LMFDB - Embedded newform 619.2.a.b.1.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [619,2,Mod(1,619)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(619, 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("619.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 619 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	619.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:	$4.94273988512$
Analytic rank:	$0$
Dimension:	$30$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.9
Character	$\chi$	$=$	619.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.26926 q^{2} +3.28637 q^{3} -0.388969 q^{4} +2.23550 q^{5} -4.17127 q^{6} +3.15236 q^{7} +3.03223 q^{8} +7.80023 q^{9} +O(q^{10})$	\(q-1.26926 q^{2} +3.28637 q^{3} -0.388969 q^{4} +2.23550 q^{5} -4.17127 q^{6} +3.15236 q^{7} +3.03223 q^{8} +7.80023 q^{9} -2.83744 q^{10} +1.25447 q^{11} -1.27830 q^{12} +0.135766 q^{13} -4.00118 q^{14} +7.34667 q^{15} -3.07076 q^{16} -8.12408 q^{17} -9.90055 q^{18} -6.16785 q^{19} -0.869540 q^{20} +10.3598 q^{21} -1.59226 q^{22} -6.32062 q^{23} +9.96504 q^{24} -0.00254610 q^{25} -0.172323 q^{26} +15.7753 q^{27} -1.22617 q^{28} +4.55365 q^{29} -9.32487 q^{30} -6.49824 q^{31} -2.16685 q^{32} +4.12266 q^{33} +10.3116 q^{34} +7.04710 q^{35} -3.03405 q^{36} -6.68758 q^{37} +7.82863 q^{38} +0.446177 q^{39} +6.77855 q^{40} +2.34133 q^{41} -13.1493 q^{42} +8.30502 q^{43} -0.487951 q^{44} +17.4374 q^{45} +8.02253 q^{46} -1.40000 q^{47} -10.0917 q^{48} +2.93738 q^{49} +0.00323167 q^{50} -26.6987 q^{51} -0.0528087 q^{52} -6.60727 q^{53} -20.0230 q^{54} +2.80437 q^{55} +9.55869 q^{56} -20.2698 q^{57} -5.77978 q^{58} +1.32957 q^{59} -2.85763 q^{60} -0.790192 q^{61} +8.24798 q^{62} +24.5891 q^{63} +8.89184 q^{64} +0.303504 q^{65} -5.23274 q^{66} -13.9783 q^{67} +3.16002 q^{68} -20.7719 q^{69} -8.94463 q^{70} +3.99597 q^{71} +23.6521 q^{72} +10.2597 q^{73} +8.48831 q^{74} -0.00836742 q^{75} +2.39910 q^{76} +3.95455 q^{77} -0.566316 q^{78} +3.82418 q^{79} -6.86469 q^{80} +28.4429 q^{81} -2.97177 q^{82} +10.1725 q^{83} -4.02965 q^{84} -18.1614 q^{85} -10.5413 q^{86} +14.9650 q^{87} +3.80385 q^{88} +3.94368 q^{89} -22.1327 q^{90} +0.427983 q^{91} +2.45852 q^{92} -21.3556 q^{93} +1.77697 q^{94} -13.7882 q^{95} -7.12108 q^{96} -1.33017 q^{97} -3.72831 q^{98} +9.78517 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 30 q + 9 q^{2} + q^{3} + 33 q^{4} + 21 q^{5} + 6 q^{6} + 2 q^{7} + 27 q^{8} + 43 q^{9}+O(q^{10}) $ 30 * q + 9 * q^2 + q^3 + 33 * q^4 + 21 * q^5 + 6 * q^6 + 2 * q^7 + 27 * q^8 + 43 * q^9	\( 30 q + 9 q^{2} + q^{3} + 33 q^{4} + 21 q^{5} + 6 q^{6} + 2 q^{7} + 27 q^{8} + 43 q^{9} + 5 q^{10} + 23 q^{11} - 6 q^{12} + 9 q^{13} + 7 q^{14} - 2 q^{15} + 35 q^{16} + 4 q^{17} + 10 q^{18} - q^{19} + 29 q^{20} + 30 q^{21} + 4 q^{23} + 4 q^{24} + 35 q^{25} + q^{26} - 5 q^{27} - 13 q^{28} + 90 q^{29} - 31 q^{30} + 2 q^{31} + 43 q^{32} - 6 q^{33} - 9 q^{34} + 9 q^{35} + 33 q^{36} + 19 q^{37} + 5 q^{38} + 32 q^{39} - 12 q^{40} + 59 q^{41} - 25 q^{42} - 4 q^{43} + 52 q^{44} + 30 q^{45} - q^{46} + 4 q^{47} - 44 q^{48} + 30 q^{49} + 31 q^{50} - 12 q^{52} + 34 q^{53} - 28 q^{54} - 17 q^{55} + 2 q^{56} - 8 q^{57} + 6 q^{58} + 13 q^{59} - 64 q^{60} + 16 q^{61} + 28 q^{62} - 40 q^{63} + 37 q^{64} + 31 q^{65} - 59 q^{66} - 11 q^{67} - 52 q^{68} + 6 q^{69} - 40 q^{70} + 42 q^{71} + 6 q^{72} - 4 q^{73} + 16 q^{74} - 52 q^{75} - 42 q^{76} + 29 q^{77} - 56 q^{78} + 3 q^{79} + 21 q^{80} + 30 q^{81} - 43 q^{82} - 11 q^{83} - 36 q^{84} + 19 q^{85} - 11 q^{86} - 20 q^{87} - 47 q^{88} + 58 q^{89} - 33 q^{90} - 39 q^{91} - 7 q^{92} - 15 q^{93} - 46 q^{94} + 23 q^{95} - 70 q^{96} - 9 q^{97} - 8 q^{99}+O(q^{100}) \) 30 * q + 9 * q^2 + q^3 + 33 * q^4 + 21 * q^5 + 6 * q^6 + 2 * q^7 + 27 * q^8 + 43 * q^9 + 5 * q^10 + 23 * q^11 - 6 * q^12 + 9 * q^13 + 7 * q^14 - 2 * q^15 + 35 * q^16 + 4 * q^17 + 10 * q^18 - q^19 + 29 * q^20 + 30 * q^21 + 4 * q^23 + 4 * q^24 + 35 * q^25 + q^26 - 5 * q^27 - 13 * q^28 + 90 * q^29 - 31 * q^30 + 2 * q^31 + 43 * q^32 - 6 * q^33 - 9 * q^34 + 9 * q^35 + 33 * q^36 + 19 * q^37 + 5 * q^38 + 32 * q^39 - 12 * q^40 + 59 * q^41 - 25 * q^42 - 4 * q^43 + 52 * q^44 + 30 * q^45 - q^46 + 4 * q^47 - 44 * q^48 + 30 * q^49 + 31 * q^50 - 12 * q^52 + 34 * q^53 - 28 * q^54 - 17 * q^55 + 2 * q^56 - 8 * q^57 + 6 * q^58 + 13 * q^59 - 64 * q^60 + 16 * q^61 + 28 * q^62 - 40 * q^63 + 37 * q^64 + 31 * q^65 - 59 * q^66 - 11 * q^67 - 52 * q^68 + 6 * q^69 - 40 * q^70 + 42 * q^71 + 6 * q^72 - 4 * q^73 + 16 * q^74 - 52 * q^75 - 42 * q^76 + 29 * q^77 - 56 * q^78 + 3 * q^79 + 21 * q^80 + 30 * q^81 - 43 * q^82 - 11 * q^83 - 36 * q^84 + 19 * q^85 - 11 * q^86 - 20 * q^87 - 47 * q^88 + 58 * q^89 - 33 * q^90 - 39 * q^91 - 7 * q^92 - 15 * q^93 - 46 * q^94 + 23 * q^95 - 70 * q^96 - 9 * q^97 - 8 * 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 $

$2$	−1.26926	−0.897505	−0.448753	−	0.893656i	$-0.648132\pi$
$2$	−1.26926	−0.897505	−0.448753	+	0.893656i	$0.648132\pi$
$3$	3.28637	1.89739	0.948693	−	0.316198i	$-0.102406\pi$
$3$	3.28637	1.89739	0.948693	+	0.316198i	$0.102406\pi$
$4$	−0.388969	−0.194485
$5$	2.23550	0.999745	0.499873	−	0.866099i	$-0.333380\pi$
$5$	2.23550	0.999745	0.499873	+	0.866099i	$0.333380\pi$
$6$	−4.17127	−1.70291
$7$	3.15236	1.19148	0.595740	−	0.803177i	$-0.296859\pi$
$7$	3.15236	1.19148	0.595740	+	0.803177i	$0.296859\pi$
$8$	3.03223	1.07206
$9$	7.80023	2.60008
$10$	−2.83744	−0.897277
$11$	1.25447	0.378238	0.189119	−	0.981954i	$-0.439437\pi$
$11$	1.25447	0.378238	0.189119	+	0.981954i	$0.439437\pi$
$12$	−1.27830	−0.369012
$13$	0.135766	0.0376547	0.0188273	−	0.999823i	$-0.494007\pi$
$13$	0.135766	0.0376547	0.0188273	+	0.999823i	$0.494007\pi$
$14$	−4.00118	−1.06936
$15$	7.34667	1.89690
$16$	−3.07076	−0.767691
$17$	−8.12408	−1.97038	−0.985189	−	0.171471i	$-0.945148\pi$
$17$	−8.12408	−1.97038	−0.985189	+	0.171471i	$0.945148\pi$
$18$	−9.90055	−2.33358
$19$	−6.16785	−1.41500	−0.707501	−	0.706713i	$-0.750177\pi$
$19$	−6.16785	−1.41500	−0.707501	+	0.706713i	$0.750177\pi$
$20$	−0.869540	−0.194435
$21$	10.3598	2.26070
$22$	−1.59226	−0.339470
$23$	−6.32062	−1.31794	−0.658970	−	0.752169i	$-0.729007\pi$
$23$	−6.32062	−1.31794	−0.658970	+	0.752169i	$0.729007\pi$
$24$	9.96504	2.03410
$25$	−0.00254610	−0.000509220 0
