LMFDB - Embedded newform 4025.2.a.ba.1.6

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:	$1$
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} + 18 x^{11} + 187 x^{10} - 118 x^{9} - 772 x^{8} + 346 x^{7} + 1581 x^{6} + \cdots - 5 $ x^14 - x^13 - 22x^12 + 18x^11 + 187x^10 - 118x^9 - 772x^8 + 346x^7 + 1581x^6 - 443x^5 - 1429x^4 + 193x^3 + 386x^2 - 3x - 5
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 3^{3} $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.6
Root			$0.704319$ 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)

$f(q)$	$=$	$q-0.704319 q^{2} +2.54639 q^{3} -1.50393 q^{4} -1.79347 q^{6} -1.00000 q^{7} +2.46789 q^{8} +3.48411 q^{9} +O(q^{10})$	\(q-0.704319 q^{2} +2.54639 q^{3} -1.50393 q^{4} -1.79347 q^{6} -1.00000 q^{7} +2.46789 q^{8} +3.48411 q^{9} -3.60653 q^{11} -3.82961 q^{12} -6.67646 q^{13} +0.704319 q^{14} +1.26969 q^{16} +7.65043 q^{17} -2.45393 q^{18} +6.35925 q^{19} -2.54639 q^{21} +2.54015 q^{22} +1.00000 q^{23} +6.28421 q^{24} +4.70236 q^{26} +1.23273 q^{27} +1.50393 q^{28} -5.44059 q^{29} -9.59588 q^{31} -5.83004 q^{32} -9.18364 q^{33} -5.38835 q^{34} -5.23987 q^{36} +10.2295 q^{37} -4.47895 q^{38} -17.0009 q^{39} -2.16374 q^{41} +1.79347 q^{42} -6.80627 q^{43} +5.42399 q^{44} -0.704319 q^{46} +1.65763 q^{47} +3.23312 q^{48} +1.00000 q^{49} +19.4810 q^{51} +10.0410 q^{52} -1.34181 q^{53} -0.868236 q^{54} -2.46789 q^{56} +16.1931 q^{57} +3.83191 q^{58} +0.0151323 q^{59} +5.55858 q^{61} +6.75857 q^{62} -3.48411 q^{63} +1.56684 q^{64} +6.46822 q^{66} -6.51195 q^{67} -11.5057 q^{68} +2.54639 q^{69} -11.3095 q^{71} +8.59839 q^{72} +2.48100 q^{73} -7.20480 q^{74} -9.56390 q^{76} +3.60653 q^{77} +11.9741 q^{78} -9.83954 q^{79} -7.31331 q^{81} +1.52396 q^{82} -1.12498 q^{83} +3.82961 q^{84} +4.79379 q^{86} -13.8539 q^{87} -8.90052 q^{88} -6.76383 q^{89} +6.67646 q^{91} -1.50393 q^{92} -24.4349 q^{93} -1.16750 q^{94} -14.8456 q^{96} -0.252247 q^{97} -0.704319 q^{98} -12.5656 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 14 q - q^{2} - 6 q^{3} + 17 q^{4} - 4 q^{6} - 14 q^{7} - 9 q^{8} + 18 q^{9}+O(q^{10}) $ 14 * q - q^2 - 6 * q^3 + 17 * q^4 - 4 * q^6 - 14 * q^7 - 9 * q^8 + 18 * q^9	$ 14 q - q^{2} - 6 q^{3} + 17 q^{4} - 4 q^{6} - 14 q^{7} - 9 q^{8} + 18 q^{9} - 3 q^{11} - 11 q^{12} - 15 q^{13} + q^{14} + 23 q^{16} - 9 q^{17} - 17 q^{18} - 4 q^{19} + 6 q^{21} - 9 q^{22} + 14 q^{23} + 10 q^{24} - 5 q^{26} - 33 q^{27} - 17 q^{28} + 11 q^{29} - q^{31} - 24 q^{32} - 26 q^{33} - 6 q^{34} + 13 q^{36} - 18 q^{37} + 6 q^{38} + 6 q^{39} - 7 q^{41} + 4 q^{42} - 18 q^{43} - 16 q^{44} - q^{46} - 10 q^{47} - 40 q^{48} + 14 q^{49} + 28 q^{51} - 46 q^{52} - 5 q^{53} - 24 q^{54} + 9 q^{56} + 26 q^{57} - 2 q^{58} - 24 q^{59} - 6 q^{61} + 16 q^{62} - 18 q^{63} + 29 q^{64} + 27 q^{66} - 61 q^{67} - 35 q^{68} - 6 q^{69} + 11 q^{71} - 12 q^{72} - 28 q^{73} - 49 q^{74} - 27 q^{76} + 3 q^{77} - 38 q^{78} + 6 q^{79} + 26 q^{81} + 14 q^{82} - 16 q^{83} + 11 q^{84} + 46 q^{86} - 61 q^{87} - 58 q^{88} - 39 q^{89} + 15 q^{91} + 17 q^{92} - 21 q^{93} - 74 q^{94} + 41 q^{96} - 19 q^{97} - q^{98} - 9 q^{99}+O(q^{100}) $ 14 * q - q^2 - 6 * q^3 + 17 * q^4 - 4 * q^6 - 14 * q^7 - 9 * q^8 + 18 * q^9 - 3 * q^11 - 11 * q^12 - 15 * q^13 + q^14 + 23 * q^16 - 9 * q^17 - 17 * q^18 - 4 * q^19 + 6 * q^21 - 9 * q^22 + 14 * q^23 + 10 * q^24 - 5 * q^26 - 33 * q^27 - 17 * q^28 + 11 * q^29 - q^31 - 24 * q^32 - 26 * q^33 - 6 * q^34 + 13 * q^36 - 18 * q^37 + 6 * q^38 + 6 * q^39 - 7 * q^41 + 4 * q^42 - 18 * q^43 - 16 * q^44 - q^46 - 10 * q^47 - 40 * q^48 + 14 * q^49 + 28 * q^51 - 46 * q^52 - 5 * q^53 - 24 * q^54 + 9 * q^56 + 26 * q^57 - 2 * q^58 - 24 * q^59 - 6 * q^61 + 16 * q^62 - 18 * q^63 + 29 * q^64 + 27 * q^66 - 61 * q^67 - 35 * q^68 - 6 * q^69 + 11 * q^71 - 12 * q^72 - 28 * q^73 - 49 * q^74 - 27 * q^76 + 3 * q^77 - 38 * q^78 + 6 * q^79 + 26 * q^81 + 14 * q^82 - 16 * q^83 + 11 * q^84 + 46 * q^86 - 61 * q^87 - 58 * q^88 - 39 * q^89 + 15 * q^91 + 17 * q^92 - 21 * q^93 - 74 * q^94 + 41 * q^96 - 19 * q^97 - q^98 - 9 * 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 $

$2$	−0.704319	−0.498029	−0.249014	−	0.968500i	$-0.580107\pi$
$2$	−0.704319	−0.498029	−0.249014	+	0.968500i	$0.580107\pi$
$3$	2.54639	1.47016	0.735080	−	0.677981i	$-0.237145\pi$
$3$	2.54639	1.47016	0.735080	+	0.677981i	$0.237145\pi$
$4$	−1.50393	−0.751967
$5$	0	0
$5$	0	0
$6$	−1.79347	−0.732182
$7$	−1.00000	−0.377964
$7$	−1.00000	−0.377964
$8$	2.46789	0.872530
$9$	3.48411	1.16137
$10$	0	0
$11$	−3.60653	−1.08741	−0.543705	−	0.839276i	$-0.682979\pi$
$11$	−3.60653	−1.08741	−0.543705	+	0.839276i	$0.682979\pi$
$12$	−3.82961	−1.10551
$13$	−6.67646	−1.85172	−0.925859	−	0.377869i	$-0.876657\pi$
$13$	−6.67646	−1.85172	−0.925859	+	0.377869i	$0.876657\pi$
$14$	0.704319	0.188237
$15$	0	0
$16$	1.26969	0.317422
$17$	7.65043	1.85550	0.927751	−	0.373199i	$-0.121739\pi$
$17$	7.65043	1.85550	0.927751	+	0.373199i	$0.121739\pi$
$18$	−2.45393	−0.578396
$19$	6.35925	1.45891	0.729456	−	0.684027i	$-0.239773\pi$
$19$	6.35925	1.45891	0.729456	+	0.684027i	$0.239773\pi$
$20$	0	0
$21$	−2.54639	−0.555668
$22$	2.54015	0.541562
$23$	1.00000	0.208514
$23$	1.00000	0.208514
$24$	6.28421	1.28276
$25$	0	0
$26$	4.70236	0.922209
$27$	1.23273	0.237239
$28$	1.50393	0.284217
$29$	−5.44059	−1.01029	−0.505146	−	0.863034i	$-0.668561\pi$
$29$	−5.44059	−1.01029	−0.505146	+	0.863034i	$0.668561\pi$
$30$	0	0
$31$	−9.59588	−1.72347	−0.861736	−	0.507357i	$-0.830622\pi$
$31$	−9.59588	−1.72347	−0.861736	+	0.507357i	$0.830622\pi$
$32$	−5.83004	−1.03062
$33$	−9.18364	−1.59867
$34$	−5.38835	−0.924094
$35$	0	0
$36$	−5.23987	−0.873312
$37$	10.2295	1.68171	0.840856	−	0.541259i	$-0.182052\pi$
