LMFDB - Embedded newform 6001.2.a.d.1.13

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6001,2,Mod(1,6001)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6001, 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("6001.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6001 = 17 \cdot 353 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6001.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:	$47.9182262530$
Analytic rank:	$0$
Dimension:	$121$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.13
Character	$\chi$	$=$	6001.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.26922 q^{2} -1.02425 q^{3} +3.14937 q^{4} -0.261054 q^{5} +2.32424 q^{6} +2.61024 q^{7} -2.60816 q^{8} -1.95092 q^{9} +O(q^{10})$	\(q-2.26922 q^{2} -1.02425 q^{3} +3.14937 q^{4} -0.261054 q^{5} +2.32424 q^{6} +2.61024 q^{7} -2.60816 q^{8} -1.95092 q^{9} +0.592389 q^{10} -3.66108 q^{11} -3.22572 q^{12} +0.188101 q^{13} -5.92322 q^{14} +0.267383 q^{15} -0.380228 q^{16} +1.00000 q^{17} +4.42707 q^{18} -5.72965 q^{19} -0.822154 q^{20} -2.67353 q^{21} +8.30781 q^{22} +6.42867 q^{23} +2.67140 q^{24} -4.93185 q^{25} -0.426843 q^{26} +5.07096 q^{27} +8.22061 q^{28} +1.16519 q^{29} -0.606752 q^{30} -0.117894 q^{31} +6.07915 q^{32} +3.74985 q^{33} -2.26922 q^{34} -0.681414 q^{35} -6.14416 q^{36} -9.59028 q^{37} +13.0018 q^{38} -0.192662 q^{39} +0.680872 q^{40} -9.94171 q^{41} +6.06683 q^{42} -4.91368 q^{43} -11.5301 q^{44} +0.509295 q^{45} -14.5881 q^{46} -1.43177 q^{47} +0.389447 q^{48} -0.186635 q^{49} +11.1915 q^{50} -1.02425 q^{51} +0.592399 q^{52} +4.56654 q^{53} -11.5071 q^{54} +0.955740 q^{55} -6.80794 q^{56} +5.86857 q^{57} -2.64407 q^{58} -12.1482 q^{59} +0.842088 q^{60} -0.202236 q^{61} +0.267527 q^{62} -5.09237 q^{63} -13.0345 q^{64} -0.0491045 q^{65} -8.50924 q^{66} +6.24354 q^{67} +3.14937 q^{68} -6.58454 q^{69} +1.54628 q^{70} -1.38354 q^{71} +5.08832 q^{72} +12.2273 q^{73} +21.7625 q^{74} +5.05143 q^{75} -18.0448 q^{76} -9.55631 q^{77} +0.437192 q^{78} +5.85241 q^{79} +0.0992600 q^{80} +0.658851 q^{81} +22.5599 q^{82} -0.703528 q^{83} -8.41992 q^{84} -0.261054 q^{85} +11.1502 q^{86} -1.19344 q^{87} +9.54870 q^{88} -0.554775 q^{89} -1.15570 q^{90} +0.490990 q^{91} +20.2462 q^{92} +0.120752 q^{93} +3.24901 q^{94} +1.49575 q^{95} -6.22655 q^{96} +15.8374 q^{97} +0.423516 q^{98} +7.14248 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 121 q + 9 q^{2} + 21 q^{3} + 127 q^{4} + 27 q^{5} + 17 q^{6} + 39 q^{7} + 24 q^{8} + 134 q^{9}+O(q^{10}) $ 121 * q + 9 * q^2 + 21 * q^3 + 127 * q^4 + 27 * q^5 + 17 * q^6 + 39 * q^7 + 24 * q^8 + 134 * q^9	\( 121 q + 9 q^{2} + 21 q^{3} + 127 q^{4} + 27 q^{5} + 17 q^{6} + 39 q^{7} + 24 q^{8} + 134 q^{9} + 19 q^{10} + 48 q^{11} + 43 q^{12} + 6 q^{13} + 40 q^{14} + 49 q^{15} + 135 q^{16} + 121 q^{17} + 30 q^{19} + 50 q^{20} + 18 q^{21} + 24 q^{22} + 75 q^{23} + 24 q^{24} + 128 q^{25} + 59 q^{26} + 75 q^{27} + 52 q^{28} + 49 q^{29} - 34 q^{30} + 101 q^{31} + 47 q^{32} + 20 q^{33} + 9 q^{34} + 47 q^{35} + 138 q^{36} + 32 q^{37} + 30 q^{38} + 101 q^{39} + 36 q^{40} + 83 q^{41} - 11 q^{42} + 8 q^{43} + 98 q^{44} + 49 q^{45} + 45 q^{46} + 135 q^{47} + 54 q^{48} + 116 q^{49} + 3 q^{50} + 21 q^{51} - 5 q^{52} + 28 q^{53} + 10 q^{54} + 37 q^{55} + 75 q^{56} + 31 q^{58} + 150 q^{59} + 50 q^{60} + 36 q^{61} + 34 q^{62} + 118 q^{63} + 110 q^{64} + 18 q^{65} - 28 q^{66} - 6 q^{67} + 127 q^{68} + 25 q^{69} - 22 q^{70} + 223 q^{71} + q^{72} + 38 q^{73} - 10 q^{74} + 88 q^{75} - 4 q^{76} + 38 q^{77} + 42 q^{78} + 74 q^{79} + 106 q^{80} + 133 q^{81} + 28 q^{82} + 55 q^{83} + 10 q^{84} + 27 q^{85} + 64 q^{86} + 14 q^{87} + 56 q^{88} + 118 q^{89} + 51 q^{90} + 73 q^{91} + 82 q^{92} + 31 q^{93} + 33 q^{94} + 106 q^{95} + 38 q^{96} + 37 q^{97} + 88 q^{98} + 81 q^{99}+O(q^{100}) \) 121 * q + 9 * q^2 + 21 * q^3 + 127 * q^4 + 27 * q^5 + 17 * q^6 + 39 * q^7 + 24 * q^8 + 134 * q^9 + 19 * q^10 + 48 * q^11 + 43 * q^12 + 6 * q^13 + 40 * q^14 + 49 * q^15 + 135 * q^16 + 121 * q^17 + 30 * q^19 + 50 * q^20 + 18 * q^21 + 24 * q^22 + 75 * q^23 + 24 * q^24 + 128 * q^25 + 59 * q^26 + 75 * q^27 + 52 * q^28 + 49 * q^29 - 34 * q^30 + 101 * q^31 + 47 * q^32 + 20 * q^33 + 9 * q^34 + 47 * q^35 + 138 * q^36 + 32 * q^37 + 30 * q^38 + 101 * q^39 + 36 * q^40 + 83 * q^41 - 11 * q^42 + 8 * q^43 + 98 * q^44 + 49 * q^45 + 45 * q^46 + 135 * q^47 + 54 * q^48 + 116 * q^49 + 3 * q^50 + 21 * q^51 - 5 * q^52 + 28 * q^53 + 10 * q^54 + 37 * q^55 + 75 * q^56 + 31 * q^58 + 150 * q^59 + 50 * q^60 + 36 * q^61 + 34 * q^62 + 118 * q^63 + 110 * q^64 + 18 * q^65 - 28 * q^66 - 6 * q^67 + 127 * q^68 + 25 * q^69 - 22 * q^70 + 223 * q^71 + q^72 + 38 * q^73 - 10 * q^74 + 88 * q^75 - 4 * q^76 + 38 * q^77 + 42 * q^78 + 74 * q^79 + 106 * q^80 + 133 * q^81 + 28 * q^82 + 55 * q^83 + 10 * q^84 + 27 * q^85 + 64 * q^86 + 14 * q^87 + 56 * q^88 + 118 * q^89 + 51 * q^90 + 73 * q^91 + 82 * q^92 + 31 * q^93 + 33 * q^94 + 106 * q^95 + 38 * q^96 + 37 * q^97 + 88 * q^98 + 81 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	−2.26922	−1.60458	−0.802291	−	0.596933i	$-0.796386\pi$
$2$	−2.26922	−1.60458	−0.802291	+	0.596933i	$0.796386\pi$
$3$	−1.02425	−0.591349	−0.295674	−	0.955289i	$-0.595544\pi$
$3$	−1.02425	−0.591349	−0.295674	+	0.955289i	$0.595544\pi$
$4$	3.14937	1.57468
$5$	−0.261054	−0.116747	−0.0583734	−	0.998295i	$-0.518591\pi$
$5$	−0.261054	−0.116747	−0.0583734	+	0.998295i	$0.518591\pi$
$6$	2.32424	0.948867
$7$	2.61024	0.986579	0.493289	−	0.869865i	$-0.335794\pi$
$7$	2.61024	0.986579	0.493289	+	0.869865i	$0.335794\pi$
$8$	−2.60816	−0.922125
$9$	−1.95092	−0.650307
$10$	0.592389	0.187330
$11$	−3.66108	−1.10386	−0.551929	−	0.833891i	$-0.686108\pi$
$11$	−3.66108	−1.10386	−0.551929	+	0.833891i	$0.686108\pi$
$12$	−3.22572	−0.931187
$13$	0.188101	0.0521699	0.0260849	−	0.999660i	$-0.491696\pi$
$13$	0.188101	0.0521699	0.0260849	+	0.999660i	$0.491696\pi$
$14$	−5.92322	−1.58305
$15$	0.267383	0.0690381
$16$	−0.380228	−0.0950570
$17$	1.00000	0.242536
$17$	1.00000	0.242536
$18$	4.42707	1.04347
$19$	−5.72965	−1.31447	−0.657236	−	0.753685i	$-0.728275\pi$
$19$	−5.72965	−1.31447	−0.657236	+	0.753685i	$0.728275\pi$
$20$	−0.822154	−0.183839
$21$	−2.67353	−0.583412
$22$	8.30781	1.77123
$23$	6.42867	1.34047	0.670235	−	0.742149i	$-0.266193\pi$
