LMFDB - Embedded newform 6047.2.a.a.1.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6047,2,Mod(1,6047)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6047, 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("6047.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6047 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6047.a (trivial)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$48.2855381023$
Analytic rank:	$1$
Dimension:	$217$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.11
Character	$\chi$	$=$	6047.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.59272 q^{2} +3.24215 q^{3} +4.72220 q^{4} -1.12445 q^{5} -8.40598 q^{6} -0.119273 q^{7} -7.05789 q^{8} +7.51153 q^{9} +O(q^{10})$	\(q-2.59272 q^{2} +3.24215 q^{3} +4.72220 q^{4} -1.12445 q^{5} -8.40598 q^{6} -0.119273 q^{7} -7.05789 q^{8} +7.51153 q^{9} +2.91540 q^{10} -1.92359 q^{11} +15.3101 q^{12} +3.49979 q^{13} +0.309241 q^{14} -3.64565 q^{15} +8.85475 q^{16} +0.738832 q^{17} -19.4753 q^{18} -7.27821 q^{19} -5.30990 q^{20} -0.386700 q^{21} +4.98733 q^{22} +7.57491 q^{23} -22.8827 q^{24} -3.73560 q^{25} -9.07397 q^{26} +14.6270 q^{27} -0.563229 q^{28} -3.31106 q^{29} +9.45215 q^{30} -10.0715 q^{31} -8.84210 q^{32} -6.23657 q^{33} -1.91558 q^{34} +0.134117 q^{35} +35.4709 q^{36} -10.2837 q^{37} +18.8704 q^{38} +11.3468 q^{39} +7.93628 q^{40} +1.50645 q^{41} +1.00260 q^{42} -0.406611 q^{43} -9.08357 q^{44} -8.44637 q^{45} -19.6396 q^{46} +1.47364 q^{47} +28.7084 q^{48} -6.98577 q^{49} +9.68537 q^{50} +2.39540 q^{51} +16.5267 q^{52} -8.19066 q^{53} -37.9238 q^{54} +2.16299 q^{55} +0.841814 q^{56} -23.5970 q^{57} +8.58464 q^{58} -12.0697 q^{59} -17.2155 q^{60} -3.82139 q^{61} +26.1126 q^{62} -0.895920 q^{63} +5.21559 q^{64} -3.93535 q^{65} +16.1697 q^{66} -5.32546 q^{67} +3.48891 q^{68} +24.5590 q^{69} -0.347727 q^{70} -11.2620 q^{71} -53.0156 q^{72} -4.10897 q^{73} +26.6627 q^{74} -12.1114 q^{75} -34.3691 q^{76} +0.229432 q^{77} -29.4191 q^{78} -4.08254 q^{79} -9.95677 q^{80} +24.8885 q^{81} -3.90581 q^{82} +3.38046 q^{83} -1.82607 q^{84} -0.830783 q^{85} +1.05423 q^{86} -10.7349 q^{87} +13.5765 q^{88} +2.04759 q^{89} +21.8991 q^{90} -0.417429 q^{91} +35.7702 q^{92} -32.6533 q^{93} -3.82075 q^{94} +8.18401 q^{95} -28.6674 q^{96} -1.22688 q^{97} +18.1122 q^{98} -14.4491 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 217 q - 20 q^{2} - 27 q^{3} + 184 q^{4} - 19 q^{5} - 17 q^{6} - 48 q^{7} - 57 q^{8} + 152 q^{9}+O(q^{10}) $ 217 * q - 20 * q^2 - 27 * q^3 + 184 * q^4 - 19 * q^5 - 17 * q^6 - 48 * q^7 - 57 * q^8 + 152 * q^9	\( 217 q - 20 q^{2} - 27 q^{3} + 184 q^{4} - 19 q^{5} - 17 q^{6} - 48 q^{7} - 57 q^{8} + 152 q^{9} - 46 q^{10} - 32 q^{11} - 72 q^{12} - 80 q^{13} - 22 q^{14} - 43 q^{15} + 122 q^{16} - 61 q^{17} - 88 q^{18} - 43 q^{19} - 41 q^{20} - 61 q^{21} - 93 q^{22} - 60 q^{23} - 41 q^{24} + 26 q^{25} - 9 q^{26} - 93 q^{27} - 126 q^{28} - 47 q^{29} - 36 q^{30} - 100 q^{31} - 114 q^{32} - 133 q^{33} - 75 q^{34} - 37 q^{35} + 75 q^{36} - 264 q^{37} - 35 q^{38} - 47 q^{39} - 118 q^{40} - 72 q^{41} - 64 q^{42} - 107 q^{43} - 59 q^{44} - 69 q^{45} - 111 q^{46} - 54 q^{47} - 135 q^{48} + 33 q^{49} - 42 q^{50} - 26 q^{51} - 173 q^{52} - 103 q^{53} - 28 q^{54} - 78 q^{55} - 44 q^{56} - 205 q^{57} - 189 q^{58} - 38 q^{59} - 105 q^{60} - 108 q^{61} - 14 q^{62} - 116 q^{63} + 39 q^{64} - 146 q^{65} + 5 q^{66} - 206 q^{67} - 62 q^{68} - 55 q^{69} - 125 q^{70} - 78 q^{71} - 225 q^{72} - 326 q^{73} + 3 q^{74} - 95 q^{75} - 84 q^{76} - 79 q^{77} - 86 q^{78} - 117 q^{79} - 39 q^{80} + q^{81} - 96 q^{82} - 23 q^{83} - 57 q^{84} - 224 q^{85} - 7 q^{86} - 45 q^{87} - 250 q^{88} - 104 q^{89} - 36 q^{90} - 96 q^{91} - 137 q^{92} - 155 q^{93} - 48 q^{94} - 38 q^{95} - 33 q^{96} - 447 q^{97} - 46 q^{98} - 94 q^{99}+O(q^{100}) \) 217 * q - 20 * q^2 - 27 * q^3 + 184 * q^4 - 19 * q^5 - 17 * q^6 - 48 * q^7 - 57 * q^8 + 152 * q^9 - 46 * q^10 - 32 * q^11 - 72 * q^12 - 80 * q^13 - 22 * q^14 - 43 * q^15 + 122 * q^16 - 61 * q^17 - 88 * q^18 - 43 * q^19 - 41 * q^20 - 61 * q^21 - 93 * q^22 - 60 * q^23 - 41 * q^24 + 26 * q^25 - 9 * q^26 - 93 * q^27 - 126 * q^28 - 47 * q^29 - 36 * q^30 - 100 * q^31 - 114 * q^32 - 133 * q^33 - 75 * q^34 - 37 * q^35 + 75 * q^36 - 264 * q^37 - 35 * q^38 - 47 * q^39 - 118 * q^40 - 72 * q^41 - 64 * q^42 - 107 * q^43 - 59 * q^44 - 69 * q^45 - 111 * q^46 - 54 * q^47 - 135 * q^48 + 33 * q^49 - 42 * q^50 - 26 * q^51 - 173 * q^52 - 103 * q^53 - 28 * q^54 - 78 * q^55 - 44 * q^56 - 205 * q^57 - 189 * q^58 - 38 * q^59 - 105 * q^60 - 108 * q^61 - 14 * q^62 - 116 * q^63 + 39 * q^64 - 146 * q^65 + 5 * q^66 - 206 * q^67 - 62 * q^68 - 55 * q^69 - 125 * q^70 - 78 * q^71 - 225 * q^72 - 326 * q^73 + 3 * q^74 - 95 * q^75 - 84 * q^76 - 79 * q^77 - 86 * q^78 - 117 * q^79 - 39 * q^80 + q^81 - 96 * q^82 - 23 * q^83 - 57 * q^84 - 224 * q^85 - 7 * q^86 - 45 * q^87 - 250 * q^88 - 104 * q^89 - 36 * q^90 - 96 * q^91 - 137 * q^92 - 155 * q^93 - 48 * q^94 - 38 * q^95 - 33 * q^96 - 447 * q^97 - 46 * q^98 - 94 * 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 $

$2$	−2.59272	−1.83333	−0.916665	−	0.399657i	$-0.869129\pi$
$2$	−2.59272	−1.83333	−0.916665	+	0.399657i	$0.869129\pi$
$3$	3.24215	1.87186	0.935928	−	0.352192i	$-0.114564\pi$
$3$	3.24215	1.87186	0.935928	+	0.352192i	$0.114564\pi$
$4$	4.72220	2.36110
$5$	−1.12445	−0.502871	−0.251436	−	0.967874i	$-0.580903\pi$
$5$	−1.12445	−0.502871	−0.251436	+	0.967874i	$0.580903\pi$
$6$	−8.40598	−3.43173
$7$	−0.119273	−0.0450808	−0.0225404	−	0.999746i	$-0.507175\pi$
$7$	−0.119273	−0.0450808	−0.0225404	+	0.999746i	$0.507175\pi$
$8$	−7.05789	−2.49534
$9$	7.51153	2.50384
$10$	2.91540	0.921929
$11$	−1.92359	−0.579984	−0.289992	−	0.957029i	$-0.593653\pi$
$11$	−1.92359	−0.579984	−0.289992	+	0.957029i	$0.593653\pi$
$12$	15.3101	4.41964
$13$	3.49979	0.970666	0.485333	−	0.874329i	$-0.338698\pi$
$13$	3.49979	0.970666	0.485333	+	0.874329i	$0.338698\pi$
$14$	0.309241	0.0826480
$15$	−3.64565	−0.941303
$16$	8.85475	2.21369
$17$	0.738832	0.179193	0.0895966	−	0.995978i	$-0.471442\pi$
$17$	0.738832	0.179193	0.0895966	+	0.995978i	$0.471442\pi$
$18$	−19.4753	−4.59037
$19$	−7.27821	−1.66974	−0.834868	−	0.550451i	$-0.814456\pi$
$19$	−7.27821	−1.66974	−0.834868	+	0.550451i	$0.814456\pi$
