LMFDB - Embedded newform 8009.2.a.b.1.17

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8009,2,Mod(1,8009)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8009, 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("8009.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8009 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8009.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:	$63.9521869788$
Analytic rank:	$0$
Dimension:	$361$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.17
Character	$\chi$	$=$	8009.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.63785 q^{2} +2.50173 q^{3} +4.95827 q^{4} +3.39410 q^{5} -6.59921 q^{6} +0.113907 q^{7} -7.80348 q^{8} +3.25867 q^{9} +O(q^{10})$	\(q-2.63785 q^{2} +2.50173 q^{3} +4.95827 q^{4} +3.39410 q^{5} -6.59921 q^{6} +0.113907 q^{7} -7.80348 q^{8} +3.25867 q^{9} -8.95313 q^{10} +6.15513 q^{11} +12.4043 q^{12} +2.57616 q^{13} -0.300469 q^{14} +8.49112 q^{15} +10.6679 q^{16} +5.53046 q^{17} -8.59590 q^{18} +2.98958 q^{19} +16.8288 q^{20} +0.284964 q^{21} -16.2363 q^{22} +6.64261 q^{23} -19.5222 q^{24} +6.51989 q^{25} -6.79553 q^{26} +0.647127 q^{27} +0.564780 q^{28} -10.0980 q^{29} -22.3983 q^{30} -6.05686 q^{31} -12.5334 q^{32} +15.3985 q^{33} -14.5885 q^{34} +0.386610 q^{35} +16.1574 q^{36} -8.55187 q^{37} -7.88608 q^{38} +6.44487 q^{39} -26.4858 q^{40} +10.5764 q^{41} -0.751693 q^{42} -6.67483 q^{43} +30.5188 q^{44} +11.0602 q^{45} -17.5222 q^{46} -1.51405 q^{47} +26.6882 q^{48} -6.98703 q^{49} -17.1985 q^{50} +13.8357 q^{51} +12.7733 q^{52} +12.3476 q^{53} -1.70703 q^{54} +20.8911 q^{55} -0.888868 q^{56} +7.47914 q^{57} +26.6370 q^{58} -8.88921 q^{59} +42.1013 q^{60} +10.7692 q^{61} +15.9771 q^{62} +0.371184 q^{63} +11.7255 q^{64} +8.74374 q^{65} -40.6190 q^{66} +1.98099 q^{67} +27.4215 q^{68} +16.6180 q^{69} -1.01982 q^{70} -4.48213 q^{71} -25.4290 q^{72} -5.31757 q^{73} +22.5586 q^{74} +16.3110 q^{75} +14.8232 q^{76} +0.701110 q^{77} -17.0006 q^{78} +13.7981 q^{79} +36.2079 q^{80} -8.15708 q^{81} -27.8991 q^{82} -1.74466 q^{83} +1.41293 q^{84} +18.7709 q^{85} +17.6072 q^{86} -25.2624 q^{87} -48.0315 q^{88} -7.32308 q^{89} -29.1753 q^{90} +0.293442 q^{91} +32.9358 q^{92} -15.1526 q^{93} +3.99384 q^{94} +10.1469 q^{95} -31.3552 q^{96} -9.07051 q^{97} +18.4307 q^{98} +20.0576 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 361 q + 10 q^{2} + 23 q^{3} + 414 q^{4} + 21 q^{5} + 49 q^{6} + 106 q^{7} + 30 q^{8} + 406 q^{9}+O(q^{10}) $ 361 * q + 10 * q^2 + 23 * q^3 + 414 * q^4 + 21 * q^5 + 49 * q^6 + 106 * q^7 + 30 * q^8 + 406 * q^9	\( 361 q + 10 q^{2} + 23 q^{3} + 414 q^{4} + 21 q^{5} + 49 q^{6} + 106 q^{7} + 30 q^{8} + 406 q^{9} + 65 q^{10} + 33 q^{11} + 52 q^{12} + 89 q^{13} + 32 q^{14} + 55 q^{15} + 512 q^{16} + 42 q^{17} + 34 q^{18} + 191 q^{19} + 48 q^{20} + 53 q^{21} + 61 q^{22} + 52 q^{23} + 139 q^{24} + 458 q^{25} + 57 q^{26} + 80 q^{27} + 194 q^{28} + 47 q^{29} + 32 q^{30} + 254 q^{31} + 55 q^{32} + 40 q^{33} + 122 q^{34} + 93 q^{35} + 519 q^{36} + 43 q^{37} + 25 q^{38} + 210 q^{39} + 184 q^{40} + 54 q^{41} + 48 q^{42} + 151 q^{43} + 56 q^{44} + 82 q^{45} + 101 q^{46} + 117 q^{47} + 77 q^{48} + 563 q^{49} + 38 q^{50} + 143 q^{51} + 241 q^{52} + 14 q^{53} + 164 q^{54} + 452 q^{55} + 52 q^{56} + 21 q^{57} + 55 q^{58} + 125 q^{59} + 39 q^{60} + 227 q^{61} + 58 q^{62} + 292 q^{63} + 710 q^{64} + 15 q^{65} + 105 q^{66} + 120 q^{67} + 125 q^{68} + 136 q^{69} + 88 q^{70} + 105 q^{71} + 78 q^{72} + 108 q^{73} + 41 q^{74} + 128 q^{75} + 461 q^{76} + 28 q^{77} + 13 q^{78} + 400 q^{79} + 59 q^{80} + 485 q^{81} + 175 q^{82} + 97 q^{83} + 76 q^{84} + 144 q^{85} - 14 q^{86} + 327 q^{87} + 145 q^{88} + 52 q^{89} + 60 q^{90} + 192 q^{91} + 11 q^{92} + 32 q^{93} + 366 q^{94} + 182 q^{95} + 275 q^{96} + 117 q^{97} + 42 q^{98} + 111 q^{99}+O(q^{100}) \) 361 * q + 10 * q^2 + 23 * q^3 + 414 * q^4 + 21 * q^5 + 49 * q^6 + 106 * q^7 + 30 * q^8 + 406 * q^9 + 65 * q^10 + 33 * q^11 + 52 * q^12 + 89 * q^13 + 32 * q^14 + 55 * q^15 + 512 * q^16 + 42 * q^17 + 34 * q^18 + 191 * q^19 + 48 * q^20 + 53 * q^21 + 61 * q^22 + 52 * q^23 + 139 * q^24 + 458 * q^25 + 57 * q^26 + 80 * q^27 + 194 * q^28 + 47 * q^29 + 32 * q^30 + 254 * q^31 + 55 * q^32 + 40 * q^33 + 122 * q^34 + 93 * q^35 + 519 * q^36 + 43 * q^37 + 25 * q^38 + 210 * q^39 + 184 * q^40 + 54 * q^41 + 48 * q^42 + 151 * q^43 + 56 * q^44 + 82 * q^45 + 101 * q^46 + 117 * q^47 + 77 * q^48 + 563 * q^49 + 38 * q^50 + 143 * q^51 + 241 * q^52 + 14 * q^53 + 164 * q^54 + 452 * q^55 + 52 * q^56 + 21 * q^57 + 55 * q^58 + 125 * q^59 + 39 * q^60 + 227 * q^61 + 58 * q^62 + 292 * q^63 + 710 * q^64 + 15 * q^65 + 105 * q^66 + 120 * q^67 + 125 * q^68 + 136 * q^69 + 88 * q^70 + 105 * q^71 + 78 * q^72 + 108 * q^73 + 41 * q^74 + 128 * q^75 + 461 * q^76 + 28 * q^77 + 13 * q^78 + 400 * q^79 + 59 * q^80 + 485 * q^81 + 175 * q^82 + 97 * q^83 + 76 * q^84 + 144 * q^85 - 14 * q^86 + 327 * q^87 + 145 * q^88 + 52 * q^89 + 60 * q^90 + 192 * q^91 + 11 * q^92 + 32 * q^93 + 366 * q^94 + 182 * q^95 + 275 * q^96 + 117 * q^97 + 42 * q^98 + 111 * 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 $

$2$	−2.63785	−1.86524	−0.932622	−	0.360855i	$-0.882485\pi$
$2$	−2.63785	−1.86524	−0.932622	+	0.360855i	$0.882485\pi$
$3$	2.50173	1.44438	0.722188	−	0.691697i	$-0.243136\pi$
$3$	2.50173	1.44438	0.722188	+	0.691697i	$0.243136\pi$
$4$	4.95827	2.47914
$5$	3.39410	1.51789	0.758943	−	0.651157i	$-0.225716\pi$
$5$	3.39410	1.51789	0.758943	+	0.651157i	$0.225716\pi$
$6$	−6.59921	−2.69411
$7$	0.113907	0.0430526	0.0215263	−	0.999768i	$-0.493147\pi$
$7$	0.113907	0.0430526	0.0215263	+	0.999768i	$0.493147\pi$
$8$	−7.80348	−2.75895
$9$	3.25867	1.08622
$10$	−8.95313	−2.83123
$11$	6.15513	1.85584	0.927921	−	0.372776i	$-0.121594\pi$
$11$	6.15513	1.85584	0.927921	+	0.372776i	$0.121594\pi$
$12$	12.4043	3.58080
$13$	2.57616	0.714498	0.357249	−	0.934009i	$-0.383715\pi$
$13$	2.57616	0.714498	0.357249	+	0.934009i	$0.383715\pi$
$14$	−0.300469	−0.0803037
$15$	8.49112	2.19240
$16$	10.6679	2.66698
$17$	5.53046	1.34133	0.670667	−	0.741759i	$-0.266008\pi$
$17$	5.53046	1.34133	0.670667	+	0.741759i	$0.266008\pi$
$18$	−8.59590	−2.02607
$19$	2.98958	0.685857	0.342929	−	0.939361i	$-0.388581\pi$
$19$	2.98958	0.685857	0.342929	+	0.939361i	$0.388581\pi$
