LMFDB - Embedded newform 525.4.d.h.274.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("525.274");

S:= CuspForms(chi, 4);

N := Newforms(S);

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

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$30.9760027530$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	$\Q(i, \sqrt{65})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} + 33x^{2} + 256 $ x^4 + 33*x^2 + 256
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 105)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			274.3
Root			$3.53113i$ of defining polynomial
Character	$\chi$	$=$	525.274
Dual form			525.4.d.h.274.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+3.53113i q^{2} +3.00000i q^{3} -4.46887 q^{4} -10.5934 q^{6} +7.00000i q^{7} +12.4689i q^{8} -9.00000 q^{9} +O(q^{10})$	\(q+3.53113i q^{2} +3.00000i q^{3} -4.46887 q^{4} -10.5934 q^{6} +7.00000i q^{7} +12.4689i q^{8} -9.00000 q^{9} -2.93774 q^{11} -13.4066i q^{12} -19.0623i q^{13} -24.7179 q^{14} -79.7802 q^{16} -122.498i q^{17} -31.7802i q^{18} -107.436 q^{19} -21.0000 q^{21} -10.3735i q^{22} +210.623i q^{23} -37.4066 q^{24} +67.3113 q^{26} -27.0000i q^{27} -31.2821i q^{28} -95.4942 q^{29} -94.3074 q^{31} -181.963i q^{32} -8.81323i q^{33} +432.556 q^{34} +40.2198 q^{36} -97.1206i q^{37} -379.370i q^{38} +57.1868 q^{39} -491.113 q^{41} -74.1537i q^{42} -43.0039i q^{43} +13.1284 q^{44} -743.735 q^{46} -473.494i q^{47} -239.340i q^{48} -49.0000 q^{49} +367.494 q^{51} +85.1868i q^{52} -183.677i q^{53} +95.3405 q^{54} -87.2821 q^{56} -322.307i q^{57} -337.202i q^{58} +760.615 q^{59} -198.747 q^{61} -333.012i q^{62} -63.0000i q^{63} +4.29373 q^{64} +31.1206 q^{66} +309.992i q^{67} +547.428i q^{68} -631.868 q^{69} +665.693 q^{71} -112.220i q^{72} +621.288i q^{73} +342.945 q^{74} +480.117 q^{76} -20.5642i q^{77} +201.934i q^{78} +24.7626 q^{79} +81.0000 q^{81} -1734.18i q^{82} -406.724i q^{83} +93.8463 q^{84} +151.852 q^{86} -286.483i q^{87} -36.6303i q^{88} -261.751 q^{89} +133.436 q^{91} -941.245i q^{92} -282.922i q^{93} +1671.97 q^{94} +545.889 q^{96} +1004.77i q^{97} -173.025i q^{98} +26.4397 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 34 q^{4} + 6 q^{6} - 36 q^{9}+O(q^{10}) $ 4 * q - 34 * q^4 + 6 * q^6 - 36 * q^9	$ 4 q - 34 q^{4} + 6 q^{6} - 36 q^{9} - 44 q^{11} + 14 q^{14} - 174 q^{16} - 204 q^{19} - 84 q^{21} - 198 q^{24} + 108 q^{26} + 392 q^{29} + 300 q^{31} + 924 q^{34} + 306 q^{36} + 132 q^{39} - 352 q^{41} + 504 q^{44} - 1040 q^{46} - 196 q^{49} + 696 q^{51} - 54 q^{54} - 462 q^{56} + 1688 q^{59} - 408 q^{61} + 1678 q^{64} - 456 q^{66} - 1560 q^{69} + 3340 q^{71} + 2436 q^{74} + 824 q^{76} + 1776 q^{79} + 324 q^{81} + 714 q^{84} - 2424 q^{86} - 1176 q^{89} + 308 q^{91} + 2560 q^{94} - 90 q^{96} + 396 q^{99}+O(q^{100}) $ 4 * q - 34 * q^4 + 6 * q^6 - 36 * q^9 - 44 * q^11 + 14 * q^14 - 174 * q^16 - 204 * q^19 - 84 * q^21 - 198 * q^24 + 108 * q^26 + 392 * q^29 + 300 * q^31 + 924 * q^34 + 306 * q^36 + 132 * q^39 - 352 * q^41 + 504 * q^44 - 1040 * q^46 - 196 * q^49 + 696 * q^51 - 54 * q^54 - 462 * q^56 + 1688 * q^59 - 408 * q^61 + 1678 * q^64 - 456 * q^66 - 1560 * q^69 + 3340 * q^71 + 2436 * q^74 + 824 * q^76 + 1776 * q^79 + 324 * q^81 + 714 * q^84 - 2424 * q^86 - 1176 * q^89 + 308 * q^91 + 2560 * q^94 - 90 * q^96 + 396 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

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

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

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

$2$	3.53113i	1.24844i	0.781248	+	0.624221i	$0.214584\pi$
$2$	3.53113i	1.24844i	−0.781248	+	0.624221i	$0.785416\pi$
$3$	3.00000i	0.577350i
$3$	3.00000i	0.577350i
$4$	−4.46887	−0.558609
$5$	0	0
$5$	0	0
$6$	−10.5934	−0.720789
$7$	7.00000i	0.377964i
$7$	7.00000i	0.377964i
$8$	12.4689i	0.551051i
$9$	−9.00000	−0.333333
$10$	0	0
$11$	−2.93774	−0.0805239	−0.0402619	−	0.999189i	$-0.512819\pi$
$11$	−2.93774	−0.0805239	−0.0402619	+	0.999189i	$0.512819\pi$
$12$	− 13.4066i	− 0.322513i
$13$	− 19.0623i	− 0.406686i	−0.979108	−	0.203343i	$-0.934819\pi$
$13$	− 19.0623i	− 0.406686i	0.979108	−	0.203343i	$-0.0651807\pi$
$14$	−24.7179	−0.471867
$15$	0	0
$16$	−79.7802	−1.24656
$17$	− 122.498i	− 1.74766i	−0.486236	−	0.873828i	$-0.661630\pi$
$17$	− 122.498i	− 1.74766i	0.486236	−	0.873828i	$-0.338370\pi$
$18$	− 31.7802i	− 0.416148i
$19$	−107.436	−1.29723	−0.648617	−	0.761115i	$-0.724652\pi$
$19$	−107.436	−1.29723	−0.648617	+	0.761115i	$0.724652\pi$
$20$	0	0
$21$	−21.0000	−0.218218
$22$	− 10.3735i	− 0.100529i
$23$	210.623i	1.90947i	0.297455	+	0.954736i	$0.403862\pi$
$23$	210.623i	1.90947i	−0.297455	+	0.954736i	$0.596138\pi$
$24$	−37.4066	−0.318150
$25$	0	0
$26$	67.3113	0.507724
$27$	− 27.0000i	− 0.192450i
$28$	− 31.2821i	− 0.211134i
$29$	−95.4942	−0.611477	−0.305738	−	0.952116i	$-0.598903\pi$
$29$	−95.4942	−0.611477	−0.305738	+	0.952116i	$0.598903\pi$
$30$	0	0
$31$	−94.3074	−0.546391	−0.273195	−	0.961959i	$-0.588081\pi$
$31$	−94.3074	−0.546391	−0.273195	+	0.961959i	$0.588081\pi$
$32$	− 181.963i	− 1.00521i
$33$	− 8.81323i	− 0.0464905i
$34$	432.556	2.18185
$35$	0	0
$36$	40.2198	0.186203
$37$	− 97.1206i	− 0.431528i	−0.976446	−	0.215764i	$-0.930776\pi$
$37$	− 97.1206i	− 0.431528i	0.976446	−	0.215764i	$-0.0692242\pi$
$38$	− 379.370i	− 1.61952i
$39$	57.1868	0.234800
$40$	0	0
$41$	−491.113	−1.87071	−0.935353	−	0.353716i	$-0.884918\pi$
$41$	−491.113	−1.87071	−0.935353	+	0.353716i	$0.884918\pi$
$42$	− 74.1537i	− 0.272433i
$43$	− 43.0039i	− 0.152512i	−0.997088	−	0.0762562i	$-0.975703\pi$
$43$	− 43.0039i	− 0.152512i	0.997088	−	0.0762562i	$-0.0242967\pi$
$44$	13.1284	0.0449814
$45$	0	0
$46$	−743.735	−2.38387
$47$	− 473.494i	− 1.46949i	−0.678341	−	0.734747i	$-0.737301\pi$
