LMFDB - Embedded newform 1764.2.e.i.1079.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1764,2,Mod(1079,1764)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1764, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 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("1764.1079");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1764 = 2^{2} \cdot 3^{2} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1764.e (of order $2$, degree $1$, 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:	$14.0856109166$
Analytic rank:	$0$
Dimension:	$16$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} + x^{12} - 10x^{10} + 4x^{8} - 40x^{6} + 16x^{4} + 256 $ x^16 + x^12 - 10x^10 + 4x^8 - 40x^6 + 16x^4 + 256
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{10} $
Twist minimal:	no (minimal twist has level 252)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			1079.8
Root			$-0.545545 + 1.30475i$ of defining polynomial
Character	$\chi$	$=$	1764.1079
Dual form			1764.2.e.i.1079.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.545545 + 1.30475i) q^{2} +(-1.40476 - 1.42360i) q^{4} +0.698240i q^{5} +(2.62381 - 1.05623i) q^{8} +O(q^{10})$	\(q+(-0.545545 + 1.30475i) q^{2} +(-1.40476 - 1.42360i) q^{4} +0.698240i q^{5} +(2.62381 - 1.05623i) q^{8} +(-0.911031 - 0.380921i) q^{10} -2.55198 q^{11} +1.88088 q^{13} +(-0.0532920 + 3.99964i) q^{16} +3.97326i q^{17} -7.05819i q^{19} +(0.994017 - 0.980861i) q^{20} +(1.39222 - 3.32971i) q^{22} +4.02656 q^{23} +4.51246 q^{25} +(-1.02610 + 2.45408i) q^{26} -1.86081i q^{29} +0.941102i q^{31} +(-5.18948 - 2.25152i) q^{32} +(-5.18413 - 2.16759i) q^{34} -7.49992 q^{37} +(9.20919 + 3.85056i) q^{38} +(0.737500 + 1.83205i) q^{40} +10.6065i q^{41} -3.97212i q^{43} +(3.58493 + 3.63301i) q^{44} +(-2.19667 + 5.25366i) q^{46} +8.90438 q^{47} +(-2.46175 + 5.88765i) q^{50} +(-2.64218 - 2.67762i) q^{52} +0.529774i q^{53} -1.78190i q^{55} +(2.42790 + 1.01516i) q^{58} +13.3007 q^{59} +10.3683 q^{61} +(-1.22791 - 0.513413i) q^{62} +(5.76877 - 5.54268i) q^{64} +1.31330i q^{65} -2.72300i q^{67} +(5.65635 - 5.58149i) q^{68} -3.51310 q^{71} -2.75071 q^{73} +(4.09155 - 9.78555i) q^{74} +(-10.0481 + 9.91507i) q^{76} +13.5338i q^{79} +(-2.79271 - 0.0372106i) q^{80} +(-13.8389 - 5.78632i) q^{82} +17.1516 q^{83} -2.77429 q^{85} +(5.18264 + 2.16697i) q^{86} +(-6.69592 + 2.69547i) q^{88} +11.8700i q^{89} +(-5.65635 - 5.73222i) q^{92} +(-4.85774 + 11.6180i) q^{94} +4.92831 q^{95} +10.8682 q^{97} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q+O(q^{10}) $ 16 * q	$ 16 q + 8 q^{13} - 4 q^{16} - 16 q^{22} - 24 q^{25} - 8 q^{34} - 8 q^{37} + 52 q^{40} + 24 q^{46} + 52 q^{52} + 12 q^{58} + 16 q^{61} + 60 q^{64} + 8 q^{73} + 36 q^{76} - 68 q^{82} - 16 q^{85} - 44 q^{88} - 60 q^{94} - 88 q^{97}+O(q^{100}) $ 16 * q + 8 * q^13 - 4 * q^16 - 16 * q^22 - 24 * q^25 - 8 * q^34 - 8 * q^37 + 52 * q^40 + 24 * q^46 + 52 * q^52 + 12 * q^58 + 16 * q^61 + 60 * q^64 + 8 * q^73 + 36 * q^76 - 68 * q^82 - 16 * q^85 - 44 * q^88 - 60 * q^94 - 88 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1764\mathbb{Z}\right)^\times$.

$n$	$785$	$883$	$1081$
$\chi(n)$	$-1$	$-1$	$1$

Coefficient data

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

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

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

$2$	−0.545545	+	1.30475i	−0.385759	+	0.922600i
$2$	−0.545545	+	1.30475i	−0.385759	+	0.922600i
$3$		0			0
$3$		0			0
$4$	−1.40476	−	1.42360i	−0.702381	−	0.711802i
$5$			0.698240i			0.312262i	0.987736	+	0.156131i	$0.0499023\pi$
$5$			0.698240i			0.312262i	−0.987736	+	0.156131i	$0.950098\pi$
$6$		0			0
$7$		0			0
$7$		0			0
$8$	2.62381	−	1.05623i	0.927657	−	0.373433i
$9$		0			0
$10$	−0.911031	−	0.380921i	−0.288093	−	0.120458i
$11$	−2.55198			−0.769452			−0.384726	−	0.923031i	$-0.625704\pi$
$11$	−2.55198			−0.769452			−0.384726	+	0.923031i	$0.625704\pi$
$12$		0			0
$13$	1.88088			0.521661			0.260831	−	0.965385i	$-0.416004\pi$
$13$	1.88088			0.521661			0.260831	+	0.965385i	$0.416004\pi$
$14$		0			0
$15$		0			0
$16$	−0.0532920	+	3.99964i	−0.0133230	+	0.999911i
$17$			3.97326i			0.963658i	0.876265	+	0.481829i	$0.160027\pi$
$17$			3.97326i			0.963658i	−0.876265	+	0.481829i	$0.839973\pi$
$18$		0			0
$19$		−	7.05819i		−	1.61926i	−0.586941	−	0.809630i	$-0.699668\pi$
$19$		−	7.05819i		−	1.61926i	0.586941	−	0.809630i	$-0.300332\pi$
$20$	0.994017	−	0.980861i	0.222269	−	0.219327i
$21$		0			0
$22$	1.39222	−	3.32971i	0.296823	−	0.709896i
$23$	4.02656			0.839595			0.419798	−	0.907618i	$-0.362101\pi$
$23$	4.02656			0.839595			0.419798	+	0.907618i	$0.362101\pi$
$24$		0			0
$25$	4.51246			0.902492
$26$	−1.02610	+	2.45408i	−0.201235	+	0.481285i
$27$		0			0
$28$		0			0
$29$		−	1.86081i		−	0.345544i	−0.984962	−	0.172772i	$-0.944728\pi$
$29$		−	1.86081i		−	0.345544i	0.984962	−	0.172772i	$-0.0552724\pi$
$30$		0			0
$31$			0.941102i			0.169027i	0.996422	+	0.0845134i	$0.0269336\pi$
$31$			0.941102i			0.169027i	−0.996422	+	0.0845134i	$0.973066\pi$
$32$	−5.18948	−	2.25152i	−0.917378	−	0.398016i