$20$	−5.30990	−1.18733
$21$	−0.386700	−0.0843848
$22$	4.98733	1.06330
$23$	7.57491	1.57948	0.789739	−	0.613443i	$-0.210216\pi$
$23$	7.57491	1.57948	0.789739	+	0.613443i	$0.210216\pi$
$24$	−22.8827	−4.67092
$25$	−3.73560	−0.747120
$26$	−9.07397	−1.77955
$27$	14.6270	2.81498
$28$	−0.563229	−0.106440
$29$	−3.31106	−0.614848	−0.307424	−	0.951573i	$-0.599467\pi$
$29$	−3.31106	−0.614848	−0.307424	+	0.951573i	$0.599467\pi$
$30$	9.45215	1.72572
$31$	−10.0715	−1.80890	−0.904448	−	0.426583i	$-0.859717\pi$
$31$	−10.0715	−1.80890	−0.904448	+	0.426583i	$0.859717\pi$
$32$	−8.84210	−1.56308
$33$	−6.23657	−1.08565
$34$	−1.91558	−0.328520
$35$	0.134117	0.0226699
$36$	35.4709	5.91182
$37$	−10.2837	−1.69062	−0.845312	−	0.534273i	$-0.820585\pi$
$37$	−10.2837	−1.69062	−0.845312	+	0.534273i	$0.820585\pi$
$38$	18.8704	3.06118
$39$	11.3468	1.81695
$40$	7.93628	1.25484
$41$	1.50645	0.235268	0.117634	−	0.993057i	$-0.462469\pi$
$41$	1.50645	0.235268	0.117634	+	0.993057i	$0.462469\pi$
$42$	1.00260	0.154705
$43$	−0.406611	−0.0620075	−0.0310038	−	0.999519i	$-0.509870\pi$
$43$	−0.406611	−0.0620075	−0.0310038	+	0.999519i	$0.509870\pi$
$44$	−9.08357	−1.36940
$45$	−8.44637	−1.25911
$46$	−19.6396	−2.89571
$47$	1.47364	0.214953	0.107477	−	0.994208i	$-0.465723\pi$
$47$	1.47364	0.214953	0.107477	+	0.994208i	$0.465723\pi$
$48$	28.7084	4.14370
$49$	−6.98577	−0.997968
$50$	9.68537	1.36972
$51$	2.39540	0.335424
$52$	16.5267	2.29184
$53$	−8.19066	−1.12507	−0.562537	−	0.826772i	$-0.690174\pi$
$53$	−8.19066	−1.12507	−0.562537	+	0.826772i	$0.690174\pi$
$54$	−37.9238	−5.16078
$55$	2.16299	0.291658
$56$	0.841814	0.112492
$57$	−23.5970	−3.12550
$58$	8.58464	1.12722
$59$	−12.0697	−1.57134	−0.785670	−	0.618645i	$-0.787682\pi$
$59$	−12.0697	−1.57134	−0.785670	+	0.618645i	$0.787682\pi$
$60$	−17.2155	−2.22251
$61$	−3.82139	−0.489279	−0.244640	−	0.969614i	$-0.578670\pi$
$61$	−3.82139	−0.489279	−0.244640	+	0.969614i	$0.578670\pi$
$62$	26.1126	3.31630
$63$	−0.895920	−0.112875
$64$	5.21559	0.651948
$65$	−3.93535	−0.488120
$66$	16.1697	1.99035
$67$	−5.32546	−0.650609	−0.325304	−	0.945609i	$-0.605467\pi$
$67$	−5.32546	−0.650609	−0.325304	+	0.945609i	$0.605467\pi$
$68$	3.48891	0.423093
$69$	24.5590	2.95656
$70$	−0.347727	−0.0415613
$71$	−11.2620	−1.33655	−0.668276	−	0.743913i	$-0.732967\pi$
$71$	−11.2620	−1.33655	−0.668276	+	0.743913i	$0.732967\pi$
$72$	−53.0156	−6.24795
$73$	−4.10897	−0.480918	−0.240459	−	0.970659i	$-0.577298\pi$
$73$	−4.10897	−0.480918	−0.240459	+	0.970659i	$0.577298\pi$
$74$	26.6627	3.09947
$75$	−12.1114	−1.39850
$76$	−34.3691	−3.94241
$77$	0.229432	0.0261462
$78$	−29.4191	−3.33106
$79$	−4.08254	−0.459321	−0.229661	−	0.973271i	$-0.573762\pi$
$79$	−4.08254	−0.459321	−0.229661	+	0.973271i	$0.573762\pi$
$80$	−9.95677	−1.11320
$81$	24.8885	2.76539
$82$	−3.90581	−0.431324
$83$	3.38046	0.371054	0.185527	−	0.982639i	$-0.440601\pi$
$83$	3.38046	0.371054	0.185527	+	0.982639i	$0.440601\pi$
$84$	−1.82607	−0.199241
$85$	−0.830783	−0.0901111
$86$	1.05423	0.113680
$87$	−10.7349	−1.15091
$88$	13.5765	1.44726
$89$	2.04759	0.217044	0.108522	−	0.994094i	$-0.465388\pi$
$89$	2.04759	0.217044	0.108522	+	0.994094i	$0.465388\pi$
$90$	21.8991	2.30837
$91$	−0.417429	−0.0437584
$92$	35.7702	3.72930
$93$	−32.6533	−3.38599
$94$	−3.82075	−0.394080
$95$	8.18401	0.839662
$96$	−28.6674	−2.92585
$97$	−1.22688	−0.124571	−0.0622853	−	0.998058i	$-0.519839\pi$
$97$	−1.22688	−0.124571	−0.0622853	+	0.998058i	$0.519839\pi$
$98$	18.1122	1.82960
$99$	−14.4491	−1.45219
$100$	−17.6402	−1.76402
$101$	−1.22866	−0.122256	−0.0611279	−	0.998130i	$-0.519470\pi$
$101$	−1.22866	−0.122256	−0.0611279	+	0.998130i	$0.519470\pi$
$102$	−6.21061	−0.614942
$103$	8.78154	0.865271	0.432635	−	0.901569i	$-0.357584\pi$
$103$	8.78154	0.865271	0.432635	+	0.901569i	$0.357584\pi$
$104$	−24.7011	−2.42214
$105$	0.434826	0.0424347
$106$	21.2361	2.06263
$107$	4.80918	0.464921	0.232461	−	0.972606i	$-0.425322\pi$
$107$	4.80918	0.464921	0.232461	+	0.972606i	$0.425322\pi$
$108$	69.0718	6.64644
$109$	5.38197	0.515499	0.257750	−	0.966212i	$-0.417019\pi$
$109$	5.38197	0.515499	0.257750	+	0.966212i	$0.417019\pi$
$110$	−5.60803	−0.534704
$111$	−33.3412	−3.16460
$112$	−1.05613	−0.0997949
$113$	9.48292	0.892079	0.446039	−	0.895013i	$-0.352834\pi$
$113$	9.48292	0.892079	0.446039	+	0.895013i	$0.352834\pi$
$114$	61.1805	5.73008
$115$	−8.51765	−0.794275
$116$	−15.6355	−1.45172
$117$	26.2887	2.43040
$118$	31.2933	2.88079
$119$	−0.0881225	−0.00807818
$120$	25.7306	2.34887
$121$	−7.29980	−0.663618
$122$	9.90780	0.897010
$123$	4.88414	0.440388
$124$	−47.5597	−4.27098
$125$	9.82279	0.878577
$126$	2.32287	0.206938
$127$	−4.00153	−0.355078	−0.177539	−	0.984114i	$-0.556814\pi$
$127$	−4.00153	−0.355078	−0.177539	+	0.984114i	$0.556814\pi$
$128$	4.16164	0.367841
$129$	−1.31829	−0.116069
$130$	10.2033	0.894885
$131$	12.6811	1.10795	0.553974	−	0.832534i	$-0.313111\pi$
$131$	12.6811	1.10795	0.553974	+	0.832534i	$0.313111\pi$
$132$	−29.4503	−2.56332
$133$	0.868091	0.0752730
$134$	13.8074	1.19278
$135$	−16.4475	−1.41557
$136$	−5.21460	−0.447148
$137$	8.03867	0.686790	0.343395	−	0.939191i	$-0.388423\pi$
$137$	8.03867	0.686790	0.343395	+	0.939191i	$0.388423\pi$
$138$	−63.6746	−5.42034
$139$	7.81365	0.662745	0.331372	−	0.943500i	$-0.392488\pi$
$139$	7.81365	0.662745	0.331372	+	0.943500i	$0.392488\pi$
$140$	0.633326	0.0535258
$141$	4.77778	0.402361
$142$	29.1992	2.45034
$143$	−6.73215	−0.562971
$144$	66.5127	5.54273
$145$	3.72313	0.309189
$146$	10.6534	0.881682
$147$	−22.6489	−1.86805
$148$	−48.5615	−3.99173
$149$	16.8025	1.37651	0.688255	−	0.725468i	$-0.258377\pi$
$149$	16.8025	1.37651	0.688255	+	0.725468i	$0.258377\pi$
$150$	31.4014	2.56391
$151$	−0.499415	−0.0406418	−0.0203209	−	0.999794i	$-0.506469\pi$
$151$	−0.499415	−0.0406418	−0.0203209	+	0.999794i	$0.506469\pi$
$152$	51.3688	4.16656
$153$	5.54976	0.448671
$154$	−0.594852	−0.0479346
$155$	11.3250	0.909643
$156$	53.5820	4.28999
$157$	7.32774	0.584818	0.292409	−	0.956293i	$-0.405543\pi$
$157$	7.32774	0.584818	0.292409	+	0.956293i	$0.405543\pi$
$158$	10.5849	0.842087
$159$	−26.5553	−2.10597
$160$	9.94254	0.786027
$161$	−0.903480	−0.0712042
$162$	−64.5289	−5.06987
$163$	−13.9224	−1.09049	−0.545244	−	0.838278i	$-0.683563\pi$