$20$	16.8288	3.76304
$21$	0.284964	0.0621842
$22$	−16.2363	−3.46160
$23$	6.64261	1.38508	0.692540	−	0.721380i	$-0.256492\pi$
$23$	6.64261	1.38508	0.692540	+	0.721380i	$0.256492\pi$
$24$	−19.5222	−3.98496
$25$	6.51989	1.30398
$26$	−6.79553	−1.33271
$27$	0.647127	0.124540
$28$	0.564780	0.106733
$29$	−10.0980	−1.87515	−0.937573	−	0.347790i	$-0.886932\pi$
$29$	−10.0980	−1.87515	−0.937573	+	0.347790i	$0.886932\pi$
$30$	−22.3983	−4.08936
$31$	−6.05686	−1.08784	−0.543922	−	0.839136i	$-0.683061\pi$
$31$	−6.05686	−1.08784	−0.543922	+	0.839136i	$0.683061\pi$
$32$	−12.5334	−2.21561
$33$	15.3985	2.68054
$34$	−14.5885	−2.50192
$35$	0.386610	0.0653490
$36$	16.1574	2.69290
$37$	−8.55187	−1.40592	−0.702959	−	0.711230i	$-0.748138\pi$
$37$	−8.55187	−1.40592	−0.702959	+	0.711230i	$0.748138\pi$
$38$	−7.88608	−1.27929
$39$	6.44487	1.03200
$40$	−26.4858	−4.18777
$41$	10.5764	1.65176	0.825881	−	0.563845i	$-0.190678\pi$
$41$	10.5764	1.65176	0.825881	+	0.563845i	$0.190678\pi$
$42$	−0.751693	−0.115989
$43$	−6.67483	−1.01790	−0.508951	−	0.860796i	$-0.669967\pi$
$43$	−6.67483	−1.01790	−0.508951	+	0.860796i	$0.669967\pi$
$44$	30.5188	4.60089
$45$	11.0602	1.64876
$46$	−17.5222	−2.58351
$47$	−1.51405	−0.220847	−0.110423	−	0.993885i	$-0.535221\pi$
$47$	−1.51405	−0.220847	−0.110423	+	0.993885i	$0.535221\pi$
$48$	26.6882	3.85212
$49$	−6.98703	−0.998146
$50$	−17.1985	−2.43224
$51$	13.8357	1.93739
$52$	12.7733	1.77134
$53$	12.3476	1.69608	0.848039	−	0.529935i	$-0.177784\pi$
$53$	12.3476	1.69608	0.848039	+	0.529935i	$0.177784\pi$
$54$	−1.70703	−0.232297
$55$	20.8911	2.81696
$56$	−0.888868	−0.118780
$57$	7.47914	0.990636
$58$	26.6370	3.49760
$59$	−8.88921	−1.15728	−0.578638	−	0.815584i	$-0.696416\pi$
$59$	−8.88921	−1.15728	−0.578638	+	0.815584i	$0.696416\pi$
$60$	42.1013	5.43525
$61$	10.7692	1.37885	0.689424	−	0.724358i	$-0.257864\pi$
$61$	10.7692	1.37885	0.689424	+	0.724358i	$0.257864\pi$
$62$	15.9771	2.02909
$63$	0.371184	0.0467648
$64$	11.7255	1.46568
$65$	8.74374	1.08453
$66$	−40.6190	−4.99985
$67$	1.98099	0.242016	0.121008	−	0.992652i	$-0.461387\pi$
$67$	1.98099	0.242016	0.121008	+	0.992652i	$0.461387\pi$
$68$	27.4215	3.32535
$69$	16.6180	2.00058
$70$	−1.01982	−0.121892
$71$	−4.48213	−0.531931	−0.265965	−	0.963983i	$-0.585691\pi$
$71$	−4.48213	−0.531931	−0.265965	+	0.963983i	$0.585691\pi$
$72$	−25.4290	−2.99683
$73$	−5.31757	−0.622375	−0.311187	−	0.950349i	$-0.600727\pi$
$73$	−5.31757	−0.622375	−0.311187	+	0.950349i	$0.600727\pi$
$74$	22.5586	2.62238
$75$	16.3110	1.88344
$76$	14.8232	1.70033
$77$	0.701110	0.0798989
$78$	−17.0006	−1.92494
$79$	13.7981	1.55241	0.776204	−	0.630482i	$-0.217143\pi$
$79$	13.7981	1.55241	0.776204	+	0.630482i	$0.217143\pi$
$80$	36.2079	4.04816
$81$	−8.15708	−0.906342
$82$	−27.8991	−3.08094
$83$	−1.74466	−0.191501	−0.0957505	−	0.995405i	$-0.530525\pi$
$83$	−1.74466	−0.191501	−0.0957505	+	0.995405i	$0.530525\pi$
$84$	1.41293	0.154163
$85$	18.7709	2.03599
$86$	17.6072	1.89864
$87$	−25.2624	−2.70842
$88$	−48.0315	−5.12017
$89$	−7.32308	−0.776245	−0.388123	−	0.921608i	$-0.626876\pi$
$89$	−7.32308	−0.776245	−0.388123	+	0.921608i	$0.626876\pi$
$90$	−29.1753	−3.07535
$91$	0.293442	0.0307610
$92$	32.9358	3.43380
$93$	−15.1526	−1.57126
$94$	3.99384	0.411933
$95$	10.1469	1.04105
$96$	−31.3552	−3.20018
$97$	−9.07051	−0.920970	−0.460485	−	0.887667i	$-0.652325\pi$
$97$	−9.07051	−0.920970	−0.460485	+	0.887667i	$0.652325\pi$
$98$	18.4307	1.86179
$99$	20.0576	2.01586
$100$	32.3274	3.23274
$101$	−13.6315	−1.35638	−0.678192	−	0.734885i	$-0.737236\pi$
$101$	−13.6315	−1.35638	−0.678192	+	0.734885i	$0.737236\pi$
$102$	−36.4967	−3.61371
$103$	−11.4743	−1.13060	−0.565299	−	0.824886i	$-0.691239\pi$
$103$	−11.4743	−1.13060	−0.565299	+	0.824886i	$0.691239\pi$
$104$	−20.1030	−1.97126
$105$	0.967195	0.0943886
$106$	−32.5712	−3.16360
$107$	−1.73189	−0.167428	−0.0837139	−	0.996490i	$-0.526678\pi$
$107$	−1.73189	−0.167428	−0.0837139	+	0.996490i	$0.526678\pi$
$108$	3.20863	0.308750
$109$	15.2924	1.46475	0.732375	−	0.680901i	$-0.238412\pi$
$109$	15.2924	1.46475	0.732375	+	0.680901i	$0.238412\pi$
$110$	−55.1077	−5.25431
$111$	−21.3945	−2.03068
$112$	1.21514	0.114820
$113$	3.81317	0.358713	0.179357	−	0.983784i	$-0.442598\pi$
$113$	3.81317	0.358713	0.179357	+	0.983784i	$0.442598\pi$
$114$	−19.7289	−1.84778
$115$	22.5457	2.10239
$116$	−50.0684	−4.64874
$117$	8.39486	0.776105
$118$	23.4484	2.15860
$119$	0.629956	0.0577480
$120$	−66.2603	−6.04871
$121$	26.8857	2.44415
$122$	−28.4074	−2.57189
$123$	26.4594	2.38577
$124$	−30.0315	−2.69691
$125$	5.15865	0.461404
$126$	−0.979129	−0.0872278
$127$	−6.95005	−0.616717	−0.308359	−	0.951270i	$-0.599780\pi$
$127$	−6.95005	−0.616717	−0.308359	+	0.951270i	$0.599780\pi$
$128$	−5.86324	−0.518242
$129$	−16.6986	−1.47023
$130$	−23.0647	−2.02291
$131$	11.1201	0.971571	0.485786	−	0.874078i	$-0.338534\pi$
$131$	11.1201	0.971571	0.485786	+	0.874078i	$0.338534\pi$
$132$	76.3500	6.64541
$133$	0.340533	0.0295280
$134$	−5.22555	−0.451419
$135$	2.19641	0.189037
$136$	−43.1569	−3.70067
$137$	2.66978	0.228095	0.114048	−	0.993475i	$-0.463618\pi$
$137$	2.66978	0.228095	0.114048	+	0.993475i	$0.463618\pi$
$138$	−43.8359	−3.73156
$139$	8.45684	0.717300	0.358650	−	0.933472i	$-0.383237\pi$
$139$	8.45684	0.717300	0.358650	+	0.933472i	$0.383237\pi$
$140$	1.91692	0.162009
$141$	−3.78775	−0.318986
$142$	11.8232	0.992181
$143$	15.8566	1.32600
$144$	34.7632	2.89693
$145$	−34.2735	−2.84626
$146$	14.0270	1.16088
$147$	−17.4797	−1.44170
$148$	−42.4025	−3.48546
$149$	−8.25931	−0.676629	−0.338315	−	0.941033i	$-0.609857\pi$
$149$	−8.25931	−0.676629	−0.338315	+	0.941033i	$0.609857\pi$
$150$	−43.0261	−3.51307
$151$	−3.12647	−0.254428	−0.127214	−	0.991875i	$-0.540604\pi$
$151$	−3.12647	−0.254428	−0.127214	+	0.991875i	$0.540604\pi$
$152$	−23.3292	−1.89224
$153$	18.0220	1.45699
$154$	−1.84943	−0.149031
$155$	−20.5575	−1.65122
$156$	31.9554	2.55848
$157$	−2.26175	−0.180507	−0.0902537	−	0.995919i	$-0.528768\pi$
$157$	−2.26175	−0.180507	−0.0902537	+	0.995919i	$0.528768\pi$
$158$	−36.3974	−2.89562
$159$	30.8905	2.44977
$160$	−42.5395	−3.36305
$161$	0.756637	0.0596313
$162$	21.5172	1.69055
$163$	20.5493	1.60955	0.804774	−	0.593581i	$-0.202286\pi$
$163$	20.5493	1.60955	0.804774	+	0.593581i	$0.202286\pi$