$47$	− 473.494i	− 1.46949i	0.678341	−	0.734747i	$-0.262699\pi$
$48$	− 239.340i	− 0.719705i
$49$	−49.0000	−0.142857
$50$	0	0
$51$	367.494	1.00901
$52$	85.1868i	0.227178i
$53$	− 183.677i	− 0.476038i	−0.971261	−	0.238019i	$-0.923502\pi$
$53$	− 183.677i	− 0.476038i	0.971261	−	0.238019i	$-0.0764980\pi$
$54$	95.3405	0.240263
$55$	0	0
$56$	−87.2821	−0.208278
$57$	− 322.307i	− 0.748959i
$58$	− 337.202i	− 0.763394i
$59$	760.615	1.67837	0.839183	−	0.543849i	$-0.183034\pi$
$59$	760.615	1.67837	0.839183	+	0.543849i	$0.183034\pi$
$60$	0	0
$61$	−198.747	−0.417163	−0.208582	−	0.978005i	$-0.566885\pi$
$61$	−198.747	−0.417163	−0.208582	+	0.978005i	$0.566885\pi$
$62$	− 333.012i	− 0.682137i
$63$	− 63.0000i	− 0.125988i
$64$	4.29373	0.00838618
$65$	0	0
$66$	31.1206	0.0580407
$67$	309.992i	0.565247i	0.959231	+	0.282624i	$0.0912048\pi$
$67$	309.992i	0.565247i	−0.959231	+	0.282624i	$0.908795\pi$
$68$	547.428i	0.976256i
$69$	−631.868	−1.10243
$70$	0	0
$71$	665.693	1.11272	0.556360	−	0.830941i	$-0.312197\pi$
$71$	665.693	1.11272	0.556360	+	0.830941i	$0.312197\pi$
$72$	− 112.220i	− 0.183684i
$73$	621.288i	0.996113i	0.867145	+	0.498057i	$0.165953\pi$
$73$	621.288i	0.996113i	−0.867145	+	0.498057i	$0.834047\pi$
$74$	342.945	0.538738
$75$	0	0
$76$	480.117	0.724647
$77$	− 20.5642i	− 0.0304352i
$78$	201.934i	0.293135i
$79$	24.7626	0.0352659	0.0176330	−	0.999845i	$-0.494387\pi$
$79$	24.7626	0.0352659	0.0176330	+	0.999845i	$0.494387\pi$
$80$	0	0
$81$	81.0000	0.111111
$82$	− 1734.18i	− 2.33547i
$83$	− 406.724i	− 0.537876i	−0.963157	−	0.268938i	$-0.913327\pi$
$83$	− 406.724i	− 0.537876i	0.963157	−	0.268938i	$-0.0866727\pi$
$84$	93.8463	0.121898
$85$	0	0
$86$	151.852	0.190403
$87$	− 286.483i	− 0.353036i
$88$	− 36.6303i	− 0.0443728i
$89$	−261.751	−0.311748	−0.155874	−	0.987777i	$-0.549819\pi$
$89$	−261.751	−0.311748	−0.155874	+	0.987777i	$0.549819\pi$
$90$	0	0
$91$	133.436	0.153713
$92$	− 941.245i	− 1.06665i
$93$	− 282.922i	− 0.315459i
$94$	1671.97	1.83458
$95$	0	0
$96$	545.889	0.580360
$97$	1004.77i	1.05175i	0.850563	+	0.525873i	$0.176261\pi$
$97$	1004.77i	1.05175i	−0.850563	+	0.525873i	$0.823739\pi$
$98$	− 173.025i	− 0.178349i
$99$	26.4397	0.0268413
$100$	0	0
$101$	−128.872	−0.126962	−0.0634812	−	0.997983i	$-0.520220\pi$
$101$	−128.872	−0.126962	−0.0634812	+	0.997983i	$0.520220\pi$
$102$	1297.67i	1.25969i
$103$	806.008i	0.771051i	0.922697	+	0.385526i	$0.125980\pi$
$103$	806.008i	0.771051i	−0.922697	+	0.385526i	$0.874020\pi$
$104$	237.685	0.224105
$105$	0	0
$106$	648.587	0.594305
$107$	769.712i	0.695429i	0.937600	+	0.347714i	$0.113042\pi$
$107$	769.712i	0.695429i	−0.937600	+	0.347714i	$0.886958\pi$
$108$	120.660i	0.107504i
$109$	780.856	0.686169	0.343085	−	0.939304i	$-0.388528\pi$
$109$	780.856	0.686169	0.343085	+	0.939304i	$0.388528\pi$
$110$	0	0
$111$	291.362	0.249143
$112$	− 558.461i	− 0.471157i
$113$	− 1115.65i	− 0.928771i	−0.885633	−	0.464386i	$-0.846275\pi$
$113$	− 1115.65i	− 0.928771i	0.885633	−	0.464386i	$-0.153725\pi$
$114$	1138.11	0.935032
$115$	0	0
$116$	426.751	0.341576
$117$	171.560i	0.135562i
$118$	2685.83i	2.09534i
$119$	857.486	0.660552
$120$	0	0
$121$	−1322.37	−0.993516
$122$	− 701.802i	− 0.520804i
$123$	− 1473.34i	− 1.08005i
$124$	421.448	0.305219
$125$	0	0
$126$	222.461	0.157289
$127$	1875.98i	1.31076i	0.755299	+	0.655381i	$0.227492\pi$
$127$	1875.98i	1.31076i	−0.755299	+	0.655381i	$0.772508\pi$
$128$	− 1440.54i	− 0.994744i
$129$	129.012	0.0880530
$130$	0	0
$131$	364.203	0.242905	0.121452	−	0.992597i	$-0.461245\pi$
$131$	364.203	0.242905	0.121452	+	0.992597i	$0.461245\pi$
$132$	39.3852i	0.0259700i
$133$	− 752.051i	− 0.490309i
$134$	−1094.62	−0.705679
$135$	0	0
$136$	1527.41	0.963048
$137$	− 1603.13i	− 0.999743i	−0.866099	−	0.499872i	$-0.833380\pi$
$137$	− 1603.13i	− 0.999743i	0.866099	−	0.499872i	$-0.166620\pi$
$138$	− 2231.21i	− 1.37633i
$139$	−2431.12	−1.48349	−0.741746	−	0.670681i	$-0.766002\pi$
$139$	−2431.12	−1.48349	−0.741746	+	0.670681i	$0.766002\pi$
$140$	0	0
$141$	1420.48	0.848413
$142$	2350.65i	1.38917i
$143$	56.0000i	0.0327479i
$144$	718.021	0.415522
$145$	0	0
$146$	−2193.85	−1.24359
$147$	− 147.000i	− 0.0824786i
$148$	434.020i	0.241055i
$149$	−2341.57	−1.28744	−0.643722	−	0.765260i	$-0.722611\pi$
$149$	−2341.57	−1.28744	−0.643722	+	0.765260i	$0.722611\pi$
$150$	0	0
$151$	−2104.07	−1.13395	−0.566976	−	0.823734i	$-0.691887\pi$
$151$	−2104.07	−1.13395	−0.566976	+	0.823734i	$0.691887\pi$
$152$	− 1339.60i	− 0.714843i
$153$	1102.48i	0.582552i
$154$	72.6148	0.0379966
$155$	0	0
$156$	−255.560	−0.131162
$157$	593.467i	0.301680i	0.988558	+	0.150840i	$0.0481979\pi$
$157$	593.467i	0.301680i	−0.988558	+	0.150840i	$0.951802\pi$
$158$	87.4399i	0.0440275i
$159$	551.031	0.274840
$160$	0	0
$161$	−1474.36	−0.721712
$162$	286.021i	0.138716i
$163$	2178.71i	1.04693i	0.852047	+	0.523465i	$0.175361\pi$
$163$	2178.71i	1.04693i	−0.852047	+	0.523465i	$0.824639\pi$
$164$	2194.72	1.04499
$165$	0	0
$166$	1436.19	0.671508
$167$	− 799.502i	− 0.370463i	−0.982695	−	0.185231i	$-0.940697\pi$
$167$	− 799.502i	− 0.370463i	0.982695	−	0.185231i	$-0.0593035\pi$
$168$	− 261.846i	− 0.120249i
$169$	1833.63	0.834606
$170$	0	0
$171$	966.922	0.432412
$172$	192.179i	0.0851947i
$173$	− 1444.36i	− 0.634754i	−0.948299	−	0.317377i	$-0.897198\pi$
$173$	− 1444.36i	− 0.634754i	0.948299	−	0.317377i	$-0.102802\pi$
$174$	1011.61	0.440745
$175$	0	0
$176$	234.374	0.100378
$177$	2281.84i	0.969005i
$178$	− 924.276i	− 0.389199i
$179$	−3343.49	−1.39611	−0.698056	−	0.716043i	$-0.745952\pi$
$179$	−3343.49	−1.39611	−0.698056	+	0.716043i	$0.745952\pi$
$180$	0	0
$181$	2251.81	0.924729	0.462365	−	0.886690i	$-0.347001\pi$
$181$	2251.81	0.924729	0.462365	+	0.886690i	$0.347001\pi$
$182$	471.179i	0.191902i
$183$	− 596.241i	− 0.240849i
