LMFDB - Embedded newform 825.4.c.o.199.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [825,4,Mod(199,825)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(825, 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("825.199");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 825 = 3 \cdot 5^{2} \cdot 11 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	825.c (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:	$48.6765757547$
Analytic rank:	$0$
Dimension:	$6$
Coefficient field:	6.0.9935104.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - 2x^{5} + 2x^{4} + 6x^{3} + 16x^{2} - 8x + 2 $ x^6 - 2x^5 + 2x^4 + 6x^3 + 16x^2 - 8*x + 2
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2^{3} $
Twist minimal:	no (minimal twist has level 165)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			199.1
Root			$-1.13973 - 1.13973i$ of defining polynomial
Character	$\chi$	$=$	825.199
Dual form			825.4.c.o.199.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-3.27945i q^{2} -3.00000i q^{3} -2.75481 q^{4} -9.83836 q^{6} +33.3329i q^{7} -17.2014i q^{8} -9.00000 q^{9} +O(q^{10})$	\(q-3.27945i q^{2} -3.00000i q^{3} -2.75481 q^{4} -9.83836 q^{6} +33.3329i q^{7} -17.2014i q^{8} -9.00000 q^{9} -11.0000 q^{11} +8.26442i q^{12} -24.2862i q^{13} +109.314 q^{14} -78.4495 q^{16} -69.7056i q^{17} +29.5151i q^{18} +125.718 q^{19} +99.9988 q^{21} +36.0740i q^{22} +130.628i q^{23} -51.6041 q^{24} -79.6453 q^{26} +27.0000i q^{27} -91.8258i q^{28} +238.181 q^{29} -133.663 q^{31} +119.661i q^{32} +33.0000i q^{33} -228.596 q^{34} +24.7933 q^{36} -166.505i q^{37} -412.285i q^{38} -72.8585 q^{39} +297.951 q^{41} -327.941i q^{42} -463.307i q^{43} +30.3029 q^{44} +428.387 q^{46} -585.981i q^{47} +235.348i q^{48} -768.085 q^{49} -209.117 q^{51} +66.9037i q^{52} -40.0845i q^{53} +88.5452 q^{54} +573.372 q^{56} -377.153i q^{57} -781.105i q^{58} +312.763 q^{59} -391.339 q^{61} +438.342i q^{62} -299.996i q^{63} -235.175 q^{64} +108.222 q^{66} -858.232i q^{67} +192.026i q^{68} +391.883 q^{69} -583.028 q^{71} +154.812i q^{72} +368.303i q^{73} -546.044 q^{74} -346.328 q^{76} -366.662i q^{77} +238.936i q^{78} +438.935 q^{79} +81.0000 q^{81} -977.117i q^{82} -877.643i q^{83} -275.478 q^{84} -1519.39 q^{86} -714.544i q^{87} +189.215i q^{88} +999.585 q^{89} +809.529 q^{91} -359.854i q^{92} +400.990i q^{93} -1921.70 q^{94} +358.982 q^{96} +1306.31i q^{97} +2518.90i q^{98} +99.0000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q + 10 q^{4} - 6 q^{6} - 54 q^{9}+O(q^{10}) $ 6 * q + 10 * q^4 - 6 * q^6 - 54 * q^9	$ 6 q + 10 q^{4} - 6 q^{6} - 54 q^{9} - 66 q^{11} + 152 q^{14} - 170 q^{16} + 560 q^{19} + 96 q^{21} - 18 q^{24} - 628 q^{26} + 580 q^{29} - 784 q^{31} - 620 q^{34} - 90 q^{36} - 252 q^{39} - 1324 q^{41} - 110 q^{44} + 1456 q^{46} - 1462 q^{49} + 204 q^{51} + 54 q^{54} + 408 q^{56} + 1224 q^{59} - 1164 q^{61} - 694 q^{64} + 66 q^{66} - 672 q^{69} - 3232 q^{71} + 1284 q^{74} + 1760 q^{76} - 248 q^{79} + 486 q^{81} - 1680 q^{84} - 2000 q^{86} - 1676 q^{89} - 3472 q^{91} - 4864 q^{94} + 138 q^{96} + 594 q^{99}+O(q^{100}) $ 6 * q + 10 * q^4 - 6 * q^6 - 54 * q^9 - 66 * q^11 + 152 * q^14 - 170 * q^16 + 560 * q^19 + 96 * q^21 - 18 * q^24 - 628 * q^26 + 580 * q^29 - 784 * q^31 - 620 * q^34 - 90 * q^36 - 252 * q^39 - 1324 * q^41 - 110 * q^44 + 1456 * q^46 - 1462 * q^49 + 204 * q^51 + 54 * q^54 + 408 * q^56 + 1224 * q^59 - 1164 * q^61 - 694 * q^64 + 66 * q^66 - 672 * q^69 - 3232 * q^71 + 1284 * q^74 + 1760 * q^76 - 248 * q^79 + 486 * q^81 - 1680 * q^84 - 2000 * q^86 - 1676 * q^89 - 3472 * q^91 - 4864 * q^94 + 138 * q^96 + 594 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/825\mathbb{Z}\right)^\times$.

$n$	$376$	$551$	$727$
$\chi(n)$	$1$	$1$	$-1$

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 $

$2$	− 3.27945i	− 1.15946i	−0.814808	−	0.579731i	$-0.803158\pi$
$2$	− 3.27945i	− 1.15946i	0.814808	−	0.579731i	$-0.196842\pi$
$3$	− 3.00000i	− 0.577350i
$3$	− 3.00000i	− 0.577350i
$4$	−2.75481	−0.344351
$5$	0	0
$5$	0	0
$6$	−9.83836	−0.669415
$7$	33.3329i	1.79981i	0.436086	+	0.899905i	$0.356364\pi$
$7$	33.3329i	1.79981i	−0.436086	+	0.899905i	$0.643636\pi$
$8$	− 17.2014i	− 0.760200i
$9$	−9.00000	−0.333333
$10$	0	0
$11$	−11.0000	−0.301511
$11$	−11.0000	−0.301511
$12$	8.26442i	0.198811i
$13$	− 24.2862i	− 0.518136i	−0.965859	−	0.259068i	$-0.916585\pi$
$13$	− 24.2862i	− 0.518136i	0.965859	−	0.259068i	$-0.0834154\pi$
$14$	109.314	2.08681
$15$	0	0
$16$	−78.4495	−1.22577
$17$	− 69.7056i	− 0.994476i	−0.867614	−	0.497238i	$-0.834348\pi$
$17$	− 69.7056i	− 0.994476i	0.867614	−	0.497238i	$-0.165652\pi$
$18$	29.5151i	0.386487i
$19$	125.718	1.51798	0.758990	−	0.651102i	$-0.225693\pi$
$19$	125.718	1.51798	0.758990	+	0.651102i	$0.225693\pi$
$20$	0	0
$21$	99.9988	1.03912
$22$	36.0740i	0.349591i
$23$	130.628i	1.18425i	0.805846	+	0.592125i	$0.201711\pi$
$23$	130.628i	1.18425i	−0.805846	+	0.592125i	$0.798289\pi$
$24$	−51.6041	−0.438902
$25$	0	0
$26$	−79.6453	−0.600759
$27$	27.0000i	0.192450i
$28$	− 91.8258i	− 0.619766i
$29$	238.181	1.52514	0.762572	−	0.646903i	$-0.223936\pi$
$29$	238.181	1.52514	0.762572	+	0.646903i	$0.223936\pi$
$30$	0	0
$31$	−133.663	−0.774408	−0.387204	−	0.921994i	$-0.626559\pi$
$31$	−133.663	−0.774408	−0.387204	+	0.921994i	$0.626559\pi$
$32$	119.661i	0.661037i
$33$	33.0000i	0.174078i
$34$	−228.596	−1.15306
$35$	0	0
$36$	24.7933	0.114784
$37$	− 166.505i	− 0.739815i	−0.929068	−	0.369908i	$-0.879389\pi$
$37$	− 166.505i	− 0.739815i	0.929068	−	0.369908i	$-0.120611\pi$
$38$	− 412.285i	− 1.76004i
$39$	−72.8585	−0.299146
$40$	0	0
$41$	297.951	1.13493	0.567466	−	0.823397i	$-0.307924\pi$
$41$	297.951	1.13493	0.567466	+	0.823397i	$0.307924\pi$
$42$	− 327.941i	− 1.20482i
