LMFDB - Embedded newform 8039.2.a.b.1.15

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8039,2,Mod(1,8039)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8039, 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("8039.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8039 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8039.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:	$64.1917381849$
Analytic rank:	$0$
Dimension:	$391$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.15
Character	$\chi$	$=$	8039.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.65165 q^{2} +1.77560 q^{3} +5.03124 q^{4} -0.216981 q^{5} -4.70826 q^{6} -4.11451 q^{7} -8.03778 q^{8} +0.152748 q^{9} +O(q^{10})$	\(q-2.65165 q^{2} +1.77560 q^{3} +5.03124 q^{4} -0.216981 q^{5} -4.70826 q^{6} -4.11451 q^{7} -8.03778 q^{8} +0.152748 q^{9} +0.575357 q^{10} -5.34387 q^{11} +8.93346 q^{12} +0.658583 q^{13} +10.9102 q^{14} -0.385271 q^{15} +11.2509 q^{16} -6.64906 q^{17} -0.405035 q^{18} +2.71183 q^{19} -1.09168 q^{20} -7.30571 q^{21} +14.1701 q^{22} -7.30424 q^{23} -14.2719 q^{24} -4.95292 q^{25} -1.74633 q^{26} -5.05557 q^{27} -20.7011 q^{28} -2.37788 q^{29} +1.02160 q^{30} +7.44945 q^{31} -13.7578 q^{32} -9.48857 q^{33} +17.6310 q^{34} +0.892769 q^{35} +0.768514 q^{36} -11.8160 q^{37} -7.19082 q^{38} +1.16938 q^{39} +1.74404 q^{40} -6.63904 q^{41} +19.3722 q^{42} -5.70237 q^{43} -26.8863 q^{44} -0.0331435 q^{45} +19.3683 q^{46} -1.05065 q^{47} +19.9770 q^{48} +9.92916 q^{49} +13.1334 q^{50} -11.8061 q^{51} +3.31349 q^{52} -5.87577 q^{53} +13.4056 q^{54} +1.15952 q^{55} +33.0715 q^{56} +4.81512 q^{57} +6.30529 q^{58} -4.54317 q^{59} -1.93839 q^{60} +15.1852 q^{61} -19.7533 q^{62} -0.628484 q^{63} +13.9792 q^{64} -0.142900 q^{65} +25.1603 q^{66} -11.9978 q^{67} -33.4530 q^{68} -12.9694 q^{69} -2.36731 q^{70} +14.0795 q^{71} -1.22776 q^{72} -3.51709 q^{73} +31.3318 q^{74} -8.79439 q^{75} +13.6439 q^{76} +21.9874 q^{77} -3.10078 q^{78} +12.1539 q^{79} -2.44123 q^{80} -9.43491 q^{81} +17.6044 q^{82} +3.98792 q^{83} -36.7568 q^{84} +1.44272 q^{85} +15.1207 q^{86} -4.22215 q^{87} +42.9528 q^{88} -10.5748 q^{89} +0.0878848 q^{90} -2.70975 q^{91} -36.7494 q^{92} +13.2272 q^{93} +2.78594 q^{94} -0.588415 q^{95} -24.4284 q^{96} +14.9775 q^{97} -26.3286 q^{98} -0.816268 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 391 q + 14 q^{2} + 12 q^{3} + 446 q^{4} + 22 q^{5} + 40 q^{6} + 63 q^{7} + 36 q^{8} + 501 q^{9}+O(q^{10}) $ 391 * q + 14 * q^2 + 12 * q^3 + 446 * q^4 + 22 * q^5 + 40 * q^6 + 63 * q^7 + 36 * q^8 + 501 * q^9	\( 391 q + 14 q^{2} + 12 q^{3} + 446 q^{4} + 22 q^{5} + 40 q^{6} + 63 q^{7} + 36 q^{8} + 501 q^{9} + 40 q^{10} + 57 q^{11} + 20 q^{12} + 83 q^{13} + 21 q^{14} + 60 q^{15} + 548 q^{16} + 59 q^{17} + 54 q^{18} + 131 q^{19} + 35 q^{20} + 121 q^{21} + 89 q^{22} + 34 q^{23} + 110 q^{24} + 609 q^{25} + 54 q^{26} + 27 q^{27} + 182 q^{28} + 102 q^{29} + 92 q^{30} + 88 q^{31} + 76 q^{32} + 131 q^{33} + 128 q^{34} + 31 q^{35} + 654 q^{36} + 135 q^{37} + 23 q^{38} + 96 q^{39} + 113 q^{40} + 128 q^{41} + 45 q^{42} + 140 q^{43} + 151 q^{44} + 77 q^{45} + 245 q^{46} + 22 q^{47} + 25 q^{48} + 712 q^{49} + 53 q^{50} + 102 q^{51} + 174 q^{52} + 54 q^{53} + 131 q^{54} + 101 q^{55} + 43 q^{56} + 226 q^{57} + 109 q^{58} + 40 q^{59} + 123 q^{60} + 249 q^{61} + 28 q^{62} + 139 q^{63} + 730 q^{64} + 227 q^{65} + 55 q^{66} + 169 q^{67} + 48 q^{68} + 89 q^{69} + 98 q^{70} + 66 q^{71} + 120 q^{72} + 324 q^{73} + 60 q^{74} + 19 q^{75} + 356 q^{76} + 83 q^{77} - 11 q^{78} + 195 q^{79} + 26 q^{80} + 807 q^{81} + 49 q^{82} + 74 q^{83} + 252 q^{84} + 373 q^{85} + 100 q^{86} + 43 q^{87} + 211 q^{88} + 207 q^{89} + 10 q^{90} + 189 q^{91} + 30 q^{92} + 172 q^{93} + 130 q^{94} + 43 q^{95} + 203 q^{96} + 254 q^{97} + 26 q^{98} + 273 q^{99}+O(q^{100}) \) 391 * q + 14 * q^2 + 12 * q^3 + 446 * q^4 + 22 * q^5 + 40 * q^6 + 63 * q^7 + 36 * q^8 + 501 * q^9 + 40 * q^10 + 57 * q^11 + 20 * q^12 + 83 * q^13 + 21 * q^14 + 60 * q^15 + 548 * q^16 + 59 * q^17 + 54 * q^18 + 131 * q^19 + 35 * q^20 + 121 * q^21 + 89 * q^22 + 34 * q^23 + 110 * q^24 + 609 * q^25 + 54 * q^26 + 27 * q^27 + 182 * q^28 + 102 * q^29 + 92 * q^30 + 88 * q^31 + 76 * q^32 + 131 * q^33 + 128 * q^34 + 31 * q^35 + 654 * q^36 + 135 * q^37 + 23 * q^38 + 96 * q^39 + 113 * q^40 + 128 * q^41 + 45 * q^42 + 140 * q^43 + 151 * q^44 + 77 * q^45 + 245 * q^46 + 22 * q^47 + 25 * q^48 + 712 * q^49 + 53 * q^50 + 102 * q^51 + 174 * q^52 + 54 * q^53 + 131 * q^54 + 101 * q^55 + 43 * q^56 + 226 * q^57 + 109 * q^58 + 40 * q^59 + 123 * q^60 + 249 * q^61 + 28 * q^62 + 139 * q^63 + 730 * q^64 + 227 * q^65 + 55 * q^66 + 169 * q^67 + 48 * q^68 + 89 * q^69 + 98 * q^70 + 66 * q^71 + 120 * q^72 + 324 * q^73 + 60 * q^74 + 19 * q^75 + 356 * q^76 + 83 * q^77 - 11 * q^78 + 195 * q^79 + 26 * q^80 + 807 * q^81 + 49 * q^82 + 74 * q^83 + 252 * q^84 + 373 * q^85 + 100 * q^86 + 43 * q^87 + 211 * q^88 + 207 * q^89 + 10 * q^90 + 189 * q^91 + 30 * q^92 + 172 * q^93 + 130 * q^94 + 43 * q^95 + 203 * q^96 + 254 * q^97 + 26 * q^98 + 273 * 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 $

$2$	−2.65165	−1.87500	−0.937499	−	0.347987i	$-0.886865\pi$
$2$	−2.65165	−1.87500	−0.937499	+	0.347987i	$0.886865\pi$
$3$	1.77560	1.02514	0.512571	−	0.858645i	$-0.328693\pi$
$3$	1.77560	1.02514	0.512571	+	0.858645i	$0.328693\pi$
$4$	5.03124	2.51562
$5$	−0.216981	−0.0970368	−0.0485184	−	0.998822i	$-0.515450\pi$
$5$	−0.216981	−0.0970368	−0.0485184	+	0.998822i	$0.515450\pi$
$6$	−4.70826	−1.92214
$7$	−4.11451	−1.55514	−0.777569	−	0.628798i	$-0.783547\pi$
$7$	−4.11451	−1.55514	−0.777569	+	0.628798i	$0.783547\pi$
$8$	−8.03778	−2.84178
$9$	0.152748	0.0509161
$10$	0.575357	0.181944
$11$	−5.34387	−1.61124	−0.805619	−	0.592434i	$-0.798167\pi$
$11$	−5.34387	−1.61124	−0.805619	+	0.592434i	$0.798167\pi$
$12$	8.93346	2.57887
$13$	0.658583	0.182658	0.0913291	−	0.995821i	$-0.470888\pi$
$13$	0.658583	0.182658	0.0913291	+	0.995821i	$0.470888\pi$
$14$	10.9102	2.91588
$15$	−0.385271	−0.0994765
$16$	11.2509	2.81272
$17$	−6.64906	−1.61263	−0.806317	−	0.591484i	$-0.798542\pi$
$17$	−6.64906	−1.61263	−0.806317	+	0.591484i	$0.798542\pi$
$18$	−0.405035	−0.0954677
$19$	2.71183	0.622137	0.311068	−	0.950388i	$-0.399313\pi$
