LMFDB - Embedded newform 6019.2.a.b.1.15

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6019,2,Mod(1,6019)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6019, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("6019.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6019 = 13 \cdot 463 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6019.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:	$48.0619569766$
Analytic rank:	$1$
Dimension:	$101$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.15
Character	$\chi$	$=$	6019.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.18475 q^{2} +1.46102 q^{3} +2.77312 q^{4} -4.12132 q^{5} -3.19197 q^{6} +2.89283 q^{7} -1.68907 q^{8} -0.865408 q^{9} +O(q^{10})$	\(q-2.18475 q^{2} +1.46102 q^{3} +2.77312 q^{4} -4.12132 q^{5} -3.19197 q^{6} +2.89283 q^{7} -1.68907 q^{8} -0.865408 q^{9} +9.00405 q^{10} -3.82290 q^{11} +4.05160 q^{12} +1.00000 q^{13} -6.32010 q^{14} -6.02135 q^{15} -1.85604 q^{16} -2.49909 q^{17} +1.89070 q^{18} -1.18283 q^{19} -11.4289 q^{20} +4.22649 q^{21} +8.35207 q^{22} +2.55393 q^{23} -2.46778 q^{24} +11.9853 q^{25} -2.18475 q^{26} -5.64746 q^{27} +8.02217 q^{28} -8.88614 q^{29} +13.1551 q^{30} +6.15307 q^{31} +7.43313 q^{32} -5.58535 q^{33} +5.45988 q^{34} -11.9223 q^{35} -2.39988 q^{36} +9.42289 q^{37} +2.58418 q^{38} +1.46102 q^{39} +6.96121 q^{40} +10.7129 q^{41} -9.23382 q^{42} +5.80061 q^{43} -10.6014 q^{44} +3.56663 q^{45} -5.57970 q^{46} +4.48649 q^{47} -2.71173 q^{48} +1.36847 q^{49} -26.1848 q^{50} -3.65123 q^{51} +2.77312 q^{52} +2.51990 q^{53} +12.3383 q^{54} +15.7554 q^{55} -4.88620 q^{56} -1.72814 q^{57} +19.4140 q^{58} -3.70438 q^{59} -16.6979 q^{60} +4.01837 q^{61} -13.4429 q^{62} -2.50348 q^{63} -12.5274 q^{64} -4.12132 q^{65} +12.2026 q^{66} -3.01438 q^{67} -6.93028 q^{68} +3.73136 q^{69} +26.0472 q^{70} +1.82785 q^{71} +1.46174 q^{72} -8.07601 q^{73} -20.5866 q^{74} +17.5108 q^{75} -3.28012 q^{76} -11.0590 q^{77} -3.19197 q^{78} +2.14492 q^{79} +7.64936 q^{80} -5.65484 q^{81} -23.4049 q^{82} +2.40836 q^{83} +11.7206 q^{84} +10.2996 q^{85} -12.6729 q^{86} -12.9829 q^{87} +6.45716 q^{88} +4.85481 q^{89} -7.79218 q^{90} +2.89283 q^{91} +7.08236 q^{92} +8.98979 q^{93} -9.80184 q^{94} +4.87481 q^{95} +10.8600 q^{96} +0.251200 q^{97} -2.98975 q^{98} +3.30837 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 101 q - 8 q^{2} - 13 q^{3} + 86 q^{4} - 43 q^{5} - 10 q^{6} - q^{7} - 24 q^{8} + 52 q^{9}+O(q^{10}) $ 101 * q - 8 * q^2 - 13 * q^3 + 86 * q^4 - 43 * q^5 - 10 * q^6 - q^7 - 24 * q^8 + 52 * q^9	\( 101 q - 8 q^{2} - 13 q^{3} + 86 q^{4} - 43 q^{5} - 10 q^{6} - q^{7} - 24 q^{8} + 52 q^{9} - 19 q^{10} - 42 q^{11} - 28 q^{12} + 101 q^{13} - 45 q^{14} - 15 q^{15} + 48 q^{16} - 83 q^{17} - 4 q^{18} - 18 q^{19} - 51 q^{20} - 50 q^{21} - 20 q^{22} - 64 q^{23} - 23 q^{24} + 46 q^{25} - 8 q^{26} - 37 q^{27} - 11 q^{28} - 117 q^{29} - 28 q^{30} - 10 q^{31} - 36 q^{32} - 20 q^{33} - 10 q^{34} - 53 q^{35} - 16 q^{36} - 27 q^{37} - 68 q^{38} - 13 q^{39} - 42 q^{40} - 60 q^{41} - 31 q^{42} - 16 q^{43} - 89 q^{44} - 56 q^{45} + 5 q^{46} - 23 q^{47} - 37 q^{48} + 48 q^{49} - 30 q^{50} - 68 q^{51} + 86 q^{52} - 189 q^{53} - 23 q^{54} + 3 q^{55} - 106 q^{56} - 25 q^{57} - 82 q^{59} + 6 q^{60} - 68 q^{61} - 57 q^{62} + 3 q^{63} - 2 q^{64} - 43 q^{65} - 40 q^{66} - 13 q^{67} - 138 q^{68} - 92 q^{69} + 18 q^{70} - 39 q^{71} - 20 q^{72} + 19 q^{73} - 88 q^{74} - 21 q^{75} - 53 q^{76} - 147 q^{77} - 10 q^{78} - 19 q^{79} - 104 q^{80} - 55 q^{81} + 27 q^{82} - 49 q^{83} - 59 q^{84} - 27 q^{85} - 99 q^{86} - 33 q^{87} - 41 q^{88} - 70 q^{89} - 49 q^{90} - q^{91} - 111 q^{92} - 84 q^{93} + 4 q^{94} - 82 q^{95} - 7 q^{96} + 25 q^{97} - 37 q^{98} - 41 q^{99}+O(q^{100}) \) 101 * q - 8 * q^2 - 13 * q^3 + 86 * q^4 - 43 * q^5 - 10 * q^6 - q^7 - 24 * q^8 + 52 * q^9 - 19 * q^10 - 42 * q^11 - 28 * q^12 + 101 * q^13 - 45 * q^14 - 15 * q^15 + 48 * q^16 - 83 * q^17 - 4 * q^18 - 18 * q^19 - 51 * q^20 - 50 * q^21 - 20 * q^22 - 64 * q^23 - 23 * q^24 + 46 * q^25 - 8 * q^26 - 37 * q^27 - 11 * q^28 - 117 * q^29 - 28 * q^30 - 10 * q^31 - 36 * q^32 - 20 * q^33 - 10 * q^34 - 53 * q^35 - 16 * q^36 - 27 * q^37 - 68 * q^38 - 13 * q^39 - 42 * q^40 - 60 * q^41 - 31 * q^42 - 16 * q^43 - 89 * q^44 - 56 * q^45 + 5 * q^46 - 23 * q^47 - 37 * q^48 + 48 * q^49 - 30 * q^50 - 68 * q^51 + 86 * q^52 - 189 * q^53 - 23 * q^54 + 3 * q^55 - 106 * q^56 - 25 * q^57 - 82 * q^59 + 6 * q^60 - 68 * q^61 - 57 * q^62 + 3 * q^63 - 2 * q^64 - 43 * q^65 - 40 * q^66 - 13 * q^67 - 138 * q^68 - 92 * q^69 + 18 * q^70 - 39 * q^71 - 20 * q^72 + 19 * q^73 - 88 * q^74 - 21 * q^75 - 53 * q^76 - 147 * q^77 - 10 * q^78 - 19 * q^79 - 104 * q^80 - 55 * q^81 + 27 * q^82 - 49 * q^83 - 59 * q^84 - 27 * q^85 - 99 * q^86 - 33 * q^87 - 41 * q^88 - 70 * q^89 - 49 * q^90 - q^91 - 111 * q^92 - 84 * q^93 + 4 * q^94 - 82 * q^95 - 7 * q^96 + 25 * q^97 - 37 * q^98 - 41 * 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 $

$2$	−2.18475	−1.54485	−0.772425	−	0.635106i	$-0.780956\pi$
$2$	−2.18475	−1.54485	−0.772425	+	0.635106i	$0.780956\pi$
$3$	1.46102	0.843523	0.421761	−	0.906707i	$-0.361412\pi$
$3$	1.46102	0.843523	0.421761	+	0.906707i	$0.361412\pi$
$4$	2.77312	1.38656
$5$	−4.12132	−1.84311	−0.921556	−	0.388246i	$-0.873081\pi$
$5$	−4.12132	−1.84311	−0.921556	+	0.388246i	$0.873081\pi$
$6$	−3.19197	−1.30312
$7$	2.89283	1.09339	0.546693	−	0.837333i	$-0.315886\pi$
$7$	2.89283	1.09339	0.546693	+	0.837333i	$0.315886\pi$
$8$	−1.68907	−0.597177
$9$	−0.865408	−0.288469
$10$	9.00405	2.84733
$11$	−3.82290	−1.15265	−0.576324	−	0.817221i	$-0.695513\pi$
$11$	−3.82290	−1.15265	−0.576324	+	0.817221i	$0.695513\pi$
$12$	4.05160	1.16959
$13$	1.00000	0.277350
$13$	1.00000	0.277350
$14$	−6.32010	−1.68912
$15$	−6.02135	−1.55471
$16$	−1.85604	−0.464011
$17$	−2.49909	−0.606119	−0.303059	−	0.952972i	$-0.598008\pi$
$17$	−2.49909	−0.606119	−0.303059	+	0.952972i	$0.598008\pi$
$18$	1.89070	0.445642
$19$	−1.18283	−0.271359	−0.135679	−	0.990753i	$-0.543322\pi$
$19$	−1.18283	−0.271359	−0.135679	+	0.990753i	$0.543322\pi$
$20$	−11.4289	−2.55558
$21$	4.22649	0.922297
$22$	8.35207	1.78067
$23$	2.55393	0.532532	0.266266	−	0.963900i	$-0.414210\pi$