$43$	− 463.307i	− 1.64311i	−0.570132	−	0.821553i	$-0.693108\pi$
$43$	− 463.307i	− 1.64311i	0.570132	−	0.821553i	$-0.306892\pi$
$44$	30.3029	0.103826
$45$	0	0
$46$	428.387	1.37309
$47$	− 585.981i	− 1.81860i	−0.416142	−	0.909300i	$-0.636618\pi$
$47$	− 585.981i	− 1.81860i	0.416142	−	0.909300i	$-0.363382\pi$
$48$	235.348i	0.707701i
$49$	−768.085	−2.23931
$50$	0	0
$51$	−209.117	−0.574161
$52$	66.9037i	0.178421i
$53$	− 40.0845i	− 0.103887i	−0.998650	−	0.0519436i	$-0.983458\pi$
$53$	− 40.0845i	− 0.103887i	0.998650	−	0.0519436i	$-0.0165416\pi$
$54$	88.5452	0.223138
$55$	0	0
$56$	573.372	1.36822
$57$	− 377.153i	− 0.876406i
$58$	− 781.105i	− 1.76835i
$59$	312.763	0.690140	0.345070	−	0.938577i	$-0.387855\pi$
$59$	312.763	0.690140	0.345070	+	0.938577i	$0.387855\pi$
$60$	0	0
$61$	−391.339	−0.821408	−0.410704	−	0.911769i	$-0.634717\pi$
$61$	−391.339	−0.821408	−0.410704	+	0.911769i	$0.634717\pi$
$62$	438.342i	0.897896i
$63$	− 299.996i	− 0.599937i
$64$	−235.175	−0.459326
$65$	0	0
$66$	108.222	0.201836
$67$	− 858.232i	− 1.56492i	−0.622700	−	0.782461i	$-0.713964\pi$
$67$	− 858.232i	− 1.56492i	0.622700	−	0.782461i	$-0.286036\pi$
$68$	192.026i	0.342449i
$69$	391.883	0.683727
$70$	0	0
$71$	−583.028	−0.974546	−0.487273	−	0.873250i	$-0.662008\pi$
$71$	−583.028	−0.974546	−0.487273	+	0.873250i	$0.662008\pi$
$72$	154.812i	0.253400i
$73$	368.303i	0.590501i	0.955420	+	0.295251i	$0.0954032\pi$
$73$	368.303i	0.590501i	−0.955420	+	0.295251i	$0.904597\pi$
$74$	−546.044	−0.857788
$75$	0	0
$76$	−346.328	−0.522718
$77$	− 366.662i	− 0.542663i
$78$	238.936i	0.346848i
$79$	438.935	0.625114	0.312557	−	0.949899i	$-0.398814\pi$
$79$	438.935	0.625114	0.312557	+	0.949899i	$0.398814\pi$
$80$	0	0
$81$	81.0000	0.111111
$82$	− 977.117i	− 1.31591i
$83$	− 877.643i	− 1.16065i	−0.814386	−	0.580324i	$-0.802926\pi$
$83$	− 877.643i	− 1.16065i	0.814386	−	0.580324i	$-0.197074\pi$
$84$	−275.478	−0.357822
$85$	0	0
$86$	−1519.39	−1.90512
$87$	− 714.544i	− 0.880542i
$88$	189.215i	0.229209i
$89$	999.585	1.19051	0.595257	−	0.803535i	$-0.297050\pi$
$89$	999.585	1.19051	0.595257	+	0.803535i	$0.297050\pi$
$90$	0	0
$91$	809.529	0.932546
$92$	− 359.854i	− 0.407797i
$93$	400.990i	0.447104i
$94$	−1921.70	−2.10860
$95$	0	0
$96$	358.982	0.381650
$97$	1306.31i	1.36738i	0.729775	+	0.683688i	$0.239625\pi$
$97$	1306.31i	1.36738i	−0.729775	+	0.683688i	$0.760375\pi$
$98$	2518.90i	2.59640i
$99$	99.0000	0.100504
$100$	0	0
$101$	67.1570	0.0661621	0.0330810	−	0.999453i	$-0.489468\pi$
$101$	67.1570	0.0661621	0.0330810	+	0.999453i	$0.489468\pi$
$102$	685.789i	0.665718i
$103$	− 813.283i	− 0.778011i	−0.921235	−	0.389005i	$-0.872819\pi$
$103$	− 813.283i	− 0.778011i	0.921235	−	0.389005i	$-0.127181\pi$
$104$	−417.755	−0.393887
$105$	0	0
$106$	−131.455	−0.120453
$107$	597.911i	0.540208i	0.962831	+	0.270104i	$0.0870580\pi$
$107$	597.911i	0.540208i	−0.962831	+	0.270104i	$0.912942\pi$
$108$	− 74.3798i	− 0.0662704i
$109$	−1176.85	−1.03414	−0.517072	−	0.855942i	$-0.672978\pi$
$109$	−1176.85	−1.03414	−0.517072	+	0.855942i	$0.672978\pi$
$110$	0	0
$111$	−499.514	−0.427133
$112$	− 2614.95i	− 2.20616i
$113$	− 1344.44i	− 1.11924i	−0.828748	−	0.559621i	$-0.810947\pi$
$113$	− 1344.44i	− 1.11924i	0.828748	−	0.559621i	$-0.189053\pi$
$114$	−1236.86	−1.01616
$115$	0	0
$116$	−656.144	−0.525185
$117$	218.575i	0.172712i
$118$	− 1025.69i	− 0.800191i
$119$	2323.49	1.78987
$120$	0	0
$121$	121.000	0.0909091
$122$	1283.38i	0.952391i
$123$	− 893.854i	− 0.655253i
$124$	368.217	0.266668
$125$	0	0
$126$	−983.824	−0.695603
$127$	− 946.021i	− 0.660990i	−0.943808	−	0.330495i	$-0.892784\pi$
$127$	− 946.021i	− 0.660990i	0.943808	−	0.330495i	$-0.107216\pi$
$128$	1728.53i	1.19361i
$129$	−1389.92	−0.948648
$130$	0	0
$131$	−974.351	−0.649843	−0.324922	−	0.945741i	$-0.605338\pi$
$131$	−974.351	−0.649843	−0.324922	+	0.945741i	$0.605338\pi$
$132$	− 90.9086i	− 0.0599438i
$133$	4190.54i	2.73207i
$134$	−2814.53	−1.81447
$135$	0	0
$136$	−1199.03	−0.756000
$137$	− 452.696i	− 0.282310i	−0.989988	−	0.141155i	$-0.954918\pi$
$137$	− 452.696i	− 0.282310i	0.989988	−	0.141155i	$-0.0450816\pi$
$138$	− 1285.16i	− 0.792755i
$139$	885.107	0.540099	0.270050	−	0.962846i	$-0.412960\pi$
$139$	885.107	0.540099	0.270050	+	0.962846i	$0.412960\pi$
$140$	0	0
$141$	−1757.94	−1.04997
$142$	1912.01i	1.12995i
$143$	267.148i	0.156224i
$144$	706.045	0.408591
$145$	0	0
$146$	1207.83	0.684664
$147$	2304.26i	1.29287i
$148$	458.688i	0.254756i
$149$	2655.48	1.46004	0.730018	−	0.683428i	$-0.239512\pi$
$149$	2655.48	1.46004	0.730018	+	0.683428i	$0.239512\pi$
$150$	0	0
$151$	−356.398	−0.192075	−0.0960373	−	0.995378i	$-0.530617\pi$
$151$	−356.398	−0.192075	−0.0960373	+	0.995378i	$0.530617\pi$
$152$	− 2162.52i	− 1.15397i
$153$	627.350i	0.331492i
$154$	−1202.45	−0.629197
$155$	0	0
$156$	200.711	0.103011
$157$	2379.88i	1.20978i	0.796310	+	0.604889i	$0.206782\pi$
$157$	2379.88i	1.20978i	−0.796310	+	0.604889i	$0.793218\pi$
$158$	− 1439.46i	− 0.724795i
$159$	−120.253	−0.0599793
$160$	0	0
$161$	−4354.20	−2.13142
$162$	− 265.636i	− 0.128829i
$163$	− 651.774i	− 0.313195i	−0.987662	−	0.156598i	$-0.949947\pi$
$163$	− 651.774i	− 0.313195i	0.987662	−	0.156598i	$-0.0500526\pi$
$164$	−820.798	−0.390815
$165$	0	0
$166$	−2878.19	−1.34573
$167$	− 2498.34i	− 1.15765i	−0.815453	−	0.578823i	$-0.803512\pi$
$167$	− 2498.34i	− 1.15765i	0.815453	−	0.578823i	$-0.196488\pi$
$168$	− 1720.12i	− 0.789939i
$169$	1607.18	0.731535
$170$	0	0
$171$	−1131.46	−0.505993
$172$	1276.32i	0.565805i
$173$	1094.34i	0.480931i	0.970658	+	0.240465i	$0.0773000\pi$
$173$	1094.34i	0.480931i	−0.970658	+	0.240465i	$0.922700\pi$
$174$	−2343.31	−1.02095
$175$	0	0
$176$	862.944	0.369585
$177$	− 938.289i	− 0.398453i
$178$	− 3278.09i	− 1.38036i
$179$	1794.49	0.749309	0.374654	−	0.927165i	$-0.377761\pi$