$37$	10.2295	1.68171	0.840856	+	0.541259i	$0.182052\pi$
$38$	−4.47895	−0.726581
$39$	−17.0009	−2.72232
$40$	0	0
$41$	−2.16374	−0.337919	−0.168960	−	0.985623i	$-0.554041\pi$
$41$	−2.16374	−0.337919	−0.168960	+	0.985623i	$0.554041\pi$
$42$	1.79347	0.276739
$43$	−6.80627	−1.03795	−0.518973	−	0.854791i	$-0.673686\pi$
$43$	−6.80627	−1.03795	−0.518973	+	0.854791i	$0.673686\pi$
$44$	5.42399	0.817697
$45$	0	0
$46$	−0.704319	−0.103846
$47$	1.65763	0.241790	0.120895	−	0.992665i	$-0.461424\pi$
$47$	1.65763	0.241790	0.120895	+	0.992665i	$0.461424\pi$
$48$	3.23312	0.466661
$49$	1.00000	0.142857
$50$	0	0
$51$	19.4810	2.72789
$52$	10.0410	1.39243
$53$	−1.34181	−0.184311	−0.0921557	−	0.995745i	$-0.529376\pi$
$53$	−1.34181	−0.184311	−0.0921557	+	0.995745i	$0.529376\pi$
$54$	−0.868236	−0.118152
$55$	0	0
$56$	−2.46789	−0.329786
$57$	16.1931	2.14483
$58$	3.83191	0.503154
$59$	0.0151323	0.00197005	0.000985027	−	1.00000i	$-0.499686\pi$
$59$	0.0151323	0.00197005	0.000985027		1.00000i	$0.499686\pi$
$60$	0	0
$61$	5.55858	0.711703	0.355851	−	0.934543i	$-0.384191\pi$
$61$	5.55858	0.711703	0.355851	+	0.934543i	$0.384191\pi$
$62$	6.75857	0.858339
$63$	−3.48411	−0.438956
$64$	1.56684	0.195855
$65$	0	0
$66$	6.46822	0.796183
$67$	−6.51195	−0.795561	−0.397780	−	0.917481i	$-0.630219\pi$
$67$	−6.51195	−0.795561	−0.397780	+	0.917481i	$0.630219\pi$
$68$	−11.5057	−1.39528
$69$	2.54639	0.306549
$70$	0	0
$71$	−11.3095	−1.34219	−0.671096	−	0.741371i	$-0.734176\pi$
$71$	−11.3095	−1.34219	−0.671096	+	0.741371i	$0.734176\pi$
$72$	8.59839	1.01333
$73$	2.48100	0.290380	0.145190	−	0.989404i	$-0.453621\pi$
$73$	2.48100	0.290380	0.145190	+	0.989404i	$0.453621\pi$
$74$	−7.20480	−0.837541
$75$	0	0
$76$	−9.56390	−1.09705
$77$	3.60653	0.411003
$78$	11.9741	1.35580
$79$	−9.83954	−1.10704	−0.553518	−	0.832838i	$-0.686715\pi$
$79$	−9.83954	−1.10704	−0.553518	+	0.832838i	$0.686715\pi$
$80$	0	0
$81$	−7.31331	−0.812590
$82$	1.52396	0.168294
$83$	−1.12498	−0.123483	−0.0617414	−	0.998092i	$-0.519665\pi$
$83$	−1.12498	−0.123483	−0.0617414	+	0.998092i	$0.519665\pi$
$84$	3.82961	0.417844
$85$	0	0
$86$	4.79379	0.516927
$87$	−13.8539	−1.48529
$88$	−8.90052	−0.948799
$89$	−6.76383	−0.716965	−0.358482	−	0.933536i	$-0.616706\pi$
$89$	−6.76383	−0.716965	−0.358482	+	0.933536i	$0.616706\pi$
$90$	0	0
$91$	6.67646	0.699884
$92$	−1.50393	−0.156796
$93$	−24.4349	−2.53378
$94$	−1.16750	−0.120419
$95$	0	0
$96$	−14.8456	−1.51517
$97$	−0.252247	−0.0256118	−0.0128059	−	0.999918i	$-0.504076\pi$
$97$	−0.252247	−0.0256118	−0.0128059	+	0.999918i	$0.504076\pi$
$98$	−0.704319	−0.0711470
$99$	−12.5656	−1.26289
$100$	0	0
$101$	−4.75447	−0.473087	−0.236544	−	0.971621i	$-0.576015\pi$
$101$	−4.75447	−0.473087	−0.236544	+	0.971621i	$0.576015\pi$
$102$	−13.7208	−1.35857
$103$	−17.5736	−1.73158	−0.865791	−	0.500405i	$-0.833184\pi$
$103$	−17.5736	−1.73158	−0.865791	+	0.500405i	$0.833184\pi$
$104$	−16.4768	−1.61568
$105$	0	0
$106$	0.945061	0.0917924
$107$	−11.3738	−1.09955	−0.549774	−	0.835313i	$-0.685286\pi$
$107$	−11.3738	−1.09955	−0.549774	+	0.835313i	$0.685286\pi$
$108$	−1.85395	−0.178396
$109$	16.8010	1.60924	0.804622	−	0.593787i	$-0.202368\pi$
$109$	16.8010	1.60924	0.804622	+	0.593787i	$0.202368\pi$
$110$	0	0
$111$	26.0482	2.47238
$112$	−1.26969	−0.119974
$113$	−7.82857	−0.736449	−0.368225	−	0.929737i	$-0.620034\pi$
$113$	−7.82857	−0.736449	−0.368225	+	0.929737i	$0.620034\pi$
$114$	−11.4051	−1.06819
$115$	0	0
$116$	8.18228	0.759706
$117$	−23.2615	−2.15053
$118$	−0.0106580	−0.000981144 0
$119$	−7.65043	−0.701314
$120$	0	0
$121$	2.00708	0.182462
$122$	−3.91501	−0.354449
$123$	−5.50973	−0.496795
$124$	14.4316	1.29599
$125$	0	0
$126$	2.45393	0.218613
$127$	−14.1867	−1.25886	−0.629431	−	0.777056i	$-0.716712\pi$
$127$	−14.1867	−1.25886	−0.629431	+	0.777056i	$0.716712\pi$
$128$	10.5565	0.933074
$129$	−17.3314	−1.52595
$130$	0	0
$131$	−12.0047	−1.04886	−0.524429	−	0.851454i	$-0.675721\pi$
$131$	−12.0047	−1.04886	−0.524429	+	0.851454i	$0.675721\pi$
$132$	13.8116	1.20215
$133$	−6.35925	−0.551417
$134$	4.58649	0.396212
$135$	0	0
$136$	18.8804	1.61898
$137$	−9.93523	−0.848824	−0.424412	−	0.905469i	$-0.639519\pi$
$137$	−9.93523	−0.848824	−0.424412	+	0.905469i	$0.639519\pi$
$138$	−1.79347	−0.152671
$139$	1.64184	0.139259	0.0696295	−	0.997573i	$-0.477818\pi$
$139$	1.64184	0.139259	0.0696295	+	0.997573i	$0.477818\pi$
$140$	0	0
$141$	4.22098	0.355470
$142$	7.96550	0.668450
$143$	24.0789	2.01358
$144$	4.42373	0.368644
$145$	0	0
$146$	−1.74742	−0.144617
$147$	2.54639	0.210023
$148$	−15.3844	−1.26459
$149$	−4.52296	−0.370536	−0.185268	−	0.982688i	$-0.559315\pi$
$149$	−4.52296	−0.370536	−0.185268	+	0.982688i	$0.559315\pi$
$150$	0	0
$151$	−6.74915	−0.549238	−0.274619	−	0.961553i	$-0.588552\pi$
$151$	−6.74915	−0.549238	−0.274619	+	0.961553i	$0.588552\pi$
$152$	15.6939	1.27295
$153$	26.6549	2.15492
$154$	−2.54015	−0.204691
$155$	0	0
$156$	25.5682	2.04710
$157$	−5.64316	−0.450373	−0.225187	−	0.974316i	$-0.572299\pi$
$157$	−5.64316	−0.450373	−0.225187	+	0.974316i	$0.572299\pi$
$158$	6.93018	0.551336
$159$	−3.41677	−0.270967
$160$	0	0
$161$	−1.00000	−0.0788110
$162$	5.15091	0.404693
$163$	−8.85100	−0.693264	−0.346632	−	0.938001i	$-0.612675\pi$
$163$	−8.85100	−0.693264	−0.346632	+	0.938001i	$0.612675\pi$
$164$	3.25412	0.254104
$165$	0	0
$166$	0.792346	0.0614980
$167$	−1.54920	−0.119881	−0.0599404	−	0.998202i	$-0.519091\pi$
$167$	−1.54920	−0.119881	−0.0599404	+	0.998202i	$0.519091\pi$
$168$	−6.28421	−0.484837
$169$	31.5752	2.42886
$170$	0	0
$171$	22.1563	1.69434
$172$	10.2362	0.780501
$173$	−21.7080	−1.65042	−0.825212	−	0.564822i	$-0.808945\pi$
$173$	−21.7080	−1.65042	−0.825212	+	0.564822i	$0.808945\pi$