$33$		0			0
$34$	−5.18413	−	2.16759i	−0.889071	−	0.371739i
$35$		0			0
$36$		0			0
$37$	−7.49992			−1.23298			−0.616490	−	0.787363i	$-0.711446\pi$
$37$	−7.49992			−1.23298			−0.616490	+	0.787363i	$0.711446\pi$
$38$	9.20919	+	3.85056i	1.49393	+	0.624643i
$39$		0			0
$40$	0.737500	+	1.83205i	0.116609	+	0.289673i
$41$			10.6065i			1.65646i	0.560392	+	0.828228i	$0.310651\pi$
$41$			10.6065i			1.65646i	−0.560392	+	0.828228i	$0.689349\pi$
$42$		0			0
$43$		−	3.97212i		−	0.605743i	−0.953031	−	0.302871i	$-0.902055\pi$
$43$		−	3.97212i		−	0.605743i	0.953031	−	0.302871i	$-0.0979452\pi$
$44$	3.58493	+	3.63301i	0.540448	+	0.547697i
$45$		0			0
$46$	−2.19667	+	5.25366i	−0.323881	+	0.774610i
$47$	8.90438			1.29884			0.649418	−	0.760431i	$-0.275012\pi$
$47$	8.90438			1.29884			0.649418	+	0.760431i	$0.275012\pi$
$48$		0			0
$49$		0			0
$50$	−2.46175	+	5.88765i	−0.348144	+	0.832639i
$51$		0			0
$52$	−2.64218	−	2.67762i	−0.366405	−	0.371319i
$53$			0.529774i			0.0727701i	0.999338	+	0.0363850i	$0.0115843\pi$
$53$			0.529774i			0.0727701i	−0.999338	+	0.0363850i	$0.988416\pi$
$54$		0			0
$55$		−	1.78190i		−	0.240271i
$56$		0			0
$57$		0			0
$58$	2.42790	+	1.01516i	0.318799	+	0.133297i
$59$	13.3007			1.73161			0.865804	−	0.500383i	$-0.166807\pi$
$59$	13.3007			1.73161			0.865804	+	0.500383i	$0.166807\pi$
$60$		0			0
$61$	10.3683			1.32752			0.663760	−	0.747946i	$-0.268960\pi$
$61$	10.3683			1.32752			0.663760	+	0.747946i	$0.268960\pi$
$62$	−1.22791	−	0.513413i	−0.155944	−	0.0652036i
$63$		0			0
$64$	5.76877	−	5.54268i	0.721096	−	0.692835i
$65$			1.31330i			0.162895i
$66$		0			0
$67$		−	2.72300i		−	0.332667i	−0.986070	−	0.166334i	$-0.946807\pi$
$67$		−	2.72300i		−	0.332667i	0.986070	−	0.166334i	$-0.0531929\pi$
$68$	5.65635	−	5.58149i	0.685933	−	0.676855i
$69$		0			0
$70$		0			0
$71$	−3.51310			−0.416928			−0.208464	−	0.978030i	$-0.566846\pi$
$71$	−3.51310			−0.416928			−0.208464	+	0.978030i	$0.566846\pi$
$72$		0			0
$73$	−2.75071			−0.321946			−0.160973	−	0.986959i	$-0.551463\pi$
$73$	−2.75071			−0.321946			−0.160973	+	0.986959i	$0.551463\pi$
$74$	4.09155	−	9.78555i	0.475632	−	1.13755i
$75$		0			0
$76$	−10.0481	+	9.91507i	−1.15259	+	1.13734i
$77$		0			0
$78$		0			0
$79$			13.5338i			1.52267i	0.648358	+	0.761335i	$0.275456\pi$
$79$			13.5338i			1.52267i	−0.648358	+	0.761335i	$0.724544\pi$
$80$	−2.79271	−	0.0372106i	−0.312235	−	0.00416027i
$81$		0			0
$82$	−13.8389	−	5.78632i	−1.52825	−	0.638992i
$83$	17.1516			1.88264			0.941319	−	0.337520i	$-0.109588\pi$
$83$	17.1516			1.88264			0.941319	+	0.337520i	$0.109588\pi$
$84$		0			0
$85$	−2.77429			−0.300914
$86$	5.18264	+	2.16697i	0.558858	+	0.233670i
$87$		0			0
$88$	−6.69592	+	2.69547i	−0.713788	+	0.287338i
$89$			11.8700i			1.25821i	0.777319	+	0.629107i	$0.216579\pi$
$89$			11.8700i			1.25821i	−0.777319	+	0.629107i	$0.783421\pi$
$90$		0			0
$91$		0			0
$92$	−5.65635	−	5.73222i	−0.589715	−	0.597625i
$93$		0			0
$94$	−4.85774	+	11.6180i	−0.501038	+	1.19831i
$95$	4.92831			0.505634
$96$		0			0
$97$	10.8682			1.10350			0.551748	−	0.834011i	$-0.313961\pi$
$97$	10.8682			1.10350			0.551748	+	0.834011i	$0.313961\pi$
$98$		0			0
$99$		0			0
$100$	−6.33893	−	6.42395i	−0.633893	−	0.642395i
$101$			10.6065i			1.05539i	0.849435	+	0.527693i	$0.176943\pi$
$101$			10.6065i			1.05539i	−0.849435	+	0.527693i	$0.823057\pi$
$102$		0			0
$103$			13.2756i			1.30808i	0.756459	+	0.654041i	$0.226928\pi$
$103$			13.2756i			1.30808i	−0.756459	+	0.654041i	$0.773072\pi$
$104$	4.93507	−	1.98663i	0.483923	−	0.194805i
$105$		0			0
$106$	−0.691224	−	0.289016i	−0.0671377	−	0.0280717i
$107$	−9.61198			−0.929225			−0.464613	−	0.885514i	$-0.653806\pi$
$107$	−9.61198			−0.929225			−0.464613	+	0.885514i	$0.653806\pi$
$108$		0			0
$109$	14.2241			1.36242			0.681209	−	0.732089i	$-0.261455\pi$
$109$	14.2241			1.36242			0.681209	+	0.732089i	$0.261455\pi$
$110$	2.32494	+	0.972105i	0.221674	+	0.0926866i
$111$		0			0
$112$		0			0
$113$		−	12.1039i		−	1.13864i	−0.822117	−	0.569319i	$-0.807207\pi$
$113$		−	12.1039i		−	1.13864i	0.822117	−	0.569319i	$-0.192793\pi$
$114$		0			0
$115$			2.81150i			0.262174i
$116$	−2.64906	+	2.61400i	−0.245959	+	0.242703i
$117$		0			0
$118$	−7.25615	+	17.3542i	−0.667983	+	1.59758i
$119$		0			0
$120$		0			0
$121$	−4.48738			−0.407944
$122$	−5.65635	+	13.5280i	−0.512102	+	1.22477i
$123$		0			0
$124$	1.33976	−	1.32202i	0.120314	−	0.118721i
$125$			6.64198i			0.594077i
$126$		0			0
$127$			0.582584i			0.0516960i	0.999666	+	0.0258480i	$0.00822859\pi$
$127$			0.582584i			0.0516960i	−0.999666	+	0.0258480i	$0.991771\pi$
$128$	4.08470	+	10.5506i	0.361040	+	0.932550i
$129$		0			0
$130$	−1.71354	−	0.716466i	−0.150287	−	0.0628382i
$131$	−10.8924			−0.951674			−0.475837	−	0.879533i	$-0.657855\pi$
$131$	−10.8924			−0.951674			−0.475837	+	0.879533i	$0.657855\pi$
$132$		0			0
$133$		0			0
$134$	3.55284	+	1.48552i	0.306919	+	0.128329i
$135$		0			0
$136$	4.19667	+	10.4251i	0.359861	+	0.893945i
$137$			13.3019i			1.13646i	0.822870	+	0.568230i	$0.192372\pi$
$137$			13.3019i			1.13646i	−0.822870	+	0.568230i	$0.807628\pi$
$138$		0			0
