LMFDB - Embedded newform 525.4.d.o.274.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [525,4,Mod(274,525)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(525, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 1, 0]))

N = Newforms(chi, 4, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("525.274");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 525 = 3 \cdot 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	525.d (of order $2$, degree $1$, not minimal)

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:	no
Analytic conductor:	$30.9760027530$
Analytic rank:	$0$
Dimension:	$8$
Coefficient field:	$\mathbb{Q}[x]/(x^{8} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} + 40x^{6} + 488x^{4} + 1945x^{2} + 1936 $ x^8 + 40x^6 + 488x^4 + 1945*x^2 + 1936
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			274.7
Root			$2.21734i$ of defining polynomial
Character	$\chi$	$=$	525.274
Dual form			525.4.d.o.274.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+3.21734i q^{2} -3.00000i q^{3} -2.35129 q^{4} +9.65203 q^{6} -7.00000i q^{7} +18.1738i q^{8} -9.00000 q^{9} +O(q^{10})$	\(q+3.21734i q^{2} -3.00000i q^{3} -2.35129 q^{4} +9.65203 q^{6} -7.00000i q^{7} +18.1738i q^{8} -9.00000 q^{9} -2.09810 q^{11} +7.05388i q^{12} -80.8215i q^{13} +22.5214 q^{14} -77.2818 q^{16} +101.965i q^{17} -28.9561i q^{18} -143.319 q^{19} -21.0000 q^{21} -6.75032i q^{22} +116.258i q^{23} +54.5215 q^{24} +260.030 q^{26} +27.0000i q^{27} +16.4590i q^{28} -181.194 q^{29} +303.614 q^{31} -103.251i q^{32} +6.29431i q^{33} -328.058 q^{34} +21.1616 q^{36} +158.336i q^{37} -461.106i q^{38} -242.465 q^{39} -379.372 q^{41} -67.5642i q^{42} +238.980i q^{43} +4.93326 q^{44} -374.041 q^{46} +125.956i q^{47} +231.845i q^{48} -49.0000 q^{49} +305.896 q^{51} +190.035i q^{52} +43.4805i q^{53} -86.8682 q^{54} +127.217 q^{56} +429.956i q^{57} -582.964i q^{58} -31.0944 q^{59} -812.675 q^{61} +976.830i q^{62} +63.0000i q^{63} -286.059 q^{64} -20.2510 q^{66} -426.225i q^{67} -239.750i q^{68} +348.774 q^{69} -1034.51 q^{71} -163.564i q^{72} +471.741i q^{73} -509.422 q^{74} +336.984 q^{76} +14.6867i q^{77} -780.091i q^{78} -1201.92 q^{79} +81.0000 q^{81} -1220.57i q^{82} -1325.72i q^{83} +49.3771 q^{84} -768.880 q^{86} +543.582i q^{87} -38.1306i q^{88} +886.226 q^{89} -565.751 q^{91} -273.356i q^{92} -910.841i q^{93} -405.245 q^{94} -309.754 q^{96} -134.908i q^{97} -157.650i q^{98} +18.8829 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 32 q^{4} + 36 q^{6} - 72 q^{9}+O(q^{10}) $ 8 * q - 32 * q^4 + 36 * q^6 - 72 * q^9	$ 8 q - 32 q^{4} + 36 q^{6} - 72 q^{9} + 114 q^{11} + 84 q^{14} + 432 q^{16} + 24 q^{19} - 168 q^{21} - 558 q^{24} - 162 q^{26} - 756 q^{29} - 186 q^{31} - 1566 q^{34} + 288 q^{36} - 258 q^{39} - 930 q^{41} - 1362 q^{44} + 620 q^{46} - 392 q^{49} + 594 q^{51} - 324 q^{54} - 1302 q^{56} - 462 q^{59} - 2706 q^{61} - 6214 q^{64} - 246 q^{66} - 936 q^{69} - 3450 q^{71} + 3906 q^{74} - 6092 q^{76} - 3258 q^{79} + 648 q^{81} + 672 q^{84} - 9084 q^{86} + 1956 q^{89} - 602 q^{91} - 4960 q^{94} + 4140 q^{96} - 1026 q^{99}+O(q^{100}) $ 8 * q - 32 * q^4 + 36 * q^6 - 72 * q^9 + 114 * q^11 + 84 * q^14 + 432 * q^16 + 24 * q^19 - 168 * q^21 - 558 * q^24 - 162 * q^26 - 756 * q^29 - 186 * q^31 - 1566 * q^34 + 288 * q^36 - 258 * q^39 - 930 * q^41 - 1362 * q^44 + 620 * q^46 - 392 * q^49 + 594 * q^51 - 324 * q^54 - 1302 * q^56 - 462 * q^59 - 2706 * q^61 - 6214 * q^64 - 246 * q^66 - 936 * q^69 - 3450 * q^71 + 3906 * q^74 - 6092 * q^76 - 3258 * q^79 + 648 * q^81 + 672 * q^84 - 9084 * q^86 + 1956 * q^89 - 602 * q^91 - 4960 * q^94 + 4140 * q^96 - 1026 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/525\mathbb{Z}\right)^\times$.

$n$	$127$	$176$	$451$
$\chi(n)$	$-1$	$1$	$1$

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 $

$2$	3.21734i	1.13750i	0.822510	+	0.568751i	$0.192573\pi$
$2$	3.21734i	1.13750i	−0.822510	+	0.568751i	$0.807427\pi$
$3$	− 3.00000i	− 0.577350i
$3$	− 3.00000i	− 0.577350i
$4$	−2.35129	−0.293911
$5$	0	0
$5$	0	0
$6$	9.65203	0.656737
$7$	− 7.00000i	− 0.377964i
$7$	− 7.00000i	− 0.377964i
$8$	18.1738i	0.803177i
$9$	−9.00000	−0.333333
$10$	0	0
$11$	−2.09810	−0.0575093	−0.0287546	−	0.999586i	$-0.509154\pi$
$11$	−2.09810	−0.0575093	−0.0287546	+	0.999586i	$0.509154\pi$
$12$	7.05388i	0.169690i
$13$	− 80.8215i	− 1.72430i	−0.506656	−	0.862148i	$-0.669119\pi$
$13$	− 80.8215i	− 1.72430i	0.506656	−	0.862148i	$-0.330881\pi$
$14$	22.5214	0.429935
$15$	0	0
$16$	−77.2818	−1.20753
$17$	101.965i	1.45472i	0.686256	+	0.727360i	$0.259253\pi$
$17$	101.965i	1.45472i	−0.686256	+	0.727360i	$0.740747\pi$
$18$	− 28.9561i	− 0.379167i
$19$	−143.319	−1.73050	−0.865252	−	0.501337i	$-0.832842\pi$
$19$	−143.319	−1.73050	−0.865252	+	0.501337i	$0.832842\pi$
$20$	0	0
$21$	−21.0000	−0.218218
$22$	− 6.75032i	− 0.0654170i
$23$	116.258i	1.05398i	0.849873	+	0.526988i	$0.176679\pi$
$23$	116.258i	1.05398i	−0.849873	+	0.526988i	$0.823321\pi$
$24$	54.5215	0.463715
$25$	0	0
$26$	260.030	1.96139
$27$	27.0000i	0.192450i
$28$	16.4590i	0.111088i
$29$	−181.194	−1.16024	−0.580119	−	0.814532i	$-0.696994\pi$
$29$	−181.194	−1.16024	−0.580119	+	0.814532i	$0.696994\pi$
$30$	0	0
$31$	303.614	1.75905	0.879527	−	0.475850i	$-0.157859\pi$
$31$	303.614	1.75905	0.879527	+	0.475850i	$0.157859\pi$
$32$	− 103.251i	− 0.570388i
$33$	6.29431i	0.0332030i
$34$	−328.058	−1.65475
$35$	0	0
$36$	21.1616	0.0979705
$37$	158.336i	0.703522i	0.936090	+	0.351761i	$0.114417\pi$
$37$	158.336i	0.703522i	−0.936090	+	0.351761i	$0.885583\pi$
$38$	− 461.106i	− 1.96845i
$39$	−242.465	−0.995523
$40$	0	0
$41$	−379.372	−1.44507	−0.722536	−	0.691333i	$-0.757024\pi$
$41$	−379.372	−1.44507	−0.722536	+	0.691333i	$0.757024\pi$
$42$	− 67.5642i	− 0.248223i
