LMFDB - Embedded newform 7935.2.a.bp.1.4

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [7935,2,Mod(1,7935)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("7935.1"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(7935, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 0, 0])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 7935 = 3 \cdot 5 \cdot 23^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	7935.a (trivial)

Newform invariants

comment:select newform

sage:traces = [15,0,-15,12,-15,0,-5] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(7)] == traces)

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

Self dual:	yes
Analytic conductor:	$63.3612940039$
Analytic rank:	$1$
Dimension:	$15$
Coefficient field:	$\mathbb{Q}[x]/(x^{15} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{15} - 21x^{13} + 172x^{11} - 696x^{9} + 1466x^{7} - 1583x^{5} + 803x^{3} - 11x^{2} - 143x + 11 $ x^15 - 21x^13 + 172x^11 - 696x^9 + 1466x^7 - 1583x^5 + 803x^3 - 11x^2 - 143x + 11
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 345)
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.4
Root			$-1.52166$ of defining polynomial
Character	$\chi$	$=$	7935.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q-1.52166 q^{2} -1.00000 q^{3} +0.315440 q^{4} -1.00000 q^{5} +1.52166 q^{6} -2.43525 q^{7} +2.56332 q^{8} +1.00000 q^{9} +1.52166 q^{10} +0.157496 q^{11} -0.315440 q^{12} -3.63908 q^{13} +3.70561 q^{14} +1.00000 q^{15} -4.53138 q^{16} -2.69280 q^{17} -1.52166 q^{18} +3.54948 q^{19} -0.315440 q^{20} +2.43525 q^{21} -0.239655 q^{22} -2.56332 q^{24} +1.00000 q^{25} +5.53743 q^{26} -1.00000 q^{27} -0.768175 q^{28} -2.74281 q^{29} -1.52166 q^{30} +8.44443 q^{31} +1.76856 q^{32} -0.157496 q^{33} +4.09752 q^{34} +2.43525 q^{35} +0.315440 q^{36} -3.24935 q^{37} -5.40110 q^{38} +3.63908 q^{39} -2.56332 q^{40} +3.80531 q^{41} -3.70561 q^{42} -4.70101 q^{43} +0.0496807 q^{44} -1.00000 q^{45} -12.7257 q^{47} +4.53138 q^{48} -1.06958 q^{49} -1.52166 q^{50} +2.69280 q^{51} -1.14791 q^{52} +7.39111 q^{53} +1.52166 q^{54} -0.157496 q^{55} -6.24232 q^{56} -3.54948 q^{57} +4.17362 q^{58} +0.00696321 q^{59} +0.315440 q^{60} -5.05027 q^{61} -12.8495 q^{62} -2.43525 q^{63} +6.37162 q^{64} +3.63908 q^{65} +0.239655 q^{66} +8.05936 q^{67} -0.849417 q^{68} -3.70561 q^{70} +0.175802 q^{71} +2.56332 q^{72} +3.72382 q^{73} +4.94439 q^{74} -1.00000 q^{75} +1.11965 q^{76} -0.383542 q^{77} -5.53743 q^{78} +8.59875 q^{79} +4.53138 q^{80} +1.00000 q^{81} -5.79037 q^{82} +7.14020 q^{83} +0.768175 q^{84} +2.69280 q^{85} +7.15332 q^{86} +2.74281 q^{87} +0.403714 q^{88} +16.7431 q^{89} +1.52166 q^{90} +8.86204 q^{91} -8.44443 q^{93} +19.3641 q^{94} -3.54948 q^{95} -1.76856 q^{96} +14.0686 q^{97} +1.62754 q^{98} +0.157496 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 15 q - 15 q^{3} + 12 q^{4} - 15 q^{5} - 5 q^{7} + 15 q^{9} + 13 q^{11} - 12 q^{12} - 24 q^{13} + 15 q^{14} + 15 q^{15} + 2 q^{16} + 2 q^{17} + 13 q^{19} - 12 q^{20} + 5 q^{21} - 9 q^{22} + 15 q^{25} - 9 q^{26}+ \cdots + 13 q^{99}+O(q^{100}) $ 15 * q - 15 * q^3 + 12 * q^4 - 15 * q^5 - 5 * q^7 + 15 * q^9 + 13 * q^11 - 12 * q^12 - 24 * q^13 + 15 * q^14 + 15 * q^15 + 2 * q^16 + 2 * q^17 + 13 * q^19 - 12 * q^20 + 5 * q^21 - 9 * q^22 + 15 * q^25 - 9 * q^26 - 15 * q^27 + q^28 - 3 * q^29 - 22 * q^31 - 13 * q^33 + q^34 + 5 * q^35 + 12 * q^36 - 6 * q^37 - 17 * q^38 + 24 * q^39 - 20 * q^41 - 15 * q^42 - 4 * q^43 - 18 * q^44 - 15 * q^45 + 7 * q^47 - 2 * q^48 - 10 * q^49 - 2 * q^51 - 55 * q^52 + 4 * q^53 - 13 * q^55 + 25 * q^56 - 13 * q^57 + 2 * q^58 + 9 * q^59 + 12 * q^60 + 13 * q^61 - 7 * q^62 - 5 * q^63 - 26 * q^64 + 24 * q^65 + 9 * q^66 - 32 * q^67 + 27 * q^68 - 15 * q^70 + 14 * q^71 - 43 * q^73 - 11 * q^74 - 15 * q^75 + 88 * q^76 - 21 * q^77 + 9 * q^78 + 33 * q^79 - 2 * q^80 + 15 * q^81 - 35 * q^82 - 12 * q^83 - q^84 - 2 * q^85 + 77 * q^86 + 3 * q^87 - 37 * q^88 + 29 * q^89 + 20 * q^91 + 22 * q^93 - 20 * q^94 - 13 * q^95 + 18 * q^97 - 19 * q^98 + 13 * q^99

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 $

$2$	−1.52166	−1.07597	−0.537987	−	0.842953i	$-0.680815\pi$
$2$	−1.52166	−1.07597	−0.537987	+	0.842953i	$0.680815\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	0.315440	0.157720
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	1.52166	0.621214
$7$	−2.43525	−0.920436	−0.460218	−	0.887806i	$-0.652229\pi$
$7$	−2.43525	−0.920436	−0.460218	+	0.887806i	$0.652229\pi$
$8$	2.56332	0.906271
$9$	1.00000	0.333333
$10$	1.52166	0.481190
$11$	0.157496	0.0474869	0.0237435	−	0.999718i	$-0.492442\pi$
$11$	0.157496	0.0474869	0.0237435	+	0.999718i	$0.492442\pi$
$12$	−0.315440	−0.0910598
$13$	−3.63908	−1.00930	−0.504649	−	0.863325i	$-0.668378\pi$
$13$	−3.63908	−1.00930	−0.504649	+	0.863325i	$0.668378\pi$
$14$	3.70561	0.990365
$15$	1.00000	0.258199
$16$	−4.53138	−1.13284
$17$	−2.69280	−0.653100	−0.326550	−	0.945180i	$-0.605886\pi$
$17$	−2.69280	−0.653100	−0.326550	+	0.945180i	$0.605886\pi$
$18$	−1.52166	−0.358658
$19$	3.54948	0.814307	0.407154	−	0.913360i	$-0.366521\pi$
$19$	3.54948	0.814307	0.407154	+	0.913360i	$0.366521\pi$
$20$	−0.315440	−0.0705346
$21$	2.43525	0.531414
$22$	−0.239655	−0.0510947
$23$	0	0
$23$	0	0
$24$	−2.56332	−0.523236
$25$	1.00000	0.200000
$26$	5.53743	1.08598
$27$	−1.00000	−0.192450
$28$	−0.768175	−0.145171
$29$	−2.74281	−0.509327	−0.254664	−	0.967030i	$-0.581965\pi$
$29$	−2.74281	−0.509327	−0.254664	+	0.967030i	$0.581965\pi$
$30$	−1.52166	−0.277815
$31$	8.44443	1.51666	0.758332	−	0.651868i	$-0.226015\pi$
$31$	8.44443	1.51666	0.758332	+	0.651868i	$0.226015\pi$
$32$	1.76856	0.312640
$33$	−0.157496	−0.0274166
$34$	4.09752	0.702718
$35$	2.43525	0.411632
$36$	0.315440	0.0525734
$37$	−3.24935	−0.534190	−0.267095	−	0.963670i	$-0.586064\pi$
$37$	−3.24935	−0.534190	−0.267095	+	0.963670i	$0.586064\pi$
$38$	−5.40110	−0.876174
$39$	3.63908	0.582719
$40$	−2.56332	−0.405297
$41$	3.80531	0.594289	0.297144	−	0.954833i	$-0.403966\pi$