$23$	6.42867	1.34047	0.670235	+	0.742149i	$0.266193\pi$
$24$	2.67140	0.545298
$25$	−4.93185	−0.986370
$26$	−0.426843	−0.0837108
$27$	5.07096	0.975907
$28$	8.22061	1.55355
$29$	1.16519	0.216370	0.108185	−	0.994131i	$-0.465496\pi$
$29$	1.16519	0.216370	0.108185	+	0.994131i	$0.465496\pi$
$30$	−0.606752	−0.110777
$31$	−0.117894	−0.0211743	−0.0105872	−	0.999944i	$-0.503370\pi$
$31$	−0.117894	−0.0211743	−0.0105872	+	0.999944i	$0.503370\pi$
$32$	6.07915	1.07465
$33$	3.74985	0.652765
$34$	−2.26922	−0.389168
$35$	−0.681414	−0.115180
$36$	−6.14416	−1.02403
$37$	−9.59028	−1.57663	−0.788316	−	0.615270i	$-0.789047\pi$
$37$	−9.59028	−1.57663	−0.788316	+	0.615270i	$0.789047\pi$
$38$	13.0018	2.10918
$39$	−0.192662	−0.0308506
$40$	0.680872	0.107655
$41$	−9.94171	−1.55263	−0.776317	−	0.630343i	$-0.782914\pi$
$41$	−9.94171	−1.55263	−0.776317	+	0.630343i	$0.782914\pi$
$42$	6.06683	0.936132
$43$	−4.91368	−0.749329	−0.374664	−	0.927160i	$-0.622242\pi$
$43$	−4.91368	−0.749329	−0.374664	+	0.927160i	$0.622242\pi$
$44$	−11.5301	−1.73823
$45$	0.509295	0.0759213
$46$	−14.5881	−2.15089
$47$	−1.43177	−0.208846	−0.104423	−	0.994533i	$-0.533300\pi$
$47$	−1.43177	−0.208846	−0.104423	+	0.994533i	$0.533300\pi$
$48$	0.389447	0.0562118
$49$	−0.186635	−0.0266621
$50$	11.1915	1.58271
$51$	−1.02425	−0.143423
$52$	0.592399	0.0821510
$53$	4.56654	0.627263	0.313631	−	0.949545i	$-0.398454\pi$
$53$	4.56654	0.627263	0.313631	+	0.949545i	$0.398454\pi$
$54$	−11.5071	−1.56592
$55$	0.955740	0.128872
$56$	−6.80794	−0.909749
$57$	5.86857	0.777312
$58$	−2.64407	−0.347184
$59$	−12.1482	−1.58156	−0.790781	−	0.612099i	$-0.790326\pi$
$59$	−12.1482	−1.58156	−0.790781	+	0.612099i	$0.790326\pi$
$60$	0.842088	0.108713
$61$	−0.202236	−0.0258937	−0.0129469	−	0.999916i	$-0.504121\pi$
$61$	−0.202236	−0.0258937	−0.0129469	+	0.999916i	$0.504121\pi$
$62$	0.267527	0.0339759
$63$	−5.09237	−0.641579
$64$	−13.0345	−1.62931
$65$	−0.0491045	−0.00609067
$66$	−8.50924	−1.04741
$67$	6.24354	0.762770	0.381385	−	0.924416i	$-0.375447\pi$
$67$	6.24354	0.762770	0.381385	+	0.924416i	$0.375447\pi$
$68$	3.14937	0.381917
$69$	−6.58454	−0.792685
$70$	1.54628	0.184816
$71$	−1.38354	−0.164196	−0.0820980	−	0.996624i	$-0.526162\pi$
$71$	−1.38354	−0.164196	−0.0820980	+	0.996624i	$0.526162\pi$
$72$	5.08832	0.599664
$73$	12.2273	1.43110	0.715551	−	0.698561i	$-0.246176\pi$
$73$	12.2273	1.43110	0.715551	+	0.698561i	$0.246176\pi$
$74$	21.7625	2.52984
$75$	5.05143	0.583289
$76$	−18.0448	−2.06988
$77$	−9.55631	−1.08904
$78$	0.437192	0.0495023
$79$	5.85241	0.658447	0.329224	−	0.944252i	$-0.393213\pi$
$79$	5.85241	0.658447	0.329224	+	0.944252i	$0.393213\pi$
$80$	0.0992600	0.0110976
$81$	0.658851	0.0732056
$82$	22.5599	2.49133
$83$	−0.703528	−0.0772222	−0.0386111	−	0.999254i	$-0.512293\pi$
$83$	−0.703528	−0.0772222	−0.0386111	+	0.999254i	$0.512293\pi$
$84$	−8.41992	−0.918689
$85$	−0.261054	−0.0283153
$86$	11.1502	1.20236
$87$	−1.19344	−0.127950
$88$	9.54870	1.01790
$89$	−0.554775	−0.0588060	−0.0294030	−	0.999568i	$-0.509361\pi$
$89$	−0.554775	−0.0588060	−0.0294030	+	0.999568i	$0.509361\pi$
$90$	−1.15570	−0.121822
$91$	0.490990	0.0514697
$92$	20.2462	2.11081
$93$	0.120752	0.0125214
$94$	3.24901	0.335110
$95$	1.49575	0.153461
$96$	−6.22655	−0.635494
$97$	15.8374	1.60805	0.804024	−	0.594597i	$-0.202688\pi$
$97$	15.8374	1.60805	0.804024	+	0.594597i	$0.202688\pi$
$98$	0.423516	0.0427816
$99$	7.14248	0.717846
$100$	−15.5322	−1.55322
$101$	17.7617	1.76735	0.883677	−	0.468096i	$-0.155060\pi$
$101$	17.7617	1.76735	0.883677	+	0.468096i	$0.155060\pi$
$102$	2.32424	0.230134
$103$	0.311787	0.0307213	0.0153606	−	0.999882i	$-0.495110\pi$
$103$	0.311787	0.0307213	0.0153606	+	0.999882i	$0.495110\pi$
$104$	−0.490599	−0.0481072
$105$	0.697935	0.0681115
$106$	−10.3625	−1.00649
$107$	−3.38784	−0.327515	−0.163757	−	0.986501i	$-0.552361\pi$
$107$	−3.38784	−0.327515	−0.163757	+	0.986501i	$0.552361\pi$
$108$	15.9703	1.53674
$109$	−15.5189	−1.48644	−0.743222	−	0.669045i	$-0.766703\pi$
$109$	−15.5189	−1.48644	−0.743222	+	0.669045i	$0.766703\pi$
$110$	−2.16878	−0.206786
$111$	9.82281	0.932340
$112$	−0.992487	−0.0937812
$113$	19.4650	1.83112	0.915559	−	0.402184i	$-0.131749\pi$
$113$	19.4650	1.83112	0.915559	+	0.402184i	$0.131749\pi$
$114$	−13.3171	−1.24726
$115$	−1.67823	−0.156496
$116$	3.66961	0.340714
$117$	−0.366970	−0.0339264
$118$	27.5670	2.53775
$119$	2.61024	0.239281
$120$	−0.697380	−0.0636618
$121$	2.40352	0.218502
$122$	0.458919	0.0415486
$123$	10.1828	0.918148
$124$	−0.371290	−0.0333428
$125$	2.59275	0.231902
$126$	11.5557	1.02947
$127$	−0.0941906	−0.00835807	−0.00417903	−	0.999991i	$-0.501330\pi$
$127$	−0.0941906	−0.00835807	−0.00417903	+	0.999991i	$0.501330\pi$
$128$	17.4198	1.53971
$129$	5.03281	0.443115
$130$	0.111429	0.00977298
$131$	−16.8285	−1.47031	−0.735157	−	0.677897i	$-0.762892\pi$
$131$	−16.8285	−1.47031	−0.735157	+	0.677897i	$0.762892\pi$
$132$	11.8096	1.02790
$133$	−14.9558	−1.29683
$134$	−14.1680	−1.22393
$135$	−1.32379	−0.113934
$136$	−2.60816	−0.223648
$137$	1.15254	0.0984678	0.0492339	−	0.998787i	$-0.484322\pi$
$137$	1.15254	0.0984678	0.0492339	+	0.998787i	$0.484322\pi$
$138$	14.9418	1.27193
$139$	−18.6215	−1.57946	−0.789729	−	0.613456i	$-0.789779\pi$
$139$	−18.6215	−1.57946	−0.789729	+	0.613456i	$0.789779\pi$
$140$	−2.14602	−0.181372
$141$	1.46649	0.123501
$142$	3.13956	0.263466
$143$	−0.688654	−0.0575881
$144$	0.741795	0.0618162
$145$	−0.304177	−0.0252605
$146$	−27.7465	−2.29632
$147$	0.191160	0.0157666
$148$	−30.2033	−2.48270
$149$	21.1182	1.73007	0.865034	−	0.501714i	$-0.167297\pi$
$149$	21.1182	1.73007	0.865034	+	0.501714i	$0.167297\pi$
$150$	−11.4628	−0.935934
$151$	17.4481	1.41991	0.709955	−	0.704247i	$-0.248715\pi$
$151$	17.4481	1.41991	0.709955	+	0.704247i	$0.248715\pi$
$152$	14.9439	1.21211
$153$	−1.95092	−0.157723
$154$	21.6854	1.74746
$155$	0.0307766	0.00247204
$156$	−0.606763	−0.0485799
$157$	4.95563	0.395503	0.197751	−	0.980252i	$-0.436636\pi$
$157$	4.95563	0.395503	0.197751	+	0.980252i	$0.436636\pi$
$158$	−13.2804	−1.05653
$159$	−4.67726	−0.370931
$160$	−1.58699	−0.125462
$161$	16.7804	1.32248
$162$	−1.49508	−0.117464
$163$	−17.9737	−1.40781	−0.703903	−	0.710297i	$-0.748561\pi$
$163$	−17.9737	−1.40781	−0.703903	+	0.710297i	$0.748561\pi$
$164$	−31.3101	−2.44491
$165$	−0.978913	−0.0762082