$139$		−	0.840795i		−	0.0713153i	−0.999364	−	0.0356577i	$-0.988647\pi$
$139$		−	0.840795i		−	0.0713153i	0.999364	−	0.0356577i	$-0.0113526\pi$
$140$		0			0
$141$		0			0
$142$	1.91655	−	4.58373i	0.160834	−	0.384658i
$143$	−4.79997			−0.401393
$144$		0			0
$145$	1.29929			0.107900
$146$	1.50063	−	3.58899i	0.124193	−	0.297027i
$147$		0			0
$148$	10.5356	+	10.6769i	0.866021	+	0.877637i
$149$			5.65685i			0.463428i	0.972784	+	0.231714i	$0.0744333\pi$
$149$			5.65685i			0.463428i	−0.972784	+	0.231714i	$0.925567\pi$
$150$		0			0
$151$		−	16.9829i		−	1.38205i	−0.722830	−	0.691026i	$-0.757159\pi$
$151$		−	16.9829i		−	1.38205i	0.722830	−	0.691026i	$-0.242841\pi$
$152$	−7.45505	−	18.5194i	−0.604684	−	1.50212i
$153$		0			0
$154$		0			0
$155$	−0.657115			−0.0527807
$156$		0			0
$157$	−1.97492			−0.157616			−0.0788079	−	0.996890i	$-0.525111\pi$
$157$	−1.97492			−0.157616			−0.0788079	+	0.996890i	$0.525111\pi$
$158$	−17.6583	−	7.38329i	−1.40482	−	0.587383i
$159$		0			0
$160$	1.57210	−	3.62350i	0.124286	−	0.286463i
$161$		0			0
$162$		0			0
$163$		−	2.81150i		−	0.220214i	−0.993920	−	0.110107i	$-0.964881\pi$
$163$		−	2.81150i		−	0.220214i	0.993920	−	0.110107i	$-0.0351194\pi$
$164$	15.0994	−	14.8996i	1.17907	−	1.16346i
$165$		0			0
$166$	−9.35699	+	22.3787i	−0.726243	+	1.73692i
$167$	−2.40833			−0.186362			−0.0931810	−	0.995649i	$-0.529704\pi$
$167$	−2.40833			−0.186362			−0.0931810	+	0.995649i	$0.529704\pi$
$168$		0			0
$169$	−9.46230			−0.727869
$170$	1.51350	−	3.61977i	0.116080	−	0.277623i
$171$		0			0
$172$	−5.65472	+	5.57988i	−0.431169	+	0.425462i
$173$			4.68026i			0.355834i	0.984046	+	0.177917i	$0.0569358\pi$
$173$			4.68026i			0.355834i	−0.984046	+	0.177917i	$0.943064\pi$
$174$		0			0
$175$		0			0
$176$	0.136000	−	10.2070i	0.0102514	−	0.769384i
$177$		0			0
$178$	−15.4874	−	6.47560i	−1.16083	−	0.485367i
$179$	13.1909			0.985933			0.492966	−	0.870048i	$-0.335913\pi$
$179$	13.1909			0.985933			0.492966	+	0.870048i	$0.335913\pi$
$180$		0			0
$181$	17.6801			1.31415			0.657075	−	0.753825i	$-0.271793\pi$
$181$	17.6801			1.31415			0.657075	+	0.753825i	$0.271793\pi$
$182$		0			0
$183$		0			0
$184$	10.5649	−	4.25296i	0.778857	−	0.313532i
$185$		−	5.23675i		−	0.385013i
$186$		0			0
$187$		−	10.1397i		−	0.741489i
$188$	−12.5085	−	12.6763i	−0.912278	−	0.924514i
$189$		0			0
$190$	−2.68862	+	6.43023i	−0.195053	+	0.466498i
$191$	21.2440			1.53716			0.768581	−	0.639753i	$-0.220963\pi$
$191$	21.2440			1.53716			0.768581	+	0.639753i	$0.220963\pi$
$192$		0			0
$193$	4.16763			0.299993			0.149996	−	0.988687i	$-0.452074\pi$
$193$	4.16763			0.299993			0.149996	+	0.988687i	$0.452074\pi$
$194$	−5.92908	+	14.1803i	−0.425683	+	1.01809i
$195$		0			0
$196$		0			0
$197$			8.04744i			0.573356i	0.958027	+	0.286678i	$0.0925510\pi$
$197$			8.04744i			0.573356i	−0.958027	+	0.286678i	$0.907449\pi$
$198$		0			0
$199$			1.52369i			0.108011i	0.998541	+	0.0540056i	$0.0171989\pi$
$199$			1.52369i			0.108011i	−0.998541	+	0.0540056i	$0.982801\pi$
$200$	11.8398	−	4.76618i	0.837203	−	0.337020i
$201$		0			0
$202$	−13.8389	−	5.78632i	−0.973698	−	0.407124i
$203$		0			0
$204$		0			0
$205$	−7.40588			−0.517249
$206$	−17.3214	−	7.24243i	−1.20684	−	0.504604i
$207$		0			0
$208$	−0.100236	+	7.52284i	−0.00695009	+	0.521615i
$209$			18.0124i			1.24594i
$210$		0			0
$211$			19.2878i			1.32783i	0.747809	+	0.663914i	$0.231106\pi$
$211$			19.2878i			1.32783i	−0.747809	+	0.663914i	$0.768894\pi$
$212$	0.754188	−	0.744206i	0.0517979	−	0.0511123i
$213$		0			0
$214$	5.24377	−	12.5413i	0.358457	−	0.857303i
$215$	2.77349			0.189151
$216$		0			0
$217$		0			0
$218$	−7.75986	+	18.5589i	−0.525564	+	1.25697i
$219$		0			0
$220$	−2.53671	+	2.50314i	−0.171025	+	0.168762i
$221$			7.47322i			0.502703i
$222$		0			0
$223$		−	18.1390i		−	1.21468i	−0.794443	−	0.607338i	$-0.792237\pi$
$223$		−	18.1390i		−	1.21468i	0.794443	−	0.607338i	$-0.207763\pi$
$224$		0			0
$225$		0			0
$226$	15.7926	+	6.60321i	1.05051	+	0.439239i
$227$	−9.57818			−0.635726			−0.317863	−	0.948137i	$-0.602965\pi$
$227$	−9.57818			−0.635726			−0.317863	+	0.948137i	$0.602965\pi$
$228$		0			0
$229$	4.84326			0.320052			0.160026	−	0.987113i	$-0.448842\pi$
$229$	4.84326			0.320052			0.160026	+	0.987113i	$0.448842\pi$
$230$	−3.66832	−	1.53380i	−0.241882	−	0.101136i
$231$		0			0
$232$	−1.96544	−	4.88242i	−0.129037	−	0.320546i
$233$		−	21.6331i		−	1.41723i	−0.705595	−	0.708615i	$-0.749320\pi$
$233$		−	21.6331i		−	1.41723i	0.705595	−	0.708615i	$-0.250680\pi$
$234$		0			0
$235$			6.21739i			0.405578i
$236$	−18.6844	−	18.9350i	−1.21625	−	1.23256i
$237$		0			0
$238$		0			0
$239$	−20.5549			−1.32958			−0.664792	−	0.747028i	$-0.731480\pi$
$239$	−20.5549			−1.32958			−0.664792	+	0.747028i	$0.731480\pi$
$240$		0			0
$241$	10.7506			0.692504			0.346252	−	0.938142i	$-0.387454\pi$
$241$	10.7506			0.692504			0.346252	+	0.938142i	$0.387454\pi$
$242$	2.44807	−	5.85493i	0.157368	−	0.376369i
$243$		0			0
$244$	−14.5649	−	14.7603i	−0.932424	−	0.944930i
$245$		0			0
$246$		0			0
$247$		−	13.2756i		−	0.844705i
$248$	0.994017	+	2.46927i	0.0631201	+	0.156799i
