LMFDB - Embedded newform 1450.2.b.h.349.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1450,2,Mod(349,1450)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1450, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([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("1450.349");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1450 = 2 \cdot 5^{2} \cdot 29 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1450.b (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:	$11.5783082931$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	$\Q(i, \sqrt{13})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} + 7x^{2} + 9 $ x^4 + 7*x^2 + 9
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 290)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			349.3
Root			$-1.30278i$ of defining polynomial
Character	$\chi$	$=$	1450.349
Dual form			1450.2.b.h.349.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000i q^{2} -1.30278i q^{3} -1.00000 q^{4} +1.30278 q^{6} +0.302776i q^{7} -1.00000i q^{8} +1.30278 q^{9} +O(q^{10})$	\(q+1.00000i q^{2} -1.30278i q^{3} -1.00000 q^{4} +1.30278 q^{6} +0.302776i q^{7} -1.00000i q^{8} +1.30278 q^{9} +4.60555 q^{11} +1.30278i q^{12} +1.30278i q^{13} -0.302776 q^{14} +1.00000 q^{16} +2.30278i q^{17} +1.30278i q^{18} -6.60555 q^{19} +0.394449 q^{21} +4.60555i q^{22} +3.90833i q^{23} -1.30278 q^{24} -1.30278 q^{26} -5.60555i q^{27} -0.302776i q^{28} +1.00000 q^{29} +10.3028 q^{31} +1.00000i q^{32} -6.00000i q^{33} -2.30278 q^{34} -1.30278 q^{36} -6.60555i q^{37} -6.60555i q^{38} +1.69722 q^{39} +1.39445 q^{41} +0.394449i q^{42} -0.302776i q^{43} -4.60555 q^{44} -3.90833 q^{46} +9.21110i q^{47} -1.30278i q^{48} +6.90833 q^{49} +3.00000 q^{51} -1.30278i q^{52} -9.69722i q^{53} +5.60555 q^{54} +0.302776 q^{56} +8.60555i q^{57} +1.00000i q^{58} +11.3028 q^{59} -3.30278 q^{61} +10.3028i q^{62} +0.394449i q^{63} -1.00000 q^{64} +6.00000 q^{66} +4.00000i q^{67} -2.30278i q^{68} +5.09167 q^{69} +9.21110 q^{71} -1.30278i q^{72} +12.1194i q^{73} +6.60555 q^{74} +6.60555 q^{76} +1.39445i q^{77} +1.69722i q^{78} +1.90833 q^{79} -3.39445 q^{81} +1.39445i q^{82} +7.81665i q^{83} -0.394449 q^{84} +0.302776 q^{86} -1.30278i q^{87} -4.60555i q^{88} +13.8167 q^{89} -0.394449 q^{91} -3.90833i q^{92} -13.4222i q^{93} -9.21110 q^{94} +1.30278 q^{96} -9.11943i q^{97} +6.90833i q^{98} +6.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 4 q^{4} - 2 q^{6} - 2 q^{9}+O(q^{10}) $ 4 * q - 4 * q^4 - 2 * q^6 - 2 * q^9	$ 4 q - 4 q^{4} - 2 q^{6} - 2 q^{9} + 4 q^{11} + 6 q^{14} + 4 q^{16} - 12 q^{19} + 16 q^{21} + 2 q^{24} + 2 q^{26} + 4 q^{29} + 34 q^{31} - 2 q^{34} + 2 q^{36} + 14 q^{39} + 20 q^{41} - 4 q^{44} + 6 q^{46} + 6 q^{49} + 12 q^{51} + 8 q^{54} - 6 q^{56} + 38 q^{59} - 6 q^{61} - 4 q^{64} + 24 q^{66} + 42 q^{69} + 8 q^{71} + 12 q^{74} + 12 q^{76} - 14 q^{79} - 28 q^{81} - 16 q^{84} - 6 q^{86} + 12 q^{89} - 16 q^{91} - 8 q^{94} - 2 q^{96} + 24 q^{99}+O(q^{100}) $ 4 * q - 4 * q^4 - 2 * q^6 - 2 * q^9 + 4 * q^11 + 6 * q^14 + 4 * q^16 - 12 * q^19 + 16 * q^21 + 2 * q^24 + 2 * q^26 + 4 * q^29 + 34 * q^31 - 2 * q^34 + 2 * q^36 + 14 * q^39 + 20 * q^41 - 4 * q^44 + 6 * q^46 + 6 * q^49 + 12 * q^51 + 8 * q^54 - 6 * q^56 + 38 * q^59 - 6 * q^61 - 4 * q^64 + 24 * q^66 + 42 * q^69 + 8 * q^71 + 12 * q^74 + 12 * q^76 - 14 * q^79 - 28 * q^81 - 16 * q^84 - 6 * q^86 + 12 * q^89 - 16 * q^91 - 8 * q^94 - 2 * q^96 + 24 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1450\mathbb{Z}\right)^\times$.

$n$	$901$	$1277$
$\chi(n)$	$1$	$-1$

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
$3$	− 1.30278i	− 0.752158i	−0.926588	−	0.376079i	$-0.877272\pi$
$3$	− 1.30278i	− 0.752158i	0.926588	−	0.376079i	$-0.122728\pi$
$4$	−1.00000	−0.500000
$5$	0	0
$5$	0	0
$6$	1.30278	0.531856
$7$	0.302776i	0.114438i	0.998362	+	0.0572192i	$0.0182234\pi$
$7$	0.302776i	0.114438i	−0.998362	+	0.0572192i	$0.981777\pi$
$8$	− 1.00000i	− 0.353553i
$9$	1.30278	0.434259
$10$	0	0
$11$	4.60555	1.38863	0.694313	−	0.719673i	$-0.255708\pi$
$11$	4.60555	1.38863	0.694313	+	0.719673i	$0.255708\pi$
$12$	1.30278i	0.376079i
$13$	1.30278i	0.361325i	0.983545	+	0.180662i	$0.0578242\pi$
$13$	1.30278i	0.361325i	−0.983545	+	0.180662i	$0.942176\pi$
$14$	−0.302776	−0.0809202
$15$	0	0
$16$	1.00000	0.250000
$17$	2.30278i	0.558505i	0.960218	+	0.279253i	$0.0900867\pi$
$17$	2.30278i	0.558505i	−0.960218	+	0.279253i	$0.909913\pi$
$18$	1.30278i	0.307067i
$19$	−6.60555	−1.51542	−0.757709	−	0.652593i	$-0.773681\pi$
$19$	−6.60555	−1.51542	−0.757709	+	0.652593i	$0.773681\pi$
$20$	0	0
$21$	0.394449	0.0860758
$22$	4.60555i	0.981907i
$23$	3.90833i	0.814942i	0.913218	+	0.407471i	$0.133589\pi$
$23$	3.90833i	0.814942i	−0.913218	+	0.407471i	$0.866411\pi$
$24$	−1.30278	−0.265928
$25$	0	0
$26$	−1.30278	−0.255495
$27$	− 5.60555i	− 1.07879i
$28$	− 0.302776i	− 0.0572192i
$29$	1.00000	0.185695
$29$	1.00000	0.185695
$30$	0	0
$31$	10.3028	1.85043	0.925217	−	0.379439i	$-0.123883\pi$
$31$	10.3028	1.85043	0.925217	+	0.379439i	$0.123883\pi$
$32$	1.00000i	0.176777i
$33$	− 6.00000i	− 1.04447i
$34$	−2.30278	−0.394923
$35$	0	0
$36$	−1.30278	−0.217129
$37$	− 6.60555i	− 1.08595i	−0.839750	−	0.542973i	$-0.817299\pi$
$37$	− 6.60555i	− 1.08595i	0.839750	−	0.542973i	$-0.182701\pi$
$38$	− 6.60555i	− 1.07156i
$39$	1.69722	0.271773
$40$	0	0
$41$	1.39445	0.217776	0.108888	−	0.994054i	$-0.465271\pi$
$41$	1.39445	0.217776	0.108888	+	0.994054i	$0.465271\pi$
$42$	0.394449i	0.0608648i
$43$	− 0.302776i	− 0.0461729i	−0.999733	−	0.0230864i	$-0.992651\pi$
$43$	− 0.302776i	− 0.0461729i	0.999733	−	0.0230864i	$-0.00734929\pi$
$44$	−4.60555	−0.694313
$45$	0	0
$46$	−3.90833	−0.576251
$47$	9.21110i	1.34358i	0.740743	+	0.671789i	$0.234474\pi$