$184$	−2626.23	−1.05222
$185$	0	0
$186$	999.035	0.393832
$187$	359.868i	0.140728i
$188$	2115.98i	0.820873i
$189$	189.000	0.0727393
$190$	0	0
$191$	−1001.93	−0.379565	−0.189782	−	0.981826i	$-0.560778\pi$
$191$	−1001.93	−0.379565	−0.189782	+	0.981826i	$0.560778\pi$
$192$	12.8812i	0.00484177i
$193$	− 4054.97i	− 1.51235i	−0.654372	−	0.756173i	$-0.727067\pi$
$193$	− 4054.97i	− 1.51235i	0.654372	−	0.756173i	$-0.272933\pi$
$194$	−3547.99	−1.31304
$195$	0	0
$196$	218.975	0.0798013
$197$	5140.23i	1.85902i	0.368802	+	0.929508i	$0.379768\pi$
$197$	5140.23i	1.85902i	−0.368802	+	0.929508i	$0.620232\pi$
$198$	93.3619i	0.0335098i
$199$	−585.631	−0.208614	−0.104307	−	0.994545i	$-0.533263\pi$
$199$	−585.631	−0.208614	−0.104307	+	0.994545i	$0.533263\pi$
$200$	0	0
$201$	−929.977	−0.326346
$202$	− 455.062i	− 0.158505i
$203$	− 668.459i	− 0.231116i
$204$	−1642.28	−0.563642
$205$	0	0
$206$	−2846.12	−0.962614
$207$	− 1895.60i	− 0.636490i
$208$	1520.79i	0.506961i
$209$	315.619	0.104458
$210$	0	0
$211$	−1055.16	−0.344266	−0.172133	−	0.985074i	$-0.555066\pi$
$211$	−1055.16	−0.344266	−0.172133	+	0.985074i	$0.555066\pi$
$212$	820.829i	0.265919i
$213$	1997.08i	0.642430i
$214$	−2717.95	−0.868203
$215$	0	0
$216$	336.660	0.106050
$217$	− 660.152i	− 0.206516i
$218$	2757.30i	0.856643i
$219$	−1863.86	−0.575106
$220$	0	0
$221$	−2335.09	−0.710747
$222$	1028.84i	0.311040i
$223$	4675.85i	1.40412i	0.712119	+	0.702059i	$0.247736\pi$
$223$	4675.85i	1.40412i	−0.712119	+	0.702059i	$0.752264\pi$
$224$	1273.74	0.379935
$225$	0	0
$226$	3939.49	1.15952
$227$	− 5443.11i	− 1.59151i	−0.605621	−	0.795754i	$-0.707075\pi$
$227$	− 5443.11i	− 1.59151i	0.605621	−	0.795754i	$-0.292925\pi$
$228$	1440.35i	0.418375i
$229$	536.303	0.154759	0.0773797	−	0.997002i	$-0.475345\pi$
$229$	536.303	0.154759	0.0773797	+	0.997002i	$0.475345\pi$
$230$	0	0
$231$	61.6926	0.0175717
$232$	− 1190.70i	− 0.336955i
$233$	− 183.490i	− 0.0515916i	−0.999667	−	0.0257958i	$-0.991788\pi$
$233$	− 183.490i	− 0.0515916i	0.999667	−	0.0257958i	$-0.00821196\pi$
$234$	−605.802	−0.169241
$235$	0	0
$236$	−3399.09	−0.937550
$237$	74.2878i	0.0203608i
$238$	3027.90i	0.824661i
$239$	−643.218	−0.174085	−0.0870425	−	0.996205i	$-0.527742\pi$
$239$	−643.218	−0.174085	−0.0870425	+	0.996205i	$0.527742\pi$
$240$	0	0
$241$	−5755.61	−1.53839	−0.769194	−	0.639015i	$-0.779342\pi$
$241$	−5755.61	−1.53839	−0.769194	+	0.639015i	$0.779342\pi$
$242$	− 4669.46i	− 1.24035i
$243$	243.000i	0.0641500i
$244$	888.175	0.233031
$245$	0	0
$246$	5202.55	1.34838
$247$	2047.97i	0.527567i
$248$	− 1175.91i	− 0.301089i
$249$	1220.17	0.310543
$250$	0	0
$251$	−5132.27	−1.29062	−0.645311	−	0.763920i	$-0.723272\pi$
$251$	−5132.27	−1.29062	−0.645311	+	0.763920i	$0.723272\pi$
$252$	281.539i	0.0703781i
$253$	− 618.755i	− 0.153758i
$254$	−6624.34	−1.63641
$255$	0	0
$256$	5121.09	1.25027
$257$	− 5041.74i	− 1.22372i	−0.790967	−	0.611859i	$-0.790422\pi$
$257$	− 5041.74i	− 1.22372i	0.790967	−	0.611859i	$-0.209578\pi$
$258$	455.557i	0.109929i
$259$	679.844	0.163102
$260$	0	0
$261$	859.448	0.203826
$262$	1286.05i	0.303253i
$263$	7577.00i	1.77649i	0.459367	+	0.888246i	$0.348076\pi$
$263$	7577.00i	1.77649i	−0.459367	+	0.888246i	$0.651924\pi$
$264$	109.891	0.0256186
$265$	0	0
$266$	2655.59	0.612122
$267$	− 785.253i	− 0.179988i
$268$	− 1385.32i	− 0.315752i
$269$	−1023.10	−0.231893	−0.115947	−	0.993255i	$-0.536990\pi$
$269$	−1023.10	−0.231893	−0.115947	+	0.993255i	$0.536990\pi$
$270$	0	0
$271$	−2251.98	−0.504790	−0.252395	−	0.967624i	$-0.581218\pi$
$271$	−2251.98	−0.504790	−0.252395	+	0.967624i	$0.581218\pi$
$272$	9772.91i	2.17857i
$273$	400.307i	0.0887462i
$274$	5660.87	1.24812
$275$	0	0
$276$	2823.74	0.615829
$277$	8630.72i	1.87209i	0.351875	+	0.936047i	$0.385544\pi$
$277$	8630.72i	1.87209i	−0.351875	+	0.936047i	$0.614456\pi$
$278$	− 8584.61i	− 1.85205i
$279$	848.767	0.182130
$280$	0	0
$281$	−7521.62	−1.59680	−0.798402	−	0.602124i	$-0.794321\pi$
$281$	−7521.62	−1.59680	−0.798402	+	0.602124i	$0.794321\pi$
$282$	5015.91i	1.05919i
$283$	14.8169i	0.00311226i	0.999999	+	0.00155613i	$0.000495333\pi$
$283$	14.8169i	0.00311226i	−0.999999	+	0.00155613i	$0.999505\pi$
$284$	−2974.89	−0.621576
$285$	0	0
$286$	−197.743	−0.0408839
$287$	− 3437.79i	− 0.707060i
$288$	1637.67i	0.335071i
$289$	−10092.8	−2.05430
$290$	0	0
$291$	−3014.32	−0.607226
$292$	− 2776.46i	− 0.556438i
$293$	6913.39i	1.37844i	0.724550	+	0.689222i	$0.242048\pi$
$293$	6913.39i	1.37844i	−0.724550	+	0.689222i	$0.757952\pi$
$294$	519.076	0.102970
$295$	0	0
$296$	1210.98	0.237794
$297$	79.3190i	0.0154968i
$298$	− 8268.39i	− 1.60730i
$299$	4014.94	0.776555
$300$	0	0
$301$	301.027	0.0576442
$302$	− 7429.74i	− 1.41567i
$303$	− 386.615i	− 0.0733018i
$304$	8571.25	1.61709
$305$	0	0
$306$	−3893.01	−0.727283
$307$	7644.12i	1.42108i	0.703655	+	0.710542i	$0.251550\pi$
$307$	7644.12i	1.42108i	−0.703655	+	0.710542i	$0.748450\pi$
$308$	91.8987i	0.0170014i
$309$	−2418.02	−0.445167
$310$	0	0
$311$	7593.99	1.38462	0.692308	−	0.721602i	$-0.256594\pi$
$311$	7593.99	1.38462	0.692308	+	0.721602i	$0.256594\pi$
$312$	713.055i	0.129387i
$313$	− 9127.84i	− 1.64836i	−0.566329	−	0.824179i	$-0.691637\pi$
$313$	− 9127.84i	− 1.64836i	0.566329	−	0.824179i	$-0.308363\pi$
$314$	−2095.61	−0.376631
$315$	0	0
$316$	−110.661	−0.0196999
$317$	4929.81i	0.873456i	0.899593	+	0.436728i	$0.143863\pi$
$317$	4929.81i	0.873456i	−0.899593	+	0.436728i	$0.856137\pi$
$318$	1945.76i	0.343122i
$319$	280.537	0.0492385
$320$	0	0
$321$	−2309.14	−0.401506
$322$	− 5206.15i	− 0.901016i
$323$	13160.7i	2.26712i
$324$	−361.979	−0.0620677
$325$	0	0
$326$	−7693.30	−1.30703
$327$	2342.57i	0.396160i
$328$	− 6123.62i	− 1.03086i
$329$	3314.46	0.555417
$330$	0	0
$331$	1221.67	0.202867	0.101433	−	0.994842i	$-0.467657\pi$
