LMFDB - Embedded newform 4025.2.a.bc.1.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4025,2,Mod(1,4025)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4025, 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("4025.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4025 = 5^{2} \cdot 7 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4025.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:	$32.1397868136$
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} - 3 x^{13} - 18 x^{12} + 58 x^{11} + 111 x^{10} - 414 x^{9} - 244 x^{8} + 1330 x^{7} - 27 x^{6} + \cdots - 9 $ x^14 - 3x^13 - 18x^12 + 58x^11 + 111x^10 - 414x^9 - 244x^8 + 1330x^7 - 27x^6 - 1853x^5 + 539x^4 + 891x^3 - 218x^2 - 133*x - 9
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 5 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.5
Root			$-0.689960$ of defining polynomial
Character	$\chi$	$=$	4025.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-0.689960 q^{2} +2.51200 q^{3} -1.52395 q^{4} -1.73318 q^{6} +1.00000 q^{7} +2.43139 q^{8} +3.31014 q^{9} +O(q^{10})$	\(q-0.689960 q^{2} +2.51200 q^{3} -1.52395 q^{4} -1.73318 q^{6} +1.00000 q^{7} +2.43139 q^{8} +3.31014 q^{9} +3.58041 q^{11} -3.82817 q^{12} +0.891289 q^{13} -0.689960 q^{14} +1.37035 q^{16} +4.87467 q^{17} -2.28386 q^{18} -3.14000 q^{19} +2.51200 q^{21} -2.47034 q^{22} +1.00000 q^{23} +6.10765 q^{24} -0.614954 q^{26} +0.779066 q^{27} -1.52395 q^{28} +8.91285 q^{29} -0.999927 q^{31} -5.80826 q^{32} +8.99397 q^{33} -3.36333 q^{34} -5.04450 q^{36} -5.32272 q^{37} +2.16648 q^{38} +2.23892 q^{39} +2.66712 q^{41} -1.73318 q^{42} +3.76793 q^{43} -5.45638 q^{44} -0.689960 q^{46} -6.09546 q^{47} +3.44231 q^{48} +1.00000 q^{49} +12.2452 q^{51} -1.35828 q^{52} +3.29021 q^{53} -0.537525 q^{54} +2.43139 q^{56} -7.88768 q^{57} -6.14951 q^{58} -4.77845 q^{59} +3.06750 q^{61} +0.689910 q^{62} +3.31014 q^{63} +1.26678 q^{64} -6.20549 q^{66} -9.01110 q^{67} -7.42877 q^{68} +2.51200 q^{69} +11.0645 q^{71} +8.04823 q^{72} +1.73604 q^{73} +3.67247 q^{74} +4.78522 q^{76} +3.58041 q^{77} -1.54476 q^{78} +3.47008 q^{79} -7.97340 q^{81} -1.84021 q^{82} +15.9049 q^{83} -3.82817 q^{84} -2.59972 q^{86} +22.3891 q^{87} +8.70536 q^{88} -1.02156 q^{89} +0.891289 q^{91} -1.52395 q^{92} -2.51182 q^{93} +4.20562 q^{94} -14.5904 q^{96} -13.8538 q^{97} -0.689960 q^{98} +11.8516 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 14 q + 3 q^{2} + 4 q^{3} + 17 q^{4} - 4 q^{6} + 14 q^{7} + 3 q^{8} + 18 q^{9}+O(q^{10}) $ 14 * q + 3 * q^2 + 4 * q^3 + 17 * q^4 - 4 * q^6 + 14 * q^7 + 3 * q^8 + 18 * q^9	$ 14 q + 3 q^{2} + 4 q^{3} + 17 q^{4} - 4 q^{6} + 14 q^{7} + 3 q^{8} + 18 q^{9} + 5 q^{11} + 17 q^{12} + 11 q^{13} + 3 q^{14} + 23 q^{16} + 3 q^{17} + 15 q^{18} - 2 q^{19} + 4 q^{21} + 23 q^{22} + 14 q^{23} - 12 q^{24} - 9 q^{26} + 25 q^{27} + 17 q^{28} + 7 q^{29} - 3 q^{31} + 24 q^{32} + 6 q^{33} - 14 q^{34} + 13 q^{36} + 22 q^{37} + 20 q^{38} - 10 q^{39} - 17 q^{41} - 4 q^{42} + 18 q^{43} + 28 q^{44} + 3 q^{46} + 30 q^{47} + 8 q^{48} + 14 q^{49} + 4 q^{51} + 8 q^{52} + 11 q^{53} + 20 q^{54} + 3 q^{56} + 18 q^{57} + 38 q^{58} - 22 q^{59} - 8 q^{61} - 22 q^{62} + 18 q^{63} + 29 q^{64} - 9 q^{66} + 39 q^{67} + q^{68} + 4 q^{69} - 5 q^{71} - 24 q^{72} + 18 q^{73} + 35 q^{74} - 41 q^{76} + 5 q^{77} - 22 q^{78} + 10 q^{79} + 2 q^{81} - 8 q^{82} + 24 q^{83} + 17 q^{84} - 26 q^{86} + 5 q^{87} + 58 q^{88} + 25 q^{89} + 11 q^{91} + 17 q^{92} + 47 q^{93} - 2 q^{94} - 117 q^{96} + 43 q^{97} + 3 q^{98} + 55 q^{99}+O(q^{100}) $ 14 * q + 3 * q^2 + 4 * q^3 + 17 * q^4 - 4 * q^6 + 14 * q^7 + 3 * q^8 + 18 * q^9 + 5 * q^11 + 17 * q^12 + 11 * q^13 + 3 * q^14 + 23 * q^16 + 3 * q^17 + 15 * q^18 - 2 * q^19 + 4 * q^21 + 23 * q^22 + 14 * q^23 - 12 * q^24 - 9 * q^26 + 25 * q^27 + 17 * q^28 + 7 * q^29 - 3 * q^31 + 24 * q^32 + 6 * q^33 - 14 * q^34 + 13 * q^36 + 22 * q^37 + 20 * q^38 - 10 * q^39 - 17 * q^41 - 4 * q^42 + 18 * q^43 + 28 * q^44 + 3 * q^46 + 30 * q^47 + 8 * q^48 + 14 * q^49 + 4 * q^51 + 8 * q^52 + 11 * q^53 + 20 * q^54 + 3 * q^56 + 18 * q^57 + 38 * q^58 - 22 * q^59 - 8 * q^61 - 22 * q^62 + 18 * q^63 + 29 * q^64 - 9 * q^66 + 39 * q^67 + q^68 + 4 * q^69 - 5 * q^71 - 24 * q^72 + 18 * q^73 + 35 * q^74 - 41 * q^76 + 5 * q^77 - 22 * q^78 + 10 * q^79 + 2 * q^81 - 8 * q^82 + 24 * q^83 + 17 * q^84 - 26 * q^86 + 5 * q^87 + 58 * q^88 + 25 * q^89 + 11 * q^91 + 17 * q^92 + 47 * q^93 - 2 * q^94 - 117 * q^96 + 43 * q^97 + 3 * q^98 + 55 * 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 $

$2$	−0.689960	−0.487876	−0.243938	−	0.969791i	$-0.578439\pi$
$2$	−0.689960	−0.487876	−0.243938	+	0.969791i	$0.578439\pi$
$3$	2.51200	1.45030	0.725152	−	0.688589i	$-0.241770\pi$
$3$	2.51200	1.45030	0.725152	+	0.688589i	$0.241770\pi$
$4$	−1.52395	−0.761977
$5$	0	0
$5$	0	0
$6$	−1.73318	−0.707568
$7$	1.00000	0.377964
$7$	1.00000	0.377964
$8$	2.43139	0.859626
$9$	3.31014	1.10338
$10$	0	0
$11$	3.58041	1.07953	0.539766	−	0.841815i	$-0.318513\pi$
$11$	3.58041	1.07953	0.539766	+	0.841815i	$0.318513\pi$
$12$	−3.82817	−1.10510
$13$	0.891289	0.247199	0.123599	−	0.992332i	$-0.460556\pi$
$13$	0.891289	0.247199	0.123599	+	0.992332i	$0.460556\pi$
$14$	−0.689960	−0.184400
$15$	0	0
$16$	1.37035	0.342587
$17$	4.87467	1.18228	0.591140	−	0.806569i	$-0.298678\pi$
$17$	4.87467	1.18228	0.591140	+	0.806569i	$0.298678\pi$
$18$	−2.28386	−0.538312
$19$	−3.14000	−0.720366	−0.360183	−	0.932882i	$-0.617286\pi$
$19$	−3.14000	−0.720366	−0.360183	+	0.932882i	$0.617286\pi$
$20$	0	0
$21$	2.51200	0.548163
$22$	−2.47034	−0.526678
$23$	1.00000	0.208514
$23$	1.00000	0.208514
$24$	6.10765	1.24672
$25$	0	0
$26$	−0.614954	−0.120602
$27$	0.779066	0.149931
$28$	−1.52395	−0.288000
$29$	8.91285	1.65507	0.827537	−	0.561411i	$-0.189741\pi$
