LMFDB - Embedded newform 8009.2.a.b.1.15

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			1.15
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)

$f(q)$	$=$	$q-2.65249 q^{2} +1.26544 q^{3} +5.03571 q^{4} +2.87387 q^{5} -3.35656 q^{6} +2.78404 q^{7} -8.05219 q^{8} -1.39867 q^{9} +O(q^{10})$	\(q-2.65249 q^{2} +1.26544 q^{3} +5.03571 q^{4} +2.87387 q^{5} -3.35656 q^{6} +2.78404 q^{7} -8.05219 q^{8} -1.39867 q^{9} -7.62292 q^{10} -1.24042 q^{11} +6.37238 q^{12} +2.24492 q^{13} -7.38464 q^{14} +3.63671 q^{15} +11.2869 q^{16} -3.96481 q^{17} +3.70995 q^{18} +0.842838 q^{19} +14.4720 q^{20} +3.52303 q^{21} +3.29020 q^{22} +3.76990 q^{23} -10.1895 q^{24} +3.25913 q^{25} -5.95462 q^{26} -5.56624 q^{27} +14.0196 q^{28} -2.74437 q^{29} -9.64633 q^{30} +9.73193 q^{31} -13.8341 q^{32} -1.56968 q^{33} +10.5166 q^{34} +8.00097 q^{35} -7.04328 q^{36} +8.32142 q^{37} -2.23562 q^{38} +2.84080 q^{39} -23.1410 q^{40} +1.50138 q^{41} -9.34481 q^{42} +9.24425 q^{43} -6.24640 q^{44} -4.01959 q^{45} -9.99963 q^{46} +7.77415 q^{47} +14.2829 q^{48} +0.750879 q^{49} -8.64482 q^{50} -5.01722 q^{51} +11.3047 q^{52} +3.18267 q^{53} +14.7644 q^{54} -3.56481 q^{55} -22.4176 q^{56} +1.06656 q^{57} +7.27941 q^{58} +3.06757 q^{59} +18.3134 q^{60} +14.9505 q^{61} -25.8139 q^{62} -3.89394 q^{63} +14.1211 q^{64} +6.45160 q^{65} +4.16355 q^{66} -11.4738 q^{67} -19.9656 q^{68} +4.77058 q^{69} -21.2225 q^{70} -8.19798 q^{71} +11.2623 q^{72} +3.21399 q^{73} -22.0725 q^{74} +4.12423 q^{75} +4.24429 q^{76} -3.45338 q^{77} -7.53520 q^{78} -9.47781 q^{79} +32.4372 q^{80} -2.84773 q^{81} -3.98241 q^{82} +14.0494 q^{83} +17.7410 q^{84} -11.3944 q^{85} -24.5203 q^{86} -3.47283 q^{87} +9.98810 q^{88} -6.54258 q^{89} +10.6619 q^{90} +6.24994 q^{91} +18.9841 q^{92} +12.3152 q^{93} -20.6209 q^{94} +2.42221 q^{95} -17.5063 q^{96} +3.77381 q^{97} -1.99170 q^{98} +1.73494 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−2.65249	−1.87559	−0.937797	−	0.347183i	$-0.887138\pi$
$2$	−2.65249	−1.87559	−0.937797	+	0.347183i	$0.887138\pi$
$3$	1.26544	0.730601	0.365300	−	0.930890i	$-0.380966\pi$
$3$	1.26544	0.730601	0.365300	+	0.930890i	$0.380966\pi$
$4$	5.03571	2.51785
$5$	2.87387	1.28523	0.642617	−	0.766188i	$-0.277849\pi$
$5$	2.87387	1.28523	0.642617	+	0.766188i	$0.277849\pi$
$6$	−3.35656	−1.37031
$7$	2.78404	1.05227	0.526134	−	0.850402i	$-0.323641\pi$
$7$	2.78404	1.05227	0.526134	+	0.850402i	$0.323641\pi$
$8$	−8.05219	−2.84688
$9$	−1.39867	−0.466222
$10$	−7.62292	−2.41058
$11$	−1.24042	−0.374001	−0.187000	−	0.982360i	$-0.559877\pi$
$11$	−1.24042	−0.374001	−0.187000	+	0.982360i	$0.559877\pi$
$12$	6.37238	1.83955
$13$	2.24492	0.622628	0.311314	−	0.950307i	$-0.399231\pi$
$13$	2.24492	0.622628	0.311314	+	0.950307i	$0.399231\pi$
$14$	−7.38464	−1.97363
$15$	3.63671	0.938993
$16$	11.2869	2.82174
$17$	−3.96481	−0.961608	−0.480804	−	0.876828i	$-0.659655\pi$
$17$	−3.96481	−0.961608	−0.480804	+	0.876828i	$0.659655\pi$
$18$	3.70995	0.874444
$19$	0.842838	0.193360	0.0966802	−	0.995315i	$-0.469178\pi$
$19$	0.842838	0.193360	0.0966802	+	0.995315i	$0.469178\pi$
$20$	14.4720	3.23603
$21$	3.52303	0.768788
$22$	3.29020	0.701474
$23$	3.76990	0.786079	0.393039	−	0.919522i	$-0.371424\pi$
$23$	3.76990	0.786079	0.393039	+	0.919522i	$0.371424\pi$
$24$	−10.1895	−2.07993
$25$	3.25913	0.651827
$26$	−5.95462	−1.16780
$27$	−5.56624	−1.07122
$28$	14.0196	2.64946
$29$	−2.74437	−0.509616	−0.254808	−	0.966992i	$-0.582012\pi$
$29$	−2.74437	−0.509616	−0.254808	+	0.966992i	$0.582012\pi$
$30$	−9.64633	−1.76117
$31$	9.73193	1.74791	0.873953	−	0.486010i	$-0.161548\pi$
$31$	9.73193	1.74791	0.873953	+	0.486010i	$0.161548\pi$
$32$	−13.8341	−2.44556
$33$	−1.56968	−0.273245
$34$	10.5166	1.80359
$35$	8.00097	1.35241
$36$	−7.04328	−1.17388
$37$	8.32142	1.36803	0.684016	−	0.729467i	$-0.260232\pi$
$37$	8.32142	1.36803	0.684016	+	0.729467i	$0.260232\pi$
$38$	−2.23562	−0.362666
$39$	2.84080	0.454892
$40$	−23.1410	−3.65891
$41$	1.50138	0.234477	0.117238	−	0.993104i	$-0.462596\pi$
$41$	1.50138	0.234477	0.117238	+	0.993104i	$0.462596\pi$
$42$	−9.34481	−1.44193
$43$	9.24425	1.40973	0.704867	−	0.709339i	$-0.251006\pi$
$43$	9.24425	1.40973	0.704867	+	0.709339i	$0.251006\pi$
$44$	−6.24640	−0.941680
$45$	−4.01959	−0.599205
$46$	−9.99963	−1.47436
$47$	7.77415	1.13398	0.566989	−	0.823726i	$-0.308108\pi$
$47$	7.77415	1.13398	0.566989	+	0.823726i	$0.308108\pi$
$48$	14.2829	2.06156
$49$	0.750879	0.107268
$50$	−8.64482	−1.22256
$51$	−5.01722	−0.702551
$52$	11.3047	1.56769
$53$	3.18267	0.437174	0.218587	−	0.975818i	$-0.429855\pi$
$53$	3.18267	0.437174	0.218587	+	0.975818i	$0.429855\pi$
$54$	14.7644	2.00918
$55$	−3.56481	−0.480679
$56$	−22.4176	−2.99568
$57$	1.06656	0.141269
$58$	7.27941	0.955833
$59$	3.06757	0.399364	0.199682	−	0.979861i	$-0.436009\pi$
$59$	3.06757	0.399364	0.199682	+	0.979861i	$0.436009\pi$
$60$	18.3134	2.36425
$61$	14.9505	1.91422	0.957110	−	0.289726i	$-0.0935642\pi$
$61$	14.9505	1.91422	0.957110	+	0.289726i	$0.0935642\pi$
$62$	−25.8139	−3.27836
$63$	−3.89394	−0.490591
$64$	14.1211	1.76513
$65$	6.45160	0.800222
$66$	4.16355	0.512498
$67$	−11.4738	−1.40175	−0.700873	−	0.713286i	$-0.747206\pi$
$67$	−11.4738	−1.40175	−0.700873	+	0.713286i	$0.747206\pi$
$68$	−19.9656	−2.42119
$69$	4.77058	0.574310
$70$	−21.2225	−2.53657
$71$	−8.19798	−0.972921	−0.486461	−	0.873702i	$-0.661712\pi$
$71$	−8.19798	−0.972921	−0.486461	+	0.873702i	$0.661712\pi$
$72$	11.2623	1.32728
$73$	3.21399	0.376169	0.188084	−	0.982153i	$-0.439772\pi$