$41$	3.80531	0.594289	0.297144	+	0.954833i	$0.403966\pi$
$42$	−3.70561	−0.571788
$43$	−4.70101	−0.716897	−0.358448	−	0.933550i	$-0.616694\pi$
$43$	−4.70101	−0.716897	−0.358448	+	0.933550i	$0.616694\pi$
$44$	0.0496807	0.00748964
$45$	−1.00000	−0.149071
$46$	0	0
$47$	−12.7257	−1.85623	−0.928116	−	0.372292i	$-0.878572\pi$
$47$	−12.7257	−1.85623	−0.928116	+	0.372292i	$0.878572\pi$
$48$	4.53138	0.654048
$49$	−1.06958	−0.152797
$50$	−1.52166	−0.215195
$51$	2.69280	0.377067
$52$	−1.14791	−0.159187
$53$	7.39111	1.01525	0.507623	−	0.861579i	$-0.330524\pi$
$53$	7.39111	1.01525	0.507623	+	0.861579i	$0.330524\pi$
$54$	1.52166	0.207071
$55$	−0.157496	−0.0212368
$56$	−6.24232	−0.834165
$57$	−3.54948	−0.470141
$58$	4.17362	0.548023
$59$	0.00696321	0.000906532 0	0.000453266	−	1.00000i	$-0.499856\pi$
$59$	0.00696321	0.000906532 0	0.000453266		1.00000i	$0.499856\pi$
$60$	0.315440	0.0407232
$61$	−5.05027	−0.646621	−0.323310	−	0.946293i	$-0.604796\pi$
$61$	−5.05027	−0.646621	−0.323310	+	0.946293i	$0.604796\pi$
$62$	−12.8495	−1.63189
$63$	−2.43525	−0.306812
$64$	6.37162	0.796452
$65$	3.63908	0.451372
$66$	0.239655	0.0294995
$67$	8.05936	0.984608	0.492304	−	0.870423i	$-0.336155\pi$
$67$	8.05936	0.984608	0.492304	+	0.870423i	$0.336155\pi$
$68$	−0.849417	−0.103007
$69$	0	0
$70$	−3.70561	−0.442905
$71$	0.175802	0.0208638	0.0104319	−	0.999946i	$-0.496679\pi$
$71$	0.175802	0.0208638	0.0104319	+	0.999946i	$0.496679\pi$
$72$	2.56332	0.302090
$73$	3.72382	0.435841	0.217920	−	0.975967i	$-0.430073\pi$
$73$	3.72382	0.435841	0.217920	+	0.975967i	$0.430073\pi$
$74$	4.94439	0.574774
$75$	−1.00000	−0.115470
$76$	1.11965	0.128433
$77$	−0.383542	−0.0437087
$78$	−5.53743	−0.626990
$79$	8.59875	0.967435	0.483717	−	0.875224i	$-0.339286\pi$
$79$	8.59875	0.967435	0.483717	+	0.875224i	$0.339286\pi$
$80$	4.53138	0.506623
$81$	1.00000	0.111111
$82$	−5.79037	−0.639440
$83$	7.14020	0.783738	0.391869	−	0.920021i	$-0.371829\pi$
$83$	7.14020	0.783738	0.391869	+	0.920021i	$0.371829\pi$
$84$	0.768175	0.0838147
$85$	2.69280	0.292075
$86$	7.15332	0.771362
$87$	2.74281	0.294060
$88$	0.403714	0.0430360
$89$	16.7431	1.77477	0.887384	−	0.461032i	$-0.152521\pi$
$89$	16.7431	1.77477	0.887384	+	0.461032i	$0.152521\pi$
$90$	1.52166	0.160397
$91$	8.86204	0.928994
$92$	0	0
$93$	−8.44443	−0.875646
$94$	19.3641	1.99726
$95$	−3.54948	−0.364169
$96$	−1.76856	−0.180503
$97$	14.0686	1.42845	0.714225	−	0.699917i	$-0.246779\pi$
$97$	14.0686	1.42845	0.714225	+	0.699917i	$0.246779\pi$
$98$	1.62754	0.164406
$99$	0.157496	0.0158290
$100$	0.315440	0.0315440
$101$	4.70030	0.467697	0.233849	−	0.972273i	$-0.424868\pi$
$101$	4.70030	0.467697	0.233849	+	0.972273i	$0.424868\pi$
$102$	−4.09752	−0.405715
$103$	−4.86693	−0.479553	−0.239776	−	0.970828i	$-0.577074\pi$
$103$	−4.86693	−0.479553	−0.239776	+	0.970828i	$0.577074\pi$
$104$	−9.32812	−0.914698
$105$	−2.43525	−0.237656
$106$	−11.2467	−1.09238
$107$	−14.8104	−1.43178	−0.715890	−	0.698213i	$-0.753979\pi$
$107$	−14.8104	−1.43178	−0.715890	+	0.698213i	$0.753979\pi$
$108$	−0.315440	−0.0303533
$109$	−4.98428	−0.477408	−0.238704	−	0.971092i	$-0.576723\pi$
$109$	−4.98428	−0.477408	−0.238704	+	0.971092i	$0.576723\pi$
$110$	0.239655	0.0228502
$111$	3.24935	0.308414
$112$	11.0350	1.04271
$113$	0.0293311	0.00275924	0.00137962	−	0.999999i	$-0.499561\pi$
$113$	0.0293311	0.00275924	0.00137962	+	0.999999i	$0.499561\pi$
$114$	5.40110	0.505859
$115$	0	0
$116$	−0.865194	−0.0803312
$117$	−3.63908	−0.336433
$118$	−0.0105956	−0.000975405 0
$119$	6.55762	0.601136
$120$	2.56332	0.233998
$121$	−10.9752	−0.997745
$122$	7.68478	0.695747
$123$	−3.80531	−0.343113
$124$	2.66371	0.239209
$125$	−1.00000	−0.0894427
$126$	3.70561	0.330122
$127$	−13.8814	−1.23177	−0.615886	−	0.787835i	$-0.711202\pi$
$127$	−13.8814	−1.23177	−0.615886	+	0.787835i	$0.711202\pi$
$128$	−13.2325	−1.16960
$129$	4.70101	0.413901
$130$	−5.53743	−0.485664
$131$	−5.91237	−0.516566	−0.258283	−	0.966069i	$-0.583157\pi$
$131$	−5.91237	−0.516566	−0.258283	+	0.966069i	$0.583157\pi$
$132$	−0.0496807	−0.00432415
$133$	−8.64386	−0.749518
$134$	−12.2636	−1.05941
$135$	1.00000	0.0860663
$136$	−6.90251	−0.591885
$137$	−0.000207022 0	−1.76871e−5 0	−8.84354e−6	−	1.00000i	$-0.500003\pi$
$137$	−0.000207022 0	−1.76871e−5 0	−8.84354e−6		1.00000i	$0.500003\pi$
$138$	0	0
$139$	−21.1954	−1.79777	−0.898886	−	0.438182i	$-0.855622\pi$
$139$	−21.1954	−1.79777	−0.898886	+	0.438182i	$0.855622\pi$
$140$	0.768175	0.0649226
$141$	12.7257	1.07170
$142$	−0.267510	−0.0224489
$143$	−0.573141	−0.0479285
$144$	−4.53138	−0.377615
$145$	2.74281	0.227778
$146$	−5.66638	−0.468953
$147$	1.06958	0.0882176
$148$	−1.02498	−0.0842525
$149$	−8.15494	−0.668079	−0.334039	−	0.942559i	$-0.608412\pi$
$149$	−8.15494	−0.668079	−0.334039	+	0.942559i	$0.608412\pi$
$150$	1.52166	0.124243
$151$	−0.294881	−0.0239971	−0.0119985	−	0.999928i	$-0.503819\pi$
$151$	−0.294881	−0.0239971	−0.0119985	+	0.999928i	$0.503819\pi$
$152$	9.09847	0.737983
$153$	−2.69280	−0.217700
$154$	0.583619	0.0470294
$155$	−8.44443	−0.678273
$156$	1.14791	0.0919065
$157$	18.2971	1.46027	0.730135	−	0.683302i	$-0.239457\pi$
$157$	18.2971	1.46027	0.730135	+	0.683302i	$0.239457\pi$
$158$	−13.0843	−1.04093
$159$	−7.39111	−0.586153
$160$	−1.76856	−0.139817
$161$	0	0
$162$	−1.52166	−0.119553
$163$	18.4174	1.44256	0.721280	−	0.692644i	$-0.243554\pi$
$163$	18.4174	1.44256	0.721280	+	0.692644i	$0.243554\pi$
$164$	1.20035	0.0937314
$165$	0.157496	0.0122611
$166$	−10.8649	−0.843282
$167$	19.6815	1.52300	0.761501	−	0.648164i	$-0.224463\pi$
$167$	19.6815	1.52300	0.761501	+	0.648164i	$0.224463\pi$
$168$	6.24232	0.481605
$169$	0.242876	0.0186827
$170$	−4.09752	−0.314265
$171$	3.54948	0.271436
$172$	−1.48289	−0.113069
$173$	19.7802	1.50386	0.751930	−	0.659243i	$-0.229123\pi$
$173$	19.7802	1.50386	0.751930	+	0.659243i	$0.229123\pi$
$174$	−4.17362	−0.316401
$175$	−2.43525	−0.184087
$176$	−0.713675	−0.0537953
$177$	−0.00696321	−0.000523387 0