$331$	1221.67	0.202867	0.101433	+	0.994842i	$0.467657\pi$
$332$	1817.60i	0.300463i
$333$	874.086i	0.143843i
$334$	2823.14	0.462502
$335$	0	0
$336$	1675.38	0.272023
$337$	8744.83i	1.41354i	0.707446	+	0.706768i	$0.249847\pi$
$337$	8744.83i	1.41354i	−0.707446	+	0.706768i	$0.750153\pi$
$338$	6474.79i	1.04196i
$339$	3346.94	0.536226
$340$	0	0
$341$	277.051	0.0439975
$342$	3414.33i	0.539841i
$343$	− 343.000i	− 0.0539949i
$344$	536.210	0.0840421
$345$	0	0
$346$	5100.21	0.792454
$347$	− 4589.56i	− 0.710031i	−0.934860	−	0.355015i	$-0.884476\pi$
$347$	− 4589.56i	− 0.710031i	0.934860	−	0.355015i	$-0.115524\pi$
$348$	1280.25i	0.197209i
$349$	3989.89	0.611960	0.305980	−	0.952038i	$-0.401016\pi$
$349$	3989.89	0.611960	0.305980	+	0.952038i	$0.401016\pi$
$350$	0	0
$351$	−514.681	−0.0782668
$352$	534.561i	0.0809437i
$353$	2416.35i	0.364333i	0.983268	+	0.182166i	$0.0583109\pi$
$353$	2416.35i	0.364333i	−0.983268	+	0.182166i	$0.941689\pi$
$354$	−8057.49	−1.20975
$355$	0	0
$356$	1169.73	0.174145
$357$	2572.46i	0.381370i
$358$	− 11806.3i	− 1.74297i
$359$	2756.24	0.405206	0.202603	−	0.979261i	$-0.435060\pi$
$359$	2756.24	0.405206	0.202603	+	0.979261i	$0.435060\pi$
$360$	0	0
$361$	4683.45	0.682818
$362$	7951.44i	1.15447i
$363$	− 3967.11i	− 0.573607i
$364$	−596.307	−0.0858654
$365$	0	0
$366$	2105.40	0.300687
$367$	− 11112.8i	− 1.58061i	−0.612711	−	0.790307i	$-0.709921\pi$
$367$	− 11112.8i	− 1.58061i	0.612711	−	0.790307i	$-0.290079\pi$
$368$	− 16803.5i	− 2.38028i
$369$	4420.02	0.623569
$370$	0	0
$371$	1285.74	0.179925
$372$	1264.34i	0.176218i
$373$	6091.09i	0.845535i	0.906238	+	0.422768i	$0.138941\pi$
$373$	6091.09i	0.845535i	−0.906238	+	0.422768i	$0.861059\pi$
$374$	−1270.74	−0.175691
$375$	0	0
$376$	5903.94	0.809767
$377$	1820.33i	0.248679i
$378$	667.383i	0.0908108i
$379$	−3984.29	−0.539998	−0.269999	−	0.962861i	$-0.587023\pi$
$379$	−3984.29	−0.539998	−0.269999	+	0.962861i	$0.587023\pi$
$380$	0	0
$381$	−5627.95	−0.756768
$382$	− 3537.93i	− 0.473865i
$383$	318.475i	0.0424890i	0.999774	+	0.0212445i	$0.00676285\pi$
$383$	318.475i	0.0424890i	−0.999774	+	0.0212445i	$0.993237\pi$
$384$	4321.63	0.574316
$385$	0	0
$386$	14318.6	1.88808
$387$	387.035i	0.0508374i
$388$	− 4490.21i	− 0.587515i
$389$	−3885.46	−0.506429	−0.253214	−	0.967410i	$-0.581488\pi$
$389$	−3885.46	−0.506429	−0.253214	+	0.967410i	$0.581488\pi$
$390$	0	0
$391$	25800.9	3.33710
$392$	− 610.975i	− 0.0787216i
$393$	1092.61i	0.140241i
$394$	−18150.8	−2.32088
$395$	0	0
$396$	−118.156	−0.0149938
$397$	− 4806.04i	− 0.607578i	−0.952739	−	0.303789i	$-0.901748\pi$
$397$	− 4806.04i	− 0.607578i	0.952739	−	0.303789i	$-0.0982518\pi$
$398$	− 2067.94i	− 0.260443i
$399$	2256.15	0.283080
$400$	0	0
$401$	3618.59	0.450633	0.225316	−	0.974286i	$-0.427658\pi$
$401$	3618.59	0.450633	0.225316	+	0.974286i	$0.427658\pi$
$402$	− 3283.87i	− 0.407424i
$403$	1797.71i	0.222209i
$404$	575.911	0.0709223
$405$	0	0
$406$	2360.42	0.288536
$407$	285.315i	0.0347483i
$408$	4582.24i	0.556016i
$409$	2109.05	0.254978	0.127489	−	0.991840i	$-0.459308\pi$
$409$	2109.05	0.254978	0.127489	+	0.991840i	$0.459308\pi$
$410$	0	0
$411$	4809.40	0.577202
$412$	− 3601.94i	− 0.430716i
$413$	5324.30i	0.634363i
$414$	6693.62	0.794622
$415$	0	0
$416$	−3468.63	−0.408806
$417$	− 7293.37i	− 0.856494i
$418$	1114.49i	0.130410i
$419$	6905.91	0.805193	0.402597	−	0.915377i	$-0.368108\pi$
$419$	6905.91	0.805193	0.402597	+	0.915377i	$0.368108\pi$
$420$	0	0
$421$	−9647.54	−1.11685	−0.558423	−	0.829556i	$-0.688593\pi$
$421$	−9647.54	−1.11685	−0.558423	+	0.829556i	$0.688593\pi$
$422$	− 3725.91i	− 0.429797i
$423$	4261.45i	0.489831i
$424$	2290.25	0.262321
$425$	0	0
$426$	−7051.94	−0.802037
$427$	− 1391.23i	− 0.157673i
$428$	− 3439.74i	− 0.388473i
$429$	−168.000	−0.0189070
$430$	0	0
$431$	−13002.7	−1.45318	−0.726589	−	0.687073i	$-0.758895\pi$
$431$	−13002.7	−1.45318	−0.726589	+	0.687073i	$0.758895\pi$
$432$	2154.06i	0.239902i
$433$	7356.07i	0.816420i	0.912888	+	0.408210i	$0.133847\pi$
$433$	7356.07i	0.816420i	−0.912888	+	0.408210i	$0.866153\pi$
$434$	2331.08	0.257824
$435$	0	0
$436$	−3489.55	−0.383300
$437$	− 22628.4i	− 2.47703i
$438$	− 6581.54i	− 0.717987i
$439$	−6909.21	−0.751159	−0.375579	−	0.926790i	$-0.622556\pi$
$439$	−6909.21	−0.751159	−0.375579	+	0.926790i	$0.622556\pi$
$440$	0	0
$441$	441.000	0.0476190
$442$	− 8245.50i	− 0.887327i
$443$	− 14812.6i	− 1.58864i	−0.607502	−	0.794318i	$-0.707828\pi$
$443$	− 14812.6i	− 1.58864i	0.607502	−	0.794318i	$-0.292172\pi$
$444$	−1302.06	−0.139173
$445$	0	0
$446$	−16511.0	−1.75296
$447$	− 7024.72i	− 0.743306i
$448$	30.0561i	0.00316968i
$449$	10654.5	1.11986	0.559932	−	0.828538i	$-0.310827\pi$
$449$	10654.5	1.11986	0.559932	+	0.828538i	$0.310827\pi$
$450$	0	0
$451$	1442.76	0.150636
$452$	4985.68i	0.518820i
$453$	− 6312.21i	− 0.654688i
$454$	19220.3	1.98691
$455$	0	0
$456$	4018.81	0.412715
$457$	5855.16i	0.599328i	0.954045	+	0.299664i	$0.0968745\pi$
$457$	5855.16i	0.599328i	−0.954045	+	0.299664i	$0.903125\pi$
$458$	1893.76i	0.193208i
$459$	−3307.45	−0.336336
$460$	0	0
$461$	3204.74	0.323774	0.161887	−	0.986809i	$-0.448242\pi$
$461$	3204.74	0.323774	0.161887	+	0.986809i	$0.448242\pi$
$462$	217.844i	0.0219373i
$463$	371.658i	0.0373054i	0.999826	+	0.0186527i	$0.00593769\pi$
$463$	371.658i	0.0373054i	−0.999826	+	0.0186527i	$0.994062\pi$
$464$	7618.54	0.762245
$465$	0	0
$466$	647.927	0.0644091
$467$	19752.3i	1.95723i	0.205703	+	0.978614i	$0.434052\pi$
$467$	19752.3i	1.95723i	−0.205703	+	0.978614i	$0.565948\pi$
$468$	− 766.681i	− 0.0757262i
$469$	−2169.95	−0.213643
$470$	0	0
$471$	−1780.40	−0.174175
$472$	9484.01i	0.924866i
$473$	126.334i	0.0122809i
$474$	−262.320	−0.0254193
$475$	0	0
$476$	−3832.00	−0.368990
$477$	1653.09i	0.158679i
$478$	− 2271.28i	− 0.217335i