$19$	2.71183	0.622137	0.311068	+	0.950388i	$0.399313\pi$
$20$	−1.09168	−0.244108
$21$	−7.30571	−1.59424
$22$	14.1701	3.02107
$23$	−7.30424	−1.52304	−0.761520	−	0.648141i	$-0.775547\pi$
$23$	−7.30424	−1.52304	−0.761520	+	0.648141i	$0.775547\pi$
$24$	−14.2719	−2.91323
$25$	−4.95292	−0.990584
$26$	−1.74633	−0.342484
$27$	−5.05557	−0.972946
$28$	−20.7011	−3.91213
$29$	−2.37788	−0.441561	−0.220780	−	0.975324i	$-0.570860\pi$
$29$	−2.37788	−0.441561	−0.220780	+	0.975324i	$0.570860\pi$
$30$	1.02160	0.186518
$31$	7.44945	1.33796	0.668980	−	0.743280i	$-0.266731\pi$
$31$	7.44945	1.33796	0.668980	+	0.743280i	$0.266731\pi$
$32$	−13.7578	−2.43206
$33$	−9.48857	−1.65175
$34$	17.6310	3.02369
$35$	0.892769	0.150905
$36$	0.768514	0.128086
$37$	−11.8160	−1.94253	−0.971266	−	0.237997i	$-0.923509\pi$
$37$	−11.8160	−1.94253	−0.971266	+	0.237997i	$0.923509\pi$
$38$	−7.19082	−1.16651
$39$	1.16938	0.187251
$40$	1.74404	0.275758
$41$	−6.63904	−1.03684	−0.518422	−	0.855125i	$-0.673480\pi$
$41$	−6.63904	−1.03684	−0.518422	+	0.855125i	$0.673480\pi$
$42$	19.3722	2.98919
$43$	−5.70237	−0.869603	−0.434801	−	0.900526i	$-0.643181\pi$
$43$	−5.70237	−0.869603	−0.434801	+	0.900526i	$0.643181\pi$
$44$	−26.8863	−4.05326
$45$	−0.0331435	−0.00494074
$46$	19.3683	2.85570
$47$	−1.05065	−0.153252	−0.0766262	−	0.997060i	$-0.524415\pi$
$47$	−1.05065	−0.153252	−0.0766262	+	0.997060i	$0.524415\pi$
$48$	19.9770	2.88344
$49$	9.92916	1.41845
$50$	13.1334	1.85734
$51$	−11.8061	−1.65318
$52$	3.31349	0.459498
$53$	−5.87577	−0.807099	−0.403549	−	0.914958i	$-0.632224\pi$
$53$	−5.87577	−0.807099	−0.403549	+	0.914958i	$0.632224\pi$
$54$	13.4056	1.82427
$55$	1.15952	0.156349
$56$	33.0715	4.41936
$57$	4.81512	0.637779
$58$	6.30529	0.827926
$59$	−4.54317	−0.591471	−0.295735	−	0.955270i	$-0.595565\pi$
$59$	−4.54317	−0.591471	−0.295735	+	0.955270i	$0.595565\pi$
$60$	−1.93839	−0.250245
$61$	15.1852	1.94427	0.972134	−	0.234427i	$-0.0753213\pi$
$61$	15.1852	1.94427	0.972134	+	0.234427i	$0.0753213\pi$
$62$	−19.7533	−2.50867
$63$	−0.628484	−0.0791816
$64$	13.9792	1.74739
$65$	−0.142900	−0.0177246
$66$	25.1603	3.09702
$67$	−11.9978	−1.46576	−0.732880	−	0.680358i	$-0.761824\pi$
$67$	−11.9978	−1.46576	−0.732880	+	0.680358i	$0.761824\pi$
$68$	−33.4530	−4.05677
$69$	−12.9694	−1.56133
$70$	−2.36731	−0.282948
$71$	14.0795	1.67093	0.835464	−	0.549546i	$-0.185199\pi$
$71$	14.0795	1.67093	0.835464	+	0.549546i	$0.185199\pi$
$72$	−1.22776	−0.144693
$73$	−3.51709	−0.411644	−0.205822	−	0.978589i	$-0.565987\pi$
$73$	−3.51709	−0.411644	−0.205822	+	0.978589i	$0.565987\pi$
$74$	31.3318	3.64224
$75$	−8.79439	−1.01549
$76$	13.6439	1.56506
$77$	21.9874	2.50570
$78$	−3.10078	−0.351095
$79$	12.1539	1.36742	0.683708	−	0.729756i	$-0.260366\pi$
$79$	12.1539	1.36742	0.683708	+	0.729756i	$0.260366\pi$
$80$	−2.44123	−0.272937
$81$	−9.43491	−1.04832
$82$	17.6044	1.94408
$83$	3.98792	0.437731	0.218866	−	0.975755i	$-0.429764\pi$
$83$	3.98792	0.437731	0.218866	+	0.975755i	$0.429764\pi$
$84$	−36.7568	−4.01049
$85$	1.44272	0.156485
$86$	15.1207	1.63050
$87$	−4.22215	−0.452662
$88$	42.9528	4.57879
$89$	−10.5748	−1.12093	−0.560466	−	0.828178i	$-0.689378\pi$
$89$	−10.5748	−1.12093	−0.560466	+	0.828178i	$0.689378\pi$
$90$	0.0878848	0.00926388
$91$	−2.70975	−0.284059
$92$	−36.7494	−3.83139
$93$	13.2272	1.37160
$94$	2.78594	0.287348
$95$	−0.588415	−0.0603701
$96$	−24.4284	−2.49321
$97$	14.9775	1.52073	0.760366	−	0.649495i	$-0.225020\pi$
$97$	14.9775	1.52073	0.760366	+	0.649495i	$0.225020\pi$
$98$	−26.3286	−2.65959
$99$	−0.816268	−0.0820380
$100$	−24.9193	−2.49193
$101$	−17.6721	−1.75844	−0.879221	−	0.476414i	$-0.841936\pi$
$101$	−17.6721	−1.75844	−0.879221	+	0.476414i	$0.841936\pi$
$102$	31.3055	3.09971
$103$	−17.1204	−1.68692	−0.843461	−	0.537190i	$-0.819486\pi$
$103$	−17.1204	−1.68692	−0.843461	+	0.537190i	$0.819486\pi$
$104$	−5.29355	−0.519075
$105$	1.58520	0.154700
$106$	15.5805	1.51331
$107$	13.2798	1.28381	0.641903	−	0.766786i	$-0.278145\pi$
$107$	13.2798	1.28381	0.641903	+	0.766786i	$0.278145\pi$
$108$	−25.4358	−2.44756
$109$	5.33713	0.511204	0.255602	−	0.966782i	$-0.417726\pi$
$109$	5.33713	0.511204	0.255602	+	0.966782i	$0.417726\pi$
$110$	−3.07463	−0.293155
$111$	−20.9804	−1.99137
$112$	−46.2918	−4.37417
$113$	−9.33308	−0.877982	−0.438991	−	0.898491i	$-0.644664\pi$
$113$	−9.33308	−0.877982	−0.438991	+	0.898491i	$0.644664\pi$
$114$	−12.7680	−1.19583
$115$	1.58488	0.147791
$116$	−11.9637	−1.11080
$117$	0.100598	0.00930025
$118$	12.0469	1.10901
$119$	27.3576	2.50787
$120$	3.09672	0.282691
$121$	17.5570	1.59609
$122$	−40.2658	−3.64550
$123$	−11.7883	−1.06291
$124$	37.4800	3.36580
$125$	2.15959	0.193160
$126$	1.66652	0.148465
$127$	−15.3289	−1.36022	−0.680109	−	0.733111i	$-0.738068\pi$
$127$	−15.3289	−1.36022	−0.680109	+	0.733111i	$0.738068\pi$
$128$	−9.55215	−0.844299
$129$	−10.1251	−0.891466
$130$	0.378920	0.0332335
$131$	−2.22905	−0.194753	−0.0973766	−	0.995248i	$-0.531045\pi$
$131$	−2.22905	−0.194753	−0.0973766	+	0.995248i	$0.531045\pi$
$132$	−47.7392	−4.15517
$133$	−11.1578	−0.967508
$134$	31.8138	2.74830
$135$	1.09696	0.0944115
$136$	53.4437	4.58276
$137$	−13.2937	−1.13576	−0.567878	−	0.823113i	$-0.692235\pi$
$137$	−13.2937	−1.13576	−0.567878	+	0.823113i	$0.692235\pi$
$138$	34.3903	2.92750
$139$	−14.7044	−1.24722	−0.623608	−	0.781738i	$-0.714334\pi$
$139$	−14.7044	−1.24722	−0.623608	+	0.781738i	$0.714334\pi$
$140$	4.49173	0.379621
$141$	−1.86552	−0.157106
$142$	−37.3338	−3.13299
$143$	−3.51938	−0.294306
$144$	1.71855	0.143213
$145$	0.515954	0.0428476
$146$	9.32608	0.771832
$147$	17.6302	1.45411
$148$	−59.4489	−4.88667
$149$	11.5742	0.948195	0.474097	−	0.880472i	$-0.342774\pi$
$149$	11.5742	0.948195	0.474097	+	0.880472i	$0.342774\pi$
$150$	23.3196	1.90404
$151$	0.549776	0.0447402	0.0223701	−	0.999750i	$-0.492879\pi$
$151$	0.549776	0.0447402	0.0223701	+	0.999750i	$0.492879\pi$
$152$	−21.7971	−1.76798
$153$	−1.01563	−0.0821091
$154$	−58.3028	−4.69818
$155$	−1.61639	−0.129831
$156$	5.88343	0.471051
$157$	3.81841	0.304743	0.152371	−	0.988323i	$-0.451309\pi$
$157$	3.81841	0.304743	0.152371	+	0.988323i	$0.451309\pi$
$158$	−32.2278	−2.56390
$159$	−10.4330	−0.827391
$160$	2.98519	0.236000
$161$	30.0534	2.36854
$162$	25.0181	1.96561
$163$	1.72702	0.135271	0.0676355	−	0.997710i	$-0.478455\pi$
