LMFDB - Embedded newform 9295.2.a.bb.1.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [9295,2,Mod(1,9295)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(9295, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 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("9295.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 9295 = 5 \cdot 11 \cdot 13^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	9295.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:	$74.2209486788$
Analytic rank:	$0$
Dimension:	$14$
Coefficient field:	$\mathbb{Q}[x]/(x^{14} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{14} - x^{13} - 22 x^{12} + 21 x^{11} + 186 x^{10} - 172 x^{9} - 755 x^{8} + 690 x^{7} + 1489 x^{6} + \cdots - 3 $ x^14 - x^13 - 22x^12 + 21x^11 + 186x^10 - 172x^9 - 755x^8 + 690x^7 + 1489x^6 - 1372x^5 - 1226x^4 + 1169x^3 + 206x^2 - 212x - 3
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	no (minimal twist has level 715)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Root			$-2.14985$ of defining polynomial
Character	$\chi$	$=$	9295.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.14985 q^{2} -1.08194 q^{3} +2.62184 q^{4} +1.00000 q^{5} +2.32601 q^{6} +2.75110 q^{7} -1.33685 q^{8} -1.82940 q^{9} +O(q^{10})$	\(q-2.14985 q^{2} -1.08194 q^{3} +2.62184 q^{4} +1.00000 q^{5} +2.32601 q^{6} +2.75110 q^{7} -1.33685 q^{8} -1.82940 q^{9} -2.14985 q^{10} -1.00000 q^{11} -2.83667 q^{12} -5.91444 q^{14} -1.08194 q^{15} -2.36964 q^{16} -1.06551 q^{17} +3.93293 q^{18} +5.38212 q^{19} +2.62184 q^{20} -2.97653 q^{21} +2.14985 q^{22} -1.63335 q^{23} +1.44640 q^{24} +1.00000 q^{25} +5.22513 q^{27} +7.21294 q^{28} +8.15779 q^{29} +2.32601 q^{30} +7.57930 q^{31} +7.76808 q^{32} +1.08194 q^{33} +2.29069 q^{34} +2.75110 q^{35} -4.79639 q^{36} -5.89912 q^{37} -11.5707 q^{38} -1.33685 q^{40} -9.91633 q^{41} +6.39908 q^{42} +6.56927 q^{43} -2.62184 q^{44} -1.82940 q^{45} +3.51145 q^{46} +10.9896 q^{47} +2.56382 q^{48} +0.568550 q^{49} -2.14985 q^{50} +1.15282 q^{51} -2.59320 q^{53} -11.2332 q^{54} -1.00000 q^{55} -3.67782 q^{56} -5.82314 q^{57} -17.5380 q^{58} +11.8826 q^{59} -2.83667 q^{60} -9.16317 q^{61} -16.2943 q^{62} -5.03287 q^{63} -11.9609 q^{64} -2.32601 q^{66} +0.236858 q^{67} -2.79360 q^{68} +1.76719 q^{69} -5.91444 q^{70} -3.07595 q^{71} +2.44564 q^{72} -14.7263 q^{73} +12.6822 q^{74} -1.08194 q^{75} +14.1110 q^{76} -2.75110 q^{77} -1.05065 q^{79} -2.36964 q^{80} -0.165081 q^{81} +21.3186 q^{82} +4.10906 q^{83} -7.80398 q^{84} -1.06551 q^{85} -14.1229 q^{86} -8.82626 q^{87} +1.33685 q^{88} +9.49872 q^{89} +3.93293 q^{90} -4.28238 q^{92} -8.20036 q^{93} -23.6260 q^{94} +5.38212 q^{95} -8.40461 q^{96} -8.36778 q^{97} -1.22230 q^{98} +1.82940 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 14 q + q^{2} + q^{3} + 17 q^{4} + 14 q^{5} + 2 q^{6} + 5 q^{7} + 27 q^{9}+O(q^{10}) $ 14 * q + q^2 + q^3 + 17 * q^4 + 14 * q^5 + 2 * q^6 + 5 * q^7 + 27 * q^9	$ 14 q + q^{2} + q^{3} + 17 q^{4} + 14 q^{5} + 2 q^{6} + 5 q^{7} + 27 q^{9} + q^{10} - 14 q^{11} - 9 q^{12} + 12 q^{14} + q^{15} + 15 q^{16} + 17 q^{17} + 23 q^{18} + 3 q^{19} + 17 q^{20} - 16 q^{21} - q^{22} + 4 q^{23} - 13 q^{24} + 14 q^{25} + 10 q^{27} + 27 q^{28} + 21 q^{29} + 2 q^{30} - 9 q^{31} + 26 q^{32} - q^{33} - 56 q^{34} + 5 q^{35} + 51 q^{36} + 8 q^{37} + 5 q^{38} + q^{41} - 42 q^{42} + 23 q^{43} - 17 q^{44} + 27 q^{45} - q^{46} - 18 q^{47} - 14 q^{48} + 41 q^{49} + q^{50} + 18 q^{53} + 8 q^{54} - 14 q^{55} + 80 q^{56} + 44 q^{57} + 22 q^{58} + 8 q^{59} - 9 q^{60} + 16 q^{61} - 5 q^{62} + 50 q^{63} + 10 q^{64} - 2 q^{66} + q^{67} - 8 q^{68} + 34 q^{69} + 12 q^{70} - 20 q^{71} + 117 q^{72} - 15 q^{73} + 49 q^{74} + q^{75} + 10 q^{76} - 5 q^{77} + 5 q^{79} + 15 q^{80} + 82 q^{81} + 32 q^{82} - 18 q^{83} - 50 q^{84} + 17 q^{85} - 74 q^{86} + 2 q^{87} - 16 q^{89} + 23 q^{90} + 7 q^{92} + 33 q^{93} + 34 q^{94} + 3 q^{95} + 56 q^{96} - 5 q^{97} + 34 q^{98} - 27 q^{99}+O(q^{100}) $ 14 * q + q^2 + q^3 + 17 * q^4 + 14 * q^5 + 2 * q^6 + 5 * q^7 + 27 * q^9 + q^10 - 14 * q^11 - 9 * q^12 + 12 * q^14 + q^15 + 15 * q^16 + 17 * q^17 + 23 * q^18 + 3 * q^19 + 17 * q^20 - 16 * q^21 - q^22 + 4 * q^23 - 13 * q^24 + 14 * q^25 + 10 * q^27 + 27 * q^28 + 21 * q^29 + 2 * q^30 - 9 * q^31 + 26 * q^32 - q^33 - 56 * q^34 + 5 * q^35 + 51 * q^36 + 8 * q^37 + 5 * q^38 + q^41 - 42 * q^42 + 23 * q^43 - 17 * q^44 + 27 * q^45 - q^46 - 18 * q^47 - 14 * q^48 + 41 * q^49 + q^50 + 18 * q^53 + 8 * q^54 - 14 * q^55 + 80 * q^56 + 44 * q^57 + 22 * q^58 + 8 * q^59 - 9 * q^60 + 16 * q^61 - 5 * q^62 + 50 * q^63 + 10 * q^64 - 2 * q^66 + q^67 - 8 * q^68 + 34 * q^69 + 12 * q^70 - 20 * q^71 + 117 * q^72 - 15 * q^73 + 49 * q^74 + q^75 + 10 * q^76 - 5 * q^77 + 5 * q^79 + 15 * q^80 + 82 * q^81 + 32 * q^82 - 18 * q^83 - 50 * q^84 + 17 * q^85 - 74 * q^86 + 2 * q^87 - 16 * q^89 + 23 * q^90 + 7 * q^92 + 33 * q^93 + 34 * q^94 + 3 * q^95 + 56 * q^96 - 5 * q^97 + 34 * q^98 - 27 * 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 $

$2$	−2.14985	−1.52017	−0.760085	−	0.649823i	$-0.774843\pi$
$2$	−2.14985	−1.52017	−0.760085	+	0.649823i	$0.774843\pi$
$3$	−1.08194	−0.624659	−0.312330	−	0.949974i	$-0.601109\pi$
$3$	−1.08194	−0.624659	−0.312330	+	0.949974i	$0.601109\pi$
$4$	2.62184	1.31092
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	2.32601	0.949589
$7$	2.75110	1.03982	0.519909	−	0.854222i	$-0.325966\pi$
$7$	2.75110	1.03982	0.519909	+	0.854222i	$0.325966\pi$
$8$	−1.33685	−0.472649
$9$	−1.82940	−0.609801
$10$	−2.14985	−0.679841
$11$	−1.00000	−0.301511
$11$	−1.00000	−0.301511
$12$	−2.83667	−0.818877
$13$	0	0
$13$	0	0
$14$	−5.91444	−1.58070
$15$	−1.08194	−0.279356
$16$	−2.36964	−0.592411
$17$	−1.06551	−0.258425	−0.129213	−	0.991617i	$-0.541245\pi$
$17$	−1.06551	−0.258425	−0.129213	+	0.991617i	$0.541245\pi$
$18$	3.93293	0.927001
$19$	5.38212	1.23474	0.617372	−	0.786672i	$-0.288198\pi$
$19$	5.38212	1.23474	0.617372	+	0.786672i	$0.288198\pi$
$20$	2.62184	0.586261
$21$	−2.97653	−0.649532
$22$	2.14985	0.458349
$23$	−1.63335	−0.340577	−0.170288	−	0.985394i	$-0.554470\pi$