$23$	2.55393	0.532532	0.266266	+	0.963900i	$0.414210\pi$
$24$	−2.46778	−0.503733
$25$	11.9853	2.39706
$26$	−2.18475	−0.428464
$27$	−5.64746	−1.08685
$28$	8.02217	1.51605
$29$	−8.88614	−1.65012	−0.825058	−	0.565049i	$-0.808857\pi$
$29$	−8.88614	−1.65012	−0.825058	+	0.565049i	$0.808857\pi$
$30$	13.1551	2.40179
$31$	6.15307	1.10512	0.552562	−	0.833472i	$-0.313650\pi$
$31$	6.15307	1.10512	0.552562	+	0.833472i	$0.313650\pi$
$32$	7.43313	1.31400
$33$	−5.58535	−0.972285
$34$	5.45988	0.936363
$35$	−11.9223	−2.01523
$36$	−2.39988	−0.399980
$37$	9.42289	1.54911	0.774557	−	0.632504i	$-0.217973\pi$
$37$	9.42289	1.54911	0.774557	+	0.632504i	$0.217973\pi$
$38$	2.58418	0.419209
$39$	1.46102	0.233951
$40$	6.96121	1.10066
$41$	10.7129	1.67307	0.836535	−	0.547913i	$-0.184577\pi$
$41$	10.7129	1.67307	0.836535	+	0.547913i	$0.184577\pi$
$42$	−9.23382	−1.42481
$43$	5.80061	0.884585	0.442293	−	0.896871i	$-0.354165\pi$
$43$	5.80061	0.884585	0.442293	+	0.896871i	$0.354165\pi$
$44$	−10.6014	−1.59822
$45$	3.56663	0.531681
$46$	−5.57970	−0.822681
$47$	4.48649	0.654421	0.327211	−	0.944951i	$-0.393891\pi$
$47$	4.48649	0.654421	0.327211	+	0.944951i	$0.393891\pi$
$48$	−2.71173	−0.391404
$49$	1.36847	0.195495
$50$	−26.1848	−3.70310
$51$	−3.65123	−0.511275
$52$	2.77312	0.384563
$53$	2.51990	0.346135	0.173068	−	0.984910i	$-0.444632\pi$
$53$	2.51990	0.346135	0.173068	+	0.984910i	$0.444632\pi$
$54$	12.3383	1.67902
$55$	15.7554	2.12446
$56$	−4.88620	−0.652946
$57$	−1.72814	−0.228897
$58$	19.4140	2.54918
$59$	−3.70438	−0.482269	−0.241135	−	0.970492i	$-0.577520\pi$
$59$	−3.70438	−0.482269	−0.241135	+	0.970492i	$0.577520\pi$
$60$	−16.6979	−2.15569
$61$	4.01837	0.514499	0.257250	−	0.966345i	$-0.417184\pi$
$61$	4.01837	0.514499	0.257250	+	0.966345i	$0.417184\pi$
$62$	−13.4429	−1.70725
$63$	−2.50348	−0.315409
$64$	−12.5274	−1.56593
$65$	−4.12132	−0.511187
$66$	12.2026	1.50203
$67$	−3.01438	−0.368265	−0.184132	−	0.982901i	$-0.558947\pi$
$67$	−3.01438	−0.368265	−0.184132	+	0.982901i	$0.558947\pi$
$68$	−6.93028	−0.840420
$69$	3.73136	0.449203
$70$	26.0472	3.11323
$71$	1.82785	0.216926	0.108463	−	0.994101i	$-0.465407\pi$
$71$	1.82785	0.216926	0.108463	+	0.994101i	$0.465407\pi$
$72$	1.46174	0.172267
$73$	−8.07601	−0.945226	−0.472613	−	0.881270i	$-0.656689\pi$
$73$	−8.07601	−0.945226	−0.472613	+	0.881270i	$0.656689\pi$
$74$	−20.5866	−2.39315
$75$	17.5108	2.02197
$76$	−3.28012	−0.376256
$77$	−11.0590	−1.26029
$78$	−3.19197	−0.361419
$79$	2.14492	0.241323	0.120661	−	0.992694i	$-0.461498\pi$
$79$	2.14492	0.241323	0.120661	+	0.992694i	$0.461498\pi$
$80$	7.64936	0.855224
$81$	−5.65484	−0.628316
$82$	−23.4049	−2.58464
$83$	2.40836	0.264351	0.132176	−	0.991226i	$-0.457804\pi$
$83$	2.40836	0.264351	0.132176	+	0.991226i	$0.457804\pi$
$84$	11.7206	1.27882
$85$	10.2996	1.11714
$86$	−12.6729	−1.36655
$87$	−12.9829	−1.39191
$88$	6.45716	0.688335
$89$	4.85481	0.514608	0.257304	−	0.966330i	$-0.417166\pi$
$89$	4.85481	0.514608	0.257304	+	0.966330i	$0.417166\pi$
$90$	−7.79218	−0.821368
$91$	2.89283	0.303251
$92$	7.08236	0.738387
$93$	8.98979	0.932197
$94$	−9.80184	−1.01098
$95$	4.87481	0.500145
$96$	10.8600	1.10839
$97$	0.251200	0.0255055	0.0127527	−	0.999919i	$-0.495941\pi$
$97$	0.251200	0.0255055	0.0127527	+	0.999919i	$0.495941\pi$
$98$	−2.98975	−0.302010
$99$	3.30837	0.332504
$100$	33.2367	3.32367
$101$	−1.16708	−0.116129	−0.0580646	−	0.998313i	$-0.518493\pi$
$101$	−1.16708	−0.116129	−0.0580646	+	0.998313i	$0.518493\pi$
$102$	7.97702	0.789843
$103$	−15.7695	−1.55382	−0.776910	−	0.629612i	$-0.783214\pi$
$103$	−15.7695	−1.55382	−0.776910	+	0.629612i	$0.783214\pi$
$104$	−1.68907	−0.165627
$105$	−17.4187	−1.69990
$106$	−5.50535	−0.534726
$107$	−9.11114	−0.880807	−0.440403	−	0.897800i	$-0.645165\pi$
$107$	−9.11114	−0.880807	−0.440403	+	0.897800i	$0.645165\pi$
$108$	−15.6611	−1.50699
$109$	−13.2581	−1.26990	−0.634948	−	0.772555i	$-0.718978\pi$
$109$	−13.2581	−1.26990	−0.634948	+	0.772555i	$0.718978\pi$
$110$	−34.4216	−3.28197
$111$	13.7671	1.30671
$112$	−5.36922	−0.507344
$113$	−17.7026	−1.66532	−0.832660	−	0.553785i	$-0.813183\pi$
$113$	−17.7026	−1.66532	−0.832660	+	0.553785i	$0.813183\pi$
$114$	3.77554	0.353612
$115$	−10.5256	−0.981515
$116$	−24.6423	−2.28798
$117$	−0.865408	−0.0800070
$118$	8.09314	0.745034
$119$	−7.22945	−0.662723
$120$	10.1705	0.928435
$121$	3.61457	0.328597
$122$	−8.77912	−0.794824
$123$	15.6518	1.41127
$124$	17.0632	1.53232
$125$	−28.7887	−2.57494
$126$	5.46947	0.487259
$127$	−0.625243	−0.0554813	−0.0277407	−	0.999615i	$-0.508831\pi$
$127$	−0.625243	−0.0554813	−0.0277407	+	0.999615i	$0.508831\pi$
$128$	12.5030	1.10512
$129$	8.47484	0.746168
$130$	9.00405	0.789707
$131$	18.5513	1.62083	0.810416	−	0.585854i	$-0.199241\pi$
$131$	18.5513	1.62083	0.810416	+	0.585854i	$0.199241\pi$
$132$	−15.4888	−1.34813
$133$	−3.42172	−0.296700
$134$	6.58565	0.568913
$135$	23.2750	2.00319
$136$	4.22115	0.361960
$137$	−12.3504	−1.05517	−0.527583	−	0.849504i	$-0.676901\pi$
$137$	−12.3504	−1.05517	−0.527583	+	0.849504i	$0.676901\pi$
$138$	−8.15207	−0.693950
$139$	0.604635	0.0512845	0.0256422	−	0.999671i	$-0.491837\pi$
$139$	0.604635	0.0512845	0.0256422	+	0.999671i	$0.491837\pi$
$140$	−33.0619	−2.79424
$141$	6.55487	0.552019
$142$	−3.99339	−0.335117
$143$	−3.82290	−0.319687
$144$	1.60624	0.133853
$145$	36.6227	3.04135
$146$	17.6440	1.46023
$147$	1.99936	0.164905
$148$	26.1308	2.14794
$149$	9.95023	0.815155	0.407577	−	0.913171i	$-0.366374\pi$
$149$	9.95023	0.815155	0.407577	+	0.913171i	$0.366374\pi$
$150$	−38.2567	−3.12365
$151$	9.39274	0.764370	0.382185	−	0.924086i	$-0.375172\pi$
$151$	9.39274	0.764370	0.382185	+	0.924086i	$0.375172\pi$
$152$	1.99788	0.162049
$153$	2.16274	0.174847
$154$	24.1611	1.94696
$155$	−25.3588	−2.03687
$156$	4.05160	0.324387
$157$	−14.1361	−1.12818	−0.564090	−	0.825713i	$-0.690773\pi$
$157$	−14.1361	−1.12818	−0.564090	+	0.825713i	$0.690773\pi$
$158$	−4.68612	−0.372807
$159$	3.68164	0.291973
$160$	−30.6343	−2.42186
$161$	7.38809	0.582263
$162$	12.3544	0.970653
$163$	5.27987	0.413551	0.206776	−	0.978388i	$-0.433703\pi$
$163$	5.27987	0.413551	0.206776	+	0.978388i	$0.433703\pi$
$164$	29.7081	2.31981
$165$	23.0190	1.79203
$166$	−5.26165	−0.408383
$167$	12.6819	0.981358	0.490679	−	0.871341i	$-0.336749\pi$