$47$	9.21110i	1.34358i	−0.740743	+	0.671789i	$0.765526\pi$
$48$	− 1.30278i	− 0.188039i
$49$	6.90833	0.986904
$50$	0	0
$51$	3.00000	0.420084
$52$	− 1.30278i	− 0.180662i
$53$	− 9.69722i	− 1.33202i	−0.745945	−	0.666008i	$-0.768002\pi$
$53$	− 9.69722i	− 1.33202i	0.745945	−	0.666008i	$-0.231998\pi$
$54$	5.60555	0.762819
$55$	0	0
$56$	0.302776	0.0404601
$57$	8.60555i	1.13983i
$58$	1.00000i	0.131306i
$59$	11.3028	1.47150	0.735748	−	0.677255i	$-0.236831\pi$
$59$	11.3028	1.47150	0.735748	+	0.677255i	$0.236831\pi$
$60$	0	0
$61$	−3.30278	−0.422877	−0.211439	−	0.977391i	$-0.567815\pi$
$61$	−3.30278	−0.422877	−0.211439	+	0.977391i	$0.567815\pi$
$62$	10.3028i	1.30845i
$63$	0.394449i	0.0496959i
$64$	−1.00000	−0.125000
$65$	0	0
$66$	6.00000	0.738549
$67$	4.00000i	0.488678i	0.969690	+	0.244339i	$0.0785709\pi$
$67$	4.00000i	0.488678i	−0.969690	+	0.244339i	$0.921429\pi$
$68$	− 2.30278i	− 0.279253i
$69$	5.09167	0.612965
$70$	0	0
$71$	9.21110	1.09316	0.546578	−	0.837408i	$-0.315930\pi$
$71$	9.21110	1.09316	0.546578	+	0.837408i	$0.315930\pi$
$72$	− 1.30278i	− 0.153534i
$73$	12.1194i	1.41847i	0.704971	+	0.709236i	$0.250960\pi$
$73$	12.1194i	1.41847i	−0.704971	+	0.709236i	$0.749040\pi$
$74$	6.60555	0.767880
$75$	0	0
$76$	6.60555	0.757709
$77$	1.39445i	0.158912i
$78$	1.69722i	0.192173i
$79$	1.90833	0.214704	0.107352	−	0.994221i	$-0.465763\pi$
$79$	1.90833	0.214704	0.107352	+	0.994221i	$0.465763\pi$
$80$	0	0
$81$	−3.39445	−0.377161
$82$	1.39445i	0.153991i
$83$	7.81665i	0.857989i	0.903307	+	0.428995i	$0.141132\pi$
$83$	7.81665i	0.857989i	−0.903307	+	0.428995i	$0.858868\pi$
$84$	−0.394449	−0.0430379
$85$	0	0
$86$	0.302776	0.0326491
$87$	− 1.30278i	− 0.139672i
$88$	− 4.60555i	− 0.490953i
$89$	13.8167	1.46456	0.732281	−	0.681002i	$-0.238456\pi$
$89$	13.8167	1.46456	0.732281	+	0.681002i	$0.238456\pi$
$90$	0	0
$91$	−0.394449	−0.0413495
$92$	− 3.90833i	− 0.407471i
$93$	− 13.4222i	− 1.39182i
$94$	−9.21110	−0.950053
$95$	0	0
$96$	1.30278	0.132964
$97$	− 9.11943i	− 0.925938i	−0.886375	−	0.462969i	$-0.846784\pi$
$97$	− 9.11943i	− 0.925938i	0.886375	−	0.462969i	$-0.153216\pi$
$98$	6.90833i	0.697846i
$99$	6.00000	0.603023
$100$	0	0
$101$	−7.11943	−0.708410	−0.354205	−	0.935168i	$-0.615248\pi$
$101$	−7.11943	−0.708410	−0.354205	+	0.935168i	$0.615248\pi$
$102$	3.00000i	0.297044i
$103$	− 10.4222i	− 1.02693i	−0.858110	−	0.513465i	$-0.828362\pi$
$103$	− 10.4222i	− 1.02693i	0.858110	−	0.513465i	$-0.171638\pi$
$104$	1.30278	0.127748
$105$	0	0
$106$	9.69722	0.941878
$107$	− 1.39445i	− 0.134806i	−0.997726	−	0.0674032i	$-0.978529\pi$
$107$	− 1.39445i	− 0.134806i	0.997726	−	0.0674032i	$-0.0214714\pi$
$108$	5.60555i	0.539394i
$109$	−6.60555	−0.632697	−0.316349	−	0.948643i	$-0.602457\pi$
$109$	−6.60555	−0.632697	−0.316349	+	0.948643i	$0.602457\pi$
$110$	0	0
$111$	−8.60555	−0.816803
$112$	0.302776i	0.0286096i
$113$	3.90833i	0.367664i	0.982958	+	0.183832i	$0.0588503\pi$
$113$	3.90833i	0.367664i	−0.982958	+	0.183832i	$0.941150\pi$
$114$	−8.60555	−0.805984
$115$	0	0
$116$	−1.00000	−0.0928477
$117$	1.69722i	0.156908i
$118$	11.3028i	1.04050i
$119$	−0.697224	−0.0639145
$120$	0	0
$121$	10.2111	0.928282
$122$	− 3.30278i	− 0.299019i
$123$	− 1.81665i	− 0.163802i
$124$	−10.3028	−0.925217
$125$	0	0
$126$	−0.394449	−0.0351403
$127$	1.21110i	0.107468i	0.998555	+	0.0537340i	$0.0171123\pi$
$127$	1.21110i	0.107468i	−0.998555	+	0.0537340i	$0.982888\pi$
$128$	− 1.00000i	− 0.0883883i
$129$	−0.394449	−0.0347293
$130$	0	0
$131$	−6.00000	−0.524222	−0.262111	−	0.965038i	$-0.584419\pi$
$131$	−6.00000	−0.524222	−0.262111	+	0.965038i	$0.584419\pi$
$132$	6.00000i	0.522233i
$133$	− 2.00000i	− 0.173422i
$134$	−4.00000	−0.345547
$135$	0	0
$136$	2.30278	0.197461
$137$	− 13.1194i	− 1.12087i	−0.828199	−	0.560434i	$-0.810634\pi$
$137$	− 13.1194i	− 1.12087i	0.828199	−	0.560434i	$-0.189366\pi$
$138$	5.09167i	0.433432i
$139$	17.3305	1.46996	0.734978	−	0.678091i	$-0.237192\pi$
$139$	17.3305	1.46996	0.734978	+	0.678091i	$0.237192\pi$
$140$	0	0
$141$	12.0000	1.01058
$142$	9.21110i	0.772979i
$143$	6.00000i	0.501745i
$144$	1.30278	0.108565
$145$	0	0
$146$	−12.1194	−1.00301
$147$	− 9.00000i	− 0.742307i
$148$	6.60555i	0.542973i
$149$	−1.81665	−0.148826	−0.0744130	−	0.997228i	$-0.523708\pi$
$149$	−1.81665	−0.148826	−0.0744130	+	0.997228i	$0.523708\pi$
$150$	0	0
$151$	6.60555	0.537552	0.268776	−	0.963203i	$-0.413381\pi$
$151$	6.60555	0.537552	0.268776	+	0.963203i	$0.413381\pi$
$152$	6.60555i	0.535781i
$153$	3.00000i	0.242536i
$154$	−1.39445	−0.112368
$155$	0	0
$156$	−1.69722	−0.135887
$157$	7.21110i	0.575509i	0.957704	+	0.287754i	$0.0929087\pi$
$157$	7.21110i	0.575509i	−0.957704	+	0.287754i	$0.907091\pi$
$158$	1.90833i	0.151818i
$159$	−12.6333	−1.00189
$160$	0	0
$161$	−1.18335	−0.0932607
$162$	− 3.39445i	− 0.266693i
$163$	− 1.21110i	− 0.0948609i	−0.998875	−	0.0474304i	$-0.984897\pi$
$163$	− 1.21110i	− 0.0948609i	0.998875	−	0.0474304i	$-0.0151032\pi$
$164$	−1.39445	−0.108888
$165$	0	0
$166$	−7.81665	−0.606690
$167$	− 15.6972i	− 1.21469i	−0.794439	−	0.607344i	$-0.792235\pi$
$167$	− 15.6972i	− 1.21469i	0.794439	−	0.607344i	$-0.207765\pi$
$168$	− 0.394449i	− 0.0304324i
$169$	11.3028	0.869444
$170$	0	0
$171$	−8.60555	−0.658083
$172$	0.302776i	0.0230864i
$173$	− 14.5139i	− 1.10347i	−0.834020	−	0.551735i	$-0.813966\pi$
$173$	− 14.5139i	− 1.10347i	0.834020	−	0.551735i	$-0.186034\pi$
$174$	1.30278	0.0987632
$175$	0	0
$176$	4.60555	0.347156
$177$	− 14.7250i	− 1.10680i
$178$	13.8167i	1.03560i
$179$	−11.3028	−0.844809	−0.422405	−	0.906407i	$-0.638814\pi$
$179$	−11.3028	−0.844809	−0.422405	+	0.906407i	$0.638814\pi$
$180$	0	0
$181$	−11.8167	−0.878325	−0.439162	−	0.898408i	$-0.644725\pi$
$181$	−11.8167	−0.878325	−0.439162	+	0.898408i	$0.644725\pi$
$182$	− 0.394449i	− 0.0292385i
