LMFDB - Embedded newform 825.4.c.o.199.3

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			199.3
Root			$0.229681 + 0.229681i$ of defining polynomial
Character	$\chi$	$=$	825.199
Dual form			825.4.c.o.199.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-0.540637i q^{2} -3.00000i q^{3} +7.70771 q^{4} -1.62191 q^{6} -24.4573i q^{7} -8.49217i q^{8} -9.00000 q^{9} +O(q^{10})$	\(q-0.540637i q^{2} -3.00000i q^{3} +7.70771 q^{4} -1.62191 q^{6} -24.4573i q^{7} -8.49217i q^{8} -9.00000 q^{9} -11.0000 q^{11} -23.1231i q^{12} -84.5976i q^{13} -13.2225 q^{14} +57.0705 q^{16} +62.8005i q^{17} +4.86573i q^{18} +159.134 q^{19} -73.3719 q^{21} +5.94701i q^{22} -114.445i q^{23} -25.4765 q^{24} -45.7366 q^{26} +27.0000i q^{27} -188.510i q^{28} -172.871 q^{29} +8.87004 q^{31} -98.7918i q^{32} +33.0000i q^{33} +33.9523 q^{34} -69.3694 q^{36} +14.9224i q^{37} -86.0336i q^{38} -253.793 q^{39} -463.669 q^{41} +39.6675i q^{42} +486.261i q^{43} -84.7848 q^{44} -61.8732 q^{46} +118.342i q^{47} -171.212i q^{48} -255.159 q^{49} +188.401 q^{51} -652.054i q^{52} -273.331i q^{53} +14.5972 q^{54} -207.695 q^{56} -477.401i q^{57} +93.4603i q^{58} +884.982 q^{59} -347.633 q^{61} -4.79547i q^{62} +220.116i q^{63} +403.154 q^{64} +17.8410 q^{66} -720.101i q^{67} +484.048i q^{68} -343.335 q^{69} -71.7282 q^{71} +76.4295i q^{72} +146.619i q^{73} +8.06763 q^{74} +1226.56 q^{76} +269.030i q^{77} +137.210i q^{78} -147.287 q^{79} +81.0000 q^{81} +250.677i q^{82} -399.060i q^{83} -565.529 q^{84} +262.891 q^{86} +518.612i q^{87} +93.4139i q^{88} -1027.83 q^{89} -2069.03 q^{91} -882.109i q^{92} -26.6101i q^{93} +63.9799 q^{94} -296.375 q^{96} -1646.09i q^{97} +137.948i q^{98} +99.0000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	− 0.540637i	− 0.191144i	−0.995423	−	0.0955720i	$-0.969532\pi$
$2$	− 0.540637i	− 0.191144i	0.995423	−	0.0955720i	$-0.0304680\pi$
$3$	− 3.00000i	− 0.577350i
$3$	− 3.00000i	− 0.577350i
$4$	7.70771	0.963464
$5$	0	0
$5$	0	0
$6$	−1.62191	−0.110357
$7$	− 24.4573i	− 1.32057i	−0.751015	−	0.660285i	$-0.770436\pi$
$7$	− 24.4573i	− 1.32057i	0.751015	−	0.660285i	$-0.229564\pi$
$8$	− 8.49217i	− 0.375304i
$9$	−9.00000	−0.333333
$10$	0	0
$11$	−11.0000	−0.301511
$11$	−11.0000	−0.301511
$12$	− 23.1231i	− 0.556256i
$13$	− 84.5976i	− 1.80486i	−0.430839	−	0.902429i	$-0.641782\pi$
$13$	− 84.5976i	− 1.80486i	0.430839	−	0.902429i	$-0.358218\pi$
$14$	−13.2225	−0.252419
$15$	0	0
$16$	57.0705	0.891727
$17$	62.8005i	0.895962i	0.894043	+	0.447981i	$0.147857\pi$
$17$	62.8005i	0.895962i	−0.894043	+	0.447981i	$0.852143\pi$
$18$	4.86573i	0.0637147i
$19$	159.134	1.92146	0.960731	−	0.277482i	$-0.0894999\pi$
$19$	159.134	1.92146	0.960731	+	0.277482i	$0.0894999\pi$
$20$	0	0
$21$	−73.3719	−0.762431
$22$	5.94701i	0.0576321i
$23$	− 114.445i	− 1.03754i	−0.854914	−	0.518770i	$-0.826390\pi$
$23$	− 114.445i	− 1.03754i	0.854914	−	0.518770i	$-0.173610\pi$
$24$	−25.4765	−0.216682
$25$	0	0
$26$	−45.7366	−0.344988
$27$	27.0000i	0.192450i
$28$	− 188.510i	− 1.27232i
$29$	−172.871	−1.10694	−0.553471	−	0.832869i	$-0.686697\pi$
$29$	−172.871	−1.10694	−0.553471	+	0.832869i	$0.686697\pi$
$30$	0	0
$31$	8.87004	0.0513905	0.0256953	−	0.999670i	$-0.491820\pi$
$31$	8.87004	0.0513905	0.0256953	+	0.999670i	$0.491820\pi$
$32$	− 98.7918i	− 0.545753i
$33$	33.0000i	0.174078i
$34$	33.9523	0.171258
$35$	0	0
$36$	−69.3694	−0.321155
$37$	14.9224i	0.0663036i	0.999450	+	0.0331518i	$0.0105545\pi$
$37$	14.9224i	0.0663036i	−0.999450	+	0.0331518i	$0.989446\pi$
$38$	− 86.0336i	− 0.367276i
$39$	−253.793	−1.04203
$40$	0	0
$41$	−463.669	−1.76617	−0.883085	−	0.469213i	$-0.844538\pi$
$41$	−463.669	−1.76617	−0.883085	+	0.469213i	$0.844538\pi$
$42$	39.6675i	0.145734i
$43$	486.261i	1.72452i	0.506469	+	0.862258i	$0.330950\pi$
$43$	486.261i	1.72452i	−0.506469	+	0.862258i	$0.669050\pi$
$44$	−84.7848	−0.290495
$45$	0	0
$46$	−61.8732	−0.198320
$47$	118.342i	0.367275i	0.982994	+	0.183637i	$0.0587872\pi$
$47$	118.342i	0.367275i	−0.982994	+	0.183637i	$0.941213\pi$
$48$	− 171.212i	− 0.514839i
$49$	−255.159	−0.743903
$50$	0	0
$51$	188.401	0.517284
$52$	− 652.054i	− 1.73891i
$53$	− 273.331i	− 0.708395i	−0.935171	−	0.354198i	$-0.884754\pi$
$53$	− 273.331i	− 0.708395i	0.935171	−	0.354198i	$-0.115246\pi$
$54$	14.5972	0.0367857
$55$	0	0
$56$	−207.695	−0.495616
$57$	− 477.401i	− 1.10936i
$58$	93.4603i	0.211585i
$59$	884.982	1.95279	0.976397	−	0.215982i	$-0.0692953\pi$
$59$	884.982	1.95279	0.976397	+	0.215982i	$0.0692953\pi$
$60$	0	0
$61$	−347.633	−0.729670	−0.364835	−	0.931072i	$-0.618875\pi$
$61$	−347.633	−0.729670	−0.364835	+	0.931072i	$0.618875\pi$
$62$	− 4.79547i	− 0.00982299i
$63$	220.116i	0.440190i
$64$	403.154	0.787409
$65$	0	0
$66$	17.8410	0.0332739
$67$	− 720.101i	− 1.31305i	−0.754305	−	0.656525i	$-0.772026\pi$
$67$	− 720.101i	− 1.31305i	0.754305	−	0.656525i	$-0.227974\pi$
$68$	484.048i	0.863227i
$69$	−343.335	−0.599024
$70$	0	0
$71$	−71.7282	−0.119895	−0.0599477	−	0.998202i	$-0.519093\pi$
$71$	−71.7282	−0.119895	−0.0599477	+	0.998202i	$0.519093\pi$
$72$	76.4295i	0.125101i
$73$	146.619i	0.235075i	0.993068	+	0.117537i	$0.0375000\pi$
$73$	146.619i	0.235075i	−0.993068	+	0.117537i	$0.962500\pi$
$74$	8.06763	0.0126735
$75$	0	0
$76$	1226.56	1.85126
$77$	269.030i	0.398167i
$78$	137.210i	0.199179i
$79$	−147.287	−0.209760	−0.104880	−	0.994485i	$-0.533446\pi$
$79$	−147.287	−0.209760	−0.104880	+	0.994485i	$0.533446\pi$
