LMFDB - Embedded newform 2013.4.a.a.1.13

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2013,4,Mod(1,2013)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2013, 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("2013.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 2013 = 3 \cdot 11 \cdot 61 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	2013.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:	$118.770844842$
Analytic rank:	$1$
Dimension:	$36$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.13
Character	$\chi$	$=$	2013.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-3.05325 q^{2} +3.00000 q^{3} +1.32235 q^{4} -6.59737 q^{5} -9.15976 q^{6} -7.71882 q^{7} +20.3886 q^{8} +9.00000 q^{9} +O(q^{10})$	\(q-3.05325 q^{2} +3.00000 q^{3} +1.32235 q^{4} -6.59737 q^{5} -9.15976 q^{6} -7.71882 q^{7} +20.3886 q^{8} +9.00000 q^{9} +20.1434 q^{10} +11.0000 q^{11} +3.96704 q^{12} -86.2701 q^{13} +23.5675 q^{14} -19.7921 q^{15} -72.8302 q^{16} +11.7524 q^{17} -27.4793 q^{18} +73.1999 q^{19} -8.72400 q^{20} -23.1565 q^{21} -33.5858 q^{22} -9.70026 q^{23} +61.1657 q^{24} -81.4747 q^{25} +263.404 q^{26} +27.0000 q^{27} -10.2070 q^{28} +120.290 q^{29} +60.4303 q^{30} +168.414 q^{31} +59.2604 q^{32} +33.0000 q^{33} -35.8830 q^{34} +50.9239 q^{35} +11.9011 q^{36} +343.691 q^{37} -223.498 q^{38} -258.810 q^{39} -134.511 q^{40} +334.621 q^{41} +70.7025 q^{42} -342.503 q^{43} +14.5458 q^{44} -59.3763 q^{45} +29.6173 q^{46} -151.927 q^{47} -218.491 q^{48} -283.420 q^{49} +248.763 q^{50} +35.2571 q^{51} -114.079 q^{52} -296.318 q^{53} -82.4378 q^{54} -72.5711 q^{55} -157.376 q^{56} +219.600 q^{57} -367.277 q^{58} +541.034 q^{59} -26.1720 q^{60} +61.0000 q^{61} -514.209 q^{62} -69.4694 q^{63} +401.705 q^{64} +569.155 q^{65} -100.757 q^{66} -787.270 q^{67} +15.5407 q^{68} -29.1008 q^{69} -155.484 q^{70} -107.252 q^{71} +183.497 q^{72} +281.800 q^{73} -1049.38 q^{74} -244.424 q^{75} +96.7956 q^{76} -84.9071 q^{77} +790.213 q^{78} -126.474 q^{79} +480.487 q^{80} +81.0000 q^{81} -1021.68 q^{82} -460.794 q^{83} -30.6209 q^{84} -77.5348 q^{85} +1045.75 q^{86} +360.871 q^{87} +224.274 q^{88} +1456.71 q^{89} +181.291 q^{90} +665.903 q^{91} -12.8271 q^{92} +505.241 q^{93} +463.871 q^{94} -482.927 q^{95} +177.781 q^{96} -591.774 q^{97} +865.352 q^{98} +99.0000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q - 14 q^{2} + 108 q^{3} + 146 q^{4} - 65 q^{5} - 42 q^{6} - 105 q^{7} - 189 q^{8} + 324 q^{9}+O(q^{10}) $ 36 * q - 14 * q^2 + 108 * q^3 + 146 * q^4 - 65 * q^5 - 42 * q^6 - 105 * q^7 - 189 * q^8 + 324 * q^9	\( 36 q - 14 q^{2} + 108 q^{3} + 146 q^{4} - 65 q^{5} - 42 q^{6} - 105 q^{7} - 189 q^{8} + 324 q^{9} - 161 q^{10} + 396 q^{11} + 438 q^{12} - 233 q^{13} - 264 q^{14} - 195 q^{15} + 574 q^{16} - 556 q^{17} - 126 q^{18} - 615 q^{19} - 136 q^{20} - 315 q^{21} - 154 q^{22} - 457 q^{23} - 567 q^{24} + 863 q^{25} + 115 q^{26} + 972 q^{27} - 424 q^{28} - 754 q^{29} - 483 q^{30} - 508 q^{31} - 1511 q^{32} + 1188 q^{33} - 860 q^{34} - 826 q^{35} + 1314 q^{36} - 412 q^{37} - 599 q^{38} - 699 q^{39} - 2791 q^{40} - 2066 q^{41} - 792 q^{42} - 2063 q^{43} + 1606 q^{44} - 585 q^{45} - 787 q^{46} - 1815 q^{47} + 1722 q^{48} + 2825 q^{49} + 808 q^{50} - 1668 q^{51} - 2882 q^{52} - 759 q^{53} - 378 q^{54} - 715 q^{55} - 1749 q^{56} - 1845 q^{57} - 335 q^{58} - 2337 q^{59} - 408 q^{60} + 2196 q^{61} - 1689 q^{62} - 945 q^{63} + 4723 q^{64} - 3550 q^{65} - 462 q^{66} - 1331 q^{67} - 6166 q^{68} - 1371 q^{69} - 1750 q^{70} - 361 q^{71} - 1701 q^{72} - 4627 q^{73} - 3394 q^{74} + 2589 q^{75} - 7214 q^{76} - 1155 q^{77} + 345 q^{78} - 2583 q^{79} - 2643 q^{80} + 2916 q^{81} + 1090 q^{82} - 6123 q^{83} - 1272 q^{84} + 295 q^{85} + 613 q^{86} - 2262 q^{87} - 2079 q^{88} - 2485 q^{89} - 1449 q^{90} - 3156 q^{91} - 6291 q^{92} - 1524 q^{93} - 1744 q^{94} - 5572 q^{95} - 4533 q^{96} - 2558 q^{97} - 2314 q^{98} + 3564 q^{99}+O(q^{100}) \) 36 * q - 14 * q^2 + 108 * q^3 + 146 * q^4 - 65 * q^5 - 42 * q^6 - 105 * q^7 - 189 * q^8 + 324 * q^9 - 161 * q^10 + 396 * q^11 + 438 * q^12 - 233 * q^13 - 264 * q^14 - 195 * q^15 + 574 * q^16 - 556 * q^17 - 126 * q^18 - 615 * q^19 - 136 * q^20 - 315 * q^21 - 154 * q^22 - 457 * q^23 - 567 * q^24 + 863 * q^25 + 115 * q^26 + 972 * q^27 - 424 * q^28 - 754 * q^29 - 483 * q^30 - 508 * q^31 - 1511 * q^32 + 1188 * q^33 - 860 * q^34 - 826 * q^35 + 1314 * q^36 - 412 * q^37 - 599 * q^38 - 699 * q^39 - 2791 * q^40 - 2066 * q^41 - 792 * q^42 - 2063 * q^43 + 1606 * q^44 - 585 * q^45 - 787 * q^46 - 1815 * q^47 + 1722 * q^48 + 2825 * q^49 + 808 * q^50 - 1668 * q^51 - 2882 * q^52 - 759 * q^53 - 378 * q^54 - 715 * q^55 - 1749 * q^56 - 1845 * q^57 - 335 * q^58 - 2337 * q^59 - 408 * q^60 + 2196 * q^61 - 1689 * q^62 - 945 * q^63 + 4723 * q^64 - 3550 * q^65 - 462 * q^66 - 1331 * q^67 - 6166 * q^68 - 1371 * q^69 - 1750 * q^70 - 361 * q^71 - 1701 * q^72 - 4627 * q^73 - 3394 * q^74 + 2589 * q^75 - 7214 * q^76 - 1155 * q^77 + 345 * q^78 - 2583 * q^79 - 2643 * q^80 + 2916 * q^81 + 1090 * q^82 - 6123 * q^83 - 1272 * q^84 + 295 * q^85 + 613 * q^86 - 2262 * q^87 - 2079 * q^88 - 2485 * q^89 - 1449 * q^90 - 3156 * q^91 - 6291 * q^92 - 1524 * q^93 - 1744 * q^94 - 5572 * q^95 - 4533 * q^96 - 2558 * q^97 - 2314 * q^98 + 3564 * 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 $

$2$	−3.05325	−1.07949	−0.539744	−	0.841829i	$-0.681479\pi$
$2$	−3.05325	−1.07949	−0.539744	+	0.841829i	$0.681479\pi$
$3$	3.00000	0.577350
$3$	3.00000	0.577350
$4$	1.32235	0.165293
$5$	−6.59737	−0.590087	−0.295043	−	0.955484i	$-0.595334\pi$
$5$	−6.59737	−0.590087	−0.295043	+	0.955484i	$0.595334\pi$
$6$	−9.15976	−0.623242
$7$	−7.71882	−0.416777	−0.208389	−	0.978046i	$-0.566822\pi$
$7$	−7.71882	−0.416777	−0.208389	+	0.978046i	$0.566822\pi$
$8$	20.3886	0.901056
$9$	9.00000	0.333333
$10$	20.1434	0.636991
$11$	11.0000	0.301511
$11$	11.0000	0.301511
$12$	3.96704	0.0954321
$13$	−86.2701	−1.84054	−0.920270	−	0.391285i	$-0.872031\pi$
$13$	−86.2701	−1.84054	−0.920270	+	0.391285i	$0.872031\pi$
$14$	23.5675	0.449906
$15$	−19.7921	−0.340687
$16$	−72.8302	−1.13797
$17$	11.7524	0.167669	0.0838344	−	0.996480i	$-0.473283\pi$
$17$	11.7524	0.167669	0.0838344	+	0.996480i	$0.473283\pi$
$18$	−27.4793	−0.359829
$19$	73.1999	0.883853	0.441927	−	0.897051i	$-0.354295\pi$
$19$	73.1999	0.883853	0.441927	+	0.897051i	$0.354295\pi$