$163$	−13.9224	−1.09049	−0.545244	+	0.838278i	$0.683563\pi$
$164$	7.11376	0.555491
$165$	7.01274	0.545941
$166$	−8.76459	−0.680264
$167$	17.3960	1.34615	0.673073	−	0.739576i	$-0.264974\pi$
$167$	17.3960	1.34615	0.673073	+	0.739576i	$0.264974\pi$
$168$	2.72929	0.210569
$169$	−0.751497	−0.0578074
$170$	2.15399	0.165203
$171$	−54.6705	−4.18075
$172$	−1.92010	−0.146406
$173$	−5.99080	−0.455472	−0.227736	−	0.973723i	$-0.573132\pi$
$173$	−5.99080	−0.455472	−0.227736	+	0.973723i	$0.573132\pi$
$174$	27.8327	2.10999
$175$	0.445555	0.0336808
$176$	−17.0329	−1.28390
$177$	−39.1318	−2.94132
$178$	−5.30884	−0.397914
$179$	−15.9540	−1.19246	−0.596229	−	0.802814i	$-0.703335\pi$
$179$	−15.9540	−1.19246	−0.596229	+	0.802814i	$0.703335\pi$
$180$	−39.8854	−2.97289
$181$	2.64305	0.196456	0.0982281	−	0.995164i	$-0.468683\pi$
$181$	2.64305	0.196456	0.0982281	+	0.995164i	$0.468683\pi$
$182$	1.08228	0.0802236
$183$	−12.3895	−0.915860
$184$	−53.4629	−3.94134
$185$	11.5635	0.850166
$186$	84.6610	6.20764
$187$	−1.42121	−0.103929
$188$	6.95884	0.507526
$189$	−1.74461	−0.126901
$190$	−21.2189	−1.53938
$191$	−13.1522	−0.951663	−0.475832	−	0.879536i	$-0.657853\pi$
$191$	−13.1522	−0.951663	−0.475832	+	0.879536i	$0.657853\pi$
$192$	16.9097	1.22035
$193$	10.7481	0.773666	0.386833	−	0.922150i	$-0.373569\pi$
$193$	10.7481	0.773666	0.386833	+	0.922150i	$0.373569\pi$
$194$	3.18095	0.228379
$195$	−12.7590	−0.913690
$196$	−32.9882	−2.35630
$197$	1.10214	0.0785240	0.0392620	−	0.999229i	$-0.487499\pi$
$197$	1.10214	0.0785240	0.0392620	+	0.999229i	$0.487499\pi$
$198$	37.4625	2.66234
$199$	10.0088	0.709508	0.354754	−	0.934960i	$-0.384565\pi$
$199$	10.0088	0.709508	0.354754	+	0.934960i	$0.384565\pi$
$200$	26.3655	1.86432
$201$	−17.2659	−1.21785
$202$	3.18556	0.224135
$203$	0.394919	0.0277179
$204$	11.3116	0.791968
$205$	−1.69394	−0.118310
$206$	−22.7681	−1.58633
$207$	56.8992	3.95477
$208$	30.9897	2.14875
$209$	14.0003	0.968420
$210$	−1.12738	−0.0777968
$211$	−4.71785	−0.324790	−0.162395	−	0.986726i	$-0.551922\pi$
$211$	−4.71785	−0.324790	−0.162395	+	0.986726i	$0.551922\pi$
$212$	−38.6779	−2.65641
$213$	−36.5130	−2.50183
$214$	−12.4689	−0.852354
$215$	0.457215	0.0311818
$216$	−103.236	−7.02433
$217$	1.20126	0.0815466
$218$	−13.9539	−0.945080
$219$	−13.3219	−0.900209
$220$	10.2141	0.688632
$221$	2.58575	0.173937
$222$	86.4443	5.80176
$223$	−2.74869	−0.184066	−0.0920329	−	0.995756i	$-0.529336\pi$
$223$	−2.74869	−0.184066	−0.0920329	+	0.995756i	$0.529336\pi$
$224$	1.05462	0.0704648
$225$	−28.0601	−1.87067
$226$	−24.5866	−1.63547
$227$	22.2245	1.47509	0.737546	−	0.675297i	$-0.235985\pi$
$227$	22.2245	1.47509	0.737546	+	0.675297i	$0.235985\pi$
$228$	−111.430	−7.37962
$229$	−13.6439	−0.901613	−0.450806	−	0.892622i	$-0.648864\pi$
$229$	−13.6439	−0.901613	−0.450806	+	0.892622i	$0.648864\pi$
$230$	22.0839	1.45617
$231$	0.743852	0.0489419
$232$	23.3691	1.53426
$233$	−9.33581	−0.611609	−0.305805	−	0.952094i	$-0.598925\pi$
$233$	−9.33581	−0.611609	−0.305805	+	0.952094i	$0.598925\pi$
$234$	−68.1594	−4.45572
$235$	−1.65705	−0.108094
$236$	−56.9955	−3.71009
$237$	−13.2362	−0.859783
$238$	0.228477	0.0148100
$239$	−12.8980	−0.834299	−0.417150	−	0.908838i	$-0.636971\pi$
$239$	−12.8980	−0.834299	−0.417150	+	0.908838i	$0.636971\pi$
$240$	−32.2813	−2.08375
$241$	−3.62854	−0.233735	−0.116867	−	0.993148i	$-0.537285\pi$
$241$	−3.62854	−0.233735	−0.116867	+	0.993148i	$0.537285\pi$
$242$	18.9263	1.21663
$243$	36.8110	2.36143
$244$	−18.0454	−1.15524
$245$	7.85519	0.501849
$246$	−12.6632	−0.807377
$247$	−25.4722	−1.62076
$248$	71.0837	4.51382
$249$	10.9600	0.694560
$250$	−25.4677	−1.61072
$251$	−28.2919	−1.78577	−0.892884	−	0.450287i	$-0.851322\pi$
$251$	−28.2919	−1.78577	−0.892884	+	0.450287i	$0.851322\pi$
$252$	−4.23071	−0.266510
$253$	−14.5710	−0.916073
$254$	10.3748	0.650975
$255$	−2.69352	−0.168675
$256$	−21.2211	−1.32632
$257$	16.0068	0.998475	0.499238	−	0.866465i	$-0.333613\pi$
$257$	16.0068	0.998475	0.499238	+	0.866465i	$0.333613\pi$
$258$	3.41796	0.212793
$259$	1.22656	0.0762147
$260$	−18.5835	−1.15250
$261$	−24.8711	−1.53948
$262$	−32.8784	−2.03124
$263$	−6.43429	−0.396755	−0.198378	−	0.980126i	$-0.563567\pi$
$263$	−6.43429	−0.396755	−0.198378	+	0.980126i	$0.563567\pi$
$264$	44.0170	2.70906
$265$	9.21002	0.565767
$266$	−2.25072	−0.138000
$267$	6.63860	0.406276
$268$	−25.1479	−1.53615
$269$	−17.3635	−1.05867	−0.529336	−	0.848412i	$-0.677559\pi$
$269$	−17.3635	−1.05867	−0.529336	+	0.848412i	$0.677559\pi$
$270$	42.6436	2.59521
$271$	19.9838	1.21393	0.606963	−	0.794730i	$-0.292387\pi$
$271$	19.9838	1.21393	0.606963	+	0.794730i	$0.292387\pi$
$272$	6.54217	0.396678
$273$	−1.35337	−0.0819095
$274$	−20.8420	−1.25911
$275$	7.18577	0.433318
$276$	115.972	6.98072
$277$	11.0608	0.664577	0.332289	−	0.943178i	$-0.392179\pi$
$277$	11.0608	0.664577	0.332289	+	0.943178i	$0.392179\pi$
$278$	−20.2586	−1.21503
$279$	−75.6525	−4.52919
$280$	−0.946582	−0.0565691
$281$	−13.8766	−0.827806	−0.413903	−	0.910321i	$-0.635835\pi$
$281$	−13.8766	−0.827806	−0.413903	+	0.910321i	$0.635835\pi$
$282$	−12.3874	−0.737661
$283$	20.3260	1.20826	0.604128	−	0.796887i	$-0.293522\pi$
$283$	20.3260	1.20826	0.604128	+	0.796887i	$0.293522\pi$
$284$	−53.1813	−3.15573
$285$	26.5338	1.57173
$286$	17.4546	1.03211
$287$	−0.179678	−0.0106061
$288$	−66.4177	−3.91370
$289$	−16.4541	−0.967890
$290$	−9.65304	−0.566846
$291$	−3.97772	−0.233178
$292$	−19.4034	−1.13550
$293$	−20.9160	−1.22192	−0.610962	−	0.791660i	$-0.709217\pi$
$293$	−20.9160	−1.22192	−0.610962	+	0.791660i	$0.709217\pi$
$294$	58.7223	3.42475
$295$	13.5718	0.790182
$296$	72.5810	4.21868
$297$	−28.1364	−1.63264
$298$	−43.5641	−2.52360
$299$	26.5106	1.53315
$300$	−57.1923	−3.30200
$301$	0.0484975	0.00279535
$302$	1.29484	0.0745099
$303$	−3.98348	−0.228845
$304$	−64.4467	−3.69627
$305$	4.29698	0.246045
$306$	−14.3890	−0.822563
$307$	−21.7354	−1.24050	−0.620251	−	0.784403i	$-0.712969\pi$
$307$	−21.7354	−1.24050	−0.620251	+	0.784403i	$0.712969\pi$
$308$	1.08342	0.0617337
$309$	28.4711	1.61966
$310$	−29.3624	−1.66767
$311$	−28.6394	−1.62399	−0.811995	−	0.583664i	$-0.801618\pi$
$311$	−28.6394	−1.62399	−0.811995	+	0.583664i	$0.801618\pi$
$312$	−80.0847	−4.53390
$313$	−13.8363	−0.782071	−0.391036	−	0.920376i	$-0.627883\pi$