$26$	−0.172323	−0.0337952
$27$	15.7753	3.03596
$28$	−1.22617	−0.231725
$29$	4.55365	0.845591	0.422796	−	0.906225i	$-0.361049\pi$
$29$	4.55365	0.845591	0.422796	+	0.906225i	$0.361049\pi$
$30$	−9.32487	−1.70248
$31$	−6.49824	−1.16712	−0.583559	−	0.812071i	$-0.698340\pi$
$31$	−6.49824	−1.16712	−0.583559	+	0.812071i	$0.698340\pi$
$32$	−2.16685	−0.383049
$33$	4.12266	0.717663
$34$	10.3116	1.76842
$35$	7.04710	1.19118
$36$	−3.03405	−0.505675
$37$	−6.68758	−1.09943	−0.549716	−	0.835352i	$-0.685264\pi$
$37$	−6.68758	−1.09943	−0.549716	+	0.835352i	$0.685264\pi$
$38$	7.82863	1.26997
$39$	0.446177	0.0714454
$40$	6.77855	1.07178
$41$	2.34133	0.365655	0.182827	−	0.983145i	$-0.441475\pi$
$41$	2.34133	0.365655	0.182827	+	0.983145i	$0.441475\pi$
$42$	−13.1493	−2.02899
$43$	8.30502	1.26650	0.633252	−	0.773946i	$-0.281720\pi$
$43$	8.30502	1.26650	0.633252	+	0.773946i	$0.281720\pi$
$44$	−0.487951	−0.0735614
$45$	17.4374	2.59941
$46$	8.02253	1.18286
$47$	−1.40000	−0.204211	−0.102106	−	0.994774i	$-0.532558\pi$
$47$	−1.40000	−0.204211	−0.102106	+	0.994774i	$0.532558\pi$
$48$	−10.0917	−1.45661
$49$	2.93738	0.419626
$50$	0.00323167	0.000457027 0
$51$	−26.6987	−3.73857
$52$	−0.0528087	−0.00732325
$53$	−6.60727	−0.907579	−0.453789	−	0.891109i	$-0.649928\pi$
$53$	−6.60727	−0.907579	−0.453789	+	0.891109i	$0.649928\pi$
$54$	−20.0230	−2.72479
$55$	2.80437	0.378141
$56$	9.55869	1.27733
$57$	−20.2698	−2.68480
$58$	−5.77978	−0.758922
$59$	1.32957	0.173096	0.0865479	−	0.996248i	$-0.472416\pi$
$59$	1.32957	0.173096	0.0865479	+	0.996248i	$0.472416\pi$
$60$	−2.85763	−0.368918
$61$	−0.790192	−0.101174	−0.0505869	−	0.998720i	$-0.516109\pi$
$61$	−0.790192	−0.101174	−0.0505869	+	0.998720i	$0.516109\pi$
$62$	8.24798	1.04749
$63$	24.5891	3.09794
$64$	8.89184	1.11148
$65$	0.303504	0.0376451
$66$	−5.23274	−0.644106
$67$	−13.9783	−1.70772	−0.853859	−	0.520504i	$-0.825744\pi$
$67$	−13.9783	−1.70772	−0.853859	+	0.520504i	$0.825744\pi$
$68$	3.16002	0.383208
$69$	−20.7719	−2.50064
$70$	−8.94463	−1.06909
$71$	3.99597	0.474234	0.237117	−	0.971481i	$-0.423797\pi$
$71$	3.99597	0.474234	0.237117	+	0.971481i	$0.423797\pi$
$72$	23.6521	2.78743
$73$	10.2597	1.20080	0.600402	−	0.799698i	$-0.295007\pi$
$73$	10.2597	1.20080	0.600402	+	0.799698i	$0.295007\pi$
$74$	8.48831	0.986746
$75$	−0.00836742	−0.000966187 0
$76$	2.39910	0.275196
$77$	3.95455	0.450663
$78$	−0.566316	−0.0641226
$79$	3.82418	0.430254	0.215127	−	0.976586i	$-0.430983\pi$
$79$	3.82418	0.430254	0.215127	+	0.976586i	$0.430983\pi$
$80$	−6.86469	−0.767496
$81$	28.4429	3.16032
$82$	−2.97177	−0.328177
$83$	10.1725	1.11658	0.558290	−	0.829646i	$-0.311458\pi$
$83$	10.1725	1.11658	0.558290	+	0.829646i	$0.311458\pi$
$84$	−4.02965	−0.439671
$85$	−18.1614	−1.96988
$86$	−10.5413	−1.13669
$87$	14.9650	1.60441
$88$	3.80385	0.405492
$89$	3.94368	0.418029	0.209014	−	0.977913i	$-0.432974\pi$
$89$	3.94368	0.418029	0.209014	+	0.977913i	$0.432974\pi$
$90$	−22.1327	−2.33299
$91$	0.427983	0.0448648
$92$	2.45852	0.256319
$93$	−21.3556	−2.21447
$94$	1.77697	0.183280
$95$	−13.7882	−1.41464
$96$	−7.12108	−0.726792
$97$	−1.33017	−0.135058	−0.0675289	−	0.997717i	$-0.521511\pi$
$97$	−1.33017	−0.135058	−0.0675289	+	0.997717i	$0.521511\pi$
$98$	−3.72831	−0.376616
$99$	9.78517	0.983446
$100$	0.000990354 0	9.90354e−5 0
$101$	5.50958	0.548224	0.274112	−	0.961698i	$-0.411616\pi$
$101$	5.50958	0.548224	0.274112	+	0.961698i	$0.411616\pi$
$102$	33.8877	3.35538
$103$	1.52947	0.150703	0.0753513	−	0.997157i	$-0.475992\pi$
$103$	1.52947	0.150703	0.0753513	+	0.997157i	$0.475992\pi$
$104$	0.411673	0.0403679
$105$	23.1594	2.26012
$106$	8.38637	0.814557
$107$	5.64779	0.545992	0.272996	−	0.962015i	$-0.411985\pi$
$107$	5.64779	0.545992	0.272996	+	0.962015i	$0.411985\pi$
$108$	−6.13611	−0.590448
$109$	1.60661	0.153885	0.0769425	−	0.997036i	$-0.475484\pi$
$109$	1.60661	0.153885	0.0769425	+	0.997036i	$0.475484\pi$
$110$	−3.55949	−0.339384
$111$	−21.9779	−2.08605
$112$	−9.68016	−0.914689
$113$	9.78658	0.920644	0.460322	−	0.887752i	$-0.347734\pi$
$113$	9.78658	0.920644	0.460322	+	0.887752i	$0.347734\pi$
$114$	25.7278	2.40963
$115$	−14.1297	−1.31760
$116$	−1.77123	−0.164454
$117$	1.05900	0.0979050
$118$	−1.68758	−0.155354
$119$	−25.6100	−2.34767
$120$	22.2768	2.03359
$121$	−9.42630	−0.856936
$122$	1.00296	0.0908040
$123$	7.69448	0.693788
$124$	2.52761	0.226986
$125$	−11.1832	−1.00025
$126$	−31.2101	−2.78042
$127$	15.0100	1.33193	0.665963	−	0.745985i	$-0.268021\pi$
$127$	15.0100	1.33193	0.665963	+	0.745985i	$0.268021\pi$
$128$	−6.95238	−0.614510
$129$	27.2934	2.40305
$130$	−0.385227	−0.0337866
$131$	5.04366	0.440667	0.220333	−	0.975425i	$-0.429285\pi$
$131$	5.04366	0.440667	0.220333	+	0.975425i	$0.429285\pi$
$132$	−1.60359	−0.139574
$133$	−19.4433	−1.68595
$134$	17.7421	1.53269
$135$	35.2657	3.03519
$136$	−24.6341	−2.11236
$137$	13.3492	1.14050	0.570248	−	0.821472i	$-0.306847\pi$
$137$	13.3492	1.14050	0.570248	+	0.821472i	$0.306847\pi$
$138$	26.3650	2.24434
$139$	−21.2420	−1.80172	−0.900860	−	0.434109i	$-0.857063\pi$
$139$	−21.2420	−1.80172	−0.900860	+	0.434109i	$0.857063\pi$
$140$	−2.74110	−0.231666
$141$	−4.60092	−0.387467
$142$	−5.07194	−0.425628
$143$	0.170314	0.0142424
$144$	−23.9527	−1.99605
$145$	10.1797	0.845376
$146$	−13.0222	−1.07773
$147$	9.65331	0.796192
$148$	2.60126	0.213823
$149$	17.7657	1.45542	0.727710	−	0.685885i	$-0.240585\pi$
$149$	17.7657	1.45542	0.727710	+	0.685885i	$0.240585\pi$
$150$	0.0106205	0.000867158 0
$151$	−15.6478	−1.27340	−0.636700	−	0.771112i	$-0.719701\pi$
$151$	−15.6478	−1.27340	−0.636700	+	0.771112i	$0.719701\pi$
$152$	−18.7023	−1.51696
$153$	−63.3696	−5.12313
$154$	−5.01937	−0.404472
$155$	−14.5268	−1.16682
$156$	−0.173549	−0.0138950
$157$	−2.59421	−0.207041	−0.103520	−	0.994627i	$-0.533011\pi$
$157$	−2.59421	−0.207041	−0.103520	+	0.994627i	$0.533011\pi$
$158$	−4.85389	−0.386155
$159$	−21.7139	−1.72203
$160$	−4.84400	−0.382952
$161$	−19.9249	−1.57030
$162$	−36.1015	−2.83640
$163$	−9.09160	−0.712109	−0.356055	−	0.934465i	$-0.615878\pi$
$163$	−9.09160	−0.712109	−0.356055	+	0.934465i	$0.615878\pi$
$164$	−0.910706	−0.0711142
$165$	9.21620	0.717480
$166$	−12.9116	−1.00214
$167$	19.6332	1.51926	0.759630	−	0.650355i	$-0.225380\pi$
$167$	19.6332	1.51926	0.759630	+	0.650355i	$0.225380\pi$