$167$	12.6819	0.981358	0.490679	+	0.871341i	$0.336749\pi$
$168$	−7.13885	−0.550775
$169$	1.00000	0.0769231
$170$	−22.5019	−1.72582
$171$	1.02363	0.0782788
$172$	16.0858	1.22653
$173$	19.8967	1.51272	0.756358	−	0.654158i	$-0.226977\pi$
$173$	19.8967	1.51272	0.756358	+	0.654158i	$0.226977\pi$
$174$	28.3643	2.15029
$175$	34.6714	2.62091
$176$	7.09547	0.534842
$177$	−5.41219	−0.406805
$178$	−10.6065	−0.794992
$179$	1.69569	0.126742	0.0633709	−	0.997990i	$-0.479815\pi$
$179$	1.69569	0.126742	0.0633709	+	0.997990i	$0.479815\pi$
$180$	9.89069	0.737208
$181$	0.106070	0.00788412	0.00394206	−	0.999992i	$-0.498745\pi$
$181$	0.106070	0.00788412	0.00394206	+	0.999992i	$0.498745\pi$
$182$	−6.32010	−0.468477
$183$	5.87093	0.433992
$184$	−4.31378	−0.318016
$185$	−38.8348	−2.85519
$186$	−19.6404	−1.44010
$187$	9.55378	0.698642
$188$	12.4416	0.907395
$189$	−16.3371	−1.18835
$190$	−10.6502	−0.772649
$191$	20.8181	1.50635	0.753174	−	0.657822i	$-0.228522\pi$
$191$	20.8181	1.50635	0.753174	+	0.657822i	$0.228522\pi$
$192$	−18.3029	−1.32090
$193$	1.90488	0.137116	0.0685582	−	0.997647i	$-0.478160\pi$
$193$	1.90488	0.137116	0.0685582	+	0.997647i	$0.478160\pi$
$194$	−0.548808	−0.0394021
$195$	−6.02135	−0.431198
$196$	3.79492	0.271066
$197$	9.41484	0.670779	0.335390	−	0.942079i	$-0.391132\pi$
$197$	9.41484	0.670779	0.335390	+	0.942079i	$0.391132\pi$
$198$	−7.22795	−0.513668
$199$	−24.3160	−1.72371	−0.861857	−	0.507152i	$-0.830698\pi$
$199$	−24.3160	−1.72371	−0.861857	+	0.507152i	$0.830698\pi$
$200$	−20.2440	−1.43147
$201$	−4.40408	−0.310640
$202$	2.54978	0.179402
$203$	−25.7061	−1.80421
$204$	−10.1253	−0.708914
$205$	−44.1512	−3.08366
$206$	34.4525	2.40042
$207$	−2.21019	−0.153619
$208$	−1.85604	−0.128694
$209$	4.52183	0.312781
$210$	38.0556	2.62608
$211$	−17.8637	−1.22979	−0.614895	−	0.788609i	$-0.710802\pi$
$211$	−17.8637	−1.22979	−0.614895	+	0.788609i	$0.710802\pi$
$212$	6.98799	0.479937
$213$	2.67053	0.182982
$214$	19.9055	1.36071
$215$	−23.9062	−1.63039
$216$	9.53896	0.649044
$217$	17.7998	1.20833
$218$	28.9656	1.96180
$219$	−11.7993	−0.797320
$220$	43.6916	2.94569
$221$	−2.49909	−0.168107
$222$	−30.0776	−2.01867
$223$	0.192240	0.0128733	0.00643665	−	0.999979i	$-0.497951\pi$
$223$	0.192240	0.0128733	0.00643665	+	0.999979i	$0.497951\pi$
$224$	21.5028	1.43672
$225$	−10.3722	−0.691479
$226$	38.6757	2.57267
$227$	−15.8023	−1.04884	−0.524418	−	0.851461i	$-0.675717\pi$
$227$	−15.8023	−1.04884	−0.524418	+	0.851461i	$0.675717\pi$
$228$	−4.79233	−0.317380
$229$	−11.2393	−0.742717	−0.371358	−	0.928490i	$-0.621108\pi$
$229$	−11.2393	−0.742717	−0.371358	+	0.928490i	$0.621108\pi$
$230$	22.9957	1.51629
$231$	−16.1575	−1.06308
$232$	15.0093	0.985411
$233$	−24.7253	−1.61981	−0.809906	−	0.586560i	$-0.800482\pi$
$233$	−24.7253	−1.61981	−0.809906	+	0.586560i	$0.800482\pi$
$234$	1.89070	0.123599
$235$	−18.4903	−1.20617
$236$	−10.2727	−0.668695
$237$	3.13379	0.203561
$238$	15.7945	1.02381
$239$	3.17623	0.205453	0.102727	−	0.994710i	$-0.467243\pi$
$239$	3.17623	0.205453	0.102727	+	0.994710i	$0.467243\pi$
$240$	11.1759	0.721401
$241$	−4.34789	−0.280072	−0.140036	−	0.990146i	$-0.544722\pi$
$241$	−4.34789	−0.280072	−0.140036	+	0.990146i	$0.544722\pi$
$242$	−7.89692	−0.507634
$243$	8.68050	0.556855
$244$	11.1434	0.713384
$245$	−5.63989	−0.360319
$246$	−34.1952	−2.18020
$247$	−1.18283	−0.0752614
$248$	−10.3930	−0.659955
$249$	3.51867	0.222986
$250$	62.8960	3.97789
$251$	8.44904	0.533298	0.266649	−	0.963794i	$-0.414083\pi$
$251$	8.44904	0.533298	0.266649	+	0.963794i	$0.414083\pi$
$252$	−6.94245	−0.437333
$253$	−9.76343	−0.613822
$254$	1.36600	0.0857103
$255$	15.0479	0.942337
$256$	−2.26103	−0.141314
$257$	3.06750	0.191345	0.0956725	−	0.995413i	$-0.469500\pi$
$257$	3.06750	0.191345	0.0956725	+	0.995413i	$0.469500\pi$
$258$	−18.5154	−1.15272
$259$	27.2588	1.69378
$260$	−11.4289	−0.708792
$261$	7.69014	0.476008
$262$	−40.5299	−2.50394
$263$	−31.1874	−1.92310	−0.961550	−	0.274630i	$-0.911445\pi$
$263$	−31.1874	−1.92310	−0.961550	+	0.274630i	$0.911445\pi$
$264$	9.43406	0.580626
$265$	−10.3853	−0.637965
$266$	7.47558	0.458357
$267$	7.09299	0.434084
$268$	−8.35923	−0.510621
$269$	7.41046	0.451824	0.225912	−	0.974148i	$-0.427464\pi$
$269$	7.41046	0.451824	0.225912	+	0.974148i	$0.427464\pi$
$270$	−50.8500	−3.09463
$271$	−1.27131	−0.0772268	−0.0386134	−	0.999254i	$-0.512294\pi$
$271$	−1.27131	−0.0772268	−0.0386134	+	0.999254i	$0.512294\pi$
$272$	4.63843	0.281246
$273$	4.22649	0.255799
$274$	26.9825	1.63007
$275$	−45.8186	−2.76297
$276$	10.3475	0.622846
$277$	−11.3579	−0.682431	−0.341215	−	0.939985i	$-0.610839\pi$
$277$	−11.3579	−0.682431	−0.341215	+	0.939985i	$0.610839\pi$
$278$	−1.32097	−0.0792268
$279$	−5.32492	−0.318795
$280$	20.1376	1.20345
$281$	−9.57996	−0.571492	−0.285746	−	0.958305i	$-0.592241\pi$
$281$	−9.57996	−0.571492	−0.285746	+	0.958305i	$0.592241\pi$
$282$	−14.3207	−0.852787
$283$	−26.7519	−1.59024	−0.795118	−	0.606455i	$-0.792591\pi$
$283$	−26.7519	−1.59024	−0.795118	+	0.606455i	$0.792591\pi$
$284$	5.06884	0.300780
$285$	7.12221	0.421884
$286$	8.35207	0.493868
$287$	30.9905	1.82931
$288$	−6.43270	−0.379050
$289$	−10.7545	−0.632620
$290$	−80.0113	−4.69842
$291$	0.367009	0.0215144
$292$	−22.3958	−1.31061
$293$	−32.5654	−1.90249	−0.951245	−	0.308436i	$-0.900195\pi$
$293$	−32.5654	−1.90249	−0.951245	+	0.308436i	$0.900195\pi$
$294$	−4.36810	−0.254753
$295$	15.2670	0.888876
$296$	−15.9159	−0.925095
$297$	21.5897	1.25276
$298$	−21.7387	−1.25929
$299$	2.55393	0.147698
$300$	48.5596	2.80359
$301$	16.7802	0.967194
$302$	−20.5208	−1.18084
$303$	−1.70514	−0.0979576
$304$	2.19538	0.125914
$305$	−16.5610	−0.948280
$306$	−4.72503	−0.270112
$307$	25.1231	1.43385	0.716925	−	0.697151i	$-0.245549\pi$
$307$	25.1231	1.43385	0.716925	+	0.697151i	$0.245549\pi$
$308$	−30.6679	−1.74747
$309$	−23.0397	−1.31068
$310$	55.4025	3.14665
$311$	6.84188	0.387967	0.193984	−	0.981005i	$-0.437859\pi$
$311$	6.84188	0.387967	0.193984	+	0.981005i	$0.437859\pi$
$312$	−2.46778	−0.139710
$313$	−15.7240	−0.888775	−0.444388	−	0.895835i	$-0.646579\pi$
$313$	−15.7240	−0.888775	−0.444388	+	0.895835i	$0.646579\pi$
$314$	30.8837	1.74287
$315$	10.3176	0.581334
$316$	5.94813	0.334609
