LMFDB - Embedded newform 2850.2.d.m.799.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2850,2,Mod(799,2850)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2850, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("2850.799");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 2850 = 2 \cdot 3 \cdot 5^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2850.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:	$22.7573645761$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(i)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} + 1 $ x^2 + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			799.1
Root			$1.00000i$ of defining polynomial
Character	$\chi$	$=$	2850.799
Dual form			2850.2.d.m.799.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000i q^{2} +1.00000i q^{3} -1.00000 q^{4} +1.00000 q^{6} +2.00000i q^{7} +1.00000i q^{8} -1.00000 q^{9} +O(q^{10})$	\(q-1.00000i q^{2} +1.00000i q^{3} -1.00000 q^{4} +1.00000 q^{6} +2.00000i q^{7} +1.00000i q^{8} -1.00000 q^{9} -3.00000 q^{11} -1.00000i q^{12} -6.00000i q^{13} +2.00000 q^{14} +1.00000 q^{16} +2.00000i q^{17} +1.00000i q^{18} +1.00000 q^{19} -2.00000 q^{21} +3.00000i q^{22} -1.00000i q^{23} -1.00000 q^{24} -6.00000 q^{26} -1.00000i q^{27} -2.00000i q^{28} +5.00000 q^{29} +7.00000 q^{31} -1.00000i q^{32} -3.00000i q^{33} +2.00000 q^{34} +1.00000 q^{36} +2.00000i q^{37} -1.00000i q^{38} +6.00000 q^{39} +2.00000 q^{41} +2.00000i q^{42} -6.00000i q^{43} +3.00000 q^{44} -1.00000 q^{46} +12.0000i q^{47} +1.00000i q^{48} +3.00000 q^{49} -2.00000 q^{51} +6.00000i q^{52} +9.00000i q^{53} -1.00000 q^{54} -2.00000 q^{56} +1.00000i q^{57} -5.00000i q^{58} +10.0000 q^{59} -13.0000 q^{61} -7.00000i q^{62} -2.00000i q^{63} -1.00000 q^{64} -3.00000 q^{66} +7.00000i q^{67} -2.00000i q^{68} +1.00000 q^{69} +12.0000 q^{71} -1.00000i q^{72} +9.00000i q^{73} +2.00000 q^{74} -1.00000 q^{76} -6.00000i q^{77} -6.00000i q^{78} -5.00000 q^{79} +1.00000 q^{81} -2.00000i q^{82} -1.00000i q^{83} +2.00000 q^{84} -6.00000 q^{86} +5.00000i q^{87} -3.00000i q^{88} -5.00000 q^{89} +12.0000 q^{91} +1.00000i q^{92} +7.00000i q^{93} +12.0000 q^{94} +1.00000 q^{96} +12.0000i q^{97} -3.00000i q^{98} +3.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - 2 q^{4} + 2 q^{6} - 2 q^{9}+O(q^{10}) $ 2 * q - 2 * q^4 + 2 * q^6 - 2 * q^9	$ 2 q - 2 q^{4} + 2 q^{6} - 2 q^{9} - 6 q^{11} + 4 q^{14} + 2 q^{16} + 2 q^{19} - 4 q^{21} - 2 q^{24} - 12 q^{26} + 10 q^{29} + 14 q^{31} + 4 q^{34} + 2 q^{36} + 12 q^{39} + 4 q^{41} + 6 q^{44} - 2 q^{46} + 6 q^{49} - 4 q^{51} - 2 q^{54} - 4 q^{56} + 20 q^{59} - 26 q^{61} - 2 q^{64} - 6 q^{66} + 2 q^{69} + 24 q^{71} + 4 q^{74} - 2 q^{76} - 10 q^{79} + 2 q^{81} + 4 q^{84} - 12 q^{86} - 10 q^{89} + 24 q^{91} + 24 q^{94} + 2 q^{96} + 6 q^{99}+O(q^{100}) $ 2 * q - 2 * q^4 + 2 * q^6 - 2 * q^9 - 6 * q^11 + 4 * q^14 + 2 * q^16 + 2 * q^19 - 4 * q^21 - 2 * q^24 - 12 * q^26 + 10 * q^29 + 14 * q^31 + 4 * q^34 + 2 * q^36 + 12 * q^39 + 4 * q^41 + 6 * q^44 - 2 * q^46 + 6 * q^49 - 4 * q^51 - 2 * q^54 - 4 * q^56 + 20 * q^59 - 26 * q^61 - 2 * q^64 - 6 * q^66 + 2 * q^69 + 24 * q^71 + 4 * q^74 - 2 * q^76 - 10 * q^79 + 2 * q^81 + 4 * q^84 - 12 * q^86 - 10 * q^89 + 24 * q^91 + 24 * q^94 + 2 * q^96 + 6 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/2850\mathbb{Z}\right)^\times$.

$n$	$1027$	$1351$	$1901$
$\chi(n)$	$-1$	$1$	$1$

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 $

$2$	− 1.00000i	− 0.707107i
$2$	− 1.00000i	− 0.707107i
$3$	1.00000i	0.577350i
$3$	1.00000i	0.577350i
$4$	−1.00000	−0.500000
$5$	0	0
$5$	0	0
$6$	1.00000	0.408248
$7$	2.00000i	0.755929i	0.925820	+	0.377964i	$0.123376\pi$
$7$	2.00000i	0.755929i	−0.925820	+	0.377964i	$0.876624\pi$
$8$	1.00000i	0.353553i
$9$	−1.00000	−0.333333
$10$	0	0
$11$	−3.00000	−0.904534	−0.452267	−	0.891883i	$-0.649385\pi$
$11$	−3.00000	−0.904534	−0.452267	+	0.891883i	$0.649385\pi$
$12$	− 1.00000i	− 0.288675i
$13$	− 6.00000i	− 1.66410i	−0.554700	−	0.832050i	$-0.687167\pi$
$13$	− 6.00000i	− 1.66410i	0.554700	−	0.832050i	$-0.312833\pi$
$14$	2.00000	0.534522
$15$	0	0
$16$	1.00000	0.250000
$17$	2.00000i	0.485071i	0.970143	+	0.242536i	$0.0779791\pi$
$17$	2.00000i	0.485071i	−0.970143	+	0.242536i	$0.922021\pi$
$18$	1.00000i	0.235702i
$19$	1.00000	0.229416
$19$	1.00000	0.229416
$20$	0	0
$21$	−2.00000	−0.436436
$22$	3.00000i	0.639602i
$23$	− 1.00000i	− 0.208514i	−0.994550	−	0.104257i	$-0.966753\pi$
$23$	− 1.00000i	− 0.208514i	0.994550	−	0.104257i	$-0.0332465\pi$
$24$	−1.00000	−0.204124
$25$	0	0
$26$	−6.00000	−1.17670
$27$	− 1.00000i	− 0.192450i
$28$	− 2.00000i	− 0.377964i
$29$	5.00000	0.928477	0.464238	−	0.885710i	$-0.346328\pi$
$29$	5.00000	0.928477	0.464238	+	0.885710i	$0.346328\pi$
$30$	0	0
$31$	7.00000	1.25724	0.628619	−	0.777714i	$-0.283621\pi$
$31$	7.00000	1.25724	0.628619	+	0.777714i	$0.283621\pi$
$32$	− 1.00000i	− 0.176777i
$33$	− 3.00000i	− 0.522233i
$34$	2.00000	0.342997
$35$	0	0
$36$	1.00000	0.166667
$37$	2.00000i	0.328798i	0.986394	+	0.164399i	$0.0525685\pi$
$37$	2.00000i	0.328798i	−0.986394	+	0.164399i	$0.947432\pi$
$38$	− 1.00000i	− 0.162221i
$39$	6.00000	0.960769
$40$	0	0
$41$	2.00000	0.312348	0.156174	−	0.987730i	$-0.450084\pi$
$41$	2.00000	0.312348	0.156174	+	0.987730i	$0.450084\pi$
$42$	2.00000i	0.308607i
$43$	− 6.00000i	− 0.914991i	−0.889212	−	0.457496i	$-0.848747\pi$
$43$	− 6.00000i	− 0.914991i	0.889212	−	0.457496i	$-0.151253\pi$
$44$	3.00000	0.452267
$45$	0	0
$46$	−1.00000	−0.147442
$47$	12.0000i	1.75038i	0.483779	+	0.875190i	$0.339264\pi$
$47$	12.0000i	1.75038i	−0.483779	+	0.875190i	$0.660736\pi$
$48$	1.00000i	0.144338i
$49$	3.00000	0.428571
