LMFDB - Embedded newform 4025.2.a.z.1.4

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

Embedding invariants

Embedding label			1.4
Root			$1.63325$ 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)

$f(q)$	$=$	$q-1.63325 q^{2} +0.456743 q^{3} +0.667506 q^{4} -0.745975 q^{6} -1.00000 q^{7} +2.17630 q^{8} -2.79139 q^{9} +O(q^{10})$	\(q-1.63325 q^{2} +0.456743 q^{3} +0.667506 q^{4} -0.745975 q^{6} -1.00000 q^{7} +2.17630 q^{8} -2.79139 q^{9} +0.335247 q^{11} +0.304879 q^{12} +4.58103 q^{13} +1.63325 q^{14} -4.88945 q^{16} -3.39509 q^{17} +4.55903 q^{18} +2.11764 q^{19} -0.456743 q^{21} -0.547542 q^{22} -1.00000 q^{23} +0.994007 q^{24} -7.48196 q^{26} -2.64517 q^{27} -0.667506 q^{28} +1.10564 q^{29} +1.68701 q^{31} +3.63310 q^{32} +0.153122 q^{33} +5.54503 q^{34} -1.86327 q^{36} -6.60823 q^{37} -3.45863 q^{38} +2.09235 q^{39} +9.47182 q^{41} +0.745975 q^{42} -9.10800 q^{43} +0.223779 q^{44} +1.63325 q^{46} -2.36690 q^{47} -2.23322 q^{48} +1.00000 q^{49} -1.55068 q^{51} +3.05786 q^{52} -1.55754 q^{53} +4.32023 q^{54} -2.17630 q^{56} +0.967216 q^{57} -1.80579 q^{58} +10.2206 q^{59} +3.04415 q^{61} -2.75531 q^{62} +2.79139 q^{63} +3.84513 q^{64} -0.250086 q^{66} +0.953507 q^{67} -2.26624 q^{68} -0.456743 q^{69} -6.97877 q^{71} -6.07488 q^{72} -7.24562 q^{73} +10.7929 q^{74} +1.41354 q^{76} -0.335247 q^{77} -3.41733 q^{78} -2.83560 q^{79} +7.16599 q^{81} -15.4699 q^{82} +8.54319 q^{83} -0.304879 q^{84} +14.8756 q^{86} +0.504994 q^{87} +0.729597 q^{88} -12.2488 q^{89} -4.58103 q^{91} -0.667506 q^{92} +0.770530 q^{93} +3.86574 q^{94} +1.65939 q^{96} +1.59216 q^{97} -1.63325 q^{98} -0.935804 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 14 q - 3 q^{2} - 4 q^{3} + 17 q^{4} - 4 q^{6} - 14 q^{7} - 3 q^{8} + 18 q^{9}+O(q^{10}) $ 14 * q - 3 * q^2 - 4 * q^3 + 17 * q^4 - 4 * q^6 - 14 * q^7 - 3 * q^8 + 18 * q^9	$ 14 q - 3 q^{2} - 4 q^{3} + 17 q^{4} - 4 q^{6} - 14 q^{7} - 3 q^{8} + 18 q^{9} + 5 q^{11} - 17 q^{12} - 11 q^{13} + 3 q^{14} + 23 q^{16} - 3 q^{17} - 15 q^{18} - 2 q^{19} + 4 q^{21} - 23 q^{22} - 14 q^{23} - 12 q^{24} - 9 q^{26} - 25 q^{27} - 17 q^{28} + 7 q^{29} - 3 q^{31} - 24 q^{32} - 6 q^{33} - 14 q^{34} + 13 q^{36} - 22 q^{37} - 20 q^{38} - 10 q^{39} - 17 q^{41} + 4 q^{42} - 18 q^{43} + 28 q^{44} + 3 q^{46} - 30 q^{47} - 8 q^{48} + 14 q^{49} + 4 q^{51} - 8 q^{52} - 11 q^{53} + 20 q^{54} + 3 q^{56} - 18 q^{57} - 38 q^{58} - 22 q^{59} - 8 q^{61} + 22 q^{62} - 18 q^{63} + 29 q^{64} - 9 q^{66} - 39 q^{67} - q^{68} + 4 q^{69} - 5 q^{71} + 24 q^{72} - 18 q^{73} + 35 q^{74} - 41 q^{76} - 5 q^{77} + 22 q^{78} + 10 q^{79} + 2 q^{81} + 8 q^{82} - 24 q^{83} + 17 q^{84} - 26 q^{86} - 5 q^{87} - 58 q^{88} + 25 q^{89} + 11 q^{91} - 17 q^{92} - 47 q^{93} - 2 q^{94} - 117 q^{96} - 43 q^{97} - 3 q^{98} + 55 q^{99}+O(q^{100}) $ 14 * q - 3 * q^2 - 4 * q^3 + 17 * q^4 - 4 * q^6 - 14 * q^7 - 3 * q^8 + 18 * q^9 + 5 * q^11 - 17 * q^12 - 11 * q^13 + 3 * q^14 + 23 * q^16 - 3 * q^17 - 15 * q^18 - 2 * q^19 + 4 * q^21 - 23 * q^22 - 14 * q^23 - 12 * q^24 - 9 * q^26 - 25 * q^27 - 17 * q^28 + 7 * q^29 - 3 * q^31 - 24 * q^32 - 6 * q^33 - 14 * q^34 + 13 * q^36 - 22 * q^37 - 20 * q^38 - 10 * q^39 - 17 * q^41 + 4 * q^42 - 18 * q^43 + 28 * q^44 + 3 * q^46 - 30 * q^47 - 8 * q^48 + 14 * q^49 + 4 * q^51 - 8 * q^52 - 11 * q^53 + 20 * q^54 + 3 * q^56 - 18 * q^57 - 38 * q^58 - 22 * q^59 - 8 * q^61 + 22 * q^62 - 18 * q^63 + 29 * q^64 - 9 * q^66 - 39 * q^67 - q^68 + 4 * q^69 - 5 * q^71 + 24 * q^72 - 18 * q^73 + 35 * q^74 - 41 * q^76 - 5 * q^77 + 22 * q^78 + 10 * q^79 + 2 * q^81 + 8 * q^82 - 24 * q^83 + 17 * q^84 - 26 * q^86 - 5 * q^87 - 58 * q^88 + 25 * q^89 + 11 * q^91 - 17 * q^92 - 47 * q^93 - 2 * q^94 - 117 * q^96 - 43 * q^97 - 3 * q^98 + 55 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−1.63325	−1.15488	−0.577441	−	0.816432i	$-0.695949\pi$
$2$	−1.63325	−1.15488	−0.577441	+	0.816432i	$0.695949\pi$
$3$	0.456743	0.263701	0.131850	−	0.991270i	$-0.457908\pi$
$3$	0.456743	0.263701	0.131850	+	0.991270i	$0.457908\pi$
$4$	0.667506	0.333753
$5$	0	0
$5$	0	0
$6$	−0.745975	−0.304543
$7$	−1.00000	−0.377964
$7$	−1.00000	−0.377964
$8$	2.17630	0.769437
$9$	−2.79139	−0.930462
$10$	0	0
$11$	0.335247	0.101081	0.0505404	−	0.998722i	$-0.483906\pi$
$11$	0.335247	0.101081	0.0505404	+	0.998722i	$0.483906\pi$
$12$	0.304879	0.0880109
$13$	4.58103	1.27055	0.635274	−	0.772287i	$-0.280887\pi$
$13$	4.58103	1.27055	0.635274	+	0.772287i	$0.280887\pi$
$14$	1.63325	0.436504
$15$	0	0
$16$	−4.88945	−1.22236
$17$	−3.39509	−0.823430	−0.411715	−	0.911313i	$-0.635070\pi$
$17$	−3.39509	−0.823430	−0.411715	+	0.911313i	$0.635070\pi$
$18$	4.55903	1.07457
$19$	2.11764	0.485819	0.242910	−	0.970049i	$-0.421898\pi$
$19$	2.11764	0.485819	0.242910	+	0.970049i	$0.421898\pi$
$20$	0	0
$21$	−0.456743	−0.0996694
$22$	−0.547542	−0.116736
$23$	−1.00000	−0.208514
$23$	−1.00000	−0.208514
$24$	0.994007	0.202901
$25$	0	0
$26$	−7.48196	−1.46733
$27$	−2.64517	−0.509064
$28$	−0.667506	−0.126147
$29$	1.10564	0.205313	0.102656	−	0.994717i	$-0.467266\pi$
$29$	1.10564	0.205313	0.102656	+	0.994717i	$0.467266\pi$
$30$	0	0
$31$	1.68701	0.302996	0.151498	−	0.988458i	$-0.451590\pi$
$31$	1.68701	0.302996	0.151498	+	0.988458i	$0.451590\pi$
$32$	3.63310	0.642247
$33$	0.153122	0.0266551
$34$	5.54503	0.950965
$35$	0	0
$36$	−1.86327	−0.310545
$37$	−6.60823	−1.08639	−0.543194	−	0.839608i	$-0.682785\pi$
$37$	−6.60823	−1.08639	−0.543194	+	0.839608i	$0.682785\pi$
$38$	−3.45863	−0.561064
$39$	2.09235	0.335044
$40$	0	0
$41$	9.47182	1.47925	0.739625	−	0.673019i	$-0.235003\pi$
$41$	9.47182	1.47925	0.739625	+	0.673019i	$0.235003\pi$
$42$	0.745975	0.115106
$43$	−9.10800	−1.38896	−0.694479	−	0.719513i	$-0.744365\pi$