$178$	−25.4773	−1.90960
$179$	25.7173	1.92220	0.961101	−	0.276199i	$-0.0890748\pi$
$179$	25.7173	1.92220	0.961101	+	0.276199i	$0.0890748\pi$
$180$	−0.315440	−0.0235115
$181$	22.4990	1.67234	0.836170	−	0.548470i	$-0.184790\pi$
$181$	22.4990	1.67234	0.836170	+	0.548470i	$0.184790\pi$
$182$	−13.4850	−0.999574
$183$	5.05027	0.373327
$184$	0	0
$185$	3.24935	0.238897
$186$	12.8495	0.942173
$187$	−0.424106	−0.0310137
$188$	−4.01419	−0.292765
$189$	2.43525	0.177138
$190$	5.40110	0.391837
$191$	14.0246	1.01478	0.507392	−	0.861715i	$-0.330609\pi$
$191$	14.0246	1.01478	0.507392	+	0.861715i	$0.330609\pi$
$192$	−6.37162	−0.459832
$193$	5.28033	0.380086	0.190043	−	0.981776i	$-0.439137\pi$
$193$	5.28033	0.380086	0.190043	+	0.981776i	$0.439137\pi$
$194$	−21.4076	−1.53697
$195$	−3.63908	−0.260600
$196$	−0.337389	−0.0240992
$197$	12.9518	0.922779	0.461390	−	0.887198i	$-0.347351\pi$
$197$	12.9518	0.922779	0.461390	+	0.887198i	$0.347351\pi$
$198$	−0.239655	−0.0170316
$199$	0.932061	0.0660720	0.0330360	−	0.999454i	$-0.489482\pi$
$199$	0.932061	0.0660720	0.0330360	+	0.999454i	$0.489482\pi$
$200$	2.56332	0.181254
$201$	−8.05936	−0.568464
$202$	−7.15224	−0.503230
$203$	6.67942	0.468803
$204$	0.849417	0.0594711
$205$	−3.80531	−0.265774
$206$	7.40580	0.515986
$207$	0	0
$208$	16.4900	1.14338
$209$	0.559030	0.0386689
$210$	3.70561	0.255711
$211$	7.66135	0.527429	0.263715	−	0.964601i	$-0.415052\pi$
$211$	7.66135	0.527429	0.263715	+	0.964601i	$0.415052\pi$
$212$	2.33145	0.160125
$213$	−0.175802	−0.0120457
$214$	22.5364	1.54056
$215$	4.70101	0.320606
$216$	−2.56332	−0.174412
$217$	−20.5643	−1.39599
$218$	7.58437	0.513678
$219$	−3.72382	−0.251633
$220$	−0.0496807	−0.00334947
$221$	9.79930	0.659172
$222$	−4.94439	−0.331846
$223$	−25.0563	−1.67789	−0.838946	−	0.544215i	$-0.816828\pi$
$223$	−25.0563	−1.67789	−0.838946	+	0.544215i	$0.816828\pi$
$224$	−4.30688	−0.287765
$225$	1.00000	0.0666667
$226$	−0.0446319	−0.00296887
$227$	−14.9400	−0.991605	−0.495802	−	0.868435i	$-0.665126\pi$
$227$	−14.9400	−0.991605	−0.495802	+	0.868435i	$0.665126\pi$
$228$	−1.11965	−0.0741507
$229$	15.4474	1.02079	0.510397	−	0.859939i	$-0.329498\pi$
$229$	15.4474	1.02079	0.510397	+	0.859939i	$0.329498\pi$
$230$	0	0
$231$	0.383542	0.0252352
$232$	−7.03071	−0.461589
$233$	11.4173	0.747971	0.373985	−	0.927435i	$-0.377991\pi$
$233$	11.4173	0.747971	0.373985	+	0.927435i	$0.377991\pi$
$234$	5.53743	0.361993
$235$	12.7257	0.830132
$236$	0.00219648	0.000142978 0
$237$	−8.59875	−0.558549
$238$	−9.97846	−0.646807
$239$	−6.47716	−0.418973	−0.209486	−	0.977812i	$-0.567179\pi$
$239$	−6.47716	−0.418973	−0.209486	+	0.977812i	$0.567179\pi$
$240$	−4.53138	−0.292499
$241$	−8.82085	−0.568201	−0.284101	−	0.958794i	$-0.591695\pi$
$241$	−8.82085	−0.568201	−0.284101	+	0.958794i	$0.591695\pi$
$242$	16.7005	1.07355
$243$	−1.00000	−0.0641500
$244$	−1.59306	−0.101985
$245$	1.06958	0.0683331
$246$	5.79037	0.369181
$247$	−12.9168	−0.821879
$248$	21.6458	1.37451
$249$	−7.14020	−0.452492
$250$	1.52166	0.0962380
$251$	6.93562	0.437773	0.218886	−	0.975750i	$-0.429758\pi$
$251$	6.93562	0.437773	0.218886	+	0.975750i	$0.429758\pi$
$252$	−0.768175	−0.0483904
$253$	0	0
$254$	21.1227	1.32536
$255$	−2.69280	−0.168630
$256$	7.39215	0.462009
$257$	−22.6644	−1.41377	−0.706884	−	0.707329i	$-0.749900\pi$
$257$	−22.6644	−1.41377	−0.706884	+	0.707329i	$0.749900\pi$
$258$	−7.15332	−0.445346
$259$	7.91296	0.491687
$260$	1.14791	0.0711904
$261$	−2.74281	−0.169776
$262$	8.99659	0.555811
$263$	−9.87610	−0.608986	−0.304493	−	0.952515i	$-0.598487\pi$
$263$	−9.87610	−0.608986	−0.304493	+	0.952515i	$0.598487\pi$
$264$	−0.403714	−0.0248469
$265$	−7.39111	−0.454032
$266$	13.1530	0.806462
$267$	−16.7431	−1.02466
$268$	2.54225	0.155293
$269$	7.09430	0.432547	0.216274	−	0.976333i	$-0.430610\pi$
$269$	7.09430	0.432547	0.216274	+	0.976333i	$0.430610\pi$
$270$	−1.52166	−0.0926051
$271$	14.2178	0.863670	0.431835	−	0.901953i	$-0.357866\pi$
$271$	14.2178	0.863670	0.431835	+	0.901953i	$0.357866\pi$
$272$	12.2021	0.739860
$273$	−8.86204	−0.536355
$274$	0.000315017 0	1.90308e−5 0
$275$	0.157496	0.00949738
$276$	0	0
$277$	−16.7847	−1.00849	−0.504246	−	0.863560i	$-0.668230\pi$
$277$	−16.7847	−1.00849	−0.504246	+	0.863560i	$0.668230\pi$
$278$	32.2522	1.93436
$279$	8.44443	0.505555
$280$	6.24232	0.373050
$281$	−0.607504	−0.0362406	−0.0181203	−	0.999836i	$-0.505768\pi$
$281$	−0.607504	−0.0362406	−0.0181203	+	0.999836i	$0.505768\pi$
$282$	−19.3641	−1.15312
$283$	−21.2552	−1.26349	−0.631746	−	0.775175i	$-0.717662\pi$
$283$	−21.2552	−1.26349	−0.631746	+	0.775175i	$0.717662\pi$
$284$	0.0554550	0.00329065
$285$	3.54948	0.210253
$286$	0.872124	0.0515698
$287$	−9.26685	−0.547005
$288$	1.76856	0.104213
$289$	−9.74884	−0.573461
$290$	−4.17362	−0.245083
$291$	−14.0686	−0.824716
$292$	1.17464	0.0687409
$293$	0.621553	0.0363115	0.0181557	−	0.999835i	$-0.494221\pi$
$293$	0.621553	0.0363115	0.0181557	+	0.999835i	$0.494221\pi$
$294$	−1.62754	−0.0949198
$295$	−0.00696321	−0.000405414 0
$296$	−8.32913	−0.484121
$297$	−0.157496	−0.00913886
$298$	12.4090	0.718836
$299$	0	0
$300$	−0.315440	−0.0182120
$301$	11.4481	0.659858
$302$	0.448708	0.0258203
$303$	−4.70030	−0.270025
$304$	−16.0841	−0.922484
$305$	5.05027	0.289178
$306$	4.09752	0.234239
$307$	−11.1010	−0.633569	−0.316785	−	0.948498i	$-0.602603\pi$
$307$	−11.1010	−0.633569	−0.316785	+	0.948498i	$0.602603\pi$
$308$	−0.120985	−0.00689374
$309$	4.86693	0.276870
$310$	12.8495	0.729804
$311$	−1.84851	−0.104819	−0.0524096	−	0.998626i	$-0.516690\pi$
$311$	−1.84851	−0.104819	−0.0524096	+	0.998626i	$0.516690\pi$
$312$	9.32812	0.528101
$313$	12.9195	0.730253	0.365127	−	0.930958i	$-0.381026\pi$
$313$	12.9195	0.730253	0.365127	+	0.930958i	$0.381026\pi$
$314$	−27.8420	−1.57121
$315$	2.43525	0.137211
$316$	2.71239	0.152584
$317$	24.1757	1.35784	0.678922	−	0.734211i	$-0.262448\pi$
$317$	24.1757	1.35784	0.678922	+	0.734211i	$0.262448\pi$
$318$	11.2467	0.630685
$319$	−0.431983	−0.0241864