$179$	1794.49	0.749309	0.374654	+	0.927165i	$0.377761\pi$
$180$	0	0
$181$	1416.94	0.581881	0.290941	−	0.956741i	$-0.406032\pi$
$181$	1416.94	0.581881	0.290941	+	0.956741i	$0.406032\pi$
$182$	− 2654.81i	− 1.08125i
$183$	1174.02i	0.474240i
$184$	2246.97	0.900266
$185$	0	0
$186$	1315.03	0.518400
$187$	766.762i	0.299846i
$188$	1614.27i	0.626236i
$189$	−899.989	−0.346374
$190$	0	0
$191$	1346.61	0.510141	0.255071	−	0.966922i	$-0.417901\pi$
$191$	1346.61	0.510141	0.255071	+	0.966922i	$0.417901\pi$
$192$	705.525i	0.265192i
$193$	− 2333.09i	− 0.870151i	−0.900394	−	0.435076i	$-0.856722\pi$
$193$	− 2333.09i	− 0.870151i	0.900394	−	0.435076i	$-0.143278\pi$
$194$	4283.97	1.58542
$195$	0	0
$196$	2115.93	0.771110
$197$	962.676i	0.348162i	0.984731	+	0.174081i	$0.0556954\pi$
$197$	962.676i	0.348162i	−0.984731	+	0.174081i	$0.944305\pi$
$198$	− 324.666i	− 0.116530i
$199$	−1337.59	−0.476477	−0.238238	−	0.971207i	$-0.576570\pi$
$199$	−1337.59	−0.476477	−0.238238	+	0.971207i	$0.576570\pi$
$200$	0	0
$201$	−2574.70	−0.903508
$202$	− 220.238i	− 0.0767124i
$203$	7939.29i	2.74497i
$204$	576.077	0.197713
$205$	0	0
$206$	−2667.12	−0.902074
$207$	− 1175.65i	− 0.394750i
$208$	1905.24i	0.635117i
$209$	−1382.89	−0.457688
$210$	0	0
$211$	4378.89	1.42870	0.714349	−	0.699790i	$-0.246723\pi$
$211$	4378.89	1.42870	0.714349	+	0.699790i	$0.246723\pi$
$212$	110.425i	0.0357737i
$213$	1749.08i	0.562654i
$214$	1960.82	0.626350
$215$	0	0
$216$	464.437	0.146301
$217$	− 4455.39i	− 1.39379i
$218$	3859.42i	1.19905i
$219$	1104.91	0.340926
$220$	0	0
$221$	−1692.88	−0.515274
$222$	1638.13i	0.495244i
$223$	− 920.657i	− 0.276465i	−0.990400	−	0.138233i	$-0.955858\pi$
$223$	− 920.657i	− 0.276465i	0.990400	−	0.138233i	$-0.0441422\pi$
$224$	−3988.64	−1.18974
$225$	0	0
$226$	−4409.03	−1.29772
$227$	− 739.810i	− 0.216313i	−0.994134	−	0.108156i	$-0.965505\pi$
$227$	− 739.810i	− 0.216313i	0.994134	−	0.108156i	$-0.0344947\pi$
$228$	1038.98i	0.301791i
$229$	−4230.73	−1.22085	−0.610425	−	0.792074i	$-0.709001\pi$
$229$	−4230.73	−1.22085	−0.610425	+	0.792074i	$0.709001\pi$
$230$	0	0
$231$	−1099.99	−0.313307
$232$	− 4097.04i	− 1.15941i
$233$	5318.96i	1.49552i	0.663968	+	0.747761i	$0.268871\pi$
$233$	5318.96i	1.49552i	−0.663968	+	0.747761i	$0.731129\pi$
$234$	716.808	0.200253
$235$	0	0
$236$	−861.602	−0.237650
$237$	− 1316.80i	− 0.360910i
$238$	− 7619.78i	− 2.07528i
$239$	−3924.28	−1.06209	−0.531047	−	0.847342i	$-0.678201\pi$
$239$	−3924.28	−1.06209	−0.531047	+	0.847342i	$0.678201\pi$
$240$	0	0
$241$	−4198.43	−1.12218	−0.561089	−	0.827756i	$-0.689617\pi$
$241$	−4198.43	−1.12218	−0.561089	+	0.827756i	$0.689617\pi$
$242$	− 396.814i	− 0.105406i
$243$	− 243.000i	− 0.0641500i
$244$	1078.06	0.282853
$245$	0	0
$246$	−2931.35	−0.759740
$247$	− 3053.20i	− 0.786520i
$248$	2299.19i	0.588705i
$249$	−2632.93	−0.670100
$250$	0	0
$251$	−654.822	−0.164669	−0.0823346	−	0.996605i	$-0.526238\pi$
$251$	−654.822	−0.164669	−0.0823346	+	0.996605i	$0.526238\pi$
$252$	826.433i	0.206589i
$253$	− 1436.90i	− 0.357065i
$254$	−3102.43	−0.766393
$255$	0	0
$256$	3787.23	0.924617
$257$	991.373i	0.240623i	0.992736	+	0.120312i	$0.0383894\pi$
$257$	991.373i	0.240623i	−0.992736	+	0.120312i	$0.961611\pi$
$258$	4558.18i	1.09992i
$259$	5550.09	1.33153
$260$	0	0
$261$	−2143.63	−0.508381
$262$	3195.34i	0.753468i
$263$	752.618i	0.176458i	0.996100	+	0.0882289i	$0.0281207\pi$
$263$	752.618i	0.176458i	−0.996100	+	0.0882289i	$0.971879\pi$
$264$	567.645	0.132334
$265$	0	0
$266$	13742.7	3.16774
$267$	− 2998.76i	− 0.687344i
$268$	2364.26i	0.538882i
$269$	4673.88	1.05937	0.529687	−	0.848193i	$-0.322309\pi$
$269$	4673.88	1.05937	0.529687	+	0.848193i	$0.322309\pi$
$270$	0	0
$271$	−8145.45	−1.82583	−0.912917	−	0.408145i	$-0.866176\pi$
$271$	−8145.45	−1.82583	−0.912917	+	0.408145i	$0.866176\pi$
$272$	5468.37i	1.21900i
$273$	− 2428.59i	− 0.538406i
$274$	−1484.60	−0.327328
$275$	0	0
$276$	−1079.56	−0.235442
$277$	− 5804.28i	− 1.25901i	−0.776997	−	0.629504i	$-0.783258\pi$
$277$	− 5804.28i	− 1.25901i	0.776997	−	0.629504i	$-0.216742\pi$
$278$	− 2902.67i	− 0.626225i
$279$	1202.97	0.258136
$280$	0	0
$281$	7850.68	1.66666	0.833332	−	0.552773i	$-0.186430\pi$
$281$	7850.68	1.66666	0.833332	+	0.552773i	$0.186430\pi$
$282$	5765.09i	1.21740i
$283$	− 7091.78i	− 1.48962i	−0.667277	−	0.744810i	$-0.732540\pi$
$283$	− 7091.78i	− 1.48962i	0.667277	−	0.744810i	$-0.267460\pi$
$284$	1606.13	0.335586
$285$	0	0
$286$	876.098	0.181136
$287$	9931.59i	2.04266i
$288$	− 1076.94i	− 0.220346i
$289$	54.1294	0.0110176
$290$	0	0
$291$	3918.92	0.789455
$292$	− 1014.60i	− 0.203340i
$293$	7796.02i	1.55443i	0.629234	+	0.777216i	$0.283369\pi$
$293$	7796.02i	1.55443i	−0.629234	+	0.777216i	$0.716631\pi$
$294$	7556.69	1.49903
$295$	0	0
$296$	−2864.10	−0.562408
$297$	− 297.000i	− 0.0580259i
$298$	− 8708.52i	− 1.69286i
$299$	3172.44	0.613602
$300$	0	0
$301$	15443.4	2.95728
$302$	1168.79i	0.222703i
$303$	− 201.471i	− 0.0381987i
$304$	−9862.49	−1.86070
$305$	0	0
$306$	2057.37	0.384352
$307$	5051.78i	0.939155i	0.882891	+	0.469577i	$0.155594\pi$
$307$	5051.78i	0.939155i	−0.882891	+	0.469577i	$0.844406\pi$
$308$	1010.08i	0.186867i
$309$	−2439.85	−0.449185
$310$	0	0
$311$	3533.10	0.644193	0.322096	−	0.946707i	$-0.395612\pi$
$311$	3533.10	0.644193	0.322096	+	0.946707i	$0.395612\pi$
$312$	1253.27i	0.227411i
$313$	3376.33i	0.609718i	0.952398	+	0.304859i	$0.0986093\pi$
$313$	3376.33i	0.609718i	−0.952398	+	0.304859i	$0.901391\pi$
$314$	7804.70	1.40269
$315$	0	0
$316$	−1209.18	−0.215259
$317$	− 2924.54i	− 0.518165i	−0.965855	−	0.259083i	$-0.916580\pi$
$317$	− 2924.54i	− 0.518165i	0.965855	−	0.259083i	$-0.0834202\pi$
$318$	394.365i	0.0695437i
$319$	−2620.00	−0.459848
$320$	0	0
$321$	1793.73	0.311889
$322$	14279.4i	2.47130i
$323$	− 8763.23i	− 1.50959i
$324$	−223.139	−0.0382612