$174$	9.75754	0.739717
$175$	0	0
$176$	−4.57917	−0.345168
$177$	0.0385327	0.00289629
$178$	4.76390	0.357069
$179$	10.2521	0.766276	0.383138	−	0.923691i	$-0.374843\pi$
$179$	10.2521	0.766276	0.383138	+	0.923691i	$0.374843\pi$
$180$	0	0
$181$	0.914362	0.0679640	0.0339820	−	0.999422i	$-0.489181\pi$
$181$	0.914362	0.0679640	0.0339820	+	0.999422i	$0.489181\pi$
$182$	−4.70236	−0.348562
$183$	14.1543	1.04632
$184$	2.46789	0.181935
$185$	0	0
$186$	17.2100	1.26190
$187$	−27.5915	−2.01769
$188$	−2.49297	−0.181818
$189$	−1.23273	−0.0896680
$190$	0	0
$191$	18.7260	1.35497	0.677484	−	0.735537i	$-0.263070\pi$
$191$	18.7260	1.35497	0.677484	+	0.735537i	$0.263070\pi$
$192$	3.98978	0.287938
$193$	7.70591	0.554684	0.277342	−	0.960771i	$-0.410547\pi$
$193$	7.70591	0.554684	0.277342	+	0.960771i	$0.410547\pi$
$194$	0.177662	0.0127554
$195$	0	0
$196$	−1.50393	−0.107424
$197$	3.12564	0.222693	0.111346	−	0.993782i	$-0.464484\pi$
$197$	3.12564	0.222693	0.111346	+	0.993782i	$0.464484\pi$
$198$	8.85016	0.628954
$199$	17.9622	1.27331	0.636653	−	0.771150i	$-0.280318\pi$
$199$	17.9622	1.27331	0.636653	+	0.771150i	$0.280318\pi$
$200$	0	0
$201$	−16.5820	−1.16960
$202$	3.34867	0.235611
$203$	5.44059	0.381854
$204$	−29.2981	−2.05128
$205$	0	0
$206$	12.3775	0.862378
$207$	3.48411	0.242162
$208$	−8.47702	−0.587775
$209$	−22.9349	−1.58644
$210$	0	0
$211$	12.3449	0.849859	0.424929	−	0.905226i	$-0.360299\pi$
$211$	12.3449	0.849859	0.424929	+	0.905226i	$0.360299\pi$
$212$	2.01799	0.138596
$213$	−28.7984	−1.97324
$214$	8.01080	0.547607
$215$	0	0
$216$	3.04224	0.206998
$217$	9.59588	0.651411
$218$	−11.8333	−0.801450
$219$	6.31761	0.426904
$220$	0	0
$221$	−51.0778	−3.43587
$222$	−18.3462	−1.23132
$223$	−5.03337	−0.337059	−0.168530	−	0.985697i	$-0.553902\pi$
$223$	−5.03337	−0.337059	−0.168530	+	0.985697i	$0.553902\pi$
$224$	5.83004	0.389536
$225$	0	0
$226$	5.51381	0.366773
$227$	13.5459	0.899073	0.449537	−	0.893262i	$-0.351589\pi$
$227$	13.5459	0.899073	0.449537	+	0.893262i	$0.351589\pi$
$228$	−24.3534	−1.61285
$229$	15.7921	1.04357	0.521785	−	0.853077i	$-0.325266\pi$
$229$	15.7921	1.04357	0.521785	+	0.853077i	$0.325266\pi$
$230$	0	0
$231$	9.18364	0.604239
$232$	−13.4268	−0.881510
$233$	−0.861392	−0.0564317	−0.0282158	−	0.999602i	$-0.508983\pi$
$233$	−0.861392	−0.0564317	−0.0282158	+	0.999602i	$0.508983\pi$
$234$	16.3835	1.07103
$235$	0	0
$236$	−0.0227579	−0.00148142
$237$	−25.0553	−1.62752
$238$	5.38835	0.349275
$239$	11.9670	0.774084	0.387042	−	0.922062i	$-0.373497\pi$
$239$	11.9670	0.774084	0.387042	+	0.922062i	$0.373497\pi$
$240$	0	0
$241$	−15.5291	−1.00032	−0.500160	−	0.865933i	$-0.666725\pi$
$241$	−15.5291	−1.00032	−0.500160	+	0.865933i	$0.666725\pi$
$242$	−1.41363	−0.0908714
$243$	−22.3207	−1.43188
$244$	−8.35974	−0.535177
$245$	0	0
$246$	3.88061	0.247419
$247$	−42.4573	−2.70150
$248$	−23.6816	−1.50378
$249$	−2.86464	−0.181539
$250$	0	0
$251$	4.49929	0.283993	0.141996	−	0.989867i	$-0.454648\pi$
$251$	4.49929	0.283993	0.141996	+	0.989867i	$0.454648\pi$
$252$	5.23987	0.330081
$253$	−3.60653	−0.226741
$254$	9.99193	0.626950
$255$	0	0
$256$	−10.5688	−0.660553
$257$	16.1212	1.00561	0.502805	−	0.864400i	$-0.332301\pi$
$257$	16.1212	1.00561	0.502805	+	0.864400i	$0.332301\pi$
$258$	12.2069	0.759966
$259$	−10.2295	−0.635627
$260$	0	0
$261$	−18.9556	−1.17332
$262$	8.45517	0.522362
$263$	−23.3091	−1.43730	−0.718651	−	0.695370i	$-0.755240\pi$
$263$	−23.3091	−1.43730	−0.718651	+	0.695370i	$0.755240\pi$
$264$	−22.6642	−1.39489
$265$	0	0
$266$	4.47895	0.274622
$267$	−17.2234	−1.05405
$268$	9.79354	0.598236
$269$	−14.0661	−0.857623	−0.428812	−	0.903394i	$-0.641068\pi$
$269$	−14.0661	−0.857623	−0.428812	+	0.903394i	$0.641068\pi$
$270$	0	0
$271$	−19.0169	−1.15520	−0.577598	−	0.816321i	$-0.696010\pi$
$271$	−19.0169	−1.15520	−0.577598	+	0.816321i	$0.696010\pi$
$272$	9.71365	0.588977
$273$	17.0009	1.02894
$274$	6.99758	0.422739
$275$	0	0
$276$	−3.82961	−0.230515
$277$	4.86313	0.292197	0.146099	−	0.989270i	$-0.453328\pi$
$277$	4.86313	0.292197	0.146099	+	0.989270i	$0.453328\pi$
$278$	−1.15638	−0.0693550
$279$	−33.4331	−2.00159
$280$	0	0
$281$	13.3767	0.797988	0.398994	−	0.916954i	$-0.369359\pi$
$281$	13.3767	0.797988	0.398994	+	0.916954i	$0.369359\pi$
$282$	−2.97291	−0.177035
$283$	10.1341	0.602411	0.301205	−	0.953559i	$-0.402611\pi$
$283$	10.1341	0.602411	0.301205	+	0.953559i	$0.402611\pi$
$284$	17.0088	1.00928
$285$	0	0
$286$	−16.9592	−1.00282
$287$	2.16374	0.127722
$288$	−20.3125	−1.19693
$289$	41.5291	2.44289
$290$	0	0
$291$	−0.642320	−0.0376534
$292$	−3.73127	−0.218356
$293$	25.3344	1.48005	0.740025	−	0.672579i	$-0.234813\pi$
$293$	25.3344	1.48005	0.740025	+	0.672579i	$0.234813\pi$
$294$	−1.79347	−0.104597
$295$	0	0
$296$	25.2452	1.46734
$297$	−4.44588	−0.257976
$298$	3.18561	0.184537
$299$	−6.67646	−0.386110
$300$	0	0
$301$	6.80627	0.392307
$302$	4.75355	0.273536
$303$	−12.1067	−0.695514
$304$	8.07426	0.463091
$305$	0	0
$306$	−18.7736	−1.07321
$307$	−25.9036	−1.47840	−0.739198	−	0.673488i	$-0.764795\pi$
$307$	−25.9036	−1.47840	−0.739198	+	0.673488i	$0.764795\pi$
$308$	−5.42399	−0.309060
$309$	−44.7494	−2.54570
$310$	0	0
$311$	29.4936	1.67243	0.836215	−	0.548402i	$-0.184764\pi$
$311$	29.4936	1.67243	0.836215	+	0.548402i	$0.184764\pi$
$312$	−41.9563	−2.37531
$313$	29.1094	1.64536	0.822682	−	0.568502i	$-0.192477\pi$
$313$	29.1094	1.64536	0.822682	+	0.568502i	$0.192477\pi$
$314$	3.97459	0.224299
$315$	0	0
$316$	14.7980	0.832454
$317$	−20.6370	−1.15909	−0.579545	−	0.814940i	$-0.696770\pi$
$317$	−20.6370	−1.15909	−0.579545	+	0.814940i	$0.696770\pi$
$318$	2.40650	0.134950
$319$	19.6217	1.09860
$320$	0	0
$321$	−28.9622	−1.61651
$322$	0.704319	0.0392502
