LMFDB - Embedded newform 980.4.i.e.961.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [980,4,Mod(361,980)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(980, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 4]))

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

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

chi := DirichletCharacter("980.361");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$N$	$=$	$980 = 2^{2} \cdot 5 \cdot 7^{2}$
Weight:	$k$	$=$	$4$
Character orbit:	$[\chi]$	$=$	980.i (of order $3$ , degree $2$ , 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:	$57.8218718056$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(\zeta_{6})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$x^{2} - x + 1$ x^2 - x + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$1$
Twist minimal:	no (minimal twist has level 20)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			961.1
Root			$0.500000 - 0.866025i$ of defining polynomial
Character	$\chi$	$=$	980.961
Dual form			980.4.i.e.361.1

$q$ -expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.00000 - 3.46410i) q^{3} +(-2.50000 + 4.33013i) q^{5} +(5.50000 - 9.52628i) q^{9} +(30.0000 + 51.9615i) q^{11} +86.0000 q^{13} +20.0000 q^{15} +(-9.00000 - 15.5885i) q^{17} +(-22.0000 + 38.1051i) q^{19} +(-24.0000 + 41.5692i) q^{23} +(-12.5000 - 21.6506i) q^{25} -152.000 q^{27} -186.000 q^{29} +(-88.0000 - 152.420i) q^{31} +(120.000 - 207.846i) q^{33} +(-127.000 + 219.970i) q^{37} +(-172.000 - 297.913i) q^{39} +186.000 q^{41} -100.000 q^{43} +(27.5000 + 47.6314i) q^{45} +(-84.0000 + 145.492i) q^{47} +(-36.0000 + 62.3538i) q^{51} +(249.000 + 431.281i) q^{53} -300.000 q^{55} +176.000 q^{57} +(126.000 + 218.238i) q^{59} +(29.0000 - 50.2295i) q^{61} +(-215.000 + 372.391i) q^{65} +(518.000 + 897.202i) q^{67} +192.000 q^{69} +168.000 q^{71} +(-253.000 - 438.209i) q^{73} +(-50.0000 + 86.6025i) q^{75} +(-136.000 + 235.559i) q^{79} +(155.500 + 269.334i) q^{81} +948.000 q^{83} +90.0000 q^{85} +(372.000 + 644.323i) q^{87} +(507.000 - 878.150i) q^{89} +(-352.000 + 609.682i) q^{93} +(-110.000 - 190.526i) q^{95} -766.000 q^{97} +660.000 q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$2 q - 4 q^{3} - 5 q^{5} + 11 q^{9} + 60 q^{11} + 172 q^{13} + 40 q^{15} - 18 q^{17} - 44 q^{19} - 48 q^{23} - 25 q^{25} - 304 q^{27} - 372 q^{29} - 176 q^{31} + 240 q^{33} - 254 q^{37} - 344 q^{39} + 372 q^{41}+ \cdots + 1320 q^{99}+O(q^{100})$ 2 * q - 4 * q^3 - 5 * q^5 + 11 * q^9 + 60 * q^11 + 172 * q^13 + 40 * q^15 - 18 * q^17 - 44 * q^19 - 48 * q^23 - 25 * q^25 - 304 * q^27 - 372 * q^29 - 176 * q^31 + 240 * q^33 - 254 * q^37 - 344 * q^39 + 372 * q^41 - 200 * q^43 + 55 * q^45 - 168 * q^47 - 72 * q^51 + 498 * q^53 - 600 * q^55 + 352 * q^57 + 252 * q^59 + 58 * q^61 - 430 * q^65 + 1036 * q^67 + 384 * q^69 + 336 * q^71 - 506 * q^73 - 100 * q^75 - 272 * q^79 + 311 * q^81 + 1896 * q^83 + 180 * q^85 + 744 * q^87 + 1014 * q^89 - 704 * q^93 - 220 * q^95 - 1532 * q^97 + 1320 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/980\mathbb{Z}\right)^\times$ .

$n$	$101$	$197$	$491$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$1$	$1$

Coefficient data

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

Display

a_p

with

p

up to: 50 250 1000 (See

a_n

instead) (See

a_n

instead) (See

a_n

instead) Display

a_n

with

n

up to: 50 250 1000 (See only

a_p

) (See only

a_p

) (See only

a_p

)