$43$	−9.10800	−1.38896	−0.694479	+	0.719513i	$0.744365\pi$
$44$	0.223779	0.0337360
$45$	0	0
$46$	1.63325	0.240810
$47$	−2.36690	−0.345248	−0.172624	−	0.984988i	$-0.555225\pi$
$47$	−2.36690	−0.345248	−0.172624	+	0.984988i	$0.555225\pi$
$48$	−2.23322	−0.322337
$49$	1.00000	0.142857
$50$	0	0
$51$	−1.55068	−0.217139
$52$	3.05786	0.424049
$53$	−1.55754	−0.213944	−0.106972	−	0.994262i	$-0.534116\pi$
$53$	−1.55754	−0.213944	−0.106972	+	0.994262i	$0.534116\pi$
$54$	4.32023	0.587909
$55$	0	0
$56$	−2.17630	−0.290820
$57$	0.967216	0.128111
$58$	−1.80579	−0.237112
$59$	10.2206	1.33061	0.665307	−	0.746570i	$-0.268301\pi$
$59$	10.2206	1.33061	0.665307	+	0.746570i	$0.268301\pi$
$60$	0	0
$61$	3.04415	0.389764	0.194882	−	0.980827i	$-0.437568\pi$
$61$	3.04415	0.389764	0.194882	+	0.980827i	$0.437568\pi$
$62$	−2.75531	−0.349925
$63$	2.79139	0.351682
$64$	3.84513	0.480642
$65$	0	0
$66$	−0.250086	−0.0307834
$67$	0.953507	0.116489	0.0582447	−	0.998302i	$-0.481450\pi$
$67$	0.953507	0.116489	0.0582447	+	0.998302i	$0.481450\pi$
$68$	−2.26624	−0.274822
$69$	−0.456743	−0.0549854
$70$	0	0
$71$	−6.97877	−0.828227	−0.414114	−	0.910225i	$-0.635908\pi$
$71$	−6.97877	−0.828227	−0.414114	+	0.910225i	$0.635908\pi$
$72$	−6.07488	−0.715932
$73$	−7.24562	−0.848036	−0.424018	−	0.905654i	$-0.639381\pi$
$73$	−7.24562	−0.848036	−0.424018	+	0.905654i	$0.639381\pi$
$74$	10.7929	1.25465
$75$	0	0
$76$	1.41354	0.162144
$77$	−0.335247	−0.0382049
$78$	−3.41733	−0.386937
$79$	−2.83560	−0.319030	−0.159515	−	0.987195i	$-0.550993\pi$
$79$	−2.83560	−0.319030	−0.159515	+	0.987195i	$0.550993\pi$
$80$	0	0
$81$	7.16599	0.796222
$82$	−15.4699	−1.70836
$83$	8.54319	0.937737	0.468869	−	0.883268i	$-0.344662\pi$
$83$	8.54319	0.937737	0.468869	+	0.883268i	$0.344662\pi$
$84$	−0.304879	−0.0332650
$85$	0	0
$86$	14.8756	1.60408
$87$	0.504994	0.0541410
$88$	0.729597	0.0777753
$89$	−12.2488	−1.29837	−0.649186	−	0.760630i	$-0.724890\pi$
$89$	−12.2488	−1.29837	−0.649186	+	0.760630i	$0.724890\pi$
$90$	0	0
$91$	−4.58103	−0.480222
$92$	−0.667506	−0.0695923
$93$	0.770530	0.0799003
$94$	3.86574	0.398721
$95$	0	0
$96$	1.65939	0.169361
$97$	1.59216	0.161660	0.0808298	−	0.996728i	$-0.474243\pi$
$97$	1.59216	0.161660	0.0808298	+	0.996728i	$0.474243\pi$
$98$	−1.63325	−0.164983
$99$	−0.935804	−0.0940518
$100$	0	0
$101$	2.27098	0.225971	0.112985	−	0.993597i	$-0.463959\pi$
$101$	2.27098	0.225971	0.112985	+	0.993597i	$0.463959\pi$
$102$	2.53265	0.250770
$103$	14.9493	1.47300	0.736501	−	0.676437i	$-0.236477\pi$
$103$	14.9493	1.47300	0.736501	+	0.676437i	$0.236477\pi$
$104$	9.96967	0.977607
$105$	0	0
$106$	2.54385	0.247080
$107$	−4.87423	−0.471210	−0.235605	−	0.971849i	$-0.575707\pi$
$107$	−4.87423	−0.471210	−0.235605	+	0.971849i	$0.575707\pi$
$108$	−1.76567	−0.169902
$109$	1.76579	0.169132	0.0845661	−	0.996418i	$-0.473050\pi$
$109$	1.76579	0.169132	0.0845661	+	0.996418i	$0.473050\pi$
$110$	0	0
$111$	−3.01826	−0.286481
$112$	4.88945	0.462009
$113$	−2.36111	−0.222114	−0.111057	−	0.993814i	$-0.535424\pi$
$113$	−2.36111	−0.222114	−0.111057	+	0.993814i	$0.535424\pi$
$114$	−1.57970	−0.147953
$115$	0	0
$116$	0.738023	0.0685237
$117$	−12.7874	−1.18220
$118$	−16.6929	−1.53670
$119$	3.39509	0.311227
$120$	0	0
$121$	−10.8876	−0.989783
$122$	−4.97186	−0.450131
$123$	4.32619	0.390079
$124$	1.12609	0.101126
$125$	0	0
$126$	−4.55903	−0.406151
$127$	−15.9550	−1.41578	−0.707890	−	0.706322i	$-0.750353\pi$
$127$	−15.9550	−1.41578	−0.707890	+	0.706322i	$0.750353\pi$
$128$	−13.5463	−1.19733
$129$	−4.16001	−0.366269
$130$	0	0
$131$	−10.4772	−0.915396	−0.457698	−	0.889108i	$-0.651326\pi$
$131$	−10.4772	−0.915396	−0.457698	+	0.889108i	$0.651326\pi$
$132$	0.102210	0.00889620
$133$	−2.11764	−0.183622
$134$	−1.55732	−0.134532
$135$	0	0
$136$	−7.38872	−0.633577
$137$	−0.0798775	−0.00682440	−0.00341220	−	0.999994i	$-0.501086\pi$
$137$	−0.0798775	−0.00682440	−0.00341220	+	0.999994i	$0.501086\pi$
$138$	0.745975	0.0635016
$139$	9.20759	0.780978	0.390489	−	0.920608i	$-0.372306\pi$
$139$	9.20759	0.780978	0.390489	+	0.920608i	$0.372306\pi$
$140$	0	0
$141$	−1.08107	−0.0910421
$142$	11.3981	0.956505
$143$	1.53578	0.128428
$144$	13.6483	1.13736
$145$	0	0
$146$	11.8339	0.979382
$147$	0.456743	0.0376715
$148$	−4.41104	−0.362585
$149$	19.3465	1.58493	0.792464	−	0.609919i	$-0.208798\pi$
$149$	19.3465	1.58493	0.792464	+	0.609919i	$0.208798\pi$
$150$	0	0
$151$	−2.19693	−0.178784	−0.0893918	−	0.995997i	$-0.528492\pi$
$151$	−2.19693	−0.178784	−0.0893918	+	0.995997i	$0.528492\pi$
$152$	4.60861	0.373807
$153$	9.47701	0.766171
$154$	0.547542	0.0441222
$155$	0	0
$156$	1.39666	0.111822
$157$	3.64204	0.290666	0.145333	−	0.989383i	$-0.453575\pi$
$157$	3.64204	0.290666	0.145333	+	0.989383i	$0.453575\pi$
$158$	4.63125	0.368442
$159$	−0.711393	−0.0564171
$160$	0	0
$161$	1.00000	0.0788110
$162$	−11.7039	−0.919542
$163$	−21.5685	−1.68938	−0.844689	−	0.535258i	$-0.820215\pi$
$163$	−21.5685	−1.68938	−0.844689	+	0.535258i	$0.820215\pi$
$164$	6.32250	0.493704
$165$	0	0
$166$	−13.9532	−1.08298
$167$	−15.3534	−1.18809	−0.594043	−	0.804433i	$-0.702469\pi$
$167$	−15.3534	−1.18809	−0.594043	+	0.804433i	$0.702469\pi$
$168$	−0.994007	−0.0766893
$169$	7.98581	0.614293
$170$	0	0
$171$	−5.91114	−0.452037
$172$	−6.07965	−0.463569
$173$	−21.6642	−1.64710	−0.823548	−	0.567246i	$-0.808009\pi$
$173$	−21.6642	−1.64710	−0.823548	+	0.567246i	$0.808009\pi$
$174$	−0.824781	−0.0625265
$175$	0	0
$176$	−1.63917	−0.123557
$177$	4.66820	0.350884
$178$	20.0054	1.49947
$179$	−11.2083	−0.837745	−0.418873	−	0.908045i	$-0.637575\pi$
$179$	−11.2083	−0.837745	−0.418873	+	0.908045i	$0.637575\pi$
$180$	0	0