$43$	238.980i	0.847537i	0.905770	+	0.423769i	$0.139293\pi$
$43$	238.980i	0.847537i	−0.905770	+	0.423769i	$0.860707\pi$
$44$	4.93326	0.0169026
$45$	0	0
$46$	−374.041	−1.19890
$47$	125.956i	0.390907i	0.980713	+	0.195453i	$0.0626178\pi$
$47$	125.956i	0.390907i	−0.980713	+	0.195453i	$0.937382\pi$
$48$	231.845i	0.697166i
$49$	−49.0000	−0.142857
$50$	0	0
$51$	305.896	0.839883
$52$	190.035i	0.506790i
$53$	43.4805i	0.112689i	0.998411	+	0.0563443i	$0.0179445\pi$
$53$	43.4805i	0.112689i	−0.998411	+	0.0563443i	$0.982056\pi$
$54$	−86.8682	−0.218912
$55$	0	0
$56$	127.217	0.303572
$57$	429.956i	0.999107i
$58$	− 582.964i	− 1.31977i
$59$	−31.0944	−0.0686127	−0.0343063	−	0.999411i	$-0.510922\pi$
$59$	−31.0944	−0.0686127	−0.0343063	+	0.999411i	$0.510922\pi$
$60$	0	0
$61$	−812.675	−1.70578	−0.852889	−	0.522093i	$-0.825151\pi$
$61$	−812.675	−1.70578	−0.852889	+	0.522093i	$0.825151\pi$
$62$	976.830i	2.00093i
$63$	63.0000i	0.125988i
$64$	−286.059	−0.558710
$65$	0	0
$66$	−20.2510	−0.0377685
$67$	− 426.225i	− 0.777189i	−0.921409	−	0.388595i	$-0.872961\pi$
$67$	− 426.225i	− 0.777189i	0.921409	−	0.388595i	$-0.127039\pi$
$68$	− 239.750i	− 0.427559i
$69$	348.774	0.608513
$70$	0	0
$71$	−1034.51	−1.72921	−0.864603	−	0.502455i	$-0.832430\pi$
$71$	−1034.51	−1.72921	−0.864603	+	0.502455i	$0.832430\pi$
$72$	− 163.564i	− 0.267726i
$73$	471.741i	0.756344i	0.925735	+	0.378172i	$0.123447\pi$
$73$	471.741i	0.756344i	−0.925735	+	0.378172i	$0.876553\pi$
$74$	−509.422	−0.800257
$75$	0	0
$76$	336.984	0.508615
$77$	14.6867i	0.0217365i
$78$	− 780.091i	− 1.13241i
$79$	−1201.92	−1.71172	−0.855861	−	0.517205i	$-0.826972\pi$
$79$	−1201.92	−1.71172	−0.855861	+	0.517205i	$0.826972\pi$
$80$	0	0
$81$	81.0000	0.111111
$82$	− 1220.57i	− 1.64377i
$83$	− 1325.72i	− 1.75321i	−0.481209	−	0.876606i	$-0.659802\pi$
$83$	− 1325.72i	− 1.75321i	0.481209	−	0.876606i	$-0.340198\pi$
$84$	49.3771	0.0641367
$85$	0	0
$86$	−768.880	−0.964076
$87$	543.582i	0.669864i
$88$	− 38.1306i	− 0.0461902i
$89$	886.226	1.05550	0.527751	−	0.849399i	$-0.323035\pi$
$89$	886.226	1.05550	0.527751	+	0.849399i	$0.323035\pi$
$90$	0	0
$91$	−565.751	−0.651723
$92$	− 273.356i	− 0.309776i
$93$	− 910.841i	− 1.01559i
$94$	−405.245	−0.444657
$95$	0	0
$96$	−309.754	−0.329314
$97$	− 134.908i	− 0.141215i	−0.997504	−	0.0706076i	$-0.977506\pi$
$97$	− 134.908i	− 0.141215i	0.997504	−	0.0706076i	$-0.0224938\pi$
$98$	− 157.650i	− 0.162500i
$99$	18.8829	0.0191698
$100$	0	0
$101$	585.617	0.576941	0.288471	−	0.957489i	$-0.406853\pi$
$101$	585.617	0.576941	0.288471	+	0.957489i	$0.406853\pi$
$102$	984.173i	0.955369i
$103$	− 850.822i	− 0.813923i	−0.913445	−	0.406961i	$-0.866588\pi$
$103$	− 850.822i	− 0.813923i	0.913445	−	0.406961i	$-0.133412\pi$
$104$	1468.84	1.38492
$105$	0	0
$106$	−139.892	−0.128184
$107$	566.799i	0.512099i	0.966664	+	0.256049i	$0.0824209\pi$
$107$	566.799i	0.512099i	−0.966664	+	0.256049i	$0.917579\pi$
$108$	− 63.4849i	− 0.0565633i
$109$	1111.49	0.976714	0.488357	−	0.872644i	$-0.337596\pi$
$109$	1111.49	0.976714	0.488357	+	0.872644i	$0.337596\pi$
$110$	0	0
$111$	475.008	0.406178
$112$	540.972i	0.456403i
$113$	− 192.740i	− 0.160455i	−0.996777	−	0.0802275i	$-0.974435\pi$
$113$	− 192.740i	− 0.160455i	0.996777	−	0.0802275i	$-0.0255647\pi$
$114$	−1383.32	−1.13649
$115$	0	0
$116$	426.040	0.341007
$117$	727.394i	0.574765i
$118$	− 100.041i	− 0.0780471i
$119$	713.758	0.549833
$120$	0	0
$121$	−1326.60	−0.996693
$122$	− 2614.65i	− 1.94033i
$123$	1138.12i	0.834313i
$124$	−713.885	−0.517006
$125$	0	0
$126$	−202.693	−0.143312
$127$	937.870i	0.655296i	0.944800	+	0.327648i	$0.106256\pi$
$127$	937.870i	0.655296i	−0.944800	+	0.327648i	$0.893744\pi$
$128$	− 1746.36i	− 1.20592i
$129$	716.940	0.489326
$130$	0	0
$131$	746.316	0.497755	0.248878	−	0.968535i	$-0.419938\pi$
$131$	746.316	0.497755	0.248878	+	0.968535i	$0.419938\pi$
$132$	− 14.7998i	− 0.00975875i
$133$	1003.23i	0.654069i
$134$	1371.31	0.884054
$135$	0	0
$136$	−1853.10	−1.16840
$137$	492.514i	0.307141i	0.988138	+	0.153570i	$0.0490772\pi$
$137$	492.514i	0.307141i	−0.988138	+	0.153570i	$0.950923\pi$
$138$	1122.12i	0.692185i
$139$	152.482	0.0930456	0.0465228	−	0.998917i	$-0.485186\pi$
$139$	152.482	0.0930456	0.0465228	+	0.998917i	$0.485186\pi$
$140$	0	0
$141$	377.869	0.225690
$142$	− 3328.37i	− 1.96698i
$143$	169.572i	0.0991631i
$144$	695.536	0.402509
$145$	0	0
$146$	−1517.75	−0.860343
$147$	147.000i	0.0824786i
$148$	− 372.294i	− 0.206773i
$149$	1433.18	0.787989	0.393994	−	0.919113i	$-0.371093\pi$
$149$	1433.18	0.787989	0.393994	+	0.919113i	$0.371093\pi$
$150$	0	0
$151$	916.243	0.493794	0.246897	−	0.969042i	$-0.420589\pi$
$151$	916.243	0.493794	0.246897	+	0.969042i	$0.420589\pi$
$152$	− 2604.65i	− 1.38990i
$153$	− 917.689i	− 0.484907i
$154$	−47.2522	−0.0247253
$155$	0	0
$156$	570.105	0.292596
$157$	169.765i	0.0862978i	0.999069	+	0.0431489i	$0.0137390\pi$
$157$	169.765i	0.0862978i	−0.999069	+	0.0431489i	$0.986261\pi$
$158$	− 3866.98i	− 1.94709i
$159$	130.441	0.0650608
$160$	0	0
$161$	813.805	0.398365
$162$	260.605i	0.126389i
$163$	− 1051.63i	− 0.505338i	−0.967553	−	0.252669i	$-0.918692\pi$
$163$	− 1051.63i	− 0.505338i	0.967553	−	0.252669i	$-0.0813084\pi$
$164$	892.014	0.424723
$165$	0	0
$166$	4265.29	1.99428
$167$	2891.32i	1.33974i	0.742478	+	0.669870i	$0.233650\pi$
$167$	2891.32i	1.33974i	−0.742478	+	0.669870i	$0.766350\pi$
$168$	− 381.650i	− 0.175268i
$169$	−4335.12	−1.97320
$170$	0	0
$171$	1289.87	0.576835
$172$	− 561.912i	− 0.249101i
$173$	868.785i	0.381806i	0.981609	+	0.190903i	$0.0611416\pi$
$173$	868.785i	0.381806i	−0.981609	+	0.190903i	$0.938858\pi$
$174$	−1748.89	−0.761972
$175$	0	0
$176$	162.145	0.0694441
$177$	93.2833i	0.0396136i
$178$	2851.29i	1.20064i
$179$	2073.48	0.865804	0.432902	−	0.901441i	$-0.357490\pi$
$179$	2073.48	0.865804	0.432902	+	0.901441i	$0.357490\pi$