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

$2$		0			0
$2$		0			0
$3$	−2.00000	−	3.46410i	−0.384900	−	0.666667i	0.606855	−	0.794812i	$-0.292431\pi$
$3$	−2.00000	−	3.46410i	−0.384900	−	0.666667i	−0.991755	+	0.128146i	$0.959097\pi$
$4$		0			0
$5$	−2.50000	+	4.33013i	−0.223607	+	0.387298i
$5$	−2.50000	+	4.33013i	−0.223607	+	0.387298i
$6$		0			0
$7$		0			0
$7$		0			0
$8$		0			0
$9$	5.50000	−	9.52628i	0.203704	−	0.352825i
$10$		0			0
$11$	30.0000	+	51.9615i	0.822304	+	1.42427i	0.903963	+	0.427611i	$0.140645\pi$
$11$	30.0000	+	51.9615i	0.822304	+	1.42427i	−0.0816590	+	0.996660i	$0.526022\pi$
$12$		0			0
$13$	86.0000			1.83478			0.917389	−	0.397992i	$-0.130293\pi$
$13$	86.0000			1.83478			0.917389	+	0.397992i	$0.130293\pi$
$14$		0			0
$15$	20.0000			0.344265
$16$		0			0
$17$	−9.00000	−	15.5885i	−0.128401	−	0.222397i	0.794656	−	0.607060i	$-0.207651\pi$
$17$	−9.00000	−	15.5885i	−0.128401	−	0.222397i	−0.923057	+	0.384662i	$0.874318\pi$
$18$		0			0
$19$	−22.0000	+	38.1051i	−0.265639	+	0.460101i	−0.967731	−	0.251986i	$-0.918916\pi$
$19$	−22.0000	+	38.1051i	−0.265639	+	0.460101i	0.702092	+	0.712087i	$0.252250\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	−24.0000	+	41.5692i	−0.217580	+	0.376860i	−0.954068	−	0.299591i	$-0.903150\pi$
$23$	−24.0000	+	41.5692i	−0.217580	+	0.376860i	0.736487	+	0.676451i	$0.236483\pi$
$24$		0			0
$25$	−12.5000	−	21.6506i	−0.100000	−	0.173205i
$26$		0			0
$27$	−152.000			−1.08342
$28$		0			0
$29$	−186.000			−1.19101			−0.595506	−	0.803351i	$-0.703048\pi$
$29$	−186.000			−1.19101			−0.595506	+	0.803351i	$0.703048\pi$
$30$		0			0
$31$	−88.0000	−	152.420i	−0.509847	−	0.883081i	−0.999935	−	0.0114083i	$-0.996369\pi$
$31$	−88.0000	−	152.420i	−0.509847	−	0.883081i	0.490088	−	0.871673i	$-0.336965\pi$
$32$		0			0
$33$	120.000	−	207.846i	0.633010	−	1.09640i
$34$		0			0
$35$		0			0
$36$		0			0
$37$	−127.000	+	219.970i	−0.564288	+	0.977376i	0.432827	+	0.901477i	$0.357516\pi$
$37$	−127.000	+	219.970i	−0.564288	+	0.977376i	−0.997115	+	0.0758992i	$0.975817\pi$
$38$		0			0
$39$	−172.000	−	297.913i	−0.706206	−	1.22319i
$40$		0			0
$41$	186.000			0.708496			0.354248	−	0.935152i	$-0.384737\pi$
$41$	186.000			0.708496			0.354248	+	0.935152i	$0.384737\pi$
$42$		0			0
$43$	−100.000			−0.354648			−0.177324	−	0.984153i	$-0.556744\pi$
$43$	−100.000			−0.354648			−0.177324	+	0.984153i	$0.556744\pi$
$44$		0			0
$45$	27.5000	+	47.6314i	0.0910991	+	0.157788i
$46$		0			0
$47$	−84.0000	+	145.492i	−0.260695	+	0.451537i	−0.966427	−	0.256942i	$-0.917285\pi$
$47$	−84.0000	+	145.492i	−0.260695	+	0.451537i	0.705732	+	0.708479i	$0.250618\pi$
$48$		0			0
$49$		0			0
$50$		0			0
$51$	−36.0000	+	62.3538i	−0.0988433	+	0.171202i
$52$		0			0
$53$	249.000	+	431.281i	0.645335	+	1.11775i	0.984224	+	0.176927i	$0.0566157\pi$
$53$	249.000	+	431.281i	0.645335	+	1.11775i	−0.338888	+	0.940827i	$0.610051\pi$
$54$		0			0
$55$	−300.000			−0.735491
$56$		0			0
$57$	176.000			0.408978
$58$		0			0
$59$	126.000	+	218.238i	0.278031	+	0.481563i	0.970895	−	0.239505i	$-0.0769850\pi$
$59$	126.000	+	218.238i	0.278031	+	0.481563i	−0.692865	+	0.721068i	$0.743652\pi$
$60$		0			0
$61$	29.0000	−	50.2295i	0.0608700	−	0.105430i	−0.833985	−	0.551788i	$-0.813946\pi$
$61$	29.0000	−	50.2295i	0.0608700	−	0.105430i	0.894855	+	0.446358i	$0.147279\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	−215.000	+	372.391i	−0.410269	+	0.710606i
$66$		0			0
$67$	518.000	+	897.202i	0.944534	+	1.63598i	0.756682	+	0.653783i	$0.226819\pi$
$67$	518.000	+	897.202i	0.944534	+	1.63598i	0.187852	+	0.982197i	$0.439847\pi$
$68$		0			0
$69$	192.000			0.334987
$70$		0			0
$71$	168.000			0.280816			0.140408	−	0.990094i	$-0.455159\pi$
$71$	168.000			0.280816			0.140408	+	0.990094i	$0.455159\pi$
$72$		0			0
$73$	−253.000	−	438.209i	−0.405636	−	0.702582i	0.588759	−	0.808308i	$-0.299617\pi$
$73$	−253.000	−	438.209i	−0.405636	−	0.702582i	−0.994395	+	0.105727i	$0.966283\pi$
$74$		0			0
$75$	−50.0000	+	86.6025i	−0.0769800	+	0.133333i
$76$		0			0
$77$		0			0
$78$		0			0
$79$	−136.000	+	235.559i	−0.193686	+	0.335474i	−0.946469	−	0.322795i	$-0.895378\pi$
$79$	−136.000	+	235.559i	−0.193686	+	0.335474i	0.752783	+	0.658269i	$0.228711\pi$
$80$		0			0
$81$	155.500	+	269.334i	0.213306	+	0.369457i
$82$		0			0
$83$	948.000			1.25369			0.626846	−	0.779143i	$-0.284345\pi$
$83$	948.000			1.25369			0.626846	+	0.779143i	$0.284345\pi$
$84$		0			0
$85$	90.0000			0.114846
$86$		0			0
$87$	372.000	+	644.323i	0.458421	+	0.794008i
$88$		0			0
$89$	507.000	−	878.150i	0.603841	−	1.04588i	−0.388392	−	0.921494i	$-0.626969\pi$
$89$	507.000	−	878.150i	0.603841	−	1.04588i	0.992233	−	0.124390i	$-0.0396973\pi$
$90$		0			0
$91$		0			0
$92$		0			0
$93$	−352.000	+	609.682i	−0.392481	+	0.679796i
$94$		0			0
$95$	−110.000	−	190.526i	−0.118797	−	0.205763i
$96$		0			0
$97$	−766.000			−0.801809			−0.400905	−	0.916120i	$-0.631304\pi$
$97$	−766.000			−0.801809			−0.400905	+	0.916120i	$0.631304\pi$
$98$		0			0
$99$	660.000			0.670025
$100$		0			0
$101$	657.000	+	1137.96i	0.647267	+	1.12110i	0.983773	+	0.179418i	$0.0574214\pi$
$101$	657.000	+	1137.96i	0.647267	+	1.12110i	−0.336506	+	0.941681i	$0.609245\pi$
$102$		0			0
$103$	224.000	−	387.979i	0.214285	−	0.371153i	−0.738766	−	0.673962i	$-0.764591\pi$
$103$	224.000	−	387.979i	0.214285	−	0.371153i	0.953051	+	0.302809i	$0.0979245\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	−774.000	+	1340.61i	−0.699303	+	1.21123i	0.269406	+	0.963027i	$0.413173\pi$
$107$	−774.000	+	1340.61i	−0.699303	+	1.21123i	−0.968708	+	0.248201i	$0.920161\pi$
$108$		0			0
$109$	−139.000	−	240.755i	−0.122145	−	0.211561i	0.798468	−	0.602037i	$-0.205644\pi$
$109$	−139.000	−	240.755i	−0.122145	−	0.211561i	−0.920613	+	0.390476i	$0.872311\pi$
$110$		0			0
$111$	1016.00			0.868779
$112$		0			0
$113$	−558.000			−0.464533			−0.232266	−	0.972652i	$-0.574614\pi$
$113$	−558.000			−0.464533			−0.232266	+	0.972652i	$0.574614\pi$
$114$		0			0
$115$	−120.000	−	207.846i	−0.0973048	−	0.168537i
$116$		0			0
$117$	473.000	−	819.260i	0.373751	−	0.647356i
$118$		0			0
$119$		0			0
$120$		0			0
$121$	−1134.50	+	1965.01i	−0.852367	+	1.47634i
$122$		0			0
$123$	−372.000	−	644.323i	−0.272700	−	0.472330i
$124$		0			0
$125$	125.000			0.0894427
$126$		0			0
$127$	344.000			0.240355			0.120177	−	0.992752i	$-0.461654\pi$
$127$	344.000			0.240355			0.120177	+	0.992752i	$0.461654\pi$
$128$		0			0
$129$	200.000	+	346.410i	0.136504	+	0.236432i
$130$		0			0
$131$	−390.000	+	675.500i	−0.260110	+	0.450524i	−0.966271	−	0.257527i	$-0.917092\pi$
$131$	−390.000	+	675.500i	−0.260110	+	0.450524i	0.706161	+	0.708052i	$0.250426\pi$
$132$		0			0
$133$		0			0
$134$		0			0
$135$	380.000	−	658.179i	0.242261	−	0.419608i
$136$		0			0
$137$	−333.000	−	576.773i	−0.207665	−	0.359686i	0.743314	−	0.668943i	$-0.233253\pi$
$137$	−333.000	−	576.773i	−0.207665	−	0.359686i	−0.950979	+	0.309257i	$0.899920\pi$
$138$		0			0
$139$	884.000			0.539424			0.269712	−	0.962941i	$-0.413072\pi$
$139$	884.000			0.539424			0.269712	+	0.962941i	$0.413072\pi$
$140$		0			0
$141$	672.000			0.401366
$142$		0			0
$143$	2580.00	+	4468.69i	1.50874	+	2.61322i
$144$		0			0
$145$	465.000	−	805.404i	0.266318	−	0.461277i
$146$		0			0
$147$		0			0
$148$		0			0
$149$	57.0000	−	98.7269i	0.0313397	−	0.0542820i	−0.849930	−	0.526895i	$-0.823356\pi$
