LMFDB - Embedded newform 6029.2.a.a.1.16

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6029,2,Mod(1,6029)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6029, 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("6029.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6029 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6029.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:	$48.1418073786$
Analytic rank:	$1$
Dimension:	$234$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.16
Character	$\chi$	$=$	6029.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.49760 q^{2} -0.682777 q^{3} +4.23800 q^{4} -3.80739 q^{5} +1.70530 q^{6} -3.54561 q^{7} -5.58962 q^{8} -2.53382 q^{9} +O(q^{10})$	\(q-2.49760 q^{2} -0.682777 q^{3} +4.23800 q^{4} -3.80739 q^{5} +1.70530 q^{6} -3.54561 q^{7} -5.58962 q^{8} -2.53382 q^{9} +9.50934 q^{10} -0.967704 q^{11} -2.89361 q^{12} -4.86783 q^{13} +8.85551 q^{14} +2.59960 q^{15} +5.48462 q^{16} -7.77370 q^{17} +6.32845 q^{18} -8.45475 q^{19} -16.1357 q^{20} +2.42086 q^{21} +2.41694 q^{22} +6.34840 q^{23} +3.81646 q^{24} +9.49625 q^{25} +12.1579 q^{26} +3.77836 q^{27} -15.0263 q^{28} -4.98093 q^{29} -6.49276 q^{30} -4.41372 q^{31} -2.51915 q^{32} +0.660726 q^{33} +19.4156 q^{34} +13.4995 q^{35} -10.7383 q^{36} +4.65744 q^{37} +21.1166 q^{38} +3.32365 q^{39} +21.2819 q^{40} +9.15045 q^{41} -6.04634 q^{42} -1.48723 q^{43} -4.10113 q^{44} +9.64723 q^{45} -15.8557 q^{46} +4.54244 q^{47} -3.74478 q^{48} +5.57135 q^{49} -23.7178 q^{50} +5.30771 q^{51} -20.6299 q^{52} +1.51150 q^{53} -9.43683 q^{54} +3.68443 q^{55} +19.8186 q^{56} +5.77271 q^{57} +12.4404 q^{58} -3.54900 q^{59} +11.0171 q^{60} -2.15353 q^{61} +11.0237 q^{62} +8.98392 q^{63} -4.67742 q^{64} +18.5338 q^{65} -1.65023 q^{66} +14.1930 q^{67} -32.9449 q^{68} -4.33454 q^{69} -33.7164 q^{70} -4.68579 q^{71} +14.1631 q^{72} -7.41318 q^{73} -11.6324 q^{74} -6.48382 q^{75} -35.8312 q^{76} +3.43110 q^{77} -8.30113 q^{78} +0.734166 q^{79} -20.8821 q^{80} +5.02166 q^{81} -22.8541 q^{82} +13.0677 q^{83} +10.2596 q^{84} +29.5976 q^{85} +3.71449 q^{86} +3.40087 q^{87} +5.40910 q^{88} -12.9481 q^{89} -24.0949 q^{90} +17.2594 q^{91} +26.9045 q^{92} +3.01359 q^{93} -11.3452 q^{94} +32.1906 q^{95} +1.72002 q^{96} -10.6495 q^{97} -13.9150 q^{98} +2.45198 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 234 q - 10 q^{2} - 43 q^{3} + 202 q^{4} - 24 q^{5} - 40 q^{6} - 61 q^{7} - 27 q^{8} + 203 q^{9}+O(q^{10}) $ 234 * q - 10 * q^2 - 43 * q^3 + 202 * q^4 - 24 * q^5 - 40 * q^6 - 61 * q^7 - 27 * q^8 + 203 * q^9	\( 234 q - 10 q^{2} - 43 q^{3} + 202 q^{4} - 24 q^{5} - 40 q^{6} - 61 q^{7} - 27 q^{8} + 203 q^{9} - 89 q^{10} - 55 q^{11} - 75 q^{12} - 49 q^{13} - 42 q^{14} - 43 q^{15} + 142 q^{16} - 40 q^{17} - 30 q^{18} - 235 q^{19} - 62 q^{20} - 62 q^{21} - 63 q^{22} - 30 q^{23} - 108 q^{24} + 170 q^{25} - 44 q^{26} - 160 q^{27} - 147 q^{28} - 76 q^{29} - 15 q^{30} - 175 q^{31} - 49 q^{32} - 43 q^{33} - 104 q^{34} - 87 q^{35} + 124 q^{36} - 77 q^{37} - 18 q^{38} - 104 q^{39} - 247 q^{40} - 60 q^{41} - 6 q^{42} - 201 q^{43} - 89 q^{44} - 102 q^{45} - 128 q^{46} - 27 q^{47} - 130 q^{48} + 123 q^{49} - 33 q^{50} - 220 q^{51} - 125 q^{52} - 34 q^{53} - 126 q^{54} - 176 q^{55} - 125 q^{56} - 17 q^{57} - 46 q^{58} - 172 q^{59} - 61 q^{60} - 243 q^{61} - 37 q^{62} - 137 q^{63} + 39 q^{64} - 31 q^{65} - 142 q^{66} - 132 q^{67} - 106 q^{68} - 115 q^{69} - 60 q^{70} - 68 q^{71} - 66 q^{72} - 109 q^{73} - 74 q^{74} - 256 q^{75} - 412 q^{76} - 32 q^{77} - 38 q^{78} - 297 q^{79} - 111 q^{80} + 142 q^{81} - 94 q^{82} - 100 q^{83} - 134 q^{84} - 90 q^{85} + q^{86} - 103 q^{87} - 143 q^{88} - 77 q^{89} - 181 q^{90} - 418 q^{91} - 19 q^{92} + 5 q^{93} - 231 q^{94} - 92 q^{95} - 189 q^{96} - 141 q^{97} - 25 q^{98} - 244 q^{99}+O(q^{100}) \) 234 * q - 10 * q^2 - 43 * q^3 + 202 * q^4 - 24 * q^5 - 40 * q^6 - 61 * q^7 - 27 * q^8 + 203 * q^9 - 89 * q^10 - 55 * q^11 - 75 * q^12 - 49 * q^13 - 42 * q^14 - 43 * q^15 + 142 * q^16 - 40 * q^17 - 30 * q^18 - 235 * q^19 - 62 * q^20 - 62 * q^21 - 63 * q^22 - 30 * q^23 - 108 * q^24 + 170 * q^25 - 44 * q^26 - 160 * q^27 - 147 * q^28 - 76 * q^29 - 15 * q^30 - 175 * q^31 - 49 * q^32 - 43 * q^33 - 104 * q^34 - 87 * q^35 + 124 * q^36 - 77 * q^37 - 18 * q^38 - 104 * q^39 - 247 * q^40 - 60 * q^41 - 6 * q^42 - 201 * q^43 - 89 * q^44 - 102 * q^45 - 128 * q^46 - 27 * q^47 - 130 * q^48 + 123 * q^49 - 33 * q^50 - 220 * q^51 - 125 * q^52 - 34 * q^53 - 126 * q^54 - 176 * q^55 - 125 * q^56 - 17 * q^57 - 46 * q^58 - 172 * q^59 - 61 * q^60 - 243 * q^61 - 37 * q^62 - 137 * q^63 + 39 * q^64 - 31 * q^65 - 142 * q^66 - 132 * q^67 - 106 * q^68 - 115 * q^69 - 60 * q^70 - 68 * q^71 - 66 * q^72 - 109 * q^73 - 74 * q^74 - 256 * q^75 - 412 * q^76 - 32 * q^77 - 38 * q^78 - 297 * q^79 - 111 * q^80 + 142 * q^81 - 94 * q^82 - 100 * q^83 - 134 * q^84 - 90 * q^85 + q^86 - 103 * q^87 - 143 * q^88 - 77 * q^89 - 181 * q^90 - 418 * q^91 - 19 * q^92 + 5 * q^93 - 231 * q^94 - 92 * q^95 - 189 * q^96 - 141 * q^97 - 25 * q^98 - 244 * 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 $

$2$	−2.49760	−1.76607	−0.883034	−	0.469308i	$-0.844503\pi$
$2$	−2.49760	−1.76607	−0.883034	+	0.469308i	$0.844503\pi$
$3$	−0.682777	−0.394202	−0.197101	−	0.980383i	$-0.563153\pi$
$3$	−0.682777	−0.394202	−0.197101	+	0.980383i	$0.563153\pi$
$4$	4.23800	2.11900
$5$	−3.80739	−1.70272	−0.851359	−	0.524583i	$-0.824221\pi$
$5$	−3.80739	−1.70272	−0.851359	+	0.524583i	$0.824221\pi$
$6$	1.70530	0.696187
$7$	−3.54561	−1.34011	−0.670057	−	0.742309i	$-0.733730\pi$
$7$	−3.54561	−1.34011	−0.670057	+	0.742309i	$0.733730\pi$
$8$	−5.58962	−1.97623
$9$	−2.53382	−0.844605
$10$	9.50934	3.00712
$11$	−0.967704	−0.291774	−0.145887	−	0.989301i	$-0.546604\pi$
$11$	−0.967704	−0.291774	−0.145887	+	0.989301i	$0.546604\pi$
$12$	−2.89361	−0.835313
$13$	−4.86783	−1.35009	−0.675047	−	0.737775i	$-0.735877\pi$
$13$	−4.86783	−1.35009	−0.675047	+	0.737775i	$0.735877\pi$
$14$	8.85551	2.36673
$15$	2.59960	0.671214
$16$	5.48462	1.37116
$17$	−7.77370	−1.88540	−0.942700	−	0.333642i	$-0.891722\pi$
$17$	−7.77370	−1.88540	−0.942700	+	0.333642i	$0.891722\pi$
$18$	6.32845	1.49163
$19$	−8.45475	−1.93965	−0.969826	−	0.243797i	$-0.921607\pi$