$163$	1.72702	0.135271	0.0676355	+	0.997710i	$0.478455\pi$
$164$	−33.4026	−2.60831
$165$	2.05884	0.160280
$166$	−10.5746	−0.820746
$167$	15.9282	1.23256	0.616282	−	0.787525i	$-0.288638\pi$
$167$	15.9282	1.23256	0.616282	+	0.787525i	$0.288638\pi$
$168$	58.7217	4.53048
$169$	−12.5663	−0.966636
$170$	−3.82558	−0.293409
$171$	0.414228	0.0316768
$172$	−28.6900	−2.18759
$173$	−5.96287	−0.453349	−0.226674	−	0.973971i	$-0.572785\pi$
$173$	−5.96287	−0.453349	−0.226674	+	0.973971i	$0.572785\pi$
$174$	11.1957	0.848741
$175$	20.3788	1.54049
$176$	−60.1233	−4.53196
$177$	−8.06685	−0.606341
$178$	28.0408	2.10174
$179$	−13.9020	−1.03909	−0.519543	−	0.854444i	$-0.673898\pi$
$179$	−13.9020	−1.03909	−0.519543	+	0.854444i	$0.673898\pi$
$180$	−0.166753	−0.0124290
$181$	2.98847	0.222131	0.111065	−	0.993813i	$-0.464574\pi$
$181$	2.98847	0.222131	0.111065	+	0.993813i	$0.464574\pi$
$182$	7.18529	0.532609
$183$	26.9628	1.99315
$184$	58.7099	4.32815
$185$	2.56384	0.188497
$186$	−35.0740	−2.57175
$187$	35.5317	2.59834
$188$	−5.28605	−0.385525
$189$	20.8012	1.51306
$190$	1.56027	0.113194
$191$	14.9712	1.08328	0.541640	−	0.840611i	$-0.317804\pi$
$191$	14.9712	1.08328	0.541640	+	0.840611i	$0.317804\pi$
$192$	24.8214	1.79133
$193$	−9.19276	−0.661709	−0.330855	−	0.943682i	$-0.607337\pi$
$193$	−9.19276	−0.661709	−0.330855	+	0.943682i	$0.607337\pi$
$194$	−39.7150	−2.85137
$195$	−0.253733	−0.0181702
$196$	49.9560	3.56828
$197$	5.30785	0.378169	0.189084	−	0.981961i	$-0.439448\pi$
$197$	5.30785	0.378169	0.189084	+	0.981961i	$0.439448\pi$
$198$	2.16445	0.153821
$199$	2.43743	0.172784	0.0863922	−	0.996261i	$-0.472466\pi$
$199$	2.43743	0.172784	0.0863922	+	0.996261i	$0.472466\pi$
$200$	39.8105	2.81503
$201$	−21.3032	−1.50261
$202$	46.8603	3.29708
$203$	9.78379	0.686687
$204$	−59.3991	−4.15877
$205$	1.44054	0.100612
$206$	45.3973	3.16298
$207$	−1.11571	−0.0775473
$208$	7.40965	0.513767
$209$	−14.4917	−1.00241
$210$	−4.20339	−0.290061
$211$	−11.7634	−0.809822	−0.404911	−	0.914356i	$-0.632698\pi$
$211$	−11.7634	−0.809822	−0.404911	+	0.914356i	$0.632698\pi$
$212$	−29.5624	−2.03035
$213$	24.9995	1.71294
$214$	−35.2134	−2.40714
$215$	1.23730	0.0843834
$216$	40.6356	2.76490
$217$	−30.6508	−2.08071
$218$	−14.1522	−0.958507
$219$	−6.24494	−0.421994
$220$	5.83381	0.393315
$221$	−4.37896	−0.294561
$222$	55.6326	3.73382
$223$	3.95952	0.265149	0.132575	−	0.991173i	$-0.457676\pi$
$223$	3.95952	0.265149	0.132575	+	0.991173i	$0.457676\pi$
$224$	56.6067	3.78219
$225$	−0.756551	−0.0504367
$226$	24.7480	1.64621
$227$	−2.42273	−0.160802	−0.0804011	−	0.996763i	$-0.525620\pi$
$227$	−2.42273	−0.160802	−0.0804011	+	0.996763i	$0.525620\pi$
$228$	24.2260	1.60441
$229$	−22.8995	−1.51324	−0.756622	−	0.653852i	$-0.773152\pi$
$229$	−22.8995	−1.51324	−0.756622	+	0.653852i	$0.773152\pi$
$230$	−4.20255	−0.277108
$231$	39.0408	2.56869
$232$	19.1128	1.25482
$233$	13.8787	0.909224	0.454612	−	0.890690i	$-0.349778\pi$
$233$	13.8787	0.909224	0.454612	+	0.890690i	$0.349778\pi$
$234$	−0.266749	−0.0174380
$235$	0.227970	0.0148711
$236$	−22.8578	−1.48792
$237$	21.5804	1.40180
$238$	−72.5427	−4.70225
$239$	−15.2274	−0.984981	−0.492490	−	0.870318i	$-0.663913\pi$
$239$	−15.2274	−0.984981	−0.492490	+	0.870318i	$0.663913\pi$
$240$	−4.33464	−0.279800
$241$	20.4418	1.31677	0.658385	−	0.752681i	$-0.271240\pi$
$241$	20.4418	1.31677	0.658385	+	0.752681i	$0.271240\pi$
$242$	−46.5549	−2.99266
$243$	−1.58589	−0.101735
$244$	76.4004	4.89104
$245$	−2.15444	−0.137642
$246$	31.2583	1.99296
$247$	1.78597	0.113638
$248$	−59.8770	−3.80220
$249$	7.08095	0.448737
$250$	−5.72648	−0.362174
$251$	0.515364	0.0325295	0.0162647	−	0.999868i	$-0.494823\pi$
$251$	0.515364	0.0325295	0.0162647	+	0.999868i	$0.494823\pi$
$252$	−3.16205	−0.199191
$253$	39.0329	2.45398
$254$	40.6468	2.55041
$255$	2.56169	0.160419
$256$	−2.62937	−0.164336
$257$	−18.7971	−1.17253	−0.586265	−	0.810120i	$-0.699402\pi$
$257$	−18.7971	−1.17253	−0.586265	+	0.810120i	$0.699402\pi$
$258$	26.8482	1.67150
$259$	48.6168	3.02090
$260$	−0.718964	−0.0445882
$261$	−0.363217	−0.0224826
$262$	5.91066	0.365162
$263$	4.34072	0.267660	0.133830	−	0.991004i	$-0.457272\pi$
$263$	4.34072	0.267660	0.133830	+	0.991004i	$0.457272\pi$
$264$	76.2670	4.69391
$265$	1.27493	0.0783183
$266$	29.5867	1.81408
$267$	−18.7767	−1.14911
$268$	−60.3636	−3.68729
$269$	−0.0778674	−0.00474766	−0.00237383	−	0.999997i	$-0.500756\pi$
$269$	−0.0778674	−0.00474766	−0.00237383	+	0.999997i	$0.500756\pi$
$270$	−2.90876	−0.177021
$271$	−27.1640	−1.65010	−0.825048	−	0.565063i	$-0.808852\pi$
$271$	−27.1640	−1.65010	−0.825048	+	0.565063i	$0.808852\pi$
$272$	−74.8078	−4.53589
$273$	−4.81142	−0.291200
$274$	35.2502	2.12954
$275$	26.4678	1.59607
$276$	−65.2522	−3.92772
$277$	24.3490	1.46299	0.731495	−	0.681847i	$-0.238823\pi$
$277$	24.3490	1.46299	0.731495	+	0.681847i	$0.238823\pi$
$278$	38.9910	2.33853
$279$	1.13789	0.0681238
$280$	−7.17588	−0.428841
$281$	32.3143	1.92771	0.963855	−	0.266429i	$-0.0858438\pi$
$281$	32.3143	1.92771	0.963855	+	0.266429i	$0.0858438\pi$
$282$	4.94672	0.294573
$283$	23.3667	1.38901	0.694503	−	0.719490i	$-0.255624\pi$
$283$	23.3667	1.38901	0.694503	+	0.719490i	$0.255624\pi$
$284$	70.8372	4.20342
$285$	−1.04479	−0.0618880
$286$	9.33217	0.551823
$287$	27.3164	1.61243
$288$	−2.10149	−0.123831
$289$	27.2100	1.60059
$290$	−1.36813	−0.0803392
$291$	26.5940	1.55897
$292$	−17.6953	−1.03554
$293$	2.17857	0.127274	0.0636368	−	0.997973i	$-0.479730\pi$
$293$	2.17857	0.127274	0.0636368	+	0.997973i	$0.479730\pi$
$294$	−46.7491	−2.72646
$295$	0.985781	0.0573944
$296$	94.9741	5.52025
$297$	27.0163	1.56765
$298$	−30.6907	−1.77786
$299$	−4.81045	−0.278196
$300$	−44.2467	−2.55458
$301$	23.4624	1.35235
$302$	−1.45781	−0.0838877
$303$	−31.3786	−1.80265
$304$	30.5105	1.74990
$305$	−3.29490	−0.188665
$306$	2.69310	0.153954
$307$	5.54252	0.316328	0.158164	−	0.987413i	$-0.449443\pi$
$307$	5.54252	0.316328	0.158164	+	0.987413i	$0.449443\pi$
$308$	110.624	6.30338
$309$	−30.3989	−1.72934
$310$	4.28609	0.243434
$311$	14.8731	0.843375	0.421687	−	0.906741i	$-0.361438\pi$
$311$	14.8731	0.843375	0.421687	+	0.906741i	$0.361438\pi$
$312$	−9.39921	−0.532126
$313$	−10.0964	−0.570683	−0.285341	−	0.958426i	$-0.592107\pi$
$313$	−10.0964	−0.570683	−0.285341	+	0.958426i	$0.592107\pi$
$314$	−10.1251	−0.571392