$149$	57.0000	−	98.7269i	0.0313397	−	0.0542820i	0.881270	+	0.472613i	$0.156689\pi$
$150$		0			0
$151$	20.0000	+	34.6410i	0.0107787	+	0.0186692i	0.871364	−	0.490636i	$-0.163236\pi$
$151$	20.0000	+	34.6410i	0.0107787	+	0.0186692i	−0.860586	+	0.509306i	$0.829902\pi$
$152$		0			0
$153$	−198.000			−0.104623
$154$		0			0
$155$	880.000			0.456021
$156$		0			0
$157$	77.0000	+	133.368i	0.0391418	+	0.0677957i	0.884933	−	0.465719i	$-0.154204\pi$
$157$	77.0000	+	133.368i	0.0391418	+	0.0677957i	−0.845791	+	0.533515i	$0.820871\pi$
$158$		0			0
$159$	996.000	−	1725.12i	0.496779	−	0.860447i
$160$		0			0
$161$		0			0
$162$		0			0
$163$	−1090.00	+	1887.94i	−0.523775	+	0.907206i	0.475842	+	0.879531i	$0.342144\pi$
$163$	−1090.00	+	1887.94i	−0.523775	+	0.907206i	−0.999617	+	0.0276746i	$0.991190\pi$
$164$		0			0
$165$	600.000	+	1039.23i	0.283091	+	0.490327i
$166$		0			0
$167$	3696.00			1.71261			0.856303	−	0.516474i	$-0.172756\pi$
$167$	3696.00			1.71261			0.856303	+	0.516474i	$0.172756\pi$
$168$		0			0
$169$	5199.00			2.36641
$170$		0			0
$171$	242.000	+	419.156i	0.108223	+	0.187448i
$172$		0			0
$173$	−651.000	+	1127.57i	−0.286096	+	0.495533i	−0.972874	−	0.231334i	$-0.925691\pi$
$173$	−651.000	+	1127.57i	−0.286096	+	0.495533i	0.686778	+	0.726867i	$0.259024\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$	504.000	−	872.954i	0.214028	−	0.370707i
$178$		0			0
$179$	2154.00	+	3730.84i	0.899427	+	1.55785i	0.828227	+	0.560392i	$0.189350\pi$
$179$	2154.00	+	3730.84i	0.899427	+	1.55785i	0.0712000	+	0.997462i	$0.477317\pi$
$180$		0			0
$181$	1550.00			0.636523			0.318261	−	0.948003i	$-0.396901\pi$
$181$	1550.00			0.636523			0.318261	+	0.948003i	$0.396901\pi$
$182$		0			0
$183$	−232.000			−0.0937155
$184$		0			0
$185$	−635.000	−	1099.85i	−0.252357	−	0.437096i
$186$		0			0
$187$	540.000	−	935.307i	0.211170	−	0.365756i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	−24.0000	+	41.5692i	−0.00909204	+	0.0157479i	−0.870536	−	0.492105i	$-0.836227\pi$
$191$	−24.0000	+	41.5692i	−0.00909204	+	0.0157479i	0.861444	+	0.507853i	$0.169561\pi$
$192$		0			0
$193$	−529.000	−	916.255i	−0.197297	−	0.341728i	0.750354	−	0.661036i	$-0.229883\pi$
$193$	−529.000	−	916.255i	−0.197297	−	0.341728i	−0.947651	+	0.319308i	$0.896550\pi$
$194$		0			0
$195$	1720.00			0.631650
$196$		0			0
$197$	−3714.00			−1.34321			−0.671603	−	0.740911i	$-0.734394\pi$
$197$	−3714.00			−1.34321			−0.671603	+	0.740911i	$0.734394\pi$
$198$		0			0
$199$	884.000	+	1531.13i	0.314900	+	0.545423i	0.979416	−	0.201851i	$-0.0646957\pi$
$199$	884.000	+	1531.13i	0.314900	+	0.545423i	−0.664516	+	0.747274i	$0.731362\pi$
$200$		0			0
$201$	2072.00	−	3588.81i	0.727103	−	1.25938i
$202$		0			0
$203$		0			0
$204$		0			0
$205$	−465.000	+	805.404i	−0.158424	+	0.274399i
$206$		0			0
$207$	264.000	+	457.261i	0.0886438	+	0.153536i
$208$		0			0
$209$	−2640.00			−0.873745
$210$		0			0
$211$	−4036.00			−1.31682			−0.658412	−	0.752658i	$-0.728771\pi$
$211$	−4036.00			−1.31682			−0.658412	+	0.752658i	$0.728771\pi$
$212$		0			0
$213$	−336.000	−	581.969i	−0.108086	−	0.187211i
$214$		0			0
$215$	250.000	−	433.013i	0.0793017	−	0.137355i
$216$		0			0
$217$		0			0
$218$		0			0
$219$	−1012.00	+	1752.84i	−0.312259	+	0.540848i
$220$		0			0
$221$	−774.000	−	1340.61i	−0.235588	−	0.408050i
$222$		0			0
$223$	680.000			0.204198			0.102099	−	0.994774i	$-0.467444\pi$
$223$	680.000			0.204198			0.102099	+	0.994774i	$0.467444\pi$
$224$		0			0
$225$	−275.000			−0.0814815
$226$		0			0
$227$	−1194.00	−	2068.07i	−0.349113	−	0.604681i	0.636979	−	0.770881i	$-0.280184\pi$
$227$	−1194.00	−	2068.07i	−0.349113	−	0.604681i	−0.986092	+	0.166200i	$0.946850\pi$
$228$		0			0
$229$	1937.00	−	3354.98i	0.558954	−	0.968137i	−0.438630	−	0.898668i	$-0.644536\pi$
$229$	1937.00	−	3354.98i	0.558954	−	0.968137i	0.997584	−	0.0694695i	$-0.0221307\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	−1581.00	+	2738.37i	−0.444527	+	0.769943i	−0.998019	−	0.0629112i	$-0.979962\pi$
$233$	−1581.00	+	2738.37i	−0.444527	+	0.769943i	0.553492	+	0.832854i	$0.313295\pi$
$234$		0			0
$235$	−420.000	−	727.461i	−0.116586	−	0.201933i
$236$		0			0
$237$	1088.00			0.298199
$238$		0			0
$239$	5424.00			1.46799			0.733995	−	0.679155i	$-0.237654\pi$
$239$	5424.00			1.46799			0.733995	+	0.679155i	$0.237654\pi$
$240$		0			0
$241$	1943.00	+	3365.37i	0.519335	+	0.899514i	0.999747	+	0.0224714i	$0.00715348\pi$
$241$	1943.00	+	3365.37i	0.519335	+	0.899514i	−0.480413	+	0.877042i	$0.659513\pi$
$242$		0			0
$243$	−1430.00	+	2476.83i	−0.377508	+	0.653864i
$244$		0			0
$245$		0			0
$246$		0			0
$247$	−1892.00	+	3277.04i	−0.487389	+	0.844182i
$248$		0			0
$249$	−1896.00	−	3283.97i	−0.482547	−	0.835795i
$250$		0			0
$251$	−5100.00			−1.28251			−0.641253	−	0.767329i	$-0.721585\pi$
$251$	−5100.00			−1.28251			−0.641253	+	0.767329i	$0.721585\pi$
$252$		0			0
$253$	−2880.00			−0.715668
$254$		0			0
$255$	−180.000	−	311.769i	−0.0442041	−	0.0765637i
$256$		0			0
$257$	−1089.00	+	1886.20i	−0.264319	+	0.457814i	−0.967385	−	0.253311i	$-0.918480\pi$
$257$	−1089.00	+	1886.20i	−0.264319	+	0.457814i	0.703066	+	0.711125i	$0.251814\pi$
$258$		0			0
$259$		0			0
$260$		0			0
$261$	−1023.00	+	1771.89i	−0.242613	+	0.420219i
$262$		0			0
$263$	3072.00	+	5320.86i	0.720257	+	1.24752i	0.960897	+	0.276907i	$0.0893095\pi$
$263$	3072.00	+	5320.86i	0.720257	+	1.24752i	−0.240639	+	0.970615i	$0.577357\pi$
$264$		0			0
$265$	−2490.00			−0.577206
$266$		0			0
$267$	−4056.00			−0.929675
$268$		0			0
$269$	−411.000	−	711.873i	−0.0931566	−	0.161352i	0.815681	−	0.578502i	$-0.196362\pi$
$269$	−411.000	−	711.873i	−0.0931566	−	0.161352i	−0.908838	+	0.417150i	$0.863029\pi$
$270$		0			0
$271$	−4240.00	+	7343.90i	−0.950412	+	1.64616i	−0.205878	+	0.978578i	$0.566005\pi$
$271$	−4240.00	+	7343.90i	−0.950412	+	1.64616i	−0.744534	+	0.667584i	$0.767328\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	750.000	−	1299.04i	0.164461	−	0.284854i
$276$		0			0
$277$	569.000	+	985.537i	0.123422	+	0.213773i	0.921115	−	0.389291i	$-0.127280\pi$
$277$	569.000	+	985.537i	0.123422	+	0.213773i	−0.797693	+	0.603064i	$0.793946\pi$
$278$		0			0
$279$	−1936.00			−0.415431
$280$		0			0
$281$	5706.00			1.21136			0.605679	−	0.795709i	$-0.292902\pi$
$281$	5706.00			1.21136			0.605679	+	0.795709i	$0.292902\pi$
$282$		0			0
$283$	1514.00	+	2622.32i	0.318014	+	0.550816i	0.980074	−	0.198635i	$-0.0636508\pi$
$283$	1514.00	+	2622.32i	0.318014	+	0.550816i	−0.662060	+	0.749451i	$0.730317\pi$
$284$		0			0
$285$	−440.000	+	762.102i	−0.0914504	+	0.158397i
$286$		0			0
$287$		0			0
$288$		0			0
$289$	2294.50	−	3974.19i	0.467026	−	0.808913i
$290$		0			0
$291$	1532.00	+	2653.50i	0.308617	+	0.534540i
$292$		0			0
$293$	3390.00			0.675925			0.337962	−	0.941160i	$-0.390262\pi$
$293$	3390.00			0.675925			0.337962	+	0.941160i	$0.390262\pi$
$294$		0			0
$295$	−1260.00			−0.248678
$296$		0			0
$297$	−4560.00	−	7898.15i	−0.890902	−	1.54309i
$298$		0			0
$299$	−2064.00	+	3574.95i	−0.399211	+	0.691454i
$300$		0			0
$301$		0			0
$302$		0			0
$303$	2628.00	−	4551.83i	0.498266	−	0.863022i
$304$		0			0
$305$	145.000	+	251.147i	0.0272219	+	0.0471497i
$306$		0			0
$307$	−4156.00			−0.772624			−0.386312	−	0.922368i	$-0.626251\pi$
$307$	−4156.00			−0.772624			−0.386312	+	0.922368i	$0.626251\pi$
$308$		0			0
$309$	−1792.00			−0.329914
$310$		0			0
$311$	−3276.00	−	5674.20i	−0.597315	−	1.03458i	−0.993216	−	0.116286i	$-0.962901\pi$