$19$	−8.45475	−1.93965	−0.969826	+	0.243797i	$0.921607\pi$
$20$	−16.1357	−3.60806
$21$	2.42086	0.528275
$22$	2.41694	0.515293
$23$	6.34840	1.32373	0.661866	−	0.749622i	$-0.269765\pi$
$23$	6.34840	1.32373	0.661866	+	0.749622i	$0.269765\pi$
$24$	3.81646	0.779032
$25$	9.49625	1.89925
$26$	12.1579	2.38436
$27$	3.77836	0.727146
$28$	−15.0263	−2.83970
$29$	−4.98093	−0.924936	−0.462468	−	0.886636i	$-0.653036\pi$
$29$	−4.98093	−0.924936	−0.462468	+	0.886636i	$0.653036\pi$
$30$	−6.49276	−1.18541
$31$	−4.41372	−0.792728	−0.396364	−	0.918093i	$-0.629728\pi$
$31$	−4.41372	−0.792728	−0.396364	+	0.918093i	$0.629728\pi$
$32$	−2.51915	−0.445327
$33$	0.660726	0.115018
$34$	19.4156	3.32975
$35$	13.4995	2.28184
$36$	−10.7383	−1.78972
$37$	4.65744	0.765679	0.382839	−	0.923815i	$-0.374946\pi$
$37$	4.65744	0.765679	0.382839	+	0.923815i	$0.374946\pi$
$38$	21.1166	3.42556
$39$	3.32365	0.532209
$40$	21.2819	3.36496
$41$	9.15045	1.42906	0.714530	−	0.699605i	$-0.246641\pi$
$41$	9.15045	1.42906	0.714530	+	0.699605i	$0.246641\pi$
$42$	−6.04634	−0.932971
$43$	−1.48723	−0.226800	−0.113400	−	0.993549i	$-0.536174\pi$
$43$	−1.48723	−0.226800	−0.113400	+	0.993549i	$0.536174\pi$
$44$	−4.10113	−0.618268
$45$	9.64723	1.43812
$46$	−15.8557	−2.33780
$47$	4.54244	0.662583	0.331292	−	0.943528i	$-0.392516\pi$
$47$	4.54244	0.662583	0.331292	+	0.943528i	$0.392516\pi$
$48$	−3.74478	−0.540512
$49$	5.57135	0.795907
$50$	−23.7178	−3.35421
$51$	5.30771	0.743228
$52$	−20.6299	−2.86085
$53$	1.51150	0.207621	0.103810	−	0.994597i	$-0.466896\pi$
$53$	1.51150	0.207621	0.103810	+	0.994597i	$0.466896\pi$
$54$	−9.43683	−1.28419
$55$	3.68443	0.496809
$56$	19.8186	2.64837
$57$	5.77271	0.764614
$58$	12.4404	1.63350
$59$	−3.54900	−0.462041	−0.231020	−	0.972949i	$-0.574206\pi$
$59$	−3.54900	−0.462041	−0.231020	+	0.972949i	$0.574206\pi$
$60$	11.0171	1.42230
$61$	−2.15353	−0.275731	−0.137865	−	0.990451i	$-0.544024\pi$
$61$	−2.15353	−0.275731	−0.137865	+	0.990451i	$0.544024\pi$
$62$	11.0237	1.40001
$63$	8.98392	1.13187
$64$	−4.67742	−0.584677
$65$	18.5338	2.29883
$66$	−1.65023	−0.203129
$67$	14.1930	1.73396	0.866978	−	0.498346i	$-0.166059\pi$
$67$	14.1930	1.73396	0.866978	+	0.498346i	$0.166059\pi$
$68$	−32.9449	−3.99516
$69$	−4.33454	−0.521818
$70$	−33.7164	−4.02988
$71$	−4.68579	−0.556100	−0.278050	−	0.960567i	$-0.589688\pi$
$71$	−4.68579	−0.556100	−0.278050	+	0.960567i	$0.589688\pi$
$72$	14.1631	1.66913
$73$	−7.41318	−0.867647	−0.433823	−	0.900998i	$-0.642836\pi$
$73$	−7.41318	−0.867647	−0.433823	+	0.900998i	$0.642836\pi$
$74$	−11.6324	−1.35224
$75$	−6.48382	−0.748688
$76$	−35.8312	−4.11012
$77$	3.43110	0.391010
$78$	−8.30113	−0.939918
$79$	0.734166	0.0826001	0.0413000	−	0.999147i	$-0.486850\pi$
$79$	0.734166	0.0826001	0.0413000	+	0.999147i	$0.486850\pi$
$80$	−20.8821	−2.33469
$81$	5.02166	0.557963
$82$	−22.8541	−2.52382
$83$	13.0677	1.43437	0.717184	−	0.696884i	$-0.245431\pi$
$83$	13.0677	1.43437	0.717184	+	0.696884i	$0.245431\pi$
$84$	10.2596	1.11941
$85$	29.5976	3.21031
$86$	3.71449	0.400544
$87$	3.40087	0.364611
$88$	5.40910	0.576612
$89$	−12.9481	−1.37249	−0.686246	−	0.727369i	$-0.740743\pi$
$89$	−12.9481	−1.37249	−0.686246	+	0.727369i	$0.740743\pi$
$90$	−24.0949	−2.53983
$91$	17.2594	1.80928
$92$	26.9045	2.80499
$93$	3.01359	0.312495
$94$	−11.3452	−1.17017
$95$	32.1906	3.30268
$96$	1.72002	0.175549
$97$	−10.6495	−1.08129	−0.540646	−	0.841250i	$-0.681820\pi$
$97$	−10.6495	−1.08129	−0.540646	+	0.841250i	$0.681820\pi$
$98$	−13.9150	−1.40563
$99$	2.45198	0.246434
$100$	40.2451	4.02451
$101$	−1.63459	−0.162648	−0.0813241	−	0.996688i	$-0.525915\pi$
$101$	−1.63459	−0.162648	−0.0813241	+	0.996688i	$0.525915\pi$
$102$	−13.2565	−1.31259
$103$	−11.2334	−1.10686	−0.553428	−	0.832897i	$-0.686681\pi$
$103$	−11.2334	−1.10686	−0.553428	+	0.832897i	$0.686681\pi$
$104$	27.2093	2.66809
$105$	−9.21718	−0.899504
$106$	−3.77512	−0.366673
$107$	7.77832	0.751959	0.375979	−	0.926628i	$-0.377306\pi$
$107$	7.77832	0.751959	0.375979	+	0.926628i	$0.377306\pi$
$108$	16.0127	1.54082
$109$	14.9036	1.42751	0.713753	−	0.700398i	$-0.246994\pi$
$109$	14.9036	1.42751	0.713753	+	0.700398i	$0.246994\pi$
$110$	−9.20223	−0.877398
$111$	−3.17999	−0.301832
$112$	−19.4463	−1.83751
$113$	−15.8035	−1.48667	−0.743334	−	0.668920i	$-0.766757\pi$
$113$	−15.8035	−1.48667	−0.743334	+	0.668920i	$0.766757\pi$
$114$	−14.4179	−1.35036
$115$	−24.1709	−2.25394
$116$	−21.1092	−1.95994
$117$	12.3342	1.14030
$118$	8.86398	0.815995
$119$	27.5625	2.52665
$120$	−14.5308	−1.32647
$121$	−10.0635	−0.914868
$122$	5.37864	0.486959
$123$	−6.24772	−0.563338
$124$	−18.7053	−1.67979
$125$	−17.1190	−1.53117
$126$	−22.4382	−1.99896
$127$	−5.30229	−0.470502	−0.235251	−	0.971935i	$-0.575591\pi$
$127$	−5.30229	−0.470502	−0.235251	+	0.971935i	$0.575591\pi$
$128$	16.7206	1.47791
$129$	1.01544	0.0894048
$130$	−46.2899	−4.05989
$131$	2.58711	0.226037	0.113018	−	0.993593i	$-0.463948\pi$
$131$	2.58711	0.226037	0.113018	+	0.993593i	$0.463948\pi$
$132$	2.80016	0.243722
$133$	29.9772	2.59936
$134$	−35.4485	−3.06229
$135$	−14.3857	−1.23813
$136$	43.4520	3.72598
$137$	16.4793	1.40792	0.703962	−	0.710238i	$-0.251413\pi$
$137$	16.4793	1.40792	0.703962	+	0.710238i	$0.251413\pi$
$138$	10.8259	0.921566
$139$	−20.5204	−1.74051	−0.870257	−	0.492597i	$-0.836048\pi$
$139$	−20.5204	−1.74051	−0.870257	+	0.492597i	$0.836048\pi$
$140$	57.2110	4.83521
$141$	−3.10148	−0.261192
$142$	11.7032	0.982112
$143$	4.71062	0.393922
$144$	−13.8970	−1.15808
$145$	18.9644	1.57491
$146$	18.5151	1.53232
$147$	−3.80399	−0.313748
$148$	19.7382	1.62247
$149$	19.9675	1.63580	0.817902	−	0.575358i	$-0.195137\pi$
$149$	19.9675	1.63580	0.817902	+	0.575358i	$0.195137\pi$
$150$	16.1940	1.32223
$151$	4.07904	0.331947	0.165974	−	0.986130i	$-0.446923\pi$
$151$	4.07904	0.331947	0.165974	+	0.986130i	$0.446923\pi$
$152$	47.2588	3.83320
$153$	19.6971	1.59242
$154$	−8.56951	−0.690551
$155$	16.8048	1.34979
$156$	14.0856	1.12775
$157$	−8.54132	−0.681671	−0.340836	−	0.940123i	$-0.610710\pi$
$157$	−8.54132	−0.681671	−0.340836	+	0.940123i	$0.610710\pi$
$158$	−1.83365	−0.145877
$159$	−1.03202	−0.0818445
$160$	9.59140	0.758267
$161$	−22.5089	−1.77395
$162$	−12.5421	−0.985400
$163$	14.1830	1.11090	0.555449	−	0.831550i	$-0.312546\pi$