$166$	1.59646	0.123909
$167$	21.8559	1.69126	0.845629	−	0.533771i	$-0.179226\pi$
$167$	21.8559	1.69126	0.845629	+	0.533771i	$0.179226\pi$
$168$	6.97301	0.537979
$169$	−12.9646	−0.997278
$170$	0.592389	0.0454342
$171$	11.1781	0.854810
$172$	−15.4750	−1.17996
$173$	−19.3743	−1.47300	−0.736501	−	0.676437i	$-0.763523\pi$
$173$	−19.3743	−1.47300	−0.736501	+	0.676437i	$0.763523\pi$
$174$	2.70818	0.205307
$175$	−12.8733	−0.973132
$176$	1.39205	0.104929
$177$	12.4428	0.935255
$178$	1.25891	0.0943590
$179$	−2.08339	−0.155720	−0.0778599	−	0.996964i	$-0.524809\pi$
$179$	−2.08339	−0.155720	−0.0778599	+	0.996964i	$0.524809\pi$
$180$	1.60396	0.119552
$181$	−11.2681	−0.837552	−0.418776	−	0.908090i	$-0.637541\pi$
$181$	−11.2681	−0.837552	−0.418776	+	0.908090i	$0.637541\pi$
$182$	−1.11416	−0.0825873
$183$	0.207140	0.0153122
$184$	−16.7670	−1.23608
$185$	2.50358	0.184067
$186$	−0.274013	−0.0200916
$187$	−3.66108	−0.267725
$188$	−4.50918	−0.328866
$189$	13.2364	0.962809
$190$	−3.39418	−0.246240
$191$	−13.3234	−0.964047	−0.482024	−	0.876158i	$-0.660098\pi$
$191$	−13.3234	−0.964047	−0.482024	+	0.876158i	$0.660098\pi$
$192$	13.3505	0.963491
$193$	−19.6130	−1.41177	−0.705886	−	0.708326i	$-0.749451\pi$
$193$	−19.6130	−1.41177	−0.705886	+	0.708326i	$0.749451\pi$
$194$	−35.9387	−2.58025
$195$	0.0502951	0.00360171
$196$	−0.587782	−0.0419844
$197$	6.48871	0.462302	0.231151	−	0.972918i	$-0.425751\pi$
$197$	6.48871	0.462302	0.231151	+	0.972918i	$0.425751\pi$
$198$	−16.2079	−1.15184
$199$	7.68122	0.544507	0.272253	−	0.962226i	$-0.412231\pi$
$199$	7.68122	0.544507	0.272253	+	0.962226i	$0.412231\pi$
$200$	12.8631	0.909557
$201$	−6.39492	−0.451063
$202$	−40.3052	−2.83587
$203$	3.04143	0.213466
$204$	−3.22572	−0.225846
$205$	2.59532	0.181265
$206$	−0.707514	−0.0492948
$207$	−12.5418	−0.871717
$208$	−0.0715213	−0.00495911
$209$	20.9767	1.45099
$210$	−1.58377	−0.109291
$211$	−6.63914	−0.457057	−0.228529	−	0.973537i	$-0.573391\pi$
$211$	−6.63914	−0.457057	−0.228529	+	0.973537i	$0.573391\pi$
$212$	14.3817	0.987740
$213$	1.41708	0.0970971
$214$	7.68775	0.525524
$215$	1.28273	0.0874818
$216$	−13.2259	−0.899908
$217$	−0.307731	−0.0208901
$218$	35.2159	2.38512
$219$	−12.5238	−0.846280
$220$	3.00997	0.202932
$221$	0.188101	0.0126531
$222$	−22.2901	−1.49602
$223$	13.7318	0.919548	0.459774	−	0.888036i	$-0.347930\pi$
$223$	13.7318	0.919548	0.459774	+	0.888036i	$0.347930\pi$
$224$	15.8681	1.06023
$225$	9.62165	0.641443
$226$	−44.1705	−2.93818
$227$	4.70353	0.312185	0.156092	−	0.987742i	$-0.450110\pi$
$227$	4.70353	0.312185	0.156092	+	0.987742i	$0.450110\pi$
$228$	18.4823	1.22402
$229$	−10.3658	−0.684992	−0.342496	−	0.939519i	$-0.611272\pi$
$229$	−10.3658	−0.684992	−0.342496	+	0.939519i	$0.611272\pi$
$230$	3.80827	0.251110
$231$	9.78801	0.644004
$232$	−3.03900	−0.199520
$233$	21.0575	1.37952	0.689762	−	0.724036i	$-0.257715\pi$
$233$	21.0575	1.37952	0.689762	+	0.724036i	$0.257715\pi$
$234$	0.832737	0.0544377
$235$	0.373770	0.0243821
$236$	−38.2592	−2.49046
$237$	−5.99430	−0.389372
$238$	−5.92322	−0.383945
$239$	−18.5434	−1.19947	−0.599736	−	0.800198i	$-0.704728\pi$
$239$	−18.5434	−1.19947	−0.599736	+	0.800198i	$0.704728\pi$
$240$	−0.101667	−0.00656255
$241$	−18.0872	−1.16510	−0.582549	−	0.812795i	$-0.697945\pi$
$241$	−18.0872	−1.16510	−0.582549	+	0.812795i	$0.697945\pi$
$242$	−5.45412	−0.350604
$243$	−15.8877	−1.01920
$244$	−0.636916	−0.0407744
$245$	0.0487218	0.00311272
$246$	−23.1069	−1.47324
$247$	−1.07775	−0.0685759
$248$	0.307486	0.0195254
$249$	0.720586	0.0456653
$250$	−5.88352	−0.372106
$251$	28.6791	1.81021	0.905105	−	0.425188i	$-0.139792\pi$
$251$	28.6791	1.81021	0.905105	+	0.425188i	$0.139792\pi$
$252$	−16.0377	−1.01028
$253$	−23.5359	−1.47969
$254$	0.213739	0.0134112
$255$	0.267383	0.0167442
$256$	−13.4605	−0.841280
$257$	−26.6483	−1.66227	−0.831136	−	0.556069i	$-0.812309\pi$
$257$	−26.6483	−1.66227	−0.831136	+	0.556069i	$0.812309\pi$
$258$	−11.4206	−0.711014
$259$	−25.0330	−1.55547
$260$	−0.154648	−0.00959087
$261$	−2.27319	−0.140707
$262$	38.1876	2.35924
$263$	20.5527	1.26733	0.633665	−	0.773607i	$-0.281550\pi$
$263$	20.5527	1.26733	0.633665	+	0.773607i	$0.281550\pi$
$264$	−9.78022	−0.601931
$265$	−1.19211	−0.0732310
$266$	33.9380	2.08087
$267$	0.568226	0.0347749
$268$	19.6632	1.20112
$269$	12.2097	0.744440	0.372220	−	0.928145i	$-0.378597\pi$
$269$	12.2097	0.744440	0.372220	+	0.928145i	$0.378597\pi$
$270$	3.00398	0.182816
$271$	−0.590600	−0.0358764	−0.0179382	−	0.999839i	$-0.505710\pi$
$271$	−0.590600	−0.0358764	−0.0179382	+	0.999839i	$0.505710\pi$
$272$	−0.380228	−0.0230547
$273$	−0.502894	−0.0304365
$274$	−2.61536	−0.158000
$275$	18.0559	1.08881
$276$	−20.7371	−1.24823
$277$	−16.5574	−0.994836	−0.497418	−	0.867511i	$-0.665718\pi$
$277$	−16.5574	−0.994836	−0.497418	+	0.867511i	$0.665718\pi$
$278$	42.2564	2.53437
$279$	0.230001	0.0137698
$280$	1.77724	0.106210
$281$	2.94326	0.175580	0.0877900	−	0.996139i	$-0.472020\pi$
$281$	2.94326	0.175580	0.0877900	+	0.996139i	$0.472020\pi$
$282$	−3.32779	−0.198167
$283$	−10.1128	−0.601144	−0.300572	−	0.953759i	$-0.597178\pi$
$283$	−10.1128	−0.601144	−0.300572	+	0.953759i	$0.597178\pi$
$284$	−4.35727	−0.258557
$285$	−1.53201	−0.0907487
$286$	1.56271	0.0924048
$287$	−25.9503	−1.53180
$288$	−11.8599	−0.698854
$289$	1.00000	0.0588235
$290$	0.690245	0.0405326
$291$	−16.2214	−0.950917
$292$	38.5084	2.25353
$293$	21.2925	1.24392	0.621960	−	0.783049i	$-0.286337\pi$
$293$	21.2925	1.24392	0.621960	+	0.783049i	$0.286337\pi$
$294$	−0.433785	−0.0252988
$295$	3.17134	0.184642
$296$	25.0130	1.45385
$297$	−18.5652	−1.07726
$298$	−47.9218	−2.77603
$299$	1.20924	0.0699321
$300$	15.9088	0.918495
$301$	−12.8259	−0.739272
$302$	−39.5937	−2.27836
$303$	−18.1923	−1.04512
$304$	2.17857	0.124950
$305$	0.0527946	0.00302301
$306$	4.42707	0.253079
$307$	16.9868	0.969488	0.484744	−	0.874656i	$-0.338913\pi$
$307$	16.9868	0.969488	0.484744	+	0.874656i	$0.338913\pi$
$308$	−30.0963	−1.71490
$309$	−0.319347	−0.0181670
$310$	−0.0698389	−0.00396658
$311$	9.42445	0.534411	0.267206	−	0.963640i	$-0.413900\pi$
$311$	9.42445	0.534411	0.267206	+	0.963640i	$0.413900\pi$
$312$	0.502494	0.0284481
$313$	19.1318	1.08139	0.540697	−	0.841217i	$-0.318161\pi$
$313$	19.1318	1.08139	0.540697	+	0.841217i	$0.318161\pi$
$314$	−11.2454	−0.634616