$29$	8.91285	1.65507	0.827537	+	0.561411i	$0.189741\pi$
$30$	0	0
$31$	−0.999927	−0.179592	−0.0897961	−	0.995960i	$-0.528622\pi$
$31$	−0.999927	−0.179592	−0.0897961	+	0.995960i	$0.528622\pi$
$32$	−5.80826	−1.02677
$33$	8.99397	1.56565
$34$	−3.36333	−0.576806
$35$	0	0
$36$	−5.04450	−0.840750
$37$	−5.32272	−0.875050	−0.437525	−	0.899206i	$-0.644145\pi$
$37$	−5.32272	−0.875050	−0.437525	+	0.899206i	$0.644145\pi$
$38$	2.16648	0.351449
$39$	2.23892	0.358513
$40$	0	0
$41$	2.66712	0.416535	0.208267	−	0.978072i	$-0.433218\pi$
$41$	2.66712	0.416535	0.208267	+	0.978072i	$0.433218\pi$
$42$	−1.73318	−0.267435
$43$	3.76793	0.574603	0.287302	−	0.957840i	$-0.407242\pi$
$43$	3.76793	0.574603	0.287302	+	0.957840i	$0.407242\pi$
$44$	−5.45638	−0.822580
$45$	0	0
$46$	−0.689960	−0.101729
$47$	−6.09546	−0.889114	−0.444557	−	0.895751i	$-0.646639\pi$
$47$	−6.09546	−0.889114	−0.444557	+	0.895751i	$0.646639\pi$
$48$	3.44231	0.496855
$49$	1.00000	0.142857
$50$	0	0
$51$	12.2452	1.71466
$52$	−1.35828	−0.188360
$53$	3.29021	0.451945	0.225972	−	0.974134i	$-0.427444\pi$
$53$	3.29021	0.451945	0.225972	+	0.974134i	$0.427444\pi$
$54$	−0.537525	−0.0731478
$55$	0	0
$56$	2.43139	0.324908
$57$	−7.88768	−1.04475
$58$	−6.14951	−0.807471
$59$	−4.77845	−0.622102	−0.311051	−	0.950393i	$-0.600681\pi$
$59$	−4.77845	−0.622102	−0.311051	+	0.950393i	$0.600681\pi$
$60$	0	0
$61$	3.06750	0.392754	0.196377	−	0.980528i	$-0.437082\pi$
$61$	3.06750	0.392754	0.196377	+	0.980528i	$0.437082\pi$
$62$	0.689910	0.0876187
$63$	3.31014	0.417038
$64$	1.26678	0.158347
$65$	0	0
$66$	−6.20549	−0.763843
$67$	−9.01110	−1.10088	−0.550441	−	0.834874i	$-0.685540\pi$
$67$	−9.01110	−1.10088	−0.550441	+	0.834874i	$0.685540\pi$
$68$	−7.42877	−0.900871
$69$	2.51200	0.302409
$70$	0	0
$71$	11.0645	1.31312	0.656559	−	0.754275i	$-0.272011\pi$
$71$	11.0645	1.31312	0.656559	+	0.754275i	$0.272011\pi$
$72$	8.04823	0.948493
$73$	1.73604	0.203188	0.101594	−	0.994826i	$-0.467606\pi$
$73$	1.73604	0.203188	0.101594	+	0.994826i	$0.467606\pi$
$74$	3.67247	0.426916
$75$	0	0
$76$	4.78522	0.548902
$77$	3.58041	0.408025
$78$	−1.54476	−0.174910
$79$	3.47008	0.390415	0.195207	−	0.980762i	$-0.437462\pi$
$79$	3.47008	0.390415	0.195207	+	0.980762i	$0.437462\pi$
$80$	0	0
$81$	−7.97340	−0.885933
$82$	−1.84021	−0.203217
$83$	15.9049	1.74579	0.872895	−	0.487909i	$-0.162240\pi$
$83$	15.9049	1.74579	0.872895	+	0.487909i	$0.162240\pi$
$84$	−3.82817	−0.417688
$85$	0	0
$86$	−2.59972	−0.280335
$87$	22.3891	2.40036
$88$	8.70536	0.927995
$89$	−1.02156	−0.108286	−0.0541428	−	0.998533i	$-0.517243\pi$
$89$	−1.02156	−0.108286	−0.0541428	+	0.998533i	$0.517243\pi$
$90$	0	0
$91$	0.891289	0.0934324
$92$	−1.52395	−0.158883
$93$	−2.51182	−0.260463
$94$	4.20562	0.433777
$95$	0	0
$96$	−14.5904	−1.48912
$97$	−13.8538	−1.40664	−0.703320	−	0.710873i	$-0.748300\pi$
$97$	−13.8538	−1.40664	−0.703320	+	0.710873i	$0.748300\pi$
$98$	−0.689960	−0.0696965
$99$	11.8516	1.19113
$100$	0	0
$101$	−6.25818	−0.622712	−0.311356	−	0.950293i	$-0.600783\pi$
$101$	−6.25818	−0.622712	−0.311356	+	0.950293i	$0.600783\pi$
$102$	−8.44867	−0.836543
$103$	−12.4084	−1.22264	−0.611320	−	0.791383i	$-0.709361\pi$
$103$	−12.4084	−1.22264	−0.611320	+	0.791383i	$0.709361\pi$
$104$	2.16707	0.212499
$105$	0	0
$106$	−2.27011	−0.220493
$107$	7.17495	0.693629	0.346814	−	0.937934i	$-0.387263\pi$
$107$	7.17495	0.693629	0.346814	+	0.937934i	$0.387263\pi$
$108$	−1.18726	−0.114244
$109$	−10.4717	−1.00301	−0.501504	−	0.865155i	$-0.667220\pi$
$109$	−10.4717	−1.00301	−0.501504	+	0.865155i	$0.667220\pi$
$110$	0	0
$111$	−13.3707	−1.26909
$112$	1.37035	0.129486
$113$	14.2747	1.34285	0.671426	−	0.741071i	$-0.265682\pi$
$113$	14.2747	1.34285	0.671426	+	0.741071i	$0.265682\pi$
$114$	5.44219	0.509707
$115$	0	0
$116$	−13.5828	−1.26113
$117$	2.95029	0.272754
$118$	3.29694	0.303508
$119$	4.87467	0.446860
$120$	0	0
$121$	1.81931	0.165391
$122$	−2.11646	−0.191615
$123$	6.69981	0.604102
$124$	1.52384	0.136845
$125$	0	0
$126$	−2.28386	−0.203463
$127$	14.0799	1.24939	0.624696	−	0.780868i	$-0.285223\pi$
$127$	14.0799	1.24939	0.624696	+	0.780868i	$0.285223\pi$
$128$	10.7425	0.949512
$129$	9.46503	0.833349
$130$	0	0
$131$	−8.57468	−0.749174	−0.374587	−	0.927192i	$-0.622215\pi$
$131$	−8.57468	−0.749174	−0.374587	+	0.927192i	$0.622215\pi$
$132$	−13.7064	−1.19299
$133$	−3.14000	−0.272273
$134$	6.21730	0.537093
$135$	0	0
$136$	11.8522	1.01632
$137$	−6.18359	−0.528299	−0.264150	−	0.964482i	$-0.585091\pi$
$137$	−6.18359	−0.528299	−0.264150	+	0.964482i	$0.585091\pi$
$138$	−1.73318	−0.147538
$139$	−6.26621	−0.531493	−0.265746	−	0.964043i	$-0.585618\pi$
$139$	−6.26621	−0.531493	−0.265746	+	0.964043i	$0.585618\pi$
$140$	0	0
$141$	−15.3118	−1.28948
$142$	−7.63409	−0.640639
$143$	3.19117	0.266859
$144$	4.53604	0.378003
$145$	0	0
$146$	−1.19780	−0.0991307
$147$	2.51200	0.207186
$148$	8.11158	0.666768
$149$	14.4728	1.18565	0.592827	−	0.805330i	$-0.298012\pi$
$149$	14.4728	1.18565	0.592827	+	0.805330i	$0.298012\pi$
$150$	0	0
$151$	13.2208	1.07589	0.537947	−	0.842979i	$-0.319200\pi$
$151$	13.2208	1.07589	0.537947	+	0.842979i	$0.319200\pi$
$152$	−7.63456	−0.619245
$153$	16.1358	1.30450
$154$	−2.47034	−0.199066
$155$	0	0
$156$	−3.41201	−0.273179
$157$	12.6678	1.01100	0.505501	−	0.862826i	$-0.331308\pi$
$157$	12.6678	1.01100	0.505501	+	0.862826i	$0.331308\pi$
$158$	−2.39422	−0.190474
$159$	8.26500	0.655457
$160$	0	0
$161$	1.00000	0.0788110
$162$	5.50133	0.432225
$163$	17.9827	1.40851	0.704257	−	0.709946i	$-0.251280\pi$
$163$	17.9827	1.40851	0.704257	+	0.709946i	$0.251280\pi$
$164$	−4.06457	−0.317390
$165$	0	0
$166$	−10.9737	−0.851728
$167$	17.5367	1.35703	0.678515	−	0.734587i	$-0.262624\pi$
$167$	17.5367	1.35703	0.678515	+	0.734587i	$0.262624\pi$
