LMFDB - Embedded newform 6019.2.a.e.1.1

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:	$0$
Dimension:	$130$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
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)

$f(q)$	$=$	$q-2.80453 q^{2} +3.24972 q^{3} +5.86540 q^{4} +2.53460 q^{5} -9.11395 q^{6} +2.92678 q^{7} -10.8406 q^{8} +7.56069 q^{9} +O(q^{10})$	\(q-2.80453 q^{2} +3.24972 q^{3} +5.86540 q^{4} +2.53460 q^{5} -9.11395 q^{6} +2.92678 q^{7} -10.8406 q^{8} +7.56069 q^{9} -7.10835 q^{10} +4.66029 q^{11} +19.0609 q^{12} +1.00000 q^{13} -8.20824 q^{14} +8.23673 q^{15} +18.6721 q^{16} +2.03520 q^{17} -21.2042 q^{18} -6.98563 q^{19} +14.8664 q^{20} +9.51121 q^{21} -13.0699 q^{22} +4.26812 q^{23} -35.2290 q^{24} +1.42418 q^{25} -2.80453 q^{26} +14.8210 q^{27} +17.1667 q^{28} -8.75361 q^{29} -23.1002 q^{30} +1.81056 q^{31} -30.6852 q^{32} +15.1446 q^{33} -5.70778 q^{34} +7.41820 q^{35} +44.3465 q^{36} -7.84924 q^{37} +19.5914 q^{38} +3.24972 q^{39} -27.4766 q^{40} -6.75887 q^{41} -26.6745 q^{42} -1.45600 q^{43} +27.3344 q^{44} +19.1633 q^{45} -11.9701 q^{46} +3.27642 q^{47} +60.6791 q^{48} +1.56602 q^{49} -3.99415 q^{50} +6.61383 q^{51} +5.86540 q^{52} +4.24682 q^{53} -41.5659 q^{54} +11.8119 q^{55} -31.7281 q^{56} -22.7014 q^{57} +24.5498 q^{58} +6.51474 q^{59} +48.3117 q^{60} -2.45928 q^{61} -5.07777 q^{62} +22.1285 q^{63} +48.7134 q^{64} +2.53460 q^{65} -42.4736 q^{66} +2.73405 q^{67} +11.9372 q^{68} +13.8702 q^{69} -20.8046 q^{70} -5.72732 q^{71} -81.9626 q^{72} +9.85464 q^{73} +22.0134 q^{74} +4.62818 q^{75} -40.9735 q^{76} +13.6396 q^{77} -9.11395 q^{78} -9.29746 q^{79} +47.3262 q^{80} +25.4820 q^{81} +18.9555 q^{82} -5.35234 q^{83} +55.7870 q^{84} +5.15841 q^{85} +4.08339 q^{86} -28.4468 q^{87} -50.5204 q^{88} -4.73837 q^{89} -53.7441 q^{90} +2.92678 q^{91} +25.0342 q^{92} +5.88381 q^{93} -9.18882 q^{94} -17.7058 q^{95} -99.7183 q^{96} -10.7613 q^{97} -4.39195 q^{98} +35.2350 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 130 q + 10 q^{2} + 11 q^{3} + 146 q^{4} + 40 q^{5} + 4 q^{6} + 8 q^{7} + 24 q^{8} + 181 q^{9}+O(q^{10}) $ 130 * q + 10 * q^2 + 11 * q^3 + 146 * q^4 + 40 * q^5 + 4 * q^6 + 8 * q^7 + 24 * q^8 + 181 * q^9	\( 130 q + 10 q^{2} + 11 q^{3} + 146 q^{4} + 40 q^{5} + 4 q^{6} + 8 q^{7} + 24 q^{8} + 181 q^{9} + 5 q^{10} + 43 q^{11} + 28 q^{12} + 130 q^{13} + 47 q^{14} + 29 q^{15} + 170 q^{16} + 85 q^{17} + 20 q^{18} + 3 q^{19} + 73 q^{20} + 62 q^{21} + 12 q^{22} + 62 q^{23} - 5 q^{24} + 178 q^{25} + 10 q^{26} + 35 q^{27} - q^{28} + 134 q^{29} + 24 q^{30} + 14 q^{31} + 48 q^{32} + 4 q^{33} + 4 q^{34} + 50 q^{35} + 244 q^{36} + 32 q^{37} + 76 q^{38} + 11 q^{39} - 6 q^{40} + 48 q^{41} + 9 q^{42} + 34 q^{43} + 123 q^{44} + 115 q^{45} + 5 q^{46} + 25 q^{47} + 35 q^{48} + 210 q^{49} + 24 q^{50} + 20 q^{51} + 146 q^{52} + 193 q^{53} - 39 q^{54} + 32 q^{55} + 122 q^{56} + 7 q^{57} - 4 q^{58} + 50 q^{59} + 42 q^{60} + 57 q^{61} + 51 q^{62} + 8 q^{63} + 172 q^{64} + 40 q^{65} - 4 q^{66} + 21 q^{67} + 132 q^{68} + 92 q^{69} - 46 q^{70} + 58 q^{71} - 26 q^{72} + 15 q^{73} + 120 q^{74} + 23 q^{75} - 65 q^{76} + 192 q^{77} + 4 q^{78} + 32 q^{79} + 66 q^{80} + 326 q^{81} + 11 q^{82} + 33 q^{83} + 5 q^{84} + 43 q^{85} + 105 q^{86} + 31 q^{87} - 17 q^{88} + 84 q^{89} - 73 q^{90} + 8 q^{91} + 161 q^{92} + 52 q^{93} + 4 q^{94} + 59 q^{95} - 77 q^{96} + 9 q^{97} - 61 q^{98} + 100 q^{99}+O(q^{100}) \) 130 * q + 10 * q^2 + 11 * q^3 + 146 * q^4 + 40 * q^5 + 4 * q^6 + 8 * q^7 + 24 * q^8 + 181 * q^9 + 5 * q^10 + 43 * q^11 + 28 * q^12 + 130 * q^13 + 47 * q^14 + 29 * q^15 + 170 * q^16 + 85 * q^17 + 20 * q^18 + 3 * q^19 + 73 * q^20 + 62 * q^21 + 12 * q^22 + 62 * q^23 - 5 * q^24 + 178 * q^25 + 10 * q^26 + 35 * q^27 - q^28 + 134 * q^29 + 24 * q^30 + 14 * q^31 + 48 * q^32 + 4 * q^33 + 4 * q^34 + 50 * q^35 + 244 * q^36 + 32 * q^37 + 76 * q^38 + 11 * q^39 - 6 * q^40 + 48 * q^41 + 9 * q^42 + 34 * q^43 + 123 * q^44 + 115 * q^45 + 5 * q^46 + 25 * q^47 + 35 * q^48 + 210 * q^49 + 24 * q^50 + 20 * q^51 + 146 * q^52 + 193 * q^53 - 39 * q^54 + 32 * q^55 + 122 * q^56 + 7 * q^57 - 4 * q^58 + 50 * q^59 + 42 * q^60 + 57 * q^61 + 51 * q^62 + 8 * q^63 + 172 * q^64 + 40 * q^65 - 4 * q^66 + 21 * q^67 + 132 * q^68 + 92 * q^69 - 46 * q^70 + 58 * q^71 - 26 * q^72 + 15 * q^73 + 120 * q^74 + 23 * q^75 - 65 * q^76 + 192 * q^77 + 4 * q^78 + 32 * q^79 + 66 * q^80 + 326 * q^81 + 11 * q^82 + 33 * q^83 + 5 * q^84 + 43 * q^85 + 105 * q^86 + 31 * q^87 - 17 * q^88 + 84 * q^89 - 73 * q^90 + 8 * q^91 + 161 * q^92 + 52 * q^93 + 4 * q^94 + 59 * q^95 - 77 * q^96 + 9 * q^97 - 61 * q^98 + 100 * 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 $

$2$	−2.80453	−1.98310	−0.991552	−	0.129713i	$-0.958594\pi$
$2$	−2.80453	−1.98310	−0.991552	+	0.129713i	$0.958594\pi$
$3$	3.24972	1.87623	0.938114	−	0.346327i	$-0.112571\pi$
$3$	3.24972	1.87623	0.938114	+	0.346327i	$0.112571\pi$
$4$	5.86540	2.93270
$5$	2.53460	1.13351	0.566753	−	0.823888i	$-0.308199\pi$
$5$	2.53460	1.13351	0.566753	+	0.823888i	$0.308199\pi$
$6$	−9.11395	−3.72075
$7$	2.92678	1.10622	0.553109	−	0.833109i	$-0.313441\pi$
$7$	2.92678	1.10622	0.553109	+	0.833109i	$0.313441\pi$
$8$	−10.8406	−3.83274
$9$	7.56069	2.52023
$10$	−7.10835	−2.24786
$11$	4.66029	1.40513	0.702564	−	0.711620i	$-0.252038\pi$
$11$	4.66029	1.40513	0.702564	+	0.711620i	$0.252038\pi$
$12$	19.0609	5.50241
$13$	1.00000	0.277350
$13$	1.00000	0.277350
$14$	−8.20824	−2.19374
$15$	8.23673	2.12672
$16$	18.6721	4.66802
$17$	2.03520	0.493608	0.246804	−	0.969065i	$-0.420620\pi$
$17$	2.03520	0.493608	0.246804	+	0.969065i	$0.420620\pi$
$18$	−21.2042	−4.99788
$19$	−6.98563	−1.60261	−0.801307	−	0.598253i	$-0.795862\pi$
$19$	−6.98563	−1.60261	−0.801307	+	0.598253i	$0.795862\pi$
$20$	14.8664	3.32423
$21$	9.51121	2.07552
$22$	−13.0699	−2.78652
$23$	4.26812	0.889964	0.444982	−	0.895540i	$-0.353210\pi$
$23$	4.26812	0.889964	0.444982	+	0.895540i	$0.353210\pi$
$24$	−35.2290	−7.19109
$25$	1.42418	0.284835
$26$	−2.80453	−0.550014
$27$	14.8210	2.85230
$28$	17.1667	3.24420
$29$	−8.75361	−1.62551	−0.812753	−	0.582609i	$-0.802032\pi$
$29$	−8.75361	−1.62551	−0.812753	+	0.582609i	$0.802032\pi$