$164$	52.4408	4.09494
$165$	52.2640	4.06875
$166$	4.60215	0.357196
$167$	−14.2636	−1.10375	−0.551874	−	0.833928i	$-0.686087\pi$
$167$	−14.2636	−1.10375	−0.551874	+	0.833928i	$0.686087\pi$
$168$	−2.22371	−0.171563
$169$	−6.36340	−0.489492
$170$	−49.5149	−3.79762
$171$	9.74207	0.744995
$172$	−33.0956	−2.52352
$173$	−1.95856	−0.148907	−0.0744534	−	0.997224i	$-0.523721\pi$
$173$	−1.95856	−0.148907	−0.0744534	+	0.997224i	$0.523721\pi$
$174$	66.6386	5.05186
$175$	0.742658	0.0561397
$176$	65.6624	4.94949
$177$	−22.2384	−1.67154
$178$	19.3172	1.44789
$179$	−25.8172	−1.92967	−0.964836	−	0.262854i	$-0.915336\pi$
$179$	−25.8172	−1.92967	−0.964836	+	0.262854i	$0.915336\pi$
$180$	54.8397	4.08751
$181$	−15.5068	−1.15261	−0.576306	−	0.817234i	$-0.695506\pi$
$181$	−15.5068	−1.15261	−0.576306	+	0.817234i	$0.695506\pi$
$182$	−0.774056	−0.0573769
$183$	26.9415	1.99158
$184$	−51.8355	−3.82136
$185$	−29.0259	−2.13402
$186$	39.9704	2.93077
$187$	34.0407	2.48931
$188$	−7.50706	−0.547509
$189$	0.0737120	0.00536176
$190$	−26.7661	−1.94182
$191$	−6.14052	−0.444313	−0.222156	−	0.975011i	$-0.571310\pi$
$191$	−6.14052	−0.444313	−0.222156	+	0.975011i	$0.571310\pi$
$192$	29.3340	2.11700
$193$	−17.7160	−1.27523	−0.637614	−	0.770356i	$-0.720079\pi$
$193$	−17.7160	−1.27523	−0.637614	+	0.770356i	$0.720079\pi$
$194$	23.9267	1.71783
$195$	21.8745	1.56647
$196$	−34.6436	−2.47454
$197$	10.8190	0.770824	0.385412	−	0.922745i	$-0.374059\pi$
$197$	10.8190	0.770824	0.385412	+	0.922745i	$0.374059\pi$
$198$	−52.9089	−3.76007
$199$	5.62760	0.398930	0.199465	−	0.979905i	$-0.436080\pi$
$199$	5.62760	0.398930	0.199465	+	0.979905i	$0.436080\pi$
$200$	−50.8778	−3.59761
$201$	4.95590	0.349562
$202$	35.9579	2.52999
$203$	−1.15022	−0.0807300
$204$	68.6013	4.80305
$205$	35.8974	2.50719
$206$	30.2676	2.10884
$207$	21.6461	1.50451
$208$	27.4822	1.90555
$209$	18.4013	1.27284
$210$	−2.55132	−0.176058
$211$	7.22927	0.497683	0.248842	−	0.968544i	$-0.419950\pi$
$211$	7.22927	0.497683	0.248842	+	0.968544i	$0.419950\pi$
$212$	61.2229	4.20480
$213$	−11.2131	−0.768308
$214$	4.56846	0.312294
$215$	−22.6550	−1.54506
$216$	−5.04984	−0.343598
$217$	−0.689916	−0.0468345
$218$	−40.3392	−2.73212
$219$	−13.3031	−0.898943
$220$	103.584	6.98362
$221$	14.2474	0.958381
$222$	56.4355	3.78770
$223$	3.66673	0.245542	0.122771	−	0.992435i	$-0.460822\pi$
$223$	3.66673	0.245542	0.122771	+	0.992435i	$0.460822\pi$
$224$	−1.42764	−0.0953879
$225$	21.2462	1.41641
$226$	−10.0586	−0.669088
$227$	−17.4381	−1.15741	−0.578703	−	0.815538i	$-0.696441\pi$
$227$	−17.4381	−1.15741	−0.578703	+	0.815538i	$0.696441\pi$
$228$	37.0836	2.45592
$229$	−25.1271	−1.66045	−0.830223	−	0.557432i	$-0.811787\pi$
$229$	−25.1271	−1.66045	−0.830223	+	0.557432i	$0.811787\pi$
$230$	−59.4721	−3.92148
$231$	1.75399	0.115404
$232$	78.7993	5.17343
$233$	−14.8329	−0.971738	−0.485869	−	0.874032i	$-0.661497\pi$
$233$	−14.8329	−0.971738	−0.485869	+	0.874032i	$0.661497\pi$
$234$	−22.1444	−1.44763
$235$	−5.13883	−0.335220
$236$	−44.0751	−2.86904
$237$	34.5192	2.24226
$238$	−1.66173	−0.107714
$239$	0.982727	0.0635673	0.0317837	−	0.999495i	$-0.489881\pi$
$239$	0.982727	0.0635673	0.0317837	+	0.999495i	$0.489881\pi$
$240$	90.5825	5.84707
$241$	−7.08195	−0.456188	−0.228094	−	0.973639i	$-0.573249\pi$
$241$	−7.08195	−0.456188	−0.228094	+	0.973639i	$0.573249\pi$
$242$	−70.9205	−4.55894
$243$	−22.3482	−1.43364
$244$	53.3964	3.41835
$245$	−23.7146	−1.51507
$246$	−69.7961	−4.45003
$247$	7.70165	0.490044
$248$	47.2646	3.00130
$249$	−4.36467	−0.276600
$250$	−13.6078	−0.860630
$251$	−5.23121	−0.330191	−0.165096	−	0.986278i	$-0.552793\pi$
$251$	−5.23121	−0.330191	−0.165096	+	0.986278i	$0.552793\pi$
$252$	1.84043	0.115936
$253$	40.8861	2.57049
$254$	18.3332	1.15033
$255$	46.9598	2.94074
$256$	−7.98455	−0.499034
$257$	−15.4448	−0.963422	−0.481711	−	0.876330i	$-0.659985\pi$
$257$	−15.4448	−0.963422	−0.481711	+	0.876330i	$0.659985\pi$
$258$	44.0486	2.74234
$259$	−0.974114	−0.0605285
$260$	43.3538	2.68869
$261$	−32.9060	−2.03683
$262$	−29.3333	−1.81222
$263$	13.5641	0.836396	0.418198	−	0.908356i	$-0.362662\pi$
$263$	13.5641	0.836396	0.418198	+	0.908356i	$0.362662\pi$
$264$	−120.162	−7.39546
$265$	41.9090	2.57445
$266$	−0.898277	−0.0550769
$267$	−18.3204	−1.12119
$268$	9.82227	0.599991
$269$	−3.52433	−0.214882	−0.107441	−	0.994211i	$-0.534266\pi$
$269$	−3.52433	−0.214882	−0.107441	+	0.994211i	$0.534266\pi$
$270$	−5.79381	−0.352600
$271$	8.54177	0.518876	0.259438	−	0.965760i	$-0.416463\pi$
$271$	8.54177	0.518876	0.259438	+	0.965760i	$0.416463\pi$
$272$	58.9984	3.57730
$273$	0.734113	0.0444305
$274$	−7.04250	−0.425453
$275$	40.1308	2.41998
$276$	82.3967	4.95970
$277$	22.2845	1.33895	0.669474	−	0.742836i	$-0.266520\pi$
$277$	22.2845	1.33895	0.669474	+	0.742836i	$0.266520\pi$
$278$	−22.3079	−1.33794
$279$	−19.7373	−1.18164
$280$	−3.01690	−0.180294
$281$	−7.74211	−0.461855	−0.230928	−	0.972971i	$-0.574176\pi$
$281$	−7.74211	−0.461855	−0.230928	+	0.972971i	$0.574176\pi$
$282$	9.99152	0.594986
$283$	−15.9454	−0.947856	−0.473928	−	0.880564i	$-0.657164\pi$
$283$	−15.9454	−0.947856	−0.473928	+	0.880564i	$0.657164\pi$
$284$	−22.2236	−1.31873
$285$	25.3849	1.50367
$286$	−41.8274	−2.47331
$287$	1.20473	0.0711127
$288$	−40.8422	−2.40665
$289$	13.5860	0.799177
$290$	90.4084	5.30896
$291$	−22.6920	−1.33023
$292$	−26.3660	−1.54295
$293$	−16.0696	−0.938795	−0.469397	−	0.882987i	$-0.655529\pi$
$293$	−16.0696	−0.938795	−0.469397	+	0.882987i	$0.655529\pi$
$294$	46.1088	2.68912
$295$	−30.1708	−1.75661
$296$	66.7343	3.87885
$297$	3.98315	0.231126
$298$	21.7869	1.26208
$299$	17.1124	0.989637
$300$	80.8745	4.66929
$301$	−0.760307	−0.0438234
$302$	8.24716	0.474571
$303$	−34.1023	−1.95913
$304$	31.8926	1.82916
$305$	36.5515	2.09293
$306$	−47.5393	−2.71764
$307$	13.8060	0.787949	0.393975	−	0.919121i	$-0.371100\pi$
$307$	13.8060	0.787949	0.393975	+	0.919121i	$0.371100\pi$
$308$	3.47629	0.198080
$309$	−28.7057	−1.63301
$310$	54.2278	3.07993
$311$	16.9545	0.961401	0.480700	−	0.876885i	$-0.340382\pi$
$311$	16.9545	0.961401	0.480700	+	0.876885i	$0.340382\pi$
$312$	−50.2924	−2.84725
$313$	−23.9016	−1.35100	−0.675499	−	0.737361i	$-0.736072\pi$
$313$	−23.9016	−1.35100	−0.675499	+	0.737361i	$0.736072\pi$