$168$	6.10765	0.471215
$169$	−12.2056	−0.938893
$170$	0	0
$171$	−10.3938	−0.794836
$172$	−5.74215	−0.437835
$173$	−20.8887	−1.58814	−0.794069	−	0.607827i	$-0.792041\pi$
$173$	−20.8887	−1.58814	−0.794069	+	0.607827i	$0.792041\pi$
$174$	−15.4476	−1.17108
$175$	0	0
$176$	4.90640	0.369834
$177$	−12.0035	−0.902236
$178$	0.704839	0.0528299
$179$	−5.07229	−0.379120	−0.189560	−	0.981869i	$-0.560706\pi$
$179$	−5.07229	−0.379120	−0.189560	+	0.981869i	$0.560706\pi$
$180$	0	0
$181$	−1.16950	−0.0869283	−0.0434642	−	0.999055i	$-0.513839\pi$
$181$	−1.16950	−0.0869283	−0.0434642	+	0.999055i	$0.513839\pi$
$182$	−0.614954	−0.0455834
$183$	7.70557	0.569612
$184$	2.43139	0.179244
$185$	0	0
$186$	1.73305	0.127074
$187$	17.4533	1.27631
$188$	9.28920	0.677485
$189$	0.779066	0.0566687
$190$	0	0
$191$	6.86267	0.496565	0.248283	−	0.968688i	$-0.420134\pi$
$191$	6.86267	0.496565	0.248283	+	0.968688i	$0.420134\pi$
$192$	3.18215	0.229652
$193$	9.64479	0.694247	0.347123	−	0.937819i	$-0.387158\pi$
$193$	9.64479	0.694247	0.347123	+	0.937819i	$0.387158\pi$
$194$	9.55857	0.686265
$195$	0	0
$196$	−1.52395	−0.108854
$197$	12.9107	0.919849	0.459924	−	0.887958i	$-0.347876\pi$
$197$	12.9107	0.919849	0.459924	+	0.887958i	$0.347876\pi$
$198$	−8.17716	−0.581125
$199$	−21.5341	−1.52651	−0.763255	−	0.646098i	$-0.776400\pi$
$199$	−21.5341	−1.52651	−0.763255	+	0.646098i	$0.776400\pi$
$200$	0	0
$201$	−22.6359	−1.59661
$202$	4.31790	0.303806
$203$	8.91285	0.625559
$204$	−18.6611	−1.30654
$205$	0	0
$206$	8.56134	0.596497
$207$	3.31014	0.230070
$208$	1.22137	0.0846871
$209$	−11.2425	−0.777658
$210$	0	0
$211$	−2.61243	−0.179847	−0.0899236	−	0.995949i	$-0.528662\pi$
$211$	−2.61243	−0.179847	−0.0899236	+	0.995949i	$0.528662\pi$
$212$	−5.01413	−0.344372
$213$	27.7941	1.90442
$214$	−4.95043	−0.338405
$215$	0	0
$216$	1.89421	0.128885
$217$	−0.999927	−0.0678795
$218$	7.22506	0.489343
$219$	4.36094	0.294685
$220$	0	0
$221$	4.34473	0.292259
$222$	9.22523	0.619157
$223$	11.8042	0.790466	0.395233	−	0.918581i	$-0.370664\pi$
$223$	11.8042	0.790466	0.395233	+	0.918581i	$0.370664\pi$
$224$	−5.80826	−0.388081
$225$	0	0
$226$	−9.84899	−0.655145
$227$	25.3347	1.68153	0.840763	−	0.541403i	$-0.182107\pi$
$227$	25.3347	1.68153	0.840763	+	0.541403i	$0.182107\pi$
$228$	12.0205	0.796075
$229$	15.8917	1.05015	0.525076	−	0.851055i	$-0.324037\pi$
$229$	15.8917	1.05015	0.525076	+	0.851055i	$0.324037\pi$
$230$	0	0
$231$	8.99397	0.591760
$232$	21.6706	1.42274
$233$	−11.1412	−0.729885	−0.364942	−	0.931030i	$-0.618911\pi$
$233$	−11.1412	−0.729885	−0.364942	+	0.931030i	$0.618911\pi$
$234$	−2.03558	−0.133070
$235$	0	0
$236$	7.28215	0.474027
$237$	8.71684	0.566220
$238$	−3.36333	−0.218012
$239$	2.91189	0.188355	0.0941773	−	0.995555i	$-0.469978\pi$
$239$	2.91189	0.188355	0.0941773	+	0.995555i	$0.469978\pi$
$240$	0	0
$241$	3.68866	0.237608	0.118804	−	0.992918i	$-0.462094\pi$
$241$	3.68866	0.237608	0.118804	+	0.992918i	$0.462094\pi$
$242$	−1.25525	−0.0806904
$243$	−22.3664	−1.43480
$244$	−4.67474	−0.299269
$245$	0	0
$246$	−4.62260	−0.294726
$247$	−2.79865	−0.178074
$248$	−2.43121	−0.154382
$249$	39.9531	2.53192
$250$	0	0
$251$	−7.56901	−0.477752	−0.238876	−	0.971050i	$-0.576779\pi$
$251$	−7.56901	−0.477752	−0.238876	+	0.971050i	$0.576779\pi$
$252$	−5.04450	−0.317774
$253$	3.58041	0.225098
$254$	−9.71460	−0.609548
$255$	0	0
$256$	−9.94546	−0.621591
$257$	16.6842	1.04073	0.520366	−	0.853943i	$-0.325795\pi$
$257$	16.6842	1.04073	0.520366	+	0.853943i	$0.325795\pi$
$258$	−6.53049	−0.406571
$259$	−5.32272	−0.330738
$260$	0	0
$261$	29.5028	1.82617
$262$	5.91619	0.365504
$263$	21.1866	1.30642	0.653210	−	0.757177i	$-0.273422\pi$
$263$	21.1866	1.30642	0.653210	+	0.757177i	$0.273422\pi$
$264$	21.8679	1.34587
$265$	0	0
$266$	2.16648	0.132835
$267$	−2.56617	−0.157047
$268$	13.7325	0.838846
$269$	−9.93782	−0.605920	−0.302960	−	0.953003i	$-0.597975\pi$
$269$	−9.93782	−0.605920	−0.302960	+	0.953003i	$0.597975\pi$
$270$	0	0
$271$	−4.13585	−0.251235	−0.125618	−	0.992079i	$-0.540091\pi$
$271$	−4.13585	−0.251235	−0.125618	+	0.992079i	$0.540091\pi$
$272$	6.67998	0.405033
$273$	2.23892	0.135505
$274$	4.26643	0.257744
$275$	0	0
$276$	−3.82817	−0.230429
$277$	2.52161	0.151509	0.0757545	−	0.997127i	$-0.475863\pi$
$277$	2.52161	0.151509	0.0757545	+	0.997127i	$0.475863\pi$
$278$	4.32343	0.259302
$279$	−3.30990	−0.198158
$280$	0	0
$281$	7.11715	0.424573	0.212287	−	0.977207i	$-0.431909\pi$
$281$	7.11715	0.424573	0.212287	+	0.977207i	$0.431909\pi$
$282$	10.5645	0.629108
$283$	−20.0584	−1.19235	−0.596175	−	0.802855i	$-0.703313\pi$
$283$	−20.0584	−1.19235	−0.596175	+	0.802855i	$0.703313\pi$
$284$	−16.8618	−1.00057
$285$	0	0
$286$	−2.20178	−0.130194
$287$	2.66712	0.157435
$288$	−19.2262	−1.13291
$289$	6.76238	0.397787
$290$	0	0
$291$	−34.8007	−2.04005
$292$	−2.64565	−0.154825
$293$	−18.1031	−1.05759	−0.528796	−	0.848749i	$-0.677356\pi$
$293$	−18.1031	−1.05759	−0.528796	+	0.848749i	$0.677356\pi$
$294$	−1.73318	−0.101081
$295$	0	0
$296$	−12.9416	−0.752215
$297$	2.78937	0.161856
$298$	−9.98563	−0.578452
$299$	0.891289	0.0515446
$300$	0	0
$301$	3.76793	0.217180
$302$	−9.12183	−0.524902
$303$	−15.7205	−0.903121
$304$	−4.30289	−0.246788
$305$	0	0
$306$	−11.1331	−0.636436
$307$	18.9880	1.08370	0.541852	−	0.840474i	$-0.317723\pi$
$307$	18.9880	1.08370	0.541852	+	0.840474i	$0.317723\pi$
$308$	−5.45638	−0.310906
$309$	−31.1700	−1.77320
$310$	0	0
$311$	−19.1681	−1.08692	−0.543461	−	0.839435i	$-0.682886\pi$
$311$	−19.1681	−1.08692	−0.543461	+	0.839435i	$0.682886\pi$
$312$	5.44368	0.308187
$313$	7.74941	0.438023	0.219011	−	0.975722i	$-0.429717\pi$
$313$	7.74941	0.438023	0.219011	+	0.975722i	$0.429717\pi$
$314$	−8.74029	−0.493243
$315$	0	0
$316$	−5.28825	−0.297487