$20$	−8.72400	−0.0975373
$21$	−23.1565	−0.240627
$22$	−33.5858	−0.325478
$23$	−9.70026	−0.0879410	−0.0439705	−	0.999033i	$-0.514001\pi$
$23$	−9.70026	−0.0879410	−0.0439705	+	0.999033i	$0.514001\pi$
$24$	61.1657	0.520225
$25$	−81.4747	−0.651798
$26$	263.404	1.98684
$27$	27.0000	0.192450
$28$	−10.2070	−0.0688905
$29$	120.290	0.770254	0.385127	−	0.922863i	$-0.374158\pi$
$29$	120.290	0.770254	0.385127	+	0.922863i	$0.374158\pi$
$30$	60.4303	0.367767
$31$	168.414	0.975741	0.487871	−	0.872916i	$-0.337774\pi$
$31$	168.414	0.975741	0.487871	+	0.872916i	$0.337774\pi$
$32$	59.2604	0.327370
$33$	33.0000	0.174078
$34$	−35.8830	−0.180996
$35$	50.9239	0.245935
$36$	11.9011	0.0550977
$37$	343.691	1.52709	0.763547	−	0.645752i	$-0.223456\pi$
$37$	343.691	1.52709	0.763547	+	0.645752i	$0.223456\pi$
$38$	−223.498	−0.954108
$39$	−258.810	−1.06264
$40$	−134.511	−0.531701
$41$	334.621	1.27461	0.637305	−	0.770612i	$-0.280049\pi$
$41$	334.621	1.27461	0.637305	+	0.770612i	$0.280049\pi$
$42$	70.7025	0.259753
$43$	−342.503	−1.21468	−0.607339	−	0.794443i	$-0.707763\pi$
$43$	−342.503	−1.21468	−0.607339	+	0.794443i	$0.707763\pi$
$44$	14.5458	0.0498378
$45$	−59.3763	−0.196696
$46$	29.6173	0.0949312
$47$	−151.927	−0.471507	−0.235753	−	0.971813i	$-0.575756\pi$
$47$	−151.927	−0.471507	−0.235753	+	0.971813i	$0.575756\pi$
$48$	−218.491	−0.657008
$49$	−283.420	−0.826297
$50$	248.763	0.703608
$51$	35.2571	0.0968037
$52$	−114.079	−0.304229
$53$	−296.318	−0.767969	−0.383985	−	0.923339i	$-0.625448\pi$
$53$	−296.318	−0.767969	−0.383985	+	0.923339i	$0.625448\pi$
$54$	−82.4378	−0.207747
$55$	−72.5711	−0.177918
$56$	−157.376	−0.375540
$57$	219.600	0.510293
$58$	−367.277	−0.831480
$59$	541.034	1.19384	0.596921	−	0.802300i	$-0.296391\pi$
$59$	541.034	1.19384	0.596921	+	0.802300i	$0.296391\pi$
$60$	−26.1720	−0.0563132
$61$	61.0000	0.128037
$61$	61.0000	0.128037
$62$	−514.209	−1.05330
$63$	−69.4694	−0.138926
$64$	401.705	0.784579
$65$	569.155	1.08608
$66$	−100.757	−0.187915
$67$	−787.270	−1.43553	−0.717764	−	0.696287i	$-0.754834\pi$
$67$	−787.270	−1.43553	−0.717764	+	0.696287i	$0.754834\pi$
$68$	15.5407	0.0277145
$69$	−29.1008	−0.0507728
$70$	−155.484	−0.265483
$71$	−107.252	−0.179274	−0.0896372	−	0.995974i	$-0.528571\pi$
$71$	−107.252	−0.179274	−0.0896372	+	0.995974i	$0.528571\pi$
$72$	183.497	0.300352
$73$	281.800	0.451811	0.225905	−	0.974149i	$-0.427466\pi$
$73$	281.800	0.451811	0.225905	+	0.974149i	$0.427466\pi$
$74$	−1049.38	−1.64848
$75$	−244.424	−0.376316
$76$	96.7956	0.146095
$77$	−84.9071	−0.125663
$78$	790.213	1.14710
$79$	−126.474	−0.180120	−0.0900598	−	0.995936i	$-0.528706\pi$
$79$	−126.474	−0.180120	−0.0900598	+	0.995936i	$0.528706\pi$
$80$	480.487	0.671502
$81$	81.0000	0.111111
$82$	−1021.68	−1.37592
$83$	−460.794	−0.609382	−0.304691	−	0.952451i	$-0.598553\pi$
$83$	−460.794	−0.609382	−0.304691	+	0.952451i	$0.598553\pi$
$84$	−30.6209	−0.0397739
$85$	−77.5348	−0.0989392
$86$	1045.75	1.31123
$87$	360.871	0.444707
$88$	224.274	0.271678
$89$	1456.71	1.73495	0.867476	−	0.497479i	$-0.165741\pi$
$89$	1456.71	1.73495	0.867476	+	0.497479i	$0.165741\pi$
$90$	181.291	0.212330
$91$	665.903	0.767095
$92$	−12.8271	−0.0145361
$93$	505.241	0.563345
$94$	463.871	0.508985
$95$	−482.927	−0.521550
$96$	177.781	0.189007
$97$	−591.774	−0.619439	−0.309719	−	0.950828i	$-0.600235\pi$
$97$	−591.774	−0.619439	−0.309719	+	0.950828i	$0.600235\pi$
$98$	865.352	0.891977
$99$	99.0000	0.100504
$100$	−107.738	−0.107738
$101$	1302.84	1.28354	0.641770	−	0.766897i	$-0.278200\pi$
$101$	1302.84	1.28354	0.641770	+	0.766897i	$0.278200\pi$
$102$	−107.649	−0.104498
$103$	1060.21	1.01422	0.507112	−	0.861880i	$-0.330713\pi$
$103$	1060.21	1.01422	0.507112	+	0.861880i	$0.330713\pi$
$104$	−1758.92	−1.65843
$105$	152.772	0.141990
$106$	904.733	0.829013
$107$	−1727.52	−1.56080	−0.780402	−	0.625278i	$-0.784985\pi$
$107$	−1727.52	−1.56080	−0.780402	+	0.625278i	$0.784985\pi$
$108$	35.7033	0.0318107
$109$	1176.87	1.03416	0.517081	−	0.855936i	$-0.327019\pi$
$109$	1176.87	1.03416	0.517081	+	0.855936i	$0.327019\pi$
$110$	221.578	0.192060
$111$	1031.07	0.881668
$112$	562.163	0.474281
$113$	976.326	0.812788	0.406394	−	0.913698i	$-0.366786\pi$
$113$	976.326	0.812788	0.406394	+	0.913698i	$0.366786\pi$
$114$	−670.493	−0.550855
$115$	63.9962	0.0518928
$116$	159.066	0.127318
$117$	−776.431	−0.613513
$118$	−1651.91	−1.28874
$119$	−90.7146	−0.0698806
$120$	−403.533	−0.306978
$121$	121.000	0.0909091
$122$	−186.248	−0.138214
$123$	1003.86	0.735896
$124$	222.701	0.161283
$125$	1362.19	0.974704
$126$	212.108	0.149969
$127$	1911.06	1.33527	0.667634	−	0.744489i	$-0.267307\pi$
$127$	1911.06	1.33527	0.667634	+	0.744489i	$0.267307\pi$
$128$	−1700.59	−1.17431
$129$	−1027.51	−0.701295
$130$	−1737.77	−1.17241
$131$	−413.662	−0.275892	−0.137946	−	0.990440i	$-0.544050\pi$
$131$	−413.662	−0.275892	−0.137946	+	0.990440i	$0.544050\pi$
$132$	43.6374	0.0287739
$133$	−565.017	−0.368370
$134$	2403.73	1.54963
$135$	−178.129	−0.113562
$136$	239.614	0.151079
$137$	−2337.21	−1.45753	−0.728763	−	0.684766i	$-0.759905\pi$
$137$	−2337.21	−1.45753	−0.728763	+	0.684766i	$0.759905\pi$
$138$	88.8520	0.0548086
$139$	−1650.89	−1.00739	−0.503693	−	0.863883i	$-0.668026\pi$
$139$	−1650.89	−1.00739	−0.503693	+	0.863883i	$0.668026\pi$
$140$	67.3390	0.0406513
$141$	−455.781	−0.272224
$142$	327.468	0.193524
$143$	−948.971	−0.554943
$144$	−655.472	−0.379324
$145$	−793.601	−0.454517
$146$	−860.406	−0.487724
$147$	−850.259	−0.477063
$148$	454.479	0.252418
$149$	−2925.81	−1.60867	−0.804336	−	0.594175i	$-0.797479\pi$
$149$	−2925.81	−1.60867	−0.804336	+	0.594175i	$0.797479\pi$
$150$	746.289	0.406228
$151$	3029.82	1.63287	0.816435	−	0.577437i	$-0.195947\pi$
$151$	3029.82	1.63287	0.816435	+	0.577437i	$0.195947\pi$
$152$	1492.44	0.796401
$153$	105.771	0.0558896
$154$	259.243	0.135652
$155$	−1111.09	−0.575772
$156$	−342.237	−0.175646
$157$	−2898.98	−1.47366	−0.736828	−	0.676080i	$-0.763677\pi$
$157$	−2898.98	−1.47366	−0.736828	+	0.676080i	$0.763677\pi$
$158$	386.157	0.194437
$159$	−888.953	−0.443387
$160$	−390.962	−0.193177
$161$	74.8746	0.0366518
$162$	−247.313	−0.119943
$163$	2448.00	1.17633	0.588165	−	0.808741i	$-0.299850\pi$
$163$	2448.00	1.17633	0.588165	+	0.808741i	$0.299850\pi$
$164$	442.484	0.210684
$165$	−217.713	−0.102721
$166$	1406.92	0.657820