$183$	4.30278i	0.318070i
$184$	3.90833	0.288126
$185$	0	0
$186$	13.4222	0.984164
$187$	10.6056i	0.775555i
$188$	− 9.21110i	− 0.671789i
$189$	1.69722	0.123455
$190$	0	0
$191$	−20.7250	−1.49961	−0.749803	−	0.661661i	$-0.769852\pi$
$191$	−20.7250	−1.49961	−0.749803	+	0.661661i	$0.769852\pi$
$192$	1.30278i	0.0940197i
$193$	10.5139i	0.756806i	0.925641	+	0.378403i	$0.123527\pi$
$193$	10.5139i	0.756806i	−0.925641	+	0.378403i	$0.876473\pi$
$194$	9.11943	0.654737
$195$	0	0
$196$	−6.90833	−0.493452
$197$	4.11943i	0.293497i	0.989174	+	0.146749i	$0.0468808\pi$
$197$	4.11943i	0.293497i	−0.989174	+	0.146749i	$0.953119\pi$
$198$	6.00000i	0.426401i
$199$	−12.6056	−0.893584	−0.446792	−	0.894638i	$-0.647434\pi$
$199$	−12.6056	−0.893584	−0.446792	+	0.894638i	$0.647434\pi$
$200$	0	0
$201$	5.21110	0.367563
$202$	− 7.11943i	− 0.500921i
$203$	0.302776i	0.0212507i
$204$	−3.00000	−0.210042
$205$	0	0
$206$	10.4222	0.726149
$207$	5.09167i	0.353896i
$208$	1.30278i	0.0903312i
$209$	−30.4222	−2.10435
$210$	0	0
$211$	9.81665	0.675806	0.337903	−	0.941181i	$-0.390282\pi$
$211$	9.81665	0.675806	0.337903	+	0.941181i	$0.390282\pi$
$212$	9.69722i	0.666008i
$213$	− 12.0000i	− 0.822226i
$214$	1.39445	0.0953226
$215$	0	0
$216$	−5.60555	−0.381409
$217$	3.11943i	0.211761i
$218$	− 6.60555i	− 0.447384i
$219$	15.7889	1.06691
$220$	0	0
$221$	−3.00000	−0.201802
$222$	− 8.60555i	− 0.577567i
$223$	27.5416i	1.84432i	0.386804	+	0.922162i	$0.373579\pi$
$223$	27.5416i	1.84432i	−0.386804	+	0.922162i	$0.626421\pi$
$224$	−0.302776	−0.0202300
$225$	0	0
$226$	−3.90833	−0.259978
$227$	18.0000i	1.19470i	0.801980	+	0.597351i	$0.203780\pi$
$227$	18.0000i	1.19470i	−0.801980	+	0.597351i	$0.796220\pi$
$228$	− 8.60555i	− 0.569917i
$229$	−8.90833	−0.588679	−0.294339	−	0.955701i	$-0.595100\pi$
$229$	−8.90833	−0.588679	−0.294339	+	0.955701i	$0.595100\pi$
$230$	0	0
$231$	1.81665	0.119527
$232$	− 1.00000i	− 0.0656532i
$233$	− 27.2111i	− 1.78266i	−0.453356	−	0.891329i	$-0.649774\pi$
$233$	− 27.2111i	− 1.78266i	0.453356	−	0.891329i	$-0.350226\pi$
$234$	−1.69722	−0.110951
$235$	0	0
$236$	−11.3028	−0.735748
$237$	− 2.48612i	− 0.161491i
$238$	− 0.697224i	− 0.0451943i
$239$	−8.78890	−0.568507	−0.284253	−	0.958749i	$-0.591746\pi$
$239$	−8.78890	−0.568507	−0.284253	+	0.958749i	$0.591746\pi$
$240$	0	0
$241$	−21.7250	−1.39943	−0.699715	−	0.714423i	$-0.746689\pi$
$241$	−21.7250	−1.39943	−0.699715	+	0.714423i	$0.746689\pi$
$242$	10.2111i	0.656395i
$243$	− 12.3944i	− 0.795104i
$244$	3.30278	0.211439
$245$	0	0
$246$	1.81665	0.115826
$247$	− 8.60555i	− 0.547558i
$248$	− 10.3028i	− 0.654227i
$249$	10.1833	0.645343
$250$	0	0
$251$	−17.0278	−1.07478	−0.537391	−	0.843333i	$-0.680590\pi$
$251$	−17.0278	−1.07478	−0.537391	+	0.843333i	$0.680590\pi$
$252$	− 0.394449i	− 0.0248479i
$253$	18.0000i	1.13165i
$254$	−1.21110	−0.0759913
$255$	0	0
$256$	1.00000	0.0625000
$257$	− 4.18335i	− 0.260950i	−0.991452	−	0.130475i	$-0.958350\pi$
$257$	− 4.18335i	− 0.260950i	0.991452	−	0.130475i	$-0.0416502\pi$
$258$	− 0.394449i	− 0.0245573i
$259$	2.00000	0.124274
$260$	0	0
$261$	1.30278	0.0806398
$262$	− 6.00000i	− 0.370681i
$263$	21.2111i	1.30793i	0.756524	+	0.653966i	$0.226896\pi$
$263$	21.2111i	1.30793i	−0.756524	+	0.653966i	$0.773104\pi$
$264$	−6.00000	−0.369274
$265$	0	0
$266$	2.00000	0.122628
$267$	− 18.0000i	− 1.10158i
$268$	− 4.00000i	− 0.244339i
$269$	−19.3305	−1.17860	−0.589302	−	0.807913i	$-0.700597\pi$
$269$	−19.3305	−1.17860	−0.589302	+	0.807913i	$0.700597\pi$
$270$	0	0
$271$	−25.2111	−1.53147	−0.765733	−	0.643159i	$-0.777623\pi$
$271$	−25.2111	−1.53147	−0.765733	+	0.643159i	$0.777623\pi$
$272$	2.30278i	0.139626i
$273$	0.513878i	0.0311013i
$274$	13.1194	0.792574
$275$	0	0
$276$	−5.09167	−0.306483
$277$	22.0000i	1.32185i	0.750451	+	0.660926i	$0.229836\pi$
$277$	22.0000i	1.32185i	−0.750451	+	0.660926i	$0.770164\pi$
$278$	17.3305i	1.03942i
$279$	13.4222	0.803566
$280$	0	0
$281$	−10.1194	−0.603675	−0.301837	−	0.953359i	$-0.597600\pi$
$281$	−10.1194	−0.603675	−0.301837	+	0.953359i	$0.597600\pi$
$282$	12.0000i	0.714590i
$283$	21.3944i	1.27177i	0.771785	+	0.635884i	$0.219364\pi$
$283$	21.3944i	1.27177i	−0.771785	+	0.635884i	$0.780636\pi$
$284$	−9.21110	−0.546578
$285$	0	0
$286$	−6.00000	−0.354787
$287$	0.422205i	0.0249220i
$288$	1.30278i	0.0767668i
$289$	11.6972	0.688072
$290$	0	0
$291$	−11.8806	−0.696451
$292$	− 12.1194i	− 0.709236i
$293$	− 17.0278i	− 0.994772i	−0.867529	−	0.497386i	$-0.834293\pi$
$293$	− 17.0278i	− 0.994772i	0.867529	−	0.497386i	$-0.165707\pi$
$294$	9.00000	0.524891
$295$	0	0
$296$	−6.60555	−0.383940
$297$	− 25.8167i	− 1.49803i
$298$	− 1.81665i	− 0.105236i
$299$	−5.09167	−0.294459
$300$	0	0
$301$	0.0916731	0.00528395
$302$	6.60555i	0.380107i
$303$	9.27502i	0.532836i
$304$	−6.60555	−0.378854
$305$	0	0
$306$	−3.00000	−0.171499
$307$	13.2111i	0.753997i	0.926214	+	0.376999i	$0.123044\pi$
$307$	13.2111i	0.753997i	−0.926214	+	0.376999i	$0.876956\pi$
$308$	− 1.39445i	− 0.0794561i
$309$	−13.5778	−0.772414
$310$	0	0
$311$	21.9083	1.24231	0.621154	−	0.783689i	$-0.286664\pi$
$311$	21.9083	1.24231	0.621154	+	0.783689i	$0.286664\pi$
$312$	− 1.69722i	− 0.0960864i
$313$	− 31.2111i	− 1.76416i	−0.471104	−	0.882078i	$-0.656144\pi$
$313$	− 31.2111i	− 1.76416i	0.471104	−	0.882078i	$-0.343856\pi$
$314$	−7.21110	−0.406946
$315$	0	0
$316$	−1.90833	−0.107352
$317$	− 25.8167i	− 1.45001i	−0.688745	−	0.725004i	$-0.741838\pi$
$317$	− 25.8167i	− 1.45001i	0.688745	−	0.725004i	$-0.258162\pi$
$318$	− 12.6333i	− 0.708441i
$319$	4.60555	0.257861
$320$	0	0
$321$	−1.81665	−0.101396
$322$	− 1.18335i	− 0.0659453i
$323$	− 15.2111i	− 0.846368i
$324$	3.39445	0.188580
$325$	0	0
$326$	1.21110	0.0670768
$327$	8.60555i	0.475888i
$328$	− 1.39445i	− 0.0769956i
$329$	−2.78890	−0.153757