$163$	14.1830	1.11090	0.555449	+	0.831550i	$0.312546\pi$
$164$	38.7796	3.02817
$165$	−2.51565	−0.195843
$166$	−32.6379	−2.53319
$167$	3.16887	0.245214	0.122607	−	0.992455i	$-0.460875\pi$
$167$	3.16887	0.245214	0.122607	+	0.992455i	$0.460875\pi$
$168$	−13.5317	−1.04399
$169$	10.6958	0.822754
$170$	−73.9228	−5.66962
$171$	21.4228	1.63824
$172$	−6.30286	−0.480588
$173$	−12.6054	−0.958368	−0.479184	−	0.877715i	$-0.659067\pi$
$173$	−12.6054	−0.958368	−0.479184	+	0.877715i	$0.659067\pi$
$174$	−8.49400	−0.643929
$175$	−33.6700	−2.54521
$176$	−5.30749	−0.400067
$177$	2.42318	0.182137
$178$	32.3391	2.42392
$179$	−19.8229	−1.48163	−0.740817	−	0.671707i	$-0.765561\pi$
$179$	−19.8229	−1.48163	−0.740817	+	0.671707i	$0.765561\pi$
$180$	40.8849	3.04738
$181$	−13.5263	−1.00540	−0.502702	−	0.864460i	$-0.667661\pi$
$181$	−13.5263	−1.00540	−0.502702	+	0.864460i	$0.667661\pi$
$182$	−43.1071	−3.19531
$183$	1.47038	0.108694
$184$	−35.4851	−2.61600
$185$	−17.7327	−1.30374
$186$	−7.52673	−0.551887
$187$	7.52265	0.550110
$188$	19.2509	1.40401
$189$	−13.3966	−0.974459
$190$	−80.3991	−5.83276
$191$	14.9768	1.08368	0.541840	−	0.840482i	$-0.317728\pi$
$191$	14.9768	1.08368	0.541840	+	0.840482i	$0.317728\pi$
$192$	3.19364	0.230481
$193$	0.583720	0.0420171	0.0210086	−	0.999779i	$-0.493312\pi$
$193$	0.583720	0.0420171	0.0210086	+	0.999779i	$0.493312\pi$
$194$	26.5981	1.90963
$195$	−12.6544	−0.906203
$196$	23.6114	1.68653
$197$	−18.4615	−1.31533	−0.657663	−	0.753313i	$-0.728455\pi$
$197$	−18.4615	−1.31533	−0.657663	+	0.753313i	$0.728455\pi$
$198$	−6.12407	−0.435219
$199$	3.00334	0.212901	0.106450	−	0.994318i	$-0.466051\pi$
$199$	3.00334	0.212901	0.106450	+	0.994318i	$0.466051\pi$
$200$	−53.0804	−3.75335
$201$	−9.69069	−0.683529
$202$	4.08256	0.287248
$203$	17.6604	1.23952
$204$	22.4940	1.57490
$205$	−34.8394	−2.43329
$206$	28.0564	1.95478
$207$	−16.0857	−1.11803
$208$	−26.6982	−1.85119
$209$	8.18170	0.565940
$210$	23.0208	1.58859
$211$	−12.4876	−0.859684	−0.429842	−	0.902904i	$-0.641431\pi$
$211$	−12.4876	−0.859684	−0.429842	+	0.902904i	$0.641431\pi$
$212$	6.40574	0.439948
$213$	3.19935	0.219216
$214$	−19.4271	−1.32801
$215$	5.66245	0.386176
$216$	−21.1196	−1.43701
$217$	15.6493	1.06235
$218$	−37.2232	−2.52107
$219$	5.06155	0.342028
$220$	15.6146	1.05274
$221$	37.8411	2.54547
$222$	7.94235	0.533056
$223$	−7.64144	−0.511709	−0.255854	−	0.966715i	$-0.582357\pi$
$223$	−7.64144	−0.511709	−0.255854	+	0.966715i	$0.582357\pi$
$224$	8.93192	0.596789
$225$	−24.0617	−1.60412
$226$	39.4708	2.62556
$227$	13.1301	0.871475	0.435738	−	0.900074i	$-0.356488\pi$
$227$	13.1301	0.871475	0.435738	+	0.900074i	$0.356488\pi$
$228$	24.4647	1.62022
$229$	−22.4134	−1.48112	−0.740558	−	0.671992i	$-0.765439\pi$
$229$	−22.4134	−1.48112	−0.740558	+	0.671992i	$0.765439\pi$
$230$	60.3691	3.98062
$231$	−2.34268	−0.154137
$232$	27.8415	1.82788
$233$	−12.1205	−0.794037	−0.397019	−	0.917811i	$-0.629955\pi$
$233$	−12.1205	−0.794037	−0.397019	+	0.917811i	$0.629955\pi$
$234$	−30.8059	−2.01384
$235$	−17.2949	−1.12819
$236$	−15.0407	−0.979063
$237$	−0.501272	−0.0325611
$238$	−68.8401	−4.46224
$239$	−4.82187	−0.311901	−0.155950	−	0.987765i	$-0.549844\pi$
$239$	−4.82187	−0.311901	−0.155950	+	0.987765i	$0.549844\pi$
$240$	14.2578	0.920339
$241$	9.49816	0.611830	0.305915	−	0.952059i	$-0.401038\pi$
$241$	9.49816	0.611830	0.305915	+	0.952059i	$0.401038\pi$
$242$	25.1347	1.61572
$243$	−14.7638	−0.947096
$244$	−9.12664	−0.584273
$245$	−21.2123	−1.35521
$246$	15.6043	0.994893
$247$	41.1563	2.61871
$248$	24.6710	1.56661
$249$	−8.92234	−0.565431
$250$	42.7564	2.70415
$251$	19.6940	1.24307	0.621537	−	0.783385i	$-0.286509\pi$
$251$	19.6940	1.24307	0.621537	+	0.783385i	$0.286509\pi$
$252$	38.0738	2.39843
$253$	−6.14337	−0.386230
$254$	13.2430	0.830938
$255$	−20.2085	−1.26551
$256$	−32.4065	−2.02541
$257$	19.3034	1.20411	0.602056	−	0.798454i	$-0.294348\pi$
$257$	19.3034	1.20411	0.602056	+	0.798454i	$0.294348\pi$
$258$	−2.53617	−0.157895
$259$	−16.5135	−1.02610
$260$	78.5460	4.87122
$261$	12.6208	0.781206
$262$	−6.46156	−0.399197
$263$	5.45023	0.336075	0.168038	−	0.985781i	$-0.446257\pi$
$263$	5.45023	0.336075	0.168038	+	0.985781i	$0.446257\pi$
$264$	−3.69321	−0.227301
$265$	−5.75488	−0.353520
$266$	−74.8711	−4.59064
$267$	8.84064	0.541039
$268$	60.1501	3.67425
$269$	−12.3419	−0.752500	−0.376250	−	0.926518i	$-0.622787\pi$
$269$	−12.3419	−0.752500	−0.376250	+	0.926518i	$0.622787\pi$
$270$	35.9297	2.18661
$271$	−17.4366	−1.05920	−0.529600	−	0.848248i	$-0.677658\pi$
$271$	−17.4366	−1.05920	−0.529600	+	0.848248i	$0.677658\pi$
$272$	−42.6358	−2.58518
$273$	−11.7844	−0.713222
$274$	−41.1587	−2.48649
$275$	−9.18956	−0.554151
$276$	−18.3698	−1.10573
$277$	−4.57469	−0.274867	−0.137433	−	0.990511i	$-0.543885\pi$
$277$	−4.57469	−0.274867	−0.137433	+	0.990511i	$0.543885\pi$
$278$	51.2516	3.07387
$279$	11.1836	0.669542
$280$	−75.4572	−4.50943
$281$	21.9805	1.31124	0.655622	−	0.755089i	$-0.272406\pi$
$281$	21.9805	1.31124	0.655622	+	0.755089i	$0.272406\pi$
$282$	7.74624	0.461282
$283$	−4.49695	−0.267316	−0.133658	−	0.991028i	$-0.542672\pi$
$283$	−4.49695	−0.267316	−0.133658	+	0.991028i	$0.542672\pi$
$284$	−19.8583	−1.17838
$285$	−21.9790	−1.30192
$286$	−11.7652	−0.695693
$287$	−32.4439	−1.91510
$288$	6.38306	0.376125
$289$	43.4305	2.55473
$290$	−47.3654	−2.78139
$291$	7.27123	0.426247
$292$	−31.4170	−1.83854
$293$	13.6252	0.795991	0.397996	−	0.917387i	$-0.369706\pi$
$293$	13.6252	0.795991	0.397996	+	0.917387i	$0.369706\pi$
$294$	9.50084	0.554100
$295$	13.5124	0.786725
$296$	−26.0333	−1.51316
$297$	−3.65634	−0.212162
$298$	−49.8709	−2.88894
$299$	−30.9029	−1.78716
$300$	−27.4784	−1.58647
$301$	5.27312	0.303938
$302$	−10.1878	−0.586242
$303$	1.11606	0.0641162
$304$	−46.3711	−2.65957
$305$	8.19932	0.469492
$306$	−49.1955	−2.81232
$307$	8.68700	0.495793	0.247897	−	0.968786i	$-0.420261\pi$
$307$	8.68700	0.495793	0.247897	+	0.968786i	$0.420261\pi$
$308$	14.5410	0.828550
$309$	7.66988	0.436324
$310$	−41.9716	−2.38383
$311$	1.57723	0.0894368	0.0447184	−	0.999000i	$-0.485761\pi$
$311$	1.57723	0.0894368	0.0447184	+	0.999000i	$0.485761\pi$
$312$	−18.5779	−1.05177
$313$	−3.15551	−0.178360	−0.0891800	−	0.996016i	$-0.528425\pi$
$313$	−3.15551	−0.178360	−0.0891800	+	0.996016i	$0.528425\pi$