$181$	4.20726	0.312723	0.156362	−	0.987700i	$-0.450023\pi$
$181$	4.20726	0.312723	0.156362	+	0.987700i	$0.450023\pi$
$182$	7.48196	0.554600
$183$	1.39039	0.102781
$184$	−2.17630	−0.160439
$185$	0	0
$186$	−1.25847	−0.0922754
$187$	−1.13819	−0.0832330
$188$	−1.57992	−0.115228
$189$	2.64517	0.192408
$190$	0	0
$191$	10.4542	0.756439	0.378219	−	0.925716i	$-0.376537\pi$
$191$	10.4542	0.756439	0.378219	+	0.925716i	$0.376537\pi$
$192$	1.75624	0.126746
$193$	0.207193	0.0149141	0.00745706	−	0.999972i	$-0.497626\pi$
$193$	0.207193	0.0149141	0.00745706	+	0.999972i	$0.497626\pi$
$194$	−2.60040	−0.186698
$195$	0	0
$196$	0.667506	0.0476790
$197$	4.58568	0.326716	0.163358	−	0.986567i	$-0.447767\pi$
$197$	4.58568	0.326716	0.163358	+	0.986567i	$0.447767\pi$
$198$	1.52840	0.108619
$199$	−17.2299	−1.22140	−0.610698	−	0.791863i	$-0.709111\pi$
$199$	−17.2299	−1.22140	−0.610698	+	0.791863i	$0.709111\pi$
$200$	0	0
$201$	0.435507	0.0307183
$202$	−3.70908	−0.260970
$203$	−1.10564	−0.0776009
$204$	−1.03509	−0.0724708
$205$	0	0
$206$	−24.4160	−1.70114
$207$	2.79139	0.194015
$208$	−22.3987	−1.55307
$209$	0.709932	0.0491070
$210$	0	0
$211$	−23.1367	−1.59280	−0.796399	−	0.604772i	$-0.793264\pi$
$211$	−23.1367	−1.59280	−0.796399	+	0.604772i	$0.793264\pi$
$212$	−1.03966	−0.0714044
$213$	−3.18750	−0.218404
$214$	7.96084	0.544192
$215$	0	0
$216$	−5.75668	−0.391692
$217$	−1.68701	−0.114522
$218$	−2.88398	−0.195328
$219$	−3.30939	−0.223628
$220$	0	0
$221$	−15.5530	−1.04621
$222$	4.92958	0.330852
$223$	14.2056	0.951278	0.475639	−	0.879641i	$-0.342217\pi$
$223$	14.2056	0.951278	0.475639	+	0.879641i	$0.342217\pi$
$224$	−3.63310	−0.242747
$225$	0	0
$226$	3.85628	0.256516
$227$	15.8588	1.05258	0.526291	−	0.850304i	$-0.323582\pi$
$227$	15.8588	1.05258	0.526291	+	0.850304i	$0.323582\pi$
$228$	0.645622	0.0427574
$229$	−1.17836	−0.0778683	−0.0389341	−	0.999242i	$-0.512396\pi$
$229$	−1.17836	−0.0778683	−0.0389341	+	0.999242i	$0.512396\pi$
$230$	0	0
$231$	−0.153122	−0.0100747
$232$	2.40620	0.157975
$233$	−15.3627	−1.00644	−0.503220	−	0.864158i	$-0.667852\pi$
$233$	−15.3627	−1.00644	−0.503220	+	0.864158i	$0.667852\pi$
$234$	20.8850	1.36530
$235$	0	0
$236$	6.82234	0.444097
$237$	−1.29514	−0.0841284
$238$	−5.54503	−0.359431
$239$	11.5814	0.749135	0.374568	−	0.927200i	$-0.377791\pi$
$239$	11.5814	0.749135	0.374568	+	0.927200i	$0.377791\pi$
$240$	0	0
$241$	8.18147	0.527015	0.263508	−	0.964657i	$-0.415121\pi$
$241$	8.18147	0.527015	0.263508	+	0.964657i	$0.415121\pi$
$242$	17.7822	1.14308
$243$	11.2085	0.719028
$244$	2.03199	0.130085
$245$	0	0
$246$	−7.06575	−0.450495
$247$	9.70096	0.617257
$248$	3.67144	0.233137
$249$	3.90204	0.247282
$250$	0	0
$251$	12.0243	0.758964	0.379482	−	0.925199i	$-0.376102\pi$
$251$	12.0243	0.758964	0.379482	+	0.925199i	$0.376102\pi$
$252$	1.86327	0.117375
$253$	−0.335247	−0.0210768
$254$	26.0586	1.63506
$255$	0	0
$256$	14.4342	0.902136
$257$	−6.13850	−0.382909	−0.191455	−	0.981501i	$-0.561320\pi$
$257$	−6.13850	−0.382909	−0.191455	+	0.981501i	$0.561320\pi$
$258$	6.79434	0.422997
$259$	6.60823	0.410616
$260$	0	0
$261$	−3.08627	−0.191036
$262$	17.1119	1.05717
$263$	−14.1956	−0.875338	−0.437669	−	0.899136i	$-0.644196\pi$
$263$	−14.1956	−0.875338	−0.437669	+	0.899136i	$0.644196\pi$
$264$	0.333238	0.0205094
$265$	0	0
$266$	3.45863	0.212062
$267$	−5.59456	−0.342381
$268$	0.636472	0.0388787
$269$	−7.12319	−0.434309	−0.217154	−	0.976137i	$-0.569677\pi$
$269$	−7.12319	−0.434309	−0.217154	+	0.976137i	$0.569677\pi$
$270$	0	0
$271$	−9.98249	−0.606393	−0.303197	−	0.952928i	$-0.598054\pi$
$271$	−9.98249	−0.606393	−0.303197	+	0.952928i	$0.598054\pi$
$272$	16.6001	1.00653
$273$	−2.09235	−0.126635
$274$	0.130460	0.00788137
$275$	0	0
$276$	−0.304879	−0.0183515
$277$	−23.5355	−1.41411	−0.707054	−	0.707159i	$-0.749976\pi$
$277$	−23.5355	−1.41411	−0.707054	+	0.707159i	$0.749976\pi$
$278$	−15.0383	−0.901937
$279$	−4.70910	−0.281927
$280$	0	0
$281$	−4.22319	−0.251934	−0.125967	−	0.992034i	$-0.540203\pi$
$281$	−4.22319	−0.251934	−0.125967	+	0.992034i	$0.540203\pi$
$282$	1.76565	0.105143
$283$	−6.96407	−0.413971	−0.206985	−	0.978344i	$-0.566365\pi$
$283$	−6.96407	−0.413971	−0.206985	+	0.978344i	$0.566365\pi$
$284$	−4.65837	−0.276423
$285$	0	0
$286$	−2.50831	−0.148319
$287$	−9.47182	−0.559104
$288$	−10.1414	−0.597587
$289$	−5.47337	−0.321963
$290$	0	0
$291$	0.727208	0.0426297
$292$	−4.83650	−0.283035
$293$	6.40853	0.374390	0.187195	−	0.982323i	$-0.440060\pi$
$293$	6.40853	0.374390	0.187195	+	0.982323i	$0.440060\pi$
$294$	−0.745975	−0.0435061
$295$	0	0
$296$	−14.3815	−0.835906
$297$	−0.886786	−0.0514566
$298$	−31.5977	−1.83041
$299$	−4.58103	−0.264928
$300$	0	0
$301$	9.10800	0.524977
$302$	3.58813	0.206474
$303$	1.03725	0.0595886
$304$	−10.3541	−0.593847
$305$	0	0
$306$	−15.4783	−0.884837
$307$	4.62513	0.263970	0.131985	−	0.991252i	$-0.457865\pi$
$307$	4.62513	0.263970	0.131985	+	0.991252i	$0.457865\pi$
$308$	−0.223779	−0.0127510
$309$	6.82800	0.388431
$310$	0	0
$311$	−2.86816	−0.162638	−0.0813191	−	0.996688i	$-0.525913\pi$
$311$	−2.86816	−0.162638	−0.0813191	+	0.996688i	$0.525913\pi$
$312$	4.55357	0.257795
$313$	16.9889	0.960267	0.480133	−	0.877195i	$-0.340588\pi$
$313$	16.9889	0.960267	0.480133	+	0.877195i	$0.340588\pi$
$314$	−5.94836	−0.335685
$315$	0	0
$316$	−1.89278	−0.106477
$317$	3.78249	0.212446	0.106223	−	0.994342i	$-0.466124\pi$
$317$	3.78249	0.212446	0.106223	+	0.994342i	$0.466124\pi$
$318$	1.16188	0.0651551
$319$	0.370663	0.0207532
$320$	0	0
$321$	−2.22627	−0.124258
$322$	−1.63325	−0.0910175
$323$	−7.18957	−0.400038
$324$	4.78335	0.265741
$325$	0	0
$326$	35.2268	1.95103
$327$	0.806513	0.0446003
$328$	20.6135	1.13819
$329$	2.36690	0.130492
$330$	0	0
