LMFDB - Embedded newform 525.4.d.o.274.6

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			274.6
Root			$3.56826i$ of defining polynomial
Character	$\chi$	$=$	525.274
Dual form			525.4.d.o.274.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+2.56826i q^{2} +3.00000i q^{3} +1.40404 q^{4} -7.70478 q^{6} +7.00000i q^{7} +24.1520i q^{8} -9.00000 q^{9} +O(q^{10})$	\(q+2.56826i q^{2} +3.00000i q^{3} +1.40404 q^{4} -7.70478 q^{6} +7.00000i q^{7} +24.1520i q^{8} -9.00000 q^{9} +66.4181 q^{11} +4.21213i q^{12} +34.0329i q^{13} -17.9778 q^{14} -50.7963 q^{16} +6.12934i q^{17} -23.1143i q^{18} +163.424 q^{19} -21.0000 q^{21} +170.579i q^{22} -35.8799i q^{23} -72.4561 q^{24} -87.4053 q^{26} -27.0000i q^{27} +9.82830i q^{28} -27.7256 q^{29} +74.3417 q^{31} +62.7581i q^{32} +199.254i q^{33} -15.7417 q^{34} -12.6364 q^{36} -260.966i q^{37} +419.716i q^{38} -102.099 q^{39} -445.485 q^{41} -53.9334i q^{42} +474.985i q^{43} +93.2538 q^{44} +92.1489 q^{46} -51.0436i q^{47} -152.389i q^{48} -49.0000 q^{49} -18.3880 q^{51} +47.7837i q^{52} +676.667i q^{53} +69.3430 q^{54} -169.064 q^{56} +490.273i q^{57} -71.2066i q^{58} +115.979 q^{59} -390.356 q^{61} +190.929i q^{62} -63.0000i q^{63} -567.550 q^{64} -511.737 q^{66} -713.721i q^{67} +8.60586i q^{68} +107.640 q^{69} +810.524 q^{71} -217.368i q^{72} -350.196i q^{73} +670.227 q^{74} +229.455 q^{76} +464.927i q^{77} -262.216i q^{78} +50.9307 q^{79} +81.0000 q^{81} -1144.12i q^{82} +84.8904i q^{83} -29.4849 q^{84} -1219.88 q^{86} -83.1769i q^{87} +1604.13i q^{88} -1521.82 q^{89} -238.230 q^{91} -50.3769i q^{92} +223.025i q^{93} +131.093 q^{94} -188.274 q^{96} -1232.08i q^{97} -125.845i q^{98} -597.763 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	2.56826i	0.908017i	0.890997	+	0.454008i	$0.150006\pi$
$2$	2.56826i	0.908017i	−0.890997	+	0.454008i	$0.849994\pi$
$3$	3.00000i	0.577350i
$3$	3.00000i	0.577350i
$4$	1.40404	0.175505
$5$	0	0
$5$	0	0
$6$	−7.70478	−0.524244
$7$	7.00000i	0.377964i
$7$	7.00000i	0.377964i
$8$	24.1520i	1.06738i
$9$	−9.00000	−0.333333
$10$	0	0
$11$	66.4181	1.82053	0.910264	−	0.414029i	$-0.135879\pi$
$11$	66.4181	1.82053	0.910264	+	0.414029i	$0.135879\pi$
$12$	4.21213i	0.101328i
$13$	34.0329i	0.726079i	0.931774	+	0.363040i	$0.118261\pi$
$13$	34.0329i	0.726079i	−0.931774	+	0.363040i	$0.881739\pi$
$14$	−17.9778	−0.343198
$15$	0	0
$16$	−50.7963	−0.793692
$17$	6.12934i	0.0874461i	0.999044	+	0.0437231i	$0.0139219\pi$
$17$	6.12934i	0.0874461i	−0.999044	+	0.0437231i	$0.986078\pi$
$18$	− 23.1143i	− 0.302672i
$19$	163.424	1.97327	0.986634	−	0.162951i	$-0.0521013\pi$
$19$	163.424	1.97327	0.986634	+	0.162951i	$0.0521013\pi$
$20$	0	0
$21$	−21.0000	−0.218218
$22$	170.579i	1.65307i
$23$	− 35.8799i	− 0.325282i	−0.986685	−	0.162641i	$-0.947999\pi$
$23$	− 35.8799i	− 0.325282i	0.986685	−	0.162641i	$-0.0520012\pi$
$24$	−72.4561	−0.616251
$25$	0	0
$26$	−87.4053	−0.659292
$27$	− 27.0000i	− 0.192450i
$28$	9.82830i	0.0663348i
$29$	−27.7256	−0.177535	−0.0887676	−	0.996052i	$-0.528293\pi$
$29$	−27.7256	−0.177535	−0.0887676	+	0.996052i	$0.528293\pi$
$30$	0	0
$31$	74.3417	0.430715	0.215358	−	0.976535i	$-0.430908\pi$
$31$	74.3417	0.430715	0.215358	+	0.976535i	$0.430908\pi$
$32$	62.7581i	0.346693i
$33$	199.254i	1.05108i
$34$	−15.7417	−0.0794026
$35$	0	0
$36$	−12.6364	−0.0585018
$37$	− 260.966i	− 1.15953i	−0.814785	−	0.579763i	$-0.803145\pi$
$37$	− 260.966i	− 1.15953i	0.814785	−	0.579763i	$-0.196855\pi$
$38$	419.716i	1.79176i
$39$	−102.099	−0.419202
$40$	0	0
$41$	−445.485	−1.69690	−0.848452	−	0.529272i	$-0.822465\pi$
$41$	−445.485	−1.69690	−0.848452	+	0.529272i	$0.822465\pi$
$42$	− 53.9334i	− 0.198146i
$43$	474.985i	1.68452i	0.539070	+	0.842261i	$0.318776\pi$
$43$	474.985i	1.68452i	−0.539070	+	0.842261i	$0.681224\pi$
$44$	93.2538	0.319512
$45$	0	0
$46$	92.1489	0.295361
$47$	− 51.0436i	− 0.158414i	−0.996858	−	0.0792072i	$-0.974761\pi$
$47$	− 51.0436i	− 0.158414i	0.996858	−	0.0792072i	$-0.0252389\pi$
$48$	− 152.389i	− 0.458239i
$49$	−49.0000	−0.142857
$50$	0	0
$51$	−18.3880	−0.0504871
$52$	47.7837i	0.127431i
$53$	676.667i	1.75372i	0.480742	+	0.876862i	$0.340367\pi$
$53$	676.667i	1.75372i	−0.480742	+	0.876862i	$0.659633\pi$
$54$	69.3430	0.174748
$55$	0	0
$56$	−169.064	−0.403431
$57$	490.273i	1.13927i
$58$	− 71.2066i	− 0.161205i
$59$	115.979	0.255917	0.127959	−	0.991779i	$-0.459158\pi$
$59$	115.979	0.255917	0.127959	+	0.991779i	$0.459158\pi$
$60$	0	0
$61$	−390.356	−0.819344	−0.409672	−	0.912233i	$-0.634357\pi$
$61$	−390.356	−0.819344	−0.409672	+	0.912233i	$0.634357\pi$
$62$	190.929i	0.391097i
$63$	− 63.0000i	− 0.125988i
$64$	−567.550	−1.10850
$65$	0	0
$66$	−511.737	−0.954400
$67$	− 713.721i	− 1.30142i	−0.759328	−	0.650708i	$-0.774472\pi$
$67$	− 713.721i	− 1.30142i	0.759328	−	0.650708i	$-0.225528\pi$
$68$	8.60586i	0.0153473i
$69$	107.640	0.187801
$70$	0	0
$71$	810.524	1.35481	0.677405	−	0.735610i	$-0.263104\pi$
$71$	810.524	1.35481	0.677405	+	0.735610i	$0.263104\pi$
$72$	− 217.368i	− 0.355793i
$73$	− 350.196i	− 0.561470i	−0.959785	−	0.280735i	$-0.909422\pi$
$73$	− 350.196i	− 0.561470i	0.959785	−	0.280735i	$-0.0905782\pi$
$74$	670.227	1.05287
$75$	0	0
$76$	229.455	0.346319
$77$	464.927i	0.688095i
$78$	− 262.216i	− 0.380642i
$79$	50.9307	0.0725336	0.0362668	−	0.999342i	$-0.488453\pi$
$79$	50.9307	0.0725336	0.0362668	+	0.999342i	$0.488453\pi$
$80$	0	0
$81$	81.0000	0.111111