$314$	5.96617	0.336690
$315$	1.25983	0.0709836
$316$	68.4147	3.84863
$317$	−5.43798	−0.305427	−0.152714	−	0.988270i	$-0.548801\pi$
$317$	−5.43798	−0.305427	−0.152714	+	0.988270i	$0.548801\pi$
$318$	−81.4845	−4.56943
$319$	−62.1543	−3.47998
$320$	39.7973	2.22474
$321$	−4.33272	−0.241829
$322$	−1.99590	−0.111227
$323$	16.5338	0.919964
$324$	−40.4450	−2.24694
$325$	16.7963	0.931690
$326$	−54.2061	−3.00220
$327$	38.2576	2.11565
$328$	−82.5330	−4.55712
$329$	−0.172460	−0.00950803
$330$	−137.865	−7.58921
$331$	−4.64880	−0.255521	−0.127761	−	0.991805i	$-0.540779\pi$
$331$	−4.64880	−0.255521	−0.127761	+	0.991805i	$0.540779\pi$
$332$	−8.65049	−0.474757
$333$	−27.8677	−1.52714
$334$	37.6252	2.05876
$335$	6.72366	0.367353
$336$	3.03997	0.165844
$337$	−6.61398	−0.360286	−0.180143	−	0.983640i	$-0.557656\pi$
$337$	−6.61398	−0.360286	−0.180143	+	0.983640i	$0.557656\pi$
$338$	16.7857	0.913022
$339$	9.53955	0.518117
$340$	93.0713	5.04750
$341$	−37.2808	−2.01887
$342$	−25.6981	−1.38960
$343$	−1.59321	−0.0860255
$344$	52.0869	2.80834
$345$	56.4032	3.03665
$346$	5.16640	0.277747
$347$	−6.82589	−0.366433	−0.183217	−	0.983073i	$-0.558651\pi$
$347$	−6.82589	−0.366433	−0.183217	+	0.983073i	$0.558651\pi$
$348$	−125.258	−6.71453
$349$	26.1476	1.39965	0.699824	−	0.714316i	$-0.253262\pi$
$349$	26.1476	1.39965	0.699824	+	0.714316i	$0.253262\pi$
$350$	−1.95902	−0.104714
$351$	1.66710	0.0889834
$352$	−77.1447	−4.11183
$353$	−7.64790	−0.407056	−0.203528	−	0.979069i	$-0.565241\pi$
$353$	−7.64790	−0.407056	−0.203528	+	0.979069i	$0.565241\pi$
$354$	58.6617	3.11783
$355$	−15.2128	−0.807410
$356$	−36.3098	−1.92442
$357$	1.57598	0.0834098
$358$	68.1021	3.59931
$359$	−2.07753	−0.109648	−0.0548239	−	0.998496i	$-0.517460\pi$
$359$	−2.07753	−0.109648	−0.0548239	+	0.998496i	$0.517460\pi$
$360$	−86.3084	−4.54885
$361$	−10.0624	−0.529600
$362$	40.9047	2.14990
$363$	67.2608	3.53028
$364$	1.45496	0.0762608
$365$	−18.0483	−0.944694
$366$	−71.0678	−3.71478
$367$	−32.7541	−1.70975	−0.854876	−	0.518833i	$-0.826367\pi$
$367$	−32.7541	−1.70975	−0.854876	+	0.518833i	$0.826367\pi$
$368$	70.8627	3.69397
$369$	34.4651	1.79418
$370$	76.5659	3.98047
$371$	1.40648	0.0730206
$372$	−75.1309	−3.89535
$373$	5.83141	0.301939	0.150969	−	0.988538i	$-0.451760\pi$
$373$	5.83141	0.301939	0.150969	+	0.988538i	$0.451760\pi$
$374$	−89.7945	−4.64316
$375$	12.9056	0.666441
$376$	11.8149	0.609305
$377$	−26.0140	−1.33979
$378$	−0.194441	−0.0100010
$379$	−27.5816	−1.41677	−0.708386	−	0.705825i	$-0.750576\pi$
$379$	−27.5816	−1.41677	−0.708386	+	0.705825i	$0.750576\pi$
$380$	50.3112	2.58091
$381$	−17.3872	−0.890772
$382$	16.1978	0.828752
$383$	36.8792	1.88444	0.942220	−	0.334996i	$-0.108735\pi$
$383$	36.8792	1.88444	0.942220	+	0.334996i	$0.108735\pi$
$384$	−14.6683	−0.748536
$385$	2.37964	0.121277
$386$	46.7323	2.37861
$387$	−21.7511	−1.10567
$388$	−44.9740	−2.28321
$389$	14.2495	0.722478	0.361239	−	0.932473i	$-0.382354\pi$
$389$	14.2495	0.722478	0.361239	+	0.932473i	$0.382354\pi$
$390$	−57.7017	−2.92184
$391$	36.7367	1.85785
$392$	54.5231	2.75383
$393$	27.8196	1.40331
$394$	−28.5390	−1.43778
$395$	46.8321	2.35638
$396$	99.4508	4.99759
$397$	38.3294	1.92370	0.961849	−	0.273582i	$-0.0882086\pi$
$397$	38.3294	1.92370	0.961849	+	0.273582i	$0.0882086\pi$
$398$	−14.8448	−0.744102
$399$	0.851923	0.0426495
$400$	69.5535	3.47768
$401$	0.984744	0.0491758	0.0245879	−	0.999698i	$-0.492173\pi$
$401$	0.984744	0.0491758	0.0245879	+	0.999698i	$0.492173\pi$
$402$	−13.0729	−0.652019
$403$	−15.6034	−0.777262
$404$	−67.5886	−3.36266
$405$	−27.6859	−1.37572
$406$	3.03412	0.150581
$407$	−52.6379	−2.60916
$408$	−107.967	−5.34516
$409$	30.7109	1.51856	0.759278	−	0.650766i	$-0.225552\pi$
$409$	30.7109	1.51856	0.759278	+	0.650766i	$0.225552\pi$
$410$	−94.6921	−4.67651
$411$	6.67909	0.329455
$412$	−56.8928	−2.80291
$413$	−1.01254	−0.0498238
$414$	−57.0992	−2.80627
$415$	−5.92154	−0.290677
$416$	−32.2880	−1.58305
$417$	21.1568	1.03605
$418$	−48.5399	−2.37416
$419$	−9.16411	−0.447696	−0.223848	−	0.974624i	$-0.571862\pi$
$419$	−9.16411	−0.447696	−0.223848	+	0.974624i	$0.571862\pi$
$420$	4.79561	0.234002
$421$	9.98399	0.486590	0.243295	−	0.969952i	$-0.421772\pi$
$421$	9.98399	0.486590	0.243295	+	0.969952i	$0.421772\pi$
$422$	−19.0697	−0.928301
$423$	−4.93379	−0.239889
$424$	−96.3545	−4.67939
$425$	36.0580	1.74907
$426$	29.5785	1.43308
$427$	1.22668	0.0593631
$428$	−8.58716	−0.415076
$429$	39.6690	1.91524
$430$	59.7606	2.88191
$431$	10.7817	0.519337	0.259668	−	0.965698i	$-0.416387\pi$
$431$	10.7817	0.519337	0.259668	+	0.965698i	$0.416387\pi$
$432$	6.90348	0.332144
$433$	4.01655	0.193023	0.0965116	−	0.995332i	$-0.469232\pi$
$433$	4.01655	0.193023	0.0965116	+	0.995332i	$0.469232\pi$
$434$	1.81990	0.0873578
$435$	−85.7431	−4.11107
$436$	75.8241	3.63131
$437$	19.8586	0.949967
$438$	35.0917	1.67675
$439$	16.8788	0.805583	0.402792	−	0.915292i	$-0.368040\pi$
$439$	16.8788	0.805583	0.402792	+	0.915292i	$0.368040\pi$
$440$	−163.023	−7.77184
$441$	−22.7684	−1.08421
$442$	−37.5824	−1.78761
$443$	−7.30807	−0.347217	−0.173608	−	0.984815i	$-0.555543\pi$
$443$	−7.30807	−0.347217	−0.173608	+	0.984815i	$0.555543\pi$
$444$	−106.080	−5.03432
$445$	−24.8552	−1.17825
$446$	−9.67229	−0.457996
$447$	−20.6626	−0.977308
$448$	1.33561	0.0631015
$449$	3.31232	0.156318	0.0781591	−	0.996941i	$-0.475096\pi$
$449$	3.31232	0.156318	0.0781591	+	0.996941i	$0.475096\pi$
$450$	−56.0443	−2.64195
$451$	65.0994	3.06541
$452$	18.9067	0.889299
$453$	−7.82158	−0.367490
$454$	45.9991	2.15885
$455$	0.995969	0.0466918
$456$	−58.3633	−2.73311
$457$	−16.5804	−0.775597	−0.387798	−	0.921744i	$-0.626764\pi$
$457$	−16.5804	−0.775597	−0.387798	+	0.921744i	$0.626764\pi$
$458$	66.2816	3.09714
$459$	3.57891	0.167049
$460$	111.787	5.21212
$461$	25.8836	1.20552	0.602760	−	0.797923i	$-0.294068\pi$
$461$	25.8836	1.20552	0.602760	+	0.797923i	$0.294068\pi$
$462$	−4.62677	−0.215257
$463$	−14.2177	−0.660750	−0.330375	−	0.943850i	$-0.607175\pi$
$463$	−14.2177	−0.660750	−0.330375	+	0.943850i	$0.607175\pi$
$464$	−107.724	−5.00097
$465$	−51.4295	−2.38499
$466$	39.1271	1.81253
$467$	17.4149	0.805864	0.402932	−	0.915230i	$-0.367991\pi$
$467$	17.4149	0.805864	0.402932	+	0.915230i	$0.367991\pi$
$468$	41.6240	1.92407
$469$	0.225647	0.0104194
