LMFDB - Embedded newform 8017.2.a.a.1.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8017,2,Mod(1,8017)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8017, 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("8017.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8017 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8017.a (trivial)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$64.0160673005$
Analytic rank:	$1$
Dimension:	$327$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.6
Character	$\chi$	$=$	8017.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.74897 q^{2} +0.108150 q^{3} +5.55686 q^{4} +1.28185 q^{5} -0.297303 q^{6} +2.70833 q^{7} -9.77771 q^{8} -2.98830 q^{9} +O(q^{10})$	\(q-2.74897 q^{2} +0.108150 q^{3} +5.55686 q^{4} +1.28185 q^{5} -0.297303 q^{6} +2.70833 q^{7} -9.77771 q^{8} -2.98830 q^{9} -3.52377 q^{10} -5.42575 q^{11} +0.600976 q^{12} +0.535174 q^{13} -7.44513 q^{14} +0.138632 q^{15} +15.7650 q^{16} -2.17026 q^{17} +8.21477 q^{18} +3.93292 q^{19} +7.12305 q^{20} +0.292907 q^{21} +14.9153 q^{22} +5.44592 q^{23} -1.05746 q^{24} -3.35687 q^{25} -1.47118 q^{26} -0.647637 q^{27} +15.0498 q^{28} -4.25960 q^{29} -0.381097 q^{30} -3.80790 q^{31} -23.7821 q^{32} -0.586797 q^{33} +5.96599 q^{34} +3.47167 q^{35} -16.6056 q^{36} +2.44297 q^{37} -10.8115 q^{38} +0.0578792 q^{39} -12.5335 q^{40} -2.75564 q^{41} -0.805194 q^{42} +6.55954 q^{43} -30.1502 q^{44} -3.83055 q^{45} -14.9707 q^{46} +0.628130 q^{47} +1.70499 q^{48} +0.335062 q^{49} +9.22794 q^{50} -0.234714 q^{51} +2.97388 q^{52} -0.296087 q^{53} +1.78034 q^{54} -6.95499 q^{55} -26.4813 q^{56} +0.425346 q^{57} +11.7095 q^{58} +4.17940 q^{59} +0.770360 q^{60} +9.52394 q^{61} +10.4678 q^{62} -8.09332 q^{63} +33.8463 q^{64} +0.686011 q^{65} +1.61309 q^{66} -4.03555 q^{67} -12.0598 q^{68} +0.588978 q^{69} -9.54353 q^{70} +2.71971 q^{71} +29.2188 q^{72} +8.14919 q^{73} -6.71565 q^{74} -0.363046 q^{75} +21.8547 q^{76} -14.6947 q^{77} -0.159108 q^{78} +0.801356 q^{79} +20.2083 q^{80} +8.89487 q^{81} +7.57519 q^{82} +6.98938 q^{83} +1.62764 q^{84} -2.78194 q^{85} -18.0320 q^{86} -0.460677 q^{87} +53.0515 q^{88} +3.64560 q^{89} +10.5301 q^{90} +1.44943 q^{91} +30.2622 q^{92} -0.411826 q^{93} -1.72671 q^{94} +5.04140 q^{95} -2.57204 q^{96} +10.6485 q^{97} -0.921077 q^{98} +16.2138 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 327 q - 23 q^{2} - 48 q^{3} + 315 q^{4} - 55 q^{5} - 38 q^{6} - 87 q^{7} - 69 q^{8} + 303 q^{9}+O(q^{10}) $ 327 * q - 23 * q^2 - 48 * q^3 + 315 * q^4 - 55 * q^5 - 38 * q^6 - 87 * q^7 - 69 * q^8 + 303 * q^9	\( 327 q - 23 q^{2} - 48 q^{3} + 315 q^{4} - 55 q^{5} - 38 q^{6} - 87 q^{7} - 69 q^{8} + 303 q^{9} - 48 q^{10} - 70 q^{11} - 120 q^{12} - 53 q^{13} - 52 q^{14} - 77 q^{15} + 295 q^{16} - 164 q^{17} - 58 q^{18} - 47 q^{19} - 153 q^{20} - 39 q^{21} - 68 q^{22} - 256 q^{23} - 107 q^{24} + 288 q^{25} - 95 q^{26} - 189 q^{27} - 167 q^{28} - 99 q^{29} - 81 q^{30} - 71 q^{31} - 146 q^{32} - 95 q^{33} - 40 q^{34} - 192 q^{35} + 261 q^{36} - 54 q^{37} - 179 q^{38} - 115 q^{39} - 121 q^{40} - 111 q^{41} - 62 q^{42} - 110 q^{43} - 157 q^{44} - 137 q^{45} - 11 q^{46} - 324 q^{47} - 236 q^{48} + 296 q^{49} - 73 q^{50} - 88 q^{51} - 138 q^{52} - 170 q^{53} - 127 q^{54} - 151 q^{55} - 151 q^{56} - 106 q^{57} - 81 q^{58} - 123 q^{59} - 83 q^{60} - 62 q^{61} - 287 q^{62} - 400 q^{63} + 263 q^{64} - 143 q^{65} - 64 q^{66} - 95 q^{67} - 442 q^{68} - 22 q^{69} - 26 q^{70} - 210 q^{71} - 129 q^{72} - 121 q^{73} - 159 q^{74} - 194 q^{75} - 86 q^{76} - 178 q^{77} - 68 q^{78} - 145 q^{79} - 338 q^{80} + 259 q^{81} - 103 q^{82} - 418 q^{83} - 102 q^{84} - 40 q^{85} - 89 q^{86} - 372 q^{87} - 186 q^{88} - 100 q^{89} - 150 q^{90} - 69 q^{91} - 458 q^{92} - 81 q^{93} - 46 q^{94} - 377 q^{95} - 190 q^{96} - 87 q^{97} - 147 q^{98} - 171 q^{99}+O(q^{100}) \) 327 * q - 23 * q^2 - 48 * q^3 + 315 * q^4 - 55 * q^5 - 38 * q^6 - 87 * q^7 - 69 * q^8 + 303 * q^9 - 48 * q^10 - 70 * q^11 - 120 * q^12 - 53 * q^13 - 52 * q^14 - 77 * q^15 + 295 * q^16 - 164 * q^17 - 58 * q^18 - 47 * q^19 - 153 * q^20 - 39 * q^21 - 68 * q^22 - 256 * q^23 - 107 * q^24 + 288 * q^25 - 95 * q^26 - 189 * q^27 - 167 * q^28 - 99 * q^29 - 81 * q^30 - 71 * q^31 - 146 * q^32 - 95 * q^33 - 40 * q^34 - 192 * q^35 + 261 * q^36 - 54 * q^37 - 179 * q^38 - 115 * q^39 - 121 * q^40 - 111 * q^41 - 62 * q^42 - 110 * q^43 - 157 * q^44 - 137 * q^45 - 11 * q^46 - 324 * q^47 - 236 * q^48 + 296 * q^49 - 73 * q^50 - 88 * q^51 - 138 * q^52 - 170 * q^53 - 127 * q^54 - 151 * q^55 - 151 * q^56 - 106 * q^57 - 81 * q^58 - 123 * q^59 - 83 * q^60 - 62 * q^61 - 287 * q^62 - 400 * q^63 + 263 * q^64 - 143 * q^65 - 64 * q^66 - 95 * q^67 - 442 * q^68 - 22 * q^69 - 26 * q^70 - 210 * q^71 - 129 * q^72 - 121 * q^73 - 159 * q^74 - 194 * q^75 - 86 * q^76 - 178 * q^77 - 68 * q^78 - 145 * q^79 - 338 * q^80 + 259 * q^81 - 103 * q^82 - 418 * q^83 - 102 * q^84 - 40 * q^85 - 89 * q^86 - 372 * q^87 - 186 * q^88 - 100 * q^89 - 150 * q^90 - 69 * q^91 - 458 * q^92 - 81 * q^93 - 46 * q^94 - 377 * q^95 - 190 * q^96 - 87 * q^97 - 147 * q^98 - 171 * 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 $

$2$	−2.74897	−1.94382	−0.971909	−	0.235356i	$-0.924374\pi$
$2$	−2.74897	−1.94382	−0.971909	+	0.235356i	$0.924374\pi$
$3$	0.108150	0.0624406	0.0312203	−	0.999513i	$-0.490061\pi$
$3$	0.108150	0.0624406	0.0312203	+	0.999513i	$0.490061\pi$
$4$	5.55686	2.77843
$5$	1.28185	0.573260	0.286630	−	0.958041i	$-0.407465\pi$
$5$	1.28185	0.573260	0.286630	+	0.958041i	$0.407465\pi$
$6$	−0.297303	−0.121373
$7$	2.70833	1.02365	0.511827	−	0.859089i	$-0.328969\pi$
$7$	2.70833	1.02365	0.511827	+	0.859089i	$0.328969\pi$
$8$	−9.77771	−3.45694
$9$	−2.98830	−0.996101
$10$	−3.52377	−1.11431
$11$	−5.42575	−1.63593	−0.817963	−	0.575271i	$-0.804897\pi$
$11$	−5.42575	−1.63593	−0.817963	+	0.575271i	$0.804897\pi$
$12$	0.600976	0.173487
$13$	0.535174	0.148430	0.0742152	−	0.997242i	$-0.476355\pi$
$13$	0.535174	0.148430	0.0742152	+	0.997242i	$0.476355\pi$
$14$	−7.44513	−1.98980
$15$	0.138632	0.0357947
$16$	15.7650	3.94124
$17$	−2.17026	−0.526365	−0.263183	−	0.964746i	$-0.584772\pi$
$17$	−2.17026	−0.526365	−0.263183	+	0.964746i	$0.584772\pi$
$18$	8.21477	1.93624
$19$	3.93292	0.902273	0.451136	−	0.892455i	$-0.351019\pi$
$19$	3.93292	0.902273	0.451136	+	0.892455i	$0.351019\pi$