$168$	31.4134	2.42360
$169$	−12.9816	−0.998582
$170$	23.0516	1.76797
$171$	−48.1106	−3.67911
$172$	−3.23040	−0.246315
$173$	22.9069	1.74158	0.870789	−	0.491657i	$-0.163609\pi$
$173$	22.9069	1.74158	0.870789	+	0.491657i	$0.163609\pi$
$174$	−18.9945	−1.43997
$175$	−0.00802622	−0.000606726 0
$176$	−3.85219	−0.290370
$177$	4.36947	0.328430
$178$	−5.00557	−0.375183
$179$	14.5618	1.08840	0.544200	−	0.838955i	$-0.316833\pi$
$179$	14.5618	1.08840	0.544200	+	0.838955i	$0.316833\pi$
$180$	−6.78261	−0.505546
$181$	−22.9942	−1.70915	−0.854574	−	0.519329i	$-0.826182\pi$
$181$	−22.9942	−1.70915	−0.854574	+	0.519329i	$0.826182\pi$
$182$	−0.543223	−0.0402664
$183$	−2.59686	−0.191966
$184$	−19.1656	−1.41290
$185$	−14.9501	−1.09915
$186$	27.1059	1.98750
$187$	−10.1914	−0.745271
$188$	0.544557	0.0397159
$189$	49.7295	3.61729
$190$	17.5009	1.26965
$191$	5.03712	0.364473	0.182236	−	0.983255i	$-0.441666\pi$
$191$	5.03712	0.364473	0.182236	+	0.983255i	$0.441666\pi$
$192$	29.2219	2.10891
$193$	−12.2667	−0.882977	−0.441488	−	0.897267i	$-0.645549\pi$
$193$	−12.2667	−0.882977	−0.441488	+	0.897267i	$0.645549\pi$
$194$	1.68833	0.121215
$195$	0.997427	0.0714272
$196$	−1.14255	−0.0816107
$197$	6.88657	0.490648	0.245324	−	0.969441i	$-0.421106\pi$
$197$	6.88657	0.490648	0.245324	+	0.969441i	$0.421106\pi$
$198$	−12.4200	−0.882648
$199$	20.5642	1.45776	0.728879	−	0.684643i	$-0.240042\pi$
$199$	20.5642	1.45776	0.728879	+	0.684643i	$0.240042\pi$
$200$	−0.00772036	−0.000545912 0
$201$	−45.9378	−3.24020
$202$	−6.99311	−0.492034
$203$	14.3547	1.00751
$204$	10.3850	0.727094
$205$	5.23405	0.365562
$206$	−1.94130	−0.135256
$207$	−49.3022	−3.42674
$208$	−0.416905	−0.0289071
$209$	−7.73739	−0.535207
$210$	−29.3954	−2.02847
$211$	22.9563	1.58038	0.790189	−	0.612863i	$-0.209982\pi$
$211$	22.9563	1.58038	0.790189	+	0.612863i	$0.209982\pi$
$212$	2.57003	0.176510
$213$	13.1322	0.899806
$214$	−7.16853	−0.490031
$215$	18.5659	1.26618
$216$	47.8344	3.25472
$217$	−20.4848	−1.39060
$218$	−2.03921	−0.138113
$219$	33.7171	2.27839
$220$	−1.09081	−0.0735426
$221$	−1.10297	−0.0741939
$222$	27.8957	1.87224
$223$	18.1325	1.21424	0.607122	−	0.794608i	$-0.292324\pi$
$223$	18.1325	1.21424	0.607122	+	0.794608i	$0.292324\pi$
$224$	−6.83070	−0.456396
$225$	−0.0198602	−0.00132401
$226$	−12.4218	−0.826283
$227$	−15.4466	−1.02523	−0.512613	−	0.858620i	$-0.671322\pi$
$227$	−15.4466	−1.02523	−0.512613	+	0.858620i	$0.671322\pi$
$228$	7.88434	0.522153
$229$	8.39998	0.555086	0.277543	−	0.960713i	$-0.410480\pi$
$229$	8.39998	0.555086	0.277543	+	0.960713i	$0.410480\pi$
$230$	17.9344	1.18256
$231$	12.9961	0.855081
$232$	13.8077	0.906521
$233$	−23.5411	−1.54223	−0.771114	−	0.636698i	$-0.780300\pi$
$233$	−23.5411	−1.54223	−0.771114	+	0.636698i	$0.780300\pi$
$234$	−1.34416	−0.0878702
$235$	−3.12970	−0.204159
$236$	−0.517163	−0.0336645
$237$	12.5677	0.816358
$238$	32.5059	2.10704
$239$	12.4408	0.804726	0.402363	−	0.915480i	$-0.368189\pi$
$239$	12.4408	0.804726	0.402363	+	0.915480i	$0.368189\pi$
$240$	−22.5599	−1.45624
$241$	−6.68701	−0.430748	−0.215374	−	0.976532i	$-0.569097\pi$
$241$	−6.68701	−0.430748	−0.215374	+	0.976532i	$0.569097\pi$
$242$	11.9645	0.769105
$243$	46.1478	2.96038
$244$	0.307360	0.0196767
$245$	6.56651	0.419519
$246$	−9.76633	−0.622679
$247$	−0.837383	−0.0532814
$248$	−19.7042	−1.25122
$249$	33.4307	2.11858
$250$	14.1944	0.897733
$251$	−21.8312	−1.37797	−0.688985	−	0.724775i	$-0.741944\pi$
$251$	−21.8312	−1.37797	−0.688985	+	0.724775i	$0.741944\pi$
$252$	−9.56441	−0.602501
$253$	−7.92903	−0.498494
$254$	−19.0517	−1.19541
$255$	−59.6850	−3.73762
$256$	−8.95927	−0.559954
$257$	12.5522	0.782985	0.391492	−	0.920181i	$-0.371959\pi$
$257$	12.5522	0.782985	0.391492	+	0.920181i	$0.371959\pi$
$258$	−34.6425	−2.15675
$259$	−21.0817	−1.30995
$260$	−0.118054	−0.00732139
$261$	35.5195	2.19860
$262$	−6.40174	−0.395501
$263$	0.979178	0.0603787	0.0301893	−	0.999544i	$-0.490389\pi$
$263$	0.979178	0.0603787	0.0301893	+	0.999544i	$0.490389\pi$
$264$	12.5009	0.769375
$265$	−14.7706	−0.907348
$266$	24.6787	1.51315
$267$	12.9604	0.793162
$268$	5.43712	0.332125
$269$	3.51069	0.214050	0.107025	−	0.994256i	$-0.465867\pi$
$269$	3.51069	0.214050	0.107025	+	0.994256i	$0.465867\pi$
$270$	−44.7615	−2.72410
$271$	15.7189	0.954852	0.477426	−	0.878672i	$-0.341570\pi$
$271$	15.7189	0.954852	0.477426	+	0.878672i	$0.341570\pi$
$272$	24.9471	1.51264
$273$	1.40651	0.0851258
$274$	−16.9436	−1.02360
$275$	−0.00319401	−0.000192606 0
$276$	8.07962	0.486336
$277$	14.9778	0.899928	0.449964	−	0.893047i	$-0.351437\pi$
$277$	14.9778	0.899928	0.449964	+	0.893047i	$0.351437\pi$
$278$	26.9617	1.61705
$279$	−50.6877	−3.03459
$280$	21.3684	1.27701
$281$	2.81144	0.167716	0.0838581	−	0.996478i	$-0.473276\pi$
$281$	2.81144	0.167716	0.0838581	+	0.996478i	$0.473276\pi$
$282$	5.83978	0.347754
$283$	6.77763	0.402888	0.201444	−	0.979500i	$-0.435437\pi$
$283$	6.77763	0.402888	0.201444	+	0.979500i	$0.435437\pi$
$284$	−1.55431	−0.0922313
$285$	−45.3132	−2.68412
$286$	−0.216174	−0.0127826
$287$	7.38072	0.435670
$288$	−16.9019	−0.995957
$289$	49.0006	2.88239
$290$	−12.9207	−0.758729
$291$	−4.37141	−0.256257
$292$	−3.99070	−0.233538
$293$	−24.1517	−1.41096	−0.705480	−	0.708730i	$-0.749268\pi$
$293$	−24.1517	−1.41096	−0.705480	+	0.708730i	$0.749268\pi$
$294$	−12.2526	−0.714586
$295$	2.97226	0.173052
$296$	−20.2783	−1.17865
$297$	19.7897	1.14831
$298$	−22.5493	−1.30625
$299$	−0.858123	−0.0496266
$300$	0.00325467	0.000187908 0
$301$	26.1804	1.50901
$302$	19.8612	1.14288
$303$	18.1065	1.04019
$304$	18.9400	1.08628
$305$	−1.76647	−0.101148
$306$	80.4328	4.59804
$307$	−30.1751	−1.72218	−0.861091	−	0.508451i	$-0.830218\pi$
$307$	−30.1751	−1.72218	−0.861091	+	0.508451i	$0.830218\pi$
$308$	−1.53820	−0.0876469
$309$	5.02639	0.285941
$310$	18.4383	1.04723
$311$	−4.94459	−0.280382	−0.140191	−	0.990124i	$-0.544772\pi$
$311$	−4.94459	−0.280382	−0.140191	+	0.990124i	$0.544772\pi$
$312$	1.35291	0.0765935
$313$	−10.3780	−0.586597	−0.293298	−	0.956021i	$-0.594753\pi$
$313$	−10.3780	−0.586597	−0.293298	+	0.956021i	$0.594753\pi$
$314$	3.29274	0.185820
$315$	54.9690	3.09715
$316$	−1.48749	−0.0836777
$317$	31.6647	1.77847	0.889234	−	0.457452i	$-0.151238\pi$