$315$	0.136369	0.00768352
$316$	61.1490	3.43990
$317$	−24.3823	−1.36945	−0.684724	−	0.728802i	$-0.740077\pi$
$317$	−24.3823	−1.36945	−0.684724	+	0.728802i	$0.740077\pi$
$318$	27.6647	1.55136
$319$	12.7071	0.711459
$320$	−3.03321	−0.169562
$321$	23.5796	1.31608
$322$	−79.6909	−4.44100
$323$	−18.0311	−1.00328
$324$	−47.4693	−2.63718
$325$	−3.26191	−0.180938
$326$	−4.57946	−0.253633
$327$	9.47659	0.524057
$328$	53.3631	2.94649
$329$	4.32289	0.238329
$330$	−5.45931	−0.300525
$331$	−3.75017	−0.206128	−0.103064	−	0.994675i	$-0.532865\pi$
$331$	−3.75017	−0.206128	−0.103064	+	0.994675i	$0.532865\pi$
$332$	20.0642	1.10117
$333$	−1.80487	−0.0989062
$334$	−42.2361	−2.31106
$335$	2.60328	0.142233
$336$	−82.1957	−4.48414
$337$	−0.0986449	−0.00537353	−0.00268676	−	0.999996i	$-0.500855\pi$
$337$	−0.0986449	−0.00537353	−0.00268676	+	0.999996i	$0.500855\pi$
$338$	33.3213	1.81244
$339$	−16.5718	−0.900056
$340$	7.25866	0.393656
$341$	−39.8089	−2.15577
$342$	−1.09839	−0.0593940
$343$	−12.0521	−0.650750
$344$	45.8343	2.47122
$345$	2.81411	0.151507
$346$	15.8114	0.850029
$347$	4.51609	0.242437	0.121218	−	0.992626i	$-0.461320\pi$
$347$	4.51609	0.242437	0.121218	+	0.992626i	$0.461320\pi$
$348$	−21.2427	−1.13873
$349$	−23.5605	−1.26116	−0.630582	−	0.776123i	$-0.717184\pi$
$349$	−23.5605	−1.26116	−0.630582	+	0.776123i	$0.717184\pi$
$350$	−54.0375	−2.88842
$351$	−3.32952	−0.177717
$352$	73.5201	3.91863
$353$	34.7546	1.84980	0.924901	−	0.380209i	$-0.124148\pi$
$353$	34.7546	1.84980	0.924901	+	0.380209i	$0.124148\pi$
$354$	21.3904	1.13689
$355$	−3.05498	−0.162141
$356$	−53.2046	−2.81984
$357$	48.5761	2.57092
$358$	36.8633	1.94829
$359$	2.87534	0.151754	0.0758772	−	0.997117i	$-0.475824\pi$
$359$	2.87534	0.151754	0.0758772	+	0.997117i	$0.475824\pi$
$360$	0.266400	0.0140405
$361$	−11.6460	−0.612946
$362$	−7.92436	−0.416495
$363$	31.1741	1.63622
$364$	−13.6334	−0.714583
$365$	0.763141	0.0399446
$366$	−71.4960	−3.73715
$367$	−12.4556	−0.650179	−0.325090	−	0.945683i	$-0.605395\pi$
$367$	−12.4556	−0.650179	−0.325090	+	0.945683i	$0.605395\pi$
$368$	−82.1792	−4.28389
$369$	−1.01410	−0.0527921
$370$	−6.79839	−0.353432
$371$	24.1759	1.25515
$372$	66.5493	3.45042
$373$	−32.2342	−1.66903	−0.834513	−	0.550988i	$-0.814251\pi$
$373$	−32.2342	−1.66903	−0.834513	+	0.550988i	$0.814251\pi$
$374$	−94.2176	−4.87188
$375$	3.83457	0.198016
$376$	8.44486	0.435510
$377$	−1.56603	−0.0806547
$378$	−55.1574	−2.83699
$379$	−24.6427	−1.26581	−0.632905	−	0.774229i	$-0.718138\pi$
$379$	−24.6427	−1.26581	−0.632905	+	0.774229i	$0.718138\pi$
$380$	−2.96046	−0.151868
$381$	−27.2179	−1.39442
$382$	−39.6984	−2.03115
$383$	−19.1368	−0.977845	−0.488923	−	0.872327i	$-0.662610\pi$
$383$	−19.1368	−0.977845	−0.488923	+	0.872327i	$0.662610\pi$
$384$	−16.9608	−0.865526
$385$	−4.77084	−0.243145
$386$	24.3760	1.24070
$387$	−0.871027	−0.0442768
$388$	75.3553	3.82558
$389$	−29.6486	−1.50324	−0.751622	−	0.659595i	$-0.770728\pi$
$389$	−29.6486	−1.50324	−0.751622	+	0.659595i	$0.770728\pi$
$390$	0.672810	0.0340691
$391$	48.5663	2.45611
$392$	−79.8084	−4.03093
$393$	−3.95790	−0.199650
$394$	−14.0746	−0.709066
$395$	−2.63715	−0.132690
$396$	−4.10684	−0.206376
$397$	18.4968	0.928329	0.464164	−	0.885749i	$-0.346355\pi$
$397$	18.4968	0.928329	0.464164	+	0.885749i	$0.346355\pi$
$398$	−6.46319	−0.323971
$399$	−19.8119	−0.991833
$400$	−55.7247	−2.78624
$401$	6.87458	0.343300	0.171650	−	0.985158i	$-0.445090\pi$
$401$	6.87458	0.343300	0.171650	+	0.985158i	$0.445090\pi$
$402$	56.4886	2.81739
$403$	4.90608	0.244389
$404$	−88.9127	−4.42357
$405$	2.04720	0.101726
$406$	−25.9432	−1.28754
$407$	63.1430	3.12988
$408$	94.8945	4.69798
$409$	−18.7320	−0.926239	−0.463119	−	0.886296i	$-0.653270\pi$
$409$	−18.7320	−0.926239	−0.463119	+	0.886296i	$0.653270\pi$
$410$	−3.81982	−0.188647
$411$	−23.6042	−1.16431
$412$	−86.1368	−4.24365
$413$	18.6929	0.919818
$414$	2.95848	0.145401
$415$	−0.865303	−0.0424760
$416$	−9.06068	−0.444236
$417$	−26.1092	−1.27857
$418$	38.4268	1.87952
$419$	−16.9563	−0.828370	−0.414185	−	0.910193i	$-0.635933\pi$
$419$	−16.9563	−0.828370	−0.414185	+	0.910193i	$0.635933\pi$
$420$	7.97551	0.389165
$421$	−5.91609	−0.288332	−0.144166	−	0.989553i	$-0.546050\pi$
$421$	−5.91609	−0.288332	−0.144166	+	0.989553i	$0.546050\pi$
$422$	31.1923	1.51842
$423$	−0.160484	−0.00780302
$424$	47.2281	2.29360
$425$	32.9322	1.59745
$426$	−66.2899	−3.21176
$427$	−62.4797	−3.02360
$428$	66.8138	3.22957
$429$	−6.24901	−0.301705
$430$	−3.28089	−0.158219
$431$	15.3119	0.737548	0.368774	−	0.929519i	$-0.379778\pi$
$431$	15.3119	0.737548	0.368774	+	0.929519i	$0.379778\pi$
$432$	−56.8797	−2.73662
$433$	−19.6718	−0.945368	−0.472684	−	0.881232i	$-0.656715\pi$
$433$	−19.6718	−0.945368	−0.472684	+	0.881232i	$0.656715\pi$
$434$	81.2752	3.90133
$435$	0.916126	0.0439249
$436$	26.8524	1.28599
$437$	−19.8079	−0.947539
$438$	16.5594	0.791237
$439$	3.75988	0.179449	0.0897247	−	0.995967i	$-0.471401\pi$
$439$	3.75988	0.179449	0.0897247	+	0.995967i	$0.471401\pi$
$440$	−9.31994	−0.444311
$441$	1.51666	0.0722221
$442$	11.6115	0.552301
$443$	−11.4012	−0.541689	−0.270844	−	0.962623i	$-0.587303\pi$
$443$	−11.4012	−0.541689	−0.270844	+	0.962623i	$0.587303\pi$
$444$	−105.557	−5.00953
$445$	2.29454	0.108772
$446$	−10.4993	−0.497154
$447$	20.5511	0.972034
$448$	−57.5173	−2.71744
$449$	−17.9606	−0.847614	−0.423807	−	0.905753i	$-0.639307\pi$
$449$	−17.9606	−0.847614	−0.423807	+	0.905753i	$0.639307\pi$
$450$	2.00611	0.0945687
$451$	35.4782	1.67060
$452$	−46.9569	−2.20867
$453$	0.976182	0.0458650
$454$	6.42423	0.301504
$455$	0.587963	0.0275641
$456$	−38.7029	−1.81243
$457$	−13.3879	−0.626261	−0.313130	−	0.949710i	$-0.601378\pi$
$457$	−13.3879	−0.626261	−0.313130	+	0.949710i	$0.601378\pi$
$458$	60.7215	2.83733
$459$	33.6148	1.56900
$460$	7.97391	0.371786
$461$	−1.08813	−0.0506795	−0.0253397	−	0.999679i	$-0.508067\pi$
$461$	−1.08813	−0.0506795	−0.0253397	+	0.999679i	$0.508067\pi$
$462$	−103.522	−4.81630
$463$	21.7970	1.01299	0.506496	−	0.862242i	$-0.330940\pi$
$463$	21.7970	1.01299	0.506496	+	0.862242i	$0.330940\pi$
$464$	−26.7532	−1.24199
$465$	−2.87005	−0.133096
$466$	−36.8014	−1.70479
$467$	9.67485	0.447699	0.223849	−	0.974624i	$-0.428138\pi$
$467$	9.67485	0.447699	0.223849	+	0.974624i	$0.428138\pi$
$468$	0.506130	0.0233959