$311$	−3276.00	−	5674.20i	−0.597315	−	1.03458i	0.395901	−	0.918293i	$-0.370432\pi$
$312$		0			0
$313$	683.000	−	1182.99i	0.123340	−	0.213631i	−0.797743	−	0.602998i	$-0.793973\pi$
$313$	683.000	−	1182.99i	0.123340	−	0.213631i	0.921083	+	0.389367i	$0.127306\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−1299.00	+	2249.93i	−0.230155	+	0.398640i	−0.957854	−	0.287257i	$-0.907257\pi$
$317$	−1299.00	+	2249.93i	−0.230155	+	0.398640i	0.727699	+	0.685897i	$0.240590\pi$
$318$		0			0
$319$	−5580.00	−	9664.84i	−0.979373	−	1.69632i
$320$		0			0
$321$	6192.00			1.07665
$322$		0			0
$323$	792.000			0.136434
$324$		0			0
$325$	−1075.00	−	1861.95i	−0.183478	−	0.317793i
$326$		0			0
$327$	−556.000	+	963.020i	−0.0940271	+	0.162860i
$328$		0			0
$329$		0			0
$330$		0			0
$331$	1646.00	−	2850.96i	0.273330	−	0.473422i	−0.696382	−	0.717671i	$-0.745208\pi$
$331$	1646.00	−	2850.96i	0.273330	−	0.473422i	0.969713	+	0.244249i	$0.0785415\pi$
$332$		0			0
$333$	1397.00	+	2419.67i	0.229895	+	0.398190i
$334$		0			0
$335$	−5180.00			−0.844817
$336$		0			0
$337$	6194.00			1.00121			0.500606	−	0.865675i	$-0.333110\pi$
$337$	6194.00			1.00121			0.500606	+	0.865675i	$0.333110\pi$
$338$		0			0
$339$	1116.00	+	1932.97i	0.178799	+	0.309689i
$340$		0			0
$341$	5280.00	−	9145.23i	0.838499	−	1.45232i
$342$		0			0
$343$		0			0
$344$		0			0
$345$	−480.000	+	831.384i	−0.0749053	+	0.129740i
$346$		0			0
$347$	5010.00	+	8677.57i	0.775075	+	1.34247i	0.934753	+	0.355299i	$0.115621\pi$
$347$	5010.00	+	8677.57i	0.775075	+	1.34247i	−0.159678	+	0.987169i	$0.551046\pi$
$348$		0			0
$349$	−3130.00			−0.480072			−0.240036	−	0.970764i	$-0.577159\pi$
$349$	−3130.00			−0.480072			−0.240036	+	0.970764i	$0.577159\pi$
$350$		0			0
$351$	−13072.0			−1.98784
$352$		0			0
$353$	−2097.00	−	3632.11i	−0.316181	−	0.547642i	0.663506	−	0.748171i	$-0.269068\pi$
$353$	−2097.00	−	3632.11i	−0.316181	−	0.547642i	−0.979688	+	0.200528i	$0.935734\pi$
$354$		0			0
$355$	−420.000	+	727.461i	−0.0627924	+	0.108760i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	2052.00	−	3554.17i	0.301672	−	0.522512i	−0.674842	−	0.737962i	$-0.735788\pi$
$359$	2052.00	−	3554.17i	0.301672	−	0.522512i	0.976515	+	0.215450i	$0.0691218\pi$
$360$		0			0
$361$	2461.50	+	4263.44i	0.358872	+	0.621584i
$362$		0			0
$363$	9076.00			1.31230
$364$		0			0
$365$	2530.00			0.362812
$366$		0			0
$367$	−3748.00	−	6491.73i	−0.533090	−	0.923339i	−0.999253	−	0.0386401i	$-0.987697\pi$
$367$	−3748.00	−	6491.73i	−0.533090	−	0.923339i	0.466163	−	0.884699i	$-0.345636\pi$
$368$		0			0
$369$	1023.00	−	1771.89i	0.144323	−	0.249975i
$370$		0			0
$371$		0			0
$372$		0			0
$373$	2921.00	−	5059.32i	0.405479	−	0.702310i	−0.588898	−	0.808207i	$-0.700438\pi$
$373$	2921.00	−	5059.32i	0.405479	−	0.702310i	0.994377	+	0.105897i	$0.0337714\pi$
$374$		0			0
$375$	−250.000	−	433.013i	−0.0344265	−	0.0596285i
$376$		0			0
$377$	−15996.0			−2.18524
$378$		0			0
$379$	−412.000			−0.0558391			−0.0279195	−	0.999610i	$-0.508888\pi$
$379$	−412.000			−0.0558391			−0.0279195	+	0.999610i	$0.508888\pi$
$380$		0			0
$381$	−688.000	−	1191.65i	−0.0925126	−	0.160237i
$382$		0			0
$383$	−1284.00	+	2223.95i	−0.171304	+	0.296707i	−0.938876	−	0.344256i	$-0.888131\pi$
$383$	−1284.00	+	2223.95i	−0.171304	+	0.296707i	0.767572	+	0.640963i	$0.221465\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$	−550.000	+	952.628i	−0.0722431	+	0.125129i
$388$		0			0
$389$	−6543.00	−	11332.8i	−0.852810	−	1.47711i	−0.878662	−	0.477445i	$-0.841563\pi$
$389$	−6543.00	−	11332.8i	−0.852810	−	1.47711i	0.0258510	−	0.999666i	$-0.491770\pi$
$390$		0			0
$391$	864.000			0.111750
$392$		0			0
$393$	3120.00			0.400466
$394$		0			0
$395$	−680.000	−	1177.79i	−0.0866190	−	0.150029i
$396$		0			0
$397$	−5227.00	+	9053.43i	−0.660795	+	1.14453i	0.319612	+	0.947548i	$0.396447\pi$
$397$	−5227.00	+	9053.43i	−0.660795	+	1.14453i	−0.980407	+	0.196982i	$0.936886\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	5415.00	−	9379.06i	0.674345	−	1.16800i	−0.302315	−	0.953208i	$-0.597760\pi$
$401$	5415.00	−	9379.06i	0.674345	−	1.16800i	0.976660	−	0.214791i	$-0.0689071\pi$
$402$		0			0
$403$	−7568.00	−	13108.2i	−0.935456	−	1.62026i
$404$		0			0
$405$	−1555.00			−0.190787
$406$		0			0
$407$	−15240.0			−1.85607
$408$		0			0
$409$	4283.00	+	7418.37i	0.517801	+	0.896858i	0.999786	+	0.0206786i	$0.00658267\pi$
$409$	4283.00	+	7418.37i	0.517801	+	0.896858i	−0.481985	+	0.876180i	$0.660084\pi$
$410$		0			0
$411$	−1332.00	+	2307.09i	−0.159861	+	0.276887i
$412$		0			0
$413$		0			0
$414$		0			0
$415$	−2370.00	+	4104.96i	−0.280334	+	0.485553i
$416$		0			0
$417$	−1768.00	−	3062.27i	−0.207624	−	0.359616i
$418$		0			0
$419$	13884.0			1.61880			0.809401	−	0.587257i	$-0.199792\pi$
$419$	13884.0			1.61880			0.809401	+	0.587257i	$0.199792\pi$
$420$		0			0
$421$	4286.00			0.496168			0.248084	−	0.968738i	$-0.420199\pi$
$421$	4286.00			0.496168			0.248084	+	0.968738i	$0.420199\pi$
$422$		0			0
$423$	924.000	+	1600.41i	0.106209	+	0.183959i
$424$		0			0
$425$	−225.000	+	389.711i	−0.0256802	+	0.0444795i
$426$		0			0
$427$		0			0
$428$		0			0
$429$	10320.0	−	17874.8i	1.16143	−	2.01166i
$430$		0			0
$431$	−3168.00	−	5487.14i	−0.354054	−	0.613239i	0.632902	−	0.774232i	$-0.281864\pi$
$431$	−3168.00	−	5487.14i	−0.354054	−	0.613239i	−0.986956	+	0.160993i	$0.948530\pi$
$432$		0			0
$433$	−8974.00			−0.995988			−0.497994	−	0.867180i	$-0.665930\pi$
$433$	−8974.00			−0.995988			−0.497994	+	0.867180i	$0.665930\pi$
$434$		0			0
$435$	−3720.00			−0.410024
$436$		0			0
$437$	−1056.00	−	1829.05i	−0.115596	−	0.200218i
$438$		0			0
$439$	1484.00	−	2570.36i	0.161338	−	0.279446i	−0.774011	−	0.633173i	$-0.781752\pi$
$439$	1484.00	−	2570.36i	0.161338	−	0.279446i	0.935349	+	0.353727i	$0.115086\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	6186.00	−	10714.5i	0.663444	−	1.14912i	−0.316261	−	0.948672i	$-0.602427\pi$
$443$	6186.00	−	10714.5i	0.663444	−	1.14912i	0.979705	−	0.200446i	$-0.0642393\pi$
$444$		0			0
$445$	2535.00	+	4390.75i	0.270046	+	0.467734i
$446$		0			0
$447$	−456.000			−0.0482507
$448$		0			0
$449$	11394.0			1.19759			0.598793	−	0.800904i	$-0.295647\pi$
$449$	11394.0			1.19759			0.598793	+	0.800904i	$0.295647\pi$
$450$		0			0
$451$	5580.00	+	9664.84i	0.582599	+	1.00909i
$452$		0			0
$453$	80.0000	−	138.564i	0.00829741	−	0.0143715i
$454$		0			0
$455$		0			0
$456$		0			0
$457$	179.000	−	310.037i	0.0183222	−	0.0317351i	−0.856719	−	0.515784i	$-0.827501\pi$
$457$	179.000	−	310.037i	0.0183222	−	0.0317351i	0.875041	+	0.484049i	$0.160834\pi$
$458$		0			0
$459$	1368.00	+	2369.45i	0.139113	+	0.240950i
$460$		0			0
$461$	−7530.00			−0.760753			−0.380376	−	0.924832i	$-0.624206\pi$
$461$	−7530.00			−0.760753			−0.380376	+	0.924832i	$0.624206\pi$
$462$		0			0
$463$	−13768.0			−1.38197			−0.690986	−	0.722868i	$-0.742823\pi$
$463$	−13768.0			−1.38197			−0.690986	+	0.722868i	$0.742823\pi$
$464$		0			0
$465$	−1760.00	−	3048.41i	−0.175523	−	0.304014i
$466$		0			0
$467$	−6690.00	+	11587.4i	−0.662904	+	1.14818i	0.316945	+	0.948444i	$0.397343\pi$
$467$	−6690.00	+	11587.4i	−0.662904	+	1.14818i	−0.979849	+	0.199740i	$0.935990\pi$
$468$		0			0
$469$		0			0
$470$		0			0
$471$	308.000	−	533.472i	0.0301314	−	0.0521891i
$472$		0			0
$473$	−3000.00	−	5196.15i	−0.291628	−	0.505115i
$474$		0			0
$475$	1100.00			0.106256