$325$	0	0
$326$	−2137.46	−0.363138
$327$	3530.55i	0.597063i
$328$	− 5125.17i	− 0.862774i
$329$	19532.5	3.27313
$330$	0	0
$331$	10052.9	1.66935	0.834675	−	0.550743i	$-0.185655\pi$
$331$	10052.9	1.66935	0.834675	+	0.550743i	$0.185655\pi$
$332$	2417.74i	0.399670i
$333$	1498.54i	0.246605i
$334$	−8193.17	−1.34225
$335$	0	0
$336$	−7844.86	−1.27373
$337$	− 6091.66i	− 0.984671i	−0.870406	−	0.492335i	$-0.836143\pi$
$337$	− 6091.66i	− 0.984671i	0.870406	−	0.492335i	$-0.163857\pi$
$338$	− 5270.68i	− 0.848187i
$339$	−4033.33	−0.646195
$340$	0	0
$341$	1470.30	0.233493
$342$	3710.57i	0.586680i
$343$	− 14169.3i	− 2.23053i
$344$	−7969.50	−1.24909
$345$	0	0
$346$	3588.83	0.557621
$347$	− 1645.57i	− 0.254578i	−0.991866	−	0.127289i	$-0.959372\pi$
$347$	− 1645.57i	− 0.254578i	0.991866	−	0.127289i	$-0.0406276\pi$
$348$	1968.43i	0.303216i
$349$	7753.75	1.18925	0.594625	−	0.804003i	$-0.297300\pi$
$349$	7753.75	1.18925	0.594625	+	0.804003i	$0.297300\pi$
$350$	0	0
$351$	655.726	0.0997153
$352$	− 1316.27i	− 0.199310i
$353$	− 8040.32i	− 1.21230i	−0.795349	−	0.606152i	$-0.792712\pi$
$353$	− 8040.32i	− 1.21230i	0.795349	−	0.606152i	$-0.207288\pi$
$354$	−3077.07	−0.461991
$355$	0	0
$356$	−2753.67	−0.409955
$357$	− 6970.48i	− 1.03338i
$358$	− 5884.94i	− 0.868795i
$359$	−9483.44	−1.39420	−0.697099	−	0.716975i	$-0.745526\pi$
$359$	−9483.44	−1.39420	−0.697099	+	0.716975i	$0.745526\pi$
$360$	0	0
$361$	8945.94	1.30426
$362$	− 4646.80i	− 0.674669i
$363$	− 363.000i	− 0.0524864i
$364$	−2230.10	−0.321123
$365$	0	0
$366$	3850.14	0.549863
$367$	− 6572.60i	− 0.934841i	−0.884035	−	0.467421i	$-0.845183\pi$
$367$	− 6572.60i	− 0.934841i	0.884035	−	0.467421i	$-0.154817\pi$
$368$	− 10247.7i	− 1.45162i
$369$	−2681.56	−0.378310
$370$	0	0
$371$	1336.13	0.186977
$372$	− 1104.65i	− 0.153961i
$373$	4148.14i	0.575825i	0.957657	+	0.287912i	$0.0929612\pi$
$373$	4148.14i	0.575825i	−0.957657	+	0.287912i	$0.907039\pi$
$374$	2514.56	0.347660
$375$	0	0
$376$	−10079.7	−1.38250
$377$	− 5784.51i	− 0.790232i
$378$	2951.47i	0.401607i
$379$	−4256.57	−0.576901	−0.288451	−	0.957495i	$-0.593140\pi$
$379$	−4256.57	−0.576901	−0.288451	+	0.957495i	$0.593140\pi$
$380$	0	0
$381$	−2838.06	−0.381623
$382$	− 4416.13i	− 0.591489i
$383$	− 5430.24i	− 0.724471i	−0.932087	−	0.362236i	$-0.882014\pi$
$383$	− 5430.24i	− 0.724471i	0.932087	−	0.362236i	$-0.117986\pi$
$384$	5185.59	0.689130
$385$	0	0
$386$	−7651.24	−1.00891
$387$	4169.76i	0.547702i
$388$	− 3598.63i	− 0.470857i
$389$	2574.81	0.335600	0.167800	−	0.985821i	$-0.446334\pi$
$389$	2574.81	0.335600	0.167800	+	0.985821i	$0.446334\pi$
$390$	0	0
$391$	9105.47	1.17771
$392$	13212.1i	1.70233i
$393$	2923.05i	0.375187i
$394$	3157.05	0.403680
$395$	0	0
$396$	−272.726	−0.0346086
$397$	14389.3i	1.81909i	0.415606	+	0.909545i	$0.363570\pi$
$397$	14389.3i	1.81909i	−0.415606	+	0.909545i	$0.636430\pi$
$398$	4386.55i	0.552457i
$399$	12571.6	1.57736
$400$	0	0
$401$	1013.21	0.126178	0.0630888	−	0.998008i	$-0.479905\pi$
$401$	1013.21	0.126178	0.0630888	+	0.998008i	$0.479905\pi$
$402$	8443.59i	1.04758i
$403$	3246.17i	0.401249i
$404$	−185.005	−0.0227830
$405$	0	0
$406$	26036.5	3.18269
$407$	1831.55i	0.223063i
$408$	3597.09i	0.436477i
$409$	−1159.14	−0.140136	−0.0700682	−	0.997542i	$-0.522322\pi$
$409$	−1159.14	−0.140136	−0.0700682	+	0.997542i	$0.522322\pi$
$410$	0	0
$411$	−1358.09	−0.162992
$412$	2240.44i	0.267909i
$413$	10425.3i	1.24212i
$414$	−3855.48	−0.457697
$415$	0	0
$416$	2906.09	0.342507
$417$	− 2655.32i	− 0.311827i
$418$	4535.14i	0.530672i
$419$	9711.04	1.13226	0.566128	−	0.824317i	$-0.308441\pi$
$419$	9711.04	1.13226	0.566128	+	0.824317i	$0.308441\pi$
$420$	0	0
$421$	3477.88	0.402616	0.201308	−	0.979528i	$-0.435481\pi$
$421$	3477.88	0.402616	0.201308	+	0.979528i	$0.435481\pi$
$422$	− 14360.4i	− 1.65652i
$423$	5273.83i	0.606200i
$424$	−689.507	−0.0789751
$425$	0	0
$426$	5736.04	0.652376
$427$	− 13044.5i	− 1.47838i
$428$	− 1647.13i	− 0.186021i
$429$	801.443	0.0901959
$430$	0	0
$431$	−6748.27	−0.754182	−0.377091	−	0.926176i	$-0.623076\pi$
$431$	−6748.27	−0.754182	−0.377091	+	0.926176i	$0.623076\pi$
$432$	− 2118.14i	− 0.235900i
$433$	5380.74i	0.597186i	0.954380	+	0.298593i	$0.0965174\pi$
$433$	5380.74i	0.597186i	−0.954380	+	0.298593i	$0.903483\pi$
$434$	−14611.2	−1.61604
$435$	0	0
$436$	3241.99	0.356108
$437$	16422.2i	1.79767i
$438$	− 3623.50i	− 0.395291i
$439$	1095.09	0.119057	0.0595283	−	0.998227i	$-0.481040\pi$
$439$	1095.09	0.119057	0.0595283	+	0.998227i	$0.481040\pi$
$440$	0	0
$441$	6912.77	0.746438
$442$	5551.72i	0.597440i
$443$	− 3167.11i	− 0.339670i	−0.985473	−	0.169835i	$-0.945677\pi$
$443$	− 3167.11i	− 0.339670i	0.985473	−	0.169835i	$-0.0543235\pi$
$444$	1376.06	0.147084
$445$	0	0
$446$	−3019.25	−0.320551
$447$	− 7966.44i	− 0.842952i
$448$	− 7839.08i	− 0.826700i
$449$	391.054	0.0411024	0.0205512	−	0.999789i	$-0.493458\pi$
$449$	391.054	0.0411024	0.0205512	+	0.999789i	$0.493458\pi$
$450$	0	0
$451$	−3277.46	−0.342195
$452$	3703.68i	0.385412i
$453$	1069.19i	0.110894i
$454$	−2426.17	−0.250806
$455$	0	0
$456$	−6487.55	−0.666244
$457$	− 2563.42i	− 0.262389i	−0.991357	−	0.131194i	$-0.958119\pi$
$457$	− 2563.42i	− 0.262389i	0.991357	−	0.131194i	$-0.0418812\pi$
$458$	13874.5i	1.41553i
$459$	1882.05	0.191387
$460$	0	0
$461$	−6151.57	−0.621491	−0.310745	−	0.950493i	$-0.600579\pi$
$461$	−6151.57	−0.621491	−0.310745	+	0.950493i	$0.600579\pi$
$462$	3607.36i	0.363267i
$463$	9833.63i	0.987058i	0.869729	+	0.493529i	$0.164293\pi$
$463$	9833.63i	0.987058i	−0.869729	+	0.493529i	$0.835707\pi$
$464$	−18685.2	−1.86948
$465$	0	0
$466$	17443.3	1.73400
$467$	7408.21i	0.734071i	0.930207	+	0.367036i	$0.119627\pi$
$467$	7408.21i	0.734071i	−0.930207	+	0.367036i	$0.880373\pi$
$468$	− 602.133i	− 0.0594736i
$469$	28607.4	2.81656
$470$	0	0
