5	−1.08062
$577$	−20457.2	−1.47599	−0.737994	−	0.674808i	$-0.764227\pi$
$577$	−20457.2	−1.47599	−0.737994	+	0.674808i	$0.764227\pi$
$578$	−11811.2	−0.849966
$579$	479.280	0.0344010
$580$	0	0
$581$	−11414.1	−0.815034
$582$	−1516.53	−0.108010
$583$	−26487.3	−1.88164
$584$	30182.1	2.13860
$585$	6694.04	0.473102
$586$	−6875.27	−0.484667
$587$	4355.22	0.306234	0.153117	−	0.988208i	$-0.451069\pi$
$587$	4355.22	0.306234	0.153117	+	0.988208i	$0.451069\pi$
$588$	−242.216	−0.0169878
$589$	8989.96	0.628905
$590$	20601.0	1.43751
$591$	1037.43	0.0722070
$592$	9857.46	0.684357
$593$	4342.49	0.300716	0.150358	−	0.988632i	$-0.451957\pi$
$593$	4342.49	0.300716	0.150358	+	0.988632i	$0.451957\pi$
$594$	3841.60	0.265358
$595$	−1072.26	−0.0738799
$596$	−6146.92	−0.422462
$597$	1072.71	0.0735392
$598$	−2403.40	−0.164352
$599$	12761.8	0.870506	0.435253	−	0.900308i	$-0.356659\pi$
$599$	12761.8	0.870506	0.435253	+	0.900308i	$0.356659\pi$
$600$	212.602	0.0144657
$601$	2804.87	0.190371	0.0951857	−	0.995460i	$-0.469656\pi$
$601$	2804.87	0.190371	0.0951857	+	0.995460i	$0.469656\pi$
$602$	−21533.6	−1.45788
$603$	13860.1	0.936032
$604$	−3703.80	−0.249512
$605$	−2296.84	−0.154346
$606$	1788.22	0.119870
$607$	−12033.5	−0.804654	−0.402327	−	0.915496i	$-0.631798\pi$
$607$	−12033.5	−0.804654	−0.402327	+	0.915496i	$0.631798\pi$
$608$	14790.7	0.986580
$609$	0	0
$610$	−5718.54	−0.379569
$611$	−5413.33	−0.358429
$612$	−260.775	−0.0172242
$613$	7993.67	0.526690	0.263345	−	0.964702i	$-0.415174\pi$
$613$	7993.67	0.526690	0.263345	+	0.964702i	$0.415174\pi$
$614$	5965.02	0.392066
$615$	−1413.74	−0.0926951
$616$	−21382.7	−1.39859
$617$	−9922.51	−0.647432	−0.323716	−	0.946154i	$-0.604932\pi$
$617$	−9922.51	−0.647432	−0.323716	+	0.946154i	$0.604932\pi$
$618$	−2225.80	−0.144878
$619$	15401.4	1.00005	0.500027	−	0.866010i	$-0.333324\pi$
$619$	15401.4	1.00005	0.500027	+	0.866010i	$0.333324\pi$
$620$	1340.03	0.0868018
$621$	1694.68	0.109509
$622$	13648.3	0.879816
$623$	−7931.74	−0.510078
$624$	−754.498	−0.0484040
$625$	−14065.4	−0.900185
$626$	−20013.2	−1.27777
$627$	−4624.08	−0.294527
$628$	−5799.92	−0.368538
$629$	1068.77	0.0677497
$630$	−15054.4	−0.952032
$631$	−3776.97	−0.238287	−0.119143	−	0.992877i	$-0.538015\pi$
$631$	−3776.97	−0.238287	−0.119143	+	0.992877i	$0.538015\pi$
$632$	15010.0	0.944724
$633$	678.921	0.0426298
$634$	−6221.57	−0.389732
$635$	−12570.6	−0.785587
$636$	−1107.74	−0.0690638
$637$	3500.64	0.217740
$638$	0	0
$639$	7450.05	0.461220
$640$	−6421.72	−0.396626
$641$	−464.125	−0.0285988	−0.0142994	−	0.999898i	$-0.504552\pi$
$641$	−464.125	−0.0285988	−0.0142994	+	0.999898i	$0.504552\pi$
$642$	−1292.78	−0.0794733