$320$	−6.37162	−0.356184
$321$	14.8104	0.826639
$322$	0	0
$323$	−9.55804	−0.531824
$324$	0.315440	0.0175245
$325$	−3.63908	−0.201860
$326$	−28.0249	−1.55216
$327$	4.98428	0.275631
$328$	9.75423	0.538587
$329$	30.9901	1.70854
$330$	−0.239655	−0.0131926
$331$	−9.41880	−0.517704	−0.258852	−	0.965917i	$-0.583344\pi$
$331$	−9.41880	−0.517704	−0.258852	+	0.965917i	$0.583344\pi$
$332$	2.25231	0.123611
$333$	−3.24935	−0.178063
$334$	−29.9485	−1.63871
$335$	−8.05936	−0.440330
$336$	−11.0350	−0.602009
$337$	−29.1059	−1.58550	−0.792750	−	0.609547i	$-0.791351\pi$
$337$	−29.1059	−1.58550	−0.792750	+	0.609547i	$0.791351\pi$
$338$	−0.369573	−0.0201021
$339$	−0.0293311	−0.00159305
$340$	0.849417	0.0460661
$341$	1.32997	0.0720217
$342$	−5.40110	−0.292058
$343$	19.6514	1.06108
$344$	−12.0502	−0.649703
$345$	0	0
$346$	−30.0987	−1.61812
$347$	12.6705	0.680189	0.340094	−	0.940391i	$-0.389541\pi$
$347$	12.6705	0.680189	0.340094	+	0.940391i	$0.389541\pi$
$348$	0.865194	0.0463792
$349$	4.06847	0.217780	0.108890	−	0.994054i	$-0.465270\pi$
$349$	4.06847	0.217780	0.108890	+	0.994054i	$0.465270\pi$
$350$	3.70561	0.198073
$351$	3.63908	0.194240
$352$	0.278542	0.0148463
$353$	10.0195	0.533284	0.266642	−	0.963796i	$-0.414086\pi$
$353$	10.0195	0.533284	0.266642	+	0.963796i	$0.414086\pi$
$354$	0.0105956	0.000563151 0
$355$	−0.175802	−0.00933059
$356$	5.28146	0.279917
$357$	−6.55762	−0.347066
$358$	−39.1329	−2.06824
$359$	36.3213	1.91697	0.958483	−	0.285151i	$-0.0920437\pi$
$359$	36.3213	1.91697	0.958483	+	0.285151i	$0.0920437\pi$
$360$	−2.56332	−0.135099
$361$	−6.40116	−0.336903
$362$	−34.2358	−1.79939
$363$	10.9752	0.576048
$364$	2.79545	0.146521
$365$	−3.72382	−0.194914
$366$	−7.68478	−0.401690
$367$	3.48523	0.181927	0.0909637	−	0.995854i	$-0.471005\pi$
$367$	3.48523	0.181927	0.0909637	+	0.995854i	$0.471005\pi$
$368$	0	0
$369$	3.80531	0.198096
$370$	−4.94439	−0.257047
$371$	−17.9992	−0.934470
$372$	−2.66371	−0.138107
$373$	−6.75585	−0.349805	−0.174902	−	0.984586i	$-0.555961\pi$
$373$	−6.75585	−0.349805	−0.174902	+	0.984586i	$0.555961\pi$
$374$	0.645343	0.0333699
$375$	1.00000	0.0516398
$376$	−32.6200	−1.68225
$377$	9.98130	0.514063
$378$	−3.70561	−0.190596
$379$	24.2905	1.24772	0.623861	−	0.781536i	$-0.285563\pi$
$379$	24.2905	1.24772	0.623861	+	0.781536i	$0.285563\pi$
$380$	−1.11965	−0.0574369
$381$	13.8814	0.711164
$382$	−21.3406	−1.09188
$383$	35.3345	1.80551	0.902755	−	0.430155i	$-0.141541\pi$
$383$	35.3345	1.80551	0.902755	+	0.430155i	$0.141541\pi$
$384$	13.2325	0.675270
$385$	0.383542	0.0195471
$386$	−8.03485	−0.408963
$387$	−4.70101	−0.238966
$388$	4.43780	0.225295
$389$	−0.133524	−0.00676996	−0.00338498	−	0.999994i	$-0.501077\pi$
$389$	−0.133524	−0.00676996	−0.00338498	+	0.999994i	$0.501077\pi$
$390$	5.53743	0.280398
$391$	0	0
$392$	−2.74168	−0.138476
$393$	5.91237	0.298239
$394$	−19.7082	−0.992887
$395$	−8.59875	−0.432650
$396$	0.0496807	0.00249655
$397$	−0.398921	−0.0200213	−0.0100106	−	0.999950i	$-0.503187\pi$
$397$	−0.398921	−0.0200213	−0.0100106	+	0.999950i	$0.503187\pi$
$398$	−1.41828	−0.0710918
$399$	8.64386	0.432734
$400$	−4.53138	−0.226569
$401$	2.97295	0.148462	0.0742310	−	0.997241i	$-0.476350\pi$
$401$	2.97295	0.148462	0.0742310	+	0.997241i	$0.476350\pi$
$402$	12.2636	0.611652
$403$	−30.7299	−1.53077
$404$	1.48266	0.0737653
$405$	−1.00000	−0.0496904
$406$	−10.1638	−0.504420
$407$	−0.511760	−0.0253670
$408$	6.90251	0.341725
$409$	−36.2392	−1.79191	−0.895957	−	0.444140i	$-0.853509\pi$
$409$	−36.2392	−1.79191	−0.895957	+	0.444140i	$0.853509\pi$
$410$	5.79037	0.285966
$411$	0.000207022 0	1.02116e−5 0
$412$	−1.53523	−0.0756351
$413$	−0.0169571	−0.000834405 0
$414$	0	0
$415$	−7.14020	−0.350498
$416$	−6.43592	−0.315547
$417$	21.1954	1.03794
$418$	−0.850653	−0.0416068
$419$	−17.9066	−0.874796	−0.437398	−	0.899268i	$-0.644100\pi$
$419$	−17.9066	−0.874796	−0.437398	+	0.899268i	$0.644100\pi$
$420$	−0.768175	−0.0374831
$421$	−10.7826	−0.525513	−0.262756	−	0.964862i	$-0.584632\pi$
$421$	−10.7826	−0.525513	−0.262756	+	0.964862i	$0.584632\pi$
$422$	−11.6580	−0.567500
$423$	−12.7257	−0.618744
$424$	18.9458	0.920089
$425$	−2.69280	−0.130620
$426$	0.267510	0.0129609
$427$	12.2986	0.595173
$428$	−4.67181	−0.225821
$429$	0.573141	0.0276715
$430$	−7.15332	−0.344964
$431$	−25.4829	−1.22747	−0.613734	−	0.789513i	$-0.710333\pi$
$431$	−25.4829	−1.22747	−0.613734	+	0.789513i	$0.710333\pi$
$432$	4.53138	0.218016
$433$	−29.6835	−1.42650	−0.713248	−	0.700911i	$-0.752777\pi$
$433$	−29.6835	−1.42650	−0.713248	+	0.700911i	$0.752777\pi$
$434$	31.2917	1.50205
$435$	−2.74281	−0.131508
$436$	−1.57224	−0.0752968
$437$	0	0
$438$	5.66638	0.270750
$439$	−10.9447	−0.522362	−0.261181	−	0.965290i	$-0.584112\pi$
$439$	−10.9447	−0.522362	−0.261181	+	0.965290i	$0.584112\pi$
$440$	−0.403714	−0.0192463
$441$	−1.06958	−0.0509324
$442$	−14.9112	−0.709252
$443$	−14.9356	−0.709612	−0.354806	−	0.934940i	$-0.615453\pi$
$443$	−14.9356	−0.709612	−0.354806	+	0.934940i	$0.615453\pi$
$444$	1.02498	0.0486432
$445$	−16.7431	−0.793700
$446$	38.1270	1.80537
$447$	8.15494	0.385716
$448$	−15.5164	−0.733083
$449$	−28.3077	−1.33592	−0.667961	−	0.744196i	$-0.732833\pi$
$449$	−28.3077	−1.33592	−0.667961	+	0.744196i	$0.732833\pi$
$450$	−1.52166	−0.0717316
$451$	0.599322	0.0282209
$452$	0.00925223	0.000435188 0
$453$	0.294881	0.0138547
$454$	22.7336	1.06694
$455$	−8.86204	−0.415459
$456$	−9.09847	−0.426075
$457$	−23.1510	−1.08296	−0.541478	−	0.840715i	$-0.682135\pi$
$457$	−23.1510	−1.08296	−0.541478	+	0.840715i	$0.682135\pi$
$458$	−23.5057	−1.09835
$459$	2.69280	0.125689
$460$	0	0
$461$	−7.63289	−0.355499	−0.177749	−	0.984076i	$-0.556882\pi$
$461$	−7.63289	−0.355499	−0.177749	+	0.984076i	$0.556882\pi$
$462$	−0.583619	−0.0271524
$463$	24.4129	1.13456	0.567281	−	0.823524i	$-0.307995\pi$
$463$	24.4129	1.13456	0.567281	+	0.823524i	$0.307995\pi$
$464$	12.4287	0.576989
$465$	8.44443	0.391601
$466$	−17.3732	−0.804797
$467$	−38.1912	−1.76728	−0.883639	−	0.468168i	$-0.844914\pi$