$471$	7139.64	0.698465
$472$	− 5379.95i	− 0.524645i
$473$	5096.37i	0.495415i
$474$	−4318.39	−0.418461
$475$	0	0
$476$	−6400.78	−0.616343
$477$	360.760i	0.0346291i
$478$	12869.5i	1.23146i
$479$	8257.19	0.787643	0.393821	−	0.919187i	$-0.371153\pi$
$479$	8257.19	0.787643	0.393821	+	0.919187i	$0.371153\pi$
$480$	0	0
$481$	−4043.76	−0.383325
$482$	13768.6i	1.30112i
$483$	13062.6i	1.23058i
$484$	−333.332	−0.0313046
$485$	0	0
$486$	−796.907	−0.0743795
$487$	10086.8i	0.938552i	0.883051	+	0.469276i	$0.155485\pi$
$487$	10086.8i	0.938552i	−0.883051	+	0.469276i	$0.844515\pi$
$488$	6731.57i	0.624434i
$489$	−1955.32	−0.180823
$490$	0	0
$491$	−6343.10	−0.583015	−0.291507	−	0.956569i	$-0.594157\pi$
$491$	−6343.10	−0.583015	−0.291507	+	0.956569i	$0.594157\pi$
$492$	2462.40i	0.225637i
$493$	− 16602.6i	− 1.51672i
$494$	−10012.8	−0.911940
$495$	0	0
$496$	10485.8	0.949248
$497$	− 19434.0i	− 1.75400i
$498$	8634.56i	0.776956i
$499$	9862.39	0.884772	0.442386	−	0.896825i	$-0.354132\pi$
$499$	9862.39	0.884772	0.442386	+	0.896825i	$0.354132\pi$
$500$	0	0
$501$	−7495.01	−0.668368
$502$	2147.46i	0.190928i
$503$	− 16774.2i	− 1.48692i	−0.668778	−	0.743462i	$-0.733182\pi$
$503$	− 16774.2i	− 1.48692i	0.668778	−	0.743462i	$-0.266818\pi$
$504$	−5160.35	−0.456072
$505$	0	0
$506$	−4712.26	−0.414003
$507$	− 4821.55i	− 0.422352i
$508$	2606.10i	0.227613i
$509$	−18723.8	−1.63049	−0.815244	−	0.579118i	$-0.803397\pi$
$509$	−18723.8	−1.63049	−0.815244	+	0.579118i	$0.803397\pi$
$510$	0	0
$511$	−12276.6	−1.06279
$512$	1408.20i	0.121551i
$513$	3394.38i	0.292135i
$514$	3251.16	0.278993
$515$	0	0
$516$	3828.96	0.326668
$517$	6445.79i	0.548328i
$518$	− 18201.2i	− 1.54385i
$519$	3283.02	0.277666
$520$	0	0
$521$	−1321.90	−0.111159	−0.0555793	−	0.998454i	$-0.517701\pi$
$521$	−1321.90	−0.111159	−0.0555793	+	0.998454i	$0.517701\pi$
$522$	7029.94i	0.589449i
$523$	4276.30i	0.357533i	0.983892	+	0.178766i	$0.0572107\pi$
$523$	4276.30i	0.357533i	−0.983892	+	0.178766i	$0.942789\pi$
$524$	2684.15	0.223774
$525$	0	0
$526$	2468.17	0.204596
$527$	9317.08i	0.770130i
$528$	− 2588.83i	− 0.213380i
$529$	−4896.57	−0.402447
$530$	0	0
$531$	−2814.87	−0.230047
$532$	− 11544.1i	− 0.940792i
$533$	− 7236.09i	− 0.588049i
$534$	−9834.28	−0.796949
$535$	0	0
$536$	−14762.8	−1.18965
$537$	− 5383.46i	− 0.432614i
$538$	− 15327.8i	− 1.22830i
$539$	8448.94	0.675179
$540$	0	0
$541$	−2941.66	−0.233774	−0.116887	−	0.993145i	$-0.537292\pi$
$541$	−2941.66	−0.233774	−0.116887	+	0.993145i	$0.537292\pi$
$542$	26712.6i	2.11698i
$543$	− 4250.83i	− 0.335949i
$544$	8341.01	0.657386
$545$	0	0
$546$	−7964.44	−0.624261
$547$	− 8717.71i	− 0.681430i	−0.940167	−	0.340715i	$-0.889331\pi$
$547$	− 8717.71i	− 0.681430i	0.940167	−	0.340715i	$-0.110669\pi$
$548$	1247.09i	0.0972137i
$549$	3522.06	0.273803
$550$	0	0
$551$	29943.6	2.31514
$552$	− 6740.92i	− 0.519769i
$553$	14631.0i	1.12509i
$554$	−19034.9	−1.45977
$555$	0	0
$556$	−2438.30	−0.185984
$557$	4154.36i	0.316025i	0.987437	+	0.158013i	$0.0505087\pi$
$557$	4154.36i	0.316025i	−0.987437	+	0.158013i	$0.949491\pi$
$558$	− 3945.08i	− 0.299299i
$559$	−11251.9	−0.851353
$560$	0	0
$561$	2300.28	0.173116
$562$	− 25745.9i	− 1.93243i
$563$	8603.87i	0.644068i	0.946728	+	0.322034i	$0.104366\pi$
$563$	8603.87i	0.644068i	−0.946728	+	0.322034i	$0.895634\pi$
$564$	4842.80	0.361558
$565$	0	0
$566$	−23257.1	−1.72716
$567$	2699.97i	0.199979i
$568$	10028.9i	0.740849i
$569$	−1598.57	−0.117778	−0.0588889	−	0.998265i	$-0.518756\pi$
$569$	−1598.57	−0.117778	−0.0588889	+	0.998265i	$0.518756\pi$
$570$	0	0
$571$	−21577.9	−1.58145	−0.790725	−	0.612171i	$-0.790296\pi$
$571$	−21577.9	−1.58145	−0.790725	+	0.612171i	$0.790296\pi$
$572$	− 735.941i	− 0.0537959i
$573$	− 4039.82i	− 0.294530i
$574$	32570.2	2.36839
$575$	0	0
$576$	2116.58	0.153109
$577$	− 7586.21i	− 0.547345i	−0.961823	−	0.273672i	$-0.911762\pi$
$577$	− 7586.21i	− 0.547345i	0.961823	−	0.273672i	$-0.0882384\pi$
$578$	− 177.515i	− 0.0127745i
$579$	−6999.26	−0.502382
$580$	0	0
$581$	29254.4	2.08895
$582$	− 12851.9i	− 0.915342i
$583$	440.929i	0.0313232i
$584$	6335.31	0.448899
$585$	0	0
$586$	25566.7	1.80230
$587$	− 4442.82i	− 0.312393i	−0.987726	−	0.156197i	$-0.950077\pi$
$587$	− 4442.82i	− 0.312393i	0.987726	−	0.156197i	$-0.0499233\pi$
$588$	− 6347.78i	− 0.445201i
$589$	−16803.8	−1.17554
$590$	0	0
$591$	2888.03	0.201011
$592$	13062.2i	0.906846i
$593$	− 15853.2i	− 1.09783i	−0.835878	−	0.548915i	$-0.815041\pi$
$593$	− 15853.2i	− 1.09783i	0.835878	−	0.548915i	$-0.184959\pi$
$594$	−973.997	−0.0672788
$595$	0	0
$596$	−7315.33	−0.502765
$597$	4012.76i	0.275094i
$598$	− 10403.9i	− 0.711448i
$599$	−3382.45	−0.230723	−0.115362	−	0.993324i	$-0.536803\pi$
$599$	−3382.45	−0.230723	−0.115362	+	0.993324i	$0.536803\pi$
$600$	0	0
$601$	−16494.3	−1.11950	−0.559748	−	0.828663i	$-0.689102\pi$
$601$	−16494.3	−1.11950	−0.559748	+	0.828663i	$0.689102\pi$
$602$	− 50645.8i	− 3.42885i
$603$	7724.09i	0.521641i
$604$	981.808	0.0661411
$605$	0	0
$606$	−660.715	−0.0442899
$607$	21074.0i	1.40917i	0.709620	+	0.704585i	$0.248867\pi$
$607$	21074.0i	1.40917i	−0.709620	+	0.704585i	$0.751133\pi$
$608$	15043.4i	1.00344i
$609$	23817.9	1.58481
$610$	0	0
$611$	−14231.2	−0.942282
$612$	− 1728.23i	− 0.114150i
$613$	20645.9i	1.36033i	0.733059	+	0.680165i	$0.238092\pi$
$613$	20645.9i	1.36033i	−0.733059	+	0.680165i	$0.761908\pi$
$614$	16567.1	1.08891
$615$	0	0
$616$	−6307.09	−0.412532
$617$	3913.54i	0.255353i	0.991816	+	0.127677i	$0.0407520\pi$
$617$	3913.54i	0.255353i	−0.991816	+	0.127677i	$0.959248\pi$
$618$	8001.37i	0.520812i
$619$	27237.9	1.76863	0.884315	−	0.466891i	$-0.154626\pi$
$619$	27237.9	1.76863	0.884315	+	0.466891i	$0.154626\pi$
$620$	0	0
$621$	−3526.94	−0.227909
$622$	− 11586.6i	− 0.746917i
$623$	33319.1i	2.14270i