$315$	1.32938	0.0749023
$316$	18.4314	1.03685
$317$	15.3104	0.859917	0.429958	−	0.902849i	$-0.358528\pi$
$317$	15.3104	0.859917	0.429958	+	0.902849i	$0.358528\pi$
$318$	10.6137	0.595189
$319$	−4.26585	−0.238842
$320$	3.40270	0.190217
$321$	3.46998	0.193675
$322$	−38.0784	−2.12203
$323$	−5.72965	−0.318806
$324$	2.07496	0.115276
$325$	−0.927687	−0.0514588
$326$	40.7862	2.25894
$327$	15.8952	0.879007
$328$	25.9296	1.43172
$329$	−3.73728	−0.206043
$330$	2.22137	0.122282
$331$	17.2604	0.948715	0.474358	−	0.880332i	$-0.342680\pi$
$331$	17.2604	0.948715	0.474358	+	0.880332i	$0.342680\pi$
$332$	−2.21567	−0.121601
$333$	18.7099	1.02529
$334$	−49.5958	−2.71376
$335$	−1.62990	−0.0890510
$336$	1.01655	0.0554574
$337$	20.1821	1.09939	0.549694	−	0.835366i	$-0.314744\pi$
$337$	20.1821	1.09939	0.549694	+	0.835366i	$0.314744\pi$
$338$	29.4196	1.60021
$339$	−19.9370	−1.08283
$340$	−0.822154	−0.0445876
$341$	0.431618	0.0233734
$342$	−25.3656	−1.37161
$343$	−18.7589	−1.01288
$344$	12.8157	0.690975
$345$	1.71892	0.0925435
$346$	43.9646	2.36355
$347$	−0.631746	−0.0339139	−0.0169569	−	0.999856i	$-0.505398\pi$
$347$	−0.631746	−0.0339139	−0.0169569	+	0.999856i	$0.505398\pi$
$348$	−3.75858	−0.201481
$349$	4.79300	0.256564	0.128282	−	0.991738i	$-0.459054\pi$
$349$	4.79300	0.256564	0.128282	+	0.991738i	$0.459054\pi$
$350$	29.2124	1.56147
$351$	0.953853	0.0509129
$352$	−22.2563	−1.18626
$353$	−1.00000	−0.0532246
$353$	−1.00000	−0.0532246
$354$	−28.2354	−1.50069
$355$	0.361178	0.0191694
$356$	−1.74719	−0.0926008
$357$	−2.67353	−0.141498
$358$	4.72767	0.249865
$359$	20.7339	1.09429	0.547147	−	0.837037i	$-0.315714\pi$
$359$	20.7339	1.09429	0.547147	+	0.837037i	$0.315714\pi$
$360$	−1.32833	−0.0700089
$361$	13.8289	0.727838
$362$	25.5698	1.34392
$363$	−2.46180	−0.129211
$364$	1.54631	0.0810484
$365$	−3.19199	−0.167077
$366$	−0.470046	−0.0245697
$367$	−13.9016	−0.725659	−0.362830	−	0.931856i	$-0.618189\pi$
$367$	−13.9016	−0.725659	−0.362830	+	0.931856i	$0.618189\pi$
$368$	−2.44436	−0.127421
$369$	19.3955	1.00969
$370$	−5.68118	−0.295350
$371$	11.9198	0.618844
$372$	0.380292	0.0197172
$373$	−11.9271	−0.617559	−0.308780	−	0.951134i	$-0.599921\pi$
$373$	−11.9271	−0.617559	−0.308780	+	0.951134i	$0.599921\pi$
$374$	8.30781	0.429586
$375$	−2.65561	−0.137135
$376$	3.73430	0.192582
$377$	0.219173	0.0112880
$378$	−30.0364	−1.54491
$379$	1.73456	0.0890985	0.0445493	−	0.999007i	$-0.485815\pi$
$379$	1.73456	0.0890985	0.0445493	+	0.999007i	$0.485815\pi$
$380$	4.71066	0.241652
$381$	0.0964744	0.00494253
$382$	30.2337	1.54689
$383$	11.5744	0.591426	0.295713	−	0.955277i	$-0.404443\pi$
$383$	11.5744	0.591426	0.295713	+	0.955277i	$0.404443\pi$
$384$	−17.8422	−0.910505
$385$	2.49471	0.127142
$386$	44.5061	2.26530
$387$	9.58619	0.487294
$388$	49.8779	2.53217
$389$	−12.8440	−0.651218	−0.325609	−	0.945504i	$-0.605569\pi$
$389$	−12.8440	−0.651218	−0.325609	+	0.945504i	$0.605569\pi$
$390$	−0.114131	−0.00577924
$391$	6.42867	0.325112
$392$	0.486775	0.0245858
$393$	17.2365	0.869468
$394$	−14.7243	−0.741801
$395$	−1.52779	−0.0768716
$396$	22.4943	1.13038
$397$	27.9607	1.40331	0.701653	−	0.712519i	$-0.252446\pi$
$397$	27.9607	1.40331	0.701653	+	0.712519i	$0.252446\pi$
$398$	−17.4304	−0.873706
$399$	15.3184	0.766879
$400$	1.87523	0.0937614
$401$	−18.9111	−0.944378	−0.472189	−	0.881497i	$-0.656536\pi$
$401$	−18.9111	−0.944378	−0.472189	+	0.881497i	$0.656536\pi$
$402$	14.5115	0.723768
$403$	−0.0221759	−0.00110466
$404$	55.9381	2.78302
$405$	−0.171996	−0.00854653
$406$	−6.90167	−0.342524
$407$	35.1108	1.74038
$408$	2.67140	0.132254
$409$	2.30224	0.113838	0.0569192	−	0.998379i	$-0.481872\pi$
$409$	2.30224	0.113838	0.0569192	+	0.998379i	$0.481872\pi$
$410$	−5.88936	−0.290855
$411$	−1.18048	−0.0582288
$412$	0.981932	0.0483763
$413$	−31.7098	−1.56034
$414$	28.4602	1.39874
$415$	0.183659	0.00901545
$416$	1.14350	0.0560645
$417$	19.0730	0.934010
$418$	−47.6008	−2.32823
$419$	−18.5387	−0.905673	−0.452836	−	0.891594i	$-0.649588\pi$
$419$	−18.5387	−0.905673	−0.452836	+	0.891594i	$0.649588\pi$
$420$	2.19805	0.107254
$421$	−26.9735	−1.31461	−0.657305	−	0.753625i	$-0.728303\pi$
$421$	−26.9735	−1.31461	−0.657305	+	0.753625i	$0.728303\pi$
$422$	15.0657	0.733386
$423$	2.79328	0.135814
$424$	−11.9103	−0.578415
$425$	−4.93185	−0.239230
$426$	−3.21568	−0.155800
$427$	−0.527886	−0.0255462
$428$	−10.6695	−0.515732
$429$	0.705351	0.0340547
$430$	−2.91081	−0.140372
$431$	14.7579	0.710863	0.355432	−	0.934702i	$-0.384334\pi$
$431$	14.7579	0.710863	0.355432	+	0.934702i	$0.384334\pi$
$432$	−1.92812	−0.0927668
$433$	−27.6514	−1.32884	−0.664422	−	0.747358i	$-0.731322\pi$
$433$	−27.6514	−1.32884	−0.664422	+	0.747358i	$0.731322\pi$
$434$	0.698310	0.0335199
$435$	0.311552	0.0149378
$436$	−48.8748	−2.34068
$437$	−36.8340	−1.76201
$438$	28.4193	1.35793
$439$	−18.1898	−0.868152	−0.434076	−	0.900876i	$-0.642925\pi$
$439$	−18.1898	−0.868152	−0.434076	+	0.900876i	$0.642925\pi$
$440$	−2.49273	−0.118836
$441$	0.364110	0.0173386
$442$	−0.426843	−0.0203029
$443$	−6.68715	−0.317716	−0.158858	−	0.987301i	$-0.550781\pi$
$443$	−6.68715	−0.317716	−0.158858	+	0.987301i	$0.550781\pi$
$444$	30.9356	1.46814
$445$	0.144826	0.00686542
$446$	−31.1604	−1.47549
$447$	−21.6302	−1.02307
$448$	−34.0232	−1.60744
$449$	21.3978	1.00983	0.504913	−	0.863170i	$-0.331525\pi$
$449$	21.3978	1.00983	0.504913	+	0.863170i	$0.331525\pi$
$450$	−21.8336	−1.02925
$451$	36.3974	1.71389
$452$	61.3025	2.88343
$453$	−17.8712	−0.839662
$454$	−10.6734	−0.500926
$455$	−0.128175	−0.00600892
$456$	−15.3062	−0.716779
$457$	−31.5753	−1.47703	−0.738516	−	0.674236i	$-0.764473\pi$
$457$	−31.5753	−1.47703	−0.738516	+	0.674236i	$0.764473\pi$
$458$	23.5223	1.09913
$459$	5.07096	0.236692
$460$	−5.28536	−0.246431
$461$	24.3344	1.13337	0.566683	−	0.823936i	$-0.308226\pi$
$461$	24.3344	1.13337	0.566683	+	0.823936i	$0.308226\pi$
$462$	−22.2112	−1.03336
$463$	1.95408	0.0908138	0.0454069	−	0.998969i	$-0.485542\pi$
$463$	1.95408	0.0908138	0.0454069	+	0.998969i	$0.485542\pi$
$464$	−0.443037	−0.0205675
$465$	−0.0315228	−0.00146183
$466$	−47.7842	−2.21356
$467$	2.50298	0.115824	0.0579120	−	0.998322i	$-0.481556\pi$
$467$	2.50298	0.115824	0.0579120	+	0.998322i	$0.481556\pi$
$468$	−1.15572	−0.0534233
$469$	16.2972	0.752533
$470$	−0.848167	−0.0391230