$317$	31.6647	1.77847	0.889234	+	0.457452i	$0.151238\pi$
$318$	27.5607	1.54553
$319$	5.71242	0.319834
$320$	19.8777	1.11120
$321$	18.5607	1.03596
$322$	25.2899	1.40935
$323$	50.1081	2.78809
$324$	−11.0634	−0.614633
$325$	−0.000345673 0	−1.91745e−5 0
$326$	11.5396	0.639122
$327$	5.27990	0.291979
$328$	7.09946	0.392002
$329$	−4.41331	−0.243314
$330$	−11.6978	−0.643942
$331$	−0.416237	−0.0228785	−0.0114392	−	0.999935i	$-0.503641\pi$
$331$	−0.416237	−0.0228785	−0.0114392	+	0.999935i	$0.503641\pi$
$332$	−3.95680	−0.217157
$333$	−52.1647	−2.85861
$334$	−24.9197	−1.36354
$335$	−31.2484	−1.70728
$336$	−31.8126	−1.73552
$337$	3.16020	0.172147	0.0860734	−	0.996289i	$-0.472568\pi$
$337$	3.16020	0.172147	0.0860734	+	0.996289i	$0.472568\pi$
$338$	16.4770	0.896233
$339$	32.1623	1.74682
$340$	7.06421	0.383111
$341$	−8.15186	−0.441448
$342$	61.0651	3.30202
$343$	−12.8068	−0.691505
$344$	25.1827	1.35776
$345$	−46.4355	−2.50000
$346$	−29.0749	−1.56307
$347$	−16.0145	−0.859705	−0.429852	−	0.902899i	$-0.641434\pi$
$347$	−16.0145	−0.859705	−0.429852	+	0.902899i	$0.641434\pi$
$348$	−5.82091	−0.312034
$349$	20.4410	1.09418	0.547092	−	0.837073i	$-0.315735\pi$
$349$	20.4410	1.09418	0.547092	+	0.837073i	$0.315735\pi$
$350$	0.0101874	0.000544539 0
$351$	2.14175	0.114318
$352$	−2.71826	−0.144884
$353$	−16.6502	−0.886203	−0.443101	−	0.896472i	$-0.646122\pi$
$353$	−16.6502	−0.886203	−0.443101	+	0.896472i	$0.646122\pi$
$354$	−5.54602	−0.294767
$355$	8.93298	0.474114
$356$	−1.53397	−0.0813002
$357$	−84.1640	−4.45443
$358$	−18.4828	−0.976845
$359$	−9.22457	−0.486854	−0.243427	−	0.969919i	$-0.578272\pi$
$359$	−9.22457	−0.486854	−0.243427	+	0.969919i	$0.578272\pi$
$360$	52.8742	2.78672
$361$	19.0423	1.00223
$362$	29.1858	1.53397
$363$	−30.9783	−1.62594
$364$	−0.166472	−0.00872551
$365$	22.9355	1.20050
$366$	3.29611	0.172290
$367$	−11.5531	−0.603065	−0.301532	−	0.953456i	$-0.597498\pi$
$367$	−11.5531	−0.603065	−0.301532	+	0.953456i	$0.597498\pi$
$368$	19.4091	1.01177
$369$	18.2629	0.950730
$370$	18.9756	0.986494
$371$	−20.8285	−1.08136
$372$	8.30667	0.430681
$373$	−3.24606	−0.168075	−0.0840374	−	0.996463i	$-0.526782\pi$
$373$	−3.24606	−0.168075	−0.0840374	+	0.996463i	$0.526782\pi$
$374$	12.9356	0.668885
$375$	−36.7521	−1.89787
$376$	−4.24513	−0.218926
$377$	0.618230	0.0318404
$378$	−63.1199	−3.24653
$379$	−17.9204	−0.920511	−0.460255	−	0.887787i	$-0.652242\pi$
$379$	−17.9204	−0.920511	−0.460255	+	0.887787i	$0.652242\pi$
$380$	5.36319	0.275126
$381$	49.3285	2.52718
$382$	−6.39343	−0.327116
$383$	17.2961	0.883787	0.441894	−	0.897067i	$-0.354307\pi$
$383$	17.2961	0.883787	0.441894	+	0.897067i	$0.354307\pi$
$384$	−22.8481	−1.16596
$385$	8.84039	0.450548
$386$	15.5697	0.792476
$387$	64.7810	3.29300
$388$	0.517393	0.0262667
$389$	2.85574	0.144792	0.0723958	−	0.997376i	$-0.476936\pi$
$389$	2.85574	0.144792	0.0723958	+	0.997376i	$0.476936\pi$
$390$	−1.26600	−0.0641063
$391$	51.3492	2.59684
$392$	8.90681	0.449862
$393$	16.5753	0.836115
$394$	−8.74088	−0.440359
$395$	8.54895	0.430144
$396$	−3.80613	−0.191265
$397$	−8.98102	−0.450745	−0.225372	−	0.974273i	$-0.572360\pi$
$397$	−8.98102	−0.450745	−0.225372	+	0.974273i	$0.572360\pi$
$398$	−26.1014	−1.30834
$399$	−63.8978	−3.19889
$400$	0.00781847	0.000390924 0
$401$	−16.8972	−0.843808	−0.421904	−	0.906640i	$-0.638638\pi$
$401$	−16.8972	−0.843808	−0.421904	+	0.906640i	$0.638638\pi$
$402$	58.3072	2.90810
$403$	−0.882238	−0.0439474
$404$	−2.14306	−0.106621
$405$	63.5840	3.15951
$406$	−18.2200	−0.904241
$407$	−8.38938	−0.415846
$408$	−80.9567	−4.00796
$409$	8.59043	0.424769	0.212385	−	0.977186i	$-0.431877\pi$
$409$	8.59043	0.424769	0.212385	+	0.977186i	$0.431877\pi$
$410$	−6.64338	−0.328093
$411$	43.8703	2.16396
$412$	−0.594915	−0.0293093
$413$	4.19130	0.206240
$414$	62.5775	3.07552
$415$	22.7407	1.11629
$416$	−0.294185	−0.0144236
$417$	−69.8090	−3.41856
$418$	9.82079	0.480351
$419$	19.9974	0.976939	0.488470	−	0.872581i	$-0.337555\pi$
$419$	19.9974	0.976939	0.488470	+	0.872581i	$0.337555\pi$
$420$	−9.00828	−0.439559
$421$	31.6643	1.54322	0.771612	−	0.636093i	$-0.219451\pi$
$421$	31.6643	1.54322	0.771612	+	0.636093i	$0.219451\pi$
$422$	−29.1376	−1.41840
$423$	−10.9203	−0.530964
$424$	−20.0348	−0.972975
$425$	0.0206847	0.00100336
$426$	−16.6683	−0.807580
$427$	−2.49097	−0.120547
$428$	−2.19682	−0.106187
$429$	0.559716	0.0270233
$430$	−23.5650	−1.13640
$431$	1.14278	0.0550459	0.0275229	−	0.999621i	$-0.491238\pi$
$431$	1.14278	0.0550459	0.0275229	+	0.999621i	$0.491238\pi$
$432$	−48.4423	−2.33068
$433$	8.47597	0.407329	0.203665	−	0.979041i	$-0.434715\pi$
$433$	8.47597	0.407329	0.203665	+	0.979041i	$0.434715\pi$
$434$	26.0006	1.24807
$435$	33.4542	1.60400
$436$	−0.624920	−0.0299282
$437$	38.9846	1.86489
$438$	−42.7959	−2.04487
$439$	−16.3741	−0.781495	−0.390747	−	0.920498i	$-0.627783\pi$
$439$	−16.3741	−0.781495	−0.390747	+	0.920498i	$0.627783\pi$
$440$	8.50350	0.405389
$441$	22.9122	1.09106
$442$	1.39996	0.0665894
$443$	−37.0812	−1.76178	−0.880891	−	0.473319i	$-0.843056\pi$
$443$	−37.0812	−1.76178	−0.880891	+	0.473319i	$0.843056\pi$
$444$	8.54871	0.405704
$445$	8.81608	0.417922
$446$	−23.0150	−1.08979
$447$	58.3845	2.76149
$448$	28.0303	1.32431
$449$	−5.57097	−0.262910	−0.131455	−	0.991322i	$-0.541965\pi$
$449$	−5.57097	−0.262910	−0.131455	+	0.991322i	$0.541965\pi$
$450$	0.0252078	0.00118831
$451$	2.93714	0.138304
$452$	−3.80668	−0.179051
$453$	−51.4245	−2.41613
$454$	19.6058	0.920145
$455$	0.956755	0.0448534
$456$	−61.4628	−2.87826
$457$	2.80831	0.131367	0.0656835	−	0.997841i	$-0.479077\pi$
$457$	2.80831	0.131367	0.0656835	+	0.997841i	$0.479077\pi$
$458$	−10.6618	−0.498193
$459$	−128.160	−5.98199
$460$	5.49603	0.256254
$461$	−31.1869	−1.45252	−0.726258	−	0.687422i	$-0.758742\pi$
$461$	−31.1869	−1.45252	−0.726258	+	0.687422i	$0.758742\pi$
$462$	−16.4955	−0.767440
$463$	−6.96104	−0.323507	−0.161753	−	0.986831i	$-0.551715\pi$
$463$	−6.96104	−0.323507	−0.161753	+	0.986831i	$0.551715\pi$
$464$	−13.9832	−0.649153
$465$	−47.7404	−2.21391
$466$	29.8798	1.38416
$467$	−18.5088	−0.856486	−0.428243	−	0.903664i	$-0.640867\pi$
$467$	−18.5088	−0.856486	−0.428243	+	0.903664i	$0.640867\pi$
$468$	−0.411920	−0.0190410
$469$	−44.0646	−2.03471
$470$	3.97241	0.183234
$471$	−8.52555	−0.392836