$80$	0	0
$81$	81.0000	0.111111
$82$	250.677i	0.337593i
$83$	− 399.060i	− 0.527742i	−0.964558	−	0.263871i	$-0.915001\pi$
$83$	− 399.060i	− 0.527742i	0.964558	−	0.263871i	$-0.0849993\pi$
$84$	−565.529	−0.734575
$85$	0	0
$86$	262.891	0.329631
$87$	518.612i	0.639093i
$88$	93.4139i	0.113159i
$89$	−1027.83	−1.22415	−0.612076	−	0.790799i	$-0.709665\pi$
$89$	−1027.83	−1.22415	−0.612076	+	0.790799i	$0.709665\pi$
$90$	0	0
$91$	−2069.03	−2.38344
$92$	− 882.109i	− 0.999633i
$93$	− 26.6101i	− 0.0296703i
$94$	63.9799	0.0702024
$95$	0	0
$96$	−296.375	−0.315090
$97$	− 1646.09i	− 1.72305i	−0.507718	−	0.861523i	$-0.669511\pi$
$97$	− 1646.09i	− 1.72305i	0.507718	−	0.861523i	$-0.330489\pi$
$98$	137.948i	0.142193i
$99$	99.0000	0.100504
$100$	0	0
$101$	665.023	0.655171	0.327586	−	0.944822i	$-0.393765\pi$
$101$	665.023	0.655171	0.327586	+	0.944822i	$0.393765\pi$
$102$	− 101.857i	− 0.0988758i
$103$	277.431i	0.265399i	0.991156	+	0.132699i	$0.0423645\pi$
$103$	277.431i	0.265399i	−0.991156	+	0.132699i	$0.957635\pi$
$104$	−718.417	−0.677371
$105$	0	0
$106$	−147.773	−0.135406
$107$	1025.77i	0.926778i	0.886155	+	0.463389i	$0.153367\pi$
$107$	1025.77i	0.926778i	−0.886155	+	0.463389i	$0.846633\pi$
$108$	208.108i	0.185419i
$109$	−276.776	−0.243214	−0.121607	−	0.992578i	$-0.538805\pi$
$109$	−276.776	−0.243214	−0.121607	+	0.992578i	$0.538805\pi$
$110$	0	0
$111$	44.7673	0.0382804
$112$	− 1395.79i	− 1.17759i
$113$	1367.93i	1.13880i	0.822062	+	0.569398i	$0.192824\pi$
$113$	1367.93i	1.13880i	−0.822062	+	0.569398i	$0.807176\pi$
$114$	−258.101	−0.212047
$115$	0	0
$116$	−1332.44	−1.06650
$117$	761.378i	0.601619i
$118$	− 478.454i	− 0.373265i
$119$	1535.93	1.18318
$120$	0	0
$121$	121.000	0.0909091
$122$	187.943i	0.139472i
$123$	1391.01i	1.01970i
$124$	68.3677	0.0495129
$125$	0	0
$126$	119.003	0.0841397
$127$	− 1778.73i	− 1.24281i	−0.783491	−	0.621404i	$-0.786563\pi$
$127$	− 1778.73i	− 1.24281i	0.783491	−	0.621404i	$-0.213437\pi$
$128$	− 1008.29i	− 0.696261i
$129$	1458.78	0.995650
$130$	0	0
$131$	−2344.56	−1.56371	−0.781853	−	0.623463i	$-0.785725\pi$
$131$	−2344.56	−1.56371	−0.781853	+	0.623463i	$0.785725\pi$
$132$	254.354i	0.167718i
$133$	− 3891.98i	− 2.53742i
$134$	−389.313	−0.250982
$135$	0	0
$136$	533.312	0.336259
$137$	− 279.153i	− 0.174085i	−0.996205	−	0.0870426i	$-0.972258\pi$
$137$	− 279.153i	− 0.174085i	0.996205	−	0.0870426i	$-0.0277416\pi$
$138$	185.620i	0.114500i
$139$	242.024	0.147685	0.0738424	−	0.997270i	$-0.476474\pi$
$139$	242.024	0.147685	0.0738424	+	0.997270i	$0.476474\pi$
$140$	0	0
$141$	355.025	0.212046
$142$	38.7789i	0.0229173i
$143$	930.573i	0.544185i
$144$	−513.635	−0.297242
$145$	0	0
$146$	79.2677	0.0449332
$147$	765.476i	0.429493i
$148$	115.018i	0.0638812i
$149$	98.5918	0.0542078	0.0271039	−	0.999633i	$-0.491372\pi$
$149$	98.5918	0.0542078	0.0271039	+	0.999633i	$0.491372\pi$
$150$	0	0
$151$	−694.131	−0.374090	−0.187045	−	0.982351i	$-0.559891\pi$
$151$	−694.131	−0.374090	−0.187045	+	0.982351i	$0.559891\pi$
$152$	− 1351.39i	− 0.721133i
$153$	− 565.204i	− 0.298654i
$154$	145.448	0.0761072
$155$	0	0
$156$	−1956.16	−1.00396
$157$	2975.80i	1.51270i	0.654165	+	0.756352i	$0.273020\pi$
$157$	2975.80i	1.51270i	−0.654165	+	0.756352i	$0.726980\pi$
$158$	79.6287i	0.0400944i
$159$	−819.994	−0.408992
$160$	0	0
$161$	−2799.01	−1.37014
$162$	− 43.7916i	− 0.0212382i
$163$	− 1225.21i	− 0.588747i	−0.955691	−	0.294373i	$-0.904889\pi$
$163$	− 1225.21i	− 0.588747i	0.955691	−	0.294373i	$-0.0951109\pi$
$164$	−3573.83	−1.70164
$165$	0	0
$166$	−215.747	−0.100875
$167$	766.003i	0.354941i	0.984126	+	0.177470i	$0.0567914\pi$
$167$	766.003i	0.354941i	−0.984126	+	0.177470i	$0.943209\pi$
$168$	623.086i	0.286144i
$169$	−4959.75	−2.25751
$170$	0	0
$171$	−1432.20	−0.640487
$172$	3747.96i	1.66151i
$173$	1578.45i	0.693683i	0.937924	+	0.346841i	$0.112746\pi$
$173$	1578.45i	0.693683i	−0.937924	+	0.346841i	$0.887254\pi$
$174$	280.381	0.122159
$175$	0	0
$176$	−627.776	−0.268866
$177$	− 2654.95i	− 1.12745i
$178$	555.682i	0.233989i
$179$	4150.20	1.73296	0.866481	−	0.499210i	$-0.166376\pi$
$179$	4150.20	1.73296	0.866481	+	0.499210i	$0.166376\pi$
$180$	0	0
$181$	2591.13	1.06407	0.532036	−	0.846722i	$-0.321427\pi$
$181$	2591.13	1.06407	0.532036	+	0.846722i	$0.321427\pi$
$182$	1118.59i	0.455580i
$183$	1042.90i	0.421275i
$184$	−971.887	−0.389394
$185$	0	0
$186$	−14.3864	−0.00567131
$187$	− 690.805i	− 0.270143i
$188$	912.144i	0.353856i
$189$	660.347	0.254144
$190$	0	0
$191$	−3830.57	−1.45115	−0.725576	−	0.688142i	$-0.758427\pi$
$191$	−3830.57	−1.45115	−0.725576	+	0.688142i	$0.758427\pi$
$192$	− 1209.46i	− 0.454611i
$193$	387.202i	0.144411i	0.997390	+	0.0722057i	$0.0230038\pi$
$193$	387.202i	0.144411i	−0.997390	+	0.0722057i	$0.976996\pi$
$194$	−889.939	−0.329350
$195$	0	0
$196$	−1966.69	−0.716724
$197$	− 2993.61i	− 1.08267i	−0.840807	−	0.541335i	$-0.817919\pi$
$197$	− 2993.61i	− 1.08267i	0.840807	−	0.541335i	$-0.182081\pi$
$198$	− 53.5231i	− 0.0192107i
$199$	689.828	0.245732	0.122866	−	0.992423i	$-0.460792\pi$
$199$	689.828	0.245732	0.122866	+	0.992423i	$0.460792\pi$
$200$	0	0
$201$	−2160.30	−0.758089
$202$	− 359.536i	− 0.125232i
$203$	4227.95i	1.46179i
$204$	1452.14	0.498384
$205$	0	0
$206$	149.989	0.0507294
$207$	1030.01i	0.345847i
$208$	− 4828.03i	− 1.60944i
$209$	−1750.47	−0.579342
$210$	0	0
$211$	−2554.57	−0.833476	−0.416738	−	0.909027i	$-0.636827\pi$