$180$	0	0
$181$	−2152.24	−0.883839	−0.441919	−	0.897055i	$-0.645702\pi$
$181$	−2152.24	−0.883839	−0.441919	+	0.897055i	$0.645702\pi$
$182$	− 1820.21i	− 0.741336i
$183$	2438.03i	0.984831i
$184$	−2112.85	−0.846529
$185$	0	0
$186$	2930.49	1.15524
$187$	− 213.934i	− 0.0836599i
$188$	− 296.160i	− 0.114892i
$189$	189.000	0.0727393
$190$	0	0
$191$	−4149.19	−1.57186	−0.785929	−	0.618316i	$-0.787815\pi$
$191$	−4149.19	−1.57186	−0.785929	+	0.618316i	$0.787815\pi$
$192$	858.178i	0.322571i
$193$	1860.51i	0.693899i	0.937884	+	0.346949i	$0.112782\pi$
$193$	1860.51i	0.693899i	−0.937884	+	0.346949i	$0.887218\pi$
$194$	434.047	0.160633
$195$	0	0
$196$	115.213	0.0419874
$197$	− 97.0507i	− 0.0350994i	−0.999846	−	0.0175497i	$-0.994413\pi$
$197$	− 97.0507i	− 0.0350994i	0.999846	−	0.0175497i	$-0.00558653\pi$
$198$	60.7529i	0.0218057i
$199$	936.970	0.333769	0.166885	−	0.985976i	$-0.446629\pi$
$199$	936.970	0.333769	0.166885	+	0.985976i	$0.446629\pi$
$200$	0	0
$201$	−1278.67	−0.448710
$202$	1884.13i	0.656272i
$203$	1268.36i	0.438529i
$204$	−719.251	−0.246851
$205$	0	0
$206$	2737.39	0.925839
$207$	− 1046.32i	− 0.351325i
$208$	6246.03i	2.08214i
$209$	300.698	0.0995201
$210$	0	0
$211$	−1342.19	−0.437915	−0.218958	−	0.975734i	$-0.570266\pi$
$211$	−1342.19	−0.437915	−0.218958	+	0.975734i	$0.570266\pi$
$212$	− 102.235i	− 0.0331205i
$213$	3103.53i	0.998358i
$214$	−1823.59	−0.582513
$215$	0	0
$216$	−490.693	−0.154572
$217$	− 2125.30i	− 0.664860i
$218$	3576.06i	1.11101i
$219$	1415.22	0.436675
$220$	0	0
$221$	8241.00	2.50837
$222$	1528.26i	0.462029i
$223$	− 810.794i	− 0.243474i	−0.992562	−	0.121737i	$-0.961153\pi$
$223$	− 810.794i	− 0.243474i	0.992562	−	0.121737i	$-0.0388465\pi$
$224$	−722.759	−0.215586
$225$	0	0
$226$	620.109	0.182518
$227$	2584.59i	0.755707i	0.925865	+	0.377853i	$0.123338\pi$
$227$	2584.59i	0.755707i	−0.925865	+	0.377853i	$0.876662\pi$
$228$	− 1010.95i	− 0.293649i
$229$	1637.36	0.472489	0.236244	−	0.971694i	$-0.424083\pi$
$229$	1637.36	0.472489	0.236244	+	0.971694i	$0.424083\pi$
$230$	0	0
$231$	44.0602	0.0125496
$232$	− 3292.99i	− 0.931877i
$233$	− 3336.49i	− 0.938115i	−0.883168	−	0.469057i	$-0.844594\pi$
$233$	− 3336.49i	− 0.938115i	0.883168	−	0.469057i	$-0.155406\pi$
$234$	−2340.27	−0.653797
$235$	0	0
$236$	73.1121	0.0201661
$237$	3605.75i	0.988264i
$238$	2296.40i	0.625436i
$239$	3983.20	1.07804	0.539020	−	0.842293i	$-0.318795\pi$
$239$	3983.20	1.07804	0.539020	+	0.842293i	$0.318795\pi$
$240$	0	0
$241$	2282.78	0.610152	0.305076	−	0.952328i	$-0.401318\pi$
$241$	2282.78	0.610152	0.305076	+	0.952328i	$0.401318\pi$
$242$	− 4268.12i	− 1.13374i
$243$	− 243.000i	− 0.0641500i
$244$	1910.84	0.501347
$245$	0	0
$246$	−3661.71	−0.949033
$247$	11583.2i	2.98390i
$248$	5517.83i	1.41283i
$249$	−3977.16	−1.01222
$250$	0	0
$251$	−855.255	−0.215073	−0.107536	−	0.994201i	$-0.534296\pi$
$251$	−855.255	−0.215073	−0.107536	+	0.994201i	$0.534296\pi$
$252$	− 148.131i	− 0.0370294i
$253$	− 243.921i	− 0.0606134i
$254$	−3017.45	−0.745400
$255$	0	0
$256$	3330.17	0.813029
$257$	− 2892.91i	− 0.702158i	−0.936346	−	0.351079i	$-0.885815\pi$
$257$	− 2892.91i	− 0.702158i	0.936346	−	0.351079i	$-0.114185\pi$
$258$	2306.64i	0.556609i
$259$	1108.35	0.265906
$260$	0	0
$261$	1630.75	0.386746
$262$	2401.15i	0.566198i
$263$	4167.10i	0.977014i	0.872560	+	0.488507i	$0.162458\pi$
$263$	4167.10i	0.977014i	−0.872560	+	0.488507i	$0.837542\pi$
$264$	−114.392	−0.0266679
$265$	0	0
$266$	−3227.74	−0.744005
$267$	− 2658.68i	− 0.609395i
$268$	1002.18i	0.228425i
$269$	7519.40	1.70433	0.852167	−	0.523270i	$-0.175288\pi$
$269$	7519.40	1.70433	0.852167	+	0.523270i	$0.175288\pi$
$270$	0	0
$271$	7793.64	1.74697	0.873487	−	0.486848i	$-0.161853\pi$
$271$	7793.64	1.74697	0.873487	+	0.486848i	$0.161853\pi$
$272$	− 7880.07i	− 1.75661i
$273$	1697.25i	0.376272i
$274$	−1584.59	−0.349373
$275$	0	0
$276$	−820.068	−0.178849
$277$	3192.46i	0.692477i	0.938147	+	0.346238i	$0.112541\pi$
$277$	3192.46i	0.692477i	−0.938147	+	0.346238i	$0.887459\pi$
$278$	490.586i	0.105840i
$279$	−2732.52	−0.586351
$280$	0	0
$281$	−2566.33	−0.544819	−0.272410	−	0.962181i	$-0.587821\pi$
$281$	−2566.33	−0.544819	−0.272410	+	0.962181i	$0.587821\pi$
$282$	1215.73i	0.256723i
$283$	6114.58i	1.28436i	0.766553	+	0.642181i	$0.221970\pi$
$283$	6114.58i	1.28436i	−0.766553	+	0.642181i	$0.778030\pi$
$284$	2432.43	0.508234
$285$	0	0
$286$	−545.571	−0.112798
$287$	2655.60i	0.546186i
$288$	929.261i	0.190129i
$289$	−5483.94	−1.11621
$290$	0	0
$291$	−404.725	−0.0815307
$292$	− 1109.20i	− 0.222298i
$293$	3546.49i	0.707127i	0.935411	+	0.353563i	$0.115030\pi$
$293$	3546.49i	0.707127i	−0.935411	+	0.353563i	$0.884970\pi$
$294$	−472.949	−0.0938196
$295$	0	0
$296$	−2877.57	−0.565053
$297$	− 56.6488i	− 0.0110677i
$298$	4611.02i	0.896339i
$299$	9396.13	1.81737
$300$	0	0
$301$	1672.86	0.320339
$302$	2947.87i	0.561691i
$303$	− 1756.85i	− 0.333097i
$304$	11075.9	2.08963
$305$	0	0
$306$	2952.52	0.551583
$307$	1705.97i	0.317150i	0.987347	+	0.158575i	$0.0506900\pi$
$307$	1705.97i	0.317150i	−0.987347	+	0.158575i	$0.949310\pi$
$308$	− 34.5328i	− 0.00638860i
$309$	−2552.47	−0.469918
$310$	0	0
$311$	−10323.6	−1.88230	−0.941152	−	0.337983i	$-0.890255\pi$
$311$	−10323.6	−1.88230	−0.941152	+	0.337983i	$0.890255\pi$
$312$	− 4406.51i	− 0.799581i
$313$	− 7118.85i	− 1.28556i	−0.766050	−	0.642781i	$-0.777780\pi$
$313$	− 7118.85i	− 1.28556i	0.766050	−	0.642781i	$-0.222220\pi$
$314$	−546.193	−0.0981640
$315$	0	0
$316$	2826.06	0.503095
$317$	− 10755.2i	− 1.90559i	−0.303607	−	0.952797i	$-0.598191\pi$
$317$	− 10755.2i	− 1.90559i	0.303607	−	0.952797i	$-0.401809\pi$
$318$	419.675i	0.0740069i
$319$	380.164	0.0667245
$320$	0	0
$321$	1700.40	0.295660
$322$	2618.29i	0.453141i
$323$	− 14613.6i	− 2.51740i
$324$	−190.455	−0.0326568
$325$	0	0