$323$	48.6510	2.70702
$324$	10.9987	0.611041
$325$	0	0
$326$	6.23393	0.345265
$327$	42.7819	2.36585
$328$	−5.33987	−0.294845
$329$	−1.65763	−0.0913881
$330$	0	0
$331$	−9.51019	−0.522727	−0.261364	−	0.965240i	$-0.584172\pi$
$331$	−9.51019	−0.522727	−0.261364	+	0.965240i	$0.584172\pi$
$332$	1.69190	0.0928549
$333$	35.6405	1.95309
$334$	1.09113	0.0597042
$335$	0	0
$336$	−3.23312	−0.176381
$337$	5.83881	0.318060	0.159030	−	0.987274i	$-0.449163\pi$
$337$	5.83881	0.318060	0.159030	+	0.987274i	$0.449163\pi$
$338$	−22.2390	−1.20964
$339$	−19.9346	−1.08270
$340$	0	0
$341$	34.6079	1.87412
$342$	−15.6051	−0.843829
$343$	−1.00000	−0.0539949
$344$	−16.7971	−0.905640
$345$	0	0
$346$	15.2893	0.821959
$347$	−30.2572	−1.62429	−0.812147	−	0.583453i	$-0.801701\pi$
$347$	−30.2572	−1.62429	−0.812147	+	0.583453i	$0.801701\pi$
$348$	20.8353	1.11689
$349$	−30.2823	−1.62097	−0.810486	−	0.585758i	$-0.800797\pi$
$349$	−30.2823	−1.62097	−0.810486	+	0.585758i	$0.800797\pi$
$350$	0	0
$351$	−8.23028	−0.439300
$352$	21.0262	1.12070
$353$	2.42599	0.129122	0.0645612	−	0.997914i	$-0.479435\pi$
$353$	2.42599	0.129122	0.0645612	+	0.997914i	$0.479435\pi$
$354$	−0.0271393	−0.00144244
$355$	0	0
$356$	10.1724	0.539134
$357$	−19.4810	−1.03104
$358$	−7.22073	−0.381628
$359$	−26.6909	−1.40869	−0.704345	−	0.709858i	$-0.748759\pi$
$359$	−26.6909	−1.40869	−0.704345	+	0.709858i	$0.748759\pi$
$360$	0	0
$361$	21.4401	1.12843
$362$	−0.644003	−0.0338480
$363$	5.11082	0.268248
$364$	−10.0410	−0.526290
$365$	0	0
$366$	−9.96916	−0.521096
$367$	11.3831	0.594192	0.297096	−	0.954848i	$-0.403982\pi$
$367$	11.3831	0.594192	0.297096	+	0.954848i	$0.403982\pi$
$368$	1.26969	0.0661870
$369$	−7.53870	−0.392449
$370$	0	0
$371$	1.34181	0.0696632
$372$	36.7484	1.90532
$373$	−19.6348	−1.01665	−0.508326	−	0.861165i	$-0.669736\pi$
$373$	−19.6348	−1.01665	−0.508326	+	0.861165i	$0.669736\pi$
$374$	19.4333	1.00487
$375$	0	0
$376$	4.09085	0.210969
$377$	36.3239	1.87078
$378$	0.868236	0.0446572
$379$	9.83437	0.505158	0.252579	−	0.967576i	$-0.418721\pi$
$379$	9.83437	0.505158	0.252579	+	0.967576i	$0.418721\pi$
$380$	0	0
$381$	−36.1248	−1.85073
$382$	−13.1891	−0.674814
$383$	−21.9906	−1.12367	−0.561835	−	0.827250i	$-0.689904\pi$
$383$	−21.9906	−1.12367	−0.561835	+	0.827250i	$0.689904\pi$
$384$	26.8811	1.37177
$385$	0	0
$386$	−5.42743	−0.276249
$387$	−23.7138	−1.20544
$388$	0.379363	0.0192592
$389$	−36.7058	−1.86106	−0.930530	−	0.366216i	$-0.880653\pi$
$389$	−36.7058	−1.86106	−0.930530	+	0.366216i	$0.880653\pi$
$390$	0	0
$391$	7.65043	0.386899
$392$	2.46789	0.124647
$393$	−30.5688	−1.54199
$394$	−2.20145	−0.110907
$395$	0	0
$396$	18.8978	0.949649
$397$	−4.48607	−0.225149	−0.112575	−	0.993643i	$-0.535910\pi$
$397$	−4.48607	−0.225149	−0.112575	+	0.993643i	$0.535910\pi$
$398$	−12.6511	−0.634144
$399$	−16.1931	−0.810671
$400$	0	0
$401$	13.2163	0.659993	0.329996	−	0.943982i	$-0.392953\pi$
$401$	13.2163	0.659993	0.329996	+	0.943982i	$0.392953\pi$
$402$	11.6790	0.582495
$403$	64.0666	3.19138
$404$	7.15041	0.355746
$405$	0	0
$406$	−3.83191	−0.190175
$407$	−36.8929	−1.82871
$408$	48.0769	2.38016
$409$	−4.11913	−0.203678	−0.101839	−	0.994801i	$-0.532473\pi$
$409$	−4.11913	−0.203678	−0.101839	+	0.994801i	$0.532473\pi$
$410$	0	0
$411$	−25.2990	−1.24791
$412$	26.4296	1.30209
$413$	−0.0151323	−0.000744611 0
$414$	−2.45393	−0.120604
$415$	0	0
$416$	38.9241	1.90841
$417$	4.18076	0.204733
$418$	16.1535	0.790092
$419$	14.2280	0.695082	0.347541	−	0.937665i	$-0.387017\pi$
$419$	14.2280	0.695082	0.347541	+	0.937665i	$0.387017\pi$
$420$	0	0
$421$	9.19185	0.447983	0.223992	−	0.974591i	$-0.428091\pi$
$421$	9.19185	0.447983	0.223992	+	0.974591i	$0.428091\pi$
$422$	−8.69476	−0.423254
$423$	5.77536	0.280808
$424$	−3.31143	−0.160817
$425$	0	0
$426$	20.2833	0.982729
$427$	−5.55858	−0.268998
$428$	17.1055	0.826824
$429$	61.3143	2.96028
$430$	0	0
$431$	29.8775	1.43915	0.719574	−	0.694416i	$-0.244337\pi$
$431$	29.8775	1.43915	0.719574	+	0.694416i	$0.244337\pi$
$432$	1.56518	0.0753048
$433$	−23.3211	−1.12074	−0.560370	−	0.828243i	$-0.689341\pi$
$433$	−23.3211	−1.12074	−0.560370	+	0.828243i	$0.689341\pi$
$434$	−6.75857	−0.324422
$435$	0	0
$436$	−25.2676	−1.21010
$437$	6.35925	0.304204
$438$	−4.44961	−0.212611
$439$	17.5959	0.839807	0.419904	−	0.907569i	$-0.362064\pi$
$439$	17.5959	0.839807	0.419904	+	0.907569i	$0.362064\pi$
$440$	0	0
$441$	3.48411	0.165910
$442$	35.9751	1.71116
$443$	−5.36299	−0.254803	−0.127402	−	0.991851i	$-0.540664\pi$
$443$	−5.36299	−0.254803	−0.127402	+	0.991851i	$0.540664\pi$
$444$	−39.1748	−1.85915
$445$	0	0
$446$	3.54510	0.167865
$447$	−11.5172	−0.544746
$448$	−1.56684	−0.0740262
$449$	14.6727	0.692449	0.346225	−	0.938152i	$-0.387463\pi$
$449$	14.6727	0.692449	0.346225	+	0.938152i	$0.387463\pi$
$450$	0	0
$451$	7.80360	0.367457
$452$	11.7736	0.553786
$453$	−17.1860	−0.807467
$454$	−9.54064	−0.447765
$455$	0	0
$456$	39.9629	1.87143
$457$	−3.24714	−0.151895	−0.0759473	−	0.997112i	$-0.524198\pi$
$457$	−3.24714	−0.151895	−0.0759473	+	0.997112i	$0.524198\pi$
$458$	−11.1227	−0.519728
$459$	9.43092	0.440198
$460$	0	0
$461$	36.2266	1.68724	0.843621	−	0.536939i	$-0.180420\pi$
$461$	36.2266	1.68724	0.843621	+	0.536939i	$0.180420\pi$
$462$	−6.46822	−0.300929
$463$	−37.2348	−1.73045	−0.865224	−	0.501385i	$-0.832824\pi$
$463$	−37.2348	−1.73045	−0.865224	+	0.501385i	$0.832824\pi$
$464$	−6.90784	−0.320688
$465$	0	0
$466$	0.606695	0.0281046
$467$	5.98939	0.277156	0.138578	−	0.990352i	$-0.455747\pi$
$467$	5.98939	0.277156	0.138578	+	0.990352i	$0.455747\pi$
$468$	34.9838	1.61713
$469$	6.51195	0.300694
$470$	0	0
$471$	−14.3697	−0.662121
$472$	0.0373448	0.00171893
$473$	24.5470	1.12867
