LMFDB - Embedded newform 6041.2.a.c.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6041,2,Mod(1,6041)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6041, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("6041.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6041 = 7 \cdot 863 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6041.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:	$48.2376278611$
Analytic rank:	$1$
Dimension:	$83$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Character	$\chi$	$=$	6041.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.73002 q^{2} -0.0142784 q^{3} +5.45300 q^{4} -0.484021 q^{5} +0.0389802 q^{6} +1.00000 q^{7} -9.42677 q^{8} -2.99980 q^{9} +O(q^{10})$	\(q-2.73002 q^{2} -0.0142784 q^{3} +5.45300 q^{4} -0.484021 q^{5} +0.0389802 q^{6} +1.00000 q^{7} -9.42677 q^{8} -2.99980 q^{9} +1.32139 q^{10} -0.554288 q^{11} -0.0778599 q^{12} -2.58000 q^{13} -2.73002 q^{14} +0.00691102 q^{15} +14.8292 q^{16} -0.480022 q^{17} +8.18950 q^{18} -4.31661 q^{19} -2.63937 q^{20} -0.0142784 q^{21} +1.51322 q^{22} +3.71486 q^{23} +0.134599 q^{24} -4.76572 q^{25} +7.04346 q^{26} +0.0856672 q^{27} +5.45300 q^{28} +7.95129 q^{29} -0.0188672 q^{30} -4.42475 q^{31} -21.6306 q^{32} +0.00791432 q^{33} +1.31047 q^{34} -0.484021 q^{35} -16.3579 q^{36} +1.58131 q^{37} +11.7844 q^{38} +0.0368382 q^{39} +4.56275 q^{40} +5.58807 q^{41} +0.0389802 q^{42} +0.117445 q^{43} -3.02254 q^{44} +1.45196 q^{45} -10.1416 q^{46} +5.93216 q^{47} -0.211737 q^{48} +1.00000 q^{49} +13.0105 q^{50} +0.00685392 q^{51} -14.0688 q^{52} +9.83101 q^{53} -0.233873 q^{54} +0.268287 q^{55} -9.42677 q^{56} +0.0616340 q^{57} -21.7072 q^{58} -1.62971 q^{59} +0.0376858 q^{60} +11.5013 q^{61} +12.0796 q^{62} -2.99980 q^{63} +29.3934 q^{64} +1.24878 q^{65} -0.0216062 q^{66} -10.3795 q^{67} -2.61756 q^{68} -0.0530421 q^{69} +1.32139 q^{70} +5.59039 q^{71} +28.2784 q^{72} +10.7023 q^{73} -4.31702 q^{74} +0.0680467 q^{75} -23.5385 q^{76} -0.554288 q^{77} -0.100569 q^{78} -1.56997 q^{79} -7.17767 q^{80} +8.99817 q^{81} -15.2555 q^{82} +16.3259 q^{83} -0.0778599 q^{84} +0.232341 q^{85} -0.320628 q^{86} -0.113531 q^{87} +5.22515 q^{88} -3.20720 q^{89} -3.96389 q^{90} -2.58000 q^{91} +20.2571 q^{92} +0.0631781 q^{93} -16.1949 q^{94} +2.08933 q^{95} +0.308849 q^{96} +4.24909 q^{97} -2.73002 q^{98} +1.66275 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 83 q - 8 q^{2} - 12 q^{3} + 48 q^{4} - 11 q^{5} - 8 q^{6} + 83 q^{7} - 18 q^{8} + 39 q^{9}+O(q^{10}) $ 83 * q - 8 * q^2 - 12 * q^3 + 48 * q^4 - 11 * q^5 - 8 * q^6 + 83 * q^7 - 18 * q^8 + 39 * q^9	\( 83 q - 8 q^{2} - 12 q^{3} + 48 q^{4} - 11 q^{5} - 8 q^{6} + 83 q^{7} - 18 q^{8} + 39 q^{9} - 20 q^{10} - 26 q^{11} - 14 q^{12} - 22 q^{13} - 8 q^{14} - 37 q^{15} - 10 q^{16} - 9 q^{17} - 27 q^{18} - 42 q^{19} - 22 q^{20} - 12 q^{21} - 44 q^{22} - 46 q^{23} - 24 q^{24} - 20 q^{25} - 9 q^{26} - 39 q^{27} + 48 q^{28} - 36 q^{29} - 11 q^{30} - 107 q^{31} - 19 q^{32} - 25 q^{33} - 24 q^{34} - 11 q^{35} - 32 q^{36} - 75 q^{37} - 16 q^{38} - 78 q^{39} - 34 q^{40} - 17 q^{41} - 8 q^{42} - 87 q^{43} - 32 q^{44} - 17 q^{45} - 56 q^{46} - 39 q^{47} - 16 q^{48} + 83 q^{49} - 26 q^{50} - 71 q^{51} - 53 q^{52} - 28 q^{53} - 25 q^{54} - 94 q^{55} - 18 q^{56} - 79 q^{57} - 69 q^{58} - 26 q^{59} - 43 q^{60} - 56 q^{61} - 6 q^{62} + 39 q^{63} - 108 q^{64} - 26 q^{65} + 10 q^{66} - 123 q^{67} - 11 q^{68} + 2 q^{69} - 20 q^{70} - 96 q^{71} - 11 q^{72} - 53 q^{73} - 26 q^{74} - 27 q^{75} - 65 q^{76} - 26 q^{77} - 43 q^{78} - 160 q^{79} + 12 q^{80} - 53 q^{81} - 20 q^{82} - 2 q^{83} - 14 q^{84} - 110 q^{85} + 24 q^{86} - 52 q^{87} - 79 q^{88} - 5 q^{89} - 4 q^{90} - 22 q^{91} - 51 q^{92} - 30 q^{93} - 9 q^{94} - 76 q^{95} - 3 q^{96} - 44 q^{97} - 8 q^{98} - 82 q^{99}+O(q^{100}) \) 83 * q - 8 * q^2 - 12 * q^3 + 48 * q^4 - 11 * q^5 - 8 * q^6 + 83 * q^7 - 18 * q^8 + 39 * q^9 - 20 * q^10 - 26 * q^11 - 14 * q^12 - 22 * q^13 - 8 * q^14 - 37 * q^15 - 10 * q^16 - 9 * q^17 - 27 * q^18 - 42 * q^19 - 22 * q^20 - 12 * q^21 - 44 * q^22 - 46 * q^23 - 24 * q^24 - 20 * q^25 - 9 * q^26 - 39 * q^27 + 48 * q^28 - 36 * q^29 - 11 * q^30 - 107 * q^31 - 19 * q^32 - 25 * q^33 - 24 * q^34 - 11 * q^35 - 32 * q^36 - 75 * q^37 - 16 * q^38 - 78 * q^39 - 34 * q^40 - 17 * q^41 - 8 * q^42 - 87 * q^43 - 32 * q^44 - 17 * q^45 - 56 * q^46 - 39 * q^47 - 16 * q^48 + 83 * q^49 - 26 * q^50 - 71 * q^51 - 53 * q^52 - 28 * q^53 - 25 * q^54 - 94 * q^55 - 18 * q^56 - 79 * q^57 - 69 * q^58 - 26 * q^59 - 43 * q^60 - 56 * q^61 - 6 * q^62 + 39 * q^63 - 108 * q^64 - 26 * q^65 + 10 * q^66 - 123 * q^67 - 11 * q^68 + 2 * q^69 - 20 * q^70 - 96 * q^71 - 11 * q^72 - 53 * q^73 - 26 * q^74 - 27 * q^75 - 65 * q^76 - 26 * q^77 - 43 * q^78 - 160 * q^79 + 12 * q^80 - 53 * q^81 - 20 * q^82 - 2 * q^83 - 14 * q^84 - 110 * q^85 + 24 * q^86 - 52 * q^87 - 79 * q^88 - 5 * q^89 - 4 * q^90 - 22 * q^91 - 51 * q^92 - 30 * q^93 - 9 * q^94 - 76 * q^95 - 3 * q^96 - 44 * q^97 - 8 * q^98 - 82 * 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 $

$2$	−2.73002	−1.93041	−0.965207	−	0.261485i	$-0.915788\pi$
$2$	−2.73002	−1.93041	−0.965207	+	0.261485i	$0.915788\pi$
$3$	−0.0142784	−0.00824361	−0.00412180	−	0.999992i	$-0.501312\pi$
$3$	−0.0142784	−0.00824361	−0.00412180	+	0.999992i	$0.501312\pi$
$4$	5.45300	2.72650
$5$	−0.484021	−0.216461	−0.108230	−	0.994126i	$-0.534518\pi$
$5$	−0.484021	−0.216461	−0.108230	+	0.994126i	$0.534518\pi$
$6$	0.0389802	0.0159136
$7$	1.00000	0.377964
$7$	1.00000	0.377964
$8$	−9.42677	−3.33287
$9$	−2.99980	−0.999932
$10$	1.32139	0.417859
$11$	−0.554288	−0.167124	−0.0835621	−	0.996503i	$-0.526630\pi$
$11$	−0.554288	−0.167124	−0.0835621	+	0.996503i	$0.526630\pi$
$12$	−0.0778599	−0.0224762
$13$	−2.58000	−0.715565	−0.357782	−	0.933805i	$-0.616467\pi$
$13$	−2.58000	−0.715565	−0.357782	+	0.933805i	$0.616467\pi$
$14$	−2.73002	−0.729628
$15$	0.00691102	0.00178442
$16$	14.8292	3.70731
$17$	−0.480022	−0.116422	−0.0582112	−	0.998304i	$-0.518540\pi$
$17$	−0.480022	−0.116422	−0.0582112	+	0.998304i	$0.518540\pi$
$18$	8.18950	1.93028
$19$	−4.31661	−0.990298	−0.495149	−	0.868808i	$-0.664886\pi$
$19$	−4.31661	−0.990298	−0.495149	+	0.868808i	$0.664886\pi$
$20$	−2.63937	−0.590181
$21$	−0.0142784	−0.00311579
$22$	1.51322	0.322619
$23$	3.71486	0.774602	0.387301	−	0.921953i	$-0.373407\pi$
$23$	3.71486	0.774602	0.387301	+	0.921953i	$0.373407\pi$