$476$		0			0
$477$	5478.00			0.525829
$478$		0			0
$479$	3168.00	+	5487.14i	0.302191	+	0.523411i	0.976632	−	0.214918i	$-0.0689485\pi$
$479$	3168.00	+	5487.14i	0.302191	+	0.523411i	−0.674441	+	0.738329i	$0.735615\pi$
$480$		0			0
$481$	−10922.0	+	18917.5i	−1.03534	+	1.79327i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	1915.00	−	3316.88i	0.179290	−	0.310539i
$486$		0			0
$487$	2504.00	+	4337.06i	0.232992	+	0.403554i	0.958687	−	0.284462i	$-0.0918151\pi$
$487$	2504.00	+	4337.06i	0.232992	+	0.403554i	−0.725695	+	0.688016i	$0.758482\pi$
$488$		0			0
$489$	8720.00			0.806405
$490$		0			0
$491$	12900.0			1.18568			0.592840	−	0.805320i	$-0.298007\pi$
$491$	12900.0			1.18568			0.592840	+	0.805320i	$0.298007\pi$
$492$		0			0
$493$	1674.00	+	2899.45i	0.152927	+	0.264878i
$494$		0			0
$495$	−1650.00	+	2857.88i	−0.149822	+	0.259500i
$496$		0			0
$497$		0			0
$498$		0			0
$499$	4058.00	−	7028.66i	0.364050	−	0.630553i	−0.624573	−	0.780966i	$-0.714727\pi$
$499$	4058.00	−	7028.66i	0.364050	−	0.630553i	0.988623	+	0.150413i	$0.0480603\pi$
$500$		0			0
$501$	−7392.00	−	12803.3i	−0.659182	−	1.14174i
$502$		0			0
$503$	−4944.00			−0.438255			−0.219127	−	0.975696i	$-0.570321\pi$
$503$	−4944.00			−0.438255			−0.219127	+	0.975696i	$0.570321\pi$
$504$		0			0
$505$	−6570.00			−0.578933
$506$		0			0
$507$	−10398.0	−	18009.9i	−0.910831	−	1.57761i
$508$		0			0
$509$	2733.00	−	4733.69i	0.237992	−	0.412215i	−0.722146	−	0.691741i	$-0.756844\pi$
$509$	2733.00	−	4733.69i	0.237992	−	0.412215i	0.960138	+	0.279526i	$0.0901774\pi$
$510$		0			0
$511$		0			0
$512$		0			0
$513$	3344.00	−	5791.98i	0.287800	−	0.498484i
$514$		0			0
$515$	1120.00	+	1939.90i	0.0958313	+	0.165985i
$516$		0			0
$517$	−10080.0			−0.857481
$518$		0			0
$519$	5208.00			0.440474
$520$		0			0
$521$	−5037.00	−	8724.34i	−0.423560	−	0.733628i	0.572724	−	0.819748i	$-0.305887\pi$
$521$	−5037.00	−	8724.34i	−0.423560	−	0.733628i	−0.996285	+	0.0861198i	$0.972553\pi$
$522$		0			0
$523$	6914.00	−	11975.4i	0.578065	−	1.00124i	−0.417636	−	0.908614i	$-0.637141\pi$
$523$	6914.00	−	11975.4i	0.578065	−	1.00124i	0.995701	−	0.0926239i	$-0.0295254\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	−1584.00	+	2743.57i	−0.130930	+	0.226777i
$528$		0			0
$529$	4931.50	+	8541.61i	0.405318	+	0.702031i
$530$		0			0
$531$	2772.00			0.226543
$532$		0			0
$533$	15996.0			1.29993
$534$		0			0
$535$	−3870.00	−	6703.04i	−0.312738	−	0.541678i
$536$		0			0
$537$	8616.00	−	14923.3i	0.692380	−	1.19924i
$538$		0			0
$539$		0			0
$540$		0			0
$541$	7613.00	−	13186.1i	0.605006	−	1.04790i	−0.387044	−	0.922061i	$-0.626504\pi$
$541$	7613.00	−	13186.1i	0.605006	−	1.04790i	0.992050	−	0.125841i	$-0.0401628\pi$
$542$		0			0
$543$	−3100.00	−	5369.36i	−0.244998	−	0.424348i
$544$		0			0
$545$	1390.00			0.109250
$546$		0			0
$547$	−13228.0			−1.03398			−0.516991	−	0.855991i	$-0.672948\pi$
$547$	−13228.0			−1.03398			−0.516991	+	0.855991i	$0.672948\pi$
$548$		0			0
$549$	−319.000	−	552.524i	−0.0247989	−	0.0429529i
$550$		0			0
$551$	4092.00	−	7087.55i	0.316379	−	0.547985i
$552$		0			0
$553$		0			0
$554$		0			0
$555$	−2540.00	+	4399.41i	−0.194265	+	0.336477i
$556$		0			0
$557$	4245.00	+	7352.56i	0.322920	+	0.559314i	0.981089	−	0.193556i	$-0.0620022\pi$
$557$	4245.00	+	7352.56i	0.322920	+	0.559314i	−0.658169	+	0.752870i	$0.728669\pi$
$558$		0			0
$559$	−8600.00			−0.650700
$560$		0			0
$561$	−4320.00			−0.325117
$562$		0			0
$563$	5142.00	+	8906.21i	0.384919	+	0.666699i	0.991758	−	0.128125i	$-0.0408960\pi$
$563$	5142.00	+	8906.21i	0.384919	+	0.666699i	−0.606839	+	0.794825i	$0.707563\pi$
$564$		0			0
$565$	1395.00	−	2416.21i	0.103873	−	0.179913i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	−885.000	+	1532.86i	−0.0652041	+	0.112937i	−0.896785	−	0.442468i	$-0.854103\pi$
$569$	−885.000	+	1532.86i	−0.0652041	+	0.112937i	0.831580	+	0.555404i	$0.187437\pi$
$570$		0			0
$571$	−3034.00	−	5255.04i	−0.222362	−	0.385143i	0.733162	−	0.680054i	$-0.238043\pi$
$571$	−3034.00	−	5255.04i	−0.222362	−	0.385143i	−0.955525	+	0.294911i	$0.904710\pi$
$572$		0			0
$573$	192.000			0.0139981
$574$		0			0
$575$	1200.00			0.0870321
$576$		0			0
$577$	−10753.0	−	18624.7i	−0.775829	−	1.34377i	−0.934327	−	0.356416i	$-0.883999\pi$
$577$	−10753.0	−	18624.7i	−0.775829	−	1.34377i	0.158499	−	0.987359i	$-0.449335\pi$
$578$		0			0
$579$	−2116.00	+	3665.02i	−0.151879	+	0.263062i
$580$		0			0
$581$		0			0
$582$		0			0
$583$	−14940.0	+	25876.8i	−1.06132	+	1.83827i
$584$		0			0
$585$	2365.00	+	4096.30i	0.167147	+	0.289506i
$586$		0			0
$587$	12108.0			0.851364			0.425682	−	0.904873i	$-0.360034\pi$
$587$	12108.0			0.851364			0.425682	+	0.904873i	$0.360034\pi$
$588$		0			0
$589$	7744.00			0.541742
$590$		0			0
$591$	7428.00	+	12865.7i	0.517000	+	0.895471i
$592$		0			0
$593$	−7737.00	+	13400.9i	−0.535785	+	0.928007i	0.463340	+	0.886181i	$0.346651\pi$
$593$	−7737.00	+	13400.9i	−0.535785	+	0.928007i	−0.999125	+	0.0418262i	$0.986682\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	3536.00	−	6124.53i	0.242410	−	0.419867i
$598$		0			0
$599$	1260.00	+	2182.38i	0.0859469	+	0.148864i	0.905794	−	0.423718i	$-0.139275\pi$
$599$	1260.00	+	2182.38i	0.0859469	+	0.148864i	−0.819847	+	0.572582i	$0.805942\pi$
$600$		0			0
$601$	−12790.0			−0.868078			−0.434039	−	0.900894i	$-0.642912\pi$
$601$	−12790.0			−0.868078			−0.434039	+	0.900894i	$0.642912\pi$
$602$		0			0
$603$	11396.0			0.769620
$604$		0			0
$605$	−5672.50	−	9825.06i	−0.381190	−	0.660240i
$606$		0			0
$607$	−5788.00	+	10025.1i	−0.387031	+	0.670357i	−0.992049	−	0.125855i	$-0.959833\pi$
$607$	−5788.00	+	10025.1i	−0.387031	+	0.670357i	0.605018	+	0.796212i	$0.293166\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	−7224.00	+	12512.3i	−0.478317	+	0.828470i
$612$		0			0
$613$	−10063.0	−	17429.6i	−0.663035	−	1.14841i	−0.979814	−	0.199912i	$-0.935935\pi$
$613$	−10063.0	−	17429.6i	−0.663035	−	1.14841i	0.316778	−	0.948500i	$-0.397399\pi$
$614$		0			0
$615$	3720.00			0.243910
$616$		0			0
$617$	−27942.0			−1.82318			−0.911590	−	0.411100i	$-0.865145\pi$
$617$	−27942.0			−1.82318			−0.911590	+	0.411100i	$0.865145\pi$
$618$		0			0
$619$	11270.0	+	19520.2i	0.731792	+	1.26750i	0.956116	+	0.292987i	$0.0946493\pi$
$619$	11270.0	+	19520.2i	0.731792	+	1.26750i	−0.224324	+	0.974515i	$0.572017\pi$
$620$		0			0
$621$	3648.00	−	6318.52i	0.235731	−	0.408299i
$622$		0			0
$623$		0			0
$624$		0			0
$625$	−312.500	+	541.266i	−0.0200000	+	0.0346410i
$626$		0			0
$627$	5280.00	+	9145.23i	0.336304	+	0.582496i
$628$		0			0
$629$	4572.00			0.289821
$630$		0			0
$631$	−5128.00			−0.323522			−0.161761	−	0.986830i	$-0.551717\pi$
$631$	−5128.00			−0.323522			−0.161761	+	0.986830i	$0.551717\pi$
$632$		0			0
$633$	8072.00	+	13981.1i	0.506845	+	0.877882i
$634$		0			0
$635$	−860.000	+	1489.56i	−0.0537450	+	0.0930890i
$636$		0			0
$637$		0			0
$638$		0			0
$639$	924.000	−	1600.41i	0.0572032	−	0.0990789i
$640$		0			0
$641$	6399.00	+	11083.4i	0.394298	+	0.682945i	0.993011	−	0.118019i	$-0.0376543\pi$
$641$	6399.00	+	11083.4i	0.394298	+	0.682945i	−0.598713	+	0.800964i	$0.704321\pi$
$642$		0			0
$643$	−21148.0			−1.29704			−0.648519	−	0.761198i	$-0.724611\pi$
$643$	−21148.0			−1.29704			−0.648519	+	0.761198i	$0.724611\pi$
$644$		0			0
$645$	−2000.00			−0.122093
$646$		0			0
$647$	−8232.00	−	14258.2i	−0.500206	−	0.866382i	−1.00000		0.000237943i	$-0.999924\pi$
