LMFDB - Embedded newform 8021.2.a.c.1.12

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8021,2,Mod(1,8021)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8021, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 0]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("8021.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8021 = 13 \cdot 617 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8021.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:	$64.0480074613$
Analytic rank:	$0$
Dimension:	$169$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.12
Character	$\chi$	$=$	8021.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.49436 q^{2} +1.22166 q^{3} +4.22181 q^{4} -2.33739 q^{5} -3.04726 q^{6} -2.97287 q^{7} -5.54199 q^{8} -1.50754 q^{9} +O(q^{10})$	\(q-2.49436 q^{2} +1.22166 q^{3} +4.22181 q^{4} -2.33739 q^{5} -3.04726 q^{6} -2.97287 q^{7} -5.54199 q^{8} -1.50754 q^{9} +5.83029 q^{10} +1.41848 q^{11} +5.15763 q^{12} -1.00000 q^{13} +7.41541 q^{14} -2.85551 q^{15} +5.38007 q^{16} -1.28698 q^{17} +3.76034 q^{18} +7.36938 q^{19} -9.86803 q^{20} -3.63185 q^{21} -3.53820 q^{22} -6.41485 q^{23} -6.77045 q^{24} +0.463404 q^{25} +2.49436 q^{26} -5.50670 q^{27} -12.5509 q^{28} -4.27815 q^{29} +7.12265 q^{30} -2.56423 q^{31} -2.33584 q^{32} +1.73291 q^{33} +3.21018 q^{34} +6.94878 q^{35} -6.36454 q^{36} -11.7195 q^{37} -18.3819 q^{38} -1.22166 q^{39} +12.9538 q^{40} +3.50633 q^{41} +9.05913 q^{42} -3.21268 q^{43} +5.98857 q^{44} +3.52371 q^{45} +16.0009 q^{46} -10.1312 q^{47} +6.57264 q^{48} +1.83798 q^{49} -1.15590 q^{50} -1.57225 q^{51} -4.22181 q^{52} -11.0482 q^{53} +13.7357 q^{54} -3.31555 q^{55} +16.4756 q^{56} +9.00290 q^{57} +10.6712 q^{58} +0.538094 q^{59} -12.0554 q^{60} +8.49392 q^{61} +6.39610 q^{62} +4.48172 q^{63} -4.93374 q^{64} +2.33739 q^{65} -4.32250 q^{66} +7.33714 q^{67} -5.43337 q^{68} -7.83679 q^{69} -17.3327 q^{70} +10.6861 q^{71} +8.35476 q^{72} +8.78270 q^{73} +29.2327 q^{74} +0.566124 q^{75} +31.1121 q^{76} -4.21698 q^{77} +3.04726 q^{78} -3.50499 q^{79} -12.5753 q^{80} -2.20472 q^{81} -8.74605 q^{82} +1.28351 q^{83} -15.3330 q^{84} +3.00817 q^{85} +8.01356 q^{86} -5.22646 q^{87} -7.86122 q^{88} -10.4129 q^{89} -8.78938 q^{90} +2.97287 q^{91} -27.0823 q^{92} -3.13262 q^{93} +25.2708 q^{94} -17.2251 q^{95} -2.85361 q^{96} +4.72191 q^{97} -4.58459 q^{98} -2.13842 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 169 q + 9 q^{2} + 9 q^{3} + 199 q^{4} + 12 q^{5} + 22 q^{6} + 36 q^{7} + 30 q^{8} + 198 q^{9}+O(q^{10}) $ 169 * q + 9 * q^2 + 9 * q^3 + 199 * q^4 + 12 * q^5 + 22 * q^6 + 36 * q^7 + 30 * q^8 + 198 * q^9	\( 169 q + 9 q^{2} + 9 q^{3} + 199 q^{4} + 12 q^{5} + 22 q^{6} + 36 q^{7} + 30 q^{8} + 198 q^{9} - 3 q^{10} + 59 q^{11} + 11 q^{12} - 169 q^{13} + 30 q^{14} + 50 q^{15} + 267 q^{16} + q^{17} + 53 q^{18} + 107 q^{19} + 48 q^{20} + 36 q^{21} + 14 q^{22} + 12 q^{23} + 78 q^{24} + 217 q^{25} - 9 q^{26} + 39 q^{27} + 99 q^{28} + 30 q^{29} - q^{30} + 106 q^{31} + 74 q^{32} + 16 q^{33} + 56 q^{34} + 46 q^{35} + 271 q^{36} + 73 q^{37} + 2 q^{38} - 9 q^{39} - 16 q^{40} + 52 q^{41} - 2 q^{42} + 64 q^{43} + 124 q^{44} + 84 q^{45} + 105 q^{46} + 55 q^{47} + 26 q^{48} + 257 q^{49} + 60 q^{50} + 117 q^{51} - 199 q^{52} + 7 q^{53} + 78 q^{54} - 4 q^{55} + 63 q^{56} + 51 q^{57} + 84 q^{58} + 98 q^{59} + 94 q^{60} + 32 q^{61} - 25 q^{62} + 128 q^{63} + 380 q^{64} - 12 q^{65} + 16 q^{66} + 170 q^{67} - 10 q^{68} + 55 q^{69} + 70 q^{70} + 124 q^{71} + 173 q^{72} + 81 q^{73} + 54 q^{74} + 120 q^{75} + 212 q^{76} + 20 q^{77} - 22 q^{78} + 92 q^{79} + 66 q^{80} + 265 q^{81} + 21 q^{82} + 62 q^{83} + 98 q^{84} + 139 q^{85} + 51 q^{86} - 33 q^{87} + 31 q^{88} + 58 q^{89} + 16 q^{90} - 36 q^{91} + 40 q^{92} + 37 q^{93} + 55 q^{94} + 23 q^{95} + 164 q^{96} + 78 q^{97} + 69 q^{98} + 307 q^{99}+O(q^{100}) \) 169 * q + 9 * q^2 + 9 * q^3 + 199 * q^4 + 12 * q^5 + 22 * q^6 + 36 * q^7 + 30 * q^8 + 198 * q^9 - 3 * q^10 + 59 * q^11 + 11 * q^12 - 169 * q^13 + 30 * q^14 + 50 * q^15 + 267 * q^16 + q^17 + 53 * q^18 + 107 * q^19 + 48 * q^20 + 36 * q^21 + 14 * q^22 + 12 * q^23 + 78 * q^24 + 217 * q^25 - 9 * q^26 + 39 * q^27 + 99 * q^28 + 30 * q^29 - q^30 + 106 * q^31 + 74 * q^32 + 16 * q^33 + 56 * q^34 + 46 * q^35 + 271 * q^36 + 73 * q^37 + 2 * q^38 - 9 * q^39 - 16 * q^40 + 52 * q^41 - 2 * q^42 + 64 * q^43 + 124 * q^44 + 84 * q^45 + 105 * q^46 + 55 * q^47 + 26 * q^48 + 257 * q^49 + 60 * q^50 + 117 * q^51 - 199 * q^52 + 7 * q^53 + 78 * q^54 - 4 * q^55 + 63 * q^56 + 51 * q^57 + 84 * q^58 + 98 * q^59 + 94 * q^60 + 32 * q^61 - 25 * q^62 + 128 * q^63 + 380 * q^64 - 12 * q^65 + 16 * q^66 + 170 * q^67 - 10 * q^68 + 55 * q^69 + 70 * q^70 + 124 * q^71 + 173 * q^72 + 81 * q^73 + 54 * q^74 + 120 * q^75 + 212 * q^76 + 20 * q^77 - 22 * q^78 + 92 * q^79 + 66 * q^80 + 265 * q^81 + 21 * q^82 + 62 * q^83 + 98 * q^84 + 139 * q^85 + 51 * q^86 - 33 * q^87 + 31 * q^88 + 58 * q^89 + 16 * q^90 - 36 * q^91 + 40 * q^92 + 37 * q^93 + 55 * q^94 + 23 * q^95 + 164 * q^96 + 78 * q^97 + 69 * q^98 + 307 * 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 $

$2$	−2.49436	−1.76378	−0.881888	−	0.471459i	$-0.843728\pi$
$2$	−2.49436	−1.76378	−0.881888	+	0.471459i	$0.843728\pi$
$3$	1.22166	0.705328	0.352664	−	0.935750i	$-0.385276\pi$
$3$	1.22166	0.705328	0.352664	+	0.935750i	$0.385276\pi$
$4$	4.22181	2.11091
$5$	−2.33739	−1.04531	−0.522657	−	0.852543i	$-0.675059\pi$
$5$	−2.33739	−1.04531	−0.522657	+	0.852543i	$0.675059\pi$
$6$	−3.04726	−1.24404
$7$	−2.97287	−1.12364	−0.561821	−	0.827259i	$-0.689899\pi$
$7$	−2.97287	−1.12364	−0.561821	+	0.827259i	$0.689899\pi$
$8$	−5.54199	−1.95939
$9$	−1.50754	−0.502513
$10$	5.83029	1.84370
$11$	1.41848	0.427689	0.213845	−	0.976868i	$-0.431401\pi$
$11$	1.41848	0.427689	0.213845	+	0.976868i	$0.431401\pi$
$12$	5.15763	1.48888
$13$	−1.00000	−0.277350
$13$	−1.00000	−0.277350
$14$	7.41541	1.98185
$15$	−2.85551	−0.737289
$16$	5.38007	1.34502
$17$	−1.28698	−0.312138	−0.156069	−	0.987746i	$-0.549882\pi$
$17$	−1.28698	−0.312138	−0.156069	+	0.987746i	$0.549882\pi$
$18$	3.76034	0.886320
$19$	7.36938	1.69065	0.845326	−	0.534251i	$-0.179406\pi$
$19$	7.36938	1.69065	0.845326	+	0.534251i	$0.179406\pi$
$20$	−9.86803	−2.20656
$21$	−3.63185	−0.792535