$331$	−17.6540	−0.970349	−0.485175	−	0.874417i	$-0.661244\pi$
$331$	−17.6540	−0.970349	−0.485175	+	0.874417i	$0.661244\pi$
$332$	5.70263	0.312973
$333$	18.4461	1.01084
$334$	25.0760	1.37210
$335$	0	0
$336$	2.23322	0.121832
$337$	−25.4009	−1.38367	−0.691837	−	0.722054i	$-0.743198\pi$
$337$	−25.4009	−1.38367	−0.691837	+	0.722054i	$0.743198\pi$
$338$	−13.0428	−0.709436
$339$	−1.07842	−0.0585716
$340$	0	0
$341$	0.565566	0.0306271
$342$	9.65438	0.522049
$343$	−1.00000	−0.0539949
$344$	−19.8217	−1.06872
$345$	0	0
$346$	35.3830	1.90220
$347$	−6.36913	−0.341913	−0.170957	−	0.985279i	$-0.554686\pi$
$347$	−6.36913	−0.341913	−0.170957	+	0.985279i	$0.554686\pi$
$348$	0.337087	0.0180697
$349$	−19.9299	−1.06682	−0.533411	−	0.845856i	$-0.679090\pi$
$349$	−19.9299	−1.06682	−0.533411	+	0.845856i	$0.679090\pi$
$350$	0	0
$351$	−12.1176	−0.646790
$352$	1.21799	0.0649189
$353$	−12.6504	−0.673314	−0.336657	−	0.941627i	$-0.609296\pi$
$353$	−12.6504	−0.673314	−0.336657	+	0.941627i	$0.609296\pi$
$354$	−7.62434	−0.405229
$355$	0	0
$356$	−8.17616	−0.433336
$357$	1.55068	0.0820708
$358$	18.3059	0.967497
$359$	15.6866	0.827907	0.413954	−	0.910298i	$-0.364148\pi$
$359$	15.6866	0.827907	0.413954	+	0.910298i	$0.364148\pi$
$360$	0	0
$361$	−14.5156	−0.763980
$362$	−6.87151	−0.361159
$363$	−4.97284	−0.261006
$364$	−3.05786	−0.160276
$365$	0	0
$366$	−2.27086	−0.118700
$367$	−16.0954	−0.840171	−0.420085	−	0.907485i	$-0.638000\pi$
$367$	−16.0954	−0.840171	−0.420085	+	0.907485i	$0.638000\pi$
$368$	4.88945	0.254880
$369$	−26.4395	−1.37639
$370$	0	0
$371$	1.55754	0.0808632
$372$	0.514334	0.0266670
$373$	−29.3402	−1.51918	−0.759590	−	0.650403i	$-0.774600\pi$
$373$	−29.3402	−1.51918	−0.759590	+	0.650403i	$0.774600\pi$
$374$	1.85895	0.0961243
$375$	0	0
$376$	−5.15108	−0.265647
$377$	5.06498	0.260860
$378$	−4.32023	−0.222209
$379$	−3.56915	−0.183335	−0.0916675	−	0.995790i	$-0.529220\pi$
$379$	−3.56915	−0.183335	−0.0916675	+	0.995790i	$0.529220\pi$
$380$	0	0
$381$	−7.28735	−0.373342
$382$	−17.0743	−0.873598
$383$	−14.5600	−0.743983	−0.371992	−	0.928236i	$-0.621325\pi$
$383$	−14.5600	−0.743983	−0.371992	+	0.928236i	$0.621325\pi$
$384$	−6.18716	−0.315737
$385$	0	0
$386$	−0.338399	−0.0172240
$387$	25.4240	1.29237
$388$	1.06278	0.0539544
$389$	−27.7276	−1.40584	−0.702922	−	0.711266i	$-0.748122\pi$
$389$	−27.7276	−1.40584	−0.702922	+	0.711266i	$0.748122\pi$
$390$	0	0
$391$	3.39509	0.171697
$392$	2.17630	0.109920
$393$	−4.78538	−0.241390
$394$	−7.48957	−0.377319
$395$	0	0
$396$	−0.624655	−0.0313901
$397$	−26.1295	−1.31140	−0.655702	−	0.755020i	$-0.727627\pi$
$397$	−26.1295	−1.31140	−0.655702	+	0.755020i	$0.727627\pi$
$398$	28.1408	1.41057
$399$	−0.967216	−0.0484213
$400$	0	0
$401$	−2.78796	−0.139224	−0.0696121	−	0.997574i	$-0.522176\pi$
$401$	−2.78796	−0.139224	−0.0696121	+	0.997574i	$0.522176\pi$
$402$	−0.711293	−0.0354761
$403$	7.72825	0.384972
$404$	1.51589	0.0754184
$405$	0	0
$406$	1.80579	0.0896199
$407$	−2.21539	−0.109813
$408$	−3.37474	−0.167075
$409$	−22.9895	−1.13676	−0.568380	−	0.822766i	$-0.692430\pi$
$409$	−22.9895	−1.13676	−0.568380	+	0.822766i	$0.692430\pi$
$410$	0	0
$411$	−0.0364835	−0.00179960
$412$	9.97877	0.491619
$413$	−10.2206	−0.502925
$414$	−4.55903	−0.224064
$415$	0	0
$416$	16.6433	0.816006
$417$	4.20550	0.205944
$418$	−1.15950	−0.0567128
$419$	−39.9990	−1.95408	−0.977038	−	0.213064i	$-0.931656\pi$
$419$	−39.9990	−1.95408	−0.977038	+	0.213064i	$0.931656\pi$
$420$	0	0
$421$	17.4910	0.852458	0.426229	−	0.904615i	$-0.359842\pi$
$421$	17.4910	0.852458	0.426229	+	0.904615i	$0.359842\pi$
$422$	37.7881	1.83949
$423$	6.60694	0.321240
$424$	−3.38966	−0.164616
$425$	0	0
$426$	5.20599	0.252231
$427$	−3.04415	−0.147317
$428$	−3.25358	−0.157268
$429$	0.701454	0.0338665
$430$	0	0
$431$	33.5444	1.61578	0.807889	−	0.589335i	$-0.200610\pi$
$431$	33.5444	1.61578	0.807889	+	0.589335i	$0.200610\pi$
$432$	12.9334	0.622260
$433$	32.2856	1.55155	0.775773	−	0.631012i	$-0.217360\pi$
$433$	32.2856	1.55155	0.775773	+	0.631012i	$0.217360\pi$
$434$	2.75531	0.132259
$435$	0	0
$436$	1.17868	0.0564484
$437$	−2.11764	−0.101300
$438$	5.40505	0.258263
$439$	14.0359	0.669899	0.334950	−	0.942236i	$-0.391281\pi$
$439$	14.0359	0.669899	0.334950	+	0.942236i	$0.391281\pi$
$440$	0	0
$441$	−2.79139	−0.132923
$442$	25.4019	1.20825
$443$	−8.02107	−0.381093	−0.190546	−	0.981678i	$-0.561026\pi$
$443$	−8.02107	−0.381093	−0.190546	+	0.981678i	$0.561026\pi$
$444$	−2.01471	−0.0956138
$445$	0	0
$446$	−23.2013	−1.09861
$447$	8.83638	0.417946
$448$	−3.84513	−0.181666
$449$	34.1493	1.61161	0.805803	−	0.592183i	$-0.201734\pi$
$449$	34.1493	1.61161	0.805803	+	0.592183i	$0.201734\pi$
$450$	0	0
$451$	3.17540	0.149524
$452$	−1.57605	−0.0741313
$453$	−1.00343	−0.0471453
$454$	−25.9013	−1.21561
$455$	0	0
$456$	2.10495	0.0985732
$457$	−29.6565	−1.38727	−0.693637	−	0.720325i	$-0.743993\pi$
$457$	−29.6565	−1.38727	−0.693637	+	0.720325i	$0.743993\pi$
$458$	1.92456	0.0899287
$459$	8.98060	0.419179
$460$	0	0
$461$	−11.4444	−0.533017	−0.266509	−	0.963833i	$-0.585870\pi$
$461$	−11.4444	−0.533017	−0.266509	+	0.963833i	$0.585870\pi$
$462$	0.250086	0.0116350
$463$	−38.4089	−1.78501	−0.892507	−	0.451033i	$-0.851056\pi$
$463$	−38.4089	−1.78501	−0.892507	+	0.451033i	$0.851056\pi$
$464$	−5.40598	−0.250966
$465$	0	0
$466$	25.0911	1.16232
$467$	4.43064	0.205026	0.102513	−	0.994732i	$-0.467312\pi$
$467$	4.43064	0.205026	0.102513	+	0.994732i	$0.467312\pi$
$468$	−8.53568	−0.394562
$469$	−0.953507	−0.0440289
$470$	0	0
$471$	1.66347	0.0766488
$472$	22.2431	1.02382
$473$	−3.05343	−0.140397
$474$	2.11529	0.0971584
$475$	0	0
$476$	2.26624	0.103873
$477$	4.34768	0.199067
$478$	−18.9152	−0.865163