$470$	13.5555	0.625267
$471$	−5.65830	−0.260721
$472$	69.3668	3.19286
$473$	−41.0845	−1.88907
$474$	−91.0565	−4.18236
$475$	19.4917	0.894343
$476$	3.12349	0.143165
$477$	40.2369	1.84232
$478$	−2.59229	−0.118569
$479$	−25.6138	−1.17033	−0.585163	−	0.810916i	$-0.698969\pi$
$479$	−25.6138	−1.17033	−0.585163	+	0.810916i	$0.698969\pi$
$480$	−106.423	−4.85751
$481$	−22.0310	−1.00453
$482$	18.6811	0.850902
$483$	1.89290	0.0861301
$484$	133.306	6.05939
$485$	−30.7862	−1.39793
$486$	58.9513	2.67409
$487$	−15.2560	−0.691314	−0.345657	−	0.938361i	$-0.612344\pi$
$487$	−15.2560	−0.691314	−0.345657	+	0.938361i	$0.612344\pi$
$488$	−84.0369	−3.80417
$489$	51.4090	2.32479
$490$	62.5557	2.82598
$491$	−17.1046	−0.771922	−0.385961	−	0.922515i	$-0.626130\pi$
$491$	−17.1046	−0.771922	−0.385961	+	0.922515i	$0.626130\pi$
$492$	131.193	5.91463
$493$	−55.8464	−2.51520
$494$	−20.3158	−0.914052
$495$	68.0773	3.05985
$496$	−64.6139	−2.90125
$497$	−0.510544	−0.0229010
$498$	11.5134	0.515926
$499$	−38.4541	−1.72144	−0.860721	−	0.509076i	$-0.829987\pi$
$499$	−38.4541	−1.72144	−0.860721	+	0.509076i	$0.829987\pi$
$500$	25.5780	1.14388
$501$	−35.6836	−1.59423
$502$	13.7992	0.615887
$503$	−32.1376	−1.43295	−0.716473	−	0.697615i	$-0.754245\pi$
$503$	−32.1376	−1.43295	−0.716473	+	0.697615i	$0.754245\pi$
$504$	−2.89653	−0.129022
$505$	−46.2666	−2.05884
$506$	−107.852	−4.79459
$507$	−15.9195	−0.707011
$508$	−34.4602	−1.52892
$509$	−2.72661	−0.120855	−0.0604274	−	0.998173i	$-0.519246\pi$
$509$	−2.72661	−0.120855	−0.0604274	+	0.998173i	$0.519246\pi$
$510$	−123.873	−5.48520
$511$	−0.605706	−0.0267949
$512$	32.7885	1.44906
$513$	1.93464	0.0854164
$514$	40.7412	1.79702
$515$	−38.9449	−1.71612
$516$	−82.7964	−3.64491
$517$	−9.31917	−0.409857
$518$	2.56957	0.112900
$519$	−4.89980	−0.215077
$520$	−68.2316	−2.99215
$521$	11.6541	0.510576	0.255288	−	0.966865i	$-0.417830\pi$
$521$	11.6541	0.510576	0.255288	+	0.966865i	$0.417830\pi$
$522$	86.8011	3.79918
$523$	36.8626	1.61189	0.805944	−	0.591991i	$-0.201658\pi$
$523$	36.8626	1.61189	0.805944	+	0.591991i	$0.201658\pi$
$524$	55.1367	2.40866
$525$	1.85793	0.0810868
$526$	−35.7800	−1.56008
$527$	−33.4972	−1.45916
$528$	164.270	7.14892
$529$	21.1242	0.918445
$530$	−110.550	−4.80198
$531$	−28.9670	−1.25706
$532$	1.68846	0.0732038
$533$	27.2466	1.18018
$534$	48.3265	2.09129
$535$	−5.87819	−0.254136
$536$	−15.4586	−0.667710
$537$	−64.5879	−2.78717
$538$	9.29666	0.400807
$539$	−43.0061	−1.85240
$540$	10.8904	0.468648
$541$	35.2524	1.51562	0.757810	−	0.652475i	$-0.226269\pi$
$541$	35.2524	1.51562	0.757810	+	0.652475i	$0.226269\pi$
$542$	−22.5319	−0.967830
$543$	−38.7939	−1.66481
$544$	−69.3155	−2.97188
$545$	51.9040	2.22332
$546$	−1.93648	−0.0828738
$547$	−12.3725	−0.529010	−0.264505	−	0.964384i	$-0.585208\pi$
$547$	−12.3725	−0.529010	−0.264505	+	0.964384i	$0.585208\pi$
$548$	13.2375	0.565478
$549$	35.0931	1.49774
$550$	−105.859	−4.51385
$551$	−30.1887	−1.28608
$552$	−129.679	−5.51949
$553$	1.57169	0.0668352
$554$	−58.7833	−2.49746
$555$	−72.6150	−3.08233
$556$	41.9313	1.77828
$557$	−39.1410	−1.65846	−0.829228	−	0.558911i	$-0.811219\pi$
$557$	−39.1410	−1.65846	−0.829228	+	0.558911i	$0.811219\pi$
$558$	52.0641	2.20405
$559$	−17.1954	−0.727289
$560$	4.12432	0.174284
$561$	85.1609	3.59549
$562$	20.4225	0.861473
$563$	−2.01594	−0.0849619	−0.0424810	−	0.999097i	$-0.513526\pi$
$563$	−2.01594	−0.0849619	−0.0424810	+	0.999097i	$0.513526\pi$
$564$	−18.7807	−0.790809
$565$	12.9423	0.544486
$566$	42.0616	1.76798
$567$	−0.929145	−0.0390204
$568$	34.9762	1.46757
$569$	−34.4410	−1.44384	−0.721921	−	0.691976i	$-0.756741\pi$
$569$	−34.4410	−1.44384	−0.721921	+	0.691976i	$0.756741\pi$
$570$	−66.9617	−2.80472
$571$	6.96795	0.291599	0.145800	−	0.989314i	$-0.453424\pi$
$571$	6.96795	0.291599	0.145800	+	0.989314i	$0.453424\pi$
$572$	78.6214	3.28733
$573$	−15.3620	−0.641755
$574$	−3.17789	−0.132642
$575$	43.3091	1.80611
$576$	38.2094	1.59206
$577$	19.3094	0.803862	0.401931	−	0.915670i	$-0.368339\pi$
$577$	19.3094	0.803862	0.401931	+	0.915670i	$0.368339\pi$
$578$	−35.8379	−1.49066
$579$	−44.3208	−1.84191
$580$	−169.937	−7.05625
$581$	−0.198728	−0.00824463
$582$	59.8581	2.48120
$583$	76.0013	3.14765
$584$	41.4956	1.71710
$585$	28.4930	1.17804
$586$	42.3892	1.75108
$587$	13.5643	0.559858	0.279929	−	0.960021i	$-0.409689\pi$
$587$	13.5643	0.559858	0.279929	+	0.960021i	$0.409689\pi$
$588$	−86.6690	−3.57417
$589$	−18.1075	−0.746105
$590$	79.5862	3.27651
$591$	27.0663	1.11336
$592$	−91.2305	−3.74955
$593$	−15.2509	−0.626278	−0.313139	−	0.949707i	$-0.601381\pi$
$593$	−15.2509	−0.626278	−0.313139	+	0.949707i	$0.601381\pi$
$594$	−10.5070	−0.431106
$595$	2.13813	0.0876548
$596$	−40.9519	−1.67746
$597$	14.0788	0.576206
$598$	−45.1401	−1.84591
$599$	29.0149	1.18552	0.592759	−	0.805380i	$-0.298039\pi$
$599$	29.0149	1.18552	0.592759	+	0.805380i	$0.298039\pi$
$600$	−127.283	−5.19630
$601$	11.2578	0.459216	0.229608	−	0.973283i	$-0.426256\pi$
$601$	11.2578	0.459216	0.229608	+	0.973283i	$0.426256\pi$
$602$	2.00558	0.0817413
$603$	6.45539	0.262884
$604$	−15.5019	−0.630762
$605$	91.2526	3.70995
$606$	89.9570	3.65425
$607$	−29.6120	−1.20191	−0.600957	−	0.799281i	$-0.705214\pi$
$607$	−29.6120	−1.20191	−0.600957	+	0.799281i	$0.705214\pi$
$608$	−37.4696	−1.51959
$609$	−2.87756	−0.116604
$610$	−96.4176	−3.90383
$611$	−3.90043	−0.157795
$612$	89.3577	3.61207
$613$	−7.95972	−0.321490	−0.160745	−	0.986996i	$-0.551390\pi$
$613$	−7.95972	−0.321490	−0.160745	+	0.986996i	$0.551390\pi$
$614$	−36.4182	−1.46972
$615$	89.8058	3.62132
$616$	−5.47110	−0.220437
$617$	−38.1174	−1.53455	−0.767274	−	0.641319i	$-0.778388\pi$
$617$	−38.1174	−1.53455	−0.767274	+	0.641319i	$0.778388\pi$
$618$	75.7214	3.04596
$619$	−35.0640	−1.40934	−0.704670	−	0.709535i	$-0.748905\pi$
$619$	−35.0640	−1.40934	−0.704670	+	0.709535i	$0.748905\pi$
$620$	−101.930	−4.09360
$621$	4.29861	0.172497
$622$	−44.7235	−1.79325
$623$	−0.834147	−0.0334194
$624$	68.7532	2.75233
$625$	−15.0905	−0.603620
$626$	63.0489	2.51994
$627$	46.0351	1.83847
$628$	−11.2144	−0.447502
$629$	−47.2958	−1.88581
$630$	−3.32326	−0.132402
$631$	36.0424	1.43482	0.717412	−	0.696649i	$-0.245326\pi$
$631$	36.0424	1.43482	0.717412	+	0.696649i	$0.245326\pi$
$632$	−107.673	−4.28301