$643$	7607.61	0.466586	0.233293	−	0.972406i	$-0.425050\pi$
$643$	7607.61	0.466586	0.233293	+	0.972406i	$0.425050\pi$
$644$	−2013.84	−0.123224
$645$	−3251.27	−0.198479
$646$	−1703.23	−0.103735
$647$	7776.85	0.472550	0.236275	−	0.971686i	$-0.424073\pi$
$647$	7776.85	0.472550	0.236275	+	0.971686i	$0.424073\pi$
$648$	−16768.7	−1.01657
$649$	31489.2	1.90456
$650$	−655.992	−0.0395848
$651$	−971.033	−0.0584605
$652$	−4673.04	−0.280691
$653$	24486.1	1.46740	0.733702	−	0.679471i	$-0.237791\pi$
$653$	24486.1	1.46740	0.733702	+	0.679471i	$0.237791\pi$
$654$	−2735.57	−0.163562
$655$	−25123.2	−1.49869
$656$	−7341.31	−0.436936
$657$	32480.6	1.92875
$658$	12174.2	0.721273
$659$	−910.966	−0.0538486	−0.0269243	−	0.999637i	$-0.508571\pi$
$659$	−910.966	−0.0538486	−0.0269243	+	0.999637i	$0.508571\pi$
$660$	−689.262	−0.0406507
$661$	5826.64	0.342859	0.171430	−	0.985196i	$-0.445161\pi$
$661$	5826.64	0.342859	0.171430	+	0.985196i	$0.445161\pi$
$662$	−18522.1	−1.08744
$663$	−81.8043	−0.00479188
$664$	−12658.6	−0.739830
$665$	36634.8	2.13629
$666$	15005.3	0.873036
$667$	0	0
$668$	−2170.24	−0.125702
$669$	−1718.40	−0.0993085
$670$	13493.8	0.778074
$671$	−8740.97	−0.502893
$672$	−1597.59	−0.0917086
$673$	27236.0	1.55999	0.779994	−	0.625788i	$-0.215222\pi$
$673$	27236.0	1.55999	0.779994	+	0.625788i	$0.215222\pi$
$674$	−8813.75	−0.503699
$675$	462.551	0.0263757
$676$	3544.03	0.201640
$677$	−8989.70	−0.510343	−0.255172	−	0.966896i	$-0.582132\pi$
$677$	−8989.70	−0.510343	−0.255172	+	0.966896i	$0.582132\pi$
$678$	1951.36	0.110533
$679$	18365.0	1.03798
$680$	−1189.18	−0.0670630
$681$	−1573.86	−0.0885616
$682$	−5497.52	−0.308667
$683$	6934.65	0.388502	0.194251	−	0.980952i	$-0.437772\pi$
$683$	6934.65	0.388502	0.194251	+	0.980952i	$0.437772\pi$
$684$	8909.59	0.498051
$685$	7699.46	0.429462
$686$	10462.7	0.582314
$687$	2813.63	0.156254
$688$	−16883.3	−0.935567
$689$	16009.6	0.885221
$690$	816.087	0.0450260
$691$	5234.54	0.288178	0.144089	−	0.989565i	$-0.453975\pi$
$691$	5234.54	0.288178	0.144089	+	0.989565i	$0.453975\pi$
$692$	5503.43	0.302325
$693$	−23011.0	−1.26135
$694$	−21093.1	−1.15372
$695$	−14900.9	−0.813270
$696$	0	0
$697$	−795.961	−0.0432556
$698$	−5175.67	−0.280662
$699$	1909.57	0.103328
$700$	−549.662	−0.0296789
$701$	−33713.7	−1.81647	−0.908237	−	0.418457i	$-0.862571\pi$
$701$	−33713.7	−1.81647	−0.908237	+	0.418457i	$0.862571\pi$
$702$	−2321.96	−0.124839
$703$	−36515.3	−1.95903
$704$	−22230.5	−1.19012
$705$	1838.12	0.0981953
$706$	−12339.4	−0.657792
$707$	−21655.2	−1.15195
$708$	1316.92	0.0699053
$709$	−12687.3	−0.672049	−0.336025	−	0.941853i	$-0.609083\pi$
$709$	−12687.3	−0.672049	−0.336025	+	0.941853i	$0.609083\pi$
$710$	7253.13	0.383388