$167$	−2016.11	−0.934199	−0.467100	−	0.884205i	$-0.654701\pi$
$167$	−2016.11	−0.934199	−0.467100	+	0.884205i	$0.654701\pi$
$168$	−472.127	−0.216818
$169$	5245.52	2.38758
$170$	236.733	0.106804
$171$	658.799	0.294618
$172$	−452.907	−0.200778
$173$	−251.061	−0.110334	−0.0551671	−	0.998477i	$-0.517569\pi$
$173$	−251.061	−0.110334	−0.0551671	+	0.998477i	$0.517569\pi$
$174$	−1101.83	−0.480055
$175$	628.889	0.271655
$176$	−801.132	−0.343111
$177$	1623.10	0.689265
$178$	−4447.69	−1.87286
$179$	2244.93	0.937398	0.468699	−	0.883358i	$-0.344723\pi$
$179$	2244.93	0.937398	0.468699	+	0.883358i	$0.344723\pi$
$180$	−78.5160	−0.0325124
$181$	−3604.70	−1.48031	−0.740153	−	0.672438i	$-0.765247\pi$
$181$	−3604.70	−1.48031	−0.740153	+	0.672438i	$0.765247\pi$
$182$	−2033.17	−0.828070
$183$	183.000	0.0739221
$184$	−197.774	−0.0792397
$185$	−2267.46	−0.901118
$186$	−1542.63	−0.608123
$187$	129.276	0.0505541
$188$	−200.900	−0.0779368
$189$	−208.408	−0.0802088
$190$	1474.50	0.563007
$191$	−3899.29	−1.47719	−0.738593	−	0.674152i	$-0.764509\pi$
$191$	−3899.29	−1.47719	−0.738593	+	0.674152i	$0.764509\pi$
$192$	1205.11	0.452977
$193$	−1809.88	−0.675016	−0.337508	−	0.941323i	$-0.609584\pi$
$193$	−1809.88	−0.675016	−0.337508	+	0.941323i	$0.609584\pi$
$194$	1806.84	0.668676
$195$	1707.47	0.627047
$196$	−374.779	−0.136581
$197$	289.167	0.104580	0.0522900	−	0.998632i	$-0.483348\pi$
$197$	289.167	0.104580	0.0522900	+	0.998632i	$0.483348\pi$
$198$	−302.272	−0.108493
$199$	837.678	0.298399	0.149200	−	0.988807i	$-0.452330\pi$
$199$	837.678	0.298399	0.149200	+	0.988807i	$0.452330\pi$
$200$	−1661.15	−0.587306
$201$	−2361.81	−0.828802
$202$	−3977.90	−1.38557
$203$	−928.501	−0.321025
$204$	46.6221	0.0160010
$205$	−2207.62	−0.752130
$206$	−3237.07	−1.09484
$207$	−87.3023	−0.0293137
$208$	6283.06	2.09448
$209$	805.199	0.266492
$210$	−466.451	−0.153277
$211$	−1036.37	−0.338137	−0.169068	−	0.985604i	$-0.554076\pi$
$211$	−1036.37	−0.338137	−0.169068	+	0.985604i	$0.554076\pi$
$212$	−391.834	−0.126940
$213$	−321.756	−0.103504
$214$	5274.56	1.68487
$215$	2259.62	0.716765
$216$	550.491	0.173408
$217$	−1299.96	−0.406667
$218$	−3593.28	−1.11637
$219$	845.400	0.260853
$220$	−95.9640	−0.0294086
$221$	−1013.88	−0.308601
$222$	−3148.13	−0.951750
$223$	4599.59	1.38122	0.690608	−	0.723229i	$-0.257343\pi$
$223$	4599.59	1.38122	0.690608	+	0.723229i	$0.257343\pi$
$224$	−457.420	−0.136441
$225$	−733.273	−0.217266
$226$	−2980.97	−0.877394
$227$	−2223.67	−0.650177	−0.325089	−	0.945684i	$-0.605394\pi$
$227$	−2223.67	−0.650177	−0.325089	+	0.945684i	$0.605394\pi$
$228$	290.387	0.0843479
$229$	2241.56	0.646842	0.323421	−	0.946255i	$-0.395167\pi$
$229$	2241.56	0.646842	0.323421	+	0.946255i	$0.395167\pi$
$230$	−195.396	−0.0560176
$231$	−254.721	−0.0725516
$232$	2452.55	0.694042
$233$	−5370.68	−1.51006	−0.755032	−	0.655687i	$-0.772379\pi$
$233$	−5370.68	−1.51006	−0.755032	+	0.655687i	$0.772379\pi$
$234$	2370.64	0.662280
$235$	1002.32	0.278230
$236$	715.434	0.197334
$237$	−379.422	−0.103992
$238$	276.974	0.0754352
$239$	5187.22	1.40391	0.701953	−	0.712224i	$-0.252312\pi$
$239$	5187.22	1.40391	0.701953	+	0.712224i	$0.252312\pi$
$240$	1441.46	0.387692
$241$	3404.24	0.909903	0.454951	−	0.890516i	$-0.349657\pi$
$241$	3404.24	0.909903	0.454951	+	0.890516i	$0.349657\pi$
$242$	−369.443	−0.0981352
$243$	243.000	0.0641500
$244$	80.6631	0.0211636
$245$	1869.82	0.487587
$246$	−3065.04	−0.794391
$247$	−6314.96	−1.62677
$248$	3433.71	0.879197
$249$	−1382.38	−0.351827
$250$	−4159.11	−1.05218
$251$	−1405.06	−0.353333	−0.176666	−	0.984271i	$-0.556531\pi$
$251$	−1405.06	−0.353333	−0.176666	+	0.984271i	$0.556531\pi$
$252$	−91.8626	−0.0229635
$253$	−106.703	−0.0265152
$254$	−5834.95	−1.44141
$255$	−232.604	−0.0571225
$256$	1978.69	0.483078
$257$	−249.451	−0.0605461	−0.0302730	−	0.999542i	$-0.509638\pi$
$257$	−249.451	−0.0605461	−0.0302730	+	0.999542i	$0.509638\pi$
$258$	3137.24	0.757039
$259$	−2652.89	−0.636458
$260$	752.620	0.179521
$261$	1082.61	0.256751
$262$	1263.01	0.297822
$263$	−2997.85	−0.702873	−0.351437	−	0.936212i	$-0.614307\pi$
$263$	−2997.85	−0.702873	−0.351437	+	0.936212i	$0.614307\pi$
$264$	672.822	0.156854
$265$	1954.92	0.453168
$266$	1725.14	0.397651
$267$	4370.12	1.00167
$268$	−1041.04	−0.237283
$269$	−2735.62	−0.620050	−0.310025	−	0.950728i	$-0.600337\pi$
$269$	−2735.62	−0.620050	−0.310025	+	0.950728i	$0.600337\pi$
$270$	543.873	0.122589
$271$	1037.95	0.232660	0.116330	−	0.993211i	$-0.462887\pi$
$271$	1037.95	0.232660	0.116330	+	0.993211i	$0.462887\pi$
$272$	−855.928	−0.190802
$273$	1997.71	0.442883
$274$	7136.08	1.57338
$275$	−896.222	−0.196524
$276$	−38.4813	−0.00839239
$277$	−6650.61	−1.44259	−0.721294	−	0.692629i	$-0.756452\pi$
$277$	−6650.61	−1.44259	−0.721294	+	0.692629i	$0.756452\pi$
$278$	5040.58	1.08746
$279$	1515.72	0.325247
$280$	1038.27	0.221601
$281$	−5425.89	−1.15189	−0.575946	−	0.817488i	$-0.695366\pi$
$281$	−5425.89	−1.15189	−0.575946	+	0.817488i	$0.695366\pi$
$282$	1391.61	0.293863
$283$	−3651.64	−0.767023	−0.383511	−	0.923536i	$-0.625285\pi$
$283$	−3651.64	−0.767023	−0.383511	+	0.923536i	$0.625285\pi$
$284$	−141.824	−0.0296328
$285$	−1448.78	−0.301117
$286$	2897.45	0.599055
$287$	−2582.88	−0.531228
$288$	533.343	0.109123
$289$	−4774.88	−0.971887
$290$	2423.06	0.490645
$291$	−1775.32	−0.357633
$292$	372.637	0.0746813
$293$	1976.62	0.394113	0.197057	−	0.980392i	$-0.436862\pi$
$293$	1976.62	0.394113	0.197057	+	0.980392i	$0.436862\pi$
$294$	2596.06	0.514983
$295$	−3569.40	−0.704470
$296$	7007.37	1.37600
$297$	297.000	0.0580259
$298$	8933.25	1.73654
$299$	836.842	0.161859
$300$	−323.213	−0.0622024
$301$	2643.72	0.506250
$302$	−9250.81	−1.76266
$303$	3908.52	0.741052
$304$	−5331.16	−1.00580
$305$	−402.439	−0.0755528
$306$	−322.947	−0.0603321
$307$	276.464	0.0513962	0.0256981	−	0.999670i	$-0.491819\pi$
$307$	276.464	0.0513962	0.0256981	+	0.999670i	$0.491819\pi$
$308$	−112.277	−0.0207713
$309$	3180.62	0.585563
$310$	3392.43	0.621539
$311$	419.040	0.0764038	0.0382019	−	0.999270i	$-0.487837\pi$
$311$	419.040	0.0764038	0.0382019	+	0.999270i	$0.487837\pi$
$312$	−5276.77	−0.957494
$313$	4281.27	0.773137	0.386568	−	0.922261i	$-0.373660\pi$
$313$	4281.27	0.773137	0.386568	+	0.922261i	$0.373660\pi$
$314$	8851.33	1.59079
$315$	458.315	0.0819782
$316$	−167.242	−0.0297725
$317$	−8422.95	−1.49237	−0.746183	−	0.665741i	$-0.768116\pi$
