LMFDB - Embedded newform 8009.2.a.b.1.14

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			1.14
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)

$f(q)$	$=$	$q-2.69232 q^{2} +2.96337 q^{3} +5.24860 q^{4} -1.91075 q^{5} -7.97835 q^{6} +3.66239 q^{7} -8.74628 q^{8} +5.78157 q^{9} +O(q^{10})$	\(q-2.69232 q^{2} +2.96337 q^{3} +5.24860 q^{4} -1.91075 q^{5} -7.97835 q^{6} +3.66239 q^{7} -8.74628 q^{8} +5.78157 q^{9} +5.14435 q^{10} -0.497890 q^{11} +15.5536 q^{12} +1.42252 q^{13} -9.86034 q^{14} -5.66225 q^{15} +13.0506 q^{16} +0.323772 q^{17} -15.5658 q^{18} -2.99118 q^{19} -10.0287 q^{20} +10.8530 q^{21} +1.34048 q^{22} +2.80456 q^{23} -25.9185 q^{24} -1.34905 q^{25} -3.82988 q^{26} +8.24282 q^{27} +19.2224 q^{28} -7.58330 q^{29} +15.2446 q^{30} +5.58309 q^{31} -17.6439 q^{32} -1.47543 q^{33} -0.871699 q^{34} -6.99790 q^{35} +30.3451 q^{36} -8.22990 q^{37} +8.05322 q^{38} +4.21545 q^{39} +16.7119 q^{40} -0.309111 q^{41} -29.2198 q^{42} +5.95437 q^{43} -2.61323 q^{44} -11.0471 q^{45} -7.55078 q^{46} +6.11758 q^{47} +38.6738 q^{48} +6.41311 q^{49} +3.63207 q^{50} +0.959457 q^{51} +7.46623 q^{52} -9.72534 q^{53} -22.1923 q^{54} +0.951342 q^{55} -32.0323 q^{56} -8.86397 q^{57} +20.4167 q^{58} +1.50314 q^{59} -29.7189 q^{60} +7.24181 q^{61} -15.0315 q^{62} +21.1744 q^{63} +21.4018 q^{64} -2.71807 q^{65} +3.97234 q^{66} -3.70882 q^{67} +1.69935 q^{68} +8.31096 q^{69} +18.8406 q^{70} -1.12372 q^{71} -50.5672 q^{72} +15.0638 q^{73} +22.1575 q^{74} -3.99772 q^{75} -15.6995 q^{76} -1.82347 q^{77} -11.3493 q^{78} +15.9087 q^{79} -24.9364 q^{80} +7.08183 q^{81} +0.832228 q^{82} -2.19779 q^{83} +56.9632 q^{84} -0.618647 q^{85} -16.0311 q^{86} -22.4721 q^{87} +4.35469 q^{88} +14.6483 q^{89} +29.7424 q^{90} +5.20982 q^{91} +14.7200 q^{92} +16.5448 q^{93} -16.4705 q^{94} +5.71539 q^{95} -52.2854 q^{96} +0.368915 q^{97} -17.2662 q^{98} -2.87859 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−2.69232	−1.90376	−0.951880	−	0.306472i	$-0.900852\pi$
$2$	−2.69232	−1.90376	−0.951880	+	0.306472i	$0.900852\pi$
$3$	2.96337	1.71090	0.855452	−	0.517883i	$-0.173280\pi$
$3$	2.96337	1.71090	0.855452	+	0.517883i	$0.173280\pi$
$4$	5.24860	2.62430
$5$	−1.91075	−0.854512	−0.427256	−	0.904131i	$-0.640520\pi$
$5$	−1.91075	−0.854512	−0.427256	+	0.904131i	$0.640520\pi$
$6$	−7.97835	−3.25715
$7$	3.66239	1.38425	0.692127	−	0.721776i	$-0.256674\pi$
$7$	3.66239	1.38425	0.692127	+	0.721776i	$0.256674\pi$
$8$	−8.74628	−3.09228
$9$	5.78157	1.92719
$10$	5.14435	1.62679
$11$	−0.497890	−0.150120	−0.0750598	−	0.997179i	$-0.523915\pi$
$11$	−0.497890	−0.150120	−0.0750598	+	0.997179i	$0.523915\pi$
$12$	15.5536	4.48992
$13$	1.42252	0.394535	0.197268	−	0.980350i	$-0.436793\pi$
$13$	1.42252	0.394535	0.197268	+	0.980350i	$0.436793\pi$
$14$	−9.86034	−2.63529
$15$	−5.66225	−1.46199
$16$	13.0506	3.26265
$17$	0.323772	0.0785263	0.0392631	−	0.999229i	$-0.487499\pi$
$17$	0.323772	0.0785263	0.0392631	+	0.999229i	$0.487499\pi$
$18$	−15.5658	−3.66891
$19$	−2.99118	−0.686224	−0.343112	−	0.939295i	$-0.611481\pi$
$19$	−2.99118	−0.686224	−0.343112	+	0.939295i	$0.611481\pi$
$20$	−10.0287	−2.24250
$21$	10.8530	2.36832
$22$	1.34048	0.285791
$23$	2.80456	0.584791	0.292396	−	0.956297i	$-0.405548\pi$
$23$	2.80456	0.584791	0.292396	+	0.956297i	$0.405548\pi$
$24$	−25.9185	−5.29059
$25$	−1.34905	−0.269809
$26$	−3.82988	−0.751100
$27$	8.24282	1.58633
$28$	19.2224	3.63270
$29$	−7.58330	−1.40818	−0.704092	−	0.710109i	$-0.748646\pi$
$29$	−7.58330	−1.40818	−0.704092	+	0.710109i	$0.748646\pi$
$30$	15.2446	2.78327
$31$	5.58309	1.00275	0.501376	−	0.865229i	$-0.332827\pi$
$31$	5.58309	1.00275	0.501376	+	0.865229i	$0.332827\pi$
$32$	−17.6439	−3.11903
$33$	−1.47543	−0.256840
$34$	−0.871699	−0.149495
$35$	−6.99790	−1.18286
$36$	30.3451	5.05752
$37$	−8.22990	−1.35299	−0.676494	−	0.736449i	$-0.736501\pi$
$37$	−8.22990	−1.35299	−0.676494	+	0.736449i	$0.736501\pi$
$38$	8.05322	1.30640
$39$	4.21545	0.675012
$40$	16.7119	2.64239
$41$	−0.309111	−0.0482751	−0.0241375	−	0.999709i	$-0.507684\pi$
$41$	−0.309111	−0.0482751	−0.0241375	+	0.999709i	$0.507684\pi$
$42$	−29.2198	−4.50872
$43$	5.95437	0.908033	0.454017	−	0.890993i	$-0.349991\pi$
$43$	5.95437	0.908033	0.454017	+	0.890993i	$0.349991\pi$
$44$	−2.61323	−0.393959
$45$	−11.0471	−1.64681
$46$	−7.55078	−1.11330
$47$	6.11758	0.892341	0.446170	−	0.894948i	$-0.352788\pi$
$47$	6.11758	0.892341	0.446170	+	0.894948i	$0.352788\pi$
$48$	38.6738	5.58208
$49$	6.41311	0.916159
$50$	3.63207	0.513652
$51$	0.959457	0.134351
$52$	7.46623	1.03538
$53$	−9.72534	−1.33588	−0.667939	−	0.744216i	$-0.732823\pi$
$53$	−9.72534	−1.33588	−0.667939	+	0.744216i	$0.732823\pi$
$54$	−22.1923	−3.01999
$55$	0.951342	0.128279
$56$	−32.0323	−4.28050
$57$	−8.86397	−1.17406
$58$	20.4167	2.68084
$59$	1.50314	0.195692	0.0978458	−	0.995202i	$-0.468805\pi$
$59$	1.50314	0.195692	0.0978458	+	0.995202i	$0.468805\pi$
$60$	−29.7189	−3.83669
$61$	7.24181	0.927219	0.463610	−	0.886040i	$-0.346554\pi$
$61$	7.24181	0.927219	0.463610	+	0.886040i	$0.346554\pi$
$62$	−15.0315	−1.90900
$63$	21.1744	2.66772
$64$	21.4018	2.67523
$65$	−2.71807	−0.337135
$66$	3.97234	0.488961
$67$	−3.70882	−0.453105	−0.226552	−	0.973999i	$-0.572745\pi$
$67$	−3.70882	−0.453105	−0.226552	+	0.973999i	$0.572745\pi$
$68$	1.69935	0.206077
$69$	8.31096	1.00052
$70$	18.8406	2.25188
$71$	−1.12372	−0.133362	−0.0666808	−	0.997774i	$-0.521241\pi$
$71$	−1.12372	−0.133362	−0.0666808	+	0.997774i	$0.521241\pi$
$72$	−50.5672	−5.95940
$73$	15.0638	1.76309	0.881545	−	0.472100i	$-0.156504\pi$
