LMFDB - Embedded newform 6011.2.a.e.1.17

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6011,2,Mod(1,6011)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6011, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("6011.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6011 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6011.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:	$47.9980766550$
Analytic rank:	$1$
Dimension:	$221$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.17
Character	$\chi$	$=$	6011.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.48261 q^{2} -2.01031 q^{3} +4.16334 q^{4} -2.06004 q^{5} +4.99080 q^{6} -1.12812 q^{7} -5.37073 q^{8} +1.04134 q^{9} +O(q^{10})$	\(q-2.48261 q^{2} -2.01031 q^{3} +4.16334 q^{4} -2.06004 q^{5} +4.99080 q^{6} -1.12812 q^{7} -5.37073 q^{8} +1.04134 q^{9} +5.11427 q^{10} +0.899239 q^{11} -8.36960 q^{12} +0.0782392 q^{13} +2.80068 q^{14} +4.14131 q^{15} +5.00674 q^{16} -2.39691 q^{17} -2.58523 q^{18} -3.04333 q^{19} -8.57664 q^{20} +2.26787 q^{21} -2.23246 q^{22} +1.99630 q^{23} +10.7968 q^{24} -0.756242 q^{25} -0.194237 q^{26} +3.93752 q^{27} -4.69676 q^{28} +0.0610137 q^{29} -10.2812 q^{30} -4.90997 q^{31} -1.68830 q^{32} -1.80775 q^{33} +5.95059 q^{34} +2.32397 q^{35} +4.33544 q^{36} +8.19210 q^{37} +7.55540 q^{38} -0.157285 q^{39} +11.0639 q^{40} -0.655606 q^{41} -5.63023 q^{42} -6.43604 q^{43} +3.74384 q^{44} -2.14519 q^{45} -4.95603 q^{46} +2.65600 q^{47} -10.0651 q^{48} -5.72734 q^{49} +1.87745 q^{50} +4.81852 q^{51} +0.325737 q^{52} +6.16517 q^{53} -9.77531 q^{54} -1.85247 q^{55} +6.05884 q^{56} +6.11803 q^{57} -0.151473 q^{58} +1.82589 q^{59} +17.2417 q^{60} -7.86067 q^{61} +12.1895 q^{62} -1.17475 q^{63} -5.82209 q^{64} -0.161176 q^{65} +4.48793 q^{66} -1.50505 q^{67} -9.97916 q^{68} -4.01317 q^{69} -5.76952 q^{70} +0.324382 q^{71} -5.59273 q^{72} +5.19069 q^{73} -20.3378 q^{74} +1.52028 q^{75} -12.6704 q^{76} -1.01445 q^{77} +0.390477 q^{78} -1.13561 q^{79} -10.3141 q^{80} -11.0396 q^{81} +1.62761 q^{82} -9.76247 q^{83} +9.44192 q^{84} +4.93773 q^{85} +15.9782 q^{86} -0.122656 q^{87} -4.82957 q^{88} +6.13459 q^{89} +5.32567 q^{90} -0.0882634 q^{91} +8.31127 q^{92} +9.87056 q^{93} -6.59380 q^{94} +6.26938 q^{95} +3.39400 q^{96} -7.36245 q^{97} +14.2187 q^{98} +0.936409 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 221 q - 15 q^{2} - 17 q^{3} + 189 q^{4} - 32 q^{5} - 33 q^{6} - 40 q^{7} - 39 q^{8} + 176 q^{9}+O(q^{10}) $ 221 * q - 15 * q^2 - 17 * q^3 + 189 * q^4 - 32 * q^5 - 33 * q^6 - 40 * q^7 - 39 * q^8 + 176 * q^9	\( 221 q - 15 q^{2} - 17 q^{3} + 189 q^{4} - 32 q^{5} - 33 q^{6} - 40 q^{7} - 39 q^{8} + 176 q^{9} - 61 q^{10} - 50 q^{11} - 43 q^{12} - 87 q^{13} - 41 q^{14} - 62 q^{15} + 129 q^{16} - 29 q^{17} - 61 q^{18} - 107 q^{19} - 59 q^{20} - 163 q^{21} - 70 q^{22} - 31 q^{23} - 98 q^{24} + 119 q^{25} - 23 q^{26} - 41 q^{27} - 112 q^{28} - 152 q^{29} - 66 q^{30} - 117 q^{31} - 93 q^{32} - 60 q^{33} - 80 q^{34} - 21 q^{35} + 92 q^{36} - 231 q^{37} + 2 q^{38} - 81 q^{39} - 143 q^{40} - 81 q^{41} - 6 q^{42} - 126 q^{43} - 115 q^{44} - 156 q^{45} - 205 q^{46} - 4 q^{47} - 55 q^{48} + 103 q^{49} - 61 q^{50} - 106 q^{51} - 164 q^{52} - 87 q^{53} - 110 q^{54} - 62 q^{55} - 73 q^{56} - 136 q^{57} - 128 q^{58} - 76 q^{59} - 148 q^{60} - 345 q^{61} + 5 q^{62} - 74 q^{63} - 25 q^{64} - 110 q^{65} - 34 q^{66} - 104 q^{67} - 48 q^{68} - 133 q^{69} - 92 q^{70} - 39 q^{71} - 177 q^{72} - 175 q^{73} - 44 q^{74} - 23 q^{75} - 268 q^{76} - 81 q^{77} - 19 q^{78} - 272 q^{79} - 60 q^{80} + 77 q^{81} - 13 q^{82} - 40 q^{83} - 221 q^{84} - 376 q^{85} - 82 q^{86} - 3 q^{87} - 234 q^{88} - 92 q^{89} - 91 q^{90} - 205 q^{91} - 11 q^{92} - 125 q^{93} - 126 q^{94} - 56 q^{95} - 148 q^{96} - 133 q^{97} - 4 q^{98} - 195 q^{99}+O(q^{100}) \) 221 * q - 15 * q^2 - 17 * q^3 + 189 * q^4 - 32 * q^5 - 33 * q^6 - 40 * q^7 - 39 * q^8 + 176 * q^9 - 61 * q^10 - 50 * q^11 - 43 * q^12 - 87 * q^13 - 41 * q^14 - 62 * q^15 + 129 * q^16 - 29 * q^17 - 61 * q^18 - 107 * q^19 - 59 * q^20 - 163 * q^21 - 70 * q^22 - 31 * q^23 - 98 * q^24 + 119 * q^25 - 23 * q^26 - 41 * q^27 - 112 * q^28 - 152 * q^29 - 66 * q^30 - 117 * q^31 - 93 * q^32 - 60 * q^33 - 80 * q^34 - 21 * q^35 + 92 * q^36 - 231 * q^37 + 2 * q^38 - 81 * q^39 - 143 * q^40 - 81 * q^41 - 6 * q^42 - 126 * q^43 - 115 * q^44 - 156 * q^45 - 205 * q^46 - 4 * q^47 - 55 * q^48 + 103 * q^49 - 61 * q^50 - 106 * q^51 - 164 * q^52 - 87 * q^53 - 110 * q^54 - 62 * q^55 - 73 * q^56 - 136 * q^57 - 128 * q^58 - 76 * q^59 - 148 * q^60 - 345 * q^61 + 5 * q^62 - 74 * q^63 - 25 * q^64 - 110 * q^65 - 34 * q^66 - 104 * q^67 - 48 * q^68 - 133 * q^69 - 92 * q^70 - 39 * q^71 - 177 * q^72 - 175 * q^73 - 44 * q^74 - 23 * q^75 - 268 * q^76 - 81 * q^77 - 19 * q^78 - 272 * q^79 - 60 * q^80 + 77 * q^81 - 13 * q^82 - 40 * q^83 - 221 * q^84 - 376 * q^85 - 82 * q^86 - 3 * q^87 - 234 * q^88 - 92 * q^89 - 91 * q^90 - 205 * q^91 - 11 * q^92 - 125 * q^93 - 126 * q^94 - 56 * q^95 - 148 * q^96 - 133 * q^97 - 4 * q^98 - 195 * 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 $

$2$	−2.48261	−1.75547	−0.877734	−	0.479147i	$-0.840946\pi$
$2$	−2.48261	−1.75547	−0.877734	+	0.479147i	$0.840946\pi$
$3$	−2.01031	−1.16065	−0.580326	−	0.814384i	$-0.697075\pi$
$3$	−2.01031	−1.16065	−0.580326	+	0.814384i	$0.697075\pi$
$4$	4.16334	2.08167
$5$	−2.06004	−0.921277	−0.460639	−	0.887588i	$-0.652380\pi$
$5$	−2.06004	−0.921277	−0.460639	+	0.887588i	$0.652380\pi$
$6$	4.99080	2.03749
$7$	−1.12812	−0.426390	−0.213195	−	0.977010i	$-0.568387\pi$
$7$	−1.12812	−0.426390	−0.213195	+	0.977010i	$0.568387\pi$
$8$	−5.37073	−1.89884
$9$	1.04134	0.347112
$10$	5.11427	1.61727
$11$	0.899239	0.271131	0.135565	−	0.990768i	$-0.456715\pi$
$11$	0.899239	0.271131	0.135565	+	0.990768i	$0.456715\pi$
$12$	−8.36960	−2.41609
$13$	0.0782392	0.0216997	0.0108498	−	0.999941i	$-0.496546\pi$
$13$	0.0782392	0.0216997	0.0108498	+	0.999941i	$0.496546\pi$
$14$	2.80068	0.748514
$15$	4.14131	1.06928
$16$	5.00674	1.25168
$17$	−2.39691	−0.581336	−0.290668	−	0.956824i	$-0.593878\pi$
$17$	−2.39691	−0.581336	−0.290668	+	0.956824i	$0.593878\pi$
$18$	−2.58523	−0.609344
$19$	−3.04333	−0.698188	−0.349094	−	0.937088i	$-0.613511\pi$
$19$	−3.04333	−0.698188	−0.349094	+	0.937088i	$0.613511\pi$
$20$	−8.57664	−1.91780
