LMFDB - Embedded newform 8027.2.a.f.1.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8027,2,Mod(1,8027)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8027, 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("8027.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8027 = 23 \cdot 349 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8027.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:	$64.0959177025$
Analytic rank:	$0$
Dimension:	$176$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.9
Character	$\chi$	$=$	8027.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.62656 q^{2} +1.97110 q^{3} +4.89882 q^{4} -2.67061 q^{5} -5.17721 q^{6} +3.82377 q^{7} -7.61393 q^{8} +0.885230 q^{9} +O(q^{10})$	\(q-2.62656 q^{2} +1.97110 q^{3} +4.89882 q^{4} -2.67061 q^{5} -5.17721 q^{6} +3.82377 q^{7} -7.61393 q^{8} +0.885230 q^{9} +7.01453 q^{10} +5.21542 q^{11} +9.65606 q^{12} -1.19149 q^{13} -10.0434 q^{14} -5.26404 q^{15} +10.2008 q^{16} +3.34464 q^{17} -2.32511 q^{18} +0.211232 q^{19} -13.0829 q^{20} +7.53702 q^{21} -13.6986 q^{22} +1.00000 q^{23} -15.0078 q^{24} +2.13217 q^{25} +3.12952 q^{26} -4.16842 q^{27} +18.7319 q^{28} -0.308608 q^{29} +13.8263 q^{30} +7.17438 q^{31} -11.5652 q^{32} +10.2801 q^{33} -8.78490 q^{34} -10.2118 q^{35} +4.33658 q^{36} -5.24394 q^{37} -0.554814 q^{38} -2.34854 q^{39} +20.3339 q^{40} -5.30350 q^{41} -19.7964 q^{42} +3.18022 q^{43} +25.5494 q^{44} -2.36411 q^{45} -2.62656 q^{46} +0.360574 q^{47} +20.1068 q^{48} +7.62118 q^{49} -5.60028 q^{50} +6.59262 q^{51} -5.83689 q^{52} +1.71032 q^{53} +10.9486 q^{54} -13.9284 q^{55} -29.1139 q^{56} +0.416359 q^{57} +0.810577 q^{58} -1.58732 q^{59} -25.7876 q^{60} +9.22123 q^{61} -18.8440 q^{62} +3.38491 q^{63} +9.97503 q^{64} +3.18200 q^{65} -27.0013 q^{66} +9.27231 q^{67} +16.3848 q^{68} +1.97110 q^{69} +26.8219 q^{70} +0.623888 q^{71} -6.74008 q^{72} +5.13126 q^{73} +13.7735 q^{74} +4.20272 q^{75} +1.03479 q^{76} +19.9425 q^{77} +6.16858 q^{78} +8.42972 q^{79} -27.2424 q^{80} -10.8721 q^{81} +13.9300 q^{82} -14.6673 q^{83} +36.9225 q^{84} -8.93224 q^{85} -8.35305 q^{86} -0.608297 q^{87} -39.7098 q^{88} +1.12919 q^{89} +6.20947 q^{90} -4.55597 q^{91} +4.89882 q^{92} +14.1414 q^{93} -0.947070 q^{94} -0.564119 q^{95} -22.7961 q^{96} +6.84287 q^{97} -20.0175 q^{98} +4.61684 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 176 q + 19 q^{2} + 22 q^{3} + 203 q^{4} + 28 q^{5} + 9 q^{6} + 30 q^{7} + 51 q^{8} + 204 q^{9}+O(q^{10}) $ 176 * q + 19 * q^2 + 22 * q^3 + 203 * q^4 + 28 * q^5 + 9 * q^6 + 30 * q^7 + 51 * q^8 + 204 * q^9	\( 176 q + 19 q^{2} + 22 q^{3} + 203 q^{4} + 28 q^{5} + 9 q^{6} + 30 q^{7} + 51 q^{8} + 204 q^{9} + 18 q^{10} + 11 q^{11} + 46 q^{12} + 87 q^{13} - 6 q^{14} + 29 q^{15} + 257 q^{16} + 14 q^{17} + 72 q^{18} + 34 q^{19} + 45 q^{20} + 23 q^{21} + 62 q^{22} + 176 q^{23} + 33 q^{24} + 272 q^{25} + 31 q^{26} + 82 q^{27} + 80 q^{28} + 75 q^{29} - 30 q^{30} + 73 q^{31} + 71 q^{32} + 30 q^{33} + 23 q^{34} + 44 q^{35} + 264 q^{36} + 236 q^{37} - 21 q^{38} + 17 q^{39} + 43 q^{40} + 51 q^{41} + 38 q^{42} + 51 q^{43} + 12 q^{44} + 127 q^{45} + 19 q^{46} + 45 q^{47} + 61 q^{48} + 268 q^{49} + 55 q^{50} - 3 q^{51} + 166 q^{52} + 63 q^{53} - 32 q^{54} + 11 q^{55} - 9 q^{56} + 72 q^{57} + 98 q^{58} + 95 q^{59} - 7 q^{60} + 73 q^{61} + 12 q^{62} + 19 q^{63} + 365 q^{64} + 19 q^{65} - 28 q^{66} + 138 q^{67} + 16 q^{68} + 22 q^{69} + 100 q^{70} + 85 q^{71} + 129 q^{72} + 118 q^{73} - 21 q^{74} - 12 q^{75} + 52 q^{76} + 75 q^{77} + 97 q^{78} + 74 q^{79} + 8 q^{80} + 280 q^{81} + 67 q^{82} + 10 q^{83} - 51 q^{84} + 169 q^{85} - 39 q^{86} - 6 q^{87} + 159 q^{88} + 38 q^{89} + 22 q^{90} + 90 q^{91} + 203 q^{92} + 230 q^{93} + 63 q^{94} + 30 q^{95} + 107 q^{96} + 161 q^{97} + 58 q^{98} + 7 q^{99}+O(q^{100}) \) 176 * q + 19 * q^2 + 22 * q^3 + 203 * q^4 + 28 * q^5 + 9 * q^6 + 30 * q^7 + 51 * q^8 + 204 * q^9 + 18 * q^10 + 11 * q^11 + 46 * q^12 + 87 * q^13 - 6 * q^14 + 29 * q^15 + 257 * q^16 + 14 * q^17 + 72 * q^18 + 34 * q^19 + 45 * q^20 + 23 * q^21 + 62 * q^22 + 176 * q^23 + 33 * q^24 + 272 * q^25 + 31 * q^26 + 82 * q^27 + 80 * q^28 + 75 * q^29 - 30 * q^30 + 73 * q^31 + 71 * q^32 + 30 * q^33 + 23 * q^34 + 44 * q^35 + 264 * q^36 + 236 * q^37 - 21 * q^38 + 17 * q^39 + 43 * q^40 + 51 * q^41 + 38 * q^42 + 51 * q^43 + 12 * q^44 + 127 * q^45 + 19 * q^46 + 45 * q^47 + 61 * q^48 + 268 * q^49 + 55 * q^50 - 3 * q^51 + 166 * q^52 + 63 * q^53 - 32 * q^54 + 11 * q^55 - 9 * q^56 + 72 * q^57 + 98 * q^58 + 95 * q^59 - 7 * q^60 + 73 * q^61 + 12 * q^62 + 19 * q^63 + 365 * q^64 + 19 * q^65 - 28 * q^66 + 138 * q^67 + 16 * q^68 + 22 * q^69 + 100 * q^70 + 85 * q^71 + 129 * q^72 + 118 * q^73 - 21 * q^74 - 12 * q^75 + 52 * q^76 + 75 * q^77 + 97 * q^78 + 74 * q^79 + 8 * q^80 + 280 * q^81 + 67 * q^82 + 10 * q^83 - 51 * q^84 + 169 * q^85 - 39 * q^86 - 6 * q^87 + 159 * q^88 + 38 * q^89 + 22 * q^90 + 90 * q^91 + 203 * q^92 + 230 * q^93 + 63 * q^94 + 30 * q^95 + 107 * q^96 + 161 * q^97 + 58 * q^98 + 7 * 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 $

$2$	−2.62656	−1.85726	−0.928629	−	0.371009i	$-0.879012\pi$
$2$	−2.62656	−1.85726	−0.928629	+	0.371009i	$0.879012\pi$
$3$	1.97110	1.13801	0.569007	−	0.822333i	$-0.307328\pi$
$3$	1.97110	1.13801	0.569007	+	0.822333i	$0.307328\pi$
$4$	4.89882	2.44941
$5$	−2.67061	−1.19433	−0.597167	−	0.802117i	$-0.703707\pi$
$5$	−2.67061	−1.19433	−0.597167	+	0.802117i	$0.703707\pi$
$6$	−5.17721	−2.11359
$7$	3.82377	1.44525	0.722624	−	0.691242i	$-0.242936\pi$
$7$	3.82377	1.44525	0.722624	+	0.691242i	$0.242936\pi$
$8$	−7.61393	−2.69193
$9$	0.885230	0.295077
$10$	7.01453	2.21819
$11$	5.21542	1.57251	0.786254	−	0.617904i	$-0.212018\pi$
$11$	5.21542	1.57251	0.786254	+	0.617904i	$0.212018\pi$
$12$	9.65606	2.78746
$13$	−1.19149	−0.330459	−0.165230	−	0.986255i	$-0.552837\pi$
$13$	−1.19149	−0.330459	−0.165230	+	0.986255i	$0.552837\pi$
$14$	−10.0434	−2.68420
$15$	−5.26404	−1.35917
$16$	10.2008	2.55020
$17$	3.34464	0.811195	0.405597	−	0.914052i	$-0.367064\pi$
$17$	3.34464	0.811195	0.405597	+	0.914052i	$0.367064\pi$
$18$	−2.32511	−0.548034
$19$	0.211232	0.0484600	0.0242300	−	0.999706i	$-0.492287\pi$
$19$	0.211232	0.0484600	0.0242300	+	0.999706i	$0.492287\pi$