$647$	−8232.00	−	14258.2i	−0.500206	−	0.866382i	0.499794	−	0.866144i	$-0.333409\pi$
$648$		0			0
$649$	−7560.00	+	13094.3i	−0.457251	+	0.791982i
$650$		0			0
$651$		0			0
$652$		0			0
$653$	12117.0	−	20987.3i	0.726148	−	1.25773i	−0.232351	−	0.972632i	$-0.574642\pi$
$653$	12117.0	−	20987.3i	0.726148	−	1.25773i	0.958500	−	0.285094i	$-0.0920248\pi$
$654$		0			0
$655$	−1950.00	−	3377.50i	−0.116325	−	0.201481i
$656$		0			0
$657$	−5566.00			−0.330518
$658$		0			0
$659$	−22836.0			−1.34987			−0.674935	−	0.737877i	$-0.735828\pi$
$659$	−22836.0			−1.34987			−0.674935	+	0.737877i	$0.735828\pi$
$660$		0			0
$661$	−13159.0	−	22792.1i	−0.774320	−	1.34116i	−0.935176	−	0.354184i	$-0.884759\pi$
$661$	−13159.0	−	22792.1i	−0.774320	−	1.34116i	0.160855	−	0.986978i	$-0.448575\pi$
$662$		0			0
$663$	−3096.00	+	5362.43i	−0.181355	+	0.314117i
$664$		0			0
$665$		0			0
$666$		0			0
$667$	4464.00	−	7731.87i	0.259141	−	0.448845i
$668$		0			0
$669$	−1360.00	−	2355.59i	−0.0785959	−	0.136132i
$670$		0			0
$671$	3480.00			0.200214
$672$		0			0
$673$	28802.0			1.64968			0.824841	−	0.565365i	$-0.191265\pi$
$673$	28802.0			1.64968			0.824841	+	0.565365i	$0.191265\pi$
$674$		0			0
$675$	1900.00	+	3290.90i	0.108342	+	0.187654i
$676$		0			0
$677$	−1263.00	+	2187.58i	−0.0717002	+	0.124188i	−0.899647	−	0.436619i	$-0.856176\pi$
$677$	−1263.00	+	2187.58i	−0.0717002	+	0.124188i	0.827946	+	0.560807i	$0.189509\pi$
$678$		0			0
$679$		0			0
$680$		0			0
$681$	−4776.00	+	8272.27i	−0.268747	+	0.465483i
$682$		0			0
$683$	11538.0	+	19984.4i	0.646397	+	1.11959i	0.983977	+	0.178296i	$0.0570584\pi$
$683$	11538.0	+	19984.4i	0.646397	+	1.11959i	−0.337580	+	0.941297i	$0.609608\pi$
$684$		0			0
$685$	3330.00			0.185741
$686$		0			0
$687$	−15496.0			−0.860567
$688$		0			0
$689$	21414.0	+	37090.1i	1.18405	+	2.05083i
$690$		0			0
$691$	−3934.00	+	6813.89i	−0.216579	+	0.375127i	−0.953760	−	0.300569i	$-0.902823\pi$
$691$	−3934.00	+	6813.89i	−0.216579	+	0.375127i	0.737181	+	0.675696i	$0.236157\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	−2210.00	+	3827.83i	−0.120619	+	0.208918i
$696$		0			0
$697$	−1674.00	−	2899.45i	−0.0909717	−	0.157568i
$698$		0			0
$699$	12648.0			0.684394
$700$		0			0
$701$	21510.0			1.15895			0.579473	−	0.814991i	$-0.303258\pi$
$701$	21510.0			1.15895			0.579473	+	0.814991i	$0.303258\pi$
$702$		0			0
$703$	−5588.00	−	9678.70i	−0.299794	−	0.519259i
$704$		0			0
$705$	−1680.00	+	2909.85i	−0.0897482	+	0.155448i
$706$		0			0
$707$		0			0
$708$		0			0
$709$	−15007.0	+	25992.9i	−0.794922	+	1.37685i	0.127967	+	0.991778i	$0.459155\pi$
$709$	−15007.0	+	25992.9i	−0.794922	+	1.37685i	−0.922889	+	0.385067i	$0.874178\pi$
$710$		0			0
$711$	1496.00	+	2591.15i	0.0789091	+	0.136675i
$712$		0			0
$713$	8448.00			0.443731
$714$		0			0
$715$	−25800.0			−1.34946
$716$		0			0
$717$	−10848.0	−	18789.3i	−0.565029	−	0.978659i
$718$		0			0
$719$	408.000	−	706.677i	0.0211625	−	0.0366545i	−0.855250	−	0.518215i	$-0.826597\pi$
$719$	408.000	−	706.677i	0.0211625	−	0.0366545i	0.876413	+	0.481561i	$0.159930\pi$
$720$		0			0
$721$		0			0
$722$		0			0
$723$	7772.00	−	13461.5i	0.399784	−	0.692446i
$724$		0			0
$725$	2325.00	+	4027.02i	0.119101	+	0.206289i
$726$		0			0
$727$	−9952.00			−0.507702			−0.253851	−	0.967243i	$-0.581697\pi$
$727$	−9952.00			−0.507702			−0.253851	+	0.967243i	$0.581697\pi$
$728$		0			0
$729$	19837.0			1.00782
$730$		0			0
$731$	900.000	+	1558.85i	0.0455372	+	0.0788728i
$732$		0			0
$733$	16973.0	−	29398.1i	0.855269	−	1.48137i	−0.0211266	−	0.999777i	$-0.506725\pi$
$733$	16973.0	−	29398.1i	0.855269	−	1.48137i	0.876395	−	0.481592i	$-0.159941\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	−31080.0	+	53832.1i	−1.55339	+	2.69055i
$738$		0			0
$739$	−11710.0	−	20282.3i	−0.582895	−	1.00960i	−0.995134	−	0.0985280i	$-0.968587\pi$
$739$	−11710.0	−	20282.3i	−0.582895	−	1.00960i	0.412239	−	0.911076i	$-0.364747\pi$
$740$		0			0
$741$	15136.0			0.750384
$742$		0			0
$743$	−14592.0			−0.720496			−0.360248	−	0.932857i	$-0.617308\pi$
$743$	−14592.0			−0.720496			−0.360248	+	0.932857i	$0.617308\pi$
$744$		0			0
$745$	285.000	+	493.634i	0.0140156	+	0.0242757i
$746$		0			0
$747$	5214.00	−	9030.91i	0.255382	−	0.442334i
$748$		0			0
$749$		0			0
$750$		0			0
$751$	−4528.00	+	7842.73i	−0.220012	+	0.381072i	−0.954811	−	0.297213i	$-0.903943\pi$
$751$	−4528.00	+	7842.73i	−0.220012	+	0.381072i	0.734799	+	0.678285i	$0.237276\pi$
$752$		0			0
$753$	10200.0	+	17666.9i	0.493637	+	0.855004i
$754$		0			0
$755$	−200.000			−0.00964072
$756$		0			0
$757$	−17554.0			−0.842815			−0.421408	−	0.906871i	$-0.638464\pi$
$757$	−17554.0			−0.842815			−0.421408	+	0.906871i	$0.638464\pi$
$758$		0			0
$759$	5760.00	+	9976.61i	0.275461	+	0.477112i
$760$		0			0
$761$	18219.0	−	31556.2i	0.867856	−	1.50317i	0.00367239	−	0.999993i	$-0.498831\pi$
$761$	18219.0	−	31556.2i	0.867856	−	1.50317i	0.864183	−	0.503177i	$-0.167836\pi$
$762$		0			0
$763$		0			0
$764$		0			0
$765$	495.000	−	857.365i	0.0233945	−	0.0405204i
$766$		0			0
$767$	10836.0	+	18768.5i	0.510124	+	0.883561i
$768$		0			0
$769$	−9022.00			−0.423071			−0.211536	−	0.977370i	$-0.567846\pi$
$769$	−9022.00			−0.423071			−0.211536	+	0.977370i	$0.567846\pi$
$770$		0			0
$771$	8712.00			0.406946
$772$		0			0
$773$	−735.000	−	1273.06i	−0.0341994	−	0.0592350i	0.848419	−	0.529325i	$-0.177555\pi$
$773$	−735.000	−	1273.06i	−0.0341994	−	0.0592350i	−0.882618	+	0.470090i	$0.844221\pi$
$774$		0			0
$775$	−2200.00	+	3810.51i	−0.101969	+	0.176616i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	−4092.00	+	7087.55i	−0.188204	+	0.325979i
$780$		0			0
$781$	5040.00	+	8729.54i	0.230916	+	0.399958i
$782$		0			0
$783$	28272.0			1.29037
$784$		0			0
$785$	−770.000			−0.0350095
$786$		0			0
$787$	−2626.00	−	4548.37i	−0.118941	−	0.206012i	0.800407	−	0.599457i	$-0.204617\pi$
$787$	−2626.00	−	4548.37i	−0.118941	−	0.206012i	−0.919348	+	0.393444i	$0.871283\pi$
$788$		0			0
$789$	12288.0	−	21283.4i	0.554454	−	0.960343i
$790$		0			0
$791$		0			0
$792$		0			0
$793$	2494.00	−	4319.73i	0.111683	−	0.193440i
$794$		0			0
$795$	4980.00	+	8625.61i	0.222167	+	0.384804i
$796$		0			0
$797$	12294.0			0.546394			0.273197	−	0.961958i	$-0.411919\pi$
$797$	12294.0			0.546394			0.273197	+	0.961958i	$0.411919\pi$
$798$		0			0
$799$	3024.00			0.133894
$800$		0			0
$801$	−5577.00	−	9659.65i	−0.246009	−	0.426101i
$802$		0			0
$803$	15180.0	−	26292.5i	0.667112	−	1.15547i
$804$		0			0
$805$		0			0
$806$		0			0
$807$	−1644.00	+	2847.49i	−0.0717119	+	0.124209i
$808$		0			0
$809$	−7773.00	−	13463.2i	−0.337805	−	0.585095i	0.646215	−	0.763156i	$-0.276351\pi$
$809$	−7773.00	−	13463.2i	−0.337805	−	0.585095i	−0.984020	+	0.178061i	$0.943018\pi$
$810$		0			0
$811$	19364.0			0.838424			0.419212	−	0.907888i	$-0.362306\pi$
$811$	19364.0			0.838424			0.419212	+	0.907888i	$0.362306\pi$
$812$		0			0
$813$	33920.0			1.46326
$814$		0			0
$815$	−5450.00	−	9439.68i	−0.234239	−	0.405715i
$816$		0			0
$817$	2200.00	−	3810.51i	0.0942084	−	0.163174i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	3657.00	−	6334.11i	0.155457	−	0.269259i	−0.777768	−	0.628551i	$-0.783648\pi$
$821$	3657.00	−	6334.11i	0.155457	−	0.269259i	0.933225	+	0.359292i	$0.116982\pi$
$822$		0			0
$823$	−5992.00	−	10378.4i	−0.253789	−	0.439575i	0.710777	−	0.703417i	$-0.248343\pi$