$21$	2.26787	0.494890
$22$	−2.23246	−0.475962
$23$	1.99630	0.416257	0.208128	−	0.978101i	$-0.433263\pi$
$23$	1.99630	0.416257	0.208128	+	0.978101i	$0.433263\pi$
$24$	10.7968	2.20389
$25$	−0.756242	−0.151248
$26$	−0.194237	−0.0380931
$27$	3.93752	0.757776
$28$	−4.69676	−0.887604
$29$	0.0610137	0.0113300	0.00566498	−	0.999984i	$-0.498197\pi$
$29$	0.0610137	0.0113300	0.00566498	+	0.999984i	$0.498197\pi$
$30$	−10.2812	−1.87709
$31$	−4.90997	−0.881858	−0.440929	−	0.897542i	$-0.645351\pi$
$31$	−4.90997	−0.881858	−0.440929	+	0.897542i	$0.645351\pi$
$32$	−1.68830	−0.298452
$33$	−1.80775	−0.314688
$34$	5.95059	1.02052
$35$	2.32397	0.392823
$36$	4.33544	0.722573
$37$	8.19210	1.34677	0.673386	−	0.739291i	$-0.264839\pi$
$37$	8.19210	1.34677	0.673386	+	0.739291i	$0.264839\pi$
$38$	7.55540	1.22565
$39$	−0.157285	−0.0251857
$40$	11.0639	1.74936
$41$	−0.655606	−0.102388	−0.0511942	−	0.998689i	$-0.516303\pi$
$41$	−0.655606	−0.102388	−0.0511942	+	0.998689i	$0.516303\pi$
$42$	−5.63023	−0.868764
$43$	−6.43604	−0.981487	−0.490744	−	0.871304i	$-0.663275\pi$
$43$	−6.43604	−0.981487	−0.490744	+	0.871304i	$0.663275\pi$
$44$	3.74384	0.564405
$45$	−2.14519	−0.319786
$46$	−4.95603	−0.730726
$47$	2.65600	0.387417	0.193708	−	0.981059i	$-0.437948\pi$
$47$	2.65600	0.387417	0.193708	+	0.981059i	$0.437948\pi$
$48$	−10.0651	−1.45277
$49$	−5.72734	−0.818192
$50$	1.87745	0.265512
$51$	4.81852	0.674728
$52$	0.325737	0.0451716
$53$	6.16517	0.846851	0.423426	−	0.905931i	$-0.360827\pi$
$53$	6.16517	0.846851	0.423426	+	0.905931i	$0.360827\pi$
$54$	−9.77531	−1.33025
$55$	−1.85247	−0.249787
$56$	6.05884	0.809646
$57$	6.11803	0.810353
$58$	−0.151473	−0.0198894
$59$	1.82589	0.237711	0.118855	−	0.992912i	$-0.462078\pi$
$59$	1.82589	0.237711	0.118855	+	0.992912i	$0.462078\pi$
$60$	17.2417	2.22589
$61$	−7.86067	−1.00646	−0.503228	−	0.864154i	$-0.667854\pi$
$61$	−7.86067	−1.00646	−0.503228	+	0.864154i	$0.667854\pi$
$62$	12.1895	1.54807
$63$	−1.17475	−0.148005
$64$	−5.82209	−0.727761
$65$	−0.161176	−0.0199914
$66$	4.48793	0.552425
$67$	−1.50505	−0.183871	−0.0919353	−	0.995765i	$-0.529305\pi$
$67$	−1.50505	−0.183871	−0.0919353	+	0.995765i	$0.529305\pi$
$68$	−9.97916	−1.21015
$69$	−4.01317	−0.483129
$70$	−5.76952	−0.689589
$71$	0.324382	0.0384971	0.0192486	−	0.999815i	$-0.493873\pi$
$71$	0.324382	0.0384971	0.0192486	+	0.999815i	$0.493873\pi$
$72$	−5.59273	−0.659110
$73$	5.19069	0.607524	0.303762	−	0.952748i	$-0.401757\pi$
$73$	5.19069	0.607524	0.303762	+	0.952748i	$0.401757\pi$
$74$	−20.3378	−2.36422
$75$	1.52028	0.175547
$76$	−12.6704	−1.45340
$77$	−1.01445	−0.115607
$78$	0.390477	0.0442128
$79$	−1.13561	−0.127766	−0.0638831	−	0.997957i	$-0.520348\pi$
$79$	−1.13561	−0.127766	−0.0638831	+	0.997957i	$0.520348\pi$
$80$	−10.3141	−1.15315
$81$	−11.0396	−1.22663
$82$	1.62761	0.179740
$83$	−9.76247	−1.07157	−0.535785	−	0.844355i	$-0.679984\pi$
$83$	−9.76247	−1.07157	−0.535785	+	0.844355i	$0.679984\pi$
$84$	9.44192	1.03020
$85$	4.93773	0.535572
$86$	15.9782	1.72297
$87$	−0.122656	−0.0131501
$88$	−4.82957	−0.514834
$89$	6.13459	0.650265	0.325132	−	0.945669i	$-0.394591\pi$
$89$	6.13459	0.650265	0.325132	+	0.945669i	$0.394591\pi$
$90$	5.32567	0.561375
$91$	−0.0882634	−0.00925252
$92$	8.31127	0.866510
$93$	9.87056	1.02353
$94$	−6.59380	−0.680098
$95$	6.26938	0.643225
$96$	3.39400	0.346399
$97$	−7.36245	−0.747543	−0.373772	−	0.927521i	$-0.621936\pi$
$97$	−7.36245	−0.747543	−0.373772	+	0.927521i	$0.621936\pi$
$98$	14.2187	1.43631
$99$	0.936409	0.0941127
$100$	−3.14850	−0.314850
$101$	15.3115	1.52355	0.761776	−	0.647841i	$-0.224328\pi$
$101$	15.3115	1.52355	0.761776	+	0.647841i	$0.224328\pi$
$102$	−11.9625	−1.18446
$103$	16.9427	1.66942	0.834708	−	0.550693i	$-0.185636\pi$
$103$	16.9427	1.66942	0.834708	+	0.550693i	$0.185636\pi$
$104$	−0.420202	−0.0412042
$105$	−4.67190	−0.455931
$106$	−15.3057	−1.48662
$107$	13.0130	1.25801	0.629007	−	0.777399i	$-0.283462\pi$
$107$	13.0130	1.25801	0.629007	+	0.777399i	$0.283462\pi$
$108$	16.3932	1.57744
$109$	8.56821	0.820685	0.410343	−	0.911931i	$-0.365409\pi$
$109$	8.56821	0.820685	0.410343	+	0.911931i	$0.365409\pi$
$110$	4.59895	0.438493
$111$	−16.4686	−1.56313
$112$	−5.64821	−0.533705
$113$	−4.52351	−0.425536	−0.212768	−	0.977103i	$-0.568248\pi$
$113$	−4.52351	−0.425536	−0.212768	+	0.977103i	$0.568248\pi$
$114$	−15.1887	−1.42255
$115$	−4.11245	−0.383488
$116$	0.254021	0.0235852
$117$	0.0814733	0.00753221
$118$	−4.53297	−0.417293
$119$	2.70401	0.247876
$120$	−22.2419	−2.03040
$121$	−10.1914	−0.926488
$122$	19.5150	1.76680
$123$	1.31797	0.118837
$124$	−20.4419	−1.83574
$125$	11.8581	1.06062
$126$	2.91645	0.259818
$127$	14.5100	1.28755	0.643775	−	0.765215i	$-0.277367\pi$
$127$	14.5100	1.28755	0.643775	+	0.765215i	$0.277367\pi$
$128$	17.8306	1.57601
$129$	12.9384	1.13916
$130$	0.400136	0.0350943
$131$	−5.11634	−0.447016	−0.223508	−	0.974702i	$-0.571751\pi$
$131$	−5.11634	−0.447016	−0.223508	+	0.974702i	$0.571751\pi$
$132$	−7.52627	−0.655078
$133$	3.43325	0.297700
$134$	3.73644	0.322779
$135$	−8.11144	−0.698121
$136$	12.8732	1.10386
$137$	−12.7890	−1.09264	−0.546321	−	0.837576i	$-0.683972\pi$
$137$	−12.7890	−1.09264	−0.546321	+	0.837576i	$0.683972\pi$
$138$	9.96313	0.848118
$139$	−16.6869	−1.41536	−0.707681	−	0.706532i	$-0.750259\pi$
$139$	−16.6869	−1.41536	−0.707681	+	0.706532i	$0.750259\pi$
$140$	9.67550	0.817729
$141$	−5.33937	−0.449656
$142$	−0.805314	−0.0675805
$143$	0.0703558	0.00588345
$144$	5.21369	0.434474
$145$	−0.125691	−0.0104380
$146$	−12.8864	−1.06649
$147$	11.5137	0.949635
$148$	34.1065	2.80354
$149$	0.584866	0.0479141	0.0239570	−	0.999713i	$-0.492374\pi$
$149$	0.584866	0.0479141	0.0239570	+	0.999713i	$0.492374\pi$
$150$	−3.77426	−0.308167
$151$	21.0058	1.70942	0.854712	−	0.519102i	$-0.173734\pi$
$151$	21.0058	1.70942	0.854712	+	0.519102i	$0.173734\pi$
$152$	16.3449	1.32575
$153$	−2.49599	−0.201789
$154$	2.51848	0.202945
$155$	10.1147	0.812435
$156$	−0.654831	−0.0524284
$157$	−12.9317	−1.03206	−0.516031	−	0.856570i	$-0.672591\pi$
$157$	−12.9317	−1.03206	−0.516031	+	0.856570i	$0.672591\pi$
$158$	2.81927	0.224289
$159$	−12.3939	−0.982899
$160$	3.47796	0.274957
$161$	−2.25207	−0.177488
$162$	27.4071	2.15330
$163$	−8.67102	−0.679166	−0.339583	−	0.940576i	$-0.610286\pi$
$163$	−8.67102	−0.679166	−0.339583	+	0.940576i	$0.610286\pi$
