LMFDB - Embedded newform 5225.2.a.j.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [5225,2,Mod(1,5225)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(5225, 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("5225.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 5225 = 5^{2} \cdot 11 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	5225.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:	$41.7218350561$
Analytic rank:	$0$
Dimension:	$5$
Coefficient field:	$\Q(\zeta_{22})^+$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{5} - x^{4} - 4x^{3} + 3x^{2} + 3x - 1 $ x^5 - x^4 - 4x^3 + 3x^2 + 3*x - 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 1045)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$0.284630$ of defining polynomial
Character	$\chi$	$=$	5225.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.22871 q^{2} +1.47889 q^{3} +2.96714 q^{4} -3.29602 q^{6} +4.42518 q^{7} -2.15546 q^{8} -0.812880 q^{9} +O(q^{10})$	\(q-2.22871 q^{2} +1.47889 q^{3} +2.96714 q^{4} -3.29602 q^{6} +4.42518 q^{7} -2.15546 q^{8} -0.812880 q^{9} -1.00000 q^{11} +4.38807 q^{12} +3.92613 q^{13} -9.86243 q^{14} -1.13037 q^{16} +1.61520 q^{17} +1.81167 q^{18} +1.00000 q^{19} +6.54436 q^{21} +2.22871 q^{22} -0.113248 q^{23} -3.18770 q^{24} -8.75019 q^{26} -5.63884 q^{27} +13.1301 q^{28} +1.08612 q^{29} -4.17296 q^{31} +6.83020 q^{32} -1.47889 q^{33} -3.59980 q^{34} -2.41193 q^{36} +5.75406 q^{37} -2.22871 q^{38} +5.80632 q^{39} +4.26750 q^{41} -14.5855 q^{42} -3.62271 q^{43} -2.96714 q^{44} +0.252396 q^{46} +6.39567 q^{47} -1.67170 q^{48} +12.5822 q^{49} +2.38870 q^{51} +11.6494 q^{52} -12.0154 q^{53} +12.5673 q^{54} -9.53832 q^{56} +1.47889 q^{57} -2.42065 q^{58} +0.883911 q^{59} +3.77712 q^{61} +9.30032 q^{62} -3.59714 q^{63} -12.9618 q^{64} +3.29602 q^{66} +12.2192 q^{67} +4.79251 q^{68} -0.167481 q^{69} +4.28400 q^{71} +1.75213 q^{72} +1.92676 q^{73} -12.8241 q^{74} +2.96714 q^{76} -4.42518 q^{77} -12.9406 q^{78} -7.81004 q^{79} -5.90059 q^{81} -9.51102 q^{82} +3.33410 q^{83} +19.4180 q^{84} +8.07397 q^{86} +1.60626 q^{87} +2.15546 q^{88} -11.9145 q^{89} +17.3738 q^{91} -0.336021 q^{92} -6.17136 q^{93} -14.2541 q^{94} +10.1011 q^{96} +13.3478 q^{97} -28.0421 q^{98} +0.812880 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 5 q + 3 q^{2} + 7 q^{3} + 5 q^{4} + 2 q^{6} + 11 q^{7} - 3 q^{8} + 8 q^{9}+O(q^{10}) $ 5 * q + 3 * q^2 + 7 * q^3 + 5 * q^4 + 2 * q^6 + 11 * q^7 - 3 * q^8 + 8 * q^9	$ 5 q + 3 q^{2} + 7 q^{3} + 5 q^{4} + 2 q^{6} + 11 q^{7} - 3 q^{8} + 8 q^{9} - 5 q^{11} + 7 q^{12} - q^{13} - 3 q^{16} + 3 q^{17} + 7 q^{18} + 5 q^{19} + 11 q^{21} - 3 q^{22} + 8 q^{23} + 9 q^{24} - 16 q^{26} + 10 q^{27} + 22 q^{28} + 11 q^{29} - 5 q^{31} + 2 q^{32} - 7 q^{33} + 4 q^{34} - 3 q^{36} + 9 q^{37} + 3 q^{38} - 8 q^{39} + 15 q^{41} - 11 q^{42} + 13 q^{43} - 5 q^{44} + 18 q^{46} + 20 q^{47} + 20 q^{48} + 20 q^{49} + 24 q^{51} - q^{52} + 5 q^{53} + 17 q^{54} + 7 q^{57} + 33 q^{58} - 17 q^{59} + 3 q^{61} - 14 q^{62} + 22 q^{63} - 17 q^{64} - 2 q^{66} + 28 q^{67} + 25 q^{68} - 2 q^{69} - 6 q^{71} + 26 q^{72} + 16 q^{73} - 21 q^{74} + 5 q^{76} - 11 q^{77} - 29 q^{78} + 3 q^{79} + q^{81} - 2 q^{82} + 33 q^{83} + 33 q^{84} + 10 q^{86} + 3 q^{88} - 16 q^{89} - 22 q^{91} + 19 q^{92} + 26 q^{93} - 10 q^{94} + 5 q^{96} + 14 q^{97} - 10 q^{98} - 8 q^{99}+O(q^{100}) $ 5 * q + 3 * q^2 + 7 * q^3 + 5 * q^4 + 2 * q^6 + 11 * q^7 - 3 * q^8 + 8 * q^9 - 5 * q^11 + 7 * q^12 - q^13 - 3 * q^16 + 3 * q^17 + 7 * q^18 + 5 * q^19 + 11 * q^21 - 3 * q^22 + 8 * q^23 + 9 * q^24 - 16 * q^26 + 10 * q^27 + 22 * q^28 + 11 * q^29 - 5 * q^31 + 2 * q^32 - 7 * q^33 + 4 * q^34 - 3 * q^36 + 9 * q^37 + 3 * q^38 - 8 * q^39 + 15 * q^41 - 11 * q^42 + 13 * q^43 - 5 * q^44 + 18 * q^46 + 20 * q^47 + 20 * q^48 + 20 * q^49 + 24 * q^51 - q^52 + 5 * q^53 + 17 * q^54 + 7 * q^57 + 33 * q^58 - 17 * q^59 + 3 * q^61 - 14 * q^62 + 22 * q^63 - 17 * q^64 - 2 * q^66 + 28 * q^67 + 25 * q^68 - 2 * q^69 - 6 * q^71 + 26 * q^72 + 16 * q^73 - 21 * q^74 + 5 * q^76 - 11 * q^77 - 29 * q^78 + 3 * q^79 + q^81 - 2 * q^82 + 33 * q^83 + 33 * q^84 + 10 * q^86 + 3 * q^88 - 16 * q^89 - 22 * q^91 + 19 * q^92 + 26 * q^93 - 10 * q^94 + 5 * q^96 + 14 * q^97 - 10 * q^98 - 8 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	−2.22871	−1.57593	−0.787967	−	0.615717i	$-0.788866\pi$
$2$	−2.22871	−1.57593	−0.787967	+	0.615717i	$0.788866\pi$
$3$	1.47889	0.853838	0.426919	−	0.904290i	$-0.359599\pi$
$3$	1.47889	0.853838	0.426919	+	0.904290i	$0.359599\pi$
$4$	2.96714	1.48357
$5$	0	0
$5$	0	0
$6$	−3.29602	−1.34559
$7$	4.42518	1.67256	0.836281	−	0.548302i	$-0.184725\pi$
$7$	4.42518	1.67256	0.836281	+	0.548302i	$0.184725\pi$
$8$	−2.15546	−0.762072
$9$	−0.812880	−0.270960
$10$	0	0
$11$	−1.00000	−0.301511
$11$	−1.00000	−0.301511
$12$	4.38807	1.26673
$13$	3.92613	1.08891	0.544456	−	0.838789i	$-0.316736\pi$
$13$	3.92613	1.08891	0.544456	+	0.838789i	$0.316736\pi$
$14$	−9.86243	−2.63585
$15$	0	0
$16$	−1.13037	−0.282593
$17$	1.61520	0.391743	0.195872	−	0.980630i	$-0.437246\pi$
$17$	1.61520	0.391743	0.195872	+	0.980630i	$0.437246\pi$
$18$	1.81167	0.427015
$19$	1.00000	0.229416
$19$	1.00000	0.229416
$20$	0	0
$21$	6.54436	1.42810
$22$	2.22871	0.475162
$23$	−0.113248	−0.0236138	−0.0118069	−	0.999930i	$-0.503758\pi$
$23$	−0.113248	−0.0236138	−0.0118069	+	0.999930i	$0.503758\pi$
$24$	−3.18770	−0.650686
$25$	0	0
$26$	−8.75019	−1.71605
$27$	−5.63884	−1.08519
$28$	13.1301	2.48136
$29$	1.08612	0.201688	0.100844	−	0.994902i	$-0.467846\pi$
$29$	1.08612	0.201688	0.100844	+	0.994902i	$0.467846\pi$
$30$	0	0
$31$	−4.17296	−0.749487	−0.374743	−	0.927129i	$-0.622269\pi$
$31$	−4.17296	−0.749487	−0.374743	+	0.927129i	$0.622269\pi$