$472$	4.03158	0.185568
$473$	10.4184	0.479039
$474$	−15.9517	−0.732685
$475$	0.0157040	0.000720547 0
$476$	9.96151	0.456585
$477$	−51.5382	−2.35977
$478$	−15.7906	−0.722245
$479$	−1.25874	−0.0575134	−0.0287567	−	0.999586i	$-0.509155\pi$
$479$	−1.25874	−0.0575134	−0.0287567	+	0.999586i	$0.509155\pi$
$480$	−15.9192	−0.726607
$481$	−0.907945	−0.0413987
$482$	8.48758	0.386599
$483$	−65.4805	−2.97946
$484$	3.66654	0.166661
$485$	−2.97358	−0.135023
$486$	−58.5737	−2.65696
$487$	−3.77174	−0.170914	−0.0854569	−	0.996342i	$-0.527235\pi$
$487$	−3.77174	−0.170914	−0.0854569	+	0.996342i	$0.527235\pi$
$488$	−2.39605	−0.108464
$489$	−29.8784	−1.35115
$490$	−8.33463	−0.376520
$491$	−22.3555	−1.00889	−0.504444	−	0.863444i	$-0.668302\pi$
$491$	−22.3555	−1.00889	−0.504444	+	0.863444i	$0.668302\pi$
$492$	−2.99292	−0.134931
$493$	−36.9942	−1.66613
$494$	1.06286	0.0478203
$495$	21.8747	0.983196
$496$	19.9546	0.895986
$497$	12.5967	0.565041
$498$	−42.4323	−1.90144
$499$	9.42498	0.421920	0.210960	−	0.977495i	$-0.432341\pi$
$499$	9.42498	0.421920	0.210960	+	0.977495i	$0.432341\pi$
$500$	4.34991	0.194534
$501$	64.5219	2.88262
$502$	27.7095	1.23674
$503$	3.30752	0.147475	0.0737374	−	0.997278i	$-0.476507\pi$
$503$	3.30752	0.147475	0.0737374	+	0.997278i	$0.476507\pi$
$504$	74.5599	3.32116
$505$	12.3167	0.548084
$506$	10.0640	0.447401
$507$	−42.6622	−1.89470
$508$	−5.83844	−0.259039
$509$	25.6399	1.13647	0.568234	−	0.822867i	$-0.307627\pi$
$509$	25.6399	1.13647	0.568234	+	0.822867i	$0.307627\pi$
$510$	75.7560	3.35453
$511$	32.3422	1.43074
$512$	25.2764	1.11707
$513$	−97.2997	−4.29589
$514$	−15.9321	−0.702733
$515$	3.41912	0.150664
$516$	−10.6163	−0.467355
$517$	−1.75626	−0.0772403
$518$	26.7582	1.17569
$519$	75.2805	3.30445
$520$	0.920295	0.0403576
$521$	20.6442	0.904440	0.452220	−	0.891907i	$-0.350632\pi$
$521$	20.6442	0.904440	0.452220	+	0.891907i	$0.350632\pi$
$522$	−45.0836	−1.97326
$523$	−42.7270	−1.86832	−0.934160	−	0.356854i	$-0.883849\pi$
$523$	−42.7270	−1.86832	−0.934160	+	0.356854i	$0.883849\pi$
$524$	−1.96183	−0.0857029
$525$	−0.0263771	−0.00115119
$526$	−1.24283	−0.0541902
$527$	52.7922	2.29966
$528$	−12.6597	−0.550943
$529$	16.9502	0.736964
$530$	18.7477	0.814349
$531$	10.3710	0.450062
$532$	7.56284	0.327890
$533$	0.317873	0.0137686
$534$	−16.4501	−0.711867
$535$	12.6256	0.545853
$536$	−42.3854	−1.83077
$537$	47.8555	2.06512
$538$	−4.45599	−0.192111
$539$	3.68486	0.158718
$540$	−13.7173	−0.590297
$541$	31.4119	1.35050	0.675252	−	0.737587i	$-0.264035\pi$
$541$	31.4119	1.35050	0.675252	+	0.737587i	$0.264035\pi$
$542$	−19.9514	−0.856985
$543$	−75.5676	−3.24292
$544$	17.6037	0.754752
$545$	3.59157	0.153846
$546$	−1.78523	−0.0764009
$547$	−42.7247	−1.82678	−0.913388	−	0.407090i	$-0.866543\pi$
$547$	−42.7247	−1.82678	−0.913388	+	0.407090i	$0.866543\pi$
$548$	−5.19241	−0.221809
$549$	−6.16368	−0.263059
$550$	0.00405404	0.000172865 0
$551$	−28.0862	−1.19651
$552$	−62.9852	−2.68083
$553$	12.0552	0.512639
$554$	−19.0108	−0.807690
$555$	−49.1315	−2.08552
$556$	8.26247	0.350407
$557$	−1.38156	−0.0585384	−0.0292692	−	0.999572i	$-0.509318\pi$
$557$	−1.38156	−0.0585384	−0.0292692	+	0.999572i	$0.509318\pi$
$558$	64.3361	2.72356
$559$	1.12754	0.0476898
$560$	−21.6400	−0.914456
$561$	−33.4928	−1.41407
$562$	−3.56845	−0.150526
$563$	11.1393	0.469466	0.234733	−	0.972060i	$-0.424578\pi$
$563$	11.1393	0.469466	0.234733	+	0.972060i	$0.424578\pi$
$564$	1.78962	0.0753564
$565$	21.8779	0.920410
$566$	−8.60260	−0.361594
$567$	89.6621	3.76546
$568$	12.1167	0.508406
$569$	−0.706950	−0.0296369	−0.0148184	−	0.999890i	$-0.504717\pi$
$569$	−0.706950	−0.0296369	−0.0148184	+	0.999890i	$0.504717\pi$
$570$	57.5144	2.40901
$571$	9.42652	0.394488	0.197244	−	0.980354i	$-0.436801\pi$
$571$	9.42652	0.394488	0.197244	+	0.980354i	$0.436801\pi$
$572$	−0.0662470	−0.00276993
$573$	16.5538	0.691546
$574$	−9.36809	−0.391016
$575$	0.0160929	0.000671121 0
$576$	69.3584	2.88993
$577$	24.1338	1.00470	0.502351	−	0.864664i	$-0.332469\pi$
$577$	24.1338	1.00470	0.502351	+	0.864664i	$0.332469\pi$
$578$	−62.1947	−2.58696
$579$	−40.3129	−1.67535
$580$	−3.95958	−0.164413
$581$	32.0675	1.33038
$582$	5.54848	0.229992
$583$	−8.28864	−0.343280
$584$	31.1097	1.28733
$585$	2.36740	0.0978800
$586$	30.6549	1.26634
$587$	4.16144	0.171761	0.0858806	−	0.996305i	$-0.472630\pi$
$587$	4.16144	0.171761	0.0858806	+	0.996305i	$0.472630\pi$
$588$	−3.75484	−0.154847
$589$	40.0801	1.65147
$590$	−3.77259	−0.155315
$591$	22.6318	0.930949
$592$	20.5360	0.844024
$593$	24.6273	1.01132	0.505661	−	0.862732i	$-0.331249\pi$
$593$	24.6273	1.01132	0.505661	+	0.862732i	$0.331249\pi$
$594$	−25.1183	−1.03062
$595$	−57.2512	−2.34707
$596$	−6.91029	−0.283057
$597$	67.5816	2.76593
$598$	1.08919	0.0445401
$599$	33.4440	1.36648	0.683242	−	0.730192i	$-0.260569\pi$
$599$	33.4440	1.36648	0.683242	+	0.730192i	$0.260569\pi$
$600$	−0.0253720	−0.00103581
$601$	12.8439	0.523913	0.261957	−	0.965080i	$-0.415632\pi$
$601$	12.8439	0.523913	0.261957	+	0.965080i	$0.415632\pi$
$602$	−33.2299	−1.35435
$603$	−109.034	−4.44020
$604$	6.08651	0.247657
$605$	−21.0725	−0.856718
$606$	−22.9819	−0.933578
$607$	−42.2651	−1.71549	−0.857743	−	0.514079i	$-0.828134\pi$
$607$	−42.2651	−1.71549	−0.857743	+	0.514079i	$0.828134\pi$
$608$	13.3648	0.542015
$609$	47.1750	1.91163
$610$	2.24212	0.0907808
$611$	−0.190072	−0.00768950
$612$	24.6488	0.996370
$613$	36.6595	1.48066	0.740332	−	0.672241i	$-0.234668\pi$
$613$	36.6595	1.48066	0.740332	+	0.672241i	$0.234668\pi$
$614$	38.3001	1.54567
$615$	17.2010	0.693612
$616$	11.9911	0.483136
$617$	30.6911	1.23558	0.617788	−	0.786345i	$-0.288029\pi$
$617$	30.6911	1.23558	0.617788	+	0.786345i	$0.288029\pi$
$618$	−6.37981	−0.256634
$619$	1.00000	0.0401934
$619$	1.00000	0.0401934
$620$	5.65048	0.226929
$621$	−99.7097	−4.00121
$622$	6.27599	0.251644
$623$	12.4319	0.498073
$624$	−1.37010	−0.0548480
$625$	−24.9873	−0.999491
$626$	13.1724	0.526474
$627$	−25.4279	−1.01549
$628$	1.00907	0.0402662
$629$	54.3304	2.16630
$630$	−69.7701	−2.77971
$631$	−42.3028	−1.68405	−0.842023	−	0.539441i	$-0.818635\pi$
$631$	−42.3028	−1.68405	−0.842023	+	0.539441i	$0.818635\pi$
$632$	11.5958	0.461256
$633$	75.4430	2.99859
$634$	−40.1909	−1.59618
$635$	33.5549	1.33159
$636$	8.44605	0.334908