$24$	0.134599	0.0274748
$25$	−4.76572	−0.953145
$26$	7.04346	1.38134
$27$	0.0856672	0.0164867
$28$	5.45300	1.03052
$29$	7.95129	1.47652	0.738259	−	0.674517i	$-0.235648\pi$
$29$	7.95129	1.47652	0.738259	+	0.674517i	$0.235648\pi$
$30$	−0.0188672	−0.00344467
$31$	−4.42475	−0.794708	−0.397354	−	0.917665i	$-0.630072\pi$
$31$	−4.42475	−0.794708	−0.397354	+	0.917665i	$0.630072\pi$
$32$	−21.6306	−3.82378
$33$	0.00791432	0.00137771
$34$	1.31047	0.224744
$35$	−0.484021	−0.0818145
$36$	−16.3579	−2.72632
$37$	1.58131	0.259966	0.129983	−	0.991516i	$-0.458508\pi$
$37$	1.58131	0.259966	0.129983	+	0.991516i	$0.458508\pi$
$38$	11.7844	1.91169
$39$	0.0368382	0.00589883
$40$	4.56275	0.721435
$41$	5.58807	0.872710	0.436355	−	0.899774i	$-0.356269\pi$
$41$	5.58807	0.872710	0.436355	+	0.899774i	$0.356269\pi$
$42$	0.0389802	0.00601477
$43$	0.117445	0.0179103	0.00895513	−	0.999960i	$-0.497149\pi$
$43$	0.117445	0.0179103	0.00895513	+	0.999960i	$0.497149\pi$
$44$	−3.02254	−0.455664
$45$	1.45196	0.216446
$46$	−10.1416	−1.49530
$47$	5.93216	0.865294	0.432647	−	0.901563i	$-0.357580\pi$
$47$	5.93216	0.865294	0.432647	+	0.901563i	$0.357580\pi$
$48$	−0.211737	−0.0305616
$49$	1.00000	0.142857
$50$	13.0105	1.83996
$51$	0.00685392	0.000959741 0
$52$	−14.0688	−1.95099
$53$	9.83101	1.35039	0.675196	−	0.737638i	$-0.264059\pi$
$53$	9.83101	1.35039	0.675196	+	0.737638i	$0.264059\pi$
$54$	−0.233873	−0.0318261
$55$	0.268287	0.0361758
$56$	−9.42677	−1.25970
$57$	0.0616340	0.00816363
$58$	−21.7072	−2.85029
$59$	−1.62971	−0.212171	−0.106085	−	0.994357i	$-0.533832\pi$
$59$	−1.62971	−0.212171	−0.106085	+	0.994357i	$0.533832\pi$
$60$	0.0376858	0.00486522
$61$	11.5013	1.47259	0.736295	−	0.676661i	$-0.236574\pi$
$61$	11.5013	1.47259	0.736295	+	0.676661i	$0.236574\pi$
$62$	12.0796	1.53412
$63$	−2.99980	−0.377939
$64$	29.3934	3.67418
$65$	1.24878	0.154892
$66$	−0.0216062	−0.00265955
$67$	−10.3795	−1.26806	−0.634031	−	0.773307i	$-0.718601\pi$
$67$	−10.3795	−1.26806	−0.634031	+	0.773307i	$0.718601\pi$
$68$	−2.61756	−0.317426
$69$	−0.0530421	−0.00638551
$70$	1.32139	0.157936
$71$	5.59039	0.663457	0.331729	−	0.943375i	$-0.392368\pi$
$71$	5.59039	0.663457	0.331729	+	0.943375i	$0.392368\pi$
$72$	28.2784	3.33264
$73$	10.7023	1.25261	0.626307	−	0.779576i	$-0.284566\pi$
$73$	10.7023	1.25261	0.626307	+	0.779576i	$0.284566\pi$
$74$	−4.31702	−0.501843
$75$	0.0680467	0.00785735
$76$	−23.5385	−2.70005
$77$	−0.554288	−0.0631670
$78$	−0.100569	−0.0113872
$79$	−1.56997	−0.176635	−0.0883177	−	0.996092i	$-0.528149\pi$
$79$	−1.56997	−0.176635	−0.0883177	+	0.996092i	$0.528149\pi$
$80$	−7.17767	−0.802488
$81$	8.99817	0.999796
$82$	−15.2555	−1.68469
$83$	16.3259	1.79200	0.896001	−	0.444053i	$-0.146460\pi$
$83$	16.3259	1.79200	0.896001	+	0.444053i	$0.146460\pi$
$84$	−0.0778599	−0.00849521
$85$	0.232341	0.0252009
$86$	−0.320628	−0.0345742
$87$	−0.113531	−0.0121718
$88$	5.22515	0.557002
$89$	−3.20720	−0.339963	−0.169981	−	0.985447i	$-0.554371\pi$
$89$	−3.20720	−0.339963	−0.169981	+	0.985447i	$0.554371\pi$
$90$	−3.96389	−0.417831
$91$	−2.58000	−0.270458
$92$	20.2571	2.11195
$93$	0.0631781	0.00655126
$94$	−16.1949	−1.67038
$95$	2.08933	0.214361
$96$	0.308849	0.0315218
$97$	4.24909	0.431430	0.215715	−	0.976456i	$-0.430792\pi$
$97$	4.24909	0.431430	0.215715	+	0.976456i	$0.430792\pi$
$98$	−2.73002	−0.275774
$99$	1.66275	0.167113
$100$	−25.9875	−2.59875
$101$	−16.1770	−1.60967	−0.804835	−	0.593499i	$-0.797746\pi$
$101$	−16.1770	−1.60967	−0.804835	+	0.593499i	$0.797746\pi$
$102$	−0.0187113	−0.00185270
$103$	−3.14162	−0.309553	−0.154776	−	0.987950i	$-0.549466\pi$
$103$	−3.14162	−0.309553	−0.154776	+	0.987950i	$0.549466\pi$
$104$	24.3211	2.38488
$105$	0.00691102	0.000674447 0
$106$	−26.8388	−2.60682
$107$	−10.2527	−0.991164	−0.495582	−	0.868561i	$-0.665045\pi$
$107$	−10.2527	−0.991164	−0.495582	+	0.868561i	$0.665045\pi$
$108$	0.467144	0.0449509
$109$	13.2085	1.26515	0.632573	−	0.774501i	$-0.281999\pi$
$109$	13.2085	1.26515	0.632573	+	0.774501i	$0.281999\pi$
$110$	−0.732429	−0.0698344
$111$	−0.0225785	−0.00214306
$112$	14.8292	1.40123
$113$	−0.00729080	−0.000685861 0	−0.000342930	−	1.00000i	$-0.500109\pi$
$113$	−0.00729080	−0.000685861 0	−0.000342930		1.00000i	$0.500109\pi$
$114$	−0.168262	−0.0157592
$115$	−1.79807	−0.167671
$116$	43.3584	4.02573
$117$	7.73949	0.715516
$118$	4.44915	0.409578
$119$	−0.480022	−0.0440036
$120$	−0.0651486	−0.00594723
$121$	−10.6928	−0.972070
$122$	−31.3987	−2.84271
$123$	−0.0797885	−0.00719428
$124$	−24.1282	−2.16677
$125$	4.72682	0.422779
$126$	8.18950	0.729579
$127$	3.44244	0.305467	0.152734	−	0.988267i	$-0.451192\pi$
$127$	3.44244	0.305467	0.152734	+	0.988267i	$0.451192\pi$
$128$	−36.9834	−3.26890
$129$	−0.00167693	−0.000147645 0
$130$	−3.40918	−0.299005
$131$	−6.15354	−0.537637	−0.268819	−	0.963191i	$-0.586633\pi$
$131$	−6.15354	−0.537637	−0.268819	+	0.963191i	$0.586633\pi$
$132$	0.0431568	0.00375632
$133$	−4.31661	−0.374297
$134$	28.3363	2.44789
$135$	−0.0414647	−0.00356872
$136$	4.52506	0.388020
$137$	−0.530417	−0.0453166	−0.0226583	−	0.999743i	$-0.507213\pi$
$137$	−0.530417	−0.0453166	−0.0226583	+	0.999743i	$0.507213\pi$
$138$	0.144806	0.0123267
$139$	−10.4506	−0.886406	−0.443203	−	0.896421i	$-0.646158\pi$
$139$	−10.4506	−0.886406	−0.443203	+	0.896421i	$0.646158\pi$
$140$	−2.63937	−0.223067
$141$	−0.0847015	−0.00713315
$142$	−15.2619	−1.28075
$143$	1.43007	0.119588
$144$	−44.4847	−3.70706
$145$	−3.84859	−0.319608
$146$	−29.2176	−2.41807
$147$	−0.0142784	−0.00117766
$148$	8.62291	0.708799
$149$	−3.51013	−0.287561	−0.143780	−	0.989610i	$-0.545926\pi$
$149$	−3.51013	−0.287561	−0.143780	+	0.989610i	$0.545926\pi$
$150$	−0.185769	−0.0151680
$151$	−21.3647	−1.73863	−0.869317	−	0.494256i	$-0.835441\pi$
$151$	−21.3647	−1.73863	−0.869317	+	0.494256i	$0.835441\pi$
$152$	40.6917	3.30053
$153$	1.43997	0.116415
$154$	1.51322	0.121939
$155$	2.14167	0.172023
$156$	0.200879	0.0160832
$157$	−21.1505	−1.68799	−0.843997	−	0.536348i	$-0.819803\pi$
$157$	−21.1505	−1.68799	−0.843997	+	0.536348i	$0.819803\pi$
$158$	4.28605	0.340980
$159$	−0.140371	−0.0111321
$160$	10.4697	0.827699
$161$	3.71486	0.292772
$162$	−24.5652	−1.93002
$163$	−9.49904	−0.744022	−0.372011	−	0.928228i	$-0.621332\pi$
$163$	−9.49904	−0.744022	−0.372011	+	0.928228i	$0.621332\pi$
$164$	30.4718	2.37945
$165$	−0.00383070	−0.000298219 0
$166$	−44.5700	−3.45931