$20$	−13.0829	−2.92541
$21$	7.53702	1.64471
$22$	−13.6986	−2.92055
$23$	1.00000	0.208514
$23$	1.00000	0.208514
$24$	−15.0078	−3.06346
$25$	2.13217	0.426434
$26$	3.12952	0.613748
$27$	−4.16842	−0.802213
$28$	18.7319	3.54000
$29$	−0.308608	−0.0573070	−0.0286535	−	0.999589i	$-0.509122\pi$
$29$	−0.308608	−0.0573070	−0.0286535	+	0.999589i	$0.509122\pi$
$30$	13.8263	2.52433
$31$	7.17438	1.28856	0.644279	−	0.764791i	$-0.277158\pi$
$31$	7.17438	1.28856	0.644279	+	0.764791i	$0.277158\pi$
$32$	−11.5652	−2.04445
$33$	10.2801	1.78954
$34$	−8.78490	−1.50660
$35$	−10.2118	−1.72611
$36$	4.33658	0.722764
$37$	−5.24394	−0.862099	−0.431049	−	0.902328i	$-0.641857\pi$
$37$	−5.24394	−0.862099	−0.431049	+	0.902328i	$0.641857\pi$
$38$	−0.554814	−0.0900027
$39$	−2.34854	−0.376067
$40$	20.3339	3.21506
$41$	−5.30350	−0.828267	−0.414134	−	0.910216i	$-0.635915\pi$
$41$	−5.30350	−0.828267	−0.414134	+	0.910216i	$0.635915\pi$
$42$	−19.7964	−3.05466
$43$	3.18022	0.484980	0.242490	−	0.970154i	$-0.422036\pi$
$43$	3.18022	0.484980	0.242490	+	0.970154i	$0.422036\pi$
$44$	25.5494	3.85172
$45$	−2.36411	−0.352420
$46$	−2.62656	−0.387265
$47$	0.360574	0.0525952	0.0262976	−	0.999654i	$-0.491628\pi$
$47$	0.360574	0.0525952	0.0262976	+	0.999654i	$0.491628\pi$
$48$	20.1068	2.90217
$49$	7.62118	1.08874
$50$	−5.60028	−0.791999
$51$	6.59262	0.923151
$52$	−5.83689	−0.809430
$53$	1.71032	0.234931	0.117466	−	0.993077i	$-0.462523\pi$
$53$	1.71032	0.234931	0.117466	+	0.993077i	$0.462523\pi$
$54$	10.9486	1.48992
$55$	−13.9284	−1.87810
$56$	−29.1139	−3.89051
$57$	0.416359	0.0551481
$58$	0.810577	0.106434
$59$	−1.58732	−0.206652	−0.103326	−	0.994648i	$-0.532948\pi$
$59$	−1.58732	−0.206652	−0.103326	+	0.994648i	$0.532948\pi$
$60$	−25.7876	−3.32916
$61$	9.22123	1.18066	0.590329	−	0.807163i	$-0.298998\pi$
$61$	9.22123	1.18066	0.590329	+	0.807163i	$0.298998\pi$
$62$	−18.8440	−2.39318
$63$	3.38491	0.426459
$64$	9.97503	1.24688
$65$	3.18200	0.394679
$66$	−27.0013	−3.32363
$67$	9.27231	1.13279	0.566397	−	0.824133i	$-0.308337\pi$
$67$	9.27231	1.13279	0.566397	+	0.824133i	$0.308337\pi$
$68$	16.3848	1.98695
$69$	1.97110	0.237292
$70$	26.8219	3.20583
$71$	0.623888	0.0740419	0.0370209	−	0.999314i	$-0.488213\pi$
$71$	0.623888	0.0740419	0.0370209	+	0.999314i	$0.488213\pi$
$72$	−6.74008	−0.794326
$73$	5.13126	0.600569	0.300285	−	0.953850i	$-0.402918\pi$
$73$	5.13126	0.600569	0.300285	+	0.953850i	$0.402918\pi$
$74$	13.7735	1.60114
$75$	4.20272	0.485288
$76$	1.03479	0.118698
$77$	19.9425	2.27266
$78$	6.16858	0.698455
$79$	8.42972	0.948418	0.474209	−	0.880412i	$-0.342734\pi$
$79$	8.42972	0.948418	0.474209	+	0.880412i	$0.342734\pi$
$80$	−27.2424	−3.04579
$81$	−10.8721	−1.20801
$82$	13.9300	1.53831
$83$	−14.6673	−1.60995	−0.804974	−	0.593311i	$-0.797821\pi$
$83$	−14.6673	−1.60995	−0.804974	+	0.593311i	$0.797821\pi$
$84$	36.9225	4.02858
$85$	−8.93224	−0.968837
$86$	−8.35305	−0.900733
$87$	−0.608297	−0.0652162
$88$	−39.7098	−4.23308
$89$	1.12919	0.119694	0.0598470	−	0.998208i	$-0.480939\pi$
$89$	1.12919	0.119694	0.0598470	+	0.998208i	$0.480939\pi$
$90$	6.20947	0.654535
$91$	−4.55597	−0.477595
$92$	4.89882	0.510737
$93$	14.1414	1.46640
$94$	−0.947070	−0.0976828
$95$	−0.564119	−0.0578774
$96$	−22.7961	−2.32662
$97$	6.84287	0.694789	0.347394	−	0.937719i	$-0.387067\pi$
$97$	6.84287	0.694789	0.347394	+	0.937719i	$0.387067\pi$
$98$	−20.0175	−2.02207
$99$	4.61684	0.464010
$100$	10.4451	1.04451
$101$	−11.3503	−1.12940	−0.564700	−	0.825296i	$-0.691008\pi$
$101$	−11.3503	−1.12940	−0.564700	+	0.825296i	$0.691008\pi$
$102$	−17.3159	−1.71453
$103$	14.4180	1.42064	0.710322	−	0.703877i	$-0.248549\pi$
$103$	14.4180	1.42064	0.710322	+	0.703877i	$0.248549\pi$
$104$	9.07190	0.889573
$105$	−20.1285	−1.96434
$106$	−4.49227	−0.436328
$107$	13.3429	1.28991	0.644954	−	0.764221i	$-0.276876\pi$
$107$	13.3429	1.28991	0.644954	+	0.764221i	$0.276876\pi$
$108$	−20.4203	−1.96495
$109$	12.8670	1.23243	0.616216	−	0.787577i	$-0.288665\pi$
$109$	12.8670	1.23243	0.616216	+	0.787577i	$0.288665\pi$
$110$	36.5837	3.48812
$111$	−10.3363	−0.981081
$112$	39.0055	3.68567
$113$	−2.09782	−0.197346	−0.0986732	−	0.995120i	$-0.531460\pi$
$113$	−2.09782	−0.197346	−0.0986732	+	0.995120i	$0.531460\pi$
$114$	−1.09359	−0.102424
$115$	−2.67061	−0.249036
$116$	−1.51181	−0.140368
$117$	−1.05474	−0.0975108
$118$	4.16920	0.383806
$119$	12.7891	1.17238
$120$	40.0800	3.65879
$121$	16.2006	1.47278
$122$	−24.2201	−2.19279
$123$	−10.4537	−0.942580
$124$	35.1460	3.15621
$125$	7.65886	0.685029
$126$	−8.89068	−0.792044
$127$	11.2255	0.996102	0.498051	−	0.867148i	$-0.334049\pi$
$127$	11.2255	0.996102	0.498051	+	0.867148i	$0.334049\pi$
$128$	−3.06966	−0.271322
$129$	6.26853	0.551914
$130$	−8.35772	−0.733021
$131$	−7.58164	−0.662411	−0.331206	−	0.943559i	$-0.607455\pi$
$131$	−7.58164	−0.662411	−0.331206	+	0.943559i	$0.607455\pi$
$132$	50.3604	4.38331
$133$	0.807702	0.0700367
$134$	−24.3543	−2.10389
$135$	11.1322	0.958110
$136$	−25.4659	−2.18368
$137$	8.62062	0.736509	0.368255	−	0.929725i	$-0.379955\pi$
$137$	8.62062	0.736509	0.368255	+	0.929725i	$0.379955\pi$
$138$	−5.17721	−0.440713
$139$	−10.5404	−0.894023	−0.447012	−	0.894528i	$-0.647512\pi$
$139$	−10.5404	−0.894023	−0.447012	+	0.894528i	$0.647512\pi$
$140$	−50.0258	−4.22795
$141$	0.710727	0.0598540
$142$	−1.63868	−0.137515
$143$	−6.21411	−0.519650
$144$	9.03006	0.752505
$145$	0.824172	0.0684438
$146$	−13.4776	−1.11541
$147$	15.0221	1.23900
$148$	−25.6891	−2.11163
$149$	6.98670	0.572373	0.286186	−	0.958174i	$-0.407612\pi$
$149$	6.98670	0.572373	0.286186	+	0.958174i	$0.407612\pi$
$150$	−11.0387	−0.901306
$151$	−17.5260	−1.42625	−0.713123	−	0.701038i	$-0.752720\pi$
$151$	−17.5260	−1.42625	−0.713123	+	0.701038i	$0.752720\pi$
$152$	−1.60831	−0.130451
$153$	2.96078	0.239365
$154$	−52.3803	−4.22092
$155$	−19.1600	−1.53897
$156$	−11.5051	−0.921143
$157$	5.45553	0.435399	0.217700	−	0.976016i	$-0.430145\pi$
$157$	5.45553	0.435399	0.217700	+	0.976016i	$0.430145\pi$
$158$	−22.1412	−1.76146
$159$	3.37122	0.267355
$160$	30.8861	2.44176
$161$	3.82377	0.301355
$162$	28.5561	2.24358
$163$	6.29409	0.492992	0.246496	−	0.969144i	$-0.420721\pi$
$163$	6.29409	0.492992	0.246496	+	0.969144i	$0.420721\pi$
$164$	−25.9809	−2.02877
$165$	−27.4542	−2.13730