$637$	0.398796	0.0158009
$638$	−7.25057	−0.287053
$639$	31.1695	1.23305
$640$	−15.5420	−0.614353
$641$	−33.3721	−1.31812	−0.659060	−	0.752090i	$-0.729046\pi$
$641$	−33.3721	−1.31812	−0.659060	+	0.752090i	$0.729046\pi$
$642$	−23.5585	−0.929778
$643$	14.1215	0.556898	0.278449	−	0.960451i	$-0.410180\pi$
$643$	14.1215	0.556898	0.278449	+	0.960451i	$0.410180\pi$
$644$	7.75016	0.305399
$645$	61.0143	2.40243
$646$	−63.6004	−2.50232
$647$	−10.6702	−0.419489	−0.209744	−	0.977756i	$-0.567263\pi$
$647$	−10.6702	−0.419489	−0.209744	+	0.977756i	$0.567263\pi$
$648$	86.2453	3.38804
$649$	1.66791	0.0654714
$650$	0.000438751 0	1.72092e−5 0
$651$	−67.3206	−2.63850
$652$	3.53635	0.138494
$653$	−3.01908	−0.118146	−0.0590728	−	0.998254i	$-0.518814\pi$
$653$	−3.01908	−0.118146	−0.0590728	+	0.998254i	$0.518814\pi$
$654$	−6.70159	−0.262053
$655$	11.2751	0.440555
$656$	−7.18968	−0.280710
$657$	80.0278	3.12218
$658$	5.60165	0.218375
$659$	−45.8116	−1.78456	−0.892282	−	0.451478i	$-0.850897\pi$
$659$	−45.8116	−1.78456	−0.892282	+	0.451478i	$0.850897\pi$
$660$	−3.58482	−0.139539
$661$	−8.99557	−0.349887	−0.174944	−	0.984578i	$-0.555974\pi$
$661$	−8.99557	−0.349887	−0.174944	+	0.984578i	$0.555974\pi$
$662$	0.528315	0.0205335
$663$	−3.62477	−0.140775
$664$	30.8454	1.19704
$665$	−43.4654	−1.68552
$666$	66.2107	2.56561
$667$	−28.7819	−1.11444
$668$	−7.63670	−0.295473
$669$	59.5902	2.30389
$670$	39.6625	1.53230
$671$	−0.991274	−0.0382677
$672$	−22.4482	−0.865959
$673$	32.1945	1.24101	0.620504	−	0.784203i	$-0.286928\pi$
$673$	32.1945	1.24101	0.620504	+	0.784203i	$0.286928\pi$
$674$	−4.01112	−0.154503
$675$	−0.0401655	−0.00154597
$676$	5.04943	0.194209
$677$	−11.3483	−0.436149	−0.218075	−	0.975932i	$-0.569978\pi$
$677$	−11.3483	−0.436149	−0.218075	+	0.975932i	$0.569978\pi$
$678$	−40.8225	−1.56778
$679$	−4.19316	−0.160919
$680$	−55.0695	−2.11182
$681$	−50.7632	−1.94525
$682$	10.3469	0.396202
$683$	−42.2406	−1.61629	−0.808147	−	0.588981i	$-0.799529\pi$
$683$	−42.2406	−1.61629	−0.808147	+	0.588981i	$0.799529\pi$
$684$	18.7135	0.715530
$685$	29.8420	1.14021
$686$	16.2553	0.620629
$687$	27.6054	1.05321
$688$	−25.5028	−0.972284
$689$	−0.897042	−0.0341746
$690$	58.9389	2.24377
$691$	28.2401	1.07431	0.537153	−	0.843485i	$-0.319500\pi$
$691$	28.2401	1.07431	0.537153	+	0.843485i	$0.319500\pi$
$692$	−8.91007	−0.338710
$693$	30.8464	1.17176
$694$	20.3267	0.771589
$695$	−47.4864	−1.80126
$696$	45.3773	1.72002
$697$	−19.0212	−0.720478
$698$	−25.9451	−0.982035
$699$	−77.3647	−2.92620
$700$	0.00312195	0.000117999 0
$701$	28.3274	1.06991	0.534956	−	0.844880i	$-0.320328\pi$
$701$	28.3274	1.06991	0.534956	+	0.844880i	$0.320328\pi$
$702$	−2.71844	−0.102601
$703$	41.2480	1.55570
$704$	11.1546	0.420403
$705$	−10.2854	−0.387369
$706$	21.1335	0.795371
$707$	17.3682	0.653198
$708$	−1.69959	−0.0638745
$709$	−38.8780	−1.46009	−0.730047	−	0.683397i	$-0.760502\pi$
$709$	−38.8780	−1.46009	−0.730047	+	0.683397i	$0.760502\pi$
$710$	−11.3383	−0.425519
$711$	29.8295	1.11869
$712$	11.9581	0.448150
$713$	41.0729	1.53819
$714$	106.826	3.99788
$715$	0.380738	0.0142388
$716$	−5.66409	−0.211677
$717$	40.8849	1.52688
$718$	11.7084	0.436954
$719$	−50.6095	−1.88741	−0.943707	−	0.330781i	$-0.892688\pi$
$719$	−50.6095	−1.88741	−0.943707	+	0.330781i	$0.892688\pi$
$720$	−53.5461	−1.99555
$721$	4.82143	0.179559
$722$	−24.1698	−0.899505
$723$	−21.9760	−0.817296
$724$	8.94405	0.332403
$725$	−0.0115940	−0.000430592 0
$726$	39.3196	1.45929
$727$	−8.08112	−0.299712	−0.149856	−	0.988708i	$-0.547881\pi$
$727$	−8.08112	−0.299712	−0.149856	+	0.988708i	$0.547881\pi$
$728$	1.29774	0.0480976
$729$	66.3301	2.45667
$730$	−29.1112	−1.07745
$731$	−67.4706	−2.49549
$732$	1.01010	0.0373344
$733$	2.64000	0.0975107	0.0487553	−	0.998811i	$-0.484475\pi$
$733$	2.64000	0.0975107	0.0487553	+	0.998811i	$0.484475\pi$
$734$	14.6639	0.541254
$735$	21.5800	0.795989
$736$	13.6958	0.504836
$737$	−17.5354	−0.645923
$738$	−23.1805	−0.853285
$739$	29.1750	1.07322	0.536609	−	0.843831i	$-0.319705\pi$
$739$	29.1750	1.07322	0.536609	+	0.843831i	$0.319705\pi$
$740$	5.81512	0.213768
$741$	−2.75195	−0.101095
$742$	26.4369	0.970528
$743$	−0.618734	−0.0226991	−0.0113496	−	0.999936i	$-0.503613\pi$
$743$	−0.618734	−0.0226991	−0.0113496	+	0.999936i	$0.503613\pi$
$744$	−64.7552	−2.37404
$745$	39.7151	1.45505
$746$	4.12011	0.150848
$747$	79.3480	2.90319
$748$	3.96415	0.144944
$749$	17.8039	0.650539
$750$	46.6481	1.70335
$751$	−13.7705	−0.502492	−0.251246	−	0.967923i	$-0.580840\pi$
$751$	−13.7705	−0.502492	−0.251246	+	0.967923i	$0.580840\pi$
$752$	4.29907	0.156771
$753$	−71.7453	−2.61454
$754$	−0.784697	−0.0285770
$755$	−34.9806	−1.27308
$756$	−19.3432	−0.703507
$757$	−28.0140	−1.01819	−0.509093	−	0.860711i	$-0.670019\pi$
$757$	−28.0140	−1.01819	−0.509093	+	0.860711i	$0.670019\pi$
$758$	22.7458	0.826163
$759$	−26.0577	−0.945836
$760$	−41.8091	−1.51657
$761$	−10.7431	−0.389436	−0.194718	−	0.980859i	$-0.562379\pi$
$761$	−10.7431	−0.389436	−0.194718	+	0.980859i	$0.562379\pi$
$762$	−62.6109	−2.26815
$763$	5.06460	0.183351
$764$	−1.95928	−0.0708844
$765$	−141.663	−5.12183
$766$	−21.9533	−0.793204
$767$	0.180511	0.00651787
$768$	−29.4435	−1.06245
$769$	−25.7299	−0.927844	−0.463922	−	0.885876i	$-0.653558\pi$
$769$	−25.7299	−0.927844	−0.463922	+	0.885876i	$0.653558\pi$
$770$	−11.2208	−0.404369
$771$	41.2512	1.48562
$772$	4.77137	0.171725
$773$	−21.8741	−0.786755	−0.393378	−	0.919377i	$-0.628694\pi$
$773$	−21.8741	−0.786755	−0.393378	+	0.919377i	$0.628694\pi$
$774$	−82.2242	−2.95549
$775$	0.0165452	0.000594320 0
$776$	−4.03337	−0.144790
$777$	−69.2822	−2.48548
$778$	−3.62468	−0.129951
$779$	−14.4410	−0.517402
$780$	−0.387968	−0.0138915
$781$	5.01283	0.179373
$782$	−65.1756	−2.33068
$783$	71.8352	2.56718
$784$	−9.02000	−0.322143
$785$	−5.79936	−0.206988
$786$	−21.0385	−0.750418
$787$	−19.6488	−0.700403	−0.350201	−	0.936674i	$-0.613887\pi$
$787$	−19.6488	−0.700403	−0.350201	+	0.936674i	$0.613887\pi$
$788$	−2.67866	−0.0954234
$789$	3.21794	0.114562
$790$	−10.8509	−0.386057
$791$	30.8508	1.09693
$792$	29.6709	1.05431
$793$	−0.107281	−0.00380966
$794$	11.3993	0.404546
$795$	−48.5415	−1.72159
$796$	−7.99884	−0.283511
$797$	−34.3265	−1.21591	−0.607953	−	0.793973i	$-0.708009\pi$