$326$	3383.46	0.574823
$327$	− 3334.48i	− 0.563906i
$328$	− 6894.64i	− 1.16065i
$329$	881.694	0.147749
$330$	0	0
$331$	−494.875	−0.0821776	−0.0410888	−	0.999155i	$-0.513083\pi$
$331$	−494.875	−0.0821776	−0.0410888	+	0.999155i	$0.513083\pi$
$332$	3117.15i	0.515289i
$333$	− 1425.03i	− 0.234507i
$334$	−9302.35	−1.52396
$335$	0	0
$336$	1622.92	0.263504
$337$	409.916i	0.0662598i	0.999451	+	0.0331299i	$0.0105475\pi$
$337$	409.916i	0.0662598i	−0.999451	+	0.0331299i	$0.989452\pi$
$338$	− 13947.6i	− 2.24452i
$339$	−578.219	−0.0926387
$340$	0	0
$341$	−637.013	−0.101162
$342$	4149.95i	0.656151i
$343$	343.000i	0.0539949i
$344$	−4343.18	−0.680723
$345$	0	0
$346$	−2795.18	−0.434306
$347$	− 7377.44i	− 1.14133i	−0.821182	−	0.570666i	$-0.806685\pi$
$347$	− 7377.44i	− 1.14133i	0.821182	−	0.570666i	$-0.193315\pi$
$348$	− 1278.12i	− 0.196881i
$349$	11284.7	1.73083	0.865413	−	0.501059i	$-0.167056\pi$
$349$	11284.7	1.73083	0.865413	+	0.501059i	$0.167056\pi$
$350$	0	0
$351$	2182.18	0.331841
$352$	216.632i	0.0328026i
$353$	3910.15i	0.589565i	0.955564	+	0.294783i	$0.0952472\pi$
$353$	3910.15i	0.589565i	−0.955564	+	0.294783i	$0.904753\pi$
$354$	−300.124	−0.0450605
$355$	0	0
$356$	−2083.78	−0.310224
$357$	− 2141.27i	− 0.317446i
$358$	6671.08i	0.984854i
$359$	−12865.9	−1.89147	−0.945733	−	0.324945i	$-0.894654\pi$
$359$	−12865.9	−1.89147	−0.945733	+	0.324945i	$0.894654\pi$
$360$	0	0
$361$	13681.3	1.99464
$362$	− 6924.50i	− 1.00537i
$363$	3979.79i	0.575441i
$364$	1330.24	0.191549
$365$	0	0
$366$	−7843.96	−1.12025
$367$	892.357i	0.126923i	0.997984	+	0.0634614i	$0.0202140\pi$
$367$	892.357i	0.126923i	−0.997984	+	0.0634614i	$0.979786\pi$
$368$	− 8984.61i	− 1.27270i
$369$	3414.35	0.481691
$370$	0	0
$371$	304.363	0.0425923
$372$	2141.65i	0.298494i
$373$	− 8666.00i	− 1.20297i	−0.798884	−	0.601486i	$-0.794576\pi$
$373$	− 8666.00i	− 1.20297i	0.798884	−	0.601486i	$-0.205424\pi$
$374$	688.299	0.0951634
$375$	0	0
$376$	−2289.11	−0.313967
$377$	14644.4i	2.00059i
$378$	608.078i	0.0827411i
$379$	7111.00	0.963767	0.481883	−	0.876235i	$-0.339953\pi$
$379$	7111.00	0.963767	0.481883	+	0.876235i	$0.339953\pi$
$380$	0	0
$381$	2813.61	0.378335
$382$	− 13349.4i	− 1.78799i
$383$	14017.9i	1.87019i	0.354401	+	0.935094i	$0.384685\pi$
$383$	14017.9i	1.87019i	−0.354401	+	0.935094i	$0.615315\pi$
$384$	−5239.08	−0.696239
$385$	0	0
$386$	−5985.90	−0.789312
$387$	− 2150.82i	− 0.282512i
$388$	317.209i	0.0415048i
$389$	4848.24	0.631917	0.315959	−	0.948773i	$-0.397674\pi$
$389$	4848.24	0.631917	0.315959	+	0.948773i	$0.397674\pi$
$390$	0	0
$391$	−11854.3	−1.53324
$392$	− 890.518i	− 0.114740i
$393$	− 2238.95i	− 0.287379i
$394$	312.245	0.0399256
$395$	0	0
$396$	−44.3993	−0.00563421
$397$	4088.76i	0.516899i	0.966025	+	0.258449i	$0.0832115\pi$
$397$	4088.76i	0.516899i	−0.966025	+	0.258449i	$0.916788\pi$
$398$	3014.55i	0.379663i
$399$	3009.69	0.377627
$400$	0	0
$401$	7187.01	0.895018	0.447509	−	0.894279i	$-0.352311\pi$
$401$	7187.01	0.895018	0.447509	+	0.894279i	$0.352311\pi$
$402$	− 4113.93i	− 0.510409i
$403$	− 24538.5i	− 3.03313i
$404$	−1376.96	−0.169570
$405$	0	0
$406$	−4080.75	−0.498828
$407$	− 332.206i	− 0.0404590i
$408$	5559.31i	0.674575i
$409$	−924.965	−0.111825	−0.0559127	−	0.998436i	$-0.517807\pi$
$409$	−924.965	−0.111825	−0.0559127	+	0.998436i	$0.517807\pi$
$410$	0	0
$411$	1477.54	0.177328
$412$	2000.53i	0.239221i
$413$	217.661i	0.0259332i
$414$	3366.37	0.399633
$415$	0	0
$416$	−8344.92	−0.983518
$417$	− 457.445i	− 0.0537199i
$418$	967.448i	0.113204i
$419$	−4460.85	−0.520112	−0.260056	−	0.965594i	$-0.583741\pi$
$419$	−4460.85	−0.520112	−0.260056	+	0.965594i	$0.583741\pi$
$420$	0	0
$421$	−3443.27	−0.398610	−0.199305	−	0.979938i	$-0.563868\pi$
$421$	−3443.27	−0.398610	−0.199305	+	0.979938i	$0.563868\pi$
$422$	− 4318.28i	− 0.498130i
$423$	− 1133.61i	− 0.130302i
$424$	−790.206	−0.0905090
$425$	0	0
$426$	−9985.11	−1.13563
$427$	5688.73i	0.644723i
$428$	− 1332.71i	− 0.150512i
$429$	508.716	0.0572518
$430$	0	0
$431$	−6214.55	−0.694535	−0.347267	−	0.937766i	$-0.612890\pi$
$431$	−6214.55	−0.694535	−0.347267	+	0.937766i	$0.612890\pi$
$432$	− 2086.61i	− 0.232389i
$433$	− 13129.1i	− 1.45714i	−0.684970	−	0.728571i	$-0.740185\pi$
$433$	− 13129.1i	− 1.45714i	0.684970	−	0.728571i	$-0.259815\pi$
$434$	6837.81	0.756279
$435$	0	0
$436$	−2613.45	−0.287067
$437$	− 16661.9i	− 1.82391i
$438$	4553.26i	0.496719i
$439$	−6830.51	−0.742602	−0.371301	−	0.928512i	$-0.621088\pi$
$439$	−6830.51	−0.742602	−0.371301	+	0.928512i	$0.621088\pi$
$440$	0	0
$441$	441.000	0.0476190
$442$	26514.1i	2.85328i
$443$	− 12837.6i	− 1.37682i	−0.725322	−	0.688410i	$-0.758309\pi$
$443$	− 12837.6i	− 1.37682i	0.725322	−	0.688410i	$-0.241691\pi$
$444$	−1116.88	−0.119380
$445$	0	0
$446$	2608.60	0.276953
$447$	− 4299.53i	− 0.454945i
$448$	2002.42i	0.211172i
$449$	16800.5	1.76585	0.882923	−	0.469518i	$-0.155572\pi$
$449$	16800.5	1.76585	0.882923	+	0.469518i	$0.155572\pi$
$450$	0	0
$451$	795.962	0.0831051
$452$	453.187i	0.0471596i
$453$	− 2748.73i	− 0.285092i
$454$	−8315.52	−0.859618
$455$	0	0
$456$	−7813.95	−0.802460
$457$	9601.60i	0.982809i	0.870931	+	0.491405i	$0.163516\pi$
$457$	9601.60i	0.982809i	−0.870931	+	0.491405i	$0.836484\pi$
$458$	5267.96i	0.537457i
$459$	−2753.07	−0.279961
$460$	0	0
$461$	3506.77	0.354287	0.177144	−	0.984185i	$-0.443314\pi$
$461$	3506.77	0.354287	0.177144	+	0.984185i	$0.443314\pi$
$462$	141.757i	0.0142752i
$463$	4212.28i	0.422810i	0.977399	+	0.211405i	$0.0678039\pi$
$463$	4212.28i	0.422810i	−0.977399	+	0.211405i	$0.932196\pi$
$464$	14003.0	1.40102
$465$	0	0
$466$	10734.6	1.06711
$467$	560.881i	0.0555771i	0.999614	+	0.0277885i	$0.00884650\pi$
$467$	560.881i	0.0555771i	−0.999614	+	0.0277885i	$0.991153\pi$
$468$	− 1710.31i	− 0.168930i
$469$	−2983.57	−0.293750
$470$	0	0
$471$	509.296	0.0498241