$166$	38.5246	2.99009
$167$	−24.3664	−1.88553	−0.942765	−	0.333457i	$-0.891785\pi$
$167$	−24.3664	−1.88553	−0.942765	+	0.333457i	$0.891785\pi$
$168$	−57.3863	−4.42745
$169$	−11.5804	−0.890797
$170$	23.4611	1.79938
$171$	0.186989	0.0142994
$172$	15.5793	1.18791
$173$	−10.3300	−0.785374	−0.392687	−	0.919672i	$-0.628454\pi$
$173$	−10.3300	−0.785374	−0.392687	+	0.919672i	$0.628454\pi$
$174$	1.59773	0.121123
$175$	8.15292	0.616303
$176$	53.2015	4.01021
$177$	−3.12877	−0.235173
$178$	−2.96589	−0.222303
$179$	6.46514	0.483227	0.241614	−	0.970373i	$-0.422323\pi$
$179$	6.46514	0.483227	0.241614	+	0.970373i	$0.422323\pi$
$180$	−11.5813	−0.863222
$181$	−7.24732	−0.538689	−0.269345	−	0.963044i	$-0.586807\pi$
$181$	−7.24732	−0.538689	−0.269345	+	0.963044i	$0.586807\pi$
$182$	11.9665	0.887018
$183$	18.1760	1.34361
$184$	−7.61393	−0.561306
$185$	14.0045	1.02963
$186$	−37.1433	−2.72348
$187$	17.4437	1.27561
$188$	1.76639	0.128827
$189$	−15.9391	−1.15940
$190$	1.48169	0.107493
$191$	−25.4287	−1.83996	−0.919978	−	0.391969i	$-0.871794\pi$
$191$	−25.4287	−1.83996	−0.919978	+	0.391969i	$0.871794\pi$
$192$	19.6618	1.41897
$193$	8.72418	0.627980	0.313990	−	0.949426i	$-0.398334\pi$
$193$	8.72418	0.627980	0.313990	+	0.949426i	$0.398334\pi$
$194$	−17.9732	−1.29040
$195$	6.27204	0.449150
$196$	37.3348	2.66677
$197$	−9.12983	−0.650474	−0.325237	−	0.945633i	$-0.605444\pi$
$197$	−9.12983	−0.650474	−0.325237	+	0.945633i	$0.605444\pi$
$198$	−12.1264	−0.861787
$199$	−0.00168745	−0.000119620 0	−5.98100e−5	−	1.00000i	$-0.500019\pi$
$199$	−0.00168745	−0.000119620 0	−5.98100e−5		1.00000i	$0.500019\pi$
$200$	−16.2342	−1.14793
$201$	18.2766	1.28913
$202$	29.8124	2.09759
$203$	−1.18004	−0.0828229
$204$	32.2961	2.26118
$205$	14.1636	0.989228
$206$	−37.8697	−2.63850
$207$	0.885230	0.0615277
$208$	−12.1541	−0.842738
$209$	1.10166	0.0762037
$210$	52.8686	3.64828
$211$	27.1276	1.86754	0.933769	−	0.357876i	$-0.116499\pi$
$211$	27.1276	1.86754	0.933769	+	0.357876i	$0.116499\pi$
$212$	8.37857	0.575443
$213$	1.22974	0.0842607
$214$	−35.0460	−2.39569
$215$	−8.49314	−0.579228
$216$	31.7381	2.15950
$217$	27.4332	1.86228
$218$	−33.7959	−2.28895
$219$	10.1142	0.683456
$220$	−68.2325	−4.60024
$221$	−3.98510	−0.268067
$222$	27.1490	1.82212
$223$	−26.3216	−1.76262	−0.881311	−	0.472537i	$-0.843338\pi$
$223$	−26.3216	−1.76262	−0.881311	+	0.472537i	$0.843338\pi$
$224$	−44.2225	−2.95474
$225$	1.88746	0.125831
$226$	5.51006	0.366523
$227$	8.92730	0.592526	0.296263	−	0.955106i	$-0.404260\pi$
$227$	8.92730	0.592526	0.296263	+	0.955106i	$0.404260\pi$
$228$	2.03967	0.135080
$229$	−5.71094	−0.377390	−0.188695	−	0.982036i	$-0.560426\pi$
$229$	−5.71094	−0.377390	−0.188695	+	0.982036i	$0.560426\pi$
$230$	7.01453	0.462524
$231$	39.3087	2.58632
$232$	2.34972	0.154267
$233$	−15.4733	−1.01369	−0.506846	−	0.862037i	$-0.669189\pi$
$233$	−15.4733	−1.01369	−0.506846	+	0.862037i	$0.669189\pi$
$234$	2.77034	0.181103
$235$	−0.962954	−0.0628162
$236$	−7.77601	−0.506175
$237$	16.6158	1.07931
$238$	−33.5914	−2.17741
$239$	12.9989	0.840828	0.420414	−	0.907332i	$-0.361885\pi$
$239$	12.9989	0.840828	0.420414	+	0.907332i	$0.361885\pi$
$240$	−53.6975	−3.46616
$241$	8.74236	0.563145	0.281573	−	0.959540i	$-0.409144\pi$
$241$	8.74236	0.563145	0.281573	+	0.959540i	$0.409144\pi$
$242$	−42.5518	−2.73533
$243$	−8.92464	−0.572516
$244$	45.1732	2.89192
$245$	−20.3532	−1.30032
$246$	27.4573	1.75061
$247$	−0.251681	−0.0160140
$248$	−54.6252	−3.46871
$249$	−28.9107	−1.83214
$250$	−20.1165	−1.27228
$251$	−15.5939	−0.984279	−0.492140	−	0.870516i	$-0.663785\pi$
$251$	−15.5939	−0.984279	−0.492140	+	0.870516i	$0.663785\pi$
$252$	16.5821	1.04457
$253$	5.21542	0.327890
$254$	−29.4845	−1.85002
$255$	−17.6063	−1.10255
$256$	−11.8874	−0.742963
$257$	−9.27085	−0.578300	−0.289150	−	0.957284i	$-0.593373\pi$
$257$	−9.27085	−0.578300	−0.289150	+	0.957284i	$0.593373\pi$
$258$	−16.4647	−1.02505
$259$	−20.0516	−1.24595
$260$	15.5881	0.966730
$261$	−0.273189	−0.0169100
$262$	19.9136	1.23027
$263$	28.4880	1.75665	0.878324	−	0.478066i	$-0.158662\pi$
$263$	28.4880	1.75665	0.878324	+	0.478066i	$0.158662\pi$
$264$	−78.2720	−4.81731
$265$	−4.56761	−0.280586
$266$	−2.12148	−0.130076
$267$	2.22575	0.136214
$268$	45.4234	2.77468
$269$	24.0681	1.46746	0.733730	−	0.679441i	$-0.237778\pi$
$269$	24.0681	1.46746	0.733730	+	0.679441i	$0.237778\pi$
$270$	−29.2395	−1.77946
$271$	20.6887	1.25675	0.628375	−	0.777910i	$-0.283720\pi$
$271$	20.6887	1.25675	0.628375	+	0.777910i	$0.283720\pi$
$272$	34.1180	2.06871
$273$	−8.98027	−0.543510
$274$	−22.6426	−1.36789
$275$	11.1202	0.670571
$276$	9.65606	0.581226
$277$	19.4390	1.16797	0.583987	−	0.811763i	$-0.301492\pi$
$277$	19.4390	1.16797	0.583987	+	0.811763i	$0.301492\pi$
$278$	27.6849	1.66043
$279$	6.35098	0.380223
$280$	77.7519	4.64656
$281$	8.23382	0.491188	0.245594	−	0.969373i	$-0.421017\pi$
$281$	8.23382	0.491188	0.245594	+	0.969373i	$0.421017\pi$
$282$	−1.86677	−0.111164
$283$	−12.7368	−0.757122	−0.378561	−	0.925576i	$-0.623581\pi$
$283$	−12.7368	−0.757122	−0.378561	+	0.925576i	$0.623581\pi$
$284$	3.05632	0.181359
$285$	−1.11193	−0.0658653
$286$	16.3217	0.965124
$287$	−20.2793	−1.19705
$288$	−10.2378	−0.603271
$289$	−5.81338	−0.341963
$290$	−2.16474	−0.127118
$291$	13.4880	0.790679
$292$	25.1371	1.47104
$293$	16.9746	0.991670	0.495835	−	0.868417i	$-0.334862\pi$
$293$	16.9746	0.991670	0.495835	+	0.868417i	$0.334862\pi$
$294$	−39.4565	−2.30115
$295$	4.23913	0.246811
$296$	39.9270	2.32071
$297$	−21.7401	−1.26149
$298$	−18.3510	−1.06304
$299$	−1.19149	−0.0689055
$300$	20.5884	1.18867
$301$	12.1604	0.700915
$302$	46.0331	2.64891
$303$	−22.3726	−1.28527
$304$	2.15474	0.123583
$305$	−24.6263	−1.41010
$306$	−7.77666	−0.444562
$307$	5.31764	0.303494	0.151747	−	0.988419i	$-0.451510\pi$
$307$	5.31764	0.303494	0.151747	+	0.988419i	$0.451510\pi$
$308$	97.6949	5.56668
$309$	28.4192	1.61671
$310$	50.3249	2.85826
$311$	−13.0110	−0.737789	−0.368894	−	0.929471i	$-0.620264\pi$
$311$	−13.0110	−0.737789	−0.368894	+	0.929471i	$0.620264\pi$
$312$	17.8816	1.01235
$313$	19.6964	1.11331	0.556653	−	0.830745i	$-0.312085\pi$
$313$	19.6964	1.11331	0.556653	+	0.830745i	$0.312085\pi$
$314$	−14.3293	−0.808649
$315$	−9.03979	−0.509334
$316$	41.2957	2.32306