$479$	0.713525	0.0326018	0.0163009	−	0.999867i	$-0.494811\pi$
$479$	0.713525	0.0326018	0.0163009	+	0.999867i	$0.494811\pi$
$480$	0	0
$481$	−30.2725	−1.38031
$482$	−13.3624	−0.608640
$483$	0.456743	0.0207825
$484$	−7.26755	−0.330343
$485$	0	0
$486$	−18.3063	−0.830393
$487$	−8.82567	−0.399929	−0.199965	−	0.979803i	$-0.564083\pi$
$487$	−8.82567	−0.399929	−0.199965	+	0.979803i	$0.564083\pi$
$488$	6.62497	0.299898
$489$	−9.85127	−0.445490
$490$	0	0
$491$	−5.73916	−0.259005	−0.129502	−	0.991579i	$-0.541338\pi$
$491$	−5.73916	−0.259005	−0.129502	+	0.991579i	$0.541338\pi$
$492$	2.88776	0.130190
$493$	−3.75375	−0.169061
$494$	−15.8441	−0.712859
$495$	0	0
$496$	−8.24856	−0.370371
$497$	6.97877	0.313040
$498$	−6.37301	−0.285581
$499$	10.5018	0.470123	0.235062	−	0.971980i	$-0.424471\pi$
$499$	10.5018	0.470123	0.235062	+	0.971980i	$0.424471\pi$
$500$	0	0
$501$	−7.01258	−0.313299
$502$	−19.6386	−0.876515
$503$	0.988754	0.0440864	0.0220432	−	0.999757i	$-0.492983\pi$
$503$	0.988754	0.0440864	0.0220432	+	0.999757i	$0.492983\pi$
$504$	6.07488	0.270597
$505$	0	0
$506$	0.547542	0.0243412
$507$	3.64746	0.161989
$508$	−10.6501	−0.472521
$509$	−30.2168	−1.33934	−0.669668	−	0.742661i	$-0.733564\pi$
$509$	−30.2168	−1.33934	−0.669668	+	0.742661i	$0.733564\pi$
$510$	0	0
$511$	7.24562	0.320528
$512$	3.51792	0.155472
$513$	−5.60152	−0.247313
$514$	10.0257	0.442215
$515$	0	0
$516$	−2.77683	−0.122243
$517$	−0.793497	−0.0348980
$518$	−10.7929	−0.474213
$519$	−9.89495	−0.434340
$520$	0	0
$521$	23.7415	1.04014	0.520068	−	0.854125i	$-0.325907\pi$
$521$	23.7415	1.04014	0.520068	+	0.854125i	$0.325907\pi$
$522$	5.04066	0.220624
$523$	−30.1770	−1.31955	−0.659774	−	0.751464i	$-0.729348\pi$
$523$	−30.1770	−1.31955	−0.659774	+	0.751464i	$0.729348\pi$
$524$	−6.99359	−0.305516
$525$	0	0
$526$	23.1850	1.01091
$527$	−5.72756	−0.249496
$528$	−0.748680	−0.0325821
$529$	1.00000	0.0434783
$530$	0	0
$531$	−28.5298	−1.23809
$532$	−1.41354	−0.0612846
$533$	43.3907	1.87946
$534$	9.13731	0.395410
$535$	0	0
$536$	2.07511	0.0896313
$537$	−5.11929	−0.220914
$538$	11.6340	0.501575
$539$	0.335247	0.0144401
$540$	0	0
$541$	31.5534	1.35658	0.678292	−	0.734792i	$-0.262720\pi$
$541$	31.5534	1.35658	0.678292	+	0.734792i	$0.262720\pi$
$542$	16.3039	0.700313
$543$	1.92164	0.0824653
$544$	−12.3347	−0.528846
$545$	0	0
$546$	3.41733	0.146248
$547$	−21.1299	−0.903449	−0.451724	−	0.892158i	$-0.649191\pi$
$547$	−21.1299	−0.903449	−0.451724	+	0.892158i	$0.649191\pi$
$548$	−0.0533187	−0.00227766
$549$	−8.49740	−0.362660
$550$	0	0
$551$	2.34135	0.0997448
$552$	−0.994007	−0.0423078
$553$	2.83560	0.120582
$554$	38.4393	1.63313
$555$	0	0
$556$	6.14612	0.260654
$557$	16.2800	0.689807	0.344903	−	0.938638i	$-0.387912\pi$
$557$	16.2800	0.689807	0.344903	+	0.938638i	$0.387912\pi$
$558$	7.69114	0.325592
$559$	−41.7240	−1.76474
$560$	0	0
$561$	−0.519862	−0.0219486
$562$	6.89752	0.290954
$563$	−35.8486	−1.51084	−0.755420	−	0.655241i	$-0.772567\pi$
$563$	−35.8486	−1.51084	−0.755420	+	0.655241i	$0.772567\pi$
$564$	−0.721618	−0.0303856
$565$	0	0
$566$	11.3741	0.478087
$567$	−7.16599	−0.300943
$568$	−15.1879	−0.637269
$569$	−24.9388	−1.04549	−0.522745	−	0.852489i	$-0.675092\pi$
$569$	−24.9388	−1.04549	−0.522745	+	0.852489i	$0.675092\pi$
$570$	0	0
$571$	−34.7684	−1.45501	−0.727507	−	0.686101i	$-0.759321\pi$
$571$	−34.7684	−1.45501	−0.727507	+	0.686101i	$0.759321\pi$
$572$	1.02514	0.0428632
$573$	4.77487	0.199473
$574$	15.4699	0.645699
$575$	0	0
$576$	−10.7333	−0.447219
$577$	−5.46961	−0.227703	−0.113851	−	0.993498i	$-0.536319\pi$
$577$	−5.46961	−0.227703	−0.113851	+	0.993498i	$0.536319\pi$
$578$	8.93938	0.371829
$579$	0.0946341	0.00393286
$580$	0	0
$581$	−8.54319	−0.354431
$582$	−1.18771	−0.0492323
$583$	−0.522159	−0.0216256
$584$	−15.7686	−0.652510
$585$	0	0
$586$	−10.4667	−0.432377
$587$	38.6017	1.59326	0.796631	−	0.604467i	$-0.206614\pi$
$587$	38.6017	1.59326	0.796631	+	0.604467i	$0.206614\pi$
$588$	0.304879	0.0125730
$589$	3.57248	0.147202
$590$	0	0
$591$	2.09448	0.0861553
$592$	32.3106	1.32796
$593$	30.2591	1.24259	0.621296	−	0.783576i	$-0.286606\pi$
$593$	30.2591	1.24259	0.621296	+	0.783576i	$0.286606\pi$
$594$	1.44834	0.0594263
$595$	0	0
$596$	12.9139	0.528975
$597$	−7.86964	−0.322083
$598$	7.48196	0.305960
$599$	−16.9792	−0.693752	−0.346876	−	0.937911i	$-0.612758\pi$
$599$	−16.9792	−0.693752	−0.346876	+	0.937911i	$0.612758\pi$
$600$	0	0
$601$	11.8894	0.484979	0.242490	−	0.970154i	$-0.422036\pi$
$601$	11.8894	0.484979	0.242490	+	0.970154i	$0.422036\pi$
$602$	−14.8756	−0.606286
$603$	−2.66161	−0.108389
$604$	−1.46646	−0.0596695
$605$	0	0
$606$	−1.69409	−0.0688178
$607$	−22.2307	−0.902315	−0.451158	−	0.892444i	$-0.648989\pi$
$607$	−22.2307	−0.902315	−0.451158	+	0.892444i	$0.648989\pi$
$608$	7.69359	0.312016
$609$	−0.504994	−0.0204634
$610$	0	0
$611$	−10.8428	−0.438655
$612$	6.32596	0.255712
$613$	−23.5668	−0.951854	−0.475927	−	0.879485i	$-0.657887\pi$
$613$	−23.5668	−0.951854	−0.475927	+	0.879485i	$0.657887\pi$
$614$	−7.55399	−0.304854
$615$	0	0
$616$	−0.729597	−0.0293963
$617$	26.9361	1.08441	0.542204	−	0.840247i	$-0.317590\pi$
$617$	26.9361	1.08441	0.542204	+	0.840247i	$0.317590\pi$
$618$	−11.1518	−0.448592
$619$	−16.7211	−0.672078	−0.336039	−	0.941848i	$-0.609087\pi$
$619$	−16.7211	−0.672078	−0.336039	+	0.941848i	$0.609087\pi$
$620$	0	0
$621$	2.64517	0.106147
$622$	4.68442	0.187828
$623$	12.2488	0.490738
$624$	−10.2304	−0.409545
$625$	0	0
$626$	−27.7470	−1.10900
$627$	0.324256	0.0129495
$628$	2.43108	0.0970107
$629$	22.4355	0.894564
$630$	0	0
$631$	−26.7787	−1.06604	−0.533021	−	0.846102i	$-0.678943\pi$
$631$	−26.7787	−1.06604	−0.533021	+	0.846102i	$0.678943\pi$