$167$	−3.01995	−0.233691	−0.116845	−	0.993150i	$-0.537278\pi$
$167$	−3.01995	−0.233691	−0.116845	+	0.993150i	$0.537278\pi$
$168$	0.134599	0.0103845
$169$	−6.34358	−0.487967
$170$	−0.634295	−0.0486482
$171$	12.9489	0.990230
$172$	0.640430	0.0488323
$173$	−24.0327	−1.82717	−0.913585	−	0.406648i	$-0.866697\pi$
$173$	−24.0327	−1.82717	−0.913585	+	0.406648i	$0.866697\pi$
$174$	0.309943	0.0234967
$175$	−4.76572	−0.360255
$176$	−8.21968	−0.619581
$177$	0.0232696	0.00174905
$178$	8.75572	0.656269
$179$	15.7042	1.17379	0.586894	−	0.809664i	$-0.300351\pi$
$179$	15.7042	1.17379	0.586894	+	0.809664i	$0.300351\pi$
$180$	7.91757	0.590141
$181$	7.97448	0.592739	0.296369	−	0.955073i	$-0.404224\pi$
$181$	7.97448	0.592739	0.296369	+	0.955073i	$0.404224\pi$
$182$	7.04346	0.522096
$183$	−0.164219	−0.0121395
$184$	−35.0191	−2.58164
$185$	−0.765389	−0.0562725
$186$	−0.172477	−0.0126467
$187$	0.266071	0.0194570
$188$	32.3481	2.35923
$189$	0.0856672	0.00623137
$190$	−5.70391	−0.413805
$191$	3.15664	0.228407	0.114203	−	0.993457i	$-0.463568\pi$
$191$	3.15664	0.228407	0.114203	+	0.993457i	$0.463568\pi$
$192$	−0.419690	−0.0302885
$193$	−23.8885	−1.71953	−0.859767	−	0.510686i	$-0.829392\pi$
$193$	−23.8885	−1.71953	−0.859767	+	0.510686i	$0.829392\pi$
$194$	−11.6001	−0.832839
$195$	−0.0178305	−0.00127687
$196$	5.45300	0.389500
$197$	−4.84093	−0.344902	−0.172451	−	0.985018i	$-0.555169\pi$
$197$	−4.84093	−0.344902	−0.172451	+	0.985018i	$0.555169\pi$
$198$	−4.53934	−0.322597
$199$	−11.6834	−0.828211	−0.414106	−	0.910229i	$-0.635906\pi$
$199$	−11.6834	−0.828211	−0.414106	+	0.910229i	$0.635906\pi$
$200$	44.9254	3.17670
$201$	0.148203	0.0104534
$202$	44.1635	3.10733
$203$	7.95129	0.558071
$204$	0.0373745	0.00261674
$205$	−2.70475	−0.188908
$206$	8.57668	0.597565
$207$	−11.1438	−0.774549
$208$	−38.2595	−2.65282
$209$	2.39264	0.165503
$210$	−0.0188672	−0.00130196
$211$	−23.9536	−1.64904	−0.824519	−	0.565835i	$-0.808554\pi$
$211$	−23.9536	−1.64904	−0.824519	+	0.565835i	$0.808554\pi$
$212$	53.6085	3.68185
$213$	−0.0798216	−0.00546928
$214$	27.9900	1.91336
$215$	−0.0568460	−0.00387687
$216$	−0.807565	−0.0549478
$217$	−4.42475	−0.300371
$218$	−36.0595	−2.44226
$219$	−0.152812	−0.0103261
$220$	1.46297	0.0986335
$221$	1.23846	0.0833078
$222$	0.0616399	0.00413700
$223$	28.8909	1.93468	0.967339	−	0.253487i	$-0.0815775\pi$
$223$	28.8909	1.93468	0.967339	+	0.253487i	$0.0815775\pi$
$224$	−21.6306	−1.44525
$225$	14.2962	0.953080
$226$	0.0199040	0.00132400
$227$	16.0458	1.06500	0.532499	−	0.846431i	$-0.321253\pi$
$227$	16.0458	1.06500	0.532499	+	0.846431i	$0.321253\pi$
$228$	0.336091	0.0222581
$229$	8.40357	0.555324	0.277662	−	0.960679i	$-0.410441\pi$
$229$	8.40357	0.555324	0.277662	+	0.960679i	$0.410441\pi$
$230$	4.90877	0.323674
$231$	0.00791432	0.000520724 0
$232$	−74.9550	−4.92104
$233$	−25.0716	−1.64250	−0.821248	−	0.570571i	$-0.806722\pi$
$233$	−25.0716	−1.64250	−0.821248	+	0.570571i	$0.806722\pi$
$234$	−21.1289	−1.38124
$235$	−2.87129	−0.187302
$236$	−8.88684	−0.578484
$237$	0.0224166	0.00145611
$238$	1.31047	0.0849451
$239$	−14.3548	−0.928537	−0.464268	−	0.885695i	$-0.653683\pi$
$239$	−14.3548	−0.928537	−0.464268	+	0.885695i	$0.653683\pi$
$240$	0.102485	0.00661539
$241$	4.05973	0.261510	0.130755	−	0.991415i	$-0.458260\pi$
$241$	4.05973	0.261510	0.130755	+	0.991415i	$0.458260\pi$
$242$	29.1915	1.87650
$243$	−0.385481	−0.0247286
$244$	62.7166	4.01502
$245$	−0.484021	−0.0309230
$246$	0.217824	0.0138880
$247$	11.1369	0.708622
$248$	41.7111	2.64866
$249$	−0.233107	−0.0147726
$250$	−12.9043	−0.816140
$251$	−11.3884	−0.718832	−0.359416	−	0.933178i	$-0.617024\pi$
$251$	−11.3884	−0.718832	−0.359416	+	0.933178i	$0.617024\pi$
$252$	−16.3579	−1.03045
$253$	−2.05910	−0.129455
$254$	−9.39793	−0.589678
$255$	−0.00331744	−0.000207746 0
$256$	42.1786	2.63616
$257$	2.39656	0.149493	0.0747466	−	0.997203i	$-0.476185\pi$
$257$	2.39656	0.149493	0.0747466	+	0.997203i	$0.476185\pi$
$258$	0.00457804	0.000285016 0
$259$	1.58131	0.0982580
$260$	6.80958	0.422313
$261$	−23.8523	−1.47642
$262$	16.7993	1.03786
$263$	31.1996	1.92385	0.961925	−	0.273312i	$-0.0881192\pi$
$263$	31.1996	1.92385	0.961925	+	0.273312i	$0.0881192\pi$
$264$	−0.0746065	−0.00459171
$265$	−4.75842	−0.292307
$266$	11.7844	0.722549
$267$	0.0457935	0.00280252
$268$	−56.5997	−3.45737
$269$	−13.6752	−0.833793	−0.416897	−	0.908954i	$-0.636882\pi$
$269$	−13.6752	−0.833793	−0.416897	+	0.908954i	$0.636882\pi$
$270$	0.113200	0.00688910
$271$	−10.8211	−0.657336	−0.328668	−	0.944446i	$-0.606600\pi$
$271$	−10.8211	−0.657336	−0.328668	+	0.944446i	$0.606600\pi$
$272$	−7.11837	−0.431614
$273$	0.0368382	0.00222955
$274$	1.44805	0.0874798
$275$	2.64158	0.159294
$276$	−0.289239	−0.0174101
$277$	−5.62084	−0.337724	−0.168862	−	0.985640i	$-0.554009\pi$
$277$	−5.62084	−0.337724	−0.168862	+	0.985640i	$0.554009\pi$
$278$	28.5303	1.71113
$279$	13.2733	0.794654
$280$	4.56275	0.272677
$281$	−12.1760	−0.726362	−0.363181	−	0.931719i	$-0.618309\pi$
$281$	−12.1760	−0.726362	−0.363181	+	0.931719i	$0.618309\pi$
$282$	0.231237	0.0137699
$283$	−8.58294	−0.510203	−0.255101	−	0.966914i	$-0.582109\pi$
$283$	−8.58294	−0.510203	−0.255101	+	0.966914i	$0.582109\pi$
$284$	30.4844	1.80892
$285$	−0.0298322	−0.00176711
$286$	−3.90411	−0.230855
$287$	5.58807	0.329854
$288$	64.8873	3.82352
$289$	−16.7696	−0.986446
$290$	10.5067	0.616977
$291$	−0.0606701	−0.00355654
$292$	58.3599	3.41526
$293$	32.6120	1.90522	0.952608	−	0.304200i	$-0.0983892\pi$
$293$	32.6120	1.90522	0.952608	+	0.304200i	$0.0983892\pi$
$294$	0.0389802	0.00227337
$295$	0.788816	0.0459266
$296$	−14.9067	−0.866433
$297$	−0.0474843	−0.00275532
$298$	9.58271	0.555111
$299$	−9.58435	−0.554278
$300$	0.371059	0.0214231
$301$	0.117445	0.00676944
$302$	58.3260	3.35628
$303$	0.230981	0.0132695
$304$	−64.0120	−3.67134
$305$	−5.56687	−0.318758
$306$	−3.93114	−0.224728
$307$	−1.01224	−0.0577715	−0.0288858	−	0.999583i	$-0.509196\pi$
$307$	−1.01224	−0.0577715	−0.0288858	+	0.999583i	$0.509196\pi$
$308$	−3.02254	−0.172225
$309$	0.0448571	0.00255183
$310$	−5.84680	−0.332076
$311$	−9.33916	−0.529575	−0.264788	−	0.964307i	$-0.585302\pi$
$311$	−9.33916	−0.529575	−0.264788	+	0.964307i	$0.585302\pi$
$312$	−0.347265	−0.0196600
$313$	−6.02979	−0.340824	−0.170412	−	0.985373i	$-0.554510\pi$
$313$	−6.02979	−0.340824	−0.170412	+	0.985373i	$0.554510\pi$
$314$	57.7413	3.25853
$315$	1.45196	0.0818089
$316$	−8.56105	−0.481597