$479$	20762.0	1.98046	0.990232	−	0.139433i	$-0.0445279\pi$
$479$	20762.0	1.98046	0.990232	+	0.139433i	$0.0445279\pi$
$480$	0	0
$481$	−1851.34	−0.175496
$482$	− 20323.8i	− 1.92059i
$483$	− 4423.07i	− 0.416681i
$484$	5909.50	0.554987
$485$	0	0
$486$	−858.064	−0.0800876
$487$	− 17647.6i	− 1.64207i	−0.570878	−	0.821035i	$-0.693397\pi$
$487$	− 17647.6i	− 1.64207i	0.570878	−	0.821035i	$-0.306603\pi$
$488$	− 2478.15i	− 0.229878i
$489$	−6536.12	−0.604445
$490$	0	0
$491$	−5637.46	−0.518157	−0.259078	−	0.965856i	$-0.583419\pi$
$491$	−5637.46	−0.518157	−0.259078	+	0.965856i	$0.583419\pi$
$492$	6584.16i	0.603327i
$493$	11697.9i	1.06865i
$494$	−7231.64	−0.658638
$495$	0	0
$496$	7523.86	0.681112
$497$	4659.85i	0.420569i
$498$	4308.58i	0.387695i
$499$	17474.1	1.56764	0.783818	−	0.620991i	$-0.213270\pi$
$499$	17474.1	1.56764	0.783818	+	0.620991i	$0.213270\pi$
$500$	0	0
$501$	2398.51	0.213887
$502$	− 18122.7i	− 1.61127i
$503$	7444.81i	0.659936i	0.943992	+	0.329968i	$0.107038\pi$
$503$	7444.81i	0.659936i	−0.943992	+	0.329968i	$0.892962\pi$
$504$	785.539	0.0694260
$505$	0	0
$506$	2184.90	0.191958
$507$	5500.89i	0.481860i
$508$	− 8383.53i	− 0.732203i
$509$	3384.48	0.294724	0.147362	−	0.989083i	$-0.452922\pi$
$509$	3384.48	0.294724	0.147362	+	0.989083i	$0.452922\pi$
$510$	0	0
$511$	−4349.02	−0.376495
$512$	6558.89i	0.566142i
$513$	2900.77i	0.249653i
$514$	17803.0	1.52774
$515$	0	0
$516$	−576.536	−0.0491872
$517$	1391.00i	0.118329i
$518$	2400.62i	0.203624i
$519$	4333.07	0.366476
$520$	0	0
$521$	2973.12	0.250009	0.125005	−	0.992156i	$-0.460105\pi$
$521$	2973.12	0.250009	0.125005	+	0.992156i	$0.460105\pi$
$522$	3034.82i	0.254465i
$523$	2689.02i	0.224823i	0.993662	+	0.112412i	$0.0358575\pi$
$523$	2689.02i	0.224823i	−0.993662	+	0.112412i	$0.964142\pi$
$524$	−1627.57	−0.135689
$525$	0	0
$526$	−26755.3	−2.21785
$527$	11552.5i	0.954903i
$528$	703.121i	0.0579534i
$529$	−32194.9	−2.64608
$530$	0	0
$531$	−6845.53	−0.559455
$532$	3360.82i	0.273891i
$533$	9361.72i	0.760790i
$534$	2772.83	0.224704
$535$	0	0
$536$	−3865.25	−0.311480
$537$	− 10030.5i	− 0.806046i
$538$	− 3612.69i	− 0.289506i
$539$	143.949	0.0115034
$540$	0	0
$541$	−14429.5	−1.14671	−0.573356	−	0.819306i	$-0.694359\pi$
$541$	−14429.5	−1.14671	−0.573356	+	0.819306i	$0.694359\pi$
$542$	− 7952.03i	− 0.630201i
$543$	6755.44i	0.533893i
$544$	−22290.1	−1.75677
$545$	0	0
$546$	−1413.54	−0.110795
$547$	− 13811.2i	− 1.07957i	−0.841804	−	0.539784i	$-0.818506\pi$
$547$	− 13811.2i	− 1.07957i	0.841804	−	0.539784i	$-0.181494\pi$
$548$	7164.19i	0.558466i
$549$	1788.72	0.139054
$550$	0	0
$551$	10259.5	0.793229
$552$	− 7878.68i	− 0.607498i
$553$	173.338i	0.0133293i
$554$	−30476.2	−2.33720
$555$	0	0
$556$	10864.4	0.828692
$557$	6033.26i	0.458954i	0.973314	+	0.229477i	$0.0737016\pi$
$557$	6033.26i	0.458954i	−0.973314	+	0.229477i	$0.926298\pi$
$558$	2997.10i	0.227379i
$559$	−819.751	−0.0620246
$560$	0	0
$561$	−1079.60	−0.0812493
$562$	− 26559.8i	− 1.99352i
$563$	− 6958.47i	− 0.520896i	−0.965488	−	0.260448i	$-0.916130\pi$
$563$	− 6958.47i	− 0.520896i	0.965488	−	0.260448i	$-0.0838703\pi$
$564$	−6347.95	−0.473931
$565$	0	0
$566$	−52.3202	−0.00388548
$567$	567.000i	0.0419961i
$568$	8300.44i	0.613166i
$569$	13396.4	0.987009	0.493505	−	0.869743i	$-0.335716\pi$
$569$	13396.4	0.987009	0.493505	+	0.869743i	$0.335716\pi$
$570$	0	0
$571$	−8055.84	−0.590414	−0.295207	−	0.955433i	$-0.595389\pi$
$571$	−8055.84	−0.590414	−0.295207	+	0.955433i	$0.595389\pi$
$572$	− 250.257i	− 0.0182933i
$573$	− 3005.78i	− 0.219142i
$574$	12139.3	0.882724
$575$	0	0
$576$	−38.6435	−0.00279539
$577$	21456.9i	1.54812i	0.633114	+	0.774059i	$0.281777\pi$
$577$	21456.9i	1.54812i	−0.633114	+	0.774059i	$0.718223\pi$
$578$	− 35638.9i	− 2.56468i
$579$	12164.9	0.873153
$580$	0	0
$581$	2847.07	0.203298
$582$	− 10644.0i	− 0.758087i
$583$	539.596i	0.0383324i
$584$	−7746.76	−0.548910
$585$	0	0
$586$	−24412.1	−1.72091
$587$	− 20156.3i	− 1.41728i	−0.705572	−	0.708638i	$-0.749310\pi$
$587$	− 20156.3i	− 1.41728i	0.705572	−	0.708638i	$-0.250690\pi$
$588$	656.924i	0.0460733i
$589$	10132.0	0.708797
$590$	0	0
$591$	−15420.7	−1.07330
$592$	7748.30i	0.537928i
$593$	599.307i	0.0415018i	0.999785	+	0.0207509i	$0.00660570\pi$
$593$	599.307i	0.0415018i	−0.999785	+	0.0207509i	$0.993394\pi$
$594$	−280.086	−0.0193469
$595$	0	0
$596$	10464.2	0.719177
$597$	− 1756.89i	− 0.120444i
$598$	14177.3i	0.969485i
$599$	5493.05	0.374691	0.187346	−	0.982294i	$-0.440012\pi$
$599$	5493.05	0.374691	0.187346	+	0.982294i	$0.440012\pi$
$600$	0	0
$601$	24292.8	1.64879	0.824396	−	0.566014i	$-0.191515\pi$
$601$	24292.8	1.64879	0.824396	+	0.566014i	$0.191515\pi$
$602$	1062.97i	0.0719655i
$603$	− 2789.93i	− 0.188416i
$604$	9402.82	0.633436
$605$	0	0
$606$	1365.19	0.0915131
$607$	− 3029.50i	− 0.202576i	−0.994857	−	0.101288i	$-0.967704\pi$
$607$	− 3029.50i	− 0.202576i	0.994857	−	0.101288i	$-0.0322964\pi$
$608$	19549.3i	1.30400i
$609$	2005.38	0.133435
$610$	0	0
$611$	−9025.87	−0.597623
$612$	− 4926.85i	− 0.325419i
$613$	− 19339.6i	− 1.27426i	−0.770757	−	0.637129i	$-0.780122\pi$
$613$	− 19339.6i	− 1.27426i	0.770757	−	0.637129i	$-0.219878\pi$
$614$	−26992.4	−1.77414
$615$	0	0
$616$	256.412	0.0167713
$617$	5743.91i	0.374783i	0.982285	+	0.187391i	$0.0600033\pi$
$617$	5743.91i	0.374783i	−0.982285	+	0.187391i	$0.939997\pi$
$618$	− 8538.35i	− 0.555765i
$619$	8243.35	0.535264	0.267632	−	0.963521i	$-0.413759\pi$
$619$	8243.35	0.535264	0.267632	+	0.963521i	$0.413759\pi$
$620$	0	0
$621$	5686.81	0.367478
$622$	26815.4i	1.72861i
$623$	− 1832.26i	− 0.117830i
$624$	−4562.37	−0.292694
$625$	0	0
$626$	32231.6	2.05788
$627$	946.856i	0.0603091i
$628$	− 2652.13i	− 0.168521i
$629$	−11897.1	−0.754162
$630$	0	0
$631$	−4376.56	−0.276114	−0.138057	−	0.990424i	$-0.544086\pi$