$317$	13.5254	0.759659	0.379830	−	0.925056i	$-0.375983\pi$
$317$	13.5254	0.759659	0.379830	+	0.925056i	$0.375983\pi$
$318$	−5.70252	−0.319782
$319$	31.9116	1.78671
$320$	0	0
$321$	18.0235	1.00597
$322$	−0.689960	−0.0384500
$323$	−15.3065	−0.851674
$324$	12.1511	0.675061
$325$	0	0
$326$	−12.4073	−0.687179
$327$	−26.3049	−1.45467
$328$	6.48481	0.358064
$329$	−6.09546	−0.336053
$330$	0	0
$331$	31.7481	1.74503	0.872517	−	0.488583i	$-0.162486\pi$
$331$	31.7481	1.74503	0.872517	+	0.488583i	$0.162486\pi$
$332$	−24.2383	−1.33025
$333$	−17.6189	−0.965512
$334$	−12.0996	−0.662062
$335$	0	0
$336$	3.44231	0.187793
$337$	−17.4286	−0.949396	−0.474698	−	0.880149i	$-0.657443\pi$
$337$	−17.4286	−0.949396	−0.474698	+	0.880149i	$0.657443\pi$
$338$	8.42138	0.458063
$339$	35.8581	1.94754
$340$	0	0
$341$	−3.58014	−0.193876
$342$	7.17133	0.387781
$343$	1.00000	0.0539949
$344$	9.16129	0.493944
$345$	0	0
$346$	14.4124	0.774814
$347$	−1.95349	−0.104869	−0.0524345	−	0.998624i	$-0.516698\pi$
$347$	−1.95349	−0.104869	−0.0524345	+	0.998624i	$0.516698\pi$
$348$	−34.1199	−1.82902
$349$	22.0562	1.18064	0.590321	−	0.807168i	$-0.299001\pi$
$349$	22.0562	1.18064	0.590321	+	0.807168i	$0.299001\pi$
$350$	0	0
$351$	0.694372	0.0370629
$352$	−20.7959	−1.10843
$353$	−22.7536	−1.21105	−0.605527	−	0.795825i	$-0.707038\pi$
$353$	−22.7536	−1.21105	−0.605527	+	0.795825i	$0.707038\pi$
$354$	8.28192	0.440179
$355$	0	0
$356$	1.55682	0.0825111
$357$	12.2452	0.648082
$358$	3.49968	0.184964
$359$	22.2448	1.17404	0.587018	−	0.809574i	$-0.300302\pi$
$359$	22.2448	1.17404	0.587018	+	0.809574i	$0.300302\pi$
$360$	0	0
$361$	−9.14040	−0.481073
$362$	0.806910	0.0424102
$363$	4.57009	0.239868
$364$	−1.35828	−0.0711934
$365$	0	0
$366$	−5.31654	−0.277900
$367$	12.5081	0.652916	0.326458	−	0.945212i	$-0.394145\pi$
$367$	12.5081	0.652916	0.326458	+	0.945212i	$0.394145\pi$
$368$	1.37035	0.0714343
$369$	8.82855	0.459596
$370$	0	0
$371$	3.29021	0.170819
$372$	3.82789	0.198467
$373$	−15.1496	−0.784418	−0.392209	−	0.919876i	$-0.628289\pi$
$373$	−15.1496	−0.784418	−0.392209	+	0.919876i	$0.628289\pi$
$374$	−12.0421	−0.622681
$375$	0	0
$376$	−14.8204	−0.764305
$377$	7.94392	0.409133
$378$	−0.537525	−0.0276473
$379$	−34.4002	−1.76702	−0.883510	−	0.468413i	$-0.844826\pi$
$379$	−34.4002	−1.76702	−0.883510	+	0.468413i	$0.844826\pi$
$380$	0	0
$381$	35.3688	1.81200
$382$	−4.73497	−0.242262
$383$	−24.7176	−1.26301	−0.631505	−	0.775371i	$-0.717563\pi$
$383$	−24.7176	−1.26301	−0.631505	+	0.775371i	$0.717563\pi$
$384$	26.9851	1.37708
$385$	0	0
$386$	−6.65452	−0.338706
$387$	12.4724	0.634005
$388$	21.1126	1.07183
$389$	6.15225	0.311931	0.155966	−	0.987762i	$-0.450151\pi$
$389$	6.15225	0.311931	0.155966	+	0.987762i	$0.450151\pi$
$390$	0	0
$391$	4.87467	0.246522
$392$	2.43139	0.122804
$393$	−21.5396	−1.08653
$394$	−8.90787	−0.448772
$395$	0	0
$396$	−18.0614	−0.907617
$397$	−16.0571	−0.805885	−0.402943	−	0.915225i	$-0.632013\pi$
$397$	−16.0571	−0.805885	−0.402943	+	0.915225i	$0.632013\pi$
$398$	14.8577	0.744747
$399$	−7.88768	−0.394878
$400$	0	0
$401$	−37.2034	−1.85785	−0.928925	−	0.370269i	$-0.879266\pi$
$401$	−37.2034	−1.85785	−0.928925	+	0.370269i	$0.879266\pi$
$402$	15.6179	0.778948
$403$	−0.891224	−0.0443950
$404$	9.53718	0.474492
$405$	0	0
$406$	−6.14951	−0.305195
$407$	−19.0575	−0.944645
$408$	29.7727	1.47397
$409$	9.68448	0.478867	0.239433	−	0.970913i	$-0.423038\pi$
$409$	9.68448	0.478867	0.239433	+	0.970913i	$0.423038\pi$
$410$	0	0
$411$	−15.5332	−0.766194
$412$	18.9099	0.931624
$413$	−4.77845	−0.235132
$414$	−2.28386	−0.112246
$415$	0	0
$416$	−5.17684	−0.253815
$417$	−15.7407	−0.770825
$418$	7.75686	0.379401
$419$	−38.4801	−1.87987	−0.939937	−	0.341347i	$-0.889117\pi$
$419$	−38.4801	−1.87987	−0.939937	+	0.341347i	$0.889117\pi$
$420$	0	0
$421$	27.8287	1.35629	0.678144	−	0.734929i	$-0.262785\pi$
$421$	27.8287	1.35629	0.678144	+	0.734929i	$0.262785\pi$
$422$	1.80247	0.0877431
$423$	−20.1768	−0.981030
$424$	7.99978	0.388503
$425$	0	0
$426$	−19.1768	−0.929120
$427$	3.06750	0.148447
$428$	−10.9343	−0.528529
$429$	8.01623	0.387027
$430$	0	0
$431$	−6.68769	−0.322134	−0.161067	−	0.986943i	$-0.551494\pi$
$431$	−6.68769	−0.322134	−0.161067	+	0.986943i	$0.551494\pi$
$432$	1.06759	0.0513644
$433$	−3.13812	−0.150809	−0.0754043	−	0.997153i	$-0.524025\pi$
$433$	−3.13812	−0.150809	−0.0754043	+	0.997153i	$0.524025\pi$
$434$	0.689910	0.0331167
$435$	0	0
$436$	15.9584	0.764269
$437$	−3.14000	−0.150207
$438$	−3.00887	−0.143770
$439$	−33.7118	−1.60898	−0.804489	−	0.593967i	$-0.797561\pi$
$439$	−33.7118	−1.60898	−0.804489	+	0.593967i	$0.797561\pi$
$440$	0	0
$441$	3.31014	0.157626
$442$	−2.99770	−0.142586
$443$	−36.0444	−1.71252	−0.856260	−	0.516544i	$-0.827218\pi$
$443$	−36.0444	−1.71252	−0.856260	+	0.516544i	$0.827218\pi$
$444$	20.3763	0.967016
$445$	0	0
$446$	−8.14441	−0.385649
$447$	36.3556	1.71956
$448$	1.26678	0.0598497
$449$	−6.76482	−0.319251	−0.159626	−	0.987178i	$-0.551029\pi$
$449$	−6.76482	−0.319251	−0.159626	+	0.987178i	$0.551029\pi$
$450$	0	0
$451$	9.54938	0.449663
$452$	−21.7540	−1.02322
$453$	33.2106	1.56037
$454$	−17.4800	−0.820376
$455$	0	0
$456$	−19.1780	−0.898093
$457$	−7.65858	−0.358253	−0.179127	−	0.983826i	$-0.557327\pi$
$457$	−7.65858	−0.358253	−0.179127	+	0.983826i	$0.557327\pi$
$458$	−10.9646	−0.512344
$459$	3.79769	0.177261
$460$	0	0
$461$	2.92441	0.136204	0.0681018	−	0.997678i	$-0.478306\pi$
$461$	2.92441	0.136204	0.0681018	+	0.997678i	$0.478306\pi$
$462$	−6.20549	−0.288705
$463$	−6.88540	−0.319992	−0.159996	−	0.987118i	$-0.551148\pi$
$463$	−6.88540	−0.319992	−0.159996	+	0.987118i	$0.551148\pi$
$464$	12.2137	0.567006
$465$	0	0
$466$	7.68699	0.356093
$467$	31.3052	1.44863	0.724316	−	0.689468i	$-0.242155\pi$