$30$	−23.1002	−4.21750
$31$	1.81056	0.325186	0.162593	−	0.986693i	$-0.448014\pi$
$31$	1.81056	0.325186	0.162593	+	0.986693i	$0.448014\pi$
$32$	−30.6852	−5.42442
$33$	15.1446	2.63634
$34$	−5.70778	−0.978876
$35$	7.41820	1.25390
$36$	44.3465	7.39108
$37$	−7.84924	−1.29041	−0.645203	−	0.764011i	$-0.723227\pi$
$37$	−7.84924	−1.29041	−0.645203	+	0.764011i	$0.723227\pi$
$38$	19.5914	3.17815
$39$	3.24972	0.520372
$40$	−27.4766	−4.34443
$41$	−6.75887	−1.05556	−0.527779	−	0.849381i	$-0.676975\pi$
$41$	−6.75887	−1.05556	−0.527779	+	0.849381i	$0.676975\pi$
$42$	−26.6745	−4.11596
$43$	−1.45600	−0.222037	−0.111019	−	0.993818i	$-0.535411\pi$
$43$	−1.45600	−0.222037	−0.111019	+	0.993818i	$0.535411\pi$
$44$	27.3344	4.12082
$45$	19.1633	2.85670
$46$	−11.9701	−1.76489
$47$	3.27642	0.477915	0.238958	−	0.971030i	$-0.423194\pi$
$47$	3.27642	0.477915	0.238958	+	0.971030i	$0.423194\pi$
$48$	60.6791	8.75827
$49$	1.56602	0.223717
$50$	−3.99415	−0.564858
$51$	6.61383	0.926122
$52$	5.86540	0.813384
$53$	4.24682	0.583345	0.291673	−	0.956518i	$-0.405788\pi$
$53$	4.24682	0.583345	0.291673	+	0.956518i	$0.405788\pi$
$54$	−41.5659	−5.65641
$55$	11.8119	1.59272
$56$	−31.7281	−4.23984
$57$	−22.7014	−3.00687
$58$	24.5498	3.22354
$59$	6.51474	0.848146	0.424073	−	0.905628i	$-0.360600\pi$
$59$	6.51474	0.848146	0.424073	+	0.905628i	$0.360600\pi$
$60$	48.3117	6.23701
$61$	−2.45928	−0.314878	−0.157439	−	0.987529i	$-0.550324\pi$
$61$	−2.45928	−0.314878	−0.157439	+	0.987529i	$0.550324\pi$
$62$	−5.07777	−0.644877
$63$	22.1285	2.78792
$64$	48.7134	6.08917
$65$	2.53460	0.314378
$66$	−42.4736	−5.22814
$67$	2.73405	0.334017	0.167009	−	0.985955i	$-0.446589\pi$
$67$	2.73405	0.334017	0.167009	+	0.985955i	$0.446589\pi$
$68$	11.9372	1.44760
$69$	13.8702	1.66977
$70$	−20.8046	−2.48662
$71$	−5.72732	−0.679707	−0.339854	−	0.940478i	$-0.610378\pi$
$71$	−5.72732	−0.679707	−0.339854	+	0.940478i	$0.610378\pi$
$72$	−81.9626	−9.65939
$73$	9.85464	1.15340	0.576699	−	0.816957i	$-0.304341\pi$
$73$	9.85464	1.15340	0.576699	+	0.816957i	$0.304341\pi$
$74$	22.0134	2.55901
$75$	4.62818	0.534416
$76$	−40.9735	−4.69998
$77$	13.6396	1.55438
$78$	−9.11395	−1.03195
$79$	−9.29746	−1.04605	−0.523023	−	0.852319i	$-0.675196\pi$
$79$	−9.29746	−1.04605	−0.523023	+	0.852319i	$0.675196\pi$
$80$	47.3262	5.29123
$81$	25.4820	2.83133
$82$	18.9555	2.09328
$83$	−5.35234	−0.587495	−0.293748	−	0.955883i	$-0.594903\pi$
$83$	−5.35234	−0.587495	−0.293748	+	0.955883i	$0.594903\pi$
$84$	55.7870	6.08686
$85$	5.15841	0.559508
$86$	4.08339	0.440323
$87$	−28.4468	−3.04982
$88$	−50.5204	−5.38549
$89$	−4.73837	−0.502266	−0.251133	−	0.967953i	$-0.580803\pi$
$89$	−4.73837	−0.502266	−0.251133	+	0.967953i	$0.580803\pi$
$90$	−53.7441	−5.66512
$91$	2.92678	0.306810
$92$	25.0342	2.61000
$93$	5.88381	0.610123
$94$	−9.18882	−0.947755
$95$	−17.7058	−1.81657
$96$	−99.7183	−10.1775
$97$	−10.7613	−1.09265	−0.546324	−	0.837574i	$-0.683973\pi$
$97$	−10.7613	−1.09265	−0.546324	+	0.837574i	$0.683973\pi$
$98$	−4.39195	−0.443654
$99$	35.2350	3.54125
$100$	8.35336	0.835336
$101$	9.90718	0.985802	0.492901	−	0.870086i	$-0.335937\pi$
$101$	9.90718	0.985802	0.492901	+	0.870086i	$0.335937\pi$
$102$	−18.5487	−1.83659
$103$	10.0116	0.986474	0.493237	−	0.869895i	$-0.335813\pi$
$103$	10.0116	0.986474	0.493237	+	0.869895i	$0.335813\pi$
$104$	−10.8406	−1.06301
$105$	24.1071	2.35261
$106$	−11.9103	−1.15683
$107$	16.1396	1.56027	0.780135	−	0.625611i	$-0.215150\pi$
$107$	16.1396	1.56027	0.780135	+	0.625611i	$0.215150\pi$
$108$	86.9310	8.36494
$109$	−20.6009	−1.97321	−0.986604	−	0.163136i	$-0.947839\pi$
$109$	−20.6009	−1.97321	−0.986604	+	0.163136i	$0.947839\pi$
$110$	−33.1270	−3.15853
$111$	−25.5078	−2.42110
$112$	54.6490	5.16384
$113$	0.861281	0.0810225	0.0405113	−	0.999179i	$-0.487101\pi$
$113$	0.861281	0.0810225	0.0405113	+	0.999179i	$0.487101\pi$
$114$	63.6667	5.96293
$115$	10.8180	1.00878
$116$	−51.3434	−4.76712
$117$	7.56069	0.698986
$118$	−18.2708	−1.68196
$119$	5.95657	0.546038
$120$	−89.2913	−8.15115
$121$	10.7183	0.974388
$122$	6.89712	0.624436
$123$	−21.9645	−1.98047
$124$	10.6196	0.953672
$125$	−9.06327	−0.810643
$126$	−62.0600	−5.52874
$127$	−6.85129	−0.607954	−0.303977	−	0.952679i	$-0.598315\pi$
$127$	−6.85129	−0.607954	−0.303977	+	0.952679i	$0.598315\pi$
$128$	−75.2479	−6.65104
$129$	−4.73158	−0.416593
$130$	−7.10835	−0.623444
$131$	0.643482	0.0562212	0.0281106	−	0.999605i	$-0.491051\pi$
$131$	0.643482	0.0562212	0.0281106	+	0.999605i	$0.491051\pi$
$132$	88.8293	7.73160
$133$	−20.4454	−1.77284
$134$	−7.66772	−0.662390
$135$	37.5652	3.23310
$136$	−22.0628	−1.89187
$137$	−15.7880	−1.34886	−0.674429	−	0.738340i	$-0.735610\pi$
$137$	−15.7880	−1.34886	−0.674429	+	0.738340i	$0.735610\pi$
$138$	−38.8994	−3.31134
$139$	14.9909	1.27151	0.635755	−	0.771891i	$-0.280689\pi$
$139$	14.9909	1.27151	0.635755	+	0.771891i	$0.280689\pi$
$140$	43.5107	3.67732
$141$	10.6475	0.896678
$142$	16.0624	1.34793
$143$	4.66029	0.389713
$144$	141.174	11.7645
$145$	−22.1869	−1.84252
$146$	−27.6376	−2.28731
$147$	5.08913	0.419744
$148$	−46.0389	−3.78437
$149$	9.44962	0.774143	0.387072	−	0.922050i	$-0.373487\pi$
$149$	9.44962	0.774143	0.387072	+	0.922050i	$0.373487\pi$
$150$	−12.9799	−1.05980
$151$	10.2239	0.832010	0.416005	−	0.909362i	$-0.363430\pi$
$151$	10.2239	0.832010	0.416005	+	0.909362i	$0.363430\pi$
$152$	75.7286	6.14240
$153$	15.3875	1.24401
$154$	−38.2527	−3.08249
$155$	4.58903	0.368600
$156$	19.0609	1.52609
$157$	−9.61153	−0.767084	−0.383542	−	0.923523i	$-0.625296\pi$
$157$	−9.61153	−0.767084	−0.383542	+	0.923523i	$0.625296\pi$
$158$	26.0750	2.07442
$159$	13.8010	1.09449
$160$	−77.7745	−6.14862
$161$	12.4918	0.984493
$162$	−71.4651	−5.61483
$163$	−17.5860	−1.37744	−0.688721	−	0.725026i	$-0.741828\pi$
$163$	−17.5860	−1.37744	−0.688721	+	0.725026i	$0.741828\pi$
$164$	−39.6435	−3.09564
$165$	38.3855	2.98831
$166$	15.0108	1.16506
$167$	19.3788	1.49958	0.749788	−	0.661678i	$-0.230155\pi$
$167$	19.3788	1.49958	0.749788	+	0.661678i	$0.230155\pi$
$168$	−103.107	−7.95491
$169$	1.00000	0.0769231
$170$	−14.4669	−1.10956
$171$	−52.8162	−4.03896