$50$	0	0
$51$	−2.00000	−0.280056
$52$	6.00000i	0.832050i
$53$	9.00000i	1.23625i	0.786082	+	0.618123i	$0.212106\pi$
$53$	9.00000i	1.23625i	−0.786082	+	0.618123i	$0.787894\pi$
$54$	−1.00000	−0.136083
$55$	0	0
$56$	−2.00000	−0.267261
$57$	1.00000i	0.132453i
$58$	− 5.00000i	− 0.656532i
$59$	10.0000	1.30189	0.650945	−	0.759125i	$-0.274373\pi$
$59$	10.0000	1.30189	0.650945	+	0.759125i	$0.274373\pi$
$60$	0	0
$61$	−13.0000	−1.66448	−0.832240	−	0.554416i	$-0.812942\pi$
$61$	−13.0000	−1.66448	−0.832240	+	0.554416i	$0.812942\pi$
$62$	− 7.00000i	− 0.889001i
$63$	− 2.00000i	− 0.251976i
$64$	−1.00000	−0.125000
$65$	0	0
$66$	−3.00000	−0.369274
$67$	7.00000i	0.855186i	0.903971	+	0.427593i	$0.140638\pi$
$67$	7.00000i	0.855186i	−0.903971	+	0.427593i	$0.859362\pi$
$68$	− 2.00000i	− 0.242536i
$69$	1.00000	0.120386
$70$	0	0
$71$	12.0000	1.42414	0.712069	−	0.702109i	$-0.247758\pi$
$71$	12.0000	1.42414	0.712069	+	0.702109i	$0.247758\pi$
$72$	− 1.00000i	− 0.117851i
$73$	9.00000i	1.05337i	0.850060	+	0.526685i	$0.176565\pi$
$73$	9.00000i	1.05337i	−0.850060	+	0.526685i	$0.823435\pi$
$74$	2.00000	0.232495
$75$	0	0
$76$	−1.00000	−0.114708
$77$	− 6.00000i	− 0.683763i
$78$	− 6.00000i	− 0.679366i
$79$	−5.00000	−0.562544	−0.281272	−	0.959628i	$-0.590756\pi$
$79$	−5.00000	−0.562544	−0.281272	+	0.959628i	$0.590756\pi$
$80$	0	0
$81$	1.00000	0.111111
$82$	− 2.00000i	− 0.220863i
$83$	− 1.00000i	− 0.109764i	−0.998493	−	0.0548821i	$-0.982522\pi$
$83$	− 1.00000i	− 0.109764i	0.998493	−	0.0548821i	$-0.0174783\pi$
$84$	2.00000	0.218218
$85$	0	0
$86$	−6.00000	−0.646997
$87$	5.00000i	0.536056i
$88$	− 3.00000i	− 0.319801i
$89$	−5.00000	−0.529999	−0.264999	−	0.964249i	$-0.585372\pi$
$89$	−5.00000	−0.529999	−0.264999	+	0.964249i	$0.585372\pi$
$90$	0	0
$91$	12.0000	1.25794
$92$	1.00000i	0.104257i
$93$	7.00000i	0.725866i
$94$	12.0000	1.23771
$95$	0	0
$96$	1.00000	0.102062
$97$	12.0000i	1.21842i	0.793011	+	0.609208i	$0.208512\pi$
$97$	12.0000i	1.21842i	−0.793011	+	0.609208i	$0.791488\pi$
$98$	− 3.00000i	− 0.303046i
$99$	3.00000	0.301511
$100$	0	0
$101$	2.00000	0.199007	0.0995037	−	0.995037i	$-0.468274\pi$
$101$	2.00000	0.199007	0.0995037	+	0.995037i	$0.468274\pi$
$102$	2.00000i	0.198030i
$103$	9.00000i	0.886796i	0.896325	+	0.443398i	$0.146227\pi$
$103$	9.00000i	0.886796i	−0.896325	+	0.443398i	$0.853773\pi$
$104$	6.00000	0.588348
$105$	0	0
$106$	9.00000	0.874157
$107$	12.0000i	1.16008i	0.814587	+	0.580042i	$0.196964\pi$
$107$	12.0000i	1.16008i	−0.814587	+	0.580042i	$0.803036\pi$
$108$	1.00000i	0.0962250i
$109$	−10.0000	−0.957826	−0.478913	−	0.877862i	$-0.658969\pi$
$109$	−10.0000	−0.957826	−0.478913	+	0.877862i	$0.658969\pi$
$110$	0	0
$111$	−2.00000	−0.189832
$112$	2.00000i	0.188982i
$113$	19.0000i	1.78737i	0.448695	+	0.893685i	$0.351889\pi$
$113$	19.0000i	1.78737i	−0.448695	+	0.893685i	$0.648111\pi$
$114$	1.00000	0.0936586
$115$	0	0
$116$	−5.00000	−0.464238
$117$	6.00000i	0.554700i
$118$	− 10.0000i	− 0.920575i
$119$	−4.00000	−0.366679
$120$	0	0
$121$	−2.00000	−0.181818
$122$	13.0000i	1.17696i
$123$	2.00000i	0.180334i
$124$	−7.00000	−0.628619
$125$	0	0
$126$	−2.00000	−0.178174
$127$	− 3.00000i	− 0.266207i	−0.991102	−	0.133103i	$-0.957506\pi$
$127$	− 3.00000i	− 0.266207i	0.991102	−	0.133103i	$-0.0424943\pi$
$128$	1.00000i	0.0883883i
$129$	6.00000	0.528271
$130$	0	0
$131$	7.00000	0.611593	0.305796	−	0.952097i	$-0.401077\pi$
$131$	7.00000	0.611593	0.305796	+	0.952097i	$0.401077\pi$
$132$	3.00000i	0.261116i
$133$	2.00000i	0.173422i
$134$	7.00000	0.604708
$135$	0	0
$136$	−2.00000	−0.171499
$137$	12.0000i	1.02523i	0.858619	+	0.512615i	$0.171323\pi$
$137$	12.0000i	1.02523i	−0.858619	+	0.512615i	$0.828677\pi$
$138$	− 1.00000i	− 0.0851257i
$139$	0	0		−	1.00000i	$-0.5\pi$
$139$	0	0			1.00000i	$0.5\pi$
$140$	0	0
$141$	−12.0000	−1.01058
$142$	− 12.0000i	− 1.00702i
$143$	18.0000i	1.50524i
$144$	−1.00000	−0.0833333
$145$	0	0
$146$	9.00000	0.744845
$147$	3.00000i	0.247436i
$148$	− 2.00000i	− 0.164399i
$149$	20.0000	1.63846	0.819232	−	0.573462i	$-0.194400\pi$
$149$	20.0000	1.63846	0.819232	+	0.573462i	$0.194400\pi$
$150$	0	0
$151$	12.0000	0.976546	0.488273	−	0.872691i	$-0.337627\pi$
$151$	12.0000	0.976546	0.488273	+	0.872691i	$0.337627\pi$
$152$	1.00000i	0.0811107i
$153$	− 2.00000i	− 0.161690i
$154$	−6.00000	−0.483494
$155$	0	0
$156$	−6.00000	−0.480384
$157$	− 18.0000i	− 1.43656i	−0.695756	−	0.718278i	$-0.744931\pi$
$157$	− 18.0000i	− 1.43656i	0.695756	−	0.718278i	$-0.255069\pi$
$158$	5.00000i	0.397779i
$159$	−9.00000	−0.713746
$160$	0	0
$161$	2.00000	0.157622
$162$	− 1.00000i	− 0.0785674i
$163$	− 6.00000i	− 0.469956i	−0.972001	−	0.234978i	$-0.924498\pi$
$163$	− 6.00000i	− 0.469956i	0.972001	−	0.234978i	$-0.0755019\pi$
$164$	−2.00000	−0.156174
$165$	0	0
$166$	−1.00000	−0.0776151
$167$	2.00000i	0.154765i	0.997001	+	0.0773823i	$0.0246562\pi$
$167$	2.00000i	0.154765i	−0.997001	+	0.0773823i	$0.975344\pi$
$168$	− 2.00000i	− 0.154303i
$169$	−23.0000	−1.76923
$170$	0	0
$171$	−1.00000	−0.0764719
$172$	6.00000i	0.457496i
$173$	− 21.0000i	− 1.59660i	−0.602260	−	0.798300i	$-0.705733\pi$
$173$	− 21.0000i	− 1.59660i	0.602260	−	0.798300i	$-0.294267\pi$
$174$	5.00000	0.379049
$175$	0	0
$176$	−3.00000	−0.226134
$177$	10.0000i	0.751646i
$178$	5.00000i	0.374766i
$179$	0	0		−	1.00000i	$-0.5\pi$
$179$	0	0			1.00000i	$0.5\pi$
$180$	0	0
$181$	2.00000	0.148659	0.0743294	−	0.997234i	$-0.476318\pi$
$181$	2.00000	0.148659	0.0743294	+	0.997234i	$0.476318\pi$
$182$	− 12.0000i	− 0.889499i
$183$	− 13.0000i	− 0.960988i
$184$	1.00000	0.0737210
$185$	0	0
$186$	7.00000	0.513265
$187$	− 6.00000i	− 0.438763i
$188$	− 12.0000i	− 0.875190i