$314$	21.3328	1.20388
$315$	−34.2053	−1.92725
$316$	3.11139	0.175029
$317$	1.94350	0.109158	0.0545788	−	0.998509i	$-0.482618\pi$
$317$	1.94350	0.109158	0.0545788	+	0.998509i	$0.482618\pi$
$318$	2.57757	0.144543
$319$	4.82007	0.269872
$320$	17.8088	0.995541
$321$	−5.31086	−0.296423
$322$	56.2183	3.13292
$323$	65.7247	3.65702
$324$	21.2818	1.18232
$325$	−46.2262	−2.56417
$326$	−35.4234	−1.96192
$327$	−10.1758	−0.562725
$328$	−51.1475	−2.82415
$329$	−16.1057	−0.887938
$330$	6.28307	0.345872
$331$	−7.82581	−0.430145	−0.215073	−	0.976598i	$-0.568999\pi$
$331$	−7.82581	−0.430145	−0.215073	+	0.976598i	$0.568999\pi$
$332$	55.3810	3.03942
$333$	−11.8011	−0.646696
$334$	−7.91455	−0.433065
$335$	−54.0385	−2.95244
$336$	13.2775	0.724348
$337$	12.2420	0.666862	0.333431	−	0.942775i	$-0.391794\pi$
$337$	12.2420	0.666862	0.333431	+	0.942775i	$0.391794\pi$
$338$	−26.7138	−1.45304
$339$	10.7903	0.586047
$340$	125.434	6.80263
$341$	4.27118	0.231297
$342$	−53.5055	−2.89324
$343$	5.06544	0.273508
$344$	8.31302	0.448208
$345$	16.5033	0.888508
$346$	31.4831	1.69254
$347$	24.7657	1.32949	0.664745	−	0.747070i	$-0.268540\pi$
$347$	24.7657	1.32949	0.664745	+	0.747070i	$0.268540\pi$
$348$	14.4129	0.772611
$349$	−29.3687	−1.57207	−0.786035	−	0.618182i	$-0.787869\pi$
$349$	−29.3687	−1.57207	−0.786035	+	0.618182i	$0.787869\pi$
$350$	84.0941	4.49502
$351$	−18.3924	−0.981716
$352$	2.43779	0.129935
$353$	15.8241	0.842231	0.421116	−	0.907007i	$-0.361639\pi$
$353$	15.8241	0.842231	0.421116	+	0.907007i	$0.361639\pi$
$354$	−6.05212	−0.321667
$355$	17.8406	0.946883
$356$	−54.8739	−2.90831
$357$	−18.8191	−0.996010
$358$	49.5097	2.61667
$359$	19.3547	1.02150	0.510751	−	0.859729i	$-0.329367\pi$
$359$	19.3547	1.02150	0.510751	+	0.859729i	$0.329367\pi$
$360$	−53.9243	−2.84206
$361$	52.4828	2.76225
$362$	33.7834	1.77561
$363$	6.87116	0.360643
$364$	73.1454	3.83386
$365$	28.2249	1.47736
$366$	−3.67242	−0.191960
$367$	30.0668	1.56947	0.784737	−	0.619829i	$-0.212798\pi$
$367$	30.0668	1.56947	0.784737	+	0.619829i	$0.212798\pi$
$368$	34.8186	1.81504
$369$	−23.1855	−1.20699
$370$	44.2892	2.30249
$371$	−5.35920	−0.278236
$372$	12.7716	0.662176
$373$	−7.70077	−0.398731	−0.199365	−	0.979925i	$-0.563888\pi$
$373$	−7.70077	−0.398731	−0.199365	+	0.979925i	$0.563888\pi$
$374$	−18.7885	−0.971533
$375$	11.6885	0.603590
$376$	−25.3905	−1.30942
$377$	24.2464	1.24875
$378$	33.4593	1.72096
$379$	16.1137	0.827705	0.413852	−	0.910344i	$-0.364183\pi$
$379$	16.1137	0.827705	0.413852	+	0.910344i	$0.364183\pi$
$380$	136.423	6.99838
$381$	3.62028	0.185473
$382$	−37.4059	−1.91385
$383$	26.2315	1.34037	0.670184	−	0.742195i	$-0.266215\pi$
$383$	26.2315	1.34037	0.670184	+	0.742195i	$0.266215\pi$
$384$	−11.4165	−0.582594
$385$	−13.0636	−0.665781
$386$	−1.45790	−0.0742051
$387$	3.76835	0.191556
$388$	−45.1325	−2.29125
$389$	−22.9768	−1.16497	−0.582484	−	0.812842i	$-0.697919\pi$
$389$	−22.9768	−1.16497	−0.582484	+	0.812842i	$0.697919\pi$
$390$	31.6057	1.60042
$391$	−49.3506	−2.49577
$392$	−31.1417	−1.57289
$393$	−1.76642	−0.0891041
$394$	46.1093	2.32295
$395$	−2.79526	−0.140645
$396$	10.3915	0.522192
$397$	28.3199	1.42134	0.710669	−	0.703527i	$-0.248393\pi$
$397$	28.3199	1.42134	0.710669	+	0.703527i	$0.248393\pi$
$398$	−7.50113	−0.375998
$399$	−20.4678	−1.02467
$400$	52.0834	2.60417
$401$	−11.4244	−0.570508	−0.285254	−	0.958452i	$-0.592078\pi$
$401$	−11.4244	−0.570508	−0.285254	+	0.958452i	$0.592078\pi$
$402$	24.2034	1.20716
$403$	21.4853	1.07026
$404$	−6.92740	−0.344651
$405$	−19.1195	−0.950053
$406$	−44.1087	−2.18908
$407$	−4.50703	−0.223405
$408$	−29.6681	−1.46879
$409$	−27.9584	−1.38245	−0.691227	−	0.722637i	$-0.742930\pi$
$409$	−27.9584	−1.38245	−0.691227	+	0.722637i	$0.742930\pi$
$410$	87.0147	4.29735
$411$	−11.2517	−0.555006
$412$	−47.6069	−2.34543
$413$	12.5834	0.619187
$414$	40.1755	1.97452
$415$	−49.7540	−2.44233
$416$	12.2628	0.601233
$417$	14.0108	0.686114
$418$	−20.4346	−0.999488
$419$	37.9318	1.85309	0.926545	−	0.376185i	$-0.122764\pi$
$419$	37.9318	1.85309	0.926545	+	0.376185i	$0.122764\pi$
$420$	−39.0624	−1.90605
$421$	−27.9490	−1.36215	−0.681075	−	0.732214i	$-0.738487\pi$
$421$	−27.9490	−1.36215	−0.681075	+	0.732214i	$0.738487\pi$
$422$	31.1891	1.51826
$423$	−11.5097	−0.559621
$424$	−8.44872	−0.410306
$425$	−73.8210	−3.58085
$426$	−7.99069	−0.387150
$427$	7.63556	0.369511
$428$	32.9645	1.59340
$429$	−3.21631	−0.155285
$430$	−14.1425	−0.682014
$431$	18.7839	0.904789	0.452395	−	0.891818i	$-0.350570\pi$
$431$	18.7839	0.904789	0.452395	+	0.891818i	$0.350570\pi$
$432$	20.7229	0.997031
$433$	4.70856	0.226279	0.113139	−	0.993579i	$-0.463909\pi$
$433$	4.70856	0.226279	0.113139	+	0.993579i	$0.463909\pi$
$434$	−39.0857	−1.87618
$435$	−12.9484	−0.620830
$436$	63.1614	3.02488
$437$	−53.6741	−2.56758
$438$	−12.6417	−0.604045
$439$	14.2004	0.677748	0.338874	−	0.940832i	$-0.389954\pi$
$439$	14.2004	0.677748	0.338874	+	0.940832i	$0.389954\pi$
$440$	−20.5946	−0.981807
$441$	−14.1168	−0.672227
$442$	−94.5118	−4.49547
$443$	25.2089	1.19771	0.598857	−	0.800856i	$-0.295622\pi$
$443$	25.2089	1.19771	0.598857	+	0.800856i	$0.295622\pi$
$444$	−13.4768	−0.639581
$445$	49.2984	2.33697
$446$	19.0852	0.903713
$447$	−13.6334	−0.644836
$448$	16.5843	0.783535
$449$	−22.9183	−1.08158	−0.540791	−	0.841157i	$-0.681875\pi$
$449$	−22.9183	−1.08158	−0.540791	+	0.841157i	$0.681875\pi$
$450$	60.0966	2.83298
$451$	−8.85492	−0.416962
$452$	−66.9752	−3.15025
$453$	−2.78507	−0.130854
$454$	−32.7937	−1.53908
$455$	−65.7135	−3.08070
$456$	−32.2672	−1.51105
$457$	1.86781	0.0873726	0.0436863	−	0.999045i	$-0.486090\pi$
$457$	1.86781	0.0873726	0.0436863	+	0.999045i	$0.486090\pi$
$458$	55.9796	2.61575
$459$	−29.3719	−1.37096
$460$	−102.436	−4.77610
$461$	26.0447	1.21302	0.606512	−	0.795074i	$-0.292568\pi$
$461$	26.0447	1.21302	0.606512	+	0.795074i	$0.292568\pi$
$462$	5.85107	0.272216
$463$	13.7142	0.637351	0.318675	−	0.947864i	$-0.396762\pi$
$463$	13.7142	0.637351	0.318675	+	0.947864i	$0.396762\pi$
$464$	−27.3185	−1.26823
$465$	−11.4739	−0.532090
$466$	30.2720	1.40232
$467$	−14.5424	−0.672944	−0.336472	−	0.941693i	$-0.609234\pi$
$467$	−14.5424	−0.672944	−0.336472	+	0.941693i	$0.609234\pi$
$468$	52.2723	2.41629
$469$	−50.3230	−2.32370
$470$	43.1956	1.99247