$172$	−8.54000	−0.651169
$173$	24.8035	1.88577	0.942886	−	0.333114i	$-0.108100\pi$
$173$	24.8035	1.88577	0.942886	+	0.333114i	$0.108100\pi$
$174$	79.7800	6.04810
$175$	4.16825	0.315090
$176$	87.0172	6.55917
$177$	21.1711	1.59132
$178$	13.2889	0.996046
$179$	3.61786	0.270412	0.135206	−	0.990818i	$-0.456830\pi$
$179$	3.61786	0.270412	0.135206	+	0.990818i	$0.456830\pi$
$180$	112.400	8.37783
$181$	−13.1861	−0.980114	−0.490057	−	0.871690i	$-0.663024\pi$
$181$	−13.1861	−0.980114	−0.490057	+	0.871690i	$0.663024\pi$
$182$	−8.20824	−0.608435
$183$	−7.99197	−0.590783
$184$	−46.2690	−3.41100
$185$	−19.8946	−1.46268
$186$	−16.5013	−1.20994
$187$	9.48461	0.693583
$188$	19.2175	1.40158
$189$	43.3777	3.15526
$190$	49.6563	3.60245
$191$	16.0111	1.15852	0.579260	−	0.815143i	$-0.303342\pi$
$191$	16.0111	1.15852	0.579260	+	0.815143i	$0.303342\pi$
$192$	158.305	11.4247
$193$	0.925361	0.0666090	0.0333045	−	0.999445i	$-0.489397\pi$
$193$	0.925361	0.0666090	0.0333045	+	0.999445i	$0.489397\pi$
$194$	30.1805	2.16683
$195$	8.23673	0.589845
$196$	9.18532	0.656094
$197$	8.75179	0.623540	0.311770	−	0.950158i	$-0.399078\pi$
$197$	8.75179	0.623540	0.311770	+	0.950158i	$0.399078\pi$
$198$	−98.8176	−7.02266
$199$	10.7183	0.759803	0.379902	−	0.925027i	$-0.375958\pi$
$199$	10.7183	0.759803	0.379902	+	0.925027i	$0.375958\pi$
$200$	−15.4390	−1.09170
$201$	8.88490	0.626692
$202$	−27.7850	−1.95495
$203$	−25.6199	−1.79816
$204$	38.7927	2.71604
$205$	−17.1310	−1.19648
$206$	−28.0779	−1.95628
$207$	32.2699	2.24291
$208$	18.6721	1.29468
$209$	−32.5550	−2.25188
$210$	−67.6090	−4.66547
$211$	−3.83177	−0.263790	−0.131895	−	0.991264i	$-0.542106\pi$
$211$	−3.83177	−0.263790	−0.131895	+	0.991264i	$0.542106\pi$
$212$	24.9093	1.71078
$213$	−18.6122	−1.27529
$214$	−45.2639	−3.09418
$215$	−3.69036	−0.251681
$216$	−160.669	−10.9321
$217$	5.29910	0.359726
$218$	57.7758	3.91307
$219$	32.0248	2.16404
$220$	69.2817	4.67097
$221$	2.03520	0.136902
$222$	71.5376	4.80129
$223$	21.5206	1.44113	0.720563	−	0.693389i	$-0.243883\pi$
$223$	21.5206	1.44113	0.720563	+	0.693389i	$0.243883\pi$
$224$	−89.8087	−6.00059
$225$	10.7678	0.717851
$226$	−2.41549	−0.160676
$227$	−1.16874	−0.0775723	−0.0387862	−	0.999248i	$-0.512349\pi$
$227$	−1.16874	−0.0775723	−0.0387862	+	0.999248i	$0.512349\pi$
$228$	−133.152	−8.81824
$229$	−16.4744	−1.08866	−0.544331	−	0.838870i	$-0.683216\pi$
$229$	−16.4744	−1.08866	−0.544331	+	0.838870i	$0.683216\pi$
$230$	−30.3393	−2.00051
$231$	44.3250	2.91637
$232$	94.8946	6.23014
$233$	−29.6747	−1.94405	−0.972027	−	0.234867i	$-0.924534\pi$
$233$	−29.6747	−1.94405	−0.972027	+	0.234867i	$0.924534\pi$
$234$	−21.2042	−1.38616
$235$	8.30440	0.541719
$236$	38.2115	2.48736
$237$	−30.2142	−1.96262
$238$	−16.7054	−1.08285
$239$	29.5826	1.91354	0.956771	−	0.290842i	$-0.0939355\pi$
$239$	29.5826	1.91354	0.956771	+	0.290842i	$0.0939355\pi$
$240$	153.797	9.92755
$241$	21.5598	1.38879	0.694394	−	0.719595i	$-0.255672\pi$
$241$	21.5598	1.38879	0.694394	+	0.719595i	$0.255672\pi$
$242$	−30.0597	−1.93231
$243$	38.3465	2.45993
$244$	−14.4246	−0.923443
$245$	3.96923	0.253584
$246$	61.6000	3.92747
$247$	−6.98563	−0.444485
$248$	−19.6276	−1.24635
$249$	−17.3936	−1.10227
$250$	25.4182	1.60759
$251$	18.8370	1.18898	0.594490	−	0.804103i	$-0.297354\pi$
$251$	18.8370	1.18898	0.594490	+	0.804103i	$0.297354\pi$
$252$	129.792	8.17614
$253$	19.8906	1.25051
$254$	19.2147	1.20563
$255$	16.7634	1.04976
$256$	113.608	7.10052
$257$	−6.00475	−0.374566	−0.187283	−	0.982306i	$-0.559968\pi$
$257$	−6.00475	−0.374566	−0.187283	+	0.982306i	$0.559968\pi$
$258$	13.2699	0.826147
$259$	−22.9730	−1.42747
$260$	14.8664	0.921976
$261$	−66.1834	−4.09665
$262$	−1.80466	−0.111493
$263$	9.24508	0.570076	0.285038	−	0.958516i	$-0.407994\pi$
$263$	9.24508	0.570076	0.285038	+	0.958516i	$0.407994\pi$
$264$	−164.177	−10.1044
$265$	10.7640	0.661225
$266$	57.3397	3.51572
$267$	−15.3984	−0.942366
$268$	16.0363	0.979571
$269$	−11.9606	−0.729249	−0.364625	−	0.931155i	$-0.618803\pi$
$269$	−11.9606	−0.729249	−0.364625	+	0.931155i	$0.618803\pi$
$270$	−105.353	−6.41157
$271$	−15.0366	−0.913410	−0.456705	−	0.889618i	$-0.650970\pi$
$271$	−15.0366	−0.913410	−0.456705	+	0.889618i	$0.650970\pi$
$272$	38.0014	2.30417
$273$	9.51121	0.575645
$274$	44.2779	2.67492
$275$	6.63707	0.400230
$276$	81.3542	4.89695
$277$	−9.62531	−0.578329	−0.289164	−	0.957279i	$-0.593377\pi$
$277$	−9.62531	−0.578329	−0.289164	+	0.957279i	$0.593377\pi$
$278$	−42.0424	−2.52154
$279$	13.6891	0.819543
$280$	−80.4179	−4.80589
$281$	−18.1929	−1.08530	−0.542648	−	0.839960i	$-0.682578\pi$
$281$	−18.1929	−1.08530	−0.542648	+	0.839960i	$0.682578\pi$
$282$	−29.8611	−1.77820
$283$	−13.9487	−0.829162	−0.414581	−	0.910012i	$-0.636072\pi$
$283$	−13.9487	−0.829162	−0.414581	+	0.910012i	$0.636072\pi$
$284$	−33.5930	−1.99338
$285$	−57.5388	−3.40830
$286$	−13.0699	−0.772840
$287$	−19.7817	−1.16768
$288$	−232.001	−13.6708
$289$	−12.8580	−0.756351
$290$	62.2238	3.65391
$291$	−34.9713	−2.05006
$292$	57.8013	3.38257
$293$	−8.59947	−0.502386	−0.251193	−	0.967937i	$-0.580823\pi$
$293$	−8.59947	−0.502386	−0.251193	+	0.967937i	$0.580823\pi$
$294$	−14.2726	−0.832396
$295$	16.5122	0.961379
$296$	85.0907	4.94579
$297$	69.0700	4.00785
$298$	−26.5018	−1.53521
$299$	4.26812	0.246832
$300$	27.1461	1.56728
$301$	−4.26138	−0.245622
$302$	−28.6733	−1.64996
$303$	32.1956	1.84959
$304$	−130.436	−7.48103
$305$	−6.23328	−0.356916
$306$	−43.1548	−2.46699
$307$	−26.5018	−1.51254	−0.756269	−	0.654260i	$-0.772980\pi$
$307$	−26.5018	−1.51254	−0.756269	+	0.654260i	$0.772980\pi$
$308$	80.0017	4.55852
$309$	32.5350	1.85085
$310$	−12.8701	−0.730972
$311$	−15.9235	−0.902939	−0.451469	−	0.892287i	$-0.649100\pi$
$311$	−15.9235	−0.902939	−0.451469	+	0.892287i	$0.649100\pi$
$312$	−35.2290	−1.99445
$313$	−8.69088	−0.491237	−0.245619	−	0.969367i	$-0.578991\pi$
$313$	−8.69088	−0.491237	−0.245619	+	0.969367i	$0.578991\pi$
$314$	26.9558	1.52121
$315$	56.0867	3.16013
$316$	−54.5333	−3.06774
$317$	9.34742	0.525003	0.262502	−	0.964932i	$-0.415452\pi$
$317$	9.34742	0.525003	0.262502	+	0.964932i	$0.415452\pi$
$318$	−38.7053	−2.17048
$319$	−40.7943	−2.28404