$82$	− 1144.12i	− 1.54082i
$83$	84.8904i	0.112264i	0.998423	+	0.0561321i	$0.0178768\pi$
$83$	84.8904i	0.112264i	−0.998423	+	0.0561321i	$0.982123\pi$
$84$	−29.4849	−0.0382984
$85$	0	0
$86$	−1219.88	−1.52957
$87$	− 83.1769i	− 0.102500i
$88$	1604.13i	1.94319i
$89$	−1521.82	−1.81251	−0.906253	−	0.422735i	$-0.861070\pi$
$89$	−1521.82	−1.81251	−0.906253	+	0.422735i	$0.861070\pi$
$90$	0	0
$91$	−238.230	−0.274432
$92$	− 50.3769i	− 0.0570887i
$93$	223.025i	0.248674i
$94$	131.093	0.143843
$95$	0	0
$96$	−188.274	−0.200163
$97$	− 1232.08i	− 1.28968i	−0.764317	−	0.644840i	$-0.776924\pi$
$97$	− 1232.08i	− 1.28968i	0.764317	−	0.644840i	$-0.223076\pi$
$98$	− 125.845i	− 0.129717i
$99$	−597.763	−0.606843
$100$	0	0
$101$	−1661.64	−1.63702	−0.818510	−	0.574492i	$-0.805200\pi$
$101$	−1661.64	−1.63702	−0.818510	+	0.574492i	$0.805200\pi$
$102$	− 47.2252i	− 0.0458431i
$103$	193.631i	0.185233i	0.995702	+	0.0926167i	$0.0295231\pi$
$103$	193.631i	0.185233i	−0.995702	+	0.0926167i	$0.970477\pi$
$104$	−821.963	−0.775001
$105$	0	0
$106$	−1737.86	−1.59241
$107$	921.040i	0.832153i	0.909330	+	0.416076i	$0.136595\pi$
$107$	921.040i	0.832153i	−0.909330	+	0.416076i	$0.863405\pi$
$108$	− 37.9092i	− 0.0337760i
$109$	−1304.73	−1.14652	−0.573260	−	0.819373i	$-0.694322\pi$
$109$	−1304.73	−1.14652	−0.573260	+	0.819373i	$0.694322\pi$
$110$	0	0
$111$	782.897	0.669453
$112$	− 355.574i	− 0.299988i
$113$	− 237.585i	− 0.197789i	−0.995098	−	0.0988945i	$-0.968469\pi$
$113$	− 237.585i	− 0.197789i	0.995098	−	0.0988945i	$-0.0315306\pi$
$114$	−1259.15	−1.03447
$115$	0	0
$116$	−38.9280	−0.0311584
$117$	− 306.296i	− 0.242026i
$118$	297.863i	0.232377i
$119$	−42.9054	−0.0330515
$120$	0	0
$121$	3080.36	2.31432
$122$	− 1002.54i	− 0.743978i
$123$	− 1336.45i	− 0.979708i
$124$	104.379	0.0755928
$125$	0	0
$126$	161.800	0.114399
$127$	− 1442.31i	− 1.00775i	−0.863776	−	0.503876i	$-0.831907\pi$
$127$	− 1442.31i	− 1.00775i	0.863776	−	0.503876i	$-0.168093\pi$
$128$	− 955.550i	− 0.659840i
$129$	−1424.95	−0.972559
$130$	0	0
$131$	644.035	0.429539	0.214770	−	0.976665i	$-0.431100\pi$
$131$	644.035	0.429539	0.214770	+	0.976665i	$0.431100\pi$
$132$	279.762i	0.184471i
$133$	1143.97i	0.745825i
$134$	1833.02	1.18171
$135$	0	0
$136$	−148.036	−0.0933381
$137$	− 355.576i	− 0.221744i	−0.993835	−	0.110872i	$-0.964636\pi$
$137$	− 355.576i	− 0.221744i	0.993835	−	0.110872i	$-0.0353644\pi$
$138$	276.447i	0.170527i
$139$	472.016	0.288028	0.144014	−	0.989576i	$-0.453999\pi$
$139$	472.016	0.288028	0.144014	+	0.989576i	$0.453999\pi$
$140$	0	0
$141$	153.131	0.0914606
$142$	2081.64i	1.23019i
$143$	2260.40i	1.32185i
$144$	457.167	0.264564
$145$	0	0
$146$	899.393	0.509824
$147$	− 147.000i	− 0.0824786i
$148$	− 366.407i	− 0.203503i
$149$	1091.53	0.600143	0.300072	−	0.953917i	$-0.402989\pi$
$149$	1091.53	0.600143	0.300072	+	0.953917i	$0.402989\pi$
$150$	0	0
$151$	2914.48	1.57071	0.785354	−	0.619047i	$-0.212481\pi$
$151$	2914.48	1.57071	0.785354	+	0.619047i	$0.212481\pi$
$152$	3947.03i	2.10622i
$153$	− 55.1641i	− 0.0291487i
$154$	−1194.05	−0.624802
$155$	0	0
$156$	−143.351	−0.0735722
$157$	− 1476.94i	− 0.750780i	−0.926867	−	0.375390i	$-0.877509\pi$
$157$	− 1476.94i	− 0.750780i	0.926867	−	0.375390i	$-0.122491\pi$
$158$	130.803i	0.0658617i
$159$	−2030.00	−1.01251
$160$	0	0
$161$	251.159	0.122945
$162$	208.029i	0.100891i
$163$	− 2764.56i	− 1.32845i	−0.747534	−	0.664224i	$-0.768762\pi$
$163$	− 2764.56i	− 1.32845i	0.747534	−	0.664224i	$-0.231238\pi$
$164$	−625.480	−0.297816
$165$	0	0
$166$	−218.020	−0.101938
$167$	− 255.508i	− 0.118394i	−0.998246	−	0.0591970i	$-0.981146\pi$
$167$	− 255.508i	− 0.118394i	0.998246	−	0.0591970i	$-0.0188540\pi$
$168$	− 507.192i	− 0.232921i
$169$	1038.76	0.472809
$170$	0	0
$171$	−1470.82	−0.657756
$172$	666.899i	0.295643i
$173$	3850.56i	1.69221i	0.533016	+	0.846105i	$0.321059\pi$
$173$	3850.56i	1.69221i	−0.533016	+	0.846105i	$0.678941\pi$
$174$	213.620	0.0930717
$175$	0	0
$176$	−3373.79	−1.44494
$177$	347.936i	0.147754i
$178$	− 3908.44i	− 1.64579i
$179$	−952.804	−0.397854	−0.198927	−	0.980014i	$-0.563746\pi$
$179$	−952.804	−0.397854	−0.198927	+	0.980014i	$0.563746\pi$
$180$	0	0
$181$	1648.83	0.677109	0.338554	−	0.940947i	$-0.390062\pi$
$181$	1648.83	0.677109	0.338554	+	0.940947i	$0.390062\pi$
$182$	− 611.837i	− 0.249189i
$183$	− 1171.07i	− 0.473048i
$184$	866.572	0.347199
$185$	0	0
$186$	−572.787	−0.225800
$187$	407.099i	0.159198i
$188$	− 71.6675i	− 0.0278026i
$189$	189.000	0.0727393
$190$	0	0
$191$	767.536	0.290769	0.145385	−	0.989375i	$-0.453558\pi$
$191$	767.536	0.290769	0.145385	+	0.989375i	$0.453558\pi$
$192$	− 1702.65i	− 0.639990i
$193$	1186.61i	0.442561i	0.975210	+	0.221280i	$0.0710236\pi$
$193$	1186.61i	0.442561i	−0.975210	+	0.221280i	$0.928976\pi$
$194$	3164.31	1.17105
$195$	0	0
$196$	−68.7981	−0.0250722
$197$	3614.72i	1.30730i	0.756797	+	0.653650i	$0.226763\pi$
$197$	3614.72i	1.30730i	−0.756797	+	0.653650i	$0.773237\pi$
$198$	− 1535.21i	− 0.551023i
$199$	3077.54	1.09629	0.548144	−	0.836384i	$-0.315335\pi$
$199$	3077.54	1.09629	0.548144	+	0.836384i	$0.315335\pi$
$200$	0	0
$201$	2141.16	0.751373
$202$	− 4267.52i	− 1.48644i
$203$	− 194.079i	− 0.0671020i
$204$	−25.8176	−0.00886075
$205$	0	0
$206$	−497.295	−0.168195
$207$	322.919i	0.108427i
$208$	− 1728.75i	− 0.576284i
$209$	10854.3	3.59239
$210$	0	0
$211$	145.901	0.0476031	0.0238016	−	0.999717i	$-0.492423\pi$