$164$	−2.72951	−0.213139
$165$	3.72403	0.289915
$166$	24.2364	1.88111
$167$	18.3401	1.41920	0.709600	−	0.704604i	$-0.248876\pi$
$167$	18.3401	1.41920	0.709600	+	0.704604i	$0.248876\pi$
$168$	−12.1801	−0.939717
$169$	−12.9939	−0.999529
$170$	−12.2584	−0.940179
$171$	−3.16913	−0.242349
$172$	−26.7954	−2.04313
$173$	−1.24364	−0.0945523	−0.0472761	−	0.998882i	$-0.515054\pi$
$173$	−1.24364	−0.0945523	−0.0472761	+	0.998882i	$0.515054\pi$
$174$	0.304507	0.0230846
$175$	0.853133	0.0644908
$176$	4.50225	0.339370
$177$	−3.67060	−0.275899
$178$	−15.2298	−1.14152
$179$	−16.3434	−1.22156	−0.610781	−	0.791799i	$-0.709145\pi$
$179$	−16.3434	−1.22156	−0.610781	+	0.791799i	$0.709145\pi$
$180$	−8.93116	−0.665690
$181$	10.6039	0.788179	0.394090	−	0.919072i	$-0.371060\pi$
$181$	10.6039	0.788179	0.394090	+	0.919072i	$0.371060\pi$
$182$	0.219123	0.0162425
$183$	15.8024	1.16814
$184$	−10.7216	−0.790405
$185$	−16.8760	−1.24075
$186$	−24.5047	−1.79677
$187$	−2.15539	−0.157618
$188$	11.0578	0.806475
$189$	−4.44200	−0.323108
$190$	−15.5644	−1.12916
$191$	17.4511	1.26272	0.631358	−	0.775492i	$-0.282498\pi$
$191$	17.4511	1.26272	0.631358	+	0.775492i	$0.282498\pi$
$192$	11.7042	0.844677
$193$	−1.45471	−0.104712	−0.0523562	−	0.998628i	$-0.516673\pi$
$193$	−1.45471	−0.104712	−0.0523562	+	0.998628i	$0.516673\pi$
$194$	18.2781	1.31229
$195$	0.324013	0.0232031
$196$	−23.8449	−1.70321
$197$	22.0316	1.56968	0.784842	−	0.619697i	$-0.212744\pi$
$197$	22.0316	1.56968	0.784842	+	0.619697i	$0.212744\pi$
$198$	−2.32474	−0.165212
$199$	3.62208	0.256762	0.128381	−	0.991725i	$-0.459022\pi$
$199$	3.62208	0.256762	0.128381	+	0.991725i	$0.459022\pi$
$200$	4.06157	0.287197
$201$	3.02561	0.213410
$202$	−38.0124	−2.67455
$203$	−0.0688308	−0.00483098
$204$	20.0612	1.40456
$205$	1.35057	0.0943281
$206$	−42.0621	−2.93061
$207$	2.07882	0.144488
$208$	0.391723	0.0271611
$209$	−2.73668	−0.189300
$210$	11.5985	0.800372
$211$	−25.0230	−1.72266	−0.861329	−	0.508048i	$-0.830367\pi$
$211$	−25.0230	−1.72266	−0.861329	+	0.508048i	$0.830367\pi$
$212$	25.6677	1.76287
$213$	−0.652108	−0.0446817
$214$	−32.3062	−2.20841
$215$	13.2585	0.904222
$216$	−21.1474	−1.43889
$217$	5.53905	0.376015
$218$	−21.2715	−1.44069
$219$	−10.4349	−0.705124
$220$	−7.71245	−0.519973
$221$	−0.187532	−0.0126148
$222$	40.8852	2.74403
$223$	26.4008	1.76793	0.883963	−	0.467556i	$-0.154866\pi$
$223$	26.4008	1.76793	0.883963	+	0.467556i	$0.154866\pi$
$224$	1.90461	0.127257
$225$	−0.787502	−0.0525001
$226$	11.2301	0.747015
$227$	25.8534	1.71595	0.857976	−	0.513690i	$-0.171722\pi$
$227$	25.8534	1.71595	0.857976	+	0.513690i	$0.171722\pi$
$228$	25.4715	1.68689
$229$	27.9834	1.84920	0.924598	−	0.380945i	$-0.124401\pi$
$229$	27.9834	1.84920	0.924598	+	0.380945i	$0.124401\pi$
$230$	10.2096	0.673201
$231$	2.03936	0.134180
$232$	−0.327688	−0.0215138
$233$	10.3168	0.675877	0.337938	−	0.941168i	$-0.390270\pi$
$233$	10.3168	0.675877	0.337938	+	0.941168i	$0.390270\pi$
$234$	−0.202266	−0.0132226
$235$	−5.47146	−0.356918
$236$	7.60180	0.494835
$237$	2.28293	0.148292
$238$	−6.71299	−0.435138
$239$	1.66872	0.107940	0.0539701	−	0.998543i	$-0.482812\pi$
$239$	1.66872	0.107940	0.0539701	+	0.998543i	$0.482812\pi$
$240$	20.7344	1.33840
$241$	−3.48671	−0.224599	−0.112299	−	0.993674i	$-0.535822\pi$
$241$	−3.48671	−0.224599	−0.112299	+	0.993674i	$0.535822\pi$
$242$	25.3012	1.62642
$243$	10.3805	0.665909
$244$	−32.7267	−2.09511
$245$	11.7985	0.753781
$246$	−3.27200	−0.208615
$247$	−0.238108	−0.0151504
$248$	26.3702	1.67451
$249$	19.6256	1.24372
$250$	−29.4390	−1.86188
$251$	20.8127	1.31369	0.656843	−	0.754028i	$-0.271892\pi$
$251$	20.8127	1.31369	0.656843	+	0.754028i	$0.271892\pi$
$252$	−4.89090	−0.308098
$253$	1.79515	0.112860
$254$	−36.0225	−2.26025
$255$	−9.92635	−0.621612
$256$	−32.6221	−2.03888
$257$	23.3403	1.45593	0.727965	−	0.685615i	$-0.240466\pi$
$257$	23.3403	1.45593	0.727965	+	0.685615i	$0.240466\pi$
$258$	−32.1210	−1.99977
$259$	−9.24168	−0.574250
$260$	−0.671030	−0.0416155
$261$	0.0635357	0.00393276
$262$	12.7019	0.784723
$263$	−21.7151	−1.33901	−0.669506	−	0.742807i	$-0.733494\pi$
$263$	−21.7151	−1.33901	−0.669506	+	0.742807i	$0.733494\pi$
$264$	9.70892	0.597543
$265$	−12.7005	−0.780185
$266$	−8.52341	−0.522604
$267$	−12.3324	−0.754731
$268$	−6.26602	−0.382758
$269$	16.0005	0.975567	0.487784	−	0.872965i	$-0.337806\pi$
$269$	16.0005	0.975567	0.487784	+	0.872965i	$0.337806\pi$
$270$	20.1375	1.22553
$271$	12.9644	0.787529	0.393765	−	0.919211i	$-0.371173\pi$
$271$	12.9644	0.787529	0.393765	+	0.919211i	$0.371173\pi$
$272$	−12.0007	−0.727649
$273$	0.177437	0.0107389
$274$	31.7502	1.91810
$275$	−0.680042	−0.0410081
$276$	−16.7082	−1.00572
$277$	−13.5028	−0.811306	−0.405653	−	0.914027i	$-0.632956\pi$
$277$	−13.5028	−0.811306	−0.405653	+	0.914027i	$0.632956\pi$
$278$	41.4270	2.48462
$279$	−5.11293	−0.306103
$280$	−12.4814	−0.745909
$281$	−2.25609	−0.134587	−0.0672934	−	0.997733i	$-0.521436\pi$
$281$	−2.25609	−0.134587	−0.0672934	+	0.997733i	$0.521436\pi$
$282$	13.2556	0.789357
$283$	9.52001	0.565906	0.282953	−	0.959134i	$-0.408686\pi$
$283$	9.52001	0.565906	0.282953	+	0.959134i	$0.408686\pi$
$284$	1.35051	0.0801383
$285$	−12.6034	−0.746560
$286$	−0.174666	−0.0103282
$287$	0.739603	0.0436574
$288$	−1.75809	−0.103596
$289$	−11.2548	−0.662048
$290$	0.312040	0.0183236
$291$	14.8008	0.867637
$292$	21.6106	1.26467
$293$	−1.19267	−0.0696763	−0.0348381	−	0.999393i	$-0.511092\pi$
$293$	−1.19267	−0.0696763	−0.0348381	+	0.999393i	$0.511092\pi$
$294$	−28.5840	−1.66706
$295$	−3.76140	−0.218997
$296$	−43.9976	−2.55731
$297$	3.54077	0.205456
$298$	−1.45199	−0.0841117
$299$	0.156189	0.00903264
$300$	6.32944	0.365431
$301$	7.26064	0.418496
$302$	−52.1491	−3.00084
$303$	−30.7808	−1.76831
$304$	−15.2372	−0.873911
$305$	16.1933	0.927225
$306$	6.19656	0.354234
$307$	−23.5344	−1.34318	−0.671591	−	0.740922i	$-0.734389\pi$
$307$	−23.5344	−1.34318	−0.671591	+	0.740922i	$0.734389\pi$
$308$	−4.22351	−0.240657
$309$	−34.0601	−1.93761
$310$	−25.1109	−1.42620
$311$	−8.77853	−0.497785	−0.248892	−	0.968531i	$-0.580067\pi$
$311$	−8.77853	−0.497785	−0.248892	+	0.968531i	$0.580067\pi$
$312$	0.844735	0.0478237
$313$	27.1526	1.53476	0.767378	−	0.641194i	$-0.221561\pi$
$313$	27.1526	1.53476	0.767378	+	0.641194i	$0.221561\pi$
$314$	32.1043	1.81175
$315$	2.42004	0.136354