$317$	−6.60266	−0.370842	−0.185421	−	0.982659i	$-0.559365\pi$
$317$	−6.60266	−0.370842	−0.185421	+	0.982659i	$0.559365\pi$
$318$	0.383214	0.0214896
$319$	−4.40731	−0.246762
$320$	−14.2270	−0.795316
$321$	0.146391	0.00817077
$322$	−10.1416	−0.565171
$323$	2.07207	0.115293
$324$	49.0670	2.72595
$325$	12.2956	0.682037
$326$	25.9326	1.43627
$327$	−0.188596	−0.0104294
$328$	−52.6775	−2.90863
$329$	5.93216	0.327051
$330$	0.0104579	0.000575687 0
$331$	4.71333	0.259068	0.129534	−	0.991575i	$-0.458652\pi$
$331$	4.71333	0.259068	0.129534	+	0.991575i	$0.458652\pi$
$332$	89.0252	4.88590
$333$	−4.74362	−0.259949
$334$	8.24451	0.451120
$335$	5.02392	0.274486
$336$	−0.211737	−0.0115512
$337$	−0.199021	−0.0108413	−0.00542067	−	0.999985i	$-0.501725\pi$
$337$	−0.199021	−0.0108413	−0.00542067	+	0.999985i	$0.501725\pi$
$338$	17.3181	0.941980
$339$	0.000104101 0	5.65397e−6 0
$340$	1.26696	0.0687103
$341$	2.45259	0.132815
$342$	−35.3509	−1.91156
$343$	1.00000	0.0539949
$344$	−1.10713	−0.0596925
$345$	0.0256735	0.00138221
$346$	65.6096	3.52720
$347$	23.1962	1.24523	0.622617	−	0.782526i	$-0.286069\pi$
$347$	23.1962	1.24523	0.622617	+	0.782526i	$0.286069\pi$
$348$	−0.619087	−0.0331865
$349$	35.8913	1.92122	0.960609	−	0.277902i	$-0.0896391\pi$
$349$	35.8913	1.92122	0.960609	+	0.277902i	$0.0896391\pi$
$350$	13.0105	0.695441
$351$	−0.221022	−0.0117973
$352$	11.9896	0.639047
$353$	−17.9868	−0.957338	−0.478669	−	0.877995i	$-0.658881\pi$
$353$	−17.9868	−0.957338	−0.478669	+	0.877995i	$0.658881\pi$
$354$	−0.0635265	−0.00337640
$355$	−2.70587	−0.143613
$356$	−17.4889	−0.926909
$357$	0.00685392	0.000362748 0
$358$	−42.8728	−2.26590
$359$	1.97366	0.104166	0.0520829	−	0.998643i	$-0.483414\pi$
$359$	1.97366	0.104166	0.0520829	+	0.998643i	$0.483414\pi$
$360$	−13.6873	−0.721386
$361$	−0.366898	−0.0193104
$362$	−21.7705	−1.14423
$363$	0.152675	0.00801336
$364$	−14.0688	−0.737404
$365$	−5.18016	−0.271142
$366$	0.448322	0.0234342
$367$	11.3185	0.590821	0.295410	−	0.955370i	$-0.404544\pi$
$367$	11.3185	0.590821	0.295410	+	0.955370i	$0.404544\pi$
$368$	55.0886	2.87169
$369$	−16.7631	−0.872651
$370$	2.08953	0.108629
$371$	9.83101	0.510401
$372$	0.344510	0.0178620
$373$	5.96043	0.308619	0.154310	−	0.988023i	$-0.450685\pi$
$373$	5.96043	0.308619	0.154310	+	0.988023i	$0.450685\pi$
$374$	−0.726378	−0.0375601
$375$	−0.0674911	−0.00348523
$376$	−55.9211	−2.88391
$377$	−20.5144	−1.05654
$378$	−0.233873	−0.0120291
$379$	−21.2151	−1.08975	−0.544873	−	0.838518i	$-0.683422\pi$
$379$	−21.2151	−1.08975	−0.544873	+	0.838518i	$0.683422\pi$
$380$	11.3931	0.584455
$381$	−0.0491524	−0.00251815
$382$	−8.61769	−0.440920
$383$	18.6188	0.951377	0.475689	−	0.879614i	$-0.342199\pi$
$383$	18.6188	0.951377	0.475689	+	0.879614i	$0.342199\pi$
$384$	0.528062	0.0269476
$385$	0.268287	0.0136732
$386$	65.2162	3.31942
$387$	−0.352312	−0.0179090
$388$	23.1703	1.17630
$389$	−21.9745	−1.11415	−0.557076	−	0.830461i	$-0.688077\pi$
$389$	−21.9745	−1.11415	−0.557076	+	0.830461i	$0.688077\pi$
$390$	0.0486775	0.00246488
$391$	−1.78321	−0.0901810
$392$	−9.42677	−0.476124
$393$	0.0878624	0.00443207
$394$	13.2158	0.665803
$395$	0.759898	0.0382346
$396$	9.06699	0.455633
$397$	25.5521	1.28242	0.641212	−	0.767364i	$-0.278432\pi$
$397$	25.5521	1.28242	0.641212	+	0.767364i	$0.278432\pi$
$398$	31.8958	1.59879
$399$	0.0616340	0.00308556
$400$	−70.6721	−3.53360
$401$	−21.4946	−1.07339	−0.536695	−	0.843776i	$-0.680328\pi$
$401$	−21.4946	−1.07339	−0.536695	+	0.843776i	$0.680328\pi$
$402$	−0.404596	−0.0201794
$403$	11.4159	0.568665
$404$	−88.2131	−4.38877
$405$	−4.35530	−0.216417
$406$	−21.7072	−1.07731
$407$	−0.876503	−0.0434467
$408$	−0.0646103	−0.00319869
$409$	−3.51894	−0.174001	−0.0870003	−	0.996208i	$-0.527728\pi$
$409$	−3.51894	−0.174001	−0.0870003	+	0.996208i	$0.527728\pi$
$410$	7.38401	0.364670
$411$	0.00757348	0.000373572 0
$412$	−17.1313	−0.843996
$413$	−1.62971	−0.0801930
$414$	30.4228	1.49520
$415$	−7.90209	−0.387898
$416$	55.8070	2.73616
$417$	0.149217	0.00730719
$418$	−6.53197	−0.319489
$419$	−5.06281	−0.247335	−0.123667	−	0.992324i	$-0.539466\pi$
$419$	−5.06281	−0.247335	−0.123667	+	0.992324i	$0.539466\pi$
$420$	0.0376858	0.00183888
$421$	−11.1786	−0.544810	−0.272405	−	0.962183i	$-0.587819\pi$
$421$	−11.1786	−0.544810	−0.272405	+	0.962183i	$0.587819\pi$
$422$	65.3939	3.18333
$423$	−17.7953	−0.865236
$424$	−92.6746	−4.50068
$425$	2.28765	0.110967
$426$	0.217914	0.0105580
$427$	11.5013	0.556586
$428$	−55.9079	−2.70241
$429$	−0.0204190	−0.000985838 0
$430$	0.155191	0.00748396
$431$	−25.9802	−1.25142	−0.625711	−	0.780055i	$-0.715191\pi$
$431$	−25.9802	−1.25142	−0.625711	+	0.780055i	$0.715191\pi$
$432$	1.27038	0.0611212
$433$	2.66796	0.128214	0.0641069	−	0.997943i	$-0.479580\pi$
$433$	2.66796	0.128214	0.0641069	+	0.997943i	$0.479580\pi$
$434$	12.0796	0.579842
$435$	0.0549516	0.00263473
$436$	72.0261	3.44942
$437$	−16.0356	−0.767086
$438$	0.417179	0.0199336
$439$	1.81868	0.0868008	0.0434004	−	0.999058i	$-0.486181\pi$
$439$	1.81868	0.0868008	0.0434004	+	0.999058i	$0.486181\pi$
$440$	−2.52908	−0.120569
$441$	−2.99980	−0.142847
$442$	−3.38102	−0.160819
$443$	−20.5852	−0.978034	−0.489017	−	0.872274i	$-0.662644\pi$
$443$	−20.5852	−0.978034	−0.489017	+	0.872274i	$0.662644\pi$
$444$	−0.123121	−0.00584306
$445$	1.55235	0.0735886
$446$	−78.8727	−3.73473
$447$	0.0501188	0.00237054
$448$	29.3934	1.38871
$449$	23.7221	1.11951	0.559757	−	0.828657i	$-0.310895\pi$
$449$	23.7221	1.11951	0.559757	+	0.828657i	$0.310895\pi$
$450$	−39.0289	−1.83984
$451$	−3.09740	−0.145851
$452$	−0.0397567	−0.00187000
$453$	0.305052	0.0143326
$454$	−43.8054	−2.05589
$455$	1.24878	0.0585436
$456$	−0.581010	−0.0272083
$457$	3.37488	0.157870	0.0789350	−	0.996880i	$-0.474848\pi$
$457$	3.37488	0.157870	0.0789350	+	0.996880i	$0.474848\pi$
$458$	−22.9419	−1.07201
$459$	−0.0411221	−0.00191942
$460$	−9.80489	−0.457155
$461$	−0.672091	−0.0313024	−0.0156512	−	0.999878i	$-0.504982\pi$
$461$	−0.672091	−0.0313024	−0.0156512	+	0.999878i	$0.504982\pi$
$462$	−0.0216062	−0.00100521
$463$	20.3682	0.946589	0.473295	−	0.880904i	$-0.343065\pi$
$463$	20.3682	0.946589	0.473295	+	0.880904i	$0.343065\pi$
$464$	117.912	5.47391
$465$	−0.0305795	−0.00141809
$466$	68.4460	3.17070
$467$	−26.4631	−1.22457	−0.612283	−	0.790639i	$-0.709749\pi$
$467$	−26.4631	−1.22457	−0.612283	+	0.790639i	$0.709749\pi$
$468$	42.2035	1.95086
$469$	−10.3795	−0.479283