$211$	−2554.57	−0.833476	−0.416738	+	0.909027i	$0.636827\pi$
$212$	− 2106.76i	− 0.682513i
$213$	215.185i	0.0692216i
$214$	554.571	0.177148
$215$	0	0
$216$	229.289	0.0722274
$217$	− 216.937i	− 0.0678647i
$218$	149.636i	0.0464890i
$219$	439.857	0.135721
$220$	0	0
$221$	5312.77	1.61708
$222$	− 24.2029i	− 0.00731708i
$223$	− 449.417i	− 0.134956i	−0.997721	−	0.0674781i	$-0.978505\pi$
$223$	− 449.417i	− 0.134956i	0.997721	−	0.0674781i	$-0.0214953\pi$
$224$	−2416.18	−0.720704
$225$	0	0
$226$	739.553	0.217674
$227$	− 4262.02i	− 1.24617i	−0.782155	−	0.623084i	$-0.785880\pi$
$227$	− 4262.02i	− 1.24617i	0.782155	−	0.623084i	$-0.214120\pi$
$228$	− 3679.67i	− 1.06882i
$229$	983.839	0.283903	0.141952	−	0.989874i	$-0.454662\pi$
$229$	983.839	0.283903	0.141952	+	0.989874i	$0.454662\pi$
$230$	0	0
$231$	807.090	0.229882
$232$	1468.05i	0.415440i
$233$	3923.18i	1.10307i	0.834151	+	0.551537i	$0.185958\pi$
$233$	3923.18i	1.10307i	−0.834151	+	0.551537i	$0.814042\pi$
$234$	411.629	0.114996
$235$	0	0
$236$	6821.19	1.88145
$237$	441.861i	0.121105i
$238$	− 830.380i	− 0.226158i
$239$	5392.18	1.45938	0.729688	−	0.683780i	$-0.239665\pi$
$239$	5392.18	1.45938	0.729688	+	0.683780i	$0.239665\pi$
$240$	0	0
$241$	2558.11	0.683743	0.341872	−	0.939747i	$-0.388939\pi$
$241$	2558.11	0.683743	0.341872	+	0.939747i	$0.388939\pi$
$242$	− 65.4171i	− 0.0173767i
$243$	− 243.000i	− 0.0641500i
$244$	−2679.46	−0.703011
$245$	0	0
$246$	752.030	0.194909
$247$	− 13462.3i	− 3.46796i
$248$	− 75.3259i	− 0.0192871i
$249$	−1197.18	−0.304692
$250$	0	0
$251$	5870.83	1.47635	0.738175	−	0.674610i	$-0.235688\pi$
$251$	5870.83	1.47635	0.738175	+	0.674610i	$0.235688\pi$
$252$	1696.59i	0.424107i
$253$	1258.90i	0.312830i
$254$	−961.646	−0.237555
$255$	0	0
$256$	2680.11	0.654323
$257$	− 4608.31i	− 1.11852i	−0.828994	−	0.559258i	$-0.811086\pi$
$257$	− 4608.31i	− 1.11852i	0.828994	−	0.559258i	$-0.188914\pi$
$258$	− 788.673i	− 0.190313i
$259$	364.962	0.0875586
$260$	0	0
$261$	1555.84	0.368980
$262$	1267.56i	0.298893i
$263$	− 6160.04i	− 1.44427i	−0.691750	−	0.722137i	$-0.743160\pi$
$263$	− 6160.04i	− 1.44427i	0.691750	−	0.722137i	$-0.256840\pi$
$264$	280.242	0.0653321
$265$	0	0
$266$	−2104.15	−0.485013
$267$	3083.48i	0.706764i
$268$	− 5550.33i	− 1.26508i
$269$	5970.28	1.35321	0.676607	−	0.736345i	$-0.263450\pi$
$269$	5970.28	1.35321	0.676607	+	0.736345i	$0.263450\pi$
$270$	0	0
$271$	−254.406	−0.0570262	−0.0285131	−	0.999593i	$-0.509077\pi$
$271$	−254.406	−0.0570262	−0.0285131	+	0.999593i	$0.509077\pi$
$272$	3584.06i	0.798953i
$273$	6207.08i	1.37608i
$274$	−150.921	−0.0332754
$275$	0	0
$276$	−2646.33	−0.577138
$277$	3348.17i	0.726254i	0.931740	+	0.363127i	$0.118291\pi$
$277$	3348.17i	0.726254i	−0.931740	+	0.363127i	$0.881709\pi$
$278$	− 130.847i	− 0.0282291i
$279$	−79.8304	−0.0171302
$280$	0	0
$281$	−5180.11	−1.09971	−0.549856	−	0.835259i	$-0.685318\pi$
$281$	−5180.11	−1.09971	−0.549856	+	0.835259i	$0.685318\pi$
$282$	− 191.940i	− 0.0405314i
$283$	103.441i	0.0217276i	0.999941	+	0.0108638i	$0.00345812\pi$
$283$	103.441i	0.0217276i	−0.999941	+	0.0108638i	$0.996542\pi$
$284$	−552.860	−0.115515
$285$	0	0
$286$	503.102	0.104018
$287$	11340.1i	2.33235i
$288$	889.126i	0.181918i
$289$	969.099	0.197252
$290$	0	0
$291$	−4938.28	−0.994801
$292$	1130.10i	0.226486i
$293$	− 1434.88i	− 0.286098i	−0.989716	−	0.143049i	$-0.954309\pi$
$293$	− 1434.88i	− 0.286098i	0.989716	−	0.143049i	$-0.0456907\pi$
$294$	413.845	0.0820950
$295$	0	0
$296$	126.724	0.0248841
$297$	− 297.000i	− 0.0580259i
$298$	− 53.3024i	− 0.0103615i
$299$	−9681.77	−1.87261
$300$	0	0
$301$	11892.6	2.27734
$302$	375.273i	0.0715050i
$303$	− 1995.07i	− 0.378263i
$304$	9081.84	1.71342
$305$	0	0
$306$	−305.570	−0.0570859
$307$	4947.74i	0.919813i	0.887967	+	0.459906i	$0.152117\pi$
$307$	4947.74i	0.919813i	−0.887967	+	0.459906i	$0.847883\pi$
$308$	2073.61i	0.383619i
$309$	832.293	0.153228
$310$	0	0
$311$	3242.80	0.591261	0.295630	−	0.955302i	$-0.404470\pi$
$311$	3242.80	0.591261	0.295630	+	0.955302i	$0.404470\pi$
$312$	2155.25i	0.391080i
$313$	4165.44i	0.752219i	0.926575	+	0.376110i	$0.122738\pi$
$313$	4165.44i	0.752219i	−0.926575	+	0.376110i	$0.877262\pi$
$314$	1608.83	0.289144
$315$	0	0
$316$	−1135.24	−0.202096
$317$	984.108i	0.174363i	0.996192	+	0.0871814i	$0.0277860\pi$
$317$	984.108i	0.174363i	−0.996192	+	0.0871814i	$0.972214\pi$
$318$	443.319i	0.0781764i
$319$	1901.58	0.333755
$320$	0	0
$321$	3077.32	0.535076
$322$	1513.25i	0.261895i
$323$	9993.67i	1.72156i
$324$	624.325	0.107052
$325$	0	0
$326$	−662.393	−0.112535
$327$	830.329i	0.140420i
$328$	3937.56i	0.662851i
$329$	2894.32	0.485012
$330$	0	0
$331$	848.615	0.140919	0.0704594	−	0.997515i	$-0.477553\pi$
$331$	848.615	0.140919	0.0704594	+	0.997515i	$0.477553\pi$
$332$	− 3075.84i	− 0.508460i
$333$	− 134.302i	− 0.0221012i
$334$	414.130	0.0678448
$335$	0	0
$336$	−4187.37	−0.679880
$337$	1641.95i	0.265408i	0.991156	+	0.132704i	$0.0423660\pi$
$337$	1641.95i	0.265408i	−0.991156	+	0.132704i	$0.957634\pi$
$338$	2681.42i	0.431510i
$339$	4103.79	0.657484
$340$	0	0
$341$	−97.5704	−0.0154948
$342$	774.302i	0.122425i
$343$	− 2148.36i	− 0.338194i
$344$	4129.42	0.647219
$345$	0	0
$346$	853.367	0.132593
$347$	5603.99i	0.866968i	0.901161	+	0.433484i	$0.142716\pi$
$347$	5603.99i	0.866968i	−0.901161	+	0.433484i	$0.857284\pi$
$348$	3997.31i	0.615743i
$349$	10498.3	1.61021	0.805104	−	0.593134i	$-0.202109\pi$
$349$	10498.3	1.61021	0.805104	+	0.593134i	$0.202109\pi$