$632$	−6.17111	−0.245474
$633$	−10.5675	−0.420022
$634$	−6.17775	−0.245350
$635$	0	0
$636$	−0.474859	−0.0188294
$637$	4.58103	0.181507
$638$	−0.605386	−0.0239675
$639$	19.4804	0.770634
$640$	0	0
$641$	49.6757	1.96207	0.981036	−	0.193825i	$-0.0620893\pi$
$641$	49.6757	1.96207	0.981036	+	0.193825i	$0.0620893\pi$
$642$	3.63605	0.143504
$643$	36.3622	1.43399	0.716993	−	0.697080i	$-0.245518\pi$
$643$	36.3622	1.43399	0.716993	+	0.697080i	$0.245518\pi$
$644$	0.667506	0.0263034
$645$	0	0
$646$	11.7424	0.461997
$647$	−10.2239	−0.401943	−0.200971	−	0.979597i	$-0.564410\pi$
$647$	−10.2239	−0.401943	−0.200971	+	0.979597i	$0.564410\pi$
$648$	15.5953	0.612642
$649$	3.42644	0.134500
$650$	0	0
$651$	−0.770530	−0.0301995
$652$	−14.3971	−0.563835
$653$	−6.87794	−0.269155	−0.134577	−	0.990903i	$-0.542968\pi$
$653$	−6.87794	−0.269155	−0.134577	+	0.990903i	$0.542968\pi$
$654$	−1.31724	−0.0515080
$655$	0	0
$656$	−46.3120	−1.80818
$657$	20.2253	0.789065
$658$	−3.86574	−0.150702
$659$	−14.2426	−0.554812	−0.277406	−	0.960753i	$-0.589475\pi$
$659$	−14.2426	−0.554812	−0.277406	+	0.960753i	$0.589475\pi$
$660$	0	0
$661$	16.1642	0.628714	0.314357	−	0.949305i	$-0.398211\pi$
$661$	16.1642	0.628714	0.314357	+	0.949305i	$0.398211\pi$
$662$	28.8333	1.12064
$663$	−7.10372	−0.275886
$664$	18.5925	0.721530
$665$	0	0
$666$	−30.1272	−1.16740
$667$	−1.10564	−0.0428106
$668$	−10.2485	−0.396527
$669$	6.48831	0.250853
$670$	0	0
$671$	1.02054	0.0393976
$672$	−1.65939	−0.0640124
$673$	1.76184	0.0679140	0.0339570	−	0.999423i	$-0.489189\pi$
$673$	1.76184	0.0679140	0.0339570	+	0.999423i	$0.489189\pi$
$674$	41.4860	1.59798
$675$	0	0
$676$	5.33058	0.205022
$677$	−4.98819	−0.191712	−0.0958560	−	0.995395i	$-0.530559\pi$
$677$	−4.98819	−0.191712	−0.0958560	+	0.995395i	$0.530559\pi$
$678$	1.76133	0.0676433
$679$	−1.59216	−0.0611016
$680$	0	0
$681$	7.24337	0.277567
$682$	−0.923710	−0.0353707
$683$	22.5273	0.861983	0.430992	−	0.902356i	$-0.358164\pi$
$683$	22.5273	0.861983	0.430992	+	0.902356i	$0.358164\pi$
$684$	−3.94572	−0.150869
$685$	0	0
$686$	1.63325	0.0623578
$687$	−0.538208	−0.0205339
$688$	44.5331	1.69781
$689$	−7.13511	−0.271826
$690$	0	0
$691$	−5.35936	−0.203880	−0.101940	−	0.994791i	$-0.532505\pi$
$691$	−5.35936	−0.203880	−0.101940	+	0.994791i	$0.532505\pi$
$692$	−14.4610	−0.549723
$693$	0.935804	0.0355482
$694$	10.4024	0.394869
$695$	0	0
$696$	1.09902	0.0416581
$697$	−32.1577	−1.21806
$698$	32.5505	1.23205
$699$	−7.01678	−0.265399
$700$	0	0
$701$	−40.7698	−1.53985	−0.769927	−	0.638132i	$-0.779707\pi$
$701$	−40.7698	−1.53985	−0.769927	+	0.638132i	$0.779707\pi$
$702$	19.7911	0.746967
$703$	−13.9938	−0.527788
$704$	1.28907	0.0485837
$705$	0	0
$706$	20.6613	0.777598
$707$	−2.27098	−0.0854089
$708$	3.11605	0.117109
$709$	−4.52746	−0.170032	−0.0850161	−	0.996380i	$-0.527094\pi$
$709$	−4.52746	−0.170032	−0.0850161	+	0.996380i	$0.527094\pi$
$710$	0	0
$711$	7.91526	0.296845
$712$	−26.6570	−0.999015
$713$	−1.68701	−0.0631791
$714$	−2.53265	−0.0947821
$715$	0	0
$716$	−7.48159	−0.279600
$717$	5.28970	0.197547
$718$	−25.6201	−0.956135
$719$	−14.6162	−0.545092	−0.272546	−	0.962143i	$-0.587866\pi$
$719$	−14.6162	−0.545092	−0.272546	+	0.962143i	$0.587866\pi$
$720$	0	0
$721$	−14.9493	−0.556742
$722$	23.7076	0.882306
$723$	3.73683	0.138974
$724$	2.80837	0.104372
$725$	0	0
$726$	8.12189	0.301431
$727$	−4.65173	−0.172523	−0.0862616	−	0.996273i	$-0.527492\pi$
$727$	−4.65173	−0.172523	−0.0862616	+	0.996273i	$0.527492\pi$
$728$	−9.96967	−0.369501
$729$	−16.3786	−0.606614
$730$	0	0
$731$	30.9225	1.14371
$732$	0.928096	0.0343034
$733$	44.5812	1.64664	0.823321	−	0.567575i	$-0.192118\pi$
$733$	44.5812	1.64664	0.823321	+	0.567575i	$0.192118\pi$
$734$	26.2877	0.970298
$735$	0	0
$736$	−3.63310	−0.133918
$737$	0.319660	0.0117748
$738$	43.1824	1.58956
$739$	2.50482	0.0921412	0.0460706	−	0.998938i	$-0.485330\pi$
$739$	2.50482	0.0921412	0.0460706	+	0.998938i	$0.485330\pi$
$740$	0	0
$741$	4.43084	0.162771
$742$	−2.54385	−0.0933875
$743$	8.92060	0.327265	0.163632	−	0.986521i	$-0.447679\pi$
$743$	8.92060	0.327265	0.163632	+	0.986521i	$0.447679\pi$
$744$	1.67690	0.0614782
$745$	0	0
$746$	47.9199	1.75447
$747$	−23.8474	−0.872529
$748$	−0.759751	−0.0277793
$749$	4.87423	0.178100
$750$	0	0
$751$	48.3798	1.76540	0.882701	−	0.469934i	$-0.155722\pi$
$751$	48.3798	1.76540	0.882701	+	0.469934i	$0.155722\pi$
$752$	11.5728	0.422018
$753$	5.49199	0.200139
$754$	−8.27237	−0.301262
$755$	0	0
$756$	1.76567	0.0642168
$757$	−11.2483	−0.408825	−0.204412	−	0.978885i	$-0.565528\pi$
$757$	−11.2483	−0.408825	−0.204412	+	0.978885i	$0.565528\pi$
$758$	5.82931	0.211730
$759$	−0.153122	−0.00555796
$760$	0	0
$761$	5.84600	0.211917	0.105959	−	0.994371i	$-0.466209\pi$
$761$	5.84600	0.211917	0.105959	+	0.994371i	$0.466209\pi$
$762$	11.9021	0.431166
$763$	−1.76579	−0.0639260
$764$	6.97824	0.252464
$765$	0	0
$766$	23.7802	0.859213
$767$	46.8210	1.69061
$768$	6.59270	0.237894
$769$	−31.2618	−1.12733	−0.563664	−	0.826004i	$-0.690609\pi$
$769$	−31.2618	−1.12733	−0.563664	+	0.826004i	$0.690609\pi$
$770$	0	0
$771$	−2.80371	−0.100973
$772$	0.138303	0.00497763
$773$	37.3451	1.34321	0.671605	−	0.740910i	$-0.265605\pi$
$773$	37.3451	1.34321	0.671605	+	0.740910i	$0.265605\pi$
$774$	−41.5237	−1.49254
$775$	0	0
$776$	3.46502	0.124387
$777$	3.01826	0.108280
$778$	45.2861	1.62359
$779$	20.0579	0.718649
$780$	0	0
$781$	−2.33961	−0.0837179
$782$	−5.54503	−0.198290
$783$	−2.92461	−0.104517
$784$	−4.88945	−0.174623
$785$	0	0
$786$	7.81572	0.278778
$787$	−16.6878	−0.594856	−0.297428	−	0.954744i	$-0.596129\pi$
$787$	−16.6878	−0.594856	−0.297428	+	0.954744i	$0.596129\pi$
$788$	3.06097	0.109043
$789$	−6.48373	−0.230827