$474$	17.6470	0.810551
$475$	0	0
$476$	11.5057	0.527365
$477$	−4.67500	−0.214054
$478$	−8.42862	−0.385516
$479$	6.69209	0.305770	0.152885	−	0.988244i	$-0.451144\pi$
$479$	6.69209	0.305770	0.152885	+	0.988244i	$0.451144\pi$
$480$	0	0
$481$	−68.2966	−3.11406
$482$	10.9375	0.498188
$483$	−2.54639	−0.115865
$484$	−3.01852	−0.137205
$485$	0	0
$486$	15.7209	0.713116
$487$	−43.8748	−1.98816	−0.994079	−	0.108659i	$-0.965344\pi$
$487$	−43.8748	−1.98816	−0.994079	+	0.108659i	$0.965344\pi$
$488$	13.7180	0.620983
$489$	−22.5381	−1.01921
$490$	0	0
$491$	−1.86242	−0.0840496	−0.0420248	−	0.999117i	$-0.513381\pi$
$491$	−1.86242	−0.0840496	−0.0420248	+	0.999117i	$0.513381\pi$
$492$	8.28627	0.373574
$493$	−41.6228	−1.87460
$494$	29.9035	1.34542
$495$	0	0
$496$	−12.1838	−0.547067
$497$	11.3095	0.507301
$498$	2.01762	0.0904118
$499$	−10.1578	−0.454724	−0.227362	−	0.973810i	$-0.573010\pi$
$499$	−10.1578	−0.454724	−0.227362	+	0.973810i	$0.573010\pi$
$500$	0	0
$501$	−3.94488	−0.176244
$502$	−3.16894	−0.141437
$503$	−7.11470	−0.317229	−0.158614	−	0.987341i	$-0.550703\pi$
$503$	−7.11470	−0.317229	−0.158614	+	0.987341i	$0.550703\pi$
$504$	−8.59839	−0.383003
$505$	0	0
$506$	2.54015	0.112923
$507$	80.4028	3.57081
$508$	21.3358	0.946623
$509$	−3.00834	−0.133342	−0.0666711	−	0.997775i	$-0.521238\pi$
$509$	−3.00834	−0.133342	−0.0666711	+	0.997775i	$0.521238\pi$
$510$	0	0
$511$	−2.48100	−0.109753
$512$	−13.6692	−0.604100
$513$	7.83925	0.346111
$514$	−11.3544	−0.500823
$515$	0	0
$516$	26.0653	1.14746
$517$	−5.97830	−0.262925
$518$	7.20480	0.316561
$519$	−55.2769	−2.42639
$520$	0	0
$521$	8.03532	0.352034	0.176017	−	0.984387i	$-0.443679\pi$
$521$	8.03532	0.352034	0.176017	+	0.984387i	$0.443679\pi$
$522$	13.3508	0.584348
$523$	30.8276	1.34800	0.673999	−	0.738732i	$-0.264575\pi$
$523$	30.8276	1.34800	0.673999	+	0.738732i	$0.264575\pi$
$524$	18.0543	0.788707
$525$	0	0
$526$	16.4171	0.715819
$527$	−73.4127	−3.19791
$528$	−11.6604	−0.507452
$529$	1.00000	0.0434783
$530$	0	0
$531$	0.0527225	0.00228796
$532$	9.56390	0.414648
$533$	14.4461	0.625731
$534$	12.1308	0.524949
$535$	0	0
$536$	−16.0708	−0.694151
$537$	26.1058	1.12655
$538$	9.90700	0.427121
$539$	−3.60653	−0.155344
$540$	0	0
$541$	−18.3413	−0.788554	−0.394277	−	0.918992i	$-0.629005\pi$
$541$	−18.3413	−0.788554	−0.394277	+	0.918992i	$0.629005\pi$
$542$	13.3940	0.575321
$543$	2.32832	0.0999179
$544$	−44.6024	−1.91231
$545$	0	0
$546$	−11.9741	−0.512442
$547$	36.1998	1.54779	0.773896	−	0.633313i	$-0.218305\pi$
$547$	36.1998	1.54779	0.773896	+	0.633313i	$0.218305\pi$
$548$	14.9419	0.638288
$549$	19.3667	0.826550
$550$	0	0
$551$	−34.5981	−1.47393
$552$	6.28421	0.267474
$553$	9.83954	0.418420
$554$	−3.42520	−0.145523
$555$	0	0
$556$	−2.46922	−0.104718
$557$	−9.36475	−0.396797	−0.198399	−	0.980121i	$-0.563574\pi$
$557$	−9.36475	−0.396797	−0.198399	+	0.980121i	$0.563574\pi$
$558$	23.5476	0.996849
$559$	45.4418	1.92198
$560$	0	0
$561$	−70.2589	−2.96633
$562$	−9.42148	−0.397421
$563$	25.0569	1.05602	0.528012	−	0.849237i	$-0.322938\pi$
$563$	25.0569	1.05602	0.528012	+	0.849237i	$0.322938\pi$
$564$	−6.34807	−0.267302
$565$	0	0
$566$	−7.13765	−0.300018
$567$	7.31331	0.307130
$568$	−27.9106	−1.17110
$569$	−4.19840	−0.176006	−0.0880030	−	0.996120i	$-0.528048\pi$
$569$	−4.19840	−0.176006	−0.0880030	+	0.996120i	$0.528048\pi$
$570$	0	0
$571$	−12.0929	−0.506071	−0.253036	−	0.967457i	$-0.581429\pi$
$571$	−12.0929	−0.506071	−0.253036	+	0.967457i	$0.581429\pi$
$572$	−36.2131	−1.51414
$573$	47.6838	1.99202
$574$	−1.52396	−0.0636090
$575$	0	0
$576$	5.45904	0.227460
$577$	39.9889	1.66476	0.832380	−	0.554205i	$-0.186978\pi$
$577$	39.9889	1.66476	0.832380	+	0.554205i	$0.186978\pi$
$578$	−29.2498	−1.21663
$579$	19.6223	0.815474
$580$	0	0
$581$	1.12498	0.0466721
$582$	0.452398	0.0187525
$583$	4.83927	0.200422
$584$	6.12284	0.253365
$585$	0	0
$586$	−17.8435	−0.737108
$587$	40.3927	1.66719	0.833593	−	0.552380i	$-0.186280\pi$
$587$	40.3927	1.66719	0.833593	+	0.552380i	$0.186280\pi$
$588$	−3.82961	−0.157930
$589$	−61.0227	−2.51440
$590$	0	0
$591$	7.95910	0.327394
$592$	12.9882	0.533812
$593$	−8.92481	−0.366498	−0.183249	−	0.983067i	$-0.558661\pi$
$593$	−8.92481	−0.366498	−0.183249	+	0.983067i	$0.558661\pi$
$594$	3.13132	0.128480
$595$	0	0
$596$	6.80224	0.278631
$597$	45.7388	1.87196
$598$	4.70236	0.192294
$599$	38.7005	1.58126	0.790630	−	0.612294i	$-0.209753\pi$
$599$	38.7005	1.58126	0.790630	+	0.612294i	$0.209753\pi$
$600$	0	0
$601$	19.6019	0.799578	0.399789	−	0.916607i	$-0.369083\pi$
$601$	19.6019	0.799578	0.399789	+	0.916607i	$0.369083\pi$
$602$	−4.79379	−0.195380
$603$	−22.6883	−0.923940
$604$	10.1503	0.413009
$605$	0	0
$606$	8.52701	0.346386
$607$	25.4201	1.03177	0.515886	−	0.856657i	$-0.327463\pi$
$607$	25.4201	1.03177	0.515886	+	0.856657i	$0.327463\pi$
$608$	−37.0747	−1.50358
$609$	13.8539	0.561387
$610$	0	0
$611$	−11.0671	−0.447727
$612$	−40.0873	−1.62043
$613$	−5.45085	−0.220158	−0.110079	−	0.993923i	$-0.535110\pi$
$613$	−5.45085	−0.220158	−0.110079	+	0.993923i	$0.535110\pi$
$614$	18.2444	0.736284
$615$	0	0
$616$	8.90052	0.358612
$617$	−38.4796	−1.54913	−0.774565	−	0.632494i	$-0.782031\pi$
$617$	−38.4796	−1.54913	−0.774565	+	0.632494i	$0.782031\pi$
$618$	31.5179	1.26783
$619$	2.21907	0.0891921	0.0445960	−	0.999005i	$-0.485800\pi$
$619$	2.21907	0.0891921	0.0445960	+	0.999005i	$0.485800\pi$
$620$	0	0
$621$	1.23273	0.0494678
$622$	−20.7729	−0.832918
$623$	6.76383	0.270987
$624$	−21.5858	−0.864124
$625$	0	0
$626$	−20.5023	−0.819439
$627$	−58.4011	−2.33232
$628$	8.48695	0.338666
$629$	78.2597	3.12042
$630$	0	0
$631$	−23.7455	−0.945295	−0.472647	−	0.881252i	$-0.656702\pi$