$350$	0	0
$351$	2284.13	0.347345
$352$	1086.71i	0.164551i
$353$	− 4641.38i	− 0.699818i	−0.936784	−	0.349909i	$-0.886213\pi$
$353$	− 4641.38i	− 0.699818i	0.936784	−	0.349909i	$-0.113787\pi$
$354$	−1435.36	−0.215505
$355$	0	0
$356$	−7922.20	−1.17943
$357$	− 4607.79i	− 0.683109i
$358$	− 2243.75i	− 0.331245i
$359$	3498.03	0.514259	0.257130	−	0.966377i	$-0.417223\pi$
$359$	3498.03	0.514259	0.257130	+	0.966377i	$0.417223\pi$
$360$	0	0
$361$	18464.5	2.69201
$362$	− 1400.86i	− 0.203391i
$363$	− 363.000i	− 0.0524864i
$364$	−15947.5	−2.29636
$365$	0	0
$366$	563.830	0.0805243
$367$	7905.90i	1.12448i	0.826974	+	0.562241i	$0.190061\pi$
$367$	7905.90i	1.12448i	−0.826974	+	0.562241i	$0.809939\pi$
$368$	− 6531.44i	− 0.925203i
$369$	4173.02	0.588723
$370$	0	0
$371$	−6684.94	−0.935485
$372$	− 205.103i	− 0.0285863i
$373$	− 6717.95i	− 0.932553i	−0.884639	−	0.466276i	$-0.845595\pi$
$373$	− 6717.95i	− 0.932553i	0.884639	−	0.466276i	$-0.154405\pi$
$374$	−373.475	−0.0516362
$375$	0	0
$376$	1004.98	0.137840
$377$	14624.4i	1.99787i
$378$	− 357.008i	− 0.0485781i
$379$	−5290.87	−0.717081	−0.358540	−	0.933514i	$-0.616725\pi$
$379$	−5290.87	−0.717081	−0.358540	+	0.933514i	$0.616725\pi$
$380$	0	0
$381$	−5336.18	−0.717535
$382$	2070.95i	0.277379i
$383$	2126.05i	0.283645i	0.989892	+	0.141822i	$0.0452962\pi$
$383$	2126.05i	0.283645i	−0.989892	+	0.141822i	$0.954704\pi$
$384$	−3024.88	−0.401987
$385$	0	0
$386$	209.336	0.0276034
$387$	− 4376.35i	− 0.574839i
$388$	− 12687.6i	− 1.66009i
$389$	6450.60	0.840766	0.420383	−	0.907347i	$-0.361896\pi$
$389$	6450.60	0.840766	0.420383	+	0.907347i	$0.361896\pi$
$390$	0	0
$391$	7187.20	0.929597
$392$	2166.85i	0.279190i
$393$	7033.69i	0.902806i
$394$	−1618.46	−0.206946
$395$	0	0
$396$	763.063	0.0968318
$397$	− 4222.91i	− 0.533858i	−0.963716	−	0.266929i	$-0.913991\pi$
$397$	− 4222.91i	− 0.533858i	0.963716	−	0.266929i	$-0.0860089\pi$
$398$	− 372.946i	− 0.0469701i
$399$	−11675.9	−1.46498
$400$	0	0
$401$	2987.95	0.372097	0.186049	−	0.982541i	$-0.440432\pi$
$401$	2987.95	0.372097	0.186049	+	0.982541i	$0.440432\pi$
$402$	1167.94i	0.144904i
$403$	− 750.384i	− 0.0927526i
$404$	5125.81	0.631234
$405$	0	0
$406$	2285.79	0.279413
$407$	− 164.147i	− 0.0199913i
$408$	− 1599.94i	− 0.194139i
$409$	286.412	0.0346263	0.0173131	−	0.999850i	$-0.494489\pi$
$409$	286.412	0.0346263	0.0173131	+	0.999850i	$0.494489\pi$
$410$	0	0
$411$	−837.460	−0.100508
$412$	2138.36i	0.255702i
$413$	− 21644.3i	− 2.57880i
$414$	556.859	0.0661066
$415$	0	0
$416$	−8357.55	−0.985006
$417$	− 726.071i	− 0.0852659i
$418$	946.369i	0.110738i
$419$	−1414.89	−0.164969	−0.0824845	−	0.996592i	$-0.526286\pi$
$419$	−1414.89	−0.164969	−0.0824845	+	0.996592i	$0.526286\pi$
$420$	0	0
$421$	8100.13	0.937710	0.468855	−	0.883275i	$-0.344667\pi$
$421$	8100.13	0.937710	0.468855	+	0.883275i	$0.344667\pi$
$422$	1381.09i	0.159314i
$423$	− 1065.08i	− 0.122425i
$424$	−2321.18	−0.265864
$425$	0	0
$426$	116.337	0.0132313
$427$	8502.17i	0.963580i
$428$	7906.37i	0.892917i
$429$	2791.72	0.314185
$430$	0	0
$431$	12755.5	1.42555	0.712775	−	0.701393i	$-0.247438\pi$
$431$	12755.5	1.42555	0.712775	+	0.701393i	$0.247438\pi$
$432$	1540.90i	0.171613i
$433$	4263.73i	0.473214i	0.971605	+	0.236607i	$0.0760354\pi$
$433$	4263.73i	0.473214i	−0.971605	+	0.236607i	$0.923965\pi$
$434$	−117.284	−0.0129719
$435$	0	0
$436$	−2133.31	−0.234328
$437$	− 18212.1i	− 1.99359i
$438$	− 237.803i	− 0.0259422i
$439$	8799.24	0.956640	0.478320	−	0.878186i	$-0.341246\pi$
$439$	8799.24	0.956640	0.478320	+	0.878186i	$0.341246\pi$
$440$	0	0
$441$	2296.43	0.247968
$442$	− 2872.28i	− 0.309096i
$443$	11232.7i	1.20470i	0.798232	+	0.602350i	$0.205769\pi$
$443$	11232.7i	1.20470i	−0.798232	+	0.602350i	$0.794231\pi$
$444$	345.054	0.0368818
$445$	0	0
$446$	−242.972	−0.0257961
$447$	− 295.775i	− 0.0312969i
$448$	− 9860.04i	− 1.03983i
$449$	−4742.40	−0.498458	−0.249229	−	0.968445i	$-0.580177\pi$
$449$	−4742.40	−0.498458	−0.249229	+	0.968445i	$0.580177\pi$
$450$	0	0
$451$	5100.36	0.532520
$452$	10543.6i	1.09719i
$453$	2082.39i	0.215981i
$454$	−2304.20	−0.238197
$455$	0	0
$456$	−4054.17	−0.416346
$457$	− 12201.9i	− 1.24897i	−0.781037	−	0.624485i	$-0.785309\pi$
$457$	− 12201.9i	− 1.24897i	0.781037	−	0.624485i	$-0.214691\pi$
$458$	− 531.900i	− 0.0542665i
$459$	−1695.61	−0.172428
$460$	0	0
$461$	−1649.61	−0.166659	−0.0833295	−	0.996522i	$-0.526555\pi$
$461$	−1649.61	−0.166659	−0.0833295	+	0.996522i	$0.526555\pi$
$462$	− 436.343i	− 0.0439405i
$463$	− 441.105i	− 0.0442762i	−0.999755	−	0.0221381i	$-0.992953\pi$
$463$	− 441.105i	− 0.0442762i	0.999755	−	0.0221381i	$-0.00704735\pi$
$464$	−9865.82	−0.987089
$465$	0	0
$466$	2121.02	0.210846
$467$	19680.6i	1.95012i	0.221936	+	0.975061i	$0.428762\pi$
$467$	19680.6i	1.95012i	−0.221936	+	0.975061i	$0.571238\pi$
$468$	5868.48i	0.579638i
$469$	−17611.7	−1.73397
$470$	0	0
$471$	8927.40	0.873360
$472$	− 7515.42i	− 0.732893i
$473$	− 5348.88i	− 0.519961i
$474$	238.886	0.0231485
$475$	0	0
$476$	11838.5	1.13995
$477$	2459.98i	0.236132i
$478$	− 2915.21i	− 0.278951i
$479$	−295.152	−0.0281541	−0.0140771	−	0.999901i	$-0.504481\pi$
$479$	−295.152	−0.0281541	−0.0140771	+	0.999901i	$0.504481\pi$
$480$	0	0
$481$	1262.40	0.119669
$482$	− 1383.01i	− 0.130694i
$483$	8397.04i	0.791053i
$484$	932.633	0.0875876
$485$	0	0
$486$	−131.375	−0.0122619
$487$	3091.36i	0.287645i	0.989604	+	0.143823i	$0.0459394\pi$