$469$	49.3649	2.27946
$470$	−0.604496	−0.0278833
$471$	6.77997	0.312404
$472$	36.5170	1.68083
$473$	30.4727	1.40114
$474$	−57.2236	−2.62836
$475$	−13.4315	−0.616279
$476$	137.643	6.30884
$477$	−0.897514	−0.0410944
$478$	40.3778	1.84684
$479$	7.10692	0.324724	0.162362	−	0.986731i	$-0.448089\pi$
$479$	7.10692	0.324724	0.162362	+	0.986731i	$0.448089\pi$
$480$	5.30049	0.241933
$481$	−7.78179	−0.354819
$482$	−54.2044	−2.46894
$483$	53.3627	2.42809
$484$	88.3332	4.01515
$485$	−3.24982	−0.147567
$486$	4.20522	0.190753
$487$	20.8949	0.946839	0.473419	−	0.880837i	$-0.343019\pi$
$487$	20.8949	0.946839	0.473419	+	0.880837i	$0.343019\pi$
$488$	−122.055	−5.52519
$489$	3.06650	0.138672
$490$	5.71281	0.258078
$491$	−41.7462	−1.88398	−0.941989	−	0.335644i	$-0.891046\pi$
$491$	−41.7462	−1.88398	−0.941989	+	0.335644i	$0.891046\pi$
$492$	−59.3096	−2.67388
$493$	15.8106	0.712076
$494$	−4.73576	−0.213072
$495$	0.177114	0.00796070
$496$	83.8129	3.76331
$497$	−57.9301	−2.59852
$498$	−18.7762	−0.841381
$499$	11.0211	0.493373	0.246687	−	0.969095i	$-0.420658\pi$
$499$	11.0211	0.493373	0.246687	+	0.969095i	$0.420658\pi$
$500$	10.8654	0.485917
$501$	28.2822	1.26355
$502$	−1.36656	−0.0609927
$503$	−16.8863	−0.752924	−0.376462	−	0.926432i	$-0.622859\pi$
$503$	−16.8863	−0.752924	−0.376462	+	0.926432i	$0.622859\pi$
$504$	5.05162	0.225017
$505$	3.83451	0.170634
$506$	−103.502	−4.60121
$507$	−22.3126	−0.990939
$508$	−77.1233	−3.42179
$509$	−44.8155	−1.98641	−0.993206	−	0.116369i	$-0.962874\pi$
$509$	−44.8155	−1.98641	−0.993206	+	0.116369i	$0.962874\pi$
$510$	−6.79269	−0.300786
$511$	14.4711	0.640163
$512$	26.0765	1.15243
$513$	−13.7099	−0.605305
$514$	49.8432	2.19849
$515$	3.71480	0.163694
$516$	−50.9418	−2.24259
$517$	5.61452	0.246926
$518$	−128.915	−5.66419
$519$	−10.5877	−0.464747
$520$	1.14860	0.0503694
$521$	−13.1990	−0.578258	−0.289129	−	0.957290i	$-0.593366\pi$
$521$	−13.1990	−0.578258	−0.289129	+	0.957290i	$0.593366\pi$
$522$	0.963124	0.0421548
$523$	12.3136	0.538435	0.269218	−	0.963079i	$-0.413235\pi$
$523$	12.3136	0.538435	0.269218	+	0.963079i	$0.413235\pi$
$524$	−11.2149	−0.489925
$525$	36.1846	1.57922
$526$	−11.5101	−0.501862
$527$	−49.5318	−2.15764
$528$	−106.755	−4.64590
$529$	30.3520	1.31965
$530$	−3.38066	−0.146847
$531$	−0.693962	−0.0301154
$532$	−56.1378	−2.43388
$533$	−4.37236	−0.189388
$534$	49.7891	2.15459
$535$	−2.88146	−0.124576
$536$	96.4353	4.16537
$537$	−24.6844	−1.06521
$538$	0.206477	0.00890186
$539$	−53.0602	−2.28546
$540$	5.51908	0.237503
$541$	42.9648	1.84720	0.923600	−	0.383358i	$-0.125232\pi$
$541$	42.9648	1.84720	0.923600	+	0.383358i	$0.125232\pi$
$542$	72.0294	3.09393
$543$	5.30631	0.227716
$544$	91.4766	3.92203
$545$	−1.15805	−0.0496056
$546$	12.7582	0.546000
$547$	−28.3018	−1.21010	−0.605048	−	0.796189i	$-0.706846\pi$
$547$	−28.3018	−1.21010	−0.605048	+	0.796189i	$0.706846\pi$
$548$	−66.8837	−2.85713
$549$	2.31952	0.0989946
$550$	−70.1832	−2.99262
$551$	−6.44840	−0.274711
$552$	104.245	4.43697
$553$	−50.0071	−2.12652
$554$	−64.5650	−2.74310
$555$	4.55234	0.193236
$556$	−73.9816	−3.13752
$557$	4.91852	0.208404	0.104202	−	0.994556i	$-0.466771\pi$
$557$	4.91852	0.208404	0.104202	+	0.994556i	$0.466771\pi$
$558$	−3.01729	−0.127732
$559$	−3.75548	−0.158840
$560$	10.0444	0.424455
$561$	63.0900	2.66366
$562$	−85.6861	−3.61445
$563$	−33.4938	−1.41160	−0.705799	−	0.708413i	$-0.749412\pi$
$563$	−33.4938	−1.41160	−0.705799	+	0.708413i	$0.749412\pi$
$564$	−9.38590	−0.395218
$565$	2.02510	0.0851965
$566$	−61.9603	−2.60438
$567$	38.8200	1.63029
$568$	−113.168	−4.74841
$569$	8.00325	0.335514	0.167757	−	0.985828i	$-0.446348\pi$
$569$	8.00325	0.335514	0.167757	+	0.985828i	$0.446348\pi$
$570$	2.77041	0.116040
$571$	15.3924	0.644151	0.322075	−	0.946714i	$-0.395620\pi$
$571$	15.3924	0.644151	0.322075	+	0.946714i	$0.395620\pi$
$572$	−17.7069	−0.740361
$573$	26.5829	1.11052
$574$	−72.4334	−3.02331
$575$	36.1773	1.50870
$576$	2.13529	0.0889706
$577$	0.199898	0.00832187	0.00416093	−	0.999991i	$-0.498676\pi$
$577$	0.199898	0.00832187	0.00416093	+	0.999991i	$0.498676\pi$
$578$	−72.1513	−3.00110
$579$	−16.3227	−0.678346
$580$	2.59589	0.107788
$581$	−16.4083	−0.680732
$582$	−70.5179	−2.92306
$583$	31.3993	1.30043
$584$	28.2696	1.16980
$585$	−0.0218277	−0.000902466 0
$586$	−5.77681	−0.238638
$587$	−16.3971	−0.676779	−0.338390	−	0.941006i	$-0.609882\pi$
$587$	−16.3971	−0.676779	−0.338390	+	0.941006i	$0.609882\pi$
$588$	88.7017	3.65800
$589$	20.2017	0.832395
$590$	−2.61395	−0.107614
$591$	9.42461	0.387677
$592$	−132.940	−5.46380
$593$	42.6130	1.74991	0.874954	−	0.484206i	$-0.160892\pi$
$593$	42.6130	1.74991	0.874954	+	0.484206i	$0.160892\pi$
$594$	−71.6378	−2.93934
$595$	−5.93607	−0.243355
$596$	58.2325	2.38530
$597$	4.32789	0.177129
$598$	12.7556	0.521617
$599$	−0.826956	−0.0337885	−0.0168942	−	0.999857i	$-0.505378\pi$
$599$	−0.826956	−0.0337885	−0.0168942	+	0.999857i	$0.505378\pi$
$600$	70.6874	2.88580
$601$	16.9376	0.690899	0.345449	−	0.938437i	$-0.387726\pi$
$601$	16.9376	0.690899	0.345449	+	0.938437i	$0.387726\pi$
$602$	−62.2141	−2.53566
$603$	−1.83264	−0.0746308
$604$	2.76606	0.112549
$605$	−3.80952	−0.154879
$606$	83.2050	3.37997
$607$	2.79889	0.113603	0.0568017	−	0.998385i	$-0.481910\pi$
$607$	2.79889	0.113603	0.0568017	+	0.998385i	$0.481910\pi$
$608$	−37.3089	−1.51308
$609$	17.3721	0.703952
$610$	8.73692	0.353747
$611$	−0.691938	−0.0279928
$612$	−5.10989	−0.206555
$613$	−12.4757	−0.503888	−0.251944	−	0.967742i	$-0.581070\pi$
$613$	−12.4757	−0.503888	−0.251944	+	0.967742i	$0.581070\pi$
$614$	−14.6968	−0.593115
$615$	2.55783	0.103142
$616$	−176.730	−7.12064
$617$	35.1143	1.41365	0.706825	−	0.707388i	$-0.250127\pi$
$617$	35.1143	1.41365	0.706825	+	0.707388i	$0.250127\pi$
$618$	80.6073	3.24250
$619$	−26.8020	−1.07726	−0.538632	−	0.842541i	$-0.681059\pi$
$619$	−26.8020	−1.07726	−0.538632	+	0.842541i	$0.681059\pi$
$620$	−8.13243	−0.326606
$621$	36.9271	1.48184
$622$	−39.4382	−1.58133
$623$	43.5103	1.74320
$624$	13.1566	0.526684
$625$	24.2960	0.971840
$626$	26.7721	1.07003
$627$	−25.7314	−1.02761
$628$	19.2113	0.766616
$629$	78.5650	3.13259
$630$	−0.361603	−0.0144066
$631$	−2.97231	−0.118326	−0.0591629	−	0.998248i	$-0.518843\pi$
$631$	−2.97231	−0.118326	−0.0591629	+	0.998248i	$0.518843\pi$
$632$	−97.6900	−3.88590