$316$	−4.72793	−0.265967
$317$	9.43014	0.529650	0.264825	−	0.964297i	$-0.414686\pi$
$317$	9.43014	0.529650	0.264825	+	0.964297i	$0.414686\pi$
$318$	30.7692	1.72545
$319$	0.0548659	0.00307190
$320$	11.9937	0.670469
$321$	−26.1601	−1.46012
$322$	5.59100	0.311574
$323$	7.29459	0.405882
$324$	−45.9617	−2.55343
$325$	−0.0591678	−0.00328204
$326$	21.5267	1.19226
$327$	−17.2247	−0.952530
$328$	3.52108	0.194419
$329$	−2.99629	−0.165191
$330$	−9.24530	−0.508937
$331$	−4.76827	−0.262088	−0.131044	−	0.991377i	$-0.541833\pi$
$331$	−4.76827	−0.262088	−0.131044	+	0.991377i	$0.541833\pi$
$332$	−40.6445	−2.23066
$333$	8.53072	0.467481
$334$	−45.5313	−2.49136
$335$	3.10045	0.169396
$336$	11.3546	0.619446
$337$	−4.48954	−0.244561	−0.122280	−	0.992496i	$-0.539021\pi$
$337$	−4.48954	−0.244561	−0.122280	+	0.992496i	$0.539021\pi$
$338$	32.2587	1.75464
$339$	9.09364	0.493899
$340$	20.5574	1.11488
$341$	−4.41524	−0.239099
$342$	7.86770	0.425437
$343$	14.3580	0.775259
$344$	34.5662	1.86369
$345$	8.26729	0.445096
$346$	3.08747	0.165984
$347$	−6.64048	−0.356480	−0.178240	−	0.983987i	$-0.557040\pi$
$347$	−6.64048	−0.356480	−0.178240	+	0.983987i	$0.557040\pi$
$348$	−0.510660	−0.0273742
$349$	25.3195	1.35532	0.677660	−	0.735376i	$-0.262994\pi$
$349$	25.3195	1.35532	0.677660	+	0.735376i	$0.262994\pi$
$350$	−2.11800	−0.113212
$351$	0.308068	0.0164435
$352$	−1.51818	−0.0809195
$353$	27.2867	1.45232	0.726162	−	0.687524i	$-0.241302\pi$
$353$	27.2867	1.45232	0.726162	+	0.687524i	$0.241302\pi$
$354$	9.11266	0.484332
$355$	−0.668240	−0.0354665
$356$	25.5404	1.35364
$357$	−5.43588	−0.287697
$358$	40.5743	2.14442
$359$	−32.1684	−1.69779	−0.848893	−	0.528565i	$-0.822730\pi$
$359$	−32.1684	−1.69779	−0.848893	+	0.528565i	$0.822730\pi$
$360$	11.5212	0.607223
$361$	−9.73814	−0.512534
$362$	−26.3253	−1.38362
$363$	20.4878	1.07533
$364$	−0.367471	−0.0192607
$365$	−10.6930	−0.559698
$366$	−39.2311	−2.05064
$367$	29.7154	1.55113	0.775565	−	0.631268i	$-0.217465\pi$
$367$	29.7154	1.55113	0.775565	+	0.631268i	$0.217465\pi$
$368$	9.99494	0.521022
$369$	−0.682705	−0.0355402
$370$	41.8966	2.17810
$371$	−6.95506	−0.361089
$372$	41.0945	2.13065
$373$	19.8064	1.02553	0.512767	−	0.858528i	$-0.328620\pi$
$373$	19.8064	1.02553	0.512767	+	0.858528i	$0.328620\pi$
$374$	5.35100	0.276694
$375$	−23.8384	−1.23101
$376$	−14.2646	−0.735643
$377$	0.00477366	0.000245856 0
$378$	11.0277	0.567206
$379$	19.0117	0.976566	0.488283	−	0.872685i	$-0.337623\pi$
$379$	19.0117	0.976566	0.488283	+	0.872685i	$0.337623\pi$
$380$	26.1016	1.33898
$381$	−29.1695	−1.49440
$382$	−43.3242	−2.21666
$383$	−17.5029	−0.894354	−0.447177	−	0.894445i	$-0.647571\pi$
$383$	−17.5029	−0.894354	−0.447177	+	0.894445i	$0.647571\pi$
$384$	−35.8449	−1.82920
$385$	2.08981	0.106506
$386$	3.61148	0.183819
$387$	−6.70208	−0.340686
$388$	−30.6524	−1.55614
$389$	16.2048	0.821614	0.410807	−	0.911722i	$-0.365247\pi$
$389$	16.2048	0.821614	0.410807	+	0.911722i	$0.365247\pi$
$390$	−0.804397	−0.0407322
$391$	−4.78495	−0.241985
$392$	30.7600	1.55362
$393$	10.2854	0.518830
$394$	−54.6957	−2.75553
$395$	2.33940	0.117708
$396$	3.89859	0.195912
$397$	−17.3410	−0.870318	−0.435159	−	0.900354i	$-0.643308\pi$
$397$	−17.3410	−0.870318	−0.435159	+	0.900354i	$0.643308\pi$
$398$	−8.99219	−0.450738
$399$	−6.90188	−0.345526
$400$	−3.78630	−0.189315
$401$	−22.2968	−1.11345	−0.556724	−	0.830697i	$-0.687942\pi$
$401$	−22.2968	−1.11345	−0.556724	+	0.830697i	$0.687942\pi$
$402$	−7.51139	−0.374634
$403$	−0.384153	−0.0191360
$404$	63.7470	3.17153
$405$	22.7421	1.13006
$406$	0.170880	0.00848063
$407$	7.36665	0.365151
$408$	−25.8790	−1.28120
$409$	−30.2637	−1.49644	−0.748222	−	0.663449i	$-0.769092\pi$
$409$	−30.2637	−1.49644	−0.748222	+	0.663449i	$0.769092\pi$
$410$	−3.35294	−0.165590
$411$	25.7099	1.26818
$412$	70.5384	3.47518
$413$	−2.05982	−0.101357
$414$	−5.16088	−0.253644
$415$	20.1111	0.987213
$416$	−0.132091	−0.00647631
$417$	33.5457	1.64274
$418$	6.79411	0.332311
$419$	16.5428	0.808170	0.404085	−	0.914722i	$-0.367590\pi$
$419$	16.5428	0.808170	0.404085	+	0.914722i	$0.367590\pi$
$420$	−19.4507	−0.949098
$421$	−16.5951	−0.808793	−0.404397	−	0.914584i	$-0.632518\pi$
$421$	−16.5951	−0.808793	−0.404397	+	0.914584i	$0.632518\pi$
$422$	62.1224	3.02407
$423$	2.76578	0.134477
$424$	−33.1115	−1.60804
$425$	1.81264	0.0879262
$426$	1.61893	0.0784374
$427$	8.86779	0.429142
$428$	54.1776	2.61877
$429$	−0.141437	−0.00682863
$430$	−32.9156	−1.58733
$431$	−26.0836	−1.25640	−0.628201	−	0.778051i	$-0.716208\pi$
$431$	−26.0836	−1.25640	−0.628201	+	0.778051i	$0.716208\pi$
$432$	19.7141	0.948496
$433$	5.46216	0.262495	0.131247	−	0.991350i	$-0.458102\pi$
$433$	5.46216	0.262495	0.131247	+	0.991350i	$0.458102\pi$
$434$	−13.7513	−0.660083
$435$	0.252677	0.0121149
$436$	35.6724	1.70840
$437$	−6.07540	−0.290626
$438$	25.9057	1.23782
$439$	25.9587	1.23894	0.619471	−	0.785020i	$-0.287347\pi$
$439$	25.9587	1.23894	0.619471	+	0.785020i	$0.287347\pi$
$440$	9.94910	0.474305
$441$	−5.96408	−0.284004
$442$	0.465569	0.0221449
$443$	−11.1067	−0.527697	−0.263849	−	0.964564i	$-0.584992\pi$
$443$	−11.1067	−0.527697	−0.263849	+	0.964564i	$0.584992\pi$
$444$	−68.5646	−3.25393
$445$	−12.6375	−0.599074
$446$	−65.5428	−3.10354
$447$	−1.17576	−0.0556115
$448$	6.56802	0.310310
$449$	21.5472	1.01688	0.508439	−	0.861098i	$-0.330223\pi$
$449$	21.5472	1.01688	0.508439	+	0.861098i	$0.330223\pi$
$450$	1.95506	0.0921623
$451$	−0.589546	−0.0277606
$452$	−18.8329	−0.885825
$453$	−42.2280	−1.98405
$454$	−64.1839	−3.01230
$455$	0.181826	0.00852413
$456$	−32.8583	−1.53873
$457$	−28.6122	−1.33842	−0.669212	−	0.743072i	$-0.733368\pi$
$457$	−28.6122	−1.33842	−0.669212	+	0.743072i	$0.733368\pi$
$458$	−69.4718	−3.24621
$459$	−9.43787	−0.440522
$460$	−17.1215	−0.798296
$461$	−16.3969	−0.763680	−0.381840	−	0.924229i	$-0.624709\pi$
$461$	−16.3969	−0.763680	−0.381840	+	0.924229i	$0.624709\pi$
$462$	−5.06293	−0.235549
$463$	−34.1225	−1.58581	−0.792904	−	0.609346i	$-0.791432\pi$
$463$	−34.1225	−1.58581	−0.792904	+	0.609346i	$0.791432\pi$
$464$	0.305479	0.0141815
$465$	−20.3337	−0.942954
$466$	−25.6126	−1.18648
$467$	−3.59434	−0.166326	−0.0831631	−	0.996536i	$-0.526502\pi$
$467$	−3.59434	−0.166326	−0.0831631	+	0.996536i	$0.526502\pi$
$468$	0.339201	0.0156796
$469$	1.69788	0.0784006
$470$	13.5835	0.626559