$317$	−8422.95	−1.49237	−0.746183	+	0.665741i	$0.768116\pi$
$318$	2714.20	0.478631
$319$	1323.20	0.232240
$320$	−2650.19	−0.462970
$321$	−5182.57	−0.901130
$322$	−228.611	−0.0395652
$323$	860.273	0.148195
$324$	107.110	0.0183659
$325$	7028.83	1.19966
$326$	−7474.35	−1.26983
$327$	3530.61	0.597074
$328$	6822.43	1.14849
$329$	1172.70	0.196513
$330$	664.733	0.110886
$331$	4143.49	0.688056	0.344028	−	0.938959i	$-0.388208\pi$
$331$	4143.49	0.688056	0.344028	+	0.938959i	$0.388208\pi$
$332$	−609.329	−0.100727
$333$	3093.22	0.509031
$334$	6155.69	1.00846
$335$	5193.91	0.847085
$336$	1686.49	0.273826
$337$	7007.61	1.13273	0.566363	−	0.824156i	$-0.308350\pi$
$337$	7007.61	1.13273	0.566363	+	0.824156i	$0.308350\pi$
$338$	−16015.9	−2.57737
$339$	2928.98	0.469263
$340$	−102.528	−0.0163540
$341$	1852.55	0.294197
$342$	−2011.48	−0.318036
$343$	4835.22	0.761159
$344$	−6983.14	−1.09449
$345$	191.988	0.0299603
$346$	766.552	0.119104
$347$	1669.53	0.258286	0.129143	−	0.991626i	$-0.458777\pi$
$347$	1669.53	0.258286	0.129143	+	0.991626i	$0.458777\pi$
$348$	477.197	0.0735070
$349$	−4123.24	−0.632412	−0.316206	−	0.948691i	$-0.602409\pi$
$349$	−4123.24	−0.632412	−0.316206	+	0.948691i	$0.602409\pi$
$350$	−1920.16	−0.293248
$351$	−2329.29	−0.354212
$352$	651.864	0.0987059
$353$	−9916.67	−1.49521	−0.747607	−	0.664141i	$-0.768797\pi$
$353$	−9916.67	−1.49521	−0.747607	+	0.664141i	$0.768797\pi$
$354$	−4955.74	−0.744052
$355$	707.582	0.105787
$356$	1926.27	0.286776
$357$	−272.144	−0.0403456
$358$	−6854.35	−1.01191
$359$	−1147.91	−0.168759	−0.0843795	−	0.996434i	$-0.526891\pi$
$359$	−1147.91	−0.168759	−0.0843795	+	0.996434i	$0.526891\pi$
$360$	−1210.60	−0.177234
$361$	−1500.77	−0.218804
$362$	11006.1	1.59797
$363$	363.000	0.0524864
$364$	880.555	0.126796
$365$	−1859.14	−0.266607
$366$	−558.745	−0.0797980
$367$	−8596.42	−1.22270	−0.611348	−	0.791362i	$-0.709372\pi$
$367$	−8596.42	−1.22270	−0.611348	+	0.791362i	$0.709372\pi$
$368$	706.471	0.100074
$369$	3011.59	0.424870
$370$	6923.12	0.972745
$371$	2287.22	0.320072
$372$	668.103	0.0931170
$373$	−6800.57	−0.944022	−0.472011	−	0.881593i	$-0.656472\pi$
$373$	−6800.57	−0.944022	−0.472011	+	0.881593i	$0.656472\pi$
$374$	−394.713	−0.0545725
$375$	4086.57	0.562745
$376$	−3097.57	−0.424854
$377$	−10377.5	−1.41768
$378$	636.323	0.0865844
$379$	−3463.22	−0.469376	−0.234688	−	0.972071i	$-0.575407\pi$
$379$	−3463.22	−0.469376	−0.234688	+	0.972071i	$0.575407\pi$
$380$	−638.596	−0.0862087
$381$	5733.18	0.770918
$382$	11905.5	1.59460
$383$	−9789.42	−1.30605	−0.653023	−	0.757338i	$-0.726500\pi$
$383$	−9789.42	−1.30605	−0.653023	+	0.757338i	$0.726500\pi$
$384$	−5101.76	−0.677990
$385$	560.163	0.0741521
$386$	5526.03	0.728672
$387$	−3082.52	−0.404893
$388$	−782.530	−0.102389
$389$	−11022.0	−1.43660	−0.718299	−	0.695735i	$-0.755079\pi$
$389$	−11022.0	−1.43660	−0.718299	+	0.695735i	$0.755079\pi$
$390$	−5213.32	−0.676890
$391$	−114.001	−0.0147450
$392$	−5778.52	−0.744539
$393$	−1240.99	−0.159286
$394$	−882.898	−0.112893
$395$	834.396	0.106286
$396$	130.912	0.0166126
$397$	−6896.84	−0.871895	−0.435947	−	0.899972i	$-0.643587\pi$
$397$	−6896.84	−0.871895	−0.435947	+	0.899972i	$0.643587\pi$
$398$	−2557.64	−0.322118
$399$	−1695.05	−0.212678
$400$	5933.82	0.741727
$401$	6774.04	0.843589	0.421794	−	0.906691i	$-0.361400\pi$
$401$	6774.04	0.843589	0.421794	+	0.906691i	$0.361400\pi$
$402$	7211.20	0.894681
$403$	−14529.1	−1.79589
$404$	1722.81	0.212161
$405$	−534.387	−0.0655652
$406$	2834.95	0.346542
$407$	3780.60	0.460436
$408$	718.842	0.0872255
$409$	−15174.3	−1.83452	−0.917260	−	0.398289i	$-0.869604\pi$
$409$	−15174.3	−1.83452	−0.917260	+	0.398289i	$0.869604\pi$
$410$	6740.41	0.811915
$411$	−7011.62	−0.841503
$412$	1401.96	0.167644
$413$	−4176.15	−0.497566
$414$	266.556	0.0316437
$415$	3040.03	0.359588
$416$	−5112.39	−0.602538
$417$	−4952.67	−0.581614
$418$	−2458.47	−0.287674
$419$	1964.50	0.229050	0.114525	−	0.993420i	$-0.463465\pi$
$419$	1964.50	0.229050	0.114525	+	0.993420i	$0.463465\pi$
$420$	202.017	0.0234701
$421$	−9427.85	−1.09141	−0.545707	−	0.837976i	$-0.683739\pi$
$421$	−9427.85	−1.09141	−0.545707	+	0.837976i	$0.683739\pi$
$422$	3164.31	0.365014
$423$	−1367.34	−0.157169
$424$	−6041.49	−0.691983
$425$	−957.522	−0.109286
$426$	982.403	0.111731
$427$	−470.848	−0.0533629
$428$	−2284.38	−0.257990
$429$	−2846.91	−0.320397
$430$	−6899.18	−0.773739
$431$	−6271.84	−0.700937	−0.350469	−	0.936575i	$-0.613978\pi$
$431$	−6271.84	−0.700937	−0.350469	+	0.936575i	$0.613978\pi$
$432$	−1966.41	−0.219003
$433$	−6767.64	−0.751113	−0.375557	−	0.926799i	$-0.622548\pi$
$433$	−6767.64	−0.751113	−0.375557	+	0.926799i	$0.622548\pi$
$434$	3969.09	0.438992
$435$	−2380.80	−0.262415
$436$	1556.23	0.170940
$437$	−710.058	−0.0777269
$438$	−2581.22	−0.281588
$439$	−1305.97	−0.141983	−0.0709915	−	0.997477i	$-0.522616\pi$
$439$	−1305.97	−0.141983	−0.0709915	+	0.997477i	$0.522616\pi$
$440$	−1479.62	−0.160314
$441$	−2550.78	−0.275432
$442$	3095.63	0.333131
$443$	−547.972	−0.0587696	−0.0293848	−	0.999568i	$-0.509355\pi$
$443$	−547.972	−0.0587696	−0.0293848	+	0.999568i	$0.509355\pi$
$444$	1363.44	0.145734
$445$	−9610.44	−1.02377
$446$	−14043.7	−1.49100
$447$	−8777.44	−0.928767
$448$	−3100.69	−0.326995
$449$	−1810.58	−0.190304	−0.0951519	−	0.995463i	$-0.530334\pi$
$449$	−1810.58	−0.190304	−0.0951519	+	0.995463i	$0.530334\pi$
$450$	2238.87	0.234536
$451$	3680.83	0.384309
$452$	1291.04	0.134348
$453$	9089.47	0.942738
$454$	6789.43	0.701858
$455$	−4393.21	−0.452653
$456$	4477.32	0.459802
$457$	−6901.11	−0.706390	−0.353195	−	0.935550i	$-0.614905\pi$
$457$	−6901.11	−0.706390	−0.353195	+	0.935550i	$0.614905\pi$
$458$	−6844.06	−0.698258
$459$	317.314	0.0322679
$460$	84.6251	0.00857753
$461$	1239.14	0.125190	0.0625950	−	0.998039i	$-0.480062\pi$
$461$	1239.14	0.125190	0.0625950	+	0.998039i	$0.480062\pi$
$462$	777.728	0.0783186
$463$	10416.7	1.04558	0.522789	−	0.852462i	$-0.324891\pi$
$463$	10416.7	1.04558	0.522789	+	0.852462i	$0.324891\pi$
$464$	−8760.77	−0.876527
$465$	−3333.26	−0.332422
$466$	16398.0	1.63010
$467$	−10240.3	−1.01470	−0.507348	−	0.861741i	$-0.669374\pi$
$467$	−10240.3	−1.01470	−0.507348	+	0.861741i	$0.669374\pi$
$468$	−1026.71	−0.101410
$469$	6076.80	0.598295
$470$	−3060.33	−0.300346
$471$	−8696.95	−0.850816
$472$	11030.9	1.07572
$473$	−3767.53	−0.366239
$474$	1158.47	0.112258