$22$	−3.53820	−0.754348
$23$	−6.41485	−1.33759	−0.668794	−	0.743448i	$-0.733189\pi$
$23$	−6.41485	−1.33759	−0.668794	+	0.743448i	$0.733189\pi$
$24$	−6.77045	−1.38201
$25$	0.463404	0.0926809
$26$	2.49436	0.489183
$27$	−5.50670	−1.05976
$28$	−12.5509	−2.37190
$29$	−4.27815	−0.794433	−0.397216	−	0.917725i	$-0.630024\pi$
$29$	−4.27815	−0.794433	−0.397216	+	0.917725i	$0.630024\pi$
$30$	7.12265	1.30041
$31$	−2.56423	−0.460549	−0.230274	−	0.973126i	$-0.573962\pi$
$31$	−2.56423	−0.460549	−0.230274	+	0.973126i	$0.573962\pi$
$32$	−2.33584	−0.412921
$33$	1.73291	0.301661
$34$	3.21018	0.550541
$35$	6.94878	1.17456
$36$	−6.36454	−1.06076
$37$	−11.7195	−1.92668	−0.963341	−	0.268282i	$-0.913544\pi$
$37$	−11.7195	−1.92668	−0.963341	+	0.268282i	$0.913544\pi$
$38$	−18.3819	−2.98193
$39$	−1.22166	−0.195623
$40$	12.9538	2.04818
$41$	3.50633	0.547597	0.273799	−	0.961787i	$-0.411720\pi$
$41$	3.50633	0.547597	0.273799	+	0.961787i	$0.411720\pi$
$42$	9.05913	1.39785
$43$	−3.21268	−0.489929	−0.244964	−	0.969532i	$-0.578776\pi$
$43$	−3.21268	−0.489929	−0.244964	+	0.969532i	$0.578776\pi$
$44$	5.98857	0.902811
$45$	3.52371	0.525283
$46$	16.0009	2.35921
$47$	−10.1312	−1.47778	−0.738892	−	0.673823i	$-0.764651\pi$
$47$	−10.1312	−1.47778	−0.738892	+	0.673823i	$0.764651\pi$
$48$	6.57264	0.948679
$49$	1.83798	0.262569
$50$	−1.15590	−0.163468
$51$	−1.57225	−0.220159
$52$	−4.22181	−0.585460
$53$	−11.0482	−1.51759	−0.758795	−	0.651330i	$-0.774211\pi$
$53$	−11.0482	−1.51759	−0.758795	+	0.651330i	$0.774211\pi$
$54$	13.7357	1.86919
$55$	−3.31555	−0.447069
$56$	16.4756	2.20165
$57$	9.00290	1.19246
$58$	10.6712	1.40120
$59$	0.538094	0.0700539	0.0350270	−	0.999386i	$-0.488848\pi$
$59$	0.538094	0.0700539	0.0350270	+	0.999386i	$0.488848\pi$
$60$	−12.0554	−1.55635
$61$	8.49392	1.08754	0.543768	−	0.839236i	$-0.316997\pi$
$61$	8.49392	1.08754	0.543768	+	0.839236i	$0.316997\pi$
$62$	6.39610	0.812305
$63$	4.48172	0.564644
$64$	−4.93374	−0.616717
$65$	2.33739	0.289918
$66$	−4.32250	−0.532062
$67$	7.33714	0.896374	0.448187	−	0.893940i	$-0.352070\pi$
$67$	7.33714	0.896374	0.448187	+	0.893940i	$0.352070\pi$
$68$	−5.43337	−0.658893
$69$	−7.83679	−0.943438
$70$	−17.3327	−2.07166
$71$	10.6861	1.26821	0.634106	−	0.773246i	$-0.281368\pi$
$71$	10.6861	1.26821	0.634106	+	0.773246i	$0.281368\pi$
$72$	8.35476	0.984618
$73$	8.78270	1.02794	0.513968	−	0.857809i	$-0.328175\pi$
$73$	8.78270	1.02794	0.513968	+	0.857809i	$0.328175\pi$
$74$	29.2327	3.39823
$75$	0.566124	0.0653704
$76$	31.1121	3.56881
$77$	−4.21698	−0.480569
$78$	3.04726	0.345035
$79$	−3.50499	−0.394342	−0.197171	−	0.980369i	$-0.563175\pi$
$79$	−3.50499	−0.394342	−0.197171	+	0.980369i	$0.563175\pi$
$80$	−12.5753	−1.40597
$81$	−2.20472	−0.244969
$82$	−8.74605	−0.965839
$83$	1.28351	0.140883	0.0704417	−	0.997516i	$-0.477559\pi$
$83$	1.28351	0.140883	0.0704417	+	0.997516i	$0.477559\pi$
$84$	−15.3330	−1.67297
$85$	3.00817	0.326282
$86$	8.01356	0.864124
$87$	−5.22646	−0.560336
$88$	−7.86122	−0.838009
$89$	−10.4129	−1.10376	−0.551882	−	0.833922i	$-0.686090\pi$
$89$	−10.4129	−1.10376	−0.551882	+	0.833922i	$0.686090\pi$
$90$	−8.78938	−0.926482
$91$	2.97287	0.311642
$92$	−27.0823	−2.82352
$93$	−3.13262	−0.324838
$94$	25.2708	2.60648
$95$	−17.2251	−1.76726
$96$	−2.85361	−0.291245
$97$	4.72191	0.479437	0.239719	−	0.970842i	$-0.422945\pi$
$97$	4.72191	0.479437	0.239719	+	0.970842i	$0.422945\pi$
$98$	−4.58459	−0.463113
$99$	−2.13842	−0.214919
$100$	1.95641	0.195641
$101$	0.526306	0.0523694	0.0261847	−	0.999657i	$-0.491664\pi$
$101$	0.526306	0.0523694	0.0261847	+	0.999657i	$0.491664\pi$
$102$	3.92176	0.388312
$103$	−2.59847	−0.256035	−0.128018	−	0.991772i	$-0.540861\pi$
$103$	−2.59847	−0.256035	−0.128018	+	0.991772i	$0.540861\pi$
$104$	5.54199	0.543437
$105$	8.48907	0.828448
$106$	27.5582	2.67669
$107$	−10.6562	−1.03018	−0.515089	−	0.857137i	$-0.672241\pi$
$107$	−10.6562	−1.03018	−0.515089	+	0.857137i	$0.672241\pi$
$108$	−23.2482	−2.23706
$109$	2.80612	0.268777	0.134389	−	0.990929i	$-0.457093\pi$
$109$	2.80612	0.268777	0.134389	+	0.990929i	$0.457093\pi$
$110$	8.27017	0.788530
$111$	−14.3173	−1.35894
$112$	−15.9943	−1.51132
$113$	−4.22149	−0.397124	−0.198562	−	0.980088i	$-0.563627\pi$
$113$	−4.22149	−0.397124	−0.198562	+	0.980088i	$0.563627\pi$
$114$	−22.4564	−2.10324
$115$	14.9940	1.39820
$116$	−18.0616	−1.67697
$117$	1.50754	0.139372
$118$	−1.34220	−0.123559
$119$	3.82602	0.350731
$120$	15.8252	1.44464
$121$	−8.98790	−0.817082
$122$	−21.1869	−1.91817
$123$	4.28356	0.386236
$124$	−10.8257	−0.972175
$125$	10.6038	0.948433
$126$	−11.1790	−0.995905
$127$	9.47878	0.841106	0.420553	−	0.907268i	$-0.361836\pi$
$127$	9.47878	0.841106	0.420553	+	0.907268i	$0.361836\pi$
$128$	16.9782	1.50067
$129$	−3.92481	−0.345560
$130$	−5.83029	−0.511350
$131$	−9.02310	−0.788351	−0.394176	−	0.919035i	$-0.628970\pi$
$131$	−9.02310	−0.788351	−0.394176	+	0.919035i	$0.628970\pi$
$132$	7.31602	0.636778
$133$	−21.9082	−1.89969
$134$	−18.3014	−1.58100
$135$	12.8713	1.10779
$136$	7.13241	0.611599
$137$	1.15943	0.0990571	0.0495285	−	0.998773i	$-0.484228\pi$
$137$	1.15943	0.0990571	0.0495285	+	0.998773i	$0.484228\pi$
$138$	19.5477	1.66401
$139$	16.4534	1.39556	0.697781	−	0.716311i	$-0.254171\pi$
$139$	16.4534	1.39556	0.697781	+	0.716311i	$0.254171\pi$
$140$	29.3364	2.47938
$141$	−12.3769	−1.04232
$142$	−26.6551	−2.23684
$143$	−1.41848	−0.118620
$144$	−8.11066	−0.675889
$145$	9.99972	0.830432
$146$	−21.9072	−1.81305
$147$	2.24540	0.185197
$148$	−49.4777	−4.06704
$149$	−3.39621	−0.278229	−0.139114	−	0.990276i	$-0.544426\pi$
$149$	−3.39621	−0.278229	−0.139114	+	0.990276i	$0.544426\pi$
$150$	−1.41212	−0.115299
$151$	−17.3088	−1.40857	−0.704284	−	0.709918i	$-0.748732\pi$
$151$	−17.3088	−1.40857	−0.704284	+	0.709918i	$0.748732\pi$
$152$	−40.8410	−3.31264
$153$	1.94016	0.156853
$154$	10.5186	0.847616
$155$	5.99361	0.481418
$156$	−5.15763	−0.412941
$157$	−20.5664	−1.64138	−0.820688	−	0.571376i	$-0.806410\pi$
$157$	−20.5664	−1.64138	−0.820688	+	0.571376i	$0.806410\pi$
$158$	8.74269	0.695531
$159$	−13.4972	−1.07040
$160$	5.45977	0.431632
$161$	19.0705	1.50297
$162$	5.49935	0.432070
$163$	−15.2198	−1.19211	−0.596054	−	0.802944i	$-0.703266\pi$
$163$	−15.2198	−1.19211	−0.596054	+	0.802944i	$0.703266\pi$