$317$	26.7688	1.50349	0.751744	−	0.659455i	$-0.229213\pi$
$317$	26.7688	1.50349	0.751744	+	0.659455i	$0.229213\pi$
$318$	−8.85471	−0.496547
$319$	−1.60952	−0.0901158
$320$	−26.6394	−1.48919
$321$	26.3002	1.46793
$322$	−10.0434	−0.559694
$323$	0.706496	0.0393105
$324$	−53.2603	−2.95890
$325$	−2.54046	−0.140919
$326$	−16.5318	−0.915613
$327$	25.3621	1.40253
$328$	40.3805	2.22964
$329$	1.37875	0.0760130
$330$	72.1100	3.96953
$331$	8.73224	0.479967	0.239984	−	0.970777i	$-0.422858\pi$
$331$	8.73224	0.479967	0.239984	+	0.970777i	$0.422858\pi$
$332$	−71.8526	−3.94342
$333$	−4.64209	−0.254385
$334$	63.9999	3.50192
$335$	−24.7628	−1.35293
$336$	76.8837	4.19435
$337$	−6.98013	−0.380232	−0.190116	−	0.981762i	$-0.560886\pi$
$337$	−6.98013	−0.380232	−0.190116	+	0.981762i	$0.560886\pi$
$338$	30.4165	1.65444
$339$	−4.13501	−0.224583
$340$	−43.7574	−2.37308
$341$	37.4174	2.02627
$342$	−0.491138	−0.0265577
$343$	2.37525	0.128251
$344$	−24.2140	−1.30553
$345$	−5.26404	−0.283406
$346$	27.1323	1.45864
$347$	23.6906	1.27178	0.635889	−	0.771780i	$-0.280634\pi$
$347$	23.6906	1.27178	0.635889	+	0.771780i	$0.280634\pi$
$348$	−2.97994	−0.159741
$349$	−1.00000	−0.0535288
$349$	−1.00000	−0.0535288
$350$	−21.4141	−1.14463
$351$	4.96662	0.265099
$352$	−60.3172	−3.21492
$353$	5.25241	0.279557	0.139779	−	0.990183i	$-0.455361\pi$
$353$	5.25241	0.279557	0.139779	+	0.990183i	$0.455361\pi$
$354$	8.21791	0.436777
$355$	−1.66616	−0.0884307
$356$	5.53171	0.293180
$357$	25.2086	1.33418
$358$	−16.9811	−0.897478
$359$	23.8299	1.25769	0.628846	−	0.777530i	$-0.283528\pi$
$359$	23.8299	1.25769	0.628846	+	0.777530i	$0.283528\pi$
$360$	18.0001	0.948691
$361$	−18.9554	−0.997652
$362$	19.0355	1.00049
$363$	31.9329	1.67604
$364$	−22.3189	−1.16983
$365$	−13.7036	−0.717280
$366$	−47.7403	−2.49542
$367$	9.82660	0.512945	0.256472	−	0.966552i	$-0.417440\pi$
$367$	9.82660	0.512945	0.256472	+	0.966552i	$0.417440\pi$
$368$	10.2008	0.531754
$369$	−4.69481	−0.244402
$370$	−36.7838	−1.91230
$371$	6.53988	0.339534
$372$	69.2763	3.59181
$373$	−12.3097	−0.637374	−0.318687	−	0.947860i	$-0.603242\pi$
$373$	−12.3097	−0.637374	−0.318687	+	0.947860i	$0.603242\pi$
$374$	−45.8169	−2.36914
$375$	15.0964	0.779573
$376$	−2.74539	−0.141583
$377$	0.367703	0.0189376
$378$	41.8649	2.15330
$379$	9.94465	0.510823	0.255411	−	0.966832i	$-0.417789\pi$
$379$	9.94465	0.510823	0.255411	+	0.966832i	$0.417789\pi$
$380$	−2.76352	−0.141766
$381$	22.1266	1.13358
$382$	66.7900	3.41728
$383$	−1.26617	−0.0646984	−0.0323492	−	0.999477i	$-0.510299\pi$
$383$	−1.26617	−0.0646984	−0.0323492	+	0.999477i	$0.510299\pi$
$384$	−6.05060	−0.308768
$385$	−53.2588	−2.71432
$386$	−22.9146	−1.16632
$387$	2.81523	0.143106
$388$	33.5220	1.70182
$389$	14.9957	0.760313	0.380157	−	0.924922i	$-0.375870\pi$
$389$	14.9957	0.760313	0.380157	+	0.924922i	$0.375870\pi$
$390$	−16.4739	−0.834188
$391$	3.34464	0.169146
$392$	−58.0271	−2.93081
$393$	−14.9442	−0.753834
$394$	23.9801	1.20810
$395$	−22.5125	−1.13273
$396$	22.6171	1.13655
$397$	−32.2714	−1.61966	−0.809828	−	0.586668i	$-0.800439\pi$
$397$	−32.2714	−1.61966	−0.809828	+	0.586668i	$0.800439\pi$
$398$	0.00443218	0.000222165 0
$399$	1.59206	0.0797027
$400$	21.7499	1.08749
$401$	5.94362	0.296810	0.148405	−	0.988927i	$-0.452586\pi$
$401$	5.94362	0.296810	0.148405	+	0.988927i	$0.452586\pi$
$402$	−48.0047	−2.39426
$403$	−8.54819	−0.425816
$404$	−55.6033	−2.76637
$405$	29.0351	1.44276
$406$	3.09946	0.153823
$407$	−27.3493	−1.35566
$408$	−50.1957	−2.48506
$409$	−25.7643	−1.27396	−0.636981	−	0.770879i	$-0.719817\pi$
$409$	−25.7643	−1.27396	−0.636981	+	0.770879i	$0.719817\pi$
$410$	−37.2015	−1.83725
$411$	16.9921	0.838158
$412$	70.6310	3.47974
$413$	−6.06955	−0.298663
$414$	−2.32511	−0.114273
$415$	39.1707	1.92282
$416$	13.7798	0.675609
$417$	−20.7761	−1.01741
$418$	−2.89359	−0.141530
$419$	−28.8829	−1.41102	−0.705512	−	0.708698i	$-0.749283\pi$
$419$	−28.8829	−1.41102	−0.705512	+	0.708698i	$0.749283\pi$
$420$	−98.6057	−4.81147
$421$	−16.7846	−0.818033	−0.409017	−	0.912527i	$-0.634128\pi$
$421$	−16.7846	−0.818033	−0.409017	+	0.912527i	$0.634128\pi$
$422$	−71.2522	−3.46850
$423$	0.319191	0.0155196
$424$	−13.0223	−0.632418
$425$	7.13135	0.345921
$426$	−3.23000	−0.156494
$427$	35.2598	1.70634
$428$	65.3646	3.15951
$429$	−12.2486	−0.591369
$430$	22.3078	1.07578
$431$	30.7285	1.48014	0.740070	−	0.672529i	$-0.234792\pi$
$431$	30.7285	1.48014	0.740070	+	0.672529i	$0.234792\pi$
$432$	−42.5212	−2.04580
$433$	−16.7548	−0.805185	−0.402592	−	0.915379i	$-0.631891\pi$
$433$	−16.7548	−0.805185	−0.402592	+	0.915379i	$0.631891\pi$
$434$	−72.0548	−3.45874
$435$	1.62452	0.0778900
$436$	63.0330	3.01873
$437$	0.211232	0.0101046
$438$	−26.5656	−1.26936
$439$	−4.81310	−0.229717	−0.114858	−	0.993382i	$-0.536641\pi$
$439$	−4.81310	−0.229717	−0.114858	+	0.993382i	$0.536641\pi$
$440$	106.050	5.05571
$441$	6.74650	0.321262
$442$	10.4671	0.497869
$443$	23.9624	1.13849	0.569245	−	0.822168i	$-0.307236\pi$
$443$	23.9624	1.13849	0.569245	+	0.822168i	$0.307236\pi$
$444$	−50.6358	−2.40307
$445$	−3.01563	−0.142955
$446$	69.1352	3.27364
$447$	13.7715	0.651368
$448$	38.1422	1.80205
$449$	−3.52890	−0.166539	−0.0832695	−	0.996527i	$-0.526536\pi$
$449$	−3.52890	−0.166539	−0.0832695	+	0.996527i	$0.526536\pi$
$450$	−4.95753	−0.233700
$451$	−27.6600	−1.30246
$452$	−10.2769	−0.483382
$453$	−34.5455	−1.62309
$454$	−23.4481	−1.10047
$455$	12.1672	0.570409
$456$	−3.17013	−0.148455
$457$	−8.14747	−0.381123	−0.190561	−	0.981675i	$-0.561031\pi$
$457$	−8.14747	−0.381123	−0.190561	+	0.981675i	$0.561031\pi$
$458$	15.0001	0.700911
$459$	−13.9419	−0.650751
$460$	−13.0829	−0.609991
$461$	−9.54569	−0.444587	−0.222293	−	0.974980i	$-0.571354\pi$
$461$	−9.54569	−0.444587	−0.222293	+	0.974980i	$0.571354\pi$
$462$	−103.247	−4.80347
$463$	−20.1439	−0.936167	−0.468084	−	0.883684i	$-0.655055\pi$
$463$	−20.1439	−0.936167	−0.468084	+	0.883684i	$0.655055\pi$
$464$	−3.14805	−0.146145
$465$	−37.7662	−1.75137
$466$	40.6417	1.88269
$467$	−21.8444	−1.01084	−0.505419	−	0.862874i	$-0.668662\pi$
$467$	−21.8444	−1.01084	−0.505419	+	0.862874i	$0.668662\pi$
$468$	−5.16699	−0.238844
$469$	35.4551	1.63717
$470$	2.52926	0.116666
$471$	10.7534	0.495490
$472$	12.0858	0.556293