$475$	−5963.94	−0.576093
$476$	−119.956	−0.0115508
$477$	−2666.86	−0.255990
$478$	−15837.9	−1.51550
$479$	−9846.93	−0.939286	−0.469643	−	0.882857i	$-0.655617\pi$
$479$	−9846.93	−0.939286	−0.469643	+	0.882857i	$0.655617\pi$
$480$	−1172.89	−0.111531
$481$	−29650.3	−2.81068
$482$	−10394.0	−0.982228
$483$	224.624	0.0211609
$484$	160.004	0.0150267
$485$	3904.15	0.365522
$486$	−741.940	−0.0692492
$487$	119.911	0.0111575	0.00557873	−	0.999984i	$-0.498224\pi$
$487$	119.911	0.0111575	0.00557873	+	0.999984i	$0.498224\pi$
$488$	1243.70	0.115368
$489$	7343.99	0.679155
$490$	−5709.04	−0.526344
$491$	2694.72	0.247681	0.123840	−	0.992302i	$-0.460479\pi$
$491$	2694.72	0.247681	0.123840	+	0.992302i	$0.460479\pi$
$492$	1327.45	0.121639
$493$	1413.70	0.129148
$494$	19281.2	1.75607
$495$	−653.139	−0.0593059
$496$	−12265.6	−1.11037
$497$	827.860	0.0747175
$498$	4220.76	0.379792
$499$	9736.71	0.873497	0.436748	−	0.899584i	$-0.356130\pi$
$499$	9736.71	0.873497	0.436748	+	0.899584i	$0.356130\pi$
$500$	1801.29	0.161112
$501$	−6048.33	−0.539360
$502$	4290.00	0.381418
$503$	−8872.67	−0.786507	−0.393253	−	0.919430i	$-0.628650\pi$
$503$	−8872.67	−0.786507	−0.393253	+	0.919430i	$0.628650\pi$
$504$	−1416.38	−0.125180
$505$	−8595.33	−0.757400
$506$	325.791	0.0286228
$507$	15736.6	1.37847
$508$	2527.08	0.220711
$509$	7921.04	0.689772	0.344886	−	0.938645i	$-0.387918\pi$
$509$	7921.04	0.689772	0.344886	+	0.938645i	$0.387918\pi$
$510$	710.200	0.0616631
$511$	−2175.16	−0.188305
$512$	7563.28	0.652837
$513$	1976.40	0.170098
$514$	761.638	0.0653588
$515$	−6994.56	−0.598480
$516$	−1358.72	−0.115919
$517$	−1671.20	−0.142165
$518$	8099.95	0.687049
$519$	−753.183	−0.0637014
$520$	11604.3	0.978616
$521$	−2080.25	−0.174928	−0.0874639	−	0.996168i	$-0.527876\pi$
$521$	−2080.25	−0.174928	−0.0874639	+	0.996168i	$0.527876\pi$
$522$	−3305.49	−0.277160
$523$	−16237.5	−1.35759	−0.678793	−	0.734330i	$-0.737497\pi$
$523$	−16237.5	−1.35759	−0.678793	+	0.734330i	$0.737497\pi$
$524$	−547.004	−0.0456030
$525$	1886.67	0.156840
$526$	9153.21	0.758743
$527$	1979.26	0.163601
$528$	−2403.40	−0.198095
$529$	−12072.9	−0.992266
$530$	−5968.85	−0.489190
$531$	4869.31	0.397947
$532$	−747.148	−0.0608891
$533$	−28867.8	−2.34597
$534$	−13343.1	−1.08130
$535$	11397.1	0.921009
$536$	−16051.3	−1.29349
$537$	6734.80	0.541207
$538$	8352.53	0.669336
$539$	−3117.62	−0.249138
$540$	−235.548	−0.0187711
$541$	11295.4	0.897646	0.448823	−	0.893621i	$-0.351843\pi$
$541$	11295.4	0.897646	0.448823	+	0.893621i	$0.351843\pi$
$542$	−3169.12	−0.251154
$543$	−10814.1	−0.854655
$544$	696.450	0.0548898
$545$	−7764.25	−0.610245
$546$	−6099.51	−0.478086
$547$	1699.79	0.132867	0.0664333	−	0.997791i	$-0.478838\pi$
$547$	1699.79	0.132867	0.0664333	+	0.997791i	$0.478838\pi$
$548$	−3090.60	−0.240919
$549$	549.000	0.0426790
$550$	2736.39	0.212146
$551$	8805.25	0.680792
$552$	−593.323	−0.0457491
$553$	976.231	0.0750698
$554$	20306.0	1.55725
$555$	−6802.37	−0.520261
$556$	−2183.05	−0.166514
$557$	−2961.46	−0.225280	−0.112640	−	0.993636i	$-0.535931\pi$
$557$	−2961.46	−0.225280	−0.112640	+	0.993636i	$0.535931\pi$
$558$	−4627.88	−0.351100
$559$	29547.7	2.23566
$560$	−3708.80	−0.279867
$561$	387.829	0.0291874
$562$	16566.6	1.24345
$563$	−15325.1	−1.14721	−0.573603	−	0.819134i	$-0.694455\pi$
$563$	−15325.1	−1.14721	−0.573603	+	0.819134i	$0.694455\pi$
$564$	−602.700	−0.0449969
$565$	−6441.18	−0.479615
$566$	11149.4	0.827992
$567$	−625.225	−0.0463086
$568$	−2186.72	−0.161536
$569$	−14180.4	−1.04477	−0.522386	−	0.852709i	$-0.674958\pi$
$569$	−14180.4	−1.04477	−0.522386	+	0.852709i	$0.674958\pi$
$570$	4423.49	0.325052
$571$	−19269.3	−1.41225	−0.706127	−	0.708085i	$-0.749559\pi$
$571$	−19269.3	−1.41225	−0.706127	+	0.708085i	$0.749559\pi$
$572$	−1254.87	−0.0917284
$573$	−11697.9	−0.852853
$574$	7886.18	0.573454
$575$	790.326	0.0573198
$576$	3615.34	0.261526
$577$	5576.08	0.402314	0.201157	−	0.979559i	$-0.435530\pi$
$577$	5576.08	0.402314	0.201157	+	0.979559i	$0.435530\pi$
$578$	14578.9	1.04914
$579$	−5429.65	−0.389721
$580$	−1049.41	−0.0751285
$581$	3556.79	0.253976
$582$	5420.51	0.386060
$583$	−3259.49	−0.231551
$584$	5745.49	0.407107
$585$	5122.40	0.362026
$586$	−6035.11	−0.425440
$587$	24950.1	1.75435	0.877173	−	0.480175i	$-0.159427\pi$
$587$	24950.1	1.75435	0.877173	+	0.480175i	$0.159427\pi$
$588$	−1124.34	−0.0788552
$589$	12327.9	0.862412
$590$	10898.3	0.760466
$591$	867.500	0.0603793
$592$	−25031.1	−1.73779
$593$	−11837.8	−0.819763	−0.409881	−	0.912139i	$-0.634430\pi$
$593$	−11837.8	−0.819763	−0.409881	+	0.912139i	$0.634430\pi$
$594$	−906.816	−0.0626382
$595$	598.477	0.0412356
$596$	−3868.94	−0.265903
$597$	2513.03	0.172281
$598$	−2555.09	−0.174725
$599$	−6753.03	−0.460637	−0.230318	−	0.973115i	$-0.573977\pi$
$599$	−6753.03	−0.460637	−0.230318	+	0.973115i	$0.573977\pi$
$600$	−4983.46	−0.339081
$601$	−1438.85	−0.0976572	−0.0488286	−	0.998807i	$-0.515549\pi$
$601$	−1438.85	−0.0976572	−0.0488286	+	0.998807i	$0.515549\pi$
$602$	−8071.94	−0.546491
$603$	−7085.43	−0.478509
$604$	4006.47	0.269902
$605$	−798.282	−0.0536442
$606$	−11933.7	−0.799957
$607$	6793.64	0.454276	0.227138	−	0.973863i	$-0.427063\pi$
$607$	6793.64	0.454276	0.227138	+	0.973863i	$0.427063\pi$
$608$	4337.85	0.289347
$609$	−2785.50	−0.185344
$610$	1228.75	0.0815584
$611$	13106.7	0.867826
$612$	139.866	0.00923818
$613$	22986.4	1.51454	0.757271	−	0.653101i	$-0.226532\pi$
$613$	22986.4	1.51454	0.757271	+	0.653101i	$0.226532\pi$
$614$	−844.114	−0.0554815
$615$	−6622.85	−0.434242
$616$	−1731.13	−0.113229
$617$	30016.5	1.95854	0.979270	−	0.202557i	$-0.0649252\pi$
$617$	30016.5	1.95854	0.979270	+	0.202557i	$0.0649252\pi$
$618$	−9711.22	−0.632108
$619$	15510.1	1.00712	0.503558	−	0.863962i	$-0.332024\pi$
$619$	15510.1	1.00712	0.503558	+	0.863962i	$0.332024\pi$
$620$	−1469.24	−0.0951712
$621$	−261.907	−0.0169243
$622$	−1279.44	−0.0824770
$623$	−11244.1	−0.723089
$624$	18849.2	1.20925
$625$	1197.47	0.0766382
$626$	−13071.8	−0.834591
$627$	2415.60	0.153859
$628$	−3833.46	−0.243585
$629$	4039.19	0.256046
$630$	−1399.35	−0.0884945
$631$	−4067.80	−0.256635	−0.128317	−	0.991733i	$-0.540958\pi$
$631$	−4067.80	−0.256635	−0.128317	+	0.991733i	$0.540958\pi$
$632$	−2578.62	−0.162298
$633$	−3109.12	−0.195223
$634$	25717.4	1.61099
$635$	−12608.0	−0.787924
$636$	−1175.50	−0.0732889
$637$	24450.6	1.52083
$638$	−4040.05	−0.250701