$164$	14.8031	1.15593
$165$	−4.05049	−0.315330
$166$	−3.20153	−0.248487
$167$	−19.1682	−1.48328	−0.741639	−	0.670800i	$-0.765951\pi$
$167$	−19.1682	−1.48328	−0.741639	+	0.670800i	$0.765951\pi$
$168$	20.1277	1.55289
$169$	1.00000	0.0769231
$170$	−7.50344	−0.575488
$171$	−11.1096	−0.849573
$172$	−13.5633	−1.03419
$173$	−15.3718	−1.16869	−0.584347	−	0.811504i	$-0.698649\pi$
$173$	−15.3718	−1.16869	−0.584347	+	0.811504i	$0.698649\pi$
$174$	13.0367	0.988307
$175$	−1.37764	−0.104140
$176$	7.63155	0.575250
$177$	0.657370	0.0494110
$178$	25.9734	1.94679
$179$	−4.13264	−0.308888	−0.154444	−	0.988002i	$-0.549359\pi$
$179$	−4.13264	−0.308888	−0.154444	+	0.988002i	$0.549359\pi$
$180$	14.8764	1.10882
$181$	−5.93620	−0.441234	−0.220617	−	0.975360i	$-0.570807\pi$
$181$	−5.93620	−0.441234	−0.220617	+	0.975360i	$0.570807\pi$
$182$	−7.41541	−0.549667
$183$	10.3767	0.767069
$184$	35.5510	2.62086
$185$	27.3932	2.01399
$186$	7.81388	0.572941
$187$	−1.82556	−0.133498
$188$	−42.7719	−3.11946
$189$	16.3707	1.19079
$190$	42.9656	3.11705
$191$	−2.03756	−0.147433	−0.0737164	−	0.997279i	$-0.523486\pi$
$191$	−2.03756	−0.147433	−0.0737164	+	0.997279i	$0.523486\pi$
$192$	−6.02737	−0.434988
$193$	−4.48959	−0.323168	−0.161584	−	0.986859i	$-0.551660\pi$
$193$	−4.48959	−0.323168	−0.161584	+	0.986859i	$0.551660\pi$
$194$	−11.7781	−0.845620
$195$	2.85551	0.204487
$196$	7.75962	0.554259
$197$	22.6973	1.61712	0.808558	−	0.588416i	$-0.200248\pi$
$197$	22.6973	1.61712	0.808558	+	0.588416i	$0.200248\pi$
$198$	5.33398	0.379069
$199$	6.38775	0.452816	0.226408	−	0.974033i	$-0.427302\pi$
$199$	6.38775	0.452816	0.226408	+	0.974033i	$0.427302\pi$
$200$	−2.56818	−0.181598
$201$	8.96352	0.632238
$202$	−1.31279	−0.0923678
$203$	12.7184	0.892657
$204$	−6.63775	−0.464736
$205$	−8.19568	−0.572411
$206$	6.48151	0.451588
$207$	9.67062	0.672155
$208$	−5.38007	−0.373041
$209$	10.4533	0.723073
$210$	−21.1748	−1.46120
$211$	−11.5367	−0.794219	−0.397110	−	0.917771i	$-0.629987\pi$
$211$	−11.5367	−0.794219	−0.397110	+	0.917771i	$0.629987\pi$
$212$	−46.6435	−3.20349
$213$	13.0549	0.894506
$214$	26.5805	1.81700
$215$	7.50929	0.512129
$216$	30.5181	2.07649
$217$	7.62313	0.517492
$218$	−6.99946	−0.474063
$219$	10.7295	0.725032
$220$	−13.9976	−0.943721
$221$	1.28698	0.0865714
$222$	35.7125	2.39687
$223$	−10.7521	−0.720014	−0.360007	−	0.932950i	$-0.617226\pi$
$223$	−10.7521	−0.720014	−0.360007	+	0.932950i	$0.617226\pi$
$224$	6.94415	0.463975
$225$	−0.698599	−0.0465733
$226$	10.5299	0.700438
$227$	−13.2425	−0.878938	−0.439469	−	0.898258i	$-0.644833\pi$
$227$	−13.2425	−0.878938	−0.439469	+	0.898258i	$0.644833\pi$
$228$	38.0086	2.51718
$229$	14.9835	0.990138	0.495069	−	0.868854i	$-0.335143\pi$
$229$	14.9835	0.990138	0.495069	+	0.868854i	$0.335143\pi$
$230$	−37.4004	−2.46611
$231$	−5.15173	−0.338959
$232$	23.7095	1.55660
$233$	−18.8710	−1.23628	−0.618139	−	0.786069i	$-0.712113\pi$
$233$	−18.8710	−1.23628	−0.618139	+	0.786069i	$0.712113\pi$
$234$	−3.76034	−0.245821
$235$	23.6806	1.54475
$236$	2.27173	0.147877
$237$	−4.28192	−0.278141
$238$	−9.54345	−0.618610
$239$	−3.62882	−0.234729	−0.117364	−	0.993089i	$-0.537445\pi$
$239$	−3.62882	−0.234729	−0.117364	+	0.993089i	$0.537445\pi$
$240$	−15.3628	−0.991667
$241$	−9.40356	−0.605736	−0.302868	−	0.953032i	$-0.597944\pi$
$241$	−9.40356	−0.605736	−0.302868	+	0.953032i	$0.597944\pi$
$242$	22.4190	1.44115
$243$	13.8267	0.886981
$244$	35.8597	2.29568
$245$	−4.29609	−0.274467
$246$	−10.6847	−0.681233
$247$	−7.36938	−0.468902
$248$	14.2109	0.902395
$249$	1.56802	0.0993690
$250$	−26.4497	−1.67282
$251$	16.7757	1.05888	0.529438	−	0.848349i	$-0.322403\pi$
$251$	16.7757	1.05888	0.529438	+	0.848349i	$0.322403\pi$
$252$	18.9210	1.19191
$253$	−9.09936	−0.572072
$254$	−23.6435	−1.48352
$255$	3.67497	0.230136
$256$	−32.4821	−2.03013
$257$	0.343395	0.0214204	0.0107102	−	0.999943i	$-0.496591\pi$
$257$	0.343395	0.0214204	0.0107102	+	0.999943i	$0.496591\pi$
$258$	9.78987	0.609491
$259$	34.8407	2.16490
$260$	9.86803	0.611989
$261$	6.44948	0.399213
$262$	22.5068	1.39048
$263$	−14.9511	−0.921926	−0.460963	−	0.887419i	$-0.652496\pi$
$263$	−14.9511	−0.921926	−0.460963	+	0.887419i	$0.652496\pi$
$264$	−9.60377	−0.591071
$265$	25.8240	1.58636
$266$	54.6469	3.35062
$267$	−12.7210	−0.778515
$268$	30.9760	1.89216
$269$	−16.6006	−1.01216	−0.506078	−	0.862488i	$-0.668905\pi$
$269$	−16.6006	−1.01216	−0.506078	+	0.862488i	$0.668905\pi$
$270$	−32.1056	−1.95389
$271$	9.83940	0.597701	0.298850	−	0.954300i	$-0.403397\pi$
$271$	9.83940	0.597701	0.298850	+	0.954300i	$0.403397\pi$
$272$	−6.92402	−0.419831
$273$	3.63185	0.219810
$274$	−2.89204	−0.174715
$275$	0.657332	0.0396386
$276$	−33.0854	−1.99151
$277$	23.6407	1.42043	0.710215	−	0.703985i	$-0.248598\pi$
$277$	23.6407	1.42043	0.710215	+	0.703985i	$0.248598\pi$
$278$	−41.0407	−2.46146
$279$	3.86567	0.231432
$280$	−38.5100	−2.30142
$281$	10.9451	0.652931	0.326466	−	0.945209i	$-0.394142\pi$
$281$	10.9451	0.652931	0.326466	+	0.945209i	$0.394142\pi$
$282$	30.8724	1.83842
$283$	18.2567	1.08525	0.542626	−	0.839975i	$-0.317430\pi$
$283$	18.2567	1.08525	0.542626	+	0.839975i	$0.317430\pi$
$284$	45.1149	2.67708
$285$	−21.0433	−1.24650
$286$	3.53820	0.209218
$287$	−10.4239	−0.615303
$288$	3.52136	0.207498
$289$	−15.3437	−0.902570
$290$	−24.9429	−1.46470
$291$	5.76859	0.338160
$292$	37.0789	2.16988
$293$	11.0719	0.646828	0.323414	−	0.946257i	$-0.395169\pi$
$293$	11.0719	0.646828	0.323414	+	0.946257i	$0.395169\pi$
$294$	−5.60082	−0.326647
$295$	−1.25774	−0.0732283
$296$	64.9496	3.77512
$297$	−7.81116	−0.453249
$298$	8.47137	0.490733
$299$	6.41485	0.370980
$300$	2.39007	0.137991
$301$	9.55088	0.550504
$302$	43.1742	2.48440
$303$	0.642968	0.0369376
$304$	39.6478	2.27396
$305$	−19.8536	−1.13682
$306$	−4.83946	−0.276654
$307$	16.4771	0.940398	0.470199	−	0.882560i	$-0.344182\pi$
$307$	16.4771	0.940398	0.470199	+	0.882560i	$0.344182\pi$
$308$	−17.8033	−1.01444
$309$	−3.17446	−0.180589
$310$	−14.9502	−0.849114
$311$	13.7519	0.779799	0.389899	−	0.920857i	$-0.372510\pi$
$311$	13.7519	0.779799	0.389899	+	0.920857i	$0.372510\pi$
$312$	6.77045	0.383301
$313$	18.6965	1.05679	0.528395	−	0.848999i	$-0.322794\pi$
$313$	18.6965	1.05679	0.528395	+	0.848999i	$0.322794\pi$
$314$	51.2999	2.89502