$472$	− 565.105i	− 0.0551082i
$473$	− 501.405i	− 0.0487413i
$474$	−11600.9	−1.12415
$475$	0	0
$476$	−1678.25	−0.161602
$477$	− 391.324i	− 0.0375629i
$478$	12815.3i	1.22627i
$479$	−13267.8	−1.26559	−0.632796	−	0.774318i	$-0.718093\pi$
$479$	−13267.8	−1.26559	−0.632796	+	0.774318i	$0.718093\pi$
$480$	0	0
$481$	12797.0	1.21308
$482$	7344.48i	0.694049i
$483$	− 2441.41i	− 0.229996i
$484$	3119.22	0.292939
$485$	0	0
$486$	781.814	0.0729708
$487$	− 16137.0i	− 1.50151i	−0.660581	−	0.750755i	$-0.729690\pi$
$487$	− 16137.0i	− 1.50151i	0.660581	−	0.750755i	$-0.270310\pi$
$488$	− 14769.4i	− 1.37004i
$489$	−3154.89	−0.291757
$490$	0	0
$491$	5186.66	0.476722	0.238361	−	0.971177i	$-0.423390\pi$
$491$	5186.66	0.476722	0.238361	+	0.971177i	$0.423390\pi$
$492$	− 2676.04i	− 0.245214i
$493$	− 18475.5i	− 1.68782i
$494$	−37267.2	−3.39420
$495$	0	0
$496$	−23463.8	−2.12411
$497$	7241.56i	0.653579i
$498$	− 12795.9i	− 1.15140i
$499$	−14822.5	−1.32975	−0.664877	−	0.746953i	$-0.731516\pi$
$499$	−14822.5	−1.32975	−0.664877	+	0.746953i	$0.731516\pi$
$500$	0	0
$501$	8673.95	0.773500
$502$	− 2751.65i	− 0.244646i
$503$	1690.53i	0.149855i	0.997189	+	0.0749273i	$0.0238725\pi$
$503$	1690.53i	0.149855i	−0.997189	+	0.0749273i	$0.976128\pi$
$504$	−1144.95	−0.101191
$505$	0	0
$506$	784.778	0.0689479
$507$	13005.3i	1.13923i
$508$	− 2205.21i	− 0.192599i
$509$	−5355.09	−0.466326	−0.233163	−	0.972438i	$-0.574908\pi$
$509$	−5355.09	−0.466326	−0.233163	+	0.972438i	$0.574908\pi$
$510$	0	0
$511$	3302.19	0.285871
$512$	− 3256.60i	− 0.281100i
$513$	− 3869.61i	− 0.333036i
$514$	9307.47	0.798706
$515$	0	0
$516$	−1685.73	−0.143818
$517$	− 264.269i	− 0.0224808i
$518$	3565.95i	0.302469i
$519$	2606.35	0.220436
$520$	0	0
$521$	−15355.6	−1.29125	−0.645624	−	0.763655i	$-0.723403\pi$
$521$	−15355.6	−1.29125	−0.645624	+	0.763655i	$0.723403\pi$
$522$	5246.67i	0.439925i
$523$	− 6142.95i	− 0.513599i	−0.966465	−	0.256800i	$-0.917332\pi$
$523$	− 6142.95i	− 0.513599i	0.966465	−	0.256800i	$-0.0826681\pi$
$524$	−1754.81	−0.146296
$525$	0	0
$526$	−13407.0	−1.11136
$527$	30958.1i	2.55893i
$528$	− 486.436i	− 0.0400935i
$529$	−1348.89	−0.110864
$530$	0	0
$531$	279.850	0.0228709
$532$	− 2358.89i	− 0.192238i
$533$	30661.4i	2.49173i
$534$	8553.88	0.693188
$535$	0	0
$536$	7746.14	0.624221
$537$	− 6220.43i	− 0.499872i
$538$	24192.5i	1.93868i
$539$	102.807	0.00821561
$540$	0	0
$541$	4877.07	0.387582	0.193791	−	0.981043i	$-0.437922\pi$
$541$	4877.07	0.387582	0.193791	+	0.981043i	$0.437922\pi$
$542$	25074.8i	1.98719i
$543$	6456.72i	0.510285i
$544$	10528.1	0.829755
$545$	0	0
$546$	−5460.64	−0.428011
$547$	3823.80i	0.298892i	0.988770	+	0.149446i	$0.0477490\pi$
$547$	3823.80i	0.298892i	−0.988770	+	0.149446i	$0.952251\pi$
$548$	− 1158.04i	− 0.0902722i
$549$	7314.08	0.568592
$550$	0	0
$551$	25968.5	2.00780
$552$	6338.55i	0.488744i
$553$	8413.41i	0.646970i
$554$	−10271.2	−0.787694
$555$	0	0
$556$	−358.529	−0.0273472
$557$	10514.6i	0.799849i	0.916548	+	0.399925i	$0.130964\pi$
$557$	10514.6i	0.799849i	−0.916548	+	0.399925i	$0.869036\pi$
$558$	− 8791.47i	− 0.666976i
$559$	19314.7	1.46141
$560$	0	0
$561$	−641.802	−0.0483011
$562$	− 8256.75i	− 0.619733i
$563$	− 1679.55i	− 0.125728i	−0.998022	−	0.0628639i	$-0.979977\pi$
$563$	− 1679.55i	− 0.125728i	0.998022	−	0.0628639i	$-0.0200234\pi$
$564$	−888.480	−0.0663329
$565$	0	0
$566$	−19672.7	−1.46096
$567$	− 567.000i	− 0.0419961i
$568$	− 18801.0i	− 1.38886i
$569$	−7067.14	−0.520686	−0.260343	−	0.965516i	$-0.583836\pi$
$569$	−7067.14	−0.520686	−0.260343	+	0.965516i	$0.583836\pi$
$570$	0	0
$571$	−10609.6	−0.777577	−0.388788	−	0.921327i	$-0.627106\pi$
$571$	−10609.6	−0.777577	−0.388788	+	0.921327i	$0.627106\pi$
$572$	− 398.713i	− 0.0291452i
$573$	12447.6i	0.907513i
$574$	−8543.99	−0.621288
$575$	0	0
$576$	2574.53	0.186237
$577$	4002.39i	0.288773i	0.989521	+	0.144386i	$0.0461208\pi$
$577$	4002.39i	0.288773i	−0.989521	+	0.144386i	$0.953879\pi$
$578$	− 17643.7i	− 1.26969i
$579$	5581.53	0.400623
$580$	0	0
$581$	−9280.03	−0.662652
$582$	− 1302.14i	− 0.0927413i
$583$	− 91.2266i	− 0.00648065i
$584$	−8573.34	−0.607478
$585$	0	0
$586$	−11410.3	−0.804358
$587$	2334.57i	0.164154i	0.996626	+	0.0820768i	$0.0261553\pi$
$587$	2334.57i	0.164154i	−0.996626	+	0.0820768i	$0.973845\pi$
$588$	− 345.640i	− 0.0242414i
$589$	−43513.6	−3.04405
$590$	0	0
$591$	−291.152	−0.0202646
$592$	− 12236.5i	− 0.849522i
$593$	− 12401.0i	− 0.858768i	−0.903122	−	0.429384i	$-0.858731\pi$
$593$	− 12401.0i	− 0.858768i	0.903122	−	0.429384i	$-0.141269\pi$
$594$	182.259	0.0125895
$595$	0	0
$596$	−3369.81	−0.231599
$597$	− 2810.91i	− 0.192702i
$598$	30230.6i	2.06726i
$599$	−15848.8	−1.08108	−0.540538	−	0.841320i	$-0.681779\pi$
$599$	−15848.8	−1.08108	−0.540538	+	0.841320i	$0.681779\pi$
$600$	0	0
$601$	298.912	0.0202877	0.0101438	−	0.999949i	$-0.496771\pi$
$601$	298.912	0.0202877	0.0101438	+	0.999949i	$0.496771\pi$
$602$	5382.16i	0.364386i
$603$	3836.02i	0.259063i
$604$	−2154.36	−0.145132
$605$	0	0
$606$	5652.39	0.378899
$607$	8731.31i	0.583843i	0.956442	+	0.291922i	$0.0942947\pi$
$607$	8731.31i	0.583843i	−0.956442	+	0.291922i	$0.905705\pi$
$608$	14797.8i	0.987059i
$609$	3805.08	0.253185
$610$	0	0
$611$	10180.0	0.674039
$612$	2157.75i	0.142520i
$613$	10037.7i	0.661368i	0.943742	+	0.330684i	$0.107279\pi$
$613$	10037.7i	0.661368i	−0.943742	+	0.330684i	$0.892721\pi$
$614$	−5488.70	−0.360759
$615$	0	0
$616$	−266.914	−0.0174582
$617$	− 20567.7i	− 1.34202i	−0.741450	−	0.671008i	$-0.765862\pi$
$617$	− 20567.7i	− 1.34202i	0.741450	−	0.671008i	$-0.234138\pi$
$618$	− 8212.16i	− 0.534533i
$619$	−15714.5	−1.02039	−0.510193	−	0.860060i	$-0.670426\pi$
$619$	−15714.5	−1.02039	−0.510193	+	0.860060i	$0.670426\pi$
$620$	0	0
$621$	−3138.96	−0.202838
$622$	− 33214.5i	− 2.14113i
$623$	− 6203.58i	− 0.398943i