$73$	3.21399	0.376169	0.188084	+	0.982153i	$0.439772\pi$
$74$	−22.0725	−2.56587
$75$	4.12423	0.476225
$76$	4.24429	0.486853
$77$	−3.45338	−0.393549
$78$	−7.53520	−0.853194
$79$	−9.47781	−1.06634	−0.533168	−	0.846009i	$-0.678999\pi$
$79$	−9.47781	−1.06634	−0.533168	+	0.846009i	$0.678999\pi$
$80$	32.4372	3.62659
$81$	−2.84773	−0.316414
$82$	−3.98241	−0.439783
$83$	14.0494	1.54212	0.771060	−	0.636762i	$-0.219727\pi$
$83$	14.0494	1.54212	0.771060	+	0.636762i	$0.219727\pi$
$84$	17.7410	1.93570
$85$	−11.3944	−1.23589
$86$	−24.5203	−2.64409
$87$	−3.47283	−0.372326
$88$	9.98810	1.06474
$89$	−6.54258	−0.693512	−0.346756	−	0.937955i	$-0.612717\pi$
$89$	−6.54258	−0.693512	−0.346756	+	0.937955i	$0.612717\pi$
$90$	10.6619	1.12387
$91$	6.24994	0.655171
$92$	18.9841	1.97923
$93$	12.3152	1.27702
$94$	−20.6209	−2.12688
$95$	2.42221	0.248513
$96$	−17.5063	−1.78672
$97$	3.77381	0.383173	0.191586	−	0.981476i	$-0.438637\pi$
$97$	3.77381	0.383173	0.191586	+	0.981476i	$0.438637\pi$
$98$	−1.99170	−0.201192
$99$	1.73494	0.174368
$100$	16.4120	1.64120
$101$	−16.7169	−1.66340	−0.831698	−	0.555228i	$-0.812631\pi$
$101$	−16.7169	−1.66340	−0.831698	+	0.555228i	$0.812631\pi$
$102$	13.3081	1.31770
$103$	−10.4124	−1.02597	−0.512984	−	0.858398i	$-0.671460\pi$
$103$	−10.4124	−1.02597	−0.512984	+	0.858398i	$0.671460\pi$
$104$	−18.0765	−1.77255
$105$	10.1247	0.988073
$106$	−8.44201	−0.819960
$107$	−6.94149	−0.671059	−0.335530	−	0.942030i	$-0.608915\pi$
$107$	−6.94149	−0.671059	−0.335530	+	0.942030i	$0.608915\pi$
$108$	−28.0300	−2.69718
$109$	17.1016	1.63804	0.819018	−	0.573768i	$-0.194519\pi$
$109$	17.1016	1.63804	0.819018	+	0.573768i	$0.194519\pi$
$110$	9.45562	0.901558
$111$	10.5302	0.999486
$112$	31.4233	2.96922
$113$	−14.9010	−1.40177	−0.700883	−	0.713276i	$-0.747211\pi$
$113$	−14.9010	−1.40177	−0.700883	+	0.713276i	$0.747211\pi$
$114$	−2.82904	−0.264964
$115$	10.8342	1.01030
$116$	−13.8198	−1.28314
$117$	−3.13989	−0.290283
$118$	−8.13671	−0.749045
$119$	−11.0382	−1.01187
$120$	−29.2834	−2.67320
$121$	−9.46136	−0.860123
$122$	−39.6562	−3.59030
$123$	1.89991	0.171309
$124$	49.0072	4.40097
$125$	−5.00303	−0.447484
$126$	10.3287	0.920150
$127$	−10.2080	−0.905810	−0.452905	−	0.891559i	$-0.649612\pi$
$127$	−10.2080	−0.905810	−0.452905	+	0.891559i	$0.649612\pi$
$128$	−9.78769	−0.865118
$129$	11.6980	1.02995
$130$	−17.1128	−1.50089
$131$	−2.91528	−0.254709	−0.127355	−	0.991857i	$-0.540649\pi$
$131$	−2.91528	−0.254709	−0.127355	+	0.991857i	$0.540649\pi$
$132$	−7.90443	−0.687992
$133$	2.34650	0.203467
$134$	30.4341	2.62911
$135$	−15.9967	−1.37677
$136$	31.9254	2.73758
$137$	−8.70559	−0.743769	−0.371885	−	0.928279i	$-0.621288\pi$
$137$	−8.70559	−0.743769	−0.371885	+	0.928279i	$0.621288\pi$
$138$	−12.6539	−1.07717
$139$	−7.75615	−0.657868	−0.328934	−	0.944353i	$-0.606689\pi$
$139$	−7.75615	−0.657868	−0.328934	+	0.944353i	$0.606689\pi$
$140$	40.2906	3.40517
$141$	9.83771	0.828485
$142$	21.7451	1.82481
$143$	−2.78464	−0.232863
$144$	−15.7867	−1.31556
$145$	−7.88696	−0.654976
$146$	−8.52507	−0.705540
$147$	0.950191	0.0783704
$148$	41.9042	3.44451
$149$	22.2735	1.82471	0.912357	−	0.409395i	$-0.134260\pi$
$149$	22.2735	1.82471	0.912357	+	0.409395i	$0.134260\pi$
$150$	−10.9395	−0.893205
$151$	5.74476	0.467502	0.233751	−	0.972296i	$-0.424900\pi$
$151$	5.74476	0.467502	0.233751	+	0.972296i	$0.424900\pi$
$152$	−6.78670	−0.550474
$153$	5.54545	0.448323
$154$	9.16006	0.738139
$155$	27.9683	2.24647
$156$	14.3055	1.14535
$157$	−2.09538	−0.167229	−0.0836147	−	0.996498i	$-0.526646\pi$
$157$	−2.09538	−0.167229	−0.0836147	+	0.996498i	$0.526646\pi$
$158$	25.1398	2.00002
$159$	4.02747	0.319399
$160$	−39.7576	−3.14311
$161$	10.4956	0.827166
$162$	7.55358	0.593465
$163$	−1.14561	−0.0897310	−0.0448655	−	0.998993i	$-0.514286\pi$
$163$	−1.14561	−0.0897310	−0.0448655	+	0.998993i	$0.514286\pi$
$164$	7.56053	0.590378
$165$	−4.51104	−0.351184
$166$	−37.2659	−2.89239
$167$	14.0671	1.08854	0.544271	−	0.838910i	$-0.316807\pi$
$167$	14.0671	1.08854	0.544271	+	0.838910i	$0.316807\pi$
$168$	−28.3681	−2.18865
$169$	−7.96035	−0.612335
$170$	30.2234	2.31803
$171$	−1.17885	−0.0901489
$172$	46.5514	3.54951
$173$	21.7243	1.65167	0.825833	−	0.563915i	$-0.190705\pi$
$173$	21.7243	1.65167	0.825833	+	0.563915i	$0.190705\pi$
$174$	9.21164	0.698333
$175$	9.07356	0.685896
$176$	−14.0006	−1.05533
$177$	3.88183	0.291776
$178$	17.3541	1.30075
$179$	−10.9816	−0.820801	−0.410401	−	0.911905i	$-0.634611\pi$
$179$	−10.9816	−0.820801	−0.410401	+	0.911905i	$0.634611\pi$
$180$	−20.2415	−1.50871
$181$	8.58111	0.637829	0.318914	−	0.947784i	$-0.396682\pi$
$181$	8.58111	0.637829	0.318914	+	0.947784i	$0.396682\pi$
$182$	−16.5779	−1.22884
$183$	18.9190	1.39853
$184$	−30.3560	−2.23787
$185$	23.9147	1.75824
$186$	−32.6658	−2.39518
$187$	4.91803	0.359642
$188$	39.1484	2.85519
$189$	−15.4966	−1.12721
$190$	−6.42489	−0.466110
$191$	−2.06181	−0.149187	−0.0745937	−	0.997214i	$-0.523766\pi$
$191$	−2.06181	−0.149187	−0.0745937	+	0.997214i	$0.523766\pi$
$192$	17.8693	1.28961
$193$	6.06828	0.436804	0.218402	−	0.975859i	$-0.429916\pi$
$193$	6.06828	0.436804	0.218402	+	0.975859i	$0.429916\pi$
$194$	−10.0100	−0.718677
$195$	8.16410	0.584643
$196$	3.78121	0.270086
$197$	2.18181	0.155448	0.0777239	−	0.996975i	$-0.475235\pi$
$197$	2.18181	0.155448	0.0777239	+	0.996975i	$0.475235\pi$
$198$	−4.60190	−0.327043
$199$	0.218966	0.0155221	0.00776105	−	0.999970i	$-0.497530\pi$
$199$	0.218966	0.0155221	0.00776105	+	0.999970i	$0.497530\pi$
$200$	−26.2432	−1.85567
$201$	−14.5194	−1.02412