$471$	5.83182	0.268716
$472$	19.8376	0.913097
$473$	1.43919	0.0661742
$474$	1.25198	0.0575051
$475$	−80.2884	−3.68389
$476$	116.810	5.35397
$477$	−3.82987	−0.175358
$478$	12.0431	0.550838
$479$	−9.91201	−0.452891	−0.226446	−	0.974024i	$-0.572711\pi$
$479$	−9.91201	−0.452891	−0.226446	+	0.974024i	$0.572711\pi$
$480$	−6.54879	−0.298910
$481$	−22.6716	−1.03374
$482$	−23.7226	−1.08053
$483$	15.3686	0.699295
$484$	−42.6493	−1.93860
$485$	40.5468	1.84113
$486$	36.8740	1.67264
$487$	34.3356	1.55590	0.777948	−	0.628328i	$-0.216261\pi$
$487$	34.3356	1.55590	0.777948	+	0.628328i	$0.216261\pi$
$488$	12.0374	0.544907
$489$	−9.68383	−0.437918
$490$	52.9799	2.39339
$491$	−33.3760	−1.50624	−0.753118	−	0.657885i	$-0.771451\pi$
$491$	−33.3760	−1.50624	−0.753118	+	0.657885i	$0.771451\pi$
$492$	−26.4778	−1.19371
$493$	38.7203	1.74387
$494$	−102.792	−4.62483
$495$	−9.33567	−0.419607
$496$	−24.2076	−1.08695
$497$	16.6140	0.745238
$498$	22.2844	0.998589
$499$	−9.38017	−0.419914	−0.209957	−	0.977711i	$-0.567332\pi$
$499$	−9.38017	−0.419914	−0.209957	+	0.977711i	$0.567332\pi$
$500$	−72.5503	−3.24455
$501$	−2.16363	−0.0966638
$502$	−49.1877	−2.19535
$503$	−24.8731	−1.10904	−0.554518	−	0.832172i	$-0.687097\pi$
$503$	−24.8731	−1.10904	−0.554518	+	0.832172i	$0.687097\pi$
$504$	−50.2167	−2.23683
$505$	6.22354	0.276944
$506$	15.3437	0.682110
$507$	−7.30285	−0.324331
$508$	−22.4711	−0.996992
$509$	21.4352	0.950099	0.475050	−	0.879959i	$-0.342430\pi$
$509$	21.4352	0.950099	0.475050	+	0.879959i	$0.342430\pi$
$510$	50.4728	2.23497
$511$	26.2842	1.16275
$512$	47.4973	2.09910
$513$	−31.9451	−1.41041
$514$	−48.2121	−2.12654
$515$	42.7698	1.88466
$516$	4.30345	0.189449
$517$	−4.39574	−0.193325
$518$	41.2440	1.81216
$519$	8.60665	0.377790
$520$	−103.597	−4.54301
$521$	−6.22049	−0.272524	−0.136262	−	0.990673i	$-0.543509\pi$
$521$	−6.22049	−0.272524	−0.136262	+	0.990673i	$0.543509\pi$
$522$	−31.5216	−1.37966
$523$	−25.1232	−1.09856	−0.549280	−	0.835638i	$-0.685098\pi$
$523$	−25.1232	−1.09856	−0.549280	+	0.835638i	$0.685098\pi$
$524$	10.9642	0.478972
$525$	22.9891	1.00333
$526$	−13.6125	−0.593532
$527$	34.3110	1.49461
$528$	3.62384	0.157707
$529$	17.3022	0.752268
$530$	14.3734	0.624340
$531$	8.99251	0.390242
$532$	127.043	5.50803
$533$	−44.5428	−1.92936
$534$	−22.0804	−0.955511
$535$	−29.6151	−1.28037
$536$	−79.3337	−3.42669
$537$	13.5346	0.584063
$538$	30.8251	1.32897
$539$	−5.39142	−0.232225
$540$	−60.9666	−2.62359
$541$	−5.15662	−0.221700	−0.110850	−	0.993837i	$-0.535357\pi$
$541$	−5.15662	−0.221700	−0.110850	+	0.993837i	$0.535357\pi$
$542$	43.5497	1.87062
$543$	9.23548	0.396332
$544$	19.5831	0.839620
$545$	−56.7439	−2.43064
$546$	29.4326	1.25960
$547$	−15.9706	−0.682854	−0.341427	−	0.939908i	$-0.610910\pi$
$547$	−15.9706	−0.682854	−0.341427	+	0.939908i	$0.610910\pi$
$548$	69.8393	2.98339
$549$	5.45664	0.232884
$550$	22.9518	0.978670
$551$	42.1125	1.79405
$552$	24.2284	1.03123
$553$	−2.60306	−0.110694
$554$	11.4257	0.485434
$555$	12.1075	0.513935
$556$	−86.9653	−3.68815
$557$	−27.6357	−1.17096	−0.585480	−	0.810687i	$-0.699094\pi$
$557$	−27.6357	−1.17096	−0.585480	+	0.810687i	$0.699094\pi$
$558$	−27.9320	−1.18246
$559$	7.23957	0.306201
$560$	74.0399	3.12875
$561$	−5.13629	−0.216854
$562$	−54.8984	−2.31575
$563$	2.45235	0.103354	0.0516771	−	0.998664i	$-0.483543\pi$
$563$	2.45235	0.103354	0.0516771	+	0.998664i	$0.483543\pi$
$564$	−13.1441	−0.553464
$565$	60.1702	2.53138
$566$	11.2316	0.472099
$567$	−17.8049	−0.747734
$568$	26.1917	1.09898
$569$	−41.9737	−1.75963	−0.879814	−	0.475318i	$-0.842333\pi$
$569$	−41.9737	−1.75963	−0.879814	+	0.475318i	$0.842333\pi$
$570$	54.8947	2.29928
$571$	2.47172	0.103438	0.0517192	−	0.998662i	$-0.483530\pi$
$571$	2.47172	0.103438	0.0517192	+	0.998662i	$0.483530\pi$
$572$	19.9636	0.834720
$573$	−10.2258	−0.427189
$574$	81.0319	3.38220
$575$	60.2860	2.51410
$576$	11.8517	0.493822
$577$	0.979907	0.0407941	0.0203970	−	0.999792i	$-0.493507\pi$
$577$	0.979907	0.0407941	0.0203970	+	0.999792i	$0.493507\pi$
$578$	−108.472	−4.51183
$579$	−0.398551	−0.0165632
$580$	80.3710	3.33722
$581$	−46.3330	−1.92222
$582$	−18.1606	−0.752781
$583$	−1.46269	−0.0605783
$584$	41.4368	1.71467
$585$	−46.9611	−1.94160
$586$	−34.0302	−1.40578
$587$	−14.5685	−0.601308	−0.300654	−	0.953733i	$-0.597205\pi$
$587$	−14.5685	−0.601308	−0.300654	+	0.953733i	$0.597205\pi$
$588$	−16.1213	−0.664831
$589$	37.3169	1.53762
$590$	−33.7487	−1.38941
$591$	12.6051	0.518503
$592$	25.5443	1.04986
$593$	12.9214	0.530618	0.265309	−	0.964163i	$-0.414526\pi$
$593$	12.9214	0.530618	0.265309	+	0.964163i	$0.414526\pi$
$594$	9.13206	0.374693
$595$	−104.941	−4.30218
$596$	84.6223	3.46626
$597$	−2.05061	−0.0839259
$598$	77.1831	3.15625
$599$	−4.68905	−0.191589	−0.0957947	−	0.995401i	$-0.530539\pi$
$599$	−4.68905	−0.191589	−0.0957947	+	0.995401i	$0.530539\pi$
$600$	36.2421	1.47958
$601$	20.3499	0.830088	0.415044	−	0.909801i	$-0.363766\pi$
$601$	20.3499	0.830088	0.415044	+	0.909801i	$0.363766\pi$
$602$	−13.1701	−0.536775
$603$	−35.9626	−1.46451
$604$	17.2869	0.703396
$605$	38.3159	1.55776
$606$	−2.78748	−0.113234
$607$	38.9294	1.58009	0.790047	−	0.613046i	$-0.210056\pi$
$607$	38.9294	1.58009	0.790047	+	0.613046i	$0.210056\pi$
$608$	21.2988	0.863780
$609$	−12.0582	−0.488621
$610$	−20.4786	−0.829155
$611$	−22.1119	−0.894550
$612$	83.4764	3.37433
$613$	36.1879	1.46162	0.730809	−	0.682582i	$-0.239143\pi$
$613$	36.1879	1.46162	0.730809	+	0.682582i	$0.239143\pi$
$614$	−21.6966	−0.875605
$615$	23.7875	0.959205
$616$	−19.1785	−0.772726
$617$	−10.4852	−0.422117	−0.211058	−	0.977473i	$-0.567691\pi$
$617$	−10.4852	−0.422117	−0.211058	+	0.977473i	$0.567691\pi$
$618$	−19.1563	−0.770579
$619$	−11.2147	−0.450755	−0.225378	−	0.974271i	$-0.572362\pi$
$619$	−11.2147	−0.450755	−0.225378	+	0.974271i	$0.572362\pi$
$620$	71.2186	2.86021
$621$	23.9866	0.962547
$622$	−3.93930	−0.157951
$623$	45.9088	1.83930
$624$	18.2289	0.729742
$625$	17.6975	0.707901
$626$	7.88120	0.314996
$627$	−5.58628	−0.223094
$628$	−36.1981	−1.44446
$629$	−36.2056	−1.44361
$630$	85.4312	3.40366
$631$	−5.75671	−0.229171	−0.114585	−	0.993413i	$-0.536554\pi$
$631$	−5.75671	−0.229171	−0.114585	+	0.993413i	$0.536554\pi$
$632$	−4.10370	−0.163237
$633$	8.52627	0.338889