$317$	−7.76434	−0.436089	−0.218044	−	0.975939i	$-0.569968\pi$
$317$	−7.76434	−0.436089	−0.218044	+	0.975939i	$0.569968\pi$
$318$	−8.04344	−0.451054
$319$	33.9708	1.90200
$320$	51.6296	2.88618
$321$	−13.3116	−0.742980
$322$	−16.1411	−0.899509
$323$	2.95599	0.164476
$324$	−15.6816	−0.871198
$325$	11.9853	0.664825
$326$	−11.5352	−0.638875
$327$	−19.3704	−1.07119
$328$	−18.0948	−0.999120
$329$	12.9786	0.715536
$330$	−50.2908	−2.76842
$331$	−16.7155	−0.918770	−0.459385	−	0.888237i	$-0.651930\pi$
$331$	−16.7155	−0.918770	−0.459385	+	0.888237i	$0.651930\pi$
$332$	6.67866	0.366539
$333$	−8.15465	−0.446872
$334$	−27.7068	−1.51605
$335$	12.4232	0.678753
$336$	−7.84456	−0.427956
$337$	24.9706	1.36023	0.680117	−	0.733103i	$-0.261929\pi$
$337$	24.9706	1.36023	0.680117	+	0.733103i	$0.261929\pi$
$338$	−2.18475	−0.118835
$339$	−25.8639	−1.40474
$340$	28.5619	1.54899
$341$	−23.5226	−1.27382
$342$	−2.23637	−0.120929
$343$	−16.2911	−0.879635
$344$	−9.79766	−0.528254
$345$	−15.3781	−0.827930
$346$	−43.4692	−2.33692
$347$	−0.657265	−0.0352839	−0.0176419	−	0.999844i	$-0.505616\pi$
$347$	−0.657265	−0.0352839	−0.0176419	+	0.999844i	$0.505616\pi$
$348$	−36.0031	−1.92997
$349$	−27.2967	−1.46116	−0.730580	−	0.682827i	$-0.760750\pi$
$349$	−27.2967	−1.46116	−0.730580	+	0.682827i	$0.760750\pi$
$350$	−75.7483	−4.04892
$351$	−5.64746	−0.301439
$352$	−28.4161	−1.51458
$353$	25.8889	1.37793	0.688964	−	0.724795i	$-0.258066\pi$
$353$	25.8889	1.37793	0.688964	+	0.724795i	$0.258066\pi$
$354$	11.8243	0.628453
$355$	−7.53315	−0.399818
$356$	13.4630	0.713535
$357$	−10.5624	−0.559021
$358$	−3.70465	−0.195797
$359$	15.6012	0.823401	0.411700	−	0.911319i	$-0.364935\pi$
$359$	15.6012	0.823401	0.411700	+	0.911319i	$0.364935\pi$
$360$	−6.02429	−0.317508
$361$	−17.6009	−0.926364
$362$	−0.231736	−0.0121798
$363$	5.28098	0.277179
$364$	8.02217	0.420476
$365$	33.2839	1.74216
$366$	−12.8265	−0.670452
$367$	−1.94971	−0.101774	−0.0508869	−	0.998704i	$-0.516205\pi$
$367$	−1.94971	−0.101774	−0.0508869	+	0.998704i	$0.516205\pi$
$368$	−4.74021	−0.247101
$369$	−9.27102	−0.482630
$370$	84.8442	4.41084
$371$	7.28964	0.378460
$372$	24.9298	1.29255
$373$	29.6670	1.53610	0.768048	−	0.640392i	$-0.221228\pi$
$373$	29.6670	1.53610	0.768048	+	0.640392i	$0.221228\pi$
$374$	−20.8726	−1.07930
$375$	−42.0609	−2.17202
$376$	−7.57800	−0.390806
$377$	−8.88614	−0.457660
$378$	35.6925	1.83582
$379$	−15.4537	−0.793801	−0.396901	−	0.917862i	$-0.629914\pi$
$379$	−15.4537	−0.793801	−0.396901	+	0.917862i	$0.629914\pi$
$380$	13.5184	0.693481
$381$	−0.913495	−0.0467998
$382$	−45.4824	−2.32708
$383$	11.4103	0.583039	0.291520	−	0.956565i	$-0.405839\pi$
$383$	11.4103	0.583039	0.291520	+	0.956565i	$0.405839\pi$
$384$	18.2672	0.932193
$385$	45.5777	2.32286
$386$	−4.16169	−0.211824
$387$	−5.01990	−0.255176
$388$	0.696607	0.0353649
$389$	22.9452	1.16337	0.581685	−	0.813414i	$-0.302394\pi$
$389$	22.9452	1.16337	0.581685	+	0.813414i	$0.302394\pi$
$390$	13.1551	0.666136
$391$	−6.38251	−0.322778
$392$	−2.31144	−0.116745
$393$	27.1039	1.36721
$394$	−20.5690	−1.03625
$395$	−8.83992	−0.444785
$396$	9.17451	0.461036
$397$	4.48468	0.225080	0.112540	−	0.993647i	$-0.464101\pi$
$397$	4.48468	0.225080	0.112540	+	0.993647i	$0.464101\pi$
$398$	53.1242	2.66288
$399$	−4.99921	−0.250273
$400$	−22.2453	−1.11226
$401$	1.45980	0.0728987	0.0364494	−	0.999336i	$-0.488395\pi$
$401$	1.45980	0.0728987	0.0364494	+	0.999336i	$0.488395\pi$
$402$	9.62179	0.479891
$403$	6.15307	0.306506
$404$	−3.23646	−0.161020
$405$	23.3054	1.15806
$406$	56.1613	2.78724
$407$	−36.0228	−1.78558
$408$	6.16720	0.305322
$409$	−27.6157	−1.36551	−0.682754	−	0.730648i	$-0.739218\pi$
$409$	−27.6157	−1.36551	−0.682754	+	0.730648i	$0.739218\pi$
$410$	96.4593	4.76378
$411$	−18.0442	−0.890056
$412$	−43.7308	−2.15446
$413$	−10.7161	−0.527307
$414$	4.82872	0.237318
$415$	−9.92561	−0.487229
$416$	7.43313	0.364439
$417$	0.883386	0.0432596
$418$	−9.87905	−0.483200
$419$	3.88202	0.189649	0.0948244	−	0.995494i	$-0.469771\pi$
$419$	3.88202	0.189649	0.0948244	+	0.995494i	$0.469771\pi$
$420$	−48.3043	−2.35701
$421$	40.0300	1.95094	0.975472	−	0.220124i	$-0.0706462\pi$
$421$	40.0300	1.95094	0.975472	+	0.220124i	$0.0706462\pi$
$422$	39.0277	1.89984
$423$	−3.88264	−0.188781
$424$	−4.25629	−0.206704
$425$	−29.9524	−1.45290
$426$	−5.83443	−0.282679
$427$	11.6245	0.562547
$428$	−25.2663	−1.22129
$429$	−5.58535	−0.269663
$430$	52.2290	2.51871
$431$	−18.2587	−0.879493	−0.439746	−	0.898122i	$-0.644932\pi$
$431$	−18.2587	−0.879493	−0.439746	+	0.898122i	$0.644932\pi$
$432$	10.4819	0.504312
$433$	−26.0078	−1.24986	−0.624929	−	0.780682i	$-0.714872\pi$
$433$	−26.0078	−1.24986	−0.624929	+	0.780682i	$0.714872\pi$
$434$	−38.8880	−1.86669
$435$	53.5066	2.56544
$436$	−36.7663	−1.76079
$437$	−3.02086	−0.144507
$438$	25.7784	1.23174
$439$	−16.2723	−0.776634	−0.388317	−	0.921526i	$-0.626943\pi$
$439$	−16.2723	−0.776634	−0.388317	+	0.921526i	$0.626943\pi$
$440$	−26.6120	−1.26868
$441$	−1.18428	−0.0563944
$442$	5.45988	0.259700
$443$	−3.80945	−0.180992	−0.0904962	−	0.995897i	$-0.528845\pi$
$443$	−3.80945	−0.180992	−0.0904962	+	0.995897i	$0.528845\pi$
$444$	38.1777	1.81184
$445$	−20.0082	−0.948481
$446$	−0.419995	−0.0198873
$447$	14.5375	0.687601
$448$	−36.2397	−1.71217
$449$	39.7225	1.87462	0.937310	−	0.348498i	$-0.113308\pi$
$449$	39.7225	1.87462	0.937310	+	0.348498i	$0.113308\pi$
$450$	22.6606	1.06823
$451$	−40.9543	−1.92846
$452$	−49.0914	−2.30907
$453$	13.7230	0.644764
$454$	34.5241	1.62029
$455$	−11.9223	−0.558925
$456$	2.91895	0.136692
$457$	28.5271	1.33444	0.667221	−	0.744860i	$-0.267484\pi$
$457$	28.5271	1.33444	0.667221	+	0.744860i	$0.267484\pi$
$458$	24.5551	1.14739
$459$	14.1135	0.658762
$460$	−29.1887	−1.36093
$461$	−32.3529	−1.50683	−0.753413	−	0.657548i	$-0.771594\pi$
$461$	−32.3529	−1.50683	−0.753413	+	0.657548i	$0.771594\pi$
$462$	35.3000	1.64230
$463$	1.00000	0.0464739
$463$	1.00000	0.0464739
$464$	16.4931	0.765672
$465$	−37.0498	−1.71814
$466$	54.0186	2.50236
$467$	−9.59450	−0.443980	−0.221990	−	0.975049i	$-0.571255\pi$
$467$	−9.59450	−0.443980	−0.221990	+	0.975049i	$0.571255\pi$
$468$	−2.39988	−0.110935
$469$	−8.72008	−0.402656
$470$	40.3965	1.86335
$471$	−20.6531	−0.951645
$472$	6.25697	0.288000