$189$	2.00000	0.145479
$190$	0	0
$191$	17.0000	1.23008	0.615038	−	0.788497i	$-0.289140\pi$
$191$	17.0000	1.23008	0.615038	+	0.788497i	$0.289140\pi$
$192$	− 1.00000i	− 0.0721688i
$193$	− 16.0000i	− 1.15171i	−0.817554	−	0.575853i	$-0.804670\pi$
$193$	− 16.0000i	− 1.15171i	0.817554	−	0.575853i	$-0.195330\pi$
$194$	12.0000	0.861550
$195$	0	0
$196$	−3.00000	−0.214286
$197$	2.00000i	0.142494i	0.997459	+	0.0712470i	$0.0226979\pi$
$197$	2.00000i	0.142494i	−0.997459	+	0.0712470i	$0.977302\pi$
$198$	− 3.00000i	− 0.213201i
$199$	10.0000	0.708881	0.354441	−	0.935079i	$-0.384671\pi$
$199$	10.0000	0.708881	0.354441	+	0.935079i	$0.384671\pi$
$200$	0	0
$201$	−7.00000	−0.493742
$202$	− 2.00000i	− 0.140720i
$203$	10.0000i	0.701862i
$204$	2.00000	0.140028
$205$	0	0
$206$	9.00000	0.627060
$207$	1.00000i	0.0695048i
$208$	− 6.00000i	− 0.416025i
$209$	−3.00000	−0.207514
$210$	0	0
$211$	17.0000	1.17033	0.585164	−	0.810915i	$-0.301030\pi$
$211$	17.0000	1.17033	0.585164	+	0.810915i	$0.301030\pi$
$212$	− 9.00000i	− 0.618123i
$213$	12.0000i	0.822226i
$214$	12.0000	0.820303
$215$	0	0
$216$	1.00000	0.0680414
$217$	14.0000i	0.950382i
$218$	10.0000i	0.677285i
$219$	−9.00000	−0.608164
$220$	0	0
$221$	12.0000	0.807207
$222$	2.00000i	0.134231i
$223$	− 11.0000i	− 0.736614i	−0.929704	−	0.368307i	$-0.879937\pi$
$223$	− 11.0000i	− 0.736614i	0.929704	−	0.368307i	$-0.120063\pi$
$224$	2.00000	0.133631
$225$	0	0
$226$	19.0000	1.26386
$227$	2.00000i	0.132745i	0.997795	+	0.0663723i	$0.0211425\pi$
$227$	2.00000i	0.132745i	−0.997795	+	0.0663723i	$0.978857\pi$
$228$	− 1.00000i	− 0.0662266i
$229$	−15.0000	−0.991228	−0.495614	−	0.868543i	$-0.665057\pi$
$229$	−15.0000	−0.991228	−0.495614	+	0.868543i	$0.665057\pi$
$230$	0	0
$231$	6.00000	0.394771
$232$	5.00000i	0.328266i
$233$	− 26.0000i	− 1.70332i	−0.524097	−	0.851658i	$-0.675597\pi$
$233$	− 26.0000i	− 1.70332i	0.524097	−	0.851658i	$-0.324403\pi$
$234$	6.00000	0.392232
$235$	0	0
$236$	−10.0000	−0.650945
$237$	− 5.00000i	− 0.324785i
$238$	4.00000i	0.259281i
$239$	0	0		−	1.00000i	$-0.5\pi$
$239$	0	0			1.00000i	$0.5\pi$
$240$	0	0
$241$	2.00000	0.128831	0.0644157	−	0.997923i	$-0.479482\pi$
$241$	2.00000	0.128831	0.0644157	+	0.997923i	$0.479482\pi$
$242$	2.00000i	0.128565i
$243$	1.00000i	0.0641500i
$244$	13.0000	0.832240
$245$	0	0
$246$	2.00000	0.127515
$247$	− 6.00000i	− 0.381771i
$248$	7.00000i	0.444500i
$249$	1.00000	0.0633724
$250$	0	0
$251$	−8.00000	−0.504956	−0.252478	−	0.967603i	$-0.581245\pi$
$251$	−8.00000	−0.504956	−0.252478	+	0.967603i	$0.581245\pi$
$252$	2.00000i	0.125988i
$253$	3.00000i	0.188608i
$254$	−3.00000	−0.188237
$255$	0	0
$256$	1.00000	0.0625000
$257$	27.0000i	1.68421i	0.539311	+	0.842107i	$0.318685\pi$
$257$	27.0000i	1.68421i	−0.539311	+	0.842107i	$0.681315\pi$
$258$	− 6.00000i	− 0.373544i
$259$	−4.00000	−0.248548
$260$	0	0
$261$	−5.00000	−0.309492
$262$	− 7.00000i	− 0.432461i
$263$	− 1.00000i	− 0.0616626i	−0.999525	−	0.0308313i	$-0.990185\pi$
$263$	− 1.00000i	− 0.0616626i	0.999525	−	0.0308313i	$-0.00981547\pi$
$264$	3.00000	0.184637
$265$	0	0
$266$	2.00000	0.122628
$267$	− 5.00000i	− 0.305995i
$268$	− 7.00000i	− 0.427593i
$269$	10.0000	0.609711	0.304855	−	0.952399i	$-0.401392\pi$
$269$	10.0000	0.609711	0.304855	+	0.952399i	$0.401392\pi$
$270$	0	0
$271$	32.0000	1.94386	0.971931	−	0.235267i	$-0.0755965\pi$
$271$	32.0000	1.94386	0.971931	+	0.235267i	$0.0755965\pi$
$272$	2.00000i	0.121268i
$273$	12.0000i	0.726273i
$274$	12.0000	0.724947
$275$	0	0
$276$	−1.00000	−0.0601929
$277$	7.00000i	0.420589i	0.977638	+	0.210295i	$0.0674423\pi$
$277$	7.00000i	0.420589i	−0.977638	+	0.210295i	$0.932558\pi$
$278$	0	0
$279$	−7.00000	−0.419079
$280$	0	0
$281$	7.00000	0.417585	0.208792	−	0.977960i	$-0.433047\pi$
$281$	7.00000	0.417585	0.208792	+	0.977960i	$0.433047\pi$
$282$	12.0000i	0.714590i
$283$	− 16.0000i	− 0.951101i	−0.879688	−	0.475551i	$-0.842249\pi$
$283$	− 16.0000i	− 0.951101i	0.879688	−	0.475551i	$-0.157751\pi$
$284$	−12.0000	−0.712069
$285$	0	0
$286$	18.0000	1.06436
$287$	4.00000i	0.236113i
$288$	1.00000i	0.0589256i
$289$	13.0000	0.764706
$290$	0	0
$291$	−12.0000	−0.703452
$292$	− 9.00000i	− 0.526685i
$293$	− 1.00000i	− 0.0584206i	−0.999573	−	0.0292103i	$-0.990701\pi$
$293$	− 1.00000i	− 0.0584206i	0.999573	−	0.0292103i	$-0.00929925\pi$
$294$	3.00000	0.174964
$295$	0	0
$296$	−2.00000	−0.116248
$297$	3.00000i	0.174078i
$298$	− 20.0000i	− 1.15857i
$299$	−6.00000	−0.346989
$300$	0	0
$301$	12.0000	0.691669
$302$	− 12.0000i	− 0.690522i
$303$	2.00000i	0.114897i
$304$	1.00000	0.0573539
$305$	0	0
$306$	−2.00000	−0.114332
$307$	7.00000i	0.399511i	0.979846	+	0.199756i	$0.0640148\pi$
$307$	7.00000i	0.399511i	−0.979846	+	0.199756i	$0.935985\pi$
$308$	6.00000i	0.341882i
$309$	−9.00000	−0.511992
$310$	0	0
$311$	12.0000	0.680458	0.340229	−	0.940343i	$-0.389495\pi$
$311$	12.0000	0.680458	0.340229	+	0.940343i	$0.389495\pi$
$312$	6.00000i	0.339683i
$313$	29.0000i	1.63918i	0.572953	+	0.819588i	$0.305798\pi$
$313$	29.0000i	1.63918i	−0.572953	+	0.819588i	$0.694202\pi$
$314$	−18.0000	−1.01580
$315$	0	0
$316$	5.00000	0.281272
$317$	− 3.00000i	− 0.168497i	−0.996445	−	0.0842484i	$-0.973151\pi$
$317$	− 3.00000i	− 0.168497i	0.996445	−	0.0842484i	$-0.0268489\pi$
$318$	9.00000i	0.504695i
$319$	−15.0000	−0.839839
$320$	0	0
$321$	−12.0000	−0.669775
$322$	− 2.00000i	− 0.111456i
$323$	2.00000i	0.111283i
$324$	−1.00000	−0.0555556
$325$	0	0
$326$	−6.00000	−0.332309
$327$	− 10.0000i	− 0.553001i
$328$	2.00000i	0.110432i
$329$	−24.0000	−1.32316
$330$	0	0
$331$	7.00000	0.384755	0.192377	−	0.981321i	$-0.438380\pi$
$331$	7.00000	0.384755	0.192377	+	0.981321i	$0.438380\pi$
$332$	1.00000i	0.0548821i