$211$	145.901	0.0476031	0.0238016	+	0.999717i	$0.492423\pi$
$212$	950.070i	0.307788i
$213$	2431.57i	0.782200i
$214$	−2365.47	−0.755609
$215$	0	0
$216$	652.105	0.205417
$217$	520.392i	0.162795i
$218$	− 3350.89i	− 1.04106i
$219$	1050.59	0.324165
$220$	0	0
$221$	−208.599	−0.0634928
$222$	2010.68i	0.607875i
$223$	− 3357.30i	− 1.00817i	−0.863655	−	0.504084i	$-0.831830\pi$
$223$	− 3357.30i	− 1.00817i	0.863655	−	0.504084i	$-0.168170\pi$
$224$	−439.306	−0.131037
$225$	0	0
$226$	610.181	0.179596
$227$	− 636.529i	− 0.186114i	−0.995661	−	0.0930570i	$-0.970336\pi$
$227$	− 636.529i	− 0.186114i	0.995661	−	0.0930570i	$-0.0296639\pi$
$228$	688.364i	0.199948i
$229$	−3652.17	−1.05389	−0.526947	−	0.849898i	$-0.676663\pi$
$229$	−3652.17	−1.05389	−0.526947	+	0.849898i	$0.676663\pi$
$230$	0	0
$231$	−1394.78	−0.397272
$232$	− 669.630i	− 0.189497i
$233$	− 3387.30i	− 0.952400i	−0.879337	−	0.476200i	$-0.842014\pi$
$233$	− 3387.30i	− 0.952400i	0.879337	−	0.476200i	$-0.157986\pi$
$234$	786.648	0.219764
$235$	0	0
$236$	162.839	0.0449149
$237$	152.792i	0.0418773i
$238$	− 110.192i	− 0.0300113i
$239$	3382.64	0.915502	0.457751	−	0.889080i	$-0.348655\pi$
$239$	3382.64	0.915502	0.457751	+	0.889080i	$0.348655\pi$
$240$	0	0
$241$	5809.63	1.55283	0.776413	−	0.630225i	$-0.217037\pi$
$241$	5809.63	1.55283	0.776413	+	0.630225i	$0.217037\pi$
$242$	7911.17i	2.10144i
$243$	243.000i	0.0641500i
$244$	−548.077	−0.143799
$245$	0	0
$246$	3432.36	0.889591
$247$	5561.80i	1.43275i
$248$	1795.50i	0.459736i
$249$	−254.671	−0.0648158
$250$	0	0
$251$	−345.006	−0.0867593	−0.0433796	−	0.999059i	$-0.513813\pi$
$251$	−345.006	−0.0867593	−0.0433796	+	0.999059i	$0.513813\pi$
$252$	− 88.4547i	− 0.0221116i
$253$	− 2383.07i	− 0.592184i
$254$	3704.23	0.915056
$255$	0	0
$256$	−2086.30	−0.509350
$257$	− 3142.39i	− 0.762712i	−0.924428	−	0.381356i	$-0.875457\pi$
$257$	− 3142.39i	− 0.762712i	0.924428	−	0.381356i	$-0.124543\pi$
$258$	− 3659.65i	− 0.883100i
$259$	1826.76	0.438260
$260$	0	0
$261$	249.531	0.0591784
$262$	1654.05i	0.390029i
$263$	4949.02i	1.16034i	0.814495	+	0.580170i	$0.197014\pi$
$263$	4949.02i	1.16034i	−0.814495	+	0.580170i	$0.802986\pi$
$264$	−4812.39	−1.12190
$265$	0	0
$266$	−2938.01	−0.677222
$267$	− 4565.47i	− 1.04645i
$268$	− 1002.10i	− 0.228406i
$269$	4570.60	1.03596	0.517982	−	0.855391i	$-0.326683\pi$
$269$	4570.60	1.03596	0.517982	+	0.855391i	$0.326683\pi$
$270$	0	0
$271$	−5338.43	−1.19663	−0.598315	−	0.801261i	$-0.704163\pi$
$271$	−5338.43	−1.19663	−0.598315	+	0.801261i	$0.704163\pi$
$272$	− 311.348i	− 0.0694053i
$273$	− 714.691i	− 0.158443i
$274$	913.213	0.201347
$275$	0	0
$276$	151.131	0.0329602
$277$	2225.98i	0.482837i	0.970421	+	0.241419i	$0.0776127\pi$
$277$	2225.98i	0.482837i	−0.970421	+	0.241419i	$0.922387\pi$
$278$	1212.26i	0.261534i
$279$	−669.076	−0.143572
$280$	0	0
$281$	1991.15	0.422712	0.211356	−	0.977409i	$-0.432212\pi$
$281$	1991.15	0.422712	0.211356	+	0.977409i	$0.432212\pi$
$282$	393.280i	0.0830478i
$283$	7350.20i	1.54390i	0.635682	+	0.771951i	$0.280719\pi$
$283$	7350.20i	1.54390i	−0.635682	+	0.771951i	$0.719281\pi$
$284$	1138.01	0.237777
$285$	0	0
$286$	−5805.29	−1.20026
$287$	− 3118.39i	− 0.641369i
$288$	− 564.823i	− 0.115564i
$289$	4875.43	0.992353
$290$	0	0
$291$	3696.25	0.744597
$292$	− 491.690i	− 0.0985410i
$293$	− 6250.16i	− 1.24621i	−0.782140	−	0.623103i	$-0.785872\pi$
$293$	− 6250.16i	− 1.24621i	0.782140	−	0.623103i	$-0.214128\pi$
$294$	377.534	0.0748920
$295$	0	0
$296$	6302.85	1.23765
$297$	− 1793.29i	− 0.350361i
$298$	2803.32i	0.544940i
$299$	1221.10	0.236180
$300$	0	0
$301$	−3324.89	−0.636690
$302$	7485.13i	1.42623i
$303$	− 4984.91i	− 0.945134i
$304$	−8301.35	−1.56617
$305$	0	0
$306$	141.676	0.0264675
$307$	− 1259.29i	− 0.234109i	−0.993126	−	0.117054i	$-0.962655\pi$
$307$	− 1259.29i	− 0.234109i	0.993126	−	0.117054i	$-0.0373452\pi$
$308$	652.777i	0.120764i
$309$	−580.893	−0.106945
$310$	0	0
$311$	−6711.92	−1.22379	−0.611894	−	0.790940i	$-0.709592\pi$
$311$	−6711.92	−1.22379	−0.611894	+	0.790940i	$0.709592\pi$
$312$	− 2465.89i	− 0.447447i
$313$	− 2436.27i	− 0.439955i	−0.975505	−	0.219978i	$-0.929402\pi$
$313$	− 2436.27i	− 0.439955i	0.975505	−	0.219978i	$-0.0705984\pi$
$314$	3793.16	0.681721
$315$	0	0
$316$	71.5089	0.0127300
$317$	1191.81i	0.211164i	0.994411	+	0.105582i	$0.0336705\pi$
$317$	1191.81i	0.211164i	−0.994411	+	0.105582i	$0.966330\pi$
$318$	− 5213.57i	− 0.919379i
$319$	−1841.48	−0.323208
$320$	0	0
$321$	−2763.12	−0.480443
$322$	645.042i	0.111636i
$323$	1001.68i	0.172555i
$324$	113.727	0.0195006
$325$	0	0
$326$	7100.11	1.20625
$327$	− 3914.20i	− 0.661944i
$328$	− 10759.4i	− 1.81124i
$329$	357.305	0.0598750
$330$	0	0
$331$	5885.63	0.977351	0.488676	−	0.872466i	$-0.337480\pi$
$331$	5885.63	0.977351	0.488676	+	0.872466i	$0.337480\pi$
$332$	119.190i	0.0197030i
$333$	2348.69i	0.386509i
$334$	656.210	0.107504
$335$	0	0
$336$	1066.72	0.173198
$337$	1209.73i	0.195544i	0.995209	+	0.0977720i	$0.0311716\pi$
$337$	1209.73i	0.195544i	−0.995209	+	0.0977720i	$0.968828\pi$
$338$	2667.81i	0.429319i
$339$	712.756	0.114193
$340$	0	0
$341$	4937.63	0.784129
$342$	− 3777.44i	− 0.597254i
$343$	− 343.000i	− 0.0539949i
$344$	−11471.8	−1.79802
$345$	0	0
$346$	−9889.23	−1.53656
$347$	− 5065.21i	− 0.783617i	−0.920047	−	0.391808i	$-0.871850\pi$
$347$	− 5065.21i	− 0.783617i	0.920047	−	0.391808i	$-0.128150\pi$