$313$	−13.8363	−0.782071	−0.391036	+	0.920376i	$0.627883\pi$
$314$	−18.9988	−1.07216
$315$	1.00742	0.0567618
$316$	−19.2785	−1.08450
$317$	24.3310	1.36657	0.683283	−	0.730154i	$-0.260552\pi$
$317$	24.3310	1.36657	0.683283	+	0.730154i	$0.260552\pi$
$318$	68.8505	3.86095
$319$	6.36912	0.356602
$320$	−5.86469	−0.327846
$321$	15.5921	0.870265
$322$	2.34247	0.130541
$323$	−5.37737	−0.299205
$324$	117.528	6.52935
$325$	−13.0738	−0.725204
$326$	36.0969	1.99922
$327$	17.4491	0.964940
$328$	−10.6324	−0.587075
$329$	−0.175766	−0.00969027
$330$	−18.1821	−1.00089
$331$	25.1735	1.38366	0.691831	−	0.722059i	$-0.256804\pi$
$331$	25.1735	1.38366	0.691831	+	0.722059i	$0.256804\pi$
$332$	15.9632	0.876095
$333$	−77.2460	−4.23306
$334$	−45.1031	−2.46793
$335$	5.98824	0.327173
$336$	−3.42413	−0.186802
$337$	6.87070	0.374271	0.187135	−	0.982334i	$-0.440080\pi$
$337$	6.87070	0.374271	0.187135	+	0.982334i	$0.440080\pi$
$338$	1.94842	0.105980
$339$	30.7451	1.66984
$340$	−3.92312	−0.212761
$341$	19.3735	1.04913
$342$	141.745	7.66470
$343$	1.66812	0.0900701
$344$	2.86981	0.154730
$345$	−27.6155	−1.48677
$346$	15.5325	0.835031
$347$	31.9611	1.71576	0.857882	−	0.513847i	$-0.171780\pi$
$347$	31.9611	1.71576	0.857882	+	0.513847i	$0.171780\pi$
$348$	−50.6925	−2.71740
$349$	13.0406	0.698047	0.349024	−	0.937114i	$-0.386513\pi$
$349$	13.0406	0.698047	0.349024	+	0.937114i	$0.386513\pi$
$350$	−1.15520	−0.0617480
$351$	51.1915	2.73240
$352$	17.0086	0.906560
$353$	26.6921	1.42068	0.710339	−	0.703860i	$-0.248542\pi$
$353$	26.6921	1.42068	0.710339	+	0.703860i	$0.248542\pi$
$354$	101.458	5.39242
$355$	12.6636	0.672114
$356$	9.66914	0.512463
$357$	−0.285706	−0.0151212
$358$	41.3643	2.18617
$359$	22.0160	1.16196	0.580980	−	0.813918i	$-0.302670\pi$
$359$	22.0160	1.16196	0.580980	+	0.813918i	$0.302670\pi$
$360$	59.6136	3.14191
$361$	33.9723	1.78802
$362$	−6.85268	−0.360169
$363$	−23.6670	−1.24220
$364$	−1.97118	−0.103318
$365$	4.62035	0.241840
$366$	32.1226	1.67907
$367$	−20.6953	−1.08029	−0.540144	−	0.841572i	$-0.681630\pi$
$367$	−20.6953	−1.08029	−0.540144	+	0.841572i	$0.681630\pi$
$368$	67.0740	3.49647
$369$	11.3158	0.589075
$370$	−29.9809	−1.55864
$371$	0.976921	0.0507192
$372$	−154.196	−7.99466
$373$	−25.1008	−1.29967	−0.649836	−	0.760074i	$-0.725162\pi$
$373$	−25.1008	−1.29967	−0.649836	+	0.760074i	$0.725162\pi$
$374$	3.68480	0.190537
$375$	31.8469	1.64457
$376$	−10.4008	−0.536382
$377$	−11.5880	−0.596812
$378$	4.52328	0.232652
$379$	22.7528	1.16873	0.584366	−	0.811490i	$-0.301343\pi$
$379$	22.7528	1.16873	0.584366	+	0.811490i	$0.301343\pi$
$380$	38.6465	1.98252
$381$	−12.9735	−0.664655
$382$	34.1001	1.74471
$383$	24.2782	1.24056	0.620278	−	0.784382i	$-0.287020\pi$
$383$	24.2782	1.24056	0.620278	+	0.784382i	$0.287020\pi$
$384$	13.4927	0.688544
$385$	−0.257986	−0.0131482
$386$	−27.8668	−1.41839
$387$	−3.05427	−0.155257
$388$	−5.79356	−0.294123
$389$	−28.6185	−1.45101	−0.725507	−	0.688215i	$-0.758394\pi$
$389$	−28.6185	−1.45101	−0.725507	+	0.688215i	$0.758394\pi$
$390$	33.0805	1.67510
$391$	5.59659	0.283032
$392$	49.3049	2.49027
$393$	41.1139	2.07392
$394$	−2.85753	−0.143960
$395$	4.59063	0.230980
$396$	−68.2315	−3.42876
$397$	3.63952	0.182662	0.0913312	−	0.995821i	$-0.470888\pi$
$397$	3.63952	0.182662	0.0913312	+	0.995821i	$0.470888\pi$
$398$	−25.9501	−1.30076
$399$	2.81448	0.140900
$400$	−33.0778	−1.65389
$401$	−3.60667	−0.180109	−0.0900543	−	0.995937i	$-0.528704\pi$
$401$	−3.60667	−0.180109	−0.0900543	+	0.995937i	$0.528704\pi$
$402$	44.7658	2.23271
$403$	−35.2481	−1.75583
$404$	−5.80195	−0.288658
$405$	−27.9860	−1.39063
$406$	−1.02391	−0.0508160
$407$	19.7816	0.980535
$408$	−16.9065	−0.836997
$409$	−19.8995	−0.983968	−0.491984	−	0.870604i	$-0.663728\pi$
$409$	−19.8995	−0.983968	−0.491984	+	0.870604i	$0.663728\pi$
$410$	4.39190	0.216901
$411$	26.0626	1.28557
$412$	41.4682	2.04299
$413$	1.43959	0.0708374
$414$	−147.524	−7.25039
$415$	−3.80118	−0.186592
$416$	−30.9455	−1.51723
$417$	25.3330	1.24056
$418$	−36.2988	−1.77543
$419$	−28.4624	−1.39048	−0.695239	−	0.718778i	$-0.744702\pi$
$419$	−28.4624	−1.39048	−0.695239	+	0.718778i	$0.744702\pi$
$420$	2.05334	0.100193
$421$	33.7126	1.64305	0.821526	−	0.570170i	$-0.193123\pi$
$421$	33.7126	1.64305	0.821526	+	0.570170i	$0.193123\pi$
$422$	12.2321	0.595447
$423$	11.0693	0.538209
$424$	57.8088	2.80744
$425$	−2.75998	−0.133879
$426$	94.6681	4.58668
$427$	0.455788	0.0220571
$428$	22.7099	1.09772
$429$	−21.8266	−1.05380
$430$	−1.18543	−0.0571666
$431$	12.3075	0.592829	0.296415	−	0.955059i	$-0.404209\pi$
$431$	12.3075	0.592829	0.296415	+	0.955059i	$0.404209\pi$
$432$	129.519	6.23148
$433$	−18.1056	−0.870098	−0.435049	−	0.900407i	$-0.643269\pi$
$433$	−18.1056	−0.870098	−0.435049	+	0.900407i	$0.643269\pi$
$434$	−3.11452	−0.149502
$435$	12.0710	0.578758
$436$	25.4147	1.21714
$437$	−55.1318	−2.63731
$438$	34.5399	1.65038
$439$	−31.7527	−1.51547	−0.757737	−	0.652560i	$-0.773695\pi$
$439$	−31.7527	−1.51547	−0.757737	+	0.652560i	$0.773695\pi$
$440$	−15.2662	−0.727785
$441$	−52.4738	−2.49875
$442$	−6.70414	−0.318883
$443$	23.8576	1.13351	0.566755	−	0.823886i	$-0.308198\pi$
$443$	23.8576	1.13351	0.566755	+	0.823886i	$0.308198\pi$
$444$	−157.444	−7.47194
$445$	−2.30243	−0.109145
$446$	7.12658	0.337453
$447$	54.4761	2.57663
$448$	−0.622077	−0.0293904
$449$	−26.8846	−1.26876	−0.634382	−	0.773019i	$-0.718745\pi$
$449$	−26.8846	−1.26876	−0.634382	+	0.773019i	$0.718745\pi$
$450$	72.7519	3.42956
$451$	−2.89780	−0.136452
$452$	44.7802	2.10629
$453$	−1.61918	−0.0760757
$454$	−57.6219	−2.70433
$455$	0.469380	0.0220049
$456$	166.545	7.79920
$457$	10.6417	0.497799	0.248899	−	0.968529i	$-0.419931\pi$
$457$	10.6417	0.497799	0.248899	+	0.968529i	$0.419931\pi$
$458$	35.3748	1.65295
$459$	10.8069	0.504424
$460$	−40.2220	−1.87536
$461$	−14.8859	−0.693306	−0.346653	−	0.937994i	$-0.612682\pi$
$461$	−14.8859	−0.693306	−0.346653	+	0.937994i	$0.612682\pi$
$462$	−1.92860	−0.0897266
$463$	−20.3444	−0.945485	−0.472743	−	0.881201i	$-0.656736\pi$
$463$	−20.3444	−0.945485	−0.472743	+	0.881201i	$0.656736\pi$
$464$	−29.3186	−1.36108
$465$	36.7172	1.70272
$466$	24.2051	1.12128
$467$	3.39329	0.157023	0.0785113	−	0.996913i	$-0.474983\pi$
$467$	3.39329	0.157023	0.0785113	+	0.996913i	$0.474983\pi$
$468$	124.141	5.73840
$469$	0.635182	0.0293300