$624$	5715.71	0.366685
$625$	0	0
$626$	11072.5	0.706944
$627$	4148.68i	0.264246i
$628$	− 6556.11i	− 0.416588i
$629$	−11606.3	−0.735729
$630$	0	0
$631$	−21440.7	−1.35268	−0.676341	−	0.736589i	$-0.736435\pi$
$631$	−21440.7	−1.35268	−0.676341	+	0.736589i	$0.736435\pi$
$632$	− 7550.27i	− 0.475211i
$633$	− 13136.7i	− 0.824859i
$634$	−9590.89	−0.600793
$635$	0	0
$636$	331.275	0.0206539
$637$	18653.8i	1.16027i
$638$	8592.15i	0.533176i
$639$	5247.25	0.324849
$640$	0	0
$641$	−2173.52	−0.133929	−0.0669647	−	0.997755i	$-0.521331\pi$
$641$	−2173.52	−0.133929	−0.0669647	+	0.997755i	$0.521331\pi$
$642$	− 5882.46i	− 0.361623i
$643$	26997.5i	1.65579i	0.560880	+	0.827897i	$0.310463\pi$
$643$	26997.5i	1.65579i	−0.560880	+	0.827897i	$0.689537\pi$
$644$	11995.0	0.733958
$645$	0	0
$646$	−28738.6	−1.75032
$647$	− 8961.19i	− 0.544514i	−0.962225	−	0.272257i	$-0.912230\pi$
$647$	− 8961.19i	− 0.544514i	0.962225	−	0.272257i	$-0.0877701\pi$
$648$	− 1393.31i	− 0.0844666i
$649$	−3440.39	−0.208085
$650$	0	0
$651$	−13366.2	−0.804703
$652$	1795.51i	0.107849i
$653$	− 27009.3i	− 1.61862i	−0.587384	−	0.809309i	$-0.699842\pi$
$653$	− 27009.3i	− 1.61862i	0.587384	−	0.809309i	$-0.300158\pi$
$654$	11578.3	0.692272
$655$	0	0
$656$	−23374.1	−1.39117
$657$	− 3314.73i	− 0.196834i
$658$	− 64055.8i	− 3.79507i
$659$	−8295.07	−0.490334	−0.245167	−	0.969481i	$-0.578843\pi$
$659$	−8295.07	−0.490334	−0.245167	+	0.969481i	$0.578843\pi$
$660$	0	0
$661$	2467.17	0.145177	0.0725883	−	0.997362i	$-0.476874\pi$
$661$	2467.17	0.145177	0.0725883	+	0.997362i	$0.476874\pi$
$662$	− 32967.9i	− 1.93555i
$663$	5078.64i	0.297494i
$664$	−15096.6	−0.882324
$665$	0	0
$666$	4914.39	0.285929
$667$	31113.1i	1.80615i
$668$	6882.43i	0.398637i
$669$	−2761.97	−0.159617
$670$	0	0
$671$	4304.73	0.247664
$672$	11965.9i	0.686897i
$673$	11725.8i	0.671614i	0.941931	+	0.335807i	$0.109009\pi$
$673$	11725.8i	0.671614i	−0.941931	+	0.335807i	$0.890991\pi$
$674$	−19977.3	−1.14169
$675$	0	0
$676$	−4427.48	−0.251905
$677$	24087.1i	1.36742i	0.729754	+	0.683710i	$0.239635\pi$
$677$	24087.1i	1.36742i	−0.729754	+	0.683710i	$0.760365\pi$
$678$	13227.1i	0.749238i
$679$	−43543.1	−2.46102
$680$	0	0
$681$	−2219.43	−0.124888
$682$	− 4821.77i	− 0.270726i
$683$	− 8183.23i	− 0.458452i	−0.973373	−	0.229226i	$-0.926381\pi$
$683$	− 8183.23i	− 0.458452i	0.973373	−	0.229226i	$-0.0736195\pi$
$684$	3116.95	0.174239
$685$	0	0
$686$	−46467.7	−2.58621
$687$	12692.2i	0.704858i
$688$	36346.2i	2.01408i
$689$	−973.498	−0.0538277
$690$	0	0
$691$	17016.4	0.936810	0.468405	−	0.883514i	$-0.344829\pi$
$691$	17016.4	0.936810	0.468405	+	0.883514i	$0.344829\pi$
$692$	− 3014.69i	− 0.165609i
$693$	3299.96i	0.180888i
$694$	−5396.56	−0.295174
$695$	0	0
$696$	−12291.1	−0.669388
$697$	− 20768.9i	− 1.12866i
$698$	− 25428.0i	− 1.37889i
$699$	15956.9	0.863440
$700$	0	0
$701$	−5983.09	−0.322365	−0.161183	−	0.986925i	$-0.551531\pi$
$701$	−5983.09	−0.322365	−0.161183	+	0.986925i	$0.551531\pi$
$702$	− 2150.42i	− 0.115616i
$703$	− 20932.6i	− 1.12302i
$704$	2586.93	0.138492
$705$	0	0
$706$	−26367.8	−1.40562
$707$	2238.54i	0.119079i
$708$	2584.81i	0.137208i
$709$	6361.76	0.336983	0.168491	−	0.985703i	$-0.446110\pi$
$709$	6361.76	0.336983	0.168491	+	0.985703i	$0.446110\pi$
$710$	0	0
$711$	−3950.41	−0.208371
$712$	− 17194.2i	− 0.905029i
$713$	− 17460.1i	− 0.917092i
$714$	−22859.4	−1.19816
$715$	0	0
$716$	−4943.47	−0.258025
$717$	11772.8i	0.613200i
$718$	31100.5i	1.61652i
$719$	4360.65	0.226182	0.113091	−	0.993585i	$-0.463925\pi$
$719$	4360.65	0.226182	0.113091	+	0.993585i	$0.463925\pi$
$720$	0	0
$721$	27109.1	1.40027
$722$	− 29337.8i	− 1.51224i
$723$	12595.3i	0.647889i
$724$	−3903.40	−0.200371
$725$	0	0
$726$	−1190.44	−0.0608559
$727$	− 11314.3i	− 0.577200i	−0.957450	−	0.288600i	$-0.906810\pi$
$727$	− 11314.3i	− 0.577200i	0.957450	−	0.288600i	$-0.0931898\pi$
$728$	− 13925.0i	− 0.708922i
$729$	−729.000	−0.0370370
$730$	0	0
$731$	−32295.1	−1.63403
$732$	− 3234.19i	− 0.163305i
$733$	22374.6i	1.12745i	0.825962	+	0.563726i	$0.190633\pi$
$733$	22374.6i	1.12745i	−0.825962	+	0.563726i	$0.809367\pi$
$734$	−21554.5	−1.08391
$735$	0	0
$736$	−15631.0	−0.782833
$737$	9440.55i	0.471842i
$738$	8794.05i	0.438636i
$739$	−31277.2	−1.55690	−0.778451	−	0.627706i	$-0.783994\pi$
$739$	−31277.2	−1.55690	−0.778451	+	0.627706i	$0.783994\pi$
$740$	0	0
$741$	−9159.60	−0.454098
$742$	− 4381.78i	− 0.216793i
$743$	35409.4i	1.74838i	0.485585	+	0.874189i	$0.338607\pi$
$743$	35409.4i	1.74838i	−0.485585	+	0.874189i	$0.661393\pi$
$744$	6897.57	0.339889
$745$	0	0
$746$	13603.6	0.667647
$747$	7898.78i	0.386883i
$748$	− 2112.28i	− 0.103252i
$749$	−19930.1	−0.972271
$750$	0	0
$751$	−24420.2	−1.18656	−0.593279	−	0.804997i	$-0.702167\pi$
$751$	−24420.2	−1.18656	−0.593279	+	0.804997i	$0.702167\pi$
$752$	45969.9i	2.22919i
$753$	1964.47i	0.0950719i
$754$	−18970.0	−0.916244
$755$	0	0
$756$	2479.30	0.119274
$757$	1017.46i	0.0488512i	0.999702	+	0.0244256i	$0.00777569\pi$
$757$	1017.46i	0.0488512i	−0.999702	+	0.0244256i	$0.992224\pi$
$758$	13959.2i	0.668895i
$759$	−4310.71	−0.206151
$760$	0	0
$761$	14539.8	0.692600	0.346300	−	0.938124i	$-0.387438\pi$
$761$	14539.8	0.692600	0.346300	+	0.938124i	$0.387438\pi$
$762$	9307.29i	0.442477i
$763$	− 39227.8i	− 1.86126i
$764$	−3709.64	−0.175668
$765$	0	0
$766$	−17808.2	−0.839996
$767$	− 7595.81i	− 0.357587i
$768$	− 11361.7i	− 0.533828i
$769$	31068.6	1.45691	0.728454	−	0.685095i	$-0.240239\pi$
$769$	31068.6	1.45691	0.728454	+	0.685095i	$0.240239\pi$
$770$	0	0
$771$	2974.12	0.138924
$772$	6427.20i	0.299637i
$773$	9031.49i	0.420233i	0.977676	+	0.210117i	$0.0673843\pi$
$773$	9031.49i	0.420233i	−0.977676	+	0.210117i	$0.932616\pi$
$774$	13674.5	0.635040
$775$	0	0
$776$	22470.3	1.03948
$777$	− 16650.3i	− 0.768758i
$778$	− 8443.98i	− 0.389115i