$711$	16153.1	0.852021
$712$	−8796.56	−0.463013
$713$	−2425.17	−0.127382
$714$	183.971	0.00964280
$715$	9961.59	0.521038
$716$	−7709.66	−0.402407
$717$	2984.02	0.155426
$718$	−10914.3	−0.567297
$719$	30604.9	1.58744	0.793720	−	0.608283i	$-0.208141\pi$
$719$	30604.9	1.58744	0.793720	+	0.608283i	$0.208141\pi$
$720$	−11803.3	−0.610947
$721$	26954.2	1.39227
$722$	41633.3	2.14602
$723$	−1494.31	−0.0768661
$724$	6590.02	0.338282
$725$	0	0
$726$	394.075	0.0201453
$727$	−3727.96	−0.190182	−0.0950911	−	0.995469i	$-0.530314\pi$
$727$	−3727.96	−0.190182	−0.0950911	+	0.995469i	$0.530314\pi$
$728$	12924.2	0.657972
$729$	−17218.3	−0.874782
$730$	31622.1	1.60327
$731$	−1830.52	−0.0926189
$732$	−365.559	−0.0184583
$733$	−1107.21	−0.0557921	−0.0278960	−	0.999611i	$-0.508881\pi$
$733$	−1107.21	−0.0557921	−0.0278960	+	0.999611i	$0.508881\pi$
$734$	1173.97	0.0590352
$735$	−1188.66	−0.0596522
$736$	−3990.00	−0.199828
$737$	20625.6	1.03087
$738$	−11175.1	−0.557401
$739$	29127.7	1.44991	0.724953	−	0.688798i	$-0.241861\pi$
$739$	29127.7	1.44991	0.724953	+	0.688798i	$0.241861\pi$
$740$	−5442.94	−0.270387
$741$	2794.91	0.138561
$742$	−36004.3	−1.78135
$743$	−12162.8	−0.600552	−0.300276	−	0.953852i	$-0.597079\pi$
$743$	−12162.8	−0.600552	−0.300276	+	0.953852i	$0.597079\pi$
$744$	−1076.91	−0.0530663
$745$	−30165.6	−1.48347
$746$	24270.2	1.19115
$747$	−13622.6	−0.667233
$748$	−388.067	−0.0189694
$749$	15655.5	0.763736
$750$	2658.41	0.129428
$751$	25067.6	1.21802	0.609008	−	0.793164i	$-0.291568\pi$
$751$	25067.6	1.21802	0.609008	+	0.793164i	$0.291568\pi$
$752$	9545.06	0.462862
$753$	936.587	0.0453269
$754$	0	0
$755$	−18176.1	−0.876156
$756$	−1945.59	−0.0935986
$757$	12020.6	0.577140	0.288570	−	0.957459i	$-0.406820\pi$
$757$	12020.6	0.577140	0.288570	+	0.957459i	$0.406820\pi$
$758$	28011.6	1.34225
$759$	1247.41	0.0596552
$760$	40629.2	1.93918
$761$	9255.42	0.440879	0.220439	−	0.975401i	$-0.429251\pi$
$761$	9255.42	0.440879	0.220439	+	0.975401i	$0.429251\pi$
$762$	2156.77	0.102535
$763$	33127.6	1.57182
$764$	4829.58	0.228702
$765$	−1279.74	−0.0604823
$766$	−10046.5	−0.473881
$767$	−19032.9	−0.896007
$768$	−2323.22	−0.109156
$769$	−28690.1	−1.34537	−0.672687	−	0.739928i	$-0.734860\pi$
$769$	−28690.1	−1.34537	−0.672687	+	0.739928i	$0.734860\pi$
$770$	−22402.8	−1.04850
$771$	2210.05	0.103233
$772$	−1374.24	−0.0640672
$773$	8984.36	0.418040	0.209020	−	0.977911i	$-0.432973\pi$
$773$	8984.36	0.418040	0.209020	+	0.977911i	$0.432973\pi$
$774$	−25700.2	−1.19351
$775$	−661.933	−0.0306804
$776$	20367.4	0.942201
$777$	3944.13	0.182104
$778$	16522.8	0.761400
$779$	27194.7	1.25077
$780$	416.607	0.0191243
$781$	11086.6	0.507952