$330$	0	0
$331$	−20.6056	−1.13258	−0.566292	−	0.824205i	$-0.691622\pi$
$331$	−20.6056	−1.13258	−0.566292	+	0.824205i	$0.691622\pi$
$332$	− 7.81665i	− 0.428995i
$333$	− 8.60555i	− 0.471581i
$334$	15.6972	0.858914
$335$	0	0
$336$	0.394449	0.0215189
$337$	− 31.5139i	− 1.71667i	−0.513089	−	0.858335i	$-0.671499\pi$
$337$	− 31.5139i	− 1.71667i	0.513089	−	0.858335i	$-0.328501\pi$
$338$	11.3028i	0.614790i
$339$	5.09167	0.276542
$340$	0	0
$341$	47.4500	2.56956
$342$	− 8.60555i	− 0.465335i
$343$	4.21110i	0.227378i
$344$	−0.302776	−0.0163246
$345$	0	0
$346$	14.5139	0.780271
$347$	− 7.81665i	− 0.419620i	−0.977742	−	0.209810i	$-0.932715\pi$
$347$	− 7.81665i	− 0.419620i	0.977742	−	0.209810i	$-0.0672845\pi$
$348$	1.30278i	0.0698361i
$349$	−23.6333	−1.26506	−0.632531	−	0.774535i	$-0.717984\pi$
$349$	−23.6333	−1.26506	−0.632531	+	0.774535i	$0.717984\pi$
$350$	0	0
$351$	7.30278	0.389793
$352$	4.60555i	0.245477i
$353$	− 6.42221i	− 0.341819i	−0.985287	−	0.170910i	$-0.945329\pi$
$353$	− 6.42221i	− 0.341819i	0.985287	−	0.170910i	$-0.0546707\pi$
$354$	14.7250	0.782624
$355$	0	0
$356$	−13.8167	−0.732281
$357$	0.908327i	0.0480738i
$358$	− 11.3028i	− 0.597370i
$359$	−21.9083	−1.15628	−0.578139	−	0.815939i	$-0.696221\pi$
$359$	−21.9083	−1.15628	−0.578139	+	0.815939i	$0.696221\pi$
$360$	0	0
$361$	24.6333	1.29649
$362$	− 11.8167i	− 0.621070i
$363$	− 13.3028i	− 0.698215i
$364$	0.394449	0.0206747
$365$	0	0
$366$	−4.30278	−0.224910
$367$	23.8167i	1.24322i	0.783327	+	0.621610i	$0.213521\pi$
$367$	23.8167i	1.24322i	−0.783327	+	0.621610i	$0.786479\pi$
$368$	3.90833i	0.203736i
$369$	1.81665	0.0945712
$370$	0	0
$371$	2.93608	0.152434
$372$	13.4222i	0.695909i
$373$	28.7250i	1.48732i	0.668556	+	0.743662i	$0.266913\pi$
$373$	28.7250i	1.48732i	−0.668556	+	0.743662i	$0.733087\pi$
$374$	−10.6056	−0.548400
$375$	0	0
$376$	9.21110	0.475026
$377$	1.30278i	0.0670964i
$378$	1.69722i	0.0872958i
$379$	2.18335	0.112151	0.0560755	−	0.998427i	$-0.482141\pi$
$379$	2.18335	0.112151	0.0560755	+	0.998427i	$0.482141\pi$
$380$	0	0
$381$	1.57779	0.0808329
$382$	− 20.7250i	− 1.06038i
$383$	3.69722i	0.188919i	0.995529	+	0.0944597i	$0.0301123\pi$
$383$	3.69722i	0.188919i	−0.995529	+	0.0944597i	$0.969888\pi$
$384$	−1.30278	−0.0664820
$385$	0	0
$386$	−10.5139	−0.535142
$387$	− 0.394449i	− 0.0200510i
$388$	9.11943i	0.462969i
$389$	24.4222	1.23825	0.619127	−	0.785290i	$-0.287486\pi$
$389$	24.4222	1.23825	0.619127	+	0.785290i	$0.287486\pi$
$390$	0	0
$391$	−9.00000	−0.455150
$392$	− 6.90833i	− 0.348923i
$393$	7.81665i	0.394298i
$394$	−4.11943	−0.207534
$395$	0	0
$396$	−6.00000	−0.301511
$397$	6.30278i	0.316327i	0.987413	+	0.158164i	$0.0505573\pi$
$397$	6.30278i	0.316327i	−0.987413	+	0.158164i	$0.949443\pi$
$398$	− 12.6056i	− 0.631859i
$399$	−2.60555	−0.130441
$400$	0	0
$401$	19.1194	0.954779	0.477389	−	0.878692i	$-0.341583\pi$
$401$	19.1194	0.954779	0.477389	+	0.878692i	$0.341583\pi$
$402$	5.21110i	0.259906i
$403$	13.4222i	0.668608i
$404$	7.11943	0.354205
$405$	0	0
$406$	−0.302776	−0.0150265
$407$	− 30.4222i	− 1.50797i
$408$	− 3.00000i	− 0.148522i
$409$	−10.7889	−0.533477	−0.266738	−	0.963769i	$-0.585946\pi$
$409$	−10.7889	−0.533477	−0.266738	+	0.963769i	$0.585946\pi$
$410$	0	0
$411$	−17.0917	−0.843070
$412$	10.4222i	0.513465i
$413$	3.42221i	0.168396i
$414$	−5.09167	−0.250242
$415$	0	0
$416$	−1.30278	−0.0638738
$417$	− 22.5778i	− 1.10564i
$418$	− 30.4222i	− 1.48800i
$419$	−12.4861	−0.609987	−0.304993	−	0.952354i	$-0.598654\pi$
$419$	−12.4861	−0.609987	−0.304993	+	0.952354i	$0.598654\pi$
$420$	0	0
$421$	−25.6333	−1.24929	−0.624645	−	0.780908i	$-0.714757\pi$
$421$	−25.6333	−1.24929	−0.624645	+	0.780908i	$0.714757\pi$
$422$	9.81665i	0.477867i
$423$	12.0000i	0.583460i
$424$	−9.69722	−0.470939
$425$	0	0
$426$	12.0000	0.581402
$427$	− 1.00000i	− 0.0483934i
$428$	1.39445i	0.0674032i
$429$	7.81665	0.377392
$430$	0	0
$431$	1.39445	0.0671682	0.0335841	−	0.999436i	$-0.489308\pi$
$431$	1.39445	0.0671682	0.0335841	+	0.999436i	$0.489308\pi$
$432$	− 5.60555i	− 0.269697i
$433$	− 13.6333i	− 0.655175i	−0.944821	−	0.327587i	$-0.893764\pi$
$433$	− 13.6333i	− 0.655175i	0.944821	−	0.327587i	$-0.106236\pi$
$434$	−3.11943	−0.149737
$435$	0	0
$436$	6.60555	0.316349
$437$	− 25.8167i	− 1.23498i
$438$	15.7889i	0.754423i
$439$	34.8444	1.66303	0.831516	−	0.555500i	$-0.187473\pi$
$439$	34.8444	1.66303	0.831516	+	0.555500i	$0.187473\pi$
$440$	0	0
$441$	9.00000	0.428571
$442$	− 3.00000i	− 0.142695i
$443$	− 27.9083i	− 1.32596i	−0.748635	−	0.662982i	$-0.769290\pi$
$443$	− 27.9083i	− 1.32596i	0.748635	−	0.662982i	$-0.230710\pi$
$444$	8.60555	0.408401
$445$	0	0
$446$	−27.5416	−1.30413
$447$	2.36669i	0.111941i
$448$	− 0.302776i	− 0.0143048i
$449$	26.2389	1.23829	0.619144	−	0.785277i	$-0.287480\pi$
$449$	26.2389	1.23829	0.619144	+	0.785277i	$0.287480\pi$
$450$	0	0
$451$	6.42221	0.302410
$452$	− 3.90833i	− 0.183832i
$453$	− 8.60555i	− 0.404324i
$454$	−18.0000	−0.844782
$455$	0	0
$456$	8.60555	0.402992
$457$	10.0000i	0.467780i	0.972263	+	0.233890i	$0.0751456\pi$
$457$	10.0000i	0.467780i	−0.972263	+	0.233890i	$0.924854\pi$
$458$	− 8.90833i	− 0.416259i
$459$	12.9083	0.602509
$460$	0	0
$461$	−14.7250	−0.685811	−0.342905	−	0.939370i	$-0.611411\pi$
$461$	−14.7250	−0.685811	−0.342905	+	0.939370i	$0.611411\pi$
$462$	1.81665i	0.0845184i
$463$	20.0000i	0.929479i	0.885448	+	0.464739i	$0.153852\pi$
$463$	20.0000i	0.929479i	−0.885448	+	0.464739i	$0.846148\pi$
$464$	1.00000	0.0464238
$465$	0	0
$466$	27.2111	1.26053
$467$	20.3028i	0.939500i	0.882799	+	0.469750i	$0.155656\pi$
$467$	20.3028i	0.939500i	−0.882799	+	0.469750i	$0.844344\pi$
$468$	− 1.69722i	− 0.0784542i
$469$	−1.21110	−0.0559235
$470$	0	0
$471$	9.39445	0.432873
$472$	− 11.3028i	− 0.520252i
$473$	− 1.39445i	− 0.0641168i