$639$	−965.269	−0.0597581
$640$	11219.4	0.692947
$641$	−7573.72	−0.466683	−0.233342	−	0.972395i	$-0.574966\pi$
$641$	−7573.72	−0.466683	−0.233342	+	0.972395i	$0.574966\pi$
$642$	15823.7	0.972759
$643$	7794.48	0.478047	0.239024	−	0.971014i	$-0.423173\pi$
$643$	7794.48	0.478047	0.239024	+	0.971014i	$0.423173\pi$
$644$	99.0101	0.00605830
$645$	6778.85	0.413825
$646$	−2626.63	−0.159974
$647$	7662.37	0.465594	0.232797	−	0.972525i	$-0.425212\pi$
$647$	7662.37	0.465594	0.232797	+	0.972525i	$0.425212\pi$
$648$	1651.47	0.100117
$649$	5951.37	0.359957
$650$	−21460.8	−1.29502
$651$	−3899.87	−0.234789
$652$	3237.10	0.194439
$653$	−3300.21	−0.197775	−0.0988875	−	0.995099i	$-0.531528\pi$
$653$	−3300.21	−0.197775	−0.0988875	+	0.995099i	$0.531528\pi$
$654$	−10779.8	−0.644534
$655$	2729.08	0.162800
$656$	−24370.5	−1.45047
$657$	2536.20	0.150604
$658$	−3580.54	−0.212134
$659$	−32759.1	−1.93644	−0.968220	−	0.250101i	$-0.919536\pi$
$659$	−32759.1	−1.93644	−0.968220	+	0.250101i	$0.919536\pi$
$660$	−287.892	−0.0169791
$661$	26446.4	1.55619	0.778097	−	0.628144i	$-0.216185\pi$
$661$	26446.4	1.55619	0.778097	+	0.628144i	$0.216185\pi$
$662$	−12651.1	−0.742748
$663$	−3041.64	−0.178171
$664$	−9394.92	−0.549087
$665$	3727.63	0.217370
$666$	−9444.38	−0.549493
$667$	−1166.85	−0.0677369
$668$	−2665.99	−0.154417
$669$	13798.8	0.797445
$670$	−15858.3	−0.914418
$671$	671.000	0.0386046
$672$	−1372.26	−0.0787740
$673$	−23973.6	−1.37312	−0.686562	−	0.727071i	$-0.740881\pi$
$673$	−23973.6	−1.37312	−0.686562	+	0.727071i	$0.740881\pi$
$674$	−21396.0	−1.22276
$675$	−2199.82	−0.125439
$676$	6936.40	0.394652
$677$	3615.46	0.205249	0.102624	−	0.994720i	$-0.467276\pi$
$677$	3615.46	0.205249	0.102624	+	0.994720i	$0.467276\pi$
$678$	−8942.90	−0.506564
$679$	4567.80	0.258168
$680$	−1580.82	−0.0891497
$681$	−6671.01	−0.375380
$682$	−5656.30	−0.317582
$683$	−3105.00	−0.173952	−0.0869761	−	0.996210i	$-0.527720\pi$
$683$	−3105.00	−0.173952	−0.0869761	+	0.996210i	$0.527720\pi$
$684$	871.160	0.0486983
$685$	15419.4	0.860067
$686$	−14763.2	−0.821662
$687$	6724.69	0.373454
$688$	24944.5	1.38227
$689$	25563.3	1.41348
$690$	−586.189	−0.0323418
$691$	28016.3	1.54239	0.771195	−	0.636599i	$-0.219659\pi$
$691$	28016.3	1.54239	0.771195	+	0.636599i	$0.219659\pi$
$692$	−331.989	−0.0182375
$693$	−764.164	−0.0418877
$694$	−5097.50	−0.278816
$695$	10891.5	0.594445
$696$	7357.65	0.400705
$697$	3932.59	0.213712
$698$	12589.3	0.682681
$699$	−16112.0	−0.871836
$700$	831.609	0.0449027
$701$	2567.11	0.138314	0.0691572	−	0.997606i	$-0.477969\pi$
$701$	2567.11	0.138314	0.0691572	+	0.997606i	$0.477969\pi$
$702$	7111.91	0.382367
$703$	25158.2	1.34973
$704$	4418.75	0.236560
$705$	3006.95	0.160636
$706$	30278.1	1.61407
$707$	−10056.4	−0.534951
$708$	2146.30	0.113931
$709$	−14077.8	−0.745700	−0.372850	−	0.927892i	$-0.621619\pi$
$709$	−14077.8	−0.745700	−0.372850	+	0.927892i	$0.621619\pi$
$710$	−2160.43	−0.114196
$711$	−1138.27	−0.0600399
$712$	29700.2	1.56329
$713$	−1633.66	−0.0858077
$714$	830.923	0.0435525
$715$	6260.71	0.327465
$716$	2968.58	0.154946
$717$	15561.7	0.810545
$718$	3504.87	0.182173
$719$	9237.38	0.479132	0.239566	−	0.970880i	$-0.422995\pi$
$719$	9237.38	0.479132	0.239566	+	0.970880i	$0.422995\pi$
$720$	4324.39	0.223834
$721$	−8183.54	−0.422706
$722$	4582.24	0.236196
$723$	10212.7	0.525333
$724$	−4766.66	−0.244685
$725$	−9800.63	−0.502050
$726$	−1108.33	−0.0566584
$727$	26453.7	1.34953	0.674767	−	0.738030i	$-0.264244\pi$
$727$	26453.7	1.34953	0.674767	+	0.738030i	$0.264244\pi$
$728$	13576.8	0.691195
$729$	729.000	0.0370370
$730$	5676.42	0.287799
$731$	−4025.22	−0.203664
$732$	241.989	0.0122188
$733$	−11038.5	−0.556229	−0.278115	−	0.960548i	$-0.589710\pi$
$733$	−11038.5	−0.556229	−0.278115	+	0.960548i	$0.589710\pi$
$734$	26247.0	1.31988
$735$	5609.47	0.281508
$736$	−574.841	−0.0287893
$737$	−8659.97	−0.432828
$738$	−9195.13	−0.458642
$739$	−23844.3	−1.18691	−0.593456	−	0.804866i	$-0.702237\pi$
$739$	−23844.3	−1.18691	−0.593456	+	0.804866i	$0.702237\pi$
$740$	−2998.36	−0.148949
$741$	−18944.9	−0.939214
$742$	−6983.47	−0.345514
$743$	−28659.9	−1.41511	−0.707556	−	0.706657i	$-0.750202\pi$
$743$	−28659.9	−1.41511	−0.707556	+	0.706657i	$0.750202\pi$
$744$	10301.1	0.507605
$745$	19302.7	0.949255
$746$	20763.8	1.01906
$747$	−4147.14	−0.203127
$748$	170.948	0.00835624
$749$	13334.5	0.650508
$750$	−12477.3	−0.607477
$751$	−21916.7	−1.06492	−0.532459	−	0.846456i	$-0.678732\pi$
$751$	−21916.7	−1.06492	−0.532459	+	0.846456i	$0.678732\pi$
$752$	11064.9	0.536561
$753$	−4215.18	−0.203997
$754$	31685.0	1.53037
$755$	−19988.9	−0.963535
$756$	−275.588	−0.0132580
$757$	22327.6	1.07201	0.536004	−	0.844216i	$-0.319933\pi$
$757$	22327.6	1.07201	0.536004	+	0.844216i	$0.319933\pi$
$758$	10574.1	0.506686
$759$	−320.108	−0.0153086
$760$	−9846.18	−0.469945
$761$	36542.4	1.74069	0.870343	−	0.492445i	$-0.163897\pi$
$761$	36542.4	1.74069	0.870343	+	0.492445i	$0.163897\pi$
$762$	−17504.8	−0.832196
$763$	−9084.05	−0.431015
$764$	−5156.20	−0.244169
$765$	−697.813	−0.0329797
$766$	29889.5	1.40986
$767$	−46675.0	−2.19731
$768$	5936.06	0.278905
$769$	−35713.9	−1.67474	−0.837372	−	0.546634i	$-0.815909\pi$
$769$	−35713.9	−1.67474	−0.837372	+	0.546634i	$0.815909\pi$
$770$	−1710.32	−0.0800463
$771$	−748.354	−0.0349563
$772$	−2393.29	−0.111576
$773$	20884.8	0.971764	0.485882	−	0.874024i	$-0.338498\pi$
$773$	20884.8	0.971764	0.485882	+	0.874024i	$0.338498\pi$
$774$	9411.72	0.437077
$775$	−13721.5	−0.635986
$776$	−12065.4	−0.558149
$777$	−7958.68	−0.367459
$778$	33652.9	1.55079
$779$	24494.2	1.12657
$780$	2257.86	0.103647
$781$	−1179.77	−0.0540533
$782$	348.074	0.0159170
$783$	3247.84	0.148236
$784$	20641.5	0.940302
$785$	19125.7	0.869585
$786$	3789.04	0.171947
$787$	2126.15	0.0963011	0.0481505	−	0.998840i	$-0.484667\pi$
$787$	2126.15	0.0963011	0.0481505	+	0.998840i	$0.484667\pi$
$788$	382.378	0.0172864
$789$	−8993.56	−0.405804
$790$	−2547.62	−0.114735
$791$	−7536.09	−0.338751
$792$	2018.47	0.0905595
$793$	−5262.47	−0.235657
$794$	21057.8	0.941200
$795$	5864.75	0.261637
$796$	1107.70	0.0493234
$797$	16450.7	0.731135	0.365568	−	0.930785i	$-0.380875\pi$
$797$	16450.7	0.731135	0.365568	+	0.930785i	$0.380875\pi$
$798$	5175.42	0.229584
$799$	−1785.50	−0.0790570
$800$	−4828.22	−0.213379
$801$	13110.4	0.578317
$802$	−20682.8	−0.910644
$803$	3099.80	0.136226