$23$	−1.63335	−0.340577	−0.170288	+	0.985394i	$0.554470\pi$
$24$	1.44640	0.295245
$25$	1.00000	0.200000
$26$	0	0
$27$	5.22513	1.00558
$28$	7.21294	1.36312
$29$	8.15779	1.51486	0.757432	−	0.652914i	$-0.226454\pi$
$29$	8.15779	1.51486	0.757432	+	0.652914i	$0.226454\pi$
$30$	2.32601	0.424669
$31$	7.57930	1.36128	0.680641	−	0.732617i	$-0.261701\pi$
$31$	7.57930	1.36128	0.680641	+	0.732617i	$0.261701\pi$
$32$	7.76808	1.37322
$33$	1.08194	0.188342
$34$	2.29069	0.392850
$35$	2.75110	0.465021
$36$	−4.79639	−0.799399
$37$	−5.89912	−0.969809	−0.484904	−	0.874567i	$-0.661146\pi$
$37$	−5.89912	−0.969809	−0.484904	+	0.874567i	$0.661146\pi$
$38$	−11.5707	−1.87702
$39$	0	0
$40$	−1.33685	−0.211375
$41$	−9.91633	−1.54867	−0.774336	−	0.632775i	$-0.781916\pi$
$41$	−9.91633	−1.54867	−0.774336	+	0.632775i	$0.781916\pi$
$42$	6.39908	0.987399
$43$	6.56927	1.00180	0.500902	−	0.865504i	$-0.333002\pi$
$43$	6.56927	1.00180	0.500902	+	0.865504i	$0.333002\pi$
$44$	−2.62184	−0.395257
$45$	−1.82940	−0.272711
$46$	3.51145	0.517735
$47$	10.9896	1.60300	0.801502	−	0.597993i	$-0.204035\pi$
$47$	10.9896	1.60300	0.801502	+	0.597993i	$0.204035\pi$
$48$	2.56382	0.370055
$49$	0.568550	0.0812214
$50$	−2.14985	−0.304034
$51$	1.15282	0.161428
$52$	0	0
$53$	−2.59320	−0.356204	−0.178102	−	0.984012i	$-0.556996\pi$
$53$	−2.59320	−0.356204	−0.178102	+	0.984012i	$0.556996\pi$
$54$	−11.2332	−1.52865
$55$	−1.00000	−0.134840
$56$	−3.67782	−0.491469
$57$	−5.82314	−0.771294
$58$	−17.5380	−2.30285
$59$	11.8826	1.54698	0.773490	−	0.633809i	$-0.218509\pi$
$59$	11.8826	1.54698	0.773490	+	0.633809i	$0.218509\pi$
$60$	−2.83667	−0.366213
$61$	−9.16317	−1.17322	−0.586612	−	0.809868i	$-0.699539\pi$
$61$	−9.16317	−1.17322	−0.586612	+	0.809868i	$0.699539\pi$
$62$	−16.2943	−2.06938
$63$	−5.03287	−0.634082
$64$	−11.9609	−1.49511
$65$	0	0
$66$	−2.32601	−0.286312
$67$	0.236858	0.0289368	0.0144684	−	0.999895i	$-0.495394\pi$
$67$	0.236858	0.0289368	0.0144684	+	0.999895i	$0.495394\pi$
$68$	−2.79360	−0.338774
$69$	1.76719	0.212745
$70$	−5.91444	−0.706911
$71$	−3.07595	−0.365048	−0.182524	−	0.983201i	$-0.558427\pi$
$71$	−3.07595	−0.365048	−0.182524	+	0.983201i	$0.558427\pi$
$72$	2.44564	0.288222
$73$	−14.7263	−1.72359	−0.861793	−	0.507260i	$-0.830658\pi$
$73$	−14.7263	−1.72359	−0.861793	+	0.507260i	$0.830658\pi$
$74$	12.6822	1.47427
$75$	−1.08194	−0.124932
$76$	14.1110	1.61865
$77$	−2.75110	−0.313517
$78$	0	0
$79$	−1.05065	−0.118207	−0.0591037	−	0.998252i	$-0.518824\pi$
$79$	−1.05065	−0.118207	−0.0591037	+	0.998252i	$0.518824\pi$
$80$	−2.36964	−0.264934
$81$	−0.165081	−0.0183423
$82$	21.3186	2.35424
$83$	4.10906	0.451028	0.225514	−	0.974240i	$-0.427594\pi$
$83$	4.10906	0.451028	0.225514	+	0.974240i	$0.427594\pi$
$84$	−7.80398	−0.851484
$85$	−1.06551	−0.115571
$86$	−14.1229	−1.52291
$87$	−8.82626	−0.946274
$88$	1.33685	0.142509
$89$	9.49872	1.00686	0.503431	−	0.864035i	$-0.332071\pi$
$89$	9.49872	1.00686	0.503431	+	0.864035i	$0.332071\pi$
$90$	3.93293	0.414568
$91$	0	0
$92$	−4.28238	−0.446469
$93$	−8.20036	−0.850338
$94$	−23.6260	−2.43684
$95$	5.38212	0.552194
$96$	−8.40461	−0.857792
$97$	−8.36778	−0.849620	−0.424810	−	0.905283i	$-0.639659\pi$
$97$	−8.36778	−0.849620	−0.424810	+	0.905283i	$0.639659\pi$
$98$	−1.22230	−0.123470
$99$	1.82940	0.183862
$100$	2.62184	0.262184
$101$	9.91449	0.986528	0.493264	−	0.869880i	$-0.335804\pi$
$101$	9.91449	0.986528	0.493264	+	0.869880i	$0.335804\pi$
$102$	−2.47839	−0.245398
$103$	4.08403	0.402411	0.201206	−	0.979549i	$-0.435514\pi$
$103$	4.08403	0.402411	0.201206	+	0.979549i	$0.435514\pi$
$104$	0	0
$105$	−2.97653	−0.290480
$106$	5.57499	0.541491
$107$	16.5003	1.59514	0.797571	−	0.603225i	$-0.206118\pi$
$107$	16.5003	1.59514	0.797571	+	0.603225i	$0.206118\pi$
$108$	13.6994	1.31823
$109$	−18.3374	−1.75641	−0.878203	−	0.478289i	$-0.841257\pi$
$109$	−18.3374	−1.75641	−0.878203	+	0.478289i	$0.841257\pi$
$110$	2.14985	0.204980
$111$	6.38250	0.605800
$112$	−6.51913	−0.616000
$113$	14.4140	1.35595	0.677977	−	0.735083i	$-0.262857\pi$
$113$	14.4140	1.35595	0.677977	+	0.735083i	$0.262857\pi$
$114$	12.5189	1.17250
$115$	−1.63335	−0.152311
$116$	21.3884	1.98586
$117$	0	0
$118$	−25.5457	−2.35167
$119$	−2.93134	−0.268715
$120$	1.44640	0.132037
$121$	1.00000	0.0909091
$122$	19.6994	1.78350
$123$	10.7289	0.967392
$124$	19.8717	1.78453
$125$	1.00000	0.0894427
$126$	10.8199	0.963912
$127$	−13.2019	−1.17148	−0.585740	−	0.810499i	$-0.699196\pi$
$127$	−13.2019	−1.17148	−0.585740	+	0.810499i	$0.699196\pi$
$128$	10.1779	0.899607
$129$	−7.10757	−0.625786
$130$	0	0
$131$	21.6849	1.89462	0.947311	−	0.320317i	$-0.103789\pi$
$131$	21.6849	1.89462	0.947311	+	0.320317i	$0.103789\pi$
$132$	2.83667	0.246901
$133$	14.8068	1.28391
$134$	−0.509208	−0.0439888
$135$	5.22513	0.449708
$136$	1.42444	0.122144
$137$	3.15484	0.269536	0.134768	−	0.990877i	$-0.456971\pi$
$137$	3.15484	0.269536	0.134768	+	0.990877i	$0.456971\pi$
$138$	−3.79918	−0.323408
$139$	10.9824	0.931518	0.465759	−	0.884911i	$-0.345781\pi$
$139$	10.9824	0.931518	0.465759	+	0.884911i	$0.345781\pi$
$140$	7.21294	0.609604
$141$	−11.8901	−1.00133
$142$	6.61282	0.554935
$143$	0	0
$144$	4.33503	0.361253
$145$	8.15779	0.677468
$146$	31.6593	2.62014
$147$	−0.615138	−0.0507357
$148$	−15.4665	−1.27134
$149$	−17.4568	−1.43011	−0.715057	−	0.699066i	$-0.753599\pi$
$149$	−17.4568	−1.43011	−0.715057	+	0.699066i	$0.753599\pi$
$150$	2.32601	0.189918
$151$	−14.2366	−1.15855	−0.579277	−	0.815130i	$-0.696665\pi$
$151$	−14.2366	−1.15855	−0.579277	+	0.815130i	$0.696665\pi$
$152$	−7.19511	−0.583600
$153$	1.94925	0.157588
$154$	5.91444	0.476599
$155$	7.57930	0.608784
$156$	0	0
$157$	4.22424	0.337131	0.168565	−	0.985690i	$-0.446087\pi$
$157$	4.22424	0.337131	0.168565	+	0.985690i	$0.446087\pi$
$158$	2.25874	0.179696
$159$	2.80570	0.222506
$160$	7.76808	0.614120
$161$	−4.49351	−0.354138
$162$	0.354899	0.0278835
$163$	17.3667	1.36027	0.680133	−	0.733089i	$-0.261922\pi$
$163$	17.3667	1.36027	0.680133	+	0.733089i	$0.261922\pi$
$164$	−25.9990	−2.03018
$165$	1.08194	0.0842290
$166$	−8.83384	−0.685639