$73$	15.0638	1.76309	0.881545	+	0.472100i	$0.156504\pi$
$74$	22.1575	2.57576
$75$	−3.99772	−0.461617
$76$	−15.6995	−1.80086
$77$	−1.82347	−0.207804
$78$	−11.3493	−1.28506
$79$	15.9087	1.78987	0.894934	−	0.446199i	$-0.147223\pi$
$79$	15.9087	1.78987	0.894934	+	0.446199i	$0.147223\pi$
$80$	−24.9364	−2.78798
$81$	7.08183	0.786870
$82$	0.832228	0.0919042
$83$	−2.19779	−0.241238	−0.120619	−	0.992699i	$-0.538488\pi$
$83$	−2.19779	−0.241238	−0.120619	+	0.992699i	$0.538488\pi$
$84$	56.9632	6.21519
$85$	−0.618647	−0.0671017
$86$	−16.0311	−1.72868
$87$	−22.4721	−2.40927
$88$	4.35469	0.464211
$89$	14.6483	1.55271	0.776356	−	0.630295i	$-0.217066\pi$
$89$	14.6483	1.55271	0.776356	+	0.630295i	$0.217066\pi$
$90$	29.7424	3.13512
$91$	5.20982	0.546137
$92$	14.7200	1.53467
$93$	16.5448	1.71561
$94$	−16.4705	−1.69880
$95$	5.71539	0.586386
$96$	−52.2854	−5.33635
$97$	0.368915	0.0374576	0.0187288	−	0.999825i	$-0.494038\pi$
$97$	0.368915	0.0374576	0.0187288	+	0.999825i	$0.494038\pi$
$98$	−17.2662	−1.74415
$99$	−2.87859	−0.289309
$100$	−7.08060	−0.708060
$101$	7.76362	0.772509	0.386255	−	0.922392i	$-0.373769\pi$
$101$	7.76362	0.772509	0.386255	+	0.922392i	$0.373769\pi$
$102$	−2.58317	−0.255772
$103$	10.5024	1.03483	0.517414	−	0.855735i	$-0.326895\pi$
$103$	10.5024	1.03483	0.517414	+	0.855735i	$0.326895\pi$
$104$	−12.4417	−1.22001
$105$	−20.7374	−2.02376
$106$	26.1837	2.54319
$107$	−0.0148292	−0.00143360	−0.000716799	−	1.00000i	$-0.500228\pi$
$107$	−0.0148292	−0.00143360	−0.000716799		1.00000i	$0.500228\pi$
$108$	43.2633	4.16301
$109$	11.1559	1.06855	0.534273	−	0.845312i	$-0.320585\pi$
$109$	11.1559	1.06855	0.534273	+	0.845312i	$0.320585\pi$
$110$	−2.56132	−0.244212
$111$	−24.3882	−2.31483
$112$	47.7964	4.51634
$113$	19.2546	1.81132	0.905659	−	0.424006i	$-0.139376\pi$
$113$	19.2546	1.81132	0.905659	+	0.424006i	$0.139376\pi$
$114$	23.8647	2.23513
$115$	−5.35881	−0.499711
$116$	−39.8017	−3.69550
$117$	8.22438	0.760344
$118$	−4.04693	−0.372550
$119$	1.18578	0.108700
$120$	49.5236	4.52087
$121$	−10.7521	−0.977464
$122$	−19.4973	−1.76520
$123$	−0.916012	−0.0825940
$124$	29.3034	2.63152
$125$	12.1314	1.08507
$126$	−57.0082	−5.07870
$127$	16.4710	1.46156	0.730782	−	0.682610i	$-0.239155\pi$
$127$	16.4710	1.46156	0.730782	+	0.682610i	$0.239155\pi$
$128$	−22.3328	−1.97396
$129$	17.6450	1.55356
$130$	7.31792	0.641824
$131$	15.5491	1.35853	0.679264	−	0.733894i	$-0.262299\pi$
$131$	15.5491	1.35853	0.679264	+	0.733894i	$0.262299\pi$
$132$	−7.74396	−0.674025
$133$	−10.9549	−0.949908
$134$	9.98534	0.862602
$135$	−15.7499	−1.35554
$136$	−2.83180	−0.242825
$137$	7.42322	0.634208	0.317104	−	0.948391i	$-0.397290\pi$
$137$	7.42322	0.634208	0.317104	+	0.948391i	$0.397290\pi$
$138$	−22.3758	−1.90475
$139$	−12.2375	−1.03797	−0.518984	−	0.854784i	$-0.673690\pi$
$139$	−12.2375	−1.03797	−0.518984	+	0.854784i	$0.673690\pi$
$140$	−36.7292	−3.10418
$141$	18.1287	1.52671
$142$	3.02543	0.253888
$143$	−0.708257	−0.0592275
$144$	75.4530	6.28775
$145$	14.4898	1.20331
$146$	−40.5567	−3.35650
$147$	19.0044	1.56746
$148$	−43.1955	−3.55064
$149$	−19.7721	−1.61980	−0.809898	−	0.586571i	$-0.800477\pi$
$149$	−19.7721	−1.61980	−0.809898	+	0.586571i	$0.800477\pi$
$150$	10.7632	0.878809
$151$	−6.15496	−0.500883	−0.250442	−	0.968132i	$-0.580576\pi$
$151$	−6.15496	−0.500883	−0.250442	+	0.968132i	$0.580576\pi$
$152$	26.1617	2.12199
$153$	1.87191	0.151335
$154$	4.90937	0.395608
$155$	−10.6679	−0.856864
$156$	22.1252	1.77143
$157$	−4.64425	−0.370652	−0.185326	−	0.982677i	$-0.559334\pi$
$157$	−4.64425	−0.370652	−0.185326	+	0.982677i	$0.559334\pi$
$158$	−42.8313	−3.40748
$159$	−28.8198	−2.28556
$160$	33.7130	2.66525
$161$	10.2714	0.809500
$162$	−19.0666	−1.49801
$163$	7.99342	0.626093	0.313047	−	0.949738i	$-0.398650\pi$
$163$	7.99342	0.626093	0.313047	+	0.949738i	$0.398650\pi$
$164$	−1.62240	−0.126688
$165$	2.81918	0.219473
$166$	5.91715	0.459260
$167$	2.16430	0.167478	0.0837391	−	0.996488i	$-0.473314\pi$
$167$	2.16430	0.167478	0.0837391	+	0.996488i	$0.473314\pi$
$168$	−94.9236	−7.32352
$169$	−10.9764	−0.844342
$170$	1.66560	0.127745
$171$	−17.2937	−1.32248
$172$	31.2521	2.38295
$173$	−4.06471	−0.309034	−0.154517	−	0.987990i	$-0.549382\pi$
$173$	−4.06471	−0.309034	−0.154517	+	0.987990i	$0.549382\pi$
$174$	60.5022	4.58666
$175$	−4.94074	−0.373484
$176$	−6.49777	−0.489788
$177$	4.45435	0.334809
$178$	−39.4378	−2.95599
$179$	7.78784	0.582090	0.291045	−	0.956709i	$-0.405997\pi$
$179$	7.78784	0.582090	0.291045	+	0.956709i	$0.405997\pi$
$180$	−57.9819	−4.32171
$181$	2.08014	0.154615	0.0773077	−	0.997007i	$-0.475368\pi$
$181$	2.08014	0.154615	0.0773077	+	0.997007i	$0.475368\pi$
$182$	−14.0265	−1.03971
$183$	21.4602	1.58638
$184$	−24.5295	−1.80834
$185$	15.7253	1.15614
$186$	−44.5438	−3.26611
$187$	−0.161203	−0.0117883
$188$	32.1087	2.34177
$189$	30.1884	2.19589
$190$	−15.3877	−1.11634
$191$	10.8976	0.788522	0.394261	−	0.918999i	$-0.371001\pi$
$191$	10.8976	0.788522	0.394261	+	0.918999i	$0.371001\pi$
$192$	63.4215	4.57705
$193$	−4.80468	−0.345848	−0.172924	−	0.984935i	$-0.555322\pi$
$193$	−4.80468	−0.345848	−0.172924	+	0.984935i	$0.555322\pi$
$194$	−0.993237	−0.0713103
$195$	−8.05465	−0.576806
$196$	33.6599	2.40428
$197$	−9.27871	−0.661080	−0.330540	−	0.943792i	$-0.607231\pi$
$197$	−9.27871	−0.661080	−0.330540	+	0.943792i	$0.607231\pi$
$198$	7.75008	0.550774
$199$	−4.19452	−0.297342	−0.148671	−	0.988887i	$-0.547500\pi$
$199$	−4.19452	−0.297342	−0.148671	+	0.988887i	$0.547500\pi$
$200$	11.7991	0.834325
$201$	−10.9906	−0.775218