$467$	31.3052	1.44863	0.724316	+	0.689468i	$0.242155\pi$
$468$	−4.49611	−0.207833
$469$	−9.01110	−0.416094
$470$	0	0
$471$	31.8215	1.46626
$472$	−11.6183	−0.534775
$473$	13.4907	0.620303
$474$	−6.01428	−0.276245
$475$	0	0
$476$	−7.42877	−0.340497
$477$	10.8910	0.498667
$478$	−2.00909	−0.0918937
$479$	23.1146	1.05613	0.528067	−	0.849202i	$-0.322917\pi$
$479$	23.1146	1.05613	0.528067	+	0.849202i	$0.322917\pi$
$480$	0	0
$481$	−4.74408	−0.216311
$482$	−2.54503	−0.115923
$483$	2.51200	0.114300
$484$	−2.77254	−0.126024
$485$	0	0
$486$	15.4319	0.700006
$487$	−43.1375	−1.95475	−0.977373	−	0.211523i	$-0.932158\pi$
$487$	−43.1375	−1.95475	−0.977373	+	0.211523i	$0.932158\pi$
$488$	7.45830	0.337621
$489$	45.1725	2.04277
$490$	0	0
$491$	−25.7117	−1.16035	−0.580175	−	0.814492i	$-0.697016\pi$
$491$	−25.7117	−1.16035	−0.580175	+	0.814492i	$0.697016\pi$
$492$	−10.2102	−0.460312
$493$	43.4472	1.95676
$494$	1.93096	0.0868778
$495$	0	0
$496$	−1.37025	−0.0615259
$497$	11.0645	0.496312
$498$	−27.5660	−1.23526
$499$	−4.28473	−0.191811	−0.0959055	−	0.995390i	$-0.530575\pi$
$499$	−4.28473	−0.191811	−0.0959055	+	0.995390i	$0.530575\pi$
$500$	0	0
$501$	44.0521	1.96810
$502$	5.22232	0.233084
$503$	13.1157	0.584802	0.292401	−	0.956296i	$-0.405546\pi$
$503$	13.1157	0.584802	0.292401	+	0.956296i	$0.405546\pi$
$504$	8.04823	0.358497
$505$	0	0
$506$	−2.47034	−0.109820
$507$	−30.6605	−1.36168
$508$	−21.4572	−0.952009
$509$	−23.2458	−1.03035	−0.515175	−	0.857085i	$-0.672273\pi$
$509$	−23.2458	−1.03035	−0.515175	+	0.857085i	$0.672273\pi$
$510$	0	0
$511$	1.73604	0.0767980
$512$	−14.6230	−0.646253
$513$	−2.44627	−0.108005
$514$	−11.5115	−0.507748
$515$	0	0
$516$	−14.4243	−0.634993
$517$	−21.8242	−0.959828
$518$	3.67247	0.161359
$519$	−52.4724	−2.30328
$520$	0	0
$521$	−3.38739	−0.148404	−0.0742020	−	0.997243i	$-0.523641\pi$
$521$	−3.38739	−0.148404	−0.0742020	+	0.997243i	$0.523641\pi$
$522$	−20.3557	−0.890946
$523$	−19.5146	−0.853313	−0.426656	−	0.904414i	$-0.640309\pi$
$523$	−19.5146	−0.853313	−0.426656	+	0.904414i	$0.640309\pi$
$524$	13.0674	0.570853
$525$	0	0
$526$	−14.6179	−0.637370
$527$	−4.87431	−0.212328
$528$	12.3249	0.536371
$529$	1.00000	0.0434783
$530$	0	0
$531$	−15.8173	−0.686414
$532$	4.78522	0.207466
$533$	2.37718	0.102967
$534$	1.77055	0.0766193
$535$	0	0
$536$	−21.9095	−0.946346
$537$	−12.7416	−0.549840
$538$	6.85671	0.295614
$539$	3.58041	0.154219
$540$	0	0
$541$	−26.7751	−1.15115	−0.575576	−	0.817748i	$-0.695222\pi$
$541$	−26.7751	−1.15115	−0.575576	+	0.817748i	$0.695222\pi$
$542$	2.85357	0.122571
$543$	−2.93779	−0.126072
$544$	−28.3133	−1.21392
$545$	0	0
$546$	−1.54476	−0.0661098
$547$	28.0410	1.19895	0.599474	−	0.800394i	$-0.295377\pi$
$547$	28.0410	1.19895	0.599474	+	0.800394i	$0.295377\pi$
$548$	9.42350	0.402552
$549$	10.1539	0.433356
$550$	0	0
$551$	−27.9864	−1.19226
$552$	6.10765	0.259959
$553$	3.47008	0.147563
$554$	−1.73981	−0.0739175
$555$	0	0
$556$	9.54941	0.404985
$557$	−17.8468	−0.756193	−0.378097	−	0.925766i	$-0.623421\pi$
$557$	−17.8468	−0.756193	−0.378097	+	0.925766i	$0.623421\pi$
$558$	2.28370	0.0966766
$559$	3.35831	0.142041
$560$	0	0
$561$	43.8426	1.85104
$562$	−4.91055	−0.207139
$563$	15.5822	0.656713	0.328356	−	0.944554i	$-0.393505\pi$
$563$	15.5822	0.656713	0.328356	+	0.944554i	$0.393505\pi$
$564$	23.3345	0.982558
$565$	0	0
$566$	13.8395	0.581718
$567$	−7.97340	−0.334851
$568$	26.9022	1.12879
$569$	−7.36438	−0.308731	−0.154365	−	0.988014i	$-0.549333\pi$
$569$	−7.36438	−0.308731	−0.154365	+	0.988014i	$0.549333\pi$
$570$	0	0
$571$	−7.33100	−0.306793	−0.153396	−	0.988165i	$-0.549021\pi$
$571$	−7.33100	−0.306793	−0.153396	+	0.988165i	$0.549021\pi$
$572$	−4.86321	−0.203341
$573$	17.2390	0.720170
$574$	−1.84021	−0.0768089
$575$	0	0
$576$	4.19321	0.174717
$577$	36.4386	1.51696	0.758480	−	0.651696i	$-0.225942\pi$
$577$	36.4386	1.51696	0.758480	+	0.651696i	$0.225942\pi$
$578$	−4.66577	−0.194071
$579$	24.2277	1.00687
$580$	0	0
$581$	15.9049	0.659846
$582$	24.0111	0.995293
$583$	11.7803	0.487889
$584$	4.22099	0.174666
$585$	0	0
$586$	12.4904	0.515974
$587$	1.43876	0.0593838	0.0296919	−	0.999559i	$-0.490547\pi$
$587$	1.43876	0.0593838	0.0296919	+	0.999559i	$0.490547\pi$
$588$	−3.82817	−0.157871
$589$	3.13977	0.129372
$590$	0	0
$591$	32.4317	1.33406
$592$	−7.29397	−0.299780
$593$	44.2007	1.81511	0.907553	−	0.419937i	$-0.137948\pi$
$593$	44.2007	1.81511	0.907553	+	0.419937i	$0.137948\pi$
$594$	−1.92456	−0.0789655
$595$	0	0
$596$	−22.0558	−0.903442
$597$	−54.0935	−2.21390
$598$	−0.614954	−0.0251473
$599$	6.19505	0.253123	0.126562	−	0.991959i	$-0.459606\pi$
$599$	6.19505	0.253123	0.126562	+	0.991959i	$0.459606\pi$
$600$	0	0
$601$	24.2485	0.989119	0.494559	−	0.869144i	$-0.335329\pi$
$601$	24.2485	0.989119	0.494559	+	0.869144i	$0.335329\pi$
$602$	−2.59972	−0.105957
$603$	−29.8280	−1.21469
$604$	−20.1479	−0.819806
$605$	0	0
$606$	10.8465	0.440611
$607$	12.3258	0.500287	0.250143	−	0.968209i	$-0.419522\pi$
$607$	12.3258	0.500287	0.250143	+	0.968209i	$0.419522\pi$
$608$	18.2380	0.739647
$609$	22.3891	0.907251
$610$	0	0
$611$	−5.43281	−0.219788
$612$	−24.5903	−0.994002
$613$	12.9375	0.522540	0.261270	−	0.965266i	$-0.415859\pi$
$613$	12.9375	0.522540	0.261270	+	0.965266i	$0.415859\pi$
$614$	−13.1010	−0.528713
$615$	0	0
$616$	8.70536	0.350749
$617$	−5.23450	−0.210733	−0.105367	−	0.994433i	$-0.533602\pi$
$617$	−5.23450	−0.210733	−0.105367	+	0.994433i	$0.533602\pi$
$618$	21.5061	0.865101
$619$	3.30329	0.132771	0.0663853	−	0.997794i	$-0.478853\pi$
$619$	3.30329	0.132771	0.0663853	+	0.997794i	$0.478853\pi$
$620$	0	0
$621$	0.779066	0.0312628
$622$	13.2252	0.530282
$623$	−1.02156	−0.0409281
$624$	3.06809	0.122822
$625$	0	0
$626$	−5.34679	−0.213701
$627$	−28.2411	−1.12784
$628$	−19.3052	−0.770360