$473$	16.5862	0.762634
$474$	−43.6424	−2.00456
$475$	0.450383	0.0206650
$476$	62.6516	2.87163
$477$	1.51403	0.0693227
$478$	−34.1424	−1.56164
$479$	11.2558	0.514291	0.257146	−	0.966373i	$-0.417218\pi$
$479$	11.2558	0.514291	0.257146	+	0.966373i	$0.417218\pi$
$480$	60.8796	2.77876
$481$	6.24809	0.284889
$482$	−22.9623	−1.04591
$483$	7.53702	0.342946
$484$	79.3637	3.60744
$485$	−18.2747	−0.829810
$486$	23.4411	1.06331
$487$	−3.66963	−0.166287	−0.0831435	−	0.996538i	$-0.526496\pi$
$487$	−3.66963	−0.166287	−0.0831435	+	0.996538i	$0.526496\pi$
$488$	−70.2098	−3.17825
$489$	12.4063	0.561031
$490$	53.4590	2.41503
$491$	2.64609	0.119416	0.0597081	−	0.998216i	$-0.480983\pi$
$491$	2.64609	0.119416	0.0597081	+	0.998216i	$0.480983\pi$
$492$	−51.2109	−2.30877
$493$	−1.03218	−0.0464872
$494$	0.661054	0.0297422
$495$	−12.3298	−0.554183
$496$	73.1845	3.28608
$497$	2.38560	0.107009
$498$	75.9358	3.40276
$499$	−15.3025	−0.685036	−0.342518	−	0.939511i	$-0.611280\pi$
$499$	−15.3025	−0.685036	−0.342518	+	0.939511i	$0.611280\pi$
$500$	37.5194	1.67792
$501$	−48.0286	−2.14576
$502$	40.9584	1.82806
$503$	−17.3798	−0.774927	−0.387463	−	0.921885i	$-0.626649\pi$
$503$	−17.3798	−0.774927	−0.387463	+	0.921885i	$0.626649\pi$
$504$	−25.7725	−1.14800
$505$	30.3124	1.34888
$506$	−13.6986	−0.608977
$507$	−22.8260	−1.01374
$508$	54.9917	2.43986
$509$	−7.92802	−0.351403	−0.175702	−	0.984443i	$-0.556219\pi$
$509$	−7.92802	−0.351403	−0.175702	+	0.984443i	$0.556219\pi$
$510$	46.2441	2.04772
$511$	19.6208	0.867971
$512$	37.3623	1.65120
$513$	−0.880504	−0.0388752
$514$	24.3505	1.07405
$515$	−38.5048	−1.69672
$516$	30.7084	1.35186
$517$	1.88055	0.0827063
$518$	52.6668	2.31404
$519$	−20.3614	−0.893767
$520$	−24.2275	−1.06245
$521$	−1.62464	−0.0711766	−0.0355883	−	0.999367i	$-0.511330\pi$
$521$	−1.62464	−0.0711766	−0.0355883	+	0.999367i	$0.511330\pi$
$522$	0.717547	0.0314062
$523$	34.5033	1.50873	0.754363	−	0.656458i	$-0.227946\pi$
$523$	34.5033	1.50873	0.754363	+	0.656458i	$0.227946\pi$
$524$	−37.1411	−1.62252
$525$	16.0702	0.701362
$526$	−74.8256	−3.26255
$527$	23.9957	1.04527
$528$	104.865	4.56368
$529$	1.00000	0.0434783
$530$	11.9971	0.521121
$531$	−1.40515	−0.0609782
$532$	3.95679	0.171549
$533$	6.31905	0.273709
$534$	−5.84606	−0.252984
$535$	−35.6338	−1.54058
$536$	−70.5987	−3.04940
$537$	12.7434	0.549920
$538$	−63.2164	−2.72545
$539$	39.7476	1.71205
$540$	54.5348	2.34681
$541$	−5.15632	−0.221688	−0.110844	−	0.993838i	$-0.535355\pi$
$541$	−5.15632	−0.221688	−0.110844	+	0.993838i	$0.535355\pi$
$542$	−54.3402	−2.33411
$543$	−14.2852	−0.613036
$544$	−38.6814	−1.65845
$545$	−34.3627	−1.47194
$546$	23.5872	1.00944
$547$	−15.2794	−0.653300	−0.326650	−	0.945145i	$-0.605920\pi$
$547$	−15.2794	−0.653300	−0.326650	+	0.945145i	$0.605920\pi$
$548$	42.2309	1.80401
$549$	8.16291	0.348385
$550$	−29.2078	−1.24542
$551$	−0.0651879	−0.00277710
$552$	−15.0078	−0.638775
$553$	32.2333	1.37070
$554$	−51.0576	−2.16923
$555$	27.6043	1.17174
$556$	−51.6354	−2.18983
$557$	3.50118	0.148350	0.0741748	−	0.997245i	$-0.476368\pi$
$557$	3.50118	0.148350	0.0741748	+	0.997245i	$0.476368\pi$
$558$	−16.6812	−0.706173
$559$	−3.78920	−0.160266
$560$	−104.169	−4.40192
$561$	34.3832	1.45166
$562$	−21.6266	−0.912264
$563$	7.87967	0.332088	0.166044	−	0.986118i	$-0.446901\pi$
$563$	7.87967	0.332088	0.166044	+	0.986118i	$0.446901\pi$
$564$	3.48173	0.146607
$565$	5.60247	0.235698
$566$	33.4539	1.40617
$567$	−41.5722	−1.74587
$568$	−4.75024	−0.199316
$569$	−22.8374	−0.957392	−0.478696	−	0.877981i	$-0.658890\pi$
$569$	−22.8374	−0.957392	−0.478696	+	0.877981i	$0.658890\pi$
$570$	2.92056	0.122329
$571$	3.72806	0.156015	0.0780073	−	0.996953i	$-0.475144\pi$
$571$	3.72806	0.156015	0.0780073	+	0.996953i	$0.475144\pi$
$572$	−30.4418	−1.27284
$573$	−50.1225	−2.09390
$574$	53.2649	2.22323
$575$	2.13217	0.0889177
$576$	8.83019	0.367925
$577$	15.1812	0.632003	0.316001	−	0.948759i	$-0.397660\pi$
$577$	15.1812	0.632003	0.316001	+	0.948759i	$0.397660\pi$
$578$	15.2692	0.635114
$579$	17.1962	0.714651
$580$	4.03747	0.167647
$581$	−56.0844	−2.32677
$582$	−35.4270	−1.46850
$583$	8.92005	0.369431
$584$	−39.0691	−1.61669
$585$	2.81680	0.116461
$586$	−44.5849	−1.84179
$587$	18.1931	0.750910	0.375455	−	0.926841i	$-0.377486\pi$
$587$	18.1931	0.750910	0.375455	+	0.926841i	$0.377486\pi$
$588$	73.5906	3.03482
$589$	1.51546	0.0624434
$590$	−11.1343	−0.458393
$591$	−17.9958	−0.740248
$592$	−53.4924	−2.19853
$593$	−10.7388	−0.440991	−0.220495	−	0.975388i	$-0.570767\pi$
$593$	−10.7388	−0.440991	−0.220495	+	0.975388i	$0.570767\pi$
$594$	57.1016	2.34291
$595$	−34.1548	−1.40021
$596$	34.2266	1.40198
$597$	−0.00332612	−0.000136129 0
$598$	3.12952	0.127975
$599$	−36.0450	−1.47276	−0.736379	−	0.676569i	$-0.763466\pi$
$599$	−36.0450	−1.47276	−0.736379	+	0.676569i	$0.763466\pi$
$600$	−31.9992	−1.30636
$601$	9.47037	0.386305	0.193152	−	0.981169i	$-0.438129\pi$
$601$	9.47037	0.386305	0.193152	+	0.981169i	$0.438129\pi$
$602$	−31.9401	−1.30178
$603$	8.20813	0.334261
$604$	−85.8568	−3.49346
$605$	−43.2655	−1.75899
$606$	58.7631	2.38709
$607$	−35.7278	−1.45015	−0.725074	−	0.688671i	$-0.758194\pi$
$607$	−35.7278	−1.45015	−0.725074	+	0.688671i	$0.758194\pi$
$608$	−2.44294	−0.0990742
$609$	−2.32598	−0.0942536
$610$	64.6826	2.61892
$611$	−0.429620	−0.0173806
$612$	14.5043	0.586302
$613$	44.2471	1.78713	0.893563	−	0.448938i	$-0.148198\pi$
$613$	44.2471	1.78713	0.893563	+	0.448938i	$0.148198\pi$
$614$	−13.9671	−0.563667
$615$	27.9178	1.12576
$616$	−151.841	−6.11785
$617$	−28.1225	−1.13217	−0.566084	−	0.824348i	$-0.691542\pi$
$617$	−28.1225	−1.13217	−0.566084	+	0.824348i	$0.691542\pi$
$618$	−74.6448	−3.00266
$619$	38.0722	1.53025	0.765126	−	0.643881i	$-0.222677\pi$
$619$	38.0722	1.53025	0.765126	+	0.643881i	$0.222677\pi$
$620$	−93.8614	−3.76956
$621$	−4.16842	−0.167273
$622$	34.1743	1.37026
$623$	4.31776	0.172988
$624$	−23.9570	−0.959048
$625$	−31.1147	−1.24459
$626$	−51.7338	−2.06770
$627$	2.17149	0.0867209
$628$	26.7257	1.06647
$629$	−17.5391	−0.699330
$630$	23.7436	0.945966
$631$	37.1951	1.48071	0.740356	−	0.672215i	$-0.234657\pi$
$631$	37.1951	1.48071	0.740356	+	0.672215i	$0.234657\pi$
$632$	−64.1833	−2.55308
$633$	53.4711	2.12529
$634$	−70.3100	−2.79236
$635$	−29.9790	−1.18968