$20$	7.12305	1.59276
$21$	0.292907	0.0639176
$22$	14.9153	3.17994
$23$	5.44592	1.13555	0.567776	−	0.823183i	$-0.307804\pi$
$23$	5.44592	1.13555	0.567776	+	0.823183i	$0.307804\pi$
$24$	−1.05746	−0.215854
$25$	−3.35687	−0.671373
$26$	−1.47118	−0.288522
$27$	−0.647637	−0.124638
$28$	15.0498	2.84415
$29$	−4.25960	−0.790987	−0.395494	−	0.918469i	$-0.629426\pi$
$29$	−4.25960	−0.790987	−0.395494	+	0.918469i	$0.629426\pi$
$30$	−0.381097	−0.0695784
$31$	−3.80790	−0.683920	−0.341960	−	0.939715i	$-0.611091\pi$
$31$	−3.80790	−0.683920	−0.341960	+	0.939715i	$0.611091\pi$
$32$	−23.7821	−4.20411
$33$	−0.586797	−0.102148
$34$	5.96599	1.02316
$35$	3.47167	0.586819
$36$	−16.6056	−2.76760
$37$	2.44297	0.401621	0.200811	−	0.979630i	$-0.435642\pi$
$37$	2.44297	0.401621	0.200811	+	0.979630i	$0.435642\pi$
$38$	−10.8115	−1.75385
$39$	0.0578792	0.00926809
$40$	−12.5335	−1.98173
$41$	−2.75564	−0.430359	−0.215180	−	0.976574i	$-0.569034\pi$
$41$	−2.75564	−0.430359	−0.215180	+	0.976574i	$0.569034\pi$
$42$	−0.805194	−0.124244
$43$	6.55954	1.00032	0.500160	−	0.865933i	$-0.333274\pi$
$43$	6.55954	1.00032	0.500160	+	0.865933i	$0.333274\pi$
$44$	−30.1502	−4.54531
$45$	−3.83055	−0.571025
$46$	−14.9707	−2.20731
$47$	0.628130	0.0916221	0.0458111	−	0.998950i	$-0.485413\pi$
$47$	0.628130	0.0916221	0.0458111	+	0.998950i	$0.485413\pi$
$48$	1.70499	0.246094
$49$	0.335062	0.0478660
$50$	9.22794	1.30503
$51$	−0.234714	−0.0328666
$52$	2.97388	0.412404
$53$	−0.296087	−0.0406706	−0.0203353	−	0.999793i	$-0.506473\pi$
$53$	−0.296087	−0.0406706	−0.0203353	+	0.999793i	$0.506473\pi$
$54$	1.78034	0.242273
$55$	−6.95499	−0.937811
$56$	−26.4813	−3.53871
$57$	0.425346	0.0563385
$58$	11.7095	1.53754
$59$	4.17940	0.544111	0.272056	−	0.962282i	$-0.412297\pi$
$59$	4.17940	0.544111	0.272056	+	0.962282i	$0.412297\pi$
$60$	0.770360	0.0994531
$61$	9.52394	1.21942	0.609708	−	0.792626i	$-0.291287\pi$
$61$	9.52394	1.21942	0.609708	+	0.792626i	$0.291287\pi$
$62$	10.4678	1.32942
$63$	−8.09332	−1.01966
$64$	33.8463	4.23079
$65$	0.686011	0.0850892
$66$	1.61309	0.198558
$67$	−4.03555	−0.493021	−0.246510	−	0.969140i	$-0.579284\pi$
$67$	−4.03555	−0.493021	−0.246510	+	0.969140i	$0.579284\pi$
$68$	−12.0598	−1.46247
$69$	0.588978	0.0709046
$70$	−9.54353	−1.14067
$71$	2.71971	0.322770	0.161385	−	0.986892i	$-0.448404\pi$
$71$	2.71971	0.322770	0.161385	+	0.986892i	$0.448404\pi$
$72$	29.2188	3.44347
$73$	8.14919	0.953790	0.476895	−	0.878960i	$-0.341762\pi$
$73$	8.14919	0.953790	0.476895	+	0.878960i	$0.341762\pi$
$74$	−6.71565	−0.780679
$75$	−0.363046	−0.0419210
$76$	21.8547	2.50690
$77$	−14.6947	−1.67462
$78$	−0.159108	−0.0180155
$79$	0.801356	0.0901596	0.0450798	−	0.998983i	$-0.485646\pi$
$79$	0.801356	0.0901596	0.0450798	+	0.998983i	$0.485646\pi$
$80$	20.2083	2.25936
$81$	8.89487	0.988319
$82$	7.57519	0.836540
$83$	6.98938	0.767184	0.383592	−	0.923503i	$-0.374687\pi$
$83$	6.98938	0.767184	0.383592	+	0.923503i	$0.374687\pi$
$84$	1.62764	0.177590
$85$	−2.78194	−0.301744
$86$	−18.0320	−1.94444
$87$	−0.460677	−0.0493897
$88$	53.0515	5.65531
$89$	3.64560	0.386433	0.193217	−	0.981156i	$-0.438108\pi$
$89$	3.64560	0.386433	0.193217	+	0.981156i	$0.438108\pi$
$90$	10.5301	1.10997
$91$	1.44943	0.151941
$92$	30.2622	3.15505
$93$	−0.411826	−0.0427044
$94$	−1.72671	−0.178097
$95$	5.04140	0.517237
$96$	−2.57204	−0.262508
$97$	10.6485	1.08119	0.540597	−	0.841282i	$-0.318199\pi$
$97$	10.6485	1.08119	0.540597	+	0.841282i	$0.318199\pi$
$98$	−0.921077	−0.0930428
$99$	16.2138	1.62955
$100$	−18.6536	−1.86536
$101$	−12.7449	−1.26816	−0.634082	−	0.773266i	$-0.718622\pi$
$101$	−12.7449	−1.26816	−0.634082	+	0.773266i	$0.718622\pi$
$102$	0.645224	0.0638867
$103$	−0.711930	−0.0701486	−0.0350743	−	0.999385i	$-0.511167\pi$
$103$	−0.711930	−0.0701486	−0.0350743	+	0.999385i	$0.511167\pi$
$104$	−5.23277	−0.513116
$105$	0.375462	0.0366414
$106$	0.813935	0.0790563
$107$	5.22967	0.505571	0.252786	−	0.967522i	$-0.418653\pi$
$107$	5.22967	0.505571	0.252786	+	0.967522i	$0.418653\pi$
$108$	−3.59883	−0.346297
$109$	−13.7450	−1.31653	−0.658264	−	0.752787i	$-0.728709\pi$
$109$	−13.7450	−1.31653	−0.658264	+	0.752787i	$0.728709\pi$
$110$	19.1191	1.82293
$111$	0.264208	0.0250775
$112$	42.6968	4.03446
$113$	2.96616	0.279033	0.139516	−	0.990220i	$-0.455445\pi$
$113$	2.96616	0.279033	0.139516	+	0.990220i	$0.455445\pi$
$114$	−1.16927	−0.109512
$115$	6.98084	0.650966
$116$	−23.6700	−2.19770
$117$	−1.59926	−0.147852
$118$	−11.4891	−1.05765
$119$	−5.87778	−0.538816
$120$	−1.35551	−0.123740
$121$	18.4388	1.67626
$122$	−26.1811	−2.37032
$123$	−0.298024	−0.0268719
$124$	−21.1600	−1.90022
$125$	−10.7122	−0.958131
$126$	22.2483	1.98204
$127$	−8.81353	−0.782074	−0.391037	−	0.920375i	$-0.627884\pi$
$127$	−8.81353	−0.782074	−0.391037	+	0.920375i	$0.627884\pi$
$128$	−45.4786	−4.01978
$129$	0.709416	0.0624606
$130$	−1.88583	−0.165398
$131$	18.6258	1.62735	0.813673	−	0.581323i	$-0.197465\pi$
$131$	18.6258	1.62735	0.813673	+	0.581323i	$0.197465\pi$
$132$	−3.26075	−0.283812
$133$	10.6516	0.923615
$134$	11.0936	0.958342
$135$	−0.830172	−0.0714499
$136$	21.2202	1.81962
$137$	−5.05390	−0.431783	−0.215892	−	0.976417i	$-0.569266\pi$
$137$	−5.05390	−0.431783	−0.215892	+	0.976417i	$0.569266\pi$
$138$	−1.61909	−0.137826
$139$	−5.66622	−0.480603	−0.240301	−	0.970698i	$-0.577246\pi$
$139$	−5.66622	−0.480603	−0.240301	+	0.970698i	$0.577246\pi$
$140$	19.2916	1.63044
$141$	0.0679324	0.00572094
$142$	−7.47640	−0.627406
$143$	−2.90372	−0.242821
$144$	−47.1105	−3.92588
$145$	−5.46015	−0.453441
$146$	−22.4019	−1.85399
$147$	0.0362371	0.00298878
$148$	13.5752	1.11588
$149$	−19.2467	−1.57675	−0.788376	−	0.615194i	$-0.789078\pi$
$149$	−19.2467	−1.57675	−0.788376	+	0.615194i	$0.789078\pi$
$150$	0.998005	0.0814868
$151$	−12.8168	−1.04302	−0.521510	−	0.853245i	$-0.674631\pi$
$151$	−12.8168	−1.04302	−0.521510	+	0.853245i	$0.674631\pi$
$152$	−38.4549	−3.11911
$153$	6.48539	0.524313
$154$	40.3955	3.25516
$155$	−4.88115	−0.392064
$156$	0.321627	0.0257507
$157$	−16.7261	−1.33489	−0.667443	−	0.744661i	$-0.732611\pi$
$157$	−16.7261	−1.33489	−0.667443	+	0.744661i	$0.732611\pi$
$158$	−2.20291	−0.175254
$159$	−0.0320219	−0.00253950
$160$	−30.4850	−2.41005
$161$	14.7494	1.16241
$162$	−24.4518	−1.92111
$163$	−3.70827	−0.290454	−0.145227	−	0.989398i	$-0.546391\pi$
$163$	−3.70827	−0.290454	−0.145227	+	0.989398i	$0.546391\pi$