$487$	3091.36i	0.287645i	−0.989604	+	0.143823i	$0.954061\pi$
$488$	2952.16i	0.273849i
$489$	−3675.62	−0.339913
$490$	0	0
$491$	−1123.13	−0.103230	−0.0516150	−	0.998667i	$-0.516437\pi$
$491$	−1123.13	−0.103230	−0.0516150	+	0.998667i	$0.516437\pi$
$492$	10721.5i	0.982443i
$493$	− 10856.4i	− 0.991777i
$494$	−7278.23	−0.662881
$495$	0	0
$496$	506.218	0.0458263
$497$	1754.28i	0.158330i
$498$	647.240i	0.0582400i
$499$	−5350.39	−0.479993	−0.239997	−	0.970774i	$-0.577146\pi$
$499$	−5350.39	−0.479993	−0.239997	+	0.970774i	$0.577146\pi$
$500$	0	0
$501$	2298.01	0.204925
$502$	− 3173.99i	− 0.282195i
$503$	5660.53i	0.501770i	0.968017	+	0.250885i	$0.0807217\pi$
$503$	5660.53i	0.501770i	−0.968017	+	0.250885i	$0.919278\pi$
$504$	1869.26	0.165205
$505$	0	0
$506$	680.605	0.0597957
$507$	14879.2i	1.30337i
$508$	− 13709.9i	− 1.19740i
$509$	12289.4	1.07017	0.535085	−	0.844798i	$-0.320280\pi$
$509$	12289.4	1.07017	0.535085	+	0.844798i	$0.320280\pi$
$510$	0	0
$511$	3585.90	0.310433
$512$	− 9515.32i	− 0.821331i
$513$	4296.61i	0.369785i
$514$	−2491.42	−0.213798
$515$	0	0
$516$	11243.9	0.959273
$517$	− 1301.76i	− 0.110737i
$518$	− 197.312i	− 0.0167363i
$519$	4735.34	0.400498
$520$	0	0
$521$	802.923	0.0675176	0.0337588	−	0.999430i	$-0.489252\pi$
$521$	802.923	0.0675176	0.0337588	+	0.999430i	$0.489252\pi$
$522$	− 841.143i	− 0.0705284i
$523$	562.939i	0.0470662i	0.999723	+	0.0235331i	$0.00749151\pi$
$523$	562.939i	0.0470662i	−0.999723	+	0.0235331i	$0.992508\pi$
$524$	−18071.2	−1.50657
$525$	0	0
$526$	−3330.34	−0.276064
$527$	557.043i	0.0460440i
$528$	1883.33i	0.155230i
$529$	−930.664	−0.0764909
$530$	0	0
$531$	−7964.84	−0.650932
$532$	− 29998.2i	− 2.44472i
$533$	39225.3i	3.18768i
$534$	1667.05	0.135094
$535$	0	0
$536$	−6115.22	−0.492793
$537$	− 12450.6i	− 1.00053i
$538$	− 3227.75i	− 0.258659i
$539$	2806.75	0.224295
$540$	0	0
$541$	−8245.16	−0.655244	−0.327622	−	0.944809i	$-0.606247\pi$
$541$	−8245.16	−0.655244	−0.327622	+	0.944809i	$0.606247\pi$
$542$	137.542i	0.0109002i
$543$	− 7773.38i	− 0.614342i
$544$	6204.17	0.488974
$545$	0	0
$546$	3355.78	0.263029
$547$	− 10946.2i	− 0.855625i	−0.903867	−	0.427813i	$-0.859284\pi$
$547$	− 10946.2i	− 0.855625i	0.903867	−	0.427813i	$-0.140716\pi$
$548$	− 2151.63i	− 0.167725i
$549$	3128.70	0.243223
$550$	0	0
$551$	−27509.6	−2.12695
$552$	2915.66i	0.224817i
$553$	3602.24i	0.277003i
$554$	1810.15	0.138819
$555$	0	0
$556$	1865.45	0.142289
$557$	6048.86i	0.460141i	0.973174	+	0.230070i	$0.0738956\pi$
$557$	6048.86i	0.460141i	−0.973174	+	0.230070i	$0.926104\pi$
$558$	43.1593i	0.00327433i
$559$	41136.5	3.11250
$560$	0	0
$561$	−2072.42	−0.155967
$562$	2800.56i	0.210204i
$563$	− 18879.8i	− 1.41330i	−0.707564	−	0.706649i	$-0.750206\pi$
$563$	− 18879.8i	− 1.41330i	0.707564	−	0.706649i	$-0.249794\pi$
$564$	2736.43	0.204299
$565$	0	0
$566$	55.9238	0.00415310
$567$	− 1981.04i	− 0.146730i
$568$	609.128i	0.0449973i
$569$	23781.0	1.75211	0.876054	−	0.482212i	$-0.160167\pi$
$569$	23781.0	1.75211	0.876054	+	0.482212i	$0.160167\pi$
$570$	0	0
$571$	−10182.2	−0.746259	−0.373129	−	0.927779i	$-0.621715\pi$
$571$	−10182.2	−0.746259	−0.373129	+	0.927779i	$0.621715\pi$
$572$	7172.59i	0.524303i
$573$	11491.7i	0.837823i
$574$	6130.87	0.445815
$575$	0	0
$576$	−3628.38	−0.262470
$577$	2750.10i	0.198420i	0.995067	+	0.0992100i	$0.0316316\pi$
$577$	2750.10i	0.198420i	−0.995067	+	0.0992100i	$0.968368\pi$
$578$	− 523.931i	− 0.0377035i
$579$	1161.61	0.0833760
$580$	0	0
$581$	−9759.93	−0.696919
$582$	2669.82i	0.190150i
$583$	3006.64i	0.213589i
$584$	1245.11	0.0882247
$585$	0	0
$586$	−775.751	−0.0546859
$587$	4733.04i	0.332800i	0.986058	+	0.166400i	$0.0532143\pi$
$587$	4733.04i	0.332800i	−0.986058	+	0.166400i	$0.946786\pi$
$588$	5900.07i	0.413801i
$589$	1411.52	0.0987449
$590$	0	0
$591$	−8980.83	−0.625079
$592$	851.632i	0.0591247i
$593$	1248.81i	0.0864797i	0.999065	+	0.0432399i	$0.0137680\pi$
$593$	1248.81i	0.0864797i	−0.999065	+	0.0432399i	$0.986232\pi$
$594$	−160.569	−0.0110913
$595$	0	0
$596$	759.917	0.0522272
$597$	− 2069.48i	− 0.141873i
$598$	5234.32i	0.357939i
$599$	6827.72	0.465731	0.232866	−	0.972509i	$-0.425190\pi$
$599$	6827.72	0.465731	0.232866	+	0.972509i	$0.425190\pi$
$600$	0	0
$601$	−14645.0	−0.993978	−0.496989	−	0.867757i	$-0.665561\pi$
$601$	−14645.0	−0.993978	−0.496989	+	0.867757i	$0.665561\pi$
$602$	− 6429.60i	− 0.435300i
$603$	6480.90i	0.437683i
$604$	−5350.16	−0.360422
$605$	0	0
$606$	−1078.61	−0.0723028
$607$	− 15358.6i	− 1.02700i	−0.858090	−	0.513499i	$-0.828349\pi$
$607$	− 15358.6i	− 1.02700i	0.858090	−	0.513499i	$-0.171651\pi$
$608$	− 15721.1i	− 1.04864i
$609$	12683.8	0.843966
$610$	0	0
$611$	10011.4	0.662878
$612$	− 4356.43i	− 0.287742i
$613$	− 1002.13i	− 0.0660287i	−0.999455	−	0.0330144i	$-0.989489\pi$
$613$	− 1002.13i	− 0.0660287i	0.999455	−	0.0330144i	$-0.0105107\pi$
$614$	2674.93	0.175817
$615$	0	0
$616$	2284.65	0.149434
$617$	− 24427.6i	− 1.59387i	−0.604063	−	0.796936i	$-0.706453\pi$
$617$	− 24427.6i	− 1.59387i	0.604063	−	0.796936i	$-0.293547\pi$
$618$	− 449.968i	− 0.0292886i
$619$	−2529.62	−0.164255	−0.0821275	−	0.996622i	$-0.526171\pi$
$619$	−2529.62	−0.164255	−0.0821275	+	0.996622i	$0.526171\pi$
$620$	0	0
$621$	3090.02	0.199675
$622$	− 1753.18i	− 0.113016i
$623$	25137.9i	1.61658i
$624$	−14484.1	−0.929210
$625$	0	0
$626$	2251.99	0.143782
$627$	5251.41i	0.334484i
$628$	22936.6i	1.45744i
$629$	−937.137	−0.0594056