$631$	−23.7455	−0.945295	−0.472647	+	0.881252i	$0.656702\pi$
$632$	−24.2829	−0.965922
$633$	31.4350	1.24943
$634$	14.5350	0.577260
$635$	0	0
$636$	5.13859	0.203758
$637$	−6.67646	−0.264531
$638$	−13.8199	−0.547136
$639$	−39.4036	−1.55878
$640$	0	0
$641$	−7.59727	−0.300074	−0.150037	−	0.988680i	$-0.547939\pi$
$641$	−7.59727	−0.300074	−0.150037	+	0.988680i	$0.547939\pi$
$642$	20.3986	0.805069
$643$	−38.8882	−1.53360	−0.766801	−	0.641885i	$-0.778153\pi$
$643$	−38.8882	−1.53360	−0.766801	+	0.641885i	$0.778153\pi$
$644$	1.50393	0.0592633
$645$	0	0
$646$	−34.2659	−1.34817
$647$	−20.0464	−0.788106	−0.394053	−	0.919088i	$-0.628927\pi$
$647$	−20.0464	−0.788106	−0.394053	+	0.919088i	$0.628927\pi$
$648$	−18.0484	−0.709010
$649$	−0.0545751	−0.00214226
$650$	0	0
$651$	24.4349	0.957678
$652$	13.3113	0.521311
$653$	−20.2141	−0.791040	−0.395520	−	0.918457i	$-0.629436\pi$
$653$	−20.2141	−0.791040	−0.395520	+	0.918457i	$0.629436\pi$
$654$	−30.1321	−1.17826
$655$	0	0
$656$	−2.74727	−0.107263
$657$	8.64409	0.337238
$658$	1.16750	0.0455139
$659$	31.7062	1.23510	0.617548	−	0.786533i	$-0.288126\pi$
$659$	31.7062	1.23510	0.617548	+	0.786533i	$0.288126\pi$
$660$	0	0
$661$	−25.9055	−1.00761	−0.503804	−	0.863818i	$-0.668066\pi$
$661$	−25.9055	−1.00761	−0.503804	+	0.863818i	$0.668066\pi$
$662$	6.69821	0.260333
$663$	−130.064	−5.05127
$664$	−2.77633	−0.107742
$665$	0	0
$666$	−25.1023	−0.972695
$667$	−5.44059	−0.210660
$668$	2.32990	0.0901465
$669$	−12.8169	−0.495531
$670$	0	0
$671$	−20.0472	−0.773913
$672$	14.8456	0.572680
$673$	44.6516	1.72119	0.860596	−	0.509289i	$-0.170091\pi$
$673$	44.6516	1.72119	0.860596	+	0.509289i	$0.170091\pi$
$674$	−4.11239	−0.158403
$675$	0	0
$676$	−47.4870	−1.82642
$677$	49.7551	1.91224	0.956122	−	0.292970i	$-0.0946437\pi$
$677$	49.7551	1.91224	0.956122	+	0.292970i	$0.0946437\pi$
$678$	14.0403	0.539215
$679$	0.252247	0.00968035
$680$	0	0
$681$	34.4932	1.32178
$682$	−24.3750	−0.933367
$683$	−14.8109	−0.566725	−0.283362	−	0.959013i	$-0.591450\pi$
$683$	−14.8109	−0.566725	−0.283362	+	0.959013i	$0.591450\pi$
$684$	−33.3217	−1.27409
$685$	0	0
$686$	0.704319	0.0268910
$687$	40.2128	1.53422
$688$	−8.64183	−0.329467
$689$	8.95853	0.341293
$690$	0	0
$691$	−22.1547	−0.842803	−0.421402	−	0.906874i	$-0.638462\pi$
$691$	−22.1547	−0.842803	−0.421402	+	0.906874i	$0.638462\pi$
$692$	32.6473	1.24107
$693$	12.5656	0.477326
$694$	21.3108	0.808945
$695$	0	0
$696$	−34.1898	−1.29596
$697$	−16.5535	−0.627010
$698$	21.3284	0.807291
$699$	−2.19344	−0.0829635
$700$	0	0
$701$	3.06173	0.115640	0.0578199	−	0.998327i	$-0.481585\pi$
$701$	3.06173	0.115640	0.0578199	+	0.998327i	$0.481585\pi$
$702$	5.79675	0.218784
$703$	65.0517	2.45347
$704$	−5.65085	−0.212975
$705$	0	0
$706$	−1.70867	−0.0643067
$707$	4.75447	0.178810
$708$	−0.0579506	−0.00217792
$709$	−43.5926	−1.63715	−0.818576	−	0.574398i	$-0.805236\pi$
$709$	−43.5926	−1.63715	−0.818576	+	0.574398i	$0.805236\pi$
$710$	0	0
$711$	−34.2820	−1.28568
$712$	−16.6924	−0.625574
$713$	−9.59588	−0.359369
$714$	13.7208	0.513490
$715$	0	0
$716$	−15.4184	−0.576214
$717$	30.4728	1.13803
$718$	18.7989	0.701569
$719$	−41.8811	−1.56190	−0.780952	−	0.624592i	$-0.785265\pi$
$719$	−41.8811	−1.56190	−0.780952	+	0.624592i	$0.785265\pi$
$720$	0	0
$721$	17.5736	0.654477
$722$	−15.1007	−0.561989
$723$	−39.5433	−1.47063
$724$	−1.37514	−0.0511067
$725$	0	0
$726$	−3.59965	−0.133595
$727$	15.2902	0.567081	0.283540	−	0.958960i	$-0.408491\pi$
$727$	15.2902	0.567081	0.283540	+	0.958960i	$0.408491\pi$
$728$	16.4768	0.610670
$729$	−34.8974	−1.29250
$730$	0	0
$731$	−52.0709	−1.92591
$732$	−21.2872	−0.786796
$733$	−19.5230	−0.721098	−0.360549	−	0.932740i	$-0.617411\pi$
$733$	−19.5230	−0.721098	−0.360549	+	0.932740i	$0.617411\pi$
$734$	−8.01733	−0.295925
$735$	0	0
$736$	−5.83004	−0.214898
$737$	23.4855	0.865101
$738$	5.30966	0.195451
$739$	34.1762	1.25719	0.628596	−	0.777732i	$-0.283630\pi$
$739$	34.1762	1.25719	0.628596	+	0.777732i	$0.283630\pi$
$740$	0	0
$741$	−108.113	−3.97163
$742$	−0.945061	−0.0346943
$743$	7.49887	0.275107	0.137553	−	0.990494i	$-0.456076\pi$
$743$	7.49887	0.275107	0.137553	+	0.990494i	$0.456076\pi$
$744$	−60.3026	−2.21080
$745$	0	0
$746$	13.8292	0.506322
$747$	−3.91956	−0.143409
$748$	41.4959	1.51724
$749$	11.3738	0.415590
$750$	0	0
$751$	−23.4336	−0.855103	−0.427551	−	0.903991i	$-0.640624\pi$
$751$	−23.4336	−0.855103	−0.427551	+	0.903991i	$0.640624\pi$
$752$	2.10467	0.0767495
$753$	11.4569	0.417514
$754$	−25.5836	−0.931700
$755$	0	0
$756$	1.85395	0.0674274
$757$	35.5807	1.29320	0.646600	−	0.762829i	$-0.276190\pi$
$757$	35.5807	1.29320	0.646600	+	0.762829i	$0.276190\pi$
$758$	−6.92654	−0.251583
$759$	−9.18364	−0.333345
$760$	0	0
$761$	40.3739	1.46355	0.731775	−	0.681546i	$-0.238692\pi$
$761$	40.3739	1.46355	0.731775	+	0.681546i	$0.238692\pi$
$762$	25.4434	0.921716
$763$	−16.8010	−0.608237
$764$	−28.1627	−1.01889
$765$	0	0
$766$	15.4884	0.559620
$767$	−0.101030	−0.00364799
$768$	−26.9124	−0.971118
$769$	7.28477	0.262695	0.131348	−	0.991336i	$-0.458070\pi$
$769$	7.28477	0.262695	0.131348	+	0.991336i	$0.458070\pi$
$770$	0	0
$771$	41.0508	1.47841
$772$	−11.5892	−0.417104
$773$	−1.08246	−0.0389335	−0.0194667	−	0.999811i	$-0.506197\pi$
$773$	−1.08246	−0.0389335	−0.0194667	+	0.999811i	$0.506197\pi$
$774$	16.7021	0.600344
$775$	0	0
$776$	−0.622518	−0.0223471
$777$	−26.0482	−0.934474
$778$	25.8526	0.926862
$779$	−13.7598	−0.492995
$780$	0	0
$781$	40.7881	1.45951
$782$	−5.38835	−0.192687
$783$	−6.70678	−0.239681
$784$	1.26969	0.0453460
$785$	0	0
$786$	21.5302	0.767956
$787$	−22.9348	−0.817538	−0.408769	−	0.912638i	$-0.634042\pi$
$787$	−22.9348	−0.817538	−0.408769	+	0.912638i	$0.634042\pi$
$788$	−4.70076	−0.167457