$32$	6.83020	1.20742
$33$	−1.47889	−0.257442
$34$	−3.59980	−0.617361
$35$	0	0
$36$	−2.41193	−0.401988
$37$	5.75406	0.945962	0.472981	−	0.881073i	$-0.343178\pi$
$37$	5.75406	0.945962	0.472981	+	0.881073i	$0.343178\pi$
$38$	−2.22871	−0.361544
$39$	5.80632	0.929755
$40$	0	0
$41$	4.26750	0.666472	0.333236	−	0.942843i	$-0.391859\pi$
$41$	4.26750	0.666472	0.333236	+	0.942843i	$0.391859\pi$
$42$	−14.5855	−2.25059
$43$	−3.62271	−0.552459	−0.276229	−	0.961092i	$-0.589085\pi$
$43$	−3.62271	−0.552459	−0.276229	+	0.961092i	$0.589085\pi$
$44$	−2.96714	−0.447313
$45$	0	0
$46$	0.252396	0.0372138
$47$	6.39567	0.932904	0.466452	−	0.884547i	$-0.345532\pi$
$47$	6.39567	0.932904	0.466452	+	0.884547i	$0.345532\pi$
$48$	−1.67170	−0.241289
$49$	12.5822	1.79746
$50$	0	0
$51$	2.38870	0.334485
$52$	11.6494	1.61548
$53$	−12.0154	−1.65044	−0.825219	−	0.564812i	$-0.808949\pi$
$53$	−12.0154	−1.65044	−0.825219	+	0.564812i	$0.808949\pi$
$54$	12.5673	1.71019
$55$	0	0
$56$	−9.53832	−1.27461
$57$	1.47889	0.195884
$58$	−2.42065	−0.317847
$59$	0.883911	0.115075	0.0575377	−	0.998343i	$-0.481675\pi$
$59$	0.883911	0.115075	0.0575377	+	0.998343i	$0.481675\pi$
$60$	0	0
$61$	3.77712	0.483611	0.241805	−	0.970325i	$-0.422260\pi$
$61$	3.77712	0.483611	0.241805	+	0.970325i	$0.422260\pi$
$62$	9.30032	1.18114
$63$	−3.59714	−0.453197
$64$	−12.9618	−1.62022
$65$	0	0
$66$	3.29602	0.405712
$67$	12.2192	1.49282	0.746409	−	0.665487i	$-0.231776\pi$
$67$	12.2192	1.49282	0.746409	+	0.665487i	$0.231776\pi$
$68$	4.79251	0.581178
$69$	−0.167481	−0.0201624
$70$	0	0
$71$	4.28400	0.508417	0.254209	−	0.967149i	$-0.418185\pi$
$71$	4.28400	0.508417	0.254209	+	0.967149i	$0.418185\pi$
$72$	1.75213	0.206491
$73$	1.92676	0.225510	0.112755	−	0.993623i	$-0.464032\pi$
$73$	1.92676	0.225510	0.112755	+	0.993623i	$0.464032\pi$
$74$	−12.8241	−1.49077
$75$	0	0
$76$	2.96714	0.340354
$77$	−4.42518	−0.504296
$78$	−12.9406	−1.46523
$79$	−7.81004	−0.878698	−0.439349	−	0.898316i	$-0.644791\pi$
$79$	−7.81004	−0.878698	−0.439349	+	0.898316i	$0.644791\pi$
$80$	0	0
$81$	−5.90059	−0.655621
$82$	−9.51102	−1.05032
$83$	3.33410	0.365964	0.182982	−	0.983116i	$-0.441425\pi$
$83$	3.33410	0.365964	0.182982	+	0.983116i	$0.441425\pi$
$84$	19.4180	2.11868
$85$	0	0
$86$	8.07397	0.870639
$87$	1.60626	0.172209
$88$	2.15546	0.229773
$89$	−11.9145	−1.26293	−0.631466	−	0.775403i	$-0.717547\pi$
$89$	−11.9145	−1.26293	−0.631466	+	0.775403i	$0.717547\pi$
$90$	0	0
$91$	17.3738	1.82127
$92$	−0.336021	−0.0350327
$93$	−6.17136	−0.639940
$94$	−14.2541	−1.47019
$95$	0	0
$96$	10.1011	1.03094
$97$	13.3478	1.35526	0.677631	−	0.735402i	$-0.263007\pi$
$97$	13.3478	1.35526	0.677631	+	0.735402i	$0.263007\pi$
$98$	−28.0421	−2.83268
$99$	0.812880	0.0816975
$100$	0	0
$101$	3.72067	0.370221	0.185110	−	0.982718i	$-0.440736\pi$
$101$	3.72067	0.370221	0.185110	+	0.982718i	$0.440736\pi$
$102$	−5.32372	−0.527127
$103$	18.7975	1.85218	0.926088	−	0.377308i	$-0.123150\pi$
$103$	18.7975	1.85218	0.926088	+	0.377308i	$0.123150\pi$
$104$	−8.46263	−0.829829
$105$	0	0
$106$	26.7788	2.60098
$107$	5.33910	0.516150	0.258075	−	0.966125i	$-0.416912\pi$
$107$	5.33910	0.516150	0.258075	+	0.966125i	$0.416912\pi$
$108$	−16.7312	−1.60996
$109$	16.7781	1.60706	0.803528	−	0.595268i	$-0.202954\pi$
$109$	16.7781	1.60706	0.803528	+	0.595268i	$0.202954\pi$
$110$	0	0
$111$	8.50963	0.807698
$112$	−5.00211	−0.472655
$113$	−9.64670	−0.907485	−0.453742	−	0.891133i	$-0.649911\pi$
$113$	−9.64670	−0.907485	−0.453742	+	0.891133i	$0.649911\pi$
$114$	−3.29602	−0.308700
$115$	0	0
$116$	3.22268	0.299218
$117$	−3.19147	−0.295052
$118$	−1.96998	−0.181351
$119$	7.14754	0.655214
$120$	0	0
$121$	1.00000	0.0909091
$122$	−8.41809	−0.762138
$123$	6.31118	0.569060
$124$	−12.3818	−1.11191
$125$	0	0
$126$	8.01698	0.714209
$127$	−0.515860	−0.0457752	−0.0228876	−	0.999738i	$-0.507286\pi$
$127$	−0.515860	−0.0457752	−0.0228876	+	0.999738i	$0.507286\pi$
$128$	15.2276	1.34594
$129$	−5.35760	−0.471710
$130$	0	0
$131$	−2.12758	−0.185888	−0.0929439	−	0.995671i	$-0.529628\pi$
$131$	−2.12758	−0.185888	−0.0929439	+	0.995671i	$0.529628\pi$
$132$	−4.38807	−0.381933
$133$	4.42518	0.383712
$134$	−27.2331	−2.35258
$135$	0	0
$136$	−3.48150	−0.298536
$137$	−3.76917	−0.322022	−0.161011	−	0.986953i	$-0.551475\pi$
$137$	−3.76917	−0.322022	−0.161011	+	0.986953i	$0.551475\pi$
$138$	0.373266	0.0317745
$139$	−11.2237	−0.951981	−0.475990	−	0.879451i	$-0.657910\pi$
$139$	−11.2237	−0.951981	−0.475990	+	0.879451i	$0.657910\pi$
$140$	0	0
$141$	9.45849	0.796549
$142$	−9.54778	−0.801232
$143$	−3.92613	−0.328319
$144$	0.918858	0.0765715
$145$	0	0
$146$	−4.29418	−0.355389
$147$	18.6077	1.53474
$148$	17.0731	1.40340
$149$	21.0620	1.72546	0.862732	−	0.505662i	$-0.168752\pi$
$149$	21.0620	1.72546	0.862732	+	0.505662i	$0.168752\pi$
$150$	0	0
$151$	7.46759	0.607704	0.303852	−	0.952719i	$-0.401727\pi$
$151$	7.46759	0.607704	0.303852	+	0.952719i	$0.401727\pi$
$152$	−2.15546	−0.174831
$153$	−1.31296	−0.106147
$154$	9.86243	0.794738
$155$	0	0
$156$	17.2281	1.37935
$157$	5.84405	0.466406	0.233203	−	0.972428i	$-0.425079\pi$
$157$	5.84405	0.466406	0.233203	+	0.972428i	$0.425079\pi$
$158$	17.4063	1.38477
$159$	−17.7694	−1.40921
$160$	0	0
$161$	−0.501142	−0.0394955
$162$	13.1507	1.03321
$163$	20.3077	1.59062	0.795311	−	0.606202i	$-0.207308\pi$
$163$	20.3077	1.59062	0.795311	+	0.606202i	$0.207308\pi$
$164$	12.6623	0.988757
$165$	0	0
$166$	−7.43072	−0.576736
$167$	−10.6177	−0.821625	−0.410812	−	0.911720i	$-0.634755\pi$
$167$	−10.6177	−0.821625	−0.410812	+	0.911720i	$0.634755\pi$
$168$	−14.1061	−1.08831
$169$	2.41448	0.185729
$170$	0	0
$171$	−0.812880	−0.0621625
$172$	−10.7491	−0.819610