$633$	18.0857	0.718842
$634$	14.3446	0.569696
$635$	−23.5891	−0.936106
$636$	153.163	6.07332
$637$	−17.9997	−0.713174
$638$	163.954	6.49100
$639$	−14.6058	−0.577796
$640$	−19.9004	−0.786632
$641$	10.7419	0.424281	0.212141	−	0.977239i	$-0.431957\pi$
$641$	10.7419	0.424281	0.212141	+	0.977239i	$0.431957\pi$
$642$	11.4291	0.451070
$643$	−37.8210	−1.49151	−0.745756	−	0.666219i	$-0.767912\pi$
$643$	−37.8210	−1.49151	−0.745756	+	0.666219i	$0.767912\pi$
$644$	3.75161	0.147834
$645$	−56.6768	−2.23165
$646$	−43.6137	−1.71596
$647$	14.8857	0.585216	0.292608	−	0.956232i	$-0.405477\pi$
$647$	14.8857	0.585216	0.292608	+	0.956232i	$0.405477\pi$
$648$	63.6536	2.50055
$649$	−54.7143	−2.14772
$650$	−44.3061	−1.73783
$651$	−1.72599	−0.0676467
$652$	101.889	3.99029
$653$	39.8868	1.56089	0.780445	−	0.625224i	$-0.214993\pi$
$653$	39.8868	1.56089	0.780445	+	0.625224i	$0.214993\pi$
$654$	−100.918	−3.94621
$655$	37.7428	1.47473
$656$	112.828	4.40521
$657$	−17.3282	−0.676038
$658$	0.454925	0.0177348
$659$	13.2269	0.515245	0.257623	−	0.966246i	$-0.417061\pi$
$659$	13.2269	0.515245	0.257623	+	0.966246i	$0.417061\pi$
$660$	259.139	10.0870
$661$	−12.2917	−0.478092	−0.239046	−	0.971008i	$-0.576835\pi$
$661$	−12.2917	−0.478092	−0.239046	+	0.971008i	$0.576835\pi$
$662$	12.2629	0.476609
$663$	35.6431	1.38426
$664$	13.6144	0.528341
$665$	1.15580	0.0448201
$666$	73.5110	2.84849
$667$	−67.0768	−2.59723
$668$	−70.7226	−2.73634
$669$	9.17318	0.354656
$670$	−17.7360	−0.685203
$671$	66.2856	2.55893
$672$	−3.57157	−0.137776
$673$	0.681185	0.0262578	0.0131289	−	0.999914i	$-0.495821\pi$
$673$	0.681185	0.0262578	0.0131289	+	0.999914i	$0.495821\pi$
$674$	17.4467	0.672022
$675$	4.21919	0.162397
$676$	−31.5514	−1.21352
$677$	18.3020	0.703404	0.351702	−	0.936112i	$-0.385603\pi$
$677$	18.3020	0.703404	0.351702	+	0.936112i	$0.385603\pi$
$678$	−25.1639	−0.966415
$679$	−1.03319	−0.0396502
$680$	−146.479	−5.61720
$681$	−43.6255	−1.67173
$682$	98.3412	3.76568
$683$	−16.6706	−0.637884	−0.318942	−	0.947774i	$-0.603328\pi$
$683$	−16.6706	−0.637884	−0.318942	+	0.947774i	$0.603328\pi$
$684$	48.3038	1.84694
$685$	9.06151	0.346222
$686$	4.20267	0.160459
$687$	−62.8613	−2.39831
$688$	−71.2064	−2.71472
$689$	31.8095	1.21184
$690$	−148.783	−5.66409
$691$	31.2023	1.18699	0.593495	−	0.804837i	$-0.297748\pi$
$691$	31.2023	1.18699	0.593495	+	0.804837i	$0.297748\pi$
$692$	−9.71108	−0.369160
$693$	2.28469	0.0867881
$694$	18.0057	0.683487
$695$	28.7033	1.08878
$696$	197.135	7.47238
$697$	58.4926	2.21556
$698$	−68.9735	−2.61068
$699$	−37.1081	−1.40356
$700$	3.68230	0.139178
$701$	12.5666	0.474635	0.237317	−	0.971432i	$-0.423732\pi$
$701$	12.5666	0.474635	0.237317	+	0.971432i	$0.423732\pi$
$702$	−4.39757	−0.165976
$703$	−25.5665	−0.964259
$704$	72.1717	2.72007
$705$	−12.8560	−0.484184
$706$	20.1740	0.759260
$707$	−1.55272	−0.0583959
$708$	−110.264	−4.14398
$709$	39.5801	1.48646	0.743232	−	0.669034i	$-0.233292\pi$
$709$	39.5801	1.48646	0.743232	+	0.669034i	$0.233292\pi$
$710$	40.1291	1.50602
$711$	44.9635	1.68626
$712$	57.1455	2.14162
$713$	−40.2333	−1.50675
$714$	−4.15721	−0.155580
$715$	53.8189	2.01271
$716$	−128.009	−4.78392
$717$	2.45852	0.0918152
$718$	5.48022	0.204520
$719$	13.6047	0.507370	0.253685	−	0.967287i	$-0.418357\pi$
$719$	13.6047	0.507370	0.253685	+	0.967287i	$0.418357\pi$
$720$	117.990	4.39721
$721$	−1.30700	−0.0486752
$722$	26.5431	0.987833
$723$	−17.7171	−0.658908
$724$	−76.8870	−2.85748
$725$	−65.8376	−2.44515
$726$	−177.424	−6.58483
$727$	51.9988	1.92853	0.964264	−	0.264942i	$-0.0853527\pi$
$727$	51.9988	1.92853	0.964264	+	0.264942i	$0.0853527\pi$
$728$	−2.28987	−0.0848681
$729$	−31.4380	−1.16437
$730$	47.6089	1.76208
$731$	−36.9149	−1.36535
$732$	133.583	4.93739
$733$	−7.57220	−0.279686	−0.139843	−	0.990174i	$-0.544660\pi$
$733$	−7.57220	−0.279686	−0.139843	+	0.990174i	$0.544660\pi$
$734$	86.4006	3.18910
$735$	−59.3277	−2.18834
$736$	−83.2544	−3.06880
$737$	12.1932	0.449144
$738$	−90.9139	−3.34659
$739$	8.98718	0.330599	0.165299	−	0.986243i	$-0.447141\pi$
$739$	8.98718	0.330599	0.165299	+	0.986243i	$0.447141\pi$
$740$	−143.918	−5.29053
$741$	19.2675	0.707808
$742$	−3.71008	−0.136201
$743$	29.7249	1.09050	0.545250	−	0.838273i	$-0.316435\pi$
$743$	29.7249	1.09050	0.545250	+	0.838273i	$0.316435\pi$
$744$	118.243	4.33501
$745$	−28.0329	−1.02705
$746$	−15.3824	−0.563190
$747$	−5.68527	−0.208013
$748$	168.783	6.17132
$749$	−0.197273	−0.00720821
$750$	−34.0430	−1.24307
$751$	30.0587	1.09686	0.548429	−	0.836197i	$-0.315226\pi$
$751$	30.0587	1.09686	0.548429	+	0.836197i	$0.315226\pi$
$752$	−16.1517	−0.588993
$753$	−13.0871	−0.476920
$754$	68.6211	2.49903
$755$	−10.6115	−0.386193
$756$	0.365484	0.0132925
$757$	45.4112	1.65050	0.825249	−	0.564770i	$-0.191035\pi$
$757$	45.4112	1.65050	0.825249	+	0.564770i	$0.191035\pi$
$758$	72.7562	2.64262
$759$	102.286	3.71276
$760$	−79.1814	−2.87221
$761$	42.4356	1.53829	0.769145	−	0.639074i	$-0.220682\pi$
$761$	42.4356	1.53829	0.769145	+	0.639074i	$0.220682\pi$
$762$	45.8648	1.66151
$763$	1.74191	0.0630614
$764$	−30.4464	−1.10151
$765$	61.1683	2.21154
$766$	−97.2819	−3.51494
$767$	−22.9000	−0.826872
$768$	−19.9752	−0.720794
$769$	38.5012	1.38839	0.694194	−	0.719788i	$-0.255761\pi$
$769$	38.5012	1.38839	0.694194	+	0.719788i	$0.255761\pi$
$770$	−6.27713	−0.226212
$771$	−38.6389	−1.39154
$772$	−87.8409	−3.16146
$773$	−16.0212	−0.576244	−0.288122	−	0.957594i	$-0.593031\pi$
$773$	−16.0212	−0.576244	−0.288122	+	0.957594i	$0.593031\pi$
$774$	57.3761	2.06234
$775$	−39.4900	−1.41852
$776$	70.7815	2.54091
$777$	−2.43697	−0.0874259
$778$	−37.5881	−1.34760
$779$	31.6191	1.13287
$780$	108.460	3.88348
$781$	−27.5881	−0.987180
$782$	−96.9060	−3.46535
$783$	−6.53466	−0.233530
$784$	−74.5369	−2.66203
$785$	−7.67660	−0.273990
$786$	−73.3841	−2.61752
$787$	−13.4333	−0.478846	−0.239423	−	0.970915i	$-0.576958\pi$
$787$	−13.4333	−0.478846	−0.239423	+	0.970915i	$0.576958\pi$
$788$	53.6437	1.91098
$789$	33.9337	1.20807
$790$	−123.536	−4.39522
$791$	0.434346	0.0154436
$792$	−156.519	−5.56165
$793$	27.7431	0.985185
$794$	−101.107	−3.58816
$795$	104.845	3.71848
$796$	27.9032	0.989002
$797$	−17.8402	−0.631933	−0.315967	−	0.948770i	$-0.602329\pi$
$797$	−17.8402	−0.631933	−0.315967	+	0.948770i	$0.602329\pi$