$320$	123.469	6.90211
$321$	52.4491	2.92742
$322$	−35.0337	−1.95235
$323$	−14.2172	−0.791063
$324$	149.462	8.30345
$325$	1.42418	0.0789991
$326$	49.3205	2.73161
$327$	−66.9472	−3.70219
$328$	73.2704	4.04568
$329$	9.58935	0.528678
$330$	−107.653	−5.92613
$331$	−21.3409	−1.17300	−0.586501	−	0.809948i	$-0.699495\pi$
$331$	−21.3409	−1.17300	−0.586501	+	0.809948i	$0.699495\pi$
$332$	−31.3936	−1.72295
$333$	−59.3457	−3.25212
$334$	−54.3484	−2.97381
$335$	6.92971	0.378610
$336$	177.594	9.68855
$337$	24.3869	1.32844	0.664221	−	0.747537i	$-0.268764\pi$
$337$	24.3869	1.32844	0.664221	+	0.747537i	$0.268764\pi$
$338$	−2.80453	−0.152546
$339$	2.79892	0.152017
$340$	30.2561	1.64087
$341$	8.43772	0.456928
$342$	148.125	8.00967
$343$	−15.9040	−0.858738
$344$	15.7839	0.851012
$345$	35.1553	1.89270
$346$	−69.5621	−3.73968
$347$	−4.52059	−0.242678	−0.121339	−	0.992611i	$-0.538719\pi$
$347$	−4.52059	−0.242678	−0.121339	+	0.992611i	$0.538719\pi$
$348$	−166.852	−8.94420
$349$	3.80851	0.203865	0.101932	−	0.994791i	$-0.467497\pi$
$349$	3.80851	0.203865	0.101932	+	0.994791i	$0.467497\pi$
$350$	−11.6900	−0.624856
$351$	14.8210	0.791086
$352$	−143.002	−7.62202
$353$	−4.79929	−0.255440	−0.127720	−	0.991810i	$-0.540766\pi$
$353$	−4.79929	−0.255440	−0.127720	+	0.991810i	$0.540766\pi$
$354$	−59.3750	−3.15574
$355$	−14.5164	−0.770452
$356$	−27.7924	−1.47300
$357$	19.3572	1.02449
$358$	−10.1464	−0.536255
$359$	14.7370	0.777788	0.388894	−	0.921283i	$-0.372857\pi$
$359$	14.7370	0.777788	0.388894	+	0.921283i	$0.372857\pi$
$360$	−207.742	−10.9490
$361$	29.7990	1.56837
$362$	36.9808	1.94367
$363$	34.8314	1.82817
$364$	17.1667	0.899780
$365$	24.9775	1.30738
$366$	22.4137	1.17158
$367$	−31.5136	−1.64500	−0.822499	−	0.568767i	$-0.807421\pi$
$367$	−31.5136	−1.64500	−0.822499	+	0.568767i	$0.807421\pi$
$368$	79.6946	4.15437
$369$	−51.1018	−2.66025
$370$	55.7952	2.90065
$371$	12.4295	0.645307
$372$	34.5109	1.78931
$373$	−30.5034	−1.57941	−0.789704	−	0.613489i	$-0.789766\pi$
$373$	−30.5034	−1.57941	−0.789704	+	0.613489i	$0.789766\pi$
$374$	−26.5999	−1.37545
$375$	−29.4531	−1.52095
$376$	−35.5184	−1.83172
$377$	−8.75361	−0.450834
$378$	−121.654	−6.25721
$379$	20.2239	1.03883	0.519416	−	0.854521i	$-0.326149\pi$
$379$	20.2239	1.03883	0.519416	+	0.854521i	$0.326149\pi$
$380$	−103.851	−5.32746
$381$	−22.2648	−1.14066
$382$	−44.9035	−2.29746
$383$	−22.2659	−1.13774	−0.568868	−	0.822429i	$-0.692618\pi$
$383$	−22.2659	−1.13774	−0.568868	+	0.822429i	$0.692618\pi$
$384$	−244.535	−12.4789
$385$	34.5709	1.76190
$386$	−2.59520	−0.132092
$387$	−11.0083	−0.559586
$388$	−63.1195	−3.20441
$389$	27.0643	1.37222	0.686108	−	0.727499i	$-0.259318\pi$
$389$	27.0643	1.37222	0.686108	+	0.727499i	$0.259318\pi$
$390$	−23.1002	−1.16972
$391$	8.68647	0.439294
$392$	−16.9766	−0.857449
$393$	2.09114	0.105484
$394$	−24.5447	−1.23654
$395$	−23.5653	−1.18570
$396$	206.667	10.3854
$397$	−27.9091	−1.40072	−0.700359	−	0.713791i	$-0.746977\pi$
$397$	−27.9091	−1.40072	−0.700359	+	0.713791i	$0.746977\pi$
$398$	−30.0599	−1.50677
$399$	−66.4418	−3.32625
$400$	26.5923	1.32962
$401$	13.4129	0.669810	0.334905	−	0.942252i	$-0.391296\pi$
$401$	13.4129	0.669810	0.334905	+	0.942252i	$0.391296\pi$
$402$	−24.9180	−1.24280
$403$	1.81056	0.0901903
$404$	58.1096	2.89106
$405$	64.5866	3.20933
$406$	71.8517	3.56594
$407$	−36.5797	−1.81319
$408$	−71.6981	−3.54958
$409$	10.5488	0.521604	0.260802	−	0.965392i	$-0.416013\pi$
$409$	10.5488	0.521604	0.260802	+	0.965392i	$0.416013\pi$
$410$	48.0445	2.37275
$411$	−51.3065	−2.53076
$412$	58.7221	2.89303
$413$	19.0672	0.938234
$414$	−90.5020	−4.44793
$415$	−13.5660	−0.665929
$416$	−30.6852	−1.50446
$417$	48.7162	2.38564
$418$	91.3016	4.46571
$419$	−13.6220	−0.665479	−0.332740	−	0.943019i	$-0.607973\pi$
$419$	−13.6220	−0.665479	−0.332740	+	0.943019i	$0.607973\pi$
$420$	141.398	6.89949
$421$	3.18766	0.155357	0.0776786	−	0.996978i	$-0.475249\pi$
$421$	3.18766	0.155357	0.0776786	+	0.996978i	$0.475249\pi$
$422$	10.7463	0.523123
$423$	24.7720	1.20446
$424$	−46.0381	−2.23581
$425$	2.89848	0.140597
$426$	52.1985	2.52902
$427$	−7.19776	−0.348324
$428$	94.6649	4.57580
$429$	15.1446	0.731190
$430$	10.3497	0.499109
$431$	−12.1601	−0.585730	−0.292865	−	0.956154i	$-0.594609\pi$
$431$	−12.1601	−0.585730	−0.292865	+	0.956154i	$0.594609\pi$
$432$	276.739	13.3146
$433$	−9.59060	−0.460895	−0.230447	−	0.973085i	$-0.574019\pi$
$433$	−9.59060	−0.460895	−0.230447	+	0.973085i	$0.574019\pi$
$434$	−14.8615	−0.713374
$435$	−72.1012	−3.45699
$436$	−120.832	−5.78682
$437$	−29.8155	−1.42627
$438$	−89.8146	−4.29151
$439$	16.8142	0.802496	0.401248	−	0.915969i	$-0.368577\pi$
$439$	16.8142	0.802496	0.401248	+	0.915969i	$0.368577\pi$
$440$	−128.049	−6.10449
$441$	11.8402	0.563819
$442$	−5.70778	−0.271491
$443$	15.7948	0.750436	0.375218	−	0.926937i	$-0.377568\pi$
$443$	15.7948	0.750436	0.375218	+	0.926937i	$0.377568\pi$
$444$	−149.614	−7.10035
$445$	−12.0099	−0.569322
$446$	−60.3552	−2.85790
$447$	30.7086	1.45247
$448$	142.573	6.73595
$449$	13.8468	0.653469	0.326735	−	0.945116i	$-0.394052\pi$
$449$	13.8468	0.653469	0.326735	+	0.945116i	$0.394052\pi$
$450$	−30.1985	−1.42357
$451$	−31.4983	−1.48320
$452$	5.05175	0.237615
$453$	33.2249	1.56104
$454$	3.27778	0.153834
$455$	7.41820	0.347770
$456$	246.097	11.5245
$457$	−24.5013	−1.14612	−0.573062	−	0.819512i	$-0.694245\pi$
$457$	−24.5013	−1.14612	−0.573062	+	0.819512i	$0.694245\pi$
$458$	46.2031	2.15893
$459$	30.1637	1.40792
$460$	63.4516	2.95844
$461$	7.23325	0.336886	0.168443	−	0.985711i	$-0.446126\pi$
$461$	7.23325	0.336886	0.168443	+	0.985711i	$0.446126\pi$
$462$	−124.311	−5.78346
$463$	−1.00000	−0.0464739
$463$	−1.00000	−0.0464739
$464$	−163.448	−7.58789
$465$	14.9131	0.691578
$466$	83.2237	3.85526
$467$	−10.7369	−0.496843	−0.248422	−	0.968652i	$-0.579912\pi$
$467$	−10.7369	−0.496843	−0.248422	+	0.968652i	$0.579912\pi$
$468$	44.3465	2.04992
$469$	8.00195	0.369496
$470$	−23.2900	−1.07429
$471$	−31.2348	−1.43922
$472$	−70.6238	−3.25072
$473$	−6.78536	−0.311991
$474$	84.7365	3.89208
$475$	−9.94877	−0.456481
$476$	34.9377	1.60136
$477$	32.1089	1.47016
$478$	−82.9654	−3.79475