$629$	−25.9465	−1.03455
$630$	0	0
$631$	7.19813	0.286553	0.143276	−	0.989683i	$-0.454236\pi$
$631$	7.19813	0.286553	0.143276	+	0.989683i	$0.454236\pi$
$632$	8.43712	0.335611
$633$	−6.56242	−0.260833
$634$	−9.33196	−0.370619
$635$	0	0
$636$	−12.5955	−0.499443
$637$	0.891289	0.0353141
$638$	−22.0178	−0.871691
$639$	36.6251	1.44887
$640$	0	0
$641$	−15.4958	−0.612049	−0.306025	−	0.952024i	$-0.598999\pi$
$641$	−15.4958	−0.612049	−0.306025	+	0.952024i	$0.598999\pi$
$642$	−12.4355	−0.490789
$643$	−18.8341	−0.742745	−0.371373	−	0.928484i	$-0.621113\pi$
$643$	−18.8341	−0.742745	−0.371373	+	0.928484i	$0.621113\pi$
$644$	−1.52395	−0.0600522
$645$	0	0
$646$	10.5608	0.415511
$647$	−10.1893	−0.400583	−0.200292	−	0.979736i	$-0.564189\pi$
$647$	−10.1893	−0.400583	−0.200292	+	0.979736i	$0.564189\pi$
$648$	−19.3864	−0.761571
$649$	−17.1088	−0.671579
$650$	0	0
$651$	−2.51182	−0.0984458
$652$	−27.4048	−1.07326
$653$	−14.4197	−0.564287	−0.282144	−	0.959372i	$-0.591045\pi$
$653$	−14.4197	−0.564287	−0.282144	+	0.959372i	$0.591045\pi$
$654$	18.1494	0.709696
$655$	0	0
$656$	3.65488	0.142699
$657$	5.74654	0.224194
$658$	4.20562	0.163952
$659$	4.54165	0.176918	0.0884589	−	0.996080i	$-0.471806\pi$
$659$	4.54165	0.176918	0.0884589	+	0.996080i	$0.471806\pi$
$660$	0	0
$661$	31.5394	1.22674	0.613370	−	0.789796i	$-0.289814\pi$
$661$	31.5394	1.22674	0.613370	+	0.789796i	$0.289814\pi$
$662$	−21.9050	−0.851360
$663$	10.9140	0.423863
$664$	38.6710	1.50073
$665$	0	0
$666$	12.1564	0.471050
$667$	8.91285	0.345107
$668$	−26.7251	−1.03403
$669$	29.6521	1.14642
$670$	0	0
$671$	10.9829	0.423991
$672$	−14.5904	−0.562835
$673$	−41.8362	−1.61267	−0.806334	−	0.591461i	$-0.798552\pi$
$673$	−41.8362	−1.61267	−0.806334	+	0.591461i	$0.798552\pi$
$674$	12.0250	0.463187
$675$	0	0
$676$	18.6008	0.715415
$677$	16.8444	0.647385	0.323692	−	0.946162i	$-0.395076\pi$
$677$	16.8444	0.647385	0.323692	+	0.946162i	$0.395076\pi$
$678$	−24.7407	−0.950159
$679$	−13.8538	−0.531660
$680$	0	0
$681$	63.6409	2.43872
$682$	2.47016	0.0945872
$683$	29.6016	1.13268	0.566338	−	0.824173i	$-0.308360\pi$
$683$	29.6016	1.13268	0.566338	+	0.824173i	$0.308360\pi$
$684$	15.8397	0.605647
$685$	0	0
$686$	−0.689960	−0.0263428
$687$	39.9199	1.52304
$688$	5.16336	0.196851
$689$	2.93252	0.111720
$690$	0	0
$691$	−32.3193	−1.22948	−0.614742	−	0.788728i	$-0.710740\pi$
$691$	−32.3193	−1.22948	−0.614742	+	0.788728i	$0.710740\pi$
$692$	31.8334	1.21013
$693$	11.8516	0.450206
$694$	1.34783	0.0511630
$695$	0	0
$696$	54.4365	2.06341
$697$	13.0013	0.492461
$698$	−15.2179	−0.576007
$699$	−27.9867	−1.05855
$700$	0	0
$701$	−15.4077	−0.581943	−0.290971	−	0.956732i	$-0.593978\pi$
$701$	−15.4077	−0.581943	−0.290971	+	0.956732i	$0.593978\pi$
$702$	−0.479089	−0.0180821
$703$	16.7133	0.630356
$704$	4.53558	0.170941
$705$	0	0
$706$	15.6991	0.590844
$707$	−6.25818	−0.235363
$708$	18.2927	0.687483
$709$	−23.0101	−0.864163	−0.432082	−	0.901834i	$-0.642221\pi$
$709$	−23.0101	−0.864163	−0.432082	+	0.901834i	$0.642221\pi$
$710$	0	0
$711$	11.4864	0.430775
$712$	−2.48382	−0.0930851
$713$	−0.999927	−0.0374476
$714$	−8.44867	−0.316184
$715$	0	0
$716$	7.72993	0.288881
$717$	7.31467	0.273171
$718$	−15.3480	−0.572784
$719$	13.0604	0.487070	0.243535	−	0.969892i	$-0.421693\pi$
$719$	13.0604	0.487070	0.243535	+	0.969892i	$0.421693\pi$
$720$	0	0
$721$	−12.4084	−0.462115
$722$	6.30651	0.234704
$723$	9.26592	0.344603
$724$	1.78227	0.0662374
$725$	0	0
$726$	−3.15318	−0.117026
$727$	30.7451	1.14027	0.570136	−	0.821550i	$-0.306890\pi$
$727$	30.7451	1.14027	0.570136	+	0.821550i	$0.306890\pi$
$728$	2.16707	0.0803169
$729$	−32.2641	−1.19497
$730$	0	0
$731$	18.3674	0.679342
$732$	−11.7429	−0.434031
$733$	−18.9260	−0.699049	−0.349524	−	0.936927i	$-0.613657\pi$
$733$	−18.9260	−0.699049	−0.349524	+	0.936927i	$0.613657\pi$
$734$	−8.63008	−0.318542
$735$	0	0
$736$	−5.80826	−0.214095
$737$	−32.2634	−1.18844
$738$	−6.09135	−0.224226
$739$	−0.966878	−0.0355672	−0.0177836	−	0.999842i	$-0.505661\pi$
$739$	−0.966878	−0.0355672	−0.0177836	+	0.999842i	$0.505661\pi$
$740$	0	0
$741$	−7.03020	−0.258261
$742$	−2.27011	−0.0833385
$743$	43.3733	1.59121	0.795606	−	0.605814i	$-0.207152\pi$
$743$	43.3733	1.59121	0.795606	+	0.605814i	$0.207152\pi$
$744$	−6.10720	−0.223901
$745$	0	0
$746$	10.4527	0.382699
$747$	52.6474	1.92627
$748$	−26.5980	−0.972520
$749$	7.17495	0.262167
$750$	0	0
$751$	13.2866	0.484834	0.242417	−	0.970172i	$-0.422060\pi$
$751$	13.2866	0.484834	0.242417	+	0.970172i	$0.422060\pi$
$752$	−8.35289	−0.304599
$753$	−19.0134	−0.692885
$754$	−5.48099	−0.199606
$755$	0	0
$756$	−1.18726	−0.0431803
$757$	29.4796	1.07145	0.535727	−	0.844391i	$-0.320038\pi$
$757$	29.4796	1.07145	0.535727	+	0.844391i	$0.320038\pi$
$758$	23.7348	0.862086
$759$	8.99397	0.326461
$760$	0	0
$761$	−17.0557	−0.618269	−0.309135	−	0.951018i	$-0.600039\pi$
$761$	−17.0557	−0.618269	−0.309135	+	0.951018i	$0.600039\pi$
$762$	−24.4031	−0.884030
$763$	−10.4717	−0.379101
$764$	−10.4584	−0.378371
$765$	0	0
$766$	17.0542	0.616192
$767$	−4.25898	−0.153783
$768$	−24.9830	−0.901496
$769$	−19.1580	−0.690857	−0.345428	−	0.938445i	$-0.612266\pi$
$769$	−19.1580	−0.690857	−0.345428	+	0.938445i	$0.612266\pi$
$770$	0	0
$771$	41.9107	1.50938
$772$	−14.6982	−0.529000
$773$	−35.1802	−1.26534	−0.632672	−	0.774420i	$-0.718042\pi$
$773$	−35.1802	−1.26534	−0.632672	+	0.774420i	$0.718042\pi$
$774$	−8.60543	−0.309316
$775$	0	0
$776$	−33.6840	−1.20918
$777$	−13.3707	−0.479670
$778$	−4.24481	−0.152184
$779$	−8.37477	−0.300057
$780$	0	0
$781$	39.6155	1.41755
$782$	−3.36333	−0.120272
$783$	6.94369	0.248147
$784$	1.37035	0.0489410
$785$	0	0
$786$	14.8615	0.530091
$787$	9.92752	0.353878	0.176939	−	0.984222i	$-0.443380\pi$
$787$	9.92752	0.353878	0.176939	+	0.984222i	$0.443380\pi$