$173$	−24.7343	−1.88051	−0.940257	−	0.340466i	$-0.889415\pi$
$173$	−24.7343	−1.88051	−0.940257	+	0.340466i	$0.889415\pi$
$174$	−3.57988	−0.271390
$175$	0	0
$176$	1.13037	0.0852051
$177$	1.30721	0.0982558
$178$	26.5539	1.99030
$179$	−14.9732	−1.11915	−0.559574	−	0.828781i	$-0.689035\pi$
$179$	−14.9732	−1.11915	−0.559574	+	0.828781i	$0.689035\pi$
$180$	0	0
$181$	−11.2782	−0.838298	−0.419149	−	0.907917i	$-0.637672\pi$
$181$	−11.2782	−0.838298	−0.419149	+	0.907917i	$0.637672\pi$
$182$	−38.7212	−2.87020
$183$	5.58595	0.412925
$184$	0.244101	0.0179954
$185$	0	0
$186$	13.7542	1.00850
$187$	−1.61520	−0.118115
$188$	18.9768	1.38403
$189$	−24.9529	−1.81505
$190$	0	0
$191$	22.3038	1.61385	0.806923	−	0.590656i	$-0.201131\pi$
$191$	22.3038	1.61385	0.806923	+	0.590656i	$0.201131\pi$
$192$	−19.1691	−1.38341
$193$	−25.1845	−1.81282	−0.906412	−	0.422395i	$-0.861189\pi$
$193$	−25.1845	−1.81282	−0.906412	+	0.422395i	$0.861189\pi$
$194$	−29.7483	−2.13580
$195$	0	0
$196$	37.3332	2.66666
$197$	10.4483	0.744413	0.372207	−	0.928150i	$-0.378601\pi$
$197$	10.4483	0.744413	0.372207	+	0.928150i	$0.378601\pi$
$198$	−1.81167	−0.128750
$199$	−6.40716	−0.454191	−0.227096	−	0.973872i	$-0.572923\pi$
$199$	−6.40716	−0.454191	−0.227096	+	0.973872i	$0.572923\pi$
$200$	0	0
$201$	18.0709	1.27463
$202$	−8.29229	−0.583444
$203$	4.80629	0.337336
$204$	7.08761	0.496232
$205$	0	0
$206$	−41.8942	−2.91891
$207$	0.0920568	0.00639839
$208$	−4.43799	−0.307719
$209$	−1.00000	−0.0691714
$210$	0	0
$211$	7.96892	0.548603	0.274302	−	0.961644i	$-0.411553\pi$
$211$	7.96892	0.548603	0.274302	+	0.961644i	$0.411553\pi$
$212$	−35.6513	−2.44854
$213$	6.33557	0.434106
$214$	−11.8993	−0.813418
$215$	0	0
$216$	12.1543	0.826996
$217$	−18.4661	−1.25356
$218$	−37.3936	−2.53261
$219$	2.84947	0.192549
$220$	0	0
$221$	6.34147	0.426574
$222$	−18.9655	−1.27288
$223$	23.9096	1.60111	0.800553	−	0.599262i	$-0.204539\pi$
$223$	23.9096	1.60111	0.800553	+	0.599262i	$0.204539\pi$
$224$	30.2249	2.01948
$225$	0	0
$226$	21.4997	1.43014
$227$	10.0128	0.664575	0.332287	−	0.943178i	$-0.392180\pi$
$227$	10.0128	0.664575	0.332287	+	0.943178i	$0.392180\pi$
$228$	4.38807	0.290607
$229$	10.4511	0.690629	0.345314	−	0.938487i	$-0.387772\pi$
$229$	10.4511	0.690629	0.345314	+	0.938487i	$0.387772\pi$
$230$	0	0
$231$	−6.54436	−0.430587
$232$	−2.34110	−0.153701
$233$	4.56505	0.299066	0.149533	−	0.988757i	$-0.452223\pi$
$233$	4.56505	0.299066	0.149533	+	0.988757i	$0.452223\pi$
$234$	7.11286	0.464982
$235$	0	0
$236$	2.62268	0.170722
$237$	−11.5502	−0.750266
$238$	−15.9298	−1.03257
$239$	−15.3794	−0.994808	−0.497404	−	0.867519i	$-0.665713\pi$
$239$	−15.3794	−0.994808	−0.497404	+	0.867519i	$0.665713\pi$
$240$	0	0
$241$	17.8737	1.15135	0.575673	−	0.817680i	$-0.304740\pi$
$241$	17.8737	1.15135	0.575673	+	0.817680i	$0.304740\pi$
$242$	−2.22871	−0.143267
$243$	8.19018	0.525400
$244$	11.2072	0.717469
$245$	0	0
$246$	−14.0658	−0.896800
$247$	3.92613	0.249814
$248$	8.99468	0.571163
$249$	4.93076	0.312475
$250$	0	0
$251$	−10.0425	−0.633878	−0.316939	−	0.948446i	$-0.602655\pi$
$251$	−10.0425	−0.633878	−0.316939	+	0.948446i	$0.602655\pi$
$252$	−10.6732	−0.672349
$253$	0.113248	0.00711982
$254$	1.14970	0.0721387
$255$	0	0
$256$	−8.01431	−0.500895
$257$	10.7636	0.671416	0.335708	−	0.941966i	$-0.391025\pi$
$257$	10.7636	0.671416	0.335708	+	0.941966i	$0.391025\pi$
$258$	11.9405	0.743385
$259$	25.4628	1.58218
$260$	0	0
$261$	−0.882888	−0.0546494
$262$	4.74176	0.292947
$263$	−22.9691	−1.41634	−0.708169	−	0.706043i	$-0.750478\pi$
$263$	−22.9691	−1.41634	−0.708169	+	0.706043i	$0.750478\pi$
$264$	3.18770	0.196189
$265$	0	0
$266$	−9.86243	−0.604705
$267$	−17.6202	−1.07834
$268$	36.2562	2.21470
$269$	−20.5868	−1.25520	−0.627600	−	0.778536i	$-0.715963\pi$
$269$	−20.5868	−1.25520	−0.627600	+	0.778536i	$0.715963\pi$
$270$	0	0
$271$	−4.27052	−0.259416	−0.129708	−	0.991552i	$-0.541404\pi$
$271$	−4.27052	−0.259416	−0.129708	+	0.991552i	$0.541404\pi$
$272$	−1.82578	−0.110704
$273$	25.6940	1.55507
$274$	8.40038	0.507485
$275$	0	0
$276$	−0.496939	−0.0299122
$277$	14.6746	0.881712	0.440856	−	0.897578i	$-0.354675\pi$
$277$	14.6746	0.881712	0.440856	+	0.897578i	$0.354675\pi$
$278$	25.0143	1.50026
$279$	3.39212	0.203081
$280$	0	0
$281$	−24.1329	−1.43965	−0.719824	−	0.694157i	$-0.755778\pi$
$281$	−24.1329	−1.43965	−0.719824	+	0.694157i	$0.755778\pi$
$282$	−21.0802	−1.25531
$283$	−0.197192	−0.0117218	−0.00586092	−	0.999983i	$-0.501866\pi$
$283$	−0.197192	−0.0117218	−0.00586092	+	0.999983i	$0.501866\pi$
$284$	12.7112	0.754272
$285$	0	0
$286$	8.75019	0.517410
$287$	18.8845	1.11472
$288$	−5.55213	−0.327163
$289$	−14.3911	−0.846537
$290$	0	0
$291$	19.7399	1.15717
$292$	5.71695	0.334559
$293$	−2.73471	−0.159763	−0.0798817	−	0.996804i	$-0.525454\pi$
$293$	−2.73471	−0.159763	−0.0798817	+	0.996804i	$0.525454\pi$
$294$	−41.4712	−2.41865
$295$	0	0
$296$	−12.4027	−0.720891
$297$	5.63884	0.327198
$298$	−46.9410	−2.71922
$299$	−0.444625	−0.0257133
$300$	0	0
$301$	−16.0312	−0.924021
$302$	−16.6431	−0.957702
$303$	5.50247	0.316109
$304$	−1.13037	−0.0648313
$305$	0	0
$306$	2.92621	0.167280
$307$	16.7313	0.954905	0.477452	−	0.878658i	$-0.341560\pi$
$307$	16.7313	0.954905	0.477452	+	0.878658i	$0.341560\pi$
$308$	−13.1301	−0.748158
$309$	27.7995	1.58146
$310$	0	0
$311$	−14.8941	−0.844565	−0.422283	−	0.906464i	$-0.638771\pi$
$311$	−14.8941	−0.844565	−0.422283	+	0.906464i	$0.638771\pi$
$312$	−12.5153	−0.708540
$313$	−8.89539	−0.502797	−0.251399	−	0.967884i	$-0.580891\pi$
$313$	−8.89539	−0.502797	−0.251399	+	0.967884i	$0.580891\pi$
$314$	−13.0247	−0.735026
$315$	0	0
$316$	−23.1735	−1.30361
$317$	−6.16319	−0.346159	−0.173079	−	0.984908i	$-0.555372\pi$