$470$	4.29626	0.198172
$471$	23.7576	1.09469
$472$	85.1867	3.92103
$473$	0.782152	0.0359634
$474$	34.3177	1.57627
$475$	27.1885	1.24749
$476$	−0.416132	−0.0190734
$477$	−61.5243	−2.81701
$478$	33.4408	1.52955
$479$	29.9813	1.36988	0.684940	−	0.728600i	$-0.259829\pi$
$479$	29.9813	1.36988	0.684940	+	0.728600i	$0.259829\pi$
$480$	32.2352	1.47133
$481$	−35.9906	−1.64103
$482$	9.40779	0.428513
$483$	−2.92922	−0.133284
$484$	−34.4711	−1.56687
$485$	1.37957	0.0626430
$486$	−95.4406	−4.32928
$487$	7.62947	0.345724	0.172862	−	0.984946i	$-0.444698\pi$
$487$	7.62947	0.345724	0.172862	+	0.984946i	$0.444698\pi$
$488$	26.9710	1.22092
$489$	−45.1385	−2.04123
$490$	−20.3663	−0.920056
$491$	−35.8022	−1.61573	−0.807865	−	0.589368i	$-0.799377\pi$
$491$	−35.8022	−1.61573	−0.807865	+	0.589368i	$0.799377\pi$
$492$	23.0639	1.03980
$493$	−2.44632	−0.110177
$494$	66.0422	2.97138
$495$	16.2474	0.730265
$496$	−89.1807	−4.00433
$497$	1.34325	0.0602529
$498$	−28.4161	−1.27336
$499$	17.8970	0.801180	0.400590	−	0.916257i	$-0.368805\pi$
$499$	17.8970	0.801180	0.400590	+	0.916257i	$0.368805\pi$
$500$	46.3851	2.07441
$501$	56.4006	2.51979
$502$	73.3529	3.27390
$503$	−22.0537	−0.983325	−0.491662	−	0.870786i	$-0.663611\pi$
$503$	−22.0537	−0.983325	−0.491662	+	0.870786i	$0.663611\pi$
$504$	6.32331	0.281663
$505$	1.38157	0.0614789
$506$	37.7786	1.67946
$507$	−2.43646	−0.108207
$508$	−18.8960	−0.838374
$509$	27.8149	1.23287	0.616436	−	0.787405i	$-0.288576\pi$
$509$	27.8149	1.23287	0.616436	+	0.787405i	$0.288576\pi$
$510$	6.98355	0.309237
$511$	0.490088	0.0216802
$512$	46.6972	2.06374
$513$	−106.459	−4.70027
$514$	−41.5011	−1.83053
$515$	−9.87444	−0.435120
$516$	−6.22523	−0.274051
$517$	−2.83469	−0.124669
$518$	−3.18013	−0.139727
$519$	−19.4231	−0.852578
$520$	27.7753	1.21803
$521$	−30.0241	−1.31538	−0.657690	−	0.753289i	$-0.728466\pi$
$521$	−30.0241	−1.31538	−0.657690	+	0.753289i	$0.728466\pi$
$522$	64.4838	2.82238
$523$	8.06979	0.352867	0.176434	−	0.984313i	$-0.443544\pi$
$523$	8.06979	0.352867	0.176434	+	0.984313i	$0.443544\pi$
$524$	59.8824	2.61598
$525$	1.44456	0.0630456
$526$	16.6823	0.727383
$527$	−7.44116	−0.324142
$528$	−55.2232	−2.40328
$529$	34.3793	1.49475
$530$	−23.8790	−1.03724
$531$	−90.6619	−3.93439
$532$	4.09930	0.177727
$533$	5.27226	0.228367
$534$	−17.2120	−0.744838
$535$	−5.40771	−0.233796
$536$	37.5866	1.62349
$537$	−51.7252	−2.23211
$538$	45.0187	1.94089
$539$	13.4378	0.578806
$540$	−77.6681	−3.34230
$541$	31.0187	1.33360	0.666799	−	0.745238i	$-0.267664\pi$
$541$	31.0187	1.33360	0.666799	+	0.745238i	$0.267664\pi$
$542$	−51.8123	−2.22553
$543$	8.56915	0.367737
$544$	−6.53283	−0.280093
$545$	−6.05178	−0.259230
$546$	3.50890	0.150167
$547$	−9.30593	−0.397893	−0.198946	−	0.980010i	$-0.563752\pi$
$547$	−9.30593	−0.397893	−0.198946	+	0.980010i	$0.563752\pi$
$548$	37.9602	1.62158
$549$	−28.7045	−1.22508
$550$	−18.6307	−0.794415
$551$	24.0986	1.02663
$552$	−173.335	−7.37762
$553$	0.486935	0.0207066
$554$	−28.6775	−1.21839
$555$	37.4906	1.59139
$556$	36.8976	1.56481
$557$	28.2686	1.19778	0.598889	−	0.800832i	$-0.295609\pi$
$557$	28.2686	1.19778	0.598889	+	0.800832i	$0.295609\pi$
$558$	196.146	8.30351
$559$	−1.42305	−0.0601886
$560$	1.18757	0.0501840
$561$	−4.60778	−0.194540
$562$	35.9780	1.51764
$563$	−42.2320	−1.77987	−0.889933	−	0.456092i	$-0.849249\pi$
$563$	−42.2320	−1.77987	−0.889933	+	0.456092i	$0.849249\pi$
$564$	22.5616	0.950015
$565$	−10.6631	−0.448601
$566$	−52.6997	−2.21513
$567$	−2.96852	−0.124666
$568$	79.4859	3.33515
$569$	−33.7707	−1.41574	−0.707872	−	0.706341i	$-0.750345\pi$
$569$	−33.7707	−1.41574	−0.707872	+	0.706341i	$0.750345\pi$
$570$	−68.7947	−2.88149
$571$	32.2616	1.35011	0.675053	−	0.737769i	$-0.264121\pi$
$571$	32.2616	1.35011	0.675053	+	0.737769i	$0.264121\pi$
$572$	−31.7906	−1.32923
$573$	−42.6415	−1.78138
$574$	0.465856	0.0194445
$575$	−28.2969	−1.18006
$576$	39.1770	1.63238
$577$	−45.7080	−1.90285	−0.951424	−	0.307882i	$-0.900380\pi$
$577$	−45.7080	−1.90285	−0.951424	+	0.307882i	$0.900380\pi$
$578$	42.6609	1.77446
$579$	34.8470	1.44819
$580$	17.5814	0.730027
$581$	−0.403197	−0.0167274
$582$	10.3131	0.427492
$583$	15.7555	0.652525
$584$	29.0007	1.20006
$585$	−29.5605	−1.22218
$586$	54.2293	2.24019
$587$	33.3919	1.37823	0.689115	−	0.724652i	$-0.258000\pi$
$587$	33.3919	1.37823	0.689115	+	0.724652i	$0.258000\pi$
$588$	−106.953	−4.41065
$589$	73.3025	3.02038
$590$	−35.1880	−1.44867
$591$	3.57329	0.146985
$592$	−91.0593	−3.74251
$593$	−34.6999	−1.42496	−0.712478	−	0.701695i	$-0.752427\pi$
$593$	−34.6999	−1.42496	−0.712478	+	0.701695i	$0.752427\pi$
$594$	72.9499	2.99317
$595$	0.0990897	0.00406228
$596$	79.3445	3.25008
$597$	32.4502	1.32810
$598$	−68.7345	−2.81076
$599$	−40.3188	−1.64738	−0.823691	−	0.567039i	$-0.808089\pi$
$599$	−40.3188	−1.64738	−0.823691	+	0.567039i	$0.808089\pi$
$600$	85.4808	3.48974
$601$	33.1497	1.35220	0.676102	−	0.736808i	$-0.263668\pi$
$601$	33.1497	1.35220	0.676102	+	0.736808i	$0.263668\pi$
$602$	−0.125741	−0.00512480
$603$	−40.0024	−1.62902
$604$	−2.35834	−0.0959594
$605$	8.20829	0.333715
$606$	10.3281	0.419549
$607$	−2.18882	−0.0888416	−0.0444208	−	0.999013i	$-0.514144\pi$
$607$	−2.18882	−0.0888416	−0.0444208	+	0.999013i	$0.514144\pi$
$608$	64.3546	2.60992
$609$	1.28039	0.0518838
$610$	−11.1409	−0.451081
$611$	5.15744	0.208648
$612$	26.2071	1.05936
$613$	−29.4892	−1.19106	−0.595529	−	0.803334i	$-0.703058\pi$
$613$	−29.4892	−1.19106	−0.595529	+	0.803334i	$0.703058\pi$
$614$	56.3537	2.27425
$615$	−5.49199	−0.221459
$616$	−1.61931	−0.0652437
$617$	−10.6977	−0.430674	−0.215337	−	0.976540i	$-0.569085\pi$
$617$	−10.6977	−0.430674	−0.215337	+	0.976540i	$0.569085\pi$
$618$	−73.8175	−2.96937
$619$	21.0858	0.847511	0.423756	−	0.905777i	$-0.360712\pi$
$619$	21.0858	0.847511	0.423756	+	0.905777i	$0.360712\pi$
$620$	53.4787	2.14776
$621$	110.799	4.44620
$622$	74.2539	2.97731
$623$	−0.244222	−0.00978454
$624$	100.473	4.02215
$625$	7.63273	0.305309
$626$	35.8735	1.43379
$627$	45.3910	1.81274
$628$	34.6030	1.38081
$629$	−7.59790	−0.302948
$630$	−2.61196	−0.104063
$631$	27.1868	1.08229	0.541145	−	0.840929i	$-0.317991\pi$
$631$	27.1868	1.08229	0.541145	+	0.840929i	$0.317991\pi$
$632$	28.8141	1.14616
$633$	−15.2960	−0.607960
$634$	−63.0835	−2.50537