$798$	−2.24725	−0.0795517
$799$	−8.37339	−0.296229
$800$	−81.7163	−2.88911
$801$	−23.8635	−0.843176
$802$	−2.59761	−0.0917248
$803$	−32.7304	−1.15503
$804$	24.5727	0.866612
$805$	2.56810	0.0905136
$806$	41.1596	1.44978
$807$	−8.81693	−0.310371
$808$	106.373	3.74219
$809$	1.84158	0.0647465	0.0323732	−	0.999476i	$-0.489693\pi$
$809$	1.84158	0.0647465	0.0323732	+	0.999476i	$0.489693\pi$
$810$	73.0313	2.56606
$811$	44.0240	1.54589	0.772946	−	0.634472i	$-0.218782\pi$
$811$	44.0240	1.54589	0.772946	+	0.634472i	$0.218782\pi$
$812$	−5.70312	−0.200140
$813$	21.3692	0.749452
$814$	138.851	4.86673
$815$	69.7464	2.44311
$816$	147.598	5.16698
$817$	−19.9550	−0.698135
$818$	−81.0108	−2.83248
$819$	0.956230	0.0334134
$820$	177.989	6.21565
$821$	−39.7334	−1.38670	−0.693352	−	0.720599i	$-0.743867\pi$
$821$	−39.7334	−1.38670	−0.693352	+	0.720599i	$0.743867\pi$
$822$	−17.6185	−0.614514
$823$	−19.7193	−0.687372	−0.343686	−	0.939085i	$-0.611676\pi$
$823$	−19.7193	−0.687372	−0.343686	+	0.939085i	$0.611676\pi$
$824$	89.5396	3.11926
$825$	100.397	3.49536
$826$	2.67093	0.0929335
$827$	−15.4232	−0.536318	−0.268159	−	0.963375i	$-0.586415\pi$
$827$	−15.4232	−0.536318	−0.268159	+	0.963375i	$0.586415\pi$
$828$	107.327	3.72987
$829$	42.7279	1.48400	0.742001	−	0.670399i	$-0.233877\pi$
$829$	42.7279	1.48400	0.742001	+	0.670399i	$0.233877\pi$
$830$	15.6201	0.542183
$831$	55.7500	1.93394
$832$	30.2067	1.04723
$833$	−38.6415	−1.33885
$834$	−55.8084	−1.93249
$835$	−48.4119	−1.67536
$836$	91.2385	3.15555
$837$	−3.91955	−0.135480
$838$	24.1736	0.835062
$839$	17.5087	0.604468	0.302234	−	0.953234i	$-0.402268\pi$
$839$	17.5087	0.604468	0.302234	+	0.953234i	$0.402268\pi$
$840$	−7.54749	−0.260413
$841$	72.9689	2.51617
$842$	−26.3363	−0.907609
$843$	−19.3687	−0.667093
$844$	35.8447	1.23382
$845$	−21.5980	−0.742993
$846$	13.0146	0.447451
$847$	3.06246	0.105227
$848$	131.723	4.52340
$849$	−39.8911	−1.36906
$850$	−95.1157	−3.26244
$851$	−56.8067	−1.94731
$852$	−55.5975	−1.90474
$853$	18.1469	0.621338	0.310669	−	0.950518i	$-0.399447\pi$
$853$	18.1469	0.621338	0.310669	+	0.950518i	$0.399447\pi$
$854$	−3.23579	−0.110727
$855$	33.0655	1.13082
$856$	13.5147	0.461924
$857$	−55.1124	−1.88260	−0.941301	−	0.337567i	$-0.890396\pi$
$857$	−55.1124	−1.88260	−0.941301	+	0.337567i	$0.890396\pi$
$858$	−104.641	−3.57239
$859$	−8.28557	−0.282700	−0.141350	−	0.989960i	$-0.545144\pi$
$859$	−8.28557	−0.282700	−0.141350	+	0.989960i	$0.545144\pi$
$860$	−112.330	−3.83041
$861$	3.01390	0.102713
$862$	−28.4406	−0.968690
$863$	−7.39487	−0.251724	−0.125862	−	0.992048i	$-0.540170\pi$
$863$	−7.39487	−0.251724	−0.125862	+	0.992048i	$0.540170\pi$
$864$	−8.11069	−0.275931
$865$	−6.64755	−0.226023
$866$	−10.5951	−0.360035
$867$	33.9886	1.15431
$868$	−3.42079	−0.116109
$869$	84.9291	2.88102
$870$	226.178	7.66814
$871$	5.10334	0.172920
$872$	−119.334	−4.04117
$873$	−29.5578	−1.00038
$874$	−52.3842	−1.77192
$875$	0.587604	0.0198646
$876$	−65.9606	−2.22860
$877$	−29.4376	−0.994036	−0.497018	−	0.867740i	$-0.665572\pi$
$877$	−29.4376	−0.994036	−0.497018	+	0.867740i	$0.665572\pi$
$878$	−44.5239	−1.50261
$879$	−40.2018	−1.35597
$880$	222.864	7.51276
$881$	47.3485	1.59521	0.797605	−	0.603180i	$-0.206100\pi$
$881$	47.3485	1.59521	0.797605	+	0.603180i	$0.206100\pi$
$882$	60.0597	2.02232
$883$	50.3237	1.69353	0.846764	−	0.531969i	$-0.178548\pi$
$883$	50.3237	1.69353	0.846764	+	0.531969i	$0.178548\pi$
$884$	70.6422	2.37596
$885$	−75.4794	−2.53721
$886$	19.2776	0.647644
$887$	−1.01424	−0.0340549	−0.0170274	−	0.999855i	$-0.505420\pi$
$887$	−1.01424	−0.0340549	−0.0170274	+	0.999855i	$0.505420\pi$
$888$	166.952	5.60253
$889$	−0.791656	−0.0265513
$890$	65.5645	2.19773
$891$	−50.2079	−1.68203
$892$	18.1806	0.608733
$893$	−4.52637	−0.151469
$894$	54.5049	1.82292
$895$	−87.6262	−2.92902
$896$	−0.667861	−0.0223117
$897$	42.8107	1.42941
$898$	−8.73742	−0.291572
$899$	61.1619	2.03986
$900$	105.344	3.51148
$901$	68.2881	2.27501
$902$	−171.723	−5.71774
$903$	−1.90209	−0.0632974
$904$	−29.7560	−0.989671
$905$	−52.6316	−1.74953
$906$	20.6322	0.685459
$907$	−16.5899	−0.550860	−0.275430	−	0.961321i	$-0.588820\pi$
$907$	−16.5899	−0.550860	−0.275430	+	0.961321i	$0.588820\pi$
$908$	−86.4628	−2.86937
$909$	−44.4205	−1.47334
$910$	−2.62722	−0.0870915
$911$	7.18323	0.237991	0.118996	−	0.992895i	$-0.462033\pi$
$911$	7.18323	0.237991	0.118996	+	0.992895i	$0.462033\pi$
$912$	79.7867	2.64200
$913$	−10.7386	−0.355396
$914$	43.7366	1.44668
$915$	91.4422	3.02299
$916$	−124.587	−4.11647
$917$	1.26666	0.0418287
$918$	−9.44064	−0.311587
$919$	33.1494	1.09350	0.546749	−	0.837297i	$-0.315865\pi$
$919$	33.1494	1.09350	0.546749	+	0.837297i	$0.315865\pi$
$920$	−175.935	−5.80039
$921$	34.5389	1.13810
$922$	−68.2772	−2.24859
$923$	−11.5467	−0.380064
$924$	8.69676	0.286102
$925$	−55.7572	−1.83329
$926$	37.5041	1.23246
$927$	−37.3910	−1.22808
$928$	126.562	4.15459
$929$	7.91553	0.259700	0.129850	−	0.991534i	$-0.458550\pi$
$929$	7.91553	0.259700	0.129850	+	0.991534i	$0.458550\pi$
$930$	135.664	4.44858
$931$	−20.8883	−0.684586
$932$	−73.5457	−2.40907
$933$	42.4156	1.38863
$934$	−45.9379	−1.50313
$935$	115.538	3.77848
$936$	−65.5092	−2.14123
$937$	25.5945	0.836135	0.418068	−	0.908416i	$-0.362708\pi$
$937$	25.5945	0.836135	0.418068	+	0.908416i	$0.362708\pi$
$938$	−0.595225	−0.0194348
$939$	−59.7954	−1.95135
$940$	−25.4797	−0.831056
$941$	11.8170	0.385223	0.192612	−	0.981275i	$-0.438304\pi$
$941$	11.8170	0.385223	0.192612	+	0.981275i	$0.438304\pi$
$942$	14.9258	0.486308
$943$	70.2551	2.28782
$944$	−94.8292	−3.08643
$945$	0.250186	0.00813854
$946$	108.375	3.52357
$947$	0.789591	0.0256583	0.0128291	−	0.999918i	$-0.495916\pi$
$947$	0.789591	0.0256583	0.0128291	+	0.999918i	$0.495916\pi$
$948$	171.155	5.55887
$949$	−13.6989	−0.444686
$950$	−51.4164	−1.66817
$951$	−13.6044	−0.441152
$952$	−4.91585	−0.159324
$953$	−21.0088	−0.680540	−0.340270	−	0.940328i	$-0.610519\pi$
$953$	−21.0088	−0.680540	−0.340270	+	0.940328i	$0.610519\pi$
$954$	−106.139	−3.43637
$955$	−20.8415	−0.674416
$956$	4.87263	0.157592
$957$	−155.494	−5.02639
$958$	67.5655	2.18294
$959$	0.304106	0.00982010
$960$	99.5623	3.21336
$961$	5.68550	0.183403
$962$	58.1145	1.87369
$963$	−5.64365	−0.181864
$964$	−35.1142	−1.13095
$965$	−60.1300	−1.93565