$471$	25.9967	1.19786
$472$	−9.80636	−0.451374
$473$	−5.78754	−0.266111
$474$	−5.66761	−0.260322
$475$	2.30150	0.105600
$476$	11.2577	0.515996
$477$	6.42001	0.293952
$478$	−4.14277	−0.189486
$479$	−31.9227	−1.45859	−0.729294	−	0.684201i	$-0.760151\pi$
$479$	−31.9227	−1.45859	−0.729294	+	0.684201i	$0.760151\pi$
$480$	−6.99177	−0.319129
$481$	0.640944	0.0292245
$482$	8.65613	0.394276
$483$	4.52735	0.206001
$484$	−42.4302	−1.92864
$485$	15.1669	0.688694
$486$	−25.7707	−1.16898
$487$	−9.91364	−0.449230	−0.224615	−	0.974448i	$-0.572112\pi$
$487$	−9.91364	−0.449230	−0.224615	+	0.974448i	$0.572112\pi$
$488$	42.2175	1.91110
$489$	17.4314	0.788275
$490$	−29.2912	−1.32324
$491$	6.83897	0.308638	0.154319	−	0.988021i	$-0.450682\pi$
$491$	6.83897	0.308638	0.154319	+	0.988021i	$0.450682\pi$
$492$	5.48716	0.247380
$493$	−0.146244	−0.00658651
$494$	0.591129	0.0265961
$495$	−1.92904	−0.0867039
$496$	−24.5829	−1.10381
$497$	−0.365943	−0.0164148
$498$	−48.7226	−2.18331
$499$	8.19769	0.366979	0.183489	−	0.983022i	$-0.441261\pi$
$499$	8.19769	0.366979	0.183489	+	0.983022i	$0.441261\pi$
$500$	49.3692	2.20786
$501$	−36.8693	−1.64720
$502$	−51.6697	−2.30613
$503$	−9.53217	−0.425018	−0.212509	−	0.977159i	$-0.568164\pi$
$503$	−9.53217	−0.425018	−0.212509	+	0.977159i	$0.568164\pi$
$504$	6.30928	0.281038
$505$	−31.5423	−1.40361
$506$	−4.45665	−0.198122
$507$	26.1217	1.16010
$508$	60.4099	2.68026
$509$	−5.63695	−0.249853	−0.124927	−	0.992166i	$-0.539870\pi$
$509$	−5.63695	−0.249853	−0.124927	+	0.992166i	$0.539870\pi$
$510$	24.6432	1.09122
$511$	−5.85573	−0.259042
$512$	45.3268	2.00318
$513$	−11.9832	−0.529070
$514$	−57.9449	−2.55584
$515$	−34.9027	−1.53800
$516$	53.8671	2.37137
$517$	2.38838	0.105041
$518$	22.9435	1.00808
$519$	2.50010	0.109742
$520$	0.865632	0.0379605
$521$	−1.08840	−0.0476838	−0.0238419	−	0.999716i	$-0.507590\pi$
$521$	−1.08840	−0.0476838	−0.0238419	+	0.999716i	$0.507590\pi$
$522$	−0.157734	−0.00690384
$523$	−11.2516	−0.492000	−0.246000	−	0.969270i	$-0.579116\pi$
$523$	−11.2516	−0.492000	−0.246000	+	0.969270i	$0.579116\pi$
$524$	−21.3011	−0.930541
$525$	−1.71506	−0.0748513
$526$	53.9101	2.35059
$527$	11.7688	0.512656
$528$	−9.05091	−0.393890
$529$	−19.0148	−0.826730
$530$	31.5303	1.36959
$531$	1.90136	0.0825121
$532$	14.2938	0.619714
$533$	−0.0512941	−0.00222179
$534$	30.6165	1.32491
$535$	−26.8073	−1.15898
$536$	8.08320	0.349141
$537$	32.8553	1.41781
$538$	−39.7230	−1.71258
$539$	−5.15025	−0.221837
$540$	−33.7707	−1.45326
$541$	2.93508	0.126189	0.0630944	−	0.998008i	$-0.479903\pi$
$541$	2.93508	0.126189	0.0630944	+	0.998008i	$0.479903\pi$
$542$	−32.1854	−1.38248
$543$	−21.3170	−0.914802
$544$	4.04670	0.173501
$545$	−17.6508	−0.756079
$546$	−0.440505	−0.0188519
$547$	−21.0011	−0.897943	−0.448972	−	0.893546i	$-0.648210\pi$
$547$	−21.0011	−0.897943	−0.448972	+	0.893546i	$0.648210\pi$
$548$	−53.2452	−2.27452
$549$	−8.18559	−0.349353
$550$	1.68828	0.0719884
$551$	−0.185685	−0.00791044
$552$	21.5537	0.917385
$553$	1.28111	0.0544782
$554$	33.5222	1.42422
$555$	33.9260	1.44008
$556$	−69.4732	−2.94632
$557$	−39.5036	−1.67382	−0.836912	−	0.547338i	$-0.815641\pi$
$557$	−39.5036	−1.67382	−0.836912	+	0.547338i	$0.815641\pi$
$558$	12.6934	0.537355
$559$	−0.503551	−0.0212979
$560$	11.6355	0.491691
$561$	4.33300	0.182940
$562$	5.60098	0.236263
$563$	37.4535	1.57848	0.789238	−	0.614087i	$-0.210476\pi$
$563$	37.4535	1.57848	0.789238	+	0.614087i	$0.210476\pi$
$564$	−22.2296	−0.936036
$565$	9.31860	0.392036
$566$	−23.6345	−0.993430
$567$	12.4540	0.523021
$568$	−1.74217	−0.0730999
$569$	−26.3325	−1.10391	−0.551957	−	0.833873i	$-0.686119\pi$
$569$	−26.3325	−1.10391	−0.551957	+	0.833873i	$0.686119\pi$
$570$	31.2892	1.31056
$571$	−25.3768	−1.06199	−0.530994	−	0.847376i	$-0.678181\pi$
$571$	−25.3768	−1.06199	−0.530994	+	0.847376i	$0.678181\pi$
$572$	0.292915	0.0122474
$573$	−35.0820	−1.46557
$574$	−1.83614	−0.0766392
$575$	−1.50969	−0.0629582
$576$	−6.06274	−0.252614
$577$	16.8906	0.703164	0.351582	−	0.936157i	$-0.385644\pi$
$577$	16.8906	0.703164	0.351582	+	0.936157i	$0.385644\pi$
$578$	27.9413	1.16221
$579$	2.92442	0.121535
$580$	−0.523293	−0.0217285
$581$	11.0132	0.456907
$582$	−36.7445	−1.52311
$583$	5.54396	0.229607
$584$	−27.8778	−1.15359
$585$	−0.167838	−0.00693925
$586$	2.96092	0.122315
$587$	20.7093	0.854763	0.427381	−	0.904071i	$-0.359436\pi$
$587$	20.7093	0.854763	0.427381	+	0.904071i	$0.359436\pi$
$588$	47.9355	1.97683
$589$	14.9427	0.615702
$590$	9.33808	0.384443
$591$	−44.2902	−1.82185
$592$	41.0157	1.68573
$593$	−13.0859	−0.537375	−0.268687	−	0.963227i	$-0.586590\pi$
$593$	−13.0859	−0.537375	−0.268687	+	0.963227i	$0.586590\pi$
$594$	−8.79034	−0.360672
$595$	−5.57035	−0.228362
$596$	2.43500	0.0997413
$597$	−7.28148	−0.298011
$598$	−0.387756	−0.0158565
$599$	−21.1444	−0.863935	−0.431968	−	0.901889i	$-0.642181\pi$
$599$	−21.1444	−0.863935	−0.431968	+	0.901889i	$0.642181\pi$
$600$	−8.16501	−0.333335
$601$	−6.07343	−0.247740	−0.123870	−	0.992298i	$-0.539531\pi$
$601$	−6.07343	−0.247740	−0.123870	+	0.992298i	$0.539531\pi$
$602$	−18.0253	−0.734657
$603$	−1.56726	−0.0638237
$604$	87.4541	3.55846
$605$	20.9946	0.853552
$606$	76.4167	3.10422
$607$	8.31464	0.337481	0.168740	−	0.985661i	$-0.446030\pi$
$607$	8.31464	0.337481	0.168740	+	0.985661i	$0.446030\pi$
$608$	5.13805	0.208376
$609$	0.138371	0.00560708
$610$	−40.2016	−1.62771
$611$	0.207803	0.00840682
$612$	−10.3916	−0.420057
$613$	−31.7943	−1.28416	−0.642080	−	0.766637i	$-0.721928\pi$
$613$	−31.7943	−1.28416	−0.642080	+	0.766637i	$0.721928\pi$
$614$	58.4268	2.35791
$615$	−2.71507	−0.109482
$616$	5.44834	0.219520
$617$	1.07286	0.0431918	0.0215959	−	0.999767i	$-0.493125\pi$
$617$	1.07286	0.0431918	0.0215959	+	0.999767i	$0.493125\pi$
$618$	84.5578	3.40142
$619$	23.5029	0.944660	0.472330	−	0.881422i	$-0.343413\pi$
$619$	23.5029	0.944660	0.472330	+	0.881422i	$0.343413\pi$
$620$	42.1111	1.69122
$621$	7.86046	0.315429
$622$	21.7936	0.873845
$623$	−6.92056	−0.277266
$624$	−0.787484	−0.0315246
$625$	−20.6469	−0.825875
$626$	−67.4093	−2.69422
$627$	5.50157	0.219712
$628$	−53.8391	−2.14841
$629$	−19.6357	−0.782927
$630$	−6.00800	−0.239364
$631$	13.4956	0.537250	0.268625	−	0.963245i	$-0.413431\pi$
$631$	13.4956	0.537250	0.268625	+	0.963245i	$0.413431\pi$
$632$	6.09906	0.242607
$633$	50.3040	1.99940