$167$	−6.27274	−0.485399	−0.242700	−	0.970101i	$-0.578033\pi$
$167$	−6.27274	−0.485399	−0.242700	+	0.970101i	$0.578033\pi$
$168$	3.97918	0.307001
$169$	0	0
$170$	2.29069	0.175688
$171$	−9.84606	−0.752947
$172$	17.2236	1.31328
$173$	10.6284	0.808059	0.404029	−	0.914746i	$-0.367609\pi$
$173$	10.6284	0.808059	0.404029	+	0.914746i	$0.367609\pi$
$174$	18.9751	1.43850
$175$	2.75110	0.207964
$176$	2.36964	0.178619
$177$	−12.8563	−0.966335
$178$	−20.4208	−1.53060
$179$	2.65723	0.198611	0.0993053	−	0.995057i	$-0.468338\pi$
$179$	2.65723	0.198611	0.0993053	+	0.995057i	$0.468338\pi$
$180$	−4.79639	−0.357502
$181$	−2.84038	−0.211124	−0.105562	−	0.994413i	$-0.533664\pi$
$181$	−2.84038	−0.211124	−0.105562	+	0.994413i	$0.533664\pi$
$182$	0	0
$183$	9.91401	0.732865
$184$	2.18355	0.160973
$185$	−5.89912	−0.433712
$186$	17.6295	1.29266
$187$	1.06551	0.0779181
$188$	28.8130	2.10141
$189$	14.3749	1.04562
$190$	−11.5707	−0.839429
$191$	−25.3980	−1.83774	−0.918869	−	0.394563i	$-0.870896\pi$
$191$	−25.3980	−1.83774	−0.918869	+	0.394563i	$0.870896\pi$
$192$	12.9410	0.933934
$193$	−3.87328	−0.278805	−0.139403	−	0.990236i	$-0.544518\pi$
$193$	−3.87328	−0.278805	−0.139403	+	0.990236i	$0.544518\pi$
$194$	17.9894	1.29157
$195$	0	0
$196$	1.49065	0.106475
$197$	10.5370	0.750733	0.375367	−	0.926876i	$-0.377517\pi$
$197$	10.5370	0.750733	0.375367	+	0.926876i	$0.377517\pi$
$198$	−3.93293	−0.279501
$199$	3.84797	0.272775	0.136388	−	0.990656i	$-0.456451\pi$
$199$	3.84797	0.272775	0.136388	+	0.990656i	$0.456451\pi$
$200$	−1.33685	−0.0945298
$201$	−0.256266	−0.0180756
$202$	−21.3146	−1.49969
$203$	22.4429	1.57518
$204$	3.02252	0.211618
$205$	−9.91633	−0.692587
$206$	−8.78003	−0.611734
$207$	2.98805	0.207684
$208$	0	0
$209$	−5.38212	−0.372289
$210$	6.39908	0.441578
$211$	−7.58198	−0.521965	−0.260982	−	0.965344i	$-0.584046\pi$
$211$	−7.58198	−0.521965	−0.260982	+	0.965344i	$0.584046\pi$
$212$	−6.79896	−0.466954
$213$	3.32800	0.228031
$214$	−35.4731	−2.42489
$215$	6.56927	0.448021
$216$	−6.98524	−0.475285
$217$	20.8514	1.41549
$218$	39.4226	2.67004
$219$	15.9330	1.07665
$220$	−2.62184	−0.176764
$221$	0	0
$222$	−13.7214	−0.920919
$223$	10.8921	0.729387	0.364694	−	0.931128i	$-0.381174\pi$
$223$	10.8921	0.729387	0.364694	+	0.931128i	$0.381174\pi$
$224$	21.3708	1.42789
$225$	−1.82940	−0.121960
$226$	−30.9879	−2.06128
$227$	15.1308	1.00427	0.502133	−	0.864790i	$-0.332549\pi$
$227$	15.1308	1.00427	0.502133	+	0.864790i	$0.332549\pi$
$228$	−15.2673	−1.01110
$229$	1.07364	0.0709481	0.0354741	−	0.999371i	$-0.488706\pi$
$229$	1.07364	0.0709481	0.0354741	+	0.999371i	$0.488706\pi$
$230$	3.51145	0.231538
$231$	2.97653	0.195841
$232$	−10.9058	−0.715999
$233$	11.8158	0.774079	0.387039	−	0.922063i	$-0.373498\pi$
$233$	11.8158	0.774079	0.387039	+	0.922063i	$0.373498\pi$
$234$	0	0
$235$	10.9896	0.716885
$236$	31.1542	2.02796
$237$	1.13674	0.0738394
$238$	6.30192	0.408493
$239$	−29.3302	−1.89721	−0.948605	−	0.316462i	$-0.897505\pi$
$239$	−29.3302	−1.89721	−0.948605	+	0.316462i	$0.897505\pi$
$240$	2.56382	0.165494
$241$	13.5037	0.869852	0.434926	−	0.900466i	$-0.356775\pi$
$241$	13.5037	0.869852	0.434926	+	0.900466i	$0.356775\pi$
$242$	−2.14985	−0.138197
$243$	−15.4968	−0.994119
$244$	−24.0243	−1.53800
$245$	0.568550	0.0363233
$246$	−23.0655	−1.47060
$247$	0	0
$248$	−10.1324	−0.643409
$249$	−4.44576	−0.281739
$250$	−2.14985	−0.135968
$251$	15.6151	0.985616	0.492808	−	0.870138i	$-0.335970\pi$
$251$	15.6151	0.985616	0.492808	+	0.870138i	$0.335970\pi$
$252$	−13.1954	−0.831230
$253$	1.63335	0.102688
$254$	28.3821	1.78085
$255$	1.15282	0.0721926
$256$	2.04086	0.127554
$257$	−24.5650	−1.53232	−0.766160	−	0.642650i	$-0.777835\pi$
$257$	−24.5650	−1.53232	−0.766160	+	0.642650i	$0.777835\pi$
$258$	15.2802	0.951302
$259$	−16.2291	−1.00842
$260$	0	0
$261$	−14.9239	−0.923765
$262$	−46.6193	−2.88015
$263$	−3.56816	−0.220022	−0.110011	−	0.993930i	$-0.535089\pi$
$263$	−3.56816	−0.220022	−0.110011	+	0.993930i	$0.535089\pi$
$264$	−1.44640	−0.0890196
$265$	−2.59320	−0.159299
$266$	−31.8322	−1.95176
$267$	−10.2771	−0.628946
$268$	0.621002	0.0379338
$269$	−17.8725	−1.08970	−0.544852	−	0.838532i	$-0.683414\pi$
$269$	−17.8725	−1.08970	−0.544852	+	0.838532i	$0.683414\pi$
$270$	−11.2332	−0.683632
$271$	0.893275	0.0542626	0.0271313	−	0.999632i	$-0.491363\pi$
$271$	0.893275	0.0542626	0.0271313	+	0.999632i	$0.491363\pi$
$272$	2.52489	0.153094
$273$	0	0
$274$	−6.78241	−0.409741
$275$	−1.00000	−0.0603023
$276$	4.63328	0.278891
$277$	22.0449	1.32455	0.662275	−	0.749261i	$-0.269591\pi$
$277$	22.0449	1.32455	0.662275	+	0.749261i	$0.269591\pi$
$278$	−23.6106	−1.41607
$279$	−13.8656	−0.830111
$280$	−3.67782	−0.219792
$281$	−11.1943	−0.667795	−0.333897	−	0.942609i	$-0.608364\pi$
$281$	−11.1943	−0.667795	−0.333897	+	0.942609i	$0.608364\pi$
$282$	25.5620	1.52219
$283$	28.8227	1.71333	0.856665	−	0.515874i	$-0.172533\pi$
$283$	28.8227	1.71333	0.856665	+	0.515874i	$0.172533\pi$
$284$	−8.06464	−0.478548
$285$	−5.82314	−0.344933
$286$	0	0
$287$	−27.2808	−1.61034
$288$	−14.2109	−0.837388
$289$	−15.8647	−0.933216
$290$	−17.5380	−1.02987
$291$	9.05346	0.530723
$292$	−38.6100	−2.25948
$293$	−12.3754	−0.722980	−0.361490	−	0.932376i	$-0.617732\pi$
$293$	−12.3754	−0.722980	−0.361490	+	0.932376i	$0.617732\pi$
$294$	1.32245	0.0771270
$295$	11.8826	0.691830
$296$	7.88625	0.458379
$297$	−5.22513	−0.303193
$298$	37.5293	2.17402
$299$	0	0
$300$	−2.83667	−0.163775
$301$	18.0727	1.04169
$302$	30.6064	1.76120
$303$	−10.7269	−0.616244
$304$	−12.7537	−0.731476
$305$	−9.16317	−0.524681
$306$	−4.19059	−0.239560
$307$	27.4526	1.56681	0.783403	−	0.621515i	$-0.213482\pi$
$307$	27.4526	1.56681	0.783403	+	0.621515i	$0.213482\pi$
$308$	−7.21294	−0.410995
$309$	−4.41868	−0.251370
$310$	−16.2943	−0.925456
$311$	−17.5072	−0.992742	−0.496371	−	0.868111i	$-0.665334\pi$
$311$	−17.5072	−0.992742	−0.496371	+	0.868111i	$0.665334\pi$
$312$	0	0
$313$	17.9914	1.01694	0.508468	−	0.861081i	$-0.330212\pi$
$313$	17.9914	1.01694	0.508468	+	0.861081i	$0.330212\pi$
$314$	−9.08146	−0.512497
$315$	−5.03287	−0.283570
$316$	−2.75464	−0.154960