$471$	−5.07579	−0.233880
$472$	31.6845	1.45840
$473$	17.9894	0.827152
$474$	13.6024	0.624779
$475$	28.2578	1.29656
$476$	8.22061	0.376791
$477$	−8.90896	−0.407913
$478$	42.0791	1.92465
$479$	11.5276	0.526709	0.263355	−	0.964699i	$-0.415171\pi$
$479$	11.5276	0.526709	0.263355	+	0.964699i	$0.415171\pi$
$480$	1.62546	0.0741919
$481$	−1.80394	−0.0822527
$482$	41.0439	1.86950
$483$	−17.1872	−0.782046
$484$	7.56957	0.344071
$485$	−4.13443	−0.187735
$486$	36.0527	1.63538
$487$	−4.63325	−0.209952	−0.104976	−	0.994475i	$-0.533477\pi$
$487$	−4.63325	−0.209952	−0.104976	+	0.994475i	$0.533477\pi$
$488$	0.527466	0.0238773
$489$	18.4094	0.832504
$490$	−0.110561	−0.00499462
$491$	−15.5822	−0.703213	−0.351607	−	0.936148i	$-0.614364\pi$
$491$	−15.5822	−0.703213	−0.351607	+	0.936148i	$0.614364\pi$
$492$	32.0692	1.44579
$493$	1.16519	0.0524775
$494$	2.44566	0.110036
$495$	−1.86457	−0.0838063
$496$	0.0448265	0.00201277
$497$	−3.61137	−0.161992
$498$	−1.63517	−0.0732737
$499$	39.7840	1.78098	0.890489	−	0.455005i	$-0.150363\pi$
$499$	39.7840	1.78098	0.890489	+	0.455005i	$0.150363\pi$
$500$	8.16551	0.365173
$501$	−22.3858	−1.00012
$502$	−65.0793	−2.90463
$503$	5.04201	0.224812	0.112406	−	0.993662i	$-0.464144\pi$
$503$	5.04201	0.224812	0.112406	+	0.993662i	$0.464144\pi$
$504$	13.2818	0.591616
$505$	−4.63676	−0.206333
$506$	53.4081	2.37428
$507$	13.2790	0.589739
$508$	−0.296641	−0.0131613
$509$	34.3319	1.52173	0.760867	−	0.648908i	$-0.224774\pi$
$509$	34.3319	1.52173	0.760867	+	0.648908i	$0.224774\pi$
$510$	−0.606752	−0.0268674
$511$	31.9163	1.41189
$512$	−4.29486	−0.189808
$513$	−29.0548	−1.28280
$514$	60.4708	2.66725
$515$	−0.0813932	−0.00358661
$516$	15.8502	0.697765
$517$	5.24184	0.230536
$518$	56.8053	2.49588
$519$	19.8441	0.871057
$520$	0.128073	0.00561636
$521$	−3.98150	−0.174433	−0.0872163	−	0.996189i	$-0.527797\pi$
$521$	−3.98150	−0.174433	−0.0872163	+	0.996189i	$0.527797\pi$
$522$	5.15837	0.225776
$523$	33.0765	1.44633	0.723167	−	0.690673i	$-0.242686\pi$
$523$	33.0765	1.44633	0.723167	+	0.690673i	$0.242686\pi$
$524$	−52.9991	−2.31528
$525$	13.1855	0.575460
$526$	−46.6385	−2.03354
$527$	−0.117894	−0.00513553
$528$	−1.42580	−0.0620499
$529$	18.3278	0.796860
$530$	2.70517	0.117505
$531$	23.7002	1.02850
$532$	−47.1012	−2.04210
$533$	−1.87005	−0.0810007
$534$	−1.28943	−0.0557991
$535$	0.884408	0.0382363
$536$	−16.2842	−0.703370
$537$	2.13390	0.0920847
$538$	−27.7066	−1.19451
$539$	0.683286	0.0294312
$540$	−4.16911	−0.179410
$541$	5.55000	0.238613	0.119307	−	0.992857i	$-0.461933\pi$
$541$	5.55000	0.238613	0.119307	+	0.992857i	$0.461933\pi$
$542$	1.34020	0.0575666
$543$	11.5413	0.495285
$544$	6.07915	0.260641
$545$	4.05128	0.173538
$546$	1.14118	0.0488379
$547$	−14.6764	−0.627518	−0.313759	−	0.949503i	$-0.601588\pi$
$547$	−14.6764	−0.627518	−0.313759	+	0.949503i	$0.601588\pi$
$548$	3.62976	0.155056
$549$	0.394547	0.0168389
$550$	−40.9729	−1.74709
$551$	−6.67613	−0.284413
$552$	17.1736	0.730955
$553$	15.2762	0.649610
$554$	37.5723	1.59630
$555$	−2.56428	−0.108848
$556$	−58.6460	−2.48715
$557$	24.9861	1.05869	0.529347	−	0.848406i	$-0.322437\pi$
$557$	24.9861	1.05869	0.529347	+	0.848406i	$0.322437\pi$
$558$	−0.521923	−0.0220948
$559$	−0.924268	−0.0390924
$560$	0.259093	0.0109487
$561$	3.74985	0.158319
$562$	−6.67890	−0.281733
$563$	−32.6496	−1.37602	−0.688009	−	0.725702i	$-0.741515\pi$
$563$	−32.6496	−1.37602	−0.688009	+	0.725702i	$0.741515\pi$
$564$	4.61851	0.194474
$565$	−5.08143	−0.213777
$566$	22.9482	0.964584
$567$	1.71976	0.0722231
$568$	3.60850	0.151409
$569$	6.26413	0.262606	0.131303	−	0.991342i	$-0.458084\pi$
$569$	6.26413	0.262606	0.131303	+	0.991342i	$0.458084\pi$
$570$	3.47648	0.145614
$571$	22.8138	0.954727	0.477364	−	0.878706i	$-0.341592\pi$
$571$	22.8138	0.954727	0.477364	+	0.878706i	$0.341592\pi$
$572$	−2.16882	−0.0906830
$573$	13.6464	0.570088
$574$	58.8869	2.45789
$575$	−31.7052	−1.32220
$576$	25.4292	1.05955
$577$	−5.90062	−0.245646	−0.122823	−	0.992429i	$-0.539195\pi$
$577$	−5.90062	−0.245646	−0.122823	+	0.992429i	$0.539195\pi$
$578$	−2.26922	−0.0943872
$579$	20.0885	0.834849
$580$	−0.957965	−0.0397773
$581$	−1.83638	−0.0761858
$582$	36.8100	1.52582
$583$	−16.7185	−0.692409
$584$	−31.8909	−1.31966
$585$	0.0957990	0.00396080
$586$	−48.3174	−1.99597
$587$	24.2350	1.00029	0.500143	−	0.865943i	$-0.333281\pi$
$587$	24.2350	1.00029	0.500143	+	0.865943i	$0.333281\pi$
$588$	0.602033	0.0248274
$589$	0.675489	0.0278331
$590$	−7.19647	−0.296274
$591$	−6.64604	−0.273381
$592$	3.64649	0.149870
$593$	42.2853	1.73645	0.868224	−	0.496173i	$-0.165262\pi$
$593$	42.2853	1.73645	0.868224	+	0.496173i	$0.165262\pi$
$594$	42.1285	1.72856
$595$	−0.681414	−0.0279352
$596$	66.5088	2.72431
$597$	−7.86745	−0.321993
$598$	−2.74403	−0.112212
$599$	19.9022	0.813182	0.406591	−	0.913610i	$-0.366717\pi$
$599$	19.9022	0.813182	0.406591	+	0.913610i	$0.366717\pi$
$600$	−13.1750	−0.537865
$601$	−25.9737	−1.05949	−0.529744	−	0.848158i	$-0.677712\pi$
$601$	−25.9737	−1.05949	−0.529744	+	0.848158i	$0.677712\pi$
$602$	29.1048	1.18622
$603$	−12.1807	−0.496035
$604$	54.9506	2.23591
$605$	−0.627449	−0.0255094
$606$	41.2825	1.67699
$607$	28.2669	1.14732	0.573658	−	0.819095i	$-0.305524\pi$
$607$	28.2669	1.14732	0.573658	+	0.819095i	$0.305524\pi$
$608$	−34.8314	−1.41260
$609$	−3.11517	−0.126233
$610$	−0.119803	−0.00485067
$611$	−0.269318	−0.0108955
$612$	−6.14416	−0.248363
$613$	47.1794	1.90556	0.952778	−	0.303668i	$-0.0982113\pi$
$613$	47.1794	1.90556	0.952778	+	0.303668i	$0.0982113\pi$
$614$	−38.5468	−1.55562
$615$	−2.65825	−0.107191
$616$	24.9244	1.00423
$617$	−15.6247	−0.629027	−0.314514	−	0.949253i	$-0.601841\pi$
$617$	−15.6247	−0.629027	−0.314514	+	0.949253i	$0.601841\pi$
$618$	0.724668	0.0291504
$619$	1.98743	0.0798816	0.0399408	−	0.999202i	$-0.487283\pi$
$619$	1.98743	0.0798816	0.0399408	+	0.999202i	$0.487283\pi$
$620$	0.0969267	0.00389267
$621$	32.5995	1.30817
$622$	−21.3862	−0.857507
$623$	−1.44810	−0.0580168
$624$	0.0732554	0.00293256
$625$	23.9824	0.959296
$626$	−43.4143	−1.73518
$627$	−21.4853	−0.858041
$628$	15.6071	0.622791
$629$	−9.59028	−0.382390
$630$	−3.01667	−0.120187
$631$	13.8012	0.549416	0.274708	−	0.961528i	$-0.411419\pi$
$631$	13.8012	0.549416	0.274708	+	0.961528i	$0.411419\pi$
$632$	−15.2640	−0.607171
$633$	6.80011	0.270280