$467$	−38.1912	−1.76728	−0.883639	+	0.468168i	$0.844914\pi$
$468$	−1.14791	−0.0530622
$469$	−19.6265	−0.906269
$470$	−19.3641	−0.893200
$471$	−18.2971	−0.843088
$472$	0.0178489	0.000821564 0
$473$	−0.740391	−0.0340432
$474$	13.0843	0.600984
$475$	3.54948	0.162861
$476$	2.06854	0.0948113
$477$	7.39111	0.338416
$478$	9.85602	0.450804
$479$	34.4555	1.57431	0.787157	−	0.616753i	$-0.211552\pi$
$479$	34.4555	1.57431	0.787157	+	0.616753i	$0.211552\pi$
$480$	1.76856	0.0807233
$481$	11.8246	0.539156
$482$	13.4223	0.611370
$483$	0	0
$484$	−3.46202	−0.157365
$485$	−14.0686	−0.638822
$486$	1.52166	0.0690238
$487$	−31.8297	−1.44234	−0.721171	−	0.692757i	$-0.756396\pi$
$487$	−31.8297	−1.44234	−0.721171	+	0.692757i	$0.756396\pi$
$488$	−12.9455	−0.586014
$489$	−18.4174	−0.832862
$490$	−1.62754	−0.0735246
$491$	3.67963	0.166059	0.0830296	−	0.996547i	$-0.473540\pi$
$491$	3.67963	0.166059	0.0830296	+	0.996547i	$0.473540\pi$
$492$	−1.20035	−0.0541158
$493$	7.38584	0.332642
$494$	19.6550	0.884320
$495$	−0.157496	−0.00707893
$496$	−38.2649	−1.71814
$497$	−0.428120	−0.0192038
$498$	10.8649	0.486869
$499$	3.39898	0.152159	0.0760796	−	0.997102i	$-0.475760\pi$
$499$	3.39898	0.152159	0.0760796	+	0.997102i	$0.475760\pi$
$500$	−0.315440	−0.0141069
$501$	−19.6815	−0.879306
$502$	−10.5536	−0.471032
$503$	0.797217	0.0355461	0.0177731	−	0.999842i	$-0.494342\pi$
$503$	0.797217	0.0355461	0.0177731	+	0.999842i	$0.494342\pi$
$504$	−6.24232	−0.278055
$505$	−4.70030	−0.209160
$506$	0	0
$507$	−0.242876	−0.0107865
$508$	−4.37875	−0.194275
$509$	16.5995	0.735759	0.367880	−	0.929873i	$-0.380084\pi$
$509$	16.5995	0.735759	0.367880	+	0.929873i	$0.380084\pi$
$510$	4.09752	0.181441
$511$	−9.06842	−0.401163
$512$	15.2168	0.672492
$513$	−3.54948	−0.156714
$514$	34.4875	1.52118
$515$	4.86693	0.214463
$516$	1.48289	0.0652805
$517$	−2.00425	−0.0881467
$518$	−12.0408	−0.529043
$519$	−19.7802	−0.868254
$520$	9.32812	0.409065
$521$	27.9606	1.22497	0.612487	−	0.790481i	$-0.290169\pi$
$521$	27.9606	1.22497	0.612487	+	0.790481i	$0.290169\pi$
$522$	4.17362	0.182674
$523$	−21.3739	−0.934614	−0.467307	−	0.884095i	$-0.654776\pi$
$523$	−21.3739	−0.934614	−0.467307	+	0.884095i	$0.654776\pi$
$524$	−1.86500	−0.0814729
$525$	2.43525	0.106283
$526$	15.0280	0.655253
$527$	−22.7391	−0.990533
$528$	0.713675	0.0310587
$529$	0	0
$530$	11.2467	0.488527
$531$	0.00696321	0.000302177 0
$532$	−2.72662	−0.118214
$533$	−13.8478	−0.599815
$534$	25.4773	1.10251
$535$	14.8104	0.640311
$536$	20.6587	0.892322
$537$	−25.7173	−1.10978
$538$	−10.7951	−0.465410
$539$	−0.168455	−0.00725587
$540$	0.315440	0.0135744
$541$	−9.59174	−0.412381	−0.206190	−	0.978512i	$-0.566107\pi$
$541$	−9.59174	−0.412381	−0.206190	+	0.978512i	$0.566107\pi$
$542$	−21.6346	−0.929286
$543$	−22.4990	−0.965526
$544$	−4.76237	−0.204185
$545$	4.98428	0.213503
$546$	13.4850	0.577104
$547$	−40.7349	−1.74170	−0.870848	−	0.491552i	$-0.836430\pi$
$547$	−40.7349	−1.74170	−0.870848	+	0.491552i	$0.836430\pi$
$548$	−6.53031e−5 0	−2.78961e−6 0
$549$	−5.05027	−0.215540
$550$	−0.239655	−0.0102189
$551$	−9.73557	−0.414749
$552$	0	0
$553$	−20.9401	−0.890462
$554$	25.5405	1.08511
$555$	−3.24935	−0.137927
$556$	−6.68589	−0.283545
$557$	42.4372	1.79812	0.899061	−	0.437823i	$-0.144250\pi$
$557$	42.4372	1.79812	0.899061	+	0.437823i	$0.144250\pi$
$558$	−12.8495	−0.543964
$559$	17.1073	0.723563
$560$	−11.0350	−0.466315
$561$	0.424106	0.0179058
$562$	0.924412	0.0389940
$563$	31.3766	1.32237	0.661184	−	0.750224i	$-0.270054\pi$
$563$	31.3766	1.32237	0.661184	+	0.750224i	$0.270054\pi$
$564$	4.01419	0.169028
$565$	−0.0293311	−0.00123397
$566$	32.3432	1.35949
$567$	−2.43525	−0.102271
$568$	0.450637	0.0189083
$569$	−12.8164	−0.537291	−0.268645	−	0.963239i	$-0.586576\pi$
$569$	−12.8164	−0.537291	−0.268645	+	0.963239i	$0.586576\pi$
$570$	−5.40110	−0.226227
$571$	−6.53822	−0.273616	−0.136808	−	0.990598i	$-0.543684\pi$
$571$	−6.53822	−0.273616	−0.136808	+	0.990598i	$0.543684\pi$
$572$	−0.180792	−0.00755928
$573$	−14.0246	−0.585886
$574$	14.1010	0.588563
$575$	0	0
$576$	6.37162	0.265484
$577$	−47.1474	−1.96277	−0.981386	−	0.192045i	$-0.938488\pi$
$577$	−47.1474	−1.96277	−0.981386	+	0.192045i	$0.938488\pi$
$578$	14.8344	0.617029
$579$	−5.28033	−0.219443
$580$	0.865194	0.0359252
$581$	−17.3881	−0.721381
$582$	21.4076	0.887373
$583$	1.16407	0.0482109
$584$	9.54536	0.394990
$585$	3.63908	0.150457
$586$	−0.945790	−0.0390702
$587$	22.2552	0.918568	0.459284	−	0.888289i	$-0.348106\pi$
$587$	22.2552	0.918568	0.459284	+	0.888289i	$0.348106\pi$
$588$	0.337389	0.0139137
$589$	29.9734	1.23503
$590$	0.0105956	0.000436215 0
$591$	−12.9518	−0.532767
$592$	14.7240	0.605154
$593$	−12.2083	−0.501334	−0.250667	−	0.968073i	$-0.580650\pi$
$593$	−12.2083	−0.501334	−0.250667	+	0.968073i	$0.580650\pi$
$594$	0.239655	0.00983318
$595$	−6.55762	−0.268836
$596$	−2.57240	−0.105370
$597$	−0.932061	−0.0381467
$598$	0	0
$599$	−18.0130	−0.735993	−0.367996	−	0.929827i	$-0.619956\pi$
$599$	−18.0130	−0.735993	−0.367996	+	0.929827i	$0.619956\pi$
$600$	−2.56332	−0.104647
$601$	−43.6266	−1.77957	−0.889783	−	0.456384i	$-0.849144\pi$
$601$	−43.6266	−1.77957	−0.889783	+	0.456384i	$0.849144\pi$
$602$	−17.4201	−0.709990
$603$	8.05936	0.328203
$604$	−0.0930174	−0.00378483
$605$	10.9752	0.446205
$606$	7.15224	0.290540
$607$	22.4241	0.910164	0.455082	−	0.890449i	$-0.349610\pi$
$607$	22.4241	0.910164	0.455082	+	0.890449i	$0.349610\pi$
$608$	6.27747	0.254585
$609$	−6.67942	−0.270664
$610$	−7.68478	−0.311148
$611$	46.3097	1.87349
$612$	−0.849417	−0.0343357
$613$	7.18234	0.290092	0.145046	−	0.989425i	$-0.453667\pi$
$613$	7.18234	0.290092	0.145046	+	0.989425i	$0.453667\pi$
$614$	16.8920	0.681704
$615$	3.80531	0.153445
$616$	−0.983142	−0.0396119
$617$	7.74481	0.311794	0.155897	−	0.987773i	$-0.450173\pi$
$617$	7.74481	0.311794	0.155897	+	0.987773i	$0.450173\pi$
$618$	−7.40580	−0.297905
$619$	40.5541	1.63001	0.815004	−	0.579455i	$-0.196735\pi$