$797$	−34.3265	−1.21591	−0.607953	+	0.793973i	$0.708009\pi$
$798$	81.1032	2.87102
$799$	11.3737	0.402373
$800$	0.00551703	0.000195056 0
$801$	30.7616	1.08691
$802$	21.4471	0.757322
$803$	12.8705	0.454189
$804$	17.8684	0.630169
$805$	−44.5420	−1.56990
$806$	1.11979	0.0394430
$807$	11.5374	0.406136
$808$	16.7063	0.587727
$809$	11.7599	0.413455	0.206728	−	0.978399i	$-0.433719\pi$
$809$	11.7599	0.413455	0.206728	+	0.978399i	$0.433719\pi$
$810$	−80.7048	−2.83568
$811$	1.74718	0.0613519	0.0306759	−	0.999529i	$-0.490234\pi$
$811$	1.74718	0.0613519	0.0306759	+	0.999529i	$0.490234\pi$
$812$	−5.58355	−0.195944
$813$	51.6580	1.81172
$814$	10.6483	0.373224
$815$	−20.3243	−0.711928
$816$	81.9855	2.87007
$817$	−51.2241	−1.79210
$818$	−10.9035	−0.381233
$819$	3.33836	0.116652
$820$	−2.03588	−0.0710961
$821$	37.6222	1.31303	0.656513	−	0.754315i	$-0.272031\pi$
$821$	37.6222	1.31303	0.656513	+	0.754315i	$0.272031\pi$
$822$	−55.6830	−1.94217
$823$	13.0158	0.453701	0.226850	−	0.973930i	$-0.427157\pi$
$823$	13.0158	0.453701	0.226850	+	0.973930i	$0.427157\pi$
$824$	4.63769	0.161562
$825$	−0.0104967	−0.000365448 0
$826$	−5.31986	−0.185102
$827$	−31.8318	−1.10690	−0.553451	−	0.832882i	$-0.686689\pi$
$827$	−31.8318	−1.10690	−0.553451	+	0.832882i	$0.686689\pi$
$828$	19.1770	0.666448
$829$	−33.8447	−1.17548	−0.587738	−	0.809051i	$-0.699981\pi$
$829$	−33.8447	−1.17548	−0.587738	+	0.809051i	$0.699981\pi$
$830$	−28.8639	−1.00188
$831$	49.2226	1.70751
$832$	1.20721	0.0418524
$833$	−23.8635	−0.826821
$834$	88.6060	3.06817
$835$	43.8899	1.51887
$836$	3.00961	0.104089
$837$	−102.512	−3.54332
$838$	−25.3820	−0.876808
$839$	6.06404	0.209354	0.104677	−	0.994506i	$-0.466619\pi$
$839$	6.06404	0.209354	0.104677	+	0.994506i	$0.466619\pi$
$840$	70.2246	2.42298
$841$	−8.26429	−0.284976
$842$	−40.1904	−1.38505
$843$	9.23942	0.318222
$844$	−8.92930	−0.307359
$845$	−29.0203	−0.998328
$846$	13.8608	0.476543
$847$	−29.7151	−1.02102
$848$	20.2894	0.696740
$849$	22.2738	0.764435
$850$	−0.0262544	−0.000900517 0
$851$	42.2696	1.44898
$852$	−5.10803	−0.174998
$853$	52.5673	1.79987	0.899935	−	0.436025i	$-0.143614\pi$
$853$	52.5673	1.79987	0.899935	+	0.436025i	$0.143614\pi$
$854$	3.16170	0.108191
$855$	−107.551	−3.67817
$856$	17.1254	0.585334
$857$	−5.55207	−0.189655	−0.0948275	−	0.995494i	$-0.530230\pi$
$857$	−5.55207	−0.189655	−0.0948275	+	0.995494i	$0.530230\pi$
$858$	−0.710427	−0.0242536
$859$	−23.7264	−0.809535	−0.404767	−	0.914420i	$-0.632647\pi$
$859$	−23.7264	−0.809535	−0.404767	+	0.914420i	$0.632647\pi$
$860$	−7.22155	−0.246253
$861$	24.2558	0.826635
$862$	−1.45049	−0.0494040
$863$	12.9344	0.440293	0.220147	−	0.975467i	$-0.429346\pi$
$863$	12.9344	0.440293	0.220147	+	0.975467i	$0.429346\pi$
$864$	−34.1828	−1.16292
$865$	51.2083	1.74113
$866$	−10.7582	−0.365580
$867$	161.034	5.46901
$868$	7.96795	0.270450
$869$	4.79733	0.162738
$870$	−42.4622	−1.43960
$871$	−1.89777	−0.0643035
$872$	4.87160	0.164973
$873$	−10.3756	−0.351160
$874$	−49.4817	−1.67374
$875$	−35.2534	−1.19178
$876$	−13.1149	−0.443112
$877$	35.5216	1.19948	0.599739	−	0.800195i	$-0.295271\pi$
$877$	35.5216	1.19948	0.599739	+	0.800195i	$0.295271\pi$
$878$	20.7831	0.701396
$879$	−79.3715	−2.67714
$880$	−8.61156	−0.290296
$881$	−15.8118	−0.532715	−0.266357	−	0.963874i	$-0.585820\pi$
$881$	−15.8118	−0.532715	−0.266357	+	0.963874i	$0.585820\pi$
$882$	−29.0817	−0.979230
$883$	−41.6550	−1.40180	−0.700902	−	0.713258i	$-0.747219\pi$
$883$	−41.6550	−1.40180	−0.700902	+	0.713258i	$0.747219\pi$
$884$	0.429022	0.0144296
$885$	9.76795	0.328346
$886$	47.0659	1.58121
$887$	−10.6948	−0.359095	−0.179548	−	0.983749i	$-0.557463\pi$
$887$	−10.6948	−0.359095	−0.179548	+	0.983749i	$0.557463\pi$
$888$	−66.6420	−2.23636
$889$	47.3171	1.58696
$890$	−11.1899	−0.375088
$891$	35.6808	1.19535
$892$	−7.05300	−0.236152
$893$	8.63499	0.288959
$894$	−74.1054	−2.47845
$895$	32.5529	1.08812
$896$	−21.9164	−0.732176
$897$	−2.82011	−0.0941608
$898$	7.07104	0.235964
$899$	−29.5907	−0.986904
$900$	0.00772499	0.000257500 0
$901$	53.6780	1.78827
$902$	−3.72800	−0.124129
$903$	86.0385	2.86318
$904$	29.6752	0.986982
$905$	−51.4036	−1.70871
$906$	65.2712	2.16849
$907$	7.55510	0.250863	0.125431	−	0.992102i	$-0.459969\pi$
$907$	7.55510	0.250863	0.125431	+	0.992102i	$0.459969\pi$
$908$	6.00824	0.199391
$909$	42.9760	1.42542
$910$	−1.21437	−0.0402561
$911$	1.47199	0.0487692	0.0243846	−	0.999703i	$-0.492237\pi$
$911$	1.47199	0.0487692	0.0243846	+	0.999703i	$0.492237\pi$
$912$	62.2439	2.06110
$913$	12.7611	0.422332
$914$	−3.56448	−0.117903
$915$	−5.80529	−0.191917
$916$	−3.26733	−0.107956
$917$	15.8994	0.525046
$918$	162.669	5.36887
$919$	−26.5075	−0.874400	−0.437200	−	0.899364i	$-0.644030\pi$
$919$	−26.5075	−0.874400	−0.437200	+	0.899364i	$0.644030\pi$
$920$	−42.8446	−1.41255
$921$	−99.1664	−3.26764
$922$	39.5844	1.30364
$923$	0.542516	0.0178571
$924$	−5.05508	−0.166300
$925$	0.0170272	0.000559852 0
$926$	8.83540	0.290349
$927$	11.9302	0.391838
$928$	−9.86709	−0.323903
$929$	−6.34088	−0.208037	−0.104019	−	0.994575i	$-0.533170\pi$
$929$	−6.34088	−0.208037	−0.104019	+	0.994575i	$0.533170\pi$
$930$	60.5952	1.98700
$931$	−18.1173	−0.593771
$932$	9.15675	0.299939
$933$	−16.2498	−0.531993
$934$	23.4926	0.768700
$935$	−22.7829	−0.745081
$936$	3.21115	0.104960
$937$	−24.0482	−0.785620	−0.392810	−	0.919620i	$-0.628497\pi$
$937$	−24.0482	−0.785620	−0.392810	+	0.919620i	$0.628497\pi$
$938$	55.9296	1.82616
$939$	−34.1058	−1.11300
$940$	1.21736	0.0397058
$941$	−18.1223	−0.590771	−0.295385	−	0.955378i	$-0.595448\pi$
$941$	−18.1223	−0.590771	−0.295385	+	0.955378i	$0.595448\pi$
$942$	10.8212	0.352573
$943$	−14.7987	−0.481911
$944$	−4.08281	−0.132884
$945$	111.170	3.61637
$946$	−13.2237	−0.429940
$947$	−20.1977	−0.656336	−0.328168	−	0.944619i	$-0.606431\pi$
$947$	−20.1977	−0.656336	−0.328168	+	0.944619i	$0.606431\pi$
$948$	−4.88844	−0.158769
$949$	1.39291	0.0452159
$950$	−0.0199325	−0.000646694 0
$951$	104.062	3.37444
$952$	−77.6555	−2.51683
$953$	32.2900	1.04598	0.522988	−	0.852340i	$-0.324817\pi$
$953$	32.2900	1.04598	0.522988	+	0.852340i	$0.324817\pi$
$954$	65.4156	2.11791
$955$	11.2605	0.364380
$956$	−4.83907	−0.156507
$957$	18.7731	0.606849
$958$	1.59767	0.0516185
$959$	42.0814	1.35888
$960$	65.3254	2.10837
$961$	11.2271	0.362164