$473$	−22.1752	−1.01962
$474$	−6.84653	−0.314471
$475$	−14.1765	−0.650464
$476$	−20.0481	−0.918905
$477$	−2.18074	−0.0998494
$478$	−6.93925	−0.317394
$479$	−19.0808	−0.871825	−0.435913	−	0.899989i	$-0.643574\pi$
$479$	−19.0808	−0.871825	−0.435913	+	0.899989i	$0.643574\pi$
$480$	−44.7575	−2.04289
$481$	9.42289	0.429647
$482$	9.49904	0.432669
$483$	10.7942	0.491152
$484$	10.0236	0.455620
$485$	−1.03528	−0.0470094
$486$	−18.9647	−0.860257
$487$	28.7685	1.30362	0.651812	−	0.758381i	$-0.274009\pi$
$487$	28.7685	1.30362	0.651812	+	0.758381i	$0.274009\pi$
$488$	−6.78732	−0.307247
$489$	7.71402	0.348840
$490$	12.3217	0.556639
$491$	−33.5913	−1.51595	−0.757977	−	0.652282i	$-0.773812\pi$
$491$	−33.5913	−1.51595	−0.757977	+	0.652282i	$0.773812\pi$
$492$	43.4043	1.95682
$493$	22.2073	1.00017
$494$	2.58418	0.116268
$495$	−13.6349	−0.612842
$496$	−11.4204	−0.512790
$497$	5.28765	0.237184
$498$	−7.68739	−0.344480
$499$	12.4132	0.555692	0.277846	−	0.960626i	$-0.410380\pi$
$499$	12.4132	0.555692	0.277846	+	0.960626i	$0.410380\pi$
$500$	−79.8345	−3.57031
$501$	18.5286	0.827797
$502$	−18.4590	−0.823866
$503$	−23.8817	−1.06483	−0.532416	−	0.846483i	$-0.678716\pi$
$503$	−23.8817	−1.06483	−0.532416	+	0.846483i	$0.678716\pi$
$504$	4.22856	0.188355
$505$	4.80993	0.214039
$506$	21.3306	0.948262
$507$	1.46102	0.0648864
$508$	−1.73387	−0.0769282
$509$	−0.826320	−0.0366260	−0.0183130	−	0.999832i	$-0.505830\pi$
$509$	−0.826320	−0.0366260	−0.0183130	+	0.999832i	$0.505830\pi$
$510$	−32.8759	−1.45577
$511$	−23.3625	−1.03350
$512$	−20.0662	−0.886810
$513$	6.67996	0.294927
$514$	−6.70170	−0.295599
$515$	64.9914	2.86386
$516$	23.5017	1.03461
$517$	−17.1514	−0.754318
$518$	−59.5536	−2.61664
$519$	29.0695	1.27601
$520$	6.96121	0.305269
$521$	−18.1152	−0.793642	−0.396821	−	0.917896i	$-0.629887\pi$
$521$	−18.1152	−0.793642	−0.396821	+	0.917896i	$0.629887\pi$
$522$	−16.8010	−0.735361
$523$	−37.4857	−1.63913	−0.819567	−	0.572983i	$-0.805786\pi$
$523$	−37.4857	−1.63913	−0.819567	+	0.572983i	$0.805786\pi$
$524$	51.4449	2.24738
$525$	50.6558	2.21080
$526$	68.1367	2.97090
$527$	−15.3771	−0.669837
$528$	10.3667	0.451151
$529$	−16.4774	−0.716410
$530$	22.6893	0.985561
$531$	3.20580	0.139120
$532$	−9.48883	−0.411393
$533$	10.7129	0.464026
$534$	−15.4964	−0.670594
$535$	37.5499	1.62342
$536$	5.09150	0.219919
$537$	2.47744	0.106910
$538$	−16.1900	−0.698000
$539$	−5.23151	−0.225337
$540$	64.5443	2.77755
$541$	3.86547	0.166190	0.0830948	−	0.996542i	$-0.473520\pi$
$541$	3.86547	0.166190	0.0830948	+	0.996542i	$0.473520\pi$
$542$	2.77750	0.119304
$543$	0.154971	0.00665043
$544$	−18.5761	−0.796443
$545$	54.6409	2.34056
$546$	−9.23382	−0.395171
$547$	24.8960	1.06448	0.532239	−	0.846594i	$-0.321351\pi$
$547$	24.8960	1.06448	0.532239	+	0.846594i	$0.321351\pi$
$548$	−34.2491	−1.46305
$549$	−3.47753	−0.148417
$550$	100.102	4.26837
$551$	10.5108	0.447774
$552$	−6.30253	−0.268254
$553$	6.20490	0.263859
$554$	24.8142	1.05425
$555$	−56.7385	−2.40842
$556$	1.67673	0.0711090
$557$	−2.69653	−0.114256	−0.0571279	−	0.998367i	$-0.518194\pi$
$557$	−2.69653	−0.114256	−0.0571279	+	0.998367i	$0.518194\pi$
$558$	11.6336	0.492490
$559$	5.80061	0.245340
$560$	22.1283	0.935091
$561$	13.9583	0.589320
$562$	20.9298	0.882870
$563$	−29.7761	−1.25491	−0.627456	−	0.778652i	$-0.715904\pi$
$563$	−29.7761	−1.25491	−0.627456	+	0.778652i	$0.715904\pi$
$564$	18.1774	0.765408
$565$	72.9581	3.06937
$566$	58.4462	2.45668
$567$	−16.3585	−0.686992
$568$	−3.08737	−0.129543
$569$	38.6374	1.61976	0.809882	−	0.586593i	$-0.199531\pi$
$569$	38.6374	1.61976	0.809882	+	0.586593i	$0.199531\pi$
$570$	−15.5602	−0.651747
$571$	29.3429	1.22796	0.613981	−	0.789321i	$-0.289567\pi$
$571$	29.3429	1.22796	0.613981	+	0.789321i	$0.289567\pi$
$572$	−10.6014	−0.443265
$573$	30.4158	1.27064
$574$	−67.7065	−2.82601
$575$	30.6096	1.27651
$576$	10.8413	0.451723
$577$	6.54757	0.272579	0.136289	−	0.990669i	$-0.456482\pi$
$577$	6.54757	0.272579	0.136289	+	0.990669i	$0.456482\pi$
$578$	23.4959	0.977302
$579$	2.78308	0.115661
$580$	101.559	4.21701
$581$	6.96696	0.289038
$582$	−0.801822	−0.0332366
$583$	−9.63333	−0.398972
$584$	13.6410	0.564467
$585$	3.56663	0.147462
$586$	71.1471	2.93906
$587$	−25.5203	−1.05334	−0.526669	−	0.850071i	$-0.676559\pi$
$587$	−25.5203	−1.05334	−0.526669	+	0.850071i	$0.676559\pi$
$588$	5.54447	0.228650
$589$	−7.27801	−0.299885
$590$	−33.3544	−1.37318
$591$	13.7553	0.565818
$592$	−17.4893	−0.718806
$593$	−37.8796	−1.55553	−0.777764	−	0.628556i	$-0.783646\pi$
$593$	−37.8796	−1.55553	−0.777764	+	0.628556i	$0.783646\pi$
$594$	−47.1680	−1.93532
$595$	29.7949	1.22147
$596$	27.5932	1.13026
$597$	−35.5262	−1.45399
$598$	−5.57970	−0.228171
$599$	−30.0766	−1.22889	−0.614447	−	0.788958i	$-0.710621\pi$
$599$	−30.0766	−1.22889	−0.614447	+	0.788958i	$0.710621\pi$
$600$	−29.5770	−1.20748
$601$	7.83491	0.319593	0.159796	−	0.987150i	$-0.448916\pi$
$601$	7.83491	0.319593	0.159796	+	0.987150i	$0.448916\pi$
$602$	−36.6605	−1.49417
$603$	2.60867	0.106233
$604$	26.0472	1.05985
$605$	−14.8968	−0.605642
$606$	3.72530	0.151330
$607$	28.7927	1.16866	0.584330	−	0.811516i	$-0.301358\pi$
$607$	28.7927	1.16866	0.584330	+	0.811516i	$0.301358\pi$
$608$	−8.79211	−0.356567
$609$	−37.5572	−1.52190
$610$	36.1816	1.46495
$611$	4.48649	0.181504
$612$	5.99753	0.242436
$613$	14.3129	0.578091	0.289045	−	0.957315i	$-0.406662\pi$
$613$	14.3129	0.578091	0.289045	+	0.957315i	$0.406662\pi$
$614$	−54.8876	−2.21508
$615$	−64.5060	−2.60113
$616$	18.6795	0.752617
$617$	−37.1044	−1.49377	−0.746884	−	0.664954i	$-0.768451\pi$
$617$	−37.1044	−1.49377	−0.746884	+	0.664954i	$0.768451\pi$
$618$	50.3359	2.02481
$619$	−36.8965	−1.48299	−0.741497	−	0.670956i	$-0.765884\pi$
$619$	−36.8965	−1.48299	−0.741497	+	0.670956i	$0.765884\pi$
$620$	−70.3230	−2.82424
$621$	−14.4232	−0.578784
$622$	−14.9478	−0.599351
$623$	14.0441	0.562666
$624$	−2.71173	−0.108556
$625$	58.7209	2.34884
$626$	34.3531	1.37302
$627$	6.60650	0.263838
$628$	−39.2010	−1.56429
$629$	−23.5487	−0.938947
$630$	−22.5415	−0.898073
$631$	15.5759	0.620067	0.310033	−	0.950726i	$-0.399660\pi$
$631$	15.5759	0.620067	0.310033	+	0.950726i	$0.399660\pi$
$632$	−3.62293	−0.144112
$633$	−26.0993	−1.03736
$634$	16.9631	0.673691