$636$	16.5150	0.654862
$637$	−9.08054	−0.359784
$638$	4.22750	0.167368
$639$	0.552284	0.0218480
$640$	8.19787	0.324049
$641$	25.8934	1.02273	0.511363	−	0.859365i	$-0.329141\pi$
$641$	25.8934	1.02273	0.511363	+	0.859365i	$0.329141\pi$
$642$	−69.0791	−2.72633
$643$	−18.7412	−0.739080	−0.369540	−	0.929215i	$-0.620485\pi$
$643$	−18.7412	−0.739080	−0.369540	+	0.929215i	$0.620485\pi$
$644$	18.7319	0.738142
$645$	−16.7408	−0.659169
$646$	−1.85565	−0.0730097
$647$	17.8529	0.701871	0.350936	−	0.936400i	$-0.385864\pi$
$647$	17.8529	0.701871	0.350936	+	0.936400i	$0.385864\pi$
$648$	82.7791	3.25187
$649$	−8.27856	−0.324962
$650$	6.67266	0.261723
$651$	54.0735	2.11931
$652$	30.8336	1.20754
$653$	−1.36185	−0.0532935	−0.0266467	−	0.999645i	$-0.508483\pi$
$653$	−1.36185	−0.0532935	−0.0266467	+	0.999645i	$0.508483\pi$
$654$	−66.6151	−2.60485
$655$	20.2476	0.791141
$656$	−54.0999	−2.11225
$657$	4.54235	0.177214
$658$	−3.62137	−0.141176
$659$	18.6674	0.727180	0.363590	−	0.931559i	$-0.381551\pi$
$659$	18.6674	0.727180	0.363590	+	0.931559i	$0.381551\pi$
$660$	−134.493	−5.23514
$661$	3.60224	0.140111	0.0700555	−	0.997543i	$-0.477682\pi$
$661$	3.60224	0.140111	0.0700555	+	0.997543i	$0.477682\pi$
$662$	−22.9358	−0.891423
$663$	−7.85502	−0.305064
$664$	111.676	4.33387
$665$	−2.15706	−0.0836472
$666$	12.1927	0.472459
$667$	−0.308608	−0.0119493
$668$	−119.367	−4.61844
$669$	−51.8824	−2.00589
$670$	65.0409	2.51275
$671$	48.0926	1.85659
$672$	−87.1669	−3.36254
$673$	−29.0556	−1.12001	−0.560006	−	0.828488i	$-0.689201\pi$
$673$	−29.0556	−1.12001	−0.560006	+	0.828488i	$0.689201\pi$
$674$	18.3337	0.706189
$675$	−8.88779	−0.342091
$676$	−56.7301	−2.18193
$677$	19.6160	0.753903	0.376951	−	0.926233i	$-0.376972\pi$
$677$	19.6160	0.753903	0.376951	+	0.926233i	$0.376972\pi$
$678$	10.8609	0.417109
$679$	26.1655	1.00414
$680$	68.0094	2.60804
$681$	17.5966	0.674303
$682$	−98.2791	−3.76330
$683$	13.3497	0.510811	0.255406	−	0.966834i	$-0.417791\pi$
$683$	13.3497	0.510811	0.255406	+	0.966834i	$0.417791\pi$
$684$	0.916026	0.0350251
$685$	−23.0223	−0.879638
$686$	−6.23874	−0.238196
$687$	−11.2568	−0.429475
$688$	32.4408	1.23680
$689$	−2.03783	−0.0776352
$690$	13.8263	0.526359
$691$	−4.16491	−0.158441	−0.0792204	−	0.996857i	$-0.525243\pi$
$691$	−4.16491	−0.158441	−0.0792204	+	0.996857i	$0.525243\pi$
$692$	−50.6047	−1.92370
$693$	17.6537	0.670610
$694$	−62.2248	−2.36202
$695$	28.1493	1.06776
$696$	4.63153	0.175558
$697$	−17.7383	−0.671886
$698$	2.62656	0.0994168
$699$	−30.4995	−1.15360
$700$	39.9397	1.50958
$701$	−5.26640	−0.198909	−0.0994546	−	0.995042i	$-0.531710\pi$
$701$	−5.26640	−0.198909	−0.0994546	+	0.995042i	$0.531710\pi$
$702$	−13.0451	−0.492357
$703$	−1.10769	−0.0417773
$704$	52.0239	1.96073
$705$	−1.89808	−0.0714857
$706$	−13.7958	−0.519210
$707$	−43.4010	−1.63226
$708$	−15.3273	−0.576035
$709$	41.7214	1.56688	0.783439	−	0.621469i	$-0.213464\pi$
$709$	41.7214	1.56688	0.783439	+	0.621469i	$0.213464\pi$
$710$	4.37628	0.164239
$711$	7.46224	0.279856
$712$	−8.59758	−0.322208
$713$	7.17438	0.268683
$714$	−66.2120	−2.47792
$715$	16.5955	0.620635
$716$	31.6716	1.18362
$717$	25.6221	0.956875
$718$	−62.5906	−2.33586
$719$	−27.8433	−1.03838	−0.519190	−	0.854659i	$-0.673766\pi$
$719$	−27.8433	−1.03838	−0.519190	+	0.854659i	$0.673766\pi$
$720$	−24.1158	−0.898742
$721$	55.1309	2.05318
$722$	49.7875	1.85290
$723$	17.2321	0.640867
$724$	−35.5033	−1.31947
$725$	−0.658005	−0.0244377
$726$	−83.8738	−3.11285
$727$	31.8230	1.18025	0.590125	−	0.807312i	$-0.299079\pi$
$727$	31.8230	1.18025	0.590125	+	0.807312i	$0.299079\pi$
$728$	34.6888	1.28565
$729$	15.0248	0.556475
$730$	35.9934	1.33218
$731$	10.6367	0.393413
$732$	89.0408	3.29104
$733$	17.3711	0.641618	0.320809	−	0.947144i	$-0.396045\pi$
$733$	17.3711	0.641618	0.320809	+	0.947144i	$0.396045\pi$
$734$	−25.8102	−0.952671
$735$	−40.1182	−1.47978
$736$	−11.5652	−0.426298
$737$	48.3590	1.78133
$738$	12.3312	0.453918
$739$	−28.3829	−1.04408	−0.522040	−	0.852921i	$-0.674829\pi$
$739$	−28.3829	−1.04408	−0.522040	+	0.852921i	$0.674829\pi$
$740$	68.6057	2.52200
$741$	−0.496087	−0.0182242
$742$	−17.1774	−0.630602
$743$	38.5200	1.41316	0.706580	−	0.707633i	$-0.250237\pi$
$743$	38.5200	1.41316	0.706580	+	0.707633i	$0.250237\pi$
$744$	−107.672	−3.94744
$745$	−18.6588	−0.683604
$746$	32.3323	1.18377
$747$	−12.9839	−0.475058
$748$	85.4536	3.12449
$749$	51.0202	1.86424
$750$	−39.6515	−1.44787
$751$	−4.04389	−0.147564	−0.0737819	−	0.997274i	$-0.523507\pi$
$751$	−4.04389	−0.147564	−0.0737819	+	0.997274i	$0.523507\pi$
$752$	3.67815	0.134128
$753$	−30.7371	−1.12012
$754$	−0.965793	−0.0351721
$755$	46.8052	1.70342
$756$	−78.0826	−2.83984
$757$	27.9758	1.01680	0.508398	−	0.861122i	$-0.330238\pi$
$757$	27.9758	1.01680	0.508398	+	0.861122i	$0.330238\pi$
$758$	−26.1202	−0.948730
$759$	10.2801	0.373144
$760$	4.29516	0.155802
$761$	2.95489	0.107115	0.0535573	−	0.998565i	$-0.482944\pi$
$761$	2.95489	0.107115	0.0535573	+	0.998565i	$0.482944\pi$
$762$	−58.1168	−2.10535
$763$	49.2003	1.78117
$764$	−124.571	−4.50681
$765$	−7.90709	−0.285881
$766$	3.32568	0.120162
$767$	1.89128	0.0682901
$768$	−23.4313	−0.845503
$769$	−17.0170	−0.613648	−0.306824	−	0.951766i	$-0.599266\pi$
$769$	−17.0170	−0.613648	−0.306824	+	0.951766i	$0.599266\pi$
$770$	139.887	5.04119
$771$	−18.2738	−0.658113
$772$	42.7382	1.53818
$773$	−21.0966	−0.758794	−0.379397	−	0.925234i	$-0.623868\pi$
$773$	−21.0966	−0.758794	−0.379397	+	0.925234i	$0.623868\pi$
$774$	−7.39437	−0.265785
$775$	15.2970	0.549485
$776$	−52.1012	−1.87032
$777$	−39.5237	−1.41790
$778$	−39.3872	−1.41210
$779$	−1.12027	−0.0401378
$780$	30.7256	1.10015
$781$	3.25384	0.116431
$782$	−8.78490	−0.314147
$783$	1.28641	0.0459724
$784$	77.7422	2.77651
$785$	−14.5696	−0.520012
$786$	39.2518	1.40006
$787$	8.57364	0.305617	0.152809	−	0.988256i	$-0.451168\pi$
$787$	8.57364	0.305617	0.152809	+	0.988256i	$0.451168\pi$
$788$	−44.7254	−1.59328
$789$	56.1527	1.99909
$790$	59.1305	2.10377
$791$	−8.02158	−0.285214
$792$	−35.1523	−1.24908
$793$	−10.9870	−0.390159
$794$	84.7628	3.00812
$795$	−9.00322	−0.319311
$796$	−0.00826650	−0.000292998 0
$797$	−6.31745	−0.223775	−0.111888	−	0.993721i	$-0.535690\pi$
$797$	−6.31745	−0.223775	−0.111888	+	0.993721i	$0.535690\pi$