$249$		0			0
$250$	−8.66615	−	3.62350i	−0.548095	−	0.229170i
$251$	−19.4316			−1.22651			−0.613257	−	0.789884i	$-0.710141\pi$
$251$	−19.4316			−1.22651			−0.613257	+	0.789884i	$0.710141\pi$
$252$		0			0
$253$	−10.2757			−0.646028
$254$	−0.760128	−	0.317826i	−0.0476947	−	0.0199422i
$255$		0			0
$256$	−15.9943	−	0.426298i	−0.999645	−	0.0266436i
$257$		−	8.73670i		−	0.544980i	−0.962159	−	0.272490i	$-0.912153\pi$
$257$		−	8.73670i		−	0.544980i	0.962159	−	0.272490i	$-0.0878472\pi$
$258$		0			0
$259$		0			0
$260$	1.86962	−	1.84488i	0.115949	−	0.114414i
$261$		0			0
$262$	5.94230	−	14.2119i	0.367117	−	0.878015i
$263$	−21.8079			−1.34474			−0.672368	−	0.740217i	$-0.734723\pi$
$263$	−21.8079			−1.34474			−0.672368	+	0.740217i	$0.734723\pi$
$264$		0			0
$265$	−0.369910			−0.0227234
$266$		0			0
$267$		0			0
$268$	−3.87647	+	3.82516i	−0.236793	+	0.233659i
$269$		−	14.7040i		−	0.896519i	−0.893904	−	0.448259i	$-0.852044\pi$
$269$		−	14.7040i		−	0.896519i	0.893904	−	0.448259i	$-0.147956\pi$
$270$		0			0
$271$		−	5.18779i		−	0.315136i	−0.987508	−	0.157568i	$-0.949635\pi$
$271$		−	5.18779i		−	0.315136i	0.987508	−	0.157568i	$-0.0503653\pi$
$272$	−15.8916	−	0.211743i	−0.963573	−	0.0128388i
$273$		0			0
$274$	−17.3557	−	7.25680i	−1.04850	−	0.438399i
$275$	−11.5157			−0.694424
$276$		0			0
$277$	23.7255			1.42553			0.712763	−	0.701405i	$-0.247444\pi$
$277$	23.7255			1.42553			0.712763	+	0.701405i	$0.247444\pi$
$278$	1.09703	+	0.458692i	0.0657955	+	0.0275105i
$279$		0			0
$280$		0			0
$281$		−	4.12400i		−	0.246017i	−0.992406	−	0.123009i	$-0.960746\pi$
$281$		−	4.12400i		−	0.246017i	0.992406	−	0.123009i	$-0.0392542\pi$
$282$		0			0
$283$			7.05819i			0.419566i	0.977748	+	0.209783i	$0.0672757\pi$
$283$			7.05819i			0.419566i	−0.977748	+	0.209783i	$0.932724\pi$
$284$	4.93507	+	5.00126i	0.292842	+	0.296770i
$285$		0			0
$286$	2.61860	−	6.26277i	0.154841	−	0.370325i
$287$		0			0
$288$		0			0
$289$	1.21317			0.0713628
$290$	−0.708823	+	1.69526i	−0.0416235	+	0.0995489i
$291$		0			0
$292$	3.86409	+	3.91592i	0.226129	+	0.229162i
$293$		−	15.9675i		−	0.932830i	−0.884566	−	0.466415i	$-0.845545\pi$
$293$		−	15.9675i		−	0.932830i	0.884566	−	0.466415i	$-0.154455\pi$
$294$		0			0
$295$			9.28711i			0.540716i
$296$	−19.6784	+	7.92162i	−1.14378	+	0.460435i
$297$		0			0
$298$	−7.38080	−	3.08607i	−0.427558	−	0.178771i
$299$	7.57346			0.437984
$300$		0			0
$301$		0			0
$302$	22.1585	+	9.26495i	1.27508	+	0.533138i
$303$		0			0
$304$	28.2302	+	0.376145i	1.61912	+	0.0215734i
$305$			7.23953i			0.414534i
$306$		0			0
$307$			5.53450i			0.315871i	0.987449	+	0.157935i	$0.0504838\pi$
$307$			5.53450i			0.315871i	−0.987449	+	0.157935i	$0.949516\pi$
$308$		0			0
$309$		0			0
$310$	0.358486	−	0.857373i	0.0203606	−	0.0486955i
$311$	−10.4888			−0.594766			−0.297383	−	0.954758i	$-0.596114\pi$
$311$	−10.4888			−0.594766			−0.297383	+	0.954758i	$0.596114\pi$
$312$		0			0
$313$	2.26317			0.127922			0.0639609	−	0.997952i	$-0.479627\pi$
$313$	2.26317			0.127922			0.0639609	+	0.997952i	$0.479627\pi$
$314$	1.07741	−	2.57678i	0.0608017	−	0.145416i
$315$		0			0
$316$	19.2668	−	19.0117i	1.08384	−	1.06949i
$317$		−	9.50588i		−	0.533903i	−0.963710	−	0.266952i	$-0.913984\pi$
$317$		−	9.50588i		−	0.533903i	0.963710	−	0.266952i	$-0.0860164\pi$
$318$		0			0
$319$			4.74876i			0.265879i
$320$	3.87012	+	4.02799i	0.216346	+	0.225171i
$321$		0			0
$322$		0			0
$323$	28.0441			1.56041
$324$		0			0
$325$	8.48738			0.470795
$326$	3.66832	+	1.53380i	0.203169	+	0.0849494i
$327$		0			0
$328$	11.2029	+	27.8294i	0.618574	+	1.53662i
$329$		0			0
$330$		0			0
$331$		−	9.94110i		−	0.546412i	−0.961956	−	0.273206i	$-0.911916\pi$
$331$		−	9.94110i		−	0.546412i	0.961956	−	0.273206i	$-0.0880841\pi$
$332$	−24.0940	−	24.4171i	−1.32233	−	1.34006i
$333$		0			0
$334$	1.31385	−	3.14227i	0.0718907	−	0.171937i
$335$	1.90131			0.103879
$336$		0			0
$337$	10.6441			0.579822			0.289911	−	0.957054i	$-0.406374\pi$
$337$	10.6441			0.579822			0.289911	+	0.957054i	$0.406374\pi$
$338$	5.16211	−	12.3460i	0.280782	−	0.671532i
$339$		0			0
$340$	3.89722	+	3.94949i	0.211356	+	0.214191i
$341$		−	2.40168i		−	0.130058i
$342$		0			0
$343$		0			0
$344$	−4.19546	−	10.4221i	−0.226204	−	0.561922i
$345$		0			0
$346$	−6.10658	−	2.55329i	−0.328292	−	0.137266i
$347$	17.5488			0.942069			0.471035	−	0.882115i	$-0.343881\pi$
$347$	17.5488			0.942069			0.471035	+	0.882115i	$0.343881\pi$
$348$		0			0
$349$	29.0703			1.55610			0.778049	−	0.628204i	$-0.216210\pi$
$349$	29.0703			1.55610			0.778049	+	0.628204i	$0.216210\pi$
$350$		0			0
$351$		0			0
$352$	13.2435	+	5.74584i	0.705879	+	0.306254i
$353$			11.2462i			0.598572i	0.954163	+	0.299286i	$0.0967485\pi$
$353$			11.2462i			0.598572i	−0.954163	+	0.299286i	$0.903251\pi$
$354$		0			0
$355$		−	2.45299i		−	0.130191i
$356$	16.8981	−	16.6745i	0.895599	−	0.883745i
$357$		0			0
$358$	−7.19622	+	17.2108i	−0.380332	+	0.909621i
$359$	−29.0436			−1.53286			−0.766431	−	0.642326i	$-0.777969\pi$
$359$	−29.0436			−1.53286			−0.766431	+	0.642326i	$0.777969\pi$
$360$		0			0
$361$	−30.8180			−1.62200