$635$	4.49954	0.178559
$636$	−125.399	−4.97241
$637$	−24.4487	−0.968693
$638$	−16.5133	−0.653769
$639$	−84.5947	−3.34652
$640$	−4.67958	−0.184977
$641$	27.0558	1.06864	0.534319	−	0.845283i	$-0.320568\pi$
$641$	27.0558	1.06864	0.534319	+	0.845283i	$0.320568\pi$
$642$	−40.4259	−1.59548
$643$	0.185986	0.00733459	0.00366729	−	0.999993i	$-0.498833\pi$
$643$	0.185986	0.00733459	0.00366729	+	0.999993i	$0.498833\pi$
$644$	−4.26641	−0.168120
$645$	1.48236	0.0583679
$646$	13.9420	0.548542
$647$	28.1939	1.10842	0.554208	−	0.832378i	$-0.313021\pi$
$647$	28.1939	1.10842	0.554208	+	0.832378i	$0.313021\pi$
$648$	−175.660	−6.90059
$649$	23.2172	0.911353
$650$	33.8967	1.32954
$651$	3.89465	0.152643
$652$	−65.7444	−2.57475
$653$	31.0888	1.21660	0.608299	−	0.793708i	$-0.291852\pi$
$653$	31.0888	1.21660	0.608299	+	0.793708i	$0.291852\pi$
$654$	−45.2407	−1.76905
$655$	−14.2593	−0.557156
$656$	13.3393	0.520810
$657$	−30.8646	−1.20414
$658$	0.455711	0.0177655
$659$	−5.22569	−0.203564	−0.101782	−	0.994807i	$-0.532454\pi$
$659$	−5.22569	−0.203564	−0.101782	+	0.994807i	$0.532454\pi$
$660$	33.1155	1.28902
$661$	−26.5381	−1.03221	−0.516106	−	0.856525i	$-0.672619\pi$
$661$	−26.5381	−1.03221	−0.516106	+	0.856525i	$0.672619\pi$
$662$	−65.2679	−2.53671
$663$	8.38340	0.325584
$664$	−23.8590	−0.925907
$665$	−0.976129	−0.0378527
$666$	200.277	7.76059
$667$	−25.0810	−0.971139
$668$	82.1476	3.17838
$669$	−8.91165	−0.344544
$670$	−15.5258	−0.599815
$671$	7.35080	0.283774
$672$	3.41924	0.131900
$673$	−30.4768	−1.17480	−0.587398	−	0.809299i	$-0.699847\pi$
$673$	−30.4768	−1.17480	−0.587398	+	0.809299i	$0.699847\pi$
$674$	−17.8138	−0.686162
$675$	−54.6408	−2.10313
$676$	−3.54871	−0.136489
$677$	21.2258	0.815773	0.407887	−	0.913033i	$-0.366266\pi$
$677$	21.2258	0.815773	0.407887	+	0.913033i	$0.366266\pi$
$678$	−79.7133	−3.06137
$679$	0.146333	0.00561575
$680$	5.86358	0.224858
$681$	72.0551	2.76116
$682$	−50.2300	−1.92340
$683$	−20.7787	−0.795077	−0.397538	−	0.917586i	$-0.630135\pi$
$683$	−20.7787	−0.795077	−0.397538	+	0.917586i	$0.630135\pi$
$684$	−258.165	−9.87117
$685$	−9.03912	−0.345367
$686$	−4.32497	−0.165128
$687$	−44.2355	−1.68769
$688$	−3.60044	−0.137265
$689$	−28.6655	−1.09207
$690$	71.5992	2.72574
$691$	−41.6051	−1.58273	−0.791366	−	0.611343i	$-0.790629\pi$
$691$	−41.6051	−1.58273	−0.791366	+	0.611343i	$0.790629\pi$
$692$	−28.2897	−1.07541
$693$	1.72338	0.0654659
$694$	−82.8663	−3.14556
$695$	−8.78609	−0.333275
$696$	75.7661	2.87191
$697$	1.11301	0.0421584
$698$	−33.8106	−1.27975
$699$	−30.2681	−1.14484
$700$	2.10400	0.0795237
$701$	17.6004	0.664758	0.332379	−	0.943146i	$-0.392149\pi$
$701$	17.6004	0.664758	0.332379	+	0.943146i	$0.392149\pi$
$702$	−132.725	−5.00939
$703$	74.8466	2.82289
$704$	−10.0327	−0.378120
$705$	−5.37239	−0.202336
$706$	−69.2051	−2.60457
$707$	0.146545	0.00551139
$708$	−184.788	−6.94475
$709$	16.2408	0.609935	0.304968	−	0.952363i	$-0.401354\pi$
$709$	16.2408	0.609935	0.304968	+	0.952363i	$0.401354\pi$
$710$	−32.8332	−1.23221
$711$	−30.6661	−1.15007
$712$	−14.4517	−0.541600
$713$	−76.2908	−2.85711
$714$	0.740756	0.0277221
$715$	7.57000	0.283102
$716$	−75.3379	−2.81551
$717$	−41.8171	−1.56169
$718$	−57.0813	−2.13026
$719$	52.2709	1.94938	0.974688	−	0.223568i	$-0.0717706\pi$
$719$	52.2709	1.94938	0.974688	+	0.223568i	$0.0717706\pi$
$720$	−74.7905	−2.78728
$721$	−1.04740	−0.0390071
$722$	−88.0806	−3.27802
$723$	−11.7643	−0.437518
$724$	12.4810	0.463852
$725$	12.3688	0.459365
$726$	61.3620	2.27736
$727$	20.4661	0.759046	0.379523	−	0.925182i	$-0.376088\pi$
$727$	20.4661	0.759046	0.379523	+	0.925182i	$0.376088\pi$
$728$	2.94617	0.109192
$729$	44.6813	1.65486
$730$	−11.9793	−0.443373
$731$	−0.300417	−0.0111113
$732$	−58.5058	−2.16244
$733$	12.4794	0.460936	0.230468	−	0.973080i	$-0.425974\pi$
$733$	12.4794	0.460936	0.230468	+	0.973080i	$0.425974\pi$
$734$	53.6572	1.98053
$735$	25.4677	0.939390
$736$	−66.9781	−2.46885
$737$	10.2440	0.377343
$738$	−29.3386	−1.07997
$739$	−36.1426	−1.32953	−0.664763	−	0.747054i	$-0.731468\pi$
$739$	−36.1426	−1.32953	−0.664763	+	0.747054i	$0.731468\pi$
$740$	54.6052	2.00733
$741$	−82.5846	−3.03382
$742$	−2.53288	−0.0929851
$743$	−5.54972	−0.203600	−0.101800	−	0.994805i	$-0.532460\pi$
$743$	−5.54972	−0.203600	−0.101800	+	0.994805i	$0.532460\pi$
$744$	230.464	8.44921
$745$	−18.8936	−0.692208
$746$	65.0794	2.38273
$747$	25.3924	0.929061
$748$	−6.71124	−0.245387
$749$	−0.573604	−0.0209590
$750$	−82.5702	−3.01504
$751$	−9.10768	−0.332344	−0.166172	−	0.986097i	$-0.553141\pi$
$751$	−9.10768	−0.332344	−0.166172	+	0.986097i	$0.553141\pi$
$752$	13.0488	0.475839
$753$	−91.7265	−3.34270
$754$	30.0444	1.09415
$755$	0.561570	0.0204376
$756$	−8.23838	−0.299627
$757$	−39.6710	−1.44187	−0.720934	−	0.693003i	$-0.756287\pi$
$757$	−39.6710	−1.44187	−0.720934	+	0.693003i	$0.756287\pi$
$758$	−58.9916	−2.14267
$759$	−47.2414	−1.71476
$760$	−57.7619	−2.09524
$761$	1.41801	0.0514028	0.0257014	−	0.999670i	$-0.491818\pi$
$761$	1.41801	0.0514028	0.0257014	+	0.999670i	$0.491818\pi$
$762$	33.6368	1.21853
$763$	−0.641922	−0.0232391
$764$	−62.1075	−2.24697
$765$	−6.24045	−0.225624
$766$	−62.9465	−2.27435
$767$	−42.2414	−1.52525
$768$	−68.8021	−2.48268
$769$	−35.8399	−1.29242	−0.646210	−	0.763160i	$-0.723647\pi$
$769$	−35.8399	−1.29242	−0.646210	+	0.763160i	$0.723647\pi$
$770$	0.668884	0.0241049
$771$	51.8963	1.86900
$772$	50.7547	1.82670
$773$	−5.41977	−0.194935	−0.0974677	−	0.995239i	$-0.531074\pi$
$773$	−5.41977	−0.194935	−0.0974677	+	0.995239i	$0.531074\pi$
$774$	7.91886	0.284638
$775$	37.6232	1.35146
$776$	8.65918	0.310846
$777$	3.97669	0.142663
$778$	74.1996	2.66019
$779$	−10.9643	−0.392836
$780$	−60.2505	−2.15731
$781$	21.6634	0.775179
$782$	−14.5104	−0.518890
$783$	−48.4310	−1.73078
$784$	−61.8573	−2.20919
$785$	−8.23971	−0.294088
$786$	−106.597	−3.80218
$787$	32.7892	1.16881	0.584404	−	0.811463i	$-0.301328\pi$
$787$	32.7892	1.16881	0.584404	+	0.811463i	$0.301328\pi$
$788$	5.20450	0.185403
$789$	−20.8609	−0.742669
$790$	−11.9022	−0.423462
$791$	−1.13105	−0.0402156
$792$	101.980	3.62371
$793$	−13.3741	−0.474927
$794$	−9.43626	−0.334880
$795$	29.8603	1.05903
$796$	47.2637	1.67522
$797$	−1.49075	−0.0528052	−0.0264026	−	0.999651i	$-0.508405\pi$
$797$	−1.49075	−0.0528052	−0.0264026	+	0.999651i	$0.508405\pi$