$634$	−4.85407	−0.192780
$635$	20.1879	0.801132
$636$	−4.37369	−0.173428
$637$	−27.1204	−1.07455
$638$	−12.0386	−0.476613
$639$	11.8729	0.469685
$640$	−63.6620	−2.51646
$641$	−13.4682	−0.531960	−0.265980	−	0.963978i	$-0.585696\pi$
$641$	−13.4682	−0.531960	−0.265980	+	0.963978i	$0.585696\pi$
$642$	13.2644	0.523504
$643$	−39.9139	−1.57405	−0.787025	−	0.616922i	$-0.788380\pi$
$643$	−39.9139	−1.57405	−0.787025	+	0.616922i	$0.788380\pi$
$644$	−95.3928	−3.75900
$645$	−3.86619	−0.152231
$646$	−164.154	−6.45855
$647$	−11.5047	−0.452295	−0.226148	−	0.974093i	$-0.572613\pi$
$647$	−11.5047	−0.452295	−0.226148	+	0.974093i	$0.572613\pi$
$648$	−28.0692	−1.10266
$649$	3.43438	0.134811
$650$	115.454	4.52849
$651$	−10.6850	−0.418779
$652$	60.1075	2.35399
$653$	34.1763	1.33742	0.668712	−	0.743522i	$-0.266846\pi$
$653$	34.1763	1.33742	0.668712	+	0.743522i	$0.266846\pi$
$654$	25.4152	0.993811
$655$	−9.85015	−0.384877
$656$	50.1867	1.95946
$657$	18.7836	0.732819
$658$	40.2256	1.56816
$659$	−49.3503	−1.92241	−0.961207	−	0.275827i	$-0.911048\pi$
$659$	−49.3503	−1.92241	−0.961207	+	0.275827i	$0.911048\pi$
$660$	−10.6613	−0.414991
$661$	11.3028	0.439629	0.219814	−	0.975542i	$-0.429455\pi$
$661$	11.3028	0.439629	0.219814	+	0.975542i	$0.429455\pi$
$662$	19.5457	0.759666
$663$	−25.8370	−1.00343
$664$	−73.0435	−2.83464
$665$	−114.135	−4.42597
$666$	29.4744	1.14211
$667$	−31.6209	−1.22437
$668$	13.4296	0.519608
$669$	5.21740	0.201716
$670$	134.967	5.21421
$671$	2.08398	0.0804510
$672$	−6.09852	−0.235255
$673$	−3.24102	−0.124932	−0.0624661	−	0.998047i	$-0.519897\pi$
$673$	−3.24102	−0.124932	−0.0624661	+	0.998047i	$0.519897\pi$
$674$	−30.5755	−1.17772
$675$	35.8803	1.38103
$676$	45.3288	1.74341
$677$	−28.8545	−1.10897	−0.554483	−	0.832195i	$-0.687084\pi$
$677$	−28.8545	−1.10897	−0.554483	+	0.832195i	$0.687084\pi$
$678$	−26.9498	−1.03500
$679$	37.7589	1.44905
$680$	−165.439	−6.34429
$681$	−8.96493	−0.343537
$682$	−10.6677	−0.408487
$683$	−21.1044	−0.807539	−0.403769	−	0.914861i	$-0.632300\pi$
$683$	−21.1044	−0.807539	−0.403769	+	0.914861i	$0.632300\pi$
$684$	90.7896	3.47143
$685$	−62.7433	−2.39730
$686$	−12.6514	−0.483034
$687$	15.3033	0.583859
$688$	−8.15687	−0.310978
$689$	−7.35774	−0.280308
$690$	−41.2186	−1.56917
$691$	13.4162	0.510375	0.255187	−	0.966892i	$-0.417863\pi$
$691$	13.4162	0.510375	0.255187	+	0.966892i	$0.417863\pi$
$692$	−53.4215	−2.03078
$693$	−8.69378	−0.330249
$694$	−61.8546	−2.34797
$695$	78.1291	2.96361
$696$	−19.0095	−0.720555
$697$	−71.1328	−2.69435
$698$	73.3512	2.77638
$699$	8.27557	0.313011
$700$	−142.693	−5.39330
$701$	−7.69058	−0.290469	−0.145235	−	0.989397i	$-0.546394\pi$
$701$	−7.69058	−0.290469	−0.145235	+	0.989397i	$0.546394\pi$
$702$	45.9369	1.73378
$703$	−39.3775	−1.48515
$704$	4.52636	0.170594
$705$	11.8085	0.444736
$706$	−39.5222	−1.48744
$707$	5.79563	0.217967
$708$	10.2694	0.385948
$709$	−9.71659	−0.364914	−0.182457	−	0.983214i	$-0.558405\pi$
$709$	−9.71659	−0.364914	−0.182457	+	0.983214i	$0.558405\pi$
$710$	−44.5587	−1.67226
$711$	−1.86024	−0.0697644
$712$	72.3747	2.71236
$713$	−28.0201	−1.04936
$714$	47.0025	1.75902
$715$	−17.9352	−0.670738
$716$	−84.0094	−3.13958
$717$	3.29226	0.122952
$718$	−48.3403	−1.80404
$719$	13.7715	0.513591	0.256796	−	0.966466i	$-0.417333\pi$
$719$	13.7715	0.513591	0.256796	+	0.966466i	$0.417333\pi$
$720$	52.9114	1.97189
$721$	39.8291	1.48331
$722$	−131.081	−4.87833
$723$	−6.48513	−0.241184
$724$	−57.3246	−2.13045
$725$	−47.3002	−1.75669
$726$	−17.1614	−0.636919
$727$	28.0247	1.03938	0.519690	−	0.854355i	$-0.326048\pi$
$727$	28.0247	1.03938	0.519690	+	0.854355i	$0.326048\pi$
$728$	−96.4736	−3.57555
$729$	−4.98463	−0.184616
$730$	−70.4944	−2.60912
$731$	11.5612	0.427608
$732$	6.23146	0.230321
$733$	−43.3441	−1.60095	−0.800475	−	0.599366i	$-0.795420\pi$
$733$	−43.3441	−1.60095	−0.800475	+	0.599366i	$0.795420\pi$
$734$	−75.0948	−2.77180
$735$	14.4833	0.534224
$736$	−15.9926	−0.589494
$737$	−13.7347	−0.505923
$738$	57.9082	2.13163
$739$	16.8754	0.620773	0.310386	−	0.950611i	$-0.399542\pi$
$739$	16.8754	0.620773	0.310386	+	0.950611i	$0.399542\pi$
$740$	−75.1512	−2.76261
$741$	−28.1006	−1.03230
$742$	13.3851	0.491383
$743$	−2.34589	−0.0860622	−0.0430311	−	0.999074i	$-0.513701\pi$
$743$	−2.34589	−0.0860622	−0.0430311	+	0.999074i	$0.513701\pi$
$744$	−16.8448	−0.617561
$745$	−76.0242	−2.78531
$746$	19.2334	0.704186
$747$	−33.1112	−1.21148
$748$	31.8809	1.16568
$749$	−27.5789	−1.00771
$750$	−29.1931	−1.06598
$751$	25.4758	0.929625	0.464812	−	0.885409i	$-0.346122\pi$
$751$	25.4758	0.929625	0.464812	+	0.885409i	$0.346122\pi$
$752$	24.9136	0.908505
$753$	−13.4466	−0.490021
$754$	−60.5576	−2.20538
$755$	−15.5305	−0.565213
$756$	−56.7748	−2.06488
$757$	−14.8089	−0.538239	−0.269120	−	0.963107i	$-0.586733\pi$
$757$	−14.8089	−0.538239	−0.269120	+	0.963107i	$0.586733\pi$
$758$	−40.2455	−1.46178
$759$	4.19455	0.152253
$760$	−179.933	−6.52685
$761$	14.5447	0.527244	0.263622	−	0.964626i	$-0.415083\pi$
$761$	14.5447	0.527244	0.263622	+	0.964626i	$0.415083\pi$
$762$	−9.04200	−0.327557
$763$	−52.8423	−1.91302
$764$	63.4714	2.29632
$765$	−74.9947	−2.71144
$766$	−65.5158	−2.36718
$767$	17.2759	0.623798
$768$	22.1265	0.798419
$769$	16.1361	0.581883	0.290941	−	0.956741i	$-0.406032\pi$
$769$	16.1361	0.581883	0.290941	+	0.956741i	$0.406032\pi$
$770$	32.6275	1.17581
$771$	−13.1799	−0.474663
$772$	2.47380	0.0890342
$773$	−41.6304	−1.49734	−0.748671	−	0.662942i	$-0.769307\pi$
$773$	−41.6304	−1.49734	−0.748671	+	0.662942i	$0.769307\pi$
$774$	−9.41183	−0.338301
$775$	−41.9138	−1.50559
$776$	59.5265	2.13688
$777$	11.2750	0.404489
$778$	57.3867	2.05741
$779$	−77.3647	−2.77188
$780$	−53.6294	−1.92024
$781$	4.53445	0.162256
$782$	123.258	4.40769
$783$	−18.8198	−0.672564
$784$	30.5568	1.09131
$785$	32.5202	1.16069
$786$	4.41181	0.157364
$787$	−34.4205	−1.22696	−0.613479	−	0.789711i	$-0.710231\pi$
$787$	−34.4205	−1.22696	−0.613479	+	0.789711i	$0.710231\pi$
$788$	−78.2396	−2.78717
$789$	−3.72129	−0.132481
$790$	6.98143	0.248388
$791$	56.0331	1.99231
$792$	−13.7056	−0.487009
$793$	10.4830	0.372263
$794$	−70.7318	−2.51018
$795$	3.92930	0.139358
$796$	12.7281	0.451137
$797$	41.2937	1.46270	0.731349	−	0.682004i	$-0.238891\pi$
$797$	41.2937	1.46270	0.731349	+	0.682004i	$0.238891\pi$