$164$	−15.3127	−1.19572
$165$	−0.752185	−0.0585575
$166$	−19.2136	−1.49127
$167$	3.30778	0.255964	0.127982	−	0.991776i	$-0.459150\pi$
$167$	3.30778	0.255964	0.127982	+	0.991776i	$0.459150\pi$
$168$	−2.86396	−0.220959
$169$	−12.7136	−0.977968
$170$	7.64749	0.586536
$171$	−11.7527	−0.898755
$172$	36.4504	2.77932
$173$	−22.2765	−1.69365	−0.846824	−	0.531873i	$-0.821488\pi$
$173$	−22.2765	−1.69365	−0.846824	+	0.531873i	$0.821488\pi$
$174$	1.26639	0.0960047
$175$	−9.09151	−0.687253
$176$	−85.5368	−6.44758
$177$	0.452003	0.0339747
$178$	−10.0217	−0.751156
$179$	2.39873	0.179289	0.0896446	−	0.995974i	$-0.471427\pi$
$179$	2.39873	0.179289	0.0896446	+	0.995974i	$0.471427\pi$
$180$	−21.2858	−1.58655
$181$	15.5921	1.15895	0.579477	−	0.814989i	$-0.303257\pi$
$181$	15.5921	1.15895	0.579477	+	0.814989i	$0.303257\pi$
$182$	−3.98444	−0.295346
$183$	1.03002	0.0761411
$184$	−53.2486	−3.92554
$185$	3.13151	0.230233
$186$	1.13210	0.0830096
$187$	11.7753	0.861095
$188$	3.49043	0.254566
$189$	−1.75402	−0.127586
$190$	−13.8587	−1.00541
$191$	−11.8548	−0.857786	−0.428893	−	0.903355i	$-0.641096\pi$
$191$	−11.8548	−0.857786	−0.428893	+	0.903355i	$0.641096\pi$
$192$	3.66049	0.264173
$193$	−4.49545	−0.323589	−0.161795	−	0.986824i	$-0.551728\pi$
$193$	−4.49545	−0.323589	−0.161795	+	0.986824i	$0.551728\pi$
$194$	−29.2725	−2.10164
$195$	0.0741923	0.00531302
$196$	1.86189	0.132992
$197$	0.844844	0.0601926	0.0300963	−	0.999547i	$-0.490419\pi$
$197$	0.844844	0.0601926	0.0300963	+	0.999547i	$0.490419\pi$
$198$	−44.5713	−3.16755
$199$	−6.83245	−0.484340	−0.242170	−	0.970234i	$-0.577859\pi$
$199$	−6.83245	−0.484340	−0.242170	+	0.970234i	$0.577859\pi$
$200$	32.8225	2.32090
$201$	−0.436446	−0.0307845
$202$	35.0354	2.46508
$203$	−11.5364	−0.809696
$204$	−1.30427	−0.0913175
$205$	−3.53232	−0.246708
$206$	1.95708	0.136356
$207$	−16.2741	−1.13112
$208$	8.43699	0.585000
$209$	−21.3390	−1.47605
$210$	−1.03214	−0.0712242
$211$	22.3118	1.53601	0.768004	−	0.640446i	$-0.221250\pi$
$211$	22.3118	1.53601	0.768004	+	0.640446i	$0.221250\pi$
$212$	−1.64531	−0.113000
$213$	0.294137	0.0201539
$214$	−14.3762	−0.982738
$215$	8.40833	0.573443
$216$	6.33241	0.430866
$217$	−10.3131	−0.700097
$218$	37.7845	2.55909
$219$	0.881337	0.0595553
$220$	−38.6479	−2.60564
$221$	−1.16147	−0.0781286
$222$	−0.726300	−0.0487461
$223$	14.4071	0.964774	0.482387	−	0.875958i	$-0.339770\pi$
$223$	14.4071	0.964774	0.482387	+	0.875958i	$0.339770\pi$
$224$	−64.4097	−4.30355
$225$	10.0313	0.668756
$226$	−8.15389	−0.542389
$227$	−19.1032	−1.26792	−0.633961	−	0.773365i	$-0.718572\pi$
$227$	−19.1032	−1.26792	−0.633961	+	0.773365i	$0.718572\pi$
$228$	2.36359	0.156533
$229$	−12.7751	−0.844205	−0.422103	−	0.906548i	$-0.638708\pi$
$229$	−12.7751	−0.844205	−0.422103	+	0.906548i	$0.638708\pi$
$230$	−19.1901	−1.26536
$231$	−1.58924	−0.104564
$232$	41.6491	2.73440
$233$	−3.86030	−0.252897	−0.126448	−	0.991973i	$-0.540358\pi$
$233$	−3.86030	−0.252897	−0.126448	+	0.991973i	$0.540358\pi$
$234$	4.39633	0.287397
$235$	0.805167	0.0525233
$236$	23.2243	1.51178
$237$	0.0866669	0.00562962
$238$	16.1579	1.04736
$239$	−15.2321	−0.985280	−0.492640	−	0.870233i	$-0.663968\pi$
$239$	−15.2321	−0.985280	−0.492640	+	0.870233i	$0.663968\pi$
$240$	2.18553	0.141076
$241$	7.47218	0.481326	0.240663	−	0.970609i	$-0.422635\pi$
$241$	7.47218	0.481326	0.240663	+	0.970609i	$0.422635\pi$
$242$	−50.6878	−3.25834
$243$	2.90489	0.186349
$244$	52.9232	3.38806
$245$	0.429498	0.0274397
$246$	0.819260	0.0522341
$247$	2.10479	0.133925
$248$	37.2326	2.36427
$249$	0.755904	0.0479034
$250$	29.4476	1.86243
$251$	−22.6705	−1.43095	−0.715474	−	0.698640i	$-0.753789\pi$
$251$	−22.6705	−1.43095	−0.715474	+	0.698640i	$0.753789\pi$
$252$	−44.9734	−2.83306
$253$	−29.5482	−1.85768
$254$	24.2282	1.52021
$255$	−0.300868	−0.0188411
$256$	57.3268	3.58292
$257$	−4.89673	−0.305450	−0.152725	−	0.988269i	$-0.548805\pi$
$257$	−4.89673	−0.305450	−0.152725	+	0.988269i	$0.548805\pi$
$258$	−1.95017	−0.121412
$259$	6.61636	0.411121
$260$	3.81207	0.236414
$261$	12.7290	0.787903
$262$	−51.2019	−3.16327
$263$	−3.37129	−0.207883	−0.103941	−	0.994583i	$-0.533145\pi$
$263$	−3.37129	−0.207883	−0.103941	+	0.994583i	$0.533145\pi$
$264$	5.73754	0.353121
$265$	−0.379538	−0.0233148
$266$	−29.2811	−1.79534
$267$	0.394273	0.0241291
$268$	−22.4250	−1.36982
$269$	1.94170	0.118388	0.0591939	−	0.998247i	$-0.481147\pi$
$269$	1.94170	0.118388	0.0591939	+	0.998247i	$0.481147\pi$
$270$	2.28212	0.138886
$271$	−22.3057	−1.35498	−0.677489	−	0.735533i	$-0.736932\pi$
$271$	−22.3057	−1.35498	−0.677489	+	0.735533i	$0.736932\pi$
$272$	−34.2141	−2.07453
$273$	0.156756	0.00948731
$274$	13.8930	0.839309
$275$	18.2135	1.09832
$276$	3.27287	0.197003
$277$	−31.2732	−1.87903	−0.939513	−	0.342512i	$-0.888722\pi$
$277$	−31.2732	−1.87903	−0.939513	+	0.342512i	$0.888722\pi$
$278$	15.5763	0.934204
$279$	11.3792	0.681253
$280$	−33.9450	−2.02860
$281$	0.723478	0.0431591	0.0215795	−	0.999767i	$-0.493130\pi$
$281$	0.723478	0.0431591	0.0215795	+	0.999767i	$0.493130\pi$
$282$	−0.186745	−0.0111205
$283$	−1.64367	−0.0977061	−0.0488531	−	0.998806i	$-0.515557\pi$
$283$	−1.64367	−0.0977061	−0.0488531	+	0.998806i	$0.515557\pi$
$284$	15.1130	0.896793
$285$	0.545229	0.0322966
$286$	7.98225	0.472000
$287$	−7.46320	−0.440539
$288$	71.0680	4.18772
$289$	−12.2900	−0.722940
$290$	15.0098	0.881407
$291$	1.15164	0.0675104
$292$	45.2839	2.65004
$293$	26.5303	1.54992	0.774958	−	0.632012i	$-0.217771\pi$
$293$	26.5303	1.54992	0.774958	+	0.632012i	$0.217771\pi$
$294$	−0.0996148	−0.00580965
$295$	5.35735	0.311917
$296$	−23.8866	−1.38838
$297$	3.51392	0.203898
$298$	52.9087	3.06492
$299$	2.91451	0.168551
$300$	−2.01740	−0.116474
$301$	17.7654	1.02398
$302$	35.2332	2.02744
$303$	−1.37836	−0.0791849
$304$	62.0023	3.55608
$305$	12.2082	0.699042
$306$	−17.8282	−1.01917
$307$	17.6418	1.00687	0.503437	−	0.864032i	$-0.332069\pi$
$307$	17.6418	1.00687	0.503437	+	0.864032i	$0.332069\pi$
$308$	−81.6566	−4.65282
$309$	−0.0769955	−0.00438012
$310$	13.4182	0.762101
$311$	−14.8675	−0.843060	−0.421530	−	0.906814i	$-0.638507\pi$
$311$	−14.8675	−0.843060	−0.421530	+	0.906814i	$0.638507\pi$
$312$	−0.565926	−0.0320393
$313$	−24.1006	−1.36225	−0.681124	−	0.732168i	$-0.738508\pi$
$313$	−24.1006	−1.36225	−0.681124	+	0.732168i	$0.738508\pi$