$474$	2.48612	0.114191
$475$	0	0
$476$	0.697224	0.0319572
$477$	− 12.6333i	− 0.578439i
$478$	− 8.78890i	− 0.401995i
$479$	−24.4861	−1.11880	−0.559400	−	0.828898i	$-0.688968\pi$
$479$	−24.4861	−1.11880	−0.559400	+	0.828898i	$0.688968\pi$
$480$	0	0
$481$	8.60555	0.392379
$482$	− 21.7250i	− 0.989546i
$483$	1.54163i	0.0701468i
$484$	−10.2111	−0.464141
$485$	0	0
$486$	12.3944	0.562224
$487$	4.27502i	0.193720i	0.995298	+	0.0968598i	$0.0308798\pi$
$487$	4.27502i	0.193720i	−0.995298	+	0.0968598i	$0.969120\pi$
$488$	3.30278i	0.149510i
$489$	−1.57779	−0.0713504
$490$	0	0
$491$	2.78890	0.125861	0.0629306	−	0.998018i	$-0.479955\pi$
$491$	2.78890	0.125861	0.0629306	+	0.998018i	$0.479955\pi$
$492$	1.81665i	0.0819011i
$493$	2.30278i	0.103712i
$494$	8.60555	0.387182
$495$	0	0
$496$	10.3028	0.462608
$497$	2.78890i	0.125099i
$498$	10.1833i	0.456327i
$499$	7.48612	0.335125	0.167562	−	0.985861i	$-0.446410\pi$
$499$	7.48612	0.335125	0.167562	+	0.985861i	$0.446410\pi$
$500$	0	0
$501$	−20.4500	−0.913637
$502$	− 17.0278i	− 0.759986i
$503$	− 5.57779i	− 0.248702i	−0.992238	−	0.124351i	$-0.960315\pi$
$503$	− 5.57779i	− 0.248702i	0.992238	−	0.124351i	$-0.0396848\pi$
$504$	0.394449	0.0175701
$505$	0	0
$506$	−18.0000	−0.800198
$507$	− 14.7250i	− 0.653959i
$508$	− 1.21110i	− 0.0537340i
$509$	−19.8167	−0.878358	−0.439179	−	0.898400i	$-0.644731\pi$
$509$	−19.8167	−0.878358	−0.439179	+	0.898400i	$0.644731\pi$
$510$	0	0
$511$	−3.66947	−0.162328
$512$	1.00000i	0.0441942i
$513$	37.0278i	1.63482i
$514$	4.18335	0.184519
$515$	0	0
$516$	0.394449	0.0173646
$517$	42.4222i	1.86573i
$518$	2.00000i	0.0878750i
$519$	−18.9083	−0.829983
$520$	0	0
$521$	−28.5416	−1.25043	−0.625216	−	0.780452i	$-0.714989\pi$
$521$	−28.5416	−1.25043	−0.625216	+	0.780452i	$0.714989\pi$
$522$	1.30278i	0.0570209i
$523$	− 21.0278i	− 0.919480i	−0.888054	−	0.459740i	$-0.847943\pi$
$523$	− 21.0278i	− 0.919480i	0.888054	−	0.459740i	$-0.152057\pi$
$524$	6.00000	0.262111
$525$	0	0
$526$	−21.2111	−0.924848
$527$	23.7250i	1.03348i
$528$	− 6.00000i	− 0.261116i
$529$	7.72498	0.335869
$530$	0	0
$531$	14.7250	0.639010
$532$	2.00000i	0.0867110i
$533$	1.81665i	0.0786880i
$534$	18.0000	0.778936
$535$	0	0
$536$	4.00000	0.172774
$537$	14.7250i	0.635430i
$538$	− 19.3305i	− 0.833398i
$539$	31.8167	1.37044
$540$	0	0
$541$	11.6972	0.502903	0.251451	−	0.967870i	$-0.419092\pi$
$541$	11.6972	0.502903	0.251451	+	0.967870i	$0.419092\pi$
$542$	− 25.2111i	− 1.08291i
$543$	15.3944i	0.660639i
$544$	−2.30278	−0.0987307
$545$	0	0
$546$	−0.513878	−0.0219920
$547$	− 30.6056i	− 1.30860i	−0.756236	−	0.654299i	$-0.772964\pi$
$547$	− 30.6056i	− 1.30860i	0.756236	−	0.654299i	$-0.227036\pi$
$548$	13.1194i	0.560434i
$549$	−4.30278	−0.183638
$550$	0	0
$551$	−6.60555	−0.281406
$552$	− 5.09167i	− 0.216716i
$553$	0.577795i	0.0245703i
$554$	−22.0000	−0.934690
$555$	0	0
$556$	−17.3305	−0.734978
$557$	− 19.5416i	− 0.828006i	−0.910276	−	0.414003i	$-0.864130\pi$
$557$	− 19.5416i	− 0.828006i	0.910276	−	0.414003i	$-0.135870\pi$
$558$	13.4222i	0.568207i
$559$	0.394449	0.0166834
$560$	0	0
$561$	13.8167	0.583340
$562$	− 10.1194i	− 0.426862i
$563$	3.90833i	0.164716i	0.996603	+	0.0823582i	$0.0262451\pi$
$563$	3.90833i	0.164716i	−0.996603	+	0.0823582i	$0.973755\pi$
$564$	−12.0000	−0.505291
$565$	0	0
$566$	−21.3944	−0.899276
$567$	− 1.02776i	− 0.0431617i
$568$	− 9.21110i	− 0.386489i
$569$	−39.6333	−1.66151	−0.830757	−	0.556635i	$-0.812092\pi$
$569$	−39.6333	−1.66151	−0.830757	+	0.556635i	$0.812092\pi$
$570$	0	0
$571$	−44.3305	−1.85518	−0.927588	−	0.373606i	$-0.878121\pi$
$571$	−44.3305	−1.85518	−0.927588	+	0.373606i	$0.878121\pi$
$572$	− 6.00000i	− 0.250873i
$573$	27.0000i	1.12794i
$574$	−0.422205	−0.0176225
$575$	0	0
$576$	−1.30278	−0.0542823
$577$	42.3028i	1.76109i	0.473965	+	0.880544i	$0.342822\pi$
$577$	42.3028i	1.76109i	−0.473965	+	0.880544i	$0.657178\pi$
$578$	11.6972i	0.486540i
$579$	13.6972	0.569237
$580$	0	0
$581$	−2.36669	−0.0981869
$582$	− 11.8806i	− 0.492465i
$583$	− 44.6611i	− 1.84967i
$584$	12.1194	0.501506
$585$	0	0
$586$	17.0278	0.703410
$587$	18.0000i	0.742940i	0.928445	+	0.371470i	$0.121146\pi$
$587$	18.0000i	0.742940i	−0.928445	+	0.371470i	$0.878854\pi$
$588$	9.00000i	0.371154i
$589$	−68.0555	−2.80418
$590$	0	0
$591$	5.36669	0.220756
$592$	− 6.60555i	− 0.271486i
$593$	− 40.6056i	− 1.66747i	−0.552165	−	0.833735i	$-0.686198\pi$
$593$	− 40.6056i	− 1.66747i	0.552165	−	0.833735i	$-0.313802\pi$
$594$	25.8167	1.05927
$595$	0	0
$596$	1.81665	0.0744130
$597$	16.4222i	0.672116i
$598$	− 5.09167i	− 0.208214i
$599$	−38.3028	−1.56501	−0.782504	−	0.622645i	$-0.786058\pi$
$599$	−38.3028	−1.56501	−0.782504	+	0.622645i	$0.786058\pi$
$600$	0	0
$601$	33.8167	1.37941	0.689705	−	0.724090i	$-0.257740\pi$
$601$	33.8167	1.37941	0.689705	+	0.724090i	$0.257740\pi$
$602$	0.0916731i	0.00373632i
$603$	5.21110i	0.212213i
$604$	−6.60555	−0.268776
$605$	0	0
$606$	−9.27502	−0.376772
$607$	16.0000i	0.649420i	0.945814	+	0.324710i	$0.105267\pi$
$607$	16.0000i	0.649420i	−0.945814	+	0.324710i	$0.894733\pi$
$608$	− 6.60555i	− 0.267890i
$609$	0.394449	0.0159839
$610$	0	0
$611$	−12.0000	−0.485468
$612$	− 3.00000i	− 0.121268i
$613$	34.3028i	1.38548i	0.721189	+	0.692738i	$0.243596\pi$
$613$	34.3028i	1.38548i	−0.721189	+	0.692738i	$0.756404\pi$
$614$	−13.2111	−0.533157
$615$	0	0
$616$	1.39445	0.0561839
$617$	34.5416i	1.39059i	0.718723	+	0.695297i	$0.244727\pi$
$617$	34.5416i	1.39059i	−0.718723	+	0.695297i	$0.755273\pi$
$618$	− 13.5778i	− 0.546179i
$619$	43.2111	1.73680	0.868400	−	0.495864i	$-0.165148\pi$
$619$	43.2111	1.73680	0.868400	+	0.495864i	$0.165148\pi$
$620$	0	0
$621$	21.9083	0.879151
$622$	21.9083i	0.878444i
$623$	4.18335i	0.167602i
$624$	1.69722	0.0679434
$625$	0	0
$626$	31.2111	1.24745