$789$	−59.3542	−2.11306
$790$	0	0
$791$	7.82857	0.278352
$792$	−31.0104	−1.10191
$793$	−37.1117	−1.31787
$794$	3.15963	0.112131
$795$	0	0
$796$	−27.0140	−0.957485
$797$	49.7826	1.76339	0.881694	−	0.471821i	$-0.156403\pi$
$797$	49.7826	1.76339	0.881694	+	0.471821i	$0.156403\pi$
$798$	11.4051	0.403738
$799$	12.6816	0.448642
$800$	0	0
$801$	−23.5659	−0.832661
$802$	−9.30852	−0.328695
$803$	−8.94783	−0.315762
$804$	24.9382	0.879502
$805$	0	0
$806$	−45.1233	−1.58940
$807$	−35.8177	−1.26084
$808$	−11.7335	−0.412783
$809$	17.7411	0.623743	0.311872	−	0.950124i	$-0.399044\pi$
$809$	17.7411	0.623743	0.311872	+	0.950124i	$0.399044\pi$
$810$	0	0
$811$	15.3166	0.537838	0.268919	−	0.963163i	$-0.413334\pi$
$811$	15.3166	0.537838	0.268919	+	0.963163i	$0.413334\pi$
$812$	−8.18228	−0.287142
$813$	−48.4245	−1.69832
$814$	25.9844	0.910751
$815$	0	0
$816$	24.7348	0.865890
$817$	−43.2828	−1.51427
$818$	2.90118	0.101437
$819$	23.2615	0.812824
$820$	0	0
$821$	−7.58010	−0.264547	−0.132274	−	0.991213i	$-0.542228\pi$
$821$	−7.58010	−0.264547	−0.132274	+	0.991213i	$0.542228\pi$
$822$	17.8186	0.621494
$823$	−18.7887	−0.654931	−0.327466	−	0.944863i	$-0.606195\pi$
$823$	−18.7887	−0.654931	−0.327466	+	0.944863i	$0.606195\pi$
$824$	−43.3698	−1.51086
$825$	0	0
$826$	0.0106580	0.000370838 0
$827$	1.21277	0.0421720	0.0210860	−	0.999778i	$-0.493288\pi$
$827$	1.21277	0.0421720	0.0210860	+	0.999778i	$0.493288\pi$
$828$	−5.23987	−0.182098
$829$	−2.68231	−0.0931606	−0.0465803	−	0.998915i	$-0.514832\pi$
$829$	−2.68231	−0.0931606	−0.0465803	+	0.998915i	$0.514832\pi$
$830$	0	0
$831$	12.3834	0.429577
$832$	−10.4609	−0.362668
$833$	7.65043	0.265072
$834$	−2.94459	−0.101963
$835$	0	0
$836$	34.4925	1.19295
$837$	−11.8291	−0.408875
$838$	−10.0210	−0.346171
$839$	16.1458	0.557416	0.278708	−	0.960376i	$-0.410094\pi$
$839$	16.1458	0.557416	0.278708	+	0.960376i	$0.410094\pi$
$840$	0	0
$841$	0.599976	0.0206888
$842$	−6.47400	−0.223109
$843$	34.0623	1.17317
$844$	−18.5659	−0.639066
$845$	0	0
$846$	−4.06770	−0.139850
$847$	−2.00708	−0.0689642
$848$	−1.70368	−0.0585044
$849$	25.8054	0.885640
$850$	0	0
$851$	10.2295	0.350661
$852$	43.3109	1.48381
$853$	−28.8563	−0.988020	−0.494010	−	0.869456i	$-0.664469\pi$
$853$	−28.8563	−0.988020	−0.494010	+	0.869456i	$0.664469\pi$
$854$	3.91501	0.133969
$855$	0	0
$856$	−28.0693	−0.959389
$857$	−23.3528	−0.797717	−0.398859	−	0.917012i	$-0.630594\pi$
$857$	−23.3528	−0.797717	−0.398859	+	0.917012i	$0.630594\pi$
$858$	−43.1848	−1.47431
$859$	28.8901	0.985718	0.492859	−	0.870109i	$-0.335952\pi$
$859$	28.8901	0.985718	0.492859	+	0.870109i	$0.335952\pi$
$860$	0	0
$861$	5.50973	0.187771
$862$	−21.0433	−0.716737
$863$	45.8189	1.55969	0.779847	−	0.625971i	$-0.215297\pi$
$863$	45.8189	1.55969	0.779847	+	0.625971i	$0.215297\pi$
$864$	−7.18687	−0.244502
$865$	0	0
$866$	16.4255	0.558161
$867$	105.749	3.59144
$868$	−14.4316	−0.489840
$869$	35.4866	1.20380
$870$	0	0
$871$	43.4768	1.47315
$872$	41.4630	1.40411
$873$	−0.878856	−0.0297448
$874$	−4.47895	−0.151503
$875$	0	0
$876$	−9.50127	−0.321018
$877$	11.5550	0.390186	0.195093	−	0.980785i	$-0.437499\pi$
$877$	11.5550	0.390186	0.195093	+	0.980785i	$0.437499\pi$
$878$	−12.3931	−0.418248
$879$	64.5113	2.17591
$880$	0	0
$881$	−39.5720	−1.33322	−0.666608	−	0.745409i	$-0.732254\pi$
$881$	−39.5720	−1.33322	−0.666608	+	0.745409i	$0.732254\pi$
$882$	−2.45393	−0.0826280
$883$	−9.27133	−0.312005	−0.156003	−	0.987757i	$-0.549861\pi$
$883$	−9.27133	−0.312005	−0.156003	+	0.987757i	$0.549861\pi$
$884$	76.8177	2.58366
$885$	0	0
$886$	3.77726	0.126900
$887$	41.0868	1.37956	0.689780	−	0.724019i	$-0.257707\pi$
$887$	41.0868	1.37956	0.689780	+	0.724019i	$0.257707\pi$
$888$	64.2840	2.15723
$889$	14.1867	0.475805
$890$	0	0
$891$	26.3757	0.883619
$892$	7.56985	0.253457
$893$	10.5413	0.352751
$894$	8.11181	0.271300
$895$	0	0
$896$	−10.5565	−0.352669
$897$	−17.0009	−0.567643
$898$	−10.3343	−0.344860
$899$	52.2072	1.74121
$900$	0	0
$901$	−10.2654	−0.341990
$902$	−5.49623	−0.183004
$903$	17.3314	0.576754
$904$	−19.3200	−0.642575
$905$	0	0
$906$	12.1044	0.402142
$907$	−31.5822	−1.04867	−0.524335	−	0.851512i	$-0.675686\pi$
$907$	−31.5822	−1.04867	−0.524335	+	0.851512i	$0.675686\pi$
$908$	−20.3722	−0.676074
$909$	−16.5651	−0.549429
$910$	0	0
$911$	−21.1977	−0.702313	−0.351156	−	0.936317i	$-0.614211\pi$
$911$	−21.1977	−0.702313	−0.351156	+	0.936317i	$0.614211\pi$
$912$	20.5602	0.680817
$913$	4.05728	0.134276
$914$	2.28702	0.0756479
$915$	0	0
$916$	−23.7503	−0.784731
$917$	12.0047	0.396431
$918$	−6.64238	−0.219231
$919$	17.8883	0.590080	0.295040	−	0.955485i	$-0.404667\pi$
$919$	17.8883	0.590080	0.295040	+	0.955485i	$0.404667\pi$
$920$	0	0
$921$	−65.9607	−2.17348
$922$	−25.5151	−0.840295
$923$	75.5075	2.48536
$924$	−13.8116	−0.454368
$925$	0	0
$926$	26.2252	0.861813
$927$	−61.2285	−2.01101
$928$	31.7188	1.04122
$929$	44.5231	1.46076	0.730378	−	0.683043i	$-0.239344\pi$
$929$	44.5231	1.46076	0.730378	+	0.683043i	$0.239344\pi$
$930$	0	0
$931$	6.35925	0.208416
$932$	1.29548	0.0424348
$933$	75.1023	2.45874
$934$	−4.21844	−0.138032
$935$	0	0
$936$	−57.4069	−1.87640
$937$	24.2044	0.790722	0.395361	−	0.918526i	$-0.370620\pi$
$937$	24.2044	0.790722	0.395361	+	0.918526i	$0.370620\pi$
$938$	−4.58649	−0.149754
$939$	74.1240	2.41895
$940$	0	0
$941$	41.5019	1.35292	0.676461	−	0.736478i	$-0.263513\pi$
$941$	41.5019	1.35292	0.676461	+	0.736478i	$0.263513\pi$
$942$	10.1209	0.329755
$943$	−2.16374	−0.0704611
$944$	0.0192132	0.000625338 0
$945$	0	0
$946$	−17.2890	−0.562112
$947$	−5.43234	−0.176527	−0.0882636	−	0.996097i	$-0.528132\pi$
$947$	−5.43234	−0.176527	−0.0882636	+	0.996097i	$0.528132\pi$
$948$	37.6816	1.22384
$949$	−16.5643	−0.537701