$635$	2.57683	0.102258
$636$	10.2096	0.404838
$637$	1.36847	0.0542206
$638$	−74.2177	−2.93831
$639$	−1.58184	−0.0625764
$640$	−51.5289	−2.03686
$641$	3.57068	0.141033	0.0705167	−	0.997511i	$-0.477535\pi$
$641$	3.57068	0.141033	0.0705167	+	0.997511i	$0.477535\pi$
$642$	29.0825	1.14779
$643$	−9.77251	−0.385390	−0.192695	−	0.981259i	$-0.561723\pi$
$643$	−9.77251	−0.385390	−0.192695	+	0.981259i	$0.561723\pi$
$644$	20.4881	0.807343
$645$	−34.9275	−1.37527
$646$	−6.45810	−0.254090
$647$	46.9149	1.84441	0.922207	−	0.386696i	$-0.126384\pi$
$647$	46.9149	1.84441	0.922207	+	0.386696i	$0.126384\pi$
$648$	9.55144	0.375216
$649$	14.1615	0.555887
$650$	−26.1848	−1.02705
$651$	26.0059	1.01925
$652$	14.6417	0.573414
$653$	−39.5671	−1.54838	−0.774190	−	0.632953i	$-0.781843\pi$
$653$	−39.5671	−1.54838	−0.774190	+	0.632953i	$0.781843\pi$
$654$	42.3194	1.65482
$655$	−76.4558	−2.98738
$656$	−19.8836	−0.776324
$657$	6.98905	0.272669
$658$	−28.3551	−1.10540
$659$	−37.2276	−1.45018	−0.725092	−	0.688652i	$-0.758203\pi$
$659$	−37.2276	−1.45018	−0.725092	+	0.688652i	$0.758203\pi$
$660$	63.8345	2.48476
$661$	−30.3335	−1.17984	−0.589918	−	0.807463i	$-0.700840\pi$
$661$	−30.3335	−1.17984	−0.589918	+	0.807463i	$0.700840\pi$
$662$	36.5192	1.41936
$663$	−3.65123	−0.141802
$664$	−4.06789	−0.157865
$665$	14.1020	0.546852
$666$	17.8158	0.690350
$667$	−22.6946	−0.878739
$668$	35.1685	1.36071
$669$	0.280867	0.0108589
$670$	−27.1416	−1.04857
$671$	−15.3618	−0.593037
$672$	31.4161	1.21190
$673$	19.7787	0.762411	0.381206	−	0.924490i	$-0.375509\pi$
$673$	19.7787	0.762411	0.381206	+	0.924490i	$0.375509\pi$
$674$	−54.5544	−2.10136
$675$	−67.6864	−2.60525
$676$	2.77312	0.106658
$677$	−7.71425	−0.296483	−0.148241	−	0.988951i	$-0.547361\pi$
$677$	−7.71425	−0.296483	−0.148241	+	0.988951i	$0.547361\pi$
$678$	56.5061	2.17010
$679$	0.726678	0.0278873
$680$	−17.3967	−0.667133
$681$	−23.0876	−0.884717
$682$	51.3909	1.96786
$683$	−29.9917	−1.14760	−0.573801	−	0.818995i	$-0.694532\pi$
$683$	−29.9917	−1.14760	−0.573801	+	0.818995i	$0.694532\pi$
$684$	2.83864	0.108538
$685$	50.8999	1.94479
$686$	35.5919	1.35890
$687$	−16.4210	−0.626499
$688$	−10.7662	−0.410458
$689$	2.51990	0.0960006
$690$	33.5973	1.27903
$691$	−32.6830	−1.24332	−0.621659	−	0.783288i	$-0.713541\pi$
$691$	−32.6830	−1.24332	−0.621659	+	0.783288i	$0.713541\pi$
$692$	55.1758	2.09747
$693$	9.57055	0.363555
$694$	1.43596	0.0545082
$695$	−2.49190	−0.0945230
$696$	21.9290	0.831217
$697$	−26.7725	−1.01408
$698$	59.6365	2.25727
$699$	−36.1243	−1.36635
$700$	96.1481	3.63405
$701$	−45.4780	−1.71768	−0.858839	−	0.512245i	$-0.828814\pi$
$701$	−45.4780	−1.71768	−0.858839	+	0.512245i	$0.828814\pi$
$702$	12.3383	0.465678
$703$	−11.1456	−0.420366
$704$	47.8911	1.80496
$705$	−27.0147	−1.01743
$706$	−56.5608	−2.12869
$707$	−3.37618	−0.126974
$708$	−15.0087	−0.564060
$709$	16.3922	0.615621	0.307810	−	0.951448i	$-0.400404\pi$
$709$	16.3922	0.615621	0.307810	+	0.951448i	$0.400404\pi$
$710$	16.4580	0.617659
$711$	−1.85624	−0.0696143
$712$	−8.20012	−0.307312
$713$	15.7145	0.588514
$714$	23.0762	0.863604
$715$	15.7554	0.589219
$716$	4.70235	0.175735
$717$	4.64055	0.173304
$718$	−34.0847	−1.27203
$719$	33.5457	1.25104	0.625522	−	0.780207i	$-0.284886\pi$
$719$	33.5457	1.25104	0.625522	+	0.780207i	$0.284886\pi$
$720$	−6.61982	−0.246706
$721$	−45.6186	−1.69893
$722$	38.4536	1.43109
$723$	−6.35237	−0.236247
$724$	0.294145	0.0109318
$725$	−106.503	−3.95543
$726$	−11.5376	−0.428200
$727$	41.1806	1.52731	0.763653	−	0.645627i	$-0.223404\pi$
$727$	41.1806	1.52731	0.763653	+	0.645627i	$0.223404\pi$
$728$	−4.88620	−0.181095
$729$	29.6470	1.09804
$730$	−72.7168	−2.69137
$731$	−14.4963	−0.536164
$732$	16.2808	0.601756
$733$	10.5141	0.388347	0.194174	−	0.980967i	$-0.437798\pi$
$733$	10.5141	0.388347	0.194174	+	0.980967i	$0.437798\pi$
$734$	4.25961	0.157225
$735$	−8.24001	−0.303937
$736$	18.9837	0.699749
$737$	11.5237	0.424479
$738$	20.2548	0.745591
$739$	−25.1878	−0.926549	−0.463275	−	0.886215i	$-0.653326\pi$
$739$	−25.1878	−0.926549	−0.463275	+	0.886215i	$0.653326\pi$
$740$	−107.693	−3.95889
$741$	−1.72814	−0.0634847
$742$	−15.9260	−0.584663
$743$	28.6062	1.04946	0.524729	−	0.851269i	$-0.324167\pi$
$743$	28.6062	1.04946	0.524729	+	0.851269i	$0.324167\pi$
$744$	−15.1844	−0.556687
$745$	−41.0081	−1.50242
$746$	−64.8148	−2.37304
$747$	−2.08421	−0.0762573
$748$	26.4938	0.968709
$749$	−26.3570	−0.963063
$750$	91.8925	3.35544
$751$	−37.7946	−1.37914	−0.689572	−	0.724217i	$-0.742202\pi$
$751$	−37.7946	−1.37914	−0.689572	+	0.724217i	$0.742202\pi$
$752$	−8.32712	−0.303659
$753$	12.3442	0.449849
$754$	19.4140	0.707015
$755$	−38.7105	−1.40882
$756$	−45.3048	−1.64772
$757$	0.889254	0.0323205	0.0161602	−	0.999869i	$-0.494856\pi$
$757$	0.889254	0.0323205	0.0161602	+	0.999869i	$0.494856\pi$
$758$	33.7623	1.22630
$759$	−14.2646	−0.517772
$760$	−8.23390	−0.298675
$761$	31.6236	1.14635	0.573177	−	0.819431i	$-0.305711\pi$
$761$	31.6236	1.14635	0.573177	+	0.819431i	$0.305711\pi$
$762$	1.99576	0.0722986
$763$	−38.3534	−1.38849
$764$	57.7312	2.08864
$765$	−8.91333	−0.322262
$766$	−24.9286	−0.900708
$767$	−3.70438	−0.133757
$768$	−3.30342	−0.119202
$769$	28.7246	1.03584	0.517918	−	0.855430i	$-0.326707\pi$
$769$	28.7246	1.03584	0.517918	+	0.855430i	$0.326707\pi$
$770$	−99.5758	−3.58846
$771$	4.48168	0.161404
$772$	5.28247	0.190120
$773$	−2.05818	−0.0740277	−0.0370139	−	0.999315i	$-0.511785\pi$
$773$	−2.05818	−0.0740277	−0.0370139	+	0.999315i	$0.511785\pi$
$774$	10.9672	0.394208
$775$	73.7464	2.64905
$776$	−0.424294	−0.0152313
$777$	39.8258	1.42874
$778$	−50.1295	−1.79723
$779$	−12.6715	−0.454003
$780$	−16.6979	−0.597882
$781$	−6.98768	−0.250039
$782$	13.9442	0.498643
$783$	50.1841	1.79343
$784$	−2.53993	−0.0907119
$785$	58.2592	2.07936
$786$	−59.2151	−2.11213
$787$	−24.8829	−0.886979	−0.443490	−	0.896279i	$-0.646260\pi$
$787$	−24.8829	−0.886979	−0.443490	+	0.896279i	$0.646260\pi$
$788$	26.1085	0.930076
$789$	−45.5656	−1.62218
$790$	19.3130	0.687126
$791$	−51.2106	−1.82084
$792$	−5.58808	−0.198564
$793$	4.01837	0.142696
$794$	−9.79790	−0.347714
$795$	−15.1732	−0.538138
$796$	−67.4311	−2.39003
$797$	−42.9408	−1.52104	−0.760521	−	0.649313i	$-0.775056\pi$