$633$	−20.8870	−0.830183
$634$	64.6534	2.56771
$635$	3.32607	0.131991
$636$	−52.4909	−2.08140
$637$	6.53918	0.259092
$638$	−33.6947	−1.33398
$639$	2.15062	0.0850772
$640$	2.07263	0.0819280
$641$	−21.5840	−0.852517	−0.426258	−	0.904601i	$-0.640169\pi$
$641$	−21.5840	−0.852517	−0.426258	+	0.904601i	$0.640169\pi$
$642$	−62.5248	−2.46766
$643$	5.05821	0.199476	0.0997381	−	0.995014i	$-0.468199\pi$
$643$	5.05821	0.199476	0.0997381	+	0.995014i	$0.468199\pi$
$644$	151.206	5.95834
$645$	2.19695	0.0865050
$646$	47.8122	1.88115
$647$	−17.3582	−0.682422	−0.341211	−	0.939987i	$-0.610837\pi$
$647$	−17.3582	−0.682422	−0.341211	+	0.939987i	$0.610837\pi$
$648$	75.8357	2.97911
$649$	24.2781	0.953000
$650$	8.64944	0.339259
$651$	−54.4235	−2.13303
$652$	8.68907	0.340290
$653$	−1.55806	−0.0609715	−0.0304857	−	0.999535i	$-0.509705\pi$
$653$	−1.55806	−0.0609715	−0.0304857	+	0.999535i	$0.509705\pi$
$654$	−25.1286	−0.982605
$655$	0.483662	0.0188982
$656$	−74.6951	−2.91635
$657$	−0.537230	−0.0209593
$658$	−11.4628	−0.446866
$659$	−27.9486	−1.08872	−0.544362	−	0.838850i	$-0.683228\pi$
$659$	−27.9486	−1.08872	−0.544362	+	0.838850i	$0.683228\pi$
$660$	10.3585	0.403204
$661$	−7.74334	−0.301181	−0.150591	−	0.988596i	$-0.548117\pi$
$661$	−7.74334	−0.301181	−0.150591	+	0.988596i	$0.548117\pi$
$662$	9.94412	0.386489
$663$	−7.77527	−0.301967
$664$	−32.0540	−1.24394
$665$	2.42104	0.0938839
$666$	4.78588	0.185449
$667$	17.3686	0.672515
$668$	80.1388	3.10066
$669$	7.03052	0.271816
$670$	−6.90299	−0.266686
$671$	−81.1478	−3.13268
$672$	100.511	3.87728
$673$	42.6558	1.64426	0.822130	−	0.569300i	$-0.192786\pi$
$673$	42.6558	1.64426	0.822130	+	0.569300i	$0.192786\pi$
$674$	0.261571	0.0100754
$675$	25.0399	0.963784
$676$	−63.2239	−2.43169
$677$	−17.9342	−0.689267	−0.344634	−	0.938737i	$-0.611997\pi$
$677$	−17.9342	−0.689267	−0.344634	+	0.938737i	$0.611997\pi$
$678$	43.9426	1.68760
$679$	−61.6249	−2.36495
$680$	−11.5962	−0.444696
$681$	−4.30179	−0.164845
$682$	105.559	4.04207
$683$	32.0505	1.22638	0.613189	−	0.789936i	$-0.289886\pi$
$683$	32.0505	1.22638	0.613189	+	0.789936i	$0.289886\pi$
$684$	2.08408	0.0796868
$685$	2.88447	0.110210
$686$	31.9578	1.22016
$687$	−40.6604	−1.55129
$688$	−64.1567	−2.44595
$689$	−3.86968	−0.147423
$690$	−7.46203	−0.284075
$691$	−10.3664	−0.394355	−0.197177	−	0.980368i	$-0.563177\pi$
$691$	−10.3664	−0.394355	−0.197177	+	0.980368i	$0.563177\pi$
$692$	−30.0006	−1.14045
$693$	3.35854	0.127580
$694$	−11.9751	−0.454568
$695$	3.19058	0.121026
$696$	33.9367	1.28637
$697$	44.1434	1.67205
$698$	62.4741	2.36468
$699$	24.6430	0.932084
$700$	102.531	3.87530
$701$	−24.6992	−0.932877	−0.466438	−	0.884554i	$-0.654463\pi$
$701$	−24.6992	−0.932877	−0.466438	+	0.884554i	$0.654463\pi$
$702$	8.82871	0.333218
$703$	−32.0429	−1.20852
$704$	−74.7028	−2.81547
$705$	0.404783	0.0152450
$706$	−92.1570	−3.46837
$707$	72.7121	2.73462
$708$	−40.5862	−1.52532
$709$	24.1154	0.905673	0.452837	−	0.891594i	$-0.350412\pi$
$709$	24.1154	0.905673	0.452837	+	0.891594i	$0.350412\pi$
$710$	8.10073	0.304015
$711$	1.85648	0.0696235
$712$	84.9983	3.18544
$713$	−54.4126	−2.03777
$714$	−128.807	−4.82047
$715$	0.763639	0.0285585
$716$	−69.9444	−2.61395
$717$	−27.0378	−1.00975
$718$	−7.62438	−0.284539
$719$	−23.7553	−0.885923	−0.442962	−	0.896541i	$-0.646072\pi$
$719$	−23.7553	−0.885923	−0.442962	+	0.896541i	$0.646072\pi$
$720$	−0.372893	−0.0138969
$721$	70.4420	2.62340
$722$	30.8810	1.14927
$723$	36.2964	1.34988
$724$	15.0357	0.558797
$725$	11.7774	0.437403
$726$	−82.6627	−3.06790
$727$	35.6852	1.32349	0.661746	−	0.749728i	$-0.269816\pi$
$727$	35.6852	1.32349	0.661746	+	0.749728i	$0.269816\pi$
$728$	21.7803	0.807233
$729$	25.4888	0.944031
$730$	−2.02358	−0.0748961
$731$	37.9154	1.40235
$732$	135.656	5.01401
$733$	9.92893	0.366733	0.183367	−	0.983045i	$-0.441300\pi$
$733$	9.92893	0.366733	0.183367	+	0.983045i	$0.441300\pi$
$734$	33.0280	1.21909
$735$	−3.82542	−0.141103
$736$	100.491	3.70413
$737$	64.1145	2.36169
$738$	2.68904	0.0989851
$739$	−32.1232	−1.18167	−0.590836	−	0.806792i	$-0.701202\pi$
$739$	−32.1232	−1.18167	−0.590836	+	0.806792i	$0.701202\pi$
$740$	12.8993	0.474187
$741$	3.17116	0.116495
$742$	−64.1059	−2.35340
$743$	−12.1374	−0.445277	−0.222638	−	0.974901i	$-0.571467\pi$
$743$	−12.1374	−0.445277	−0.222638	+	0.974901i	$0.571467\pi$
$744$	−106.318	−3.89779
$745$	−2.51138	−0.0920097
$746$	85.4739	3.12942
$747$	0.609149	0.0222876
$748$	178.768	6.53642
$749$	−54.6398	−1.99650
$750$	−10.1679	−0.371280
$751$	4.96246	0.181083	0.0905413	−	0.995893i	$-0.471140\pi$
$751$	4.96246	0.181083	0.0905413	+	0.995893i	$0.471140\pi$
$752$	−11.8207	−0.431056
$753$	0.915079	0.0333473
$754$	4.15256	0.151227
$755$	−0.119291	−0.00434144
$756$	104.656	3.80629
$757$	24.4302	0.887931	0.443965	−	0.896044i	$-0.353571\pi$
$757$	24.4302	0.887931	0.443965	+	0.896044i	$0.353571\pi$
$758$	65.3438	2.37339
$759$	69.3068	2.51568
$760$	4.72955	0.171559
$761$	5.48101	0.198686	0.0993432	−	0.995053i	$-0.468326\pi$
$761$	5.48101	0.198686	0.0993432	+	0.995053i	$0.468326\pi$
$762$	72.1724	2.61453
$763$	−21.9596	−0.794992
$764$	75.3238	2.72512
$765$	0.220373	0.00796760
$766$	50.7441	1.83346
$767$	−2.99206	−0.108037
$768$	−4.66870	−0.168467
$769$	−1.21998	−0.0439936	−0.0219968	−	0.999758i	$-0.507002\pi$
$769$	−1.21998	−0.0439936	−0.0219968	+	0.999758i	$0.507002\pi$
$770$	12.6506	0.455896
$771$	−33.3760	−1.20201
$772$	−46.2510	−1.66461
$773$	−1.08909	−0.0391719	−0.0195860	−	0.999808i	$-0.506235\pi$
$773$	−1.08909	−0.0391719	−0.0195860	+	0.999808i	$0.506235\pi$
$774$	2.30966	0.0830189
$775$	−36.8965	−1.32536
$776$	−120.386	−4.32159
$777$	86.3240	3.09685
$778$	78.6176	2.81858
$779$	−18.0040	−0.645059
$780$	−1.27659	−0.0457093
$781$	−75.2389	−2.69226
$782$	−128.781	−4.60519
$783$	12.0215	0.429615
$784$	111.712	3.98971
$785$	−0.828522	−0.0295712
$786$	10.4950	0.374343
$787$	−16.1241	−0.574762	−0.287381	−	0.957816i	$-0.592785\pi$
$787$	−16.1241	−0.574762	−0.287381	+	0.957816i	$0.592785\pi$
$788$	26.7051	0.951329
$789$	7.70737	0.274390
$790$	6.99281	0.248793
$791$	38.4010	1.36538
$792$	6.56098	0.233134
$793$	10.0007	0.355136
$794$	−49.0471	−1.74062
$795$	2.26376	0.0802873
$796$	12.2633	0.434660
$797$	37.6057	1.33206	0.666031	−	0.745924i	$-0.267992\pi$
$797$	37.6057	1.33206	0.666031	+	0.745924i	$0.267992\pi$