$362$	−9.64529	+	23.0682i	−0.506945	+	1.21244i
$363$		0			0
$364$		0			0
$365$		−	1.92065i		−	0.100532i
$366$		0			0
$367$		−	24.0864i		−	1.25730i	−0.777689	−	0.628649i	$-0.783608\pi$
$367$		−	24.0864i		−	1.25730i	0.777689	−	0.628649i	$-0.216392\pi$
$368$	−0.214583	+	16.1048i	−0.0111859	+	0.839521i
$369$		0			0
$370$	6.83266	+	2.85688i	0.355213	+	0.148522i
$371$		0			0
$372$		0			0
$373$	13.3947			0.693550			0.346775	−	0.937948i	$-0.387277\pi$
$373$	13.3947			0.693550			0.346775	+	0.937948i	$0.387277\pi$
$374$	13.2298	+	5.53167i	0.684097	+	0.286036i
$375$		0			0
$376$	23.3634	−	9.40504i	1.20488	−	0.485028i
$377$		−	3.49996i		−	0.180257i
$378$		0			0
$379$		−	12.9558i		−	0.665493i	−0.943016	−	0.332746i	$-0.892025\pi$
$379$		−	12.9558i		−	0.665493i	0.943016	−	0.332746i	$-0.107975\pi$
$380$	−6.92310	−	7.01596i	−0.355147	−	0.359911i
$381$		0			0
$382$	−11.5896	+	27.7182i	−0.592973	+	1.41819i
$383$	2.53349			0.129455			0.0647277	−	0.997903i	$-0.479382\pi$
$383$	2.53349			0.129455			0.0647277	+	0.997903i	$0.479382\pi$
$384$		0			0
$385$		0			0
$386$	−2.27363	+	5.43773i	−0.115725	+	0.276773i
$387$		0			0
$388$	−15.2672	−	15.4720i	−0.775075	−	0.785471i
$389$		−	15.3047i		−	0.775979i	−0.921664	−	0.387990i	$-0.873170\pi$
$389$		−	15.3047i		−	0.775979i	0.921664	−	0.387990i	$-0.126830\pi$
$390$		0			0
$391$			15.9986i			0.809083i
$392$		0			0
$393$		0			0
$394$	−10.4999	−	4.39024i	−0.528978	−	0.221177i
$395$	−9.44984			−0.475473
$396$		0			0
$397$	13.1066			0.657801			0.328900	−	0.944365i	$-0.393322\pi$
$397$	13.1066			0.657801			0.328900	+	0.944365i	$0.393322\pi$
$398$	−1.98803	−	0.831239i	−0.0996511	−	0.0416663i
$399$		0			0
$400$	−0.240478	+	18.0482i	−0.0120239	+	0.902412i
$401$			1.16046i			0.0579505i	0.999580	+	0.0289753i	$0.00922440\pi$
$401$			1.16046i			0.0579505i	−0.999580	+	0.0289753i	$0.990776\pi$
$402$		0			0
$403$			1.77010i			0.0881748i
$404$	15.0994	−	14.8996i	0.751225	−	0.741282i
$405$		0			0
$406$		0			0
$407$	19.1397			0.948718
$408$		0			0
$409$	7.18809			0.355428			0.177714	−	0.984082i	$-0.443130\pi$
$409$	7.18809			0.355428			0.177714	+	0.984082i	$0.443130\pi$
$410$	4.04024	−	9.66284i	0.199533	−	0.477214i
$411$		0			0
$412$	18.8992	−	18.6490i	0.931095	−	0.918771i
$413$		0			0
$414$		0			0
$415$			11.9760i			0.587877i
$416$	−9.76076	−	4.23483i	−0.478561	−	0.207630i
$417$		0			0
$418$	−23.5017	−	9.82656i	−1.14951	−	0.480633i
$419$	16.1127			0.787155			0.393578	−	0.919291i	$-0.371237\pi$
$419$	16.1127			0.787155			0.393578	+	0.919291i	$0.371237\pi$
$420$		0			0
$421$	5.49992			0.268050			0.134025	−	0.990978i	$-0.457210\pi$
$421$	5.49992			0.268050			0.134025	+	0.990978i	$0.457210\pi$
$422$	−25.1658	−	10.5224i	−1.22505	−	0.512221i
$423$		0			0
$424$	0.559562	+	1.39003i	0.0271747	+	0.0675057i
$425$			17.9292i			0.869694i
$426$		0			0
$427$		0			0
$428$	13.5025	+	13.6836i	0.652670	+	0.661424i
$429$		0			0
$430$	−1.51307	+	3.61872i	−0.0729665	+	0.174510i
$431$	13.4106			0.645965			0.322983	−	0.946405i	$-0.395314\pi$
$431$	13.4106			0.645965			0.322983	+	0.946405i	$0.395314\pi$
$432$		0			0
$433$	−31.6801			−1.52245			−0.761224	−	0.648489i	$-0.775401\pi$
$433$	−31.6801			−1.52245			−0.761224	+	0.648489i	$0.775401\pi$
$434$		0			0
$435$		0			0
$436$	−19.9814	−	20.2494i	−0.956936	−	0.969771i
$437$		−	28.4202i		−	1.35952i
$438$		0			0
$439$		−	19.4812i		−	0.929786i	−0.885367	−	0.464893i	$-0.846093\pi$
$439$		−	19.4812i		−	0.929786i	0.885367	−	0.464893i	$-0.153907\pi$
$440$	−1.88209	−	4.67536i	−0.0897250	−	0.222889i
$441$		0			0
$442$	−9.75071	−	4.07698i	−0.463794	−	0.193922i
$443$	−6.88254			−0.326999			−0.163500	−	0.986543i	$-0.552278\pi$
$443$	−6.88254			−0.326999			−0.163500	+	0.986543i	$0.552278\pi$
$444$		0			0
$445$	−8.28809			−0.392893
$446$	23.6669	+	9.89564i	1.12066	+	0.468572i
$447$		0			0
$448$		0			0
$449$			19.3255i			0.912025i	0.889973	+	0.456012i	$0.150723\pi$
$449$			19.3255i			0.912025i	−0.889973	+	0.456012i	$0.849277\pi$
$450$		0			0
$451$		−	27.0676i		−	1.27456i
$452$	−17.2311	+	17.0031i	−0.810484	+	0.799757i
$453$		0			0
$454$	5.22533	−	12.4972i	0.245237	−	0.586521i
$455$		0			0
$456$		0			0
$457$	4.83699			0.226265			0.113132	−	0.993580i	$-0.463912\pi$
$457$	4.83699			0.226265			0.113132	+	0.993580i	$0.463912\pi$
$458$	−2.64222	+	6.31926i	−0.123463	+	0.295279i
$459$		0			0
$460$	4.00247	−	3.94949i	0.186616	−	0.184146i
$461$		−	26.3490i		−	1.22720i	−0.789618	−	0.613599i	$-0.789721\pi$
$461$		−	26.3490i		−	1.22720i	0.789618	−	0.613599i	$-0.210279\pi$
$462$		0			0
$463$		−	38.1024i		−	1.77077i	−0.464858	−	0.885385i	$-0.653895\pi$
$463$		−	38.1024i		−	1.77077i	0.464858	−	0.885385i	$-0.346105\pi$
$464$	7.44258	+	0.0991663i	0.345513	+	0.00460368i
$465$		0			0
$466$	28.2258	+	11.8018i	1.30754	+	0.546709i
$467$	−6.38439			−0.295435			−0.147717	−	0.989030i	$-0.547193\pi$
$467$	−6.38439			−0.295435			−0.147717	+	0.989030i	$0.547193\pi$
$468$		0			0
$469$		0			0
$470$	−8.11216	−	3.39187i	−0.374186	−	0.156455i
$471$		0			0
$472$	34.8986	−	14.0486i	1.60634	−	0.646639i
$473$			10.1368i			0.466090i
$474$		0			0
$475$		−	31.8498i		−	1.46137i