$627$	39.6333i	1.58280i
$628$	− 7.21110i	− 0.287754i
$629$	15.2111	0.606506
$630$	0	0
$631$	8.42221	0.335283	0.167641	−	0.985848i	$-0.446385\pi$
$631$	8.42221	0.335283	0.167641	+	0.985848i	$0.446385\pi$
$632$	− 1.90833i	− 0.0759092i
$633$	− 12.7889i	− 0.508313i
$634$	25.8167	1.02531
$635$	0	0
$636$	12.6333	0.500943
$637$	9.00000i	0.356593i
$638$	4.60555i	0.182336i
$639$	12.0000	0.474713
$640$	0	0
$641$	23.4500	0.926218	0.463109	−	0.886301i	$-0.346734\pi$
$641$	23.4500	0.926218	0.463109	+	0.886301i	$0.346734\pi$
$642$	− 1.81665i	− 0.0716976i
$643$	9.81665i	0.387131i	0.981087	+	0.193566i	$0.0620052\pi$
$643$	9.81665i	0.387131i	−0.981087	+	0.193566i	$0.937995\pi$
$644$	1.18335	0.0466304
$645$	0	0
$646$	15.2111	0.598473
$647$	26.7889i	1.05318i	0.850119	+	0.526590i	$0.176530\pi$
$647$	26.7889i	1.05318i	−0.850119	+	0.526590i	$0.823470\pi$
$648$	3.39445i	0.133347i
$649$	52.0555	2.04336
$650$	0	0
$651$	4.06392	0.159277
$652$	1.21110i	0.0474304i
$653$	− 44.2389i	− 1.73120i	−0.500736	−	0.865600i	$-0.666937\pi$
$653$	− 44.2389i	− 1.73120i	0.500736	−	0.865600i	$-0.333063\pi$
$654$	−8.60555	−0.336504
$655$	0	0
$656$	1.39445	0.0544441
$657$	15.7889i	0.615984i
$658$	− 2.78890i	− 0.108723i
$659$	−1.81665	−0.0707668	−0.0353834	−	0.999374i	$-0.511265\pi$
$659$	−1.81665	−0.0707668	−0.0353834	+	0.999374i	$0.511265\pi$
$660$	0	0
$661$	4.23886	0.164873	0.0824363	−	0.996596i	$-0.473730\pi$
$661$	4.23886	0.164873	0.0824363	+	0.996596i	$0.473730\pi$
$662$	− 20.6056i	− 0.800857i
$663$	3.90833i	0.151787i
$664$	7.81665	0.303345
$665$	0	0
$666$	8.60555	0.333458
$667$	3.90833i	0.151331i
$668$	15.6972i	0.607344i
$669$	35.8806	1.38722
$670$	0	0
$671$	−15.2111	−0.587218
$672$	0.394449i	0.0152162i
$673$	6.60555i	0.254625i	0.991863	+	0.127313i	$0.0406352\pi$
$673$	6.60555i	0.254625i	−0.991863	+	0.127313i	$0.959365\pi$
$674$	31.5139	1.21387
$675$	0	0
$676$	−11.3028	−0.434722
$677$	0	0	1.00000			$0$
$677$	0	0	−1.00000			$\pi$
$678$	5.09167i	0.195545i
$679$	2.76114	0.105963
$680$	0	0
$681$	23.4500	0.898604
$682$	47.4500i	1.81695i
$683$	− 32.6611i	− 1.24974i	−0.780728	−	0.624870i	$-0.785152\pi$
$683$	− 32.6611i	− 1.24974i	0.780728	−	0.624870i	$-0.214848\pi$
$684$	8.60555	0.329041
$685$	0	0
$686$	−4.21110	−0.160781
$687$	11.6056i	0.442779i
$688$	− 0.302776i	− 0.0115432i
$689$	12.6333	0.481291
$690$	0	0
$691$	−20.1194	−0.765379	−0.382690	−	0.923877i	$-0.625002\pi$
$691$	−20.1194	−0.765379	−0.382690	+	0.923877i	$0.625002\pi$
$692$	14.5139i	0.551735i
$693$	1.81665i	0.0690090i
$694$	7.81665	0.296716
$695$	0	0
$696$	−1.30278	−0.0493816
$697$	3.21110i	0.121629i
$698$	− 23.6333i	− 0.894534i
$699$	−35.4500	−1.34084
$700$	0	0
$701$	23.0278	0.869746	0.434873	−	0.900492i	$-0.356793\pi$
$701$	23.0278	0.869746	0.434873	+	0.900492i	$0.356793\pi$
$702$	7.30278i	0.275626i
$703$	43.6333i	1.64566i
$704$	−4.60555	−0.173578
$705$	0	0
$706$	6.42221	0.241703
$707$	− 2.15559i	− 0.0810693i
$708$	14.7250i	0.553399i
$709$	2.18335	0.0819973	0.0409986	−	0.999159i	$-0.486946\pi$
$709$	2.18335	0.0819973	0.0409986	+	0.999159i	$0.486946\pi$
$710$	0	0
$711$	2.48612	0.0932369
$712$	− 13.8167i	− 0.517801i
$713$	40.2666i	1.50800i
$714$	−0.908327	−0.0339933
$715$	0	0
$716$	11.3028	0.422405
$717$	11.4500i	0.427607i
$718$	− 21.9083i	− 0.817611i
$719$	−19.8167	−0.739036	−0.369518	−	0.929223i	$-0.620477\pi$
$719$	−19.8167	−0.739036	−0.369518	+	0.929223i	$0.620477\pi$
$720$	0	0
$721$	3.15559	0.117520
$722$	24.6333i	0.916757i
$723$	28.3028i	1.05259i
$724$	11.8167	0.439162
$725$	0	0
$726$	13.3028	0.493712
$727$	29.8167i	1.10584i	0.833235	+	0.552919i	$0.186486\pi$
$727$	29.8167i	1.10584i	−0.833235	+	0.552919i	$0.813514\pi$
$728$	0.394449i	0.0146192i
$729$	−26.3305	−0.975205
$730$	0	0
$731$	0.697224	0.0257878
$732$	− 4.30278i	− 0.159035i
$733$	− 18.7889i	− 0.693984i	−0.937868	−	0.346992i	$-0.887203\pi$
$733$	− 18.7889i	− 0.693984i	0.937868	−	0.346992i	$-0.112797\pi$
$734$	−23.8167	−0.879089
$735$	0	0
$736$	−3.90833	−0.144063
$737$	18.4222i	0.678591i
$738$	1.81665i	0.0668720i
$739$	37.2111	1.36883	0.684416	−	0.729091i	$-0.260057\pi$
$739$	37.2111	1.36883	0.684416	+	0.729091i	$0.260057\pi$
$740$	0	0
$741$	−11.2111	−0.411850
$742$	2.93608i	0.107787i
$743$	46.0555i	1.68961i	0.535072	+	0.844806i	$0.320284\pi$
$743$	46.0555i	1.68961i	−0.535072	+	0.844806i	$0.679716\pi$
$744$	−13.4222	−0.492082
$745$	0	0
$746$	−28.7250	−1.05170
$747$	10.1833i	0.372589i
$748$	− 10.6056i	− 0.387777i
$749$	0.422205	0.0154270
$750$	0	0
$751$	−35.2666	−1.28690	−0.643449	−	0.765489i	$-0.722497\pi$
$751$	−35.2666	−1.28690	−0.643449	+	0.765489i	$0.722497\pi$
$752$	9.21110i	0.335894i
$753$	22.1833i	0.808406i
$754$	−1.30278	−0.0474443
$755$	0	0
$756$	−1.69722	−0.0617275
$757$	− 31.4500i	− 1.14307i	−0.820578	−	0.571534i	$-0.806348\pi$
$757$	− 31.4500i	− 1.14307i	0.820578	−	0.571534i	$-0.193652\pi$
$758$	2.18335i	0.0793027i
$759$	23.4500	0.851180
$760$	0	0
$761$	−29.5139	−1.06988	−0.534939	−	0.844891i	$-0.679665\pi$
$761$	−29.5139	−1.06988	−0.534939	+	0.844891i	$0.679665\pi$
$762$	1.57779i	0.0571575i
$763$	− 2.00000i	− 0.0724049i
$764$	20.7250	0.749803
$765$	0	0
$766$	−3.69722	−0.133586
$767$	14.7250i	0.531688i
$768$	− 1.30278i	− 0.0470099i
$769$	−31.0278	−1.11889	−0.559445	−	0.828868i	$-0.688986\pi$
$769$	−31.0278	−1.11889	−0.559445	+	0.828868i	$0.688986\pi$
$770$	0	0
$771$	−5.44996	−0.196276
$772$	− 10.5139i	− 0.378403i
$773$	− 42.0000i	− 1.51064i	−0.655359	−	0.755318i	$-0.727483\pi$
$773$	− 42.0000i	− 1.51064i	0.655359	−	0.755318i	$-0.272517\pi$
$774$	0.394449	0.0141782
$775$	0	0
$776$	−9.11943	−0.327368
$777$	− 2.60555i	− 0.0934736i
$778$	24.4222i	0.875578i
$779$	−9.21110	−0.330022
$780$	0	0
$781$	42.4222	1.51799
$782$	− 9.00000i	− 0.321839i
$783$	− 5.60555i	− 0.200326i