$314$	45.9796	2.59478
$315$	−10.3744	−0.584531
$316$	4.45302	0.250502
$317$	5.89250	0.330956	0.165478	−	0.986213i	$-0.447083\pi$
$317$	5.89250	0.330956	0.165478	+	0.986213i	$0.447083\pi$
$318$	0.0880273	0.00493633
$319$	23.1115	1.29400
$320$	43.3858	2.42534
$321$	0.565590	0.0315682
$322$	−40.5456	−2.25952
$323$	−8.53545	−0.474925
$324$	49.4275	2.74597
$325$	−1.79651	−0.0996522
$326$	10.1939	0.564590
$327$	−1.48652	−0.0822048
$328$	26.9439	1.48773
$329$	1.70118	0.0937893
$330$	2.06774	0.113825
$331$	2.88324	0.158477	0.0792387	−	0.996856i	$-0.474751\pi$
$331$	2.88324	0.158477	0.0792387	+	0.996856i	$0.474751\pi$
$332$	38.8390	2.13157
$333$	−7.30033	−0.400055
$334$	−9.09301	−0.497548
$335$	−5.17296	−0.282629
$336$	4.61767	0.251915
$337$	−12.2578	−0.667725	−0.333862	−	0.942622i	$-0.608352\pi$
$337$	−12.2578	−0.667725	−0.333862	+	0.942622i	$0.608352\pi$
$338$	34.9493	1.90099
$339$	0.320791	0.0174230
$340$	−15.4589	−0.838375
$341$	20.6608	1.11884
$342$	32.3080	1.74702
$343$	−18.0509	−0.974655
$344$	−64.1373	−3.45805
$345$	0.754980	0.0406468
$346$	61.2374	3.29214
$347$	−13.4059	−0.719668	−0.359834	−	0.933016i	$-0.617167\pi$
$347$	−13.4059	−0.719668	−0.359834	+	0.933016i	$0.617167\pi$
$348$	−2.55992	−0.137226
$349$	1.65665	0.0886787	0.0443393	−	0.999017i	$-0.485882\pi$
$349$	1.65665	0.0886787	0.0443393	+	0.999017i	$0.485882\pi$
$350$	24.9923	1.33590
$351$	−0.346598	−0.0185000
$352$	129.036	6.87762
$353$	−18.5711	−0.988441	−0.494220	−	0.869337i	$-0.664546\pi$
$353$	−18.5711	−0.988441	−0.494220	+	0.869337i	$0.664546\pi$
$354$	−1.24255	−0.0660406
$355$	3.48625	0.185031
$356$	20.2581	1.07368
$357$	−0.635684	−0.0336440
$358$	−6.59404	−0.348506
$359$	24.1319	1.27363	0.636815	−	0.771016i	$-0.280251\pi$
$359$	24.1319	1.27363	0.636815	+	0.771016i	$0.280251\pi$
$360$	37.4540	1.97400
$361$	−3.53217	−0.185903
$362$	−42.8623	−2.25279
$363$	1.99416	0.104666
$364$	8.05427	0.422158
$365$	10.4460	0.546770
$366$	−2.83149	−0.148004
$367$	11.2597	0.587754	0.293877	−	0.955843i	$-0.405054\pi$
$367$	11.2597	0.587754	0.293877	+	0.955843i	$0.405054\pi$
$368$	85.8547	4.47549
$369$	8.23470	0.428681
$370$	−8.60845	−0.447532
$371$	−0.801901	−0.0416326
$372$	−2.28846	−0.118651
$373$	−14.7645	−0.764477	−0.382239	−	0.924064i	$-0.624847\pi$
$373$	−14.7645	−0.764477	−0.382239	+	0.924064i	$0.624847\pi$
$374$	−32.3700	−1.67381
$375$	−1.15853	−0.0598263
$376$	−6.14167	−0.316733
$377$	−2.27962	−0.117407
$378$	4.82175	0.248004
$379$	7.75539	0.398367	0.199184	−	0.979962i	$-0.436171\pi$
$379$	7.75539	0.398367	0.199184	+	0.979962i	$0.436171\pi$
$380$	28.0144	1.43711
$381$	−0.953186	−0.0488332
$382$	32.5886	1.66738
$383$	−11.9219	−0.609181	−0.304590	−	0.952483i	$-0.598520\pi$
$383$	−11.9219	−0.609181	−0.304590	+	0.952483i	$0.598520\pi$
$384$	−4.91852	−0.250997
$385$	−18.8364	−0.959993
$386$	12.3579	0.628999
$387$	−19.6019	−0.996420
$388$	59.1723	3.00402
$389$	−17.7304	−0.898967	−0.449484	−	0.893289i	$-0.648392\pi$
$389$	−17.7304	−0.898967	−0.449484	+	0.893289i	$0.648392\pi$
$390$	−0.203953	−0.0103276
$391$	−11.8191	−0.597715
$392$	−3.27614	−0.165470
$393$	2.01439	0.101613
$394$	−2.32245	−0.117004
$395$	1.02722	0.0516849
$396$	90.0978	4.52759
$397$	−26.8262	−1.34637	−0.673183	−	0.739476i	$-0.735074\pi$
$397$	−26.8262	−1.34637	−0.673183	+	0.739476i	$0.735074\pi$
$398$	18.7822	0.941468
$399$	1.15198	0.0576711
$400$	−52.9209	−2.64604
$401$	−3.69765	−0.184652	−0.0923260	−	0.995729i	$-0.529430\pi$
$401$	−3.69765	−0.184652	−0.0923260	+	0.995729i	$0.529430\pi$
$402$	1.19978	0.0598395
$403$	−2.03789	−0.101515
$404$	−70.8215	−3.52350
$405$	11.4019	0.566563
$406$	31.7133	1.57390
$407$	−13.2549	−0.657023
$408$	2.29497	0.113618
$409$	−12.4332	−0.614782	−0.307391	−	0.951583i	$-0.599456\pi$
$409$	−12.4332	−0.614782	−0.307391	+	0.951583i	$0.599456\pi$
$410$	9.71024	0.479555
$411$	−0.546581	−0.0269608
$412$	−3.95610	−0.194903
$413$	11.3192	0.556981
$414$	44.7370	2.19870
$415$	8.95932	0.439796
$416$	−12.7275	−0.624018
$417$	−0.612804	−0.0300091
$418$	58.6605	2.86918
$419$	11.3395	0.553970	0.276985	−	0.960874i	$-0.410665\pi$
$419$	11.3395	0.553970	0.276985	+	0.960874i	$0.410665\pi$
$420$	2.08639	0.101805
$421$	−22.0492	−1.07461	−0.537306	−	0.843387i	$-0.680558\pi$
$421$	−22.0492	−1.07461	−0.537306	+	0.843387i	$0.680558\pi$
$422$	−61.3345	−2.98572
$423$	−1.87704	−0.0912649
$424$	2.89505	0.140596
$425$	7.28527	0.353388
$426$	−0.808576	−0.0391756
$427$	25.7940	1.24826
$428$	29.0605	1.40469
$429$	−0.314038	−0.0151619
$430$	−23.1143	−1.11467
$431$	−9.23059	−0.444622	−0.222311	−	0.974976i	$-0.571360\pi$
$431$	−9.23059	−0.444622	−0.222311	+	0.974976i	$0.571360\pi$
$432$	−10.2100	−0.491228
$433$	−23.8377	−1.14557	−0.572783	−	0.819707i	$-0.694136\pi$
$433$	−23.8377	−1.14557	−0.572783	+	0.819707i	$0.694136\pi$
$434$	28.3504	1.36086
$435$	−0.590518	−0.0283132
$436$	−76.3788	−3.65788
$437$	21.4183	1.02458
$438$	−2.42277	−0.115765
$439$	7.85657	0.374973	0.187487	−	0.982267i	$-0.439966\pi$
$439$	7.85657	0.374973	0.187487	+	0.982267i	$0.439966\pi$
$440$	68.0039	3.24196
$441$	−1.00127	−0.0476794
$442$	3.19284	0.151868
$443$	−4.72574	−0.224526	−0.112263	−	0.993679i	$-0.535810\pi$
$443$	−4.72574	−0.224526	−0.112263	+	0.993679i	$0.535810\pi$
$444$	1.46817	0.0696760
$445$	4.67311	0.221527
$446$	−39.6049	−1.87534
$447$	−2.08154	−0.0984533
$448$	91.6671	4.33086
$449$	38.4186	1.81308	0.906542	−	0.422115i	$-0.138712\pi$
$449$	38.4186	1.81308	0.906542	+	0.422115i	$0.138712\pi$
$450$	−27.5759	−1.29994
$451$	14.9514	0.704036
$452$	16.4825	0.775272
$453$	−1.38615	−0.0651268
$454$	52.5141	2.46461
$455$	1.85795	0.0871018
$456$	−4.15892	−0.194759
$457$	16.3280	0.763792	0.381896	−	0.924205i	$-0.375271\pi$
$457$	16.3280	0.763792	0.381896	+	0.924205i	$0.375271\pi$
$458$	35.1185	1.64098
$459$	1.40554	0.0656050
$460$	38.7915	1.80866
$461$	−10.5648	−0.492052	−0.246026	−	0.969263i	$-0.579125\pi$
$461$	−10.5648	−0.492052	−0.246026	+	0.969263i	$0.579125\pi$
$462$	4.36878	0.203254
$463$	−25.1526	−1.16894	−0.584471	−	0.811414i	$-0.698698\pi$
$463$	−25.1526	−1.16894	−0.584471	+	0.811414i	$0.698698\pi$
$464$	−67.1524	−3.11747
$465$	−0.527899	−0.0244807
$466$	10.6119	0.491586
$467$	−0.180362	−0.00834616	−0.00417308	−	0.999991i	$-0.501328\pi$
$467$	−0.180362	−0.00834616	−0.00417308	+	0.999991i	$0.501328\pi$
$468$	−8.88687	−0.410796
$469$	−10.9296	−0.504682