$479$	−24.4519	−1.11724	−0.558618	−	0.829425i	$-0.688668\pi$
$479$	−24.4519	−1.11724	−0.558618	+	0.829425i	$0.688668\pi$
$480$	−252.746	−11.5362
$481$	−7.84924	−0.357894
$482$	−60.4651	−2.75411
$483$	40.5949	1.84713
$484$	62.8669	2.85758
$485$	−27.2756	−1.23852
$486$	−107.544	−4.87829
$487$	−40.2519	−1.82399	−0.911994	−	0.410203i	$-0.865458\pi$
$487$	−40.2519	−1.82399	−0.911994	+	0.410203i	$0.865458\pi$
$488$	26.6601	1.20685
$489$	−57.1497	−2.58440
$490$	−11.1318	−0.502884
$491$	−35.0480	−1.58169	−0.790847	−	0.612014i	$-0.790359\pi$
$491$	−35.0480	−1.58169	−0.790847	+	0.612014i	$0.790359\pi$
$492$	−128.830	−5.80812
$493$	−17.8153	−0.802363
$494$	19.5914	0.881460
$495$	89.3065	4.01403
$496$	33.8069	1.51797
$497$	−16.7626	−0.751904
$498$	48.7809	2.18592
$499$	22.1663	0.992298	0.496149	−	0.868237i	$-0.334747\pi$
$499$	22.1663	0.992298	0.496149	+	0.868237i	$0.334747\pi$
$500$	−53.1597	−2.37737
$501$	62.9757	2.81355
$502$	−52.8289	−2.35787
$503$	31.6648	1.41186	0.705932	−	0.708279i	$-0.250528\pi$
$503$	31.6648	1.41186	0.705932	+	0.708279i	$0.250528\pi$
$504$	−239.886	−10.6854
$505$	25.1107	1.11741
$506$	−55.7839	−2.47990
$507$	3.24972	0.144325
$508$	−40.1855	−1.78294
$509$	17.4522	0.773556	0.386778	−	0.922173i	$-0.373588\pi$
$509$	17.4522	0.773556	0.386778	+	0.922173i	$0.373588\pi$
$510$	−47.0135	−2.08179
$511$	28.8423	1.27591
$512$	−168.122	−7.43002
$513$	−103.534	−4.57114
$514$	16.8405	0.742803
$515$	25.3754	1.11817
$516$	−27.7526	−1.22174
$517$	15.2691	0.671532
$518$	64.4284	2.83082
$519$	80.6044	3.53814
$520$	−27.4766	−1.20493
$521$	−21.1418	−0.926239	−0.463119	−	0.886296i	$-0.653270\pi$
$521$	−21.1418	−0.926239	−0.463119	+	0.886296i	$0.653270\pi$
$522$	185.613	8.12408
$523$	13.3803	0.585078	0.292539	−	0.956254i	$-0.405500\pi$
$523$	13.3803	0.585078	0.292539	+	0.956254i	$0.405500\pi$
$524$	3.77427	0.164880
$525$	13.5456	0.591180
$526$	−25.9281	−1.13052
$527$	3.68485	0.160514
$528$	282.782	12.3065
$529$	−4.78318	−0.207964
$530$	−30.1879	−1.31128
$531$	49.2559	2.13752
$532$	−119.920	−5.19920
$533$	−6.75887	−0.292759
$534$	43.1853	1.86881
$535$	40.9073	1.76858
$536$	−29.6388	−1.28020
$537$	11.7571	0.507354
$538$	33.5438	1.44618
$539$	7.29810	0.314351
$540$	220.335	9.48170
$541$	−8.93575	−0.384178	−0.192089	−	0.981378i	$-0.561526\pi$
$541$	−8.93575	−0.384178	−0.192089	+	0.981378i	$0.561526\pi$
$542$	42.1707	1.81139
$543$	−42.8511	−1.83892
$544$	−62.4505	−2.67754
$545$	−52.2149	−2.23664
$546$	−26.6745	−1.14156
$547$	−22.0436	−0.942517	−0.471258	−	0.881995i	$-0.656200\pi$
$547$	−22.0436	−0.942517	−0.471258	+	0.881995i	$0.656200\pi$
$548$	−92.6027	−3.95579
$549$	−18.5938	−0.793566
$550$	−18.6139	−0.793698
$551$	61.1495	2.60506
$552$	−150.362	−6.39981
$553$	−27.2116	−1.15715
$554$	26.9945	1.14689
$555$	−64.6521	−2.74433
$556$	87.9275	3.72896
$557$	16.0651	0.680699	0.340350	−	0.940299i	$-0.389455\pi$
$557$	16.0651	0.680699	0.340350	+	0.940299i	$0.389455\pi$
$558$	−38.3914	−1.62524
$559$	−1.45600	−0.0615821
$560$	138.513	5.85325
$561$	30.8223	1.30132
$562$	51.0225	2.15225
$563$	−1.72205	−0.0725758	−0.0362879	−	0.999341i	$-0.511553\pi$
$563$	−1.72205	−0.0725758	−0.0362879	+	0.999341i	$0.511553\pi$
$564$	62.4515	2.62968
$565$	2.18300	0.0918395
$566$	39.1195	1.64431
$567$	74.5801	3.13207
$568$	62.0877	2.60514
$569$	38.3571	1.60801	0.804007	−	0.594619i	$-0.202697\pi$
$569$	38.3571	1.60801	0.804007	+	0.594619i	$0.202697\pi$
$570$	161.369	6.75902
$571$	33.0759	1.38418	0.692092	−	0.721809i	$-0.256689\pi$
$571$	33.0759	1.38418	0.692092	+	0.721809i	$0.256689\pi$
$572$	27.3344	1.14291
$573$	52.0315	2.17365
$574$	55.4784	2.31562
$575$	6.07855	0.253493
$576$	368.307	15.3461
$577$	−23.2325	−0.967182	−0.483591	−	0.875294i	$-0.660668\pi$
$577$	−23.2325	−0.967182	−0.483591	+	0.875294i	$0.660668\pi$
$578$	36.0606	1.49992
$579$	3.00717	0.124974
$580$	−130.135	−5.40355
$581$	−15.6651	−0.649897
$582$	98.0782	4.06547
$583$	19.7914	0.819675
$584$	−106.830	−4.42067
$585$	19.1633	0.792305
$586$	24.1175	0.996284
$587$	−0.391217	−0.0161473	−0.00807363	−	0.999967i	$-0.502570\pi$
$587$	−0.391217	−0.0161473	−0.00807363	+	0.999967i	$0.502570\pi$
$588$	29.8497	1.23098
$589$	−12.6479	−0.521147
$590$	−46.3090	−1.90651
$591$	28.4409	1.16990
$592$	−146.562	−6.02364
$593$	−2.69122	−0.110515	−0.0552575	−	0.998472i	$-0.517598\pi$
$593$	−2.69122	−0.110515	−0.0552575	+	0.998472i	$0.517598\pi$
$594$	−193.709	−7.94798
$595$	15.0975	0.618937
$596$	55.4258	2.27033
$597$	34.8316	1.42556
$598$	−11.9701	−0.489492
$599$	7.25425	0.296401	0.148200	−	0.988957i	$-0.452652\pi$
$599$	7.25425	0.296401	0.148200	+	0.988957i	$0.452652\pi$
$600$	−50.1723	−2.04828
$601$	32.5648	1.32834	0.664172	−	0.747580i	$-0.268784\pi$
$601$	32.5648	1.32834	0.664172	+	0.747580i	$0.268784\pi$
$602$	11.9512	0.487093
$603$	20.6713	0.841800
$604$	59.9673	2.44003
$605$	27.1665	1.10447
$606$	−90.2935	−3.66792
$607$	−11.0874	−0.450022	−0.225011	−	0.974356i	$-0.572242\pi$
$607$	−11.0874	−0.450022	−0.225011	+	0.974356i	$0.572242\pi$
$608$	214.355	8.69326
$609$	−83.2574	−3.37376
$610$	17.4814	0.707802
$611$	3.27642	0.132550
$612$	90.2539	3.64830
$613$	4.26849	0.172403	0.0862013	−	0.996278i	$-0.472527\pi$
$613$	4.26849	0.172403	0.0862013	+	0.996278i	$0.472527\pi$
$614$	74.3252	2.99952
$615$	−55.6710	−2.24487
$616$	−147.862	−5.95753
$617$	−32.4001	−1.30438	−0.652190	−	0.758056i	$-0.726149\pi$
$617$	−32.4001	−1.30438	−0.652190	+	0.758056i	$0.726149\pi$
$618$	−91.2454	−3.67043
$619$	4.05068	0.162811	0.0814054	−	0.996681i	$-0.474059\pi$
$619$	4.05068	0.162811	0.0814054	+	0.996681i	$0.474059\pi$
$620$	26.9165	1.08099
$621$	63.2577	2.53844
$622$	44.6579	1.79062
$623$	−13.8682	−0.555616
$624$	60.6791	2.42911
$625$	−30.0926	−1.20370
$626$	24.3738	0.974174
$627$	−105.795	−4.22504
$628$	−56.3754	−2.24962
$629$	−15.9748	−0.636956
$630$	−157.297	−6.26686
$631$	1.72740	0.0687669	0.0343834	−	0.999409i	$-0.489053\pi$
$631$	1.72740	0.0687669	0.0343834	+	0.999409i	$0.489053\pi$
$632$	100.790	4.00922
$633$	−12.4522	−0.494930
$634$	−26.2151	−1.04114
$635$	−17.3652	−0.689119
$636$	80.9482	3.20980
$637$	1.56602	0.0620479