$315$	−10.4755	−0.590230
$316$	−14.7974	−0.832419
$317$	−17.3424	−0.974046	−0.487023	−	0.873389i	$-0.661917\pi$
$317$	−17.3424	−0.974046	−0.487023	+	0.873389i	$0.661917\pi$
$318$	33.6668	1.88794
$319$	−6.06849	−0.339770
$320$	11.5321	0.644663
$321$	−13.0184	−0.726613
$322$	−47.5687	−2.65090
$323$	−9.48421	−0.527716
$324$	−9.30790	−0.517106
$325$	−0.463404	−0.0257050
$326$	37.9636	2.10261
$327$	3.42813	0.189576
$328$	−19.4321	−1.07296
$329$	30.1187	1.66050
$330$	10.1034	0.556172
$331$	−26.1161	−1.43547	−0.717735	−	0.696316i	$-0.754821\pi$
$331$	−26.1161	−1.43547	−0.717735	+	0.696316i	$0.754821\pi$
$332$	5.41873	0.297392
$333$	17.6677	0.968181
$334$	47.8122	2.61617
$335$	−17.1498	−0.936992
$336$	−19.5396	−1.06597
$337$	14.7554	0.803776	0.401888	−	0.915689i	$-0.368354\pi$
$337$	14.7554	0.803776	0.401888	+	0.915689i	$0.368354\pi$
$338$	−2.49436	−0.135675
$339$	−5.15724	−0.280103
$340$	12.6999	0.688750
$341$	−3.63732	−0.196972
$342$	27.7113	1.49846
$343$	15.3460	0.828608
$344$	17.8046	0.959961
$345$	18.3176	0.986189
$346$	38.3427	2.06132
$347$	9.37558	0.503308	0.251654	−	0.967817i	$-0.419026\pi$
$347$	9.37558	0.503308	0.251654	+	0.967817i	$0.419026\pi$
$348$	−22.0651	−1.18282
$349$	32.6794	1.74929	0.874645	−	0.484765i	$-0.161095\pi$
$349$	32.6794	1.74929	0.874645	+	0.484765i	$0.161095\pi$
$350$	3.43633	0.183680
$351$	5.50670	0.293926
$352$	−3.31335	−0.176602
$353$	−12.2676	−0.652940	−0.326470	−	0.945207i	$-0.605859\pi$
$353$	−12.2676	−0.652940	−0.326470	+	0.945207i	$0.605859\pi$
$354$	−1.63972	−0.0871499
$355$	−24.9777	−1.32568
$356$	−43.9612	−2.32994
$357$	4.67411	0.247380
$358$	10.3083	0.544809
$359$	−7.27296	−0.383852	−0.191926	−	0.981409i	$-0.561473\pi$
$359$	−7.27296	−0.383852	−0.191926	+	0.981409i	$0.561473\pi$
$360$	−19.5284	−1.02923
$361$	35.3077	1.85830
$362$	14.8070	0.778238
$363$	−10.9802	−0.576311
$364$	12.5509	0.657847
$365$	−20.5286	−1.07452
$366$	−25.8832	−1.35294
$367$	−3.76634	−0.196601	−0.0983007	−	0.995157i	$-0.531341\pi$
$367$	−3.76634	−0.196601	−0.0983007	+	0.995157i	$0.531341\pi$
$368$	−34.5123	−1.79908
$369$	−5.28593	−0.275175
$370$	−68.3283	−3.55222
$371$	32.8450	1.70523
$372$	−13.2253	−0.685702
$373$	0.428055	0.0221638	0.0110819	−	0.999939i	$-0.496472\pi$
$373$	0.428055	0.0221638	0.0110819	+	0.999939i	$0.496472\pi$
$374$	4.55358	0.235460
$375$	12.9543	0.668956
$376$	56.1469	2.89556
$377$	4.27815	0.220336
$378$	−40.8344	−2.10029
$379$	28.9161	1.48532	0.742660	−	0.669668i	$-0.233564\pi$
$379$	28.9161	1.48532	0.742660	+	0.669668i	$0.233564\pi$
$380$	−72.7213	−3.73052
$381$	11.5799	0.593255
$382$	5.08240	0.260038
$383$	−17.3207	−0.885046	−0.442523	−	0.896757i	$-0.645917\pi$
$383$	−17.3207	−0.885046	−0.442523	+	0.896757i	$0.645917\pi$
$384$	20.7416	1.05847
$385$	9.85673	0.502345
$386$	11.1986	0.569996
$387$	4.84323	0.246195
$388$	19.9350	1.01205
$389$	0.113453	0.00575228	0.00287614	−	0.999996i	$-0.499084\pi$
$389$	0.113453	0.00575228	0.00287614	+	0.999996i	$0.499084\pi$
$390$	−7.12265	−0.360670
$391$	8.25575	0.417511
$392$	−10.1861	−0.514475
$393$	−11.0232	−0.556046
$394$	−56.6152	−2.85223
$395$	8.19254	0.412211
$396$	−9.02800	−0.453674
$397$	26.4708	1.32853	0.664265	−	0.747497i	$-0.268745\pi$
$397$	26.4708	1.32853	0.664265	+	0.747497i	$0.268745\pi$
$398$	−15.9333	−0.798665
$399$	−26.7645	−1.33990
$400$	2.49315	0.124657
$401$	−11.5656	−0.577560	−0.288780	−	0.957395i	$-0.593250\pi$
$401$	−11.5656	−0.577560	−0.288780	+	0.957395i	$0.593250\pi$
$402$	−22.3582	−1.11513
$403$	2.56423	0.127733
$404$	2.22196	0.110547
$405$	5.15329	0.256069
$406$	−31.7242	−1.57445
$407$	−16.6240	−0.824020
$408$	8.71340	0.431378
$409$	−6.21147	−0.307138	−0.153569	−	0.988138i	$-0.549077\pi$
$409$	−6.21147	−0.307138	−0.153569	+	0.988138i	$0.549077\pi$
$410$	20.4429	1.00961
$411$	1.41644	0.0698677
$412$	−10.9703	−0.540466
$413$	−1.59969	−0.0787155
$414$	−24.1220	−1.18553
$415$	−3.00006	−0.147267
$416$	2.33584	0.114524
$417$	20.1006	0.984329
$418$	−26.0744	−1.27534
$419$	17.0707	0.833960	0.416980	−	0.908916i	$-0.363089\pi$
$419$	17.0707	0.833960	0.416980	+	0.908916i	$0.363089\pi$
$420$	35.8392	1.74878
$421$	13.0373	0.635397	0.317699	−	0.948192i	$-0.397090\pi$
$421$	13.0373	0.635397	0.317699	+	0.948192i	$0.397090\pi$
$422$	28.7766	1.40083
$423$	15.2731	0.742605
$424$	61.2291	2.97355
$425$	−0.596390	−0.0289292
$426$	−32.5635	−1.57771
$427$	−25.2514	−1.22200
$428$	−44.9887	−2.17461
$429$	−1.73291	−0.0836657
$430$	−18.7308	−0.903281
$431$	−14.7607	−0.710999	−0.355500	−	0.934676i	$-0.615689\pi$
$431$	−14.7607	−0.710999	−0.355500	+	0.934676i	$0.615689\pi$
$432$	−29.6264	−1.42540
$433$	18.5813	0.892959	0.446480	−	0.894794i	$-0.352678\pi$
$433$	18.5813	0.892959	0.446480	+	0.894794i	$0.352678\pi$
$434$	−19.0148	−0.912739
$435$	12.2163	0.585727
$436$	11.8469	0.567364
$437$	−47.2734	−2.26140
$438$	−26.7632	−1.27879
$439$	−7.37082	−0.351790	−0.175895	−	0.984409i	$-0.556282\pi$
$439$	−7.37082	−0.351790	−0.175895	+	0.984409i	$0.556282\pi$
$440$	18.3748	0.875983
$441$	−2.77083	−0.131944
$442$	−3.21018	−0.152693
$443$	−6.45693	−0.306778	−0.153389	−	0.988166i	$-0.549019\pi$
$443$	−6.45693	−0.306778	−0.153389	+	0.988166i	$0.549019\pi$
$444$	−60.4451	−2.86860
$445$	24.3390	1.15378
$446$	26.8196	1.26994
$447$	−4.14903	−0.196243
$448$	14.6674	0.692969
$449$	15.4757	0.730345	0.365172	−	0.930940i	$-0.381010\pi$
$449$	15.4757	0.730345	0.365172	+	0.930940i	$0.381010\pi$
$450$	1.74256	0.0821449
$451$	4.97368	0.234201
$452$	−17.8223	−0.838291
$453$	−21.1455	−0.993502
$454$	33.0316	1.55025
$455$	−6.94878	−0.325764
$456$	−49.8940	−2.33650
$457$	22.3671	1.04629	0.523143	−	0.852245i	$-0.324759\pi$
$457$	22.3671	1.04629	0.523143	+	0.852245i	$0.324759\pi$
$458$	−37.3742	−1.74638
$459$	7.08699	0.330792
$460$	63.3019	2.95147
$461$	−26.1554	−1.21818	−0.609089	−	0.793102i	$-0.708465\pi$
$461$	−26.1554	−1.21818	−0.609089	+	0.793102i	$0.708465\pi$
$462$	12.8502	0.597847
$463$	−18.3003	−0.850486	−0.425243	−	0.905079i	$-0.639811\pi$
$463$	−18.3003	−0.850486	−0.425243	+	0.905079i	$0.639811\pi$
$464$	−23.0168	−1.06853
$465$	7.32217	0.339558
$466$	47.0709	2.18052
$467$	27.9823	1.29487	0.647433	−	0.762122i	$-0.275843\pi$
$467$	27.9823	1.29487	0.647433	+	0.762122i	$0.275843\pi$
$468$	6.36454	0.294201