$624$	18738.1	1.20212
$625$	0	0
$626$	22903.8	1.46233
$627$	− 902.093i	− 0.0574579i
$628$	− 399.168i	− 0.0253639i
$629$	−16144.8	−1.02343
$630$	0	0
$631$	−8962.39	−0.565431	−0.282716	−	0.959204i	$-0.591235\pi$
$631$	−8962.39	−0.565431	−0.282716	+	0.959204i	$0.591235\pi$
$632$	− 21843.4i	− 1.37482i
$633$	4026.57i	0.252831i
$634$	34603.2	2.16762
$635$	0	0
$636$	−306.706	−0.0191221
$637$	3960.25i	0.246328i
$638$	1223.12i	0.0758993i
$639$	9310.58	0.576402
$640$	0	0
$641$	26919.8	1.65877	0.829383	−	0.558681i	$-0.188692\pi$
$641$	26919.8	1.65877	0.829383	+	0.558681i	$0.188692\pi$
$642$	5470.76i	0.336314i
$643$	5675.19i	0.348068i	0.984740	+	0.174034i	$0.0556803\pi$
$643$	5675.19i	0.348068i	−0.984740	+	0.174034i	$0.944320\pi$
$644$	−1913.49	−0.117084
$645$	0	0
$646$	47016.8	2.86355
$647$	8444.54i	0.513121i	0.966528	+	0.256560i	$0.0825893\pi$
$647$	8444.54i	0.513121i	−0.966528	+	0.256560i	$0.917411\pi$
$648$	1472.08i	0.0892419i
$649$	65.2393	0.00394587
$650$	0	0
$651$	−6375.89	−0.383857
$652$	2472.69i	0.148525i
$653$	25968.1i	1.55622i	0.628130	+	0.778108i	$0.283820\pi$
$653$	25968.1i	1.55622i	−0.628130	+	0.778108i	$0.716180\pi$
$654$	10728.2	0.641444
$655$	0	0
$656$	29318.5	1.74496
$657$	− 4245.67i	− 0.252115i
$658$	2836.71i	0.168065i
$659$	21195.4	1.25289	0.626446	−	0.779465i	$-0.284509\pi$
$659$	21195.4	1.25289	0.626446	+	0.779465i	$0.284509\pi$
$660$	0	0
$661$	−9283.40	−0.546267	−0.273134	−	0.961976i	$-0.588060\pi$
$661$	−9283.40	−0.546267	−0.273134	+	0.961976i	$0.588060\pi$
$662$	− 1592.18i	− 0.0934773i
$663$	− 24723.0i	− 1.44821i
$664$	24093.4	1.40814
$665$	0	0
$666$	4584.79	0.266752
$667$	− 21065.2i	− 1.22286i
$668$	− 6798.33i	− 0.393765i
$669$	−2432.38	−0.140570
$670$	0	0
$671$	1705.08	0.0980980
$672$	2168.28i	0.124469i
$673$	25358.3i	1.45244i	0.687463	+	0.726219i	$0.258724\pi$
$673$	25358.3i	1.45244i	−0.687463	+	0.726219i	$0.741276\pi$
$674$	−1318.84	−0.0753707
$675$	0	0
$676$	10193.1	0.579945
$677$	7140.67i	0.405374i	0.979244	+	0.202687i	$0.0649674\pi$
$677$	7140.67i	0.405374i	−0.979244	+	0.202687i	$0.935033\pi$
$678$	− 1860.33i	− 0.105377i
$679$	−944.359	−0.0533743
$680$	0	0
$681$	7753.78	0.436308
$682$	− 2049.49i	− 0.115072i
$683$	− 10666.3i	− 0.597561i	−0.954322	−	0.298780i	$-0.903420\pi$
$683$	− 10666.3i	− 0.597561i	0.954322	−	0.298780i	$-0.0965798\pi$
$684$	−3032.86	−0.169538
$685$	0	0
$686$	−1103.55	−0.0614194
$687$	− 4912.09i	− 0.272792i
$688$	− 18468.8i	− 1.02342i
$689$	3514.16	0.194309
$690$	0	0
$691$	−19360.0	−1.06583	−0.532915	−	0.846169i	$-0.678903\pi$
$691$	−19360.0	−1.06583	−0.532915	+	0.846169i	$0.678903\pi$
$692$	− 2042.77i	− 0.112217i
$693$	− 132.181i	− 0.00724549i
$694$	23735.8	1.29827
$695$	0	0
$696$	−9878.97	−0.538019
$697$	− 38682.8i	− 2.10218i
$698$	36306.9i	1.96882i
$699$	−10009.5	−0.541621
$700$	0	0
$701$	−19252.3	−1.03730	−0.518651	−	0.854986i	$-0.673566\pi$
$701$	−19252.3	−1.03730	−0.518651	+	0.854986i	$0.673566\pi$
$702$	7020.82i	0.377470i
$703$	− 22692.5i	− 1.21745i
$704$	600.183	0.0321310
$705$	0	0
$706$	−12580.3	−0.670632
$707$	− 4099.32i	− 0.218063i
$708$	− 219.336i	− 0.0116429i
$709$	19553.0	1.03572	0.517861	−	0.855465i	$-0.326728\pi$
$709$	19553.0	1.03572	0.517861	+	0.855465i	$0.326728\pi$
$710$	0	0
$711$	10817.2	0.570574
$712$	16106.1i	0.847756i
$713$	35297.5i	1.85400i
$714$	6889.21	0.361096
$715$	0	0
$716$	−4875.35	−0.254470
$717$	− 11949.6i	− 0.622407i
$718$	− 41394.0i	− 2.15155i
$719$	16334.8	0.847265	0.423633	−	0.905834i	$-0.360755\pi$
$719$	16334.8	0.847265	0.423633	+	0.905834i	$0.360755\pi$
$720$	0	0
$721$	−5955.76	−0.307634
$722$	44017.3i	2.26891i
$723$	− 6848.33i	− 0.352272i
$724$	5060.55	0.259770
$725$	0	0
$726$	−12804.4	−0.654565
$727$	− 30698.8i	− 1.56610i	−0.621957	−	0.783051i	$-0.713662\pi$
$727$	− 30698.8i	− 1.56610i	0.621957	−	0.783051i	$-0.286338\pi$
$728$	− 10281.9i	− 0.523449i
$729$	−729.000	−0.0370370
$730$	0	0
$731$	−24367.7	−1.23293
$732$	− 5732.51i	− 0.289453i
$733$	− 7388.56i	− 0.372309i	−0.982520	−	0.186155i	$-0.940397\pi$
$733$	− 7388.56i	− 0.372309i	0.982520	−	0.186155i	$-0.0596025\pi$
$734$	−2871.02	−0.144375
$735$	0	0
$736$	12003.8	0.601175
$737$	894.264i	0.0446956i
$738$	10985.1i	0.547924i
$739$	−22650.8	−1.12750	−0.563751	−	0.825945i	$-0.690642\pi$
$739$	−22650.8	−1.12750	−0.563751	+	0.825945i	$0.690642\pi$
$740$	0	0
$741$	34749.7	1.72276
$742$	979.241i	0.0484489i
$743$	17656.4i	0.871806i	0.899994	+	0.435903i	$0.143571\pi$
$743$	17656.4i	0.871806i	−0.899994	+	0.435903i	$0.856429\pi$
$744$	16553.5	0.815699
$745$	0	0
$746$	27881.5	1.36838
$747$	11931.5i	0.584404i
$748$	503.021i	0.0245886i
$749$	3967.59	0.193555
$750$	0	0
$751$	22109.0	1.07426	0.537130	−	0.843500i	$-0.319508\pi$
$751$	22109.0	1.07426	0.537130	+	0.843500i	$0.319508\pi$
$752$	− 9734.12i	− 0.472031i
$753$	2565.77i	0.124172i
$754$	−47116.0	−2.27568
$755$	0	0
$756$	−444.394	−0.0213789
$757$	− 11034.2i	− 0.529784i	−0.964278	−	0.264892i	$-0.914664\pi$
$757$	− 11034.2i	− 0.529784i	0.964278	−	0.264892i	$-0.0853363\pi$
$758$	22878.5i	1.09629i
$759$	−731.763	−0.0349952
$760$	0	0
$761$	−6357.12	−0.302819	−0.151410	−	0.988471i	$-0.548381\pi$
$761$	−6357.12	−0.302819	−0.151410	+	0.988471i	$0.548381\pi$
$762$	9052.35i	0.430357i
$763$	− 7780.46i	− 0.369163i
$764$	9755.96	0.461987
$765$	0	0
$766$	−45100.4	−2.12734
$767$	2513.10i	0.118309i
$768$	− 9990.50i	− 0.469402i
$769$	35810.1	1.67925	0.839627	−	0.543163i	$-0.182774\pi$
$769$	35810.1	1.67925	0.839627	+	0.543163i	$0.182774\pi$
$770$	0	0
$771$	−8678.72	−0.405391
$772$	− 4374.60i	− 0.203945i
$773$	− 3158.57i	− 0.146967i	−0.997296	−	0.0734837i	$-0.976588\pi$
$773$	− 3158.57i	− 0.146967i	0.997296	−	0.0734837i	$-0.0234117\pi$
$774$	6919.92	0.321359
$775$	0	0
$776$	2451.80	0.113421
$777$	− 3325.06i	− 0.153521i