$317$	−3.37829	−0.189744	−0.0948718	−	0.995489i	$-0.530244\pi$
$317$	−3.37829	−0.189744	−0.0948718	+	0.995489i	$0.530244\pi$
$318$	−6.03181	−0.338247
$319$	−8.15779	−0.456749
$320$	−11.9609	−0.668634
$321$	−17.8523	−0.996420
$322$	9.66035	0.538350
$323$	−5.73472	−0.319089
$324$	−0.432816	−0.0240453
$325$	0	0
$326$	−37.3357	−2.06784
$327$	19.8400	1.09715
$328$	13.2567	0.731978
$329$	30.2336	1.66683
$330$	−2.32601	−0.128043
$331$	−7.03495	−0.386676	−0.193338	−	0.981132i	$-0.561931\pi$
$331$	−7.03495	−0.386676	−0.193338	+	0.981132i	$0.561931\pi$
$332$	10.7733	0.591261
$333$	10.7919	0.591390
$334$	13.4854	0.737890
$335$	0.236858	0.0129409
$336$	7.05332	0.384790
$337$	−4.96442	−0.270429	−0.135215	−	0.990816i	$-0.543172\pi$
$337$	−4.96442	−0.270429	−0.135215	+	0.990816i	$0.543172\pi$
$338$	0	0
$339$	−15.5951	−0.847009
$340$	−2.79360	−0.151504
$341$	−7.57930	−0.410442
$342$	21.1675	1.14461
$343$	−17.6936	−0.955362
$344$	−8.78215	−0.473502
$345$	1.76719	0.0951422
$346$	−22.8493	−1.22839
$347$	−25.4217	−1.36471	−0.682354	−	0.731022i	$-0.739044\pi$
$347$	−25.4217	−1.36471	−0.682354	+	0.731022i	$0.739044\pi$
$348$	−23.1410	−1.24049
$349$	−28.5913	−1.53045	−0.765227	−	0.643760i	$-0.777373\pi$
$349$	−28.5913	−1.53045	−0.765227	+	0.643760i	$0.777373\pi$
$350$	−5.91444	−0.316140
$351$	0	0
$352$	−7.76808	−0.414040
$353$	18.3223	0.975198	0.487599	−	0.873068i	$-0.337873\pi$
$353$	18.3223	0.975198	0.487599	+	0.873068i	$0.337873\pi$
$354$	27.6390	1.46899
$355$	−3.07595	−0.163255
$356$	24.9041	1.31991
$357$	3.17153	0.167855
$358$	−5.71263	−0.301922
$359$	21.1551	1.11652	0.558261	−	0.829665i	$-0.311469\pi$
$359$	21.1551	1.11652	0.558261	+	0.829665i	$0.311469\pi$
$360$	2.44564	0.128897
$361$	9.96722	0.524591
$362$	6.10637	0.320944
$363$	−1.08194	−0.0567872
$364$	0	0
$365$	−14.7263	−0.770811
$366$	−21.3136	−1.11408
$367$	−10.5098	−0.548608	−0.274304	−	0.961643i	$-0.588448\pi$
$367$	−10.5098	−0.548608	−0.274304	+	0.961643i	$0.588448\pi$
$368$	3.87046	0.201762
$369$	18.1410	0.944381
$370$	12.6822	0.659316
$371$	−7.13416	−0.370387
$372$	−21.5000	−1.11472
$373$	−6.09673	−0.315677	−0.157838	−	0.987465i	$-0.550453\pi$
$373$	−6.09673	−0.315677	−0.157838	+	0.987465i	$0.550453\pi$
$374$	−2.29069	−0.118449
$375$	−1.08194	−0.0558712
$376$	−14.6915	−0.757658
$377$	0	0
$378$	−30.9037	−1.58952
$379$	−26.2822	−1.35003	−0.675013	−	0.737806i	$-0.735862\pi$
$379$	−26.2822	−1.35003	−0.675013	+	0.737806i	$0.735862\pi$
$380$	14.1110	0.723881
$381$	14.2837	0.731776
$382$	54.6019	2.79368
$383$	19.6920	1.00622	0.503108	−	0.864224i	$-0.332190\pi$
$383$	19.6920	1.00622	0.503108	+	0.864224i	$0.332190\pi$
$384$	−11.0119	−0.561948
$385$	−2.75110	−0.140209
$386$	8.32696	0.423831
$387$	−12.0178	−0.610901
$388$	−21.9390	−1.11378
$389$	−6.30020	−0.319433	−0.159716	−	0.987163i	$-0.551058\pi$
$389$	−6.30020	−0.319433	−0.159716	+	0.987163i	$0.551058\pi$
$390$	0	0
$391$	1.74036	0.0880136
$392$	−0.760068	−0.0383892
$393$	−23.4618	−1.18349
$394$	−22.6530	−1.14124
$395$	−1.05065	−0.0528640
$396$	4.79639	0.241028
$397$	7.61154	0.382012	0.191006	−	0.981589i	$-0.438825\pi$
$397$	7.61154	0.382012	0.191006	+	0.981589i	$0.438825\pi$
$398$	−8.27254	−0.414665
$399$	−16.0200	−0.802005
$400$	−2.36964	−0.118482
$401$	21.6060	1.07895	0.539476	−	0.842001i	$-0.318622\pi$
$401$	21.6060	1.07895	0.539476	+	0.842001i	$0.318622\pi$
$402$	0.550933	0.0274780
$403$	0	0
$404$	25.9942	1.29326
$405$	−0.165081	−0.00820294
$406$	−48.2488	−2.39455
$407$	5.89912	0.292408
$408$	−1.54116	−0.0762986
$409$	−8.93547	−0.441831	−0.220915	−	0.975293i	$-0.570904\pi$
$409$	−8.93547	−0.441831	−0.220915	+	0.975293i	$0.570904\pi$
$410$	21.3186	1.05285
$411$	−3.41335	−0.168368
$412$	10.7077	0.527528
$413$	32.6902	1.60858
$414$	−6.42385	−0.315715
$415$	4.10906	0.201706
$416$	0	0
$417$	−11.8824	−0.581882
$418$	11.5707	0.565943
$419$	0.0364025	0.00177838	0.000889188	−	1.00000i	$-0.499717\pi$
$419$	0.0364025	0.00177838	0.000889188		1.00000i	$0.499717\pi$
$420$	−7.80398	−0.380795
$421$	2.32492	0.113310	0.0566549	−	0.998394i	$-0.481957\pi$
$421$	2.32492	0.113310	0.0566549	+	0.998394i	$0.481957\pi$
$422$	16.3001	0.793476
$423$	−20.1045	−0.977512
$424$	3.46673	0.168359
$425$	−1.06551	−0.0516850
$426$	−7.15468	−0.346646
$427$	−25.2088	−1.21994
$428$	43.2610	2.09110
$429$	0	0
$430$	−14.1229	−0.681068
$431$	5.22945	0.251894	0.125947	−	0.992037i	$-0.459803\pi$
$431$	5.22945	0.251894	0.125947	+	0.992037i	$0.459803\pi$
$432$	−12.3817	−0.595715
$433$	0.100475	0.00482852	0.00241426	−	0.999997i	$-0.499232\pi$
$433$	0.100475	0.00482852	0.00241426	+	0.999997i	$0.499232\pi$
$434$	−44.8273	−2.15178
$435$	−8.82626	−0.423187
$436$	−48.0777	−2.30250
$437$	−8.79088	−0.420525
$438$	−34.2535	−1.63670
$439$	30.9534	1.47733	0.738664	−	0.674074i	$-0.235457\pi$
$439$	30.9534	1.47733	0.738664	+	0.674074i	$0.235457\pi$
$440$	1.33685	0.0637320
$441$	−1.04011	−0.0495289
$442$	0	0
$443$	17.8185	0.846581	0.423291	−	0.905994i	$-0.360875\pi$
$443$	17.8185	0.846581	0.423291	+	0.905994i	$0.360875\pi$
$444$	16.7339	0.794154
$445$	9.49872	0.450282
$446$	−23.4163	−1.10879
$447$	18.8872	0.893334
$448$	−32.9056	−1.55464
$449$	−37.6891	−1.77866	−0.889330	−	0.457266i	$-0.848829\pi$
$449$	−37.6891	−1.77866	−0.889330	+	0.457266i	$0.848829\pi$
$450$	3.93293	0.185400
$451$	9.91633	0.466942
$452$	37.7911	1.77755
$453$	15.4031	0.723702
$454$	−32.5289	−1.52666
$455$	0	0
$456$	7.78469	0.364551
$457$	17.0608	0.798070	0.399035	−	0.916936i	$-0.369345\pi$
$457$	17.0608	0.798070	0.399035	+	0.916936i	$0.369345\pi$
$458$	−2.30816	−0.107853
$459$	−5.56745	−0.259866
$460$	−4.28238	−0.199667
$461$	−32.0709	−1.49369	−0.746846	−	0.664997i	$-0.768433\pi$
$461$	−32.0709	−1.49369	−0.746846	+	0.664997i	$0.768433\pi$
$462$	−6.39908	−0.297712
$463$	−2.54597	−0.118321	−0.0591606	−	0.998248i	$-0.518842\pi$
$463$	−2.54597	−0.118321	−0.0591606	+	0.998248i	$0.518842\pi$
$464$	−19.3311	−0.897423
$465$	−8.20036	−0.380283
$466$	−25.4021	−1.17673
$467$	19.8439	0.918266	0.459133	−	0.888367i	$-0.348160\pi$
$467$	19.8439	0.918266	0.459133	+	0.888367i	$0.348160\pi$