$470$	7.83868	0.361571
$471$	0.301994	0.0139152
$472$	15.3629	0.707136
$473$	−0.0650986	−0.00299324
$474$	−0.0611977	−0.00281090
$475$	20.5718	0.943897
$476$	−2.61756	−0.119976
$477$	−29.4910	−1.35030
$478$	39.1890	1.79246
$479$	18.8265	0.860205	0.430103	−	0.902780i	$-0.358477\pi$
$479$	18.8265	0.860205	0.430103	+	0.902780i	$0.358477\pi$
$480$	−0.149489	−0.00682323
$481$	−4.07980	−0.186023
$482$	−11.0832	−0.504824
$483$	−0.0530421	−0.00241350
$484$	−58.3077	−2.65035
$485$	−2.05665	−0.0933877
$486$	1.05237	0.0477364
$487$	32.4491	1.47041	0.735205	−	0.677845i	$-0.237086\pi$
$487$	32.4491	1.47041	0.735205	+	0.677845i	$0.237086\pi$
$488$	−108.420	−4.90794
$489$	0.135631	0.00613343
$490$	1.32139	0.0596942
$491$	14.0640	0.634700	0.317350	−	0.948308i	$-0.397207\pi$
$491$	14.0640	0.634700	0.317350	+	0.948308i	$0.397207\pi$
$492$	−0.435087	−0.0196152
$493$	−3.81680	−0.171900
$494$	−30.4039	−1.36793
$495$	−0.804807	−0.0361734
$496$	−65.6157	−2.94623
$497$	5.59039	0.250763
$498$	0.636387	0.0285172
$499$	−40.2237	−1.80066	−0.900331	−	0.435206i	$-0.856676\pi$
$499$	−40.2237	−1.80066	−0.900331	+	0.435206i	$0.856676\pi$
$500$	25.7754	1.15271
$501$	0.0431199	0.00192645
$502$	31.0906	1.38764
$503$	−10.6827	−0.476318	−0.238159	−	0.971226i	$-0.576544\pi$
$503$	−10.6827	−0.476318	−0.238159	+	0.971226i	$0.576544\pi$
$504$	28.2784	1.25962
$505$	7.83000	0.348430
$506$	5.62139	0.249901
$507$	0.0905758	0.00402261
$508$	18.7716	0.832857
$509$	0.704585	0.0312302	0.0156151	−	0.999878i	$-0.495029\pi$
$509$	0.704585	0.0312302	0.0156151	+	0.999878i	$0.495029\pi$
$510$	0.00905669	0.000401037 0
$511$	10.7023	0.473444
$512$	−41.1816	−1.81999
$513$	−0.369792	−0.0163267
$514$	−6.54265	−0.288584
$515$	1.52061	0.0670061
$516$	−0.00914428	−0.000402555 0
$517$	−3.28813	−0.144612
$518$	−4.31702	−0.189679
$519$	0.343147	0.0150625
$520$	−11.7719	−0.516233
$521$	−35.0996	−1.53774	−0.768871	−	0.639404i	$-0.779181\pi$
$521$	−35.0996	−1.53774	−0.768871	+	0.639404i	$0.779181\pi$
$522$	65.1171	2.85010
$523$	−35.1894	−1.53872	−0.769362	−	0.638814i	$-0.779426\pi$
$523$	−35.1894	−1.53872	−0.769362	+	0.638814i	$0.779426\pi$
$524$	−33.5553	−1.46587
$525$	0.0680467	0.00296980
$526$	−85.1756	−3.71383
$527$	2.12398	0.0925219
$528$	0.117363	0.00510759
$529$	−9.19982	−0.399992
$530$	12.9906	0.564274
$531$	4.88881	0.212156
$532$	−23.5385	−1.02052
$533$	−14.4173	−0.624481
$534$	−0.125017	−0.00541002
$535$	4.96251	0.214548
$536$	97.8455	4.22628
$537$	−0.224230	−0.00967624
$538$	37.3336	1.60957
$539$	−0.554288	−0.0238749
$540$	−0.226107	−0.00973011
$541$	24.6291	1.05889	0.529445	−	0.848344i	$-0.322400\pi$
$541$	24.6291	1.05889	0.529445	+	0.848344i	$0.322400\pi$
$542$	29.5419	1.26893
$543$	−0.113862	−0.00488630
$544$	10.3832	0.445174
$545$	−6.39320	−0.273855
$546$	−0.100569	−0.00430396
$547$	17.0758	0.730106	0.365053	−	0.930987i	$-0.381051\pi$
$547$	17.0758	0.730106	0.365053	+	0.930987i	$0.381051\pi$
$548$	−2.89237	−0.123556
$549$	−34.5015	−1.47249
$550$	−7.21158	−0.307503
$551$	−34.3226	−1.46219
$552$	0.500015	0.0212821
$553$	−1.56997	−0.0667619
$554$	15.3450	0.651947
$555$	0.0109285	0.000463889 0
$556$	−56.9870	−2.41679
$557$	22.8524	0.968286	0.484143	−	0.874989i	$-0.339131\pi$
$557$	22.8524	0.968286	0.484143	+	0.874989i	$0.339131\pi$
$558$	−36.2365	−1.53401
$559$	−0.303010	−0.0128159
$560$	−7.17767	−0.303312
$561$	−0.00379905	−0.000160396 0
$562$	33.2408	1.40218
$563$	2.94256	0.124014	0.0620070	−	0.998076i	$-0.480250\pi$
$563$	2.94256	0.124014	0.0620070	+	0.998076i	$0.480250\pi$
$564$	−0.461877	−0.0194485
$565$	0.00352890	0.000148462 0
$566$	23.4316	0.984903
$567$	8.99817	0.377887
$568$	−52.6993	−2.21121
$569$	15.8778	0.665630	0.332815	−	0.942992i	$-0.392001\pi$
$569$	15.8778	0.665630	0.332815	+	0.942992i	$0.392001\pi$
$570$	0.0814424	0.00341125
$571$	−1.09794	−0.0459473	−0.0229736	−	0.999736i	$-0.507313\pi$
$571$	−1.09794	−0.0459473	−0.0229736	+	0.999736i	$0.507313\pi$
$572$	7.79816	0.326057
$573$	−0.0450716	−0.00188289
$574$	−15.2555	−0.636754
$575$	−17.7040	−0.738308
$576$	−88.1743	−3.67393
$577$	−30.6372	−1.27544	−0.637722	−	0.770267i	$-0.720123\pi$
$577$	−30.6372	−1.27544	−0.637722	+	0.770267i	$0.720123\pi$
$578$	45.7813	1.90425
$579$	0.341089	0.0141752
$580$	−20.9864	−0.871413
$581$	16.3259	0.677313
$582$	0.165630	0.00686560
$583$	−5.44921	−0.225683
$584$	−100.889	−4.17480
$585$	−3.74608	−0.154881
$586$	−89.0315	−3.67786
$587$	0.188754	0.00779073	0.00389537	−	0.999992i	$-0.498760\pi$
$587$	0.188754	0.00779073	0.00389537	+	0.999992i	$0.498760\pi$
$588$	−0.0778599	−0.00321089
$589$	19.0999	0.786998
$590$	−2.15348	−0.0886575
$591$	0.0691204	0.00284323
$592$	23.4497	0.963776
$593$	19.4362	0.798148	0.399074	−	0.916919i	$-0.369332\pi$
$593$	19.4362	0.798148	0.399074	+	0.916919i	$0.369332\pi$
$594$	0.129633	0.00531891
$595$	0.232341	0.00952505
$596$	−19.1407	−0.784035
$597$	0.166819	0.00682745
$598$	26.1655	1.06999
$599$	18.5029	0.756007	0.378003	−	0.925804i	$-0.376611\pi$
$599$	18.5029	0.756007	0.378003	+	0.925804i	$0.376611\pi$
$600$	−0.641460	−0.0261875
$601$	2.25345	0.0919202	0.0459601	−	0.998943i	$-0.485365\pi$
$601$	2.25345	0.0919202	0.0459601	+	0.998943i	$0.485365\pi$
$602$	−0.320628	−0.0130678
$603$	31.1365	1.26798
$604$	−116.502	−4.74039
$605$	5.17552	0.210415
$606$	−0.630581	−0.0256156
$607$	36.9857	1.50120	0.750601	−	0.660756i	$-0.229764\pi$
$607$	36.9857	1.50120	0.750601	+	0.660756i	$0.229764\pi$
$608$	93.3708	3.78668
$609$	−0.113531	−0.00460052
$610$	15.1977	0.615335
$611$	−15.3050	−0.619174
$612$	7.85215	0.317405
$613$	16.9543	0.684776	0.342388	−	0.939559i	$-0.388764\pi$
$613$	16.9543	0.684776	0.342388	+	0.939559i	$0.388764\pi$
$614$	2.76343	0.111523
$615$	0.0386193	0.00155728
$616$	5.22515	0.210527
$617$	−22.5432	−0.907557	−0.453778	−	0.891115i	$-0.649924\pi$
$617$	−22.5432	−0.907557	−0.453778	+	0.891115i	$0.649924\pi$
$618$	−0.122461	−0.00492610
$619$	−14.9751	−0.601900	−0.300950	−	0.953640i	$-0.597304\pi$
$619$	−14.9751	−0.601900	−0.300950	+	0.953640i	$0.597304\pi$
$620$	11.6785	0.469022
$621$	0.318242	0.0127706
$622$	25.4961	1.02230
$623$	−3.20720	−0.128494
$624$	0.546283	0.0218688
$625$	21.5407	0.861630
$626$	16.4615	0.657932
$627$	−0.0341630	−0.00136434
$628$	−115.334	−4.60232
$629$	−0.759065	−0.0302659
$630$	−3.96389	−0.157925
$631$	14.3125	0.569772	0.284886	−	0.958561i	$-0.408044\pi$
$631$	14.3125	0.569772	0.284886	+	0.958561i	$0.408044\pi$