$202$	44.3415	3.11986
$203$	−7.64043	−0.536253
$204$	−25.2653	−1.76892
$205$	4.31478	0.301357
$206$	27.6189	1.92430
$207$	−5.27284	−0.366487
$208$	25.3383	1.75689
$209$	−1.04547	−0.0723169
$210$	−26.8558	−1.85322
$211$	5.21397	0.358944	0.179472	−	0.983763i	$-0.442561\pi$
$211$	5.21397	0.358944	0.179472	+	0.983763i	$0.442561\pi$
$212$	16.0270	1.10074
$213$	−10.3740	−0.710817
$214$	18.4122	1.25864
$215$	26.5668	1.81184
$216$	44.8204	3.04964
$217$	27.0941	1.83927
$218$	−45.3618	−3.07229
$219$	4.06710	0.274829
$220$	−17.9513	−1.21028
$221$	−8.90067	−0.598724
$222$	−27.9314	−1.87463
$223$	−15.4113	−1.03202	−0.516008	−	0.856584i	$-0.672582\pi$
$223$	−15.4113	−1.03202	−0.516008	+	0.856584i	$0.672582\pi$
$224$	−38.5148	−2.57338
$225$	−4.55844	−0.303896
$226$	39.5247	2.62915
$227$	−7.30836	−0.485073	−0.242537	−	0.970142i	$-0.577979\pi$
$227$	−7.30836	−0.485073	−0.242537	+	0.970142i	$0.577979\pi$
$228$	5.37088	0.355695
$229$	4.60417	0.304252	0.152126	−	0.988361i	$-0.451388\pi$
$229$	4.60417	0.304252	0.152126	+	0.988361i	$0.451388\pi$
$230$	−28.7376	−1.89490
$231$	−4.37004	−0.287527
$232$	22.0982	1.45082
$233$	5.47008	0.358357	0.179179	−	0.983817i	$-0.442656\pi$
$233$	5.47008	0.358357	0.179179	+	0.983817i	$0.442656\pi$
$234$	8.32853	0.544453
$235$	22.3419	1.45743
$236$	15.4474	1.00554
$237$	−11.9936	−0.779067
$238$	29.2787	1.89786
$239$	19.9846	1.29269	0.646347	−	0.763044i	$-0.276296\pi$
$239$	19.9846	1.29269	0.646347	+	0.763044i	$0.276296\pi$
$240$	41.0473	2.64959
$241$	−3.57206	−0.230097	−0.115048	−	0.993360i	$-0.536702\pi$
$241$	−3.57206	−0.230097	−0.115048	+	0.993360i	$0.536702\pi$
$242$	25.0962	1.61324
$243$	13.0951	0.840051
$244$	75.2865	4.81973
$245$	2.15793	0.137865
$246$	−5.03949	−0.321306
$247$	1.89210	0.120392
$248$	−78.3634	−4.97608
$249$	17.7786	1.12667
$250$	13.2705	0.839299
$251$	11.7544	0.741932	0.370966	−	0.928646i	$-0.379027\pi$
$251$	11.7544	0.741932	0.370966	+	0.928646i	$0.379027\pi$
$252$	−19.6088	−1.23524
$253$	−4.67626	−0.293994
$254$	27.0765	1.69893
$255$	−14.4188	−0.902943
$256$	−2.28036	−0.142523
$257$	−10.8585	−0.677336	−0.338668	−	0.940906i	$-0.609976\pi$
$257$	−10.8585	−0.677336	−0.338668	+	0.940906i	$0.609976\pi$
$258$	−31.0289	−1.93178
$259$	23.1672	1.43954
$260$	32.4884	2.01484
$261$	3.83846	0.237594
$262$	7.73275	0.477731
$263$	20.2113	1.24628	0.623141	−	0.782109i	$-0.285856\pi$
$263$	20.2113	1.24628	0.623141	+	0.782109i	$0.285856\pi$
$264$	12.6393	0.777897
$265$	9.14659	0.561870
$266$	−6.22406	−0.381622
$267$	−8.27923	−0.506681
$268$	−57.7786	−3.52939
$269$	17.3608	1.05850	0.529252	−	0.848465i	$-0.322473\pi$
$269$	17.3608	1.05850	0.529252	+	0.848465i	$0.322473\pi$
$270$	42.4310	2.58227
$271$	−1.24144	−0.0754122	−0.0377061	−	0.999289i	$-0.512005\pi$
$271$	−1.24144	−0.0754122	−0.0377061	+	0.999289i	$0.512005\pi$
$272$	−44.7506	−2.71340
$273$	7.90891	0.478669
$274$	23.0915	1.39501
$275$	−4.04270	−0.243784
$276$	24.0232	1.44603
$277$	5.25739	0.315886	0.157943	−	0.987448i	$-0.449514\pi$
$277$	5.25739	0.315886	0.157943	+	0.987448i	$0.449514\pi$
$278$	20.5731	1.23389
$279$	−13.6117	−0.814913
$280$	−64.4254	−3.85015
$281$	−7.77260	−0.463674	−0.231837	−	0.972755i	$-0.574474\pi$
$281$	−7.77260	−0.463674	−0.231837	+	0.972755i	$0.574474\pi$
$282$	−26.0944	−1.55390
$283$	6.93915	0.412490	0.206245	−	0.978500i	$-0.433876\pi$
$283$	6.93915	0.412490	0.206245	+	0.978500i	$0.433876\pi$
$284$	−41.2826	−2.44967
$285$	3.06515	0.181564
$286$	7.38623	0.436757
$287$	4.17991	0.246732
$288$	19.3494	1.14017
$289$	−1.28028	−0.0753106
$290$	20.9201	1.22847
$291$	4.77553	0.279946
$292$	16.1847	0.947138
$293$	15.2295	0.889718	0.444859	−	0.895601i	$-0.353254\pi$
$293$	15.2295	0.889718	0.444859	+	0.895601i	$0.353254\pi$
$294$	−2.52037	−0.146991
$295$	8.81581	0.513277
$296$	−67.0057	−3.89462
$297$	6.90448	0.400638
$298$	−59.0802	−3.42242
$299$	8.46311	0.489434
$300$	20.7684	1.19907
$301$	25.7364	1.48342
$302$	−15.2379	−0.876844
$303$	−21.1542	−1.21528
$304$	9.51307	0.545612
$305$	42.9659	2.46022
$306$	−14.7093	−0.840872
$307$	8.46783	0.483285	0.241642	−	0.970365i	$-0.422314\pi$
$307$	8.46783	0.483285	0.241642	+	0.970365i	$0.422314\pi$
$308$	−17.3902	−0.990900
$309$	−13.1763	−0.749573
$310$	−74.1857	−4.21346
$311$	−33.1336	−1.87883	−0.939417	−	0.342775i	$-0.888633\pi$
$311$	−33.1336	−1.87883	−0.939417	+	0.342775i	$0.888633\pi$
$312$	−22.8747	−1.29502
$313$	24.4476	1.38186	0.690929	−	0.722922i	$-0.257202\pi$
$313$	24.4476	1.38186	0.690929	+	0.722922i	$0.257202\pi$
$314$	5.55797	0.313655
$315$	−11.1907	−0.630524
$316$	−47.7275	−2.68488
$317$	22.7984	1.28048	0.640242	−	0.768174i	$-0.278834\pi$
$317$	22.7984	1.28048	0.640242	+	0.768174i	$0.278834\pi$
$318$	−10.6828	−0.599064
$319$	3.40417	0.190597
$320$	40.5821	2.26861
$321$	−8.78403	−0.490277
$322$	−27.8394	−1.55143
$323$	−3.34169	−0.185937
$324$	−14.3403	−0.796686
$325$	7.31648	0.405845
$326$	3.03872	0.168299
$327$	21.6410	1.19675
$328$	−12.0894	−0.667527
$329$	21.6436	1.19325
$330$	11.9655	0.658679
$331$	−1.72329	−0.0947205	−0.0473602	−	0.998878i	$-0.515081\pi$
$331$	−1.72329	−0.0947205	−0.0473602	+	0.998878i	$0.515081\pi$
$332$	70.7486	3.88284
$333$	−11.6389	−0.637807
$334$	−37.3127	−2.04166
$335$	−32.9742	−1.80157
$336$	39.7643	2.16932
$337$	−18.8666	−1.02773	−0.513864	−	0.857872i	$-0.671786\pi$
$337$	−18.8666	−1.02773	−0.513864	+	0.857872i	$0.671786\pi$
$338$	21.1148	1.14849
$339$	−18.8563	−1.02413
$340$	−57.3786	−3.11179
$341$	−12.0717	−0.653719
$342$	3.12689	0.169083
$343$	−17.3978	−0.939393
$344$	−74.4365	−4.01335