$966$	−4.99320	−0.160654
$967$	−27.7245	−0.891559	−0.445779	−	0.895143i	$-0.647073\pi$
$967$	−27.7245	−0.891559	−0.445779	+	0.895143i	$0.647073\pi$
$968$	−209.802	−6.74329
$969$	41.3631	1.32877
$970$	81.2094	2.60748
$971$	−8.25587	−0.264943	−0.132472	−	0.991187i	$-0.542291\pi$
$971$	−8.25587	−0.264943	−0.132472	+	0.991187i	$0.542291\pi$
$972$	−110.808	−3.55418
$973$	0.963289	0.0308816
$974$	40.2430	1.28947
$975$	42.0198	1.34571
$976$	114.884	3.67735
$977$	25.1900	0.805899	0.402949	−	0.915222i	$-0.367985\pi$
$977$	25.1900	0.805899	0.402949	+	0.915222i	$0.367985\pi$
$978$	−135.609	−4.33631
$979$	−45.0746	−1.44059
$980$	−117.584	−3.75607
$981$	49.8331	1.59105
$982$	45.1196	1.43982
$983$	17.6493	0.562924	0.281462	−	0.959572i	$-0.409181\pi$
$983$	17.6493	0.562924	0.281462	+	0.959572i	$0.409181\pi$
$984$	−206.476	−6.58220
$985$	36.7208	1.17002
$986$	147.315	4.69145
$987$	−0.431449	−0.0137332
$988$	38.1868	1.21489
$989$	−44.3383	−1.40987
$990$	−179.578	−5.70736
$991$	6.39439	0.203124	0.101562	−	0.994829i	$-0.467616\pi$
$991$	6.39439	0.203124	0.101562	+	0.994829i	$0.467616\pi$
$992$	75.9130	2.41024
$993$	−11.6301	−0.369069
$994$	1.34674	0.0427160
$995$	19.1006	0.605531
$996$	−21.6412	−0.685728
$997$	−53.7858	−1.70341	−0.851707	−	0.524018i	$-0.824432\pi$
$997$	−53.7858	−1.70341	−0.851707	+	0.524018i	$0.824432\pi$
$998$	101.436	3.21091
$999$	−5.53414	−0.175092

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8009.2.a.b.1.17	✓	361

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8009.2.a.b.1.17	✓	361	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:	\( N \)	\(=\)	\( 8009 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8009.a (trivial)

\(f(q)\)	\(=\)	\(q-2.63785 q^{2} +2.50173 q^{3} +4.95827 q^{4} +3.39410 q^{5} -6.59921 q^{6} +0.113907 q^{7} -7.80348 q^{8} +3.25867 q^{9} +O(q^{10})\)	\(q-2.63785 q^{2} +2.50173 q^{3} +4.95827 q^{4} +3.39410 q^{5} -6.59921 q^{6} +0.113907 q^{7} -7.80348 q^{8} +3.25867 q^{9} -8.95313 q^{10} +6.15513 q^{11} +12.4043 q^{12} +2.57616 q^{13} -0.300469 q^{14} +8.49112 q^{15} +10.6679 q^{16} +5.53046 q^{17} -8.59590 q^{18} +2.98958 q^{19} +16.8288 q^{20} +0.284964 q^{21} -16.2363 q^{22} +6.64261 q^{23} -19.5222 q^{24} +6.51989 q^{25} -6.79553 q^{26} +0.647127 q^{27} +0.564780 q^{28} -10.0980 q^{29} -22.3983 q^{30} -6.05686 q^{31} -12.5334 q^{32} +15.3985 q^{33} -14.5885 q^{34} +0.386610 q^{35} +16.1574 q^{36} -8.55187 q^{37} -7.88608 q^{38} +6.44487 q^{39} -26.4858 q^{40} +10.5764 q^{41} -0.751693 q^{42} -6.67483 q^{43} +30.5188 q^{44} +11.0602 q^{45} -17.5222 q^{46} -1.51405 q^{47} +26.6882 q^{48} -6.98703 q^{49} -17.1985 q^{50} +13.8357 q^{51} +12.7733 q^{52} +12.3476 q^{53} -1.70703 q^{54} +20.8911 q^{55} -0.888868 q^{56} +7.47914 q^{57} +26.6370 q^{58} -8.88921 q^{59} +42.1013 q^{60} +10.7692 q^{61} +15.9771 q^{62} +0.371184 q^{63} +11.7255 q^{64} +8.74374 q^{65} -40.6190 q^{66} +1.98099 q^{67} +27.4215 q^{68} +16.6180 q^{69} -1.01982 q^{70} -4.48213 q^{71} -25.4290 q^{72} -5.31757 q^{73} +22.5586 q^{74} +16.3110 q^{75} +14.8232 q^{76} +0.701110 q^{77} -17.0006 q^{78} +13.7981 q^{79} +36.2079 q^{80} -8.15708 q^{81} -27.8991 q^{82} -1.74466 q^{83} +1.41293 q^{84} +18.7709 q^{85} +17.6072 q^{86} -25.2624 q^{87} -48.0315 q^{88} -7.32308 q^{89} -29.1753 q^{90} +0.293442 q^{91} +32.9358 q^{92} -15.1526 q^{93} +3.99384 q^{94} +10.1469 q^{95} -31.3552 q^{96} -9.07051 q^{97} +18.4307 q^{98} +20.0576 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 361 q + 10 q^{2} + 23 q^{3} + 414 q^{4} + 21 q^{5} + 49 q^{6} + 106 q^{7} + 30 q^{8} + 406 q^{9}+O(q^{10}) \) 361 * q + 10 * q^2 + 23 * q^3 + 414 * q^4 + 21 * q^5 + 49 * q^6 + 106 * q^7 + 30 * q^8 + 406 * q^9	\( 361 q + 10 q^{2} + 23 q^{3} + 414 q^{4} + 21 q^{5} + 49 q^{6} + 106 q^{7} + 30 q^{8} + 406 q^{9} + 65 q^{10} + 33 q^{11} + 52 q^{12} + 89 q^{13} + 32 q^{14} + 55 q^{15} + 512 q^{16} + 42 q^{17} + 34 q^{18} + 191 q^{19} + 48 q^{20} + 53 q^{21} + 61 q^{22} + 52 q^{23} + 139 q^{24} + 458 q^{25} + 57 q^{26} + 80 q^{27} + 194 q^{28} + 47 q^{29} + 32 q^{30} + 254 q^{31} + 55 q^{32} + 40 q^{33} + 122 q^{34} + 93 q^{35} + 519 q^{36} + 43 q^{37} + 25 q^{38} + 210 q^{39} + 184 q^{40} + 54 q^{41} + 48 q^{42} + 151 q^{43} + 56 q^{44} + 82 q^{45} + 101 q^{46} + 117 q^{47} + 77 q^{48} + 563 q^{49} + 38 q^{50} + 143 q^{51} + 241 q^{52} + 14 q^{53} + 164 q^{54} + 452 q^{55} + 52 q^{56} + 21 q^{57} + 55 q^{58} + 125 q^{59} + 39 q^{60} + 227 q^{61} + 58 q^{62} + 292 q^{63} + 710 q^{64} + 15 q^{65} + 105 q^{66} + 120 q^{67} + 125 q^{68} + 136 q^{69} + 88 q^{70} + 105 q^{71} + 78 q^{72} + 108 q^{73} + 41 q^{74} + 128 q^{75} + 461 q^{76} + 28 q^{77} + 13 q^{78} + 400 q^{79} + 59 q^{80} + 485 q^{81} + 175 q^{82} + 97 q^{83} + 76 q^{84} + 144 q^{85} - 14 q^{86} + 327 q^{87} + 145 q^{88} + 52 q^{89} + 60 q^{90} + 192 q^{91} + 11 q^{92} + 32 q^{93} + 366 q^{94} + 182 q^{95} + 275 q^{96} + 117 q^{97} + 42 q^{98} + 111 q^{99}+O(q^{100}) \) 361 * q + 10 * q^2 + 23 * q^3 + 414 * q^4 + 21 * q^5 + 49 * q^6 + 106 * q^7 + 30 * q^8 + 406 * q^9 + 65 * q^10 + 33 * q^11 + 52 * q^12 + 89 * q^13 + 32 * q^14 + 55 * q^15 + 512 * q^16 + 42 * q^17 + 34 * q^18 + 191 * q^19 + 48 * q^20 + 53 * q^21 + 61 * q^22 + 52 * q^23 + 139 * q^24 + 458 * q^25 + 57 * q^26 + 80 * q^27 + 194 * q^28 + 47 * q^29 + 32 * q^30 + 254 * q^31 + 55 * q^32 + 40 * q^33 + 122 * q^34 + 93 * q^35 + 519 * q^36 + 43 * q^37 + 25 * q^38 + 210 * q^39 + 184 * q^40 + 54 * q^41 + 48 * q^42 + 151 * q^43 + 56 * q^44 + 82 * q^45 + 101 * q^46 + 117 * q^47 + 77 * q^48 + 563 * q^49 + 38 * q^50 + 143 * q^51 + 241 * q^52 + 14 * q^53 + 164 * q^54 + 452 * q^55 + 52 * q^56 + 21 * q^57 + 55 * q^58 + 125 * q^59 + 39 * q^60 + 227 * q^61 + 58 * q^62 + 292 * q^63 + 710 * q^64 + 15 * q^65 + 105 * q^66 + 120 * q^67 + 125 * q^68 + 136 * q^69 + 88 * q^70 + 105 * q^71 + 78 * q^72 + 108 * q^73 + 41 * q^74 + 128 * q^75 + 461 * q^76 + 28 * q^77 + 13 * q^78 + 400 * q^79 + 59 * q^80 + 485 * q^81 + 175 * q^82 + 97 * q^83 + 76 * q^84 + 144 * q^85 - 14 * q^86 + 327 * q^87 + 145 * q^88 + 52 * q^89 + 60 * q^90 + 192 * q^91 + 11 * q^92 + 32 * q^93 + 366 * q^94 + 182 * q^95 + 275 * q^96 + 117 * q^97 + 42 * q^98 + 111 * q^99

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