$333$	− 2.00000i	− 0.109599i
$334$	2.00000	0.109435
$335$	0	0
$336$	−2.00000	−0.109109
$337$	− 8.00000i	− 0.435788i	−0.975972	−	0.217894i	$-0.930081\pi$
$337$	− 8.00000i	− 0.435788i	0.975972	−	0.217894i	$-0.0699187\pi$
$338$	23.0000i	1.25104i
$339$	−19.0000	−1.03194
$340$	0	0
$341$	−21.0000	−1.13721
$342$	1.00000i	0.0540738i
$343$	20.0000i	1.07990i
$344$	6.00000	0.323498
$345$	0	0
$346$	−21.0000	−1.12897
$347$	12.0000i	0.644194i	0.946707	+	0.322097i	$0.104388\pi$
$347$	12.0000i	0.644194i	−0.946707	+	0.322097i	$0.895612\pi$
$348$	− 5.00000i	− 0.268028i
$349$	−25.0000	−1.33822	−0.669110	−	0.743164i	$-0.733324\pi$
$349$	−25.0000	−1.33822	−0.669110	+	0.743164i	$0.733324\pi$
$350$	0	0
$351$	−6.00000	−0.320256
$352$	3.00000i	0.159901i
$353$	− 6.00000i	− 0.319348i	−0.987170	−	0.159674i	$-0.948956\pi$
$353$	− 6.00000i	− 0.319348i	0.987170	−	0.159674i	$-0.0510443\pi$
$354$	10.0000	0.531494
$355$	0	0
$356$	5.00000	0.264999
$357$	− 4.00000i	− 0.211702i
$358$	0	0
$359$	0	0		−	1.00000i	$-0.5\pi$
$359$	0	0			1.00000i	$0.5\pi$
$360$	0	0
$361$	1.00000	0.0526316
$362$	− 2.00000i	− 0.105118i
$363$	− 2.00000i	− 0.104973i
$364$	−12.0000	−0.628971
$365$	0	0
$366$	−13.0000	−0.679521
$367$	− 28.0000i	− 1.46159i	−0.682598	−	0.730794i	$-0.739150\pi$
$367$	− 28.0000i	− 1.46159i	0.682598	−	0.730794i	$-0.260850\pi$
$368$	− 1.00000i	− 0.0521286i
$369$	−2.00000	−0.104116
$370$	0	0
$371$	−18.0000	−0.934513
$372$	− 7.00000i	− 0.362933i
$373$	− 6.00000i	− 0.310668i	−0.987862	−	0.155334i	$-0.950355\pi$
$373$	− 6.00000i	− 0.310668i	0.987862	−	0.155334i	$-0.0496454\pi$
$374$	−6.00000	−0.310253
$375$	0	0
$376$	−12.0000	−0.618853
$377$	− 30.0000i	− 1.54508i
$378$	− 2.00000i	− 0.102869i
$379$	−20.0000	−1.02733	−0.513665	−	0.857991i	$-0.671713\pi$
$379$	−20.0000	−1.02733	−0.513665	+	0.857991i	$0.671713\pi$
$380$	0	0
$381$	3.00000	0.153695
$382$	− 17.0000i	− 0.869796i
$383$	24.0000i	1.22634i	0.789950	+	0.613171i	$0.210106\pi$
$383$	24.0000i	1.22634i	−0.789950	+	0.613171i	$0.789894\pi$
$384$	−1.00000	−0.0510310
$385$	0	0
$386$	−16.0000	−0.814379
$387$	6.00000i	0.304997i
$388$	− 12.0000i	− 0.609208i
$389$	30.0000	1.52106	0.760530	−	0.649303i	$-0.224939\pi$
$389$	30.0000	1.52106	0.760530	+	0.649303i	$0.224939\pi$
$390$	0	0
$391$	2.00000	0.101144
$392$	3.00000i	0.151523i
$393$	7.00000i	0.353103i
$394$	2.00000	0.100759
$395$	0	0
$396$	−3.00000	−0.150756
$397$	37.0000i	1.85698i	0.371361	+	0.928488i	$0.378891\pi$
$397$	37.0000i	1.85698i	−0.371361	+	0.928488i	$0.621109\pi$
$398$	− 10.0000i	− 0.501255i
$399$	−2.00000	−0.100125
$400$	0	0
$401$	−3.00000	−0.149813	−0.0749064	−	0.997191i	$-0.523866\pi$
$401$	−3.00000	−0.149813	−0.0749064	+	0.997191i	$0.523866\pi$
$402$	7.00000i	0.349128i
$403$	− 42.0000i	− 2.09217i
$404$	−2.00000	−0.0995037
$405$	0	0
$406$	10.0000	0.496292
$407$	− 6.00000i	− 0.297409i
$408$	− 2.00000i	− 0.0990148i
$409$	10.0000	0.494468	0.247234	−	0.968956i	$-0.420478\pi$
$409$	10.0000	0.494468	0.247234	+	0.968956i	$0.420478\pi$
$410$	0	0
$411$	−12.0000	−0.591916
$412$	− 9.00000i	− 0.443398i
$413$	20.0000i	0.984136i
$414$	1.00000	0.0491473
$415$	0	0
$416$	−6.00000	−0.294174
$417$	0	0
$418$	3.00000i	0.146735i
$419$	20.0000	0.977064	0.488532	−	0.872546i	$-0.337533\pi$
$419$	20.0000	0.977064	0.488532	+	0.872546i	$0.337533\pi$
$420$	0	0
$421$	22.0000	1.07221	0.536107	−	0.844150i	$-0.319894\pi$
$421$	22.0000	1.07221	0.536107	+	0.844150i	$0.319894\pi$
$422$	− 17.0000i	− 0.827547i
$423$	− 12.0000i	− 0.583460i
$424$	−9.00000	−0.437079
$425$	0	0
$426$	12.0000	0.581402
$427$	− 26.0000i	− 1.25823i
$428$	− 12.0000i	− 0.580042i
$429$	−18.0000	−0.869048
$430$	0	0
$431$	−18.0000	−0.867029	−0.433515	−	0.901146i	$-0.642727\pi$
$431$	−18.0000	−0.867029	−0.433515	+	0.901146i	$0.642727\pi$
$432$	− 1.00000i	− 0.0481125i
$433$	− 36.0000i	− 1.73005i	−0.501729	−	0.865025i	$-0.667303\pi$
$433$	− 36.0000i	− 1.73005i	0.501729	−	0.865025i	$-0.332697\pi$
$434$	14.0000	0.672022
$435$	0	0
$436$	10.0000	0.478913
$437$	− 1.00000i	− 0.0478365i
$438$	9.00000i	0.430037i
$439$	35.0000	1.67046	0.835229	−	0.549902i	$-0.185335\pi$
$439$	35.0000	1.67046	0.835229	+	0.549902i	$0.185335\pi$
$440$	0	0
$441$	−3.00000	−0.142857
$442$	− 12.0000i	− 0.570782i
$443$	− 21.0000i	− 0.997740i	−0.866677	−	0.498870i	$-0.833748\pi$
$443$	− 21.0000i	− 0.997740i	0.866677	−	0.498870i	$-0.166252\pi$
$444$	2.00000	0.0949158
$445$	0	0
$446$	−11.0000	−0.520865
$447$	20.0000i	0.945968i
$448$	− 2.00000i	− 0.0944911i
$449$	−35.0000	−1.65175	−0.825876	−	0.563852i	$-0.809319\pi$
$449$	−35.0000	−1.65175	−0.825876	+	0.563852i	$0.809319\pi$
$450$	0	0
$451$	−6.00000	−0.282529
$452$	− 19.0000i	− 0.893685i
$453$	12.0000i	0.563809i
$454$	2.00000	0.0938647
$455$	0	0
$456$	−1.00000	−0.0468293
$457$	− 38.0000i	− 1.77757i	−0.458329	−	0.888783i	$-0.651552\pi$
$457$	− 38.0000i	− 1.77757i	0.458329	−	0.888783i	$-0.348448\pi$
$458$	15.0000i	0.700904i
$459$	2.00000	0.0933520
$460$	0	0
$461$	−28.0000	−1.30409	−0.652045	−	0.758180i	$-0.726089\pi$
$461$	−28.0000	−1.30409	−0.652045	+	0.758180i	$0.726089\pi$
$462$	− 6.00000i	− 0.279145i
$463$	− 16.0000i	− 0.743583i	−0.928316	−	0.371792i	$-0.878744\pi$
$463$	− 16.0000i	− 0.743583i	0.928316	−	0.371792i	$-0.121256\pi$
$464$	5.00000	0.232119
$465$	0	0
$466$	−26.0000	−1.20443
$467$	7.00000i	0.323921i	0.986797	+	0.161961i	$0.0517818\pi$
$467$	7.00000i	0.323921i	−0.986797	+	0.161961i	$0.948218\pi$
$468$	− 6.00000i	− 0.277350i
$469$	−14.0000	−0.646460
$470$	0	0
$471$	18.0000	0.829396
$472$	10.0000i	0.460287i
$473$	18.0000i	0.827641i
$474$	−5.00000	−0.229658
$475$	0	0
$476$	4.00000	0.183340
$477$	− 9.00000i	− 0.412082i