$345$	13.7100	0.738123
$346$	−57.6234	−3.09786
$347$	−26.2395	−1.40861	−0.704304	−	0.709898i	$-0.748741\pi$
$347$	−26.2395	−1.40861	−0.704304	+	0.709898i	$0.748741\pi$
$348$	−17.4881	−0.937463
$349$	21.7488	1.16419	0.582093	−	0.813122i	$-0.302234\pi$
$349$	21.7488	1.16419	0.582093	+	0.813122i	$0.302234\pi$
$350$	−24.0675	−1.28646
$351$	−12.4957	−0.666973
$352$	17.1602	0.914640
$353$	9.73968	0.518391	0.259195	−	0.965825i	$-0.416543\pi$
$353$	9.73968	0.518391	0.259195	+	0.965825i	$0.416543\pi$
$354$	−10.2965	−0.547253
$355$	−23.5599	−1.25043
$356$	−32.9465	−1.74616
$357$	−13.9681	−0.739273
$358$	29.1285	1.53949
$359$	21.4459	1.13187	0.565935	−	0.824450i	$-0.308515\pi$
$359$	21.4459	1.13187	0.565935	+	0.824450i	$0.308515\pi$
$360$	32.3665	1.70586
$361$	−18.2896	−0.962612
$362$	−22.7613	−1.19631
$363$	−11.9728	−0.628407
$364$	31.4729	1.64963
$365$	9.23658	0.483465
$366$	−50.1824	−2.62308
$367$	26.8015	1.39903	0.699513	−	0.714620i	$-0.253400\pi$
$367$	26.8015	1.39903	0.699513	+	0.714620i	$0.253400\pi$
$368$	42.5507	2.21811
$369$	−2.09994	−0.109318
$370$	−63.4335	−3.29775
$371$	8.86068	0.460024
$372$	62.0155	3.21536
$373$	26.0350	1.34804	0.674021	−	0.738713i	$-0.264566\pi$
$373$	26.0350	1.34804	0.674021	+	0.738713i	$0.264566\pi$
$374$	−13.0450	−0.674543
$375$	−6.33102	−0.326932
$376$	−62.5990	−3.22830
$377$	−6.16087	−0.317301
$378$	41.1047	2.11420
$379$	23.7545	1.22019	0.610094	−	0.792329i	$-0.291132\pi$
$379$	23.7545	1.22019	0.610094	+	0.792329i	$0.291132\pi$
$380$	12.1975	0.625720
$381$	−12.9175	−0.661785
$382$	5.46893	0.279815
$383$	−34.6008	−1.76802	−0.884010	−	0.467468i	$-0.845166\pi$
$383$	−34.6008	−1.76802	−0.884010	+	0.467468i	$0.845166\pi$
$384$	−12.3857	−0.632056
$385$	−9.92457	−0.505803
$386$	−16.0961	−0.819267
$387$	−12.9296	−0.657250
$388$	19.0038	0.964774
$389$	−17.7285	−0.898868	−0.449434	−	0.893313i	$-0.648374\pi$
$389$	−17.7285	−0.898868	−0.449434	+	0.893313i	$0.648374\pi$
$390$	−21.6552	−1.09655
$391$	−14.9469	−0.755899
$392$	−6.04622	−0.305380
$393$	−3.68910	−0.186091
$394$	−5.78724	−0.291557
$395$	−27.2380	−1.37049
$396$	8.73663	0.439032
$397$	3.15502	0.158346	0.0791730	−	0.996861i	$-0.474772\pi$
$397$	3.15502	0.158346	0.0791730	+	0.996861i	$0.474772\pi$
$398$	−0.580806	−0.0291132
$399$	2.96934	0.148653
$400$	36.7857	1.83928
$401$	19.3248	0.965037	0.482518	−	0.875886i	$-0.339722\pi$
$401$	19.3248	0.965037	0.482518	+	0.875886i	$0.339722\pi$
$402$	38.5125	1.92083
$403$	21.8474	1.08829
$404$	−84.1816	−4.18819
$405$	−8.18401	−0.406667
$406$	20.2662	1.00579
$407$	−10.3221	−0.511645
$408$	40.3996	2.00008
$409$	−9.33762	−0.461715	−0.230858	−	0.972988i	$-0.574153\pi$
$409$	−9.33762	−0.461715	−0.230858	+	0.972988i	$0.574153\pi$
$410$	−11.4449	−0.565224
$411$	−11.0164	−0.543398
$412$	−52.4340	−2.58324
$413$	8.54025	0.420238
$414$	13.9862	0.687382
$415$	40.3761	1.98199
$416$	−31.0565	−1.52267
$417$	−9.81493	−0.480639
$418$	2.77311	0.135637
$419$	−0.124070	−0.00606123	−0.00303061	−	0.999995i	$-0.500965\pi$
$419$	−0.124070	−0.00606123	−0.00303061	+	0.999995i	$0.500965\pi$
$420$	50.9852	2.48782
$421$	12.4531	0.606927	0.303463	−	0.952843i	$-0.401857\pi$
$421$	12.4531	0.606927	0.303463	+	0.952843i	$0.401857\pi$
$422$	−13.8300	−0.673234
$423$	−10.8735	−0.528685
$424$	−25.6275	−1.24458
$425$	−12.9218	−0.626802
$426$	27.5170	1.33320
$427$	41.6229	2.01427
$428$	−34.9553	−1.68963
$429$	−3.52379	−0.170130
$430$	−70.4681	−3.39828
$431$	−28.1625	−1.35654	−0.678269	−	0.734814i	$-0.737269\pi$
$431$	−28.1625	−1.35654	−0.678269	+	0.734814i	$0.737269\pi$
$432$	−62.8259	−3.02271
$433$	20.4257	0.981594	0.490797	−	0.871274i	$-0.336706\pi$
$433$	20.4257	0.981594	0.490797	+	0.871274i	$0.336706\pi$
$434$	−71.8668	−3.44972
$435$	−9.98045	−0.478526
$436$	86.1186	4.12433
$437$	3.17742	0.151996
$438$	−10.7879	−0.515468
$439$	−30.4665	−1.45409	−0.727043	−	0.686592i	$-0.759106\pi$
$439$	−30.4665	−1.45409	−0.727043	+	0.686592i	$0.759106\pi$
$440$	28.7045	1.36843
$441$	−1.05023	−0.0500109
$442$	23.6089	1.12296
$443$	−33.2876	−1.58154	−0.790771	−	0.612112i	$-0.790320\pi$
$443$	−33.2876	−1.58154	−0.790771	+	0.612112i	$0.790320\pi$
$444$	53.0272	2.51656
$445$	−18.8025	−0.891326
$446$	40.8783	1.93564
$447$	28.1857	1.33314
$448$	39.3136	1.85739
$449$	−17.7031	−0.835461	−0.417730	−	0.908571i	$-0.637174\pi$
$449$	−17.7031	−0.835461	−0.417730	+	0.908571i	$0.637174\pi$
$450$	12.0912	0.569986
$451$	−1.86235	−0.0876945
$452$	−75.0370	−3.52945
$453$	7.26964	0.341557
$454$	19.3854	0.909800
$455$	17.9615	0.842049
$456$	−8.58814	−0.402177
$457$	7.44361	0.348197	0.174099	−	0.984728i	$-0.444299\pi$
$457$	7.44361	0.348197	0.174099	+	0.984728i	$0.444299\pi$
$458$	−12.2125	−0.570654
$459$	22.0691	1.03010
$460$	54.5579	2.54378
$461$	36.1756	1.68487	0.842433	−	0.538802i	$-0.181123\pi$
$461$	36.1756	1.68487	0.842433	+	0.538802i	$0.181123\pi$
$462$	11.5915	0.539285
$463$	7.66174	0.356071	0.178036	−	0.984024i	$-0.443026\pi$
$463$	7.66174	0.356071	0.178036	+	0.984024i	$0.443026\pi$
$464$	−30.9755	−1.43800
$465$	35.3922	1.64127
$466$	−14.5094	−0.672133
$467$	20.4807	0.947736	0.473868	−	0.880596i	$-0.342857\pi$
$467$	20.4807	0.947736	0.473868	+	0.880596i	$0.342857\pi$
$468$	−15.8116	−0.730890
$469$	−31.9435	−1.47501
$470$	−59.2617	−2.73354
$471$	−2.65157	−0.122178
$472$	−24.7007	−1.13694
$473$	−11.4668	−0.527242
$474$	31.8129	1.46121
$475$	2.74692	0.126037
$476$	−55.5851	−2.54774
$477$	−4.45150	−0.203820
$478$	−53.0088	−2.42457
$479$	−11.8926	−0.543388	−0.271694	−	0.962384i	$-0.587584\pi$