$470$	−2.21338	−0.102096
$471$	−1.80893	−0.0833512
$472$	−40.8650	−1.88096
$473$	−35.5904	−1.63645
$474$	−0.238245	−0.0109430
$475$	−13.2023	−0.605762
$476$	−32.6620	−1.49706
$477$	0.884797	0.0405121
$478$	41.8726	1.91521
$479$	−10.6315	−0.485768	−0.242884	−	0.970055i	$-0.578093\pi$
$479$	−10.6315	−0.485768	−0.242884	+	0.970055i	$0.578093\pi$
$480$	−3.29696	−0.150485
$481$	1.30741	0.0596128
$482$	−20.5408	−0.935609
$483$	1.59515	0.0725817
$484$	102.462	4.65736
$485$	13.6498	0.619805
$486$	−7.98548	−0.362229
$487$	−15.8163	−0.716707	−0.358353	−	0.933586i	$-0.616662\pi$
$487$	−15.8163	−0.716707	−0.358353	+	0.933586i	$0.616662\pi$
$488$	−93.1223	−4.21545
$489$	−0.401051	−0.0181361
$490$	−1.18068	−0.0533377
$491$	14.9551	0.674913	0.337456	−	0.941341i	$-0.390433\pi$
$491$	14.9551	0.674913	0.337456	+	0.941341i	$0.390433\pi$
$492$	−1.65608	−0.0746617
$493$	9.24443	0.416348
$494$	−5.78602	−0.260325
$495$	20.7836	0.934155
$496$	−60.0315	−2.69549
$497$	7.36587	0.330404
$498$	−2.07796	−0.0931156
$499$	0.693018	0.0310237	0.0155119	−	0.999880i	$-0.495062\pi$
$499$	0.693018	0.0310237	0.0155119	+	0.999880i	$0.495062\pi$
$500$	−59.5264	−2.66210
$501$	0.357738	0.0159826
$502$	62.3205	2.78150
$503$	−17.1039	−0.762625	−0.381312	−	0.924446i	$-0.624528\pi$
$503$	−17.1039	−0.762625	−0.381312	+	0.924446i	$0.624528\pi$
$504$	79.1342	3.52492
$505$	−16.3370	−0.726987
$506$	81.2273	3.61099
$507$	−1.37498	−0.0610650
$508$	−48.9755	−2.17294
$509$	−28.2728	−1.25317	−0.626584	−	0.779354i	$-0.715547\pi$
$509$	−28.2728	−1.25317	−0.626584	+	0.779354i	$0.715547\pi$
$510$	0.827079	0.0366237
$511$	22.0707	0.976350
$512$	−66.6327	−2.94478
$513$	−2.54710	−0.112457
$514$	13.4610	0.593739
$515$	−0.912586	−0.0402134
$516$	3.94213	0.173542
$517$	−3.40808	−0.149887
$518$	−18.1882	−0.799144
$519$	−2.40921	−0.105752
$520$	−6.70762	−0.294149
$521$	37.1443	1.62732	0.813660	−	0.581341i	$-0.197472\pi$
$521$	37.1443	1.62732	0.813660	+	0.581341i	$0.197472\pi$
$522$	−34.9916	−1.53154
$523$	−42.3822	−1.85324	−0.926622	−	0.375993i	$-0.877302\pi$
$523$	−42.3822	−1.85324	−0.926622	+	0.375993i	$0.877302\pi$
$524$	103.501	4.52147
$525$	−0.983250	−0.0429125
$526$	9.26758	0.404086
$527$	8.26414	0.359992
$528$	−9.25084	−0.402591
$529$	6.65802	0.289479
$530$	1.04334	0.0453198
$531$	−12.4893	−0.541990
$532$	59.1897	2.56620
$533$	−1.47475	−0.0638784
$534$	−1.08385	−0.0469026
$535$	6.70364	0.289824
$536$	39.4584	1.70434
$537$	0.259423	0.0111949
$538$	−5.33770	−0.230124
$539$	−1.81796	−0.0783052
$540$	−4.61315	−0.198518
$541$	22.3118	0.959259	0.479630	−	0.877471i	$-0.340771\pi$
$541$	22.3118	0.959259	0.479630	+	0.877471i	$0.340771\pi$
$542$	61.3179	2.63383
$543$	1.68629	0.0723658
$544$	51.6132	2.21290
$545$	−17.6189	−0.754712
$546$	−0.430919	−0.0184416
$547$	6.49934	0.277892	0.138946	−	0.990300i	$-0.455629\pi$
$547$	6.49934	0.277892	0.138946	+	0.990300i	$0.455629\pi$
$548$	−28.0838	−1.19968
$549$	−28.4604	−1.21466
$550$	−50.0685	−2.13493
$551$	−16.7526	−0.713686
$552$	−5.75886	−0.245113
$553$	2.17034	0.0922922
$554$	85.9693	3.65249
$555$	0.338674	0.0143759
$556$	−31.4864	−1.33532
$557$	−40.8114	−1.72923	−0.864617	−	0.502431i	$-0.832439\pi$
$557$	−40.8114	−1.72923	−0.864617	+	0.502431i	$0.832439\pi$
$558$	−31.2811	−1.32423
$559$	3.51049	0.148478
$560$	54.7308	2.31280
$561$	1.27350	0.0537673
$562$	−1.98882	−0.0838934
$563$	−15.3538	−0.647087	−0.323543	−	0.946213i	$-0.604874\pi$
$563$	−15.3538	−0.647087	−0.323543	+	0.946213i	$0.604874\pi$
$564$	0.377491	0.0158952
$565$	3.80216	0.159958
$566$	4.51841	0.189923
$567$	24.0903	1.01170
$568$	−26.5925	−1.11580
$569$	−37.2193	−1.56031	−0.780157	−	0.625584i	$-0.784861\pi$
$569$	−37.2193	−1.56031	−0.780157	+	0.625584i	$0.784861\pi$
$570$	−1.49882	−0.0627787
$571$	−26.4720	−1.10782	−0.553910	−	0.832577i	$-0.686865\pi$
$571$	−26.4720	−1.10782	−0.553910	+	0.832577i	$0.686865\pi$
$572$	−16.1356	−0.674662
$573$	−1.28210	−0.0535607
$574$	20.5161	0.856327
$575$	−18.2812	−0.762379
$576$	−101.143	−4.21430
$577$	28.4469	1.18426	0.592129	−	0.805843i	$-0.298287\pi$
$577$	28.4469	1.18426	0.592129	+	0.805843i	$0.298287\pi$
$578$	33.7848	1.40526
$579$	−0.486184	−0.0202051
$580$	−30.3413	−1.25985
$581$	18.9296	0.785330
$582$	−3.16583	−0.131228
$583$	1.60649	0.0665342
$584$	−79.6804	−3.29720
$585$	−2.05001	−0.0847575
$586$	−72.9311	−3.01276
$587$	42.9586	1.77309	0.886546	−	0.462641i	$-0.153098\pi$
$587$	42.9586	1.77309	0.886546	+	0.462641i	$0.153098\pi$
$588$	0.201364	0.00830412
$589$	−14.9762	−0.617082
$590$	−14.7272	−0.606310
$591$	0.0913702	0.00375847
$592$	38.5133	1.58289
$593$	10.7250	0.440422	0.220211	−	0.975452i	$-0.429325\pi$
$593$	10.7250	0.440422	0.220211	+	0.975452i	$0.429325\pi$
$594$	−9.65968	−0.396341
$595$	−7.53442	−0.308881
$596$	−106.951	−4.38089
$597$	−0.738932	−0.0302425
$598$	−8.01192	−0.327632
$599$	30.3910	1.24174	0.620872	−	0.783912i	$-0.286779\pi$
$599$	30.3910	1.24174	0.620872	+	0.783912i	$0.286779\pi$
$600$	3.54976	0.144918
$601$	−7.28613	−0.297207	−0.148604	−	0.988897i	$-0.547478\pi$
$601$	−7.28613	−0.297207	−0.148604	+	0.988897i	$0.547478\pi$
$602$	−48.8366	−1.99043
$603$	12.0594	0.491098
$604$	−71.2214	−2.89796
$605$	23.6357	0.960930
$606$	3.78909	0.153921
$607$	20.8764	0.847345	0.423673	−	0.905815i	$-0.360741\pi$
$607$	20.8764	0.847345	0.423673	+	0.905815i	$0.360741\pi$
$608$	−93.5328	−3.79326
$609$	−1.24767	−0.0505580
$610$	−33.5601	−1.35881
$611$	0.336158	0.0135995
$612$	36.0384	1.45677
$613$	−5.95917	−0.240689	−0.120344	−	0.992732i	$-0.538400\pi$
$613$	−5.95917	−0.240689	−0.120344	+	0.992732i	$0.538400\pi$
$614$	−48.4970	−1.95718
$615$	−0.382021	−0.0154046
$616$	143.681	5.78907
$617$	14.5058	0.583980	0.291990	−	0.956421i	$-0.405683\pi$
$617$	14.5058	0.583980	0.291990	+	0.956421i	$0.405683\pi$
$618$	0.211659	0.00851416
$619$	16.7061	0.671474	0.335737	−	0.941956i	$-0.391015\pi$
$619$	16.7061	0.671474	0.335737	+	0.941956i	$0.391015\pi$
$620$	−27.1239	−1.08932
$621$	−3.52698	−0.141533
$622$	40.8704	1.63876
$623$	9.87350	0.395573
$624$	0.912464	0.0365278
$625$	3.05288	0.122115
$626$	66.2520	2.64796
$627$	−2.30782	−0.0921656
$628$	−92.9445	−3.70889
$629$	−5.30187	−0.211399
$630$	28.5190	1.13622
$631$	36.7455	1.46282	0.731409	−	0.681940i	$-0.238863\pi$
$631$	36.7455	1.46282	0.731409	+	0.681940i	$0.238863\pi$
$632$	−7.83543	−0.311677