$478$	0	0
$479$	15.0000	0.685367	0.342684	−	0.939451i	$-0.388664\pi$
$479$	15.0000	0.685367	0.342684	+	0.939451i	$0.388664\pi$
$480$	0	0
$481$	12.0000	0.547153
$482$	− 2.00000i	− 0.0910975i
$483$	2.00000i	0.0910032i
$484$	2.00000	0.0909091
$485$	0	0
$486$	1.00000	0.0453609
$487$	− 8.00000i	− 0.362515i	−0.983436	−	0.181257i	$-0.941983\pi$
$487$	− 8.00000i	− 0.362515i	0.983436	−	0.181257i	$-0.0580167\pi$
$488$	− 13.0000i	− 0.588482i
$489$	6.00000	0.271329
$490$	0	0
$491$	−28.0000	−1.26362	−0.631811	−	0.775122i	$-0.717688\pi$
$491$	−28.0000	−1.26362	−0.631811	+	0.775122i	$0.717688\pi$
$492$	− 2.00000i	− 0.0901670i
$493$	10.0000i	0.450377i
$494$	−6.00000	−0.269953
$495$	0	0
$496$	7.00000	0.314309
$497$	24.0000i	1.07655i
$498$	− 1.00000i	− 0.0448111i
$499$	−30.0000	−1.34298	−0.671492	−	0.741012i	$-0.734346\pi$
$499$	−30.0000	−1.34298	−0.671492	+	0.741012i	$0.734346\pi$
$500$	0	0
$501$	−2.00000	−0.0893534
$502$	8.00000i	0.357057i
$503$	44.0000i	1.96186i	0.194354	+	0.980932i	$0.437739\pi$
$503$	44.0000i	1.96186i	−0.194354	+	0.980932i	$0.562261\pi$
$504$	2.00000	0.0890871
$505$	0	0
$506$	3.00000	0.133366
$507$	− 23.0000i	− 1.02147i
$508$	3.00000i	0.133103i
$509$	15.0000	0.664863	0.332432	−	0.943127i	$-0.392131\pi$
$509$	15.0000	0.664863	0.332432	+	0.943127i	$0.392131\pi$
$510$	0	0
$511$	−18.0000	−0.796273
$512$	− 1.00000i	− 0.0441942i
$513$	− 1.00000i	− 0.0441511i
$514$	27.0000	1.19092
$515$	0	0
$516$	−6.00000	−0.264135
$517$	− 36.0000i	− 1.58328i
$518$	4.00000i	0.175750i
$519$	21.0000	0.921798
$520$	0	0
$521$	−3.00000	−0.131432	−0.0657162	−	0.997838i	$-0.520933\pi$
$521$	−3.00000	−0.131432	−0.0657162	+	0.997838i	$0.520933\pi$
$522$	5.00000i	0.218844i
$523$	4.00000i	0.174908i	0.996169	+	0.0874539i	$0.0278730\pi$
$523$	4.00000i	0.174908i	−0.996169	+	0.0874539i	$0.972127\pi$
$524$	−7.00000	−0.305796
$525$	0	0
$526$	−1.00000	−0.0436021
$527$	14.0000i	0.609850i
$528$	− 3.00000i	− 0.130558i
$529$	22.0000	0.956522
$530$	0	0
$531$	−10.0000	−0.433963
$532$	− 2.00000i	− 0.0867110i
$533$	− 12.0000i	− 0.519778i
$534$	−5.00000	−0.216371
$535$	0	0
$536$	−7.00000	−0.302354
$537$	0	0
$538$	− 10.0000i	− 0.431131i
$539$	−9.00000	−0.387657
$540$	0	0
$541$	17.0000	0.730887	0.365444	−	0.930834i	$-0.380917\pi$
$541$	17.0000	0.730887	0.365444	+	0.930834i	$0.380917\pi$
$542$	− 32.0000i	− 1.37452i
$543$	2.00000i	0.0858282i
$544$	2.00000	0.0857493
$545$	0	0
$546$	12.0000	0.513553
$547$	− 23.0000i	− 0.983409i	−0.870762	−	0.491704i	$-0.836374\pi$
$547$	− 23.0000i	− 0.983409i	0.870762	−	0.491704i	$-0.163626\pi$
$548$	− 12.0000i	− 0.512615i
$549$	13.0000	0.554826
$550$	0	0
$551$	5.00000	0.213007
$552$	1.00000i	0.0425628i
$553$	− 10.0000i	− 0.425243i
$554$	7.00000	0.297402
$555$	0	0
$556$	0	0
$557$	2.00000i	0.0847427i	0.999102	+	0.0423714i	$0.0134913\pi$
$557$	2.00000i	0.0847427i	−0.999102	+	0.0423714i	$0.986509\pi$
$558$	7.00000i	0.296334i
$559$	−36.0000	−1.52264
$560$	0	0
$561$	6.00000	0.253320
$562$	− 7.00000i	− 0.295277i
$563$	− 16.0000i	− 0.674320i	−0.941447	−	0.337160i	$-0.890534\pi$
$563$	− 16.0000i	− 0.674320i	0.941447	−	0.337160i	$-0.109466\pi$
$564$	12.0000	0.505291
$565$	0	0
$566$	−16.0000	−0.672530
$567$	2.00000i	0.0839921i
$568$	12.0000i	0.503509i
$569$	−10.0000	−0.419222	−0.209611	−	0.977785i	$-0.567220\pi$
$569$	−10.0000	−0.419222	−0.209611	+	0.977785i	$0.567220\pi$
$570$	0	0
$571$	−8.00000	−0.334790	−0.167395	−	0.985890i	$-0.553535\pi$
$571$	−8.00000	−0.334790	−0.167395	+	0.985890i	$0.553535\pi$
$572$	− 18.0000i	− 0.752618i
$573$	17.0000i	0.710185i
$574$	4.00000	0.166957
$575$	0	0
$576$	1.00000	0.0416667
$577$	7.00000i	0.291414i	0.989328	+	0.145707i	$0.0465456\pi$
$577$	7.00000i	0.291414i	−0.989328	+	0.145707i	$0.953454\pi$
$578$	− 13.0000i	− 0.540729i
$579$	16.0000	0.664937
$580$	0	0
$581$	2.00000	0.0829740
$582$	12.0000i	0.497416i
$583$	− 27.0000i	− 1.11823i
$584$	−9.00000	−0.372423
$585$	0	0
$586$	−1.00000	−0.0413096
$587$	− 3.00000i	− 0.123823i	−0.998082	−	0.0619116i	$-0.980280\pi$
$587$	− 3.00000i	− 0.123823i	0.998082	−	0.0619116i	$-0.0197197\pi$
$588$	− 3.00000i	− 0.123718i
$589$	7.00000	0.288430
$590$	0	0
$591$	−2.00000	−0.0822690
$592$	2.00000i	0.0821995i
$593$	4.00000i	0.164260i	0.996622	+	0.0821302i	$0.0261723\pi$
$593$	4.00000i	0.164260i	−0.996622	+	0.0821302i	$0.973828\pi$
$594$	3.00000	0.123091
$595$	0	0
$596$	−20.0000	−0.819232
$597$	10.0000i	0.409273i
$598$	6.00000i	0.245358i
$599$	−30.0000	−1.22577	−0.612883	−	0.790173i	$-0.709990\pi$
$599$	−30.0000	−1.22577	−0.612883	+	0.790173i	$0.709990\pi$
$600$	0	0
$601$	−28.0000	−1.14214	−0.571072	−	0.820900i	$-0.693472\pi$
$601$	−28.0000	−1.14214	−0.571072	+	0.820900i	$0.693472\pi$
$602$	− 12.0000i	− 0.489083i
$603$	− 7.00000i	− 0.285062i
$604$	−12.0000	−0.488273
$605$	0	0
$606$	2.00000	0.0812444
$607$	− 23.0000i	− 0.933541i	−0.884378	−	0.466771i	$-0.845417\pi$
$607$	− 23.0000i	− 0.933541i	0.884378	−	0.466771i	$-0.154583\pi$
$608$	− 1.00000i	− 0.0405554i
$609$	−10.0000	−0.405220
$610$	0	0
$611$	72.0000	2.91281
$612$	2.00000i	0.0808452i
$613$	34.0000i	1.37325i	0.727013	+	0.686624i	$0.240908\pi$
$613$	34.0000i	1.37325i	−0.727013	+	0.686624i	$0.759092\pi$
$614$	7.00000	0.282497
$615$	0	0
$616$	6.00000	0.241747
$617$	22.0000i	0.885687i	0.896599	+	0.442843i	$0.146030\pi$
$617$	22.0000i	0.885687i	−0.896599	+	0.442843i	$0.853970\pi$
$618$	9.00000i	0.362033i
$619$	−10.0000	−0.401934	−0.200967	−	0.979598i	$-0.564408\pi$
$619$	−10.0000	−0.401934	−0.200967	+	0.979598i	$0.564408\pi$
$620$	0	0
$621$	−1.00000	−0.0401286
$622$	− 12.0000i	− 0.481156i
$623$	− 10.0000i	− 0.400642i
$624$	6.00000	0.240192
$625$	0	0
$626$	29.0000	1.15907