$479$	−11.8926	−0.543388	−0.271694	+	0.962384i	$0.587584\pi$
$480$	−50.3107	−2.29636
$481$	18.6809	0.851775
$482$	9.47486	0.431568
$483$	13.2815	0.604328
$484$	−47.6446	−2.16567
$485$	10.8455	0.492467
$486$	−34.7346	−1.57559
$487$	39.3400	1.78267	0.891334	−	0.453348i	$-0.149770\pi$
$487$	39.3400	1.78267	0.891334	+	0.453348i	$0.149770\pi$
$488$	−120.385	−5.44955
$489$	−1.44970	−0.0655576
$490$	−5.72389	−0.258579
$491$	28.0283	1.26490	0.632449	−	0.774602i	$-0.282050\pi$
$491$	28.0283	1.26490	0.632449	+	0.774602i	$0.282050\pi$
$492$	9.56738	0.431331
$493$	10.8809	0.490051
$494$	−5.01878	−0.225806
$495$	4.98598	0.224103
$496$	109.844	4.93213
$497$	−22.8235	−1.02377
$498$	−47.1577	−2.11319
$499$	44.3989	1.98757	0.993785	−	0.111318i	$-0.0355072\pi$
$499$	44.3989	1.98757	0.993785	+	0.111318i	$0.0355072\pi$
$500$	−25.1938	−1.12670
$501$	17.8010	0.795289
$502$	−31.1785	−1.39156
$503$	−20.7926	−0.927095	−0.463548	−	0.886072i	$-0.653424\pi$
$503$	−20.7926	−0.927095	−0.463548	+	0.886072i	$0.653424\pi$
$504$	31.3548	1.39665
$505$	−48.0423	−2.13785
$506$	12.4037	0.551414
$507$	−10.0733	−0.447372
$508$	−51.4043	−2.28070
$509$	−12.7789	−0.566416	−0.283208	−	0.959059i	$-0.591399\pi$
$509$	−12.7789	−0.566416	−0.283208	+	0.959059i	$0.591399\pi$
$510$	38.2459	1.69356
$511$	8.94787	0.395830
$512$	25.6240	1.13243
$513$	−4.69144	−0.207132
$514$	28.8021	1.27041
$515$	−29.9240	−1.31861
$516$	58.9078	2.59327
$517$	−9.64322	−0.424108
$518$	−61.4507	−2.69999
$519$	27.4907	1.20671
$520$	−51.9495	−2.27814
$521$	23.3324	1.02221	0.511106	−	0.859518i	$-0.329236\pi$
$521$	23.3324	1.02221	0.511106	+	0.859518i	$0.329236\pi$
$522$	−10.1815	−0.445631
$523$	−15.3093	−0.669430	−0.334715	−	0.942319i	$-0.608640\pi$
$523$	−15.3093	−0.669430	−0.334715	+	0.942319i	$0.608640\pi$
$524$	−14.6805	−0.641320
$525$	11.4820	0.501117
$526$	−53.6103	−2.33752
$527$	−38.5853	−1.68080
$528$	−17.7168	−0.771027
$529$	−8.78784	−0.382080
$530$	−24.2612	−1.05384
$531$	−4.29052	−0.186193
$532$	11.8163	0.512300
$533$	3.37048	0.145992
$534$	21.9606	0.950328
$535$	−19.9490	−0.862468
$536$	92.3891	3.99060
$537$	−13.8965	−0.599678
$538$	−46.0493	−1.98532
$539$	−0.931406	−0.0401185
$540$	−80.5545	−3.46651
$541$	−5.02343	−0.215974	−0.107987	−	0.994152i	$-0.534441\pi$
$541$	−5.02343	−0.215974	−0.107987	+	0.994152i	$0.534441\pi$
$542$	3.29291	0.141443
$543$	10.8589	0.465998
$544$	54.8498	2.35166
$545$	49.1478	2.10526
$546$	−20.9783	−0.897789
$547$	−31.4188	−1.34337	−0.671686	−	0.740836i	$-0.734429\pi$
$547$	−31.4188	−1.34337	−0.671686	+	0.740836i	$0.734429\pi$
$548$	−43.8388	−1.87270
$549$	−20.9108	−0.892452
$550$	10.7232	0.457239
$551$	−2.31306	−0.0985396
$552$	−38.4136	−1.63499
$553$	−26.3866	−1.12207
$554$	−13.9452	−0.592473
$555$	30.2625	1.28457
$556$	−39.0577	−1.65642
$557$	0.820296	0.0347570	0.0173785	−	0.999849i	$-0.494468\pi$
$557$	0.820296	0.0347570	0.0173785	+	0.999849i	$0.494468\pi$
$558$	36.1050	1.52845
$559$	20.7526	0.877740
$560$	90.3066	3.81615
$561$	6.22346	0.262755
$562$	20.6167	0.869665
$563$	22.1192	0.932212	0.466106	−	0.884729i	$-0.345657\pi$
$563$	22.1192	0.932212	0.466106	+	0.884729i	$0.345657\pi$
$564$	49.5398	2.08600
$565$	−42.8235	−1.80160
$566$	−18.4060	−0.773664
$567$	−7.92819	−0.332953
$568$	66.0117	2.76979
$569$	28.9291	1.21277	0.606386	−	0.795170i	$-0.292618\pi$
$569$	28.9291	1.21277	0.606386	+	0.795170i	$0.292618\pi$
$570$	−8.13029	−0.340541
$571$	31.1170	1.30221	0.651104	−	0.758989i	$-0.274306\pi$
$571$	31.1170	1.30221	0.651104	+	0.758989i	$0.274306\pi$
$572$	−14.0226	−0.586316
$573$	−2.60909	−0.108996
$574$	−11.0872	−0.462770
$575$	12.2866	0.512387
$576$	−19.7507	−0.822944
$577$	−12.8064	−0.533137	−0.266568	−	0.963816i	$-0.585890\pi$
$577$	−12.8064	−0.533137	−0.266568	+	0.963816i	$0.585890\pi$
$578$	3.39593	0.141252
$579$	7.67903	0.319129
$580$	−39.7164	−1.64913
$581$	39.1141	1.62272
$582$	−12.6670	−0.525066
$583$	−3.94785	−0.163503
$584$	−25.8796	−1.07091
$585$	−9.02364	−0.373082
$586$	−40.3962	−1.66875
$587$	47.2062	1.94841	0.974204	−	0.225669i	$-0.0724566\pi$
$587$	47.2062	1.94841	0.974204	+	0.225669i	$0.0724566\pi$
$588$	4.78489	0.197325
$589$	8.20244	0.337976
$590$	−23.3839	−0.962699
$591$	2.76095	0.113570
$592$	93.9234	3.86023
$593$	−3.60409	−0.148002	−0.0740011	−	0.997258i	$-0.523577\pi$
$593$	−3.60409	−0.148002	−0.0740011	+	0.997258i	$0.523577\pi$
$594$	−18.3141	−0.751435
$595$	−31.7223	−1.30049
$596$	112.163	4.59437
$597$	0.277088	0.0113405
$598$	−22.4483	−0.917980
$599$	−27.2360	−1.11283	−0.556416	−	0.830904i	$-0.687824\pi$
$599$	−27.2360	−1.11283	−0.556416	+	0.830904i	$0.687824\pi$
$600$	−33.2091	−1.35576
$601$	8.76927	0.357706	0.178853	−	0.983876i	$-0.442761\pi$
$601$	8.76927	0.357706	0.178853	+	0.983876i	$0.442761\pi$
$602$	−68.2655	−2.78229
$603$	16.0480	0.653525
$604$	28.9289	1.17710
$605$	−27.1907	−1.10546
$606$	56.1114	2.27937
$607$	4.00640	0.162615	0.0813074	−	0.996689i	$-0.474090\pi$
$607$	4.00640	0.162615	0.0813074	+	0.996689i	$0.474090\pi$
$608$	−11.6600	−0.472873
$609$	−9.66849	−0.391787
$610$	−113.967	−4.61437
$611$	17.4523	0.706045
$612$	27.9253	1.12881
$613$	−24.0493	−0.971344	−0.485672	−	0.874141i	$-0.661425\pi$
$613$	−24.0493	−0.971344	−0.485672	+	0.874141i	$0.661425\pi$
$614$	−22.4608	−0.906446
$615$	5.46009	0.220172
$616$	27.8073	1.12039
$617$	−2.74317	−0.110436	−0.0552179	−	0.998474i	$-0.517585\pi$
$617$	−2.74317	−0.110436	−0.0552179	+	0.998474i	$0.517585\pi$
$618$	34.9500	1.40589
$619$	18.6605	0.750027	0.375014	−	0.927019i	$-0.377638\pi$