$804$	−3123.13	−0.136995
$805$	−493.975	−0.0216277
$806$	44360.9	1.93864
$807$	−8206.85	−0.357986
$808$	26563.1	1.15654
$809$	44490.9	1.93352	0.966760	−	0.255685i	$-0.0823011\pi$
$809$	44490.9	1.93352	0.966760	+	0.255685i	$0.0823011\pi$
$810$	1631.62	0.0707768
$811$	−16494.4	−0.714174	−0.357087	−	0.934071i	$-0.616230\pi$
$811$	−16494.4	−0.714174	−0.357087	+	0.934071i	$0.616230\pi$
$812$	−1227.80	−0.0530632
$813$	3113.84	0.134326
$814$	−11543.1	−0.497035
$815$	−16150.3	−0.694137
$816$	−2567.78	−0.110160
$817$	−25071.2	−1.07360
$818$	46330.8	1.98034
$819$	5993.13	0.255698
$820$	−2919.23	−0.124322
$821$	−3775.16	−0.160480	−0.0802399	−	0.996776i	$-0.525569\pi$
$821$	−3775.16	−0.160480	−0.0802399	+	0.996776i	$0.525569\pi$
$822$	21408.2	0.908392
$823$	27677.0	1.17225	0.586123	−	0.810222i	$-0.300653\pi$
$823$	27677.0	1.17225	0.586123	+	0.810222i	$0.300653\pi$
$824$	21616.1	0.913873
$825$	−2688.67	−0.113463
$826$	12750.8	0.537116
$827$	−1569.53	−0.0659951	−0.0329976	−	0.999455i	$-0.510505\pi$
$827$	−1569.53	−0.0659951	−0.0329976	+	0.999455i	$0.510505\pi$
$828$	−115.444	−0.00484535
$829$	−1833.83	−0.0768293	−0.0384147	−	0.999262i	$-0.512231\pi$
$829$	−1833.83	−0.0768293	−0.0384147	+	0.999262i	$0.512231\pi$
$830$	−9281.96	−0.388171
$831$	−19951.8	−0.832878
$832$	−34655.1	−1.44405
$833$	−3330.86	−0.138544
$834$	15121.7	0.627845
$835$	13301.0	0.551258
$836$	1064.75	0.0440493
$837$	4547.17	0.187782
$838$	−5998.12	−0.247257
$839$	−18066.1	−0.743399	−0.371699	−	0.928353i	$-0.621225\pi$
$839$	−18066.1	−0.743399	−0.371699	+	0.928353i	$0.621225\pi$
$840$	3114.80	0.127941
$841$	−9919.20	−0.406708
$842$	28785.6	1.17817
$843$	−16277.7	−0.665045
$844$	−1370.44	−0.0558917
$845$	−34606.7	−1.40888
$846$	4174.84	0.169662
$847$	−933.978	−0.0378889
$848$	21580.9	0.873927
$849$	−10954.9	−0.442841
$850$	2923.56	0.117973
$851$	−3333.89	−0.134294
$852$	−425.473	−0.0171085
$853$	7885.07	0.316506	0.158253	−	0.987399i	$-0.449414\pi$
$853$	7885.07	0.316506	0.158253	+	0.987399i	$0.449414\pi$
$854$	1437.62	0.0576046
$855$	−4346.34	−0.173850
$856$	−35221.7	−1.40637
$857$	28314.2	1.12858	0.564292	−	0.825575i	$-0.309149\pi$
$857$	28314.2	1.12858	0.564292	+	0.825575i	$0.309149\pi$
$858$	8692.34	0.345864
$859$	1903.38	0.0756025	0.0378013	−	0.999285i	$-0.487965\pi$
$859$	1903.38	0.0756025	0.0378013	+	0.999285i	$0.487965\pi$
$860$	2987.99	0.118476
$861$	−7748.64	−0.306705
$862$	19149.5	0.756653
$863$	6882.41	0.271471	0.135736	−	0.990745i	$-0.456660\pi$
$863$	6882.41	0.271471	0.135736	+	0.990745i	$0.456660\pi$
$864$	1600.03	0.0630025
$865$	1656.34	0.0651067
$866$	20663.3	0.810818
$867$	−14324.6	−0.561119
$868$	−1718.99	−0.0672193
$869$	−1391.22	−0.0543081
$870$	7269.19	0.283274
$871$	67917.8	2.64214
$872$	23994.7	0.931838
$873$	−5325.97	−0.206480
$874$	2167.98	0.0839052
$875$	−10514.5	−0.406234
$876$	1117.91	0.0431172
$877$	−17895.6	−0.689043	−0.344521	−	0.938778i	$-0.611959\pi$
$877$	−17895.6	−0.689043	−0.344521	+	0.938778i	$0.611959\pi$
$878$	3987.46	0.153269
$879$	5929.85	0.227541
$880$	5285.36	0.202465
$881$	−660.136	−0.0252446	−0.0126223	−	0.999920i	$-0.504018\pi$
$881$	−660.136	−0.0252446	−0.0126223	+	0.999920i	$0.504018\pi$
$882$	7788.17	0.297326
$883$	−13352.9	−0.508904	−0.254452	−	0.967085i	$-0.581895\pi$
$883$	−13352.9	−0.508904	−0.254452	+	0.967085i	$0.581895\pi$
$884$	−1340.70	−0.0510097
$885$	−10708.2	−0.406726
$886$	1673.10	0.0634411
$887$	23458.0	0.887983	0.443992	−	0.896031i	$-0.353562\pi$
$887$	23458.0	0.887983	0.443992	+	0.896031i	$0.353562\pi$
$888$	21022.1	0.794432
$889$	−14751.1	−0.556510
$890$	29343.1	1.10515
$891$	891.000	0.0335013
$892$	6082.24	0.228306
$893$	−11121.0	−0.416743
$894$	26799.7	1.00259
$895$	−14810.7	−0.553146
$896$	13126.5	0.489427
$897$	2510.52	0.0934493
$898$	5528.15	0.205431
$899$	20258.6	0.751569
$900$	−969.640	−0.0359126
$901$	−3482.44	−0.128765
$902$	−11238.5	−0.414857
$903$	7931.15	0.292284
$904$	19905.9	0.732367
$905$	23781.6	0.873509
$906$	−27752.4	−1.01767
$907$	9408.37	0.344432	0.172216	−	0.985059i	$-0.444907\pi$
$907$	9408.37	0.344432	0.172216	+	0.985059i	$0.444907\pi$
$908$	−2940.46	−0.107470
$909$	11725.6	0.427847
$910$	13413.6	0.488633
$911$	−38200.2	−1.38927	−0.694636	−	0.719361i	$-0.744435\pi$
$911$	−38200.2	−1.38927	−0.694636	+	0.719361i	$0.744435\pi$
$912$	−15993.5	−0.580699
$913$	−5068.73	−0.183735
$914$	21070.8	0.762539
$915$	−1207.32	−0.0436205
$916$	2964.12	0.106919
$917$	3192.98	0.114985
$918$	−968.840	−0.0348328
$919$	−21887.3	−0.785632	−0.392816	−	0.919617i	$-0.628499\pi$
$919$	−21887.3	−0.785632	−0.392816	+	0.919617i	$0.628499\pi$
$920$	1304.79	0.0467583
$921$	829.392	0.0296736
$922$	−3783.41	−0.135141
$923$	9252.65	0.329962
$924$	−336.830	−0.0119923
$925$	−28002.1	−0.995357
$926$	−31804.7	−1.12869
$927$	9541.85	0.338075
$928$	7128.46	0.252158
$929$	−25782.0	−0.910528	−0.455264	−	0.890357i	$-0.650455\pi$
$929$	−25782.0	−0.910528	−0.455264	+	0.890357i	$0.650455\pi$
$930$	10177.3	0.358845
$931$	−20746.3	−0.730325
$932$	−7101.90	−0.249604
$933$	1257.12	0.0441118
$934$	31266.1	1.09535
$935$	−852.883	−0.0298313
$936$	−15830.3	−0.552809
$937$	20063.6	0.699519	0.349760	−	0.936840i	$-0.386263\pi$
$937$	20063.6	0.699519	0.349760	+	0.936840i	$0.386263\pi$
$938$	−18554.0	−0.645852
$939$	12843.8	0.446371
$940$	1325.41	0.0459895
$941$	−6186.32	−0.214313	−0.107156	−	0.994242i	$-0.534175\pi$
$941$	−6186.32	−0.214313	−0.107156	+	0.994242i	$0.534175\pi$
$942$	26554.0	0.918445
$943$	−3245.91	−0.112090
$944$	−39403.6	−1.35856
$945$	1374.95	0.0473302
$946$	11503.2	0.395351
$947$	−3293.69	−0.113021	−0.0565103	−	0.998402i	$-0.517997\pi$
$947$	−3293.69	−0.113021	−0.0565103	+	0.998402i	$0.517997\pi$
$948$	−501.727	−0.0171892
$949$	−24310.9	−0.831575
$950$	18209.4	0.621886
$951$	−25268.9	−0.861618
$952$	−1849.54	−0.0629663
$953$	−54816.4	−1.86325	−0.931626	−	0.363420i	$-0.881609\pi$
$953$	−54816.4	−1.86325	−0.931626	+	0.363420i	$0.881609\pi$
$954$	8142.59	0.276338
$955$	25725.0	0.871667
$956$	6859.30	0.232056
$957$	3969.59	0.134084
$958$	30065.2	1.01395
$959$	18040.5	0.607464
$960$	−7950.58	−0.267296
$961$	−1427.85	−0.0479288
$962$	90529.7	3.03409
$963$	−15547.7	−0.520268
$964$	4501.59	0.150401
$965$	11940.5	0.398318
$966$	−685.833	−0.0228430
$967$	−18205.7	−0.605435	−0.302718	−	0.953080i	$-0.597894\pi$
$967$	−18205.7	−0.605435	−0.302718	+	0.953080i	$0.597894\pi$