$630$	0	0
$631$	−10750.5	−0.678245	−0.339122	−	0.940742i	$-0.610130\pi$
$631$	−10750.5	−0.678245	−0.339122	+	0.940742i	$0.610130\pi$
$632$	1250.79i	0.0787240i
$633$	7663.70i	0.481208i
$634$	532.045	0.0333284
$635$	0	0
$636$	−6320.28	−0.394049
$637$	21585.8i	1.34264i
$638$	− 1028.06i	− 0.0637954i
$639$	645.554	0.0399651
$640$	0	0
$641$	16369.4	1.00866	0.504331	−	0.863510i	$-0.331739\pi$
$641$	16369.4	1.00866	0.504331	+	0.863510i	$0.331739\pi$
$642$	− 1663.71i	− 0.102277i
$643$	− 15097.7i	− 0.925966i	−0.886367	−	0.462983i	$-0.846779\pi$
$643$	− 15097.7i	− 0.925966i	0.886367	−	0.462983i	$-0.153221\pi$
$644$	−21574.0	−1.32008
$645$	0	0
$646$	5402.95	0.329065
$647$	1680.02i	0.102084i	0.998697	+	0.0510419i	$0.0162542\pi$
$647$	1680.02i	0.102084i	−0.998697	+	0.0510419i	$0.983746\pi$
$648$	− 687.866i	− 0.0417005i
$649$	−9734.81	−0.588790
$650$	0	0
$651$	−650.811	−0.0391817
$652$	− 9443.55i	− 0.567236i
$653$	− 22943.0i	− 1.37493i	−0.726219	−	0.687464i	$-0.758724\pi$
$653$	− 22943.0i	− 1.37493i	0.726219	−	0.687464i	$-0.241276\pi$
$654$	448.907	0.0268404
$655$	0	0
$656$	−26461.8	−1.57494
$657$	− 1319.57i	− 0.0783583i
$658$	− 1564.77i	− 0.0927071i
$659$	19062.4	1.12680	0.563402	−	0.826183i	$-0.309492\pi$
$659$	19062.4	1.12680	0.563402	+	0.826183i	$0.309492\pi$
$660$	0	0
$661$	15141.1	0.890952	0.445476	−	0.895294i	$-0.353034\pi$
$661$	15141.1	0.890952	0.445476	+	0.895294i	$0.353034\pi$
$662$	− 458.793i	− 0.0269358i
$663$	− 15938.3i	− 0.933624i
$664$	−3388.89	−0.198064
$665$	0	0
$666$	−72.6086	−0.00422452
$667$	19784.2i	1.14850i
$668$	5904.13i	0.341973i
$669$	−1348.25	−0.0779169
$670$	0	0
$671$	3823.97	0.220004
$672$	7248.54i	0.416099i
$673$	− 32674.0i	− 1.87146i	−0.352723	−	0.935728i	$-0.614744\pi$
$673$	− 32674.0i	− 1.87146i	0.352723	−	0.935728i	$-0.385256\pi$
$674$	887.697	0.0507312
$675$	0	0
$676$	−38228.3	−2.17503
$677$	− 8497.87i	− 0.482422i	−0.970473	−	0.241211i	$-0.922455\pi$
$677$	− 8497.87i	− 0.482422i	0.970473	−	0.241211i	$-0.0775446\pi$
$678$	− 2218.66i	− 0.125674i
$679$	−40259.0	−2.27540
$680$	0	0
$681$	−12786.0	−0.719475
$682$	52.7502i	0.00296174i
$683$	2499.51i	0.140031i	0.997546	+	0.0700154i	$0.0223048\pi$
$683$	2499.51i	0.140031i	−0.997546	+	0.0700154i	$0.977695\pi$
$684$	−11039.0	−0.617086
$685$	0	0
$686$	−1161.48	−0.0646437
$687$	− 2951.52i	− 0.163912i
$688$	27751.2i	1.53780i
$689$	−23123.2	−1.27855
$690$	0	0
$691$	−7519.96	−0.413998	−0.206999	−	0.978341i	$-0.566370\pi$
$691$	−7519.96	−0.413998	−0.206999	+	0.978341i	$0.566370\pi$
$692$	12166.2i	0.668338i
$693$	− 2421.27i	− 0.132722i
$694$	3029.72	0.165716
$695$	0	0
$696$	4404.14	0.239854
$697$	− 29118.7i	− 1.58242i
$698$	− 5675.78i	− 0.307782i
$699$	11769.5	0.636860
$700$	0	0
$701$	9761.60	0.525949	0.262975	−	0.964803i	$-0.415296\pi$
$701$	9761.60	0.525949	0.262975	+	0.964803i	$0.415296\pi$
$702$	− 1234.89i	− 0.0663929i
$703$	2374.66i	0.127400i
$704$	−4434.69	−0.237413
$705$	0	0
$706$	−2509.30	−0.133766
$707$	− 16264.7i	− 0.865199i
$708$	− 20463.6i	− 1.08625i
$709$	25103.8	1.32975	0.664875	−	0.746955i	$-0.268485\pi$
$709$	25103.8	1.32975	0.664875	+	0.746955i	$0.268485\pi$
$710$	0	0
$711$	1325.58	0.0699201
$712$	8728.49i	0.459430i
$713$	− 1015.13i	− 0.0533198i
$714$	−2491.14	−0.130572
$715$	0	0
$716$	31988.5	1.66965
$717$	− 16176.5i	− 0.842571i
$718$	− 1891.17i	− 0.0982976i
$719$	−33039.4	−1.71371	−0.856857	−	0.515554i	$-0.827586\pi$
$719$	−33039.4	−1.71371	−0.856857	+	0.515554i	$0.827586\pi$
$720$	0	0
$721$	6785.21	0.350478
$722$	− 9982.61i	− 0.514563i
$723$	− 7674.32i	− 0.394759i
$724$	19971.7	1.02519
$725$	0	0
$726$	−196.251	−0.0100325
$727$	− 1256.17i	− 0.0640834i	−0.999487	−	0.0320417i	$-0.989799\pi$
$727$	− 1256.17i	− 0.0640834i	0.999487	−	0.0320417i	$-0.0102009\pi$
$728$	17570.5i	0.894515i
$729$	−729.000	−0.0370370
$730$	0	0
$731$	−30537.5	−1.54510
$732$	8038.37i	0.405884i
$733$	6515.94i	0.328338i	0.986432	+	0.164169i	$0.0524942\pi$
$733$	6515.94i	0.328338i	−0.986432	+	0.164169i	$0.947506\pi$
$734$	4274.22	0.214938
$735$	0	0
$736$	−11306.2	−0.566241
$737$	7921.11i	0.395899i
$738$	− 2256.09i	− 0.112531i
$739$	32622.4	1.62386	0.811932	−	0.583753i	$-0.198416\pi$
$739$	32622.4	1.62386	0.811932	+	0.583753i	$0.198416\pi$
$740$	0	0
$741$	−40387.0	−2.00223
$742$	3614.13i	0.178812i
$743$	− 8898.83i	− 0.439390i	−0.975569	−	0.219695i	$-0.929494\pi$
$743$	− 8898.83i	− 0.439390i	0.975569	−	0.219695i	$-0.0705062\pi$
$744$	−225.978	−0.0111354
$745$	0	0
$746$	−3631.97	−0.178252
$747$	3591.54i	0.175914i
$748$	− 5324.53i	− 0.260273i
$749$	25087.6	1.22387
$750$	0	0
$751$	36939.2	1.79485	0.897424	−	0.441169i	$-0.145436\pi$
$751$	36939.2	1.79485	0.897424	+	0.441169i	$0.145436\pi$
$752$	6753.82i	0.327509i
$753$	− 17612.5i	− 0.852371i
$754$	7906.52	0.381881
$755$	0	0
$756$	5089.76	0.244858
$757$	− 1889.05i	− 0.0906982i	−0.998971	−	0.0453491i	$-0.985560\pi$
$757$	− 1889.05i	− 0.0906982i	0.998971	−	0.0453491i	$-0.0144400\pi$
$758$	2860.44i	0.137066i
$759$	3776.69	0.180613
$760$	0	0
$761$	−22384.0	−1.06625	−0.533127	−	0.846035i	$-0.678983\pi$
$761$	−22384.0	−1.06625	−0.533127	+	0.846035i	$0.678983\pi$
$762$	2884.94i	0.137153i
$763$	6769.20i	0.321181i
$764$	−29524.9	−1.39813
$765$	0	0
$766$	1149.42	0.0542170
$767$	− 74867.3i	− 3.52452i
$768$	− 8040.32i	− 0.377774i
$769$	−71.2505	−0.00334117	−0.00167058	−	0.999999i	$-0.500532\pi$
$769$	−71.2505	−0.00334117	−0.00167058	+	0.999999i	$0.500532\pi$