$627$	− 3.00000i	− 0.119808i
$628$	18.0000i	0.718278i
$629$	−4.00000	−0.159490
$630$	0	0
$631$	−48.0000	−1.91085	−0.955425	−	0.295234i	$-0.904602\pi$
$631$	−48.0000	−1.91085	−0.955425	+	0.295234i	$0.904602\pi$
$632$	− 5.00000i	− 0.198889i
$633$	17.0000i	0.675689i
$634$	−3.00000	−0.119145
$635$	0	0
$636$	9.00000	0.356873
$637$	− 18.0000i	− 0.713186i
$638$	15.0000i	0.593856i
$639$	−12.0000	−0.474713
$640$	0	0
$641$	−18.0000	−0.710957	−0.355479	−	0.934684i	$-0.615682\pi$
$641$	−18.0000	−0.710957	−0.355479	+	0.934684i	$0.615682\pi$
$642$	12.0000i	0.473602i
$643$	14.0000i	0.552106i	0.961142	+	0.276053i	$0.0890266\pi$
$643$	14.0000i	0.552106i	−0.961142	+	0.276053i	$0.910973\pi$
$644$	−2.00000	−0.0788110
$645$	0	0
$646$	2.00000	0.0786889
$647$	27.0000i	1.06148i	0.847535	+	0.530740i	$0.178086\pi$
$647$	27.0000i	1.06148i	−0.847535	+	0.530740i	$0.821914\pi$
$648$	1.00000i	0.0392837i
$649$	−30.0000	−1.17760
$650$	0	0
$651$	−14.0000	−0.548703
$652$	6.00000i	0.234978i
$653$	24.0000i	0.939193i	0.882881	+	0.469596i	$0.155601\pi$
$653$	24.0000i	0.939193i	−0.882881	+	0.469596i	$0.844399\pi$
$654$	−10.0000	−0.391031
$655$	0	0
$656$	2.00000	0.0780869
$657$	− 9.00000i	− 0.351123i
$658$	24.0000i	0.935617i
$659$	−30.0000	−1.16863	−0.584317	−	0.811525i	$-0.698638\pi$
$659$	−30.0000	−1.16863	−0.584317	+	0.811525i	$0.698638\pi$
$660$	0	0
$661$	−28.0000	−1.08907	−0.544537	−	0.838737i	$-0.683295\pi$
$661$	−28.0000	−1.08907	−0.544537	+	0.838737i	$0.683295\pi$
$662$	− 7.00000i	− 0.272063i
$663$	12.0000i	0.466041i
$664$	1.00000	0.0388075
$665$	0	0
$666$	−2.00000	−0.0774984
$667$	− 5.00000i	− 0.193601i
$668$	− 2.00000i	− 0.0773823i
$669$	11.0000	0.425285
$670$	0	0
$671$	39.0000	1.50558
$672$	2.00000i	0.0771517i
$673$	− 26.0000i	− 1.00223i	−0.865382	−	0.501113i	$-0.832924\pi$
$673$	− 26.0000i	− 1.00223i	0.865382	−	0.501113i	$-0.167076\pi$
$674$	−8.00000	−0.308148
$675$	0	0
$676$	23.0000	0.884615
$677$	7.00000i	0.269032i	0.990911	+	0.134516i	$0.0429479\pi$
$677$	7.00000i	0.269032i	−0.990911	+	0.134516i	$0.957052\pi$
$678$	19.0000i	0.729691i
$679$	−24.0000	−0.921035
$680$	0	0
$681$	−2.00000	−0.0766402
$682$	21.0000i	0.804132i
$683$	24.0000i	0.918334i	0.888350	+	0.459167i	$0.151852\pi$
$683$	24.0000i	0.918334i	−0.888350	+	0.459167i	$0.848148\pi$
$684$	1.00000	0.0382360
$685$	0	0
$686$	20.0000	0.763604
$687$	− 15.0000i	− 0.572286i
$688$	− 6.00000i	− 0.228748i
$689$	54.0000	2.05724
$690$	0	0
$691$	−8.00000	−0.304334	−0.152167	−	0.988355i	$-0.548625\pi$
$691$	−8.00000	−0.304334	−0.152167	+	0.988355i	$0.548625\pi$
$692$	21.0000i	0.798300i
$693$	6.00000i	0.227921i
$694$	12.0000	0.455514
$695$	0	0
$696$	−5.00000	−0.189525
$697$	4.00000i	0.151511i
$698$	25.0000i	0.946264i
$699$	26.0000	0.983410
$700$	0	0
$701$	−48.0000	−1.81293	−0.906467	−	0.422276i	$-0.861231\pi$
$701$	−48.0000	−1.81293	−0.906467	+	0.422276i	$0.861231\pi$
$702$	6.00000i	0.226455i
$703$	2.00000i	0.0754314i
$704$	3.00000	0.113067
$705$	0	0
$706$	−6.00000	−0.225813
$707$	4.00000i	0.150435i
$708$	− 10.0000i	− 0.375823i
$709$	25.0000	0.938895	0.469447	−	0.882960i	$-0.344453\pi$
$709$	25.0000	0.938895	0.469447	+	0.882960i	$0.344453\pi$
$710$	0	0
$711$	5.00000	0.187515
$712$	− 5.00000i	− 0.187383i
$713$	− 7.00000i	− 0.262152i
$714$	−4.00000	−0.149696
$715$	0	0
$716$	0	0
$717$	0	0
$718$	0	0
$719$	−5.00000	−0.186469	−0.0932343	−	0.995644i	$-0.529721\pi$
$719$	−5.00000	−0.186469	−0.0932343	+	0.995644i	$0.529721\pi$
$720$	0	0
$721$	−18.0000	−0.670355
$722$	− 1.00000i	− 0.0372161i
$723$	2.00000i	0.0743808i
$724$	−2.00000	−0.0743294
$725$	0	0
$726$	−2.00000	−0.0742270
$727$	2.00000i	0.0741759i	0.999312	+	0.0370879i	$0.0118082\pi$
$727$	2.00000i	0.0741759i	−0.999312	+	0.0370879i	$0.988192\pi$
$728$	12.0000i	0.444750i
$729$	−1.00000	−0.0370370
$730$	0	0
$731$	12.0000	0.443836
$732$	13.0000i	0.480494i
$733$	39.0000i	1.44050i	0.693716	+	0.720249i	$0.255972\pi$
$733$	39.0000i	1.44050i	−0.693716	+	0.720249i	$0.744028\pi$
$734$	−28.0000	−1.03350
$735$	0	0
$736$	−1.00000	−0.0368605
$737$	− 21.0000i	− 0.773545i
$738$	2.00000i	0.0736210i
$739$	40.0000	1.47142	0.735712	−	0.677295i	$-0.236848\pi$
$739$	40.0000	1.47142	0.735712	+	0.677295i	$0.236848\pi$
$740$	0	0
$741$	6.00000	0.220416
$742$	18.0000i	0.660801i
$743$	− 16.0000i	− 0.586983i	−0.955962	−	0.293492i	$-0.905183\pi$
$743$	− 16.0000i	− 0.586983i	0.955962	−	0.293492i	$-0.0948173\pi$
$744$	−7.00000	−0.256632
$745$	0	0
$746$	−6.00000	−0.219676
$747$	1.00000i	0.0365881i
$748$	6.00000i	0.219382i
$749$	−24.0000	−0.876941
$750$	0	0
$751$	52.0000	1.89751	0.948753	−	0.316017i	$-0.102346\pi$
$751$	52.0000	1.89751	0.948753	+	0.316017i	$0.102346\pi$
$752$	12.0000i	0.437595i
$753$	− 8.00000i	− 0.291536i
$754$	−30.0000	−1.09254
$755$	0	0
$756$	−2.00000	−0.0727393
$757$	− 23.0000i	− 0.835949i	−0.908459	−	0.417975i	$-0.862740\pi$
$757$	− 23.0000i	− 0.835949i	0.908459	−	0.417975i	$-0.137260\pi$
$758$	20.0000i	0.726433i
$759$	−3.00000	−0.108893
$760$	0	0
$761$	−48.0000	−1.74000	−0.869999	−	0.493053i	$-0.835881\pi$
$761$	−48.0000	−1.74000	−0.869999	+	0.493053i	$0.835881\pi$
$762$	− 3.00000i	− 0.108679i
$763$	− 20.0000i	− 0.724049i
$764$	−17.0000	−0.615038
$765$	0	0
$766$	24.0000	0.867155
$767$	− 60.0000i	− 2.16647i
$768$	1.00000i	0.0360844i
$769$	5.00000	0.180305	0.0901523	−	0.995928i	$-0.471265\pi$
$769$	5.00000	0.180305	0.0901523	+	0.995928i	$0.471265\pi$
$770$	0	0
$771$	−27.0000	−0.972381
$772$	16.0000i	0.575853i
$773$	− 6.00000i	− 0.215805i	−0.994161	−	0.107903i	$-0.965587\pi$
$773$	− 6.00000i	− 0.215805i	0.994161	−	0.107903i	$-0.0344134\pi$
$774$	6.00000	0.215666
$775$	0	0
$776$	−12.0000	−0.430775