$469$	−21.8124	−1.00720
$470$	−59.0677	−2.72459
$471$	−25.1252	−1.15771
$472$	−2.98211	−0.137263
$473$	−4.55713	−0.209537
$474$	10.6806	0.490578
$475$	3.41500	0.156691
$476$	16.1527	0.740359
$477$	16.6556	0.762608
$478$	9.05157	0.414009
$479$	4.88384	0.223149	0.111574	−	0.993756i	$-0.464411\pi$
$479$	4.88384	0.223149	0.111574	+	0.993756i	$0.464411\pi$
$480$	6.67000	0.304442
$481$	11.7195	0.534365
$482$	23.4558	1.06838
$483$	23.2978	1.06009
$484$	−37.9452	−1.72478
$485$	−11.0370	−0.501162
$486$	−34.4886	−1.56444
$487$	19.9330	0.903250	0.451625	−	0.892208i	$-0.350845\pi$
$487$	19.9330	0.903250	0.451625	+	0.892208i	$0.350845\pi$
$488$	−47.0732	−2.13091
$489$	−18.5935	−0.840827
$490$	10.7160	0.484099
$491$	5.00720	0.225972	0.112986	−	0.993597i	$-0.463958\pi$
$491$	5.00720	0.225972	0.112986	+	0.993597i	$0.463958\pi$
$492$	18.0844	0.815307
$493$	5.50588	0.247972
$494$	18.3819	0.827039
$495$	4.99832	0.224658
$496$	−13.7957	−0.619447
$497$	−31.7686	−1.42502
$498$	−3.91119	−0.175265
$499$	−29.2155	−1.30787	−0.653933	−	0.756552i	$-0.726882\pi$
$499$	−29.2155	−1.30787	−0.653933	+	0.756552i	$0.726882\pi$
$500$	44.7673	2.00205
$501$	−23.4171	−1.04620
$502$	−41.8447	−1.86762
$503$	0.915667	0.0408276	0.0204138	−	0.999792i	$-0.493502\pi$
$503$	0.915667	0.0408276	0.0204138	+	0.999792i	$0.493502\pi$
$504$	−24.8377	−1.10636
$505$	−1.23018	−0.0547424
$506$	22.6970	1.00901
$507$	1.22166	0.0542560
$508$	40.0176	1.77550
$509$	−41.5852	−1.84323	−0.921617	−	0.388101i	$-0.873131\pi$
$509$	−41.5852	−1.84323	−0.921617	+	0.388101i	$0.873131\pi$
$510$	−9.16668	−0.405908
$511$	−26.1099	−1.15503
$512$	47.0657	2.08003
$513$	−40.5809	−1.79169
$514$	−0.856550	−0.0377808
$515$	6.07365	0.267637
$516$	−16.5698	−0.729445
$517$	−14.3709	−0.632032
$518$	−86.9052	−3.81839
$519$	−18.7791	−0.824313
$520$	−12.9538	−0.568062
$521$	29.3716	1.28679	0.643396	−	0.765533i	$-0.277525\pi$
$521$	29.3716	1.28679	0.643396	+	0.765533i	$0.277525\pi$
$522$	−16.0873	−0.704122
$523$	6.26847	0.274101	0.137051	−	0.990564i	$-0.456238\pi$
$523$	6.26847	0.274101	0.137051	+	0.990564i	$0.456238\pi$
$524$	−38.0938	−1.66414
$525$	−1.68302	−0.0734529
$526$	37.2934	1.62607
$527$	3.30010	0.143755
$528$	9.32318	0.405740
$529$	18.1503	0.789142
$530$	−64.4143	−2.79798
$531$	−0.811198	−0.0352030
$532$	−92.4925	−4.01006
$533$	−3.50633	−0.151876
$534$	31.7308	1.37313
$535$	24.9078	1.07686
$536$	−40.6624	−1.75635
$537$	−5.04870	−0.217867
$538$	41.4078	1.78522
$539$	2.60715	0.112298
$540$	54.3402	2.33843
$541$	24.3271	1.04590	0.522952	−	0.852362i	$-0.324831\pi$
$541$	24.3271	1.04590	0.522952	+	0.852362i	$0.324831\pi$
$542$	−24.5430	−1.05421
$543$	−7.25204	−0.311215
$544$	3.00617	0.128888
$545$	−6.55900	−0.280957
$546$	−9.05913	−0.387695
$547$	−19.6167	−0.838749	−0.419375	−	0.907813i	$-0.637751\pi$
$547$	−19.6167	−0.838749	−0.419375	+	0.907813i	$0.637751\pi$
$548$	4.89491	0.209100
$549$	−12.8049	−0.546500
$550$	−1.63962	−0.0699136
$551$	−31.5273	−1.34311
$552$	43.4314	1.84856
$553$	10.4199	0.443099
$554$	−58.9683	−2.50532
$555$	33.4652	1.42052
$556$	69.4633	2.94590
$557$	39.2764	1.66419	0.832097	−	0.554630i	$-0.187140\pi$
$557$	39.2764	1.66419	0.832097	+	0.554630i	$0.187140\pi$
$558$	−9.64236	−0.408194
$559$	3.21268	0.135882
$560$	37.3849	1.57980
$561$	−2.23021	−0.0941597
$562$	−27.3010	−1.15162
$563$	2.36937	0.0998572	0.0499286	−	0.998753i	$-0.484101\pi$
$563$	2.36937	0.0998572	0.0499286	+	0.998753i	$0.484101\pi$
$564$	−52.2529	−2.20025
$565$	9.86727	0.415119
$566$	−45.5388	−1.91414
$567$	6.55435	0.275257
$568$	−59.2225	−2.48492
$569$	−22.9722	−0.963045	−0.481523	−	0.876434i	$-0.659916\pi$
$569$	−22.9722	−0.963045	−0.481523	+	0.876434i	$0.659916\pi$
$570$	52.4895	2.19854
$571$	−30.1747	−1.26277	−0.631385	−	0.775469i	$-0.717513\pi$
$571$	−30.1747	−1.26277	−0.631385	+	0.775469i	$0.717513\pi$
$572$	−5.98857	−0.250395
$573$	−2.48922	−0.103988
$574$	26.0009	1.08526
$575$	−2.97267	−0.123969
$576$	7.43780	0.309908
$577$	43.2110	1.79890	0.899448	−	0.437028i	$-0.143969\pi$
$577$	43.2110	1.79890	0.899448	+	0.437028i	$0.143969\pi$
$578$	38.2726	1.59193
$579$	−5.48477	−0.227939
$580$	42.2169	1.75296
$581$	−3.81571	−0.158302
$582$	−14.3889	−0.596439
$583$	−15.6717	−0.649056
$584$	−48.6736	−2.01413
$585$	−3.52371	−0.145687
$586$	−27.6173	−1.14086
$587$	−3.05765	−0.126203	−0.0631013	−	0.998007i	$-0.520099\pi$
$587$	−3.05765	−0.126203	−0.0631013	+	0.998007i	$0.520099\pi$
$588$	9.47965	0.390934
$589$	−18.8968	−0.778628
$590$	3.13725	0.129158
$591$	27.7285	1.14060
$592$	−63.0520	−2.59142
$593$	16.0425	0.658786	0.329393	−	0.944193i	$-0.393156\pi$
$593$	16.0425	0.658786	0.329393	+	0.944193i	$0.393156\pi$
$594$	19.4838	0.799431
$595$	−8.94291	−0.366623
$596$	−14.3382	−0.587315
$597$	7.80368	0.319383
$598$	−16.0009	−0.654326
$599$	31.1018	1.27079	0.635393	−	0.772189i	$-0.280838\pi$
$599$	31.1018	1.27079	0.635393	+	0.772189i	$0.280838\pi$
$600$	−3.13745	−0.128086
$601$	1.78030	0.0726201	0.0363101	−	0.999341i	$-0.488440\pi$
$601$	1.78030	0.0726201	0.0363101	+	0.999341i	$0.488440\pi$
$602$	−23.8233	−0.970965
$603$	−11.0610	−0.450439
$604$	−73.0744	−2.97335
$605$	21.0083	0.854107
$606$	−1.60379	−0.0651496
$607$	36.0691	1.46400	0.732000	−	0.681305i	$-0.238587\pi$
$607$	36.0691	1.46400	0.732000	+	0.681305i	$0.238587\pi$
$608$	−17.2137	−0.698106
$609$	15.5376	0.629616
$610$	49.5220	2.00509
$611$	10.1312	0.409864
$612$	8.19101	0.331102
$613$	−4.36004	−0.176100	−0.0880502	−	0.996116i	$-0.528064\pi$
$613$	−4.36004	−0.176100	−0.0880502	+	0.996116i	$0.528064\pi$
$614$	−41.0998	−1.65865
$615$	−10.0124	−0.403738
$616$	23.3704	0.941622
$617$	1.00000	0.0402585
$617$	1.00000	0.0402585
$618$	7.91823	0.318518
$619$	−6.30868	−0.253567	−0.126784	−	0.991930i	$-0.540465\pi$
$619$	−6.30868	−0.253567	−0.126784	+	0.991930i	$0.540465\pi$
$620$	25.3039	1.01623
$621$	35.3246	1.41753
$622$	−34.3021	−1.37539
$623$	30.9562	1.24023
$624$	−6.57264	−0.263116
$625$	−27.1023	−1.08409
$626$	−46.6358	−1.86394
$627$	12.7705	0.510004
$628$	−86.8274	−3.46479
$629$	15.0828	0.601389
$630$	26.1297	1.04103
$631$	−14.5844	−0.580597	−0.290299	−	0.956936i	$-0.593755\pi$
$631$	−14.5844	−0.580597	−0.290299	+	0.956936i	$0.593755\pi$
$632$	19.4246	0.772670
$633$	−14.0940	−0.560185