$634$	−34.7427	−1.37981
$635$	0.0245888	0.000975778 0
$636$	−14.7304	−0.584099
$637$	−0.0351063	−0.00139096
$638$	9.68016	0.383241
$639$	2.69918	0.106778
$640$	−4.54751	−0.179756
$641$	48.9494	1.93338	0.966692	−	0.255942i	$-0.0823857\pi$
$641$	48.9494	1.93338	0.966692	+	0.255942i	$0.0823857\pi$
$642$	−7.87415	−0.310768
$643$	−30.2371	−1.19243	−0.596217	−	0.802823i	$-0.703330\pi$
$643$	−30.2371	−1.19243	−0.596217	+	0.802823i	$0.703330\pi$
$644$	52.8476	2.08249
$645$	−1.31384	−0.0517322
$646$	13.0018	0.511551
$647$	−31.5786	−1.24148	−0.620741	−	0.784016i	$-0.713168\pi$
$647$	−31.5786	−1.24148	−0.620741	+	0.784016i	$0.713168\pi$
$648$	−1.71839	−0.0675048
$649$	44.4756	1.74582
$650$	2.10513	0.0825699
$651$	0.315192	0.0123534
$652$	−56.6056	−2.21685
$653$	21.4932	0.841096	0.420548	−	0.907270i	$-0.361838\pi$
$653$	21.4932	0.841096	0.420548	+	0.907270i	$0.361838\pi$
$654$	−36.0697	−1.41044
$655$	4.39315	0.171655
$656$	3.78012	0.147589
$657$	−23.8546	−0.930655
$658$	8.48071	0.330612
$659$	1.65772	0.0645755	0.0322877	−	0.999479i	$-0.489721\pi$
$659$	1.65772	0.0645755	0.0322877	+	0.999479i	$0.489721\pi$
$660$	−3.08295	−0.120004
$661$	39.5301	1.53754	0.768770	−	0.639525i	$-0.220869\pi$
$661$	39.5301	1.53754	0.768770	+	0.639525i	$0.220869\pi$
$662$	−39.1676	−1.52229
$663$	−0.192662	−0.00748237
$664$	1.83492	0.0712086
$665$	3.90426	0.151401
$666$	−42.4569	−1.64517
$667$	7.49061	0.290038
$668$	68.8321	2.66319
$669$	−14.0647	−0.543773
$670$	3.69861	0.142890
$671$	0.740404	0.0285830
$672$	−16.2528	−0.626965
$673$	7.60349	0.293093	0.146547	−	0.989204i	$-0.453184\pi$
$673$	7.60349	0.293093	0.146547	+	0.989204i	$0.453184\pi$
$674$	−45.7976	−1.76406
$675$	−25.0092	−0.962605
$676$	−40.8303	−1.57040
$677$	−46.9268	−1.80354	−0.901771	−	0.432215i	$-0.857732\pi$
$677$	−46.9268	−1.80354	−0.901771	+	0.432215i	$0.857732\pi$
$678$	45.2415	1.73749
$679$	41.3396	1.58647
$680$	0.680872	0.0261102
$681$	−4.81758	−0.184610
$682$	−0.979437	−0.0375046
$683$	47.5297	1.81867	0.909337	−	0.416061i	$-0.136590\pi$
$683$	47.5297	1.81867	0.909337	+	0.416061i	$0.136590\pi$
$684$	35.2039	1.34606
$685$	−0.300874	−0.0114958
$686$	42.5680	1.62525
$687$	10.6171	0.405069
$688$	1.86832	0.0712290
$689$	0.858972	0.0327242
$690$	−3.90061	−0.148494
$691$	34.1189	1.29794	0.648972	−	0.760813i	$-0.275199\pi$
$691$	34.1189	1.29794	0.648972	+	0.760813i	$0.275199\pi$
$692$	−61.0168	−2.31951
$693$	18.6436	0.708212
$694$	1.43357	0.0544176
$695$	4.86122	0.184397
$696$	3.11269	0.117986
$697$	−9.94171	−0.376569
$698$	−10.8764	−0.411677
$699$	−21.5681	−0.815780
$700$	−40.5428	−1.53237
$701$	−42.7264	−1.61375	−0.806876	−	0.590720i	$-0.798844\pi$
$701$	−42.7264	−1.61375	−0.806876	+	0.590720i	$0.798844\pi$
$702$	−2.16450	−0.0816940
$703$	54.9490	2.07244
$704$	47.7203	1.79853
$705$	−0.382832	−0.0144183
$706$	2.26922	0.0854033
$707$	46.3623	1.74363
$708$	39.1868	1.47273
$709$	−52.2315	−1.96159	−0.980797	−	0.195033i	$-0.937519\pi$
$709$	−52.2315	−1.96159	−0.980797	+	0.195033i	$0.937519\pi$
$710$	−0.819594	−0.0307588
$711$	−11.4176	−0.428193
$712$	1.44694	0.0542265
$713$	−0.757899	−0.0283835
$714$	6.06683	0.227045
$715$	0.179776	0.00672323
$716$	−6.56135	−0.245209
$717$	18.9930	0.709306
$718$	−47.0498	−1.75588
$719$	27.3320	1.01931	0.509655	−	0.860379i	$-0.329773\pi$
$719$	27.3320	1.01931	0.509655	+	0.860379i	$0.329773\pi$
$720$	−0.193648	−0.00721685
$721$	0.813840	0.0303090
$722$	−31.3809	−1.16788
$723$	18.5257	0.688980
$724$	−35.4874	−1.31888
$725$	−5.74654	−0.213421
$726$	5.58636	0.207329
$727$	−28.9801	−1.07481	−0.537407	−	0.843323i	$-0.680596\pi$
$727$	−28.9801	−1.07481	−0.537407	+	0.843323i	$0.680596\pi$
$728$	−1.28058	−0.0474615
$729$	14.2964	0.529495
$730$	7.24334	0.268088
$731$	−4.91368	−0.181739
$732$	0.652359	0.0241119
$733$	30.3523	1.12109	0.560545	−	0.828124i	$-0.310592\pi$
$733$	30.3523	1.12109	0.560545	+	0.828124i	$0.310592\pi$
$734$	31.5459	1.16438
$735$	−0.0499031	−0.00184070
$736$	39.0808	1.44054
$737$	−22.8581	−0.841990
$738$	−44.0126	−1.62013
$739$	45.1340	1.66028	0.830141	−	0.557553i	$-0.188260\pi$
$739$	45.1340	1.66028	0.830141	+	0.557553i	$0.188260\pi$
$740$	7.88469	0.289847
$741$	1.10389	0.0405522
$742$	−27.0486	−0.992986
$743$	−45.1424	−1.65611	−0.828057	−	0.560644i	$-0.810554\pi$
$743$	−45.1424	−1.65611	−0.828057	+	0.560644i	$0.810554\pi$
$744$	−0.314941	−0.0115463
$745$	−5.51298	−0.201980
$746$	27.0651	0.990925
$747$	1.37253	0.0502181
$748$	−11.5301	−0.421582
$749$	−8.84308	−0.323119
$750$	6.02617	0.220045
$751$	−27.6825	−1.01015	−0.505074	−	0.863076i	$-0.668535\pi$
$751$	−27.6825	−1.01015	−0.505074	+	0.863076i	$0.668535\pi$
$752$	0.544400	0.0198522
$753$	−29.3745	−1.07047
$754$	−0.497353	−0.0181125
$755$	−4.55491	−0.165770
$756$	41.6864	1.51612
$757$	10.7888	0.392125	0.196063	−	0.980591i	$-0.437184\pi$
$757$	10.7888	0.392125	0.196063	+	0.980591i	$0.437184\pi$
$758$	−3.93611	−0.142966
$759$	24.1065	0.875012
$760$	−3.90116	−0.141510
$761$	−20.6249	−0.747652	−0.373826	−	0.927499i	$-0.621954\pi$
$761$	−20.6249	−0.747652	−0.373826	+	0.927499i	$0.621954\pi$
$762$	−0.218922	−0.00793070
$763$	−40.5082	−1.46649
$764$	−41.9603	−1.51807
$765$	0.509295	0.0184136
$766$	−26.2649	−0.948991
$767$	−2.28509	−0.0825099
$768$	13.7868	0.497490
$769$	49.3078	1.77808	0.889042	−	0.457825i	$-0.151371\pi$
$769$	49.3078	1.77808	0.889042	+	0.457825i	$0.151371\pi$
$770$	−5.66105	−0.204010
$771$	27.2944	0.982983
$772$	−61.7684	−2.22309
$773$	−32.3239	−1.16261	−0.581305	−	0.813686i	$-0.697458\pi$
$773$	−32.3239	−1.16261	−0.581305	+	0.813686i	$0.697458\pi$
$774$	−21.7532	−0.781902
$775$	0.581434	0.0208857
$776$	−41.3067	−1.48282
$777$	25.6399	0.919827
$778$	29.1460	1.04493
$779$	56.9625	2.04089
$780$	0.158398	0.00567155
$781$	5.06525	0.181249
$782$	−14.5881	−0.521668
$783$	5.90863	0.211157
$784$	0.0709639	0.00253442
$785$	−1.29369	−0.0461737
$786$	−39.1135	−1.39513
$787$	26.9077	0.959157	0.479578	−	0.877499i	$-0.340790\pi$
$787$	26.9077	0.959157	0.479578	+	0.877499i	$0.340790\pi$
$788$	20.4353	0.727978
$789$	−21.0510	−0.749434
$790$	3.46690	0.123347
$791$	50.8085	1.80654
$792$	−18.6288	−0.661944
$793$	−0.0380409	−0.00135087
$794$	−63.4489	−2.25172
$795$	1.22102	0.0433050
$796$	24.1910	0.857426
$797$	−14.6233	−0.517982	−0.258991	−	0.965880i	$-0.583390\pi$