$202$	−20.9022	−1.47067
$203$	−27.7730	−1.94928
$204$	5.03581	0.352577
$205$	0.590634	0.0412516
$206$	−28.2757	−1.97006
$207$	16.2148	1.12700
$208$	18.5647	1.28723
$209$	1.48928	0.103016
$210$	55.8317	3.85276
$211$	12.2404	0.842664	0.421332	−	0.906906i	$-0.361563\pi$
$211$	12.2404	0.842664	0.421332	+	0.906906i	$0.361563\pi$
$212$	−51.0444	−3.50575
$213$	−3.33001	−0.228169
$214$	0.0399251	0.00272922
$215$	−11.3773	−0.775925
$216$	−72.0940	−4.90538
$217$	20.4475	1.38806
$218$	−30.0354	−2.03425
$219$	44.6398	3.01648
$220$	4.99321	0.336642
$221$	0.460572	0.0309814
$222$	65.6610	4.40688
$223$	1.00718	0.0674457	0.0337228	−	0.999431i	$-0.489264\pi$
$223$	1.00718	0.0674457	0.0337228	+	0.999431i	$0.489264\pi$
$224$	−64.6188	−4.31753
$225$	−7.79960	−0.519974
$226$	−51.8395	−3.44832
$227$	−18.3708	−1.21931	−0.609656	−	0.792666i	$-0.708692\pi$
$227$	−18.3708	−1.21931	−0.609656	+	0.792666i	$0.708692\pi$
$228$	−46.5235	−3.08109
$229$	17.8231	1.17779	0.588893	−	0.808211i	$-0.299564\pi$
$229$	17.8231	1.17779	0.588893	+	0.808211i	$0.299564\pi$
$230$	14.4276	0.951330
$231$	−5.40361	−0.355532
$232$	66.3257	4.35450
$233$	19.6742	1.28890	0.644449	−	0.764647i	$-0.277087\pi$
$233$	19.6742	1.28890	0.644449	+	0.764647i	$0.277087\pi$
$234$	−22.1427	−1.44751
$235$	−11.6891	−0.762516
$236$	7.88936	0.513553
$237$	47.1434	3.06229
$238$	−3.19250	−0.206939
$239$	−1.98343	−0.128297	−0.0641487	−	0.997940i	$-0.520433\pi$
$239$	−1.98343	−0.128297	−0.0641487	+	0.997940i	$0.520433\pi$
$240$	−73.8958	−4.76996
$241$	−12.4682	−0.803145	−0.401573	−	0.915827i	$-0.631536\pi$
$241$	−12.4682	−0.803145	−0.401573	+	0.915827i	$0.631536\pi$
$242$	28.9481	1.86086
$243$	−3.74238	−0.240074
$244$	38.0094	2.43330
$245$	−12.2538	−0.782869
$246$	2.46620	0.157239
$247$	−4.25500	−0.270739
$248$	−48.8312	−3.10079
$249$	−6.51285	−0.412735
$250$	−32.6617	−2.06571
$251$	22.4379	1.41627	0.708135	−	0.706077i	$-0.249537\pi$
$251$	22.4379	1.41627	0.708135	+	0.706077i	$0.249537\pi$
$252$	111.136	7.00090
$253$	−1.39636	−0.0877886
$254$	−44.3452	−2.78247
$255$	−1.83328	−0.114804
$256$	17.3235	1.08272
$257$	13.8445	0.863593	0.431797	−	0.901971i	$-0.357880\pi$
$257$	13.8445	0.863593	0.431797	+	0.901971i	$0.357880\pi$
$258$	−47.5061	−2.95760
$259$	−30.1411	−1.87288
$260$	−14.2661	−0.884744
$261$	−43.8434	−2.71384
$262$	−41.8631	−2.58631
$263$	5.01694	0.309357	0.154679	−	0.987965i	$-0.450566\pi$
$263$	5.01694	0.309357	0.154679	+	0.987965i	$0.450566\pi$
$264$	12.9046	0.794220
$265$	18.5827	1.14152
$266$	29.4940	1.80840
$267$	43.4082	2.65654
$268$	−19.4661	−1.18908
$269$	−17.2530	−1.05193	−0.525966	−	0.850506i	$-0.676296\pi$
$269$	−17.2530	−1.05193	−0.525966	+	0.850506i	$0.676296\pi$
$270$	42.4039	2.58062
$271$	1.46088	0.0887424	0.0443712	−	0.999015i	$-0.485872\pi$
$271$	1.46088	0.0887424	0.0443712	+	0.999015i	$0.485872\pi$
$272$	4.22542	0.256204
$273$	15.4386	0.934388
$274$	−19.9857	−1.20738
$275$	0.671677	0.0405036
$276$	43.6209	2.62567
$277$	30.4654	1.83049	0.915246	−	0.402896i	$-0.131996\pi$
$277$	30.4654	1.83049	0.915246	+	0.402896i	$0.131996\pi$
$278$	32.9472	1.97604
$279$	32.2790	1.93249
$280$	61.2056	3.65774
$281$	7.62379	0.454797	0.227399	−	0.973802i	$-0.426978\pi$
$281$	7.62379	0.454797	0.227399	+	0.973802i	$0.426978\pi$
$282$	−48.8082	−2.90649
$283$	2.85437	0.169674	0.0848372	−	0.996395i	$-0.472963\pi$
$283$	2.85437	0.169674	0.0848372	+	0.996395i	$0.472963\pi$
$284$	−5.89798	−0.349981
$285$	16.9368	1.00325
$286$	1.90686	0.112755
$287$	−1.13209	−0.0668250
$288$	−102.009	−6.01096
$289$	−16.8952	−0.993834
$290$	−39.0111	−2.29081
$291$	1.09323	0.0640863
$292$	79.0641	4.62688
$293$	10.6571	0.622594	0.311297	−	0.950313i	$-0.399237\pi$
$293$	10.6571	0.622594	0.311297	+	0.950313i	$0.399237\pi$
$294$	−51.1661	−2.98406
$295$	−2.87211	−0.167221
$296$	71.9810	4.18381
$297$	−4.10402	−0.238139
$298$	53.2329	3.08370
$299$	3.98954	0.230721
$300$	−20.9825	−1.21142
$301$	21.8072	1.25695
$302$	16.5711	0.953562
$303$	23.0065	1.32169
$304$	−39.0367	−2.23891
$305$	−13.8373	−0.792320
$306$	−5.03979	−0.288106
$307$	−11.8585	−0.676801	−0.338401	−	0.941002i	$-0.609886\pi$
$307$	−11.8585	−0.676801	−0.338401	+	0.941002i	$0.609886\pi$
$308$	−9.57066	−0.545339
$309$	31.1224	1.77049
$310$	28.7213	1.63126
$311$	−13.7411	−0.779186	−0.389593	−	0.920987i	$-0.627384\pi$
$311$	−13.7411	−0.779186	−0.389593	+	0.920987i	$0.627384\pi$
$312$	−36.8695	−2.08732
$313$	22.0507	1.24638	0.623189	−	0.782071i	$-0.285837\pi$
$313$	22.0507	1.24638	0.623189	+	0.782071i	$0.285837\pi$
$314$	12.5038	0.705632
$315$	−40.4589	−2.27960
$316$	83.4984	4.69715
$317$	−4.18821	−0.235233	−0.117617	−	0.993059i	$-0.537525\pi$
$317$	−4.18821	−0.235233	−0.117617	+	0.993059i	$0.537525\pi$
$318$	77.5922	4.35115
$319$	3.77565	0.211396
$320$	−40.8934	−2.28601
$321$	−0.0439446	−0.00245275
$322$	−27.6539	−1.54109
$323$	−0.968461	−0.0538866
$324$	37.1697	2.06498
$325$	−1.91904	−0.106449
$326$	−21.5209	−1.19193
$327$	33.0592	1.82818
$328$	2.70358	0.149280
$329$	22.4050	1.23523
$330$	−7.59014	−0.417823
$331$	−10.2772	−0.564887	−0.282444	−	0.959284i	$-0.591145\pi$
$331$	−10.2772	−0.564887	−0.282444	+	0.959284i	$0.591145\pi$
$332$	−11.5353	−0.633082
$333$	−47.5817	−2.60746
$334$	−5.82698	−0.318838
$335$	7.08662	0.387183
$336$	141.639	7.72702
$337$	14.9560	0.814704	0.407352	−	0.913271i	$-0.366452\pi$
$337$	14.9560	0.814704	0.407352	+	0.913271i	$0.366452\pi$
$338$	29.5521	1.60742
$339$	57.0585	3.09899
$340$	−3.24703	−0.176095
$341$	−2.77976	−0.150533
$342$	46.5602	2.51769
$343$	−2.14942	−0.116058
$344$	−52.0786	−2.80789