$348$	− 116.784i	− 0.0179893i
$349$	−5481.35	−0.840716	−0.420358	−	0.907358i	$-0.638096\pi$
$349$	−5481.35	−0.840716	−0.420358	+	0.907358i	$0.638096\pi$
$350$	0	0
$351$	918.888	0.139734
$352$	4168.27i	0.631163i
$353$	602.190i	0.0907970i	0.998969	+	0.0453985i	$0.0144558\pi$
$353$	602.190i	0.0907970i	−0.998969	+	0.0453985i	$0.985544\pi$
$354$	−893.589	−0.134163
$355$	0	0
$356$	−2136.71	−0.318105
$357$	− 128.716i	− 0.0190823i
$358$	− 2447.05i	− 0.361259i
$359$	−2004.84	−0.294740	−0.147370	−	0.989081i	$-0.547081\pi$
$359$	−2004.84	−0.294740	−0.147370	+	0.989081i	$0.547081\pi$
$360$	0	0
$361$	19848.5	2.89379
$362$	4234.63i	0.614826i
$363$	9241.08i	1.33617i
$364$	−334.486	−0.0481643
$365$	0	0
$366$	3007.61	0.429536
$367$	− 7770.37i	− 1.10520i	−0.833445	−	0.552602i	$-0.813635\pi$
$367$	− 7770.37i	− 1.10520i	0.833445	−	0.552602i	$-0.186365\pi$
$368$	1822.57i	0.258174i
$369$	4009.36	0.565635
$370$	0	0
$371$	−4736.67	−0.662846
$372$	313.137i	0.0436435i
$373$	− 7485.06i	− 1.03904i	−0.854458	−	0.519520i	$-0.826111\pi$
$373$	− 7485.06i	− 1.03904i	0.854458	−	0.519520i	$-0.173889\pi$
$374$	−1045.54	−0.144555
$375$	0	0
$376$	1232.81	0.169088
$377$	− 943.583i	− 0.128905i
$378$	485.401i	0.0660485i
$379$	4053.61	0.549393	0.274697	−	0.961531i	$-0.411423\pi$
$379$	4053.61	0.549393	0.274697	+	0.961531i	$0.411423\pi$
$380$	0	0
$381$	4326.94	0.581826
$382$	1971.23i	0.264023i
$383$	4531.33i	0.604543i	0.953222	+	0.302272i	$0.0977450\pi$
$383$	4531.33i	0.604543i	−0.953222	+	0.302272i	$0.902255\pi$
$384$	2866.65	0.380959
$385$	0	0
$386$	−3047.53	−0.401853
$387$	− 4274.86i	− 0.561507i
$388$	− 1729.90i	− 0.226346i
$389$	1160.19	0.151219	0.0756093	−	0.997138i	$-0.475910\pi$
$389$	1160.19	0.151219	0.0756093	+	0.997138i	$0.475910\pi$
$390$	0	0
$391$	219.920	0.0284446
$392$	− 1183.45i	− 0.152483i
$393$	1932.11i	0.247995i
$394$	−9283.53	−1.18705
$395$	0	0
$396$	−839.285	−0.106504
$397$	6720.74i	0.849632i	0.905280	+	0.424816i	$0.139661\pi$
$397$	6720.74i	0.849632i	−0.905280	+	0.424816i	$0.860339\pi$
$398$	7903.93i	0.995448i
$399$	−3431.91	−0.430602
$400$	0	0
$401$	2769.06	0.344839	0.172419	−	0.985024i	$-0.444842\pi$
$401$	2769.06	0.344839	0.172419	+	0.985024i	$0.444842\pi$
$402$	5499.06i	0.682260i
$403$	2530.07i	0.312733i
$404$	−2333.01	−0.287306
$405$	0	0
$406$	498.446	0.0609297
$407$	− 17332.8i	− 2.11095i
$408$	− 444.108i	− 0.0538888i
$409$	−14438.9	−1.74561	−0.872806	−	0.488067i	$-0.837702\pi$
$409$	−14438.9	−1.74561	−0.872806	+	0.488067i	$0.837702\pi$
$410$	0	0
$411$	1066.73	0.128024
$412$	271.866i	0.0325095i
$413$	811.850i	0.0967277i
$414$	−829.340	−0.0984537
$415$	0	0
$416$	−2135.84	−0.251726
$417$	1416.05i	0.166293i
$418$	27876.7i	3.26195i
$419$	−6396.35	−0.745780	−0.372890	−	0.927875i	$-0.621633\pi$
$419$	−6396.35	−0.745780	−0.372890	+	0.927875i	$0.621633\pi$
$420$	0	0
$421$	−8231.07	−0.952868	−0.476434	−	0.879210i	$-0.658071\pi$
$421$	−8231.07	−0.952868	−0.476434	+	0.879210i	$0.658071\pi$
$422$	374.712i	0.0432244i
$423$	459.393i	0.0528048i
$424$	−16342.9	−1.87189
$425$	0	0
$426$	−6244.91	−0.710251
$427$	− 2732.49i	− 0.309683i
$428$	1293.18i	0.146047i
$429$	−6781.20	−0.763169
$430$	0	0
$431$	−5975.72	−0.667843	−0.333922	−	0.942601i	$-0.608372\pi$
$431$	−5975.72	−0.667843	−0.333922	+	0.942601i	$0.608372\pi$
$432$	1371.50i	0.152746i
$433$	− 10912.9i	− 1.21118i	−0.795776	−	0.605591i	$-0.792937\pi$
$433$	− 10912.9i	− 1.21118i	0.795776	−	0.605591i	$-0.207063\pi$
$434$	−1336.50	−0.147821
$435$	0	0
$436$	−1831.90	−0.201221
$437$	− 5863.65i	− 0.641868i
$438$	2698.18i	0.294347i
$439$	−3784.05	−0.411396	−0.205698	−	0.978616i	$-0.565946\pi$
$439$	−3784.05	−0.411396	−0.205698	+	0.978616i	$0.565946\pi$
$440$	0	0
$441$	441.000	0.0476190
$442$	− 535.737i	− 0.0576526i
$443$	7869.34i	0.843981i	0.906600	+	0.421991i	$0.138669\pi$
$443$	7869.34i	0.843981i	−0.906600	+	0.421991i	$0.861331\pi$
$444$	1099.22	0.117493
$445$	0	0
$446$	8622.42	0.915434
$447$	3274.58i	0.346493i
$448$	− 3972.85i	− 0.418972i
$449$	15601.8	1.63986	0.819929	−	0.572465i	$-0.194013\pi$
$449$	15601.8	1.63986	0.819929	+	0.572465i	$0.194013\pi$
$450$	0	0
$451$	−29588.3	−3.08926
$452$	− 333.580i	− 0.0347130i
$453$	8743.43i	0.906848i
$454$	1634.77	0.168995
$455$	0	0
$456$	−11841.1	−1.21603
$457$	− 8840.78i	− 0.904933i	−0.891781	−	0.452466i	$-0.850544\pi$
$457$	− 8840.78i	− 0.904933i	0.891781	−	0.452466i	$-0.149456\pi$
$458$	− 9379.71i	− 0.956954i
$459$	165.492	0.0168290
$460$	0	0
$461$	−10523.7	−1.06321	−0.531605	−	0.846993i	$-0.678411\pi$
$461$	−10523.7	−1.06321	−0.531605	+	0.846993i	$0.678411\pi$
$462$	− 3582.16i	− 0.360729i
$463$	− 10781.6i	− 1.08221i	−0.840954	−	0.541107i	$-0.818006\pi$
$463$	− 10781.6i	− 1.08221i	0.840954	−	0.541107i	$-0.181994\pi$
$464$	1408.36	0.140908
$465$	0	0
$466$	8699.46	0.864795
$467$	− 5592.55i	− 0.554160i	−0.960847	−	0.277080i	$-0.910633\pi$
$467$	− 5592.55i	− 0.554160i	0.960847	−	0.277080i	$-0.0893666\pi$
$468$	− 430.053i	− 0.0424769i
$469$	4996.05	0.491889
$470$	0	0
$471$	4430.82	0.433463
$472$	2801.12i	0.273161i
$473$	31547.6i	3.06672i
$474$	−392.410	−0.0380253
$475$	0	0
$476$	−60.2410	−0.00580072
$477$	− 6090.01i	− 0.584575i
$478$	8687.51i	0.831292i
$479$	7835.28	0.747397	0.373698	−	0.927550i	$-0.378089\pi$
$479$	7835.28	0.747397	0.373698	+	0.927550i	$0.378089\pi$
$480$	0	0
$481$	8881.42	0.841908
$482$	14920.6i	1.40999i
$483$	753.478i	0.0709823i