$634$	43.2581	1.71800
$635$	−22.1556	−0.879220
$636$	−56.9827	−2.25951
$637$	−1.83798	−0.0728236
$638$	15.1370	0.599279
$639$	−16.1098	−0.637293
$640$	−39.6847	−1.56867
$641$	37.9321	1.49823	0.749115	−	0.662440i	$-0.230479\pi$
$641$	37.9321	1.49823	0.749115	+	0.662440i	$0.230479\pi$
$642$	32.4724	1.28158
$643$	12.8461	0.506601	0.253301	−	0.967388i	$-0.418484\pi$
$643$	12.8461	0.506601	0.253301	+	0.967388i	$0.418484\pi$
$644$	80.5122	3.17263
$645$	9.17382	0.361219
$646$	23.6570	0.930772
$647$	18.4071	0.723659	0.361829	−	0.932244i	$-0.382152\pi$
$647$	18.4071	0.723659	0.361829	+	0.932244i	$0.382152\pi$
$648$	12.2185	0.479989
$649$	0.763278	0.0299613
$650$	1.15590	0.0453379
$651$	9.31290	0.365001
$652$	−64.2552	−2.51643
$653$	−15.2036	−0.594961	−0.297481	−	0.954728i	$-0.596146\pi$
$653$	−15.2036	−0.594961	−0.297481	+	0.954728i	$0.596146\pi$
$654$	−8.55099	−0.334370
$655$	21.0905	0.824075
$656$	18.8643	0.736529
$657$	−13.2402	−0.516551
$658$	−75.1268	−2.92875
$659$	14.8269	0.577575	0.288788	−	0.957393i	$-0.406748\pi$
$659$	14.8269	0.577575	0.288788	+	0.957393i	$0.406748\pi$
$660$	−17.1004	−0.665633
$661$	10.6124	0.412773	0.206387	−	0.978471i	$-0.433830\pi$
$661$	10.6124	0.412773	0.206387	+	0.978471i	$0.433830\pi$
$662$	65.1429	2.53185
$663$	1.57225	0.0610612
$664$	−7.11320	−0.276046
$665$	51.2082	1.98577
$666$	−44.0694	−1.70766
$667$	27.4437	1.06262
$668$	−80.9244	−3.13106
$669$	−13.1355	−0.507846
$670$	42.7776	1.65264
$671$	12.0485	0.465127
$672$	8.48341	0.327255
$673$	49.5986	1.91188	0.955942	−	0.293556i	$-0.0948387\pi$
$673$	49.5986	1.91188	0.955942	+	0.293556i	$0.0948387\pi$
$674$	−36.8052	−1.41768
$675$	−2.55183	−0.0982198
$676$	4.22181	0.162377
$677$	2.75014	0.105696	0.0528482	−	0.998603i	$-0.483170\pi$
$677$	2.75014	0.105696	0.0528482	+	0.998603i	$0.483170\pi$
$678$	12.8640	0.494038
$679$	−14.0376	−0.538715
$680$	−16.6712	−0.639313
$681$	−16.1779	−0.619939
$682$	9.07276	0.347414
$683$	−21.3050	−0.815212	−0.407606	−	0.913158i	$-0.633636\pi$
$683$	−21.3050	−0.815212	−0.407606	+	0.913158i	$0.633636\pi$
$684$	−46.9027	−1.79337
$685$	−2.71005	−0.103546
$686$	−38.2785	−1.46148
$687$	18.3048	0.698372
$688$	−17.2844	−0.658963
$689$	11.0482	0.420904
$690$	−45.6907	−1.73942
$691$	−5.06602	−0.192720	−0.0963602	−	0.995347i	$-0.530720\pi$
$691$	−5.06602	−0.192720	−0.0963602	+	0.995347i	$0.530720\pi$
$692$	−64.8967	−2.46700
$693$	6.35725	0.241492
$694$	−23.3860	−0.887722
$695$	−38.4581	−1.45880
$696$	28.9650	1.09792
$697$	−4.51257	−0.170926
$698$	−81.5141	−3.08535
$699$	−23.0540	−0.871981
$700$	−5.81615	−0.219830
$701$	−9.67818	−0.365540	−0.182770	−	0.983156i	$-0.558506\pi$
$701$	−9.67818	−0.365540	−0.182770	+	0.983156i	$0.558506\pi$
$702$	−13.7357	−0.518419
$703$	−86.3657	−3.25735
$704$	−6.99843	−0.263763
$705$	28.9297	1.08955
$706$	30.5999	1.15164
$707$	−1.56464	−0.0588444
$708$	2.77529	0.104302
$709$	−38.5711	−1.44857	−0.724284	−	0.689501i	$-0.757830\pi$
$709$	−38.5711	−1.44857	−0.724284	+	0.689501i	$0.757830\pi$
$710$	62.3033	2.33820
$711$	5.28390	0.198162
$712$	57.7081	2.16270
$713$	16.4491	0.616025
$714$	−11.6589	−0.436323
$715$	3.31555	0.123995
$716$	−17.4472	−0.652034
$717$	−4.43320	−0.165561
$718$	18.1414	0.677030
$719$	18.2022	0.678826	0.339413	−	0.940637i	$-0.389772\pi$
$719$	18.2022	0.678826	0.339413	+	0.940637i	$0.389772\pi$
$720$	18.9578	0.706516
$721$	7.72493	0.287691
$722$	−88.0700	−3.27763
$723$	−11.4880	−0.427243
$724$	−25.0615	−0.931404
$725$	−1.98251	−0.0736287
$726$	27.3885	1.01648
$727$	32.3277	1.19897	0.599483	−	0.800387i	$-0.295373\pi$
$727$	32.3277	1.19897	0.599483	+	0.800387i	$0.295373\pi$
$728$	−16.4756	−0.610628
$729$	23.5057	0.870581
$730$	51.2057	1.89521
$731$	4.13464	0.152925
$732$	43.8085	1.61921
$733$	40.7021	1.50337	0.751683	−	0.659525i	$-0.229242\pi$
$733$	40.7021	1.50337	0.751683	+	0.659525i	$0.229242\pi$
$734$	9.39459	0.346761
$735$	−5.24838	−0.193589
$736$	14.9840	0.552319
$737$	10.4076	0.383369
$738$	13.1850	0.485346
$739$	−0.359462	−0.0132230	−0.00661152	−	0.999978i	$-0.502105\pi$
$739$	−0.359462	−0.0132230	−0.00661152	+	0.999978i	$0.502105\pi$
$740$	115.649	4.25134
$741$	−9.00290	−0.330730
$742$	−81.9271	−3.00764
$743$	36.9548	1.35574	0.677871	−	0.735181i	$-0.262903\pi$
$743$	36.9548	1.35574	0.677871	+	0.735181i	$0.262903\pi$
$744$	17.3610	0.636484
$745$	7.93829	0.290836
$746$	−1.06772	−0.0390920
$747$	−1.93494	−0.0707957
$748$	−7.70715	−0.281801
$749$	31.6797	1.15755
$750$	−32.3126	−1.17989
$751$	−14.8316	−0.541214	−0.270607	−	0.962690i	$-0.587224\pi$
$751$	−14.8316	−0.541214	−0.270607	+	0.962690i	$0.587224\pi$
$752$	−54.5065	−1.98765
$753$	20.4943	0.746855
$754$	−10.6712	−0.388623
$755$	40.4574	1.47240
$756$	69.1141	2.51365
$757$	−15.8925	−0.577624	−0.288812	−	0.957386i	$-0.593260\pi$
$757$	−15.8925	−0.577624	−0.288812	+	0.957386i	$0.593260\pi$
$758$	−72.1271	−2.61977
$759$	−11.1164	−0.403498
$760$	95.4615	3.46275
$761$	41.0427	1.48780	0.743898	−	0.668294i	$-0.232975\pi$
$761$	41.0427	1.48780	0.743898	+	0.668294i	$0.232975\pi$
$762$	−28.8844	−1.04637
$763$	−8.34224	−0.302009
$764$	−8.60220	−0.311217
$765$	−4.53493	−0.163961
$766$	43.2040	1.56102
$767$	−0.538094	−0.0194295
$768$	−39.6822	−1.43191
$769$	16.2031	0.584300	0.292150	−	0.956372i	$-0.405629\pi$
$769$	16.2031	0.584300	0.292150	+	0.956372i	$0.405629\pi$
$770$	−24.5862	−0.886025
$771$	0.419514	0.0151084
$772$	−18.9542	−0.682177
$773$	−6.13282	−0.220582	−0.110291	−	0.993899i	$-0.535178\pi$
$773$	−6.13282	−0.220582	−0.110291	+	0.993899i	$0.535178\pi$
$774$	−12.0807	−0.434233
$775$	−1.18827	−0.0426841
$776$	−26.1688	−0.939404
$777$	42.5637	1.52696
$778$	−0.282991	−0.0101457
$779$	25.8395	0.925796
$780$	12.0554	0.431653
$781$	15.1581	0.542401
$782$	−20.5928	−0.736397
$783$	23.5585	0.841911
$784$	9.88849	0.353160
$785$	48.0717	1.71575
$786$	27.4958	0.980741
$787$	22.3758	0.797612	0.398806	−	0.917035i	$-0.369425\pi$
$787$	22.3758	0.797612	0.398806	+	0.917035i	$0.369425\pi$
$788$	95.8238	3.41358
$789$	−18.2653	−0.650260
$790$	−20.4351	−0.727048
$791$	12.5499	0.446225
$792$	11.8511	0.421110
$793$	−8.49392	−0.301628
$794$	−66.0276	−2.34323
$795$	31.5483	1.11890
$796$	26.9679	0.955851
$797$	21.3715	0.757019	0.378509	−	0.925597i	$-0.376437\pi$