$633$	2.41303	0.0959093
$634$	−16.1983	−0.643318
$635$	−11.2976	−0.448332
$636$	−0.177941	−0.00705582
$637$	0.179316	0.00710477
$638$	−63.5330	−2.51529
$639$	−8.12731	−0.321511
$640$	−58.2966	−2.30438
$641$	17.8095	0.703433	0.351716	−	0.936107i	$-0.385598\pi$
$641$	17.8095	0.703433	0.351716	+	0.936107i	$0.385598\pi$
$642$	−1.55479	−0.0613628
$643$	−9.52978	−0.375818	−0.187909	−	0.982186i	$-0.560171\pi$
$643$	−9.52978	−0.375818	−0.187909	+	0.982186i	$0.560171\pi$
$644$	81.9601	3.22968
$645$	0.909364	0.0358062
$646$	23.4637	0.923168
$647$	6.30341	0.247813	0.123906	−	0.992294i	$-0.460458\pi$
$647$	6.30341	0.247813	0.123906	+	0.992294i	$0.460458\pi$
$648$	−86.9715	−3.41656
$649$	−22.6764	−0.890126
$650$	4.93855	0.193706
$651$	−1.11536	−0.0437145
$652$	−20.6063	−0.807007
$653$	33.1045	1.29548	0.647739	−	0.761862i	$-0.275715\pi$
$653$	33.1045	1.29548	0.647739	+	0.761862i	$0.275715\pi$
$654$	4.08641	0.159791
$655$	23.8755	0.932892
$656$	−43.4426	−1.69615
$657$	−24.3522	−0.950071
$658$	−4.67651	−0.182309
$659$	−14.2166	−0.553801	−0.276901	−	0.960899i	$-0.589307\pi$
$659$	−14.2166	−0.553801	−0.276901	+	0.960899i	$0.589307\pi$
$660$	−4.17979	−0.162698
$661$	−4.81558	−0.187304	−0.0936521	−	0.995605i	$-0.529854\pi$
$661$	−4.81558	−0.187304	−0.0936521	+	0.995605i	$0.529854\pi$
$662$	−7.92596	−0.308051
$663$	−0.125613	−0.00487840
$664$	−68.3401	−2.65211
$665$	13.6538	0.529471
$666$	20.0684	0.777635
$667$	−23.1974	−0.898207
$668$	18.3809	0.711178
$669$	1.55814	0.0602411
$670$	14.2203	0.549379
$671$	−51.6745	−1.99487
$672$	−6.96593	−0.268717
$673$	37.2297	1.43510	0.717550	−	0.696507i	$-0.245263\pi$
$673$	37.2297	1.43510	0.717550	+	0.696507i	$0.245263\pi$
$674$	33.6964	1.29794
$675$	2.17403	0.0836785
$676$	−70.6476	−2.71722
$677$	12.1587	0.467295	0.233648	−	0.972321i	$-0.424934\pi$
$677$	12.1587	0.467295	0.233648	+	0.972321i	$0.424934\pi$
$678$	−0.881846	−0.0338671
$679$	28.8397	1.10677
$680$	27.2010	1.04311
$681$	−2.06602	−0.0791699
$682$	−56.7959	−2.17483
$683$	−22.4773	−0.860071	−0.430035	−	0.902812i	$-0.641499\pi$
$683$	−22.4773	−0.860071	−0.430035	+	0.902812i	$0.641499\pi$
$684$	−65.3084	−2.49713
$685$	−6.47833	−0.247524
$686$	49.6214	1.89455
$687$	−1.38164	−0.0527127
$688$	103.411	3.94250
$689$	−0.158458	−0.00603676
$690$	−2.07542	−0.0790099
$691$	6.86588	0.261190	0.130595	−	0.991436i	$-0.458311\pi$
$691$	6.86588	0.261190	0.130595	+	0.991436i	$0.458311\pi$
$692$	−123.787	−4.70568
$693$	43.9124	1.66809
$694$	36.8526	1.39890
$695$	−7.26324	−0.275510
$696$	4.50437	0.170738
$697$	5.98046	0.226526
$698$	−4.55410	−0.172375
$699$	−0.417493	−0.0157910
$700$	−50.5202	−1.90949
$701$	5.66075	0.213804	0.106902	−	0.994270i	$-0.465907\pi$
$701$	5.66075	0.213804	0.106902	+	0.994270i	$0.465907\pi$
$702$	0.952790	0.0359607
$703$	9.60798	0.362372
$704$	−183.642	−6.92126
$705$	0.0870791	0.00327959
$706$	51.0515	1.92135
$707$	−34.5174	−1.29816
$708$	2.51172	0.0943962
$709$	−40.6231	−1.52563	−0.762817	−	0.646615i	$-0.776184\pi$
$709$	−40.6231	−1.52563	−0.762817	+	0.646615i	$0.776184\pi$
$710$	−9.58361	−0.359666
$711$	−2.39469	−0.0898081
$712$	−35.6457	−1.33588
$713$	−20.7375	−0.776627
$714$	1.74748	0.0653978
$715$	−3.72213	−0.139200
$716$	13.3294	0.498143
$717$	−1.64735	−0.0615215
$718$	−66.3379	−2.47571
$719$	38.6426	1.44113	0.720564	−	0.693389i	$-0.243883\pi$
$719$	38.6426	1.44113	0.720564	+	0.693389i	$0.243883\pi$
$720$	−60.3885	−2.25055
$721$	−1.92814	−0.0718078
$722$	9.70983	0.361363
$723$	0.808119	0.0300543
$724$	86.6432	3.22007
$725$	14.2989	0.531047
$726$	−5.48190	−0.203453
$727$	16.3411	0.606059	0.303029	−	0.952981i	$-0.402002\pi$
$727$	16.3411	0.606059	0.303029	+	0.952981i	$0.402002\pi$
$728$	−14.1721	−0.525253
$729$	−26.3704	−0.976683
$730$	−28.7158	−1.06282
$731$	−14.2359	−0.526534
$732$	5.72366	0.211553
$733$	1.07390	0.0396654	0.0198327	−	0.999803i	$-0.493687\pi$
$733$	1.07390	0.0396654	0.0198327	+	0.999803i	$0.493687\pi$
$734$	−30.9528	−1.14249
$735$	0.0464504	0.00171335
$736$	−129.515	−4.77399
$737$	21.8959	0.806545
$738$	−22.6370	−0.833279
$739$	20.3002	0.746757	0.373378	−	0.927679i	$-0.378199\pi$
$739$	20.3002	0.746757	0.373378	+	0.927679i	$0.378199\pi$
$740$	17.4014	0.639687
$741$	0.227634	0.00836235
$742$	2.20440	0.0809262
$743$	−35.9993	−1.32069	−0.660343	−	0.750964i	$-0.729589\pi$
$743$	−35.9993	−1.32069	−0.660343	+	0.750964i	$0.729589\pi$
$744$	4.02672	0.147627
$745$	−24.6713	−0.903888
$746$	40.5872	1.48600
$747$	−20.8864	−0.764193
$748$	65.4337	2.39249
$749$	14.1637	0.517529
$750$	3.18477	0.116291
$751$	2.42034	0.0883195	0.0441598	−	0.999024i	$-0.485939\pi$
$751$	2.42034	0.0883195	0.0441598	+	0.999024i	$0.485939\pi$
$752$	9.90244	0.361105
$753$	−2.45182	−0.0893493
$754$	6.26662	0.228217
$755$	−16.4292	−0.597922
$756$	−9.74682	−0.354489
$757$	27.1055	0.985167	0.492584	−	0.870265i	$-0.336053\pi$
$757$	27.1055	0.985167	0.492584	+	0.870265i	$0.336053\pi$
$758$	−21.3194	−0.774354
$759$	−3.19565	−0.115995
$760$	−49.2934	−1.78806
$761$	−0.960721	−0.0348261	−0.0174131	−	0.999848i	$-0.505543\pi$
$761$	−0.960721	−0.0348261	−0.0174131	+	0.999848i	$0.505543\pi$
$762$	2.62028	0.0949229
$763$	−37.2259	−1.34767
$764$	−65.8757	−2.38330
$765$	8.31329	0.300568
$766$	32.7730	1.18414
$767$	2.23670	0.0807627
$768$	6.19991	0.223720
$769$	−25.6386	−0.924552	−0.462276	−	0.886736i	$-0.652967\pi$
$769$	−25.6386	−0.924552	−0.462276	+	0.886736i	$0.652967\pi$
$770$	51.7808	1.86605
$771$	−0.529583	−0.0190725
$772$	−24.9806	−0.899071
$773$	−2.83949	−0.102129	−0.0510646	−	0.998695i	$-0.516261\pi$
$773$	−2.83949	−0.102129	−0.0510646	+	0.998695i	$0.516261\pi$
$774$	53.8851	1.93686
$775$	12.7826	0.459165
$776$	−104.118	−3.73762
$777$	0.715562	0.0256707
$778$	48.7404	1.74743
$779$	−10.8377	−0.388301
$780$	0.412276	0.0147619
$781$	−14.7565	−0.528028
$782$	32.4903	1.16185
$783$	2.75867	0.0985869
$784$	5.28224	0.188651
$785$	−21.4403	−0.765237
$786$	−5.53751	−0.197516
$787$	42.7969	1.52554	0.762772	−	0.646668i	$-0.223838\pi$
$787$	42.7969	1.52554	0.762772	+	0.646668i	$0.223838\pi$
$788$	4.69468	0.167241
$789$	−0.364606	−0.0129803
$790$	−2.82379	−0.100466
$791$	8.03334	0.285633
$792$	−158.534	−5.63326
$793$	5.09696	0.180998
$794$	73.7444	2.61709
$795$	−0.0410472	−0.00145579
$796$	−37.9670	−1.34570
$797$	−14.3079	−0.506812	−0.253406	−	0.967360i	$-0.581551\pi$