$790$	0	0
$791$	2.36111	0.0839513
$792$	−2.03659	−0.0723669
$793$	13.9453	0.495213
$794$	42.6761	1.51452
$795$	0	0
$796$	−11.5011	−0.407645
$797$	49.9631	1.76978	0.884892	−	0.465796i	$-0.154232\pi$
$797$	49.9631	1.76978	0.884892	+	0.465796i	$0.154232\pi$
$798$	1.57970	0.0559209
$799$	8.03585	0.284288
$800$	0	0
$801$	34.1912	1.20809
$802$	4.55344	0.160788
$803$	−2.42907	−0.0857201
$804$	0.290704	0.0102523
$805$	0	0
$806$	−12.6222	−0.444597
$807$	−3.25347	−0.114527
$808$	4.94232	0.173870
$809$	−26.2425	−0.922635	−0.461318	−	0.887235i	$-0.652623\pi$
$809$	−26.2425	−0.922635	−0.461318	+	0.887235i	$0.652623\pi$
$810$	0	0
$811$	−2.59171	−0.0910074	−0.0455037	−	0.998964i	$-0.514489\pi$
$811$	−2.59171	−0.0910074	−0.0455037	+	0.998964i	$0.514489\pi$
$812$	−0.738023	−0.0258995
$813$	−4.55943	−0.159906
$814$	3.61829	0.126821
$815$	0	0
$816$	7.58198	0.265422
$817$	−19.2875	−0.674783
$818$	37.5477	1.31282
$819$	12.7874	0.446828
$820$	0	0
$821$	6.49572	0.226702	0.113351	−	0.993555i	$-0.463842\pi$
$821$	6.49572	0.226702	0.113351	+	0.993555i	$0.463842\pi$
$822$	0.0595866	0.00207832
$823$	−8.51260	−0.296731	−0.148365	−	0.988933i	$-0.547401\pi$
$823$	−8.51260	−0.296731	−0.148365	+	0.988933i	$0.547401\pi$
$824$	32.5342	1.13338
$825$	0	0
$826$	16.6929	0.580819
$827$	−4.09417	−0.142368	−0.0711842	−	0.997463i	$-0.522678\pi$
$827$	−4.09417	−0.142368	−0.0711842	+	0.997463i	$0.522678\pi$
$828$	1.86327	0.0647530
$829$	−24.1706	−0.839481	−0.419740	−	0.907644i	$-0.637879\pi$
$829$	−24.1706	−0.839481	−0.419740	+	0.907644i	$0.637879\pi$
$830$	0	0
$831$	−10.7496	−0.372901
$832$	17.6147	0.610679
$833$	−3.39509	−0.117633
$834$	−6.86863	−0.237841
$835$	0	0
$836$	0.473884	0.0163896
$837$	−4.46244	−0.154244
$838$	65.3283	2.25673
$839$	22.7688	0.786066	0.393033	−	0.919524i	$-0.371426\pi$
$839$	22.7688	0.786066	0.393033	+	0.919524i	$0.371426\pi$
$840$	0	0
$841$	−27.7776	−0.957847
$842$	−28.5671	−0.984489
$843$	−1.92891	−0.0664352
$844$	−15.4439	−0.531601
$845$	0	0
$846$	−10.7908	−0.370995
$847$	10.8876	0.374103
$848$	7.61549	0.261517
$849$	−3.18079	−0.109164
$850$	0	0
$851$	6.60823	0.226527
$852$	−2.12768	−0.0728930
$853$	43.9698	1.50550	0.752749	−	0.658308i	$-0.228727\pi$
$853$	43.9698	1.50550	0.752749	+	0.658308i	$0.228727\pi$
$854$	4.97186	0.170134
$855$	0	0
$856$	−10.6078	−0.362566
$857$	−6.03103	−0.206016	−0.103008	−	0.994681i	$-0.532847\pi$
$857$	−6.03103	−0.206016	−0.103008	+	0.994681i	$0.532847\pi$
$858$	−1.14565	−0.0391119
$859$	−20.2416	−0.690636	−0.345318	−	0.938486i	$-0.612229\pi$
$859$	−20.2416	−0.690636	−0.345318	+	0.938486i	$0.612229\pi$
$860$	0	0
$861$	−4.32619	−0.147436
$862$	−54.7864	−1.86603
$863$	41.6744	1.41861	0.709307	−	0.704900i	$-0.249008\pi$
$863$	41.6744	1.41861	0.709307	+	0.704900i	$0.249008\pi$
$864$	−9.61018	−0.326945
$865$	0	0
$866$	−52.7304	−1.79185
$867$	−2.49992	−0.0849017
$868$	−1.12609	−0.0382220
$869$	−0.950627	−0.0322478
$870$	0	0
$871$	4.36804	0.148005
$872$	3.84289	0.130137
$873$	−4.44434	−0.150418
$874$	3.45863	0.116990
$875$	0	0
$876$	−2.20904	−0.0746364
$877$	−56.0744	−1.89350	−0.946749	−	0.321973i	$-0.895654\pi$
$877$	−56.0744	−1.89350	−0.946749	+	0.321973i	$0.895654\pi$
$878$	−22.9242	−0.773655
$879$	2.92705	0.0987269
$880$	0	0
$881$	29.7638	1.00277	0.501385	−	0.865225i	$-0.332824\pi$
$881$	29.7638	1.00277	0.501385	+	0.865225i	$0.332824\pi$
$882$	4.55903	0.153511
$883$	10.5038	0.353482	0.176741	−	0.984257i	$-0.443445\pi$
$883$	10.5038	0.353482	0.176741	+	0.984257i	$0.443445\pi$
$884$	−10.3817	−0.349175
$885$	0	0
$886$	13.1004	0.440117
$887$	48.7845	1.63802	0.819012	−	0.573777i	$-0.194522\pi$
$887$	48.7845	1.63802	0.819012	+	0.573777i	$0.194522\pi$
$888$	−6.56863	−0.220429
$889$	15.9550	0.535115
$890$	0	0
$891$	2.40238	0.0804827
$892$	9.48233	0.317492
$893$	−5.01224	−0.167728
$894$	−14.4320	−0.482679
$895$	0	0
$896$	13.5463	0.452549
$897$	−2.09235	−0.0698616
$898$	−55.7744	−1.86122
$899$	1.86523	0.0622090
$900$	0	0
$901$	5.28797	0.176168
$902$	−5.18622	−0.172682
$903$	4.16001	0.138437
$904$	−5.13846	−0.170903
$905$	0	0
$906$	1.63885	0.0544473
$907$	1.62527	0.0539664	0.0269832	−	0.999636i	$-0.491410\pi$
$907$	1.62527	0.0539664	0.0269832	+	0.999636i	$0.491410\pi$
$908$	10.5858	0.351303
$909$	−6.33918	−0.210257
$910$	0	0
$911$	−11.8739	−0.393401	−0.196700	−	0.980464i	$-0.563023\pi$
$911$	−11.8739	−0.393401	−0.196700	+	0.980464i	$0.563023\pi$
$912$	−4.72915	−0.156598
$913$	2.86408	0.0947872
$914$	48.4365	1.60214
$915$	0	0
$916$	−0.786563	−0.0259888
$917$	10.4772	0.345987
$918$	−14.6676	−0.484102
$919$	−18.9944	−0.626568	−0.313284	−	0.949659i	$-0.601429\pi$
$919$	−18.9944	−0.626568	−0.313284	+	0.949659i	$0.601429\pi$
$920$	0	0
$921$	2.11249	0.0696090
$922$	18.6915	0.615572
$923$	−31.9699	−1.05230
$924$	−0.102210	−0.00336245
$925$	0	0
$926$	62.7314	2.06148
$927$	−41.7294	−1.37057
$928$	4.01691	0.131861
$929$	56.1778	1.84313	0.921567	−	0.388218i	$-0.126909\pi$
$929$	56.1778	1.84313	0.921567	+	0.388218i	$0.126909\pi$
$930$	0	0
$931$	2.11764	0.0694028
$932$	−10.2547	−0.335903
$933$	−1.31001	−0.0428878
$934$	−7.23635	−0.236781
$935$	0	0
$936$	−27.8292	−0.909626
$937$	−50.1197	−1.63734	−0.818669	−	0.574266i	$-0.805288\pi$
$937$	−50.1197	−1.63734	−0.818669	+	0.574266i	$0.805288\pi$
$938$	1.55732	0.0508482
$939$	7.75953	0.253223
$940$	0	0
$941$	16.0121	0.521979	0.260989	−	0.965342i	$-0.415951\pi$
$941$	16.0121	0.521979	0.260989	+	0.965342i	$0.415951\pi$
$942$	−2.71687	−0.0885203
$943$	−9.47182	−0.308445
$944$	−49.9733	−1.62649
$945$	0	0
$946$	4.98702	0.162142
$947$	−47.0892	−1.53019	−0.765097	−	0.643915i	$-0.777309\pi$
$947$	−47.0892	−1.53019	−0.765097	+	0.643915i	$0.777309\pi$