$798$	52.5341	1.85969
$799$	6.98581	0.247140
$800$	68.1414	2.40916
$801$	−1.61529	−0.0570735
$802$	−18.2290	−0.643687
$803$	18.7949	0.663256
$804$	−107.181	−3.78000
$805$	−6.52100	−0.229835
$806$	−13.0092	−0.458230
$807$	−0.138261	−0.00486703
$808$	142.045	4.99711
$809$	10.6881	0.375775	0.187887	−	0.982191i	$-0.439836\pi$
$809$	10.6881	0.375775	0.187887	+	0.982191i	$0.439836\pi$
$810$	−5.42844	−0.190736
$811$	14.8284	0.520697	0.260349	−	0.965515i	$-0.416163\pi$
$811$	14.8284	0.520697	0.260349	+	0.965515i	$0.416163\pi$
$812$	49.2246	1.72744
$813$	−48.2324	−1.69158
$814$	−167.433	−5.86852
$815$	−0.374731	−0.0131263
$816$	−132.829	−4.64993
$817$	−15.4639	−0.541012
$818$	49.6707	1.73670
$819$	−0.413909	−0.0144632
$820$	7.24772	0.253101
$821$	−46.7735	−1.63241	−0.816203	−	0.577765i	$-0.803925\pi$
$821$	−46.7735	−1.63241	−0.816203	+	0.577765i	$0.803925\pi$
$822$	62.5901	2.18308
$823$	−36.0880	−1.25795	−0.628975	−	0.777426i	$-0.716525\pi$
$823$	−36.0880	−1.25795	−0.628975	+	0.777426i	$0.716525\pi$
$824$	137.610	4.79387
$825$	46.9961	1.63619
$826$	−49.5670	−1.72466
$827$	−42.3034	−1.47103	−0.735516	−	0.677507i	$-0.763060\pi$
$827$	−42.3034	−1.47103	−0.735516	+	0.677507i	$0.763060\pi$
$828$	−5.61341	−0.195080
$829$	21.2156	0.736848	0.368424	−	0.929658i	$-0.379897\pi$
$829$	21.2156	0.736848	0.368424	+	0.929658i	$0.379897\pi$
$830$	2.29448	0.0796425
$831$	43.2340	1.49977
$832$	9.20644	0.319176
$833$	−66.0196	−2.28744
$834$	69.2324	2.39732
$835$	−3.45612	−0.119604
$836$	−72.9111	−2.52168
$837$	−37.6612	−1.30176
$838$	44.9622	1.55319
$839$	26.8813	0.928045	0.464022	−	0.885823i	$-0.346406\pi$
$839$	26.8813	0.928045	0.464022	+	0.885823i	$0.346406\pi$
$840$	−12.7415	−0.439623
$841$	−23.3457	−0.805024
$842$	15.6874	0.540623
$843$	57.3772	1.97618
$844$	−59.1842	−2.03720
$845$	2.72664	0.0937992
$846$	0.425548	0.0146307
$847$	−72.2382	−2.48213
$848$	−66.1076	−2.27014
$849$	41.4899	1.42393
$850$	−87.3247	−2.99521
$851$	86.3066	2.95855
$852$	125.778	4.30910
$853$	17.3676	0.594655	0.297327	−	0.954776i	$-0.403905\pi$
$853$	17.3676	0.594655	0.297327	+	0.954776i	$0.403905\pi$
$854$	165.674	5.66925
$855$	−0.0898795	−0.00307381
$856$	−106.740	−3.64830
$857$	−31.3359	−1.07042	−0.535208	−	0.844721i	$-0.679767\pi$
$857$	−31.3359	−1.07042	−0.535208	+	0.844721i	$0.679767\pi$
$858$	16.5702	0.565697
$859$	−28.7848	−0.982126	−0.491063	−	0.871124i	$-0.663392\pi$
$859$	−28.7848	−0.982126	−0.491063	+	0.871124i	$0.663392\pi$
$860$	6.22517	0.212277
$861$	48.5029	1.65297
$862$	−40.6017	−1.38290
$863$	20.2164	0.688173	0.344087	−	0.938938i	$-0.388189\pi$
$863$	20.2164	0.688173	0.344087	+	0.938938i	$0.388189\pi$
$864$	69.5537	2.36627
$865$	1.29383	0.0439915
$866$	52.1628	1.77256
$867$	48.3140	1.64083
$868$	−154.212	−5.23428
$869$	−64.9487	−2.20323
$870$	−2.42924	−0.0823591
$871$	−7.90153	−0.267733
$872$	−42.8986	−1.45273
$873$	2.28779	0.0774298
$874$	52.5235	1.77663
$875$	−8.88566	−0.300390
$876$	−31.4198	−1.06158
$877$	49.4373	1.66938	0.834689	−	0.550721i	$-0.185647\pi$
$877$	49.4373	1.66938	0.834689	+	0.550721i	$0.185647\pi$
$878$	−9.96989	−0.336467
$879$	3.86827	0.130474
$880$	13.0456	0.439767
$881$	18.7808	0.632740	0.316370	−	0.948636i	$-0.397536\pi$
$881$	18.7808	0.632740	0.316370	+	0.948636i	$0.397536\pi$
$882$	−4.02166	−0.135416
$883$	−48.3151	−1.62593	−0.812966	−	0.582310i	$-0.802149\pi$
$883$	−48.3151	−1.62593	−0.812966	+	0.582310i	$0.802149\pi$
$884$	−22.0316	−0.741003
$885$	1.75035	0.0588374
$886$	30.2320	1.01567
$887$	−2.29120	−0.0769311	−0.0384655	−	0.999260i	$-0.512247\pi$
$887$	−2.29120	−0.0769311	−0.0384655	+	0.999260i	$0.512247\pi$
$888$	168.636	5.65905
$889$	63.0708	2.11533
$890$	−6.08431	−0.203946
$891$	50.4190	1.68910
$892$	19.9213	0.667015
$893$	−2.84917	−0.0953440
$894$	−54.4943	−1.82256
$895$	3.01647	0.100830
$896$	39.3024	1.31300
$897$	−8.54143	−0.285190
$898$	47.6252	1.58927
$899$	−17.7139	−0.590791
$900$	−3.80639	−0.126880
$901$	39.0683	1.30155
$902$	−94.0757	−3.13238
$903$	41.6598	1.38635
$904$	75.0172	2.49503
$905$	−0.648440	−0.0215549
$906$	−2.58849	−0.0859968
$907$	−25.2039	−0.836881	−0.418441	−	0.908244i	$-0.637423\pi$
$907$	−25.2039	−0.836881	−0.418441	+	0.908244i	$0.637423\pi$
$908$	−12.1893	−0.404517
$909$	−2.69939	−0.0895331
$910$	−1.55907	−0.0516827
$911$	−38.4953	−1.27540	−0.637702	−	0.770283i	$-0.720115\pi$
$911$	−38.4953	−1.27540	−0.637702	+	0.770283i	$0.720115\pi$
$912$	54.1744	1.79389
$913$	−21.3109	−0.705289
$914$	35.5001	1.17424
$915$	−5.85042	−0.193409
$916$	−115.213	−3.80675
$917$	9.17145	0.302868
$918$	−89.1346	−2.94188
$919$	−51.5224	−1.69957	−0.849783	−	0.527133i	$-0.823267\pi$
$919$	−51.5224	−1.69957	−0.849783	+	0.527133i	$0.823267\pi$
$920$	−12.7389	−0.419990
$921$	9.84128	0.324281
$922$	2.88535	0.0950239
$923$	9.27251	0.305209
$924$	196.423	6.46186
$925$	58.5235	1.92424
$926$	−57.7980	−1.89936
$927$	−2.61511	−0.0858916
$928$	32.7144	1.07390
$929$	−11.7848	−0.386647	−0.193323	−	0.981135i	$-0.561927\pi$
$929$	−11.7848	−0.386647	−0.193323	+	0.981135i	$0.561927\pi$
$930$	7.61038	0.249554
$931$	26.9262	0.882471
$932$	69.8271	2.28726
$933$	26.4086	0.864579
$934$	−25.6543	−0.839435
$935$	−7.70970	−0.252134
$936$	−0.808581	−0.0264293
$937$	−47.5576	−1.55364	−0.776820	−	0.629722i	$-0.783169\pi$
$937$	−47.5576	−1.55364	−0.776820	+	0.629722i	$0.783169\pi$
$938$	−130.898	−4.27398
$939$	−17.9272	−0.585031
$940$	1.14697	0.0374101
$941$	2.76175	0.0900305	0.0450153	−	0.998986i	$-0.485666\pi$
$941$	2.76175	0.0900305	0.0450153	+	0.998986i	$0.485666\pi$
$942$	−17.9781	−0.585758
$943$	48.4932	1.57916
$944$	−51.1147	−1.66364
$945$	−4.51346	−0.146823
$946$	−80.8029	−2.62713
$947$	−44.8446	−1.45725	−0.728627	−	0.684910i	$-0.759841\pi$
$947$	−44.8446	−1.45725	−0.728627	+	0.684910i	$0.759841\pi$
$948$	108.576	3.52638
$949$	−2.31630	−0.0751902
$950$	35.6156	1.15552
$951$	−43.2932	−1.40388
$952$	−219.894	−7.12681
$953$	−6.69222	−0.216782	−0.108391	−	0.994108i	$-0.534570\pi$
$953$	−6.69222	−0.216782	−0.108391	+	0.994108i	$0.534570\pi$
$954$	2.37989	0.0770519
$955$	−3.24847	−0.105118
$956$	−76.6129	−2.47784
$957$	22.5626	0.729347
$958$	−18.8451	−0.608856
$959$	54.6970	1.76626
$960$	−5.38576	−0.173825
$961$	24.4943	0.790139
$962$	20.6346	0.665286
$963$	2.02847	0.0653665
$964$	102.847	3.31249