$778$	15598.5i	0.718807i
$779$	54371.1	2.50070
$780$	0	0
$781$	2170.51	0.0994455
$782$	− 38139.3i	− 1.74406i
$783$	− 4892.24i	− 0.223288i
$784$	3786.81	0.172504
$785$	0	0
$786$	7203.46	0.326894
$787$	− 20371.2i	− 0.922687i	−0.887222	−	0.461344i	$-0.847368\pi$
$787$	− 20371.2i	− 0.922687i	0.887222	−	0.461344i	$-0.152632\pi$
$788$	228.195i	0.0103161i
$789$	12501.3	0.564079
$790$	0	0
$791$	−1349.18	−0.0606463
$792$	343.175i	0.0153967i
$793$	65681.6i	2.94127i
$794$	−13154.9	−0.587973
$795$	0	0
$796$	−2203.09	−0.0980986
$797$	31056.5i	1.38027i	0.723680	+	0.690136i	$0.242449\pi$
$797$	31056.5i	1.38027i	−0.723680	+	0.690136i	$0.757551\pi$
$798$	9683.22i	0.429552i
$799$	−12843.2	−0.568660
$800$	0	0
$801$	−7976.03	−0.351834
$802$	23123.1i	1.01809i
$803$	− 989.761i	− 0.0434968i
$804$	3006.54	0.131881
$805$	0	0
$806$	78948.8	3.45019
$807$	− 22558.2i	− 0.983998i
$808$	10642.9i	0.463386i
$809$	−9549.52	−0.415010	−0.207505	−	0.978234i	$-0.566534\pi$
$809$	−9549.52	−0.415010	−0.207505	+	0.978234i	$0.566534\pi$
$810$	0	0
$811$	−26730.9	−1.15740	−0.578698	−	0.815542i	$-0.696439\pi$
$811$	−26730.9	−1.15740	−0.578698	+	0.815542i	$0.696439\pi$
$812$	− 2982.28i	− 0.128889i
$813$	− 23380.9i	− 1.00862i
$814$	1068.82	0.0460222
$815$	0	0
$816$	−23640.2	−1.01418
$817$	− 34250.3i	− 1.46667i
$818$	− 2975.93i	− 0.127202i
$819$	5091.75	0.217241
$820$	0	0
$821$	−30878.1	−1.31261	−0.656305	−	0.754496i	$-0.727882\pi$
$821$	−30878.1	−1.31261	−0.656305	+	0.754496i	$0.727882\pi$
$822$	4753.76i	0.201711i
$823$	− 20618.3i	− 0.873280i	−0.899636	−	0.436640i	$-0.856168\pi$
$823$	− 20618.3i	− 0.873280i	0.899636	−	0.436640i	$-0.143832\pi$
$824$	15462.7	0.653724
$825$	0	0
$826$	−700.290	−0.0294990
$827$	12493.2i	0.525311i	0.964890	+	0.262656i	$0.0845983\pi$
$827$	12493.2i	0.525311i	−0.964890	+	0.262656i	$0.915402\pi$
$828$	2460.21i	0.103259i
$829$	36795.9	1.54158	0.770792	−	0.637087i	$-0.219861\pi$
$829$	36795.9	1.54158	0.770792	+	0.637087i	$0.219861\pi$
$830$	0	0
$831$	9577.37	0.399802
$832$	23119.8i	0.963381i
$833$	− 4996.31i	− 0.207817i
$834$	1471.76	0.0611065
$835$	0	0
$836$	−707.028	−0.0292501
$837$	8197.57i	0.338530i
$838$	− 14352.1i	− 0.591628i
$839$	−6904.41	−0.284108	−0.142054	−	0.989859i	$-0.545371\pi$
$839$	−6904.41	−0.284108	−0.142054	+	0.989859i	$0.545371\pi$
$840$	0	0
$841$	8442.32	0.346153
$842$	− 11078.2i	− 0.453419i
$843$	7698.98i	0.314552i
$844$	3155.88	0.128708
$845$	0	0
$846$	3647.20	0.148219
$847$	9286.19i	0.376714i
$848$	− 3360.25i	− 0.136075i
$849$	18343.8	0.741527
$850$	0	0
$851$	−18407.8	−0.741495
$852$	− 7297.30i	− 0.293429i
$853$	− 34285.8i	− 1.37623i	−0.725602	−	0.688115i	$-0.758439\pi$
$853$	− 34285.8i	− 1.37623i	0.725602	−	0.688115i	$-0.241561\pi$
$854$	−18302.6	−0.733374
$855$	0	0
$856$	−10300.9	−0.411306
$857$	34301.1i	1.36722i	0.729849	+	0.683608i	$0.239590\pi$
$857$	34301.1i	1.36722i	−0.729849	+	0.683608i	$0.760410\pi$
$858$	1636.71i	0.0651241i
$859$	−6823.12	−0.271015	−0.135507	−	0.990776i	$-0.543266\pi$
$859$	−6823.12	−0.271015	−0.135507	+	0.990776i	$0.543266\pi$
$860$	0	0
$861$	7966.81	0.315341
$862$	− 19994.3i	− 0.790035i
$863$	8059.34i	0.317895i	0.987287	+	0.158947i	$0.0508100\pi$
$863$	8059.34i	0.317895i	−0.987287	+	0.158947i	$0.949190\pi$
$864$	2787.78	0.109771
$865$	0	0
$866$	42240.7	1.65750
$867$	16451.8i	0.644445i
$868$	4997.19i	0.195410i
$869$	2521.75	0.0984400
$870$	0	0
$871$	−34448.1	−1.34010
$872$	20200.1i	0.784474i
$873$	1214.18i	0.0470717i
$874$	53607.1	2.07470
$875$	0	0
$876$	−3327.60	−0.128344
$877$	− 162.992i	− 0.00627577i	−0.999995	−	0.00313789i	$-0.999001\pi$
$877$	− 162.992i	− 0.00627577i	0.999995	−	0.00313789i	$-0.000998822\pi$
$878$	− 21976.1i	− 0.844712i
$879$	10639.5	0.408260
$880$	0	0
$881$	10633.9	0.406658	0.203329	−	0.979110i	$-0.434824\pi$
$881$	10633.9	0.406658	0.203329	+	0.979110i	$0.434824\pi$
$882$	1418.85i	0.0541668i
$883$	42208.3i	1.60863i	0.594201	+	0.804317i	$0.297468\pi$
$883$	42208.3i	1.60863i	−0.594201	+	0.804317i	$0.702532\pi$
$884$	−19377.0	−0.737238
$885$	0	0
$886$	41302.8	1.56614
$887$	− 15696.0i	− 0.594161i	−0.954852	−	0.297080i	$-0.903987\pi$
$887$	− 15696.0i	− 0.594161i	0.954852	−	0.297080i	$-0.0960129\pi$
$888$	8632.72i	0.326233i
$889$	6565.09	0.247678
$890$	0	0
$891$	−169.946	−0.00638992
$892$	1906.41i	0.0715599i
$893$	− 18051.9i	− 0.676466i
$894$	13833.0	0.517501
$895$	0	0
$896$	−12224.5	−0.455796
$897$	− 28188.4i	− 1.04926i
$898$	54053.0i	2.00865i
$899$	−55013.0	−2.04092
$900$	0	0
$901$	−4433.50	−0.163931
$902$	2560.88i	0.0945322i
$903$	− 5018.58i	− 0.184948i
$904$	3502.82	0.128874
$905$	0	0
$906$	8843.61	0.324293
$907$	− 24251.5i	− 0.887827i	−0.896070	−	0.443913i	$-0.853590\pi$
$907$	− 24251.5i	− 0.887827i	0.896070	−	0.443913i	$-0.146410\pi$
$908$	− 6077.13i	− 0.222111i
$909$	−5270.55	−0.192314
$910$	0	0
$911$	−34110.8	−1.24055	−0.620276	−	0.784384i	$-0.712979\pi$
$911$	−34110.8	−1.24055	−0.620276	+	0.784384i	$0.712979\pi$
$912$	− 33227.8i	− 1.20645i
$913$	2781.50i	0.100826i
$914$	−30891.6	−1.11795
$915$	0	0
$916$	−3849.92	−0.138870
$917$	− 5224.21i	− 0.188134i
$918$	− 8857.56i	− 0.318456i
$919$	−55153.2	−1.97969	−0.989846	−	0.142146i	$-0.954600\pi$
$919$	−55153.2	−1.97969	−0.989846	+	0.142146i	$0.954600\pi$
$920$	0	0
$921$	5117.92	0.183107
$922$	11282.5i	0.403003i
$923$	83610.6i	2.98166i
$924$	−103.598	−0.00368846
$925$	0	0
$926$	−13552.3	−0.480947
$927$	7657.40i	0.271308i
$928$	18708.5i	0.661786i
$929$	−14429.8	−0.509607	−0.254804	−	0.966993i	$-0.582011\pi$
$929$	−14429.8	−0.509607	−0.254804	+	0.966993i	$0.582011\pi$
$930$	0	0
$931$	7022.62	0.247215
$932$	7845.06i	0.275723i
$933$	30970.7i	1.08675i
$934$	−1804.55	−0.0632190
$935$	0	0
$936$	−13219.5	−0.461639
$937$	3625.32i	0.126397i	0.998001	+	0.0631985i	$0.0201301\pi$
$937$	3625.32i	0.126397i	−0.998001	+	0.0631985i	$0.979870\pi$