$345$	−15.8801	−0.854958
$346$	10.9435	0.588327
$347$	10.1075	0.542597	0.271299	−	0.962495i	$-0.412547\pi$
$347$	10.1075	0.542597	0.271299	+	0.962495i	$0.412547\pi$
$348$	−117.947	−6.32264
$349$	2.65973	0.142372	0.0711861	−	0.997463i	$-0.477322\pi$
$349$	2.65973	0.142372	0.0711861	+	0.997463i	$0.477322\pi$
$350$	13.3021	0.711025
$351$	11.7256	0.625864
$352$	8.78471	0.468227
$353$	−15.4869	−0.824286	−0.412143	−	0.911119i	$-0.635220\pi$
$353$	−15.4869	−0.824286	−0.412143	+	0.911119i	$0.635220\pi$
$354$	−11.9925	−0.637396
$355$	2.14715	0.113959
$356$	76.8829	4.07478
$357$	3.51391	0.185976
$358$	−20.9674	−1.10816
$359$	12.1919	0.643461	0.321731	−	0.946831i	$-0.395735\pi$
$359$	12.1919	0.643461	0.321731	+	0.946831i	$0.395735\pi$
$360$	96.6212	5.09238
$361$	−10.0528	−0.529097
$362$	−5.60040	−0.294351
$363$	−31.8625	−1.67235
$364$	27.3442	1.43323
$365$	−28.7832	−1.50658
$366$	−57.7777	−3.02009
$367$	9.71497	0.507117	0.253559	−	0.967320i	$-0.418399\pi$
$367$	9.71497	0.507117	0.253559	+	0.967320i	$0.418399\pi$
$368$	36.6012	1.90797
$369$	−1.78715	−0.0930353
$370$	−42.3375	−2.20102
$371$	−35.6180	−1.84919
$372$	86.8368	4.50228
$373$	12.7541	0.660383	0.330191	−	0.943914i	$-0.392887\pi$
$373$	12.7541	0.660383	0.330191	+	0.943914i	$0.392887\pi$
$374$	0.434010	0.0224421
$375$	35.9499	1.85644
$376$	−53.5061	−2.75937
$377$	−10.7874	−0.555578
$378$	−81.2770	−4.18044
$379$	−6.19553	−0.318243	−0.159122	−	0.987259i	$-0.550866\pi$
$379$	−6.19553	−0.318243	−0.159122	+	0.987259i	$0.550866\pi$
$380$	29.9978	1.53885
$381$	48.8097	2.50060
$382$	−29.3398	−1.50116
$383$	−18.4454	−0.942517	−0.471259	−	0.881995i	$-0.656200\pi$
$383$	−18.4454	−0.942517	−0.471259	+	0.881995i	$0.656200\pi$
$384$	−66.1804	−3.37725
$385$	3.48419	0.177571
$386$	12.9357	0.658412
$387$	34.4256	1.74995
$388$	1.93629	0.0983000
$389$	−8.05746	−0.408530	−0.204265	−	0.978916i	$-0.565480\pi$
$389$	−8.05746	−0.408530	−0.204265	+	0.978916i	$0.565480\pi$
$390$	21.6857	1.09810
$391$	0.908039	0.0459215
$392$	−56.0909	−2.83302
$393$	46.0777	2.32431
$394$	24.9813	1.25854
$395$	−30.3975	−1.52946
$396$	−15.1085	−0.759233
$397$	7.69615	0.386259	0.193129	−	0.981173i	$-0.438136\pi$
$397$	7.69615	0.386259	0.193129	+	0.981173i	$0.438136\pi$
$398$	11.2930	0.566067
$399$	−32.4633	−1.62520
$400$	−17.6059	−0.880294
$401$	5.18131	0.258742	0.129371	−	0.991596i	$-0.458704\pi$
$401$	5.18131	0.258742	0.129371	+	0.991596i	$0.458704\pi$
$402$	29.5903	1.47583
$403$	7.94204	0.395621
$404$	40.7481	2.02730
$405$	−13.5316	−0.672390
$406$	74.7739	3.71097
$407$	4.09759	0.203110
$408$	−8.39168	−0.415450
$409$	−11.4305	−0.565203	−0.282602	−	0.959237i	$-0.591197\pi$
$409$	−11.4305	−0.565203	−0.282602	+	0.959237i	$0.591197\pi$
$410$	−1.59018	−0.0785332
$411$	21.9977	1.08507
$412$	55.1227	2.71570
$413$	5.50507	0.270887
$414$	−43.6554	−2.14554
$415$	4.19941	0.206141
$416$	−25.0987	−1.23057
$417$	−36.2641	−1.77586
$418$	−4.00962	−0.196117
$419$	19.6687	0.960877	0.480438	−	0.877028i	$-0.340478\pi$
$419$	19.6687	0.960877	0.480438	+	0.877028i	$0.340478\pi$
$420$	−108.842	−5.31096
$421$	−17.9617	−0.875402	−0.437701	−	0.899121i	$-0.644207\pi$
$421$	−17.9617	−0.875402	−0.437701	+	0.899121i	$0.644207\pi$
$422$	−32.9551	−1.60423
$423$	35.3692	1.71971
$424$	85.0605	4.13091
$425$	−0.436784	−0.0211871
$426$	8.96546	0.434378
$427$	26.5224	1.28351
$428$	−0.0778328	−0.00376219
$429$	−2.09883	−0.101332
$430$	30.6314	1.47717
$431$	25.0914	1.20861	0.604305	−	0.796753i	$-0.293451\pi$
$431$	25.0914	1.20861	0.604305	+	0.796753i	$0.293451\pi$
$432$	107.574	5.17565
$433$	18.0844	0.869082	0.434541	−	0.900652i	$-0.356911\pi$
$433$	18.0844	0.869082	0.434541	+	0.900652i	$0.356911\pi$
$434$	−55.0511	−2.64254
$435$	42.9386	2.05875
$436$	58.5531	2.80419
$437$	−8.38895	−0.401298
$438$	−120.185	−5.74265
$439$	−1.71999	−0.0820907	−0.0410454	−	0.999157i	$-0.513069\pi$
$439$	−1.71999	−0.0820907	−0.0410454	+	0.999157i	$0.513069\pi$
$440$	−8.32070	−0.396674
$441$	37.0778	1.76561
$442$	−1.24001	−0.0589811
$443$	−29.0125	−1.37843	−0.689214	−	0.724558i	$-0.742044\pi$
$443$	−29.0125	−1.37843	−0.689214	+	0.724558i	$0.742044\pi$
$444$	−128.004	−6.07481
$445$	−27.9891	−1.32681
$446$	−2.71165	−0.128400
$447$	−58.5921	−2.77131
$448$	78.3818	3.70319
$449$	−8.72598	−0.411805	−0.205902	−	0.978573i	$-0.566013\pi$
$449$	−8.72598	−0.411805	−0.205902	+	0.978573i	$0.566013\pi$
$450$	20.9990	0.989905
$451$	0.153904	0.00724703
$452$	101.060	4.75344
$453$	−18.2394	−0.856963
$454$	49.4601	2.32128
$455$	−9.95464	−0.466681
$456$	77.5268	3.63053
$457$	−25.7385	−1.20399	−0.601997	−	0.798498i	$-0.705628\pi$
$457$	−25.7385	−1.20399	−0.601997	+	0.798498i	$0.705628\pi$
$458$	−47.9857	−2.24222
$459$	2.66880	0.124569
$460$	−28.1262	−1.31139
$461$	−9.56863	−0.445656	−0.222828	−	0.974858i	$-0.571529\pi$
$461$	−9.56863	−0.445656	−0.222828	+	0.974858i	$0.571529\pi$
$462$	14.5483	0.676847
$463$	−17.2181	−0.800193	−0.400096	−	0.916473i	$-0.631023\pi$
$463$	−17.2181	−0.800193	−0.400096	+	0.916473i	$0.631023\pi$
$464$	−98.9667	−4.59441
$465$	−31.6128	−1.46601
$466$	−52.9693	−2.45375
$467$	−41.2882	−1.91059	−0.955295	−	0.295653i	$-0.904463\pi$
$467$	−41.2882	−1.91059	−0.955295	+	0.295653i	$0.904463\pi$
$468$	43.1665	1.99537
$469$	−13.5832	−0.627212
$470$	31.4710	1.45165
$471$	−13.7626	−0.634149
$472$	−13.1468	−0.605133
$473$	−2.96462	−0.136313
$474$	−126.925	−5.82986
$475$	4.03524	0.185149
$476$	6.22369	0.285262
$477$	−56.2277	−2.57449
$478$	5.34004	0.244248
$479$	−6.45978	−0.295155	−0.147578	−	0.989050i	$-0.547148\pi$