$619$	18.6605	0.750027	0.375014	+	0.927019i	$0.377638\pi$
$620$	140.840	5.65628
$621$	−20.9842	−0.842066
$622$	87.8866	3.52393
$623$	−18.2148	−0.729761
$624$	32.0640	1.28359
$625$	−30.6737	−1.22695
$626$	−64.8470	−2.59181
$627$	−1.32298	−0.0528348
$628$	−10.5517	−0.421059
$629$	−32.9928	−1.31551
$630$	29.6832	1.18261
$631$	15.4675	0.615753	0.307877	−	0.951426i	$-0.400382\pi$
$631$	15.4675	0.615753	0.307877	+	0.951426i	$0.400382\pi$
$632$	76.3172	3.03573
$633$	6.59795	0.262245
$634$	−60.4724	−2.40167
$635$	−29.3363	−1.16418
$636$	20.2812	0.804201
$637$	1.68566	0.0667883
$638$	−9.02953	−0.357483
$639$	11.4662	0.453598
$640$	−28.1285	−1.11188
$641$	34.6149	1.36721	0.683603	−	0.729854i	$-0.260412\pi$
$641$	34.6149	1.36721	0.683603	+	0.729854i	$0.260412\pi$
$642$	23.2996	0.919560
$643$	−7.02700	−0.277118	−0.138559	−	0.990354i	$-0.544247\pi$
$643$	−7.02700	−0.277118	−0.138559	+	0.990354i	$0.544247\pi$
$644$	52.8526	2.08268
$645$	33.6186	1.32373
$646$	8.86381	0.348742
$647$	−31.0635	−1.22123	−0.610616	−	0.791927i	$-0.709078\pi$
$647$	−31.0635	−1.22123	−0.610616	+	0.791927i	$0.709078\pi$
$648$	22.9305	0.900794
$649$	−3.80508	−0.149363
$650$	−19.4069	−0.761201
$651$	34.2859	1.34377
$652$	−5.76895	−0.225930
$653$	−34.7758	−1.36088	−0.680441	−	0.732803i	$-0.738212\pi$
$653$	−34.7758	−1.36088	−0.680441	+	0.732803i	$0.738212\pi$
$654$	−57.4026	−2.24462
$655$	−8.37813	−0.327361
$656$	16.9460	0.661632
$657$	−4.49530	−0.175378
$658$	−57.4093	−2.23805
$659$	4.72250	0.183962	0.0919812	−	0.995761i	$-0.470680\pi$
$659$	4.72250	0.183962	0.0919812	+	0.995761i	$0.470680\pi$
$660$	−22.7163	−0.884231
$661$	−13.4690	−0.523882	−0.261941	−	0.965084i	$-0.584363\pi$
$661$	−13.4690	−0.523882	−0.261941	+	0.965084i	$0.584363\pi$
$662$	4.57101	0.177657
$663$	−11.2632	−0.437428
$664$	−113.128	−4.39023
$665$	6.74353	0.261503
$666$	30.8721	1.19627
$667$	−10.3460	−0.400598
$668$	70.8376	2.74079
$669$	−19.5020	−0.753992
$670$	87.4637	3.37902
$671$	−18.5449	−0.715920
$672$	−48.7381	−1.88011
$673$	−16.9700	−0.654146	−0.327073	−	0.944999i	$-0.606062\pi$
$673$	−16.9700	−0.654146	−0.327073	+	0.944999i	$0.606062\pi$
$674$	50.0434	1.92760
$675$	−18.1411	−0.698252
$676$	−40.0860	−1.54177
$677$	−2.79940	−0.107590	−0.0537949	−	0.998552i	$-0.517132\pi$
$677$	−2.79940	−0.107590	−0.0537949	+	0.998552i	$0.517132\pi$
$678$	50.0161	1.92086
$679$	10.5065	0.403201
$680$	91.7495	3.51843
$681$	−9.24828	−0.354395
$682$	32.0200	1.22611
$683$	18.3704	0.702922	0.351461	−	0.936203i	$-0.385685\pi$
$683$	18.3704	0.702922	0.351461	+	0.936203i	$0.385685\pi$
$684$	−5.93635	−0.226982
$685$	−25.0188	−0.955917
$686$	46.1475	1.76192
$687$	5.82629	0.222287
$688$	104.339	3.97790
$689$	7.14483	0.272196
$690$	−36.3657	−1.38442
$691$	47.0835	1.79114	0.895570	−	0.444922i	$-0.146768\pi$
$691$	47.0835	1.79114	0.895570	+	0.444922i	$0.146768\pi$
$692$	109.397	4.15865
$693$	4.83013	0.183481
$694$	69.5999	2.64198
$695$	−22.2902	−0.845515
$696$	27.9639	1.05997
$697$	−5.95270	−0.225475
$698$	−57.6885	−2.18354
$699$	6.92205	0.261816
$700$	45.6918	1.72699
$701$	32.4444	1.22541	0.612704	−	0.790313i	$-0.290082\pi$
$701$	32.4444	1.22541	0.612704	+	0.790313i	$0.290082\pi$
$702$	33.1448	1.25097
$703$	7.01361	0.264523
$704$	−17.5161	−0.660161
$705$	28.2723	1.06480
$706$	−25.8344	−0.972291
$707$	−46.5406	−1.75034
$708$	19.5477	0.734649
$709$	25.1317	0.943839	0.471920	−	0.881642i	$-0.343561\pi$
$709$	25.1317	0.943839	0.471920	+	0.881642i	$0.343561\pi$
$710$	62.4925	2.34530
$711$	13.2563	0.497150
$712$	52.6821	1.97435
$713$	36.6884	1.37399
$714$	37.0504	1.38658
$715$	−8.00270	−0.299284
$716$	−55.3000	−2.06666
$717$	25.2892	0.944443
$718$	−56.8850	−2.12293
$719$	32.3819	1.20764	0.603820	−	0.797120i	$-0.293644\pi$
$719$	32.3819	1.20764	0.603820	+	0.797120i	$0.293644\pi$
$720$	−45.3689	−1.69080
$721$	−28.9886	−1.07959
$722$	48.5131	1.80547
$723$	−4.52022	−0.168109
$724$	43.2120	1.60596
$725$	−8.94426	−0.332181
$726$	31.7576	1.17864
$727$	−24.5649	−0.911063	−0.455532	−	0.890220i	$-0.650551\pi$
$727$	−24.5649	−0.911063	−0.455532	+	0.890220i	$0.650551\pi$
$728$	−50.3257	−1.86519
$729$	25.1142	0.930156
$730$	−24.5000	−0.906784
$731$	−36.6517	−1.35561
$732$	95.2704	3.52130
$733$	−18.3935	−0.679379	−0.339689	−	0.940538i	$-0.610322\pi$
$733$	−18.3935	−0.679379	−0.339689	+	0.940538i	$0.610322\pi$
$734$	−71.0907	−2.62401
$735$	2.73073	0.100724
$736$	−52.1534	−1.92240
$737$	14.2323	0.524254
$738$	5.57006	0.205037
$739$	17.2849	0.635836	0.317918	−	0.948118i	$-0.397016\pi$
$739$	17.2849	0.635836	0.317918	+	0.948118i	$0.397016\pi$
$740$	120.427	4.42700
$741$	2.39434	0.0879582
$742$	−23.5029	−0.862818
$743$	40.9052	1.50066	0.750332	−	0.661061i	$-0.229893\pi$
$743$	40.9052	1.50066	0.750332	+	0.661061i	$0.229893\pi$
$744$	−99.1640	−3.63553
$745$	64.0111	2.34519
$746$	−69.0576	−2.52838
$747$	−19.6504	−0.718971
$748$	24.7658	0.905527
$749$	−19.3254	−0.706135
$750$	16.7930	0.613193
$751$	−28.2845	−1.03212	−0.516058	−	0.856554i	$-0.672601\pi$
$751$	−28.2845	−1.03212	−0.516058	+	0.856554i	$0.672601\pi$
$752$	87.7465	3.19979
$753$	14.8745	0.542056
$754$	16.3417	0.595128
$755$	16.5097	0.600850
$756$	−78.0365	−2.83816
$757$	−28.3360	−1.02989	−0.514945	−	0.857223i	$-0.672188\pi$
$757$	−28.3360	−1.02989	−0.514945	+	0.857223i	$0.672188\pi$
$758$	−63.0087	−2.28858
$759$	−5.91752	−0.214792
$760$	−19.5041	−0.707488
$761$	−10.5454	−0.382272	−0.191136	−	0.981564i	$-0.561217\pi$
$761$	−10.5454	−0.382272	−0.191136	+	0.981564i	$0.561217\pi$
$762$	34.2636	1.24124
$763$	47.6115	1.72365
$764$	−10.3827	−0.375632