$965$	1.99465	0.0642101
$966$	−141.499	−4.55266
$967$	−25.3316	−0.814609	−0.407305	−	0.913292i	$-0.633531\pi$
$967$	−25.3316	−0.814609	−0.407305	+	0.913292i	$0.633531\pi$
$968$	−141.119	−4.53573
$969$	−32.0160	−1.02850
$970$	8.61739	0.276688
$971$	27.5351	0.883642	0.441821	−	0.897103i	$-0.354333\pi$
$971$	27.5351	0.883642	0.441821	+	0.897103i	$0.354333\pi$
$972$	−7.97899	−0.255926
$973$	60.5016	1.93959
$974$	−55.4060	−1.77532
$975$	−5.79184	−0.185487
$976$	170.847	5.46868
$977$	48.0725	1.53798	0.768988	−	0.639263i	$-0.220761\pi$
$977$	48.0725	1.53798	0.768988	+	0.639263i	$0.220761\pi$
$978$	−8.13128	−0.260010
$979$	56.5106	1.80609
$980$	−10.8395	−0.346255
$981$	0.815238	0.0260285
$982$	110.696	3.53246
$983$	58.7646	1.87430	0.937150	−	0.348927i	$-0.113454\pi$
$983$	58.7646	1.87430	0.937150	+	0.348927i	$0.113454\pi$
$984$	94.7515	3.02057
$985$	−1.15170	−0.0366963
$986$	−41.9243	−1.33514
$987$	7.67571	0.244321
$988$	8.98563	0.285871
$989$	41.6515	1.32444
$990$	−0.469645	−0.0149263
$991$	−48.2629	−1.53312	−0.766561	−	0.642172i	$-0.778034\pi$
$991$	−48.2629	−1.53312	−0.766561	+	0.642172i	$0.778034\pi$
$992$	−102.488	−3.25401
$993$	−6.65879	−0.211310
$994$	153.610	4.87222
$995$	−0.528874	−0.0167664
$996$	35.6259	1.12885
$997$	−31.1815	−0.987527	−0.493763	−	0.869596i	$-0.664379\pi$
$997$	−31.1815	−0.987527	−0.493763	+	0.869596i	$0.664379\pi$
$998$	−29.2241	−0.925074
$999$	59.7365	1.88998

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8039.2.a.b.1.15	✓	391

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8039.2.a.b.1.15	✓	391	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:	\( N \)	\(=\)	\( 8039 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8039.a (trivial)

\(f(q)\)	\(=\)	\(q-2.65165 q^{2} +1.77560 q^{3} +5.03124 q^{4} -0.216981 q^{5} -4.70826 q^{6} -4.11451 q^{7} -8.03778 q^{8} +0.152748 q^{9} +O(q^{10})\)	\(q-2.65165 q^{2} +1.77560 q^{3} +5.03124 q^{4} -0.216981 q^{5} -4.70826 q^{6} -4.11451 q^{7} -8.03778 q^{8} +0.152748 q^{9} +0.575357 q^{10} -5.34387 q^{11} +8.93346 q^{12} +0.658583 q^{13} +10.9102 q^{14} -0.385271 q^{15} +11.2509 q^{16} -6.64906 q^{17} -0.405035 q^{18} +2.71183 q^{19} -1.09168 q^{20} -7.30571 q^{21} +14.1701 q^{22} -7.30424 q^{23} -14.2719 q^{24} -4.95292 q^{25} -1.74633 q^{26} -5.05557 q^{27} -20.7011 q^{28} -2.37788 q^{29} +1.02160 q^{30} +7.44945 q^{31} -13.7578 q^{32} -9.48857 q^{33} +17.6310 q^{34} +0.892769 q^{35} +0.768514 q^{36} -11.8160 q^{37} -7.19082 q^{38} +1.16938 q^{39} +1.74404 q^{40} -6.63904 q^{41} +19.3722 q^{42} -5.70237 q^{43} -26.8863 q^{44} -0.0331435 q^{45} +19.3683 q^{46} -1.05065 q^{47} +19.9770 q^{48} +9.92916 q^{49} +13.1334 q^{50} -11.8061 q^{51} +3.31349 q^{52} -5.87577 q^{53} +13.4056 q^{54} +1.15952 q^{55} +33.0715 q^{56} +4.81512 q^{57} +6.30529 q^{58} -4.54317 q^{59} -1.93839 q^{60} +15.1852 q^{61} -19.7533 q^{62} -0.628484 q^{63} +13.9792 q^{64} -0.142900 q^{65} +25.1603 q^{66} -11.9978 q^{67} -33.4530 q^{68} -12.9694 q^{69} -2.36731 q^{70} +14.0795 q^{71} -1.22776 q^{72} -3.51709 q^{73} +31.3318 q^{74} -8.79439 q^{75} +13.6439 q^{76} +21.9874 q^{77} -3.10078 q^{78} +12.1539 q^{79} -2.44123 q^{80} -9.43491 q^{81} +17.6044 q^{82} +3.98792 q^{83} -36.7568 q^{84} +1.44272 q^{85} +15.1207 q^{86} -4.22215 q^{87} +42.9528 q^{88} -10.5748 q^{89} +0.0878848 q^{90} -2.70975 q^{91} -36.7494 q^{92} +13.2272 q^{93} +2.78594 q^{94} -0.588415 q^{95} -24.4284 q^{96} +14.9775 q^{97} -26.3286 q^{98} -0.816268 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 391 q + 14 q^{2} + 12 q^{3} + 446 q^{4} + 22 q^{5} + 40 q^{6} + 63 q^{7} + 36 q^{8} + 501 q^{9}+O(q^{10}) \) 391 * q + 14 * q^2 + 12 * q^3 + 446 * q^4 + 22 * q^5 + 40 * q^6 + 63 * q^7 + 36 * q^8 + 501 * q^9	\( 391 q + 14 q^{2} + 12 q^{3} + 446 q^{4} + 22 q^{5} + 40 q^{6} + 63 q^{7} + 36 q^{8} + 501 q^{9} + 40 q^{10} + 57 q^{11} + 20 q^{12} + 83 q^{13} + 21 q^{14} + 60 q^{15} + 548 q^{16} + 59 q^{17} + 54 q^{18} + 131 q^{19} + 35 q^{20} + 121 q^{21} + 89 q^{22} + 34 q^{23} + 110 q^{24} + 609 q^{25} + 54 q^{26} + 27 q^{27} + 182 q^{28} + 102 q^{29} + 92 q^{30} + 88 q^{31} + 76 q^{32} + 131 q^{33} + 128 q^{34} + 31 q^{35} + 654 q^{36} + 135 q^{37} + 23 q^{38} + 96 q^{39} + 113 q^{40} + 128 q^{41} + 45 q^{42} + 140 q^{43} + 151 q^{44} + 77 q^{45} + 245 q^{46} + 22 q^{47} + 25 q^{48} + 712 q^{49} + 53 q^{50} + 102 q^{51} + 174 q^{52} + 54 q^{53} + 131 q^{54} + 101 q^{55} + 43 q^{56} + 226 q^{57} + 109 q^{58} + 40 q^{59} + 123 q^{60} + 249 q^{61} + 28 q^{62} + 139 q^{63} + 730 q^{64} + 227 q^{65} + 55 q^{66} + 169 q^{67} + 48 q^{68} + 89 q^{69} + 98 q^{70} + 66 q^{71} + 120 q^{72} + 324 q^{73} + 60 q^{74} + 19 q^{75} + 356 q^{76} + 83 q^{77} - 11 q^{78} + 195 q^{79} + 26 q^{80} + 807 q^{81} + 49 q^{82} + 74 q^{83} + 252 q^{84} + 373 q^{85} + 100 q^{86} + 43 q^{87} + 211 q^{88} + 207 q^{89} + 10 q^{90} + 189 q^{91} + 30 q^{92} + 172 q^{93} + 130 q^{94} + 43 q^{95} + 203 q^{96} + 254 q^{97} + 26 q^{98} + 273 q^{99}+O(q^{100}) \) 391 * q + 14 * q^2 + 12 * q^3 + 446 * q^4 + 22 * q^5 + 40 * q^6 + 63 * q^7 + 36 * q^8 + 501 * q^9 + 40 * q^10 + 57 * q^11 + 20 * q^12 + 83 * q^13 + 21 * q^14 + 60 * q^15 + 548 * q^16 + 59 * q^17 + 54 * q^18 + 131 * q^19 + 35 * q^20 + 121 * q^21 + 89 * q^22 + 34 * q^23 + 110 * q^24 + 609 * q^25 + 54 * q^26 + 27 * q^27 + 182 * q^28 + 102 * q^29 + 92 * q^30 + 88 * q^31 + 76 * q^32 + 131 * q^33 + 128 * q^34 + 31 * q^35 + 654 * q^36 + 135 * q^37 + 23 * q^38 + 96 * q^39 + 113 * q^40 + 128 * q^41 + 45 * q^42 + 140 * q^43 + 151 * q^44 + 77 * q^45 + 245 * q^46 + 22 * q^47 + 25 * q^48 + 712 * q^49 + 53 * q^50 + 102 * q^51 + 174 * q^52 + 54 * q^53 + 131 * q^54 + 101 * q^55 + 43 * q^56 + 226 * q^57 + 109 * q^58 + 40 * q^59 + 123 * q^60 + 249 * q^61 + 28 * q^62 + 139 * q^63 + 730 * q^64 + 227 * q^65 + 55 * q^66 + 169 * q^67 + 48 * q^68 + 89 * q^69 + 98 * q^70 + 66 * q^71 + 120 * q^72 + 324 * q^73 + 60 * q^74 + 19 * q^75 + 356 * q^76 + 83 * q^77 - 11 * q^78 + 195 * q^79 + 26 * q^80 + 807 * q^81 + 49 * q^82 + 74 * q^83 + 252 * q^84 + 373 * q^85 + 100 * q^86 + 43 * q^87 + 211 * q^88 + 207 * q^89 + 10 * q^90 + 189 * q^91 + 30 * q^92 + 172 * q^93 + 130 * q^94 + 43 * q^95 + 203 * q^96 + 254 * q^97 + 26 * q^98 + 273 * q^99

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