$484$	4324.96	0.406176
$485$	0	0
$486$	−624.087	−0.0582493
$487$	5979.24i	0.556356i	0.960530	+	0.278178i	$0.0897305\pi$
$487$	5979.24i	0.556356i	−0.960530	+	0.278178i	$0.910269\pi$
$488$	− 9427.89i	− 0.874550i
$489$	8293.68	0.766980
$490$	0	0
$491$	−1792.66	−0.164769	−0.0823846	−	0.996601i	$-0.526254\pi$
$491$	−1792.66	−0.164769	−0.0823846	+	0.996601i	$0.526254\pi$
$492$	− 1876.44i	− 0.171944i
$493$	− 169.940i	− 0.0155248i
$494$	−14284.2	−1.30096
$495$	0	0
$496$	−3776.29	−0.341855
$497$	5673.67i	0.512070i
$498$	− 654.061i	− 0.0588538i
$499$	20514.4	1.84038	0.920191	−	0.391470i	$-0.128033\pi$
$499$	20514.4	1.84038	0.920191	+	0.391470i	$0.128033\pi$
$500$	0	0
$501$	766.523	0.0683548
$502$	− 886.065i	− 0.0787789i
$503$	− 16294.5i	− 1.44441i	−0.691679	−	0.722205i	$-0.743129\pi$
$503$	− 16294.5i	− 1.44441i	0.691679	−	0.722205i	$-0.256871\pi$
$504$	1521.58	0.134477
$505$	0	0
$506$	6120.35	0.537713
$507$	3116.28i	0.272976i
$508$	− 2025.07i	− 0.176866i
$509$	−12183.8	−1.06097	−0.530487	−	0.847693i	$-0.677991\pi$
$509$	−12183.8	−1.06097	−0.530487	+	0.847693i	$0.677991\pi$
$510$	0	0
$511$	2451.37	0.212216
$512$	− 13002.5i	− 1.12234i
$513$	− 4412.46i	− 0.379756i
$514$	8070.48	0.692555
$515$	0	0
$516$	−2000.70	−0.170689
$517$	− 3390.22i	− 0.288398i
$518$	4691.59i	0.397947i
$519$	−11551.7	−0.976998
$520$	0	0
$521$	−11251.3	−0.946116	−0.473058	−	0.881031i	$-0.656850\pi$
$521$	−11251.3	−0.946116	−0.473058	+	0.881031i	$0.656850\pi$
$522$	640.859i	0.0537350i
$523$	13493.7i	1.12818i	0.825713	+	0.564090i	$0.190773\pi$
$523$	13493.7i	1.12818i	−0.825713	+	0.564090i	$0.809227\pi$
$524$	904.254	0.0753865
$525$	0	0
$526$	−12710.4	−1.05361
$527$	455.666i	0.0376644i
$528$	− 10121.4i	− 0.834236i
$529$	10879.6	0.894192
$530$	0	0
$531$	−1043.81	−0.0853058
$532$	1606.18i	0.130896i
$533$	− 15161.1i	− 1.23209i
$534$	11725.3	0.950195
$535$	0	0
$536$	17237.8	1.38910
$537$	− 2858.41i	− 0.229701i
$538$	11738.5i	0.940673i
$539$	−3254.49	−0.260075
$540$	0	0
$541$	−18810.8	−1.49490	−0.747449	−	0.664319i	$-0.768722\pi$
$541$	−18810.8	−1.49490	−0.747449	+	0.664319i	$0.768722\pi$
$542$	− 13710.5i	− 1.08656i
$543$	4946.49i	0.390929i
$544$	−384.666	−0.0303169
$545$	0	0
$546$	1835.51	0.143869
$547$	9822.68i	0.767801i	0.923374	+	0.383901i	$0.125419\pi$
$547$	9822.68i	0.767801i	−0.923374	+	0.383901i	$0.874581\pi$
$548$	− 499.245i	− 0.0389173i
$549$	3513.20	0.273115
$550$	0	0
$551$	−4531.04	−0.350324
$552$	2599.72i	0.200455i
$553$	356.515i	0.0274151i
$554$	−5716.89	−0.438424
$555$	0	0
$556$	662.731	0.0505504
$557$	23627.9i	1.79739i	0.438571	+	0.898696i	$0.355485\pi$
$557$	23627.9i	1.79739i	−0.438571	+	0.898696i	$0.644515\pi$
$558$	− 1718.36i	− 0.130366i
$559$	−16165.1	−1.22310
$560$	0	0
$561$	−1221.30	−0.0919131
$562$	5113.79i	0.383830i
$563$	966.441i	0.0723457i	0.999346	+	0.0361729i	$0.0115167\pi$
$563$	966.441i	0.0723457i	−0.999346	+	0.0361729i	$0.988483\pi$
$564$	215.002	0.0160518
$565$	0	0
$566$	−18877.2	−1.40189
$567$	567.000i	0.0419961i
$568$	19575.8i	1.44610i
$569$	−16451.2	−1.21208	−0.606038	−	0.795435i	$-0.707242\pi$
$569$	−16451.2	−1.21208	−0.606038	+	0.795435i	$0.707242\pi$
$570$	0	0
$571$	37.8467	0.00277379	0.00138690	−	0.999999i	$-0.499559\pi$
$571$	37.8467	0.00277379	0.00138690	+	0.999999i	$0.499559\pi$
$572$	3173.70i	0.231991i
$573$	2302.61i	0.167876i
$574$	8008.85	0.582374
$575$	0	0
$576$	5107.95	0.369498
$577$	− 23779.1i	− 1.71566i	−0.513933	−	0.857830i	$-0.671812\pi$
$577$	− 23779.1i	− 1.71566i	0.513933	−	0.857830i	$-0.328188\pi$
$578$	12521.4i	0.901073i
$579$	−3559.84	−0.255513
$580$	0	0
$581$	−594.233	−0.0424319
$582$	9492.92i	0.676107i
$583$	44942.9i	3.19270i
$584$	8457.93	0.599301
$585$	0	0
$586$	16052.0	1.13158
$587$	− 12556.0i	− 0.882863i	−0.897295	−	0.441432i	$-0.854471\pi$
$587$	− 12556.0i	− 0.882863i	0.897295	−	0.441432i	$-0.145529\pi$
$588$	− 206.394i	− 0.0144754i
$589$	12149.2	0.849917
$590$	0	0
$591$	−10844.2	−0.754770
$592$	13256.1i	0.920307i
$593$	− 26489.2i	− 1.83437i	−0.398461	−	0.917185i	$-0.630456\pi$
$593$	− 26489.2i	− 1.83437i	0.398461	−	0.917185i	$-0.369544\pi$
$594$	4605.63	0.318133
$595$	0	0
$596$	1532.55	0.105328
$597$	9232.63i	0.632942i
$598$	3136.09i	0.214456i
$599$	−8910.78	−0.607821	−0.303910	−	0.952701i	$-0.598292\pi$
$599$	−8910.78	−0.607821	−0.303910	+	0.952701i	$0.598292\pi$
$600$	0	0
$601$	2943.50	0.199780	0.0998902	−	0.994998i	$-0.468151\pi$
$601$	2943.50	0.199780	0.0998902	+	0.994998i	$0.468151\pi$
$602$	− 8539.18i	− 0.578125i
$603$	6423.49i	0.433806i
$604$	4092.05	0.275668
$605$	0	0
$606$	12802.5	0.858198
$607$	20445.4i	1.36714i	0.729886	+	0.683569i	$0.239573\pi$
$607$	20445.4i	1.36714i	−0.729886	+	0.683569i	$0.760427\pi$
$608$	10256.2i	0.684117i
$609$	582.238	0.0387413
$610$	0	0
$611$	1737.16	0.115021
$612$	− 77.4528i	− 0.00511576i
$613$	− 19174.7i	− 1.26339i	−0.775215	−	0.631697i	$-0.782359\pi$
$613$	− 19174.7i	− 1.26339i	0.775215	−	0.631697i	$-0.217641\pi$
$614$	3234.18	0.212575
$615$	0	0
$616$	−11228.9	−0.734458
$617$	− 21445.6i	− 1.39930i	−0.714486	−	0.699650i	$-0.753339\pi$
$617$	− 21445.6i	− 1.39930i	0.714486	−	0.699650i	$-0.246661\pi$
$618$	− 1491.88i	− 0.0971074i
$619$	17031.2	1.10588	0.552941	−	0.833220i	$-0.313505\pi$
$619$	17031.2	1.10588	0.552941	+	0.833220i	$0.313505\pi$
$620$	0	0
$621$	−968.757	−0.0626005
$622$	− 17237.9i	− 1.11122i
$623$	− 10652.8i	− 0.685063i