$779$	37457.7	1.72280
$780$	0	0
$781$	6413.31	0.293837
$782$	− 29861.0i	− 1.36551i
$783$	6430.90i	0.293514i
$784$	60255.9	2.74489
$785$	0	0
$786$	9586.02	0.435015
$787$	− 4975.83i	− 0.225374i	−0.993631	−	0.112687i	$-0.964054\pi$
$787$	− 4975.83i	− 0.225374i	0.993631	−	0.112687i	$-0.0359457\pi$
$788$	− 2651.99i	− 0.119890i
$789$	2257.85	0.101878
$790$	0	0
$791$	44814.2	2.01442
$792$	− 1702.93i	− 0.0764030i
$793$	9504.13i	0.425601i
$794$	47189.0	2.10916
$795$	0	0
$796$	3684.79	0.164075
$797$	13663.9i	0.607276i	0.952787	+	0.303638i	$0.0982014\pi$
$797$	13663.9i	0.607276i	−0.952787	+	0.303638i	$0.901799\pi$
$798$	− 41228.0i	− 1.82889i
$799$	−40846.2	−1.80855
$800$	0	0
$801$	−8996.27	−0.396838
$802$	− 3322.77i	− 0.146298i
$803$	− 4051.33i	− 0.178043i
$804$	7092.79	0.311124
$805$	0	0
$806$	10645.7	0.465232
$807$	− 14021.6i	− 0.611630i
$808$	− 1155.19i	− 0.0502964i
$809$	536.654	0.0233223	0.0116612	−	0.999932i	$-0.496288\pi$
$809$	536.654	0.0233223	0.0116612	+	0.999932i	$0.496288\pi$
$810$	0	0
$811$	7711.19	0.333880	0.166940	−	0.985967i	$-0.446611\pi$
$811$	7711.19	0.333880	0.166940	+	0.985967i	$0.446611\pi$
$812$	− 21871.2i	− 0.945233i
$813$	24436.4i	1.05415i
$814$	6006.48	0.258633
$815$	0	0
$816$	16405.1	0.703791
$817$	− 58245.8i	− 2.49420i
$818$	3801.34i	0.162483i
$819$	−7285.76	−0.310849
$820$	0	0
$821$	10451.9	0.444305	0.222152	−	0.975012i	$-0.428692\pi$
$821$	10451.9	0.444305	0.222152	+	0.975012i	$0.428692\pi$
$822$	4453.79i	0.188983i
$823$	17400.3i	0.736983i	0.929631	+	0.368491i	$0.120126\pi$
$823$	17400.3i	0.736983i	−0.929631	+	0.368491i	$0.879874\pi$
$824$	−13989.6	−0.591444
$825$	0	0
$826$	34189.3	1.44019
$827$	18828.3i	0.791684i	0.918319	+	0.395842i	$0.129547\pi$
$827$	18828.3i	0.791684i	−0.918319	+	0.395842i	$0.870453\pi$
$828$	3238.68i	0.135932i
$829$	−34431.9	−1.44254	−0.721272	−	0.692652i	$-0.756442\pi$
$829$	−34431.9	−1.44254	−0.721272	+	0.692652i	$0.756442\pi$
$830$	0	0
$831$	−17412.8	−0.726889
$832$	5711.50i	0.237994i
$833$	53539.8i	2.22694i
$834$	−8708.00	−0.361551
$835$	0	0
$836$	3809.61	0.157605
$837$	− 3608.91i	− 0.149035i
$838$	− 31846.9i	− 1.31281i
$839$	−39094.5	−1.60869	−0.804346	−	0.594162i	$-0.797484\pi$
$839$	−39094.5	−1.60869	−0.804346	+	0.594162i	$0.797484\pi$
$840$	0	0
$841$	32341.4	1.32606
$842$	− 11405.5i	− 0.466818i
$843$	− 23552.0i	− 0.962249i
$844$	−12063.0	−0.491973
$845$	0	0
$846$	17295.3	0.702865
$847$	4033.29i	0.163619i
$848$	3144.61i	0.127342i
$849$	−21275.3	−0.860032
$850$	0	0
$851$	21750.1	0.876126
$852$	− 4818.39i	− 0.193750i
$853$	− 38765.9i	− 1.55606i	−0.628228	−	0.778029i	$-0.716220\pi$
$853$	− 38765.9i	− 1.55606i	0.628228	−	0.778029i	$-0.283780\pi$
$854$	−42778.8	−1.71412
$855$	0	0
$856$	10284.9	0.410666
$857$	4057.20i	0.161717i	0.996726	+	0.0808584i	$0.0257661\pi$
$857$	4057.20i	0.161717i	−0.996726	+	0.0808584i	$0.974234\pi$
$858$	− 2628.30i	− 0.104579i
$859$	−32753.0	−1.30095	−0.650477	−	0.759526i	$-0.725431\pi$
$859$	−32753.0	−1.30095	−0.650477	+	0.759526i	$0.725431\pi$
$860$	0	0
$861$	29794.8	1.17933
$862$	22130.6i	0.874445i
$863$	47506.8i	1.87387i	0.349501	+	0.936936i	$0.386351\pi$
$863$	47506.8i	1.87387i	−0.349501	+	0.936936i	$0.613649\pi$
$864$	−3230.83	−0.127217
$865$	0	0
$866$	17645.9	0.692415
$867$	− 162.388i	− 0.00636100i
$868$	12273.7i	0.479952i
$869$	−4828.28	−0.188479
$870$	0	0
$871$	−20843.2	−0.810842
$872$	20243.4i	0.786156i
$873$	− 11756.8i	− 0.455792i
$874$	53855.8	2.08433
$875$	0	0
$876$	−3043.81	−0.117398
$877$	− 22933.4i	− 0.883016i	−0.897257	−	0.441508i	$-0.854444\pi$
$877$	− 22933.4i	− 0.883016i	0.897257	−	0.441508i	$-0.145556\pi$
$878$	− 3591.30i	− 0.138042i
$879$	23388.1	0.897452
$880$	0	0
$881$	152.937	0.00584854	0.00292427	−	0.999996i	$-0.499069\pi$
$881$	152.937	0.00584854	0.00292427	+	0.999996i	$0.499069\pi$
$882$	− 22670.1i	− 0.865466i
$883$	− 41553.9i	− 1.58369i	−0.610722	−	0.791845i	$-0.709121\pi$
$883$	− 41553.9i	− 1.58369i	0.610722	−	0.791845i	$-0.290879\pi$
$884$	4663.56	0.177435
$885$	0	0
$886$	−10386.4	−0.393834
$887$	− 41795.1i	− 1.58212i	−0.611736	−	0.791062i	$-0.709529\pi$
$887$	− 41795.1i	− 1.58212i	0.611736	−	0.791062i	$-0.290471\pi$
$888$	8592.31i	0.324706i
$889$	31533.7	1.18966
$890$	0	0
$891$	−891.000	−0.0335013
$892$	2536.23i	0.0952011i
$893$	− 73668.2i	− 2.76060i
$894$	−26125.5	−0.977370
$895$	0	0
$896$	−57617.0	−2.14827
$897$	− 9517.33i	− 0.354264i
$898$	− 1282.44i	− 0.0476566i
$899$	−31836.1	−1.18108
$900$	0	0
$901$	−2794.11	−0.103313
$902$	10748.3i	0.396761i
$903$	− 46330.1i	− 1.70739i
$904$	−23126.2	−0.850848
$905$	0	0
$906$	3506.37	0.128578
$907$	11144.0i	0.407973i	0.978974	+	0.203987i	$0.0653899\pi$
$907$	11144.0i	0.407973i	−0.978974	+	0.203987i	$0.934610\pi$
$908$	2038.04i	0.0744874i
$909$	−604.413	−0.0220540
$910$	0	0
$911$	38572.8	1.40282	0.701412	−	0.712756i	$-0.252553\pi$
$911$	38572.8	1.40282	0.701412	+	0.712756i	$0.252553\pi$
$912$	29587.5i	1.07428i
$913$	9654.07i	0.349949i
$914$	−8406.61	−0.304230
$915$	0	0
$916$	11654.9	0.420401
$917$	− 32478.0i	− 1.16959i
$918$	− 6172.10i	− 0.221906i
$919$	15020.5	0.539152	0.269576	−	0.962979i	$-0.413117\pi$
$919$	15020.5	0.539152	0.269576	+	0.962979i	$0.413117\pi$
$920$	0	0
$921$	15155.3	0.542221
$922$	20173.8i	0.720595i
$923$	14159.5i	0.504947i
$924$	3030.25	0.107887
$925$	0	0
$926$	32248.9	1.14446
$927$	7319.54i	0.259337i
$928$	28500.9i	1.00818i
$929$	32208.5	1.13749	0.568744	−	0.822515i	$-0.307430\pi$
$929$	32208.5	1.13749	0.568744	+	0.822515i	$0.307430\pi$
$930$	0	0
$931$	−96561.9	−3.39923
$932$	− 14652.7i	− 0.514984i
$933$	− 10599.3i	− 0.371925i
$934$	24294.9	0.851127
$935$	0	0
$936$	3759.80	0.131296
$937$	34189.4i	1.19202i	0.802979	+	0.596008i	$0.203247\pi$
$937$	34189.4i	1.19202i	−0.802979	+	0.596008i	$0.796753\pi$