$798$	−4.18164	−0.148029
$799$	1.20599	0.0426649
$800$	−24.6589	−0.871825
$801$	0.999594	0.0353189
$802$	−15.6113	−0.551254
$803$	26.7617	0.944399
$804$	89.5340	3.15762
$805$	−10.2118	−0.359918
$806$	22.4523	0.790850
$807$	47.4407	1.66999
$808$	86.4207	3.04027
$809$	19.4280	0.683051	0.341526	−	0.939872i	$-0.389056\pi$
$809$	19.4280	0.683051	0.341526	+	0.939872i	$0.389056\pi$
$810$	−76.2623	−2.67959
$811$	43.0651	1.51222	0.756111	−	0.654444i	$-0.227097\pi$
$811$	43.0651	1.51222	0.756111	+	0.654444i	$0.227097\pi$
$812$	−5.78082	−0.202867
$813$	40.7795	1.43020
$814$	71.8347	2.51781
$815$	−16.8091	−0.588797
$816$	67.2500	2.35422
$817$	0.671765	0.0235021
$818$	67.6715	2.36608
$819$	−4.03308	−0.140927
$820$	69.3849	2.42302
$821$	7.40859	0.258562	0.129281	−	0.991608i	$-0.458733\pi$
$821$	7.40859	0.258562	0.129281	+	0.991608i	$0.458733\pi$
$822$	−44.6308	−1.55668
$823$	1.25403	0.0437129	0.0218564	−	0.999761i	$-0.493042\pi$
$823$	1.25403	0.0437129	0.0218564	+	0.999761i	$0.493042\pi$
$824$	−109.777	−3.82428
$825$	21.9189	0.763119
$826$	15.9420	0.554695
$827$	34.7288	1.20764	0.603819	−	0.797121i	$-0.293645\pi$
$827$	34.7288	1.20764	0.603819	+	0.797121i	$0.293645\pi$
$828$	4.33658	0.150707
$829$	41.2183	1.43157	0.715786	−	0.698320i	$-0.246069\pi$
$829$	41.2183	1.43157	0.715786	+	0.698320i	$0.246069\pi$
$830$	−102.884	−3.57117
$831$	38.3161	1.32917
$832$	−11.8851	−0.412042
$833$	25.4901	0.883180
$834$	54.5698	1.88960
$835$	65.0733	2.25195
$836$	5.39685	0.186654
$837$	−29.9058	−1.03370
$838$	75.8628	2.62064
$839$	35.5481	1.22726	0.613628	−	0.789596i	$-0.289710\pi$
$839$	35.5481	1.22726	0.613628	+	0.789596i	$0.289710\pi$
$840$	153.257	5.28786
$841$	−28.9048	−0.996716
$842$	44.0859	1.51930
$843$	16.2297	0.558979
$844$	132.893	4.57437
$845$	30.9266	1.06391
$846$	−0.838375	−0.0288239
$847$	61.9472	2.12853
$848$	17.4467	0.599122
$849$	−25.1054	−0.861615
$850$	−18.7309	−0.642465
$851$	−5.24394	−0.179760
$852$	6.02430	0.206389
$853$	−28.5245	−0.976659	−0.488329	−	0.872659i	$-0.662394\pi$
$853$	−28.5245	−0.976659	−0.488329	+	0.872659i	$0.662394\pi$
$854$	−92.6121	−3.16912
$855$	−0.499375	−0.0170783
$856$	−101.592	−3.47234
$857$	34.6553	1.18380	0.591900	−	0.806011i	$-0.298378\pi$
$857$	34.6553	1.18380	0.591900	+	0.806011i	$0.298378\pi$
$858$	32.1717	1.09832
$859$	24.9302	0.850607	0.425304	−	0.905051i	$-0.360167\pi$
$859$	24.9302	0.850607	0.425304	+	0.905051i	$0.360167\pi$
$860$	−41.6064	−1.41877
$861$	−39.9726	−1.36226
$862$	−80.7103	−2.74900
$863$	−26.2800	−0.894580	−0.447290	−	0.894389i	$-0.647611\pi$
$863$	−26.2800	−0.894580	−0.447290	+	0.894389i	$0.647611\pi$
$864$	48.2085	1.64009
$865$	27.5874	0.937999
$866$	44.0075	1.49544
$867$	−11.4587	−0.389159
$868$	134.390	4.56150
$869$	43.9645	1.49139
$870$	−4.26691	−0.144662
$871$	−11.0478	−0.374342
$872$	−97.9683	−3.31762
$873$	6.05752	0.205016
$874$	−0.554814	−0.0187669
$875$	29.2857	0.990037
$876$	49.5478	1.67406
$877$	−22.7884	−0.769508	−0.384754	−	0.923019i	$-0.625714\pi$
$877$	−22.7884	−0.769508	−0.384754	+	0.923019i	$0.625714\pi$
$878$	12.6419	0.426644
$879$	33.4587	1.12853
$880$	−142.080	−4.78953
$881$	−35.3506	−1.19099	−0.595497	−	0.803358i	$-0.703045\pi$
$881$	−35.3506	−1.19099	−0.595497	+	0.803358i	$0.703045\pi$
$882$	−17.7201	−0.596666
$883$	−25.3421	−0.852829	−0.426414	−	0.904528i	$-0.640223\pi$
$883$	−25.3421	−0.852829	−0.426414	+	0.904528i	$0.640223\pi$
$884$	−19.5223	−0.656606
$885$	8.35574	0.280875
$886$	−62.9388	−2.11447
$887$	−7.49068	−0.251512	−0.125756	−	0.992061i	$-0.540136\pi$
$887$	−7.49068	−0.251512	−0.125756	+	0.992061i	$0.540136\pi$
$888$	78.7001	2.64100
$889$	42.9237	1.43961
$890$	7.92074	0.265504
$891$	−56.7023	−1.89960
$892$	−128.945	−4.31738
$893$	0.0761649	0.00254876
$894$	−36.1716	−1.20976
$895$	−17.2659	−0.577135
$896$	−11.7377	−0.392127
$897$	−2.34854	−0.0784155
$898$	9.26887	0.309306
$899$	−2.21407	−0.0738434
$900$	9.24634	0.308211
$901$	5.72042	0.190575
$902$	72.6505	2.41900
$903$	23.9694	0.797652
$904$	15.9727	0.531243
$905$	19.3548	0.643375
$906$	90.7359	3.01450
$907$	51.0827	1.69617	0.848087	−	0.529856i	$-0.177754\pi$
$907$	51.0827	1.69617	0.848087	+	0.529856i	$0.177754\pi$
$908$	43.7333	1.45134
$909$	−10.0477	−0.333260
$910$	−31.9580	−1.05940
$911$	26.5780	0.880568	0.440284	−	0.897859i	$-0.354878\pi$
$911$	26.5780	0.880568	0.440284	+	0.897859i	$0.354878\pi$
$912$	4.24720	0.140639
$913$	−76.4962	−2.53165
$914$	21.3998	0.707843
$915$	−48.5409	−1.60471
$916$	−27.9769	−0.924383
$917$	−28.9904	−0.957348
$918$	36.6192	1.20861
$919$	22.1758	0.731512	0.365756	−	0.930711i	$-0.380810\pi$
$919$	22.1758	0.731512	0.365756	+	0.930711i	$0.380810\pi$
$920$	20.3339	0.670387
$921$	10.4816	0.345380
$922$	25.0723	0.825713
$923$	−0.743355	−0.0244678
$924$	192.566	6.33497
$925$	−11.1810	−0.367628
$926$	52.9092	1.73871
$927$	12.7632	0.419199
$928$	3.56910	0.117162
$929$	−2.16222	−0.0709401	−0.0354701	−	0.999371i	$-0.511293\pi$
$929$	−2.16222	−0.0709401	−0.0354701	+	0.999371i	$0.511293\pi$
$930$	99.1953	3.25274
$931$	1.60984	0.0527603
$932$	−75.8011	−2.48295
$933$	−25.6461	−0.839614
$934$	57.3756	1.87739
$935$	−46.5854	−1.52350
$936$	8.03072	0.262492
$937$	16.4794	0.538360	0.269180	−	0.963090i	$-0.413247\pi$
$937$	16.4794	0.538360	0.269180	+	0.963090i	$0.413247\pi$
$938$	−93.1251	−3.04064
$939$	38.8235	1.26696
$940$	−4.71734	−0.153863
$941$	−31.5114	−1.02724	−0.513620	−	0.858018i	$-0.671696\pi$
$941$	−31.5114	−1.02724	−0.513620	+	0.858018i	$0.671696\pi$
$942$	−28.2444	−0.920254
$943$	−5.30350	−0.172706
$944$	−16.1920	−0.527004
$945$	42.5671	1.38471
$946$	−43.5646	−1.41641
$947$	49.0380	1.59352	0.796760	−	0.604296i	$-0.206545\pi$
$947$	49.0380	1.59352	0.796760	+	0.604296i	$0.206545\pi$
$948$	81.3979	2.64368
$949$	−6.11384	−0.198464
$950$	−1.18296	−0.0383802
$951$	52.7640	1.71099
$952$	−97.3755	−3.15596
$953$	−58.0513	−1.88047	−0.940234	−	0.340530i	$-0.889394\pi$
$953$	−58.0513	−1.88047	−0.940234	+	0.340530i	$0.889394\pi$
$954$	−3.97669	−0.128750
$955$	67.9102	2.19752
$956$	63.6792	2.05953
$957$	−3.17252	−0.102553
$958$	−29.5641	−0.955172
$959$	32.9632	1.06444
$960$	−52.5089	−1.69472
$961$	20.4718	0.660380
$962$	−16.4110	−0.529112
$963$	11.8115	0.380622
$964$	42.8273	1.37937