$624$	5186.24	0.332717
$625$	0	0
$626$	6256.97	0.399487
$627$	32563.0i	2.07407i
$628$	− 2073.69i	− 0.131766i
$629$	1599.55	0.101396
$630$	0	0
$631$	25190.1	1.58923	0.794614	−	0.607115i	$-0.207673\pi$
$631$	25190.1	1.58923	0.794614	+	0.607115i	$0.207673\pi$
$632$	1230.08i	0.0774208i
$633$	437.704i	0.0274837i
$634$	−3060.88	−0.191740
$635$	0	0
$636$	−2850.21	−0.177702
$637$	− 1667.61i	− 0.103726i
$638$	− 4729.40i	− 0.293478i
$639$	−7294.72	−0.451603
$640$	0	0
$641$	11755.1	0.724335	0.362168	−	0.932113i	$-0.382037\pi$
$641$	11755.1	0.724335	0.362168	+	0.932113i	$0.382037\pi$
$642$	− 7096.41i	− 0.436251i
$643$	− 24044.2i	− 1.47467i	−0.675530	−	0.737333i	$-0.736085\pi$
$643$	− 24044.2i	− 1.47467i	0.675530	−	0.737333i	$-0.263915\pi$
$644$	352.639	0.0215775
$645$	0	0
$646$	−2572.58	−0.156683
$647$	− 5138.50i	− 0.312234i	−0.987739	−	0.156117i	$-0.950102\pi$
$647$	− 5138.50i	− 0.312234i	0.987739	−	0.156117i	$-0.0498976\pi$
$648$	1956.31i	0.118598i
$649$	7703.07	0.465905
$650$	0	0
$651$	−1561.18	−0.0939897
$652$	− 3881.56i	− 0.233150i
$653$	− 6665.57i	− 0.399455i	−0.979851	−	0.199727i	$-0.935994\pi$
$653$	− 6665.57i	− 0.399455i	0.979851	−	0.199727i	$-0.0640057\pi$
$654$	10052.7	0.601056
$655$	0	0
$656$	22629.0	1.34682
$657$	3151.76i	0.187157i
$658$	917.653i	0.0543675i
$659$	−8996.31	−0.531785	−0.265893	−	0.964003i	$-0.585667\pi$
$659$	−8996.31	−0.531785	−0.265893	+	0.964003i	$0.585667\pi$
$660$	0	0
$661$	24565.6	1.44553	0.722763	−	0.691096i	$-0.242872\pi$
$661$	24565.6	1.44553	0.722763	+	0.691096i	$0.242872\pi$
$662$	15115.8i	0.887451i
$663$	− 625.798i	− 0.0366576i
$664$	−2050.27	−0.119828
$665$	0	0
$666$	−6032.05	−0.350957
$667$	994.793i	0.0577489i
$668$	− 358.744i	− 0.0207788i
$669$	10071.9	0.582066
$670$	0	0
$671$	−25926.7	−1.49164
$672$	− 1317.92i	− 0.0756545i
$673$	22046.9i	1.26277i	0.775468	+	0.631387i	$0.217514\pi$
$673$	22046.9i	1.26277i	−0.775468	+	0.631387i	$0.782486\pi$
$674$	−3106.91	−0.177557
$675$	0	0
$676$	1458.47	0.0829805
$677$	25109.8i	1.42548i	0.701430	+	0.712738i	$0.252545\pi$
$677$	25109.8i	1.42548i	−0.701430	+	0.712738i	$0.747455\pi$
$678$	1830.54i	0.103690i
$679$	8624.58	0.487453
$680$	0	0
$681$	1909.59	0.107453
$682$	12681.1i	0.712002i
$683$	− 20540.1i	− 1.15073i	−0.817898	−	0.575363i	$-0.804861\pi$
$683$	− 20540.1i	− 1.15073i	0.817898	−	0.575363i	$-0.195139\pi$
$684$	−2065.09	−0.115440
$685$	0	0
$686$	880.913	0.0490283
$687$	− 10956.5i	− 0.608466i
$688$	− 24127.5i	− 1.33699i
$689$	−23029.0	−1.27334
$690$	0	0
$691$	−1635.59	−0.0900446	−0.0450223	−	0.998986i	$-0.514336\pi$
$691$	−1635.59	−0.0900446	−0.0450223	+	0.998986i	$0.514336\pi$
$692$	5406.35i	0.296992i
$693$	− 4184.34i	− 0.229365i
$694$	13008.8	0.711537
$695$	0	0
$696$	2008.89	0.109406
$697$	− 2730.53i	− 0.148388i
$698$	− 14077.5i	− 0.763385i
$699$	10161.9	0.549868
$700$	0	0
$701$	16895.6	0.910325	0.455163	−	0.890408i	$-0.349581\pi$
$701$	16895.6	0.910325	0.455163	+	0.890408i	$0.349581\pi$
$702$	2359.94i	0.126881i
$703$	− 42648.1i	− 2.28806i
$704$	−37695.5	−2.01805
$705$	0	0
$706$	−1546.58	−0.0824452
$707$	− 11631.5i	− 0.618736i
$708$	488.517i	0.0259316i
$709$	3527.13	0.186833	0.0934163	−	0.995627i	$-0.470221\pi$
$709$	3527.13	0.186833	0.0934163	+	0.995627i	$0.470221\pi$
$710$	0	0
$711$	−458.376	−0.0241779
$712$	− 36755.1i	− 1.93463i
$713$	− 2667.37i	− 0.140104i
$714$	330.577	0.0173271
$715$	0	0
$716$	−1337.78	−0.0698256
$717$	10147.9i	0.528566i
$718$	− 5148.95i	− 0.267628i
$719$	35693.3	1.85137	0.925687	−	0.378291i	$-0.123488\pi$
$719$	35693.3	1.85137	0.925687	+	0.378291i	$0.123488\pi$
$720$	0	0
$721$	−1355.42	−0.0700116
$722$	50976.1i	2.62761i
$723$	17428.9i	0.896524i
$724$	2315.03	0.118836
$725$	0	0
$726$	−23733.5	−1.21327
$727$	− 18829.9i	− 0.960611i	−0.877101	−	0.480305i	$-0.840526\pi$
$727$	− 18829.9i	− 0.960611i	0.877101	−	0.480305i	$-0.159474\pi$
$728$	− 5753.74i	− 0.292923i
$729$	−729.000	−0.0370370
$730$	0	0
$731$	−2911.34	−0.147305
$732$	− 1644.23i	− 0.0830225i
$733$	14895.4i	0.750577i	0.926908	+	0.375288i	$0.122456\pi$
$733$	14895.4i	0.750577i	−0.926908	+	0.375288i	$0.877544\pi$
$734$	19956.3	1.00354
$735$	0	0
$736$	2251.75	0.112773
$737$	− 47404.0i	− 2.36926i
$738$	10297.1i	0.513606i
$739$	−8866.34	−0.441345	−0.220672	−	0.975348i	$-0.570825\pi$
$739$	−8866.34	−0.441345	−0.220672	+	0.975348i	$0.570825\pi$
$740$	0	0
$741$	−16685.4	−0.827198
$742$	− 12165.0i	− 0.601875i
$743$	− 14225.4i	− 0.702394i	−0.936302	−	0.351197i	$-0.885775\pi$
$743$	− 14225.4i	− 0.702394i	0.936302	−	0.351197i	$-0.114225\pi$
$744$	−5386.51	−0.265429
$745$	0	0
$746$	19223.6	0.943465
$747$	− 764.013i	− 0.0374214i
$748$	571.585i	0.0279401i
$749$	−6447.28	−0.314524
$750$	0	0
$751$	34300.2	1.66662	0.833311	−	0.552804i	$-0.186442\pi$
$751$	34300.2	1.66662	0.833311	+	0.552804i	$0.186442\pi$
$752$	2592.83i	0.125732i
$753$	− 1035.02i	− 0.0500905i
$754$	2423.37	0.117047
$755$	0	0
$756$	265.364	0.0127661
$757$	− 2340.98i	− 0.112397i	−0.998420	−	0.0561984i	$-0.982102\pi$
$757$	− 2340.98i	− 0.112397i	0.998420	−	0.0561984i	$-0.0178979\pi$
$758$	10410.7i	0.498858i
$759$	7149.22	0.341898
$760$	0	0
$761$	23894.9	1.13823	0.569113	−	0.822259i	$-0.307287\pi$
$761$	23894.9	1.13823	0.569113	+	0.822259i	$0.307287\pi$
$762$	11112.7i	0.528308i
$763$	− 9133.13i	− 0.433344i
$764$	1077.65	0.0510316
$765$	0	0
$766$	−11637.6	−0.548935
$767$	3947.09i	0.185816i