$638$	114.409	4.52950
$639$	−43.3025	−1.71302
$640$	−190.723	−7.53899
$641$	−21.1886	−0.836899	−0.418450	−	0.908240i	$-0.637426\pi$
$641$	−21.1886	−0.836899	−0.418450	+	0.908240i	$0.637426\pi$
$642$	−147.095	−5.80538
$643$	35.1084	1.38454	0.692271	−	0.721638i	$-0.256610\pi$
$643$	35.1084	1.38454	0.692271	+	0.721638i	$0.256610\pi$
$644$	73.2695	2.88722
$645$	−11.9927	−0.472210
$646$	39.8724	1.56876
$647$	−45.3979	−1.78478	−0.892388	−	0.451269i	$-0.850971\pi$
$647$	−45.3979	−1.78478	−0.892388	+	0.451269i	$0.850971\pi$
$648$	−276.241	−10.8518
$649$	30.3605	1.19176
$650$	−3.99415	−0.156663
$651$	17.2206	0.674928
$652$	−103.149	−4.03962
$653$	−27.6572	−1.08231	−0.541154	−	0.840923i	$-0.682013\pi$
$653$	−27.6572	−1.08231	−0.541154	+	0.840923i	$0.682013\pi$
$654$	187.755	7.34182
$655$	1.63097	0.0637271
$656$	−126.202	−4.92737
$657$	74.5079	2.90683
$658$	−26.8936	−1.04842
$659$	22.1102	0.861293	0.430647	−	0.902521i	$-0.358286\pi$
$659$	22.1102	0.861293	0.430647	+	0.902521i	$0.358286\pi$
$660$	225.146	8.76381
$661$	7.94176	0.308899	0.154449	−	0.988001i	$-0.450640\pi$
$661$	7.94176	0.308899	0.154449	+	0.988001i	$0.450640\pi$
$662$	59.8513	2.32619
$663$	6.61383	0.256860
$664$	58.0227	2.25172
$665$	−51.8208	−2.00952
$666$	166.437	6.44930
$667$	−37.3614	−1.44664
$668$	113.664	4.39780
$669$	69.9360	2.70388
$670$	−19.4346	−0.750823
$671$	−11.4609	−0.442445
$672$	−291.853	−11.2585
$673$	−4.77296	−0.183984	−0.0919921	−	0.995760i	$-0.529323\pi$
$673$	−4.77296	−0.183984	−0.0919921	+	0.995760i	$0.529323\pi$
$674$	−68.3939	−2.63444
$675$	21.1077	0.812436
$676$	5.86540	0.225592
$677$	−23.5302	−0.904339	−0.452169	−	0.891932i	$-0.649350\pi$
$677$	−23.5302	−0.904339	−0.452169	+	0.891932i	$0.649350\pi$
$678$	−7.84967	−0.301465
$679$	−31.4960	−1.20871
$680$	−55.9204	−2.14445
$681$	−3.79810	−0.145543
$682$	−23.6638	−0.906135
$683$	−6.61026	−0.252935	−0.126467	−	0.991971i	$-0.540364\pi$
$683$	−6.61026	−0.252935	−0.126467	+	0.991971i	$0.540364\pi$
$684$	−309.788	−11.8450
$685$	−40.0161	−1.52894
$686$	44.6034	1.70297
$687$	−53.5374	−2.04258
$688$	−27.1865	−1.03648
$689$	4.24682	0.161791
$690$	−98.5942	−3.75342
$691$	−0.625195	−0.0237835	−0.0118918	−	0.999929i	$-0.503785\pi$
$691$	−0.625195	−0.0237835	−0.0118918	+	0.999929i	$0.503785\pi$
$692$	145.482	5.53040
$693$	103.125	3.91739
$694$	12.6781	0.481255
$695$	37.9958	1.44126
$696$	308.381	11.6892
$697$	−13.7557	−0.521033
$698$	−10.6811	−0.404285
$699$	−96.4346	−3.64749
$700$	24.4484	0.924063
$701$	10.6060	0.400582	0.200291	−	0.979736i	$-0.435811\pi$
$701$	10.6060	0.400582	0.200291	+	0.979736i	$0.435811\pi$
$702$	−41.5659	−1.56880
$703$	54.8319	2.06802
$704$	227.018	8.55608
$705$	26.9870	1.01639
$706$	13.4597	0.506564
$707$	28.9961	1.09051
$708$	124.177	4.66685
$709$	−21.9496	−0.824336	−0.412168	−	0.911108i	$-0.635228\pi$
$709$	−21.9496	−0.824336	−0.412168	+	0.911108i	$0.635228\pi$
$710$	40.7118	1.52789
$711$	−70.2952	−2.63628
$712$	51.3669	1.92506
$713$	7.72767	0.289404
$714$	−54.2879	−2.03167
$715$	11.8119	0.441742
$716$	21.2202	0.793036
$717$	96.1354	3.59024
$718$	−41.3303	−1.54243
$719$	−28.9232	−1.07865	−0.539327	−	0.842097i	$-0.681321\pi$
$719$	−28.9232	−1.07865	−0.539327	+	0.842097i	$0.681321\pi$
$720$	357.819	13.3351
$721$	29.3018	1.09126
$722$	−83.5724	−3.11024
$723$	70.0633	2.60568
$724$	−77.3416	−2.87438
$725$	−12.4667	−0.463001
$726$	−97.6857	−3.62546
$727$	31.9086	1.18343	0.591713	−	0.806149i	$-0.298452\pi$
$727$	31.9086	1.18343	0.591713	+	0.806149i	$0.298452\pi$
$728$	−31.7281	−1.17592
$729$	48.1694	1.78405
$730$	−70.0502	−2.59268
$731$	−2.96324	−0.109600
$732$	−46.8761	−1.73259
$733$	27.2120	1.00510	0.502549	−	0.864549i	$-0.332396\pi$
$733$	27.2120	1.00510	0.502549	+	0.864549i	$0.332396\pi$
$734$	88.3809	3.26220
$735$	12.8989	0.475782
$736$	−130.968	−4.82754
$737$	12.7414	0.469337
$738$	143.317	5.27555
$739$	−30.2426	−1.11249	−0.556245	−	0.831018i	$-0.687759\pi$
$739$	−30.2426	−1.11249	−0.556245	+	0.831018i	$0.687759\pi$
$740$	−116.690	−4.28961
$741$	−22.7014	−0.833955
$742$	−34.8589	−1.27971
$743$	10.9348	0.401159	0.200579	−	0.979677i	$-0.435718\pi$
$743$	10.9348	0.401159	0.200579	+	0.979677i	$0.435718\pi$
$744$	−63.7842	−2.33844
$745$	23.9510	0.877496
$746$	85.5478	3.13213
$747$	−40.4674	−1.48062
$748$	55.6310	2.03407
$749$	47.2369	1.72600
$750$	82.6021	3.01620
$751$	11.1749	0.407778	0.203889	−	0.978994i	$-0.434642\pi$
$751$	11.1749	0.407778	0.203889	+	0.978994i	$0.434642\pi$
$752$	61.1776	2.23092
$753$	61.2149	2.23080
$754$	24.5498	0.894050
$755$	25.9135	0.943088
$756$	254.427	9.25344
$757$	−42.6217	−1.54911	−0.774555	−	0.632506i	$-0.782026\pi$
$757$	−42.6217	−1.54911	−0.774555	+	0.632506i	$0.782026\pi$
$758$	−56.7186	−2.06011
$759$	64.6391	2.34625
$760$	191.941	6.96245
$761$	−5.54940	−0.201166	−0.100583	−	0.994929i	$-0.532071\pi$
$761$	−5.54940	−0.201166	−0.100583	+	0.994929i	$0.532071\pi$
$762$	62.4423	2.26205
$763$	−60.2942	−2.18280
$764$	93.9112	3.39759
$765$	39.0011	1.41009
$766$	62.4455	2.25625
$767$	6.51474	0.235233
$768$	369.195	13.3222
$769$	−7.88581	−0.284369	−0.142185	−	0.989840i	$-0.545413\pi$
$769$	−7.88581	−0.284369	−0.142185	+	0.989840i	$0.545413\pi$
$770$	−96.9552	−3.49402
$771$	−19.5138	−0.702772
$772$	5.42761	0.195344
$773$	1.11621	0.0401472	0.0200736	−	0.999799i	$-0.493610\pi$
$773$	1.11621	0.0401472	0.0200736	+	0.999799i	$0.493610\pi$
$774$	30.8733	1.10972
$775$	2.57855	0.0926244
$776$	116.660	4.18783
$777$	−74.6558	−2.67826
$778$	−75.9028	−2.72125
$779$	47.2150	1.69165
$780$	48.3117	1.72984
$781$	−26.6909	−0.955077
$782$	−24.3615	−0.871164
$783$	−129.737	−4.63643
$784$	29.2408	1.04432
$785$	−24.3613	−0.869494
$786$	−5.86466	−0.209185
$787$	35.7962	1.27600	0.637999	−	0.770037i	$-0.279763\pi$
$787$	35.7962	1.27600	0.637999	+	0.770037i	$0.279763\pi$
$788$	51.3327	1.82865
$789$	30.0439	1.06959
$790$	66.0896	2.35136
$791$	2.52078	0.0896285
$792$	−381.969	−13.5727
$793$	−2.45928	−0.0873315
$794$	78.2719	2.77777
$795$	34.9799	1.24061
$796$	62.8673	2.22827
$797$	−33.4841	−1.18607	−0.593033	−	0.805178i	$-0.702070\pi$
$797$	−33.4841	−1.18607	−0.593033	+	0.805178i	$0.702070\pi$