$798$	−7.29716	−0.258317
$799$	1.08878	0.0385181
$800$	33.0306	1.16781
$801$	15.3806	0.543445
$802$	9.35109	0.330199
$803$	7.90397	0.278925
$804$	−81.5332	−2.87545
$805$	1.01592	0.0358066
$806$	91.3886	3.21902
$807$	−56.2951	−1.98168
$808$	8.67172	0.305070
$809$	−26.6165	−0.935788	−0.467894	−	0.883785i	$-0.654987\pi$
$809$	−26.6165	−0.935788	−0.467894	+	0.883785i	$0.654987\pi$
$810$	72.5598	2.54949
$811$	29.9915	1.05315	0.526573	−	0.850130i	$-0.323477\pi$
$811$	29.9915	1.05315	0.526573	+	0.850130i	$0.323477\pi$
$812$	1.86488	0.0654446
$813$	64.7903	2.27230
$814$	−51.2880	−1.79764
$815$	15.6551	0.548375
$816$	21.2107	0.742523
$817$	2.95940	0.103536
$818$	51.5939	1.80394
$819$	−3.13553	−0.109564
$820$	−7.99910	−0.279341
$821$	53.3974	1.86358	0.931790	−	0.362997i	$-0.118246\pi$
$821$	53.3974	1.86358	0.931790	+	0.362997i	$0.118246\pi$
$822$	−67.5730	−2.35688
$823$	8.09162	0.282056	0.141028	−	0.990006i	$-0.454959\pi$
$823$	8.09162	0.282056	0.141028	+	0.990006i	$0.454959\pi$
$824$	−61.9792	−2.15915
$825$	23.2973	0.811109
$826$	−3.73244	−0.129868
$827$	8.74577	0.304120	0.152060	−	0.988371i	$-0.451409\pi$
$827$	8.74577	0.304120	0.152060	+	0.988371i	$0.451409\pi$
$828$	268.689	9.33759
$829$	18.6336	0.647170	0.323585	−	0.946199i	$-0.395112\pi$
$829$	18.6336	0.647170	0.323585	+	0.946199i	$0.395112\pi$
$830$	9.85539	0.342086
$831$	35.8607	1.24399
$832$	18.2534	0.632824
$833$	−5.16131	−0.178829
$834$	−65.6814	−2.27436
$835$	−19.5611	−0.676939
$836$	66.1121	2.28654
$837$	−147.316	−5.09200
$838$	73.7950	2.54921
$839$	−33.9259	−1.17125	−0.585627	−	0.810581i	$-0.699152\pi$
$839$	−33.9259	−1.17125	−0.585627	+	0.810581i	$0.699152\pi$
$840$	−3.06896	−0.105889
$841$	−18.0369	−0.621962
$842$	−87.4074	−3.01226
$843$	−44.9899	−1.54953
$844$	−22.2786	−0.766861
$845$	0.845024	0.0290697
$846$	−28.6997	−0.986715
$847$	0.870667	0.0299165
$848$	−72.5262	−2.49056
$849$	65.8999	2.26168
$850$	7.15586	0.245444
$851$	−77.8978	−2.67030
$852$	−172.422	−5.90707
$853$	−38.5876	−1.32121	−0.660607	−	0.750732i	$-0.729701\pi$
$853$	−38.5876	−1.32121	−0.660607	+	0.750732i	$0.729701\pi$
$854$	−1.18173	−0.0404380
$855$	61.4745	2.10238
$856$	−33.9427	−1.16014
$857$	−32.0381	−1.09440	−0.547201	−	0.837001i	$-0.684307\pi$
$857$	−32.0381	−1.09440	−0.547201	+	0.837001i	$0.684307\pi$
$858$	56.5904	1.93196
$859$	25.3434	0.864705	0.432352	−	0.901705i	$-0.357684\pi$
$859$	25.3434	0.864705	0.432352	+	0.901705i	$0.357684\pi$
$860$	2.15906	0.0736233
$861$	−0.582544	−0.0198531
$862$	−31.9098	−1.08685
$863$	−26.7100	−0.909218	−0.454609	−	0.890691i	$-0.650221\pi$
$863$	−26.7100	−0.909218	−0.454609	+	0.890691i	$0.650221\pi$
$864$	−129.334	−4.40003
$865$	6.73638	0.229044
$866$	46.9426	1.59518
$867$	−53.3467	−1.81175
$868$	5.67257	0.192540
$869$	7.85313	0.266399
$870$	−31.2966	−1.06105
$871$	−18.6380	−0.631524
$872$	−37.9854	−1.28635
$873$	−9.21573	−0.311905
$874$	142.941	4.83506
$875$	−1.17159	−0.0396070
$876$	−62.9086	−2.12548
$877$	−3.65822	−0.123529	−0.0617647	−	0.998091i	$-0.519673\pi$
$877$	−3.65822	−0.123529	−0.0617647	+	0.998091i	$0.519673\pi$
$878$	82.3259	2.77836
$879$	−67.8127	−2.28727
$880$	19.1527	0.645639
$881$	34.1044	1.14901	0.574503	−	0.818502i	$-0.305195\pi$
$881$	34.1044	1.14901	0.574503	+	0.818502i	$0.305195\pi$
$882$	136.050	4.58104
$883$	−0.738932	−0.0248670	−0.0124335	−	0.999923i	$-0.503958\pi$
$883$	−0.738932	−0.0248670	−0.0124335	+	0.999923i	$0.503958\pi$
$884$	12.2104	0.410682
$885$	44.0019	1.47911
$886$	−61.8562	−2.07810
$887$	−40.0494	−1.34473	−0.672364	−	0.740221i	$-0.734721\pi$
$887$	−40.0494	−1.34473	−0.672364	+	0.740221i	$0.734721\pi$
$888$	235.318	7.89677
$889$	0.477273	0.0160072
$890$	5.96954	0.200100
$891$	−47.8752	−1.60388
$892$	−12.9798	−0.434597
$893$	−10.7255	−0.358915
$894$	−141.241	−4.72381
$895$	17.9396	0.599653
$896$	−0.496370	−0.0165826
$897$	85.9512	2.86983
$898$	69.7043	2.32606
$899$	33.3474	1.11220
$900$	−132.505	−4.41684
$901$	−6.05152	−0.201605
$902$	7.51317	0.250161
$903$	0.157236	0.00523249
$904$	−66.9295	−2.22604
$905$	−2.97199	−0.0987922
$906$	4.19808	0.139472
$907$	−29.3966	−0.976097	−0.488048	−	0.872817i	$-0.662291\pi$
$907$	−29.3966	−0.976097	−0.488048	+	0.872817i	$0.662291\pi$
$908$	104.948	3.48284
$909$	−9.22908	−0.306109
$910$	−1.21697	−0.0403422
$911$	25.0465	0.829827	0.414913	−	0.909861i	$-0.363812\pi$
$911$	25.0465	0.829827	0.414913	+	0.909861i	$0.363812\pi$
$912$	−208.946	−6.91889
$913$	−6.50263	−0.215206
$914$	−27.5910	−0.912629
$915$	13.9315	0.460560
$916$	−64.4291	−2.12880
$917$	−1.51250	−0.0499473
$918$	−28.0194	−0.924776
$919$	48.9471	1.61462	0.807308	−	0.590130i	$-0.200924\pi$
$919$	48.9471	1.61462	0.807308	+	0.590130i	$0.200924\pi$
$920$	60.1167	1.98199
$921$	−70.4693	−2.32204
$922$	38.5950	1.27106
$923$	−39.4145	−1.29735
$924$	3.51262	0.115557
$925$	38.4157	1.26310
$926$	52.7474	1.73339
$927$	65.9628	2.16650
$928$	29.2767	0.961055
$929$	−48.0397	−1.57613	−0.788066	−	0.615590i	$-0.788918\pi$
$929$	−48.0397	−1.57613	−0.788066	+	0.615590i	$0.788918\pi$
$930$	−95.1974	−3.12165
$931$	50.8439	1.66634
$932$	−44.0855	−1.44407
$933$	−92.8531	−3.03988
$934$	−8.79784	−0.287874
$935$	1.59809	0.0522630
$936$	−185.543	−6.06467
$937$	49.1965	1.60718	0.803589	−	0.595184i	$-0.202921\pi$
$937$	49.1965	1.60718	0.803589	+	0.595184i	$0.202921\pi$
$938$	−1.64685	−0.0537715
$939$	−44.8592	−1.46392
$940$	−7.82490	−0.255220
$941$	−22.4504	−0.731862	−0.365931	−	0.930642i	$-0.619249\pi$
$941$	−22.4504	−0.731862	−0.365931	+	0.930642i	$0.619249\pi$
$942$	−61.5969	−2.00694
$943$	11.4112	0.371601
$944$	−106.874	−3.47846
$945$	1.96173	0.0638151
$946$	−2.02790	−0.0659328
$947$	−25.4133	−0.825820	−0.412910	−	0.910772i	$-0.635488\pi$
$947$	−25.4133	−0.825820	−0.412910	+	0.910772i	$0.635488\pi$
$948$	−62.5039	−2.03003
$949$	−14.3805	−0.466811
$950$	−70.4921	−2.28707
$951$	78.8848	2.55801
$952$	0.621959	0.0201578
$953$	−33.3017	−1.07875	−0.539374	−	0.842066i	$-0.681339\pi$
$953$	−33.3017	−1.07875	−0.539374	+	0.842066i	$0.681339\pi$
$954$	159.515	5.16450
$955$	14.7891	0.478564
$956$	−60.9067	−1.96986
$957$	20.6496	0.667508
$958$	−77.7330	−2.51144
$959$	−0.958794	−0.0309611
$960$	−19.0142	−0.613681
$961$	70.4354	2.27211
$962$	93.3136	3.00855
$963$	36.1243	1.16409