$784$	6.90833	0.246726
$785$	0	0
$786$	−7.81665	−0.278811
$787$	9.02776i	0.321805i	0.986970	+	0.160902i	$0.0514404\pi$
$787$	9.02776i	0.321805i	−0.986970	+	0.160902i	$0.948560\pi$
$788$	− 4.11943i	− 0.146749i
$789$	27.6333	0.983772
$790$	0	0
$791$	−1.18335	−0.0420749
$792$	− 6.00000i	− 0.213201i
$793$	− 4.30278i	− 0.152796i
$794$	−6.30278	−0.223677
$795$	0	0
$796$	12.6056	0.446792
$797$	3.63331i	0.128698i	0.997927	+	0.0643492i	$0.0204971\pi$
$797$	3.63331i	0.128698i	−0.997927	+	0.0643492i	$0.979503\pi$
$798$	− 2.60555i	− 0.0922355i
$799$	−21.2111	−0.750395
$800$	0	0
$801$	18.0000	0.635999
$802$	19.1194i	0.675131i
$803$	55.8167i	1.96973i
$804$	−5.21110	−0.183781
$805$	0	0
$806$	−13.4222	−0.472777
$807$	25.1833i	0.886496i
$808$	7.11943i	0.250461i
$809$	−39.6333	−1.39343	−0.696716	−	0.717347i	$-0.745356\pi$
$809$	−39.6333	−1.39343	−0.696716	+	0.717347i	$0.745356\pi$
$810$	0	0
$811$	48.1194	1.68970	0.844851	−	0.535002i	$-0.179689\pi$
$811$	48.1194	1.68970	0.844851	+	0.535002i	$0.179689\pi$
$812$	− 0.302776i	− 0.0106253i
$813$	32.8444i	1.15190i
$814$	30.4222	1.06630
$815$	0	0
$816$	3.00000	0.105021
$817$	2.00000i	0.0699711i
$818$	− 10.7889i	− 0.377225i
$819$	−0.513878	−0.0179564
$820$	0	0
$821$	20.2389	0.706341	0.353171	−	0.935559i	$-0.385104\pi$
$821$	20.2389	0.706341	0.353171	+	0.935559i	$0.385104\pi$
$822$	− 17.0917i	− 0.596141i
$823$	− 13.6333i	− 0.475227i	−0.971360	−	0.237614i	$-0.923635\pi$
$823$	− 13.6333i	− 0.475227i	0.971360	−	0.237614i	$-0.0763652\pi$
$824$	−10.4222	−0.363075
$825$	0	0
$826$	−3.42221	−0.119074
$827$	− 21.1472i	− 0.735360i	−0.929952	−	0.367680i	$-0.880152\pi$
$827$	− 21.1472i	− 0.735360i	0.929952	−	0.367680i	$-0.119848\pi$
$828$	− 5.09167i	− 0.176948i
$829$	15.0917	0.524155	0.262078	−	0.965047i	$-0.415592\pi$
$829$	15.0917	0.524155	0.262078	+	0.965047i	$0.415592\pi$
$830$	0	0
$831$	28.6611	0.994241
$832$	− 1.30278i	− 0.0451656i
$833$	15.9083i	0.551191i
$834$	22.5778	0.781805
$835$	0	0
$836$	30.4222	1.05217
$837$	− 57.7527i	− 1.99623i
$838$	− 12.4861i	− 0.431326i
$839$	−51.6333	−1.78258	−0.891290	−	0.453434i	$-0.850199\pi$
$839$	−51.6333	−1.78258	−0.891290	+	0.453434i	$0.850199\pi$
$840$	0	0
$841$	1.00000	0.0344828
$842$	− 25.6333i	− 0.883382i
$843$	13.1833i	0.454059i
$844$	−9.81665	−0.337903
$845$	0	0
$846$	−12.0000	−0.412568
$847$	3.09167i	0.106231i
$848$	− 9.69722i	− 0.333004i
$849$	27.8722	0.956570
$850$	0	0
$851$	25.8167	0.884983
$852$	12.0000i	0.411113i
$853$	− 2.60555i	− 0.0892124i	−0.999005	−	0.0446062i	$-0.985797\pi$
$853$	− 2.60555i	− 0.0892124i	0.999005	−	0.0446062i	$-0.0142033\pi$
$854$	1.00000	0.0342193
$855$	0	0
$856$	−1.39445	−0.0476613
$857$	16.6056i	0.567235i	0.958938	+	0.283617i	$0.0915346\pi$
$857$	16.6056i	0.567235i	−0.958938	+	0.283617i	$0.908465\pi$
$858$	7.81665i	0.266856i
$859$	−49.0278	−1.67281	−0.836403	−	0.548115i	$-0.815345\pi$
$859$	−49.0278	−1.67281	−0.836403	+	0.548115i	$0.815345\pi$
$860$	0	0
$861$	0.550039	0.0187453
$862$	1.39445i	0.0474951i
$863$	4.45837i	0.151765i	0.997117	+	0.0758823i	$0.0241773\pi$
$863$	4.45837i	0.151765i	−0.997117	+	0.0758823i	$0.975823\pi$
$864$	5.60555	0.190705
$865$	0	0
$866$	13.6333	0.463279
$867$	− 15.2389i	− 0.517539i
$868$	− 3.11943i	− 0.105880i
$869$	8.78890	0.298143
$870$	0	0
$871$	−5.21110	−0.176571
$872$	6.60555i	0.223692i
$873$	− 11.8806i	− 0.402096i
$874$	25.8167	0.873261
$875$	0	0
$876$	−15.7889	−0.533457
$877$	− 14.6972i	− 0.496290i	−0.968723	−	0.248145i	$-0.920179\pi$
$877$	− 14.6972i	− 0.496290i	0.968723	−	0.248145i	$-0.0798209\pi$
$878$	34.8444i	1.17594i
$879$	−22.1833	−0.748226
$880$	0	0
$881$	31.8167	1.07193	0.535965	−	0.844240i	$-0.319948\pi$
$881$	31.8167	1.07193	0.535965	+	0.844240i	$0.319948\pi$
$882$	9.00000i	0.303046i
$883$	− 18.2389i	− 0.613786i	−0.951744	−	0.306893i	$-0.900711\pi$
$883$	− 18.2389i	− 0.613786i	0.951744	−	0.306893i	$-0.0992895\pi$
$884$	3.00000	0.100901
$885$	0	0
$886$	27.9083	0.937599
$887$	− 46.0555i	− 1.54639i	−0.634167	−	0.773196i	$-0.718657\pi$
$887$	− 46.0555i	− 1.54639i	0.634167	−	0.773196i	$-0.281343\pi$
$888$	8.60555i	0.288783i
$889$	−0.366692	−0.0122985
$890$	0	0
$891$	−15.6333	−0.523736
$892$	− 27.5416i	− 0.922162i
$893$	− 60.8444i	− 2.03608i
$894$	−2.36669	−0.0791540
$895$	0	0
$896$	0.302776	0.0101150
$897$	6.63331i	0.221480i
$898$	26.2389i	0.875602i
$899$	10.3028	0.343617
$900$	0	0
$901$	22.3305	0.743938
$902$	6.42221i	0.213836i
$903$	− 0.119429i	− 0.00397436i
$904$	3.90833	0.129989
$905$	0	0
$906$	8.60555	0.285900
$907$	− 10.7250i	− 0.356117i	−0.984020	−	0.178059i	$-0.943018\pi$
$907$	− 10.7250i	− 0.356117i	0.984020	−	0.178059i	$-0.0569817\pi$
$908$	− 18.0000i	− 0.597351i
$909$	−9.27502	−0.307633
$910$	0	0
$911$	−21.3583	−0.707632	−0.353816	−	0.935315i	$-0.615116\pi$
$911$	−21.3583	−0.707632	−0.353816	+	0.935315i	$0.615116\pi$
$912$	8.60555i	0.284958i
$913$	36.0000i	1.19143i
$914$	−10.0000	−0.330771
$915$	0	0
$916$	8.90833	0.294339
$917$	− 1.81665i	− 0.0599912i
$918$	12.9083i	0.426038i
$919$	30.7889	1.01563	0.507816	−	0.861466i	$-0.330453\pi$
$919$	30.7889	1.01563	0.507816	+	0.861466i	$0.330453\pi$
$920$	0	0
$921$	17.2111	0.567125
$922$	− 14.7250i	− 0.484941i
$923$	12.0000i	0.394985i
$924$	−1.81665	−0.0597635
$925$	0	0
$926$	−20.0000	−0.657241
$927$	− 13.5778i	− 0.445953i
$928$	1.00000i	0.0328266i
$929$	38.7250	1.27053	0.635263	−	0.772296i	$-0.280892\pi$
$929$	38.7250	1.27053	0.635263	+	0.772296i	$0.280892\pi$
$930$	0	0
$931$	−45.6333	−1.49557
$932$	27.2111i	0.891329i
$933$	− 28.5416i	− 0.934411i
$934$	−20.3028	−0.664327
$935$	0	0
$936$	1.69722	0.0554755
$937$	27.4500i	0.896751i	0.893845	+	0.448376i	$0.147997\pi$
$937$	27.4500i	0.896751i	−0.893845	+	0.448376i	$0.852003\pi$
$938$	− 1.21110i	− 0.0395439i