$797$	−42.9408	−1.52104	−0.760521	+	0.649313i	$0.775056\pi$
$798$	10.9220	0.386635
$799$	−11.2121	−0.396657
$800$	89.0883	3.14975
$801$	−4.20139	−0.148449
$802$	−3.18928	−0.112618
$803$	30.8738	1.08951
$804$	−12.2130	−0.430720
$805$	−30.4487	−1.07318
$806$	−13.4429	−0.473506
$807$	10.8269	0.381124
$808$	1.97129	0.0693497
$809$	3.59737	0.126477	0.0632384	−	0.997998i	$-0.479857\pi$
$809$	3.59737	0.126477	0.0632384	+	0.997998i	$0.479857\pi$
$810$	−50.9165	−1.78902
$811$	−46.7441	−1.64141	−0.820704	−	0.571354i	$-0.806418\pi$
$811$	−46.7441	−1.64141	−0.820704	+	0.571354i	$0.806418\pi$
$812$	−71.2861	−2.50165
$813$	−1.85742	−0.0651426
$814$	78.7007	2.75846
$815$	−21.7600	−0.762221
$816$	6.77685	0.237237
$817$	−6.86112	−0.240040
$818$	60.3333	2.10951
$819$	−2.50348	−0.0874787
$820$	−122.437	−4.27567
$821$	−34.7988	−1.21449	−0.607244	−	0.794516i	$-0.707725\pi$
$821$	−34.7988	−1.21449	−0.607244	+	0.794516i	$0.707725\pi$
$822$	39.4221	1.37500
$823$	13.1442	0.458177	0.229088	−	0.973406i	$-0.426426\pi$
$823$	13.1442	0.458177	0.229088	+	0.973406i	$0.426426\pi$
$824$	26.6359	0.927905
$825$	−66.9421	−2.33062
$826$	23.4121	0.814610
$827$	6.76362	0.235194	0.117597	−	0.993061i	$-0.462481\pi$
$827$	6.76362	0.235194	0.117597	+	0.993061i	$0.462481\pi$
$828$	−6.12914	−0.213002
$829$	30.2615	1.05102	0.525512	−	0.850786i	$-0.323874\pi$
$829$	30.2615	1.05102	0.525512	+	0.850786i	$0.323874\pi$
$830$	21.6849	0.752696
$831$	−16.5942	−0.575646
$832$	−12.5274	−0.434310
$833$	−3.41992	−0.118493
$834$	−1.92998	−0.0668296
$835$	−52.2663	−1.80875
$836$	12.5396	0.433690
$837$	−34.7492	−1.20111
$838$	−8.48122	−0.292979
$839$	39.4118	1.36065	0.680324	−	0.732912i	$-0.261839\pi$
$839$	39.4118	1.36065	0.680324	+	0.732912i	$0.261839\pi$
$840$	29.4215	1.01514
$841$	49.9635	1.72288
$842$	−87.4555	−3.01391
$843$	−13.9965	−0.482067
$844$	−49.5383	−1.70518
$845$	−4.12132	−0.141778
$846$	8.48260	0.291638
$847$	10.4563	0.359284
$848$	−4.67705	−0.160611
$849$	−39.0852	−1.34140
$850$	65.4384	2.24452
$851$	24.0654	0.824952
$852$	7.40570	0.253715
$853$	−56.2989	−1.92764	−0.963819	−	0.266557i	$-0.914114\pi$
$853$	−56.2989	−1.92764	−0.963819	+	0.266557i	$0.914114\pi$
$854$	−25.3965	−0.869051
$855$	−4.21870	−0.144277
$856$	15.3894	0.525998
$857$	49.1923	1.68038	0.840189	−	0.542294i	$-0.182444\pi$
$857$	49.1923	1.68038	0.840189	+	0.542294i	$0.182444\pi$
$858$	12.2026	0.416589
$859$	12.2444	0.417772	0.208886	−	0.977940i	$-0.433016\pi$
$859$	12.2444	0.417772	0.208886	+	0.977940i	$0.433016\pi$
$860$	−66.2948	−2.26063
$861$	45.2779	1.54307
$862$	39.8907	1.35868
$863$	−33.4065	−1.13717	−0.568585	−	0.822625i	$-0.692509\pi$
$863$	−33.4065	−1.13717	−0.568585	+	0.822625i	$0.692509\pi$
$864$	−41.9783	−1.42813
$865$	−82.0006	−2.78810
$866$	56.8206	1.93084
$867$	−15.7126	−0.533629
$868$	49.3610	1.67542
$869$	−8.19983	−0.278160
$870$	−116.898	−3.96323
$871$	−3.01438	−0.102138
$872$	22.3939	0.758353
$873$	−0.217390	−0.00735755
$874$	6.59981	0.223242
$875$	−83.2807	−2.81540
$876$	−32.7207	−1.10553
$877$	−28.5944	−0.965564	−0.482782	−	0.875741i	$-0.660374\pi$
$877$	−28.5944	−0.965564	−0.482782	+	0.875741i	$0.660374\pi$
$878$	35.5508	1.19978
$879$	−47.5788	−1.60479
$880$	−29.2427	−0.985773
$881$	−13.1062	−0.441558	−0.220779	−	0.975324i	$-0.570860\pi$
$881$	−13.1062	−0.441558	−0.220779	+	0.975324i	$0.570860\pi$
$882$	2.58736	0.0871208
$883$	−21.5477	−0.725139	−0.362570	−	0.931957i	$-0.618101\pi$
$883$	−21.5477	−0.725139	−0.362570	+	0.931957i	$0.618101\pi$
$884$	−6.93028	−0.233091
$885$	22.3054	0.749787
$886$	8.32269	0.279606
$887$	−18.2422	−0.612514	−0.306257	−	0.951949i	$-0.599077\pi$
$887$	−18.2422	−0.612514	−0.306257	+	0.951949i	$0.599077\pi$
$888$	−23.2536	−0.780339
$889$	−1.80872	−0.0606626
$890$	43.7129	1.46526
$891$	21.6179	0.724227
$892$	0.533103	0.0178496
$893$	−5.30674	−0.177583
$894$	−31.7608	−1.06224
$895$	−6.98848	−0.233599
$896$	36.1690	1.20832
$897$	3.73136	0.124586
$898$	−86.7835	−2.89600
$899$	−54.6771	−1.82358
$900$	−28.7633	−0.958777
$901$	−6.29746	−0.209799
$902$	89.4747	2.97918
$903$	24.5163	0.815850
$904$	29.9010	0.994491
$905$	−0.437149	−0.0145313
$906$	−29.9813	−0.996063
$907$	−45.3951	−1.50732	−0.753660	−	0.657264i	$-0.771714\pi$
$907$	−45.3951	−1.50732	−0.753660	+	0.657264i	$0.771714\pi$
$908$	−43.8217	−1.45427
$909$	1.01000	0.0334997
$910$	26.0472	0.863456
$911$	26.5524	0.879720	0.439860	−	0.898066i	$-0.355028\pi$
$911$	26.5524	0.879720	0.439860	+	0.898066i	$0.355028\pi$
$912$	3.20750	0.106211
$913$	−9.20690	−0.304704
$914$	−62.3245	−2.06151
$915$	−24.1960	−0.799896
$916$	−31.1681	−1.02982
$917$	53.6657	1.77220
$918$	−30.8345	−1.01769
$919$	−10.0414	−0.331234	−0.165617	−	0.986190i	$-0.552962\pi$
$919$	−10.0414	−0.331234	−0.165617	+	0.986190i	$0.552962\pi$
$920$	17.7785	0.586139
$921$	36.7054	1.20948
$922$	70.6829	2.32782
$923$	1.82785	0.0601643
$924$	−44.8066	−1.47403
$925$	112.936	3.71332
$926$	−2.18475	−0.0717952
$927$	13.6471	0.448229
$928$	−66.0519	−2.16826
$929$	22.4693	0.737195	0.368598	−	0.929589i	$-0.379838\pi$
$929$	22.4693	0.737195	0.368598	+	0.929589i	$0.379838\pi$
$930$	80.9445	2.65427
$931$	−1.61866	−0.0530493
$932$	−68.5664	−2.24597
$933$	9.99615	0.327259
$934$	20.9616	0.685883
$935$	−39.3742	−1.28767
$936$	1.46174	0.0477784
$937$	33.4955	1.09425	0.547125	−	0.837051i	$-0.315722\pi$
$937$	33.4955	1.09425	0.547125	+	0.837051i	$0.315722\pi$
$938$	19.0512	0.622043
$939$	−22.9732	−0.749702
$940$	−51.2757	−1.67243
$941$	14.5207	0.473362	0.236681	−	0.971587i	$-0.423940\pi$
$941$	14.5207	0.473362	0.236681	+	0.971587i	$0.423940\pi$
$942$	45.1218	1.47015
$943$	27.3600	0.890963
$944$	6.87550	0.223778
$945$	67.3306	2.19026
$946$	48.4471	1.57515
$947$	−28.6386	−0.930631	−0.465315	−	0.885145i	$-0.654059\pi$
$947$	−28.6386	−0.930631	−0.465315	+	0.885145i	$0.654059\pi$
$948$	8.69036	0.282250
$949$	−8.07601	−0.262159
$950$	30.9721	1.00487
$951$	−11.3439	−0.367851
$952$	12.2111	0.395763
$953$	−3.76140	−0.121844	−0.0609219	−	0.998143i	$-0.519404\pi$
$953$	−3.76140	−0.121844	−0.0609219	+	0.998143i	$0.519404\pi$
$954$	4.76437	0.154252
$955$	−85.7982	−2.77637
$956$	8.80806	0.284873
$957$	49.6322	1.60438
$958$	41.6868	1.34684
$959$	−35.7276	−1.15370
$960$	75.4320	2.43456
$961$	6.86029	0.221300