$317$	−6.16319	−0.346159	−0.173079	+	0.984908i	$0.555372\pi$
$318$	39.6029	2.22082
$319$	−1.08612	−0.0608112
$320$	0	0
$321$	7.89595	0.440709
$322$	1.11690	0.0622423
$323$	1.61520	0.0898720
$324$	−17.5078	−0.972658
$325$	0	0
$326$	−45.2599	−2.50671
$327$	24.8131	1.37217
$328$	−9.19846	−0.507900
$329$	28.3020	1.56034
$330$	0	0
$331$	17.5144	0.962681	0.481340	−	0.876534i	$-0.340150\pi$
$331$	17.5144	0.962681	0.481340	+	0.876534i	$0.340150\pi$
$332$	9.89272	0.542933
$333$	−4.67736	−0.256318
$334$	23.6638	1.29483
$335$	0	0
$336$	−7.39757	−0.403571
$337$	34.0733	1.85609	0.928045	−	0.372467i	$-0.121488\pi$
$337$	34.0733	1.85609	0.928045	+	0.372467i	$0.121488\pi$
$338$	−5.38117	−0.292697
$339$	−14.2664	−0.774845
$340$	0	0
$341$	4.17296	0.225979
$342$	1.81167	0.0979640
$343$	24.7024	1.33380
$344$	7.80863	0.421013
$345$	0	0
$346$	55.1255	2.96357
$347$	−14.8065	−0.794856	−0.397428	−	0.917633i	$-0.630097\pi$
$347$	−14.8065	−0.794856	−0.397428	+	0.917633i	$0.630097\pi$
$348$	4.76599	0.255484
$349$	−20.2032	−1.08145	−0.540727	−	0.841198i	$-0.681851\pi$
$349$	−20.2032	−1.08145	−0.540727	+	0.841198i	$0.681851\pi$
$350$	0	0
$351$	−22.1388	−1.18168
$352$	−6.83020	−0.364051
$353$	34.8488	1.85481	0.927407	−	0.374053i	$-0.122032\pi$
$353$	34.8488	1.85481	0.927407	+	0.374053i	$0.122032\pi$
$354$	−2.91338	−0.154845
$355$	0	0
$356$	−35.3519	−1.87365
$357$	10.5704	0.559447
$358$	33.3708	1.76370
$359$	−25.8010	−1.36173	−0.680863	−	0.732410i	$-0.738395\pi$
$359$	−25.8010	−1.36173	−0.680863	+	0.732410i	$0.738395\pi$
$360$	0	0
$361$	1.00000	0.0526316
$362$	25.1357	1.32110
$363$	1.47889	0.0776217
$364$	51.5505	2.70198
$365$	0	0
$366$	−12.4494	−0.650743
$367$	−12.6344	−0.659510	−0.329755	−	0.944066i	$-0.606966\pi$
$367$	−12.6344	−0.659510	−0.329755	+	0.944066i	$0.606966\pi$
$368$	0.128012	0.00667310
$369$	−3.46897	−0.180587
$370$	0	0
$371$	−53.1702	−2.76046
$372$	−18.3113	−0.949395
$373$	−31.3623	−1.62388	−0.811940	−	0.583741i	$-0.801588\pi$
$373$	−31.3623	−1.62388	−0.811940	+	0.583741i	$0.801588\pi$
$374$	3.59980	0.186141
$375$	0	0
$376$	−13.7856	−0.710940
$377$	4.26426	0.219620
$378$	55.6126	2.86041
$379$	−17.2730	−0.887256	−0.443628	−	0.896211i	$-0.646309\pi$
$379$	−17.2730	−0.887256	−0.443628	+	0.896211i	$0.646309\pi$
$380$	0	0
$381$	−0.762901	−0.0390846
$382$	−49.7086	−2.54332
$383$	−1.96340	−0.100325	−0.0501625	−	0.998741i	$-0.515974\pi$
$383$	−1.96340	−0.100325	−0.0501625	+	0.998741i	$0.515974\pi$
$384$	22.5200	1.14922
$385$	0	0
$386$	56.1290	2.85689
$387$	2.94483	0.149694
$388$	39.6047	2.01062
$389$	27.2460	1.38143	0.690714	−	0.723128i	$-0.257296\pi$
$389$	27.2460	1.38143	0.690714	+	0.723128i	$0.257296\pi$
$390$	0	0
$391$	−0.182917	−0.00925054
$392$	−27.1206	−1.36979
$393$	−3.14646	−0.158718
$394$	−23.2863	−1.17315
$395$	0	0
$396$	2.41193	0.121204
$397$	−24.1194	−1.21052	−0.605258	−	0.796029i	$-0.706930\pi$
$397$	−24.1194	−1.21052	−0.605258	+	0.796029i	$0.706930\pi$
$398$	14.2797	0.715776
$399$	6.54436	0.327628
$400$	0	0
$401$	−18.6773	−0.932699	−0.466349	−	0.884601i	$-0.654431\pi$
$401$	−18.6773	−0.932699	−0.466349	+	0.884601i	$0.654431\pi$
$402$	−40.2748	−2.00873
$403$	−16.3836	−0.816125
$404$	11.0397	0.549248
$405$	0	0
$406$	−10.7118	−0.531619
$407$	−5.75406	−0.285218
$408$	−5.14876	−0.254902
$409$	−19.9442	−0.986176	−0.493088	−	0.869979i	$-0.664132\pi$
$409$	−19.9442	−0.986176	−0.493088	+	0.869979i	$0.664132\pi$
$410$	0	0
$411$	−5.57419	−0.274955
$412$	55.7748	2.74783
$413$	3.91146	0.192471
$414$	−0.205168	−0.0100834
$415$	0	0
$416$	26.8162	1.31477
$417$	−16.5986	−0.812838
$418$	2.22871	0.109010
$419$	22.0961	1.07946	0.539731	−	0.841837i	$-0.318526\pi$
$419$	22.0961	1.07946	0.539731	+	0.841837i	$0.318526\pi$
$420$	0	0
$421$	−25.4045	−1.23814	−0.619070	−	0.785336i	$-0.712490\pi$
$421$	−25.4045	−1.23814	−0.619070	+	0.785336i	$0.712490\pi$
$422$	−17.7604	−0.864563
$423$	−5.19891	−0.252780
$424$	25.8987	1.25775
$425$	0	0
$426$	−14.1201	−0.684123
$427$	16.7144	0.808868
$428$	15.8418	0.765744
$429$	−5.80632	−0.280332
$430$	0	0
$431$	−3.51614	−0.169367	−0.0846833	−	0.996408i	$-0.526988\pi$
$431$	−3.51614	−0.169367	−0.0846833	+	0.996408i	$0.526988\pi$
$432$	6.37399	0.306669
$433$	9.71737	0.466987	0.233493	−	0.972358i	$-0.424984\pi$
$433$	9.71737	0.466987	0.233493	+	0.972358i	$0.424984\pi$
$434$	41.1556	1.97553
$435$	0	0
$436$	49.7831	2.38418
$437$	−0.113248	−0.00541737
$438$	−6.35062	−0.303445
$439$	0.888955	0.0424275	0.0212138	−	0.999775i	$-0.493247\pi$
$439$	0.888955	0.0424275	0.0212138	+	0.999775i	$0.493247\pi$
$440$	0	0
$441$	−10.2278	−0.487040
$442$	−14.1333	−0.672252
$443$	−5.44113	−0.258516	−0.129258	−	0.991611i	$-0.541260\pi$
$443$	−5.44113	−0.258516	−0.129258	+	0.991611i	$0.541260\pi$
$444$	25.2492	1.19828
$445$	0	0
$446$	−53.2875	−2.52324
$447$	31.1484	1.47327
$448$	−57.3582	−2.70992
$449$	21.6076	1.01972	0.509862	−	0.860256i	$-0.329697\pi$
$449$	21.6076	1.01972	0.509862	+	0.860256i	$0.329697\pi$
$450$	0	0
$451$	−4.26750	−0.200949
$452$	−28.6231	−1.34632
$453$	11.0438	0.518881
$454$	−22.3157	−1.04733
$455$	0	0
$456$	−3.18770	−0.149278
$457$	29.1996	1.36590	0.682950	−	0.730465i	$-0.260697\pi$
$457$	29.1996	1.36590	0.682950	+	0.730465i	$0.260697\pi$
$458$	−23.2925	−1.08839
$459$	−9.10784	−0.425117
$460$	0	0
$461$	−32.2335	−1.50126	−0.750631	−	0.660722i	$-0.770250\pi$
$461$	−32.2335	−1.50126	−0.750631	+	0.660722i	$0.770250\pi$
$462$	14.5855	0.678577
$463$	11.8543	0.550917	0.275459	−	0.961313i	$-0.411170\pi$
$463$	11.8543	0.550917	0.275459	+	0.961313i	$0.411170\pi$
$464$	−1.22772	−0.0569957
$465$	0	0
$466$	−10.1742	−0.471309
$467$	31.4900	1.45718	0.728592	−	0.684948i	$-0.240175\pi$
$467$	31.4900	1.45718	0.728592	+	0.684948i	$0.240175\pi$
$468$	−9.46953	−0.437729