$782$	459.472	0.0210111
$783$	0	0
$784$	−6172.51	−0.281182
$785$	−28462.7	−1.29411
$786$	4310.46	0.195609
$787$	−5257.13	−0.238115	−0.119058	−	0.992887i	$-0.537987\pi$
$787$	−5257.13	−0.238115	−0.119058	+	0.992887i	$0.537987\pi$
$788$	−2974.63	−0.134476
$789$	235.379	0.0106207
$790$	15726.1	0.708240
$791$	−23630.9	−1.06222
$792$	−25520.0	−1.14497
$793$	5283.26	0.236588
$794$	13217.2	0.590755
$795$	−5436.14	−0.242516
$796$	−3075.76	−0.136957
$797$	−7623.92	−0.338837	−0.169419	−	0.985544i	$-0.554189\pi$
$797$	−7623.92	−0.338837	−0.169419	+	0.985544i	$0.554189\pi$
$798$	−6285.54	−0.278829
$799$	1034.90	0.0458223
$800$	−1089.04	−0.0481293
$801$	−9466.45	−0.417579
$802$	2148.68	0.0946042
$803$	48335.3	2.12418
$804$	862.591	0.0378373
$805$	−9882.77	−0.432698
$806$	3322.84	0.145213
$807$	1393.53	0.0607862
$808$	−24016.4	−1.04566
$809$	28238.7	1.22722	0.613609	−	0.789610i	$-0.289717\pi$
$809$	28238.7	1.22722	0.613609	+	0.789610i	$0.289717\pi$
$810$	−17568.8	−0.762103
$811$	29851.2	1.29250	0.646251	−	0.763125i	$-0.276336\pi$
$811$	29851.2	1.29250	0.646251	+	0.763125i	$0.276336\pi$
$812$	0	0
$813$	−3928.69	−0.169478
$814$	22329.8	0.961496
$815$	−22932.7	−0.985640
$816$	144.242	0.00618807
$817$	62541.4	2.67815
$818$	−19574.0	−0.836661
$819$	13908.4	0.593407
$820$	4053.61	0.172632
$821$	2043.20	0.0868552	0.0434276	−	0.999057i	$-0.486172\pi$
$821$	2043.20	0.0868552	0.0434276	+	0.999057i	$0.486172\pi$
$822$	−1321.02	−0.0560533
$823$	−123.242	−0.00521988	−0.00260994	−	0.999997i	$-0.500831\pi$
$823$	−123.242	−0.00521988	−0.00260994	+	0.999997i	$0.500831\pi$
$824$	29893.1	1.26381
$825$	340.473	0.0143682
$826$	42803.4	1.80305
$827$	−34335.2	−1.44371	−0.721857	−	0.692043i	$-0.756711\pi$
$827$	−34335.2	−1.44371	−0.721857	+	0.692043i	$0.756711\pi$
$828$	−2403.49	−0.100878
$829$	14705.0	0.616073	0.308037	−	0.951375i	$-0.400328\pi$
$829$	14705.0	0.616073	0.308037	+	0.951375i	$0.400328\pi$
$830$	−13262.5	−0.554636
$831$	6563.58	0.273993
$832$	13436.7	0.559894
$833$	−669.237	−0.0278364
$834$	2556.59	0.106148
$835$	−10650.3	−0.441401
$836$	13258.6	0.548515
$837$	−2342.99	−0.0967570
$838$	10230.4	0.421724
$839$	22204.3	0.913679	0.456840	−	0.889549i	$-0.348981\pi$
$839$	22204.3	0.913679	0.456840	+	0.889549i	$0.348981\pi$
$840$	−4388.48	−0.180258
$841$	0	0
$842$	2302.28	0.0942300
$843$	5950.54	0.243117
$844$	−1946.67	−0.0793922
$845$	17392.1	0.708054
$846$	14529.7	0.590475
$847$	−4772.22	−0.193595
$848$	−28228.9	−1.14314
$849$	−2313.51	−0.0935212
$850$	125.410	0.00506060
$851$	9850.54	0.396794
$852$	463.657	0.0186439
$853$	40095.2	1.60942	0.804710	−	0.593669i	$-0.202321\pi$
$853$	40095.2	1.60942	0.804710	+	0.593669i	$0.202321\pi$