$798$	51.1203	1.80964
$799$	−35.3116	−1.24923
$800$	−23.9225	−0.845788
$801$	32.8080	1.15921
$802$	28.5336	1.00756
$803$	7.17376	0.253157
$804$	−41.0691	−1.44840
$805$	85.7004	3.02054
$806$	−53.6615	−1.89015
$807$	8.42678	0.296637
$808$	9.13675	0.321430
$809$	−1.66490	−0.0585349	−0.0292674	−	0.999572i	$-0.509317\pi$
$809$	−1.66490	−0.0585349	−0.0292674	+	0.999572i	$0.509317\pi$
$810$	47.7527	1.67786
$811$	41.2540	1.44862	0.724311	−	0.689473i	$-0.242158\pi$
$811$	41.2540	1.44862	0.724311	+	0.689473i	$0.242158\pi$
$812$	74.8449	2.62654
$813$	11.9053	0.417538
$814$	11.2567	0.394548
$815$	−54.0003	−1.89155
$816$	29.1108	1.01908
$817$	12.5741	0.439913
$818$	69.8289	2.44151
$819$	−43.7322	−1.52813
$820$	−147.649	−5.15613
$821$	12.3505	0.431034	0.215517	−	0.976500i	$-0.430856\pi$
$821$	12.3505	0.431034	0.215517	+	0.976500i	$0.430856\pi$
$822$	28.1022	0.980178
$823$	−39.1997	−1.36642	−0.683208	−	0.730223i	$-0.739416\pi$
$823$	−39.1997	−1.36642	−0.683208	+	0.730223i	$0.739416\pi$
$824$	62.7902	2.18740
$825$	6.27442	0.218447
$826$	−31.4282	−1.09353
$827$	−21.5522	−0.749442	−0.374721	−	0.927138i	$-0.622261\pi$
$827$	−21.5522	−0.749442	−0.374721	+	0.927138i	$0.622261\pi$
$828$	−68.1710	−2.36911
$829$	34.3822	1.19414	0.597072	−	0.802188i	$-0.296331\pi$
$829$	34.3822	1.19414	0.597072	+	0.802188i	$0.296331\pi$
$830$	124.265	4.31332
$831$	3.12350	0.108353
$832$	22.7689	0.789370
$833$	−43.3100	−1.50060
$834$	−34.9935	−1.21172
$835$	−12.0651	−0.417531
$836$	34.6740	1.19923
$837$	−16.6766	−0.576429
$838$	−94.7384	−3.27268
$839$	−1.08534	−0.0374700	−0.0187350	−	0.999824i	$-0.505964\pi$
$839$	−1.08534	−0.0374700	−0.0187350	+	0.999824i	$0.505964\pi$
$840$	51.5205	1.77763
$841$	−4.19030	−0.144493
$842$	69.8053	2.40565
$843$	−15.0078	−0.516895
$844$	−52.9225	−1.82167
$845$	−40.7231	−1.40092
$846$	28.7466	0.988330
$847$	35.6814	1.22603
$848$	8.29002	0.284680
$849$	3.07042	0.105376
$850$	184.375	6.32402
$851$	29.5673	1.01355
$852$	13.5588	0.464518
$853$	−4.83849	−0.165667	−0.0828334	−	0.996563i	$-0.526397\pi$
$853$	−4.83849	−0.165667	−0.0828334	+	0.996563i	$0.526397\pi$
$854$	−19.0706	−0.652582
$855$	−81.5649	−2.78946
$856$	−43.4778	−1.48604
$857$	17.7069	0.604855	0.302428	−	0.953172i	$-0.402203\pi$
$857$	17.7069	0.604855	0.302428	+	0.953172i	$0.402203\pi$
$858$	8.03304	0.274244
$859$	15.2423	0.520059	0.260030	−	0.965601i	$-0.416268\pi$
$859$	15.2423	0.520059	0.260030	+	0.965601i	$0.416268\pi$
$860$	23.9975	0.818307
$861$	22.1520	0.754937
$862$	−46.9147	−1.59792
$863$	26.7946	0.912098	0.456049	−	0.889955i	$-0.349264\pi$
$863$	26.7946	0.912098	0.456049	+	0.889955i	$0.349264\pi$
$864$	−9.51827	−0.323818
$865$	47.9936	1.63183
$866$	−11.7601	−0.399624
$867$	−29.6533	−1.00708
$868$	66.3218	2.25111
$869$	−0.710455	−0.0241005
$870$	32.3400	1.09643
$871$	−69.0894	−2.34100
$872$	−83.3054	−2.82108
$873$	26.9838	0.913264
$874$	134.056	4.53452
$875$	60.6973	2.05194
$876$	21.4508	0.724757
$877$	−20.8591	−0.704361	−0.352181	−	0.935932i	$-0.614560\pi$
$877$	−20.8591	−0.704361	−0.352181	+	0.935932i	$0.614560\pi$
$878$	−35.4669	−1.19695
$879$	−9.30296	−0.313781
$880$	20.2077	0.681202
$881$	19.3302	0.651250	0.325625	−	0.945499i	$-0.394425\pi$
$881$	19.3302	0.651250	0.325625	+	0.945499i	$0.394425\pi$
$882$	35.2580	1.18720
$883$	−32.9912	−1.11024	−0.555122	−	0.831769i	$-0.687328\pi$
$883$	−32.9912	−1.11024	−0.555122	+	0.831769i	$0.687328\pi$
$884$	160.370	5.39384
$885$	−9.22599	−0.310128
$886$	−62.9618	−2.11524
$887$	−24.8769	−0.835284	−0.417642	−	0.908612i	$-0.637143\pi$
$887$	−24.8769	−0.835284	−0.417642	+	0.908612i	$0.637143\pi$
$888$	17.7750	0.596488
$889$	18.7998	0.630526
$890$	−123.128	−4.12725
$891$	−4.85949	−0.162799
$892$	−32.3844	−1.08431
$893$	−38.4052	−1.28518
$894$	34.0507	1.13883
$895$	75.4737	2.52281
$896$	−59.2848	−1.98057
$897$	21.0998	0.704503
$898$	57.2407	1.91015
$899$	21.9845	0.733223
$900$	−101.974	−3.39912
$901$	−11.7500	−0.391448
$902$	22.1160	0.736384
$903$	−3.60037	−0.119813
$904$	88.3355	2.93800
$905$	51.5001	1.71192
$906$	6.95600	0.231097
$907$	−6.81735	−0.226366	−0.113183	−	0.993574i	$-0.536105\pi$
$907$	−6.81735	−0.226366	−0.113183	+	0.993574i	$0.536105\pi$
$908$	55.6453	1.84665
$909$	4.14176	0.137373
$910$	164.126	5.44072
$911$	−48.8185	−1.61743	−0.808714	−	0.588202i	$-0.799836\pi$
$911$	−48.8185	−1.61743	−0.808714	+	0.588202i	$0.799836\pi$
$912$	31.6611	1.04841
$913$	−12.6457	−0.418511
$914$	−4.66505	−0.154306
$915$	−5.59831	−0.185074
$916$	−94.9877	−3.13848
$917$	−9.17288	−0.302915
$918$	73.3591	2.42121
$919$	−0.173690	−0.00572949	−0.00286475	−	0.999996i	$-0.500912\pi$
$919$	−0.173690	−0.00572949	−0.00286475	+	0.999996i	$0.500912\pi$
$920$	135.106	4.45431
$921$	−5.93129	−0.195443
$922$	−65.0492	−2.14228
$923$	22.8096	0.750788
$924$	−9.92826	−0.326616
$925$	44.2282	1.45422
$926$	−34.2524	−1.12561
$927$	28.4633	0.934856
$928$	12.5477	0.411899
$929$	33.2704	1.09157	0.545784	−	0.837926i	$-0.316232\pi$
$929$	33.2704	1.09157	0.545784	+	0.837926i	$0.316232\pi$
$930$	28.6572	0.939708
$931$	−47.1044	−1.54378
$932$	−51.3664	−1.68256
$933$	−1.07690	−0.0352561
$934$	36.3212	1.18847
$935$	−28.6417	−0.936683
$936$	−68.9434	−2.25349
$937$	6.66765	0.217823	0.108911	−	0.994051i	$-0.465264\pi$
$937$	6.66765	0.217823	0.108911	+	0.994051i	$0.465264\pi$
$938$	125.687	4.10381
$939$	2.15451	0.0703098
$940$	−73.2956	−2.39064
$941$	−1.80759	−0.0589257	−0.0294629	−	0.999566i	$-0.509380\pi$
$941$	−1.80759	−0.0589257	−0.0294629	+	0.999566i	$0.509380\pi$
$942$	−14.5655	−0.474571
$943$	58.0907	1.89169
$944$	−19.4649	−0.633529
$945$	51.0061	1.65923
$946$	−3.59453	−0.116868
$947$	32.4443	1.05430	0.527149	−	0.849773i	$-0.323261\pi$
$947$	32.4443	1.05430	0.527149	+	0.849773i	$0.323261\pi$
$948$	−2.12439	−0.0689969
$949$	36.0861	1.17141
$950$	200.528	6.50599
$951$	−1.32697	−0.0430301
$952$	−154.064	−4.99324
$953$	−10.4539	−0.338635	−0.169318	−	0.985562i	$-0.554156\pi$
$953$	−10.4539	−0.338635	−0.169318	+	0.985562i	$0.554156\pi$
$954$	9.56547	0.309693
$955$	−57.0224	−1.84520
$956$	−20.4351	−0.660917
$957$	−3.29103	−0.106384
$958$	24.7562	0.799837
$959$	−58.4293	−1.88678
$960$	−12.1594	−0.392444
$961$	−11.5191	−0.371583
$962$	56.6247	1.82565
$963$	−19.7088	−0.635108
$964$	40.2532	1.29647