$476$		0			0
$477$		0			0
$478$	11.2136	−	26.8190i	0.512899	−	1.22667i
$479$	21.0410			0.961387			0.480693	−	0.876889i	$-0.340385\pi$
$479$	21.0410			0.961387			0.480693	+	0.876889i	$0.340385\pi$
$480$		0			0
$481$	−14.1064			−0.643198
$482$	−5.86491	+	14.0268i	−0.267139	+	0.638904i
$483$		0			0
$484$	6.30370	+	6.38825i	0.286532	+	0.290375i
$485$			7.58860i			0.344581i
$486$		0			0
$487$			15.7836i			0.715224i	0.933870	+	0.357612i	$0.116409\pi$
$487$			15.7836i			0.715224i	−0.933870	+	0.357612i	$0.883591\pi$
$488$	27.2044	−	10.9512i	1.23148	−	0.495739i
$489$		0			0
$490$		0			0
$491$	−18.8204			−0.849351			−0.424675	−	0.905346i	$-0.639612\pi$
$491$	−18.8204			−0.849351			−0.424675	+	0.905346i	$0.639612\pi$
$492$		0			0
$493$	7.39349			0.332986
$494$	17.3214	+	7.24243i	0.779325	+	0.325852i
$495$		0			0
$496$	−3.76407	−	0.0501532i	−0.169012	−	0.00225194i
$497$		0			0
$498$		0			0
$499$			8.05889i			0.360766i	0.983596	+	0.180383i	$0.0577337\pi$
$499$			8.05889i			0.360766i	−0.983596	+	0.180383i	$0.942266\pi$
$500$	9.45555	−	9.33040i	0.422865	−	0.417268i
$501$		0			0
$502$	10.6008	−	25.3535i	0.473138	−	1.13158i
$503$	−0.823898			−0.0367358			−0.0183679	−	0.999831i	$-0.505847\pi$
$503$	−0.823898			−0.0367358			−0.0183679	+	0.999831i	$0.505847\pi$
$504$		0			0
$505$	−7.40588			−0.329557
$506$	5.60586	−	13.4073i	0.249211	−	0.596025i
$507$		0			0
$508$	0.829368	−	0.818391i	0.0367973	−	0.0363102i
$509$		−	39.1011i		−	1.73313i	−0.499067	−	0.866563i	$-0.666324\pi$
$509$		−	39.1011i		−	1.73313i	0.499067	−	0.866563i	$-0.333676\pi$
$510$		0			0
$511$		0			0
$512$	9.28184	−	20.6361i	0.410203	−	0.911994i
$513$		0			0
$514$	11.3992	+	4.76626i	0.502799	+	0.210231i
$515$	−9.26954			−0.408465
$516$		0			0
$517$	−22.7238			−0.999392
$518$		0			0
$519$		0			0
$520$	1.38715	+	3.44586i	0.0608304	+	0.151111i
$521$		−	0.523131i		−	0.0229188i	−0.999934	−	0.0114594i	$-0.996352\pi$
$521$		−	0.523131i		−	0.0229188i	0.999934	−	0.0114594i	$-0.00364772\pi$
$522$		0			0
$523$			37.5317i			1.64115i	0.571542	+	0.820573i	$0.306345\pi$
$523$			37.5317i			1.64115i	−0.571542	+	0.820573i	$0.693655\pi$
$524$	15.3012	+	15.5065i	0.668438	+	0.677403i
$525$		0			0
$526$	11.8972	−	28.4540i	0.518743	−	1.24065i
$527$	−3.73925			−0.162884
$528$		0			0
$529$	−6.78683			−0.295080
$530$	0.201802	−	0.482641i	0.00876573	−	0.0209646i
$531$		0			0
$532$		0			0
$533$			19.9495i			0.864109i
$534$		0			0
$535$		−	6.71147i		−	0.290162i
$536$	−2.87610	−	7.14463i	−0.124229	−	0.308601i
$537$		0			0
$538$	19.1851	+	8.02169i	0.827128	+	0.345840i
$539$		0			0
$540$		0			0
$541$	22.3541			0.961076			0.480538	−	0.876974i	$-0.340441\pi$
$541$	22.3541			0.961076			0.480538	+	0.876974i	$0.340441\pi$
$542$	6.76878	+	2.83017i	0.290744	+	0.121566i
$543$		0			0
$544$	8.94588	−	20.6192i	0.383552	−	0.884039i
$545$			9.93181i			0.425432i
$546$		0			0
$547$			8.09960i			0.346314i	0.984894	+	0.173157i	$0.0553968\pi$
$547$			8.09960i			0.346314i	−0.984894	+	0.173157i	$0.944603\pi$
$548$	18.9367	−	18.6860i	0.808934	−	0.798227i
$549$		0			0
$550$	6.28235	−	15.0252i	0.267880	−	0.640676i
$551$	−13.1340			−0.559525
$552$		0			0
$553$		0			0
$554$	−12.9433	+	30.9559i	−0.549909	+	1.31519i
$555$		0			0
$556$	−1.19696	+	1.18112i	−0.0507624	+	0.0500905i
$557$		−	31.5924i		−	1.33861i	−0.742986	−	0.669307i	$-0.766591\pi$
$557$		−	31.5924i		−	1.33861i	0.742986	−	0.669307i	$-0.233409\pi$
$558$		0			0
$559$		−	7.47107i		−	0.315992i
$560$		0			0
$561$		0			0
$562$	5.38080	+	2.24983i	0.226975	+	0.0949032i
$563$	−8.35892			−0.352286			−0.176143	−	0.984365i	$-0.556362\pi$
$563$	−8.35892			−0.352286			−0.176143	+	0.984365i	$0.556362\pi$
$564$		0			0
$565$	8.45141			0.355554
$566$	−9.20919	−	3.85056i	−0.387091	−	0.161851i
$567$		0			0
$568$	−9.21771	+	3.71063i	−0.386766	+	0.155695i
$569$		−	13.0294i		−	0.546220i	−0.961983	−	0.273110i	$-0.911948\pi$
$569$		−	13.0294i		−	0.546220i	0.961983	−	0.273110i	$-0.0880524\pi$
$570$		0			0
$571$			14.3864i			0.602052i	0.953616	+	0.301026i	$0.0973290\pi$
$571$			14.3864i			0.602052i	−0.953616	+	0.301026i	$0.902671\pi$
$572$	6.74281	+	6.83325i	0.281931	+	0.285712i
$573$		0			0
$574$		0			0
$575$	18.1697			0.757728
$576$		0			0
$577$	−25.7616			−1.07247			−0.536235	−	0.844069i	$-0.680154\pi$
$577$	−25.7616			−1.07247			−0.536235	+	0.844069i	$0.680154\pi$
$578$	−0.661838	+	1.58288i	−0.0275288	+	0.0658393i
$579$		0			0
$580$	−1.82520	−	1.84968i	−0.0757871	−	0.0768037i
$581$		0			0
$582$		0			0
$583$		−	1.35197i		−	0.0559931i
$584$	−7.21734	+	2.90537i	−0.298656	+	0.120225i
$585$		0			0
$586$	20.8336	+	8.71098i	0.860629	+	0.359847i
$587$	−33.3927			−1.37826			−0.689131	−	0.724637i	$-0.742008\pi$
$587$	−33.3927			−1.37826			−0.689131	+	0.724637i	$0.742008\pi$
$588$		0			0
$589$	6.64247			0.273698
$590$	−12.1174	−	5.06654i	−0.498865	−	0.208586i
$591$		0			0
$592$	0.399686	−	29.9970i	0.0164270	−	1.23287i
$593$			29.5496i			1.21346i	0.794909	+	0.606729i	$0.207519\pi$
$593$			29.5496i			1.21346i	−0.794909	+	0.606729i	$0.792481\pi$
$594$		0			0
$595$		0			0
$596$	8.05312	−	7.94653i	0.329868	−	0.325503i