$854$	−11881.6	−0.476090
$855$	43723.2	1.74889
$856$	17362.4	0.693265
$857$	−12883.7	−0.513536	−0.256768	−	0.966473i	$-0.582658\pi$
$857$	−12883.7	−0.513536	−0.256768	+	0.966473i	$0.582658\pi$
$858$	−1709.14	−0.0680059
$859$	34336.9	1.36386	0.681932	−	0.731416i	$-0.261140\pi$
$859$	34336.9	1.36386	0.681932	+	0.731416i	$0.261140\pi$
$860$	9322.36	0.369639
$861$	−2937.38	−0.116267
$862$	−24380.7	−0.963351
$863$	10864.2	0.428531	0.214266	−	0.976775i	$-0.431264\pi$
$863$	10864.2	0.428531	0.214266	+	0.976775i	$0.431264\pi$
$864$	−3854.79	−0.151785
$865$	27007.7	1.06161
$866$	30981.9	1.21571
$867$	−3705.27	−0.145141
$868$	2784.24	0.108875
$869$	24037.8	0.938352
$870$	0	0
$871$	−12466.6	−0.484978
$872$	36739.6	1.42679
$873$	21918.5	0.849745
$874$	−15698.2	−0.607552
$875$	−32193.1	−1.24380
$876$	2021.45	0.0779662
$877$	4818.40	0.185525	0.0927626	−	0.995688i	$-0.470430\pi$
$877$	4818.40	0.185525	0.0927626	+	0.995688i	$0.470430\pi$
$878$	−34848.6	−1.33950
$879$	−2156.83	−0.0827623
$880$	−17564.8	−0.672851
$881$	30195.7	1.15473	0.577366	−	0.816485i	$-0.304080\pi$
$881$	30195.7	1.15473	0.577366	+	0.816485i	$0.304080\pi$
$882$	−9395.94	−0.358705
$883$	30734.0	1.17133	0.585663	−	0.810555i	$-0.300834\pi$
$883$	30734.0	1.17133	0.585663	+	0.810555i	$0.300834\pi$
$884$	234.557	0.00892422
$885$	6462.71	0.245471
$886$	16949.3	0.642691
$887$	43409.3	1.64323	0.821614	−	0.570045i	$-0.193074\pi$
$887$	43409.3	1.64323	0.821614	+	0.570045i	$0.193074\pi$
$888$	4374.17	0.165301
$889$	−26118.3	−0.985355
$890$	−9216.24	−0.347111
$891$	−26854.4	−1.00972
$892$	4927.17	0.184948
$893$	−35358.1	−1.32499
$894$	5175.60	0.193622
$895$	−37834.7	−1.41304
$896$	−13342.6	−0.497485
$897$	−753.968	−0.0280650
$898$	−31892.9	−1.18517
$899$	0	0
$900$	−656.016	−0.0242969
$901$	−3060.64	−0.113169
$902$	−16630.0	−0.613880
$903$	−6755.29	−0.248950
$904$	−26207.4	−0.964209
$905$	32340.1	1.18787
$906$	3118.53	0.114356
$907$	7991.51	0.292562	0.146281	−	0.989243i	$-0.453270\pi$
$907$	7991.51	0.292562	0.146281	+	0.989243i	$0.453270\pi$
$908$	4512.72	0.164934
$909$	−25845.3	−0.943052
$910$	13540.8	0.493268
$911$	−24188.5	−0.879694	−0.439847	−	0.898073i	$-0.644967\pi$
$911$	−24188.5	−0.879694	−0.439847	+	0.898073i	$0.644967\pi$
$912$	−4928.13	−0.178933
$913$	−20272.1	−0.734840
$914$	−6786.79	−0.245609
$915$	−1793.96	−0.0648157
$916$	−8067.50	−0.291002
$917$	−52199.4	−1.87980
$918$	443.902	0.0159596
$919$	27421.3	0.984273	0.492136	−	0.870518i	$-0.336216\pi$
$919$	27421.3	0.984273	0.492136	+	0.870518i	$0.336216\pi$
$920$	−10960.3	−0.392773
$921$	1871.28	0.0669497
$922$	23285.3	0.831737
$923$	−6701.03	−0.238968
$924$	−1432.10	−0.0509878
$925$	2688.63	0.0955694