$965$	−23.2989	−0.750018
$966$	−19.7964	−0.636940
$967$	41.9562	1.34922	0.674610	−	0.738174i	$-0.264312\pi$
$967$	41.9562	1.34922	0.674610	+	0.738174i	$0.264312\pi$
$968$	−123.350	−3.96462
$969$	1.39257	0.0447359
$970$	47.9995	1.54117
$971$	−57.2201	−1.83628	−0.918141	−	0.396254i	$-0.870310\pi$
$971$	−57.2201	−1.83628	−0.918141	+	0.396254i	$0.870310\pi$
$972$	−43.7202	−1.40233
$973$	−40.3039	−1.29208
$974$	9.63852	0.308838
$975$	−5.00749	−0.160368
$976$	94.0640	3.01091
$977$	14.4731	0.463034	0.231517	−	0.972831i	$-0.425631\pi$
$977$	14.4731	0.463034	0.231517	+	0.972831i	$0.425631\pi$
$978$	−32.5859	−1.04198
$979$	5.88920	0.188220
$980$	−99.7068	−3.18502
$981$	11.3902	0.363662
$982$	−6.95011	−0.221787
$983$	61.0151	1.94608	0.973039	−	0.230639i	$-0.0740818\pi$
$983$	61.0151	1.94608	0.973039	+	0.230639i	$0.0740818\pi$
$984$	79.5939	2.53736
$985$	24.3822	0.776883
$986$	2.71109	0.0863387
$987$	2.71765	0.0865039
$988$	−1.23294	−0.0392250
$989$	3.18022	0.101125
$990$	32.3850	1.02926
$991$	−15.7813	−0.501308	−0.250654	−	0.968077i	$-0.580646\pi$
$991$	−15.7813	−0.501308	−0.250654	+	0.968077i	$0.580646\pi$
$992$	−82.9730	−2.63440
$993$	17.2121	0.546210
$994$	−6.26593	−0.198743
$995$	0.00450652	0.000142866 0
$996$	−141.628	−4.48767
$997$	0.171832	0.00544199	0.00272099	−	0.999996i	$-0.499134\pi$
$997$	0.171832	0.00544199	0.00272099	+	0.999996i	$0.499134\pi$
$998$	40.1931	1.27229
$999$	21.8590	0.691587

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8027.2.a.f.1.9	✓	176

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8027.2.a.f.1.9	✓	176	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:	\( N \)	\(=\)	\( 8027 = 23 \cdot 349 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8027.a (trivial)

\(f(q)\)	\(=\)	\(q-2.62656 q^{2} +1.97110 q^{3} +4.89882 q^{4} -2.67061 q^{5} -5.17721 q^{6} +3.82377 q^{7} -7.61393 q^{8} +0.885230 q^{9} +O(q^{10})\)	\(q-2.62656 q^{2} +1.97110 q^{3} +4.89882 q^{4} -2.67061 q^{5} -5.17721 q^{6} +3.82377 q^{7} -7.61393 q^{8} +0.885230 q^{9} +7.01453 q^{10} +5.21542 q^{11} +9.65606 q^{12} -1.19149 q^{13} -10.0434 q^{14} -5.26404 q^{15} +10.2008 q^{16} +3.34464 q^{17} -2.32511 q^{18} +0.211232 q^{19} -13.0829 q^{20} +7.53702 q^{21} -13.6986 q^{22} +1.00000 q^{23} -15.0078 q^{24} +2.13217 q^{25} +3.12952 q^{26} -4.16842 q^{27} +18.7319 q^{28} -0.308608 q^{29} +13.8263 q^{30} +7.17438 q^{31} -11.5652 q^{32} +10.2801 q^{33} -8.78490 q^{34} -10.2118 q^{35} +4.33658 q^{36} -5.24394 q^{37} -0.554814 q^{38} -2.34854 q^{39} +20.3339 q^{40} -5.30350 q^{41} -19.7964 q^{42} +3.18022 q^{43} +25.5494 q^{44} -2.36411 q^{45} -2.62656 q^{46} +0.360574 q^{47} +20.1068 q^{48} +7.62118 q^{49} -5.60028 q^{50} +6.59262 q^{51} -5.83689 q^{52} +1.71032 q^{53} +10.9486 q^{54} -13.9284 q^{55} -29.1139 q^{56} +0.416359 q^{57} +0.810577 q^{58} -1.58732 q^{59} -25.7876 q^{60} +9.22123 q^{61} -18.8440 q^{62} +3.38491 q^{63} +9.97503 q^{64} +3.18200 q^{65} -27.0013 q^{66} +9.27231 q^{67} +16.3848 q^{68} +1.97110 q^{69} +26.8219 q^{70} +0.623888 q^{71} -6.74008 q^{72} +5.13126 q^{73} +13.7735 q^{74} +4.20272 q^{75} +1.03479 q^{76} +19.9425 q^{77} +6.16858 q^{78} +8.42972 q^{79} -27.2424 q^{80} -10.8721 q^{81} +13.9300 q^{82} -14.6673 q^{83} +36.9225 q^{84} -8.93224 q^{85} -8.35305 q^{86} -0.608297 q^{87} -39.7098 q^{88} +1.12919 q^{89} +6.20947 q^{90} -4.55597 q^{91} +4.89882 q^{92} +14.1414 q^{93} -0.947070 q^{94} -0.564119 q^{95} -22.7961 q^{96} +6.84287 q^{97} -20.0175 q^{98} +4.61684 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 176 q + 19 q^{2} + 22 q^{3} + 203 q^{4} + 28 q^{5} + 9 q^{6} + 30 q^{7} + 51 q^{8} + 204 q^{9}+O(q^{10}) \) 176 * q + 19 * q^2 + 22 * q^3 + 203 * q^4 + 28 * q^5 + 9 * q^6 + 30 * q^7 + 51 * q^8 + 204 * q^9	\( 176 q + 19 q^{2} + 22 q^{3} + 203 q^{4} + 28 q^{5} + 9 q^{6} + 30 q^{7} + 51 q^{8} + 204 q^{9} + 18 q^{10} + 11 q^{11} + 46 q^{12} + 87 q^{13} - 6 q^{14} + 29 q^{15} + 257 q^{16} + 14 q^{17} + 72 q^{18} + 34 q^{19} + 45 q^{20} + 23 q^{21} + 62 q^{22} + 176 q^{23} + 33 q^{24} + 272 q^{25} + 31 q^{26} + 82 q^{27} + 80 q^{28} + 75 q^{29} - 30 q^{30} + 73 q^{31} + 71 q^{32} + 30 q^{33} + 23 q^{34} + 44 q^{35} + 264 q^{36} + 236 q^{37} - 21 q^{38} + 17 q^{39} + 43 q^{40} + 51 q^{41} + 38 q^{42} + 51 q^{43} + 12 q^{44} + 127 q^{45} + 19 q^{46} + 45 q^{47} + 61 q^{48} + 268 q^{49} + 55 q^{50} - 3 q^{51} + 166 q^{52} + 63 q^{53} - 32 q^{54} + 11 q^{55} - 9 q^{56} + 72 q^{57} + 98 q^{58} + 95 q^{59} - 7 q^{60} + 73 q^{61} + 12 q^{62} + 19 q^{63} + 365 q^{64} + 19 q^{65} - 28 q^{66} + 138 q^{67} + 16 q^{68} + 22 q^{69} + 100 q^{70} + 85 q^{71} + 129 q^{72} + 118 q^{73} - 21 q^{74} - 12 q^{75} + 52 q^{76} + 75 q^{77} + 97 q^{78} + 74 q^{79} + 8 q^{80} + 280 q^{81} + 67 q^{82} + 10 q^{83} - 51 q^{84} + 169 q^{85} - 39 q^{86} - 6 q^{87} + 159 q^{88} + 38 q^{89} + 22 q^{90} + 90 q^{91} + 203 q^{92} + 230 q^{93} + 63 q^{94} + 30 q^{95} + 107 q^{96} + 161 q^{97} + 58 q^{98} + 7 q^{99}+O(q^{100}) \) 176 * q + 19 * q^2 + 22 * q^3 + 203 * q^4 + 28 * q^5 + 9 * q^6 + 30 * q^7 + 51 * q^8 + 204 * q^9 + 18 * q^10 + 11 * q^11 + 46 * q^12 + 87 * q^13 - 6 * q^14 + 29 * q^15 + 257 * q^16 + 14 * q^17 + 72 * q^18 + 34 * q^19 + 45 * q^20 + 23 * q^21 + 62 * q^22 + 176 * q^23 + 33 * q^24 + 272 * q^25 + 31 * q^26 + 82 * q^27 + 80 * q^28 + 75 * q^29 - 30 * q^30 + 73 * q^31 + 71 * q^32 + 30 * q^33 + 23 * q^34 + 44 * q^35 + 264 * q^36 + 236 * q^37 - 21 * q^38 + 17 * q^39 + 43 * q^40 + 51 * q^41 + 38 * q^42 + 51 * q^43 + 12 * q^44 + 127 * q^45 + 19 * q^46 + 45 * q^47 + 61 * q^48 + 268 * q^49 + 55 * q^50 - 3 * q^51 + 166 * q^52 + 63 * q^53 - 32 * q^54 + 11 * q^55 - 9 * q^56 + 72 * q^57 + 98 * q^58 + 95 * q^59 - 7 * q^60 + 73 * q^61 + 12 * q^62 + 19 * q^63 + 365 * q^64 + 19 * q^65 - 28 * q^66 + 138 * q^67 + 16 * q^68 + 22 * q^69 + 100 * q^70 + 85 * q^71 + 129 * q^72 + 118 * q^73 - 21 * q^74 - 12 * q^75 + 52 * q^76 + 75 * q^77 + 97 * q^78 + 74 * q^79 + 8 * q^80 + 280 * q^81 + 67 * q^82 + 10 * q^83 - 51 * q^84 + 169 * q^85 - 39 * q^86 - 6 * q^87 + 159 * q^88 + 38 * q^89 + 22 * q^90 + 90 * q^91 + 203 * q^92 + 230 * q^93 + 63 * q^94 + 30 * q^95 + 107 * q^96 + 161 * q^97 + 58 * q^98 + 7 * q^99

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