$469$	54.0724	2.49683
$470$	0	0
$471$	8.64272	0.398236
$472$	−1.90524	−0.0876957
$473$	3.62271	0.166573
$474$	25.7420	1.18237
$475$	0	0
$476$	21.2077	0.972055
$477$	9.76706	0.447203
$478$	34.2761	1.56775
$479$	15.1565	0.692519	0.346259	−	0.938139i	$-0.387452\pi$
$479$	15.1565	0.692519	0.346259	+	0.938139i	$0.387452\pi$
$480$	0	0
$481$	22.5912	1.03007
$482$	−39.8353	−1.81445
$483$	−0.741134	−0.0337228
$484$	2.96714	0.134870
$485$	0	0
$486$	−18.2535	−0.827996
$487$	−28.0154	−1.26950	−0.634749	−	0.772718i	$-0.718897\pi$
$487$	−28.0154	−1.26950	−0.634749	+	0.772718i	$0.718897\pi$
$488$	−8.14145	−0.368546
$489$	30.0329	1.35813
$490$	0	0
$491$	−1.56411	−0.0705873	−0.0352937	−	0.999377i	$-0.511237\pi$
$491$	−1.56411	−0.0705873	−0.0352937	+	0.999377i	$0.511237\pi$
$492$	18.7261	0.844239
$493$	1.75430	0.0790099
$494$	−8.75019	−0.393690
$495$	0	0
$496$	4.71701	0.211800
$497$	18.9575	0.850359
$498$	−10.9892	−0.492439
$499$	15.4416	0.691263	0.345631	−	0.938370i	$-0.387665\pi$
$499$	15.4416	0.691263	0.345631	+	0.938370i	$0.387665\pi$
$500$	0	0
$501$	−15.7025	−0.701535
$502$	22.3818	0.998950
$503$	23.3185	1.03972	0.519861	−	0.854251i	$-0.325984\pi$
$503$	23.3185	1.03972	0.519861	+	0.854251i	$0.325984\pi$
$504$	7.75351	0.345369
$505$	0	0
$506$	−0.252396	−0.0112204
$507$	3.57075	0.158583
$508$	−1.53063	−0.0679106
$509$	32.7538	1.45178	0.725892	−	0.687808i	$-0.241427\pi$
$509$	32.7538	1.45178	0.725892	+	0.687808i	$0.241427\pi$
$510$	0	0
$511$	8.52625	0.377179
$512$	−12.5936	−0.556565
$513$	−5.63884	−0.248961
$514$	−23.9889	−1.05811
$515$	0	0
$516$	−15.8967	−0.699815
$517$	−6.39567	−0.281281
$518$	−56.7490	−2.49341
$519$	−36.5793	−1.60565
$520$	0	0
$521$	38.5714	1.68984	0.844922	−	0.534889i	$-0.179647\pi$
$521$	38.5714	1.68984	0.844922	+	0.534889i	$0.179647\pi$
$522$	1.96770	0.0861238
$523$	−34.9926	−1.53012	−0.765060	−	0.643959i	$-0.777291\pi$
$523$	−34.9926	−1.53012	−0.765060	+	0.643959i	$0.777291\pi$
$524$	−6.31283	−0.275777
$525$	0	0
$526$	51.1915	2.23205
$527$	−6.74016	−0.293606
$528$	1.67170	0.0727514
$529$	−22.9872	−0.999442
$530$	0	0
$531$	−0.718513	−0.0311808
$532$	13.1301	0.569263
$533$	16.7548	0.725730
$534$	39.2703	1.69939
$535$	0	0
$536$	−26.3382	−1.13764
$537$	−22.1437	−0.955571
$538$	45.8820	1.97811
$539$	−12.5822	−0.541955
$540$	0	0
$541$	35.1455	1.51102	0.755511	−	0.655136i	$-0.227389\pi$
$541$	35.1455	1.51102	0.755511	+	0.655136i	$0.227389\pi$
$542$	9.51774	0.408822
$543$	−16.6792	−0.715771
$544$	11.0321	0.472999
$545$	0	0
$546$	−57.2644	−2.45069
$547$	−2.79933	−0.119691	−0.0598454	−	0.998208i	$-0.519061\pi$
$547$	−2.79933	−0.119691	−0.0598454	+	0.998208i	$0.519061\pi$
$548$	−11.1836	−0.477741
$549$	−3.07035	−0.131039
$550$	0	0
$551$	1.08612	0.0462704
$552$	0.361000	0.0153652
$553$	−34.5608	−1.46968
$554$	−32.7054	−1.38952
$555$	0	0
$556$	−33.3022	−1.41233
$557$	27.8118	1.17843	0.589213	−	0.807978i	$-0.299438\pi$
$557$	27.8118	1.17843	0.589213	+	0.807978i	$0.299438\pi$
$558$	−7.56004	−0.320042
$559$	−14.2232	−0.601579
$560$	0	0
$561$	−2.38870	−0.100851
$562$	53.7852	2.26879
$563$	−26.4265	−1.11374	−0.556872	−	0.830598i	$-0.687999\pi$
$563$	−26.4265	−1.11374	−0.556872	+	0.830598i	$0.687999\pi$
$564$	28.0646	1.18173
$565$	0	0
$566$	0.439483	0.0184728
$567$	−26.1112	−1.09657
$568$	−9.23401	−0.387451
$569$	15.1625	0.635643	0.317822	−	0.948151i	$-0.397049\pi$
$569$	15.1625	0.635643	0.317822	+	0.948151i	$0.397049\pi$
$570$	0	0
$571$	−11.4144	−0.477677	−0.238838	−	0.971059i	$-0.576767\pi$
$571$	−11.4144	−0.477677	−0.238838	+	0.971059i	$0.576767\pi$
$572$	−11.6494	−0.487084
$573$	32.9849	1.37796
$574$	−42.0880	−1.75672
$575$	0	0
$576$	10.5364	0.439015
$577$	9.33855	0.388769	0.194385	−	0.980925i	$-0.437729\pi$
$577$	9.33855	0.388769	0.194385	+	0.980925i	$0.437729\pi$
$578$	32.0736	1.33409
$579$	−37.2452	−1.54786
$580$	0	0
$581$	14.7540	0.612098
$582$	−43.9945	−1.82363
$583$	12.0154	0.497626
$584$	−4.15306	−0.171855
$585$	0	0
$586$	6.09486	0.251776
$587$	−9.38542	−0.387378	−0.193689	−	0.981063i	$-0.562045\pi$
$587$	−9.38542	−0.387378	−0.193689	+	0.981063i	$0.562045\pi$
$588$	55.2117	2.27689
$589$	−4.17296	−0.171944
$590$	0	0
$591$	15.4520	0.635609
$592$	−6.50424	−0.267322
$593$	35.6523	1.46406	0.732032	−	0.681270i	$-0.238572\pi$
$593$	35.6523	1.46406	0.732032	+	0.681270i	$0.238572\pi$
$594$	−12.5673	−0.515643
$595$	0	0
$596$	62.4937	2.55984
$597$	−9.47549	−0.387806
$598$	0.990939	0.0405225
$599$	37.1404	1.51751	0.758757	−	0.651373i	$-0.225807\pi$
$599$	37.1404	1.51751	0.758757	+	0.651373i	$0.225807\pi$
$600$	0	0
$601$	12.2448	0.499474	0.249737	−	0.968314i	$-0.419656\pi$
$601$	12.2448	0.499474	0.249737	+	0.968314i	$0.419656\pi$
$602$	35.7288	1.45620
$603$	−9.93278	−0.404494
$604$	22.1574	0.901571
$605$	0	0
$606$	−12.2634	−0.498167
$607$	−31.3652	−1.27307	−0.636536	−	0.771247i	$-0.719634\pi$
$607$	−31.3652	−1.27307	−0.636536	+	0.771247i	$0.719634\pi$
$608$	6.83020	0.277001
$609$	7.10798	0.288030
$610$	0	0
$611$	25.1102	1.01585
$612$	−3.89574	−0.157476
$613$	5.48484	0.221531	0.110765	−	0.993847i	$-0.464670\pi$
$613$	5.48484	0.221531	0.110765	+	0.993847i	$0.464670\pi$
$614$	−37.2891	−1.50487
$615$	0	0
$616$	9.53832	0.384310
$617$	32.6913	1.31610	0.658052	−	0.752973i	$-0.271381\pi$
$617$	32.6913	1.31610	0.658052	+	0.752973i	$0.271381\pi$
$618$	−61.9570	−2.49227
$619$	1.71800	0.0690522	0.0345261	−	0.999404i	$-0.489008\pi$
$619$	1.71800	0.0690522	0.0345261	+	0.999404i	$0.489008\pi$
$620$	0	0
$621$	0.638585	0.0256255
$622$	33.1945	1.33098
$623$	−52.7238	−2.11233
$624$	−6.56330	−0.262742
$625$	0	0
$626$	19.8252	0.792375
$627$	−1.47889	−0.0590612
$628$	17.3401	0.691946
$629$	9.29395	0.370574
$630$	0	0