$788$	−19.6753	−0.700904
$789$	53.2206	1.89470
$790$	0	0
$791$	14.2747	0.507551
$792$	28.8159	1.02393
$793$	2.73403	0.0970883
$794$	11.0788	0.393172
$795$	0	0
$796$	32.8169	1.16317
$797$	6.08546	0.215558	0.107779	−	0.994175i	$-0.465626\pi$
$797$	6.08546	0.215558	0.107779	+	0.994175i	$0.465626\pi$
$798$	5.44219	0.192651
$799$	−29.7133	−1.05118
$800$	0	0
$801$	−3.38152	−0.119480
$802$	25.6689	0.906400
$803$	6.21574	0.219349
$804$	34.4960	1.21658
$805$	0	0
$806$	0.614909	0.0216592
$807$	−24.9638	−0.878767
$808$	−15.2161	−0.535299
$809$	10.4836	0.368583	0.184291	−	0.982872i	$-0.441001\pi$
$809$	10.4836	0.368583	0.184291	+	0.982872i	$0.441001\pi$
$810$	0	0
$811$	−19.4801	−0.684041	−0.342020	−	0.939693i	$-0.611111\pi$
$811$	−19.4801	−0.684041	−0.342020	+	0.939693i	$0.611111\pi$
$812$	−13.5828	−0.476662
$813$	−10.3893	−0.364367
$814$	13.1489	0.460869
$815$	0	0
$816$	16.7801	0.587421
$817$	−11.8313	−0.413924
$818$	−6.68191	−0.233627
$819$	2.95029	0.103091
$820$	0	0
$821$	29.9796	1.04630	0.523148	−	0.852242i	$-0.324757\pi$
$821$	29.9796	1.04630	0.523148	+	0.852242i	$0.324757\pi$
$822$	10.7173	0.373808
$823$	20.9283	0.729514	0.364757	−	0.931103i	$-0.381152\pi$
$823$	20.9283	0.729514	0.364757	+	0.931103i	$0.381152\pi$
$824$	−30.1698	−1.05101
$825$	0	0
$826$	3.29694	0.114715
$827$	−43.7316	−1.52070	−0.760348	−	0.649516i	$-0.774971\pi$
$827$	−43.7316	−1.52070	−0.760348	+	0.649516i	$0.774971\pi$
$828$	−5.04450	−0.175308
$829$	−39.3713	−1.36742	−0.683710	−	0.729754i	$-0.739635\pi$
$829$	−39.3713	−1.36742	−0.683710	+	0.729754i	$0.739635\pi$
$830$	0	0
$831$	6.33428	0.219734
$832$	1.12907	0.0391433
$833$	4.87467	0.168897
$834$	10.8605	0.376067
$835$	0	0
$836$	17.1330	0.592558
$837$	−0.779009	−0.0269265
$838$	26.5497	0.917145
$839$	31.9928	1.10451	0.552256	−	0.833674i	$-0.313767\pi$
$839$	31.9928	1.10451	0.552256	+	0.833674i	$0.313767\pi$
$840$	0	0
$841$	50.4389	1.73927
$842$	−19.2007	−0.661700
$843$	17.8783	0.615760
$844$	3.98123	0.137039
$845$	0	0
$846$	13.9212	0.478621
$847$	1.81931	0.0625121
$848$	4.50873	0.154830
$849$	−50.3867	−1.72927
$850$	0	0
$851$	−5.32272	−0.182460
$852$	−42.3569	−1.45112
$853$	13.3259	0.456271	0.228135	−	0.973629i	$-0.426737\pi$
$853$	13.3259	0.456271	0.228135	+	0.973629i	$0.426737\pi$
$854$	−2.11646	−0.0724237
$855$	0	0
$856$	17.4451	0.596261
$857$	13.5884	0.464170	0.232085	−	0.972695i	$-0.425445\pi$
$857$	13.5884	0.464170	0.232085	+	0.972695i	$0.425445\pi$
$858$	−5.53088	−0.188821
$859$	−49.0122	−1.67227	−0.836137	−	0.548521i	$-0.815191\pi$
$859$	−49.0122	−1.67227	−0.836137	+	0.548521i	$0.815191\pi$
$860$	0	0
$861$	6.69981	0.228329
$862$	4.61424	0.157162
$863$	−44.8430	−1.52647	−0.763237	−	0.646119i	$-0.776391\pi$
$863$	−44.8430	−1.52647	−0.763237	+	0.646119i	$0.776391\pi$
$864$	−4.52502	−0.153944
$865$	0	0
$866$	2.16518	0.0735759
$867$	16.9871	0.576911
$868$	1.52384	0.0517226
$869$	12.4243	0.421466
$870$	0	0
$871$	−8.03149	−0.272137
$872$	−25.4608	−0.862211
$873$	−45.8580	−1.55206
$874$	2.16648	0.0732822
$875$	0	0
$876$	−6.64587	−0.224543
$877$	−38.7185	−1.30743	−0.653716	−	0.756740i	$-0.726791\pi$
$877$	−38.7185	−1.30743	−0.653716	+	0.756740i	$0.726791\pi$
$878$	23.2598	0.784982
$879$	−45.4749	−1.53383
$880$	0	0
$881$	−18.9857	−0.639644	−0.319822	−	0.947478i	$-0.603623\pi$
$881$	−18.9857	−0.639644	−0.319822	+	0.947478i	$0.603623\pi$
$882$	−2.28386	−0.0769017
$883$	38.6212	1.29971	0.649854	−	0.760059i	$-0.274830\pi$
$883$	38.6212	1.29971	0.649854	+	0.760059i	$0.274830\pi$
$884$	−6.62118	−0.222694
$885$	0	0
$886$	24.8692	0.835497
$887$	−36.8732	−1.23808	−0.619041	−	0.785359i	$-0.712479\pi$
$887$	−36.8732	−1.23808	−0.619041	+	0.785359i	$0.712479\pi$
$888$	−32.5093	−1.09094
$889$	14.0799	0.472226
$890$	0	0
$891$	−28.5480	−0.956394
$892$	−17.9890	−0.602317
$893$	19.1397	0.640487
$894$	−25.0839	−0.838931
$895$	0	0
$896$	10.7425	0.358882
$897$	2.23892	0.0747552
$898$	4.66746	0.155755
$899$	−8.91220	−0.297238
$900$	0	0
$901$	16.0387	0.534325
$902$	−6.58870	−0.219380
$903$	9.46503	0.314976
$904$	34.7074	1.15435
$905$	0	0
$906$	−22.9140	−0.761267
$907$	−17.3188	−0.575061	−0.287531	−	0.957771i	$-0.592834\pi$
$907$	−17.3188	−0.575061	−0.287531	+	0.957771i	$0.592834\pi$
$908$	−38.6090	−1.28128
$909$	−20.7154	−0.687087
$910$	0	0
$911$	−51.5109	−1.70663	−0.853316	−	0.521394i	$-0.825412\pi$
$911$	−51.5109	−1.70663	−0.853316	+	0.521394i	$0.825412\pi$
$912$	−10.8089	−0.357917
$913$	56.9460	1.88464
$914$	5.28412	0.174783
$915$	0	0
$916$	−24.2182	−0.800192
$917$	−8.57468	−0.283161
$918$	−2.62025	−0.0864812
$919$	−50.6546	−1.67094	−0.835471	−	0.549534i	$-0.814805\pi$
$919$	−50.6546	−1.67094	−0.835471	+	0.549534i	$0.814805\pi$
$920$	0	0
$921$	47.6979	1.57170
$922$	−2.01773	−0.0664504
$923$	9.86169	0.324602
$924$	−13.7064	−0.450908
$925$	0	0
$926$	4.75065	0.156116
$927$	−41.0737	−1.34904
$928$	−51.7682	−1.69937
$929$	−49.8957	−1.63703	−0.818513	−	0.574489i	$-0.805201\pi$
$929$	−49.8957	−1.63703	−0.818513	+	0.574489i	$0.805201\pi$
$930$	0	0
$931$	−3.14000	−0.102909
$932$	16.9787	0.556156
$933$	−48.1502	−1.57637
$934$	−21.5994	−0.706753
$935$	0	0
$936$	7.17330	0.234467
$937$	−27.4405	−0.896441	−0.448220	−	0.893923i	$-0.647942\pi$
$937$	−27.4405	−0.896441	−0.448220	+	0.893923i	$0.647942\pi$
$938$	6.21730	0.203002
$939$	19.4665	0.635266
$940$	0	0
$941$	36.0538	1.17532	0.587660	−	0.809108i	$-0.300049\pi$
$941$	36.0538	1.17532	0.587660	+	0.809108i	$0.300049\pi$
$942$	−21.9556	−0.715352
$943$	2.66712	0.0868535
$944$	−6.54814	−0.213124
$945$	0	0
$946$	−9.30805	−0.302631
$947$	−42.4621	−1.37983	−0.689917	−	0.723888i	$-0.742353\pi$
$947$	−42.4621	−1.37983	−0.689917	+	0.723888i	$0.742353\pi$
$948$	−13.2841	−0.431447
$949$	1.54731	0.0502280