$823$	−5992.00	−	10378.4i	−0.253789	−	0.439575i	−0.964566	+	0.263843i	$0.915010\pi$
$824$		0			0
$825$	−6000.00			−0.253204
$826$		0			0
$827$	13500.0			0.567643			0.283822	−	0.958877i	$-0.408398\pi$
$827$	13500.0			0.567643			0.283822	+	0.958877i	$0.408398\pi$
$828$		0			0
$829$	22301.0	+	38626.5i	0.934313	+	1.61828i	0.775854	+	0.630913i	$0.217319\pi$
$829$	22301.0	+	38626.5i	0.934313	+	1.61828i	0.158459	+	0.987365i	$0.449347\pi$
$830$		0			0
$831$	2276.00	−	3942.15i	0.0950103	−	0.164563i
$832$		0			0
$833$		0			0
$834$		0			0
$835$	−9240.00	+	16004.1i	−0.382950	+	0.663289i
$836$		0			0
$837$	13376.0	+	23167.9i	0.552380	+	0.956751i
$838$		0			0
$839$	35448.0			1.45864			0.729321	−	0.684172i	$-0.239836\pi$
$839$	35448.0			1.45864			0.729321	+	0.684172i	$0.239836\pi$
$840$		0			0
$841$	10207.0			0.418508
$842$		0			0
$843$	−11412.0	−	19766.2i	−0.466252	−	0.807572i
$844$		0			0
$845$	−12997.5	+	22512.3i	−0.529145	+	0.916506i
$846$		0			0
$847$		0			0
$848$		0			0
$849$	6056.00	−	10489.3i	0.244807	−	0.424019i
$850$		0			0
$851$	−6096.00	−	10558.6i	−0.245556	−	0.425316i
$852$		0			0
$853$	12590.0			0.505362			0.252681	−	0.967550i	$-0.418688\pi$
$853$	12590.0			0.505362			0.252681	+	0.967550i	$0.418688\pi$
$854$		0			0
$855$	−2420.00			−0.0967980
$856$		0			0
$857$	−12453.0	−	21569.2i	−0.496367	−	0.859733i	0.503624	−	0.863923i	$-0.332000\pi$
$857$	−12453.0	−	21569.2i	−0.496367	−	0.859733i	−0.999991	+	0.00419015i	$0.998666\pi$
$858$		0			0
$859$	−11602.0	+	20095.3i	−0.460833	+	0.798185i	−0.999003	−	0.0446509i	$-0.985782\pi$
$859$	−11602.0	+	20095.3i	−0.460833	+	0.798185i	0.538170	+	0.842836i	$0.319116\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	−9924.00	+	17188.9i	−0.391445	+	0.678002i	−0.992640	−	0.121100i	$-0.961358\pi$
$863$	−9924.00	+	17188.9i	−0.391445	+	0.678002i	0.601196	+	0.799102i	$0.294691\pi$
$864$		0			0
$865$	−3255.00	−	5637.83i	−0.127946	−	0.221609i
$866$		0			0
$867$	−18356.0			−0.719034
$868$		0			0
$869$	−16320.0			−0.637075
$870$		0			0
$871$	44548.0	+	77159.4i	1.73301	+	3.00166i
$872$		0			0
$873$	−4213.00	+	7297.13i	−0.163332	+	0.282899i
$874$		0			0
$875$		0			0
$876$		0			0
$877$	−13771.0	+	23852.1i	−0.530232	+	0.918389i	0.469146	+	0.883121i	$0.344562\pi$
$877$	−13771.0	+	23852.1i	−0.530232	+	0.918389i	−0.999378	+	0.0352683i	$0.988771\pi$
$878$		0			0
$879$	−6780.00	−	11743.3i	−0.260164	−	0.450616i
$880$		0			0
$881$	−20718.0			−0.792290			−0.396145	−	0.918188i	$-0.629652\pi$
$881$	−20718.0			−0.792290			−0.396145	+	0.918188i	$0.629652\pi$
$882$		0			0
$883$	25172.0			0.959349			0.479675	−	0.877446i	$-0.340755\pi$
$883$	25172.0			0.959349			0.479675	+	0.877446i	$0.340755\pi$
$884$		0			0
$885$	2520.00	+	4364.77i	0.0957162	+	0.165785i
$886$		0			0
$887$	6432.00	−	11140.6i	0.243478	−	0.421717i	−0.718224	−	0.695812i	$-0.755045\pi$
$887$	6432.00	−	11140.6i	0.243478	−	0.421717i	0.961703	+	0.274095i	$0.0883781\pi$
$888$		0			0
$889$		0			0
$890$		0			0
$891$	−9330.00	+	16160.0i	−0.350804	+	0.607611i
$892$		0			0
$893$	−3696.00	−	6401.66i	−0.138502	−	0.239892i
$894$		0			0
$895$	−21540.0			−0.804472
$896$		0			0
$897$	16512.0			0.614626
$898$		0			0
$899$	16368.0	+	28350.2i	0.607234	+	1.05176i
$900$		0			0
$901$	4482.00	−	7763.05i	0.165724	−	0.287042i
$902$		0			0
$903$		0			0
$904$		0			0
$905$	−3875.00	+	6711.70i	−0.142331	+	0.246524i
$906$		0			0
$907$	11546.0	+	19998.3i	0.422689	+	0.732118i	0.996201	−	0.0870783i	$-0.0277530\pi$
$907$	11546.0	+	19998.3i	0.422689	+	0.732118i	−0.573513	+	0.819197i	$0.694420\pi$
$908$		0			0
$909$	14454.0			0.527403
$910$		0			0
$911$	−14208.0			−0.516720			−0.258360	−	0.966049i	$-0.583182\pi$
$911$	−14208.0			−0.516720			−0.258360	+	0.966049i	$0.583182\pi$
$912$		0			0
$913$	28440.0	+	49259.5i	1.03092	+	1.78560i
$914$		0			0
$915$	580.000	−	1004.59i	0.0209554	−	0.0362959i
$916$		0			0
$917$		0			0
$918$		0			0
$919$	13292.0	−	23022.4i	0.477108	−	0.826376i	−0.522547	−	0.852610i	$-0.675018\pi$
$919$	13292.0	−	23022.4i	0.477108	−	0.826376i	0.999656	+	0.0262342i	$0.00835157\pi$
$920$		0			0
$921$	8312.00	+	14396.8i	0.297383	+	0.515082i
$922$		0			0
$923$	14448.0			0.515235
$924$		0			0
$925$	6350.00			0.225715
$926$		0			0
$927$	−2464.00	−	4267.77i	−0.0873014	−	0.151210i
$928$		0			0
$929$	−81.0000	+	140.296i	−0.00286063	+	0.00495475i	−0.867452	−	0.497521i	$-0.834244\pi$
$929$	−81.0000	+	140.296i	−0.00286063	+	0.00495475i	0.864592	+	0.502475i	$0.167577\pi$
$930$		0			0
$931$		0			0
$932$		0			0
$933$	−13104.0	+	22696.8i	−0.459813	+	0.796420i
$934$		0			0
$935$	2700.00	+	4676.54i	0.0944379	+	0.163571i
$936$		0			0
$937$	−29734.0			−1.03668			−0.518339	−	0.855175i	$-0.673449\pi$
$937$	−29734.0			−1.03668			−0.518339	+	0.855175i	$0.673449\pi$
$938$		0			0
$939$	−5464.00			−0.189894
$940$		0			0
$941$	−8571.00	−	14845.4i	−0.296925	−	0.514290i	0.678506	−	0.734595i	$-0.262628\pi$
$941$	−8571.00	−	14845.4i	−0.296925	−	0.514290i	−0.975431	+	0.220306i	$0.929295\pi$
$942$		0			0
$943$	−4464.00	+	7731.87i	−0.154155	+	0.267004i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−13218.0	+	22894.2i	−0.453566	+	0.785600i	−0.998605	−	0.0528113i	$-0.983182\pi$
$947$	−13218.0	+	22894.2i	−0.453566	+	0.785600i	0.545038	+	0.838411i	$0.316515\pi$
$948$		0			0
$949$	−21758.0	−	37686.0i	−0.744251	−	1.28908i
$950$		0			0
$951$	10392.0			0.354347
$952$		0			0
$953$	27882.0			0.947730			0.473865	−	0.880598i	$-0.342858\pi$
$953$	27882.0			0.947730			0.473865	+	0.880598i	$0.342858\pi$
$954$		0			0
$955$	−120.000	−	207.846i	−0.00406608	−	0.00704266i
$956$		0			0
$957$	−22320.0	+	38659.4i	−0.753922	+	1.30583i
$958$		0			0
$959$		0			0
$960$		0			0
$961$	−592.500	+	1026.24i	−0.0198886	+	0.0344480i
$962$		0			0
$963$	8514.00	+	14746.7i	0.284901	+	0.493463i
$964$		0			0
$965$	5290.00			0.176467
$966$		0			0
$967$	12656.0			0.420879			0.210439	−	0.977607i	$-0.432511\pi$
$967$	12656.0			0.420879			0.210439	+	0.977607i	$0.432511\pi$
$968$		0			0
$969$	−1584.00	−	2743.57i	−0.0525133	−	0.0909557i
$970$		0			0
$971$	−1458.00	+	2525.33i	−0.0481869	+	0.0834621i	−0.889113	−	0.457688i	$-0.848678\pi$
$971$	−1458.00	+	2525.33i	−0.0481869	+	0.0834621i	0.840926	+	0.541150i	$0.182011\pi$
$972$		0			0
$973$		0			0
$974$		0			0
$975$	−4300.00	+	7447.82i	−0.141241	+	0.244637i
$976$		0			0
$977$	3447.00	+	5970.38i	0.112875	+	0.195506i	0.916928	−	0.399052i	$-0.130661\pi$
$977$	3447.00	+	5970.38i	0.112875	+	0.195506i	−0.804053	+	0.594558i	$0.797327\pi$
$978$		0			0
$979$	60840.0			1.98616
$980$		0			0
$981$	−3058.00			−0.0995254
$982$		0			0
$983$	22632.0	+	39199.8i	0.734332	+	1.27190i	0.955016	+	0.296555i	$0.0958379\pi$
$983$	22632.0	+	39199.8i	0.734332	+	1.27190i	−0.220683	+	0.975346i	$0.570829\pi$
$984$		0			0
$985$	9285.00	−	16082.1i	0.300350	−	0.520221i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	2400.00	−	4156.92i	0.0771644	−	0.133653i
$990$		0			0
$991$	−26008.0	−	45047.2i	−0.833674	−	1.44397i	−0.895105	−	0.445855i	$-0.852900\pi$
$991$	−26008.0	−	45047.2i	−0.833674	−	1.44397i	0.0614307	−	0.998111i	$-0.480434\pi$
$992$		0			0
$993$	−13168.0			−0.420820
$994$		0			0
$995$	−8840.00			−0.281655
$996$		0			0
$997$	6929.00	+	12001.4i	0.220104	+	0.381231i	0.954839	−	0.297123i	$-0.0960270\pi$
$997$	6929.00	+	12001.4i	0.220104	+	0.381231i	−0.734735	+	0.678354i	$0.762694\pi$
$998$		0			0
$999$	19304.0	−	33435.5i	0.611363	−	1.05891i