$597$		0			0
$598$	−4.13166	+	9.88149i	−0.168956	+	0.404084i
$599$	−5.99928			−0.245124			−0.122562	−	0.992461i	$-0.539111\pi$
$599$	−5.99928			−0.245124			−0.122562	+	0.992461i	$0.539111\pi$
$600$		0			0
$601$	−5.44843			−0.222246			−0.111123	−	0.993807i	$-0.535445\pi$
$601$	−5.44843			−0.222246			−0.111123	+	0.993807i	$0.535445\pi$
$602$		0			0
$603$		0			0
$604$	−24.1770	+	23.8570i	−0.983746	+	0.970726i
$605$		−	3.13327i		−	0.127386i
$606$		0			0
$607$		−	4.34699i		−	0.176439i	−0.996101	−	0.0882195i	$-0.971882\pi$
$607$		−	4.34699i		−	0.176439i	0.996101	−	0.0882195i	$-0.0281177\pi$
$608$	−15.8916	+	36.6283i	−0.644491	+	1.48547i
$609$		0			0
$610$	−9.44580	−	3.94949i	−0.382449	−	0.159910i
$611$	16.7480			0.677553
$612$		0			0
$613$	−14.9621			−0.604312			−0.302156	−	0.953258i	$-0.597706\pi$
$613$	−14.9621			−0.604312			−0.302156	+	0.953258i	$0.597706\pi$
$614$	−7.22116	−	3.01932i	−0.291422	−	0.121850i
$615$		0			0
$616$		0			0
$617$		−	21.4967i		−	0.865425i	−0.901532	−	0.432713i	$-0.857557\pi$
$617$		−	21.4967i		−	0.865425i	0.901532	−	0.432713i	$-0.142443\pi$
$618$		0			0
$619$			14.3864i			0.578238i	0.957293	+	0.289119i	$0.0933623\pi$
$619$			14.3864i			0.578238i	−0.957293	+	0.289119i	$0.906638\pi$
$620$	0.923089	+	0.935471i	0.0370722	+	0.0375694i
$621$		0			0
$622$	5.72212	−	13.6853i	0.229436	−	0.548731i
$623$		0			0
$624$		0			0
$625$	17.9246			0.716984
$626$	−1.23466	+	2.95288i	−0.0493470	+	0.118021i
$627$		0			0
$628$	2.77429	+	2.81150i	0.110706	+	0.112191i
$629$		−	29.7992i		−	1.18817i
$630$		0			0
$631$			15.8983i			0.632900i	0.948609	+	0.316450i	$0.102491\pi$
$631$			15.8983i			0.632900i	−0.948609	+	0.316450i	$0.897509\pi$
$632$	14.2948	+	35.5101i	0.568615	+	1.41252i
$633$		0			0
$634$	12.4028	+	5.18588i	0.492579	+	0.205958i
$635$	−0.406784			−0.0161427
$636$		0			0
$637$		0			0
$638$	−6.19596	−	2.59066i	−0.245300	−	0.102565i
$639$		0			0
$640$	−7.36685	+	2.85210i	−0.291200	+	0.112739i
$641$		−	1.56599i		−	0.0618528i	−0.999522	−	0.0309264i	$-0.990154\pi$
$641$		−	1.56599i		−	0.0618528i	0.999522	−	0.0309264i	$-0.00984576\pi$
$642$		0			0
$643$			33.5314i			1.32235i	0.750232	+	0.661174i	$0.229942\pi$
$643$			33.5314i			1.32235i	−0.750232	+	0.661174i	$0.770058\pi$
$644$		0			0
$645$		0			0
$646$	−15.2993	+	36.5906i	−0.601943	+	1.43964i
$647$	−17.3184			−0.680857			−0.340429	−	0.940270i	$-0.610572\pi$
$647$	−17.3184			−0.680857			−0.340429	+	0.940270i	$0.610572\pi$
$648$		0			0
$649$	−33.9433			−1.33239
$650$	−4.63025	+	11.0739i	−0.181613	+	0.434356i
$651$		0			0
$652$	−4.00247	+	3.94949i	−0.156749	+	0.154674i
$653$			27.0948i			1.06030i	0.847904	+	0.530150i	$0.177864\pi$
$653$			27.0948i			1.06030i	−0.847904	+	0.530150i	$0.822136\pi$
$654$		0			0
$655$		−	7.60552i		−	0.297172i
$656$	−42.4222	−	0.565241i	−1.65631	−	0.0220690i
$657$		0			0
$658$		0			0
$659$	−10.9749			−0.427521			−0.213761	−	0.976886i	$-0.568571\pi$
$659$	−10.9749			−0.427521			−0.213761	+	0.976886i	$0.568571\pi$
$660$		0			0
$661$	2.88072			0.112047			0.0560235	−	0.998429i	$-0.482158\pi$
$661$	2.88072			0.112047			0.0560235	+	0.998429i	$0.482158\pi$
$662$	12.9707	+	5.42332i	0.504120	+	0.210783i
$663$		0			0
$664$	45.0027	−	18.1160i	1.74644	−	0.703038i
$665$		0			0
$666$		0			0
$667$		−	7.49266i		−	0.290117i
$668$	3.38312	+	3.42850i	0.130897	+	0.132653i
$669$		0			0
$670$	−1.03725	+	2.48074i	−0.0400724	+	0.0958392i
$671$	−26.4596			−1.02146
$672$		0			0
$673$	9.09255			0.350492			0.175246	−	0.984525i	$-0.443928\pi$
$673$	9.09255			0.350492			0.175246	+	0.984525i	$0.443928\pi$
$674$	−5.80685	+	13.8880i	−0.223671	+	0.534944i
$675$		0			0
$676$	13.2923	+	13.4706i	0.511241	+	0.518099i
$677$		−	15.9675i		−	0.613680i	−0.951761	−	0.306840i	$-0.900728\pi$
$677$		−	15.9675i		−	0.613680i	0.951761	−	0.306840i	$-0.0992717\pi$
$678$		0			0
$679$		0			0
$680$	−7.27922	+	2.93028i	−0.279145	+	0.112371i
$681$		0			0
$682$	3.13359	+	1.31022i	0.119991	+	0.0501710i
$683$	−44.5539			−1.70481			−0.852404	−	0.522885i	$-0.824856\pi$
$683$	−44.5539			−1.70481			−0.852404	+	0.522885i	$0.824856\pi$
$684$		0			0
$685$	−9.28793			−0.354874
$686$		0			0
$687$		0			0
$688$	15.8871	+	0.211682i	0.605689	+	0.00807031i
$689$			0.996440i			0.0379613i
$690$		0			0
$691$		−	13.9926i		−	0.532304i	−0.963931	−	0.266152i	$-0.914248\pi$
$691$		−	13.9926i		−	0.532304i	0.963931	−	0.266152i	$-0.0857523\pi$
$692$	6.66283	−	6.57465i	0.253283	−	0.249931i
$693$		0			0
$694$	−9.57366	+	22.8969i	−0.363411	+	0.869153i
$695$	0.587077			0.0222691
$696$		0			0
$697$	−42.1424			−1.59626
$698$	−15.8592	+	37.9296i	−0.600278	+	1.43566i
$699$		0			0
$700$		0			0
$701$			14.4059i			0.544104i	0.962283	+	0.272052i	$0.0877022\pi$
$701$			14.4059i			0.544104i	−0.962283	+	0.272052i	$0.912298\pi$
$702$		0			0
$703$			52.9359i			1.99651i
$704$	−14.7218	+	14.1448i	−0.554849	+	0.533103i
$705$		0			0
$706$	−14.6735	−	6.13528i	−0.552243	−	0.230904i
$707$		0			0
$708$		0			0
$709$	−44.1878			−1.65951			−0.829753	−	0.558130i	$-0.811519\pi$
$709$	−44.1878			−1.65951			−0.829753	+	0.558130i	$0.811519\pi$