$962$	1.15242	0.0371556
$963$	44.0540	1.41962
$964$	2.60104	0.0837739
$965$	−27.4222	−0.882752
$966$	83.1120	2.67408
$967$	−17.9586	−0.577508	−0.288754	−	0.957403i	$-0.593241\pi$
$967$	−17.9586	−0.577508	−0.288754	+	0.957403i	$0.593241\pi$
$968$	−28.5827	−0.918684
$969$	164.674	5.29008
$970$	3.77426	0.121184
$971$	23.0632	0.740134	0.370067	−	0.929005i	$-0.379335\pi$
$971$	23.0632	0.740134	0.370067	+	0.929005i	$0.379335\pi$
$972$	−17.9501	−0.575748
$973$	−66.9624	−2.14671
$974$	4.78733	0.153396
$975$	−0.00113601	−3.63814e−5 0
$976$	2.42649	0.0776702
$977$	−22.2539	−0.711966	−0.355983	−	0.934492i	$-0.615854\pi$
$977$	−22.2539	−0.711966	−0.355983	+	0.934492i	$0.615854\pi$
$978$	37.9235	1.21266
$979$	4.94723	0.158114
$980$	−2.55417	−0.0815899
$981$	12.5319	0.400112
$982$	28.3750	0.905482
$983$	−34.9063	−1.11334	−0.556669	−	0.830735i	$-0.687921\pi$
$983$	−34.9063	−1.11334	−0.556669	+	0.830735i	$0.687921\pi$
$984$	23.3315	0.743780
$985$	15.3949	0.490523
$986$	46.9554	1.49536
$987$	−14.5038	−0.461660
$988$	0.325716	0.0103624
$989$	−52.4928	−1.66917
$990$	−27.7648	−0.882423
$991$	−19.4547	−0.617999	−0.309000	−	0.951062i	$-0.599994\pi$
$991$	−19.4547	−0.617999	−0.309000	+	0.951062i	$0.599994\pi$
$992$	14.0807	0.447064
$993$	−1.36791	−0.0434093
$994$	−15.9886	−0.507127
$995$	45.9712	1.45739
$996$	−13.0035	−0.412032
$997$	−58.4225	−1.85026	−0.925129	−	0.379652i	$-0.876044\pi$
$997$	−58.4225	−1.85026	−0.925129	+	0.379652i	$0.876044\pi$
$998$	−11.9628	−0.378676
$999$	−105.499	−3.33783

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	619.2.a.b.1.9	✓	30
3.2	odd	2		5571.2.a.g.1.22		30
4.3	odd	2		9904.2.a.n.1.1		30

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
619.2.a.b.1.9	✓	30	1.1	even	1	trivial
5571.2.a.g.1.22		30	3.2	odd	2
9904.2.a.n.1.1		30	4.3	odd	2

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:	\( N \)	\(=\)	\( 619 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	619.a (trivial)

\(f(q)\)	\(=\)	\(q-1.26926 q^{2} +3.28637 q^{3} -0.388969 q^{4} +2.23550 q^{5} -4.17127 q^{6} +3.15236 q^{7} +3.03223 q^{8} +7.80023 q^{9} +O(q^{10})\)	\(q-1.26926 q^{2} +3.28637 q^{3} -0.388969 q^{4} +2.23550 q^{5} -4.17127 q^{6} +3.15236 q^{7} +3.03223 q^{8} +7.80023 q^{9} -2.83744 q^{10} +1.25447 q^{11} -1.27830 q^{12} +0.135766 q^{13} -4.00118 q^{14} +7.34667 q^{15} -3.07076 q^{16} -8.12408 q^{17} -9.90055 q^{18} -6.16785 q^{19} -0.869540 q^{20} +10.3598 q^{21} -1.59226 q^{22} -6.32062 q^{23} +9.96504 q^{24} -0.00254610 q^{25} -0.172323 q^{26} +15.7753 q^{27} -1.22617 q^{28} +4.55365 q^{29} -9.32487 q^{30} -6.49824 q^{31} -2.16685 q^{32} +4.12266 q^{33} +10.3116 q^{34} +7.04710 q^{35} -3.03405 q^{36} -6.68758 q^{37} +7.82863 q^{38} +0.446177 q^{39} +6.77855 q^{40} +2.34133 q^{41} -13.1493 q^{42} +8.30502 q^{43} -0.487951 q^{44} +17.4374 q^{45} +8.02253 q^{46} -1.40000 q^{47} -10.0917 q^{48} +2.93738 q^{49} +0.00323167 q^{50} -26.6987 q^{51} -0.0528087 q^{52} -6.60727 q^{53} -20.0230 q^{54} +2.80437 q^{55} +9.55869 q^{56} -20.2698 q^{57} -5.77978 q^{58} +1.32957 q^{59} -2.85763 q^{60} -0.790192 q^{61} +8.24798 q^{62} +24.5891 q^{63} +8.89184 q^{64} +0.303504 q^{65} -5.23274 q^{66} -13.9783 q^{67} +3.16002 q^{68} -20.7719 q^{69} -8.94463 q^{70} +3.99597 q^{71} +23.6521 q^{72} +10.2597 q^{73} +8.48831 q^{74} -0.00836742 q^{75} +2.39910 q^{76} +3.95455 q^{77} -0.566316 q^{78} +3.82418 q^{79} -6.86469 q^{80} +28.4429 q^{81} -2.97177 q^{82} +10.1725 q^{83} -4.02965 q^{84} -18.1614 q^{85} -10.5413 q^{86} +14.9650 q^{87} +3.80385 q^{88} +3.94368 q^{89} -22.1327 q^{90} +0.427983 q^{91} +2.45852 q^{92} -21.3556 q^{93} +1.77697 q^{94} -13.7882 q^{95} -7.12108 q^{96} -1.33017 q^{97} -3.72831 q^{98} +9.78517 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 30 q + 9 q^{2} + q^{3} + 33 q^{4} + 21 q^{5} + 6 q^{6} + 2 q^{7} + 27 q^{8} + 43 q^{9}+O(q^{10}) \) 30 * q + 9 * q^2 + q^3 + 33 * q^4 + 21 * q^5 + 6 * q^6 + 2 * q^7 + 27 * q^8 + 43 * q^9	\( 30 q + 9 q^{2} + q^{3} + 33 q^{4} + 21 q^{5} + 6 q^{6} + 2 q^{7} + 27 q^{8} + 43 q^{9} + 5 q^{10} + 23 q^{11} - 6 q^{12} + 9 q^{13} + 7 q^{14} - 2 q^{15} + 35 q^{16} + 4 q^{17} + 10 q^{18} - q^{19} + 29 q^{20} + 30 q^{21} + 4 q^{23} + 4 q^{24} + 35 q^{25} + q^{26} - 5 q^{27} - 13 q^{28} + 90 q^{29} - 31 q^{30} + 2 q^{31} + 43 q^{32} - 6 q^{33} - 9 q^{34} + 9 q^{35} + 33 q^{36} + 19 q^{37} + 5 q^{38} + 32 q^{39} - 12 q^{40} + 59 q^{41} - 25 q^{42} - 4 q^{43} + 52 q^{44} + 30 q^{45} - q^{46} + 4 q^{47} - 44 q^{48} + 30 q^{49} + 31 q^{50} - 12 q^{52} + 34 q^{53} - 28 q^{54} - 17 q^{55} + 2 q^{56} - 8 q^{57} + 6 q^{58} + 13 q^{59} - 64 q^{60} + 16 q^{61} + 28 q^{62} - 40 q^{63} + 37 q^{64} + 31 q^{65} - 59 q^{66} - 11 q^{67} - 52 q^{68} + 6 q^{69} - 40 q^{70} + 42 q^{71} + 6 q^{72} - 4 q^{73} + 16 q^{74} - 52 q^{75} - 42 q^{76} + 29 q^{77} - 56 q^{78} + 3 q^{79} + 21 q^{80} + 30 q^{81} - 43 q^{82} - 11 q^{83} - 36 q^{84} + 19 q^{85} - 11 q^{86} - 20 q^{87} - 47 q^{88} + 58 q^{89} - 33 q^{90} - 39 q^{91} - 7 q^{92} - 15 q^{93} - 46 q^{94} + 23 q^{95} - 70 q^{96} - 9 q^{97} - 8 q^{99}+O(q^{100}) \) 30 * q + 9 * q^2 + q^3 + 33 * q^4 + 21 * q^5 + 6 * q^6 + 2 * q^7 + 27 * q^8 + 43 * q^9 + 5 * q^10 + 23 * q^11 - 6 * q^12 + 9 * q^13 + 7 * q^14 - 2 * q^15 + 35 * q^16 + 4 * q^17 + 10 * q^18 - q^19 + 29 * q^20 + 30 * q^21 + 4 * q^23 + 4 * q^24 + 35 * q^25 + q^26 - 5 * q^27 - 13 * q^28 + 90 * q^29 - 31 * q^30 + 2 * q^31 + 43 * q^32 - 6 * q^33 - 9 * q^34 + 9 * q^35 + 33 * q^36 + 19 * q^37 + 5 * q^38 + 32 * q^39 - 12 * q^40 + 59 * q^41 - 25 * q^42 - 4 * q^43 + 52 * q^44 + 30 * q^45 - q^46 + 4 * q^47 - 44 * q^48 + 30 * q^49 + 31 * q^50 - 12 * q^52 + 34 * q^53 - 28 * q^54 - 17 * q^55 + 2 * q^56 - 8 * q^57 + 6 * q^58 + 13 * q^59 - 64 * q^60 + 16 * q^61 + 28 * q^62 - 40 * q^63 + 37 * q^64 + 31 * q^65 - 59 * q^66 - 11 * q^67 - 52 * q^68 + 6 * q^69 - 40 * q^70 + 42 * q^71 + 6 * q^72 - 4 * q^73 + 16 * q^74 - 52 * q^75 - 42 * q^76 + 29 * q^77 - 56 * q^78 + 3 * q^79 + 21 * q^80 + 30 * q^81 - 43 * q^82 - 11 * q^83 - 36 * q^84 + 19 * q^85 - 11 * q^86 - 20 * q^87 - 47 * q^88 + 58 * q^89 - 33 * q^90 - 39 * q^91 - 7 * q^92 - 15 * q^93 - 46 * q^94 + 23 * q^95 - 70 * q^96 - 9 * q^97 - 8 * q^99

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