$634$	−23.4113	−0.929783
$635$	−29.8911	−1.18619
$636$	−51.6000	−2.04607
$637$	−0.448103	−0.0177545
$638$	−0.136210	−0.00539262
$639$	0.337791	0.0133628
$640$	−36.7316	−1.45195
$641$	−15.7935	−0.623805	−0.311902	−	0.950114i	$-0.600966\pi$
$641$	−15.7935	−0.623805	−0.311902	+	0.950114i	$0.600966\pi$
$642$	64.9454	2.56319
$643$	−33.0909	−1.30498	−0.652489	−	0.757798i	$-0.726275\pi$
$643$	−33.0909	−1.30498	−0.652489	+	0.757798i	$0.726275\pi$
$644$	−9.37613	−0.369471
$645$	−26.6536	−1.04949
$646$	−18.1096	−0.712513
$647$	−18.1328	−0.712873	−0.356437	−	0.934320i	$-0.616008\pi$
$647$	−18.1328	−0.712873	−0.356437	+	0.934320i	$0.616008\pi$
$648$	59.2909	2.32917
$649$	1.64191	0.0644506
$650$	0.146891	0.00576152
$651$	−11.1352	−0.436422
$652$	−36.1004	−1.41380
$653$	−12.7669	−0.499609	−0.249805	−	0.968296i	$-0.580366\pi$
$653$	−12.7669	−0.499609	−0.249805	+	0.968296i	$0.580366\pi$
$654$	42.7623	1.67214
$655$	10.5398	0.411826
$656$	−3.28244	−0.128158
$657$	5.40525	0.210879
$658$	7.43861	0.289987
$659$	13.4976	0.525793	0.262896	−	0.964824i	$-0.415322\pi$
$659$	13.4976	0.525793	0.262896	+	0.964824i	$0.415322\pi$
$660$	15.5044	0.603508
$661$	−37.3501	−1.45275	−0.726375	−	0.687299i	$-0.758796\pi$
$661$	−37.3501	−1.45275	−0.726375	+	0.687299i	$0.758796\pi$
$662$	11.8377	0.460087
$663$	0.376998	0.0146414
$664$	52.4316	2.03474
$665$	−7.07262	−0.274264
$666$	−21.1784	−0.820648
$667$	0.121801	0.00471617
$668$	76.3562	2.95431
$669$	−53.0737	−2.05195
$670$	−7.69721	−0.297369
$671$	−7.06862	−0.272881
$672$	−3.82884	−0.147701
$673$	−5.23072	−0.201629	−0.100815	−	0.994905i	$-0.532145\pi$
$673$	−5.23072	−0.201629	−0.100815	+	0.994905i	$0.532145\pi$
$674$	11.1458	0.429319
$675$	−2.97772	−0.114612
$676$	−54.0980	−2.08069
$677$	24.8855	0.956428	0.478214	−	0.878243i	$-0.341284\pi$
$677$	24.8855	0.956428	0.478214	+	0.878243i	$0.341284\pi$
$678$	−22.5759	−0.867024
$679$	8.30574	0.318745
$680$	−26.5192	−1.01696
$681$	−51.9733	−1.99162
$682$	10.9613	0.419730
$683$	−17.7356	−0.678634	−0.339317	−	0.940672i	$-0.610196\pi$
$683$	−17.7356	−0.678634	−0.339317	+	0.940672i	$0.610196\pi$
$684$	−13.1942	−0.504492
$685$	26.3459	1.00663
$686$	−35.6453	−1.36094
$687$	−56.2552	−2.14627
$688$	−32.2236	−1.22851
$689$	0.482358	0.0183764
$690$	−20.5244	−0.781352
$691$	−10.3710	−0.394531	−0.197265	−	0.980350i	$-0.563206\pi$
$691$	−10.3710	−0.394531	−0.197265	+	0.980350i	$0.563206\pi$
$692$	−5.17770	−0.196827
$693$	−1.05638	−0.0401287
$694$	16.4857	0.625789
$695$	34.3756	1.30394
$696$	0.658754	0.0249700
$697$	1.57143	0.0595221
$698$	−62.8583	−2.37922
$699$	−20.7400	−0.784458
$700$	3.55189	0.134249
$701$	−20.8767	−0.788502	−0.394251	−	0.919003i	$-0.628996\pi$
$701$	−20.8767	−0.788502	−0.394251	+	0.919003i	$0.628996\pi$
$702$	−0.764813	−0.0288660
$703$	−24.9313	−0.940301
$704$	−5.23545	−0.197318
$705$	10.9993	0.414258
$706$	−67.7422	−2.54951
$707$	−17.2732	−0.649627
$708$	−15.2820	−0.574331
$709$	−24.2175	−0.909506	−0.454753	−	0.890618i	$-0.650273\pi$
$709$	−24.2175	−0.909506	−0.454753	+	0.890618i	$0.650273\pi$
$710$	1.65898	0.0622603
$711$	−1.18255	−0.0443491
$712$	−32.9472	−1.23475
$713$	−9.80177	−0.367079
$714$	13.4952	0.505044
$715$	−0.144936	−0.00542028
$716$	−68.0432	−2.54289
$717$	−3.35463	−0.125281
$718$	79.8616	2.98041
$719$	21.9019	0.816803	0.408401	−	0.912802i	$-0.366086\pi$
$719$	21.9019	0.816803	0.408401	+	0.912802i	$0.366086\pi$
$720$	−10.7404	−0.400271
$721$	−19.1135	−0.711822
$722$	24.1760	0.899737
$723$	7.00936	0.260681
$724$	44.1475	1.64073
$725$	−0.0461411	−0.00171364
$726$	−50.8631	−1.88771
$727$	51.0968	1.89507	0.947537	−	0.319646i	$-0.103564\pi$
$727$	51.0968	1.89507	0.947537	+	0.319646i	$0.103564\pi$
$728$	0.474039	0.0175691
$729$	12.2509	0.453737
$730$	26.5466	0.982533
$731$	15.4266	0.570574
$732$	65.7906	2.43169
$733$	−5.89043	−0.217568	−0.108784	−	0.994065i	$-0.534696\pi$
$733$	−5.89043	−0.217568	−0.108784	+	0.994065i	$0.534696\pi$
$734$	−73.7716	−2.72296
$735$	−23.7187	−0.874877
$736$	−3.37035	−0.124233
$737$	−1.35340	−0.0498530
$738$	1.69489	0.0623898
$739$	−41.7427	−1.53553	−0.767766	−	0.640731i	$-0.778632\pi$
$739$	−41.7427	−1.53553	−0.767766	+	0.640731i	$0.778632\pi$
$740$	−70.2607	−2.58284
$741$	0.478670	0.0175844
$742$	17.2667	0.633880
$743$	−41.6554	−1.52819	−0.764095	−	0.645104i	$-0.776814\pi$
$743$	−41.6554	−1.52819	−0.764095	+	0.645104i	$0.776814\pi$
$744$	−53.0121	−1.94352
$745$	−1.20485	−0.0441421
$746$	−49.1714	−1.80029
$747$	−10.1660	−0.371955
$748$	−8.97364	−0.328109
$749$	−14.6802	−0.536405
$750$	59.1814	2.16100
$751$	−0.632416	−0.0230772	−0.0115386	−	0.999933i	$-0.503673\pi$
$751$	−0.632416	−0.0230772	−0.0115386	+	0.999933i	$0.503673\pi$
$752$	13.2979	0.484924
$753$	−41.8399	−1.52473
$754$	−0.0118511	−0.000431593 0
$755$	−43.2727	−1.57485
$756$	−18.4936	−0.672604
$757$	−4.66181	−0.169436	−0.0847182	−	0.996405i	$-0.526999\pi$
$757$	−4.66181	−0.169436	−0.0847182	+	0.996405i	$0.526999\pi$
$758$	−47.1986	−1.71433
$759$	−3.60880	−0.130991
$760$	−33.6711	−1.22138
$761$	4.79488	0.173814	0.0869071	−	0.996216i	$-0.472302\pi$
$761$	4.79488	0.173814	0.0869071	+	0.996216i	$0.472302\pi$
$762$	72.4163	2.62337
$763$	−9.66598	−0.349932
$764$	72.6548	2.62856
$765$	5.14183	0.185903
$766$	43.4527	1.57001
$767$	0.142856	0.00515824
$768$	65.5805	2.36643
$769$	−16.1022	−0.580660	−0.290330	−	0.956927i	$-0.593765\pi$
$769$	−16.1022	−0.580660	−0.290330	+	0.956927i	$0.593765\pi$
$770$	−5.18817	−0.186969
$771$	−46.9212	−1.68983
$772$	−6.05646	−0.217977
$773$	−39.2141	−1.41043	−0.705217	−	0.708991i	$-0.749150\pi$
$773$	−39.2141	−1.41043	−0.705217	+	0.708991i	$0.749150\pi$
$774$	16.6386	0.598063
$775$	3.71313	0.133380
$776$	39.5417	1.41947
$777$	18.5786	0.666504
$778$	−40.2301	−1.44232
$779$	1.99522	0.0714863
$780$	1.34898	0.0483011
$781$	0.291697	0.0104377
$782$	11.8791	0.424797
$783$	0.240242	0.00858556
$784$	−28.6753	−1.02412
$785$	26.6398	0.950815
$786$	−25.5346	−0.910790
$787$	−14.2267	−0.507127	−0.253564	−	0.967319i	$-0.581603\pi$
$787$	−14.2267	−0.507127	−0.253564	+	0.967319i	$0.581603\pi$
$788$	91.7249	3.26756
$789$	43.6540	1.55413
$790$	−5.80781	−0.206633
$791$	5.10307	0.181444
$792$	−5.02920	−0.178705
$793$	−0.615013	−0.0218397
$794$	43.0508	1.52782
$795$	25.5319	0.905523
$796$	15.0799	0.534494
$797$	−30.0542	−1.06457	−0.532286	−	0.846564i	$-0.678667\pi$