$770$	0	0
$771$	−13824.9	−0.645775
$772$	2984.44i	0.139135i
$773$	35710.2i	1.66159i	0.556582	+	0.830793i	$0.312113\pi$
$773$	35710.2i	1.66159i	−0.556582	+	0.830793i	$0.687887\pi$
$774$	−2366.02	−0.109877
$775$	0	0
$776$	−13978.9	−0.646667
$777$	− 1094.89i	− 0.0505520i
$778$	− 3487.43i	− 0.160708i
$779$	−73785.4	−3.39363
$780$	0	0
$781$	789.010	0.0361498
$782$	− 3885.67i	− 0.177687i
$783$	− 4667.51i	− 0.213031i
$784$	−14562.0	−0.663358
$785$	0	0
$786$	3802.67	0.172566
$787$	− 1457.17i	− 0.0660005i	−0.999455	−	0.0330003i	$-0.989494\pi$
$787$	− 1457.17i	− 0.0660005i	0.999455	−	0.0330003i	$-0.0105062\pi$
$788$	− 23073.9i	− 1.04311i
$789$	−18480.1	−0.833852
$790$	0	0
$791$	33455.8	1.50386
$792$	− 840.725i	− 0.0377195i
$793$	29408.9i	1.31695i
$794$	−2283.06	−0.102044
$795$	0	0
$796$	5316.99	0.236753
$797$	− 10331.8i	− 0.459187i	−0.973287	−	0.229594i	$-0.926260\pi$
$797$	− 10331.8i	− 0.459187i	0.973287	−	0.229594i	$-0.0737397\pi$
$798$	6312.44i	0.280023i
$799$	−7431.92	−0.329064
$800$	0	0
$801$	9250.45	0.408051
$802$	− 1615.40i	− 0.0711242i
$803$	− 1612.81i	− 0.0708777i
$804$	−16651.0	−0.730392
$805$	0	0
$806$	−405.685	−0.0177291
$807$	− 17910.8i	− 0.781278i
$808$	− 5647.49i	− 0.245889i
$809$	3265.67	0.141922	0.0709610	−	0.997479i	$-0.477393\pi$
$809$	3265.67	0.141922	0.0709610	+	0.997479i	$0.477393\pi$
$810$	0	0
$811$	−27533.0	−1.19213	−0.596063	−	0.802938i	$-0.703269\pi$
$811$	−27533.0	−1.19213	−0.596063	+	0.802938i	$0.703269\pi$
$812$	32587.8i	1.40838i
$813$	763.219i	0.0329241i
$814$	−88.7439	−0.00382122
$815$	0	0
$816$	10752.2	0.461276
$817$	77380.6i	3.31359i
$818$	− 154.845i	− 0.00661861i
$819$	18621.2	0.794480
$820$	0	0
$821$	−8580.31	−0.364744	−0.182372	−	0.983230i	$-0.558378\pi$
$821$	−8580.31	−0.364744	−0.182372	+	0.983230i	$0.558378\pi$
$822$	452.762i	0.0192115i
$823$	35119.7i	1.48748i	0.668470	+	0.743739i	$0.266950\pi$
$823$	35119.7i	1.48748i	−0.668470	+	0.743739i	$0.733050\pi$
$824$	2355.99	0.0996054
$825$	0	0
$826$	−11701.7	−0.492922
$827$	− 15896.7i	− 0.668420i	−0.942499	−	0.334210i	$-0.891530\pi$
$827$	− 15896.7i	− 0.668420i	0.942499	−	0.334210i	$-0.108470\pi$
$828$	7938.98i	0.333211i
$829$	−24243.4	−1.01569	−0.507845	−	0.861449i	$-0.669558\pi$
$829$	−24243.4	−1.01569	−0.507845	+	0.861449i	$0.669558\pi$
$830$	0	0
$831$	10044.5	0.419303
$832$	− 34105.8i	− 1.42116i
$833$	− 16024.1i	− 0.666509i
$834$	−392.541	−0.0162981
$835$	0	0
$836$	−13492.1	−0.558176
$837$	239.491i	0.00989011i
$838$	764.944i	0.0315329i
$839$	−2056.93	−0.0846402	−0.0423201	−	0.999104i	$-0.513475\pi$
$839$	−2056.93	−0.0846402	−0.0423201	+	0.999104i	$0.513475\pi$
$840$	0	0
$841$	5495.31	0.225319
$842$	− 4379.23i	− 0.179238i
$843$	15540.3i	0.634919i
$844$	−19689.9	−0.803025
$845$	0	0
$846$	−575.819	−0.0234008
$847$	− 2959.33i	− 0.120052i
$848$	− 15599.2i	− 0.631695i
$849$	310.322	0.0125444
$850$	0	0
$851$	1707.80	0.0687927
$852$	1658.58i	0.0666925i
$853$	20756.8i	0.833176i	0.909095	+	0.416588i	$0.136774\pi$
$853$	20756.8i	0.833176i	−0.909095	+	0.416588i	$0.863226\pi$
$854$	4596.59	0.184183
$855$	0	0
$856$	8711.04	0.347824
$857$	17345.5i	0.691380i	0.938349	+	0.345690i	$0.112355\pi$
$857$	17345.5i	0.691380i	−0.938349	+	0.345690i	$0.887645\pi$
$858$	− 1509.31i	− 0.0600547i
$859$	−16066.6	−0.638166	−0.319083	−	0.947727i	$-0.603375\pi$
$859$	−16066.6	−0.638166	−0.319083	+	0.947727i	$0.603375\pi$
$860$	0	0
$861$	34020.3	1.34658
$862$	− 6896.11i	− 0.272485i
$863$	− 10155.0i	− 0.400556i	−0.979739	−	0.200278i	$-0.935815\pi$
$863$	− 10155.0i	− 0.400556i	0.979739	−	0.200278i	$-0.0641846\pi$
$864$	2667.38	0.105030
$865$	0	0
$866$	2305.13	0.0904521
$867$	− 2907.30i	− 0.113883i
$868$	− 1672.09i	− 0.0653852i
$869$	1620.16	0.0632451
$870$	0	0
$871$	−60918.8	−2.36987
$872$	2350.43i	0.0912794i
$873$	14814.8i	0.574349i
$874$	−9846.11	−0.381064
$875$	0	0
$876$	3390.29	0.130762
$877$	− 23346.1i	− 0.898908i	−0.893304	−	0.449454i	$-0.851619\pi$
$877$	− 23346.1i	− 0.898908i	0.893304	−	0.449454i	$-0.148381\pi$
$878$	− 4757.20i	− 0.182856i
$879$	−4304.65	−0.165179
$880$	0	0
$881$	−4750.08	−0.181651	−0.0908253	−	0.995867i	$-0.528950\pi$
$881$	−4750.08	−0.181651	−0.0908253	+	0.995867i	$0.528950\pi$
$882$	− 1241.53i	− 0.0473975i
$883$	− 14394.2i	− 0.548587i	−0.961646	−	0.274294i	$-0.911556\pi$
$883$	− 14394.2i	− 0.548587i	0.961646	−	0.274294i	$-0.0884440\pi$
$884$	40949.3	1.55800
$885$	0	0
$886$	6072.82	0.230271
$887$	− 50185.5i	− 1.89973i	−0.312656	−	0.949867i	$-0.601219\pi$
$887$	− 50185.5i	− 1.89973i	0.312656	−	0.949867i	$-0.398781\pi$
$888$	− 380.172i	− 0.0143668i
$889$	−43502.8	−1.64121
$890$	0	0
$891$	−891.000	−0.0335013
$892$	− 3463.98i	− 0.130025i
$893$	18832.1i	0.705704i
$894$	−159.907	−0.00598221
$895$	0	0
$896$	−24660.1	−0.919461
$897$	29045.3i	1.08115i
$898$	2563.91i	0.0952772i
$899$	−1533.37	−0.0568863
$900$	0	0
$901$	17165.3	0.634695
$902$	− 2757.44i	− 0.101788i
$903$	− 35677.9i	− 1.31482i
$904$	11616.7	0.427395
$905$	0	0
$906$	1125.82	0.0412835
$907$	11675.6i	0.427433i	0.976896	+	0.213716i	$0.0685569\pi$
$907$	11675.6i	0.427433i	−0.976896	+	0.213716i	$0.931443\pi$
$908$	− 32850.4i	− 1.20064i
$909$	−5985.21	−0.218390
$910$	0	0
$911$	26483.7	0.963165	0.481582	−	0.876401i	$-0.340062\pi$
$911$	26483.7	0.963165	0.481582	+	0.876401i	$0.340062\pi$
$912$	− 27245.5i	− 0.989243i
$913$	4389.66i	0.159120i
$914$	−6596.78	−0.238733
$915$	0	0
$916$	7583.15	0.273531