$950$	0	0
$951$	−52.5499	−1.70405
$952$	−18.8804	−0.611918
$953$	2.28832	0.0741260	0.0370630	−	0.999313i	$-0.488200\pi$
$953$	2.28832	0.0741260	0.0370630	+	0.999313i	$0.488200\pi$
$954$	3.29270	0.106605
$955$	0	0
$956$	−17.9977	−0.582086
$957$	49.9644	1.61512
$958$	−4.71337	−0.152282
$959$	9.93523	0.320825
$960$	0	0
$961$	61.0810	1.97035
$962$	48.1026	1.55089
$963$	−39.6276	−1.27698
$964$	23.3548	0.752207
$965$	0	0
$966$	1.79347	0.0577040
$967$	−8.94796	−0.287747	−0.143873	−	0.989596i	$-0.545956\pi$
$967$	−8.94796	−0.287747	−0.143873	+	0.989596i	$0.545956\pi$
$968$	4.95325	0.159204
$969$	123.885	3.97975
$970$	0	0
$971$	14.6730	0.470878	0.235439	−	0.971889i	$-0.424347\pi$
$971$	14.6730	0.470878	0.235439	+	0.971889i	$0.424347\pi$
$972$	33.5689	1.07672
$973$	−1.64184	−0.0526349
$974$	30.9019	0.990160
$975$	0	0
$976$	7.05765	0.225910
$977$	3.87938	0.124112	0.0620562	−	0.998073i	$-0.480234\pi$
$977$	3.87938	0.124112	0.0620562	+	0.998073i	$0.480234\pi$
$978$	15.8740	0.507595
$979$	24.3940	0.779635
$980$	0	0
$981$	58.5365	1.86893
$982$	1.31174	0.0418591
$983$	−26.5731	−0.847550	−0.423775	−	0.905767i	$-0.639295\pi$
$983$	−26.5731	−0.847550	−0.423775	+	0.905767i	$0.639295\pi$
$984$	−13.5974	−0.433469
$985$	0	0
$986$	29.3158	0.933604
$987$	−4.22098	−0.134355
$988$	63.8530	2.03144
$989$	−6.80627	−0.216427
$990$	0	0
$991$	53.4073	1.69654	0.848269	−	0.529566i	$-0.177645\pi$
$991$	53.4073	1.69654	0.848269	+	0.529566i	$0.177645\pi$
$992$	55.9444	1.77624
$993$	−24.2167	−0.768492
$994$	−7.96550	−0.252650
$995$	0	0
$996$	4.30823	0.136512
$997$	−49.3362	−1.56249	−0.781247	−	0.624222i	$-0.785416\pi$
$997$	−49.3362	−1.56249	−0.781247	+	0.624222i	$0.785416\pi$
$998$	7.15431	0.226466
$999$	12.6102	0.398968

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4025.2.a.ba.1.6	✓	14
5.4	even	2		4025.2.a.bb.1.9	yes	14

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4025.2.a.ba.1.6	✓	14	1.1	even	1	trivial
4025.2.a.bb.1.9	yes	14	5.4	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 4025 = 5^{2} \cdot 7 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4025.a (trivial)

\(f(q)\)	\(=\)	\(q-0.704319 q^{2} +2.54639 q^{3} -1.50393 q^{4} -1.79347 q^{6} -1.00000 q^{7} +2.46789 q^{8} +3.48411 q^{9} +O(q^{10})\)	\(q-0.704319 q^{2} +2.54639 q^{3} -1.50393 q^{4} -1.79347 q^{6} -1.00000 q^{7} +2.46789 q^{8} +3.48411 q^{9} -3.60653 q^{11} -3.82961 q^{12} -6.67646 q^{13} +0.704319 q^{14} +1.26969 q^{16} +7.65043 q^{17} -2.45393 q^{18} +6.35925 q^{19} -2.54639 q^{21} +2.54015 q^{22} +1.00000 q^{23} +6.28421 q^{24} +4.70236 q^{26} +1.23273 q^{27} +1.50393 q^{28} -5.44059 q^{29} -9.59588 q^{31} -5.83004 q^{32} -9.18364 q^{33} -5.38835 q^{34} -5.23987 q^{36} +10.2295 q^{37} -4.47895 q^{38} -17.0009 q^{39} -2.16374 q^{41} +1.79347 q^{42} -6.80627 q^{43} +5.42399 q^{44} -0.704319 q^{46} +1.65763 q^{47} +3.23312 q^{48} +1.00000 q^{49} +19.4810 q^{51} +10.0410 q^{52} -1.34181 q^{53} -0.868236 q^{54} -2.46789 q^{56} +16.1931 q^{57} +3.83191 q^{58} +0.0151323 q^{59} +5.55858 q^{61} +6.75857 q^{62} -3.48411 q^{63} +1.56684 q^{64} +6.46822 q^{66} -6.51195 q^{67} -11.5057 q^{68} +2.54639 q^{69} -11.3095 q^{71} +8.59839 q^{72} +2.48100 q^{73} -7.20480 q^{74} -9.56390 q^{76} +3.60653 q^{77} +11.9741 q^{78} -9.83954 q^{79} -7.31331 q^{81} +1.52396 q^{82} -1.12498 q^{83} +3.82961 q^{84} +4.79379 q^{86} -13.8539 q^{87} -8.90052 q^{88} -6.76383 q^{89} +6.67646 q^{91} -1.50393 q^{92} -24.4349 q^{93} -1.16750 q^{94} -14.8456 q^{96} -0.252247 q^{97} -0.704319 q^{98} -12.5656 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 14 q - q^{2} - 6 q^{3} + 17 q^{4} - 4 q^{6} - 14 q^{7} - 9 q^{8} + 18 q^{9}+O(q^{10}) \) 14 * q - q^2 - 6 * q^3 + 17 * q^4 - 4 * q^6 - 14 * q^7 - 9 * q^8 + 18 * q^9	\( 14 q - q^{2} - 6 q^{3} + 17 q^{4} - 4 q^{6} - 14 q^{7} - 9 q^{8} + 18 q^{9} - 3 q^{11} - 11 q^{12} - 15 q^{13} + q^{14} + 23 q^{16} - 9 q^{17} - 17 q^{18} - 4 q^{19} + 6 q^{21} - 9 q^{22} + 14 q^{23} + 10 q^{24} - 5 q^{26} - 33 q^{27} - 17 q^{28} + 11 q^{29} - q^{31} - 24 q^{32} - 26 q^{33} - 6 q^{34} + 13 q^{36} - 18 q^{37} + 6 q^{38} + 6 q^{39} - 7 q^{41} + 4 q^{42} - 18 q^{43} - 16 q^{44} - q^{46} - 10 q^{47} - 40 q^{48} + 14 q^{49} + 28 q^{51} - 46 q^{52} - 5 q^{53} - 24 q^{54} + 9 q^{56} + 26 q^{57} - 2 q^{58} - 24 q^{59} - 6 q^{61} + 16 q^{62} - 18 q^{63} + 29 q^{64} + 27 q^{66} - 61 q^{67} - 35 q^{68} - 6 q^{69} + 11 q^{71} - 12 q^{72} - 28 q^{73} - 49 q^{74} - 27 q^{76} + 3 q^{77} - 38 q^{78} + 6 q^{79} + 26 q^{81} + 14 q^{82} - 16 q^{83} + 11 q^{84} + 46 q^{86} - 61 q^{87} - 58 q^{88} - 39 q^{89} + 15 q^{91} + 17 q^{92} - 21 q^{93} - 74 q^{94} + 41 q^{96} - 19 q^{97} - q^{98} - 9 q^{99}+O(q^{100}) \) 14 * q - q^2 - 6 * q^3 + 17 * q^4 - 4 * q^6 - 14 * q^7 - 9 * q^8 + 18 * q^9 - 3 * q^11 - 11 * q^12 - 15 * q^13 + q^14 + 23 * q^16 - 9 * q^17 - 17 * q^18 - 4 * q^19 + 6 * q^21 - 9 * q^22 + 14 * q^23 + 10 * q^24 - 5 * q^26 - 33 * q^27 - 17 * q^28 + 11 * q^29 - q^31 - 24 * q^32 - 26 * q^33 - 6 * q^34 + 13 * q^36 - 18 * q^37 + 6 * q^38 + 6 * q^39 - 7 * q^41 + 4 * q^42 - 18 * q^43 - 16 * q^44 - q^46 - 10 * q^47 - 40 * q^48 + 14 * q^49 + 28 * q^51 - 46 * q^52 - 5 * q^53 - 24 * q^54 + 9 * q^56 + 26 * q^57 - 2 * q^58 - 24 * q^59 - 6 * q^61 + 16 * q^62 - 18 * q^63 + 29 * q^64 + 27 * q^66 - 61 * q^67 - 35 * q^68 - 6 * q^69 + 11 * q^71 - 12 * q^72 - 28 * q^73 - 49 * q^74 - 27 * q^76 + 3 * q^77 - 38 * q^78 + 6 * q^79 + 26 * q^81 + 14 * q^82 - 16 * q^83 + 11 * q^84 + 46 * q^86 - 61 * q^87 - 58 * q^88 - 39 * q^89 + 15 * q^91 + 17 * q^92 - 21 * q^93 - 74 * q^94 + 41 * q^96 - 19 * q^97 - q^98 - 9 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more