$631$	39.9355	1.58981	0.794903	−	0.606737i	$-0.207522\pi$
$631$	39.9355	1.58981	0.794903	+	0.606737i	$0.207522\pi$
$632$	16.8343	0.669631
$633$	11.7852	0.468419
$634$	13.7359	0.545524
$635$	0	0
$636$	−52.7243	−2.09066
$637$	49.3994	1.95728
$638$	2.42065	0.0958345
$639$	−3.48238	−0.137761
$640$	0	0
$641$	−3.50123	−0.138290	−0.0691452	−	0.997607i	$-0.522027\pi$
$641$	−3.50123	−0.138290	−0.0691452	+	0.997607i	$0.522027\pi$
$642$	−17.5978	−0.694528
$643$	−6.59740	−0.260176	−0.130088	−	0.991502i	$-0.541526\pi$
$643$	−6.59740	−0.260176	−0.130088	+	0.991502i	$0.541526\pi$
$644$	−1.48696	−0.0585943
$645$	0	0
$646$	−3.59980	−0.141632
$647$	24.8389	0.976518	0.488259	−	0.872699i	$-0.337632\pi$
$647$	24.8389	0.976518	0.488259	+	0.872699i	$0.337632\pi$
$648$	12.7185	0.499630
$649$	−0.883911	−0.0346965
$650$	0	0
$651$	−27.3094	−1.07034
$652$	60.2557	2.35980
$653$	17.5186	0.685555	0.342778	−	0.939417i	$-0.388632\pi$
$653$	17.5186	0.685555	0.342778	+	0.939417i	$0.388632\pi$
$654$	−55.3011	−2.16244
$655$	0	0
$656$	−4.82387	−0.188341
$657$	−1.56622	−0.0611042
$658$	−63.0768	−2.45899
$659$	3.56748	0.138969	0.0694846	−	0.997583i	$-0.477865\pi$
$659$	3.56748	0.138969	0.0694846	+	0.997583i	$0.477865\pi$
$660$	0	0
$661$	−48.5242	−1.88737	−0.943687	−	0.330841i	$-0.892668\pi$
$661$	−48.5242	−1.88737	−0.943687	+	0.330841i	$0.892668\pi$
$662$	−39.0346	−1.51712
$663$	9.37835	0.364225
$664$	−7.18652	−0.278891
$665$	0	0
$666$	10.4245	0.403940
$667$	−0.123001	−0.00476262
$668$	−31.5043	−1.21894
$669$	35.3597	1.36709
$670$	0	0
$671$	−3.77712	−0.145814
$672$	44.6993	1.72431
$673$	0.476829	0.0183804	0.00919020	−	0.999958i	$-0.497075\pi$
$673$	0.476829	0.0183804	0.00919020	+	0.999958i	$0.497075\pi$
$674$	−75.9394	−2.92508
$675$	0	0
$676$	7.16409	0.275542
$677$	−3.68052	−0.141454	−0.0707269	−	0.997496i	$-0.522532\pi$
$677$	−3.68052	−0.141454	−0.0707269	+	0.997496i	$0.522532\pi$
$678$	31.7957	1.22111
$679$	59.0664	2.26676
$680$	0	0
$681$	14.8079	0.567439
$682$	−9.30032	−0.356128
$683$	−0.701724	−0.0268507	−0.0134254	−	0.999910i	$-0.504274\pi$
$683$	−0.701724	−0.0268507	−0.0134254	+	0.999910i	$0.504274\pi$
$684$	−2.41193	−0.0922223
$685$	0	0
$686$	−55.0544	−2.10199
$687$	15.4561	0.589685
$688$	4.09502	0.156121
$689$	−47.1739	−1.79718
$690$	0	0
$691$	3.65425	0.139014	0.0695071	−	0.997581i	$-0.477857\pi$
$691$	3.65425	0.139014	0.0695071	+	0.997581i	$0.477857\pi$
$692$	−73.3900	−2.78987
$693$	3.59714	0.136644
$694$	32.9994	1.25264
$695$	0	0
$696$	−3.46223	−0.131236
$697$	6.89287	0.261086
$698$	45.0271	1.70430
$699$	6.75121	0.255354
$700$	0	0
$701$	−45.3852	−1.71417	−0.857087	−	0.515171i	$-0.827728\pi$
$701$	−45.3852	−1.71417	−0.857087	+	0.515171i	$0.827728\pi$
$702$	49.3409	1.86225
$703$	5.75406	0.217019
$704$	12.9618	0.488515
$705$	0	0
$706$	−77.6678	−2.92307
$707$	16.4647	0.619217
$708$	3.87866	0.145769
$709$	16.6965	0.627051	0.313525	−	0.949580i	$-0.398490\pi$
$709$	16.6965	0.627051	0.313525	+	0.949580i	$0.398490\pi$
$710$	0	0
$711$	6.34862	0.238092
$712$	25.6813	0.962446
$713$	0.472579	0.0176982
$714$	−23.5584	−0.881652
$715$	0	0
$716$	−44.4274	−1.66033
$717$	−22.7444	−0.849405
$718$	57.5030	2.14599
$719$	16.1346	0.601718	0.300859	−	0.953669i	$-0.402727\pi$
$719$	16.1346	0.601718	0.300859	+	0.953669i	$0.402727\pi$
$720$	0	0
$721$	83.1825	3.09788
$722$	−2.22871	−0.0829439
$723$	26.4333	0.983064
$724$	−33.4638	−1.24367
$725$	0	0
$726$	−3.29602	−0.122327
$727$	21.9546	0.814251	0.407126	−	0.913372i	$-0.366531\pi$
$727$	21.9546	0.814251	0.407126	+	0.913372i	$0.366531\pi$
$728$	−37.4487	−1.38794
$729$	29.8141	1.10423
$730$	0	0
$731$	−5.85140	−0.216422
$732$	16.5743	0.612603
$733$	47.5004	1.75447	0.877234	−	0.480063i	$-0.159386\pi$
$733$	47.5004	1.75447	0.877234	+	0.480063i	$0.159386\pi$
$734$	28.1584	1.03935
$735$	0	0
$736$	−0.773505	−0.0285118
$737$	−12.2192	−0.450102
$738$	7.73132	0.284594
$739$	29.9890	1.10316	0.551581	−	0.834122i	$-0.314025\pi$
$739$	29.9890	1.10316	0.551581	+	0.834122i	$0.314025\pi$
$740$	0	0
$741$	5.80632	0.213300
$742$	118.501	4.35030
$743$	−2.24383	−0.0823181	−0.0411590	−	0.999153i	$-0.513105\pi$
$743$	−2.24383	−0.0823181	−0.0411590	+	0.999153i	$0.513105\pi$
$744$	13.3022	0.487681
$745$	0	0
$746$	69.8974	2.55913
$747$	−2.71022	−0.0991618
$748$	−4.79251	−0.175232
$749$	23.6265	0.863293
$750$	0	0
$751$	29.0275	1.05923	0.529614	−	0.848239i	$-0.322337\pi$
$751$	29.0275	1.05923	0.529614	+	0.848239i	$0.322337\pi$
$752$	−7.22949	−0.263632
$753$	−14.8518	−0.541229
$754$	−9.50378	−0.346107
$755$	0	0
$756$	−74.0386	−2.69276
$757$	−47.0009	−1.70828	−0.854138	−	0.520046i	$-0.825915\pi$
$757$	−47.0009	−1.70828	−0.854138	+	0.520046i	$0.825915\pi$
$758$	38.4965	1.39826
$759$	0.167481	0.00607918
$760$	0	0
$761$	46.6332	1.69045	0.845226	−	0.534409i	$-0.179466\pi$
$761$	46.6332	1.69045	0.845226	+	0.534409i	$0.179466\pi$
$762$	1.70028	0.0615948
$763$	74.2463	2.68790
$764$	66.1784	2.39425
$765$	0	0
$766$	4.37584	0.158106
$767$	3.47035	0.125307
$768$	−11.8523	−0.427683
$769$	−22.6169	−0.815585	−0.407793	−	0.913075i	$-0.633701\pi$
$769$	−22.6169	−0.815585	−0.407793	+	0.913075i	$0.633701\pi$
$770$	0	0
$771$	15.9182	0.573280
$772$	−74.7260	−2.68945
$773$	−16.1951	−0.582499	−0.291249	−	0.956647i	$-0.594071\pi$
$773$	−16.1951	−0.582499	−0.291249	+	0.956647i	$0.594071\pi$
$774$	−6.56317	−0.235908
$775$	0	0
$776$	−28.7707	−1.03281
$777$	37.6567	1.35093
$778$	−60.7234	−2.17704
$779$	4.26750	0.152899
$780$	0	0
$781$	−4.28400	−0.153294
$782$	0.407670	0.0145782
$783$	−6.12447	−0.218871
$784$	−14.2226	−0.507950
$785$	0	0
$786$	7.01255	0.250129
$787$	27.6814	0.986736	0.493368	−	0.869821i	$-0.335766\pi$
$787$	27.6814	0.986736	0.493368	+	0.869821i	$0.335766\pi$