$479$	−6.45978	−0.295155	−0.147578	+	0.989050i	$0.547148\pi$
$480$	99.9041	4.55998
$481$	−11.7072	−0.533801
$482$	33.5683	1.52900
$483$	30.4380	1.38498
$484$	−56.4335	−2.56516
$485$	−0.704902	−0.0320080
$486$	10.0757	0.457042
$487$	−26.0014	−1.17823	−0.589117	−	0.808048i	$-0.700524\pi$
$487$	−26.0014	−1.17823	−0.589117	+	0.808048i	$0.700524\pi$
$488$	−63.3389	−2.86722
$489$	23.6875	1.07118
$490$	32.9913	1.49039
$491$	7.75396	0.349931	0.174966	−	0.984575i	$-0.444019\pi$
$491$	7.75396	0.349931	0.174966	+	0.984575i	$0.444019\pi$
$492$	−4.80778	−0.216751
$493$	−2.45526	−0.110579
$494$	11.4558	0.515423
$495$	5.50025	0.247218
$496$	72.8627	3.27163
$497$	−4.11552	−0.184606
$498$	17.5347	0.785749
$499$	−25.6632	−1.14884	−0.574421	−	0.818560i	$-0.694773\pi$
$499$	−25.6632	−1.14884	−0.574421	+	0.818560i	$0.694773\pi$
$500$	63.6730	2.84754
$501$	6.41361	0.286539
$502$	−60.4102	−2.69624
$503$	28.6354	1.27679	0.638394	−	0.769709i	$-0.279599\pi$
$503$	28.6354	1.27679	0.638394	+	0.769709i	$0.279599\pi$
$504$	−185.197	−8.24933
$505$	−14.8343	−0.660118
$506$	3.75946	0.167128
$507$	−32.5273	−1.44459
$508$	86.4497	3.83559
$509$	−43.4230	−1.92469	−0.962345	−	0.271833i	$-0.912370\pi$
$509$	−43.4230	−1.92469	−0.962345	+	0.271833i	$0.912370\pi$
$510$	4.93578	0.218560
$511$	55.1697	2.44056
$512$	−1.97484	−0.0872766
$513$	−24.6557	−1.08858
$514$	−37.2737	−1.64407
$515$	−20.0674	−0.884273
$516$	92.6116	4.07700
$517$	−3.04588	−0.133958
$518$	81.1496	3.56551
$519$	−12.0452	−0.528727
$520$	23.7730	1.04252
$521$	11.6085	0.508576	0.254288	−	0.967129i	$-0.418159\pi$
$521$	11.6085	0.508576	0.254288	+	0.967129i	$0.418159\pi$
$522$	118.041	5.16649
$523$	7.77497	0.339975	0.169988	−	0.985446i	$-0.445627\pi$
$523$	7.77497	0.339975	0.169988	+	0.985446i	$0.445627\pi$
$524$	81.6109	3.56519
$525$	−14.6412	−0.638996
$526$	−13.5072	−0.588942
$527$	1.80765	0.0787424
$528$	−19.2553	−0.837979
$529$	−15.1344	−0.658019
$530$	−50.0305	−2.17319
$531$	8.69048	0.377135
$532$	−57.4977	−2.49284
$533$	−0.439716	−0.0190462
$534$	−116.869	−5.05741
$535$	0.0283349	0.00122503
$536$	32.4384	1.40113
$537$	23.0783	0.995900
$538$	46.4506	2.00263
$539$	−3.19302	−0.137533
$540$	−82.6651	−3.55734
$541$	−27.3393	−1.17541	−0.587704	−	0.809076i	$-0.699968\pi$
$541$	−27.3393	−1.17541	−0.587704	+	0.809076i	$0.699968\pi$
$542$	−3.93317	−0.168944
$543$	6.16422	0.264532
$544$	−5.71260	−0.244926
$545$	−21.3162	−0.913085
$546$	−41.5657	−1.77885
$547$	25.1098	1.07362	0.536809	−	0.843704i	$-0.319629\pi$
$547$	25.1098	1.07362	0.536809	+	0.843704i	$0.319629\pi$
$548$	38.9615	1.66435
$549$	41.8690	1.78693
$550$	−1.80837	−0.0771092
$551$	22.6830	0.966329
$552$	−72.6900	−3.09389
$553$	58.2639	2.47763
$554$	−82.0228	−3.48482
$555$	46.5998	1.97805
$556$	−64.2296	−2.72394
$557$	27.3686	1.15964	0.579822	−	0.814743i	$-0.303122\pi$
$557$	27.3686	1.15964	0.579822	+	0.814743i	$0.303122\pi$
$558$	−86.9055	−3.67900
$559$	8.47020	0.358251
$560$	−91.3269	−3.85927
$561$	−0.477704	−0.0201687
$562$	−20.5257	−0.865824
$563$	−35.7792	−1.50791	−0.753956	−	0.656925i	$-0.771857\pi$
$563$	−35.7792	−1.50791	−0.753956	+	0.656925i	$0.771857\pi$
$564$	95.1501	4.00654
$565$	−36.7906	−1.54779
$566$	−7.68487	−0.323019
$567$	25.9364	1.08923
$568$	9.82841	0.412391
$569$	−4.10043	−0.171899	−0.0859495	−	0.996299i	$-0.527392\pi$
$569$	−4.10043	−0.171899	−0.0859495	+	0.996299i	$0.527392\pi$
$570$	−45.5994	−1.90995
$571$	−3.76658	−0.157626	−0.0788132	−	0.996889i	$-0.525113\pi$
$571$	−3.76658	−0.157626	−0.0788132	+	0.996889i	$0.525113\pi$
$572$	−3.71736	−0.155431
$573$	32.2936	1.34908
$574$	3.04794	0.127219
$575$	−3.78348	−0.157782
$576$	123.736	5.15567
$577$	13.7966	0.574358	0.287179	−	0.957877i	$-0.407283\pi$
$577$	13.7966	0.574358	0.287179	+	0.957877i	$0.407283\pi$
$578$	45.4873	1.89202
$579$	−14.2381	−0.591713
$580$	76.0510	3.15785
$581$	−8.04915	−0.333935
$582$	−2.94333	−0.122005
$583$	4.84215	0.200541
$584$	−131.753	−5.45196
$585$	−15.7147	−0.649723
$586$	−28.6923	−1.18527
$587$	−30.0924	−1.24205	−0.621023	−	0.783792i	$-0.713283\pi$
$587$	−30.0924	−1.24205	−0.621023	+	0.783792i	$0.713283\pi$
$588$	99.7467	4.11348
$589$	−16.7000	−0.688112
$590$	7.73265	0.318348
$591$	−27.4963	−1.13104
$592$	−107.405	−4.41433
$593$	−45.4669	−1.86710	−0.933551	−	0.358445i	$-0.883307\pi$
$593$	−45.4669	−1.86710	−0.933551	+	0.358445i	$0.883307\pi$
$594$	11.0493	0.453360
$595$	−2.26573	−0.0928857
$596$	−103.776	−4.25083
$597$	−12.4299	−0.508723
$598$	−10.7411	−0.439237
$599$	46.5624	1.90249	0.951245	−	0.308437i	$-0.0998060\pi$
$599$	46.5624	1.90249	0.951245	+	0.308437i	$0.0998060\pi$
$600$	34.9652	1.42745
$601$	−2.76984	−0.112984	−0.0564920	−	0.998403i	$-0.517992\pi$
$601$	−2.76984	−0.112984	−0.0564920	+	0.998403i	$0.517992\pi$
$602$	−58.7121	−2.39293
$603$	−21.4428	−0.873218
$604$	−32.3049	−1.31447
$605$	20.5446	0.835255
$606$	−61.9409	−2.51618
$607$	26.3606	1.06994	0.534971	−	0.844870i	$-0.320322\pi$
$607$	26.3606	1.06994	0.534971	+	0.844870i	$0.320322\pi$
$608$	52.7760	2.14035
$609$	−82.3018	−3.33504
$610$	37.2544	1.50839
$611$	8.70237	0.352060
$612$	9.82491	0.397149
$613$	−17.5730	−0.709767	−0.354884	−	0.934910i	$-0.615480\pi$
$613$	−17.5730	−0.709767	−0.354884	+	0.934910i	$0.615480\pi$
$614$	31.9270	1.28847
$615$	1.75027	0.0705776
$616$	15.9486	0.642586
$617$	−9.86620	−0.397198	−0.198599	−	0.980081i	$-0.563639\pi$
$617$	−9.86620	−0.397198	−0.198599	+	0.980081i	$0.563639\pi$
$618$	−83.7915	−3.37059
$619$	6.20431	0.249372	0.124686	−	0.992196i	$-0.460208\pi$
$619$	6.20431	0.249372	0.124686	+	0.992196i	$0.460208\pi$