$468$	0	0
$469$	0.651619	0.0300890
$470$	−23.6260	−1.08979
$471$	−4.57038	−0.210592
$472$	−15.8853	−0.731179
$473$	−6.56927	−0.302055
$474$	−2.44382	−0.112248
$475$	5.38212	0.246949
$476$	−7.68548	−0.352264
$477$	4.74401	0.217213
$478$	63.0553	2.88408
$479$	21.0364	0.961179	0.480589	−	0.876946i	$-0.340423\pi$
$479$	21.0364	0.961179	0.480589	+	0.876946i	$0.340423\pi$
$480$	−8.40461	−0.383616
$481$	0	0
$482$	−29.0309	−1.32232
$483$	4.86171	0.221216
$484$	2.62184	0.119174
$485$	−8.36778	−0.379962
$486$	33.3157	1.51123
$487$	−9.96422	−0.451522	−0.225761	−	0.974183i	$-0.572487\pi$
$487$	−9.96422	−0.451522	−0.225761	+	0.974183i	$0.572487\pi$
$488$	12.2498	0.554523
$489$	−18.7898	−0.849703
$490$	−1.22230	−0.0552177
$491$	1.12213	0.0506411	0.0253205	−	0.999679i	$-0.491939\pi$
$491$	1.12213	0.0506411	0.0253205	+	0.999679i	$0.491939\pi$
$492$	28.1294	1.26817
$493$	−8.69224	−0.391479
$494$	0	0
$495$	1.82940	0.0822255
$496$	−17.9603	−0.806439
$497$	−8.46225	−0.379584
$498$	9.55770	0.428291
$499$	2.19814	0.0984022	0.0492011	−	0.998789i	$-0.484332\pi$
$499$	2.19814	0.0984022	0.0492011	+	0.998789i	$0.484332\pi$
$500$	2.62184	0.117252
$501$	6.78674	0.303209
$502$	−33.5701	−1.49830
$503$	−6.32312	−0.281934	−0.140967	−	0.990014i	$-0.545021\pi$
$503$	−6.32312	−0.281934	−0.140967	+	0.990014i	$0.545021\pi$
$504$	6.72821	0.299698
$505$	9.91449	0.441189
$506$	−3.51145	−0.156103
$507$	0	0
$508$	−34.6132	−1.53571
$509$	13.5463	0.600428	0.300214	−	0.953872i	$-0.402942\pi$
$509$	13.5463	0.600428	0.300214	+	0.953872i	$0.402942\pi$
$510$	−2.47839	−0.109745
$511$	−40.5136	−1.79222
$512$	−24.7433	−1.09351
$513$	28.1223	1.24163
$514$	52.8109	2.32939
$515$	4.08403	0.179964
$516$	−18.6349	−0.820355
$517$	−10.9896	−0.483324
$518$	34.8900	1.53298
$519$	−11.4993	−0.504761
$520$	0	0
$521$	19.4285	0.851178	0.425589	−	0.904917i	$-0.360067\pi$
$521$	19.4285	0.851178	0.425589	+	0.904917i	$0.360067\pi$
$522$	32.0841	1.40428
$523$	12.1543	0.531470	0.265735	−	0.964046i	$-0.414385\pi$
$523$	12.1543	0.531470	0.265735	+	0.964046i	$0.414385\pi$
$524$	56.8544	2.48369
$525$	−2.97653	−0.129906
$526$	7.67098	0.334471
$527$	−8.07585	−0.351790
$528$	−2.56382	−0.111576
$529$	−20.3322	−0.884007
$530$	5.57499	0.242162
$531$	−21.7380	−0.943350
$532$	38.8209	1.68310
$533$	0	0
$534$	22.0941	0.956105
$535$	16.5003	0.713369
$536$	−0.316644	−0.0136769
$537$	−2.87497	−0.124064
$538$	38.4231	1.65654
$539$	−0.568550	−0.0244892
$540$	13.6994	0.589530
$541$	18.0332	0.775308	0.387654	−	0.921805i	$-0.373286\pi$
$541$	18.0332	0.775308	0.387654	+	0.921805i	$0.373286\pi$
$542$	−1.92040	−0.0824884
$543$	3.07312	0.131880
$544$	−8.27700	−0.354873
$545$	−18.3374	−0.785488
$546$	0	0
$547$	26.7326	1.14300	0.571502	−	0.820600i	$-0.306361\pi$
$547$	26.7326	1.14300	0.571502	+	0.820600i	$0.306361\pi$
$548$	8.27147	0.353340
$549$	16.7631	0.715433
$550$	2.14985	0.0916697
$551$	43.9062	1.87047
$552$	−2.36247	−0.100554
$553$	−2.89045	−0.122914
$554$	−47.3932	−2.01354
$555$	6.38250	0.270922
$556$	28.7942	1.22114
$557$	35.7655	1.51543	0.757717	−	0.652583i	$-0.226315\pi$
$557$	35.7655	1.51543	0.757717	+	0.652583i	$0.226315\pi$
$558$	29.8089	1.26191
$559$	0	0
$560$	−6.51913	−0.275483
$561$	−1.15282	−0.0486723
$562$	24.0660	1.01516
$563$	0.139004	0.00585832	0.00292916	−	0.999996i	$-0.499068\pi$
$563$	0.139004	0.00585832	0.00292916	+	0.999996i	$0.499068\pi$
$564$	−31.1740	−1.31266
$565$	14.4140	0.606401
$566$	−61.9643	−2.60455
$567$	−0.454154	−0.0190727
$568$	4.11210	0.172540
$569$	14.9284	0.625831	0.312915	−	0.949781i	$-0.398694\pi$
$569$	14.9284	0.625831	0.312915	+	0.949781i	$0.398694\pi$
$570$	12.5189	0.524357
$571$	13.1593	0.550699	0.275349	−	0.961344i	$-0.411206\pi$
$571$	13.1593	0.550699	0.275349	+	0.961344i	$0.411206\pi$
$572$	0	0
$573$	27.4792	1.14796
$574$	58.6496	2.44799
$575$	−1.63335	−0.0681154
$576$	21.8813	0.911719
$577$	−7.73801	−0.322138	−0.161069	−	0.986943i	$-0.551494\pi$
$577$	−7.73801	−0.322138	−0.161069	+	0.986943i	$0.551494\pi$
$578$	34.1066	1.41865
$579$	4.19067	0.174158
$580$	21.3884	0.888105
$581$	11.3044	0.468987
$582$	−19.4635	−0.806789
$583$	2.59320	0.107400
$584$	19.6869	0.814652
$585$	0	0
$586$	26.6053	1.09905
$587$	−27.5154	−1.13568	−0.567840	−	0.823139i	$-0.692221\pi$
$587$	−27.5154	−1.13568	−0.567840	+	0.823139i	$0.692221\pi$
$588$	−1.61279	−0.0665104
$589$	40.7927	1.68083
$590$	−25.5457	−1.05170
$591$	−11.4005	−0.468953
$592$	13.9788	0.574525
$593$	41.5326	1.70554	0.852770	−	0.522286i	$-0.174921\pi$
$593$	41.5326	1.70554	0.852770	+	0.522286i	$0.174921\pi$
$594$	11.2332	0.460905
$595$	−2.93134	−0.120173
$596$	−45.7688	−1.87476
$597$	−4.16328	−0.170392
$598$	0	0
$599$	1.71243	0.0699679	0.0349839	−	0.999388i	$-0.488862\pi$
$599$	1.71243	0.0699679	0.0349839	+	0.999388i	$0.488862\pi$
$600$	1.44640	0.0590489
$601$	32.4351	1.32305	0.661527	−	0.749921i	$-0.269909\pi$
$601$	32.4351	1.32305	0.661527	+	0.749921i	$0.269909\pi$
$602$	−38.8536	−1.58355
$603$	−0.433308	−0.0176457
$604$	−37.3259	−1.51877
$605$	1.00000	0.0406558
$606$	23.0612	0.936796
$607$	−25.0183	−1.01546	−0.507730	−	0.861516i	$-0.669515\pi$
$607$	−25.0183	−1.01546	−0.507730	+	0.861516i	$0.669515\pi$
$608$	41.8087	1.69557
$609$	−24.2819	−0.983953
$610$	19.6994	0.797605
$611$	0	0
$612$	5.11063	0.206585
$613$	−31.6724	−1.27924	−0.639618	−	0.768693i	$-0.720908\pi$
$613$	−31.6724	−1.27924	−0.639618	+	0.768693i	$0.720908\pi$
$614$	−59.0189	−2.38181
$615$	10.7289	0.432631
$616$	3.67782	0.148184
$617$	23.6860	0.953562	0.476781	−	0.879022i	$-0.341804\pi$
$617$	23.6860	0.953562	0.476781	+	0.879022i	$0.341804\pi$
$618$	9.49948	0.382125
$619$	18.1958	0.731351	0.365675	−	0.930742i	$-0.380838\pi$
$619$	18.1958	0.731351	0.365675	+	0.930742i	$0.380838\pi$
$620$	19.8717	0.798066
$621$	−8.53446	−0.342476
$622$	37.6378	1.50914
$623$	26.1319	1.04695
$624$	0	0
$625$	1.00000	0.0400000
$626$	−38.6788	−1.54592
$627$	5.82314	0.232554
$628$	11.0753	0.441951
$629$	6.28559	0.250623
$630$	10.8199	0.431075
$631$	−12.8671	−0.512230	−0.256115	−	0.966646i	$-0.582443\pi$