$619$	40.5541	1.63001	0.815004	+	0.579455i	$0.196735\pi$
$620$	−2.66371	−0.106977
$621$	0	0
$622$	2.81279	0.112783
$623$	−40.7736	−1.63356
$624$	−16.4900	−0.660130
$625$	1.00000	0.0400000
$626$	−19.6590	−0.785733
$627$	−0.559030	−0.0223255
$628$	5.77166	0.230314
$629$	8.74984	0.348879
$630$	−3.70561	−0.147635
$631$	8.44572	0.336219	0.168109	−	0.985768i	$-0.446234\pi$
$631$	8.44572	0.336219	0.168109	+	0.985768i	$0.446234\pi$
$632$	22.0414	0.876758
$633$	−7.66135	−0.304512
$634$	−36.7871	−1.46100
$635$	13.8814	0.550866
$636$	−2.33145	−0.0924482
$637$	3.89229	0.154218
$638$	0.657330	0.0260239
$639$	0.175802	0.00695461
$640$	13.2325	0.523062
$641$	−44.1783	−1.74494	−0.872468	−	0.488671i	$-0.837482\pi$
$641$	−44.1783	−1.74494	−0.872468	+	0.488671i	$0.837482\pi$
$642$	−22.5364	−0.889442
$643$	−42.6078	−1.68029	−0.840144	−	0.542363i	$-0.817530\pi$
$643$	−42.6078	−1.68029	−0.840144	+	0.542363i	$0.817530\pi$
$644$	0	0
$645$	−4.70101	−0.185102
$646$	14.5441	0.572229
$647$	−24.3515	−0.957355	−0.478677	−	0.877991i	$-0.658884\pi$
$647$	−24.3515	−0.957355	−0.478677	+	0.877991i	$0.658884\pi$
$648$	2.56332	0.100697
$649$	0.00109668	4.30484e−5 0
$650$	5.53743	0.217196
$651$	20.5643	0.805977
$652$	5.80958	0.227521
$653$	16.2424	0.635613	0.317806	−	0.948156i	$-0.397054\pi$
$653$	16.2424	0.635613	0.317806	+	0.948156i	$0.397054\pi$
$654$	−7.58437	−0.296572
$655$	5.91237	0.231015
$656$	−17.2433	−0.673237
$657$	3.72382	0.145280
$658$	−47.1564	−1.83835
$659$	33.2244	1.29424	0.647120	−	0.762388i	$-0.275973\pi$
$659$	33.2244	1.29424	0.647120	+	0.762388i	$0.275973\pi$
$660$	0.0496807	0.00193382
$661$	−42.3167	−1.64593	−0.822965	−	0.568092i	$-0.807682\pi$
$661$	−42.3167	−1.64593	−0.822965	+	0.568092i	$0.807682\pi$
$662$	14.3322	0.557036
$663$	−9.79930	−0.380573
$664$	18.3026	0.710279
$665$	8.64386	0.335195
$666$	4.94439	0.191591
$667$	0	0
$668$	6.20835	0.240208
$669$	25.0563	0.968731
$670$	12.2636	0.473784
$671$	−0.795398	−0.0307060
$672$	4.30688	0.166141
$673$	−41.9872	−1.61849	−0.809244	−	0.587472i	$-0.800123\pi$
$673$	−41.9872	−1.61849	−0.809244	+	0.587472i	$0.800123\pi$
$674$	44.2892	1.70596
$675$	−1.00000	−0.0384900
$676$	0.0766127	0.00294664
$677$	−41.5658	−1.59750	−0.798751	−	0.601661i	$-0.794506\pi$
$677$	−41.5658	−1.59750	−0.798751	+	0.601661i	$0.794506\pi$
$678$	0.0446319	0.00171408
$679$	−34.2605	−1.31480
$680$	6.90251	0.264699
$681$	14.9400	0.572503
$682$	−2.02375	−0.0774935
$683$	−51.5327	−1.97184	−0.985922	−	0.167203i	$-0.946526\pi$
$683$	−51.5327	−1.97184	−0.985922	+	0.167203i	$0.946526\pi$
$684$	1.11965	0.0428109
$685$	0.000207022 0	7.90991e−6 0
$686$	−29.9027	−1.14169
$687$	−15.4474	−0.589356
$688$	21.3020	0.812133
$689$	−26.8968	−1.02469
$690$	0	0
$691$	−29.7608	−1.13215	−0.566077	−	0.824352i	$-0.691540\pi$
$691$	−29.7608	−1.13215	−0.566077	+	0.824352i	$0.691540\pi$
$692$	6.23947	0.237189
$693$	−0.383542	−0.0145696
$694$	−19.2802	−0.731866
$695$	21.1954	0.803988
$696$	7.03071	0.266498
$697$	−10.2469	−0.388130
$698$	−6.19082	−0.234326
$699$	−11.4173	−0.431841
$700$	−0.768175	−0.0290343
$701$	−31.8878	−1.20438	−0.602192	−	0.798351i	$-0.705706\pi$
$701$	−31.8878	−1.20438	−0.602192	+	0.798351i	$0.705706\pi$
$702$	−5.53743	−0.208997
$703$	−11.5335	−0.434995
$704$	1.00351	0.0378210
$705$	−12.7257	−0.479277
$706$	−15.2462	−0.573800
$707$	−11.4464	−0.430485
$708$	−0.00219648	−8.25486e−5 0
$709$	25.0272	0.939915	0.469957	−	0.882689i	$-0.344269\pi$
$709$	25.0272	0.939915	0.469957	+	0.882689i	$0.344269\pi$
$710$	0.267510	0.0100395
$711$	8.59875	0.322478
$712$	42.9180	1.60842
$713$	0	0
$714$	9.97846	0.373434
$715$	0.573141	0.0214343
$716$	8.11227	0.303170
$717$	6.47716	0.241894
$718$	−55.2686	−2.06260
$719$	−19.8536	−0.740413	−0.370206	−	0.928950i	$-0.620713\pi$
$719$	−19.8536	−0.740413	−0.370206	+	0.928950i	$0.620713\pi$
$720$	4.53138	0.168874
$721$	11.8522	0.441398
$722$	9.74038	0.362499
$723$	8.82085	0.328051
$724$	7.09710	0.263762
$725$	−2.74281	−0.101865
$726$	−16.7005	−0.619813
$727$	−12.5712	−0.466240	−0.233120	−	0.972448i	$-0.574894\pi$
$727$	−12.5712	−0.466240	−0.233120	+	0.972448i	$0.574894\pi$
$728$	22.7163	0.841921
$729$	1.00000	0.0370370
$730$	5.66638	0.209722
$731$	12.6589	0.468205
$732$	1.59306	0.0588811
$733$	−36.9438	−1.36455	−0.682276	−	0.731095i	$-0.739010\pi$
$733$	−36.9438	−1.36455	−0.682276	+	0.731095i	$0.739010\pi$
$734$	−5.30332	−0.195749
$735$	−1.06958	−0.0394521
$736$	0	0
$737$	1.26932	0.0467560
$738$	−5.79037	−0.213147
$739$	11.7160	0.430978	0.215489	−	0.976506i	$-0.430865\pi$
$739$	11.7160	0.430978	0.215489	+	0.976506i	$0.430865\pi$
$740$	1.02498	0.0376788
$741$	12.9168	0.474512
$742$	27.3885	1.00547
$743$	31.3983	1.15189	0.575945	−	0.817488i	$-0.304634\pi$
$743$	31.3983	1.15189	0.575945	+	0.817488i	$0.304634\pi$
$744$	−21.6458	−0.793573
$745$	8.15494	0.298774
$746$	10.2801	0.376381
$747$	7.14020	0.261246
$748$	−0.133780	−0.00489148
$749$	36.0671	1.31786
$750$	−1.52166	−0.0555631
$751$	25.0180	0.912919	0.456460	−	0.889744i	$-0.349117\pi$
$751$	25.0180	0.912919	0.456460	+	0.889744i	$0.349117\pi$
$752$	57.6649	2.10282
$753$	−6.93562	−0.252748
$754$	−15.1881	−0.553119
$755$	0.294881	0.0107318
$756$	0.768175	0.0279382
$757$	25.2872	0.919079	0.459540	−	0.888157i	$-0.348014\pi$
$757$	25.2872	0.919079	0.459540	+	0.888157i	$0.348014\pi$
$758$	−36.9619	−1.34252
$759$	0	0
$760$	−9.09847	−0.330036
$761$	−20.5818	−0.746088	−0.373044	−	0.927814i	$-0.621686\pi$
$761$	−20.5818	−0.746088	−0.373044	+	0.927814i	$0.621686\pi$
$762$	−21.1227	−0.765194
$763$	12.1380	0.439423
$764$	4.42393	0.160052
$765$	2.69280	0.0973583
$766$	−53.7670	−1.94268
$767$	−0.0253396	−0.000914961 0
$768$	−7.39215	−0.266741
$769$	14.5430	0.524433	0.262216	−	0.965009i	$-0.415547\pi$
$769$	14.5430	0.524433	0.262216	+	0.965009i	$0.415547\pi$
$770$	−0.583619	−0.0210322
$771$	22.6644	0.816240
$772$	1.66563	0.0599473
$773$	−22.1136	−0.795372	−0.397686	−	0.917522i	$-0.630187\pi$
$773$	−22.1136	−0.795372	−0.397686	+	0.917522i	$0.630187\pi$