$797$	−14.3079	−0.506812	−0.253406	+	0.967360i	$0.581551\pi$
$798$	−3.16676	−0.112102
$799$	−1.36320	−0.0482267
$800$	79.8332	2.82253
$801$	−10.8942	−0.384926
$802$	10.1648	0.358930
$803$	−44.2155	−1.56033
$804$	−2.42527	−0.0855326
$805$	18.9064	0.666364
$806$	5.60211	0.197326
$807$	0.209996	0.00739221
$808$	124.616	4.38397
$809$	51.1858	1.79960	0.899799	−	0.436305i	$-0.143713\pi$
$809$	51.1858	1.79960	0.899799	+	0.436305i	$0.143713\pi$
$810$	−31.3434	−1.10130
$811$	−17.9128	−0.629003	−0.314502	−	0.949257i	$-0.601837\pi$
$811$	−17.9128	−0.629003	−0.314502	+	0.949257i	$0.601837\pi$
$812$	−64.1061	−2.24968
$813$	−2.41237	−0.0846057
$814$	36.4375	1.27713
$815$	−4.75344	−0.166506
$816$	−3.70026	−0.129535
$817$	25.7981	0.902562
$818$	34.1786	1.19503
$819$	−4.33133	−0.151349
$820$	−19.6286	−0.685460
$821$	15.1941	0.530279	0.265139	−	0.964210i	$-0.414582\pi$
$821$	15.1941	0.530279	0.265139	+	0.964210i	$0.414582\pi$
$822$	1.50254	0.0524070
$823$	35.2424	1.22847	0.614236	−	0.789123i	$-0.289464\pi$
$823$	35.2424	1.22847	0.614236	+	0.789123i	$0.289464\pi$
$824$	6.96105	0.242500
$825$	1.96980	0.0685796
$826$	−31.1162	−1.08267
$827$	−6.74492	−0.234544	−0.117272	−	0.993100i	$-0.537415\pi$
$827$	−6.74492	−0.234544	−0.117272	+	0.993100i	$0.537415\pi$
$828$	−90.4326	−3.14275
$829$	21.7467	0.755295	0.377647	−	0.925949i	$-0.376733\pi$
$829$	21.7467	0.755295	0.377647	+	0.925949i	$0.376733\pi$
$830$	−24.6289	−0.854883
$831$	−3.38221	−0.117328
$832$	18.1137	0.627978
$833$	−0.727172	−0.0251950
$834$	1.68458	0.0583323
$835$	4.24008	0.146734
$836$	−118.578	−4.10111
$837$	2.46614	0.0852423
$838$	−31.1720	−1.07682
$839$	18.0853	0.624375	0.312187	−	0.950021i	$-0.398938\pi$
$839$	18.0853	0.624375	0.312187	+	0.950021i	$0.398938\pi$
$840$	−3.67116	−0.126667
$841$	−10.8558	−0.374340
$842$	60.6126	2.08885
$843$	0.0782444	0.00269488
$844$	123.983	4.26769
$845$	−16.2969	−0.560630
$846$	5.15994	0.177402
$847$	49.9384	1.71590
$848$	−4.66780	−0.160293
$849$	−0.177764	−0.00610083
$850$	−20.0270	−0.686921
$851$	13.3042	0.456062
$852$	1.63448	0.0559963
$853$	12.7129	0.435283	0.217641	−	0.976029i	$-0.430164\pi$
$853$	12.7129	0.435283	0.217641	+	0.976029i	$0.430164\pi$
$854$	−70.9070	−2.42639
$855$	−15.0652	−0.515220
$856$	−51.1342	−1.74773
$857$	−41.0556	−1.40243	−0.701216	−	0.712949i	$-0.747359\pi$
$857$	−41.0556	−1.40243	−0.701216	+	0.712949i	$0.747359\pi$
$858$	0.863283	0.0294720
$859$	9.13785	0.311779	0.155890	−	0.987774i	$-0.450176\pi$
$859$	9.13785	0.311779	0.155890	+	0.987774i	$0.450176\pi$
$860$	46.7239	1.59327
$861$	−0.807147	−0.0275075
$862$	25.3746	0.864264
$863$	−44.8133	−1.52546	−0.762731	−	0.646716i	$-0.776142\pi$
$863$	−44.8133	−1.52546	−0.762731	+	0.646716i	$0.776142\pi$
$864$	15.4021	0.523992
$865$	−28.5550	−0.970900
$866$	65.5291	2.22677
$867$	−1.32916	−0.0451408
$868$	−57.3083	−1.94517
$869$	−4.34796	−0.147494
$870$	1.62332	0.0550356
$871$	−2.15972	−0.0731792
$872$	134.394	4.55116
$873$	−31.8210	−1.07698
$874$	−58.8785	−1.99159
$875$	−29.0123	−0.980794
$876$	4.89747	0.165470
$877$	−40.8481	−1.37934	−0.689671	−	0.724123i	$-0.742245\pi$
$877$	−40.8481	−1.37934	−0.689671	+	0.724123i	$0.742245\pi$
$878$	−21.5975	−0.728880
$879$	2.86926	0.0967778
$880$	−109.645	−3.69614
$881$	43.4103	1.46253	0.731264	−	0.682094i	$-0.238931\pi$
$881$	43.4103	1.46253	0.731264	+	0.682094i	$0.238931\pi$
$882$	2.75246	0.0926800
$883$	−55.9905	−1.88423	−0.942116	−	0.335288i	$-0.891166\pi$
$883$	−55.9905	−1.88423	−0.942116	+	0.335288i	$0.891166\pi$
$884$	−6.45410	−0.217075
$885$	0.579400	0.0194763
$886$	12.9909	0.436439
$887$	−2.11885	−0.0711441	−0.0355721	−	0.999367i	$-0.511325\pi$
$887$	−2.11885	−0.0711441	−0.0355721	+	0.999367i	$0.511325\pi$
$888$	−2.58335	−0.0866915
$889$	−23.8700	−0.800573
$890$	−12.8463	−0.430607
$891$	−48.2614	−1.61682
$892$	80.0585	2.68056
$893$	2.47038	0.0826682
$894$	5.72209	0.191375
$895$	3.07480	0.102779
$896$	−123.171	−4.11486
$897$	0.315205	0.0105244
$898$	−105.612	−3.52431
$899$	16.2201	0.540972
$900$	55.7427	1.85809
$901$	0.642585	0.0214076
$902$	−41.1011	−1.36852
$903$	1.92134	0.0639380
$904$	−29.0022	−0.964600
$905$	19.9867	0.664381
$906$	3.81048	0.126595
$907$	−41.4664	−1.37687	−0.688435	−	0.725298i	$-0.741702\pi$
$907$	−41.4664	−1.37687	−0.688435	+	0.725298i	$0.741702\pi$
$908$	−106.154	−3.52283
$909$	38.0856	1.26322
$910$	−5.10744	−0.169310
$911$	21.0410	0.697119	0.348560	−	0.937287i	$-0.386671\pi$
$911$	21.0410	0.697119	0.348560	+	0.937287i	$0.386671\pi$
$912$	6.70557	0.222044
$913$	−37.9226	−1.25506
$914$	−44.8853	−1.48467
$915$	1.32033	0.0436486
$916$	−70.9897	−2.34557
$917$	50.4449	1.66584
$918$	−3.86380	−0.127524
$919$	−5.44581	−0.179641	−0.0898204	−	0.995958i	$-0.528629\pi$
$919$	−5.44581	−0.179641	−0.0898204	+	0.995958i	$0.528629\pi$
$920$	−68.2566	−2.25035
$921$	1.90797	0.0628698
$922$	29.0424	0.956460
$923$	1.45551	0.0479088
$924$	−8.83119	−0.290525
$925$	−8.20071	−0.269638
$926$	69.1440	2.27221
$927$	2.12746	0.0698751
$928$	101.302	3.32540
$929$	35.2603	1.15685	0.578426	−	0.815735i	$-0.303667\pi$
$929$	35.2603	1.15685	0.578426	+	0.815735i	$0.303667\pi$
$930$	1.45118	0.0475861
$931$	1.31777	0.0431882
$932$	−21.4512	−0.702656
$933$	−1.60793	−0.0526412
$934$	0.495811	0.0162234
$935$	15.0941	0.493631
$936$	15.6371	0.511115
$937$	−50.0837	−1.63616	−0.818081	−	0.575103i	$-0.804962\pi$
$937$	−50.0837	−1.63616	−0.818081	+	0.575103i	$0.804962\pi$
$938$	30.0452	0.981010
$939$	−2.60649	−0.0850596
$940$	4.47420	0.145932
$941$	5.89824	0.192277	0.0961385	−	0.995368i	$-0.469351\pi$
$941$	5.89824	0.192277	0.0961385	+	0.995368i	$0.469351\pi$
$942$	4.97271	0.162020
$943$	−15.0070	−0.488695
$944$	65.8881	2.14447
$945$	−2.24838	−0.0731399
$946$	97.8372	3.18096
$947$	37.0930	1.20536	0.602681	−	0.797982i	$-0.294099\pi$
$947$	37.0930	1.20536	0.602681	+	0.797982i	$0.294099\pi$
$948$	0.481596	0.0156415
$949$	4.36123	0.141571
$950$	36.2927	1.17749
$951$	0.637276	0.0206651
$952$	57.4713	1.86266
$953$	11.9178	0.386056	0.193028	−	0.981193i	$-0.438169\pi$
$953$	11.9178	0.386056	0.193028	+	0.981193i	$0.438169\pi$
$954$	−2.43228	−0.0787481
$955$	−15.1961	−0.491734
$956$	−84.6424	−2.73753
$957$	2.49952	0.0807980
$958$	29.2258	0.944244
$959$	−13.6876	−0.441997
$960$	4.69220	0.151440
$961$	−16.4999	−0.532254
$962$	−3.59404	−0.115876
$963$	−15.6278	−0.503600
$964$	41.5219	1.33733
$965$	−5.76248	−0.185501