$797$	21.3715	0.757019	0.378509	+	0.925597i	$0.376437\pi$
$798$	66.7602	2.36328
$799$	13.0386	0.461272
$800$	−1.08244	−0.0382699
$801$	15.6978	0.554655
$802$	28.8488	1.01869
$803$	12.4581	0.439637
$804$	37.8423	1.33459
$805$	−44.5753	−1.57107
$806$	−6.39610	−0.225293
$807$	−20.2803	−0.713901
$808$	−2.91678	−0.102612
$809$	24.1417	0.848777	0.424388	−	0.905480i	$-0.360489\pi$
$809$	24.1417	0.848777	0.424388	+	0.905480i	$0.360489\pi$
$810$	−12.8541	−0.451648
$811$	−55.7377	−1.95721	−0.978607	−	0.205739i	$-0.934040\pi$
$811$	−55.7377	−1.95721	−0.978607	+	0.205739i	$0.934040\pi$
$812$	53.6947	1.88432
$813$	12.0204	0.421575
$814$	41.4661	1.45339
$815$	35.5747	1.24613
$816$	−8.45883	−0.296118
$817$	−23.6754	−0.828298
$818$	15.4936	0.541722
$819$	−4.48172	−0.156604
$820$	−34.6006	−1.20831
$821$	29.0772	1.01480	0.507401	−	0.861710i	$-0.330606\pi$
$821$	29.0772	1.01480	0.507401	+	0.861710i	$0.330606\pi$
$822$	−3.53310	−0.123231
$823$	−28.4658	−0.992254	−0.496127	−	0.868250i	$-0.665245\pi$
$823$	−28.4658	−0.992254	−0.496127	+	0.868250i	$0.665245\pi$
$824$	14.4007	0.501672
$825$	0.803038	0.0279582
$826$	3.99019	0.138836
$827$	−16.3826	−0.569680	−0.284840	−	0.958575i	$-0.591940\pi$
$827$	−16.3826	−0.569680	−0.284840	+	0.958575i	$0.591940\pi$
$828$	40.8276	1.41886
$829$	−3.14296	−0.109160	−0.0545798	−	0.998509i	$-0.517382\pi$
$829$	−3.14296	−0.109160	−0.0545798	+	0.998509i	$0.517382\pi$
$830$	7.48323	0.259747
$831$	28.8810	1.00187
$832$	4.93374	0.171047
$833$	−2.36544	−0.0819577
$834$	−50.1380	−1.73614
$835$	44.8035	1.55049
$836$	44.1321	1.52634
$837$	14.1204	0.488073
$838$	−42.5805	−1.47092
$839$	48.8084	1.68505	0.842526	−	0.538655i	$-0.181067\pi$
$839$	48.8084	1.68505	0.842526	+	0.538655i	$0.181067\pi$
$840$	−47.0463	−1.62325
$841$	−10.6974	−0.368876
$842$	−32.5196	−1.12070
$843$	13.3713	0.460531
$844$	−48.7058	−1.67652
$845$	−2.33739	−0.0804088
$846$	−38.0966	−1.30979
$847$	26.7199	0.918107
$848$	−59.4402	−2.04119
$849$	22.3036	0.765458
$850$	1.48761	0.0510246
$851$	75.1791	2.57711
$852$	55.1153	1.88822
$853$	40.4780	1.38594	0.692971	−	0.720965i	$-0.256301\pi$
$853$	40.4780	1.38594	0.692971	+	0.720965i	$0.256301\pi$
$854$	62.9859	2.15533
$855$	25.9675	0.888071
$856$	59.0568	2.01852
$857$	47.4644	1.62135	0.810677	−	0.585493i	$-0.199099\pi$
$857$	47.4644	1.62135	0.810677	+	0.585493i	$0.199099\pi$
$858$	4.32250	0.147568
$859$	38.6371	1.31828	0.659140	−	0.752020i	$-0.270920\pi$
$859$	38.6371	1.31828	0.659140	+	0.752020i	$0.270920\pi$
$860$	31.7028	1.08106
$861$	−12.7345	−0.433990
$862$	36.8185	1.25404
$863$	−55.0293	−1.87322	−0.936609	−	0.350376i	$-0.886054\pi$
$863$	−55.0293	−1.87322	−0.936609	+	0.350376i	$0.886054\pi$
$864$	12.8627	0.437599
$865$	35.9299	1.22165
$866$	−46.3483	−1.57498
$867$	−18.7448	−0.636608
$868$	32.1834	1.09238
$869$	−4.97177	−0.168656
$870$	−30.4718	−1.03309
$871$	−7.33714	−0.248609
$872$	−15.5515	−0.526640
$873$	−7.11846	−0.240923
$874$	117.917	3.98859
$875$	−31.5238	−1.06570
$876$	45.2979	1.53048
$877$	14.7724	0.498829	0.249415	−	0.968397i	$-0.419762\pi$
$877$	14.7724	0.498829	0.249415	+	0.968397i	$0.419762\pi$
$878$	18.3855	0.620479
$879$	13.5262	0.456226
$880$	−17.8379	−0.601316
$881$	−38.8747	−1.30972	−0.654861	−	0.755750i	$-0.727273\pi$
$881$	−38.8747	−1.30972	−0.654861	+	0.755750i	$0.727273\pi$
$882$	6.91144	0.232720
$883$	−19.4598	−0.654874	−0.327437	−	0.944873i	$-0.606185\pi$
$883$	−19.4598	−0.654874	−0.327437	+	0.944873i	$0.606185\pi$
$884$	5.43337	0.182744
$885$	−1.53653	−0.0516500
$886$	16.1059	0.541088
$887$	−33.7925	−1.13464	−0.567321	−	0.823497i	$-0.692020\pi$
$887$	−33.7925	−1.13464	−0.567321	+	0.823497i	$0.692020\pi$
$888$	79.3466	2.66270
$889$	−28.1792	−0.945101
$890$	−60.7101	−2.03501
$891$	−3.12736	−0.104770
$892$	−45.3934	−1.51988
$893$	−74.6605	−2.49842
$894$	10.3492	0.346128
$895$	9.65960	0.322885
$896$	−50.4740	−1.68622
$897$	7.83679	0.261663
$898$	−38.6020	−1.28816
$899$	10.9702	0.365875
$900$	−2.94936	−0.0983118
$901$	14.2188	0.473697
$902$	−12.4061	−0.413079
$903$	11.6680	0.388286
$904$	23.3954	0.778121
$905$	13.8752	0.461228
$906$	52.7444	1.75232
$907$	46.3184	1.53798	0.768988	−	0.639263i	$-0.220760\pi$
$907$	46.3184	1.53798	0.768988	+	0.639263i	$0.220760\pi$
$908$	−55.9075	−1.85535
$909$	−0.793425	−0.0263163
$910$	17.3327	0.574574
$911$	−21.3944	−0.708828	−0.354414	−	0.935089i	$-0.615320\pi$
$911$	−21.3944	−0.708828	−0.354414	+	0.935089i	$0.615320\pi$
$912$	48.4363	1.60388
$913$	1.82064	0.0602543
$914$	−55.7914	−1.84542
$915$	−24.2545	−0.801828
$916$	63.2575	2.09009
$917$	26.8245	0.885824
$918$	−17.6775	−0.583443
$919$	−17.0810	−0.563451	−0.281726	−	0.959495i	$-0.590907\pi$
$919$	−17.0810	−0.563451	−0.281726	+	0.959495i	$0.590907\pi$
$920$	−83.0967	−2.73962
$921$	20.1295	0.663289
$922$	65.2408	2.14859
$923$	−10.6861	−0.351739
$924$	−21.7496	−0.715510
$925$	−5.43089	−0.178566
$926$	45.6474	1.50007
$927$	3.91729	0.128661
$928$	9.99306	0.328038
$929$	−46.2450	−1.51725	−0.758625	−	0.651527i	$-0.774129\pi$
$929$	−46.2450	−1.51725	−0.758625	+	0.651527i	$0.774129\pi$
$930$	−18.2641	−0.598904
$931$	13.5448	0.443913
$932$	−79.6696	−2.60967
$933$	16.8002	0.550014
$934$	−69.7978	−2.28385
$935$	4.26704	0.139547
$936$	−8.35476	−0.273084
$937$	−10.9404	−0.357407	−0.178704	−	0.983903i	$-0.557190\pi$
$937$	−10.9404	−0.357407	−0.178704	+	0.983903i	$0.557190\pi$
$938$	54.4079	1.77648
$939$	22.8409	0.745383
$940$	99.9748	3.26082
$941$	−10.2180	−0.333097	−0.166549	−	0.986033i	$-0.553262\pi$
$941$	−10.2180	−0.333097	−0.166549	+	0.986033i	$0.553262\pi$
$942$	62.6712	2.04194
$943$	−22.4926	−0.732460
$944$	2.89499	0.0942238
$945$	−38.2648	−1.24475
$946$	11.3671	0.369576
$947$	33.2958	1.08197	0.540984	−	0.841033i	$-0.318052\pi$
$947$	33.2958	1.08197	0.540984	+	0.841033i	$0.318052\pi$
$948$	−18.0775	−0.587129
$949$	−8.78270	−0.285098
$950$	−8.51823	−0.276368
$951$	−21.1866	−0.687022
$952$	−21.2038	−0.687218
$953$	−35.3698	−1.14574	−0.572871	−	0.819646i	$-0.694170\pi$
$953$	−35.3698	−1.14574	−0.572871	+	0.819646i	$0.694170\pi$
$954$	−41.5450	−1.34507
$955$	4.76258	0.154114
$956$	−15.3202	−0.495491
$957$	−7.41366	−0.239649
$958$	−12.1820	−0.393584
$959$	−3.44685	−0.111305
$960$	14.0883	0.454699
$961$	−24.4247	−0.787895
$962$	−29.2327	−0.942500