$797$	−14.6233	−0.517982	−0.258991	+	0.965880i	$0.583390\pi$
$798$	−34.7608	−1.23052
$799$	−1.43177	−0.0506525
$800$	−29.9815	−1.06000
$801$	1.08232	0.0382419
$802$	42.9136	1.51533
$803$	−44.7653	−1.57973
$804$	−20.1400	−0.710281
$805$	−4.38058	−0.154395
$806$	0.0503221	0.00177252
$807$	−12.5058	−0.440223
$808$	−46.3254	−1.62972
$809$	29.4584	1.03570	0.517850	−	0.855471i	$-0.326732\pi$
$809$	29.4584	1.03570	0.517850	+	0.855471i	$0.326732\pi$
$810$	0.390296	0.0137136
$811$	39.7001	1.39406	0.697030	−	0.717042i	$-0.254504\pi$
$811$	39.7001	1.39406	0.697030	+	0.717042i	$0.254504\pi$
$812$	9.57856	0.336142
$813$	0.604920	0.0212155
$814$	−79.6742	−2.79258
$815$	4.69209	0.164357
$816$	0.389447	0.0136334
$817$	28.1537	0.984972
$818$	−5.22429	−0.182663
$819$	−0.957882	−0.0334711
$820$	8.17361	0.285435
$821$	−11.5370	−0.402643	−0.201322	−	0.979525i	$-0.564524\pi$
$821$	−11.5370	−0.402643	−0.201322	+	0.979525i	$0.564524\pi$
$822$	2.67877	0.0934329
$823$	22.6789	0.790538	0.395269	−	0.918565i	$-0.370651\pi$
$823$	22.6789	0.790538	0.395269	+	0.918565i	$0.370651\pi$
$824$	−0.813192	−0.0283289
$825$	−18.4937	−0.643868
$826$	71.9565	2.50369
$827$	9.07701	0.315638	0.157819	−	0.987468i	$-0.449554\pi$
$827$	9.07701	0.315638	0.157819	+	0.987468i	$0.449554\pi$
$828$	−39.4988	−1.37268
$829$	−25.1705	−0.874209	−0.437104	−	0.899411i	$-0.643996\pi$
$829$	−25.1705	−0.874209	−0.437104	+	0.899411i	$0.643996\pi$
$830$	−0.416762	−0.0144660
$831$	16.9588	0.588295
$832$	−2.45180	−0.0850009
$833$	−0.186635	−0.00646652
$834$	−43.2809	−1.49870
$835$	−5.70556	−0.197449
$836$	66.0634	2.28485
$837$	−0.597834	−0.0206642
$838$	42.0683	1.45323
$839$	8.59556	0.296752	0.148376	−	0.988931i	$-0.452595\pi$
$839$	8.59556	0.296752	0.148376	+	0.988931i	$0.452595\pi$
$840$	−1.82033	−0.0628074
$841$	−27.6423	−0.953184
$842$	61.2089	2.10940
$843$	−3.01462	−0.103829
$844$	−20.9091	−0.719720
$845$	3.38446	0.116429
$846$	−6.33856	−0.217924
$847$	6.27377	0.215569
$848$	−1.73633	−0.0596257
$849$	10.3580	0.355486
$850$	11.1915	0.383864
$851$	−61.6527	−2.11343
$852$	4.46292	0.152897
$853$	−27.9160	−0.955825	−0.477912	−	0.878407i	$-0.658606\pi$
$853$	−27.9160	−0.955825	−0.477912	+	0.878407i	$0.658606\pi$
$854$	1.19789	0.0409910
$855$	−2.91809	−0.0997964
$856$	8.83604	0.302010
$857$	57.5848	1.96706	0.983529	−	0.180750i	$-0.0578524\pi$
$857$	57.5848	1.96706	0.983529	+	0.180750i	$0.0578524\pi$
$858$	−1.60060	−0.0546435
$859$	32.9890	1.12557	0.562785	−	0.826603i	$-0.309730\pi$
$859$	32.9890	1.12557	0.562785	+	0.826603i	$0.309730\pi$
$860$	4.03980	0.137756
$861$	26.5794	0.905825
$862$	−33.4890	−1.14064
$863$	4.84337	0.164870	0.0824351	−	0.996596i	$-0.473730\pi$
$863$	4.84337	0.164870	0.0824351	+	0.996596i	$0.473730\pi$
$864$	30.8271	1.04876
$865$	5.05774	0.171968
$866$	62.7472	2.13224
$867$	−1.02425	−0.0347852
$868$	−0.969157	−0.0328953
$869$	−21.4261	−0.726832
$870$	−0.706981	−0.0239689
$871$	1.17442	0.0397936
$872$	40.4759	1.37069
$873$	−30.8976	−1.04572
$874$	83.5846	2.82729
$875$	6.76770	0.228790
$876$	−39.4420	−1.33262
$877$	−31.4974	−1.06359	−0.531796	−	0.846872i	$-0.678483\pi$
$877$	−31.4974	−1.06359	−0.531796	+	0.846872i	$0.678483\pi$
$878$	41.2767	1.39302
$879$	−21.8087	−0.735590
$880$	−0.363399	−0.0122502
$881$	−31.1249	−1.04862	−0.524312	−	0.851526i	$-0.675678\pi$
$881$	−31.1249	−1.04862	−0.524312	+	0.851526i	$0.675678\pi$
$882$	−0.826246	−0.0278212
$883$	48.8828	1.64504	0.822519	−	0.568737i	$-0.192568\pi$
$883$	48.8828	1.64504	0.822519	+	0.568737i	$0.192568\pi$
$884$	0.592399	0.0199245
$885$	−3.24823	−0.109188
$886$	15.1746	0.509802
$887$	−1.91025	−0.0641400	−0.0320700	−	0.999486i	$-0.510210\pi$
$887$	−1.91025	−0.0641400	−0.0320700	+	0.999486i	$0.510210\pi$
$888$	−25.6195	−0.859734
$889$	−0.245860	−0.00824589
$890$	−0.328643	−0.0110161
$891$	−2.41211	−0.0808086
$892$	43.2464	1.44800
$893$	8.20356	0.274522
$894$	49.0837	1.64160
$895$	0.543877	0.0181798
$896$	45.4700	1.51904
$897$	−1.23856	−0.0413543
$898$	−48.5564	−1.62035
$899$	−0.137368	−0.00458149
$900$	30.3021	1.01007
$901$	4.56654	0.152134
$902$	−82.5938	−2.75007
$903$	13.1369	0.437167
$904$	−50.7680	−1.68852
$905$	2.94158	0.0977816
$906$	40.5537	1.34731
$907$	51.2411	1.70143	0.850716	−	0.525625i	$-0.176169\pi$
$907$	51.2411	1.70143	0.850716	+	0.525625i	$0.176169\pi$
$908$	14.8131	0.491592
$909$	−34.6517	−1.14932
$910$	0.290857	0.00964181
$911$	−25.6317	−0.849216	−0.424608	−	0.905377i	$-0.639588\pi$
$911$	−25.6317	−0.849216	−0.424608	+	0.905377i	$0.639588\pi$
$912$	−2.23140	−0.0738889
$913$	2.57567	0.0852424
$914$	71.6514	2.37002
$915$	−0.0540747	−0.00178765
$916$	−32.6457	−1.07865
$917$	−43.9265	−1.45058
$918$	−11.5071	−0.379792
$919$	−34.5643	−1.14017	−0.570085	−	0.821586i	$-0.693090\pi$
$919$	−34.5643	−1.14017	−0.570085	+	0.821586i	$0.693090\pi$
$920$	4.37710	0.144309
$921$	−17.3987	−0.573305
$922$	−55.2202	−1.81858
$923$	−0.260245	−0.00856608
$924$	30.8260	1.01410
$925$	47.2978	1.55514
$926$	−4.43424	−0.145718
$927$	−0.608272	−0.0199783
$928$	7.08336	0.232523
$929$	−27.3989	−0.898930	−0.449465	−	0.893298i	$-0.648385\pi$
$929$	−27.3989	−0.898930	−0.449465	+	0.893298i	$0.648385\pi$
$930$	0.0715322	0.00234563
$931$	1.06935	0.0350467
$932$	66.3178	2.17231
$933$	−9.65295	−0.316023
$934$	−5.67981	−0.185849
$935$	0.955740	0.0312560
$936$	0.957119	0.0312844
$937$	−6.44316	−0.210489	−0.105244	−	0.994446i	$-0.533562\pi$
$937$	−6.44316	−0.210489	−0.105244	+	0.994446i	$0.533562\pi$
$938$	−36.9819	−1.20750
$939$	−19.5957	−0.639481
$940$	1.17714	0.0383940
$941$	−35.7110	−1.16414	−0.582072	−	0.813137i	$-0.697758\pi$
$941$	−35.7110	−1.16414	−0.582072	+	0.813137i	$0.697758\pi$
$942$	11.5181	0.375280
$943$	−63.9119	−2.08126
$944$	4.61909	0.150339
$945$	−3.45542	−0.112405
$946$	−40.8219	−1.32723
$947$	−10.0170	−0.325507	−0.162754	−	0.986667i	$-0.552038\pi$
$947$	−10.0170	−0.325507	−0.162754	+	0.986667i	$0.552038\pi$
$948$	−18.8782	−0.613137
$949$	2.29998	0.0746604
$950$	−64.1232	−2.08043
$951$	−15.6816	−0.508511
$952$	−6.80794	−0.220647
$953$	52.7523	1.70881	0.854407	−	0.519605i	$-0.173921\pi$
$953$	52.7523	1.70881	0.854407	+	0.519605i	$0.173921\pi$
$954$	20.2164	0.654530
$955$	3.47812	0.112549
$956$	−58.3999	−1.88879
$957$	4.36928	0.141239
$958$	−26.1587	−0.845148
$959$	3.00840	0.0971463
$960$	−3.48520	−0.112484