$948$	−0.864514	−0.0280781
$949$	−33.1924	−1.07747
$950$	0	0
$951$	1.72762	0.0560220
$952$	7.38872	0.239470
$953$	38.3796	1.24324	0.621618	−	0.783320i	$-0.286476\pi$
$953$	38.3796	1.24324	0.621618	+	0.783320i	$0.286476\pi$
$954$	−7.10085	−0.229899
$955$	0	0
$956$	7.73062	0.250026
$957$	0.169298	0.00547262
$958$	−1.16536	−0.0376512
$959$	0.0798775	0.00257938
$960$	0	0
$961$	−28.1540	−0.908193
$962$	49.4426	1.59409
$963$	13.6059	0.438443
$964$	5.46118	0.175893
$965$	0	0
$966$	−0.745975	−0.0240014
$967$	−14.8104	−0.476272	−0.238136	−	0.971232i	$-0.576536\pi$
$967$	−14.8104	−0.476272	−0.238136	+	0.971232i	$0.576536\pi$
$968$	−23.6947	−0.761575
$969$	−3.28378	−0.105490
$970$	0	0
$971$	29.1730	0.936205	0.468102	−	0.883674i	$-0.344938\pi$
$971$	29.1730	0.936205	0.468102	+	0.883674i	$0.344938\pi$
$972$	7.48177	0.239978
$973$	−9.20759	−0.295182
$974$	14.4145	0.461871
$975$	0	0
$976$	−14.8842	−0.476432
$977$	49.0835	1.57032	0.785161	−	0.619292i	$-0.212580\pi$
$977$	49.0835	1.57032	0.785161	+	0.619292i	$0.212580\pi$
$978$	16.0896	0.514488
$979$	−4.10638	−0.131240
$980$	0	0
$981$	−4.92901	−0.157371
$982$	9.37348	0.299120
$983$	−27.9923	−0.892815	−0.446408	−	0.894830i	$-0.647297\pi$
$983$	−27.9923	−0.892815	−0.446408	+	0.894830i	$0.647297\pi$
$984$	9.41506	0.300141
$985$	0	0
$986$	6.13082	0.195245
$987$	1.08107	0.0344107
$988$	6.47545	0.206011
$989$	9.10800	0.289618
$990$	0	0
$991$	53.1269	1.68763	0.843816	−	0.536633i	$-0.180304\pi$
$991$	53.1269	1.68763	0.843816	+	0.536633i	$0.180304\pi$
$992$	6.12908	0.194599
$993$	−8.06332	−0.255882
$994$	−11.3981	−0.361525
$995$	0	0
$996$	2.60464	0.0825311
$997$	28.9207	0.915928	0.457964	−	0.888971i	$-0.348579\pi$
$997$	28.9207	0.915928	0.457964	+	0.888971i	$0.348579\pi$
$998$	−17.1520	−0.542937
$999$	17.4799	0.553040

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4025.2.a.z.1.4	✓	14
5.4	even	2		4025.2.a.bc.1.11	yes	14

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4025.2.a.z.1.4	✓	14	1.1	even	1	trivial
4025.2.a.bc.1.11	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)

\(f(q)\)	\(=\)	\(q-1.63325 q^{2} +0.456743 q^{3} +0.667506 q^{4} -0.745975 q^{6} -1.00000 q^{7} +2.17630 q^{8} -2.79139 q^{9} +O(q^{10})\)	\(q-1.63325 q^{2} +0.456743 q^{3} +0.667506 q^{4} -0.745975 q^{6} -1.00000 q^{7} +2.17630 q^{8} -2.79139 q^{9} +0.335247 q^{11} +0.304879 q^{12} +4.58103 q^{13} +1.63325 q^{14} -4.88945 q^{16} -3.39509 q^{17} +4.55903 q^{18} +2.11764 q^{19} -0.456743 q^{21} -0.547542 q^{22} -1.00000 q^{23} +0.994007 q^{24} -7.48196 q^{26} -2.64517 q^{27} -0.667506 q^{28} +1.10564 q^{29} +1.68701 q^{31} +3.63310 q^{32} +0.153122 q^{33} +5.54503 q^{34} -1.86327 q^{36} -6.60823 q^{37} -3.45863 q^{38} +2.09235 q^{39} +9.47182 q^{41} +0.745975 q^{42} -9.10800 q^{43} +0.223779 q^{44} +1.63325 q^{46} -2.36690 q^{47} -2.23322 q^{48} +1.00000 q^{49} -1.55068 q^{51} +3.05786 q^{52} -1.55754 q^{53} +4.32023 q^{54} -2.17630 q^{56} +0.967216 q^{57} -1.80579 q^{58} +10.2206 q^{59} +3.04415 q^{61} -2.75531 q^{62} +2.79139 q^{63} +3.84513 q^{64} -0.250086 q^{66} +0.953507 q^{67} -2.26624 q^{68} -0.456743 q^{69} -6.97877 q^{71} -6.07488 q^{72} -7.24562 q^{73} +10.7929 q^{74} +1.41354 q^{76} -0.335247 q^{77} -3.41733 q^{78} -2.83560 q^{79} +7.16599 q^{81} -15.4699 q^{82} +8.54319 q^{83} -0.304879 q^{84} +14.8756 q^{86} +0.504994 q^{87} +0.729597 q^{88} -12.2488 q^{89} -4.58103 q^{91} -0.667506 q^{92} +0.770530 q^{93} +3.86574 q^{94} +1.65939 q^{96} +1.59216 q^{97} -1.63325 q^{98} -0.935804 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 14 q - 3 q^{2} - 4 q^{3} + 17 q^{4} - 4 q^{6} - 14 q^{7} - 3 q^{8} + 18 q^{9}+O(q^{10}) \) 14 * q - 3 * q^2 - 4 * q^3 + 17 * q^4 - 4 * q^6 - 14 * q^7 - 3 * q^8 + 18 * q^9	\( 14 q - 3 q^{2} - 4 q^{3} + 17 q^{4} - 4 q^{6} - 14 q^{7} - 3 q^{8} + 18 q^{9} + 5 q^{11} - 17 q^{12} - 11 q^{13} + 3 q^{14} + 23 q^{16} - 3 q^{17} - 15 q^{18} - 2 q^{19} + 4 q^{21} - 23 q^{22} - 14 q^{23} - 12 q^{24} - 9 q^{26} - 25 q^{27} - 17 q^{28} + 7 q^{29} - 3 q^{31} - 24 q^{32} - 6 q^{33} - 14 q^{34} + 13 q^{36} - 22 q^{37} - 20 q^{38} - 10 q^{39} - 17 q^{41} + 4 q^{42} - 18 q^{43} + 28 q^{44} + 3 q^{46} - 30 q^{47} - 8 q^{48} + 14 q^{49} + 4 q^{51} - 8 q^{52} - 11 q^{53} + 20 q^{54} + 3 q^{56} - 18 q^{57} - 38 q^{58} - 22 q^{59} - 8 q^{61} + 22 q^{62} - 18 q^{63} + 29 q^{64} - 9 q^{66} - 39 q^{67} - q^{68} + 4 q^{69} - 5 q^{71} + 24 q^{72} - 18 q^{73} + 35 q^{74} - 41 q^{76} - 5 q^{77} + 22 q^{78} + 10 q^{79} + 2 q^{81} + 8 q^{82} - 24 q^{83} + 17 q^{84} - 26 q^{86} - 5 q^{87} - 58 q^{88} + 25 q^{89} + 11 q^{91} - 17 q^{92} - 47 q^{93} - 2 q^{94} - 117 q^{96} - 43 q^{97} - 3 q^{98} + 55 q^{99}+O(q^{100}) \) 14 * q - 3 * q^2 - 4 * q^3 + 17 * q^4 - 4 * q^6 - 14 * q^7 - 3 * q^8 + 18 * q^9 + 5 * q^11 - 17 * q^12 - 11 * q^13 + 3 * q^14 + 23 * q^16 - 3 * q^17 - 15 * q^18 - 2 * q^19 + 4 * q^21 - 23 * q^22 - 14 * q^23 - 12 * q^24 - 9 * q^26 - 25 * q^27 - 17 * q^28 + 7 * q^29 - 3 * q^31 - 24 * q^32 - 6 * q^33 - 14 * q^34 + 13 * q^36 - 22 * q^37 - 20 * q^38 - 10 * q^39 - 17 * q^41 + 4 * q^42 - 18 * q^43 + 28 * q^44 + 3 * q^46 - 30 * q^47 - 8 * q^48 + 14 * q^49 + 4 * q^51 - 8 * q^52 - 11 * q^53 + 20 * q^54 + 3 * q^56 - 18 * q^57 - 38 * q^58 - 22 * q^59 - 8 * q^61 + 22 * q^62 - 18 * q^63 + 29 * q^64 - 9 * q^66 - 39 * q^67 - q^68 + 4 * q^69 - 5 * q^71 + 24 * q^72 - 18 * q^73 + 35 * q^74 - 41 * q^76 - 5 * q^77 + 22 * q^78 + 10 * q^79 + 2 * q^81 + 8 * q^82 - 24 * q^83 + 17 * q^84 - 26 * q^86 - 5 * q^87 - 58 * q^88 + 25 * q^89 + 11 * q^91 - 17 * q^92 - 47 * q^93 - 2 * q^94 - 117 * q^96 - 43 * q^97 - 3 * q^98 + 55 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more