$962$	−20.5866	−0.663740
$963$	7.88485	0.254086
$964$	−12.0572	−0.388337
$965$	−7.85064	−0.252721
$966$	−23.5826	−0.758756
$967$	3.93959	0.126689	0.0633444	−	0.997992i	$-0.479823\pi$
$967$	3.93959	0.126689	0.0633444	+	0.997992i	$0.479823\pi$
$968$	−6.10527	−0.196231
$969$	4.31878	0.138739
$970$	2.26181	0.0726225
$971$	51.9463	1.66703	0.833517	−	0.552493i	$-0.186323\pi$
$971$	51.9463	1.66703	0.833517	+	0.552493i	$0.186323\pi$
$972$	24.0721	0.772112
$973$	1.74911	0.0560738
$974$	−62.8518	−2.01390
$975$	17.5108	0.560795
$976$	−7.45827	−0.238734
$977$	−26.5806	−0.850388	−0.425194	−	0.905102i	$-0.639794\pi$
$977$	−26.5806	−0.850388	−0.425194	+	0.905102i	$0.639794\pi$
$978$	−16.8532	−0.538905
$979$	−18.5594	−0.593162
$980$	−15.6401	−0.499604
$981$	11.4737	0.366326
$982$	73.3885	2.34192
$983$	−11.7611	−0.375120	−0.187560	−	0.982253i	$-0.560058\pi$
$983$	−11.7611	−0.375120	−0.187560	+	0.982253i	$0.560058\pi$
$984$	−26.4370	−0.842780
$985$	−38.8016	−1.23632
$986$	−48.5173	−1.54511
$987$	18.9621	0.603571
$988$	−3.28012	−0.104355
$989$	14.8144	0.471070
$990$	29.7887	0.946748
$991$	−2.46570	−0.0783256	−0.0391628	−	0.999233i	$-0.512469\pi$
$991$	−2.46570	−0.0783256	−0.0391628	+	0.999233i	$0.512469\pi$
$992$	45.7366	1.45214
$993$	−24.4218	−0.775003
$994$	−11.5522	−0.366413
$995$	100.214	3.17700
$996$	9.75768	0.309184
$997$	−24.6496	−0.780659	−0.390330	−	0.920675i	$-0.627639\pi$
$997$	−24.6496	−0.780659	−0.390330	+	0.920675i	$0.627639\pi$
$998$	−27.1197	−0.858460
$999$	−53.2154	−1.68366

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6019.2.a.b.1.15	✓	101

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6019.2.a.b.1.15	✓	101	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:	\( N \)	\(=\)	\( 6019 = 13 \cdot 463 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6019.a (trivial)

\(f(q)\)	\(=\)	\(q-2.18475 q^{2} +1.46102 q^{3} +2.77312 q^{4} -4.12132 q^{5} -3.19197 q^{6} +2.89283 q^{7} -1.68907 q^{8} -0.865408 q^{9} +O(q^{10})\)	\(q-2.18475 q^{2} +1.46102 q^{3} +2.77312 q^{4} -4.12132 q^{5} -3.19197 q^{6} +2.89283 q^{7} -1.68907 q^{8} -0.865408 q^{9} +9.00405 q^{10} -3.82290 q^{11} +4.05160 q^{12} +1.00000 q^{13} -6.32010 q^{14} -6.02135 q^{15} -1.85604 q^{16} -2.49909 q^{17} +1.89070 q^{18} -1.18283 q^{19} -11.4289 q^{20} +4.22649 q^{21} +8.35207 q^{22} +2.55393 q^{23} -2.46778 q^{24} +11.9853 q^{25} -2.18475 q^{26} -5.64746 q^{27} +8.02217 q^{28} -8.88614 q^{29} +13.1551 q^{30} +6.15307 q^{31} +7.43313 q^{32} -5.58535 q^{33} +5.45988 q^{34} -11.9223 q^{35} -2.39988 q^{36} +9.42289 q^{37} +2.58418 q^{38} +1.46102 q^{39} +6.96121 q^{40} +10.7129 q^{41} -9.23382 q^{42} +5.80061 q^{43} -10.6014 q^{44} +3.56663 q^{45} -5.57970 q^{46} +4.48649 q^{47} -2.71173 q^{48} +1.36847 q^{49} -26.1848 q^{50} -3.65123 q^{51} +2.77312 q^{52} +2.51990 q^{53} +12.3383 q^{54} +15.7554 q^{55} -4.88620 q^{56} -1.72814 q^{57} +19.4140 q^{58} -3.70438 q^{59} -16.6979 q^{60} +4.01837 q^{61} -13.4429 q^{62} -2.50348 q^{63} -12.5274 q^{64} -4.12132 q^{65} +12.2026 q^{66} -3.01438 q^{67} -6.93028 q^{68} +3.73136 q^{69} +26.0472 q^{70} +1.82785 q^{71} +1.46174 q^{72} -8.07601 q^{73} -20.5866 q^{74} +17.5108 q^{75} -3.28012 q^{76} -11.0590 q^{77} -3.19197 q^{78} +2.14492 q^{79} +7.64936 q^{80} -5.65484 q^{81} -23.4049 q^{82} +2.40836 q^{83} +11.7206 q^{84} +10.2996 q^{85} -12.6729 q^{86} -12.9829 q^{87} +6.45716 q^{88} +4.85481 q^{89} -7.79218 q^{90} +2.89283 q^{91} +7.08236 q^{92} +8.98979 q^{93} -9.80184 q^{94} +4.87481 q^{95} +10.8600 q^{96} +0.251200 q^{97} -2.98975 q^{98} +3.30837 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 101 q - 8 q^{2} - 13 q^{3} + 86 q^{4} - 43 q^{5} - 10 q^{6} - q^{7} - 24 q^{8} + 52 q^{9}+O(q^{10}) \) 101 * q - 8 * q^2 - 13 * q^3 + 86 * q^4 - 43 * q^5 - 10 * q^6 - q^7 - 24 * q^8 + 52 * q^9	\( 101 q - 8 q^{2} - 13 q^{3} + 86 q^{4} - 43 q^{5} - 10 q^{6} - q^{7} - 24 q^{8} + 52 q^{9} - 19 q^{10} - 42 q^{11} - 28 q^{12} + 101 q^{13} - 45 q^{14} - 15 q^{15} + 48 q^{16} - 83 q^{17} - 4 q^{18} - 18 q^{19} - 51 q^{20} - 50 q^{21} - 20 q^{22} - 64 q^{23} - 23 q^{24} + 46 q^{25} - 8 q^{26} - 37 q^{27} - 11 q^{28} - 117 q^{29} - 28 q^{30} - 10 q^{31} - 36 q^{32} - 20 q^{33} - 10 q^{34} - 53 q^{35} - 16 q^{36} - 27 q^{37} - 68 q^{38} - 13 q^{39} - 42 q^{40} - 60 q^{41} - 31 q^{42} - 16 q^{43} - 89 q^{44} - 56 q^{45} + 5 q^{46} - 23 q^{47} - 37 q^{48} + 48 q^{49} - 30 q^{50} - 68 q^{51} + 86 q^{52} - 189 q^{53} - 23 q^{54} + 3 q^{55} - 106 q^{56} - 25 q^{57} - 82 q^{59} + 6 q^{60} - 68 q^{61} - 57 q^{62} + 3 q^{63} - 2 q^{64} - 43 q^{65} - 40 q^{66} - 13 q^{67} - 138 q^{68} - 92 q^{69} + 18 q^{70} - 39 q^{71} - 20 q^{72} + 19 q^{73} - 88 q^{74} - 21 q^{75} - 53 q^{76} - 147 q^{77} - 10 q^{78} - 19 q^{79} - 104 q^{80} - 55 q^{81} + 27 q^{82} - 49 q^{83} - 59 q^{84} - 27 q^{85} - 99 q^{86} - 33 q^{87} - 41 q^{88} - 70 q^{89} - 49 q^{90} - q^{91} - 111 q^{92} - 84 q^{93} + 4 q^{94} - 82 q^{95} - 7 q^{96} + 25 q^{97} - 37 q^{98} - 41 q^{99}+O(q^{100}) \) 101 * q - 8 * q^2 - 13 * q^3 + 86 * q^4 - 43 * q^5 - 10 * q^6 - q^7 - 24 * q^8 + 52 * q^9 - 19 * q^10 - 42 * q^11 - 28 * q^12 + 101 * q^13 - 45 * q^14 - 15 * q^15 + 48 * q^16 - 83 * q^17 - 4 * q^18 - 18 * q^19 - 51 * q^20 - 50 * q^21 - 20 * q^22 - 64 * q^23 - 23 * q^24 + 46 * q^25 - 8 * q^26 - 37 * q^27 - 11 * q^28 - 117 * q^29 - 28 * q^30 - 10 * q^31 - 36 * q^32 - 20 * q^33 - 10 * q^34 - 53 * q^35 - 16 * q^36 - 27 * q^37 - 68 * q^38 - 13 * q^39 - 42 * q^40 - 60 * q^41 - 31 * q^42 - 16 * q^43 - 89 * q^44 - 56 * q^45 + 5 * q^46 - 23 * q^47 - 37 * q^48 + 48 * q^49 - 30 * q^50 - 68 * q^51 + 86 * q^52 - 189 * q^53 - 23 * q^54 + 3 * q^55 - 106 * q^56 - 25 * q^57 - 82 * q^59 + 6 * q^60 - 68 * q^61 - 57 * q^62 + 3 * q^63 - 2 * q^64 - 43 * q^65 - 40 * q^66 - 13 * q^67 - 138 * q^68 - 92 * q^69 + 18 * q^70 - 39 * q^71 - 20 * q^72 + 19 * q^73 - 88 * q^74 - 21 * q^75 - 53 * q^76 - 147 * q^77 - 10 * q^78 - 19 * q^79 - 104 * q^80 - 55 * q^81 + 27 * q^82 - 49 * q^83 - 59 * q^84 - 27 * q^85 - 99 * q^86 - 33 * q^87 - 41 * q^88 - 70 * q^89 - 49 * q^90 - q^91 - 111 * q^92 - 84 * q^93 + 4 * q^94 - 82 * q^95 - 7 * q^96 + 25 * q^97 - 37 * q^98 - 41 * q^99

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