$964$	−17.1347	−0.551871
$965$	−12.0858	−0.389055
$966$	7.59464	0.244354
$967$	51.7462	1.66405	0.832023	−	0.554742i	$-0.187183\pi$
$967$	51.7462	1.66405	0.832023	+	0.554742i	$0.187183\pi$
$968$	51.5212	1.65595
$969$	−17.4342	−0.560069
$970$	−3.57684	−0.114845
$971$	−39.6891	−1.27368	−0.636842	−	0.770994i	$-0.719760\pi$
$971$	−39.6891	−1.27368	−0.636842	+	0.770994i	$0.719760\pi$
$972$	173.829	5.57556
$973$	−0.931955	−0.0298771
$974$	−19.7811	−0.633827
$975$	−42.3872	−1.35748
$976$	−33.8375	−1.08311
$977$	13.4665	0.430833	0.215416	−	0.976522i	$-0.430889\pi$
$977$	13.4665	0.430833	0.215416	+	0.976522i	$0.430889\pi$
$978$	117.032	3.74226
$979$	−3.93873	−0.125882
$980$	37.0937	1.18492
$981$	40.4268	1.29073
$982$	92.8250	2.96217
$983$	16.6239	0.530219	0.265110	−	0.964218i	$-0.414592\pi$
$983$	16.6239	0.530219	0.265110	+	0.964218i	$0.414592\pi$
$984$	−34.4717	−1.09892
$985$	−1.23930	−0.0394875
$986$	6.34261	0.201990
$987$	−0.569858	−0.0181388
$988$	−120.285	−3.82676
$989$	−3.08004	−0.0979396
$990$	−42.1249	−1.33882
$991$	20.1224	0.639208	0.319604	−	0.947551i	$-0.396450\pi$
$991$	20.1224	0.639208	0.319604	+	0.947551i	$0.396450\pi$
$992$	89.0533	2.82745
$993$	81.6163	2.59002
$994$	−3.48266	−0.110463
$995$	−11.2545	−0.356791
$996$	51.7551	1.63992
$997$	−3.27490	−0.103717	−0.0518585	−	0.998654i	$-0.516514\pi$
$997$	−3.27490	−0.103717	−0.0518585	+	0.998654i	$0.516514\pi$
$998$	−46.4019	−1.46883
$999$	−150.420	−4.75907

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6047.2.a.a.1.11	✓	217

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6047.2.a.a.1.11	✓	217	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:	\( N \)	\(=\)	\( 6047 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6047.a (trivial)

\(f(q)\)	\(=\)	\(q-2.59272 q^{2} +3.24215 q^{3} +4.72220 q^{4} -1.12445 q^{5} -8.40598 q^{6} -0.119273 q^{7} -7.05789 q^{8} +7.51153 q^{9} +O(q^{10})\)	\(q-2.59272 q^{2} +3.24215 q^{3} +4.72220 q^{4} -1.12445 q^{5} -8.40598 q^{6} -0.119273 q^{7} -7.05789 q^{8} +7.51153 q^{9} +2.91540 q^{10} -1.92359 q^{11} +15.3101 q^{12} +3.49979 q^{13} +0.309241 q^{14} -3.64565 q^{15} +8.85475 q^{16} +0.738832 q^{17} -19.4753 q^{18} -7.27821 q^{19} -5.30990 q^{20} -0.386700 q^{21} +4.98733 q^{22} +7.57491 q^{23} -22.8827 q^{24} -3.73560 q^{25} -9.07397 q^{26} +14.6270 q^{27} -0.563229 q^{28} -3.31106 q^{29} +9.45215 q^{30} -10.0715 q^{31} -8.84210 q^{32} -6.23657 q^{33} -1.91558 q^{34} +0.134117 q^{35} +35.4709 q^{36} -10.2837 q^{37} +18.8704 q^{38} +11.3468 q^{39} +7.93628 q^{40} +1.50645 q^{41} +1.00260 q^{42} -0.406611 q^{43} -9.08357 q^{44} -8.44637 q^{45} -19.6396 q^{46} +1.47364 q^{47} +28.7084 q^{48} -6.98577 q^{49} +9.68537 q^{50} +2.39540 q^{51} +16.5267 q^{52} -8.19066 q^{53} -37.9238 q^{54} +2.16299 q^{55} +0.841814 q^{56} -23.5970 q^{57} +8.58464 q^{58} -12.0697 q^{59} -17.2155 q^{60} -3.82139 q^{61} +26.1126 q^{62} -0.895920 q^{63} +5.21559 q^{64} -3.93535 q^{65} +16.1697 q^{66} -5.32546 q^{67} +3.48891 q^{68} +24.5590 q^{69} -0.347727 q^{70} -11.2620 q^{71} -53.0156 q^{72} -4.10897 q^{73} +26.6627 q^{74} -12.1114 q^{75} -34.3691 q^{76} +0.229432 q^{77} -29.4191 q^{78} -4.08254 q^{79} -9.95677 q^{80} +24.8885 q^{81} -3.90581 q^{82} +3.38046 q^{83} -1.82607 q^{84} -0.830783 q^{85} +1.05423 q^{86} -10.7349 q^{87} +13.5765 q^{88} +2.04759 q^{89} +21.8991 q^{90} -0.417429 q^{91} +35.7702 q^{92} -32.6533 q^{93} -3.82075 q^{94} +8.18401 q^{95} -28.6674 q^{96} -1.22688 q^{97} +18.1122 q^{98} -14.4491 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 217 q - 20 q^{2} - 27 q^{3} + 184 q^{4} - 19 q^{5} - 17 q^{6} - 48 q^{7} - 57 q^{8} + 152 q^{9}+O(q^{10}) \) 217 * q - 20 * q^2 - 27 * q^3 + 184 * q^4 - 19 * q^5 - 17 * q^6 - 48 * q^7 - 57 * q^8 + 152 * q^9	\( 217 q - 20 q^{2} - 27 q^{3} + 184 q^{4} - 19 q^{5} - 17 q^{6} - 48 q^{7} - 57 q^{8} + 152 q^{9} - 46 q^{10} - 32 q^{11} - 72 q^{12} - 80 q^{13} - 22 q^{14} - 43 q^{15} + 122 q^{16} - 61 q^{17} - 88 q^{18} - 43 q^{19} - 41 q^{20} - 61 q^{21} - 93 q^{22} - 60 q^{23} - 41 q^{24} + 26 q^{25} - 9 q^{26} - 93 q^{27} - 126 q^{28} - 47 q^{29} - 36 q^{30} - 100 q^{31} - 114 q^{32} - 133 q^{33} - 75 q^{34} - 37 q^{35} + 75 q^{36} - 264 q^{37} - 35 q^{38} - 47 q^{39} - 118 q^{40} - 72 q^{41} - 64 q^{42} - 107 q^{43} - 59 q^{44} - 69 q^{45} - 111 q^{46} - 54 q^{47} - 135 q^{48} + 33 q^{49} - 42 q^{50} - 26 q^{51} - 173 q^{52} - 103 q^{53} - 28 q^{54} - 78 q^{55} - 44 q^{56} - 205 q^{57} - 189 q^{58} - 38 q^{59} - 105 q^{60} - 108 q^{61} - 14 q^{62} - 116 q^{63} + 39 q^{64} - 146 q^{65} + 5 q^{66} - 206 q^{67} - 62 q^{68} - 55 q^{69} - 125 q^{70} - 78 q^{71} - 225 q^{72} - 326 q^{73} + 3 q^{74} - 95 q^{75} - 84 q^{76} - 79 q^{77} - 86 q^{78} - 117 q^{79} - 39 q^{80} + q^{81} - 96 q^{82} - 23 q^{83} - 57 q^{84} - 224 q^{85} - 7 q^{86} - 45 q^{87} - 250 q^{88} - 104 q^{89} - 36 q^{90} - 96 q^{91} - 137 q^{92} - 155 q^{93} - 48 q^{94} - 38 q^{95} - 33 q^{96} - 447 q^{97} - 46 q^{98} - 94 q^{99}+O(q^{100}) \) 217 * q - 20 * q^2 - 27 * q^3 + 184 * q^4 - 19 * q^5 - 17 * q^6 - 48 * q^7 - 57 * q^8 + 152 * q^9 - 46 * q^10 - 32 * q^11 - 72 * q^12 - 80 * q^13 - 22 * q^14 - 43 * q^15 + 122 * q^16 - 61 * q^17 - 88 * q^18 - 43 * q^19 - 41 * q^20 - 61 * q^21 - 93 * q^22 - 60 * q^23 - 41 * q^24 + 26 * q^25 - 9 * q^26 - 93 * q^27 - 126 * q^28 - 47 * q^29 - 36 * q^30 - 100 * q^31 - 114 * q^32 - 133 * q^33 - 75 * q^34 - 37 * q^35 + 75 * q^36 - 264 * q^37 - 35 * q^38 - 47 * q^39 - 118 * q^40 - 72 * q^41 - 64 * q^42 - 107 * q^43 - 59 * q^44 - 69 * q^45 - 111 * q^46 - 54 * q^47 - 135 * q^48 + 33 * q^49 - 42 * q^50 - 26 * q^51 - 173 * q^52 - 103 * q^53 - 28 * q^54 - 78 * q^55 - 44 * q^56 - 205 * q^57 - 189 * q^58 - 38 * q^59 - 105 * q^60 - 108 * q^61 - 14 * q^62 - 116 * q^63 + 39 * q^64 - 146 * q^65 + 5 * q^66 - 206 * q^67 - 62 * q^68 - 55 * q^69 - 125 * q^70 - 78 * q^71 - 225 * q^72 - 326 * q^73 + 3 * q^74 - 95 * q^75 - 84 * q^76 - 79 * q^77 - 86 * q^78 - 117 * q^79 - 39 * q^80 + q^81 - 96 * q^82 - 23 * q^83 - 57 * q^84 - 224 * q^85 - 7 * q^86 - 45 * q^87 - 250 * q^88 - 104 * q^89 - 36 * q^90 - 96 * q^91 - 137 * q^92 - 155 * q^93 - 48 * q^94 - 38 * q^95 - 33 * q^96 - 447 * q^97 - 46 * q^98 - 94 * q^99

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