$620$	−55.9914	−2.24867
$621$	23.1175	0.927673
$622$	36.9955	1.48338
$623$	53.6477	2.14935
$624$	55.0141	2.20233
$625$	−16.4348	−0.657394
$626$	−59.3675	−2.37280
$627$	4.41328	0.176250
$628$	−24.3758	−0.972702
$629$	−2.66461	−0.106245
$630$	108.928	4.33981
$631$	−13.9941	−0.557096	−0.278548	−	0.960422i	$-0.589853\pi$
$631$	−13.9941	−0.557096	−0.278548	+	0.960422i	$0.589853\pi$
$632$	−139.142	−5.53477
$633$	36.2729	1.44172
$634$	11.2760	0.447827
$635$	−31.4719	−1.24892
$636$	−151.264	−5.99799
$637$	9.12276	0.361457
$638$	−10.1653	−0.402447
$639$	−6.49689	−0.257013
$640$	42.6723	1.68677
$641$	−1.57045	−0.0620291	−0.0310145	−	0.999519i	$-0.509874\pi$
$641$	−1.57045	−0.0620291	−0.0310145	+	0.999519i	$0.509874\pi$
$642$	0.118313	0.00466944
$643$	−37.1291	−1.46423	−0.732114	−	0.681182i	$-0.761466\pi$
$643$	−37.1291	−1.46423	−0.732114	+	0.681182i	$0.761466\pi$
$644$	53.9105	2.12437
$645$	−33.7151	−1.32753
$646$	2.60741	0.102587
$647$	6.06275	0.238351	0.119176	−	0.992873i	$-0.461975\pi$
$647$	6.06275	0.238351	0.119176	+	0.992873i	$0.461975\pi$
$648$	−61.9396	−2.43322
$649$	−0.748396	−0.0293771
$650$	5.16668	0.202654
$651$	60.5934	2.37484
$652$	41.9543	1.64306
$653$	−20.6088	−0.806483	−0.403242	−	0.915094i	$-0.632117\pi$
$653$	−20.6088	−0.806483	−0.403242	+	0.915094i	$0.632117\pi$
$654$	−89.0061	−3.48041
$655$	−29.7103	−1.16088
$656$	−4.03409	−0.157505
$657$	87.0927	3.39781
$658$	−60.3214	−2.35157
$659$	−20.5714	−0.801350	−0.400675	−	0.916220i	$-0.631224\pi$
$659$	−20.5714	−0.801350	−0.400675	+	0.916220i	$0.631224\pi$
$660$	14.7967	0.575963
$661$	−1.73750	−0.0675810	−0.0337905	−	0.999429i	$-0.510758\pi$
$661$	−1.73750	−0.0675810	−0.0337905	+	0.999429i	$0.510758\pi$
$662$	27.6696	1.07541
$663$	1.36484	0.0530062
$664$	19.2225	0.745976
$665$	20.9320	0.811707
$666$	128.105	4.96398
$667$	−21.2678	−0.823494
$668$	11.3595	0.439513
$669$	2.98464	0.115393
$670$	−19.0795	−0.737104
$671$	−3.60563	−0.139194
$672$	−191.490	−7.38687
$673$	41.3833	1.59521	0.797605	−	0.603180i	$-0.206100\pi$
$673$	41.3833	1.59521	0.797605	+	0.603180i	$0.206100\pi$
$674$	−40.2663	−1.55100
$675$	−11.1199	−0.428007
$676$	−57.6110	−2.21581
$677$	−31.0891	−1.19485	−0.597426	−	0.801924i	$-0.703810\pi$
$677$	−31.0891	−1.19485	−0.597426	+	0.801924i	$0.703810\pi$
$678$	−153.620	−5.89973
$679$	1.35111	0.0518508
$680$	5.41086	0.207497
$681$	−54.4395	−2.08612
$682$	7.48402	0.286578
$683$	21.3712	0.817747	0.408874	−	0.912591i	$-0.365922\pi$
$683$	21.3712	0.817747	0.408874	+	0.912591i	$0.365922\pi$
$684$	−90.7678	−3.47059
$685$	−14.1839	−0.541938
$686$	5.78692	0.220946
$687$	52.8166	2.01508
$688$	77.7082	2.96260
$689$	−13.8345	−0.527051
$690$	42.7544	1.62763
$691$	−12.0864	−0.459787	−0.229893	−	0.973216i	$-0.573838\pi$
$691$	−12.0864	−0.459787	−0.229893	+	0.973216i	$0.573838\pi$
$692$	−21.3340	−0.810998
$693$	−10.5425	−0.400477
$694$	−27.2126	−1.03298
$695$	23.3827	0.886956
$696$	196.548	7.45012
$697$	−0.100082	−0.00379086
$698$	−7.16086	−0.271043
$699$	58.3019	2.20518
$700$	−25.9319	−0.980135
$701$	13.3202	0.503096	0.251548	−	0.967845i	$-0.419060\pi$
$701$	13.3202	0.503096	0.251548	+	0.967845i	$0.419060\pi$
$702$	−31.5690	−1.19149
$703$	24.6171	0.928452
$704$	−10.6557	−0.401604
$705$	−34.6393	−1.30459
$706$	41.6958	1.56924
$707$	28.4334	1.06935
$708$	23.3791	0.878640
$709$	−16.7627	−0.629535	−0.314768	−	0.949169i	$-0.601927\pi$
$709$	−16.7627	−0.629535	−0.314768	+	0.949169i	$0.601927\pi$
$710$	−5.78083	−0.216951
$711$	91.9772	3.44941
$712$	−128.118	−4.80142
$713$	15.6581	0.586401
$714$	−9.46057	−0.354053
$715$	1.35330	0.0506106
$716$	40.8753	1.52758
$717$	−5.87764	−0.219505
$718$	−32.8244	−1.22500
$719$	−7.59969	−0.283421	−0.141710	−	0.989908i	$-0.545260\pi$
$719$	−7.59969	−0.283421	−0.141710	+	0.989908i	$0.545260\pi$
$720$	−144.172	−5.37296
$721$	38.4638	1.43247
$722$	27.0655	1.00727
$723$	−36.9478	−1.37410
$724$	10.9178	0.405757
$725$	10.2302	0.379941
$726$	85.7841	3.18375
$727$	−36.1248	−1.33980	−0.669898	−	0.742453i	$-0.733662\pi$
$727$	−36.1248	−1.33980	−0.669898	+	0.742453i	$0.733662\pi$
$728$	−45.5665	−1.68881
$729$	−32.3355	−1.19761
$730$	77.4937	2.86817
$731$	1.92786	0.0713045
$732$	112.636	4.16314
$733$	−10.8879	−0.402152	−0.201076	−	0.979576i	$-0.564444\pi$
$733$	−10.8879	−0.402152	−0.201076	+	0.979576i	$0.564444\pi$
$734$	−26.1558	−0.965429
$735$	−36.3127	−1.33941
$736$	−49.4834	−1.82398
$737$	1.84659	0.0680198
$738$	4.81158	0.177117
$739$	52.4152	1.92812	0.964062	−	0.265679i	$-0.0855960\pi$
$739$	52.4152	1.92812	0.964062	+	0.265679i	$0.0855960\pi$
$740$	82.5356	3.03407
$741$	−12.6092	−0.463209
$742$	95.8951	3.52042
$743$	50.0732	1.83701	0.918504	−	0.395412i	$-0.129398\pi$
$743$	50.0732	1.83701	0.918504	+	0.395412i	$0.129398\pi$
$744$	−144.705	−5.30515
$745$	37.7795	1.38413
$746$	−34.3382	−1.25721
$747$	−12.7066	−0.464912
$748$	−0.846090	−0.0309361
$749$	−0.0543105	−0.00198446
$750$	−96.7887	−3.53422
$751$	−40.8762	−1.49159	−0.745797	−	0.666173i	$-0.767931\pi$
$751$	−40.8762	−1.49159	−0.745797	+	0.666173i	$0.767931\pi$
$752$	79.8381	2.91140
$753$	66.4920	2.42310
$754$	29.0431	1.05769
$755$	11.7606	0.428011
$756$	158.447	5.76266
$757$	27.7544	1.00875	0.504376	−	0.863484i	$-0.331722\pi$
$757$	27.7544	1.00875	0.504376	+	0.863484i	$0.331722\pi$
$758$	16.6804	0.605858
$759$	−4.13794	−0.150198
$760$	−49.9884	−1.81327
$761$	45.0938	1.63465	0.817324	−	0.576178i	$-0.195457\pi$
$761$	45.0938	1.63465	0.817324	+	0.576178i	$0.195457\pi$
$762$	−131.411	−4.76053
$763$	40.8574	1.47914