$788$	31.0016	1.10439
$789$	−33.9689	−1.20932
$790$	0	0
$791$	−42.6884	−1.51782
$792$	−1.75213	−0.0622594
$793$	14.8295	0.526609
$794$	53.7550	1.90769
$795$	0	0
$796$	−19.0109	−0.673824
$797$	4.49477	0.159213	0.0796065	−	0.996826i	$-0.474634\pi$
$797$	4.49477	0.159213	0.0796065	+	0.996826i	$0.474634\pi$
$798$	−14.5855	−0.516320
$799$	10.3303	0.365459
$800$	0	0
$801$	9.68505	0.342204
$802$	41.6262	1.46987
$803$	−1.92676	−0.0679938
$804$	53.6189	1.89099
$805$	0	0
$806$	36.5142	1.28616
$807$	−30.4456	−1.07174
$808$	−8.01978	−0.282135
$809$	48.0468	1.68924	0.844618	−	0.535369i	$-0.179828\pi$
$809$	48.0468	1.68924	0.844618	+	0.535369i	$0.179828\pi$
$810$	0	0
$811$	20.9156	0.734448	0.367224	−	0.930133i	$-0.380308\pi$
$811$	20.9156	0.734448	0.367224	+	0.930133i	$0.380308\pi$
$812$	14.2609	0.500460
$813$	−6.31564	−0.221499
$814$	12.8241	0.449485
$815$	0	0
$816$	−2.70013	−0.0945233
$817$	−3.62271	−0.126743
$818$	44.4497	1.55415
$819$	−14.1228	−0.493492
$820$	0	0
$821$	10.7228	0.374227	0.187114	−	0.982338i	$-0.440087\pi$
$821$	10.7228	0.374227	0.187114	+	0.982338i	$0.440087\pi$
$822$	12.4232	0.433310
$823$	−42.5971	−1.48484	−0.742420	−	0.669935i	$-0.766322\pi$
$823$	−42.5971	−1.48484	−0.742420	+	0.669935i	$0.766322\pi$
$824$	−40.5174	−1.41149
$825$	0	0
$826$	−8.71751	−0.303321
$827$	15.3377	0.533343	0.266672	−	0.963787i	$-0.414076\pi$
$827$	15.3377	0.533343	0.266672	+	0.963787i	$0.414076\pi$
$828$	0.273145	0.00949245
$829$	−9.78901	−0.339986	−0.169993	−	0.985445i	$-0.554375\pi$
$829$	−9.78901	−0.339986	−0.169993	+	0.985445i	$0.554375\pi$
$830$	0	0
$831$	21.7022	0.752840
$832$	−50.8896	−1.76428
$833$	20.3228	0.704143
$834$	36.9935	1.28098
$835$	0	0
$836$	−2.96714	−0.102621
$837$	23.5307	0.813339
$838$	−49.2456	−1.70116
$839$	−48.1417	−1.66204	−0.831019	−	0.556244i	$-0.812242\pi$
$839$	−48.1417	−1.66204	−0.831019	+	0.556244i	$0.812242\pi$
$840$	0	0
$841$	−27.8203	−0.959322
$842$	56.6192	1.95123
$843$	−35.6899	−1.22923
$844$	23.6449	0.813891
$845$	0	0
$846$	11.5868	0.398364
$847$	4.42518	0.152051
$848$	13.5819	0.466403
$849$	−0.291625	−0.0100086
$850$	0	0
$851$	−0.651634	−0.0223377
$852$	18.7985	0.644026
$853$	41.0884	1.40684	0.703420	−	0.710775i	$-0.251655\pi$
$853$	41.0884	1.40684	0.703420	+	0.710775i	$0.251655\pi$
$854$	−37.2516	−1.27472
$855$	0	0
$856$	−11.5082	−0.393343
$857$	30.0628	1.02693	0.513464	−	0.858111i	$-0.328362\pi$
$857$	30.0628	1.02693	0.513464	+	0.858111i	$0.328362\pi$
$858$	12.9406	0.441784
$859$	9.99982	0.341190	0.170595	−	0.985341i	$-0.445431\pi$
$859$	9.99982	0.341190	0.170595	+	0.985341i	$0.445431\pi$
$860$	0	0
$861$	27.9281	0.951787
$862$	7.83646	0.266911
$863$	−18.3253	−0.623800	−0.311900	−	0.950115i	$-0.600965\pi$
$863$	−18.3253	−0.623800	−0.311900	+	0.950115i	$0.600965\pi$
$864$	−38.5144	−1.31029
$865$	0	0
$866$	−21.6572	−0.735940
$867$	−21.2829	−0.722806
$868$	−54.7915	−1.85975
$869$	7.81004	0.264937
$870$	0	0
$871$	47.9743	1.62555
$872$	−36.1647	−1.22469
$873$	−10.8501	−0.367222
$874$	0.252396	0.00853742
$875$	0	0
$876$	8.45475	0.285660
$877$	−54.2556	−1.83208	−0.916040	−	0.401086i	$-0.868633\pi$
$877$	−54.2556	−1.83208	−0.916040	+	0.401086i	$0.868633\pi$
$878$	−1.98122	−0.0668629
$879$	−4.04434	−0.136412
$880$	0	0
$881$	−20.9741	−0.706636	−0.353318	−	0.935503i	$-0.614947\pi$
$881$	−20.9741	−0.706636	−0.353318	+	0.935503i	$0.614947\pi$
$882$	22.7949	0.767543
$883$	16.2916	0.548256	0.274128	−	0.961693i	$-0.411611\pi$
$883$	16.2916	0.548256	0.274128	+	0.961693i	$0.411611\pi$
$884$	18.8160	0.632851
$885$	0	0
$886$	12.1267	0.407404
$887$	−41.2926	−1.38647	−0.693234	−	0.720712i	$-0.743815\pi$
$887$	−41.2926	−1.38647	−0.693234	+	0.720712i	$0.743815\pi$
$888$	−18.3422	−0.615524
$889$	−2.28277	−0.0765618
$890$	0	0
$891$	5.90059	0.197677
$892$	70.9431	2.37535
$893$	6.39567	0.214023
$894$	−69.4206	−2.32177
$895$	0	0
$896$	67.3849	2.25117
$897$	−0.657552	−0.0219550
$898$	−48.1569	−1.60702
$899$	−4.53235	−0.151162
$900$	0	0
$901$	−19.4072	−0.646548
$902$	9.51102	0.316682
$903$	−23.7084	−0.788965
$904$	20.7931	0.691569
$905$	0	0
$906$	−24.6133	−0.817722
$907$	−35.5669	−1.18098	−0.590490	−	0.807045i	$-0.701065\pi$
$907$	−35.5669	−1.18098	−0.590490	+	0.807045i	$0.701065\pi$
$908$	29.7094	0.985942
$909$	−3.02446	−0.100315
$910$	0	0
$911$	26.1812	0.867422	0.433711	−	0.901052i	$-0.357204\pi$
$911$	26.1812	0.867422	0.433711	+	0.901052i	$0.357204\pi$
$912$	−1.67170	−0.0553555
$913$	−3.33410	−0.110342
$914$	−65.0774	−2.15257
$915$	0	0
$916$	31.0099	1.02459
$917$	−9.41494	−0.310909
$918$	20.2987	0.669957
$919$	0.328420	0.0108336	0.00541678	−	0.999985i	$-0.498276\pi$
$919$	0.328420	0.0108336	0.00541678	+	0.999985i	$0.498276\pi$
$920$	0	0
$921$	24.7438	0.815334
$922$	71.8390	2.36589
$923$	16.8195	0.553622
$924$	−19.4180	−0.638806
$925$	0	0
$926$	−26.4198	−0.868210
$927$	−15.2801	−0.501866
$928$	7.41844	0.243522
$929$	0.642511	0.0210801	0.0105401	−	0.999944i	$-0.496645\pi$
$929$	0.642511	0.0210801	0.0105401	+	0.999944i	$0.496645\pi$
$930$	0	0
$931$	12.5822	0.412366
$932$	13.5451	0.443685
$933$	−22.0267	−0.721122
$934$	−70.1820	−2.29643
$935$	0	0
$936$	6.87910	0.224851
$937$	−19.2863	−0.630055	−0.315027	−	0.949083i	$-0.602014\pi$
$937$	−19.2863	−0.630055	−0.315027	+	0.949083i	$0.602014\pi$
$938$	−120.512	−3.93484
$939$	−13.1553	−0.429308
$940$	0	0
$941$	19.4348	0.633556	0.316778	−	0.948500i	$-0.397399\pi$
$941$	19.4348	0.633556	0.316778	+	0.948500i	$0.397399\pi$
$942$	−19.2621	−0.627593
$943$	−0.483285	−0.0157379
$944$	−0.999149	−0.0325195
$945$	0	0
$946$	−8.07397	−0.262507
$947$	61.1924	1.98849	0.994243	−	0.107147i	$-0.0341716\pi$
$947$	61.1924	1.98849	0.994243	+	0.107147i	$0.0341716\pi$
$948$	−34.2710	−1.11307