$926$	16714.1	0.593154
$927$	32169.6	1.13979
$928$	0	0
$929$	−9284.12	−0.327882	−0.163941	−	0.986470i	$-0.552421\pi$
$929$	−9284.12	−0.327882	−0.163941	+	0.986470i	$0.552421\pi$
$930$	−1128.29	−0.0397828
$931$	22865.0	0.804910
$932$	−5475.29	−0.192435
$933$	4281.57	0.150238
$934$	300.210	0.0105173
$935$	−1904.41	−0.0666106
$936$	15424.9	0.538653
$937$	−1891.00	−0.0659297	−0.0329649	−	0.999457i	$-0.510495\pi$
$937$	−1891.00	−0.0659297	−0.0329649	+	0.999457i	$0.510495\pi$
$938$	28036.5	0.975932
$939$	−6278.30	−0.218194
$940$	−5270.44	−0.182875
$941$	15163.9	0.525322	0.262661	−	0.964888i	$-0.415400\pi$
$941$	15163.9	0.525322	0.262661	+	0.964888i	$0.415400\pi$
$942$	4883.43	0.168907
$943$	−7336.16	−0.253338
$944$	33559.7	1.15707
$945$	−9547.87	−0.328669
$946$	−38245.2	−1.31444
$947$	31251.8	1.07238	0.536192	−	0.844096i	$-0.319862\pi$
$947$	31251.8	1.07238	0.536192	+	0.844096i	$0.319862\pi$
$948$	1005.29	0.0344414
$949$	−29215.1	−0.999327
$950$	−4284.72	−0.146331
$951$	−1951.76	−0.0665512
$952$	−2470.79	−0.0841165
$953$	−12521.4	−0.425612	−0.212806	−	0.977094i	$-0.568260\pi$
$953$	−12521.4	−0.425612	−0.212806	+	0.977094i	$0.568260\pi$
$954$	−42970.8	−1.45831
$955$	23700.9	0.803081
$956$	−8556.07	−0.289459
$957$	0	0
$958$	10771.0	0.363251
$959$	15997.5	0.538670
$960$	−4562.48	−0.153389
$961$	−26438.1	−0.887451
$962$	−13496.7	−0.452339
$963$	18684.6	0.625237
$964$	4284.64	0.143152
$965$	−6743.98	−0.224970
$966$	1695.61	0.0564757
$967$	18348.5	0.610183	0.305091	−	0.952323i	$-0.401313\pi$
$967$	18348.5	0.610183	0.305091	+	0.952323i	$0.401313\pi$
$968$	−5292.55	−0.175732
$969$	−534.319	−0.0177139
$970$	21339.1	0.706349
$971$	−27188.0	−0.898564	−0.449282	−	0.893390i	$-0.648320\pi$
$971$	−27188.0	−0.898564	−0.449282	+	0.893390i	$0.648320\pi$
$972$	−3495.53	−0.115349
$973$	−30960.1	−1.02008
$974$	−13666.2	−0.449582
$975$	−205.790	−0.00675955
$976$	−9315.71	−0.305521
$977$	4733.67	0.155009	0.0775044	−	0.996992i	$-0.475305\pi$
$977$	4733.67	0.155009	0.0775044	+	0.996992i	$0.475305\pi$
$978$	3934.62	0.128646
$979$	−14087.3	−0.459890
$980$	3408.24	0.111094
$981$	39537.5	1.28678
$982$	−13489.4	−0.438355
$983$	43971.5	1.42673	0.713363	−	0.700795i	$-0.247171\pi$
$983$	43971.5	1.42673	0.713363	+	0.700795i	$0.247171\pi$
$984$	−3257.65	−0.105539
$985$	−14597.8	−0.472208
$986$	0	0
$987$	3819.13	0.123166
$988$	−8013.84	−0.258051
$989$	−16871.4	−0.542448
$990$	−26737.5	−0.858359
$991$	−14031.4	−0.449769	−0.224885	−	0.974385i	$-0.572201\pi$
$991$	−14031.4	−0.449769	−0.224885	+	0.974385i	$0.572201\pi$
$992$	5516.39	0.176558
$993$	−5810.56	−0.185692
$994$	15070.1	0.480880
$995$	−15094.1	−0.480920
$996$	−847.807	−0.0269717