$938$	− 9599.18i	− 0.334141i
$939$	−21356.5	−0.742220
$940$	0	0
$941$	−15634.7	−0.541632	−0.270816	−	0.962631i	$-0.587293\pi$
$941$	−15634.7	−0.541632	−0.270816	+	0.962631i	$0.587293\pi$
$942$	1638.58i	0.0566750i
$943$	− 44105.0i	− 1.52307i
$944$	2403.03	0.0828517
$945$	0	0
$946$	1613.19	0.0554433
$947$	32438.0i	1.11309i	0.830818	+	0.556544i	$0.187873\pi$
$947$	32438.0i	1.11309i	−0.830818	+	0.556544i	$0.812127\pi$
$948$	− 8478.17i	− 0.290462i
$949$	38126.8	1.30416
$950$	0	0
$951$	−32265.7	−1.10020
$952$	12971.7i	0.441613i
$953$	10940.1i	0.371862i	0.982563	+	0.185931i	$0.0595300\pi$
$953$	10940.1i	0.371862i	−0.982563	+	0.185931i	$0.940470\pi$
$954$	1259.02	0.0427279
$955$	0	0
$956$	−9365.66	−0.316849
$957$	− 1140.49i	− 0.0385234i
$958$	− 42686.9i	− 1.43961i
$959$	3447.60	0.116088
$960$	0	0
$961$	62390.3	2.09427
$962$	41172.2i	1.37988i
$963$	− 5101.19i	− 0.170700i
$964$	−5367.48	−0.179331
$965$	0	0
$966$	7854.87	0.261621
$967$	27827.5i	0.925412i	0.886512	+	0.462706i	$0.153121\pi$
$967$	27827.5i	0.925412i	−0.886512	+	0.462706i	$0.846879\pi$
$968$	− 24109.4i	− 0.800521i
$969$	−43840.7	−1.45342
$970$	0	0
$971$	−58041.1	−1.91826	−0.959129	−	0.282970i	$-0.908680\pi$
$971$	−58041.1	−1.91826	−0.959129	+	0.282970i	$0.908680\pi$
$972$	571.364i	0.0188544i
$973$	− 1067.37i	− 0.0351679i
$974$	51918.1	1.70797
$975$	0	0
$976$	62805.0	2.05977
$977$	− 28430.6i	− 0.930988i	−0.885051	−	0.465494i	$-0.845877\pi$
$977$	− 28430.6i	− 0.930988i	0.885051	−	0.465494i	$-0.154123\pi$
$978$	− 10150.4i	− 0.331874i
$979$	−1859.39	−0.0607012
$980$	0	0
$981$	−10003.4	−0.325571
$982$	16687.2i	0.542272i
$983$	9356.47i	0.303586i	0.988412	+	0.151793i	$0.0485047\pi$
$983$	9356.47i	0.303586i	−0.988412	+	0.151793i	$0.951495\pi$
$984$	−20683.9	−0.670101
$985$	0	0
$986$	59442.1	1.91990
$987$	− 2645.08i	− 0.0853028i
$988$	− 27235.6i	− 0.877003i
$989$	−27783.3	−0.893284
$990$	0	0
$991$	−9199.90	−0.294898	−0.147449	−	0.989070i	$-0.547106\pi$
$991$	−9199.90	−0.294898	−0.147449	+	0.989070i	$0.547106\pi$
$992$	− 31348.5i	− 1.00334i
$993$	1484.63i	0.0474453i
$994$	−23298.6	−0.743447
$995$	0	0
$996$	9351.46	0.297502
$997$	5396.25i	0.171415i	0.996320	+	0.0857076i	$0.0273151\pi$
$997$	5396.25i	0.171415i	−0.996320	+	0.0857076i	$0.972685\pi$
$998$	− 47689.1i	− 1.51260i
$999$	−4275.08	−0.135393

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	525.4.d.o.274.7		8
5.2	odd	4		525.4.a.s.1.2	✓	4
5.3	odd	4		525.4.a.v.1.3	yes	4
5.4	even	2	inner	525.4.d.o.274.2		8
15.2	even	4		1575.4.a.bm.1.3		4
15.8	even	4		1575.4.a.bf.1.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
525.4.a.s.1.2	✓	4	5.2	odd	4
525.4.a.v.1.3	yes	4	5.3	odd	4
525.4.d.o.274.2		8	5.4	even	2	inner
525.4.d.o.274.7		8	1.1	even	1	trivial
1575.4.a.bf.1.2		4	15.8	even	4
1575.4.a.bm.1.3		4	15.2	even	4

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:	\( N \)	\(=\)	\( 525 = 3 \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	525.d (of order \(2\), degree \(1\), not minimal)

\(f(q)\)	\(=\)	\(q+3.21734i q^{2} -3.00000i q^{3} -2.35129 q^{4} +9.65203 q^{6} -7.00000i q^{7} +18.1738i q^{8} -9.00000 q^{9} +O(q^{10})\)	\(q+3.21734i q^{2} -3.00000i q^{3} -2.35129 q^{4} +9.65203 q^{6} -7.00000i q^{7} +18.1738i q^{8} -9.00000 q^{9} -2.09810 q^{11} +7.05388i q^{12} -80.8215i q^{13} +22.5214 q^{14} -77.2818 q^{16} +101.965i q^{17} -28.9561i q^{18} -143.319 q^{19} -21.0000 q^{21} -6.75032i q^{22} +116.258i q^{23} +54.5215 q^{24} +260.030 q^{26} +27.0000i q^{27} +16.4590i q^{28} -181.194 q^{29} +303.614 q^{31} -103.251i q^{32} +6.29431i q^{33} -328.058 q^{34} +21.1616 q^{36} +158.336i q^{37} -461.106i q^{38} -242.465 q^{39} -379.372 q^{41} -67.5642i q^{42} +238.980i q^{43} +4.93326 q^{44} -374.041 q^{46} +125.956i q^{47} +231.845i q^{48} -49.0000 q^{49} +305.896 q^{51} +190.035i q^{52} +43.4805i q^{53} -86.8682 q^{54} +127.217 q^{56} +429.956i q^{57} -582.964i q^{58} -31.0944 q^{59} -812.675 q^{61} +976.830i q^{62} +63.0000i q^{63} -286.059 q^{64} -20.2510 q^{66} -426.225i q^{67} -239.750i q^{68} +348.774 q^{69} -1034.51 q^{71} -163.564i q^{72} +471.741i q^{73} -509.422 q^{74} +336.984 q^{76} +14.6867i q^{77} -780.091i q^{78} -1201.92 q^{79} +81.0000 q^{81} -1220.57i q^{82} -1325.72i q^{83} +49.3771 q^{84} -768.880 q^{86} +543.582i q^{87} -38.1306i q^{88} +886.226 q^{89} -565.751 q^{91} -273.356i q^{92} -910.841i q^{93} -405.245 q^{94} -309.754 q^{96} -134.908i q^{97} -157.650i q^{98} +18.8829 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 32 q^{4} + 36 q^{6} - 72 q^{9}+O(q^{10}) \) 8 * q - 32 * q^4 + 36 * q^6 - 72 * q^9	\( 8 q - 32 q^{4} + 36 q^{6} - 72 q^{9} + 114 q^{11} + 84 q^{14} + 432 q^{16} + 24 q^{19} - 168 q^{21} - 558 q^{24} - 162 q^{26} - 756 q^{29} - 186 q^{31} - 1566 q^{34} + 288 q^{36} - 258 q^{39} - 930 q^{41} - 1362 q^{44} + 620 q^{46} - 392 q^{49} + 594 q^{51} - 324 q^{54} - 1302 q^{56} - 462 q^{59} - 2706 q^{61} - 6214 q^{64} - 246 q^{66} - 936 q^{69} - 3450 q^{71} + 3906 q^{74} - 6092 q^{76} - 3258 q^{79} + 648 q^{81} + 672 q^{84} - 9084 q^{86} + 1956 q^{89} - 602 q^{91} - 4960 q^{94} + 4140 q^{96} - 1026 q^{99}+O(q^{100}) \) 8 * q - 32 * q^4 + 36 * q^6 - 72 * q^9 + 114 * q^11 + 84 * q^14 + 432 * q^16 + 24 * q^19 - 168 * q^21 - 558 * q^24 - 162 * q^26 - 756 * q^29 - 186 * q^31 - 1566 * q^34 + 288 * q^36 - 258 * q^39 - 930 * q^41 - 1362 * q^44 + 620 * q^46 - 392 * q^49 + 594 * q^51 - 324 * q^54 - 1302 * q^56 - 462 * q^59 - 2706 * q^61 - 6214 * q^64 - 246 * q^66 - 936 * q^69 - 3450 * q^71 + 3906 * q^74 - 6092 * q^76 - 3258 * q^79 + 648 * q^81 + 672 * q^84 - 9084 * q^86 + 1956 * q^89 - 602 * q^91 - 4960 * q^94 + 4140 * q^96 - 1026 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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