$764$	57.1971	2.06932
$765$	−3.57675	−0.129318
$766$	49.6610	1.79433
$767$	2.13824	0.0772072
$768$	51.3360	1.85243
$769$	−53.7491	−1.93824	−0.969121	−	0.246587i	$-0.920691\pi$
$769$	−53.7491	−1.93824	−0.969121	+	0.246587i	$0.920691\pi$
$770$	−9.38055	−0.338052
$771$	41.0263	1.47752
$772$	−25.2178	−0.907610
$773$	−21.0431	−0.756868	−0.378434	−	0.925628i	$-0.623537\pi$
$773$	−21.0431	−0.756868	−0.378434	+	0.925628i	$0.623537\pi$
$774$	−92.6848	−3.33149
$775$	−7.53184	−0.270552
$776$	−3.22663	−0.115829
$777$	−89.3193	−3.20431
$778$	21.6933	0.777742
$779$	0.924608	0.0331275
$780$	−42.2757	−1.51371
$781$	0.559491	0.0200202
$782$	−2.44473	−0.0874235
$783$	−62.5078	−2.23385
$784$	83.6950	2.98911
$785$	8.87399	0.316726
$786$	−124.056	−4.42493
$787$	−16.2351	−0.578718	−0.289359	−	0.957221i	$-0.593442\pi$
$787$	−16.2351	−0.578718	−0.289359	+	0.957221i	$0.593442\pi$
$788$	−48.7002	−1.73487
$789$	14.8670	0.529281
$790$	81.8398	2.91173
$791$	70.5178	2.50732
$792$	25.1769	0.894623
$793$	10.3016	0.365821
$794$	−20.7205	−0.735344
$795$	55.0673	1.95304
$796$	−22.0154	−0.780314
$797$	−15.0764	−0.534035	−0.267018	−	0.963692i	$-0.586038\pi$
$797$	−15.0764	−0.534035	−0.267018	+	0.963692i	$0.586038\pi$
$798$	87.4018	3.09399
$799$	1.98070	0.0700722
$800$	23.8024	0.841542
$801$	84.6899	2.99237
$802$	−13.9497	−0.492583
$803$	−7.50014	−0.264674
$804$	−57.6853	−2.03441
$805$	−19.6260	−0.691727
$806$	−21.3825	−0.753168
$807$	−51.1269	−1.79975
$808$	−67.9028	−2.38881
$809$	−23.3751	−0.821825	−0.410913	−	0.911675i	$-0.634790\pi$
$809$	−23.3751	−0.821825	−0.410913	+	0.911675i	$0.634790\pi$
$810$	36.4314	1.28007
$811$	38.0185	1.33501	0.667504	−	0.744606i	$-0.267362\pi$
$811$	38.0185	1.33501	0.667504	+	0.744606i	$0.267362\pi$
$812$	−145.770	−5.11551
$813$	4.32914	0.151830
$814$	−11.0320	−0.386672
$815$	−15.2734	−0.535004
$816$	12.5215	0.438340
$817$	−17.8106	−0.623114
$818$	30.7747	1.07601
$819$	30.1209	1.05251
$820$	3.10000	0.108257
$821$	55.3557	1.93193	0.965964	−	0.258676i	$-0.0832862\pi$
$821$	55.3557	1.93193	0.965964	+	0.258676i	$0.0832862\pi$
$822$	−59.2250	−2.06571
$823$	41.9558	1.46249	0.731243	−	0.682117i	$-0.238941\pi$
$823$	41.9558	1.46249	0.731243	+	0.682117i	$0.238941\pi$
$824$	−91.8566	−3.19998
$825$	1.99043	0.0692978
$826$	−14.8214	−0.515703
$827$	−9.61658	−0.334401	−0.167201	−	0.985923i	$-0.553473\pi$
$827$	−9.61658	−0.334401	−0.167201	+	0.985923i	$0.553473\pi$
$828$	85.1048	2.95760
$829$	32.0943	1.11468	0.557341	−	0.830284i	$-0.311822\pi$
$829$	32.0943	1.11468	0.557341	+	0.830284i	$0.311822\pi$
$830$	−11.3062	−0.392443
$831$	90.2804	3.13179
$832$	30.4444	1.05547
$833$	2.07639	0.0719426
$834$	97.6348	3.38082
$835$	−4.13542	−0.143112
$836$	7.81663	0.270344
$837$	46.0204	1.59070
$838$	−52.9544	−1.82928
$839$	−42.1196	−1.45413	−0.727066	−	0.686568i	$-0.759116\pi$
$839$	−42.1196	−1.45413	−0.727066	+	0.686568i	$0.759116\pi$
$840$	181.375	6.25803
$841$	28.5065	0.982982
$842$	48.3588	1.66655
$843$	22.5921	0.778114
$844$	64.2450	2.21140
$845$	20.9732	0.721500
$846$	−95.2253	−3.27391
$847$	−39.3784	−1.35306
$848$	−126.922	−4.35851
$849$	8.45854	0.290296
$850$	1.17596	0.0403352
$851$	−23.0813	−0.791215
$852$	−17.4779	−0.598783
$853$	23.7828	0.814306	0.407153	−	0.913360i	$-0.366522\pi$
$853$	23.7828	0.814306	0.407153	+	0.913360i	$0.366522\pi$
$854$	−71.4067	−2.44349
$855$	33.0439	1.13008
$856$	0.129701	0.00443308
$857$	−25.4459	−0.869215	−0.434607	−	0.900620i	$-0.643113\pi$
$857$	−25.4459	−0.869215	−0.434607	+	0.900620i	$0.643113\pi$
$858$	5.65073	0.192913
$859$	−18.9684	−0.647192	−0.323596	−	0.946195i	$-0.604892\pi$
$859$	−18.9684	−0.647192	−0.323596	+	0.946195i	$0.604892\pi$
$860$	−59.7149	−2.03626
$861$	−3.35479	−0.114331
$862$	−67.5541	−2.30090
$863$	−48.3115	−1.64454	−0.822271	−	0.569095i	$-0.807293\pi$
$863$	−48.3115	−1.64454	−0.822271	+	0.569095i	$0.807293\pi$
$864$	−145.435	−4.94781
$865$	7.76663	0.264073
$866$	−48.6891	−1.65452
$867$	−50.0667	−1.70035
$868$	107.321	3.64270
$869$	−7.92078	−0.268694
$870$	−115.604	−3.91936
$871$	−5.27586	−0.178766
$872$	−97.5730	−3.30424
$873$	2.13290	0.0721879
$874$	22.5857	0.763974
$875$	44.4300	1.50201
$876$	234.296	7.91614
$877$	27.2307	0.919516	0.459758	−	0.888044i	$-0.347936\pi$
$877$	27.2307	0.919516	0.459758	+	0.888044i	$0.347936\pi$
$878$	4.63077	0.156281
$879$	31.5809	1.06520
$880$	12.4156	0.418529
$881$	19.1683	0.645796	0.322898	−	0.946434i	$-0.395343\pi$
$881$	19.1683	0.645796	0.322898	+	0.946434i	$0.395343\pi$
$882$	−99.8255	−3.36130
$883$	15.2847	0.514370	0.257185	−	0.966362i	$-0.417205\pi$
$883$	15.2847	0.514370	0.257185	+	0.966362i	$0.417205\pi$
$884$	2.41736	0.0813045
$885$	−8.51113	−0.286099
$886$	78.1111	2.62419
$887$	−40.1629	−1.34854	−0.674269	−	0.738486i	$-0.735541\pi$
$887$	−40.1629	−1.34854	−0.674269	+	0.738486i	$0.735541\pi$
$888$	213.306	7.15810
$889$	60.3232	2.02318
$890$	75.3557	2.52593
$891$	−3.52597	−0.118124
$892$	5.28628	0.176998
$893$	−18.2988	−0.612345
$894$	157.749	5.27591
$895$	−14.8806	−0.497403
$896$	−81.7915	−2.73246
$897$	11.8225	0.394741
$898$	23.4932	0.783977
$899$	−42.3382	−1.41206
$900$	−40.9370	−1.36457
$901$	−3.14879	−0.104902
$902$	−0.414358	−0.0137966
$903$	64.6229	2.15052
$904$	−168.406	−5.60110
$905$	−3.97462	−0.132121
$906$	49.1064	1.63145
$907$	−14.6965	−0.487990	−0.243995	−	0.969776i	$-0.578458\pi$
$907$	−14.6965	−0.487990	−0.243995	+	0.969776i	$0.578458\pi$
$908$	−96.4209	−3.19984
$909$	44.8859	1.48877
$910$	26.8011	0.888448
$911$	43.5708	1.44356	0.721782	−	0.692120i	$-0.243323\pi$