$997$	−43177.4	−1.37156	−0.685779	−	0.727810i	$-0.740538\pi$
$997$	−43177.4	−1.37156	−0.685779	+	0.727810i	$0.740538\pi$
$998$	−10164.3	−0.322390
$999$	9516.73	0.301397

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	841.4.a.a.1.2		2
29.28	even	2		29.4.a.a.1.1	✓	2
87.86	odd	2		261.4.a.b.1.2		2
116.115	odd	2		464.4.a.f.1.1		2
145.144	even	2		725.4.a.b.1.2		2
203.202	odd	2		1421.4.a.c.1.1		2
232.115	odd	2		1856.4.a.h.1.2		2
232.173	even	2		1856.4.a.n.1.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
29.4.a.a.1.1	✓	2	29.28	even	2
261.4.a.b.1.2		2	87.86	odd	2
464.4.a.f.1.1		2	116.115	odd	2
725.4.a.b.1.2		2	145.144	even	2
841.4.a.a.1.2		2	1.1	even	1	trivial
1421.4.a.c.1.1		2	203.202	odd	2
1856.4.a.h.1.2		2	232.115	odd	2
1856.4.a.n.1.1		2	232.173	even	2

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:	\( N \)	\(=\)	\( 841 = 29^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	841.a (trivial)

\(f(q)\)	\(=\)	\(q+2.41421 q^{2} +0.757359 q^{3} -2.17157 q^{4} -10.6569 q^{5} +1.82843 q^{6} -22.1421 q^{7} -24.5563 q^{8} -26.4264 q^{9} +O(q^{10})\)	\(q+2.41421 q^{2} +0.757359 q^{3} -2.17157 q^{4} -10.6569 q^{5} +1.82843 q^{6} -22.1421 q^{7} -24.5563 q^{8} -26.4264 q^{9} -25.7279 q^{10} -39.3259 q^{11} -1.64466 q^{12} +23.7696 q^{13} -53.4558 q^{14} -8.07107 q^{15} -41.9117 q^{16} -4.54416 q^{17} -63.7990 q^{18} +155.255 q^{19} +23.1421 q^{20} -16.7696 q^{21} -94.9411 q^{22} -41.8823 q^{23} -18.5980 q^{24} -11.4315 q^{25} +57.3848 q^{26} -40.4630 q^{27} +48.0833 q^{28} -19.4853 q^{30} +57.9045 q^{31} +95.2670 q^{32} -29.7838 q^{33} -10.9706 q^{34} +235.966 q^{35} +57.3869 q^{36} -235.196 q^{37} +374.818 q^{38} +18.0021 q^{39} +261.693 q^{40} +175.161 q^{41} -40.4853 q^{42} +402.831 q^{43} +85.3991 q^{44} +281.622 q^{45} -101.113 q^{46} -227.742 q^{47} -31.7422 q^{48} +147.274 q^{49} -27.5980 q^{50} -3.44156 q^{51} -51.6173 q^{52} +673.534 q^{53} -97.6863 q^{54} +419.090 q^{55} +543.730 q^{56} +117.584 q^{57} -800.725 q^{59} +17.5269 q^{60} +222.270 q^{61} +139.794 q^{62} +585.137 q^{63} +565.288 q^{64} -253.309 q^{65} -71.9045 q^{66} -524.479 q^{67} +9.86797 q^{68} -31.7199 q^{69} +569.671 q^{70} -281.917 q^{71} +648.936 q^{72} -1229.10 q^{73} -567.813 q^{74} -8.65772 q^{75} -337.147 q^{76} +870.759 q^{77} +43.4609 q^{78} -611.247 q^{79} +446.647 q^{80} +682.868 q^{81} +422.877 q^{82} +515.490 q^{83} +36.4163 q^{84} +48.4264 q^{85} +972.519 q^{86} +965.701 q^{88} +358.219 q^{89} +679.897 q^{90} -526.309 q^{91} +90.9504 q^{92} +43.8545 q^{93} -549.818 q^{94} -1654.53 q^{95} +72.1514 q^{96} -829.415 q^{97} +355.551 q^{98} +1039.24 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + 2 q^{2} + 