$777$	− 4.00000i	− 0.143499i
$778$	− 30.0000i	− 1.07555i
$779$	2.00000	0.0716574
$780$	0	0
$781$	−36.0000	−1.28818
$782$	− 2.00000i	− 0.0715199i
$783$	− 5.00000i	− 0.178685i
$784$	3.00000	0.107143
$785$	0	0
$786$	7.00000	0.249682
$787$	− 43.0000i	− 1.53278i	−0.642373	−	0.766392i	$-0.722050\pi$
$787$	− 43.0000i	− 1.53278i	0.642373	−	0.766392i	$-0.277950\pi$
$788$	− 2.00000i	− 0.0712470i
$789$	1.00000	0.0356009
$790$	0	0
$791$	−38.0000	−1.35112
$792$	3.00000i	0.106600i
$793$	78.0000i	2.76986i
$794$	37.0000	1.31308
$795$	0	0
$796$	−10.0000	−0.354441
$797$	2.00000i	0.0708436i	0.999372	+	0.0354218i	$0.0112775\pi$
$797$	2.00000i	0.0708436i	−0.999372	+	0.0354218i	$0.988723\pi$
$798$	2.00000i	0.0707992i
$799$	−24.0000	−0.849059
$800$	0	0
$801$	5.00000	0.176666
$802$	3.00000i	0.105934i
$803$	− 27.0000i	− 0.952809i
$804$	7.00000	0.246871
$805$	0	0
$806$	−42.0000	−1.47939
$807$	10.0000i	0.352017i
$808$	2.00000i	0.0703598i
$809$	−30.0000	−1.05474	−0.527372	−	0.849635i	$-0.676823\pi$
$809$	−30.0000	−1.05474	−0.527372	+	0.849635i	$0.676823\pi$
$810$	0	0
$811$	−13.0000	−0.456492	−0.228246	−	0.973604i	$-0.573299\pi$
$811$	−13.0000	−0.456492	−0.228246	+	0.973604i	$0.573299\pi$
$812$	− 10.0000i	− 0.350931i
$813$	32.0000i	1.12229i
$814$	−6.00000	−0.210300
$815$	0	0
$816$	−2.00000	−0.0700140
$817$	− 6.00000i	− 0.209913i
$818$	− 10.0000i	− 0.349642i
$819$	−12.0000	−0.419314
$820$	0	0
$821$	−8.00000	−0.279202	−0.139601	−	0.990208i	$-0.544582\pi$
$821$	−8.00000	−0.279202	−0.139601	+	0.990208i	$0.544582\pi$
$822$	12.0000i	0.418548i
$823$	34.0000i	1.18517i	0.805510	+	0.592583i	$0.201892\pi$
$823$	34.0000i	1.18517i	−0.805510	+	0.592583i	$0.798108\pi$
$824$	−9.00000	−0.313530
$825$	0	0
$826$	20.0000	0.695889
$827$	− 18.0000i	− 0.625921i	−0.949766	−	0.312961i	$-0.898679\pi$
$827$	− 18.0000i	− 0.625921i	0.949766	−	0.312961i	$-0.101321\pi$
$828$	− 1.00000i	− 0.0347524i
$829$	0	0		−	1.00000i	$-0.5\pi$
$829$	0	0			1.00000i	$0.5\pi$
$830$	0	0
$831$	−7.00000	−0.242827
$832$	6.00000i	0.208013i
$833$	6.00000i	0.207888i
$834$	0	0
$835$	0	0
$836$	3.00000	0.103757
$837$	− 7.00000i	− 0.241955i
$838$	− 20.0000i	− 0.690889i
$839$	30.0000	1.03572	0.517858	−	0.855467i	$-0.326730\pi$
$839$	30.0000	1.03572	0.517858	+	0.855467i	$0.326730\pi$
$840$	0	0
$841$	−4.00000	−0.137931
$842$	− 22.0000i	− 0.758170i
$843$	7.00000i	0.241093i
$844$	−17.0000	−0.585164
$845$	0	0
$846$	−12.0000	−0.412568
$847$	− 4.00000i	− 0.137442i
$848$	9.00000i	0.309061i
$849$	16.0000	0.549119
$850$	0	0
$851$	2.00000	0.0685591
$852$	− 12.0000i	− 0.411113i
$853$	− 26.0000i	− 0.890223i	−0.895475	−	0.445112i	$-0.853164\pi$
$853$	− 26.0000i	− 0.890223i	0.895475	−	0.445112i	$-0.146836\pi$
$854$	−26.0000	−0.889702
$855$	0	0
$856$	−12.0000	−0.410152
$857$	42.0000i	1.43469i	0.696717	+	0.717346i	$0.254643\pi$
$857$	42.0000i	1.43469i	−0.696717	+	0.717346i	$0.745357\pi$
$858$	18.0000i	0.614510i
$859$	10.0000	0.341196	0.170598	−	0.985341i	$-0.445430\pi$
$859$	10.0000	0.341196	0.170598	+	0.985341i	$0.445430\pi$
$860$	0	0
$861$	−4.00000	−0.136320
$862$	18.0000i	0.613082i
$863$	− 36.0000i	− 1.22545i	−0.790295	−	0.612727i	$-0.790072\pi$
$863$	− 36.0000i	− 1.22545i	0.790295	−	0.612727i	$-0.209928\pi$
$864$	−1.00000	−0.0340207
$865$	0	0
$866$	−36.0000	−1.22333
$867$	13.0000i	0.441503i
$868$	− 14.0000i	− 0.475191i
$869$	15.0000	0.508840
$870$	0	0
$871$	42.0000	1.42312
$872$	− 10.0000i	− 0.338643i
$873$	− 12.0000i	− 0.406138i
$874$	−1.00000	−0.0338255
$875$	0	0
$876$	9.00000	0.304082
$877$	− 38.0000i	− 1.28317i	−0.767052	−	0.641584i	$-0.778277\pi$
$877$	− 38.0000i	− 1.28317i	0.767052	−	0.641584i	$-0.221723\pi$
$878$	− 35.0000i	− 1.18119i
$879$	1.00000	0.0337292
$880$	0	0
$881$	32.0000	1.07811	0.539054	−	0.842271i	$-0.318782\pi$
$881$	32.0000	1.07811	0.539054	+	0.842271i	$0.318782\pi$
$882$	3.00000i	0.101015i
$883$	4.00000i	0.134611i	0.997732	+	0.0673054i	$0.0214402\pi$
$883$	4.00000i	0.134611i	−0.997732	+	0.0673054i	$0.978560\pi$
$884$	−12.0000	−0.403604
$885$	0	0
$886$	−21.0000	−0.705509
$887$	52.0000i	1.74599i	0.487730	+	0.872995i	$0.337825\pi$
$887$	52.0000i	1.74599i	−0.487730	+	0.872995i	$0.662175\pi$
$888$	− 2.00000i	− 0.0671156i
$889$	6.00000	0.201234
$890$	0	0
$891$	−3.00000	−0.100504
$892$	11.0000i	0.368307i
$893$	12.0000i	0.401565i
$894$	20.0000	0.668900
$895$	0	0
$896$	−2.00000	−0.0668153
$897$	− 6.00000i	− 0.200334i
$898$	35.0000i	1.16797i
$899$	35.0000	1.16732
$900$	0	0
$901$	−18.0000	−0.599667
$902$	6.00000i	0.199778i
$903$	12.0000i	0.399335i
$904$	−19.0000	−0.631931
$905$	0	0
$906$	12.0000	0.398673
$907$	32.0000i	1.06254i	0.847202	+	0.531271i	$0.178286\pi$
$907$	32.0000i	1.06254i	−0.847202	+	0.531271i	$0.821714\pi$
$908$	− 2.00000i	− 0.0663723i
$909$	−2.00000	−0.0663358
$910$	0	0
$911$	22.0000	0.728893	0.364446	−	0.931224i	$-0.381258\pi$
$911$	22.0000	0.728893	0.364446	+	0.931224i	$0.381258\pi$
$912$	1.00000i	0.0331133i
$913$	3.00000i	0.0992855i
$914$	−38.0000	−1.25693
$915$	0	0
$916$	15.0000	0.495614
$917$	14.0000i	0.462321i
$918$	− 2.00000i	− 0.0660098i
$919$	−20.0000	−0.659739	−0.329870	−	0.944027i	$-0.607005\pi$
$919$	−20.0000	−0.659739	−0.329870	+	0.944027i	$0.607005\pi$
$920$	0	0
$921$	−7.00000	−0.230658
$922$	28.0000i	0.922131i
$923$	− 72.0000i	− 2.36991i
$924$	−6.00000	−0.197386
$925$	0	0
$926$	−16.0000	−0.525793
$927$	− 9.00000i	− 0.295599i
$928$	− 5.00000i	− 0.164133i
$929$	0	0		−	1.00000i	$-0.5\pi$
$929$	0	0			1.00000i	$0.5\pi$
$930$	0	0
$931$	3.00000	0.0983210
$932$	26.0000i	0.851658i
$933$	12.0000i	0.392862i
$934$	7.00000	0.229047
$935$	0	0
$936$	−6.00000	−0.196116
$937$	2.00000i	0.0653372i	0.999466	+	0.0326686i	$0.0104006\pi$