$965$	−2.22245	−0.0715433
$966$	−38.3846	−1.23500
$967$	55.1991	1.77508	0.887542	−	0.460726i	$-0.152411\pi$
$967$	55.1991	1.77508	0.887542	+	0.460726i	$0.152411\pi$
$968$	56.2514	1.80799
$969$	−44.8753	−1.44160
$970$	−101.270	−3.25157
$971$	45.1695	1.44956	0.724780	−	0.688981i	$-0.241942\pi$
$971$	45.1695	1.44956	0.724780	+	0.688981i	$0.241942\pi$
$972$	−62.5688	−2.00690
$973$	72.7572	2.33249
$974$	−85.7566	−2.74782
$975$	31.5622	1.01080
$976$	−11.8113	−0.378070
$977$	48.6434	1.55624	0.778120	−	0.628115i	$-0.216173\pi$
$977$	48.6434	1.55624	0.778120	+	0.628115i	$0.216173\pi$
$978$	24.1863	0.773393
$979$	12.5299	0.400457
$980$	−89.8978	−2.87168
$981$	−37.7630	−1.20568
$982$	83.3597	2.66012
$983$	13.1368	0.418998	0.209499	−	0.977809i	$-0.432817\pi$
$983$	13.1368	0.418998	0.209499	+	0.977809i	$0.432817\pi$
$984$	34.9223	1.11328
$985$	70.2901	2.23963
$986$	−96.7077	−3.07980
$987$	10.9966	0.350027
$988$	174.420	5.54905
$989$	−9.44150	−0.300222
$990$	23.3167	0.741055
$991$	37.3293	1.18580	0.592901	−	0.805275i	$-0.297982\pi$
$991$	37.3293	1.18580	0.592901	+	0.805275i	$0.297982\pi$
$992$	11.1188	0.353023
$993$	5.34329	0.169564
$994$	−41.4950	−1.31614
$995$	−11.4349	−0.362510
$996$	−37.8129	−1.19815
$997$	−25.3787	−0.803750	−0.401875	−	0.915694i	$-0.631641\pi$
$997$	−25.3787	−0.803750	−0.401875	+	0.915694i	$0.631641\pi$
$998$	23.4279	0.741597
$999$	17.5975	0.556760

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6029.2.a.a.1.16	✓	234

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6029.2.a.a.1.16	✓	234	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:	\( N \)	\(=\)	\( 6029 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6029.a (trivial)

\(f(q)\)	\(=\)	\(q-2.49760 q^{2} -0.682777 q^{3} +4.23800 q^{4} -3.80739 q^{5} +1.70530 q^{6} -3.54561 q^{7} -5.58962 q^{8} -2.53382 q^{9} +O(q^{10})\)	\(q-2.49760 q^{2} -0.682777 q^{3} +4.23800 q^{4} -3.80739 q^{5} +1.70530 q^{6} -3.54561 q^{7} -5.58962 q^{8} -2.53382 q^{9} +9.50934 q^{10} -0.967704 q^{11} -2.89361 q^{12} -4.86783 q^{13} +8.85551 q^{14} +2.59960 q^{15} +5.48462 q^{16} -7.77370 q^{17} +6.32845 q^{18} -8.45475 q^{19} -16.1357 q^{20} +2.42086 q^{21} +2.41694 q^{22} +6.34840 q^{23} +3.81646 q^{24} +9.49625 q^{25} +12.1579 q^{26} +3.77836 q^{27} -15.0263 q^{28} -4.98093 q^{29} -6.49276 q^{30} -4.41372 q^{31} -2.51915 q^{32} +0.660726 q^{33} +19.4156 q^{34} +13.4995 q^{35} -10.7383 q^{36} +4.65744 q^{37} +21.1166 q^{38} +3.32365 q^{39} +21.2819 q^{40} +9.15045 q^{41} -6.04634 q^{42} -1.48723 q^{43} -4.10113 q^{44} +9.64723 q^{45} -15.8557 q^{46} +4.54244 q^{47} -3.74478 q^{48} +5.57135 q^{49} -23.7178 q^{50} +5.30771 q^{51} -20.6299 q^{52} +1.51150 q^{53} -9.43683 q^{54} +3.68443 q^{55} +19.8186 q^{56} +5.77271 q^{57} +12.4404 q^{58} -3.54900 q^{59} +11.0171 q^{60} -2.15353 q^{61} +11.0237 q^{62} +8.98392 q^{63} -4.67742 q^{64} +18.5338 q^{65} -1.65023 q^{66} +14.1930 q^{67} -32.9449 q^{68} -4.33454 q^{69} -33.7164 q^{70} -4.68579 q^{71} +14.1631 q^{72} -7.41318 q^{73} -11.6324 q^{74} -6.48382 q^{75} -35.8312 q^{76} +3.43110 q^{77} -8.30113 q^{78} +0.734166 q^{79} -20.8821 q^{80} +5.02166 q^{81} -22.8541 q^{82} +13.0677 q^{83} +10.2596 q^{84} +29.5976 q^{85} +3.71449 q^{86} +3.40087 q^{87} +5.40910 q^{88} -12.9481 q^{89} -24.0949 q^{90} +17.2594 q^{91} +26.9045 q^{92} +3.01359 q^{93} -11.3452 q^{94} +32.1906 q^{95} +1.72002 q^{96} -10.6495 q^{97} -13.9150 q^{98} +2.45198 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 234 q - 10 q^{2} - 43 q^{3} + 202 q^{4} - 24 q^{5} - 40 q^{6} - 61 q^{7} - 27 q^{8} + 203 q^{9}+O(q^{10}) \) 234 * q - 10 * q^2 - 43 * q^3 + 202 * q^4 - 24 * q^5 - 40 * q^6 - 61 * q^7 - 27 * q^8 + 203 * q^9	\( 234 q - 10 q^{2} - 43 q^{3} + 202 q^{4} - 24 q^{5} - 40 q^{6} - 61 q^{7} - 27 q^{8} + 203 q^{9} - 89 q^{10} - 55 q^{11} - 75 q^{12} - 49 q^{13} - 42 q^{14} - 43 q^{15} + 142 q^{16} - 40 q^{17} - 30 q^{18} - 235 q^{19} - 62 q^{20} - 62 q^{21} - 63 q^{22} - 30 q^{23} - 108 q^{24} + 170 q^{25} - 44 q^{26} - 160 q^{27} - 147 q^{28} - 76 q^{29} - 15 q^{30} - 175 q^{31} - 49 q^{32} - 43 q^{33} - 104 q^{34} - 87 q^{35} + 124 q^{36} - 77 q^{37} - 18 q^{38} - 104 q^{39} - 247 q^{40} - 60 q^{41} - 6 q^{42} - 201 q^{43} - 89 q^{44} - 102 q^{45} - 128 q^{46} - 27 q^{47} - 130 q^{48} + 123 q^{49} - 33 q^{50} - 220 q^{51} - 125 q^{52} - 34 q^{53} - 126 q^{54} - 176 q^{55} - 125 q^{56} - 17 q^{57} - 46 q^{58} - 172 q^{59} - 61 q^{60} - 243 q^{61} - 37 q^{62} - 137 q^{63} + 39 q^{64} - 31 q^{65} - 142 q^{66} - 132 q^{67} - 106 q^{68} - 115 q^{69} - 60 q^{70} - 68 q^{71} - 66 q^{72} - 109 q^{73} - 74 q^{74} - 256 q^{75} - 412 q^{76} - 32 q^{77} - 38 q^{78} - 297 q^{79} - 111 q^{80} + 142 q^{81} - 94 q^{82} - 100 q^{83} - 134 q^{84} - 90 q^{85} + q^{86} - 103 q^{87} - 143 q^{88} - 77 q^{89} - 181 q^{90} - 418 q^{91} - 19 q^{92} + 5 q^{93} - 231 q^{94} - 92 q^{95} - 189 q^{96} - 141 q^{97} - 25 q^{98} - 244 q^{99}+O(q^{100}) \) 234 * q - 10 * q^2 - 43 * q^3 + 202 * q^4 - 24 * q^5 - 40 * q^6 - 61 * q^7 - 27 * q^8 + 203 * q^9 - 89 * q^10 - 55 * q^11 - 75 * q^12 - 49 * q^13 - 42 * q^14 - 43 * q^15 + 142 * q^16 - 40 * q^17 - 30 * q^18 - 235 * q^19 - 62 * q^20 - 62 * q^21 - 63 * q^22 - 30 * q^23 - 108 * q^24 + 170 * q^25 - 44 * q^26 - 160 * q^27 - 147 * q^28 - 76 * q^29 - 15 * q^30 - 175 * q^31 - 49 * q^32 - 43 * q^33 - 104 * q^34 - 87 * q^35 + 124 * q^36 - 77 * q^37 - 18 * q^38 - 104 * q^39 - 247 * q^40 - 60 * q^41 - 6 * q^42 - 201 * q^43 - 89 * q^44 - 102 * q^45 - 128 * q^46 - 27 * q^47 - 130 * q^48 + 123 * q^49 - 33 * q^50 - 220 * q^51 - 125 * q^52 - 34 * q^53 - 126 * q^54 - 176 * q^55 - 125 * q^56 - 17 * q^57 - 46 * q^58 - 172 * q^59 - 61 * q^60 - 243 * q^61 - 37 * q^62 - 137 * q^63 + 39 * q^64 - 31 * q^65 - 142 * q^66 - 132 * q^67 - 106 * q^68 - 115 * q^69 - 60 * q^70 - 68 * q^71 - 66 * q^72 - 109 * q^73 - 74 * q^74 - 256 * q^75 - 412 * q^76 - 32 * q^77 - 38 * q^78 - 297 * q^79 - 111 * q^80 + 142 * q^81 - 94 * q^82 - 100 * q^83 - 134 * q^84 - 90 * q^85 + q^86 - 103 * q^87 - 143 * q^88 - 77 * q^89 - 181 * q^90 - 418 * q^91 - 19 * q^92 + 5 * q^93 - 231 * q^94 - 92 * q^95 - 189 * q^96 - 141 * q^97 - 25 * q^98 - 244 * q^99

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