$798$	186.338	6.59630
$799$	6.66817	0.235903
$800$	−43.7011	−1.54507
$801$	−35.8254	−1.26583
$802$	−37.6170	−1.32830
$803$	45.9254	1.62067
$804$	52.1134	1.83790
$805$	31.6617	1.11593
$806$	−5.07777	−0.178857
$807$	−38.8685	−1.36824
$808$	−107.400	−3.77832
$809$	−32.8101	−1.15354	−0.576770	−	0.816906i	$-0.695687\pi$
$809$	−32.8101	−1.15354	−0.576770	+	0.816906i	$0.695687\pi$
$810$	−181.135	−6.36444
$811$	39.1275	1.37395	0.686976	−	0.726680i	$-0.258938\pi$
$811$	39.1275	1.37395	0.686976	+	0.726680i	$0.258938\pi$
$812$	−150.271	−5.27347
$813$	−48.8648	−1.71376
$814$	102.589	3.59574
$815$	−44.5734	−1.56134
$816$	123.494	4.32315
$817$	10.1711	0.355840
$818$	−29.5844	−1.03439
$819$	22.1285	0.773231
$820$	−100.480	−3.50892
$821$	2.45718	0.0857562	0.0428781	−	0.999080i	$-0.486347\pi$
$821$	2.45718	0.0857562	0.0428781	+	0.999080i	$0.486347\pi$
$822$	143.891	5.01877
$823$	−8.45068	−0.294572	−0.147286	−	0.989094i	$-0.547054\pi$
$823$	−8.45068	−0.294572	−0.147286	+	0.989094i	$0.547054\pi$
$824$	−108.532	−3.78090
$825$	21.5686	0.750923
$826$	−53.4745	−1.86062
$827$	5.96590	0.207455	0.103727	−	0.994606i	$-0.466923\pi$
$827$	5.96590	0.207455	0.103727	+	0.994606i	$0.466923\pi$
$828$	189.276	6.57779
$829$	27.1910	0.944384	0.472192	−	0.881496i	$-0.343463\pi$
$829$	27.1910	0.944384	0.472192	+	0.881496i	$0.343463\pi$
$830$	38.0463	1.32061
$831$	−31.2796	−1.08508
$832$	48.7134	1.68883
$833$	3.18716	0.110429
$834$	−136.626	−4.73098
$835$	49.1174	1.69978
$836$	−190.948	−6.60408
$837$	26.8343	0.927527
$838$	38.2034	1.31971
$839$	12.2756	0.423800	0.211900	−	0.977291i	$-0.432035\pi$
$839$	12.2756	0.423800	0.211900	+	0.977291i	$0.432035\pi$
$840$	−261.336	−9.01694
$841$	47.6257	1.64227
$842$	−8.93990	−0.308089
$843$	−59.1218	−2.03626
$844$	−22.4749	−0.773617
$845$	2.53460	0.0871928
$846$	−69.4739	−2.38856
$847$	31.3700	1.07788
$848$	79.2969	2.72307
$849$	−45.3293	−1.55570
$850$	−8.12889	−0.278819
$851$	−33.5015	−1.14842
$852$	−109.168	−3.74003
$853$	23.5541	0.806478	0.403239	−	0.915095i	$-0.367884\pi$
$853$	23.5541	0.806478	0.403239	+	0.915095i	$0.367884\pi$
$854$	20.1863	0.690762
$855$	−133.868	−4.57818
$856$	−174.963	−5.98011
$857$	43.6245	1.49018	0.745092	−	0.666962i	$-0.232406\pi$
$857$	43.6245	1.49018	0.745092	+	0.666962i	$0.232406\pi$
$858$	−42.4736	−1.45002
$859$	−1.67048	−0.0569960	−0.0284980	−	0.999594i	$-0.509072\pi$
$859$	−1.67048	−0.0569960	−0.0284980	+	0.999594i	$0.509072\pi$
$860$	−21.6454	−0.738104
$861$	−64.2851	−2.19083
$862$	34.1033	1.16156
$863$	−28.3547	−0.965205	−0.482602	−	0.875840i	$-0.660308\pi$
$863$	−28.3547	−0.965205	−0.482602	+	0.875840i	$0.660308\pi$
$864$	−454.785	−15.4721
$865$	62.8668	2.13753
$866$	26.8971	0.914002
$867$	−41.7848	−1.41909
$868$	31.0813	1.05497
$869$	−43.3288	−1.46983
$870$	202.210	6.85556
$871$	2.73405	0.0926397
$872$	223.326	7.56279
$873$	−81.3631	−2.75372
$874$	83.6185	2.82844
$875$	−26.5262	−0.896748
$876$	187.838	6.34647
$877$	−31.9839	−1.08002	−0.540010	−	0.841659i	$-0.681579\pi$
$877$	−31.9839	−1.08002	−0.540010	+	0.841659i	$0.681579\pi$
$878$	−47.1558	−1.59143
$879$	−27.9459	−0.942591
$880$	220.553	7.43486
$881$	44.5966	1.50250	0.751249	−	0.660019i	$-0.229452\pi$
$881$	44.5966	1.50250	0.751249	+	0.660019i	$0.229452\pi$
$882$	−33.2062	−1.11811
$883$	48.8015	1.64230	0.821151	−	0.570710i	$-0.193332\pi$
$883$	48.8015	1.64230	0.821151	+	0.570710i	$0.193332\pi$
$884$	11.9372	0.401493
$885$	53.6601	1.80377
$886$	−44.2971	−1.48819
$887$	10.2669	0.344727	0.172364	−	0.985033i	$-0.444860\pi$
$887$	10.2669	0.344727	0.172364	+	0.985033i	$0.444860\pi$
$888$	276.521	9.27944
$889$	−20.0522	−0.672529
$890$	33.6820	1.12902
$891$	118.753	3.97839
$892$	126.227	4.22639
$893$	−22.8879	−0.765913
$894$	−86.1234	−2.88040
$895$	9.16983	0.306513
$896$	−220.234	−7.35749
$897$	13.8702	0.463112
$898$	−38.8337	−1.29590
$899$	−15.8489	−0.528591
$900$	63.1572	2.10524
$901$	8.64312	0.287944
$902$	88.3379	2.94133
$903$	−13.8483	−0.460842
$904$	−9.33682	−0.310538
$905$	−33.4214	−1.11096
$906$	−93.1802	−3.09570
$907$	48.6017	1.61379	0.806896	−	0.590694i	$-0.201146\pi$
$907$	48.6017	1.61379	0.806896	+	0.590694i	$0.201146\pi$
$908$	−6.85515	−0.227496
$909$	74.9052	2.48445
$910$	−20.8046	−0.689664
$911$	−33.0382	−1.09461	−0.547303	−	0.836935i	$-0.684345\pi$
$911$	−33.0382	−1.09461	−0.547303	+	0.836935i	$0.684345\pi$
$912$	−423.882	−14.0361
$913$	−24.9434	−0.825507
$914$	68.7148	2.27288
$915$	−20.2564	−0.669656
$916$	−96.6292	−3.19272
$917$	1.88333	0.0621929
$918$	−84.5949	−2.79205
$919$	9.89529	0.326415	0.163208	−	0.986592i	$-0.447816\pi$
$919$	9.89529	0.326415	0.163208	+	0.986592i	$0.447816\pi$
$920$	−117.273	−3.86639
$921$	−86.1235	−2.83787
$922$	−20.2859	−0.668080
$923$	−5.72732	−0.188517
$924$	259.983	8.55283
$925$	−11.1787	−0.367554
$926$	2.80453	0.0921626
$927$	75.6948	2.48614
$928$	268.606	8.81743
$929$	−29.3662	−0.963475	−0.481737	−	0.876316i	$-0.659994\pi$
$929$	−29.3662	−0.963475	−0.481737	+	0.876316i	$0.659994\pi$
$930$	−41.8242	−1.37147
$931$	−10.9396	−0.358532
$932$	−174.054	−5.70133
$933$	−51.7469	−1.69412
$934$	30.1119	0.985291
$935$	24.0397	0.786181
$936$	−81.9626	−2.67903
$937$	59.5162	1.94431	0.972155	−	0.234339i	$-0.0752925\pi$
$937$	59.5162	1.94431	0.972155	+	0.234339i	$0.0752925\pi$
$938$	−22.4417	−0.732748
$939$	−28.2429	−0.921673
$940$	48.7086	1.58870
$941$	41.1461	1.34132	0.670662	−	0.741764i	$-0.266010\pi$
$941$	41.1461	1.34132	0.670662	+	0.741764i	$0.266010\pi$
$942$	87.5990	2.85413
$943$	−28.8477	−0.939409
$944$	121.644	3.95916
$945$	109.945	3.57651
$946$	19.0298	0.618711
$947$	33.7347	1.09623	0.548116	−	0.836402i	$-0.315345\pi$
$947$	33.7347	1.09623	0.548116	+	0.836402i	$0.315345\pi$
$948$	−177.218	−5.75577
$949$	9.85464	0.319895
$950$	27.9016	0.905249
$951$	30.3765	0.985026
$952$	−64.5730	−2.09282
$953$	−30.2851	−0.981031	−0.490516	−	0.871432i	$-0.663192\pi$
$953$	−30.2851	−0.981031	−0.490516	+	0.871432i	$0.663192\pi$
$954$	−90.0504	−2.91549
$955$	40.5816	1.31319
$956$	173.514	5.61184
$957$	−132.570	−4.28539
$958$	68.5762	2.21560
$959$	−46.2079	−1.49213
$960$	401.239	12.9499
$961$	−27.7219	−0.894254
$962$	22.0134	0.709742