$911$	43.5708	1.44356	0.721782	+	0.692120i	$0.243323\pi$
$912$	−115.680	−3.83056
$913$	1.09426	0.0362146
$914$	69.2962	2.29212
$915$	−41.0050	−1.35558
$916$	93.5466	3.09087
$917$	56.9468	1.88055
$918$	−7.18526	−0.237149
$919$	−16.2147	−0.534873	−0.267436	−	0.963575i	$-0.586177\pi$
$919$	−16.2147	−0.534873	−0.267436	+	0.963575i	$0.586177\pi$
$920$	46.8696	1.54525
$921$	−35.1412	−1.15794
$922$	25.7618	0.848421
$923$	−1.59852	−0.0526158
$924$	−28.3614	−0.933022
$925$	11.1025	0.365048
$926$	46.3567	1.52337
$927$	60.7201	1.99431
$928$	133.799	4.39216
$929$	45.0966	1.47957	0.739785	−	0.672843i	$-0.234927\pi$
$929$	45.0966	1.47957	0.739785	+	0.672843i	$0.234927\pi$
$930$	85.1120	2.79093
$931$	−19.1828	−0.628690
$932$	103.262	3.38246
$933$	−40.7200	−1.33311
$934$	111.161	3.63731
$935$	0.308018	0.0100733
$936$	−71.9328	−2.35120
$937$	−23.7273	−0.775139	−0.387569	−	0.921841i	$-0.626685\pi$
$937$	−23.7273	−0.775139	−0.387569	+	0.921841i	$0.626685\pi$
$938$	36.5702	1.19406
$939$	65.3443	2.13243
$940$	−61.3517	−2.00107
$941$	−42.6692	−1.39098	−0.695489	−	0.718537i	$-0.744812\pi$
$941$	−42.6692	−1.39098	−0.695489	+	0.718537i	$0.744812\pi$
$942$	37.0535	1.20727
$943$	−0.866922	−0.0282309
$944$	19.6168	0.638473
$945$	−57.6824	−1.87641
$946$	7.98172	0.259508
$947$	10.4694	0.340210	0.170105	−	0.985426i	$-0.445589\pi$
$947$	10.4694	0.340210	0.170105	+	0.985426i	$0.445589\pi$
$948$	247.437	8.03637
$949$	21.4286	0.695601
$950$	−10.8642	−0.352480
$951$	−12.4112	−0.402461
$952$	−10.3712	−0.336132
$953$	21.1162	0.684021	0.342010	−	0.939696i	$-0.388892\pi$
$953$	21.1162	0.684021	0.342010	+	0.939696i	$0.388892\pi$
$954$	151.383	4.90121
$955$	−20.8225	−0.673801
$956$	−10.4102	−0.336691
$957$	11.1887	0.361678
$958$	17.3918	0.561904
$959$	27.1867	0.877905
$960$	−121.182	−3.91115
$961$	0.170864	0.00551174
$962$	31.5195	1.01623
$963$	−0.0857363	−0.00276281
$964$	−65.4404	−2.10769
$965$	9.18053	0.295532
$966$	−81.9488	−2.63666
$967$	44.8646	1.44275	0.721374	−	0.692546i	$-0.243511\pi$
$967$	44.8646	1.44275	0.721374	+	0.692546i	$0.243511\pi$
$968$	94.0409	3.02259
$969$	−2.86991	−0.0921947
$970$	1.89782	0.0609355
$971$	19.5646	0.627857	0.313929	−	0.949447i	$-0.398355\pi$
$971$	19.5646	0.627857	0.313929	+	0.949447i	$0.398355\pi$
$972$	−19.6422	−0.630025
$973$	−44.8184	−1.43681
$974$	70.0040	2.24307
$975$	−5.68683	−0.182124
$976$	94.5101	3.02519
$977$	11.4252	0.365524	0.182762	−	0.983157i	$-0.441496\pi$
$977$	11.4252	0.365524	0.182762	+	0.983157i	$0.441496\pi$
$978$	−63.7743	−2.03928
$979$	−7.29322	−0.233092
$980$	−64.3155	−2.05448
$981$	64.4989	2.05929
$982$	−20.8762	−0.666185
$983$	−45.9694	−1.46620	−0.733098	−	0.680123i	$-0.761926\pi$
$983$	−45.9694	−1.46620	−0.733098	+	0.680123i	$0.761926\pi$
$984$	8.01170	0.255404
$985$	17.7293	0.564901
$986$	6.61036	0.210517
$987$	66.3943	2.11335
$988$	−22.3328	−0.710502
$989$	16.6994	0.531010
$990$	−14.8084	−0.470643
$991$	−40.2192	−1.27761	−0.638803	−	0.769371i	$-0.720570\pi$
$991$	−40.2192	−1.27761	−0.638803	+	0.769371i	$0.720570\pi$
$992$	−98.5073	−3.12761
$993$	−30.4552	−0.966467
$994$	11.0803	0.351446
$995$	8.01467	0.254082
$996$	−34.1834	−1.08314
$997$	−59.7465	−1.89219	−0.946096	−	0.323887i	$-0.895010\pi$
$997$	−59.7465	−1.89219	−0.946096	+	0.323887i	$0.895010\pi$
$998$	69.0936	2.18712
$999$	−67.8376	−2.14629

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8009.2.a.b.1.14	✓	361

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8009.2.a.b.1.14	✓	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)

\(f(q)\)	\(=\)	\(q-2.69232 q^{2} +2.96337 q^{3} +5.24860 q^{4} -1.91075 q^{5} -7.97835 q^{6} +3.66239 q^{7} -8.74628 q^{8} +5.78157 q^{9} +O(q^{10})\)	\(q-2.69232 q^{2} +2.96337 q^{3} +5.24860 q^{4} -1.91075 q^{5} -7.97835 q^{6} +3.66239 q^{7} -8.74628 q^{8} +5.78157 q^{9} +5.14435 q^{10} -0.497890 q^{11} +15.5536 q^{12} +1.42252 q^{13} -9.86034 q^{14} -5.66225 q^{15} +13.0506 q^{16} +0.323772 q^{17} -15.5658 q^{18} -2.99118 q^{19} -10.0287 q^{20} +10.8530 q^{21} +1.34048 q^{22} +2.80456 q^{23} -25.9185 q^{24} -1.34905 q^{25} -3.82988 q^{26} +8.24282 q^{27} +19.2224 q^{28} -7.58330 q^{29} +15.2446 q^{30} +5.58309 q^{31} -17.6439 q^{32} -1.47543 q^{33} -0.871699 q^{34} -6.99790 q^{35} +30.3451 q^{36} -8.22990 q^{37} +8.05322 q^{38} +4.21545 q^{39} +16.7119 q^{40} -0.309111 q^{41} -29.2198 q^{42} +5.95437 q^{43} -2.61323 q^{44} -11.0471 q^{45} -7.55078 q^{46} +6.11758 q^{47} +38.6738 q^{48} +6.41311 q^{49} +3.63207 q^{50} +0.959457 q^{51} +7.46623 q^{52} -9.72534 q^{53} -22.1923 q^{54} +0.951342 q^{55} -32.0323 q^{56} -8.86397 q^{57} +20.4167 q^{58} +1.50314 q^{59} -29.7189 q^{60} +7.24181 q^{61} -15.0315 q^{62} +21.1744 q^{63} +21.4018 q^{64} -2.71807 q^{65} +3.97234 q^{66} -3.70882 q^{67} +1.69935 q^{68} +8.31096 q^{69} +18.8406 q^{70} -1.12372 q^{71} -50.5672 q^{72} +15.0638 q^{73} +22.1575 q^{74} -3.99772 q^{75} -15.6995 q^{76} -1.82347 q^{77} -11.3493 q^{78} +15.9087 q^{79} -24.9364 q^{80} +7.08183 q^{81} +0.832228 q^{82} -2.19779 q^{83} +56.9632 q^{84} -0.618647 q^{85} -16.0311 q^{86} -22.4721 q^{87} +4.35469 q^{88} +14.6483 q^{89} +29.7424 q^{90} +5.20982 q^{91} +14.7200 q^{92} +16.5448 q^{93} -16.4705 q^{94} +5.71539 q^{95} -52.2854 q^{96} +0.368915 q^{97} -17.2662 q^{98} -2.87859 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 361 q + 10 q^{2} + 23 q^{3} + 414 q^{4} + 21 q^{5} + 49 q^{6} + 106 q^{7} + 30 q^{8} + 406 q^{9}+O(q^{10}) \) 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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