$631$	−12.8671	−0.512230	−0.256115	+	0.966646i	$0.582443\pi$
$632$	1.40457	0.0558707
$633$	8.20326	0.326050
$634$	7.26280	0.288443
$635$	−13.2019	−0.523902
$636$	7.35608	0.291687
$637$	0	0
$638$	17.5380	0.694336
$639$	5.62715	0.222607
$640$	10.1779	0.402317
$641$	41.7050	1.64725	0.823623	−	0.567137i	$-0.191949\pi$
$641$	41.7050	1.64725	0.823623	+	0.567137i	$0.191949\pi$
$642$	38.3798	1.51473
$643$	−19.3323	−0.762390	−0.381195	−	0.924495i	$-0.624487\pi$
$643$	−19.3323	−0.762390	−0.381195	+	0.924495i	$0.624487\pi$
$644$	−11.7812	−0.464246
$645$	−7.10757	−0.279860
$646$	12.3288	0.485069
$647$	−5.67962	−0.223289	−0.111644	−	0.993748i	$-0.535612\pi$
$647$	−5.67962	−0.223289	−0.111644	+	0.993748i	$0.535612\pi$
$648$	0.220689	0.00866949
$649$	−11.8826	−0.466432
$650$	0	0
$651$	−22.5600	−0.884197
$652$	45.5327	1.78320
$653$	−6.09068	−0.238347	−0.119173	−	0.992873i	$-0.538024\pi$
$653$	−6.09068	−0.238347	−0.119173	+	0.992873i	$0.538024\pi$
$654$	−42.6530	−1.66786
$655$	21.6849	0.847300
$656$	23.4982	0.917450
$657$	26.9404	1.05104
$658$	−64.9975	−2.53387
$659$	−4.77111	−0.185856	−0.0929281	−	0.995673i	$-0.529623\pi$
$659$	−4.77111	−0.185856	−0.0929281	+	0.995673i	$0.529623\pi$
$660$	2.83667	0.110417
$661$	−27.0274	−1.05125	−0.525623	−	0.850718i	$-0.676168\pi$
$661$	−27.0274	−1.05125	−0.525623	+	0.850718i	$0.676168\pi$
$662$	15.1241	0.587814
$663$	0	0
$664$	−5.49321	−0.213178
$665$	14.8068	0.574181
$666$	−23.2008	−0.899014
$667$	−13.3245	−0.515928
$668$	−16.4461	−0.636319
$669$	−11.7846	−0.455619
$670$	−0.509208	−0.0196724
$671$	9.16317	0.353740
$672$	−23.1219	−0.891947
$673$	−3.65814	−0.141011	−0.0705055	−	0.997511i	$-0.522461\pi$
$673$	−3.65814	−0.141011	−0.0705055	+	0.997511i	$0.522461\pi$
$674$	10.6727	0.411099
$675$	5.22513	0.201115
$676$	0	0
$677$	−13.2418	−0.508924	−0.254462	−	0.967083i	$-0.581898\pi$
$677$	−13.2418	−0.508924	−0.254462	+	0.967083i	$0.581898\pi$
$678$	33.5271	1.28760
$679$	−23.0206	−0.883450
$680$	1.42444	0.0546246
$681$	−16.3706	−0.627324
$682$	16.2943	0.623942
$683$	−2.17478	−0.0832156	−0.0416078	−	0.999134i	$-0.513248\pi$
$683$	−2.17478	−0.0832156	−0.0416078	+	0.999134i	$0.513248\pi$
$684$	−25.8148	−0.987052
$685$	3.15484	0.120540
$686$	38.0384	1.45231
$687$	−1.16162	−0.0443184
$688$	−15.5668	−0.593480
$689$	0	0
$690$	−3.79918	−0.144632
$691$	−44.8225	−1.70513	−0.852564	−	0.522623i	$-0.824953\pi$
$691$	−44.8225	−1.70513	−0.852564	+	0.522623i	$0.824953\pi$
$692$	27.8658	1.05930
$693$	5.03287	0.191183
$694$	54.6527	2.07459
$695$	10.9824	0.416588
$696$	11.7994	0.447256
$697$	10.5660	0.400216
$698$	61.4668	2.32655
$699$	−12.7840	−0.483536
$700$	7.21294	0.272623
$701$	32.8117	1.23928	0.619640	−	0.784886i	$-0.287279\pi$
$701$	32.8117	1.23928	0.619640	+	0.784886i	$0.287279\pi$
$702$	0	0
$703$	−31.7497	−1.19746
$704$	11.9609	0.450793
$705$	−11.8901	−0.447809
$706$	−39.3901	−1.48247
$707$	27.2757	1.02581
$708$	−33.7070	−1.26679
$709$	−0.245066	−0.00920366	−0.00460183	−	0.999989i	$-0.501465\pi$
$709$	−0.245066	−0.00920366	−0.00460183	+	0.999989i	$0.501465\pi$
$710$	6.61282	0.248175
$711$	1.92206	0.0720830
$712$	−12.6984	−0.475893
$713$	−12.3796	−0.463621
$714$	−6.81831	−0.255169
$715$	0	0
$716$	6.96682	0.260362
$717$	31.7335	1.18511
$718$	−45.4801	−1.69730
$719$	17.7961	0.663681	0.331841	−	0.943335i	$-0.392330\pi$
$719$	17.7961	0.663681	0.331841	+	0.943335i	$0.392330\pi$
$720$	4.33503	0.161557
$721$	11.2356	0.418434
$722$	−21.4280	−0.797467
$723$	−14.6102	−0.543361
$724$	−7.44700	−0.276766
$725$	8.15779	0.302973
$726$	2.32601	0.0863262
$727$	−40.5448	−1.50372	−0.751861	−	0.659321i	$-0.770844\pi$
$727$	−40.5448	−1.50372	−0.751861	+	0.659321i	$0.770844\pi$
$728$	0	0
$729$	17.2619	0.639328
$730$	31.6593	1.17176
$731$	−6.99965	−0.258891
$732$	25.9929	0.960726
$733$	−4.28706	−0.158346	−0.0791730	−	0.996861i	$-0.525228\pi$
$733$	−4.28706	−0.158346	−0.0791730	+	0.996861i	$0.525228\pi$
$734$	22.5945	0.833978
$735$	−0.615138	−0.0226897
$736$	−12.6880	−0.467685
$737$	−0.236858	−0.00872477
$738$	−39.0003	−1.43562
$739$	−4.62049	−0.169967	−0.0849837	−	0.996382i	$-0.527084\pi$
$739$	−4.62049	−0.169967	−0.0849837	+	0.996382i	$0.527084\pi$
$740$	−15.4665	−0.568561
$741$	0	0
$742$	15.3373	0.563052
$743$	−18.9260	−0.694328	−0.347164	−	0.937804i	$-0.612855\pi$
$743$	−18.9260	−0.694328	−0.347164	+	0.937804i	$0.612855\pi$
$744$	10.9627	0.401911
$745$	−17.4568	−0.639566
$746$	13.1070	0.479883
$747$	−7.51712	−0.275037
$748$	2.79360	0.102144
$749$	45.3939	1.65866
$750$	2.32601	0.0849338
$751$	0.265161	0.00967588	0.00483794	−	0.999988i	$-0.498460\pi$
$751$	0.265161	0.00967588	0.00483794	+	0.999988i	$0.498460\pi$
$752$	−26.0415	−0.949637
$753$	−16.8946	−0.615674
$754$	0	0
$755$	−14.2366	−0.518122
$756$	37.6885	1.37072
$757$	−47.9222	−1.74176	−0.870881	−	0.491494i	$-0.836451\pi$
$757$	−47.9222	−1.74176	−0.870881	+	0.491494i	$0.836451\pi$
$758$	56.5027	2.05227
$759$	−1.76719	−0.0641449
$760$	−7.19511	−0.260994
$761$	18.0906	0.655785	0.327893	−	0.944715i	$-0.393662\pi$
$761$	18.0906	0.655785	0.327893	+	0.944715i	$0.393662\pi$
$762$	−30.7077	−1.11242
$763$	−50.4480	−1.82634
$764$	−66.5895	−2.40912
$765$	1.94925	0.0704754
$766$	−42.3348	−1.52962
$767$	0	0
$768$	−2.20809	−0.0796777
$769$	17.2635	0.622540	0.311270	−	0.950322i	$-0.399246\pi$
$769$	17.2635	0.622540	0.311270	+	0.950322i	$0.399246\pi$
$770$	5.91444	0.213142
$771$	26.5778	0.957178
$772$	−10.1551	−0.365491
$773$	−24.3414	−0.875498	−0.437749	−	0.899097i	$-0.644224\pi$
$773$	−24.3414	−0.875498	−0.437749	+	0.899097i	$0.644224\pi$
$774$	25.8365	0.928674
$775$	7.57930	0.272257
$776$	11.1865	0.401572
$777$	17.5589	0.629922
$778$	13.5445	0.485592
$779$	−53.3709	−1.91221
$780$	0	0
$781$	3.07595	0.110066
$782$	−3.74150	−0.133796
$783$	42.6256	1.52331
$784$	−1.34726	−0.0481165
$785$	4.22424	0.150770
$786$	50.4393	1.79911
$787$	5.74525	0.204796	0.102398	−	0.994744i	$-0.467348\pi$
$787$	5.74525	0.204796	0.102398	+	0.994744i	$0.467348\pi$
$788$	27.6264	0.984150
$789$	3.86054	0.137439
$790$	2.25874	0.0803623
$791$	39.6543	1.40995
$792$	−2.44564	−0.0869021
$793$	0	0