$632$	14.7997	0.588702
$633$	0.342019	0.0135940
$634$	18.0254	0.715879
$635$	−1.66621	−0.0661217
$636$	−0.765441	−0.0303517
$637$	−2.58000	−0.102224
$638$	12.0320	0.476353
$639$	−16.7700	−0.663412
$640$	17.9008	0.707590
$641$	−6.60075	−0.260714	−0.130357	−	0.991467i	$-0.541612\pi$
$641$	−6.60075	−0.260714	−0.130357	+	0.991467i	$0.541612\pi$
$642$	−0.399651	−0.0157730
$643$	−26.3274	−1.03825	−0.519126	−	0.854698i	$-0.673742\pi$
$643$	−26.3274	−1.03825	−0.519126	+	0.854698i	$0.673742\pi$
$644$	20.2571	0.798243
$645$	0.000811668 0	3.19594e−5 0
$646$	−5.65678	−0.222563
$647$	−32.0830	−1.26131	−0.630656	−	0.776062i	$-0.717214\pi$
$647$	−32.0830	−1.26131	−0.630656	+	0.776062i	$0.717214\pi$
$648$	−84.8236	−3.33219
$649$	0.903331	0.0354589
$650$	−33.5672	−1.31661
$651$	0.0631781	0.00247614
$652$	−51.7983	−2.02858
$653$	−37.2295	−1.45690	−0.728451	−	0.685098i	$-0.759760\pi$
$653$	−37.2295	−1.45690	−0.728451	+	0.685098i	$0.759760\pi$
$654$	0.514870	0.0201330
$655$	2.97844	0.116377
$656$	82.8669	3.23541
$657$	−32.1049	−1.25253
$658$	−16.1949	−0.631343
$659$	−31.9781	−1.24569	−0.622845	−	0.782345i	$-0.714023\pi$
$659$	−31.9781	−1.24569	−0.622845	+	0.782345i	$0.714023\pi$
$660$	−0.0208888	−0.000813096 0
$661$	−12.1257	−0.471633	−0.235817	−	0.971798i	$-0.575776\pi$
$661$	−12.1257	−0.471633	−0.235817	+	0.971798i	$0.575776\pi$
$662$	−12.8675	−0.500109
$663$	−0.0176832	−0.000686757 0
$664$	−153.901	−5.97250
$665$	2.08933	0.0810207
$666$	12.9502	0.501809
$667$	29.5379	1.14371
$668$	−16.4678	−0.637158
$669$	−0.412514	−0.0159487
$670$	−13.7154	−0.529872
$671$	−6.37503	−0.246105
$672$	0.308849	0.0119141
$673$	−10.9804	−0.423263	−0.211631	−	0.977350i	$-0.567878\pi$
$673$	−10.9804	−0.423263	−0.211631	+	0.977350i	$0.567878\pi$
$674$	0.543330	0.0209283
$675$	−0.408266	−0.0157142
$676$	−34.5915	−1.33044
$677$	−15.5147	−0.596278	−0.298139	−	0.954522i	$-0.596366\pi$
$677$	−15.5147	−0.596278	−0.298139	+	0.954522i	$0.596366\pi$
$678$	−0.000284197 0	−1.09145e−5 0
$679$	4.24909	0.163065
$680$	−2.19022	−0.0839912
$681$	−0.229108	−0.00877943
$682$	−6.69560	−0.256388
$683$	−21.7885	−0.833714	−0.416857	−	0.908972i	$-0.636868\pi$
$683$	−21.7885	−0.833714	−0.416857	+	0.908972i	$0.636868\pi$
$684$	70.6106	2.69987
$685$	0.256733	0.00980926
$686$	−2.73002	−0.104233
$687$	−0.119989	−0.00457787
$688$	1.74163	0.0663989
$689$	−25.3640	−0.966293
$690$	−0.0700891	−0.00266825
$691$	−20.8204	−0.792046	−0.396023	−	0.918241i	$-0.629610\pi$
$691$	−20.8204	−0.792046	−0.396023	+	0.918241i	$0.629610\pi$
$692$	−131.050	−4.98178
$693$	1.66275	0.0631627
$694$	−63.3259	−2.40382
$695$	5.05830	0.191872
$696$	1.07023	0.0405671
$697$	−2.68240	−0.101603
$698$	−97.9840	−3.70875
$699$	0.357981	0.0135401
$700$	−25.9875	−0.982236
$701$	−29.3106	−1.10705	−0.553523	−	0.832834i	$-0.686717\pi$
$701$	−29.3106	−1.10705	−0.553523	+	0.832834i	$0.686717\pi$
$702$	0.603394	0.0227736
$703$	−6.82591	−0.257444
$704$	−16.2924	−0.614044
$705$	0.0409973	0.00154405
$706$	49.1042	1.84806
$707$	−16.1770	−0.608398
$708$	0.126889	0.00476879
$709$	−13.3390	−0.500957	−0.250478	−	0.968122i	$-0.580588\pi$
$709$	−13.3390	−0.500957	−0.250478	+	0.968122i	$0.580588\pi$
$710$	7.38707	0.277232
$711$	4.70959	0.176623
$712$	30.2335	1.13305
$713$	−16.4373	−0.615582
$714$	−0.0187113	−0.000700254 0
$715$	−0.692182	−0.0258861
$716$	85.6351	3.20033
$717$	0.204963	0.00765450
$718$	−5.38813	−0.201083
$719$	−14.0496	−0.523963	−0.261982	−	0.965073i	$-0.584376\pi$
$719$	−14.0496	−0.523963	−0.261982	+	0.965073i	$0.584376\pi$
$720$	21.5315	0.802433
$721$	−3.14162	−0.117000
$722$	1.00164	0.0372771
$723$	−0.0579663	−0.00215579
$724$	43.4849	1.61610
$725$	−37.8937	−1.40734
$726$	−0.416806	−0.0154691
$727$	22.4284	0.831824	0.415912	−	0.909405i	$-0.363462\pi$
$727$	22.4284	0.831824	0.415912	+	0.909405i	$0.363462\pi$
$728$	24.3211	0.901400
$729$	−26.9890	−0.999592
$730$	14.1419	0.523417
$731$	−0.0563764	−0.00208516
$732$	−0.895489	−0.0330982
$733$	23.2274	0.857924	0.428962	−	0.903323i	$-0.358879\pi$
$733$	23.2274	0.857924	0.428962	+	0.903323i	$0.358879\pi$
$734$	−30.8997	−1.14053
$735$	0.00691102	0.000254917 0
$736$	−80.3546	−2.96191
$737$	5.75326	0.211924
$738$	45.7635	1.68458
$739$	−35.0767	−1.29032	−0.645159	−	0.764049i	$-0.723209\pi$
$739$	−35.0767	−1.29032	−0.645159	+	0.764049i	$0.723209\pi$
$740$	−4.17367	−0.153427
$741$	−0.159016	−0.00584160
$742$	−26.8388	−0.985285
$743$	−25.9929	−0.953588	−0.476794	−	0.879015i	$-0.658201\pi$
$743$	−25.9929	−0.953588	−0.476794	+	0.879015i	$0.658201\pi$
$744$	−0.595565	−0.0218345
$745$	1.69897	0.0622456
$746$	−16.2721	−0.595763
$747$	−48.9744	−1.79188
$748$	1.45088	0.0530496
$749$	−10.2527	−0.374625
$750$	0.184252	0.00672794
$751$	41.8289	1.52636	0.763179	−	0.646187i	$-0.223637\pi$
$751$	41.8289	1.52636	0.763179	+	0.646187i	$0.223637\pi$
$752$	87.9695	3.20792
$753$	0.162608	0.00592577
$754$	56.0046	2.03957
$755$	10.3410	0.376346
$756$	0.467144	0.0169898
$757$	15.5885	0.566572	0.283286	−	0.959035i	$-0.408575\pi$
$757$	15.5885	0.566572	0.283286	+	0.959035i	$0.408575\pi$
$758$	57.9176	2.10366
$759$	0.0294006	0.00106717
$760$	−19.6956	−0.714435
$761$	−48.9780	−1.77545	−0.887725	−	0.460374i	$-0.847715\pi$
$761$	−48.9780	−1.77545	−0.887725	+	0.460374i	$0.847715\pi$
$762$	0.134187	0.00486108
$763$	13.2085	0.478180
$764$	17.2132	0.622751
$765$	−0.696975	−0.0251992
$766$	−50.8297	−1.83655
$767$	4.20467	0.151822
$768$	−0.602241	−0.0217315
$769$	−26.3856	−0.951487	−0.475744	−	0.879584i	$-0.657821\pi$
$769$	−26.3856	−0.951487	−0.475744	+	0.879584i	$0.657821\pi$
$770$	−0.732429	−0.0263949
$771$	−0.0342189	−0.00123236
$772$	−130.264	−4.68832
$773$	36.3625	1.30787	0.653934	−	0.756552i	$-0.273117\pi$
$773$	36.3625	1.30787	0.653934	+	0.756552i	$0.273117\pi$
$774$	0.961819	0.0345719
$775$	21.0871	0.757472
$776$	−40.0552	−1.43790
$777$	−0.0225785	−0.000810001 0
$778$	59.9909	2.15078
$779$	−24.1215	−0.864243
$780$	−0.0972296	−0.00348138
$781$	−3.09869	−0.110880
$782$	4.86821	0.174087
$783$	0.681165	0.0243428
$784$	14.8292	0.529616
$785$	10.2373	0.365384
$786$	−0.239866	−0.00855574
$787$	−22.8881	−0.815872	−0.407936	−	0.913011i	$-0.633751\pi$
$787$	−22.8881	−0.815872	−0.407936	+	0.913011i	$0.633751\pi$
$788$	−26.3976	−0.940375
$789$	−0.445479	−0.0158595
$790$	−2.07454	−0.0738087
$791$	−0.00729080	−0.000259231 0
$792$	−15.6744	−0.556965
$793$	−29.6734	−1.05373