$917$	57341.7i	2.06498i
$918$	916.711i	0.0329586i
$919$	−7212.79	−0.258899	−0.129449	−	0.991586i	$-0.541321\pi$
$919$	−7212.79	−0.258899	−0.129449	+	0.991586i	$0.541321\pi$
$920$	0	0
$921$	14843.2	0.531054
$922$	891.839i	0.0318559i
$923$	6068.03i	0.216394i
$924$	6220.82	0.221483
$925$	0	0
$926$	−238.478	−0.00846313
$927$	− 2496.88i	− 0.0884663i
$928$	17078.2i	0.604116i
$929$	15483.7	0.546828	0.273414	−	0.961896i	$-0.411847\pi$
$929$	15483.7	0.546828	0.273414	+	0.961896i	$0.411847\pi$
$930$	0	0
$931$	−40604.3	−1.42938
$932$	30238.8i	1.06277i
$933$	− 9728.39i	− 0.341365i
$934$	10640.0	0.372754
$935$	0	0
$936$	6465.75	0.225790
$937$	34091.5i	1.18860i	0.804242	+	0.594302i	$0.202572\pi$
$937$	34091.5i	1.18860i	−0.804242	+	0.594302i	$0.797428\pi$
$938$	9521.54i	0.331438i
$939$	12496.3	0.434294
$940$	0	0
$941$	−21424.1	−0.742195	−0.371097	−	0.928594i	$-0.621018\pi$
$941$	−21424.1	−0.742195	−0.371097	+	0.928594i	$0.621018\pi$
$942$	− 4826.48i	− 0.166938i
$943$	53064.6i	1.83247i
$944$	50506.4	1.74136
$945$	0	0
$946$	−2891.80	−0.0993875
$947$	6068.12i	0.208223i	0.994566	+	0.104112i	$0.0331999\pi$
$947$	6068.12i	0.208223i	−0.994566	+	0.104112i	$0.966800\pi$
$948$	3405.73i	0.116680i
$949$	12403.6	0.424277
$950$	0	0
$951$	2952.32	0.100668
$952$	− 13043.4i	− 0.444053i
$953$	36918.5i	1.25489i	0.778662	+	0.627443i	$0.215899\pi$
$953$	36918.5i	1.25489i	−0.778662	+	0.627443i	$0.784101\pi$
$954$	1329.96	0.0451352
$955$	0	0
$956$	41561.3	1.40606
$957$	− 5704.74i	− 0.192694i
$958$	159.570i	0.00538150i
$959$	−6827.33	−0.229892
$960$	0	0
$961$	−29712.3	−0.997359
$962$	− 682.502i	− 0.0228739i
$963$	− 9231.96i	− 0.308926i
$964$	19717.2	0.658762
$965$	0	0
$966$	4539.75	0.151205
$967$	52866.7i	1.75810i	0.476733	+	0.879048i	$0.341821\pi$
$967$	52866.7i	1.75810i	−0.476733	+	0.879048i	$0.658179\pi$
$968$	− 1027.55i	− 0.0341186i
$969$	29981.0	0.993941
$970$	0	0
$971$	25052.7	0.827990	0.413995	−	0.910279i	$-0.364133\pi$
$971$	25052.7	0.827990	0.413995	+	0.910279i	$0.364133\pi$
$972$	− 1872.97i	− 0.0618062i
$973$	− 5919.24i	− 0.195028i
$974$	1671.31	0.0549816
$975$	0	0
$976$	−19839.6	−0.650667
$977$	21534.7i	0.705175i	0.935779	+	0.352588i	$0.114698\pi$
$977$	21534.7i	0.705175i	−0.935779	+	0.352588i	$0.885302\pi$
$978$	1987.18i	0.0649724i
$979$	11306.1	0.369096
$980$	0	0
$981$	2490.99	0.0810715
$982$	607.204i	0.0197318i
$983$	− 39303.1i	− 1.27525i	−0.770346	−	0.637626i	$-0.779916\pi$
$983$	− 39303.1i	− 1.27525i	0.770346	−	0.637626i	$-0.220084\pi$
$984$	11812.7	0.382697
$985$	0	0
$986$	−5869.36	−0.189572
$987$	− 8682.95i	− 0.280022i
$988$	− 103764.i	− 3.34126i
$989$	55650.2	1.78926
$990$	0	0
$991$	19325.5	0.619471	0.309735	−	0.950823i	$-0.399760\pi$
$991$	19325.5	0.619471	0.309735	+	0.950823i	$0.399760\pi$
$992$	− 876.287i	− 0.0280465i
$993$	− 2545.84i	− 0.0813595i
$994$	948.427	0.0302639
$995$	0	0
$996$	−9227.53	−0.293560
$997$	− 30296.3i	− 0.962379i	−0.876617	−	0.481190i	$-0.840205\pi$
$997$	− 30296.3i	− 0.962379i	0.876617	−	0.481190i	$-0.159795\pi$
$998$	2892.62i	0.0917478i
$999$	−402.906	−0.0127601

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	825.4.c.o.199.3		6
5.2	odd	4		165.4.a.f.1.2	✓	3
5.3	odd	4		825.4.a.n.1.2		3
5.4	even	2	inner	825.4.c.o.199.4		6
15.2	even	4		495.4.a.g.1.2		3
15.8	even	4		2475.4.a.w.1.2		3
55.32	even	4		1815.4.a.p.1.2		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
165.4.a.f.1.2	✓	3	5.2	odd	4
495.4.a.g.1.2		3	15.2	even	4
825.4.a.n.1.2		3	5.3	odd	4
825.4.c.o.199.3		6	1.1	even	1	trivial
825.4.c.o.199.4		6	5.4	even	2	inner
1815.4.a.p.1.2		3	55.32	even	4
2475.4.a.w.1.2		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)

\(f(q)\)	\(=\)	\(q-0.540637i q^{2} -3.00000i q^{3} +7.70771 q^{4} -1.62191 q^{6} -24.4573i q^{7} -8.49217i q^{8} -9.00000 q^{9} +O(q^{10})\)	\(q-0.540637i q^{2} -3.00000i q^{3} +7.70771 q^{4} -1.62191 q^{6} -24.4573i q^{7} -8.49217i q^{8} -9.00000 q^{9} -11.0000 q^{11} -23.1231i q^{12} -84.5976i q^{13} -13.2225 q^{14} +57.0705 q^{16} +62.8005i q^{17} +4.86573i q^{18} +159.134 q^{19} -73.3719 q^{21} +5.94701i q^{22} -114.445i q^{23} -25.4765 q^{24} -45.7366 q^{26} +27.0000i q^{27} -188.510i q^{28} -172.871 q^{29} +8.87004 q^{31} -98.7918i q^{32} +33.0000i q^{33} +33.9523 q^{34} -69.3694 q^{36} +14.9224i q^{37} -86.0336i q^{38} -253.793 q^{39} -463.669 q^{41} +39.6675i q^{42} +486.261i q^{43} -84.7848 q^{44} -61.8732 q^{46} +118.342i q^{47} -171.212i q^{48} -255.159 q^{49} +188.401 q^{51} -652.054i q^{52} -273.331i q^{53} +14.5972 q^{54} -207.695 q^{56} -477.401i q^{57} +93.4603i q^{58} +884.982 q^{59} -347.633 q^{61} -4.79547i q^{62} +220.116i q^{63} +403.154 q^{64} +17.8410 q^{66} -720.101i q^{67} +484.048i q^{68} -343.335 q^{69} -71.7282 q^{71} +76.4295i q^{72} +146.619i q^{73} +8.06763 q^{74} +1226.56 q^{76} +269.030i q^{77} +137.210i q^{78} -147.287 q^{79} +81.0000 q^{81} +250.677i q^{82} -399.060i q^{83} -565.529 q^{84} +262.891 q^{86} +518.612i q^{87} +93.4139i q^{88} -1027.83 q^{89} -2069.03 q^{91} -882.109i q^{92} -26.6101i q^{93} +63.9799 q^{94} -296.375 q^{96} -1646.09i q^{97} +137.948i q^{98} +99.0000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + 10 q^{4} - 6 q^{6} - 54 q^{9}+O(q^{10}) \) 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

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Groups

Database

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