$966$	−4.38502	−0.141086
$967$	−47.9758	−1.54280	−0.771399	−	0.636352i	$-0.780443\pi$
$967$	−47.9758	−1.54280	−0.771399	+	0.636352i	$0.780443\pi$
$968$	−180.289	−5.79472
$969$	−0.923112	−0.0296546
$970$	−37.5229	−1.20479
$971$	−20.1475	−0.646563	−0.323281	−	0.946303i	$-0.604786\pi$
$971$	−20.1475	−0.646563	−0.323281	+	0.946303i	$0.604786\pi$
$972$	16.1421	0.517758
$973$	−15.3460	−0.491971
$974$	43.4787	1.39315
$975$	−0.194293	−0.00622235
$976$	150.145	4.80601
$977$	−23.2869	−0.745014	−0.372507	−	0.928029i	$-0.621502\pi$
$977$	−23.2869	−0.745014	−0.372507	+	0.928029i	$0.621502\pi$
$978$	1.10248	0.0352534
$979$	−19.7801	−0.632176
$980$	2.38666	0.0762391
$981$	41.0741	1.31139
$982$	−41.1111	−1.31191
$983$	−4.79894	−0.153062	−0.0765312	−	0.997067i	$-0.524384\pi$
$983$	−4.79894	−0.153062	−0.0765312	+	0.997067i	$0.524384\pi$
$984$	2.91399	0.0928947
$985$	1.08296	0.0345060
$986$	−25.4127	−0.809305
$987$	0.183984	0.00585626
$988$	11.6960	0.372101
$989$	35.7227	1.13592
$990$	−57.1337	−1.81583
$991$	−31.9627	−1.01533	−0.507664	−	0.861555i	$-0.669491\pi$
$991$	−31.9627	−1.01533	−0.507664	+	0.861555i	$0.669491\pi$
$992$	90.5598	2.87528
$993$	0.311824	0.00989543
$994$	−20.2486	−0.642246
$995$	−8.75816	−0.277652
$996$	4.20045	0.133096
$997$	5.02717	0.159212	0.0796061	−	0.996826i	$-0.474634\pi$
$997$	5.02717	0.159212	0.0796061	+	0.996826i	$0.474634\pi$
$998$	−1.90509	−0.0603045
$999$	−1.58216	−0.0500572

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8017.2.a.a.1.6	✓	327

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8017.2.a.a.1.6	✓	327	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:	\( N \)	\(=\)	\( 8017 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8017.a (trivial)

\(f(q)\)	\(=\)	\(q-2.74897 q^{2} +0.108150 q^{3} +5.55686 q^{4} +1.28185 q^{5} -0.297303 q^{6} +2.70833 q^{7} -9.77771 q^{8} -2.98830 q^{9} +O(q^{10})\)	\(q-2.74897 q^{2} +0.108150 q^{3} +5.55686 q^{4} +1.28185 q^{5} -0.297303 q^{6} +2.70833 q^{7} -9.77771 q^{8} -2.98830 q^{9} -3.52377 q^{10} -5.42575 q^{11} +0.600976 q^{12} +0.535174 q^{13} -7.44513 q^{14} +0.138632 q^{15} +15.7650 q^{16} -2.17026 q^{17} +8.21477 q^{18} +3.93292 q^{19} +7.12305 q^{20} +0.292907 q^{21} +14.9153 q^{22} +5.44592 q^{23} -1.05746 q^{24} -3.35687 q^{25} -1.47118 q^{26} -0.647637 q^{27} +15.0498 q^{28} -4.25960 q^{29} -0.381097 q^{30} -3.80790 q^{31} -23.7821 q^{32} -0.586797 q^{33} +5.96599 q^{34} +3.47167 q^{35} -16.6056 q^{36} +2.44297 q^{37} -10.8115 q^{38} +0.0578792 q^{39} -12.5335 q^{40} -2.75564 q^{41} -0.805194 q^{42} +6.55954 q^{43} -30.1502 q^{44} -3.83055 q^{45} -14.9707 q^{46} +0.628130 q^{47} +1.70499 q^{48} +0.335062 q^{49} +9.22794 q^{50} -0.234714 q^{51} +2.97388 q^{52} -0.296087 q^{53} +1.78034 q^{54} -6.95499 q^{55} -26.4813 q^{56} +0.425346 q^{57} +11.7095 q^{58} +4.17940 q^{59} +0.770360 q^{60} +9.52394 q^{61} +10.4678 q^{62} -8.09332 q^{63} +33.8463 q^{64} +0.686011 q^{65} +1.61309 q^{66} -4.03555 q^{67} -12.0598 q^{68} +0.588978 q^{69} -9.54353 q^{70} +2.71971 q^{71} +29.2188 q^{72} +8.14919 q^{73} -6.71565 q^{74} -0.363046 q^{75} +21.8547 q^{76} -14.6947 q^{77} -0.159108 q^{78} +0.801356 q^{79} +20.2083 q^{80} +8.89487 q^{81} +7.57519 q^{82} +6.98938 q^{83} +1.62764 q^{84} -2.78194 q^{85} -18.0320 q^{86} -0.460677 q^{87} +53.0515 q^{88} +3.64560 q^{89} +10.5301 q^{90} +1.44943 q^{91} +30.2622 q^{92} -0.411826 q^{93} -1.72671 q^{94} +5.04140 q^{95} -2.57204 q^{96} +10.6485 q^{97} -0.921077 q^{98} +16.2138 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 327 q - 23 q^{2} - 48 q^{3} + 315 q^{4} - 55 q^{5} - 38 q^{6} - 87 q^{7} - 69 q^{8} + 303 q^{9}+O(q^{10}) \) 327 * q - 23 * q^2 - 48 * q^3 + 315 * q^4 - 55 * q^5 - 38 * q^6 - 87 * q^7 - 69 * q^8 + 303 * q^9	\( 327 q - 23 q^{2} - 48 q^{3} + 315 q^{4} - 55 q^{5} - 38 q^{6} - 87 q^{7} - 69 q^{8} + 303 q^{9} - 48 q^{10} - 70 q^{11} - 120 q^{12} - 53 q^{13} - 52 q^{14} - 77 q^{15} + 295 q^{16} - 164 q^{17} - 58 q^{18} - 47 q^{19} - 153 q^{20} - 39 q^{21} - 68 q^{22} - 256 q^{23} - 107 q^{24} + 288 q^{25} - 95 q^{26} - 189 q^{27} - 167 q^{28} - 99 q^{29} - 81 q^{30} - 71 q^{31} - 146 q^{32} - 95 q^{33} - 40 q^{34} - 192 q^{35} + 261 q^{36} - 54 q^{37} - 179 q^{38} - 115 q^{39} - 121 q^{40} - 111 q^{41} - 62 q^{42} - 110 q^{43} - 157 q^{44} - 137 q^{45} - 11 q^{46} - 324 q^{47} - 236 q^{48} + 296 q^{49} - 73 q^{50} - 88 q^{51} - 138 q^{52} - 170 q^{53} - 127 q^{54} - 151 q^{55} - 151 q^{56} - 106 q^{57} - 81 q^{58} - 123 q^{59} - 83 q^{60} - 62 q^{61} - 287 q^{62} - 400 q^{63} + 263 q^{64} - 143 q^{65} - 64 q^{66} - 95 q^{67} - 442 q^{68} - 22 q^{69} - 26 q^{70} - 210 q^{71} - 129 q^{72} - 121 q^{73} - 159 q^{74} - 194 q^{75} - 86 q^{76} - 178 q^{77} - 68 q^{78} - 145 q^{79} - 338 q^{80} + 259 q^{81} - 103 q^{82} - 418 q^{83} - 102 q^{84} - 40 q^{85} - 89 q^{86} - 372 q^{87} - 186 q^{88} - 100 q^{89} - 150 q^{90} - 69 q^{91} - 458 q^{92} - 81 q^{93} - 46 q^{94} - 377 q^{95} - 190 q^{96} - 87 q^{97} - 147 q^{98} - 171 q^{99}+O(q^{100}) \) 327 * q - 23 * q^2 - 48 * q^3 + 315 * q^4 - 55 * q^5 - 38 * q^6 - 87 * q^7 - 69 * q^8 + 303 * q^9 - 48 * q^10 - 70 * q^11 - 120 * q^12 - 53 * q^13 - 52 * q^14 - 77 * q^15 + 295 * q^16 - 164 * q^17 - 58 * q^18 - 47 * q^19 - 153 * q^20 - 39 * q^21 - 68 * q^22 - 256 * q^23 - 107 * q^24 + 288 * q^25 - 95 * q^26 - 189 * q^27 - 167 * q^28 - 99 * q^29 - 81 * q^30 - 71 * q^31 - 146 * q^32 - 95 * q^33 - 40 * q^34 - 192 * q^35 + 261 * q^36 - 54 * q^37 - 179 * q^38 - 115 * q^39 - 121 * q^40 - 111 * q^41 - 62 * q^42 - 110 * q^43 - 157 * q^44 - 137 * q^45 - 11 * q^46 - 324 * q^47 - 236 * q^48 + 296 * q^49 - 73 * q^50 - 88 * q^51 - 138 * q^52 - 170 * q^53 - 127 * q^54 - 151 * q^55 - 151 * q^56 - 106 * q^57 - 81 * q^58 - 123 * q^59 - 83 * q^60 - 62 * q^61 - 287 * q^62 - 400 * q^63 + 263 * q^64 - 143 * q^65 - 64 * q^66 - 95 * q^67 - 442 * q^68 - 22 * q^69 - 26 * q^70 - 210 * q^71 - 129 * q^72 - 121 * q^73 - 159 * q^74 - 194 * q^75 - 86 * q^76 - 178 * q^77 - 68 * q^78 - 145 * q^79 - 338 * q^80 + 259 * q^81 - 103 * q^82 - 418 * q^83 - 102 * q^84 - 40 * q^85 - 89 * q^86 - 372 * q^87 - 186 * q^88 - 100 * q^89 - 150 * q^90 - 69 * q^91 - 458 * q^92 - 81 * q^93 - 46 * q^94 - 377 * q^95 - 190 * q^96 - 87 * q^97 - 147 * q^98 - 171 * q^99

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