$794$	−69.7578	−2.47561
$795$	0.0679423	0.00240967
$796$	−63.7094	−2.25812
$797$	8.21283	0.290913	0.145457	−	0.989365i	$-0.453535\pi$
$797$	8.21283	0.290913	0.145457	+	0.989365i	$0.453535\pi$
$798$	−0.168262	−0.00595641
$799$	−2.84757	−0.100740
$800$	103.085	3.64462
$801$	9.62095	0.339939
$802$	58.6808	2.07209
$803$	−5.93218	−0.209342
$804$	0.808150	0.0285012
$805$	−1.79807	−0.0633737
$806$	−31.1655	−1.09776
$807$	0.195260	0.00687347
$808$	152.497	5.36481
$809$	14.3235	0.503587	0.251793	−	0.967781i	$-0.418980\pi$
$809$	14.3235	0.503587	0.251793	+	0.967781i	$0.418980\pi$
$810$	11.8901	0.417774
$811$	−2.43463	−0.0854913	−0.0427457	−	0.999086i	$-0.513611\pi$
$811$	−2.43463	−0.0854913	−0.0427457	+	0.999086i	$0.513611\pi$
$812$	43.3584	1.52158
$813$	0.154508	0.00541882
$814$	2.39287	0.0838701
$815$	4.59774	0.161052
$816$	0.101639	0.00355806
$817$	−0.506966	−0.0177365
$818$	9.60679	0.335893
$819$	7.73949	0.270440
$820$	−14.7490	−0.515057
$821$	44.5818	1.55592	0.777958	−	0.628316i	$-0.216255\pi$
$821$	44.5818	1.55592	0.777958	+	0.628316i	$0.216255\pi$
$822$	−0.0206757	−0.000721149 0
$823$	−25.0344	−0.872646	−0.436323	−	0.899790i	$-0.643719\pi$
$823$	−25.0344	−0.872646	−0.436323	+	0.899790i	$0.643719\pi$
$824$	29.6153	1.03170
$825$	−0.0377175	−0.00131315
$826$	4.44915	0.154806
$827$	2.49490	0.0867561	0.0433781	−	0.999059i	$-0.486188\pi$
$827$	2.49490	0.0867561	0.0433781	+	0.999059i	$0.486188\pi$
$828$	−60.7673	−2.11181
$829$	23.6825	0.822528	0.411264	−	0.911516i	$-0.365087\pi$
$829$	23.6825	0.822528	0.411264	+	0.911516i	$0.365087\pi$
$830$	21.5728	0.748804
$831$	0.0802564	0.00278406
$832$	−75.8352	−2.62911
$833$	−0.480022	−0.0166318
$834$	−0.407365	−0.0141059
$835$	1.46172	0.0505849
$836$	13.0471	0.451243
$837$	−0.379056	−0.0131021
$838$	13.8216	0.477459
$839$	−25.8432	−0.892207	−0.446104	−	0.894981i	$-0.647189\pi$
$839$	−25.8432	−0.892207	−0.446104	+	0.894981i	$0.647189\pi$
$840$	−0.0651486	−0.00224784
$841$	34.2231	1.18011
$842$	30.5177	1.05171
$843$	0.173854	0.00598785
$844$	−130.619	−4.49610
$845$	3.07042	0.105626
$846$	48.5814	1.67026
$847$	−10.6928	−0.367408
$848$	145.786	5.00633
$849$	0.122550	0.00420591
$850$	−6.24534	−0.214213
$851$	5.87436	0.201370
$852$	−0.435267	−0.0149120
$853$	16.5781	0.567623	0.283811	−	0.958880i	$-0.408401\pi$
$853$	16.5781	0.567623	0.283811	+	0.958880i	$0.408401\pi$
$854$	−31.3987	−1.07444
$855$	−6.26756	−0.214346
$856$	96.6496	3.30342
$857$	22.9564	0.784177	0.392088	−	0.919928i	$-0.371753\pi$
$857$	22.9564	0.784177	0.392088	+	0.919928i	$0.371753\pi$
$858$	0.0557442	0.00190308
$859$	5.98840	0.204322	0.102161	−	0.994768i	$-0.467424\pi$
$859$	5.98840	0.204322	0.102161	+	0.994768i	$0.467424\pi$
$860$	−0.309982	−0.0105703
$861$	−0.0797885	−0.00271918
$862$	70.9265	2.41577
$863$	1.00000	0.0340404
$863$	1.00000	0.0340404
$864$	−1.85303	−0.0630414
$865$	11.6323	0.395511
$866$	−7.28357	−0.247506
$867$	0.239442	0.00813187
$868$	−24.1282	−0.818963
$869$	0.870216	0.0295200
$870$	−0.150019	−0.00508611
$871$	26.7793	0.907380
$872$	−124.514	−4.21656
$873$	−12.7464	−0.431401
$874$	43.7775	1.48079
$875$	4.72682	0.159796
$876$	−0.833283	−0.0281540
$877$	16.2421	0.548456	0.274228	−	0.961665i	$-0.411578\pi$
$877$	16.2421	0.548456	0.274228	+	0.961665i	$0.411578\pi$
$878$	−4.96503	−0.167561
$879$	−0.465646	−0.0157059
$880$	3.97850	0.134115
$881$	24.9272	0.839818	0.419909	−	0.907566i	$-0.362062\pi$
$881$	24.9272	0.839818	0.419909	+	0.907566i	$0.362062\pi$
$882$	8.18950	0.275755
$883$	30.8263	1.03739	0.518693	−	0.854960i	$-0.326419\pi$
$883$	30.8263	1.03739	0.518693	+	0.854960i	$0.326419\pi$
$884$	6.75332	0.227139
$885$	−0.0112630	−0.000378601 0
$886$	56.1981	1.88801
$887$	31.7573	1.06631	0.533153	−	0.846019i	$-0.321007\pi$
$887$	31.7573	1.06631	0.533153	+	0.846019i	$0.321007\pi$
$888$	0.212843	0.00714253
$889$	3.44244	0.115456
$890$	−4.23795	−0.142056
$891$	−4.98758	−0.167090
$892$	157.542	5.27490
$893$	−25.6068	−0.856899
$894$	−0.136825	−0.00457612
$895$	−7.60117	−0.254079
$896$	−36.9834	−1.23553
$897$	0.136849	0.00456925
$898$	−64.7617	−2.16112
$899$	−35.1825	−1.17340
$900$	77.9572	2.59857
$901$	−4.71910	−0.157216
$902$	8.45597	0.281553
$903$	−0.00167693	−5.58046e−5 0
$904$	0.0687286	0.00228588
$905$	−3.85982	−0.128305
$906$	−0.832799	−0.0276679
$907$	−35.1197	−1.16613	−0.583066	−	0.812425i	$-0.698147\pi$
$907$	−35.1197	−1.16613	−0.583066	+	0.812425i	$0.698147\pi$
$908$	87.4979	2.90372
$909$	48.5276	1.60956
$910$	−3.40918	−0.113013
$911$	−26.5447	−0.879466	−0.439733	−	0.898128i	$-0.644927\pi$
$911$	−26.5447	−0.879466	−0.439733	+	0.898128i	$0.644927\pi$
$912$	0.913986	0.0302651
$913$	−9.04926	−0.299487
$914$	−9.21347	−0.304755
$915$	0.0794857	0.00262772
$916$	45.8247	1.51409
$917$	−6.15354	−0.203208
$918$	0.112264	0.00370527
$919$	−52.2778	−1.72449	−0.862244	−	0.506494i	$-0.830941\pi$
$919$	−52.2778	−1.72449	−0.862244	+	0.506494i	$0.830941\pi$
$920$	16.9500	0.558825
$921$	0.0144531	0.000476246 0
$922$	1.83482	0.0604266
$923$	−14.4232	−0.474747
$924$	0.0431568	0.00141976
$925$	−7.53610	−0.247786
$926$	−55.6055	−1.82731
$927$	9.42421	0.309532
$928$	−171.991	−5.64589
$929$	3.39474	0.111378	0.0556889	−	0.998448i	$-0.482264\pi$
$929$	3.39474	0.111378	0.0556889	+	0.998448i	$0.482264\pi$
$930$	0.0834827	0.00273751
$931$	−4.31661	−0.141471
$932$	−136.716	−4.47827
$933$	0.133348	0.00436561
$934$	72.2448	2.36392
$935$	−0.128784	−0.00421168
$936$	−72.9583	−2.38472
$937$	−46.1258	−1.50687	−0.753433	−	0.657525i	$-0.771603\pi$
$937$	−46.1258	−1.50687	−0.753433	+	0.657525i	$0.771603\pi$
$938$	28.3363	0.925214
$939$	0.0860955	0.00280962
$940$	−15.6572	−0.510680
$941$	−54.1057	−1.76380	−0.881898	−	0.471441i	$-0.843734\pi$
$941$	−54.1057	−1.76380	−0.881898	+	0.471441i	$0.843734\pi$
$942$	−0.824450	−0.0268620
$943$	20.7589	0.676003
$944$	−24.1674	−0.786583
$945$	−0.0414647	−0.00134885
$946$	0.177720	0.00577819
$947$	−19.5715	−0.635987	−0.317993	−	0.948093i	$-0.603009\pi$
$947$	−19.5715	−0.635987	−0.317993	+	0.948093i	$0.603009\pi$
$948$	0.122238	0.00397009
$949$	−27.6121	−0.896327
$950$	−56.1613	−1.82211
$951$	0.0942750	0.00305708
$952$	4.52506	0.146658
$953$	−31.8350	−1.03124	−0.515619	−	0.856818i	$-0.672438\pi$
$953$	−31.8350	−1.03124	−0.515619	+	0.856818i	$0.672438\pi$
$954$	80.5111	2.60664
$955$	−1.52788	−0.0494411
$956$	−78.2770	−2.53166
$957$	0.0629291	0.00203421
$958$	−51.3967	−1.66055