$963$	16.0647	0.517678
$964$	−39.7000	−1.27865
$965$	10.4939	0.337812
$966$	−58.1130	−1.86975
$967$	58.3618	1.87679	0.938395	−	0.345565i	$-0.112313\pi$
$967$	58.3618	1.87679	0.938395	+	0.345565i	$0.112313\pi$
$968$	49.8109	1.60098
$969$	−11.5865	−0.372213
$970$	27.5301	0.883938
$971$	−4.32728	−0.138869	−0.0694345	−	0.997587i	$-0.522119\pi$
$971$	−4.32728	−0.138869	−0.0694345	+	0.997587i	$0.522119\pi$
$972$	58.3736	1.87233
$973$	−48.9140	−1.56811
$974$	−49.7199	−1.59313
$975$	−0.566124	−0.0181305
$976$	45.6979	1.46275
$977$	9.47131	0.303014	0.151507	−	0.988456i	$-0.451587\pi$
$977$	9.47131	0.303014	0.151507	+	0.988456i	$0.451587\pi$
$978$	46.3788	1.48303
$979$	−14.7705	−0.472067
$980$	−18.1373	−0.579374
$981$	−4.23033	−0.135064
$982$	−12.4898	−0.398564
$983$	17.8366	0.568900	0.284450	−	0.958691i	$-0.408189\pi$
$983$	17.8366	0.568900	0.284450	+	0.958691i	$0.408189\pi$
$984$	−23.7395	−0.756786
$985$	−53.0525	−1.69039
$986$	−13.7336	−0.437368
$987$	36.7950	1.17120
$988$	−31.1121	−0.989809
$989$	20.6088	0.655323
$990$	−12.4676	−0.396246
$991$	−36.2577	−1.15176	−0.575881	−	0.817533i	$-0.695341\pi$
$991$	−36.2577	−1.15176	−0.575881	+	0.817533i	$0.695341\pi$
$992$	5.98962	0.190170
$993$	−31.9051	−1.01248
$994$	79.2422	2.51341
$995$	−14.9307	−0.473334
$996$	6.61987	0.209759
$997$	5.21008	0.165005	0.0825024	−	0.996591i	$-0.473709\pi$
$997$	5.21008	0.165005	0.0825024	+	0.996591i	$0.473709\pi$
$998$	72.8739	2.30678
$999$	64.5360	2.04183

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8021.2.a.c.1.12	✓	169

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8021.2.a.c.1.12	✓	169	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:	\( N \)	\(=\)	\( 8021 = 13 \cdot 617 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8021.a (trivial)

\(f(q)\)	\(=\)	\(q-2.49436 q^{2} +1.22166 q^{3} +4.22181 q^{4} -2.33739 q^{5} -3.04726 q^{6} -2.97287 q^{7} -5.54199 q^{8} -1.50754 q^{9} +O(q^{10})\)	\(q-2.49436 q^{2} +1.22166 q^{3} +4.22181 q^{4} -2.33739 q^{5} -3.04726 q^{6} -2.97287 q^{7} -5.54199 q^{8} -1.50754 q^{9} +5.83029 q^{10} +1.41848 q^{11} +5.15763 q^{12} -1.00000 q^{13} +7.41541 q^{14} -2.85551 q^{15} +5.38007 q^{16} -1.28698 q^{17} +3.76034 q^{18} +7.36938 q^{19} -9.86803 q^{20} -3.63185 q^{21} -3.53820 q^{22} -6.41485 q^{23} -6.77045 q^{24} +0.463404 q^{25} +2.49436 q^{26} -5.50670 q^{27} -12.5509 q^{28} -4.27815 q^{29} +7.12265 q^{30} -2.56423 q^{31} -2.33584 q^{32} +1.73291 q^{33} +3.21018 q^{34} +6.94878 q^{35} -6.36454 q^{36} -11.7195 q^{37} -18.3819 q^{38} -1.22166 q^{39} +12.9538 q^{40} +3.50633 q^{41} +9.05913 q^{42} -3.21268 q^{43} +5.98857 q^{44} +3.52371 q^{45} +16.0009 q^{46} -10.1312 q^{47} +6.57264 q^{48} +1.83798 q^{49} -1.15590 q^{50} -1.57225 q^{51} -4.22181 q^{52} -11.0482 q^{53} +13.7357 q^{54} -3.31555 q^{55} +16.4756 q^{56} +9.00290 q^{57} +10.6712 q^{58} +0.538094 q^{59} -12.0554 q^{60} +8.49392 q^{61} +6.39610 q^{62} +4.48172 q^{63} -4.93374 q^{64} +2.33739 q^{65} -4.32250 q^{66} +7.33714 q^{67} -5.43337 q^{68} -7.83679 q^{69} -17.3327 q^{70} +10.6861 q^{71} +8.35476 q^{72} +8.78270 q^{73} +29.2327 q^{74} +0.566124 q^{75} +31.1121 q^{76} -4.21698 q^{77} +3.04726 q^{78} -3.50499 q^{79} -12.5753 q^{80} -2.20472 q^{81} -8.74605 q^{82} +1.28351 q^{83} -15.3330 q^{84} +3.00817 q^{85} +8.01356 q^{86} -5.22646 q^{87} -7.86122 q^{88} -10.4129 q^{89} -8.78938 q^{90} +2.97287 q^{91} -27.0823 q^{92} -3.13262 q^{93} +25.2708 q^{94} -17.2251 q^{95} -2.85361 q^{96} +4.72191 q^{97} -4.58459 q^{98} -2.13842 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 169 q + 9 q^{2} + 9 q^{3} + 199 q^{4} + 12 q^{5} + 22 q^{6} + 36 q^{7} + 30 q^{8} + 198 q^{9}+O(q^{10}) \) 169 * q + 9 * q^2 + 9 * q^3 + 199 * q^4 + 12 * q^5 + 22 * q^6 + 36 * q^7 + 30 * q^8 + 198 * q^9	\( 169 q + 9 q^{2} + 9 q^{3} + 199 q^{4} + 12 q^{5} + 22 q^{6} + 36 q^{7} + 30 q^{8} + 198 q^{9} - 3 q^{10} + 59 q^{11} + 11 q^{12} - 169 q^{13} + 30 q^{14} + 50 q^{15} + 267 q^{16} + q^{17} + 53 q^{18} + 107 q^{19} + 48 q^{20} + 36 q^{21} + 14 q^{22} + 12 q^{23} + 78 q^{24} + 217 q^{25} - 9 q^{26} + 39 q^{27} + 99 q^{28} + 30 q^{29} - q^{30} + 106 q^{31} + 74 q^{32} + 16 q^{33} + 56 q^{34} + 46 q^{35} + 271 q^{36} + 73 q^{37} + 2 q^{38} - 9 q^{39} - 16 q^{40} + 52 q^{41} - 2 q^{42} + 64 q^{43} + 124 q^{44} + 84 q^{45} + 105 q^{46} + 55 q^{47} + 26 q^{48} + 257 q^{49} + 60 q^{50} + 117 q^{51} - 199 q^{52} + 7 q^{53} + 78 q^{54} - 4 q^{55} + 63 q^{56} + 51 q^{57} + 84 q^{58} + 98 q^{59} + 94 q^{60} + 32 q^{61} - 25 q^{62} + 128 q^{63} + 380 q^{64} - 12 q^{65} + 16 q^{66} + 170 q^{67} - 10 q^{68} + 55 q^{69} + 70 q^{70} + 124 q^{71} + 173 q^{72} + 81 q^{73} + 54 q^{74} + 120 q^{75} + 212 q^{76} + 20 q^{77} - 22 q^{78} + 92 q^{79} + 66 q^{80} + 265 q^{81} + 21 q^{82} + 62 q^{83} + 98 q^{84} + 139 q^{85} + 51 q^{86} - 33 q^{87} + 31 q^{88} + 58 q^{89} + 16 q^{90} - 36 q^{91} + 40 q^{92} + 37 q^{93} + 55 q^{94} + 23 q^{95} + 164 q^{96} + 78 q^{97} + 69 q^{98} + 307 q^{99}+O(q^{100}) \) 169 * q + 9 * q^2 + 9 * q^3 + 199 * q^4 + 12 * q^5 + 22 * q^6 + 36 * q^7 + 30 * q^8 + 198 * q^9 - 3 * q^10 + 59 * q^11 + 11 * q^12 - 169 * q^13 + 30 * q^14 + 50 * q^15 + 267 * q^16 + q^17 + 53 * q^18 + 107 * q^19 + 48 * q^20 + 36 * q^21 + 14 * q^22 + 12 * q^23 + 78 * q^24 + 217 * q^25 - 9 * q^26 + 39 * q^27 + 99 * q^28 + 30 * q^29 - q^30 + 106 * q^31 + 74 * q^32 + 16 * q^33 + 56 * q^34 + 46 * q^35 + 271 * q^36 + 73 * q^37 + 2 * q^38 - 9 * q^39 - 16 * q^40 + 52 * q^41 - 2 * q^42 + 64 * q^43 + 124 * q^44 + 84 * q^45 + 105 * q^46 + 55 * q^47 + 26 * q^48 + 257 * q^49 + 60 * q^50 + 117 * q^51 - 199 * q^52 + 7 * q^53 + 78 * q^54 - 4 * q^55 + 63 * q^56 + 51 * q^57 + 84 * q^58 + 98 * q^59 + 94 * q^60 + 32 * q^61 - 25 * q^62 + 128 * q^63 + 380 * q^64 - 12 * q^65 + 16 * q^66 + 170 * q^67 - 10 * q^68 + 55 * q^69 + 70 * q^70 + 124 * q^71 + 173 * q^72 + 81 * q^73 + 54 * q^74 + 120 * q^75 + 212 * q^76 + 20 * q^77 - 22 * q^78 + 92 * q^79 + 66 * q^80 + 265 * q^81 + 21 * q^82 + 62 * q^83 + 98 * q^84 + 139 * q^85 + 51 * q^86 - 33 * q^87 + 31 * q^88 + 58 * q^89 + 16 * q^90 - 36 * q^91 + 40 * q^92 + 37 * q^93 + 55 * q^94 + 23 * q^95 + 164 * q^96 + 78 * q^97 + 69 * q^98 + 307 * q^99

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