$963$	122.026	3.93224
$964$	126.457	4.07290
$965$	2.34542	0.0755016
$966$	−113.850	−3.66306
$967$	22.1191	0.711303	0.355652	−	0.934619i	$-0.384259\pi$
$967$	22.1191	0.711303	0.355652	+	0.934619i	$0.384259\pi$
$968$	−116.193	−3.73457
$969$	−46.2018	−1.48422
$970$	76.4953	2.45612
$971$	−41.9567	−1.34645	−0.673227	−	0.739435i	$-0.735093\pi$
$971$	−41.9567	−1.34645	−0.673227	+	0.739435i	$0.735093\pi$
$972$	224.917	7.21423
$973$	43.8750	1.40657
$974$	112.888	3.61716
$975$	4.62818	0.148220
$976$	−45.9198	−1.46986
$977$	−13.8967	−0.444595	−0.222298	−	0.974979i	$-0.571356\pi$
$977$	−13.8967	−0.444595	−0.222298	+	0.974979i	$0.571356\pi$
$978$	160.278	5.12513
$979$	−22.0822	−0.705749
$980$	23.2811	0.743687
$981$	−155.757	−4.97294
$982$	98.2932	3.13666
$983$	21.4378	0.683759	0.341879	−	0.939744i	$-0.388937\pi$
$983$	21.4378	0.683759	0.341879	+	0.939744i	$0.388937\pi$
$984$	238.108	7.59062
$985$	22.1823	0.706786
$986$	49.9637	1.59117
$987$	31.1627	0.991920
$988$	−40.9735	−1.30354
$989$	−6.21436	−0.197605
$990$	−250.463	−7.96023
$991$	−16.1499	−0.513017	−0.256508	−	0.966542i	$-0.582572\pi$
$991$	−16.1499	−0.513017	−0.256508	+	0.966542i	$0.582572\pi$
$992$	−55.5573	−1.76395
$993$	−69.3520	−2.20082
$994$	47.0112	1.49110
$995$	27.1667	0.861241
$996$	−102.020	−3.23264
$997$	−5.26945	−0.166885	−0.0834425	−	0.996513i	$-0.526591\pi$
$997$	−5.26945	−0.166885	−0.0834425	+	0.996513i	$0.526591\pi$
$998$	−62.1659	−1.96783
$999$	−116.333	−3.68063

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6019.2.a.e.1.1	✓	130

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6019.2.a.e.1.1	✓	130	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)

\(f(q)\)	\(=\)	\(q-2.80453 q^{2} +3.24972 q^{3} +5.86540 q^{4} +2.53460 q^{5} -9.11395 q^{6} +2.92678 q^{7} -10.8406 q^{8} +7.56069 q^{9} +O(q^{10})\)	\(q-2.80453 q^{2} +3.24972 q^{3} +5.86540 q^{4} +2.53460 q^{5} -9.11395 q^{6} +2.92678 q^{7} -10.8406 q^{8} +7.56069 q^{9} -7.10835 q^{10} +4.66029 q^{11} +19.0609 q^{12} +1.00000 q^{13} -8.20824 q^{14} +8.23673 q^{15} +18.6721 q^{16} +2.03520 q^{17} -21.2042 q^{18} -6.98563 q^{19} +14.8664 q^{20} +9.51121 q^{21} -13.0699 q^{22} +4.26812 q^{23} -35.2290 q^{24} +1.42418 q^{25} -2.80453 q^{26} +14.8210 q^{27} +17.1667 q^{28} -8.75361 q^{29} -23.1002 q^{30} +1.81056 q^{31} -30.6852 q^{32} +15.1446 q^{33} -5.70778 q^{34} +7.41820 q^{35} +44.3465 q^{36} -7.84924 q^{37} +19.5914 q^{38} +3.24972 q^{39} -27.4766 q^{40} -6.75887 q^{41} -26.6745 q^{42} -1.45600 q^{43} +27.3344 q^{44} +19.1633 q^{45} -11.9701 q^{46} +3.27642 q^{47} +60.6791 q^{48} +1.56602 q^{49} -3.99415 q^{50} +6.61383 q^{51} +5.86540 q^{52} +4.24682 q^{53} -41.5659 q^{54} +11.8119 q^{55} -31.7281 q^{56} -22.7014 q^{57} +24.5498 q^{58} +6.51474 q^{59} +48.3117 q^{60} -2.45928 q^{61} -5.07777 q^{62} +22.1285 q^{63} +48.7134 q^{64} +2.53460 q^{65} -42.4736 q^{66} +2.73405 q^{67} +11.9372 q^{68} +13.8702 q^{69} -20.8046 q^{70} -5.72732 q^{71} -81.9626 q^{72} +9.85464 q^{73} +22.0134 q^{74} +4.62818 q^{75} -40.9735 q^{76} +13.6396 q^{77} -9.11395 q^{78} -9.29746 q^{79} +47.3262 q^{80} +25.4820 q^{81} +18.9555 q^{82} -5.35234 q^{83} +55.7870 q^{84} +5.15841 q^{85} +4.08339 q^{86} -28.4468 q^{87} -50.5204 q^{88} -4.73837 q^{89} -53.7441 q^{90} +2.92678 q^{91} +25.0342 q^{92} +5.88381 q^{93} -9.18882 q^{94} -17.7058 q^{95} -99.7183 q^{96} -10.7613 q^{97} -4.39195 q^{98} +35.2350 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 130 q + 10 q^{2} + 11 q^{3} + 146 q^{4} + 40 q^{5} + 4 q^{6} + 8 q^{7} + 24 q^{8} + 181 q^{9}+O(q^{10}) \) 130 * q + 10 * q^2 + 11 * q^3 + 146 * q^4 + 40 * q^5 + 4 * q^6 + 8 * q^7 + 24 * q^8 + 181 * q^9	\( 130 q + 10 q^{2} + 11 q^{3} + 146 q^{4} + 40 q^{5} + 4 q^{6} + 8 q^{7} + 24 q^{8} + 181 q^{9} + 5 q^{10} + 43 q^{11} + 28 q^{12} + 130 q^{13} + 47 q^{14} + 29 q^{15} + 170 q^{16} + 85 q^{17} + 20 q^{18} + 3 q^{19} + 73 q^{20} + 62 q^{21} + 12 q^{22} + 62 q^{23} - 5 q^{24} + 178 q^{25} + 10 q^{26} + 35 q^{27} - q^{28} + 134 q^{29} + 24 q^{30} + 14 q^{31} + 48 q^{32} + 4 q^{33} + 4 q^{34} + 50 q^{35} + 244 q^{36} + 32 q^{37} + 76 q^{38} + 11 q^{39} - 6 q^{40} + 48 q^{41} + 9 q^{42} + 34 q^{43} + 123 q^{44} + 115 q^{45} + 5 q^{46} + 25 q^{47} + 35 q^{48} + 210 q^{49} + 24 q^{50} + 20 q^{51} + 146 q^{52} + 193 q^{53} - 39 q^{54} + 32 q^{55} + 122 q^{56} + 7 q^{57} - 4 q^{58} + 50 q^{59} + 42 q^{60} + 57 q^{61} + 51 q^{62} + 8 q^{63} + 172 q^{64} + 40 q^{65} - 4 q^{66} + 21 q^{67} + 132 q^{68} + 92 q^{69} - 46 q^{70} + 58 q^{71} - 26 q^{72} + 15 q^{73} + 120 q^{74} + 23 q^{75} - 65 q^{76} + 192 q^{77} + 4 q^{78} + 32 q^{79} + 66 q^{80} + 326 q^{81} + 11 q^{82} + 33 q^{83} + 5 q^{84} + 43 q^{85} + 105 q^{86} + 31 q^{87} - 17 q^{88} + 84 q^{89} - 73 q^{90} + 8 q^{91} + 161 q^{92} + 52 q^{93} + 4 q^{94} + 59 q^{95} - 77 q^{96} + 9 q^{97} - 61 q^{98} + 100 q^{99}+O(q^{100}) \) 130 * q + 10 * q^2 + 11 * q^3 + 146 * q^4 + 40 * q^5 + 4 * q^6 + 8 * q^7 + 24 * q^8 + 181 * q^9 + 5 * q^10 + 43 * q^11 + 28 * q^12 + 130 * q^13 + 47 * q^14 + 29 * q^15 + 170 * q^16 + 85 * q^17 + 20 * q^18 + 3 * q^19 + 73 * q^20 + 62 * q^21 + 12 * q^22 + 62 * q^23 - 5 * q^24 + 178 * q^25 + 10 * q^26 + 35 * q^27 - q^28 + 134 * q^29 + 24 * q^30 + 14 * q^31 + 48 * q^32 + 4 * q^33 + 4 * q^34 + 50 * q^35 + 244 * q^36 + 32 * q^37 + 76 * q^38 + 11 * q^39 - 6 * q^40 + 48 * q^41 + 9 * q^42 + 34 * q^43 + 123 * q^44 + 115 * q^45 + 5 * q^46 + 25 * q^47 + 35 * q^48 + 210 * q^49 + 24 * q^50 + 20 * q^51 + 146 * q^52 + 193 * q^53 - 39 * q^54 + 32 * q^55 + 122 * q^56 + 7 * q^57 - 4 * q^58 + 50 * q^59 + 42 * q^60 + 57 * q^61 + 51 * q^62 + 8 * q^63 + 172 * q^64 + 40 * q^65 - 4 * q^66 + 21 * q^67 + 132 * q^68 + 92 * q^69 - 46 * q^70 + 58 * q^71 - 26 * q^72 + 15 * q^73 + 120 * q^74 + 23 * q^75 - 65 * q^76 + 192 * q^77 + 4 * q^78 + 32 * q^79 + 66 * q^80 + 326 * q^81 + 11 * q^82 + 33 * q^83 + 5 * q^84 + 43 * q^85 + 105 * q^86 + 31 * q^87 - 17 * q^88 + 84 * q^89 - 73 * q^90 + 8 * q^91 + 161 * q^92 + 52 * q^93 + 4 * q^94 + 59 * q^95 - 77 * q^96 + 9 * q^97 - 61 * q^98 + 100 * q^99

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