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

)

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	980.4.i.e.961.1		2
7.2	even	3		20.4.a.a.1.1	✓	1
7.3	odd	6		980.4.i.n.361.1		2
7.4	even	3	inner	980.4.i.e.361.1		2
7.5	odd	6		980.4.a.c.1.1		1
7.6	odd	2		980.4.i.n.961.1		2
21.2	odd	6		180.4.a.a.1.1		1
28.23	odd	6		80.4.a.c.1.1		1
35.2	odd	12		100.4.c.a.49.1		2
35.9	even	6		100.4.a.a.1.1		1
35.23	odd	12		100.4.c.a.49.2		2
56.37	even	6		320.4.a.d.1.1		1
56.51	odd	6		320.4.a.k.1.1		1
63.2	odd	6		1620.4.i.j.1081.1		2
63.16	even	3		1620.4.i.d.1081.1		2
63.23	odd	6		1620.4.i.j.541.1		2
63.58	even	3		1620.4.i.d.541.1		2
77.65	odd	6		2420.4.a.d.1.1		1
84.23	even	6		720.4.a.k.1.1		1
105.2	even	12		900.4.d.k.649.1		2
105.23	even	12		900.4.d.k.649.2		2
105.44	odd	6		900.4.a.m.1.1		1
112.37	even	12		1280.4.d.n.641.1		2
112.51	odd	12		1280.4.d.c.641.1		2
112.93	even	12		1280.4.d.n.641.2		2
112.107	odd	12		1280.4.d.c.641.2		2
140.23	even	12		400.4.c.j.49.1		2
140.79	odd	6		400.4.a.o.1.1		1
140.107	even	12		400.4.c.j.49.2		2
280.149	even	6		1600.4.a.bl.1.1		1
280.219	odd	6		1600.4.a.p.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
20.4.a.a.1.1	✓	1	7.2	even	3
80.4.a.c.1.1		1	28.23	odd	6
100.4.a.a.1.1		1	35.9	even	6
100.4.c.a.49.1		2	35.2	odd	12
100.4.c.a.49.2		2	35.23	odd	12
180.4.a.a.1.1		1	21.2	odd	6
320.4.a.d.1.1		1	56.37	even	6
320.4.a.k.1.1		1	56.51	odd	6
400.4.a.o.1.1		1	140.79	odd	6
400.4.c.j.49.1		2	140.23	even	12
400.4.c.j.49.2		2	140.107	even	12
720.4.a.k.1.1		1	84.23	even	6
900.4.a.m.1.1		1	105.44	odd	6
900.4.d.k.649.1		2	105.2	even	12
900.4.d.k.649.2		2	105.23	even	12
980.4.a.c.1.1		1	7.5	odd	6
980.4.i.e.361.1		2	7.4	even	3	inner
980.4.i.e.961.1		2	1.1	even	1	trivial
980.4.i.n.361.1		2	7.3	odd	6
980.4.i.n.961.1		2	7.6	odd	2
1280.4.d.c.641.1		2	112.51	odd	12
1280.4.d.c.641.2		2	112.107	odd	12
1280.4.d.n.641.1		2	112.37	even	12
1280.4.d.n.641.2		2	112.93	even	12
1600.4.a.p.1.1		1	280.219	odd	6
1600.4.a.bl.1.1		1	280.149	even	6
1620.4.i.d.541.1		2	63.58	even	3
1620.4.i.d.1081.1		2	63.16	even	3
1620.4.i.j.541.1		2	63.23	odd	6
1620.4.i.j.1081.1		2	63.2	odd	6
2420.4.a.d.1.1		1	77.65	odd	6

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 $\F_{q}$
Belyi maps

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more

Newspace parameters

Newform invariants

Embedding invariants

$q$ -expansion

Character values

Coefficient data

Twists

This project is supported by grants from the US National Science Foundation, the UK Engineering and Physical Sciences Research Council, and the Simons Foundation.

Label	980.4.i.e.961.1

Level	$980$
Weight	$4$
Character	980.961
Analytic conductor	$57.822$
Analytic rank	$0$
Dimension	$2$
Inner twists	$2$