$961$	−30.9861	−0.999552
$962$	4.09355	0.131981
$963$	6.60940	0.212985
$964$	−56.9632	−1.83466
$965$	5.12004	0.164820
$966$	39.0016	1.25486
$967$	−21.9876	−0.707072	−0.353536	−	0.935421i	$-0.615021\pi$
$967$	−21.9876	−0.707072	−0.353536	+	0.935421i	$0.615021\pi$
$968$	−6.26878	−0.201486
$969$	5.86857	0.188526
$970$	9.38193	0.301235
$971$	9.93393	0.318795	0.159398	−	0.987214i	$-0.449045\pi$
$971$	9.93393	0.318795	0.159398	+	0.987214i	$0.449045\pi$
$972$	−50.0362	−1.60491
$973$	−48.6067	−1.55826
$974$	10.5139	0.336886
$975$	0.950179	0.0304301
$976$	0.0768960	0.00246138
$977$	19.4550	0.622421	0.311211	−	0.950341i	$-0.399266\pi$
$977$	19.4550	0.622421	0.311211	+	0.950341i	$0.399266\pi$
$978$	−41.7751	−1.33582
$979$	2.03108	0.0649135
$980$	0.153443	0.00490155
$981$	30.2762	0.966645
$982$	35.3594	1.12836
$983$	42.8746	1.36749	0.683744	−	0.729722i	$-0.260350\pi$
$983$	42.8746	1.36749	0.683744	+	0.729722i	$0.260350\pi$
$984$	−26.5583	−0.846647
$985$	−1.69390	−0.0539723
$986$	−2.64407	−0.0842044
$987$	3.82789	0.121843
$988$	−3.39424	−0.107985
$989$	−31.5884	−1.00445
$990$	4.23113	0.134474
$991$	−2.67623	−0.0850133	−0.0425066	−	0.999096i	$-0.513534\pi$
$991$	−2.67623	−0.0850133	−0.0425066	+	0.999096i	$0.513534\pi$
$992$	−0.716693	−0.0227550
$993$	−17.6789	−0.561021
$994$	8.19501	0.259930
$995$	−2.00521	−0.0635695
$996$	2.26939	0.0719083
$997$	31.6978	1.00388	0.501939	−	0.864903i	$-0.332620\pi$
$997$	31.6978	1.00388	0.501939	+	0.864903i	$0.332620\pi$
$998$	−90.2788	−2.85772
$999$	−48.6319	−1.53865

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6001.2.a.d.1.13	✓	121

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6001.2.a.d.1.13	✓	121	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:	\( N \)	\(=\)	\( 6001 = 17 \cdot 353 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6001.a (trivial)

\(f(q)\)	\(=\)	\(q-2.26922 q^{2} -1.02425 q^{3} +3.14937 q^{4} -0.261054 q^{5} +2.32424 q^{6} +2.61024 q^{7} -2.60816 q^{8} -1.95092 q^{9} +O(q^{10})\)	\(q-2.26922 q^{2} -1.02425 q^{3} +3.14937 q^{4} -0.261054 q^{5} +2.32424 q^{6} +2.61024 q^{7} -2.60816 q^{8} -1.95092 q^{9} +0.592389 q^{10} -3.66108 q^{11} -3.22572 q^{12} +0.188101 q^{13} -5.92322 q^{14} +0.267383 q^{15} -0.380228 q^{16} +1.00000 q^{17} +4.42707 q^{18} -5.72965 q^{19} -0.822154 q^{20} -2.67353 q^{21} +8.30781 q^{22} +6.42867 q^{23} +2.67140 q^{24} -4.93185 q^{25} -0.426843 q^{26} +5.07096 q^{27} +8.22061 q^{28} +1.16519 q^{29} -0.606752 q^{30} -0.117894 q^{31} +6.07915 q^{32} +3.74985 q^{33} -2.26922 q^{34} -0.681414 q^{35} -6.14416 q^{36} -9.59028 q^{37} +13.0018 q^{38} -0.192662 q^{39} +0.680872 q^{40} -9.94171 q^{41} +6.06683 q^{42} -4.91368 q^{43} -11.5301 q^{44} +0.509295 q^{45} -14.5881 q^{46} -1.43177 q^{47} +0.389447 q^{48} -0.186635 q^{49} +11.1915 q^{50} -1.02425 q^{51} +0.592399 q^{52} +4.56654 q^{53} -11.5071 q^{54} +0.955740 q^{55} -6.80794 q^{56} +5.86857 q^{57} -2.64407 q^{58} -12.1482 q^{59} +0.842088 q^{60} -0.202236 q^{61} +0.267527 q^{62} -5.09237 q^{63} -13.0345 q^{64} -0.0491045 q^{65} -8.50924 q^{66} +6.24354 q^{67} +3.14937 q^{68} -6.58454 q^{69} +1.54628 q^{70} -1.38354 q^{71} +5.08832 q^{72} +12.2273 q^{73} +21.7625 q^{74} +5.05143 q^{75} -18.0448 q^{76} -9.55631 q^{77} +0.437192 q^{78} +5.85241 q^{79} +0.0992600 q^{80} +0.658851 q^{81} +22.5599 q^{82} -0.703528 q^{83} -8.41992 q^{84} -0.261054 q^{85} +11.1502 q^{86} -1.19344 q^{87} +9.54870 q^{88} -0.554775 q^{89} -1.15570 q^{90} +0.490990 q^{91} +20.2462 q^{92} +0.120752 q^{93} +3.24901 q^{94} +1.49575 q^{95} -6.22655 q^{96} +15.8374 q^{97} +0.423516 q^{98} +7.14248 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 121 q + 9 q^{2} + 21 q^{3} + 127 q^{4} + 27 q^{5} + 17 q^{6} + 39 q^{7} + 24 q^{8} + 134 q^{9}+O(q^{10}) \) 121 * q + 9 * q^2 + 21 * q^3 + 127 * q^4 + 27 * q^5 + 17 * q^6 + 39 * q^7 + 24 * q^8 + 134 * q^9	\( 121 q + 9 q^{2} + 21 q^{3} + 127 q^{4} + 27 q^{5} + 17 q^{6} + 39 q^{7} + 24 q^{8} + 134 q^{9} + 19 q^{10} + 48 q^{11} + 43 q^{12} + 6 q^{13} + 40 q^{14} + 49 q^{15} + 135 q^{16} + 121 q^{17} + 30 q^{19} + 50 q^{20} + 18 q^{21} + 24 q^{22} + 75 q^{23} + 24 q^{24} + 128 q^{25} + 59 q^{26} + 75 q^{27} + 52 q^{28} + 49 q^{29} - 34 q^{30} + 101 q^{31} + 47 q^{32} + 20 q^{33} + 9 q^{34} + 47 q^{35} + 138 q^{36} + 32 q^{37} + 30 q^{38} + 101 q^{39} + 36 q^{40} + 83 q^{41} - 11 q^{42} + 8 q^{43} + 98 q^{44} + 49 q^{45} + 45 q^{46} + 135 q^{47} + 54 q^{48} + 116 q^{49} + 3 q^{50} + 21 q^{51} - 5 q^{52} + 28 q^{53} + 10 q^{54} + 37 q^{55} + 75 q^{56} + 31 q^{58} + 150 q^{59} + 50 q^{60} + 36 q^{61} + 34 q^{62} + 118 q^{63} + 110 q^{64} + 18 q^{65} - 28 q^{66} - 6 q^{67} + 127 q^{68} + 25 q^{69} - 22 q^{70} + 223 q^{71} + q^{72} + 38 q^{73} - 10 q^{74} + 88 q^{75} - 4 q^{76} + 38 q^{77} + 42 q^{78} + 74 q^{79} + 106 q^{80} + 133 q^{81} + 28 q^{82} + 55 q^{83} + 10 q^{84} + 27 q^{85} + 64 q^{86} + 14 q^{87} + 56 q^{88} + 118 q^{89} + 51 q^{90} + 73 q^{91} + 82 q^{92} + 31 q^{93} + 33 q^{94} + 106 q^{95} + 38 q^{96} + 37 q^{97} + 88 q^{98} + 81 q^{99}+O(q^{100}) \) 121 * q + 9 * q^2 + 21 * q^3 + 127 * q^4 + 27 * q^5 + 17 * q^6 + 39 * q^7 + 24 * q^8 + 134 * q^9 + 19 * q^10 + 48 * q^11 + 43 * q^12 + 6 * q^13 + 40 * q^14 + 49 * q^15 + 135 * q^16 + 121 * q^17 + 30 * q^19 + 50 * q^20 + 18 * q^21 + 24 * q^22 + 75 * q^23 + 24 * q^24 + 128 * q^25 + 59 * q^26 + 75 * q^27 + 52 * q^28 + 49 * q^29 - 34 * q^30 + 101 * q^31 + 47 * q^32 + 20 * q^33 + 9 * q^34 + 47 * q^35 + 138 * q^36 + 32 * q^37 + 30 * q^38 + 101 * q^39 + 36 * q^40 + 83 * q^41 - 11 * q^42 + 8 * q^43 + 98 * q^44 + 49 * q^45 + 45 * q^46 + 135 * q^47 + 54 * q^48 + 116 * q^49 + 3 * q^50 + 21 * q^51 - 5 * q^52 + 28 * q^53 + 10 * q^54 + 37 * q^55 + 75 * q^56 + 31 * q^58 + 150 * q^59 + 50 * q^60 + 36 * q^61 + 34 * q^62 + 118 * q^63 + 110 * q^64 + 18 * q^65 - 28 * q^66 - 6 * q^67 + 127 * q^68 + 25 * q^69 - 22 * q^70 + 223 * q^71 + q^72 + 38 * q^73 - 10 * q^74 + 88 * q^75 - 4 * q^76 + 38 * q^77 + 42 * q^78 + 74 * q^79 + 106 * q^80 + 133 * q^81 + 28 * q^82 + 55 * q^83 + 10 * q^84 + 27 * q^85 + 64 * q^86 + 14 * q^87 + 56 * q^88 + 118 * q^89 + 51 * q^90 + 73 * q^91 + 82 * q^92 + 31 * q^93 + 33 * q^94 + 106 * q^95 + 38 * q^96 + 37 * q^97 + 88 * q^98 + 81 * q^99

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