$959$	−0.530417	−0.0171281
$960$	0.203139	0.00655627
$961$	−11.4216	−0.368439
$962$	11.1379	0.359101
$963$	30.7559	0.991096
$964$	22.1377	0.713009
$965$	11.5626	0.372212
$966$	0.144806	0.00465905
$967$	−22.9076	−0.736660	−0.368330	−	0.929695i	$-0.620070\pi$
$967$	−22.9076	−0.736660	−0.368330	+	0.929695i	$0.620070\pi$
$968$	100.798	3.23978
$969$	−0.0295857	−0.000950430 0
$970$	5.61470	0.180277
$971$	41.6915	1.33794	0.668972	−	0.743288i	$-0.266735\pi$
$971$	41.6915	1.33794	0.668972	+	0.743288i	$0.266735\pi$
$972$	−2.10203	−0.0674225
$973$	−10.4506	−0.335030
$974$	−88.5867	−2.83850
$975$	−0.175561	−0.00562244
$976$	170.555	5.45935
$977$	44.7962	1.43316	0.716579	−	0.697506i	$-0.245707\pi$
$977$	44.7962	1.43316	0.716579	+	0.697506i	$0.245707\pi$
$978$	−0.370274	−0.0118401
$979$	1.77771	0.0568160
$980$	−2.63937	−0.0843116
$981$	−39.6228	−1.26506
$982$	−38.3950	−1.22523
$983$	4.16108	0.132718	0.0663589	−	0.997796i	$-0.478862\pi$
$983$	4.16108	0.132718	0.0663589	+	0.997796i	$0.478862\pi$
$984$	0.752147	0.0239776
$985$	2.34311	0.0746577
$986$	10.4199	0.331838
$987$	−0.0847015	−0.00269608
$988$	60.7294	1.93206
$989$	0.436293	0.0138733
$990$	2.19714	0.0698296
$991$	−46.0570	−1.46305	−0.731524	−	0.681815i	$-0.761191\pi$
$991$	−46.0570	−1.46305	−0.731524	+	0.681815i	$0.761191\pi$
$992$	95.7099	3.03879
$993$	−0.0672985	−0.00213565
$994$	−15.2619	−0.484077
$995$	5.65499	0.179275
$996$	−1.27113	−0.0402774
$997$	−11.4046	−0.361189	−0.180594	−	0.983558i	$-0.557802\pi$
$997$	−11.4046	−0.361189	−0.180594	+	0.983558i	$0.557802\pi$
$998$	109.812	3.47603
$999$	0.135467	0.00428598

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6041.2.a.c.1.1	✓	83

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6041.2.a.c.1.1	✓	83	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:	\( N \)	\(=\)	\( 6041 = 7 \cdot 863 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6041.a (trivial)

\(f(q)\)	\(=\)	\(q-2.73002 q^{2} -0.0142784 q^{3} +5.45300 q^{4} -0.484021 q^{5} +0.0389802 q^{6} +1.00000 q^{7} -9.42677 q^{8} -2.99980 q^{9} +O(q^{10})\)	\(q-2.73002 q^{2} -0.0142784 q^{3} +5.45300 q^{4} -0.484021 q^{5} +0.0389802 q^{6} +1.00000 q^{7} -9.42677 q^{8} -2.99980 q^{9} +1.32139 q^{10} -0.554288 q^{11} -0.0778599 q^{12} -2.58000 q^{13} -2.73002 q^{14} +0.00691102 q^{15} +14.8292 q^{16} -0.480022 q^{17} +8.18950 q^{18} -4.31661 q^{19} -2.63937 q^{20} -0.0142784 q^{21} +1.51322 q^{22} +3.71486 q^{23} +0.134599 q^{24} -4.76572 q^{25} +7.04346 q^{26} +0.0856672 q^{27} +5.45300 q^{28} +7.95129 q^{29} -0.0188672 q^{30} -4.42475 q^{31} -21.6306 q^{32} +0.00791432 q^{33} +1.31047 q^{34} -0.484021 q^{35} -16.3579 q^{36} +1.58131 q^{37} +11.7844 q^{38} +0.0368382 q^{39} +4.56275 q^{40} +5.58807 q^{41} +0.0389802 q^{42} +0.117445 q^{43} -3.02254 q^{44} +1.45196 q^{45} -10.1416 q^{46} +5.93216 q^{47} -0.211737 q^{48} +1.00000 q^{49} +13.0105 q^{50} +0.00685392 q^{51} -14.0688 q^{52} +9.83101 q^{53} -0.233873 q^{54} +0.268287 q^{55} -9.42677 q^{56} +0.0616340 q^{57} -21.7072 q^{58} -1.62971 q^{59} +0.0376858 q^{60} +11.5013 q^{61} +12.0796 q^{62} -2.99980 q^{63} +29.3934 q^{64} +1.24878 q^{65} -0.0216062 q^{66} -10.3795 q^{67} -2.61756 q^{68} -0.0530421 q^{69} +1.32139 q^{70} +5.59039 q^{71} +28.2784 q^{72} +10.7023 q^{73} -4.31702 q^{74} +0.0680467 q^{75} -23.5385 q^{76} -0.554288 q^{77} -0.100569 q^{78} -1.56997 q^{79} -7.17767 q^{80} +8.99817 q^{81} -15.2555 q^{82} +16.3259 q^{83} -0.0778599 q^{84} +0.232341 q^{85} -0.320628 q^{86} -0.113531 q^{87} +5.22515 q^{88} -3.20720 q^{89} -3.96389 q^{90} -2.58000 q^{91} +20.2571 q^{92} +0.0631781 q^{93} -16.1949 q^{94} +2.08933 q^{95} +0.308849 q^{96} +4.24909 q^{97} -2.73002 q^{98} +1.66275 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 83 q - 8 q^{2} - 12 q^{3} + 48 q^{4} - 11 q^{5} - 8 q^{6} + 83 q^{7} - 18 q^{8} + 39 q^{9}+O(q^{10}) \) 83 * q - 8 * q^2 - 12 * q^3 + 48 * q^4 - 11 * q^5 - 8 * q^6 + 83 * q^7 - 18 * q^8 + 39 * q^9	\( 83 q - 8 q^{2} - 12 q^{3} + 48 q^{4} - 11 q^{5} - 8 q^{6} + 83 q^{7} - 18 q^{8} + 39 q^{9} - 20 q^{10} - 26 q^{11} - 14 q^{12} - 22 q^{13} - 8 q^{14} - 37 q^{15} - 10 q^{16} - 9 q^{17} - 27 q^{18} - 42 q^{19} - 22 q^{20} - 12 q^{21} - 44 q^{22} - 46 q^{23} - 24 q^{24} - 20 q^{25} - 9 q^{26} - 39 q^{27} + 48 q^{28} - 36 q^{29} - 11 q^{30} - 107 q^{31} - 19 q^{32} - 25 q^{33} - 24 q^{34} - 11 q^{35} - 32 q^{36} - 75 q^{37} - 16 q^{38} - 78 q^{39} - 34 q^{40} - 17 q^{41} - 8 q^{42} - 87 q^{43} - 32 q^{44} - 17 q^{45} - 56 q^{46} - 39 q^{47} - 16 q^{48} + 83 q^{49} - 26 q^{50} - 71 q^{51} - 53 q^{52} - 28 q^{53} - 25 q^{54} - 94 q^{55} - 18 q^{56} - 79 q^{57} - 69 q^{58} - 26 q^{59} - 43 q^{60} - 56 q^{61} - 6 q^{62} + 39 q^{63} - 108 q^{64} - 26 q^{65} + 10 q^{66} - 123 q^{67} - 11 q^{68} + 2 q^{69} - 20 q^{70} - 96 q^{71} - 11 q^{72} - 53 q^{73} - 26 q^{74} - 27 q^{75} - 65 q^{76} - 26 q^{77} - 43 q^{78} - 160 q^{79} + 12 q^{80} - 53 q^{81} - 20 q^{82} - 2 q^{83} - 14 q^{84} - 110 q^{85} + 24 q^{86} - 52 q^{87} - 79 q^{88} - 5 q^{89} - 4 q^{90} - 22 q^{91} - 51 q^{92} - 30 q^{93} - 9 q^{94} - 76 q^{95} - 3 q^{96} - 44 q^{97} - 8 q^{98} - 82 q^{99}+O(q^{100}) \) 83 * q - 8 * q^2 - 12 * q^3 + 48 * q^4 - 11 * q^5 - 8 * q^6 + 83 * q^7 - 18 * q^8 + 39 * q^9 - 20 * q^10 - 26 * q^11 - 14 * q^12 - 22 * q^13 - 8 * q^14 - 37 * q^15 - 10 * q^16 - 9 * q^17 - 27 * q^18 - 42 * q^19 - 22 * q^20 - 12 * q^21 - 44 * q^22 - 46 * q^23 - 24 * q^24 - 20 * q^25 - 9 * q^26 - 39 * q^27 + 48 * q^28 - 36 * q^29 - 11 * q^30 - 107 * q^31 - 19 * q^32 - 25 * q^33 - 24 * q^34 - 11 * q^35 - 32 * q^36 - 75 * q^37 - 16 * q^38 - 78 * q^39 - 34 * q^40 - 17 * q^41 - 8 * q^42 - 87 * q^43 - 32 * q^44 - 17 * q^45 - 56 * q^46 - 39 * q^47 - 16 * q^48 + 83 * q^49 - 26 * q^50 - 71 * q^51 - 53 * q^52 - 28 * q^53 - 25 * q^54 - 94 * q^55 - 18 * q^56 - 79 * q^57 - 69 * q^58 - 26 * q^59 - 43 * q^60 - 56 * q^61 - 6 * q^62 + 39 * q^63 - 108 * q^64 - 26 * q^65 + 10 * q^66 - 123 * q^67 - 11 * q^68 + 2 * q^69 - 20 * q^70 - 96 * q^71 - 11 * q^72 - 53 * q^73 - 26 * q^74 - 27 * q^75 - 65 * q^76 - 26 * q^77 - 43 * q^78 - 160 * q^79 + 12 * q^80 - 53 * q^81 - 20 * q^82 - 2 * q^83 - 14 * q^84 - 110 * q^85 + 24 * q^86 - 52 * q^87 - 79 * q^88 - 5 * q^89 - 4 * q^90 - 22 * q^91 - 51 * q^92 - 30 * q^93 - 9 * q^94 - 76 * q^95 - 3 * q^96 - 44 * q^97 - 8 * q^98 - 82 * q^99

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