$765$	15.9369	0.576200
$766$	91.7784	3.31609
$767$	6.88645	0.248655
$768$	−2.88566	−0.104127
$769$	9.70048	0.349808	0.174904	−	0.984585i	$-0.444038\pi$
$769$	9.70048	0.349808	0.174904	+	0.984585i	$0.444038\pi$
$770$	26.3248	0.948681
$771$	−13.7408	−0.494862
$772$	30.5581	1.09981
$773$	21.1457	0.760558	0.380279	−	0.924872i	$-0.375828\pi$
$773$	21.1457	0.760558	0.380279	+	0.924872i	$0.375828\pi$
$774$	34.2957	1.23273
$775$	31.7177	1.13933
$776$	−30.3875	−1.09085
$777$	29.3166	1.05173
$778$	47.0246	1.68591
$779$	1.26542	0.0453385
$780$	41.1120	1.47205
$781$	10.1689	0.363873
$782$	39.6466	1.41776
$783$	15.2758	0.545913
$784$	8.47514	0.302683
$785$	−6.02185	−0.214929
$786$	9.78531	0.349031
$787$	4.23756	0.151053	0.0755264	−	0.997144i	$-0.475936\pi$
$787$	4.23756	0.151053	0.0755264	+	0.997144i	$0.475936\pi$
$788$	10.9870	0.391395
$789$	25.5762	0.910535
$790$	72.2486	2.57049
$791$	−41.4849	−1.47503
$792$	−13.9700	−0.496403
$793$	33.5627	1.19185
$794$	−8.36867	−0.296993
$795$	11.5744	0.410503
$796$	1.10265	0.0390824
$797$	−49.8459	−1.76563	−0.882816	−	0.469719i	$-0.844355\pi$
$797$	−49.8459	−1.76563	−0.882816	+	0.469719i	$0.844355\pi$
$798$	−7.87616	−0.278813
$799$	−30.8230	−1.09044
$800$	−45.0873	−1.59408
$801$	9.15090	0.323331
$802$	−51.2590	−1.81002
$803$	−3.98670	−0.140687
$804$	−73.1153	−2.57858
$805$	30.1629	1.06310
$806$	−57.9500	−2.04120
$807$	21.9690	0.773344
$808$	134.608	4.73549
$809$	17.0236	0.598516	0.299258	−	0.954172i	$-0.403261\pi$
$809$	17.0236	0.598516	0.299258	+	0.954172i	$0.403261\pi$
$810$	21.7080	0.762742
$811$	−12.0950	−0.424713	−0.212357	−	0.977192i	$-0.568114\pi$
$811$	−12.0950	−0.424713	−0.212357	+	0.977192i	$0.568114\pi$
$812$	−38.4750	−1.35021
$813$	−1.57097	−0.0550962
$814$	27.3792	0.959639
$815$	−3.29233	−0.115325
$816$	−56.6291	−1.98242
$817$	7.79141	0.272587
$818$	24.7679	0.865991
$819$	−8.74158	−0.305455
$820$	21.7280	0.758774
$821$	−24.0863	−0.840616	−0.420308	−	0.907381i	$-0.638078\pi$
$821$	−24.0863	−0.840616	−0.420308	+	0.907381i	$0.638078\pi$
$822$	29.2209	1.01919
$823$	−20.5348	−0.715799	−0.357899	−	0.933760i	$-0.616507\pi$
$823$	−20.5348	−0.715799	−0.357899	+	0.933760i	$0.616507\pi$
$824$	83.8429	2.92081
$825$	−5.11578	−0.178109
$826$	−22.6529	−0.788197
$827$	6.41811	0.223180	0.111590	−	0.993754i	$-0.464406\pi$
$827$	6.41811	0.223180	0.111590	+	0.993754i	$0.464406\pi$
$828$	−26.5525	−0.922762
$829$	−27.3569	−0.950143	−0.475071	−	0.879947i	$-0.657578\pi$
$829$	−27.3569	−0.950143	−0.475071	+	0.879947i	$0.657578\pi$
$830$	−107.097	−3.71740
$831$	6.65289	0.230786
$832$	31.7006	1.09902
$833$	−2.97709	−0.103150
$834$	26.0340	0.901484
$835$	40.4269	1.39903
$836$	−5.26470	−0.182084
$837$	−54.1703	−1.87240
$838$	0.329095	0.0113684
$839$	−36.2452	−1.25132	−0.625661	−	0.780095i	$-0.715171\pi$
$839$	−36.2452	−1.25132	−0.625661	+	0.780095i	$0.715171\pi$
$840$	−81.5263	−2.81292
$841$	−21.4684	−0.740291
$842$	−33.0317	−1.13835
$843$	−9.83574	−0.338761
$844$	26.2560	0.903769
$845$	−22.8770	−0.786993
$846$	28.8417	0.991599
$847$	−26.3408	−0.905080
$848$	35.9227	1.23359
$849$	8.78107	0.301365
$850$	34.2751	1.17563
$851$	31.3709	1.07538
$852$	−52.2406	−1.78973
$853$	−32.8473	−1.12467	−0.562336	−	0.826909i	$-0.690097\pi$
$853$	−32.8473	−1.12467	−0.562336	+	0.826909i	$0.690097\pi$
$854$	−110.404	−3.77796
$855$	−3.38786	−0.115862
$856$	55.8942	1.91043
$857$	−38.9621	−1.33092	−0.665460	−	0.746433i	$-0.731765\pi$
$857$	−38.9621	−1.33092	−0.665460	+	0.746433i	$0.731765\pi$
$858$	9.34682	0.319095
$859$	−35.7158	−1.21861	−0.609304	−	0.792937i	$-0.708551\pi$
$859$	−35.7158	−1.21861	−0.609304	+	0.792937i	$0.708551\pi$
$860$	133.783	4.56195
$861$	5.28942	0.180263
$862$	74.7007	2.54431
$863$	46.6588	1.58828	0.794142	−	0.607732i	$-0.207921\pi$
$863$	46.6588	1.58828	0.794142	+	0.607732i	$0.207921\pi$
$864$	77.0042	2.61974
$865$	62.4327	2.12278
$866$	−54.1789	−1.84107
$867$	−1.62011	−0.0550220
$868$	136.438	4.63101
$869$	11.7565	0.398811
$870$	26.4731	0.897521
$871$	−25.7577	−0.872766
$872$	−137.705	−4.66329
$873$	−5.27831	−0.178644
$874$	−8.42807	−0.285084
$875$	−13.9286	−0.470873
$876$	20.4807	0.691980
$877$	−17.6556	−0.596189	−0.298094	−	0.954536i	$-0.596351\pi$
$877$	−17.6556	−0.596189	−0.298094	+	0.954536i	$0.596351\pi$
$878$	80.8121	2.72727
$879$	19.2720	0.650029
$880$	−40.2358	−1.35635
$881$	−35.4475	−1.19426	−0.597128	−	0.802146i	$-0.703692\pi$
$881$	−35.4475	−1.19426	−0.597128	+	0.802146i	$0.703692\pi$
$882$	2.78573	0.0938003
$883$	48.7035	1.63900	0.819502	−	0.573076i	$-0.194250\pi$
$883$	48.7035	1.63900	0.819502	+	0.573076i	$0.194250\pi$
$884$	−44.8212	−1.50750
$885$	11.1559	0.375000
$886$	88.2951	2.96633
$887$	15.0706	0.506021	0.253011	−	0.967464i	$-0.418579\pi$
$887$	15.0706	0.506021	0.253011	+	0.967464i	$0.418579\pi$
$888$	−84.7915	−2.84542
$889$	−28.4194	−0.953155
$890$	49.8736	1.67177
$891$	3.53238	0.118339
$892$	−77.6067	−2.59847
$893$	6.55236	0.219266
$894$	−74.7623	−2.50043
$895$	−31.5596	−1.05492
$896$	−27.2493	−0.910336
$897$	10.7095	0.357581
$898$	46.9573	1.56699
$899$	−26.7080	−0.890762
$900$	−22.9550	−0.765166
$901$	−12.6187	−0.420389
$902$	4.93986	0.164479
$903$	32.5678	1.08379
$904$	119.986	3.99066
$905$	24.6610	0.819759
$906$	−19.2827	−0.640623
$907$	−0.487736	−0.0161950	−0.00809751	−	0.999967i	$-0.502578\pi$
$907$	−0.487736	−0.0161950	−0.00809751	+	0.999967i	$0.502578\pi$
$908$	−36.8028	−1.22134
$909$	23.3814	0.775512
$910$	−47.6427	−1.57934
$911$	4.85534	0.160865	0.0804324	−	0.996760i	$-0.474370\pi$