$938$	− 93816.6i	− 3.26569i
$939$	10129.0	0.352021
$940$	0	0
$941$	−31309.9	−1.08467	−0.542334	−	0.840163i	$-0.682459\pi$
$941$	−31309.9	−1.08467	−0.542334	+	0.840163i	$0.682459\pi$
$942$	− 23414.1i	− 0.809844i
$943$	38920.7i	1.34404i
$944$	−24536.1	−0.845956
$945$	0	0
$946$	16713.3	0.574415
$947$	14608.5i	0.501281i	0.968080	+	0.250641i	$0.0806412\pi$
$947$	14608.5i	0.501281i	−0.968080	+	0.250641i	$0.919359\pi$
$948$	3627.54i	0.124280i
$949$	8944.67	0.305960
$950$	0	0
$951$	−8773.62	−0.299163
$952$	− 39967.2i	− 1.36066i
$953$	− 25778.5i	− 0.876230i	−0.898919	−	0.438115i	$-0.855646\pi$
$953$	− 25778.5i	− 0.876230i	0.898919	−	0.438115i	$-0.144354\pi$
$954$	1183.10	0.0401511
$955$	0	0
$956$	10810.6	0.365733
$957$	7859.99i	0.265493i
$958$	− 27079.1i	− 0.913241i
$959$	15089.7	0.508104
$960$	0	0
$961$	−11925.1	−0.400293
$962$	13261.3i	0.444451i
$963$	− 5381.20i	− 0.180069i
$964$	11565.9	0.386423
$965$	0	0
$966$	42838.2	1.42681
$967$	17308.2i	0.575588i	0.957692	+	0.287794i	$0.0929219\pi$
$967$	17308.2i	0.575588i	−0.957692	+	0.287794i	$0.907078\pi$
$968$	− 2081.36i	− 0.0691091i
$969$	−26289.7	−0.871565
$970$	0	0
$971$	22356.6	0.738886	0.369443	−	0.929253i	$-0.379549\pi$
$971$	22356.6	0.738886	0.369443	+	0.929253i	$0.379549\pi$
$972$	669.418i	0.0220901i
$973$	29503.2i	0.972076i
$974$	33079.1	1.08822
$975$	0	0
$976$	30700.4	1.00686
$977$	− 3453.54i	− 0.113090i	−0.998400	−	0.0565449i	$-0.981992\pi$
$977$	− 3453.54i	− 0.113090i	0.998400	−	0.0565449i	$-0.0180084\pi$
$978$	6412.38i	0.209658i
$979$	−10995.4	−0.358954
$980$	0	0
$981$	10591.6	0.344715
$982$	20801.9i	0.675983i
$983$	− 16391.6i	− 0.531853i	−0.963993	−	0.265926i	$-0.914322\pi$
$983$	− 16391.6i	− 0.531853i	0.963993	−	0.265926i	$-0.0856778\pi$
$984$	−15375.5	−0.498123
$985$	0	0
$986$	−54447.4	−1.75858
$987$	− 58597.4i	− 1.88974i
$988$	8410.98i	0.270839i
$989$	60520.6	1.94585
$990$	0	0
$991$	−36513.7	−1.17043	−0.585216	−	0.810878i	$-0.698990\pi$
$991$	−36513.7	−1.17043	−0.585216	+	0.810878i	$0.698990\pi$
$992$	− 15994.2i	− 0.511912i
$993$	− 30158.6i	− 0.963800i
$994$	−63733.0	−2.03369
$995$	0	0
$996$	7253.21	0.230750
$997$	32452.1i	1.03086i	0.856931	+	0.515430i	$0.172368\pi$
$997$	32452.1i	1.03086i	−0.856931	+	0.515430i	$0.827632\pi$
$998$	− 32343.2i	− 1.02586i
$999$	4495.62	0.142378

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	825.4.c.o.199.1		6
5.2	odd	4		165.4.a.f.1.3	✓	3
5.3	odd	4		825.4.a.n.1.1		3
5.4	even	2	inner	825.4.c.o.199.6		6
15.2	even	4		495.4.a.g.1.1		3
15.8	even	4		2475.4.a.w.1.3		3
55.32	even	4		1815.4.a.p.1.1		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
165.4.a.f.1.3	✓	3	5.2	odd	4
495.4.a.g.1.1		3	15.2	even	4
825.4.a.n.1.1		3	5.3	odd	4
825.4.c.o.199.1		6	1.1	even	1	trivial
825.4.c.o.199.6		6	5.4	even	2	inner
1815.4.a.p.1.1		3	55.32	even	4
2475.4.a.w.1.3		3	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:	\( N \)	\(=\)	\( 825 = 3 \cdot 5^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	825.c (of order \(2\), degree \(1\), not minimal)

\(f(q)\)	\(=\)	\(q-3.27945i q^{2} -3.00000i q^{3} -2.75481 q^{4} -9.83836 q^{6} +33.3329i q^{7} -17.2014i q^{8} -9.00000 q^{9} +O(q^{10})\)	\(q-3.27945i q^{2} -3.00000i q^{3} -2.75481 q^{4} -9.83836 q^{6} +33.3329i q^{7} -17.2014i q^{8} -9.00000 q^{9} -11.0000 q^{11} +8.26442i q^{12} -24.2862i q^{13} +109.314 q^{14} -78.4495 q^{16} -69.7056i q^{17} +29.5151i q^{18} +125.718 q^{19} +99.9988 q^{21} +36.0740i q^{22} +130.628i q^{23} -51.6041 q^{24} -79.6453 q^{26} +27.0000i q^{27} -91.8258i q^{28} +238.181 q^{29} -133.663 q^{31} +119.661i q^{32} +33.0000i q^{33} -228.596 q^{34} +24.7933 q^{36} -166.505i q^{37} -412.285i q^{38} -72.8585 q^{39} +297.951 q^{41} -327.941i q^{42} -463.307i q^{43} +30.3029 q^{44} +428.387 q^{46} -585.981i q^{47} +235.348i q^{48} -768.085 q^{49} -209.117 q^{51} +66.9037i q^{52} -40.0845i q^{53} +88.5452 q^{54} +573.372 q^{56} -377.153i q^{57} -781.105i q^{58} +312.763 q^{59} -391.339 q^{61} +438.342i q^{62} -299.996i q^{63} -235.175 q^{64} +108.222 q^{66} -858.232i q^{67} +192.026i q^{68} +391.883 q^{69} -583.028 q^{71} +154.812i q^{72} +368.303i q^{73} -546.044 q^{74} -346.328 q^{76} -366.662i q^{77} +238.936i q^{78} +438.935 q^{79} +81.0000 q^{81} -977.117i q^{82} -877.643i q^{83} -275.478 q^{84} -1519.39 q^{86} -714.544i q^{87} +189.215i q^{88} +999.585 q^{89} +809.529 q^{91} -359.854i q^{92} +400.990i q^{93} -1921.70 q^{94} +358.982 q^{96} +1306.31i q^{97} +2518.90i q^{98} +99.0000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + 10 q^{4} - 6 q^{6} - 54 q^{9}+O(q^{10}) \) 6 * q + 10 * q^4 - 6 * q^6 - 54 * q^9	\( 6 q + 10 q^{4} - 6 q^{6} - 54 q^{9} - 66 q^{11} + 152 q^{14} - 170 q^{16} + 560 q^{19} + 96 q^{21} - 18 q^{24} - 628 q^{26} + 580 q^{29} - 784 q^{31} - 620 q^{34} - 90 q^{36} - 252 q^{39} - 1324 q^{41} - 110 q^{44} + 1456 q^{46} - 1462 q^{49} + 204 q^{51} + 54 q^{54} + 408 q^{56} + 1224 q^{59} - 1164 q^{61} - 694 q^{64} + 66 q^{66} - 672 q^{69} - 3232 q^{71} + 1284 q^{74} + 1760 q^{76} - 248 q^{79} + 486 q^{81} - 1680 q^{84} - 2000 q^{86} - 1676 q^{89} - 3472 q^{91} - 4864 q^{94} + 138 q^{96} + 594 q^{99}+O(q^{100}) \) 6 * q + 10 * q^4 - 6 * q^6 - 54 * q^9 - 66 * q^11 + 152 * q^14 - 170 * q^16 + 560 * q^19 + 96 * q^21 - 18 * q^24 - 628 * q^26 + 580 * q^29 - 784 * q^31 - 620 * q^34 - 90 * q^36 - 252 * q^39 - 1324 * q^41 - 110 * q^44 + 1456 * q^46 - 1462 * q^49 + 204 * q^51 + 54 * q^54 + 408 * q^56 + 1224 * q^59 - 1164 * q^61 - 694 * q^64 + 66 * q^66 - 672 * q^69 - 3232 * q^71 + 1284 * q^74 + 1760 * q^76 - 248 * q^79 + 486 * q^81 - 1680 * q^84 - 2000 * q^86 - 1676 * q^89 - 3472 * q^91 - 4864 * q^94 + 138 * q^96 + 594 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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