$631$	−4376.56	−0.276114	−0.138057	+	0.990424i	$0.544086\pi$
$632$	308.762i	0.0194334i
$633$	− 3165.48i	− 0.198762i
$634$	−17407.8	−1.09046
$635$	0	0
$636$	−2462.49	−0.153528
$637$	934.051i	0.0580980i
$638$	990.613i	0.0614714i
$639$	−5991.23	−0.370907
$640$	0	0
$641$	11836.6	0.729357	0.364678	−	0.931133i	$-0.381179\pi$
$641$	11836.6	0.729357	0.364678	+	0.931133i	$0.381179\pi$
$642$	− 8153.86i	− 0.501257i
$643$	1448.21i	0.0888209i	0.999013	+	0.0444104i	$0.0141409\pi$
$643$	1448.21i	0.0888209i	−0.999013	+	0.0444104i	$0.985859\pi$
$644$	6588.72	0.403155
$645$	0	0
$646$	−46472.0	−2.83037
$647$	8732.95i	0.530646i	0.964160	+	0.265323i	$0.0854785\pi$
$647$	8732.95i	0.530646i	−0.964160	+	0.265323i	$0.914521\pi$
$648$	1009.98i	0.0612279i
$649$	−2234.49	−0.135149
$650$	0	0
$651$	1980.46	0.119232
$652$	− 9736.37i	− 0.584824i
$653$	− 21978.4i	− 1.31712i	−0.752527	−	0.658562i	$-0.771165\pi$
$653$	− 21978.4i	− 1.31712i	0.752527	−	0.658562i	$-0.228835\pi$
$654$	−8271.91	−0.494583
$655$	0	0
$656$	39181.1	2.33196
$657$	− 5591.59i	− 0.332038i
$658$	11703.8i	0.693406i
$659$	27761.7	1.64103	0.820516	−	0.571623i	$-0.193686\pi$
$659$	27761.7	1.64103	0.820516	+	0.571623i	$0.193686\pi$
$660$	0	0
$661$	−8573.72	−0.504507	−0.252254	−	0.967661i	$-0.581172\pi$
$661$	−8573.72	−0.504507	−0.252254	+	0.967661i	$0.581172\pi$
$662$	4313.86i	0.253267i
$663$	− 7005.27i	− 0.410350i
$664$	5071.39	0.296398
$665$	0	0
$666$	−3086.51	−0.179579
$667$	− 20113.2i	− 1.16760i
$668$	3572.87i	0.206944i
$669$	−14027.6	−0.810668
$670$	0	0
$671$	583.868	0.0335916
$672$	3821.22i	0.219356i
$673$	27159.2i	1.55559i	0.628518	+	0.777795i	$0.283662\pi$
$673$	27159.2i	1.55559i	−0.628518	+	0.777795i	$0.716338\pi$
$674$	−30879.1	−1.76472
$675$	0	0
$676$	−8194.26	−0.466219
$677$	1392.30i	0.0790404i	0.999219	+	0.0395202i	$0.0125829\pi$
$677$	1392.30i	0.0790404i	−0.999219	+	0.0395202i	$0.987417\pi$
$678$	11818.5i	0.669448i
$679$	−7033.42	−0.397523
$680$	0	0
$681$	16329.3	0.918857
$682$	978.302i	0.0549283i
$683$	− 8675.09i	− 0.486007i	−0.970025	−	0.243004i	$-0.921867\pi$
$683$	− 8675.09i	− 0.486007i	0.970025	−	0.243004i	$-0.0781327\pi$
$684$	−4321.05	−0.241549
$685$	0	0
$686$	1211.18	0.0674096
$687$	1608.91i	0.0893504i
$688$	3430.86i	0.190117i
$689$	−3501.30	−0.193598
$690$	0	0
$691$	−21426.0	−1.17957	−0.589785	−	0.807561i	$-0.700787\pi$
$691$	−21426.0	−1.17957	−0.589785	+	0.807561i	$0.700787\pi$
$692$	6454.65i	0.354579i
$693$	185.078i	0.0101451i
$694$	16206.3	0.886433
$695$	0	0
$696$	3572.11	0.194541
$697$	60160.4i	3.26935i
$698$	14088.8i	0.763997i
$699$	550.470	0.0297864
$700$	0	0
$701$	24840.5	1.33839	0.669197	−	0.743085i	$-0.266638\pi$
$701$	24840.5	1.33839	0.669197	+	0.743085i	$0.266638\pi$
$702$	− 1817.40i	− 0.0977116i
$703$	10434.2i	0.559793i
$704$	−12.6139	−0.000675288 0
$705$	0	0
$706$	−8532.45	−0.454848
$707$	− 902.101i	− 0.0479873i
$708$	− 10197.3i	− 0.541295i
$709$	−12525.0	−0.663450	−0.331725	−	0.943376i	$-0.607631\pi$
$709$	−12525.0	−0.663450	−0.331725	+	0.943376i	$0.607631\pi$
$710$	0	0
$711$	−222.863	−0.0117553
$712$	− 3263.74i	− 0.171789i
$713$	− 19863.3i	− 1.04332i
$714$	−9083.69	−0.476118
$715$	0	0
$716$	14941.6	0.779881
$717$	− 1929.65i	− 0.100508i
$718$	9732.66i	0.505877i
$719$	−28085.0	−1.45674	−0.728369	−	0.685185i	$-0.759721\pi$
$719$	−28085.0	−1.45674	−0.728369	+	0.685185i	$0.759721\pi$
$720$	0	0
$721$	−5642.05	−0.291430
$722$	16537.9i	0.852460i
$723$	− 17266.8i	− 0.888189i
$724$	−10063.1	−0.516562
$725$	0	0
$726$	14008.4	0.716115
$727$	14326.2i	0.730851i	0.930841	+	0.365426i	$0.119077\pi$
$727$	14326.2i	0.730851i	−0.930841	+	0.365426i	$0.880923\pi$
$728$	1663.79i	0.0847037i
$729$	−729.000	−0.0370370
$730$	0	0
$731$	−5267.89	−0.266539
$732$	2664.53i	0.134541i
$733$	6727.85i	0.339016i	0.985529	+	0.169508i	$0.0542179\pi$
$733$	6727.85i	0.339016i	−0.985529	+	0.169508i	$0.945782\pi$
$734$	39240.8	1.97331
$735$	0	0
$736$	38325.5	1.91943
$737$	− 910.677i	− 0.0455159i
$738$	15607.6i	0.778490i
$739$	3418.51	0.170165	0.0850826	−	0.996374i	$-0.472885\pi$
$739$	3418.51	0.170165	0.0850826	+	0.996374i	$0.472885\pi$
$740$	0	0
$741$	−6143.91	−0.304591
$742$	4540.11i	0.224626i
$743$	8095.50i	0.399724i	0.979824	+	0.199862i	$0.0640494\pi$
$743$	8095.50i	0.399724i	−0.979824	+	0.199862i	$0.935951\pi$
$744$	3527.72	0.173834
$745$	0	0
$746$	−21508.4	−1.05560
$747$	3660.51i	0.179292i
$748$	− 1608.20i	− 0.0786119i
$749$	−5387.99	−0.262847
$750$	0	0
$751$	13446.8	0.653371	0.326686	−	0.945133i	$-0.394068\pi$
$751$	13446.8	0.653371	0.326686	+	0.945133i	$0.394068\pi$
$752$	37775.4i	1.83182i
$753$	− 15396.8i	− 0.745141i
$754$	−6427.84	−0.310462
$755$	0	0
$756$	−844.617	−0.0406328
$757$	2593.24i	0.124508i	0.998060	+	0.0622541i	$0.0198289\pi$
$757$	2593.24i	0.124508i	−0.998060	+	0.0622541i	$0.980171\pi$
$758$	− 14069.0i	− 0.674156i
$759$	1856.26	0.0887722
$760$	0	0
$761$	27079.4	1.28992	0.644959	−	0.764217i	$-0.276875\pi$
$761$	27079.4	1.28992	0.644959	+	0.764217i	$0.276875\pi$
$762$	− 19873.0i	− 0.944782i
$763$	5465.99i	0.259348i
$764$	4477.48	0.212028
$765$	0	0
$766$	−1124.58	−0.0530451
$767$	− 14499.0i	− 0.682568i
$768$	15363.3i	0.721842i
$769$	−2138.72	−0.100292	−0.0501458	−	0.998742i	$-0.515969\pi$
$769$	−2138.72	−0.100292	−0.0501458	+	0.998742i	$0.515969\pi$
$770$	0	0
$771$	15125.2	0.706513
$772$	18121.1i	0.844810i
$773$	25864.0i	1.20345i	0.798704	+	0.601724i	$0.205519\pi$
$773$	25864.0i	1.20345i	−0.798704	+	0.601724i	$0.794481\pi$
$774$	−1366.67	−0.0634676
$775$	0	0
$776$	−12528.4	−0.579566
$777$	2039.53i	0.0941671i
$778$	− 13720.1i	− 0.632247i
$779$	52763.1	2.42675
$780$	0	0
$781$	−1955.63	−0.0896006
$782$	91106.2i	4.16618i
$783$	2578.34i	0.117679i
$784$	3909.23	0.178081
$785$	0	0
$786$	−3858.14	−0.175083