$768$	− 6258.89i	− 0.294073i
$769$	−22951.1	−1.07625	−0.538126	−	0.842864i	$-0.680868\pi$
$769$	−22951.1	−1.07625	−0.538126	+	0.842864i	$0.680868\pi$
$770$	0	0
$771$	9427.17	0.440352
$772$	1666.05i	0.0776718i
$773$	− 13526.7i	− 0.629393i	−0.949192	−	0.314696i	$-0.898097\pi$
$773$	− 13526.7i	− 0.629393i	0.949192	−	0.314696i	$-0.101903\pi$
$774$	10979.0	0.509858
$775$	0	0
$776$	29757.3	1.37658
$777$	5480.28i	0.253029i
$778$	2979.67i	0.137309i
$779$	−72803.1	−3.34845
$780$	0	0
$781$	53833.5	2.46647
$782$	564.812i	0.0258282i
$783$	748.592i	0.0341666i
$784$	2489.02	0.113385
$785$	0	0
$786$	−4962.15	−0.225183
$787$	− 1611.55i	− 0.0729929i	−0.999334	−	0.0364965i	$-0.988380\pi$
$787$	− 1611.55i	− 0.0729929i	0.999334	−	0.0364965i	$-0.0116198\pi$
$788$	5075.22i	0.229438i
$789$	−14847.1	−0.669923
$790$	0	0
$791$	1663.10	0.0747572
$792$	− 14437.2i	− 0.647731i
$793$	− 13285.0i	− 0.594909i
$794$	−17260.6	−0.771481
$795$	0	0
$796$	4321.00	0.192404
$797$	− 7064.99i	− 0.313996i	−0.987599	−	0.156998i	$-0.949818\pi$
$797$	− 7064.99i	− 0.313996i	0.987599	−	0.156998i	$-0.0501816\pi$
$798$	− 8814.03i	− 0.390994i
$799$	312.864	0.0138527
$800$	0	0
$801$	13696.4	0.604169
$802$	7111.67i	0.313119i
$803$	− 23259.3i	− 1.02217i
$804$	3006.29	0.131870
$805$	0	0
$806$	−6497.86	−0.283967
$807$	13711.8i	0.598114i
$808$	− 40131.9i	− 1.74732i
$809$	6352.68	0.276079	0.138040	−	0.990427i	$-0.455920\pi$
$809$	6352.68	0.276079	0.138040	+	0.990427i	$0.455920\pi$
$810$	0	0
$811$	−16809.3	−0.727810	−0.363905	−	0.931436i	$-0.618557\pi$
$811$	−16809.3	−0.727810	−0.363905	+	0.931436i	$0.618557\pi$
$812$	− 272.496i	− 0.0117768i
$813$	− 16015.3i	− 0.690874i
$814$	44515.2	1.91678
$815$	0	0
$816$	934.044	0.0400712
$817$	77624.0i	3.32401i
$818$	− 37082.7i	− 1.58505i
$819$	2144.07	0.0914774
$820$	0	0
$821$	−41992.9	−1.78510	−0.892548	−	0.450952i	$-0.851084\pi$
$821$	−41992.9	−1.78510	−0.892548	+	0.450952i	$0.851084\pi$
$822$	2739.64i	0.116248i
$823$	37046.2i	1.56908i	0.620080	+	0.784538i	$0.287100\pi$
$823$	37046.2i	1.56908i	−0.620080	+	0.784538i	$0.712900\pi$
$824$	−4676.58	−0.197714
$825$	0	0
$826$	−2085.04	−0.0878304
$827$	− 14371.8i	− 0.604301i	−0.953260	−	0.302151i	$-0.902295\pi$
$827$	− 14371.8i	− 0.604301i	0.953260	−	0.302151i	$-0.0977046\pi$
$828$	453.392i	0.0190296i
$829$	43252.1	1.81207	0.906037	−	0.423199i	$-0.139093\pi$
$829$	43252.1	1.81207	0.906037	+	0.423199i	$0.139093\pi$
$830$	0	0
$831$	−6677.93	−0.278766
$832$	− 19315.4i	− 0.804855i
$833$	− 300.338i	− 0.0124923i
$834$	−3636.78	−0.150997
$835$	0	0
$836$	15239.9	0.630484
$837$	− 2007.23i	− 0.0828912i
$838$	− 16427.5i	− 0.677181i
$839$	6400.97	0.263392	0.131696	−	0.991290i	$-0.457958\pi$
$839$	6400.97	0.263392	0.131696	+	0.991290i	$0.457958\pi$
$840$	0	0
$841$	−23620.3	−0.968481
$842$	− 21139.5i	− 0.865221i
$843$	5973.45i	0.244053i
$844$	204.852	0.00835460
$845$	0	0
$846$	−1179.84	−0.0479477
$847$	21562.5i	0.874731i
$848$	− 34372.2i	− 1.39192i
$849$	−22050.6	−0.891372
$850$	0	0
$851$	−9363.42	−0.377173
$852$	3414.03i	0.137280i
$853$	− 17772.0i	− 0.713368i	−0.934225	−	0.356684i	$-0.883907\pi$
$853$	− 17772.0i	− 0.713368i	0.934225	−	0.356684i	$-0.116093\pi$
$854$	7017.75	0.281197
$855$	0	0
$856$	−22245.0	−0.888222
$857$	29094.3i	1.15968i	0.814731	+	0.579839i	$0.196885\pi$
$857$	29094.3i	1.15968i	−0.814731	+	0.579839i	$0.803115\pi$
$858$	− 17415.9i	− 0.692970i
$859$	599.045	0.0237941	0.0118971	−	0.999929i	$-0.496213\pi$
$859$	599.045	0.0237941	0.0118971	+	0.999929i	$0.496213\pi$
$860$	0	0
$861$	9355.18	0.370295
$862$	− 15347.2i	− 0.606413i
$863$	19253.4i	0.759435i	0.925103	+	0.379717i	$0.123979\pi$
$863$	19253.4i	0.759435i	−0.925103	+	0.379717i	$0.876021\pi$
$864$	1694.47	0.0667210
$865$	0	0
$866$	28027.2	1.09977
$867$	14626.3i	0.572935i
$868$	730.653i	0.0285714i
$869$	3382.72	0.132049
$870$	0	0
$871$	24290.0	0.944931
$872$	− 31511.9i	− 1.22377i
$873$	11088.7i	0.429893i
$874$	15059.4	0.582827
$875$	0	0
$876$	1475.07	0.0568927
$877$	42907.7i	1.65210i	0.563598	+	0.826049i	$0.309417\pi$
$877$	42907.7i	1.65210i	−0.563598	+	0.826049i	$0.690583\pi$
$878$	− 9718.41i	− 0.373554i
$879$	18750.5	0.719498
$880$	0	0
$881$	−5765.54	−0.220484	−0.110242	−	0.993905i	$-0.535163\pi$
$881$	−5765.54	−0.220484	−0.110242	+	0.993905i	$0.535163\pi$
$882$	1132.60i	0.0432389i
$883$	35426.8i	1.35018i	0.737736	+	0.675089i	$0.235895\pi$
$883$	35426.8i	1.35018i	−0.737736	+	0.675089i	$0.764105\pi$
$884$	−292.883	−0.0111433
$885$	0	0
$886$	−20210.5	−0.766349
$887$	− 24413.1i	− 0.924138i	−0.886844	−	0.462069i	$-0.847107\pi$
$887$	− 24413.1i	− 0.924138i	0.886844	−	0.462069i	$-0.152893\pi$
$888$	18908.5i	0.714560i
$889$	10096.2	0.380895
$890$	0	0
$891$	5379.86	0.202281
$892$	− 4713.80i	− 0.176939i
$893$	− 8341.77i	− 0.312594i
$894$	−8409.97	−0.314621
$895$	0	0
$896$	6688.85	0.249396
$897$	3663.29i	0.136359i
$898$	40069.6i	1.48902i
$899$	−2061.17	−0.0764671
$900$	0	0
$901$	−4147.53	−0.153356
$902$	− 75990.3i	− 2.80510i
$903$	− 9974.67i	− 0.367593i
$904$	5738.17	0.211116
$905$	0	0
$906$	−22455.4	−0.823434
$907$	− 23459.2i	− 0.858818i	−0.903110	−	0.429409i	$-0.858722\pi$
$907$	− 23459.2i	− 0.858818i	0.903110	−	0.429409i	$-0.141278\pi$
$908$	− 893.714i	− 0.0326640i
$909$	14954.7	0.545674
$910$	0	0
$911$	−45803.8	−1.66580	−0.832902	−	0.553421i	$-0.813322\pi$
$911$	−45803.8	−1.66580	−0.832902	+	0.553421i	$0.813322\pi$