$968$	2467.02	0.0819141
$969$	2580.82	0.0855602
$970$	−11920.4	−0.394577
$971$	−3181.18	−0.105138	−0.0525689	−	0.998617i	$-0.516741\pi$
$971$	−3181.18	−0.105138	−0.0525689	+	0.998617i	$0.516741\pi$
$972$	321.330	0.0106036
$973$	12742.9	0.419856
$974$	−366.118	−0.0120443
$975$	21086.5	0.692624
$976$	−4442.64	−0.145702
$977$	−19758.1	−0.646999	−0.323499	−	0.946228i	$-0.604859\pi$
$977$	−19758.1	−0.646999	−0.323499	+	0.946228i	$0.604859\pi$
$978$	−22423.0	−0.733139
$979$	16023.8	0.523108
$980$	2472.55	0.0805948
$981$	10591.8	0.344721
$982$	−8227.67	−0.267368
$983$	−16196.2	−0.525514	−0.262757	−	0.964862i	$-0.584632\pi$
$983$	−16196.2	−0.525514	−0.262757	+	0.964862i	$0.584632\pi$
$984$	20467.3	0.663083
$985$	−1907.74	−0.0617113
$986$	−4316.38	−0.139413
$987$	3518.09	0.113457
$988$	−8350.56	−0.268893
$989$	3322.36	0.106820
$990$	1994.20	0.0640200
$991$	9814.47	0.314598	0.157299	−	0.987551i	$-0.449721\pi$
$991$	9814.47	0.314598	0.157299	+	0.987551i	$0.449721\pi$
$992$	9980.25	0.319429
$993$	12430.5	0.397250
$994$	−2527.67	−0.0806566
$995$	−5526.47	−0.176081
$996$	−1827.99	−0.0581546
$997$	29528.5	0.937991	0.468996	−	0.883200i	$-0.344616\pi$
$997$	29528.5	0.937991	0.468996	+	0.883200i	$0.344616\pi$
$998$	−29728.6	−0.942929
$999$	9279.66	0.293889

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2013.4.a.a.1.13	✓	36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2013.4.a.a.1.13	✓	36	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:	\( N \)	\(=\)	\( 2013 = 3 \cdot 11 \cdot 61 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	2013.a (trivial)

\(f(q)\)	\(=\)	\(q-3.05325 q^{2} +3.00000 q^{3} +1.32235 q^{4} -6.59737 q^{5} -9.15976 q^{6} -7.71882 q^{7} +20.3886 q^{8} +9.00000 q^{9} +O(q^{10})\)	\(q-3.05325 q^{2} +3.00000 q^{3} +1.32235 q^{4} -6.59737 q^{5} -9.15976 q^{6} -7.71882 q^{7} +20.3886 q^{8} +9.00000 q^{9} +20.1434 q^{10} +11.0000 q^{11} +3.96704 q^{12} -86.2701 q^{13} +23.5675 q^{14} -19.7921 q^{15} -72.8302 q^{16} +11.7524 q^{17} -27.4793 q^{18} +73.1999 q^{19} -8.72400 q^{20} -23.1565 q^{21} -33.5858 q^{22} -9.70026 q^{23} +61.1657 q^{24} -81.4747 q^{25} +263.404 q^{26} +27.0000 q^{27} -10.2070 q^{28} +120.290 q^{29} +60.4303 q^{30} +168.414 q^{31} +59.2604 q^{32} +33.0000 q^{33} -35.8830 q^{34} +50.9239 q^{35} +11.9011 q^{36} +343.691 q^{37} -223.498 q^{38} -258.810 q^{39} -134.511 q^{40} +334.621 q^{41} +70.7025 q^{42} -342.503 q^{43} +14.5458 q^{44} -59.3763 q^{45} +29.6173 q^{46} -151.927 q^{47} -218.491 q^{48} -283.420 q^{49} +248.763 q^{50} +35.2571 q^{51} -114.079 q^{52} -296.318 q^{53} -82.4378 q^{54} -72.5711 q^{55} -157.376 q^{56} +219.600 q^{57} -367.277 q^{58} +541.034 q^{59} -26.1720 q^{60} +61.0000 q^{61} -514.209 q^{62} -69.4694 q^{63} +401.705 q^{64} +569.155 q^{65} -100.757 q^{66} -787.270 q^{67} +15.5407 q^{68} -29.1008 q^{69} -155.484 q^{70} -107.252 q^{71} +183.497 q^{72} +281.800 q^{73} -1049.38 q^{74} -244.424 q^{75} +96.7956 q^{76} -84.9071 q^{77} +790.213 q^{78} -126.474 q^{79} +480.487 q^{80} +81.0000 q^{81} -1021.68 q^{82} -460.794 q^{83} -30.6209 q^{84} -77.5348 q^{85} +1045.75 q^{86} +360.871 q^{87} +224.274 q^{88} +1456.71 q^{89} +181.291 q^{90} +665.903 q^{91} -12.8271 q^{92} +505.241 q^{93} +463.871 q^{94} -482.927 q^{95} +177.781 q^{96} -591.774 q^{97} +865.352 q^{98} +99.0000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q - 14 q^{2} + 108 q^{3} + 146 q^{4} - 65 q^{5} - 42 q^{6} - 105 q^{7} - 189 q^{8} + 324 q^{9}+O(q^{10}) \) 36 * q - 14 * q^2 + 108 * q^3 + 146 * q^4 - 65 * q^5 - 42 * q^6 - 105 * q^7 - 189 * q^8 + 324 * q^9	\( 36 q - 14 q^{2} + 108 q^{3} + 146 q^{4} - 65 q^{5} - 42 q^{6} - 105 q^{7} - 189 q^{8} + 324 q^{9} - 161 q^{10} + 396 q^{11} + 438 q^{12} - 233 q^{13} - 264 q^{14} - 195 q^{15} + 574 q^{16} - 556 q^{17} - 126 q^{18} - 615 q^{19} - 136 q^{20} - 315 q^{21} - 154 q^{22} - 457 q^{23} - 567 q^{24} + 863 q^{25} + 115 q^{26} + 972 q^{27} - 424 q^{28} - 754 q^{29} - 483 q^{30} - 508 q^{31} - 1511 q^{32} + 1188 q^{33} - 860 q^{34} - 826 q^{35} + 1314 q^{36} - 412 q^{37} - 599 q^{38} - 699 q^{39} - 2791 q^{40} - 2066 q^{41} - 792 q^{42} - 2063 q^{43} + 1606 q^{44} - 585 q^{45} - 787 q^{46} - 1815 q^{47} + 1722 q^{48} + 2825 q^{49} + 808 q^{50} - 1668 q^{51} - 2882 q^{52} - 759 q^{53} - 378 q^{54} - 715 q^{55} - 1749 q^{56} - 1845 q^{57} - 335 q^{58} - 2337 q^{59} - 408 q^{60} + 2196 q^{61} - 1689 q^{62} - 945 q^{63} + 4723 q^{64} - 3550 q^{65} - 462 q^{66} - 1331 q^{67} - 6166 q^{68} - 1371 q^{69} - 1750 q^{70} - 361 q^{71} - 1701 q^{72} - 4627 q^{73} - 3394 q^{74} + 2589 q^{75} - 7214 q^{76} - 1155 q^{77} + 345 q^{78} - 2583 q^{79} - 2643 q^{80} + 2916 q^{81} + 1090 q^{82} - 6123 q^{83} - 1272 q^{84} + 295 q^{85} + 613 q^{86} - 2262 q^{87} - 2079 q^{88} - 2485 q^{89} - 1449 q^{90} - 3156 q^{91} - 6291 q^{92} - 1524 q^{93} - 1744 q^{94} - 5572 q^{95} - 4533 q^{96} - 2558 q^{97} - 2314 q^{98} + 3564 q^{99}+O(q^{100}) \) 36 * q - 14 * q^2 + 108 * q^3 + 146 * q^4 - 65 * q^5 - 42 * q^6 - 105 * q^7 - 189 * q^8 + 324 * q^9 - 161 * q^10 + 396 * q^11 + 438 * q^12 - 233 * q^13 - 264 * q^14 - 195 * q^15 + 574 * q^16 - 556 * q^17 - 126 * q^18 - 615 * q^19 - 136 * q^20 - 315 * q^21 - 154 * q^22 - 457 * q^23 - 567 * q^24 + 863 * q^25 + 115 * q^26 + 972 * q^27 - 424 * q^28 - 754 * q^29 - 483 * q^30 - 508 * q^31 - 1511 * q^32 + 1188 * q^33 - 860 * q^34 - 826 * q^35 + 1314 * q^36 - 412 * q^37 - 599 * q^38 - 699 * q^39 - 2791 * q^40 - 2066 * q^41 - 792 * q^42 - 2063 * q^43 + 1606 * q^44 - 585 * q^45 - 787 * q^46 - 1815 * q^47 + 1722 * q^48 + 2825 * q^49 + 808 * q^50 - 1668 * q^51 - 2882 * q^52 - 759 * q^53 - 378 * q^54 - 715 * q^55 - 1749 * q^56 - 1845 * q^57 - 335 * q^58 - 2337 * q^59 - 408 * q^60 + 2196 * q^61 - 1689 * q^62 - 945 * q^63 + 4723 * q^64 - 3550 * q^65 - 462 * q^66 - 1331 * q^67 - 6166 * q^68 - 1371 * q^69 - 1750 * q^70 - 361 * q^71 - 1701 * q^72 - 4627 * q^73 - 3394 * q^74 + 2589 * q^75 - 7214 * q^76 - 1155 * q^77 + 345 * q^78 - 2583 * q^79 - 2643 * q^80 + 2916 * q^81 + 1090 * q^82 - 6123 * q^83 - 1272 * q^84 + 295 * q^85 + 613 * q^86 - 2262 * q^87 - 2079 * q^88 - 2485 * q^89 - 1449 * q^90 - 3156 * q^91 - 6291 * q^92 - 1524 * q^93 - 1744 * q^94 - 5572 * q^95 - 4533 * q^96 - 2558 * q^97 - 2314 * q^98 + 3564 * q^99

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