$950$	0	0
$951$	33.9757	1.10174
$952$	11.8522	0.384132
$953$	11.4477	0.370826	0.185413	−	0.982661i	$-0.440638\pi$
$953$	11.4477	0.370826	0.185413	+	0.982661i	$0.440638\pi$
$954$	−7.51439	−0.243287
$955$	0	0
$956$	−4.43759	−0.143522
$957$	80.1619	2.59127
$958$	−15.9482	−0.515263
$959$	−6.18359	−0.199678
$960$	0	0
$961$	−30.0001	−0.967747
$962$	3.27323	0.105533
$963$	23.7501	0.765335
$964$	−5.62135	−0.181052
$965$	0	0
$966$	−1.73318	−0.0557641
$967$	10.0912	0.324510	0.162255	−	0.986749i	$-0.448123\pi$
$967$	10.0912	0.324510	0.162255	+	0.986749i	$0.448123\pi$
$968$	4.42344	0.142175
$969$	−38.4498	−1.23519
$970$	0	0
$971$	32.1946	1.03317	0.516587	−	0.856235i	$-0.327202\pi$
$971$	32.1946	1.03317	0.516587	+	0.856235i	$0.327202\pi$
$972$	34.0853	1.09329
$973$	−6.26621	−0.200885
$974$	29.7632	0.953673
$975$	0	0
$976$	4.20354	0.134552
$977$	−42.8142	−1.36975	−0.684875	−	0.728661i	$-0.740143\pi$
$977$	−42.8142	−1.36975	−0.684875	+	0.728661i	$0.740143\pi$
$978$	−31.1672	−0.996618
$979$	−3.65761	−0.116898
$980$	0	0
$981$	−34.6628	−1.10670
$982$	17.7400	0.566107
$983$	14.0817	0.449138	0.224569	−	0.974458i	$-0.427903\pi$
$983$	14.0817	0.449138	0.224569	+	0.974458i	$0.427903\pi$
$984$	16.2898	0.519301
$985$	0	0
$986$	−29.9768	−0.954657
$987$	−15.3118	−0.487379
$988$	4.26501	0.135688
$989$	3.76793	0.119813
$990$	0	0
$991$	−54.8730	−1.74310	−0.871549	−	0.490308i	$-0.836884\pi$
$991$	−54.8730	−1.74310	−0.871549	+	0.490308i	$0.836884\pi$
$992$	5.80784	0.184399
$993$	79.7513	2.53083
$994$	−7.63409	−0.242139
$995$	0	0
$996$	−60.8867	−1.92927
$997$	−13.3811	−0.423783	−0.211891	−	0.977293i	$-0.567962\pi$
$997$	−13.3811	−0.423783	−0.211891	+	0.977293i	$0.567962\pi$
$998$	2.95630	0.0935799
$999$	−4.14675	−0.131197

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4025.2.a.bc.1.5	yes	14
5.4	even	2		4025.2.a.z.1.10	✓	14

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4025.2.a.z.1.10	✓	14	5.4	even	2
4025.2.a.bc.1.5	yes	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:	\( N \)	\(=\)	\( 4025 = 5^{2} \cdot 7 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4025.a (trivial)

\(f(q)\)	\(=\)	\(q-0.689960 q^{2} +2.51200 q^{3} -1.52395 q^{4} -1.73318 q^{6} +1.00000 q^{7} +2.43139 q^{8} +3.31014 q^{9} +O(q^{10})\)	\(q-0.689960 q^{2} +2.51200 q^{3} -1.52395 q^{4} -1.73318 q^{6} +1.00000 q^{7} +2.43139 q^{8} +3.31014 q^{9} +3.58041 q^{11} -3.82817 q^{12} +0.891289 q^{13} -0.689960 q^{14} +1.37035 q^{16} +4.87467 q^{17} -2.28386 q^{18} -3.14000 q^{19} +2.51200 q^{21} -2.47034 q^{22} +1.00000 q^{23} +6.10765 q^{24} -0.614954 q^{26} +0.779066 q^{27} -1.52395 q^{28} +8.91285 q^{29} -0.999927 q^{31} -5.80826 q^{32} +8.99397 q^{33} -3.36333 q^{34} -5.04450 q^{36} -5.32272 q^{37} +2.16648 q^{38} +2.23892 q^{39} +2.66712 q^{41} -1.73318 q^{42} +3.76793 q^{43} -5.45638 q^{44} -0.689960 q^{46} -6.09546 q^{47} +3.44231 q^{48} +1.00000 q^{49} +12.2452 q^{51} -1.35828 q^{52} +3.29021 q^{53} -0.537525 q^{54} +2.43139 q^{56} -7.88768 q^{57} -6.14951 q^{58} -4.77845 q^{59} +3.06750 q^{61} +0.689910 q^{62} +3.31014 q^{63} +1.26678 q^{64} -6.20549 q^{66} -9.01110 q^{67} -7.42877 q^{68} +2.51200 q^{69} +11.0645 q^{71} +8.04823 q^{72} +1.73604 q^{73} +3.67247 q^{74} +4.78522 q^{76} +3.58041 q^{77} -1.54476 q^{78} +3.47008 q^{79} -7.97340 q^{81} -1.84021 q^{82} +15.9049 q^{83} -3.82817 q^{84} -2.59972 q^{86} +22.3891 q^{87} +8.70536 q^{88} -1.02156 q^{89} +0.891289 q^{91} -1.52395 q^{92} -2.51182 q^{93} +4.20562 q^{94} -14.5904 q^{96} -13.8538 q^{97} -0.689960 q^{98} +11.8516 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 14 q + 3 q^{2} + 4 q^{3} + 17 q^{4} - 4 q^{6} + 14 q^{7} + 3 q^{8} + 18 q^{9}+O(q^{10}) \) 14 * q + 3 * q^2 + 4 * q^3 + 17 * q^4 - 4 * q^6 + 14 * q^7 + 3 * q^8 + 18 * q^9	\( 14 q + 3 q^{2} + 4 q^{3} + 17 q^{4} - 4 q^{6} + 14 q^{7} + 3 q^{8} + 18 q^{9} + 5 q^{11} + 17 q^{12} + 11 q^{13} + 3 q^{14} + 23 q^{16} + 3 q^{17} + 15 q^{18} - 2 q^{19} + 4 q^{21} + 23 q^{22} + 14 q^{23} - 12 q^{24} - 9 q^{26} + 25 q^{27} + 17 q^{28} + 7 q^{29} - 3 q^{31} + 24 q^{32} + 6 q^{33} - 14 q^{34} + 13 q^{36} + 22 q^{37} + 20 q^{38} - 10 q^{39} - 17 q^{41} - 4 q^{42} + 18 q^{43} + 28 q^{44} + 3 q^{46} + 30 q^{47} + 8 q^{48} + 14 q^{49} + 4 q^{51} + 8 q^{52} + 11 q^{53} + 20 q^{54} + 3 q^{56} + 18 q^{57} + 38 q^{58} - 22 q^{59} - 8 q^{61} - 22 q^{62} + 18 q^{63} + 29 q^{64} - 9 q^{66} + 39 q^{67} + q^{68} + 4 q^{69} - 5 q^{71} - 24 q^{72} + 18 q^{73} + 35 q^{74} - 41 q^{76} + 5 q^{77} - 22 q^{78} + 10 q^{79} + 2 q^{81} - 8 q^{82} + 24 q^{83} + 17 q^{84} - 26 q^{86} + 5 q^{87} + 58 q^{88} + 25 q^{89} + 11 q^{91} + 17 q^{92} + 47 q^{93} - 2 q^{94} - 117 q^{96} + 43 q^{97} + 3 q^{98} + 55 q^{99}+O(q^{100}) \) 14 * q + 3 * q^2 + 4 * q^3 + 17 * q^4 - 4 * q^6 + 14 * q^7 + 3 * q^8 + 18 * q^9 + 5 * q^11 + 17 * q^12 + 11 * q^13 + 3 * q^14 + 23 * q^16 + 3 * q^17 + 15 * q^18 - 2 * q^19 + 4 * q^21 + 23 * q^22 + 14 * q^23 - 12 * q^24 - 9 * q^26 + 25 * q^27 + 17 * q^28 + 7 * q^29 - 3 * q^31 + 24 * q^32 + 6 * q^33 - 14 * q^34 + 13 * q^36 + 22 * q^37 + 20 * q^38 - 10 * q^39 - 17 * q^41 - 4 * q^42 + 18 * q^43 + 28 * q^44 + 3 * q^46 + 30 * q^47 + 8 * q^48 + 14 * q^49 + 4 * q^51 + 8 * q^52 + 11 * q^53 + 20 * q^54 + 3 * q^56 + 18 * q^57 + 38 * q^58 - 22 * q^59 - 8 * q^61 - 22 * q^62 + 18 * q^63 + 29 * q^64 - 9 * q^66 + 39 * q^67 + q^68 + 4 * q^69 - 5 * q^71 - 24 * q^72 + 18 * q^73 + 35 * q^74 - 41 * q^76 + 5 * q^77 - 22 * q^78 + 10 * q^79 + 2 * q^81 - 8 * q^82 + 24 * q^83 + 17 * q^84 - 26 * q^86 + 5 * q^87 + 58 * q^88 + 25 * q^89 + 11 * q^91 + 17 * q^92 + 47 * q^93 - 2 * q^94 - 117 * q^96 + 43 * q^97 + 3 * q^98 + 55 * q^99

Introduction

L-functions

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