$787$	32371.3i	1.46621i	0.680113	+	0.733107i	$0.261931\pi$
$787$	32371.3i	1.46621i	−0.680113	+	0.733107i	$0.738069\pi$
$788$	− 22971.0i	− 1.03846i
$789$	−22731.0	−1.02566
$790$	0	0
$791$	7809.52	0.351043
$792$	329.673i	0.0147909i
$793$	3788.57i	0.169654i
$794$	16970.8	0.758526
$795$	0	0
$796$	2617.11	0.116534
$797$	− 2024.33i	− 0.0899691i	−0.998988	−	0.0449845i	$-0.985676\pi$
$797$	− 2024.33i	− 0.0899691i	0.998988	−	0.0449845i	$-0.0143239\pi$
$798$	7966.76i	0.353409i
$799$	−58002.1	−2.56817
$800$	0	0
$801$	2355.76	0.103916
$802$	12777.7i	0.562589i
$803$	− 1825.18i	− 0.0802109i
$804$	4155.95	0.182300
$805$	0	0
$806$	−6347.95	−0.277416
$807$	− 3069.29i	− 0.133884i
$808$	− 1606.88i	− 0.0699628i
$809$	−12391.7	−0.538526	−0.269263	−	0.963067i	$-0.586780\pi$
$809$	−12391.7	−0.538526	−0.269263	+	0.963067i	$0.586780\pi$
$810$	0	0
$811$	14654.5	0.634511	0.317256	−	0.948340i	$-0.397239\pi$
$811$	14654.5	0.634511	0.317256	+	0.948340i	$0.397239\pi$
$812$	2987.26i	0.129104i
$813$	− 6755.94i	− 0.291441i
$814$	−1007.49	−0.0433813
$815$	0	0
$816$	−29318.7	−1.25780
$817$	4620.16i	0.197844i
$818$	7447.33i	0.318325i
$819$	−1200.92	−0.0512376
$820$	0	0
$821$	23887.9	1.01546	0.507731	−	0.861516i	$-0.330485\pi$
$821$	23887.9	1.01546	0.507731	+	0.861516i	$0.330485\pi$
$822$	16982.6i	0.720604i
$823$	− 4008.41i	− 0.169774i	−0.996391	−	0.0848871i	$-0.972947\pi$
$823$	− 4008.41i	− 0.169774i	0.996391	−	0.0848871i	$-0.0270530\pi$
$824$	−10050.0	−0.424889
$825$	0	0
$826$	−18800.8	−0.791966
$827$	45110.4i	1.89679i	0.317096	+	0.948394i	$0.397292\pi$
$827$	45110.4i	1.89679i	−0.317096	+	0.948394i	$0.602708\pi$
$828$	8471.21i	0.355549i
$829$	−16165.4	−0.677260	−0.338630	−	0.940920i	$-0.609964\pi$
$829$	−16165.4	−0.677260	−0.338630	+	0.940920i	$0.609964\pi$
$830$	0	0
$831$	−25892.2	−1.08085
$832$	− 81.8481i	− 0.00341054i
$833$	6002.41i	0.249665i
$834$	25753.8	1.06928
$835$	0	0
$836$	−1410.46	−0.0583514
$837$	2546.30i	0.105153i
$838$	24385.7i	1.00524i
$839$	25244.4	1.03878	0.519388	−	0.854538i	$-0.326160\pi$
$839$	25244.4	1.03878	0.519388	+	0.854538i	$0.326160\pi$
$840$	0	0
$841$	−15269.9	−0.626096
$842$	− 34066.7i	− 1.39432i
$843$	− 22564.9i	− 0.921916i
$844$	4715.37	0.192310
$845$	0	0
$846$	−15047.7	−0.611526
$847$	− 9256.59i	− 0.375514i
$848$	14653.8i	0.593412i
$849$	−44.4506	−0.00179687
$850$	0	0
$851$	20455.8	0.823990
$852$	− 8924.68i	− 0.358867i
$853$	− 30168.1i	− 1.21094i	−0.795867	−	0.605472i	$-0.792984\pi$
$853$	− 30168.1i	− 1.21094i	0.795867	−	0.605472i	$-0.207016\pi$
$854$	4912.61	0.196846
$855$	0	0
$856$	−9597.44	−0.383217
$857$	13393.6i	0.533857i	0.963716	+	0.266929i	$0.0860088\pi$
$857$	13393.6i	0.533857i	−0.963716	+	0.266929i	$0.913991\pi$
$858$	− 593.230i	− 0.0236043i
$859$	−19060.4	−0.757081	−0.378541	−	0.925585i	$-0.623574\pi$
$859$	−19060.4	−0.757081	−0.378541	+	0.925585i	$0.623574\pi$
$860$	0	0
$861$	10313.4	0.408222
$862$	− 45914.3i	− 1.81421i
$863$	− 9466.86i	− 0.373413i	−0.982416	−	0.186707i	$-0.940219\pi$
$863$	− 9466.86i	− 0.373413i	0.982416	−	0.186707i	$-0.0597814\pi$
$864$	−4913.00	−0.193453
$865$	0	0
$866$	−25975.2	−1.01925
$867$	− 30278.3i	− 1.18605i
$868$	2950.13i	0.115362i
$869$	−72.7461	−0.00283975
$870$	0	0
$871$	5909.15	0.229878
$872$	9736.39i	0.378115i
$873$	− 9042.97i	− 0.350582i
$874$	79903.8	3.09243
$875$	0	0
$876$	8329.37	0.321259
$877$	− 37740.6i	− 1.45315i	−0.687090	−	0.726573i	$-0.741112\pi$
$877$	− 37740.6i	− 1.45315i	0.687090	−	0.726573i	$-0.258888\pi$
$878$	− 24397.3i	− 0.937778i
$879$	−20740.2	−0.795845
$880$	0	0
$881$	25991.5	0.993957	0.496979	−	0.867763i	$-0.334443\pi$
$881$	25991.5	0.993957	0.496979	+	0.867763i	$0.334443\pi$
$882$	1557.23i	0.0594496i
$883$	39420.3i	1.50238i	0.660087	+	0.751189i	$0.270519\pi$
$883$	39420.3i	1.50238i	−0.660087	+	0.751189i	$0.729481\pi$
$884$	10435.2	0.397030
$885$	0	0
$886$	52305.0	1.98332
$887$	− 46005.2i	− 1.74149i	−0.491735	−	0.870745i	$-0.663637\pi$
$887$	− 46005.2i	− 1.74149i	0.491735	−	0.870745i	$-0.336363\pi$
$888$	3632.95i	0.137290i
$889$	−13131.9	−0.495421
$890$	0	0
$891$	−237.957	−0.00894710
$892$	− 20895.8i	− 0.784353i
$893$	50870.2i	1.90628i
$894$	24805.2	0.927975
$895$	0	0
$896$	10083.8	0.375978
$897$	12044.8i	0.448345i
$898$	37622.6i	1.39809i
$899$	9005.81	0.334105
$900$	0	0
$901$	−22500.1	−0.831950
$902$	5094.58i	0.188061i
$903$	903.081i	0.0332809i
$904$	13910.8	0.511801
$905$	0	0
$906$	22289.2	0.817340
$907$	2838.97i	0.103932i	0.998649	+	0.0519661i	$0.0165488\pi$
$907$	2838.97i	0.103932i	−0.998649	+	0.0519661i	$0.983451\pi$
$908$	24324.6i	0.889030i
$909$	1159.84	0.0423208
$910$	0	0
$911$	39890.9	1.45076	0.725382	−	0.688347i	$-0.241663\pi$
$911$	39890.9	1.45076	0.725382	+	0.688347i	$0.241663\pi$
$912$	25713.7i	0.933626i
$913$	1194.85i	0.0433119i
$914$	−20675.3	−0.748226
$915$	0	0
$916$	−2396.67	−0.0864500
$917$	2549.42i	0.0918094i
$918$	− 11679.0i	− 0.419897i
$919$	646.475	0.0232048	0.0116024	−	0.999933i	$-0.496307\pi$
$919$	646.475	0.0232048	0.0116024	+	0.999933i	$0.496307\pi$
$920$	0	0
$921$	−22932.4	−0.820463
$922$	11316.3i	0.404213i
$923$	− 12689.6i	− 0.452528i
$924$	−275.696	−0.00981574
$925$	0	0
$926$	−1312.37	−0.0465737
$927$	− 7254.07i	− 0.257017i
$928$	17376.4i	0.614665i
$929$	−51188.2	−1.80778	−0.903892	−	0.427760i	$-0.859303\pi$
$929$	−51188.2	−1.80778	−0.903892	+	0.427760i	$0.859303\pi$
$930$	0	0
$931$	5264.35	0.185319
$932$	819.993i	0.0288195i
$933$	22782.0i	0.799409i
$934$	−69747.8	−2.44349
$935$	0	0
$936$	−2139.16	−0.0747017
$937$	− 29786.1i	− 1.03849i	−0.854624	−	0.519247i	$-0.826212\pi$
$937$	− 29786.1i	− 1.03849i	0.854624	−	0.519247i	$-0.173788\pi$
$938$	− 7662.36i	− 0.266722i
$939$	27383.5	0.951680
$940$	0	0
$941$	−44817.4	−1.55261	−0.776304	−	0.630358i	$-0.782908\pi$