$797$	−30.0542	−1.06457	−0.532286	+	0.846564i	$0.678667\pi$
$798$	17.1347	0.606561
$799$	−6.36618	−0.225219
$800$	1.27676	0.0451404
$801$	6.38816	0.225715
$802$	55.3542	1.95462
$803$	4.66767	0.164718
$804$	12.5966	0.444249
$805$	4.63934	0.163515
$806$	0.953701	0.0335927
$807$	−32.1659	−1.13229
$808$	−82.2339	−2.89298
$809$	−3.80181	−0.133664	−0.0668322	−	0.997764i	$-0.521289\pi$
$809$	−3.80181	−0.133664	−0.0668322	+	0.997764i	$0.521289\pi$
$810$	−56.4596	−1.98379
$811$	−4.24558	−0.149082	−0.0745412	−	0.997218i	$-0.523749\pi$
$811$	−4.24558	−0.149082	−0.0745412	+	0.997218i	$0.523749\pi$
$812$	−0.286566	−0.0100565
$813$	−26.0624	−0.914047
$814$	−18.2885	−0.641012
$815$	17.8626	0.625700
$816$	24.1251	0.844547
$817$	19.5870	0.685262
$818$	75.1329	2.62696
$819$	−0.0919118	−0.00321166
$820$	5.62290	0.196360
$821$	32.0247	1.11767	0.558835	−	0.829279i	$-0.311248\pi$
$821$	32.0247	1.11767	0.558835	+	0.829279i	$0.311248\pi$
$822$	−63.8276	−2.22624
$823$	19.5077	0.679994	0.339997	−	0.940427i	$-0.389574\pi$
$823$	19.5077	0.679994	0.339997	+	0.940427i	$0.389574\pi$
$824$	−90.9948	−3.16996
$825$	1.36709	0.0475961
$826$	5.11374	0.177930
$827$	1.59305	0.0553958	0.0276979	−	0.999616i	$-0.491182\pi$
$827$	1.59305	0.0553958	0.0276979	+	0.999616i	$0.491182\pi$
$828$	8.65482	0.300776
$829$	25.2615	0.877368	0.438684	−	0.898641i	$-0.355445\pi$
$829$	25.2615	0.877368	0.438684	+	0.898641i	$0.355445\pi$
$830$	−49.9279	−1.73302
$831$	27.1448	0.941644
$832$	−0.455516	−0.0157922
$833$	13.7279	0.475644
$834$	−83.2809	−2.88378
$835$	−37.7813	−1.30748
$836$	−11.3937	−0.394061
$837$	−19.3331	−0.668250
$838$	−41.0693	−1.41872
$839$	−50.5653	−1.74571	−0.872855	−	0.487980i	$-0.837734\pi$
$839$	−50.5653	−1.74571	−0.872855	+	0.487980i	$0.837734\pi$
$840$	25.0915	0.865740
$841$	−28.9963	−0.999872
$842$	41.1990	1.41981
$843$	4.53543	0.156208
$844$	−104.179	−3.58601
$845$	26.7679	0.920843
$846$	−6.86636	−0.236070
$847$	11.4971	0.395045
$848$	30.8674	1.05999
$849$	−19.1381	−0.656820
$850$	−4.50009	−0.154352
$851$	16.3539	0.560604
$852$	−2.71495	−0.0930127
$853$	1.96591	0.0673114	0.0336557	−	0.999433i	$-0.489285\pi$
$853$	1.96591	0.0673114	0.0336557	+	0.999433i	$0.489285\pi$
$854$	−22.0152	−0.753346
$855$	6.52852	0.223271
$856$	−69.8893	−2.38877
$857$	39.8018	1.35960	0.679801	−	0.733397i	$-0.262066\pi$
$857$	39.8018	1.35960	0.679801	+	0.733397i	$0.262066\pi$
$858$	0.351132	0.0119874
$859$	50.6159	1.72699	0.863495	−	0.504357i	$-0.168270\pi$
$859$	50.6159	1.72699	0.863495	+	0.504357i	$0.168270\pi$
$860$	55.1996	1.88229
$861$	−1.48683	−0.0506710
$862$	64.7553	2.20557
$863$	6.64784	0.226295	0.113148	−	0.993578i	$-0.463907\pi$
$863$	6.64784	0.226295	0.113148	+	0.993578i	$0.463907\pi$
$864$	−6.64771	−0.226160
$865$	2.56195	0.0871088
$866$	−13.5604	−0.460801
$867$	22.6257	0.768408
$868$	23.0610	0.782740
$869$	−1.02118	−0.0346413
$870$	−0.627297	−0.0212674
$871$	−0.117754	−0.00398993
$872$	−46.0175	−1.55835
$873$	−7.66678	−0.259481
$874$	15.0828	0.510184
$875$	−13.3774	−0.452237
$876$	−43.4440	−1.46784
$877$	−35.8073	−1.20913	−0.604564	−	0.796557i	$-0.706653\pi$
$877$	−35.8073	−1.20913	−0.604564	+	0.796557i	$0.706653\pi$
$878$	−64.4453	−2.17492
$879$	2.39763	0.0808699
$880$	−9.27481	−0.312654
$881$	−43.4433	−1.46364	−0.731822	−	0.681496i	$-0.761330\pi$
$881$	−43.4433	−1.46364	−0.731822	+	0.681496i	$0.761330\pi$
$882$	14.8065	0.498560
$883$	−5.78393	−0.194645	−0.0973223	−	0.995253i	$-0.531028\pi$
$883$	−5.78393	−0.194645	−0.0973223	+	0.995253i	$0.531028\pi$
$884$	−0.780762	−0.0262599
$885$	7.56157	0.254179
$886$	27.5737	0.926356
$887$	11.3807	0.382125	0.191063	−	0.981578i	$-0.438807\pi$
$887$	11.3807	0.382125	0.191063	+	0.981578i	$0.438807\pi$
$888$	88.4486	2.96814
$889$	−16.3690	−0.548998
$890$	31.3739	1.05166
$891$	−9.92726	−0.332576
$892$	109.915	3.68024
$893$	−8.08308	−0.270490
$894$	2.91895	0.0976243
$895$	33.6680	1.12540
$896$	−20.1150	−0.671996
$897$	−0.313988	−0.0104837
$898$	−53.4934	−1.78510
$899$	−0.299576	−0.00999141
$900$	−3.27864	−0.109288
$901$	−14.7774	−0.492305
$902$	1.46361	0.0487329
$903$	−14.5961	−0.485728
$904$	24.2945	0.808024
$905$	−21.8444	−0.726132
$906$	104.836	3.48293
$907$	51.1804	1.69942	0.849709	−	0.527252i	$-0.176778\pi$
$907$	51.1804	1.69942	0.849709	+	0.527252i	$0.176778\pi$
$908$	107.637	3.57205
$909$	15.9444	0.528843
$910$	−0.451403	−0.0149638
$911$	57.9014	1.91836	0.959179	−	0.282800i	$-0.0912632\pi$
$911$	57.9014	1.91836	0.959179	+	0.282800i	$0.0912632\pi$
$912$	30.6314	1.01431
$913$	−8.77879	−0.290535
$914$	71.0329	2.34956
$915$	−32.5535	−1.07618
$916$	116.504	3.84942
$917$	5.77185	0.190603
$918$	23.4305	0.773323
$919$	9.89923	0.326545	0.163273	−	0.986581i	$-0.447795\pi$
$919$	9.89923	0.326545	0.163273	+	0.986581i	$0.447795\pi$
$920$	22.0869	0.728182
$921$	47.3115	1.55897
$922$	40.7071	1.34062
$923$	0.0253794	0.000835374 0
$924$	8.49054	0.279318
$925$	−6.19521	−0.203697
$926$	84.7129	2.78384
$927$	17.6431	0.579474
$928$	−0.103009	−0.00338145
$929$	19.5463	0.641294	0.320647	−	0.947199i	$-0.396100\pi$
$929$	19.5463	0.641294	0.320647	+	0.947199i	$0.396100\pi$
$930$	50.4807	1.65533
$931$	17.4302	0.571252
$932$	42.9524	1.40695
$933$	17.6475	0.577754
$934$	8.92334	0.291981
$935$	4.44019	0.145210
$936$	−0.437571	−0.0143025
$937$	−41.4214	−1.35318	−0.676589	−	0.736361i	$-0.736543\pi$
$937$	−41.4214	−1.35318	−0.676589	+	0.736361i	$0.736543\pi$
$938$	−4.21516	−0.137630
$939$	−54.5851	−1.78132
$940$	−22.7795	−0.742987
$941$	1.65772	0.0540401	0.0270201	−	0.999635i	$-0.491398\pi$
$941$	1.65772	0.0540401	0.0270201	+	0.999635i	$0.491398\pi$
$942$	−64.5396	−2.10281
$943$	−1.30878	−0.0426199
$944$	9.14174	0.297538
$945$	9.15069	0.297672
$946$	14.3682	0.467150
$947$	−18.9035	−0.614282	−0.307141	−	0.951664i	$-0.599372\pi$
$947$	−18.9035	−0.614282	−0.307141	+	0.951664i	$0.599372\pi$
$948$	9.50460	0.308695
$949$	0.406116	0.0131831
$950$	−5.71371	−0.185377
$951$	−18.9575	−0.614739
$952$	−14.5225	−0.470677
$953$	19.3103	0.625521	0.312760	−	0.949832i	$-0.398746\pi$
$953$	19.3103	0.625521	0.312760	+	0.949832i	$0.398746\pi$
$954$	−15.9384	−0.516024
$955$	−35.9499	−1.16331
$956$	6.94743	0.224696
$957$	−0.110297	−0.00356540
$958$	79.2517	2.56050
$959$	14.4276	0.465892
$960$	−24.1111	−0.778181
$961$	−6.89215	−0.222327
$962$	−1.59121	−0.0513027