$911$	4.85534	0.160865	0.0804324	+	0.996760i	$0.474370\pi$
$912$	12.0382	0.398625
$913$	−17.4272	−0.576755
$914$	−19.7441	−0.653077
$915$	54.3707	1.79744
$916$	23.1853	0.766063
$917$	−8.11625	−0.268022
$918$	−58.5381	−1.93204
$919$	−18.7126	−0.617272	−0.308636	−	0.951180i	$-0.599872\pi$
$919$	−18.7126	−0.617272	−0.308636	+	0.951180i	$0.599872\pi$
$920$	−87.2391	−2.87619
$921$	10.7155	0.353088
$922$	−95.9554	−3.16012
$923$	−18.4038	−0.605768
$924$	−22.0062	−0.723952
$925$	27.1206	0.891720
$926$	−20.3227	−0.667845
$927$	14.5635	0.478329
$928$	37.9660	1.24629
$929$	−36.4166	−1.19479	−0.597396	−	0.801947i	$-0.703798\pi$
$929$	−36.4166	−1.19479	−0.597396	+	0.801947i	$0.703798\pi$
$930$	−93.8774	−3.07836
$931$	0.632870	0.0207415
$932$	27.5458	0.902291
$933$	−41.9285	−1.37268
$934$	−54.3250	−1.77757
$935$	14.1338	0.462224
$936$	25.2830	0.826401
$937$	20.9867	0.685605	0.342802	−	0.939408i	$-0.388624\pi$
$937$	20.9867	0.685605	0.342802	+	0.939408i	$0.388624\pi$
$938$	84.7298	2.76653
$939$	30.9369	1.00959
$940$	112.507	3.66959
$941$	56.2367	1.83327	0.916633	−	0.399730i	$-0.130896\pi$
$941$	56.2367	1.83327	0.916633	+	0.399730i	$0.130896\pi$
$942$	7.03327	0.229156
$943$	5.66007	0.184317
$944$	34.6236	1.12690
$945$	−44.5353	−1.44873
$946$	30.4155	0.988892
$947$	−11.0355	−0.358606	−0.179303	−	0.983794i	$-0.557384\pi$
$947$	−11.0355	−0.358606	−0.179303	+	0.983794i	$0.557384\pi$
$948$	−60.3962	−1.96158
$949$	7.21513	0.234213
$950$	−7.28619	−0.236395
$951$	28.8499	0.935522
$952$	88.8816	2.88067
$953$	8.47633	0.274575	0.137288	−	0.990531i	$-0.456162\pi$
$953$	8.47633	0.274575	0.137288	+	0.990531i	$0.456162\pi$
$954$	11.8076	0.382284
$955$	−5.92537	−0.191741
$956$	100.636	3.25481
$957$	4.30777	0.139250
$958$	31.5451	1.01918
$959$	−24.2367	−0.782645
$960$	51.3541	1.65745
$961$	63.7105	2.05518
$962$	−49.5509	−1.59758
$963$	9.70884	0.312863
$964$	−17.9879	−0.579350
$965$	17.4394	0.561396
$966$	−35.2290	−1.13347
$967$	3.24026	0.104200	0.0520999	−	0.998642i	$-0.483409\pi$
$967$	3.24026	0.104200	0.0520999	+	0.998642i	$0.483409\pi$
$968$	76.1847	2.44867
$969$	−4.22871	−0.135846
$970$	−28.7675	−0.923668
$971$	−11.6409	−0.373573	−0.186787	−	0.982401i	$-0.559807\pi$
$971$	−11.6409	−0.373573	−0.186787	+	0.982401i	$0.559807\pi$
$972$	65.9431	2.11513
$973$	−21.5934	−0.692254
$974$	−104.349	−3.34356
$975$	9.25855	0.296511
$976$	168.746	5.40142
$977$	33.7853	1.08089	0.540444	−	0.841380i	$-0.318256\pi$
$977$	33.7853	1.08089	0.540444	+	0.841380i	$0.318256\pi$
$978$	3.84531	0.122959
$979$	8.11556	0.259374
$980$	10.8667	0.347124
$981$	−23.9194	−0.763688
$982$	−74.3447	−2.37244
$983$	25.2255	0.804567	0.402284	−	0.915515i	$-0.368217\pi$
$983$	25.2255	0.804567	0.402284	+	0.915515i	$0.368217\pi$
$984$	−15.2984	−0.487696
$985$	6.27025	0.199787
$986$	−28.8615	−0.919137
$987$	27.3886	0.871788
$988$	9.52807	0.303128
$989$	34.8499	1.10816
$990$	−13.2253	−0.420327
$991$	16.2803	0.517162	0.258581	−	0.965990i	$-0.416745\pi$
$991$	16.2803	0.517162	0.258581	+	0.965990i	$0.416745\pi$
$992$	−134.633	−4.27460
$993$	−2.18071	−0.0692029
$994$	60.5391	1.92019
$995$	0.629280	0.0199495
$996$	89.5280	2.83680
$997$	5.26938	0.166883	0.0834414	−	0.996513i	$-0.473409\pi$
$997$	5.26938	0.166883	0.0834414	+	0.996513i	$0.473409\pi$
$998$	−117.768	−3.72787
$999$	−46.3190	−1.46547

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8009.2.a.b.1.15	✓	361

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8009.2.a.b.1.15	✓	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)

\(f(q)\)	\(=\)	\(q-2.65249 q^{2} +1.26544 q^{3} +5.03571 q^{4} +2.87387 q^{5} -3.35656 q^{6} +2.78404 q^{7} -8.05219 q^{8} -1.39867 q^{9} +O(q^{10})\)	\(q-2.65249 q^{2} +1.26544 q^{3} +5.03571 q^{4} +2.87387 q^{5} -3.35656 q^{6} +2.78404 q^{7} -8.05219 q^{8} -1.39867 q^{9} -7.62292 q^{10} -1.24042 q^{11} +6.37238 q^{12} +2.24492 q^{13} -7.38464 q^{14} +3.63671 q^{15} +11.2869 q^{16} -3.96481 q^{17} +3.70995 q^{18} +0.842838 q^{19} +14.4720 q^{20} +3.52303 q^{21} +3.29020 q^{22} +3.76990 q^{23} -10.1895 q^{24} +3.25913 q^{25} -5.95462 q^{26} -5.56624 q^{27} +14.0196 q^{28} -2.74437 q^{29} -9.64633 q^{30} +9.73193 q^{31} -13.8341 q^{32} -1.56968 q^{33} +10.5166 q^{34} +8.00097 q^{35} -7.04328 q^{36} +8.32142 q^{37} -2.23562 q^{38} +2.84080 q^{39} -23.1410 q^{40} +1.50138 q^{41} -9.34481 q^{42} +9.24425 q^{43} -6.24640 q^{44} -4.01959 q^{45} -9.99963 q^{46} +7.77415 q^{47} +14.2829 q^{48} +0.750879 q^{49} -8.64482 q^{50} -5.01722 q^{51} +11.3047 q^{52} +3.18267 q^{53} +14.7644 q^{54} -3.56481 q^{55} -22.4176 q^{56} +1.06656 q^{57} +7.27941 q^{58} +3.06757 q^{59} +18.3134 q^{60} +14.9505 q^{61} -25.8139 q^{62} -3.89394 q^{63} +14.1211 q^{64} +6.45160 q^{65} +4.16355 q^{66} -11.4738 q^{67} -19.9656 q^{68} +4.77058 q^{69} -21.2225 q^{70} -8.19798 q^{71} +11.2623 q^{72} +3.21399 q^{73} -22.0725 q^{74} +4.12423 q^{75} +4.24429 q^{76} -3.45338 q^{77} -7.53520 q^{78} -9.47781 q^{79} +32.4372 q^{80} -2.84773 q^{81} -3.98241 q^{82} +14.0494 q^{83} +17.7410 q^{84} -11.3944 q^{85} -24.5203 q^{86} -3.47283 q^{87} +9.98810 q^{88} -6.54258 q^{89} +10.6619 q^{90} +6.24994 q^{91} +18.9841 q^{92} +12.3152 q^{93} -20.6209 q^{94} +2.42221 q^{95} -17.5063 q^{96} +3.77381 q^{97} -1.99170 q^{98} +1.73494 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 361 q + 10 q^{2} + 23 q^{3} + 414 q^{4} + 21 q^{5} + 49 q^{6} + 106 q^{7} + 30 q^{8} + 406 q^{9}+O(q^{10}) \) 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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