$794$	−16.3636	−0.580724
$795$	2.80570	0.0995078
$796$	10.0888	0.357586
$797$	−10.5941	−0.375263	−0.187632	−	0.982239i	$-0.560081\pi$
$797$	−10.5941	−0.375263	−0.187632	+	0.982239i	$0.560081\pi$
$798$	34.4406	1.21918
$799$	−11.7096	−0.414256
$800$	7.76808	0.274643
$801$	−17.3770	−0.613985
$802$	−46.4496	−1.64019
$803$	14.7263	0.519681
$804$	−0.671888	−0.0236957
$805$	−4.49351	−0.158375
$806$	0	0
$807$	19.3370	0.680694
$808$	−13.2542	−0.466282
$809$	−29.2109	−1.02700	−0.513500	−	0.858090i	$-0.671651\pi$
$809$	−29.2109	−1.02700	−0.513500	+	0.858090i	$0.671651\pi$
$810$	0.354899	0.0124699
$811$	−32.3324	−1.13535	−0.567673	−	0.823254i	$-0.692156\pi$
$811$	−32.3324	−1.13535	−0.567673	+	0.823254i	$0.692156\pi$
$812$	58.8416	2.06494
$813$	−0.966472	−0.0338956
$814$	−12.6822	−0.444510
$815$	17.3667	0.608329
$816$	−2.73178	−0.0956315
$817$	35.3566	1.23697
$818$	19.2099	0.671658
$819$	0	0
$820$	−25.9990	−0.907925
$821$	−12.1719	−0.424803	−0.212402	−	0.977182i	$-0.568129\pi$
$821$	−12.1719	−0.424803	−0.212402	+	0.977182i	$0.568129\pi$
$822$	7.33818	0.255948
$823$	−16.5420	−0.576618	−0.288309	−	0.957537i	$-0.593093\pi$
$823$	−16.5420	−0.576618	−0.288309	+	0.957537i	$0.593093\pi$
$824$	−5.45975	−0.190199
$825$	1.08194	0.0376684
$826$	−70.2788	−2.44531
$827$	45.0533	1.56666	0.783329	−	0.621608i	$-0.213520\pi$
$827$	45.0533	1.56666	0.783329	+	0.621608i	$0.213520\pi$
$828$	7.83419	0.272257
$829$	−37.1165	−1.28911	−0.644554	−	0.764559i	$-0.722957\pi$
$829$	−37.1165	−1.28911	−0.644554	+	0.764559i	$0.722957\pi$
$830$	−8.83384	−0.306627
$831$	−23.8513	−0.827393
$832$	0	0
$833$	−0.605798	−0.0209897
$834$	25.5452	0.884559
$835$	−6.27274	−0.217077
$836$	−14.1110	−0.488041
$837$	39.6028	1.36887
$838$	−0.0782597	−0.00270344
$839$	34.7366	1.19924	0.599621	−	0.800284i	$-0.295318\pi$
$839$	34.7366	1.19924	0.599621	+	0.800284i	$0.295318\pi$
$840$	3.97918	0.137295
$841$	37.5496	1.29481
$842$	−4.99823	−0.172250
$843$	12.1116	0.417144
$844$	−19.8787	−0.684253
$845$	0	0
$846$	43.2215	1.48599
$847$	2.75110	0.0945289
$848$	6.14497	0.211019
$849$	−31.1844	−1.07025
$850$	2.29069	0.0785700
$851$	9.63532	0.330294
$852$	8.72547	0.298930
$853$	50.0958	1.71525	0.857623	−	0.514278i	$-0.171940\pi$
$853$	50.0958	1.71525	0.857623	+	0.514278i	$0.171940\pi$
$854$	54.1950	1.85452
$855$	−9.84606	−0.336728
$856$	−22.0585	−0.753943
$857$	19.4896	0.665752	0.332876	−	0.942971i	$-0.391981\pi$
$857$	19.4896	0.665752	0.332876	+	0.942971i	$0.391981\pi$
$858$	0	0
$859$	36.1569	1.23366	0.616828	−	0.787098i	$-0.288417\pi$
$859$	36.1569	1.23366	0.616828	+	0.787098i	$0.288417\pi$
$860$	17.2236	0.587318
$861$	29.5163	1.00591
$862$	−11.2425	−0.382922
$863$	25.1739	0.856928	0.428464	−	0.903559i	$-0.359055\pi$
$863$	25.1739	0.856928	0.428464	+	0.903559i	$0.359055\pi$
$864$	40.5892	1.38087
$865$	10.6284	0.361375
$866$	−0.216006	−0.00734017
$867$	17.1647	0.582942
$868$	54.6690	1.85559
$869$	1.05065	0.0356409
$870$	18.9751	0.643316
$871$	0	0
$872$	24.5144	0.830163
$873$	15.3080	0.518099
$874$	18.8990	0.639270
$875$	2.75110	0.0930041
$876$	41.7738	1.41141
$877$	15.4612	0.522088	0.261044	−	0.965327i	$-0.415933\pi$
$877$	15.4612	0.522088	0.261044	+	0.965327i	$0.415933\pi$
$878$	−66.5451	−2.24579
$879$	13.3895	0.451616
$880$	2.36964	0.0798807
$881$	25.4248	0.856584	0.428292	−	0.903640i	$-0.359115\pi$
$881$	25.4248	0.856584	0.428292	+	0.903640i	$0.359115\pi$
$882$	2.23607	0.0752924
$883$	51.9801	1.74927	0.874635	−	0.484782i	$-0.161101\pi$
$883$	51.9801	1.74927	0.874635	+	0.484782i	$0.161101\pi$
$884$	0	0
$885$	−12.8563	−0.432158
$886$	−38.3070	−1.28695
$887$	51.4814	1.72858	0.864288	−	0.502997i	$-0.167769\pi$
$887$	51.4814	1.72858	0.864288	+	0.502997i	$0.167769\pi$
$888$	−8.53247	−0.286331
$889$	−36.3198	−1.21813
$890$	−20.4208	−0.684506
$891$	0.165081	0.00553042
$892$	28.5573	0.956167
$893$	59.1475	1.97930
$894$	−40.6046	−1.35802
$895$	2.65723	0.0888214
$896$	28.0004	0.935428
$897$	0	0
$898$	81.0258	2.70387
$899$	61.8304	2.06216
$900$	−4.79639	−0.159880
$901$	2.76309	0.0920520
$902$	−21.3186	−0.709831
$903$	−19.5536	−0.650704
$904$	−19.2694	−0.640891
$905$	−2.84038	−0.0944173
$906$	−33.1144	−1.10015
$907$	31.9407	1.06057	0.530286	−	0.847819i	$-0.322084\pi$
$907$	31.9407	1.06057	0.530286	+	0.847819i	$0.322084\pi$
$908$	39.6705	1.31651
$909$	−18.1376	−0.601586
$910$	0	0
$911$	34.9657	1.15846	0.579232	−	0.815163i	$-0.303353\pi$
$911$	34.9657	1.15846	0.579232	+	0.815163i	$0.303353\pi$
$912$	13.7988	0.456923
$913$	−4.10906	−0.135990
$914$	−36.6781	−1.21320
$915$	9.91401	0.327747
$916$	2.81491	0.0930072
$917$	59.6574	1.97006
$918$	11.9692	0.395041
$919$	36.5141	1.20449	0.602244	−	0.798312i	$-0.294273\pi$
$919$	36.5141	1.20449	0.602244	+	0.798312i	$0.294273\pi$
$920$	2.18355	0.0719895
$921$	−29.7022	−0.978719
$922$	68.9476	2.27067
$923$	0	0
$924$	7.80398	0.256732
$925$	−5.89912	−0.193962
$926$	5.47344	0.179868
$927$	−7.47133	−0.245391
$928$	63.3704	2.08023
$929$	20.7766	0.681659	0.340830	−	0.940125i	$-0.389292\pi$
$929$	20.7766	0.681659	0.340830	+	0.940125i	$0.389292\pi$
$930$	17.6295	0.578095
$931$	3.06001	0.100288
$932$	30.9791	1.01475
$933$	18.9418	0.620125
$934$	−42.6613	−1.39592
$935$	1.06551	0.0348460
$936$	0	0
$937$	−5.11109	−0.166972	−0.0834860	−	0.996509i	$-0.526605\pi$
$937$	−5.11109	−0.166972	−0.0834860	+	0.996509i	$0.526605\pi$
$938$	−1.40088	−0.0457404
$939$	−19.4657	−0.635239
$940$	28.8130	0.939778
$941$	18.2306	0.594300	0.297150	−	0.954831i	$-0.403964\pi$
$941$	18.2306	0.594300	0.297150	+	0.954831i	$0.403964\pi$
$942$	9.82561	0.320136
$943$	16.1968	0.527442
$944$	−28.1575	−0.916448
$945$	14.3749	0.467614
$946$	14.1229	0.459176
$947$	7.70784	0.250471	0.125236	−	0.992127i	$-0.460031\pi$
$947$	7.70784	0.250471	0.125236	+	0.992127i	$0.460031\pi$
$948$	2.98036	0.0967974
$949$	0	0
$950$	−11.5707	−0.375404
$951$	3.65511	0.118525
$952$	3.91877	0.127008
$953$	−46.4805	−1.50565	−0.752825	−	0.658220i	$-0.771310\pi$
$953$	−46.4805	−1.50565	−0.752825	+	0.658220i	$0.771310\pi$
$954$	−10.1989	−0.330201
$955$	−25.3980	−0.821861
$956$	−76.8989	−2.48709