$941$	−44817.4	−1.55261	−0.776304	+	0.630358i	$0.782908\pi$
$942$	− 6286.82i	− 0.217448i
$943$	− 103439.i	− 3.57206i
$944$	−60682.0	−2.09219
$945$	0	0
$946$	−446.103	−0.0153320
$947$	− 54697.1i	− 1.87689i	−0.345425	−	0.938446i	$-0.612265\pi$
$947$	− 54697.1i	− 1.87689i	0.345425	−	0.938446i	$-0.387735\pi$
$948$	− 331.983i	− 0.0113737i
$949$	11843.2	0.405105
$950$	0	0
$951$	−14789.4	−0.504290
$952$	10691.9i	0.363998i
$953$	− 7577.51i	− 0.257565i	−0.991673	−	0.128783i	$-0.958893\pi$
$953$	− 7577.51i	− 0.257565i	0.991673	−	0.128783i	$-0.0411069\pi$
$954$	−5837.29	−0.198102
$955$	0	0
$956$	2874.46	0.0972454
$957$	841.612i	0.0284278i
$958$	73313.4i	2.47249i
$959$	11221.9	0.377868
$960$	0	0
$961$	−20897.1	−0.701457
$962$	− 6537.32i	− 0.219097i
$963$	− 6927.41i	− 0.231810i
$964$	25721.1	0.859357
$965$	0	0
$966$	15618.4	0.520202
$967$	− 50779.0i	− 1.68867i	−0.535817	−	0.844334i	$-0.679996\pi$
$967$	− 50779.0i	− 1.68867i	0.535817	−	0.844334i	$-0.320004\pi$
$968$	− 16488.5i	− 0.547478i
$969$	−39482.0	−1.30892
$970$	0	0
$971$	−15313.2	−0.506102	−0.253051	−	0.967453i	$-0.581434\pi$
$971$	−15313.2	−0.506102	−0.253051	+	0.967453i	$0.581434\pi$
$972$	− 1085.94i	− 0.0358348i
$973$	− 17017.9i	− 0.560707i
$974$	62315.9	2.05003
$975$	0	0
$976$	15856.1	0.520021
$977$	− 46620.4i	− 1.52663i	−0.646025	−	0.763316i	$-0.723570\pi$
$977$	− 46620.4i	− 1.52663i	0.646025	−	0.763316i	$-0.276430\pi$
$978$	− 23079.9i	− 0.754615i
$979$	768.957	0.0251031
$980$	0	0
$981$	−7027.70	−0.228723
$982$	− 19906.6i	− 0.646889i
$983$	− 2824.37i	− 0.0916414i	−0.998950	−	0.0458207i	$-0.985410\pi$
$983$	− 2824.37i	− 0.0916414i	0.998950	−	0.0458207i	$-0.0145903\pi$
$984$	18370.9	0.595165
$985$	0	0
$986$	−41306.6	−1.33415
$987$	9943.38i	0.320670i
$988$	− 9152.11i	− 0.294704i
$989$	9057.59	0.291218
$990$	0	0
$991$	16951.4	0.543370	0.271685	−	0.962386i	$-0.412419\pi$
$991$	16951.4	0.543370	0.271685	+	0.962386i	$0.412419\pi$
$992$	17160.5i	0.549239i
$993$	3665.00i	0.117125i
$994$	−16454.5	−0.525056
$995$	0	0
$996$	−5452.79	−0.173472
$997$	− 23847.8i	− 0.757540i	−0.925491	−	0.378770i	$-0.876347\pi$
$997$	− 23847.8i	− 0.757540i	0.925491	−	0.378770i	$-0.123653\pi$
$998$	61703.4i	1.95710i
$999$	−2622.26	−0.0830476

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	525.4.d.h.274.3		4
5.2	odd	4		105.4.a.f.1.1	✓	2
5.3	odd	4		525.4.a.k.1.2		2
5.4	even	2	inner	525.4.d.h.274.2		4
15.2	even	4		315.4.a.i.1.2		2
15.8	even	4		1575.4.a.w.1.1		2
20.7	even	4		1680.4.a.bg.1.1		2
35.27	even	4		735.4.a.p.1.1		2
105.62	odd	4		2205.4.a.z.1.2		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
105.4.a.f.1.1	✓	2	5.2	odd	4
315.4.a.i.1.2		2	15.2	even	4
525.4.a.k.1.2		2	5.3	odd	4
525.4.d.h.274.2		4	5.4	even	2	inner
525.4.d.h.274.3		4	1.1	even	1	trivial
735.4.a.p.1.1		2	35.27	even	4
1575.4.a.w.1.1		2	15.8	even	4
1680.4.a.bg.1.1		2	20.7	even	4
2205.4.a.z.1.2		2	105.62	odd	4

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

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

\(f(q)\)	\(=\)	\(q+3.53113i q^{2} +3.00000i q^{3} -4.46887 q^{4} -10.5934 q^{6} +7.00000i q^{7} +12.4689i q^{8} -9.00000 q^{9} +O(q^{10})\)	\(q+3.53113i q^{2} +3.00000i q^{3} -4.46887 q^{4} -10.5934 q^{6} +7.00000i q^{7} +12.4689i q^{8} -9.00000 q^{9} -2.93774 q^{11} -13.4066i q^{12} -19.0623i q^{13} -24.7179 q^{14} -79.7802 q^{16} -122.498i q^{17} -31.7802i q^{18} -107.436 q^{19} -21.0000 q^{21} -10.3735i q^{22} +210.623i q^{23} -37.4066 q^{24} +67.3113 q^{26} -27.0000i q^{27} -31.2821i q^{28} -95.4942 q^{29} -94.3074 q^{31} -181.963i q^{32} -8.81323i q^{33} +432.556 q^{34} +40.2198 q^{36} -97.1206i q^{37} -379.370i q^{38} +57.1868 q^{39} -491.113 q^{41} -74.1537i q^{42} -43.0039i q^{43} +13.1284 q^{44} -743.735 q^{46} -473.494i q^{47} -239.340i q^{48} -49.0000 q^{49} +367.494 q^{51} +85.1868i q^{52} -183.677i q^{53} +95.3405 q^{54} -87.2821 q^{56} -322.307i q^{57} -337.202i q^{58} +760.615 q^{59} -198.747 q^{61} -333.012i q^{62} -63.0000i q^{63} +4.29373 q^{64} +31.1206 q^{66} +309.992i q^{67} +547.428i q^{68} -631.868 q^{69} +665.693 q^{71} -112.220i q^{72} +621.288i q^{73} +342.945 q^{74} +480.117 q^{76} -20.5642i q^{77} +201.934i q^{78} +24.7626 q^{79} +81.0000 q^{81} -1734.18i q^{82} -406.724i q^{83} +93.8463 q^{84} +151.852 q^{86} -286.483i q^{87} -36.6303i q^{88} -261.751 q^{89} +133.436 q^{91} -941.245i q^{92} -282.922i q^{93} +1671.97 q^{94} +545.889 q^{96} +1004.77i q^{97} -173.025i q^{98} +26.4397 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 34 q^{4} + 6 q^{6} - 36 q^{9}+O(q^{10}) \) 4 * q - 34 * q^4 + 6 * q^6 - 36 * q^9	\( 4 q - 34 q^{4} + 6 q^{6} - 36 q^{9} - 44 q^{11} + 14 q^{14} - 174 q^{16} - 204 q^{19} - 84 q^{21} - 198 q^{24} + 108 q^{26} + 392 q^{29} + 300 q^{31} + 924 q^{34} + 306 q^{36} + 132 q^{39} - 352 q^{41} + 504 q^{44} - 1040 q^{46} - 196 q^{49} + 696 q^{51} - 54 q^{54} - 462 q^{56} + 1688 q^{59} - 408 q^{61} + 1678 q^{64} - 456 q^{66} - 1560 q^{69} + 3340 q^{71} + 2436 q^{74} + 824 q^{76} + 1776 q^{79} + 324 q^{81} + 714 q^{84} - 2424 q^{86} - 1176 q^{89} + 308 q^{91} + 2560 q^{94} - 90 q^{96} + 396 q^{99}+O(q^{100}) \) 4 * q - 34 * q^4 + 6 * q^6 - 36 * q^9 - 44 * q^11 + 14 * q^14 - 174 * q^16 - 204 * q^19 - 84 * q^21 - 198 * q^24 + 108 * q^26 + 392 * q^29 + 300 * q^31 + 924 * q^34 + 306 * q^36 + 132 * q^39 - 352 * q^41 + 504 * q^44 - 1040 * q^46 - 196 * q^49 + 696 * q^51 - 54 * q^54 - 462 * q^56 + 1688 * q^59 - 408 * q^61 + 1678 * q^64 - 456 * q^66 - 1560 * q^69 + 3340 * q^71 + 2436 * q^74 + 824 * q^76 + 1776 * q^79 + 324 * q^81 + 714 * q^84 - 2424 * q^86 - 1176 * q^89 + 308 * q^91 + 2560 * q^94 - 90 * q^96 + 396 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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