$912$	− 24904.1i	− 0.904228i
$913$	5638.25i	0.204380i
$914$	22705.4	0.821694
$915$	0	0
$916$	−5127.80	−0.184964
$917$	4508.25i	0.162351i
$918$	425.027i	0.0152810i
$919$	−33360.4	−1.19745	−0.598725	−	0.800955i	$-0.704326\pi$
$919$	−33360.4	−1.19745	−0.598725	+	0.800955i	$0.704326\pi$
$920$	0	0
$921$	3777.86	0.135163
$922$	− 27027.7i	− 0.965412i
$923$	27584.5i	0.983700i
$924$	−1958.33	−0.0697233
$925$	0	0
$926$	27690.0	0.982668
$927$	− 1742.68i	− 0.0617444i
$928$	− 1740.01i	− 0.0615501i
$929$	−11194.3	−0.395341	−0.197670	−	0.980269i	$-0.563338\pi$
$929$	−11194.3	−0.395341	−0.197670	+	0.980269i	$0.563338\pi$
$930$	0	0
$931$	−8007.79	−0.281895
$932$	− 4755.91i	− 0.167151i
$933$	− 20135.8i	− 0.706554i
$934$	14363.1	0.503186
$935$	0	0
$936$	7397.67	0.258334
$937$	4383.20i	0.152821i	0.997076	+	0.0764103i	$0.0243459\pi$
$937$	4383.20i	0.152821i	−0.997076	+	0.0764103i	$0.975654\pi$
$938$	12831.1i	0.446644i
$939$	7308.80	0.254008
$940$	0	0
$941$	−27642.7	−0.957626	−0.478813	−	0.877917i	$-0.658933\pi$
$941$	−27642.7	−0.957626	−0.478813	+	0.877917i	$0.658933\pi$
$942$	11379.5i	0.393592i
$943$	15984.0i	0.551972i
$944$	−5891.29	−0.203120
$945$	0	0
$946$	−81022.3	−2.78463
$947$	25657.8i	0.880428i	0.897893	+	0.440214i	$0.145098\pi$
$947$	25657.8i	0.880428i	−0.897893	+	0.440214i	$0.854902\pi$
$948$	214.527i	0.00734969i
$949$	11918.2	0.407672
$950$	0	0
$951$	−3575.44	−0.121915
$952$	− 1036.25i	− 0.0352785i
$953$	− 48210.6i	− 1.63871i	−0.573285	−	0.819356i	$-0.694331\pi$
$953$	− 48210.6i	− 1.63871i	0.573285	−	0.819356i	$-0.305669\pi$
$954$	15640.7	0.530804
$955$	0	0
$956$	4749.38	0.160676
$957$	− 5524.45i	− 0.186604i
$958$	20123.0i	0.678649i
$959$	2489.04	0.0838114
$960$	0	0
$961$	−24264.3	−0.814484
$962$	22809.8i	0.764467i
$963$	− 8289.36i	− 0.277384i
$964$	8156.97	0.272529
$965$	0	0
$966$	−1935.13	−0.0644531
$967$	− 17711.5i	− 0.589002i	−0.955651	−	0.294501i	$-0.904847\pi$
$967$	− 17711.5i	− 0.589002i	0.955651	−	0.294501i	$-0.0951534\pi$
$968$	74396.9i	2.47026i
$969$	−3005.05	−0.0996245
$970$	0	0
$971$	35777.8	1.18245	0.591227	−	0.806505i	$-0.298644\pi$
$971$	35777.8	1.18245	0.591227	+	0.806505i	$0.298644\pi$
$972$	341.182i	0.0112587i
$973$	3304.11i	0.108864i
$974$	−15356.2	−0.505181
$975$	0	0
$976$	19828.7	0.650307
$977$	30436.2i	0.996662i	0.866987	+	0.498331i	$0.166054\pi$
$977$	30436.2i	0.996662i	−0.866987	+	0.498331i	$0.833946\pi$
$978$	21300.3i	0.696430i
$979$	−101077.	−3.29972
$980$	0	0
$981$	11742.6	0.382174
$982$	− 4604.02i	− 0.149613i
$983$	57841.2i	1.87675i	0.345617	+	0.938376i	$0.387670\pi$
$983$	57841.2i	1.87675i	−0.345617	+	0.938376i	$0.612330\pi$
$984$	32278.1	1.04572
$985$	0	0
$986$	436.450	0.0140967
$987$	1071.92i	0.0345689i
$988$	7809.01i	0.251455i
$989$	17042.4	0.547944
$990$	0	0
$991$	1521.84	0.0487819	0.0243909	−	0.999702i	$-0.492235\pi$
$991$	1521.84	0.0487819	0.0243909	+	0.999702i	$0.492235\pi$
$992$	4665.54i	0.149326i
$993$	17656.9i	0.564274i
$994$	−14571.5	−0.464968
$995$	0	0
$996$	−357.569	−0.0113755
$997$	46899.5i	1.48979i	0.667181	+	0.744896i	$0.267501\pi$
$997$	46899.5i	1.48979i	−0.667181	+	0.744896i	$0.732499\pi$
$998$	52686.3i	1.67110i
$999$	−7046.07	−0.223151

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	525.4.d.o.274.6		8
5.2	odd	4		525.4.a.v.1.1	yes	4
5.3	odd	4		525.4.a.s.1.4	✓	4
5.4	even	2	inner	525.4.d.o.274.3		8
15.2	even	4		1575.4.a.bf.1.4		4
15.8	even	4		1575.4.a.bm.1.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
525.4.a.s.1.4	✓	4	5.3	odd	4
525.4.a.v.1.1	yes	4	5.2	odd	4
525.4.d.o.274.3		8	5.4	even	2	inner
525.4.d.o.274.6		8	1.1	even	1	trivial
1575.4.a.bf.1.4		4	15.2	even	4
1575.4.a.bm.1.1		4	15.8	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)

\(f(q)\)	\(=\)	\(q+2.56826i q^{2} +3.00000i q^{3} +1.40404 q^{4} -7.70478 q^{6} +7.00000i q^{7} +24.1520i q^{8} -9.00000 q^{9} +O(q^{10})\)	\(q+2.56826i q^{2} +3.00000i q^{3} +1.40404 q^{4} -7.70478 q^{6} +7.00000i q^{7} +24.1520i q^{8} -9.00000 q^{9} +66.4181 q^{11} +4.21213i q^{12} +34.0329i q^{13} -17.9778 q^{14} -50.7963 q^{16} +6.12934i q^{17} -23.1143i q^{18} +163.424 q^{19} -21.0000 q^{21} +170.579i q^{22} -35.8799i q^{23} -72.4561 q^{24} -87.4053 q^{26} -27.0000i q^{27} +9.82830i q^{28} -27.7256 q^{29} +74.3417 q^{31} +62.7581i q^{32} +199.254i q^{33} -15.7417 q^{34} -12.6364 q^{36} -260.966i q^{37} +419.716i q^{38} -102.099 q^{39} -445.485 q^{41} -53.9334i q^{42} +474.985i q^{43} +93.2538 q^{44} +92.1489 q^{46} -51.0436i q^{47} -152.389i q^{48} -49.0000 q^{49} -18.3880 q^{51} +47.7837i q^{52} +676.667i q^{53} +69.3430 q^{54} -169.064 q^{56} +490.273i q^{57} -71.2066i q^{58} +115.979 q^{59} -390.356 q^{61} +190.929i q^{62} -63.0000i q^{63} -567.550 q^{64} -511.737 q^{66} -713.721i q^{67} +8.60586i q^{68} +107.640 q^{69} +810.524 q^{71} -217.368i q^{72} -350.196i q^{73} +670.227 q^{74} +229.455 q^{76} +464.927i q^{77} -262.216i q^{78} +50.9307 q^{79} +81.0000 q^{81} -1144.12i q^{82} +84.8904i q^{83} -29.4849 q^{84} -1219.88 q^{86} -83.1769i q^{87} +1604.13i q^{88} -1521.82 q^{89} -238.230 q^{91} -50.3769i q^{92} +223.025i q^{93} +131.093 q^{94} -188.274 q^{96} -1232.08i q^{97} -125.845i q^{98} -597.763 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 32 q^{4} + 36 q^{6} - 72 q^{9}+O(q^{10}) \) 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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