$957$	8.82626	0.285312
$958$	−45.2251	−1.46116
$959$	8.67927	0.280268
$960$	12.9410	0.417668
$961$	26.4458	0.853091
$962$	0	0
$963$	−30.1856	−0.972719
$964$	35.4046	1.14030
$965$	−3.87328	−0.124685
$966$	−10.4519	−0.336285
$967$	18.4315	0.592718	0.296359	−	0.955077i	$-0.404228\pi$
$967$	18.4315	0.592718	0.296359	+	0.955077i	$0.404228\pi$
$968$	−1.33685	−0.0429681
$969$	6.20464	0.199322
$970$	17.9894	0.577606
$971$	15.8309	0.508038	0.254019	−	0.967199i	$-0.418247\pi$
$971$	15.8309	0.508038	0.254019	+	0.967199i	$0.418247\pi$
$972$	−40.6300	−1.30321
$973$	30.2138	0.968610
$974$	21.4215	0.686390
$975$	0	0
$976$	21.7135	0.695031
$977$	18.0618	0.577848	0.288924	−	0.957352i	$-0.406702\pi$
$977$	18.0618	0.577848	0.288924	+	0.957352i	$0.406702\pi$
$978$	40.3951	1.29169
$979$	−9.49872	−0.303580
$980$	1.49065	0.0476169
$981$	33.5465	1.07106
$982$	−2.41241	−0.0769831
$983$	31.2331	0.996182	0.498091	−	0.867125i	$-0.334035\pi$
$983$	31.2331	0.996182	0.498091	+	0.867125i	$0.334035\pi$
$984$	−14.3430	−0.457237
$985$	10.5370	0.335738
$986$	18.6870	0.595115
$987$	−32.7110	−1.04120
$988$	0	0
$989$	−10.7299	−0.341191
$990$	−3.93293	−0.124997
$991$	−12.3980	−0.393835	−0.196918	−	0.980420i	$-0.563093\pi$
$991$	−12.3980	−0.393835	−0.196918	+	0.980420i	$0.563093\pi$
$992$	58.8766	1.86933
$993$	7.61141	0.241541
$994$	18.1925	0.577032
$995$	3.84797	0.121989
$996$	−11.6561	−0.369337
$997$	17.4240	0.551825	0.275913	−	0.961183i	$-0.411020\pi$
$997$	17.4240	0.551825	0.275913	+	0.961183i	$0.411020\pi$
$998$	−4.72566	−0.149588
$999$	−30.8237	−0.975217

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	9295.2.a.bb.1.3		14
13.4	even	6		715.2.i.e.276.3	✓	28
13.10	even	6		715.2.i.e.386.3	yes	28
13.12	even	2		9295.2.a.ba.1.12		14

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
715.2.i.e.276.3	✓	28	13.4	even	6
715.2.i.e.386.3	yes	28	13.10	even	6
9295.2.a.ba.1.12		14	13.12	even	2
9295.2.a.bb.1.3		14	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:	\( N \)	\(=\)	\( 9295 = 5 \cdot 11 \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	9295.a (trivial)

\(f(q)\)	\(=\)	\(q-2.14985 q^{2} -1.08194 q^{3} +2.62184 q^{4} +1.00000 q^{5} +2.32601 q^{6} +2.75110 q^{7} -1.33685 q^{8} -1.82940 q^{9} +O(q^{10})\)	\(q-2.14985 q^{2} -1.08194 q^{3} +2.62184 q^{4} +1.00000 q^{5} +2.32601 q^{6} +2.75110 q^{7} -1.33685 q^{8} -1.82940 q^{9} -2.14985 q^{10} -1.00000 q^{11} -2.83667 q^{12} -5.91444 q^{14} -1.08194 q^{15} -2.36964 q^{16} -1.06551 q^{17} +3.93293 q^{18} +5.38212 q^{19} +2.62184 q^{20} -2.97653 q^{21} +2.14985 q^{22} -1.63335 q^{23} +1.44640 q^{24} +1.00000 q^{25} +5.22513 q^{27} +7.21294 q^{28} +8.15779 q^{29} +2.32601 q^{30} +7.57930 q^{31} +7.76808 q^{32} +1.08194 q^{33} +2.29069 q^{34} +2.75110 q^{35} -4.79639 q^{36} -5.89912 q^{37} -11.5707 q^{38} -1.33685 q^{40} -9.91633 q^{41} +6.39908 q^{42} +6.56927 q^{43} -2.62184 q^{44} -1.82940 q^{45} +3.51145 q^{46} +10.9896 q^{47} +2.56382 q^{48} +0.568550 q^{49} -2.14985 q^{50} +1.15282 q^{51} -2.59320 q^{53} -11.2332 q^{54} -1.00000 q^{55} -3.67782 q^{56} -5.82314 q^{57} -17.5380 q^{58} +11.8826 q^{59} -2.83667 q^{60} -9.16317 q^{61} -16.2943 q^{62} -5.03287 q^{63} -11.9609 q^{64} -2.32601 q^{66} +0.236858 q^{67} -2.79360 q^{68} +1.76719 q^{69} -5.91444 q^{70} -3.07595 q^{71} +2.44564 q^{72} -14.7263 q^{73} +12.6822 q^{74} -1.08194 q^{75} +14.1110 q^{76} -2.75110 q^{77} -1.05065 q^{79} -2.36964 q^{80} -0.165081 q^{81} +21.3186 q^{82} +4.10906 q^{83} -7.80398 q^{84} -1.06551 q^{85} -14.1229 q^{86} -8.82626 q^{87} +1.33685 q^{88} +9.49872 q^{89} +3.93293 q^{90} -4.28238 q^{92} -8.20036 q^{93} -23.6260 q^{94} +5.38212 q^{95} -8.40461 q^{96} -8.36778 q^{97} -1.22230 q^{98} +1.82940 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 14 q + q^{2} + q^{3} + 17 q^{4} + 14 q^{5} + 2 q^{6} + 5 q^{7} + 27 q^{9}+O(q^{10}) \) 14 * q + q^2 + q^3 + 17 * q^4 + 14 * q^5 + 2 * q^6 + 5 * q^7 + 27 * q^9	\( 14 q + q^{2} + q^{3} + 17 q^{4} + 14 q^{5} + 2 q^{6} + 5 q^{7} + 27 q^{9} + q^{10} - 14 q^{11} - 9 q^{12} + 12 q^{14} + q^{15} + 15 q^{16} + 17 q^{17} + 23 q^{18} + 3 q^{19} + 17 q^{20} - 16 q^{21} - q^{22} + 4 q^{23} - 13 q^{24} + 14 q^{25} + 10 q^{27} + 27 q^{28} + 21 q^{29} + 2 q^{30} - 9 q^{31} + 26 q^{32} - q^{33} - 56 q^{34} + 5 q^{35} + 51 q^{36} + 8 q^{37} + 5 q^{38} + q^{41} - 42 q^{42} + 23 q^{43} - 17 q^{44} + 27 q^{45} - q^{46} - 18 q^{47} - 14 q^{48} + 41 q^{49} + q^{50} + 18 q^{53} + 8 q^{54} - 14 q^{55} + 80 q^{56} + 44 q^{57} + 22 q^{58} + 8 q^{59} - 9 q^{60} + 16 q^{61} - 5 q^{62} + 50 q^{63} + 10 q^{64} - 2 q^{66} + q^{67} - 8 q^{68} + 34 q^{69} + 12 q^{70} - 20 q^{71} + 117 q^{72} - 15 q^{73} + 49 q^{74} + q^{75} + 10 q^{76} - 5 q^{77} + 5 q^{79} + 15 q^{80} + 82 q^{81} + 32 q^{82} - 18 q^{83} - 50 q^{84} + 17 q^{85} - 74 q^{86} + 2 q^{87} - 16 q^{89} + 23 q^{90} + 7 q^{92} + 33 q^{93} + 34 q^{94} + 3 q^{95} + 56 q^{96} - 5 q^{97} + 34 q^{98} - 27 q^{99}+O(q^{100}) \) 14 * q + q^2 + q^3 + 17 * q^4 + 14 * q^5 + 2 * q^6 + 5 * q^7 + 27 * q^9 + q^10 - 14 * q^11 - 9 * q^12 + 12 * q^14 + q^15 + 15 * q^16 + 17 * q^17 + 23 * q^18 + 3 * q^19 + 17 * q^20 - 16 * q^21 - q^22 + 4 * q^23 - 13 * q^24 + 14 * q^25 + 10 * q^27 + 27 * q^28 + 21 * q^29 + 2 * q^30 - 9 * q^31 + 26 * q^32 - q^33 - 56 * q^34 + 5 * q^35 + 51 * q^36 + 8 * q^37 + 5 * q^38 + q^41 - 42 * q^42 + 23 * q^43 - 17 * q^44 + 27 * q^45 - q^46 - 18 * q^47 - 14 * q^48 + 41 * q^49 + q^50 + 18 * q^53 + 8 * q^54 - 14 * q^55 + 80 * q^56 + 44 * q^57 + 22 * q^58 + 8 * q^59 - 9 * q^60 + 16 * q^61 - 5 * q^62 + 50 * q^63 + 10 * q^64 - 2 * q^66 + q^67 - 8 * q^68 + 34 * q^69 + 12 * q^70 - 20 * q^71 + 117 * q^72 - 15 * q^73 + 49 * q^74 + q^75 + 10 * q^76 - 5 * q^77 + 5 * q^79 + 15 * q^80 + 82 * q^81 + 32 * q^82 - 18 * q^83 - 50 * q^84 + 17 * q^85 - 74 * q^86 + 2 * q^87 - 16 * q^89 + 23 * q^90 + 7 * q^92 + 33 * q^93 + 34 * q^94 + 3 * q^95 + 56 * q^96 - 5 * q^97 + 34 * q^98 - 27 * q^99

Introduction

L-functions

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Database

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