$949$	7.56470	0.245560
$950$	0	0
$951$	−9.11468	−0.295564
$952$	−15.4063	−0.499320
$953$	−3.19828	−0.103602	−0.0518012	−	0.998657i	$-0.516496\pi$
$953$	−3.19828	−0.103602	−0.0518012	+	0.998657i	$0.516496\pi$
$954$	−21.7679	−0.704762
$955$	0	0
$956$	−45.6327	−1.47587
$957$	−1.60626	−0.0519230
$958$	−33.7794	−1.09136
$959$	−16.6793	−0.538601
$960$	0	0
$961$	−13.5864	−0.438270
$962$	−50.3491	−1.62332
$963$	−4.34005	−0.139856
$964$	53.0337	1.70810
$965$	0	0
$966$	1.65177	0.0531449
$967$	−45.2536	−1.45526	−0.727629	−	0.685970i	$-0.759378\pi$
$967$	−45.2536	−1.45526	−0.727629	+	0.685970i	$0.759378\pi$
$968$	−2.15546	−0.0692793
$969$	2.38870	0.0767362
$970$	0	0
$971$	−49.4103	−1.58565	−0.792826	−	0.609448i	$-0.791391\pi$
$971$	−49.4103	−1.58565	−0.792826	+	0.609448i	$0.791391\pi$
$972$	24.3014	0.779467
$973$	−49.6668	−1.59225
$974$	62.4381	2.00065
$975$	0	0
$976$	−4.26955	−0.136665
$977$	−48.8753	−1.56366	−0.781830	−	0.623492i	$-0.785714\pi$
$977$	−48.8753	−1.56366	−0.781830	+	0.623492i	$0.785714\pi$
$978$	−66.9345	−2.14033
$979$	11.9145	0.380789
$980$	0	0
$981$	−13.6386	−0.435448
$982$	3.48594	0.111241
$983$	−16.7325	−0.533684	−0.266842	−	0.963740i	$-0.585980\pi$
$983$	−16.7325	−0.533684	−0.266842	+	0.963740i	$0.585980\pi$
$984$	−13.6035	−0.433664
$985$	0	0
$986$	−3.90983	−0.124514
$987$	41.8556	1.33228
$988$	11.6494	0.370615
$989$	0.410264	0.0130456
$990$	0	0
$991$	−46.6422	−1.48164	−0.740820	−	0.671704i	$-0.765563\pi$
$991$	−46.6422	−1.48164	−0.740820	+	0.671704i	$0.765563\pi$
$992$	−28.5022	−0.904945
$993$	25.9020	0.821974
$994$	−42.2507	−1.34011
$995$	0	0
$996$	14.6303	0.463577
$997$	−30.3768	−0.962043	−0.481021	−	0.876709i	$-0.659734\pi$
$997$	−30.3768	−0.962043	−0.481021	+	0.876709i	$0.659734\pi$
$998$	−34.4149	−1.08938
$999$	−32.4462	−1.02655

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	5225.2.a.j.1.1		5
5.4	even	2		1045.2.a.d.1.5	✓	5
15.14	odd	2		9405.2.a.v.1.1		5

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1045.2.a.d.1.5	✓	5	5.4	even	2
5225.2.a.j.1.1		5	1.1	even	1	trivial
9405.2.a.v.1.1		5	15.14	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 5225 = 5^{2} \cdot 11 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	5225.a (trivial)

\(f(q)\)	\(=\)	\(q-2.22871 q^{2} +1.47889 q^{3} +2.96714 q^{4} -3.29602 q^{6} +4.42518 q^{7} -2.15546 q^{8} -0.812880 q^{9} +O(q^{10})\)	\(q-2.22871 q^{2} +1.47889 q^{3} +2.96714 q^{4} -3.29602 q^{6} +4.42518 q^{7} -2.15546 q^{8} -0.812880 q^{9} -1.00000 q^{11} +4.38807 q^{12} +3.92613 q^{13} -9.86243 q^{14} -1.13037 q^{16} +1.61520 q^{17} +1.81167 q^{18} +1.00000 q^{19} +6.54436 q^{21} +2.22871 q^{22} -0.113248 q^{23} -3.18770 q^{24} -8.75019 q^{26} -5.63884 q^{27} +13.1301 q^{28} +1.08612 q^{29} -4.17296 q^{31} +6.83020 q^{32} -1.47889 q^{33} -3.59980 q^{34} -2.41193 q^{36} +5.75406 q^{37} -2.22871 q^{38} +5.80632 q^{39} +4.26750 q^{41} -14.5855 q^{42} -3.62271 q^{43} -2.96714 q^{44} +0.252396 q^{46} +6.39567 q^{47} -1.67170 q^{48} +12.5822 q^{49} +2.38870 q^{51} +11.6494 q^{52} -12.0154 q^{53} +12.5673 q^{54} -9.53832 q^{56} +1.47889 q^{57} -2.42065 q^{58} +0.883911 q^{59} +3.77712 q^{61} +9.30032 q^{62} -3.59714 q^{63} -12.9618 q^{64} +3.29602 q^{66} +12.2192 q^{67} +4.79251 q^{68} -0.167481 q^{69} +4.28400 q^{71} +1.75213 q^{72} +1.92676 q^{73} -12.8241 q^{74} +2.96714 q^{76} -4.42518 q^{77} -12.9406 q^{78} -7.81004 q^{79} -5.90059 q^{81} -9.51102 q^{82} +3.33410 q^{83} +19.4180 q^{84} +8.07397 q^{86} +1.60626 q^{87} +2.15546 q^{88} -11.9145 q^{89} +17.3738 q^{91} -0.336021 q^{92} -6.17136 q^{93} -14.2541 q^{94} +10.1011 q^{96} +13.3478 q^{97} -28.0421 q^{98} +0.812880 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 5 q + 3 q^{2} + 7 q^{3} + 5 q^{4} + 2 q^{6} + 11 q^{7} - 3 q^{8} + 8 q^{9}+O(q^{10}) \) 5 * q + 3 * q^2 + 7 * q^3 + 5 * q^4 + 2 * q^6 + 11 * q^7 - 3 * q^8 + 8 * q^9	\( 5 q + 3 q^{2} + 7 q^{3} + 5 q^{4} + 2 q^{6} + 11 q^{7} - 3 q^{8} + 8 q^{9} - 5 q^{11} + 7 q^{12} - q^{13} - 3 q^{16} + 3 q^{17} + 7 q^{18} + 5 q^{19} + 11 q^{21} - 3 q^{22} + 8 q^{23} + 9 q^{24} - 16 q^{26} + 10 q^{27} + 22 q^{28} + 11 q^{29} - 5 q^{31} + 2 q^{32} - 7 q^{33} + 4 q^{34} - 3 q^{36} + 9 q^{37} + 3 q^{38} - 8 q^{39} + 15 q^{41} - 11 q^{42} + 13 q^{43} - 5 q^{44} + 18 q^{46} + 20 q^{47} + 20 q^{48} + 20 q^{49} + 24 q^{51} - q^{52} + 5 q^{53} + 17 q^{54} + 7 q^{57} + 33 q^{58} - 17 q^{59} + 3 q^{61} - 14 q^{62} + 22 q^{63} - 17 q^{64} - 2 q^{66} + 28 q^{67} + 25 q^{68} - 2 q^{69} - 6 q^{71} + 26 q^{72} + 16 q^{73} - 21 q^{74} + 5 q^{76} - 11 q^{77} - 29 q^{78} + 3 q^{79} + q^{81} - 2 q^{82} + 33 q^{83} + 33 q^{84} + 10 q^{86} + 3 q^{88} - 16 q^{89} - 22 q^{91} + 19 q^{92} + 26 q^{93} - 10 q^{94} + 5 q^{96} + 14 q^{97} - 10 q^{98} - 8 q^{99}+O(q^{100}) \) 5 * q + 3 * q^2 + 7 * q^3 + 5 * q^4 + 2 * q^6 + 11 * q^7 - 3 * q^8 + 8 * q^9 - 5 * q^11 + 7 * q^12 - q^13 - 3 * q^16 + 3 * q^17 + 7 * q^18 + 5 * q^19 + 11 * q^21 - 3 * q^22 + 8 * q^23 + 9 * q^24 - 16 * q^26 + 10 * q^27 + 22 * q^28 + 11 * q^29 - 5 * q^31 + 2 * q^32 - 7 * q^33 + 4 * q^34 - 3 * q^36 + 9 * q^37 + 3 * q^38 - 8 * q^39 + 15 * q^41 - 11 * q^42 + 13 * q^43 - 5 * q^44 + 18 * q^46 + 20 * q^47 + 20 * q^48 + 20 * q^49 + 24 * q^51 - q^52 + 5 * q^53 + 17 * q^54 + 7 * q^57 + 33 * q^58 - 17 * q^59 + 3 * q^61 - 14 * q^62 + 22 * q^63 - 17 * q^64 - 2 * q^66 + 28 * q^67 + 25 * q^68 - 2 * q^69 - 6 * q^71 + 26 * q^72 + 16 * q^73 - 21 * q^74 + 5 * q^76 - 11 * q^77 - 29 * q^78 + 3 * q^79 + q^81 - 2 * q^82 + 33 * q^83 + 33 * q^84 + 10 * q^86 + 3 * q^88 - 16 * q^89 - 22 * q^91 + 19 * q^92 + 26 * q^93 - 10 * q^94 + 5 * q^96 + 14 * q^97 - 10 * q^98 - 8 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more