$937$	2.00000i	0.0653372i	−0.999466	+	0.0326686i	$0.989599\pi$
$938$	14.0000i	0.457116i
$939$	−29.0000	−0.946379
$940$	0	0
$941$	−43.0000	−1.40176	−0.700880	−	0.713279i	$-0.747209\pi$
$941$	−43.0000	−1.40176	−0.700880	+	0.713279i	$0.747209\pi$
$942$	− 18.0000i	− 0.586472i
$943$	− 2.00000i	− 0.0651290i
$944$	10.0000	0.325472
$945$	0	0
$946$	18.0000	0.585230
$947$	− 28.0000i	− 0.909878i	−0.890523	−	0.454939i	$-0.849661\pi$
$947$	− 28.0000i	− 0.909878i	0.890523	−	0.454939i	$-0.150339\pi$
$948$	5.00000i	0.162392i
$949$	54.0000	1.75291
$950$	0	0
$951$	3.00000	0.0972817
$952$	− 4.00000i	− 0.129641i
$953$	− 11.0000i	− 0.356325i	−0.984001	−	0.178162i	$-0.942985\pi$
$953$	− 11.0000i	− 0.356325i	0.984001	−	0.178162i	$-0.0570153\pi$
$954$	−9.00000	−0.291386
$955$	0	0
$956$	0	0
$957$	− 15.0000i	− 0.484881i
$958$	− 15.0000i	− 0.484628i
$959$	−24.0000	−0.775000
$960$	0	0
$961$	18.0000	0.580645
$962$	− 12.0000i	− 0.386896i
$963$	− 12.0000i	− 0.386695i
$964$	−2.00000	−0.0644157
$965$	0	0
$966$	2.00000	0.0643489
$967$	42.0000i	1.35063i	0.737530	+	0.675314i	$0.235992\pi$
$967$	42.0000i	1.35063i	−0.737530	+	0.675314i	$0.764008\pi$
$968$	− 2.00000i	− 0.0642824i
$969$	−2.00000	−0.0642493
$970$	0	0
$971$	42.0000	1.34784	0.673922	−	0.738802i	$-0.264608\pi$
$971$	42.0000	1.34784	0.673922	+	0.738802i	$0.264608\pi$
$972$	− 1.00000i	− 0.0320750i
$973$	0	0
$974$	−8.00000	−0.256337
$975$	0	0
$976$	−13.0000	−0.416120
$977$	42.0000i	1.34370i	0.740688	+	0.671850i	$0.234500\pi$
$977$	42.0000i	1.34370i	−0.740688	+	0.671850i	$0.765500\pi$
$978$	− 6.00000i	− 0.191859i
$979$	15.0000	0.479402
$980$	0	0
$981$	10.0000	0.319275
$982$	28.0000i	0.893516i
$983$	24.0000i	0.765481i	0.923856	+	0.382741i	$0.125020\pi$
$983$	24.0000i	0.765481i	−0.923856	+	0.382741i	$0.874980\pi$
$984$	−2.00000	−0.0637577
$985$	0	0
$986$	10.0000	0.318465
$987$	− 24.0000i	− 0.763928i
$988$	6.00000i	0.190885i
$989$	−6.00000	−0.190789
$990$	0	0
$991$	17.0000	0.540023	0.270011	−	0.962857i	$-0.412973\pi$
$991$	17.0000	0.540023	0.270011	+	0.962857i	$0.412973\pi$
$992$	− 7.00000i	− 0.222250i
$993$	7.00000i	0.222138i
$994$	24.0000	0.761234
$995$	0	0
$996$	−1.00000	−0.0316862
$997$	17.0000i	0.538395i	0.963085	+	0.269198i	$0.0867585\pi$
$997$	17.0000i	0.538395i	−0.963085	+	0.269198i	$0.913241\pi$
$998$	30.0000i	0.949633i
$999$	2.00000	0.0632772

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2850.2.d.m.799.1		2
5.2	odd	4		2850.2.a.z.1.1	yes	1
5.3	odd	4		2850.2.a.d.1.1	✓	1
5.4	even	2	inner	2850.2.d.m.799.2		2
15.2	even	4		8550.2.a.f.1.1		1
15.8	even	4		8550.2.a.bi.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2850.2.a.d.1.1	✓	1	5.3	odd	4
2850.2.a.z.1.1	yes	1	5.2	odd	4
2850.2.d.m.799.1		2	1.1	even	1	trivial
2850.2.d.m.799.2		2	5.4	even	2	inner
8550.2.a.f.1.1		1	15.2	even	4
8550.2.a.bi.1.1		1	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:	\( N \)	\(=\)	\( 2850 = 2 \cdot 3 \cdot 5^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2850.d (of order \(2\), degree \(1\), not minimal)

\(f(q)\)	\(=\)	\(q-1.00000i q^{2} +1.00000i q^{3} -1.00000 q^{4} +1.00000 q^{6} +2.00000i q^{7} +1.00000i q^{8} -1.00000 q^{9} +O(q^{10})\)	\(q-1.00000i q^{2} +1.00000i q^{3} -1.00000 q^{4} +1.00000 q^{6} +2.00000i q^{7} +1.00000i q^{8} -1.00000 q^{9} -3.00000 q^{11} -1.00000i q^{12} -6.00000i q^{13} +2.00000 q^{14} +1.00000 q^{16} +2.00000i q^{17} +1.00000i q^{18} +1.00000 q^{19} -2.00000 q^{21} +3.00000i q^{22} -1.00000i q^{23} -1.00000 q^{24} -6.00000 q^{26} -1.00000i q^{27} -2.00000i q^{28} +5.00000 q^{29} +7.00000 q^{31} -1.00000i q^{32} -3.00000i q^{33} +2.00000 q^{34} +1.00000 q^{36} +2.00000i q^{37} -1.00000i q^{38} +6.00000 q^{39} +2.00000 q^{41} +2.00000i q^{42} -6.00000i q^{43} +3.00000 q^{44} -1.00000 q^{46} +12.0000i q^{47} +1.00000i q^{48} +3.00000 q^{49} -2.00000 q^{51} +6.00000i q^{52} +9.00000i q^{53} -1.00000 q^{54} -2.00000 q^{56} +1.00000i q^{57} -5.00000i q^{58} +10.0000 q^{59} -13.0000 q^{61} -7.00000i q^{62} -2.00000i q^{63} -1.00000 q^{64} -3.00000 q^{66} +7.00000i q^{67} -2.00000i q^{68} +1.00000 q^{69} +12.0000 q^{71} -1.00000i q^{72} +9.00000i q^{73} +2.00000 q^{74} -1.00000 q^{76} -6.00000i q^{77} -6.00000i q^{78} -5.00000 q^{79} +1.00000 q^{81} -2.00000i q^{82} -1.00000i q^{83} +2.00000 q^{84} -6.00000 q^{86} +5.00000i q^{87} -3.00000i q^{88} -5.00000 q^{89} +12.0000 q^{91} +1.00000i q^{92} +7.00000i q^{93} +12.0000 q^{94} +1.00000 q^{96} +12.0000i q^{97} -3.00000i q^{98} +3.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 2 q^{4} + 2 q^{6} - 2 q^{9}+O(q^{10}) \) 2 * q - 2 * q^4 + 2 * q^6 - 2 * q^9	\( 2 q - 2 q^{4} + 2 q^{6} - 2 q^{9} - 6 q^{11} + 4 q^{14} + 2 q^{16} + 2 q^{19} - 4 q^{21} - 2 q^{24} - 12 q^{26} + 10 q^{29} + 14 q^{31} + 4 q^{34} + 2 q^{36} + 12 q^{39} + 4 q^{41} + 6 q^{44} - 2 q^{46} + 6 q^{49} - 4 q^{51} - 2 q^{54} - 4 q^{56} + 20 q^{59} - 26 q^{61} - 2 q^{64} - 6 q^{66} + 2 q^{69} + 24 q^{71} + 4 q^{74} - 2 q^{76} - 10 q^{79} + 2 q^{81} + 4 q^{84} - 12 q^{86} - 10 q^{89} + 24 q^{91} + 24 q^{94} + 2 q^{96} + 6 q^{99}+O(q^{100}) \) 2 * q - 2 * q^4 + 2 * q^6 - 2 * q^9 - 6 * q^11 + 4 * q^14 + 2 * q^16 + 2 * q^19 - 4 * q^21 - 2 * q^24 - 12 * q^26 + 10 * q^29 + 14 * q^31 + 4 * q^34 + 2 * q^36 + 12 * q^39 + 4 * q^41 + 6 * q^44 - 2 * q^46 + 6 * q^49 - 4 * q^51 - 2 * q^54 - 4 * q^56 + 20 * q^59 - 26 * q^61 - 2 * q^64 - 6 * q^66 + 2 * q^69 + 24 * q^71 + 4 * q^74 - 2 * q^76 - 10 * q^79 + 2 * q^81 + 4 * q^84 - 12 * q^86 - 10 * q^89 + 24 * q^91 + 24 * q^94 + 2 * q^96 + 6 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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