$774$	7.15332	0.257121
$775$	8.44443	0.303333
$776$	36.0623	1.29456
$777$	−7.91296	−0.283876
$778$	0.203178	0.00728430
$779$	13.5069	0.483934
$780$	−1.14791	−0.0411018
$781$	0.0276881	0.000990759 0
$782$	0	0
$783$	2.74281	0.0980201
$784$	4.84668	0.173096
$785$	−18.2971	−0.653053
$786$	−8.99659	−0.320898
$787$	−32.0415	−1.14216	−0.571079	−	0.820895i	$-0.693475\pi$
$787$	−32.0415	−1.14216	−0.571079	+	0.820895i	$0.693475\pi$
$788$	4.08553	0.145541
$789$	9.87610	0.351598
$790$	13.0843	0.465520
$791$	−0.0714285	−0.00253971
$792$	0.403714	0.0143453
$793$	18.3783	0.652633
$794$	0.607021	0.0215424
$795$	7.39111	0.262136
$796$	0.294010	0.0104209
$797$	16.4004	0.580931	0.290465	−	0.956886i	$-0.406190\pi$
$797$	16.4004	0.580931	0.290465	+	0.956886i	$0.406190\pi$
$798$	−13.1530	−0.465611
$799$	34.2677	1.21230
$800$	1.76856	0.0625280
$801$	16.7431	0.591589
$802$	−4.52381	−0.159741
$803$	0.586488	0.0206967
$804$	−2.54225	−0.0896582
$805$	0	0
$806$	46.7604	1.64706
$807$	−7.09430	−0.249731
$808$	12.0484	0.423860
$809$	−24.2277	−0.851800	−0.425900	−	0.904770i	$-0.640042\pi$
$809$	−24.2277	−0.851800	−0.425900	+	0.904770i	$0.640042\pi$
$810$	1.52166	0.0534656
$811$	−6.97340	−0.244869	−0.122435	−	0.992477i	$-0.539070\pi$
$811$	−6.97340	−0.244869	−0.122435	+	0.992477i	$0.539070\pi$
$812$	2.10696	0.0739398
$813$	−14.2178	−0.498640
$814$	0.778724	0.0272942
$815$	−18.4174	−0.645132
$816$	−12.2021	−0.427159
$817$	−16.6861	−0.583774
$818$	55.1437	1.92805
$819$	8.86204	0.309665
$820$	−1.20035	−0.0419179
$821$	−23.9944	−0.837412	−0.418706	−	0.908122i	$-0.637516\pi$
$821$	−23.9944	−0.837412	−0.418706	+	0.908122i	$0.637516\pi$
$822$	−0.000315017 0	−1.09875e−5 0
$823$	−7.14292	−0.248987	−0.124493	−	0.992220i	$-0.539731\pi$
$823$	−7.14292	−0.248987	−0.124493	+	0.992220i	$0.539731\pi$
$824$	−12.4755	−0.434605
$825$	−0.157496	−0.00548332
$826$	0.0258029	0.000897798 0
$827$	−25.7772	−0.896360	−0.448180	−	0.893943i	$-0.647928\pi$
$827$	−25.7772	−0.896360	−0.448180	+	0.893943i	$0.647928\pi$
$828$	0	0
$829$	31.3952	1.09040	0.545200	−	0.838306i	$-0.316454\pi$
$829$	31.3952	1.09040	0.545200	+	0.838306i	$0.316454\pi$
$830$	10.8649	0.377127
$831$	16.7847	0.582254
$832$	−23.1868	−0.803857
$833$	2.88017	0.0997919
$834$	−32.2522	−1.11680
$835$	−19.6815	−0.681107
$836$	0.176341	0.00609887
$837$	−8.44443	−0.291882
$838$	27.2477	0.941257
$839$	−40.1381	−1.38572	−0.692860	−	0.721072i	$-0.743650\pi$
$839$	−40.1381	−1.38572	−0.692860	+	0.721072i	$0.743650\pi$
$840$	−6.24232	−0.215380
$841$	−21.4770	−0.740586
$842$	16.4075	0.565438
$843$	0.607504	0.0209235
$844$	2.41670	0.0831863
$845$	−0.242876	−0.00835517
$846$	19.3641	0.665752
$847$	26.7273	0.918361
$848$	−33.4919	−1.15012
$849$	21.2552	0.729478
$850$	4.09752	0.140544
$851$	0	0
$852$	−0.0554550	−0.00189986
$853$	−26.1529	−0.895458	−0.447729	−	0.894169i	$-0.647767\pi$
$853$	−26.1529	−0.895458	−0.447729	+	0.894169i	$0.647767\pi$
$854$	−18.7143	−0.640391
$855$	−3.54948	−0.121390
$856$	−37.9639	−1.29758
$857$	−20.4093	−0.697168	−0.348584	−	0.937278i	$-0.613337\pi$
$857$	−20.4093	−0.697168	−0.348584	+	0.937278i	$0.613337\pi$
$858$	−0.872124	−0.0297738
$859$	35.1123	1.19802	0.599008	−	0.800743i	$-0.295562\pi$
$859$	35.1123	1.19802	0.599008	+	0.800743i	$0.295562\pi$
$860$	1.48289	0.0505660
$861$	9.26685	0.315814
$862$	38.7763	1.32072
$863$	32.3970	1.10281	0.551403	−	0.834239i	$-0.314093\pi$
$863$	32.3970	1.10281	0.551403	+	0.834239i	$0.314093\pi$
$864$	−1.76856	−0.0601676
$865$	−19.7802	−0.672547
$866$	45.1681	1.53487
$867$	9.74884	0.331088
$868$	−6.48680	−0.220176
$869$	1.35427	0.0459405
$870$	4.17362	0.141499
$871$	−29.3286	−0.993763
$872$	−12.7763	−0.432661
$873$	14.0686	0.476150
$874$	0	0
$875$	2.43525	0.0823263
$876$	−1.17464	−0.0396876
$877$	7.27420	0.245632	0.122816	−	0.992429i	$-0.460807\pi$
$877$	7.27420	0.245632	0.122816	+	0.992429i	$0.460807\pi$
$878$	16.6541	0.562048
$879$	−0.621553	−0.0209645
$880$	0.713675	0.0240580
$881$	−15.3987	−0.518795	−0.259398	−	0.965771i	$-0.583524\pi$
$881$	−15.3987	−0.518795	−0.259398	+	0.965771i	$0.583524\pi$
$882$	1.62754	0.0548020
$883$	8.36662	0.281559	0.140780	−	0.990041i	$-0.455039\pi$
$883$	8.36662	0.281559	0.140780	+	0.990041i	$0.455039\pi$
$884$	3.09109	0.103965
$885$	0.00696321	0.000234066 0
$886$	22.7269	0.763524
$887$	6.69161	0.224682	0.112341	−	0.993670i	$-0.464165\pi$
$887$	6.69161	0.224682	0.112341	+	0.993670i	$0.464165\pi$
$888$	8.32913	0.279507
$889$	33.8046	1.13377
$890$	25.4773	0.854001
$891$	0.157496	0.00527632
$892$	−7.90376	−0.264637
$893$	−45.1696	−1.51154
$894$	−12.4090	−0.415020
$895$	−25.7173	−0.859634
$896$	32.2245	1.07654
$897$	0	0
$898$	43.0746	1.43742
$899$	−23.1615	−0.772479
$900$	0.315440	0.0105147
$901$	−19.9028	−0.663057
$902$	−0.911962	−0.0303650
$903$	−11.4481	−0.380969
$904$	0.0751852	0.00250062
$905$	−22.4990	−0.747893
$906$	−0.448708	−0.0149073
$907$	−23.1663	−0.769223	−0.384611	−	0.923079i	$-0.625665\pi$
$907$	−23.1663	−0.769223	−0.384611	+	0.923079i	$0.625665\pi$
$908$	−4.71269	−0.156396
$909$	4.70030	0.155899
$910$	13.4850	0.447023
$911$	−44.4071	−1.47127	−0.735637	−	0.677376i	$-0.763117\pi$
$911$	−44.4071	−1.47127	−0.735637	+	0.677376i	$0.763117\pi$
$912$	16.0841	0.532596
$913$	1.12455	0.0372173
$914$	35.2278	1.16523
$915$	−5.05027	−0.166957
$916$	4.87274	0.161000
$917$	14.3981	0.475466
$918$	−4.09752	−0.135238
$919$	−28.0150	−0.924130	−0.462065	−	0.886846i	$-0.652891\pi$
$919$	−28.0150	−0.924130	−0.462065	+	0.886846i	$0.652891\pi$
$920$	0	0
$921$	11.1010	0.365791
$922$	11.6146	0.382508
$923$	−0.639756	−0.0210578
$924$	0.120985	0.00398010
$925$	−3.24935	−0.106838
$926$	−37.1480	−1.22076
$927$	−4.86693	−0.159851
$928$	−4.85083	−0.159236
$929$	−56.4774	−1.85296	−0.926482	−	0.376339i	$-0.877183\pi$
$929$	−56.4774	−1.85296	−0.926482	+	0.376339i	$0.877183\pi$
$930$	−12.8495	−0.421353
$931$	−3.79646	−0.124424
$932$	3.60147	0.117970
$933$	1.84851	0.0605174
$934$	58.1139	1.90155