10 q^{3} - 10 q^{4} - 10 q^{5} - 2 q^{6} - 16 q^{7} - 18 q^{8} + 32 q^{9}+O(q^{10}) \) 2 * q + 2 * q^2 + 10 * q^3 - 10 * q^4 - 10 * q^5 - 2 * q^6 - 16 * q^7 - 18 * q^8 + 32 * q^9	\( 2 q + 2 q^{2} + 10 q^{3} - 10 q^{4} - 10 q^{5} - 2 q^{6} - 16 q^{7} - 18 q^{8} + 32 q^{9} - 26 q^{10} + 26 q^{11} - 74 q^{12} - 26 q^{13} - 56 q^{14} - 2 q^{15} + 18 q^{16} - 60 q^{17} - 88 q^{18} + 220 q^{19} + 18 q^{20} + 40 q^{21} - 122 q^{22} + 52 q^{23} + 42 q^{24} - 136 q^{25} + 78 q^{26} + 250 q^{27} - 22 q^{30} + 294 q^{31} + 18 q^{32} + 574 q^{33} + 12 q^{34} + 240 q^{35} - 400 q^{36} - 312 q^{37} + 348 q^{38} - 442 q^{39} + 266 q^{40} - 40 q^{41} - 64 q^{42} + 322 q^{43} - 426 q^{44} + 320 q^{45} - 140 q^{46} + 130 q^{47} + 522 q^{48} - 158 q^{49} + 24 q^{50} - 516 q^{51} + 338 q^{52} + 1002 q^{53} - 218 q^{54} + 462 q^{55} + 584 q^{56} + 716 q^{57} - 900 q^{59} - 30 q^{60} + 948 q^{61} + 42 q^{62} + 944 q^{63} + 118 q^{64} - 286 q^{65} - 322 q^{66} + 320 q^{67} + 444 q^{68} + 836 q^{69} + 568 q^{70} - 660 q^{71} + 1032 q^{72} - 648 q^{73} - 536 q^{74} - 1160 q^{75} - 844 q^{76} + 1272 q^{77} + 234 q^{78} - 258 q^{79} + 486 q^{80} + 1790 q^{81} + 512 q^{82} + 1212 q^{83} - 408 q^{84} + 12 q^{85} + 1006 q^{86} + 1394 q^{88} - 760 q^{89} + 664 q^{90} - 832 q^{91} - 644 q^{92} + 2226 q^{93} - 698 q^{94} - 1612 q^{95} - 642 q^{96} - 24 q^{97} + 482 q^{98} + 4856 q^{99}+O(q^{100}) \) 2 * q + 2 * q^2 + 10 * q^3 - 10 * q^4 - 10 * q^5 - 2 * q^6 - 16 * q^7 - 18 * q^8 + 32 * q^9 - 26 * q^10 + 26 * q^11 - 74 * q^12 - 26 * q^13 - 56 * q^14 - 2 * q^15 + 18 * q^16 - 60 * q^17 - 88 * q^18 + 220 * q^19 + 18 * q^20 + 40 * q^21 - 122 * q^22 + 52 * q^23 + 42 * q^24 - 136 * q^25 + 78 * q^26 + 250 * q^27 - 22 * q^30 + 294 * q^31 + 18 * q^32 + 574 * q^33 + 12 * q^34 + 240 * q^35 - 400 * q^36 - 312 * q^37 + 348 * q^38 - 442 * q^39 + 266 * q^40 - 40 * q^41 - 64 * q^42 + 322 * q^43 - 426 * q^44 + 320 * q^45 - 140 * q^46 + 130 * q^47 + 522 * q^48 - 158 * q^49 + 24 * q^50 - 516 * q^51 + 338 * q^52 + 1002 * q^53 - 218 * q^54 + 462 * q^55 + 584 * q^56 + 716 * q^57 - 900 * q^59 - 30 * q^60 + 948 * q^61 + 42 * q^62 + 944 * q^63 + 118 * q^64 - 286 * q^65 - 322 * q^66 + 320 * q^67 + 444 * q^68 + 836 * q^69 + 568 * q^70 - 660 * q^71 + 1032 * q^72 - 648 * q^73 - 536 * q^74 - 1160 * q^75 - 844 * q^76 + 1272 * q^77 + 234 * q^78 - 258 * q^79 + 486 * q^80 + 1790 * q^81 + 512 * q^82 + 1212 * q^83 - 408 * q^84 + 12 * q^85 + 1006 * q^86 + 1394 * q^88 - 760 * q^89 + 664 * q^90 - 832 * q^91 - 644 * q^92 + 2226 * q^93 - 698 * q^94 - 1612 * q^95 - 642 * q^96 - 24 * q^97 + 482 * q^98 + 4856 * q^99

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