$939$	−40.6611	−1.32692
$940$	0	0
$941$	12.0000	0.391189	0.195594	−	0.980685i	$-0.437336\pi$
$941$	12.0000	0.391189	0.195594	+	0.980685i	$0.437336\pi$
$942$	9.39445i	0.306088i
$943$	5.44996i	0.177475i
$944$	11.3028	0.367874
$945$	0	0
$946$	1.39445	0.0453374
$947$	23.7250i	0.770958i	0.922717	+	0.385479i	$0.125964\pi$
$947$	23.7250i	0.770958i	−0.922717	+	0.385479i	$0.874036\pi$
$948$	2.48612i	0.0807455i
$949$	−15.7889	−0.512529
$950$	0	0
$951$	−33.6333	−1.09063
$952$	0.697224i	0.0225972i
$953$	− 45.6333i	− 1.47821i	−0.673591	−	0.739104i	$-0.735249\pi$
$953$	− 45.6333i	− 1.47821i	0.673591	−	0.739104i	$-0.264751\pi$
$954$	12.6333	0.409018
$955$	0	0
$956$	8.78890	0.284253
$957$	− 6.00000i	− 0.193952i
$958$	− 24.4861i	− 0.791111i
$959$	3.97224	0.128270
$960$	0	0
$961$	75.1472	2.42410
$962$	8.60555i	0.277454i
$963$	− 1.81665i	− 0.0585409i
$964$	21.7250	0.699715
$965$	0	0
$966$	−1.54163	−0.0496013
$967$	− 57.8167i	− 1.85926i	−0.368497	−	0.929629i	$-0.620127\pi$
$967$	− 57.8167i	− 1.85926i	0.368497	−	0.929629i	$-0.379873\pi$
$968$	− 10.2111i	− 0.328197i
$969$	−19.8167	−0.636603
$970$	0	0
$971$	14.2389	0.456947	0.228473	−	0.973550i	$-0.426627\pi$
$971$	14.2389	0.456947	0.228473	+	0.973550i	$0.426627\pi$
$972$	12.3944i	0.397552i
$973$	5.24726i	0.168220i
$974$	−4.27502	−0.136980
$975$	0	0
$976$	−3.30278	−0.105719
$977$	4.60555i	0.147345i	0.997283	+	0.0736723i	$0.0234719\pi$
$977$	4.60555i	0.147345i	−0.997283	+	0.0736723i	$0.976528\pi$
$978$	− 1.57779i	− 0.0504523i
$979$	63.6333	2.03373
$980$	0	0
$981$	−8.60555	−0.274754
$982$	2.78890i	0.0889973i
$983$	9.63331i	0.307255i	0.988129	+	0.153627i	$0.0490955\pi$
$983$	9.63331i	0.307255i	−0.988129	+	0.153627i	$0.950904\pi$
$984$	−1.81665	−0.0579128
$985$	0	0
$986$	−2.30278	−0.0733353
$987$	3.63331i	0.115649i
$988$	8.60555i	0.273779i
$989$	1.18335	0.0376282
$990$	0	0
$991$	49.4500	1.57083	0.785415	−	0.618970i	$-0.212450\pi$
$991$	49.4500	1.57083	0.785415	+	0.618970i	$0.212450\pi$
$992$	10.3028i	0.327113i
$993$	26.8444i	0.851882i
$994$	−2.78890	−0.0884585
$995$	0	0
$996$	−10.1833	−0.322672
$997$	7.76114i	0.245798i	0.992419	+	0.122899i	$0.0392191\pi$
$997$	7.76114i	0.245798i	−0.992419	+	0.122899i	$0.960781\pi$
$998$	7.48612i	0.236969i
$999$	−37.0278	−1.17151

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1450.2.b.h.349.3		4
5.2	odd	4		290.2.a.c.1.1	✓	2
5.3	odd	4		1450.2.a.n.1.2		2
5.4	even	2	inner	1450.2.b.h.349.2		4
15.2	even	4		2610.2.a.s.1.1		2
20.7	even	4		2320.2.a.j.1.2		2
40.27	even	4		9280.2.a.bb.1.1		2
40.37	odd	4		9280.2.a.x.1.2		2
145.57	odd	4		8410.2.a.s.1.2		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
290.2.a.c.1.1	✓	2	5.2	odd	4
1450.2.a.n.1.2		2	5.3	odd	4
1450.2.b.h.349.2		4	5.4	even	2	inner
1450.2.b.h.349.3		4	1.1	even	1	trivial
2320.2.a.j.1.2		2	20.7	even	4
2610.2.a.s.1.1		2	15.2	even	4
8410.2.a.s.1.2		2	145.57	odd	4
9280.2.a.x.1.2		2	40.37	odd	4
9280.2.a.bb.1.1		2	40.27	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:	\( N \)	\(=\)	\( 1450 = 2 \cdot 5^{2} \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1450.b (of order \(2\), degree \(1\), not minimal)

\(f(q)\)	\(=\)	\(q+1.00000i q^{2} -1.30278i q^{3} -1.00000 q^{4} +1.30278 q^{6} +0.302776i q^{7} -1.00000i q^{8} +1.30278 q^{9} +O(q^{10})\)	\(q+1.00000i q^{2} -1.30278i q^{3} -1.00000 q^{4} +1.30278 q^{6} +0.302776i q^{7} -1.00000i q^{8} +1.30278 q^{9} +4.60555 q^{11} +1.30278i q^{12} +1.30278i q^{13} -0.302776 q^{14} +1.00000 q^{16} +2.30278i q^{17} +1.30278i q^{18} -6.60555 q^{19} +0.394449 q^{21} +4.60555i q^{22} +3.90833i q^{23} -1.30278 q^{24} -1.30278 q^{26} -5.60555i q^{27} -0.302776i q^{28} +1.00000 q^{29} +10.3028 q^{31} +1.00000i q^{32} -6.00000i q^{33} -2.30278 q^{34} -1.30278 q^{36} -6.60555i q^{37} -6.60555i q^{38} +1.69722 q^{39} +1.39445 q^{41} +0.394449i q^{42} -0.302776i q^{43} -4.60555 q^{44} -3.90833 q^{46} +9.21110i q^{47} -1.30278i q^{48} +6.90833 q^{49} +3.00000 q^{51} -1.30278i q^{52} -9.69722i q^{53} +5.60555 q^{54} +0.302776 q^{56} +8.60555i q^{57} +1.00000i q^{58} +11.3028 q^{59} -3.30278 q^{61} +10.3028i q^{62} +0.394449i q^{63} -1.00000 q^{64} +6.00000 q^{66} +4.00000i q^{67} -2.30278i q^{68} +5.09167 q^{69} +9.21110 q^{71} -1.30278i q^{72} +12.1194i q^{73} +6.60555 q^{74} +6.60555 q^{76} +1.39445i q^{77} +1.69722i q^{78} +1.90833 q^{79} -3.39445 q^{81} +1.39445i q^{82} +7.81665i q^{83} -0.394449 q^{84} +0.302776 q^{86} -1.30278i q^{87} -4.60555i q^{88} +13.8167 q^{89} -0.394449 q^{91} -3.90833i q^{92} -13.4222i q^{93} -9.21110 q^{94} +1.30278 q^{96} -9.11943i q^{97} +6.90833i q^{98} +6.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 4 q^{4} - 2 q^{6} - 2 q^{9}+O(q^{10}) \) 4 * q - 4 * q^4 - 2 * q^6 - 2 * q^9	\( 4 q - 4 q^{4} - 2 q^{6} - 2 q^{9} + 4 q^{11} + 6 q^{14} + 4 q^{16} - 12 q^{19} + 16 q^{21} + 2 q^{24} + 2 q^{26} + 4 q^{29} + 34 q^{31} - 2 q^{34} + 2 q^{36} + 14 q^{39} + 20 q^{41} - 4 q^{44} + 6 q^{46} + 6 q^{49} + 12 q^{51} + 8 q^{54} - 6 q^{56} + 38 q^{59} - 6 q^{61} - 4 q^{64} + 24 q^{66} + 42 q^{69} + 8 q^{71} + 12 q^{74} + 12 q^{76} - 14 q^{79} - 28 q^{81} - 16 q^{84} - 6 q^{86} + 12 q^{89} - 16 q^{91} - 8 q^{94} - 2 q^{96} + 24 q^{99}+O(q^{100}) \) 4 * q - 4 * q^4 - 2 * q^6 - 2 * q^9 + 4 * q^11 + 6 * q^14 + 4 * q^16 - 12 * q^19 + 16 * q^21 + 2 * q^24 + 2 * q^26 + 4 * q^29 + 34 * q^31 - 2 * q^34 + 2 * q^36 + 14 * q^39 + 20 * q^41 - 4 * q^44 + 6 * q^46 + 6 * q^49 + 12 * q^51 + 8 * q^54 - 6 * q^56 + 38 * q^59 - 6 * q^61 - 4 * q^64 + 24 * q^66 + 42 * q^69 + 8 * q^71 + 12 * q^74 + 12 * q^76 - 14 * q^79 - 28 * q^81 - 16 * q^84 - 6 * q^86 + 12 * q^89 - 16 * q^91 - 8 * q^94 - 2 * q^96 + 24 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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