$935$	0.424106	0.0138697
$936$	−9.32812	−0.304899
$937$	8.17235	0.266979	0.133489	−	0.991050i	$-0.457382\pi$
$937$	8.17235	0.266979	0.133489	+	0.991050i	$0.457382\pi$
$938$	29.8648	0.975122
$939$	−12.9195	−0.421612
$940$	4.01419	0.130929
$941$	−11.2938	−0.368168	−0.184084	−	0.982911i	$-0.558932\pi$
$941$	−11.2938	−0.368168	−0.184084	+	0.982911i	$0.558932\pi$
$942$	27.8420	0.907141
$943$	0	0
$944$	−0.0315529	−0.00102696
$945$	−2.43525	−0.0792185
$946$	1.12662	0.0366296
$947$	15.7080	0.510442	0.255221	−	0.966883i	$-0.417852\pi$
$947$	15.7080	0.510442	0.255221	+	0.966883i	$0.417852\pi$
$948$	−2.71239	−0.0880944
$949$	−13.5513	−0.439893
$950$	−5.40110	−0.175235
$951$	−24.1757	−0.783951
$952$	16.8093	0.544793
$953$	10.8638	0.351912	0.175956	−	0.984398i	$-0.443698\pi$
$953$	10.8638	0.351912	0.175956	+	0.984398i	$0.443698\pi$
$954$	−11.2467	−0.364126
$955$	−14.0246	−0.453826
$956$	−2.04316	−0.0660805
$957$	0.431983	0.0139640
$958$	−52.4295	−1.69392
$959$	0.000504149 0	1.62798e−5 0
$960$	6.37162	0.205643
$961$	40.3084	1.30027
$962$	−17.9930	−0.580118
$963$	−14.8104	−0.477260
$964$	−2.78245	−0.0896168
$965$	−5.28033	−0.169980
$966$	0	0
$967$	42.2130	1.35748	0.678740	−	0.734379i	$-0.262526\pi$
$967$	42.2130	1.35748	0.678740	+	0.734379i	$0.262526\pi$
$968$	−28.1330	−0.904228
$969$	9.55804	0.307049
$970$	21.4076	0.687356
$971$	−6.43699	−0.206573	−0.103286	−	0.994652i	$-0.532936\pi$
$971$	−6.43699	−0.206573	−0.103286	+	0.994652i	$0.532936\pi$
$972$	−0.315440	−0.0101178
$973$	51.6160	1.65473
$974$	48.4339	1.55192
$975$	3.63908	0.116544
$976$	22.8847	0.732521
$977$	−27.4184	−0.877192	−0.438596	−	0.898684i	$-0.644524\pi$
$977$	−27.4184	−0.877192	−0.438596	+	0.898684i	$0.644524\pi$
$978$	28.0249	0.896138
$979$	2.63698	0.0842782
$980$	0.337389	0.0107775
$981$	−4.98428	−0.159136
$982$	−5.59913	−0.178675
$983$	−9.62397	−0.306957	−0.153478	−	0.988152i	$-0.549048\pi$
$983$	−9.62397	−0.306957	−0.153478	+	0.988152i	$0.549048\pi$
$984$	−9.75423	−0.310953
$985$	−12.9518	−0.412679
$986$	−11.2387	−0.357914
$987$	−30.9901	−0.986427
$988$	−4.07449	−0.129627
$989$	0	0
$990$	0.239655	0.00761675
$991$	−24.7842	−0.787296	−0.393648	−	0.919261i	$-0.628787\pi$
$991$	−24.7842	−0.787296	−0.393648	+	0.919261i	$0.628787\pi$
$992$	14.9345	0.474170
$993$	9.41880	0.298897
$994$	0.651452	0.0206628
$995$	−0.932061	−0.0295483
$996$	−2.25231	−0.0713670
$997$	−60.2847	−1.90924	−0.954618	−	0.297832i	$-0.903736\pi$
$997$	−60.2847	−1.90924	−0.954618	+	0.297832i	$0.903736\pi$
$998$	−5.17208	−0.163719
$999$	3.24935	0.102805

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	7935.2.a.bp.1.4		15
23.4	even	11		345.2.m.a.16.3	✓	30
23.6	even	11		345.2.m.a.151.3	yes	30
23.22	odd	2		7935.2.a.bq.1.4		15

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
345.2.m.a.16.3	✓	30	23.4	even	11
345.2.m.a.151.3	yes	30	23.6	even	11
7935.2.a.bp.1.4		15	1.1	even	1	trivial
7935.2.a.bq.1.4		15	23.22	odd	2

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 7935 = 3 \cdot 5 \cdot 23^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	7935.a (trivial)

\(f(q)\)	\(=\)	\(q-1.52166 q^{2} -1.00000 q^{3} +0.315440 q^{4} -1.00000 q^{5} +1.52166 q^{6} -2.43525 q^{7} +2.56332 q^{8} +1.00000 q^{9} +1.52166 q^{10} +0.157496 q^{11} -0.315440 q^{12} -3.63908 q^{13} +3.70561 q^{14} +1.00000 q^{15} -4.53138 q^{16} -2.69280 q^{17} -1.52166 q^{18} +3.54948 q^{19} -0.315440 q^{20} +2.43525 q^{21} -0.239655 q^{22} -2.56332 q^{24} +1.00000 q^{25} +5.53743 q^{26} -1.00000 q^{27} -0.768175 q^{28} -2.74281 q^{29} -1.52166 q^{30} +8.44443 q^{31} +1.76856 q^{32} -0.157496 q^{33} +4.09752 q^{34} +2.43525 q^{35} +0.315440 q^{36} -3.24935 q^{37} -5.40110 q^{38} +3.63908 q^{39} -2.56332 q^{40} +3.80531 q^{41} -3.70561 q^{42} -4.70101 q^{43} +0.0496807 q^{44} -1.00000 q^{45} -12.7257 q^{47} +4.53138 q^{48} -1.06958 q^{49} -1.52166 q^{50} +2.69280 q^{51} -1.14791 q^{52} +7.39111 q^{53} +1.52166 q^{54} -0.157496 q^{55} -6.24232 q^{56} -3.54948 q^{57} +4.17362 q^{58} +0.00696321 q^{59} +0.315440 q^{60} -5.05027 q^{61} -12.8495 q^{62} -2.43525 q^{63} +6.37162 q^{64} +3.63908 q^{65} +0.239655 q^{66} +8.05936 q^{67} -0.849417 q^{68} -3.70561 q^{70} +0.175802 q^{71} +2.56332 q^{72} +3.72382 q^{73} +4.94439 q^{74} -1.00000 q^{75} +1.11965 q^{76} -0.383542 q^{77} -5.53743 q^{78} +8.59875 q^{79} +4.53138 q^{80} +1.00000 q^{81} -5.79037 q^{82} +7.14020 q^{83} +0.768175 q^{84} +2.69280 q^{85} +7.15332 q^{86} +2.74281 q^{87} +0.403714 q^{88} +16.7431 q^{89} +1.52166 q^{90} +8.86204 q^{91} -8.44443 q^{93} +19.3641 q^{94} -3.54948 q^{95} -1.76856 q^{96} +14.0686 q^{97} +1.62754 q^{98} +0.157496 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 15 q - 15 q^{3} + 12 q^{4} - 15 q^{5} - 5 q^{7} + 15 q^{9} + 13 q^{11} - 12 q^{12} - 24 q^{13} + 15 q^{14} + 15 q^{15} + 2 q^{16} + 2 q^{17} + 13 q^{19} - 12 q^{20} + 5 q^{21} - 9 q^{22} + 15 q^{25} - 9 q^{26}+ \cdots + 13 q^{99}+O(q^{100}) \) 15 * q - 15 * q^3 + 12 * q^4 - 15 * q^5 - 5 * q^7 + 15 * q^9 + 13 * q^11 - 12 * q^12 - 24 * q^13 + 15 * q^14 + 15 * q^15 + 2 * q^16 + 2 * q^17 + 13 * q^19 - 12 * q^20 + 5 * q^21 - 9 * q^22 + 15 * q^25 - 9 * q^26 - 15 * q^27 + q^28 - 3 * q^29 - 22 * q^31 - 13 * q^33 + q^34 + 5 * q^35 + 12 * q^36 - 6 * q^37 - 17 * q^38 + 24 * q^39 - 20 * q^41 - 15 * q^42 - 4 * q^43 - 18 * q^44 - 15 * q^45 + 7 * q^47 - 2 * q^48 - 10 * q^49 - 2 * q^51 - 55 * q^52 + 4 * q^53 - 13 * q^55 + 25 * q^56 - 13 * q^57 + 2 * q^58 + 9 * q^59 + 12 * q^60 + 13 * q^61 - 7 * q^62 - 5 * q^63 - 26 * q^64 + 24 * q^65 + 9 * q^66 - 32 * q^67 + 27 * q^68 - 15 * q^70 + 14 * q^71 - 43 * q^73 - 11 * q^74 - 15 * q^75 + 88 * q^76 - 21 * q^77 + 9 * q^78 + 33 * q^79 - 2 * q^80 + 15 * q^81 - 35 * q^82 - 12 * q^83 - q^84 - 2 * q^85 + 77 * q^86 + 3 * q^87 - 37 * q^88 + 29 * q^89 + 20 * q^91 + 22 * q^93 - 20 * q^94 - 13 * q^95 + 18 * q^97 - 19 * q^98 + 13 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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