$963$	13.5509	0.436672
$964$	−14.5164	−0.467541
$965$	2.99676	0.0964691
$966$	−11.2396	−0.361629
$967$	29.9913	0.964455	0.482227	−	0.876046i	$-0.339828\pi$
$967$	29.9913	0.964455	0.482227	+	0.876046i	$0.339828\pi$
$968$	54.7351	1.75925
$969$	−14.6644	−0.471087
$970$	−37.6535	−1.20898
$971$	14.2161	0.456217	0.228108	−	0.973636i	$-0.426746\pi$
$971$	14.2161	0.456217	0.228108	+	0.973636i	$0.426746\pi$
$972$	43.2175	1.38620
$973$	18.8248	0.603496
$974$	24.6117	0.788609
$975$	0.118946	0.00380930
$976$	−39.3563	−1.25976
$977$	−21.9841	−0.703334	−0.351667	−	0.936125i	$-0.614385\pi$
$977$	−21.9841	−0.703334	−0.351667	+	0.936125i	$0.614385\pi$
$978$	−43.2754	−1.38379
$979$	5.51646	0.176307
$980$	49.1214	1.56912
$981$	8.92238	0.284870
$982$	−16.9785	−0.541805
$983$	−37.4292	−1.19381	−0.596903	−	0.802313i	$-0.703602\pi$
$983$	−37.4292	−1.19381	−0.596903	+	0.802313i	$0.703602\pi$
$984$	−7.07846	−0.225653
$985$	−45.3858	−1.44611
$986$	0.363067	0.0115624
$987$	6.02346	0.191729
$988$	−0.991325	−0.0315382
$989$	−12.8483	−0.408551
$990$	4.78905	0.152206
$991$	16.0295	0.509193	0.254597	−	0.967047i	$-0.418057\pi$
$991$	16.0295	0.509193	0.254597	+	0.967047i	$0.418057\pi$
$992$	8.28951	0.263192
$993$	9.58569	0.304193
$994$	0.908492	0.0288156
$995$	−7.46161	−0.236549
$996$	81.7079	2.58901
$997$	−52.8151	−1.67267	−0.836335	−	0.548219i	$-0.815306\pi$
$997$	−52.8151	−1.67267	−0.836335	+	0.548219i	$0.815306\pi$
$998$	−20.3517	−0.644220
$999$	32.2565	1.02055

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6011.2.a.e.1.17	✓	221

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6011.2.a.e.1.17	✓	221	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:	\( N \)	\(=\)	\( 6011 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6011.a (trivial)

\(f(q)\)	\(=\)	\(q-2.48261 q^{2} -2.01031 q^{3} +4.16334 q^{4} -2.06004 q^{5} +4.99080 q^{6} -1.12812 q^{7} -5.37073 q^{8} +1.04134 q^{9} +O(q^{10})\)	\(q-2.48261 q^{2} -2.01031 q^{3} +4.16334 q^{4} -2.06004 q^{5} +4.99080 q^{6} -1.12812 q^{7} -5.37073 q^{8} +1.04134 q^{9} +5.11427 q^{10} +0.899239 q^{11} -8.36960 q^{12} +0.0782392 q^{13} +2.80068 q^{14} +4.14131 q^{15} +5.00674 q^{16} -2.39691 q^{17} -2.58523 q^{18} -3.04333 q^{19} -8.57664 q^{20} +2.26787 q^{21} -2.23246 q^{22} +1.99630 q^{23} +10.7968 q^{24} -0.756242 q^{25} -0.194237 q^{26} +3.93752 q^{27} -4.69676 q^{28} +0.0610137 q^{29} -10.2812 q^{30} -4.90997 q^{31} -1.68830 q^{32} -1.80775 q^{33} +5.95059 q^{34} +2.32397 q^{35} +4.33544 q^{36} +8.19210 q^{37} +7.55540 q^{38} -0.157285 q^{39} +11.0639 q^{40} -0.655606 q^{41} -5.63023 q^{42} -6.43604 q^{43} +3.74384 q^{44} -2.14519 q^{45} -4.95603 q^{46} +2.65600 q^{47} -10.0651 q^{48} -5.72734 q^{49} +1.87745 q^{50} +4.81852 q^{51} +0.325737 q^{52} +6.16517 q^{53} -9.77531 q^{54} -1.85247 q^{55} +6.05884 q^{56} +6.11803 q^{57} -0.151473 q^{58} +1.82589 q^{59} +17.2417 q^{60} -7.86067 q^{61} +12.1895 q^{62} -1.17475 q^{63} -5.82209 q^{64} -0.161176 q^{65} +4.48793 q^{66} -1.50505 q^{67} -9.97916 q^{68} -4.01317 q^{69} -5.76952 q^{70} +0.324382 q^{71} -5.59273 q^{72} +5.19069 q^{73} -20.3378 q^{74} +1.52028 q^{75} -12.6704 q^{76} -1.01445 q^{77} +0.390477 q^{78} -1.13561 q^{79} -10.3141 q^{80} -11.0396 q^{81} +1.62761 q^{82} -9.76247 q^{83} +9.44192 q^{84} +4.93773 q^{85} +15.9782 q^{86} -0.122656 q^{87} -4.82957 q^{88} +6.13459 q^{89} +5.32567 q^{90} -0.0882634 q^{91} +8.31127 q^{92} +9.87056 q^{93} -6.59380 q^{94} +6.26938 q^{95} +3.39400 q^{96} -7.36245 q^{97} +14.2187 q^{98} +0.936409 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 221 q - 15 q^{2} - 17 q^{3} + 189 q^{4} - 32 q^{5} - 33 q^{6} - 40 q^{7} - 39 q^{8} + 176 q^{9}+O(q^{10}) \) 221 * q - 15 * q^2 - 17 * q^3 + 189 * q^4 - 32 * q^5 - 33 * q^6 - 40 * q^7 - 39 * q^8 + 176 * q^9	\( 221 q - 15 q^{2} - 17 q^{3} + 189 q^{4} - 32 q^{5} - 33 q^{6} - 40 q^{7} - 39 q^{8} + 176 q^{9} - 61 q^{10} - 50 q^{11} - 43 q^{12} - 87 q^{13} - 41 q^{14} - 62 q^{15} + 129 q^{16} - 29 q^{17} - 61 q^{18} - 107 q^{19} - 59 q^{20} - 163 q^{21} - 70 q^{22} - 31 q^{23} - 98 q^{24} + 119 q^{25} - 23 q^{26} - 41 q^{27} - 112 q^{28} - 152 q^{29} - 66 q^{30} - 117 q^{31} - 93 q^{32} - 60 q^{33} - 80 q^{34} - 21 q^{35} + 92 q^{36} - 231 q^{37} + 2 q^{38} - 81 q^{39} - 143 q^{40} - 81 q^{41} - 6 q^{42} - 126 q^{43} - 115 q^{44} - 156 q^{45} - 205 q^{46} - 4 q^{47} - 55 q^{48} + 103 q^{49} - 61 q^{50} - 106 q^{51} - 164 q^{52} - 87 q^{53} - 110 q^{54} - 62 q^{55} - 73 q^{56} - 136 q^{57} - 128 q^{58} - 76 q^{59} - 148 q^{60} - 345 q^{61} + 5 q^{62} - 74 q^{63} - 25 q^{64} - 110 q^{65} - 34 q^{66} - 104 q^{67} - 48 q^{68} - 133 q^{69} - 92 q^{70} - 39 q^{71} - 177 q^{72} - 175 q^{73} - 44 q^{74} - 23 q^{75} - 268 q^{76} - 81 q^{77} - 19 q^{78} - 272 q^{79} - 60 q^{80} + 77 q^{81} - 13 q^{82} - 40 q^{83} - 221 q^{84} - 376 q^{85} - 82 q^{86} - 3 q^{87} - 234 q^{88} - 92 q^{89} - 91 q^{90} - 205 q^{91} - 11 q^{92} - 125 q^{93} - 126 q^{94} - 56 q^{95} - 148 q^{96} - 133 q^{97} - 4 q^{98} - 195 q^{99}+O(q^{100}) \) 221 * q - 15 * q^2 - 17 * q^3 + 189 * q^4 - 32 * q^5 - 33 * q^6 - 40 * q^7 - 39 * q^8 + 176 * q^9 - 61 * q^10 - 50 * q^11 - 43 * q^12 - 87 * q^13 - 41 * q^14 - 62 * q^15 + 129 * q^16 - 29 * q^17 - 61 * q^18 - 107 * q^19 - 59 * q^20 - 163 * q^21 - 70 * q^22 - 31 * q^23 - 98 * q^24 + 119 * q^25 - 23 * q^26 - 41 * q^27 - 112 * q^28 - 152 * q^29 - 66 * q^30 - 117 * q^31 - 93 * q^32 - 60 * q^33 - 80 * q^34 - 21 * q^35 + 92 * q^36 - 231 * q^37 + 2 * q^38 - 81 * q^39 - 143 * q^40 - 81 * q^41 - 6 * q^42 - 126 * q^43 - 115 * q^44 - 156 * q^45 - 205 * q^46 - 4 * q^47 - 55 * q^48 + 103 * q^49 - 61 * q^50 - 106 * q^51 - 164 * q^52 - 87 * q^53 - 110 * q^54 - 62 * q^55 - 73 * q^56 - 136 * q^57 - 128 * q^58 - 76 * q^59 - 148 * q^60 - 345 * q^61 + 5 * q^62 - 74 * q^63 - 25 * q^64 - 110 * q^65 - 34 * q^66 - 104 * q^67 - 48 * q^68 - 133 * q^69 - 92 * q^70 - 39 * q^71 - 177 * q^72 - 175 * q^73 - 44 * q^74 - 23 * q^75 - 268 * q^76 - 81 * q^77 - 19 * q^78 - 272 * q^79 - 60 * q^80 + 77 * q^81 - 13 * q^82 - 40 * q^83 - 221 * q^84 - 376 * q^85 - 82 * q^86 - 3 * q^87 - 234 * q^88 - 92 * q^89 - 91 * q^90 - 205 * q^91 - 11 * q^92 - 125 * q^93 - 126 * q^94 - 56 * q^95 - 148 * q^96 - 133 * q^97 - 4 * q^98 - 195 * q^99

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