$710$	3.20054	+	1.33821i	0.120114	+	0.0502223i
$711$		0			0
$712$	12.5374	+	31.1446i	0.469858	+	1.16719i
$713$			3.78940i			0.141914i
$714$		0			0
$715$		−	3.35153i		−	0.125340i
$716$	−18.5300	−	18.7786i	−0.692500	−	0.701789i
$717$		0			0
$718$	15.8446	−	37.8947i	0.591315	−	1.41422i
$719$	12.1366			0.452619			0.226309	−	0.974055i	$-0.427334\pi$
$719$	12.1366			0.452619			0.226309	+	0.974055i	$0.427334\pi$
$720$		0			0
$721$		0			0
$722$	16.8126	−	40.2099i	0.625701	−	1.49646i
$723$		0			0
$724$	−24.8363	−	25.1694i	−0.923034	−	0.935415i
$725$		−	8.39684i		−	0.311851i
$726$		0			0
$727$			27.8081i			1.03134i	0.856786	+	0.515672i	$0.172458\pi$
$727$			27.8081i			1.03134i	−0.856786	+	0.515672i	$0.827542\pi$
$728$		0			0
$729$		0			0
$730$	2.50598	+	1.04780i	0.0927505	+	0.0387809i
$731$	15.7823			0.583729
$732$		0			0
$733$	−39.6626			−1.46497			−0.732486	−	0.680782i	$-0.761640\pi$
$733$	−39.6626			−1.46497			−0.732486	+	0.680782i	$0.761640\pi$
$734$	31.4268	+	13.1402i	1.15998	+	0.485014i
$735$		0			0
$736$	−20.8957	−	9.06587i	−0.770227	−	0.334173i
$737$			6.94905i			0.255971i
$738$		0			0
$739$		−	32.6564i		−	1.20129i	−0.799517	−	0.600643i	$-0.794911\pi$
$739$		−	32.6564i		−	1.20129i	0.799517	−	0.600643i	$-0.205089\pi$
$740$	−7.45505	+	7.35638i	−0.274053	+	0.270426i
$741$		0			0
$742$		0			0
$743$	33.8538			1.24198			0.620988	−	0.783820i	$-0.286732\pi$
$743$	33.8538			1.24198			0.620988	+	0.783820i	$0.286732\pi$
$744$		0			0
$745$	−3.94984			−0.144711
$746$	−7.30740	+	17.4767i	−0.267543	+	0.639869i
$747$		0			0
$748$	−14.4349	+	14.2439i	−0.527793	+	0.520807i
$749$		0			0
$750$		0			0
$751$		−	29.7617i		−	1.08602i	−0.839726	−	0.543010i	$-0.817285\pi$
$751$		−	29.7617i		−	1.08602i	0.839726	−	0.543010i	$-0.182715\pi$
$752$	−0.474532	+	35.6143i	−0.0173044	+	1.29872i
$753$		0			0
$754$	4.56658	+	1.90938i	0.166305	+	0.0695357i
$755$	11.8582			0.431563
$756$		0			0
$757$	21.4183			0.778460			0.389230	−	0.921141i	$-0.372741\pi$
$757$	21.4183			0.778460			0.389230	+	0.921141i	$0.372741\pi$
$758$	16.9041	+	7.06795i	0.613983	+	0.256720i
$759$		0			0
$760$	12.9310	−	5.20541i	0.469055	−	0.188820i
$761$		−	43.7901i		−	1.58739i	−0.608315	−	0.793696i	$-0.708154\pi$
$761$		−	43.7901i		−	1.58739i	0.608315	−	0.793696i	$-0.291846\pi$
$762$		0			0
$763$		0			0
$764$	−29.8427	−	30.2430i	−1.07967	−	1.09415i
$765$		0			0
$766$	−1.38213	+	3.30558i	−0.0499385	+	0.119436i
$767$	25.0170			0.903313
$768$		0			0
$769$	−53.6687			−1.93534			−0.967672	−	0.252212i	$-0.918842\pi$
$769$	−53.6687			−1.93534			−0.967672	+	0.252212i	$0.918842\pi$
$770$		0			0
$771$		0			0
$772$	−5.85452	−	5.93305i	−0.210709	−	0.213535i
$773$			43.5231i			1.56542i	0.622389	+	0.782708i	$0.286162\pi$
$773$			43.5231i			1.56542i	−0.622389	+	0.782708i	$0.713838\pi$
$774$		0			0
$775$			4.24668i			0.152545i
$776$	28.5161	−	11.4793i	1.02367	−	0.412082i
$777$		0			0
$778$	19.9689	+	8.34941i	0.715918	+	0.299341i
$779$	74.8626			2.68223
$780$		0			0
$781$	8.96537			0.320806
$782$	−20.8742	−	8.72795i	−0.746460	−	0.312111i
$783$		0			0
$784$		0			0
$785$		−	1.37897i		−	0.0492175i
$786$		0			0
$787$			11.3049i			0.402975i	0.979491	+	0.201488i	$0.0645776\pi$
$787$			11.3049i			0.402975i	−0.979491	+	0.201488i	$0.935422\pi$
$788$	11.4564	−	11.3047i	0.408116	−	0.402714i
$789$		0			0
$790$	5.15531	−	12.3297i	0.183418	−	0.438671i
$791$		0			0
$792$		0			0
$793$	19.5014			0.692516
$794$	−7.15023	+	17.1009i	−0.253752	+	0.606887i
$795$		0			0
$796$	2.16912	−	2.14041i	0.0768826	−	0.0758650i
$797$		−	52.0507i		−	1.84373i	−0.387511	−	0.921865i	$-0.626665\pi$
$797$		−	52.0507i		−	1.84373i	0.387511	−	0.921865i	$-0.373335\pi$
$798$		0			0
$799$			35.3794i			1.25163i
$800$	−23.4173	−	10.1599i	−0.827927	−	0.359206i
$801$		0			0
$802$	−1.51411	−	0.633082i	−0.0534651	−	0.0223549i
$803$	7.01976			0.247722
$804$		0			0
$805$		0			0
$806$	−2.30954	−	0.965667i	−0.0813500	−	0.0340142i
$807$		0			0
$808$	11.2029	+	27.8294i	0.394115	+	0.979036i
$809$			12.7602i			0.448626i	0.974517	+	0.224313i	$0.0720138\pi$
$809$			12.7602i			0.448626i	−0.974517	+	0.224313i	$0.927986\pi$
$810$		0			0
$811$			37.2617i			1.30843i	0.756307	+	0.654217i	$0.227002\pi$
$811$			37.2617i			1.30843i	−0.756307	+	0.654217i	$0.772998\pi$
$812$		0			0
$813$		0			0
$814$	−10.4416	+	24.9725i	−0.365976	+	0.875287i
$815$	1.96310			0.0687646
$816$		0			0
$817$	−28.0360			−0.980854
$818$	−3.92143	+	9.37868i	−0.137109	+	0.327918i
$819$		0			0
$820$	10.4035	+	10.5430i	0.363306	+	0.368179i
$821$			39.4205i			1.37579i	0.725812	+	0.687893i	$0.241464\pi$
$821$			39.4205i			1.37579i	−0.725812	+	0.687893i	$0.758536\pi$
$822$		0			0
$823$			49.8543i			1.73781i	0.494976	+	0.868907i	$0.335177\pi$
$823$			49.8543i			1.73781i	−0.494976	+	0.868907i	$0.664823\pi$
$824$	14.0220	+	34.8326i	0.488480	+	1.21345i
$825$		0			0
$826$		0			0
$827$	−48.4688			−1.68542			−0.842712	−	0.538364i	$-0.819043\pi$
$827$	−48.4688			−1.68542			−0.842712	+	0.538364i	$0.819043\pi$
$828$		0			0
$829$	−8.61739			−0.299294			−0.149647	−	0.988739i	$-0.547814\pi$
$829$	−8.61739			−0.299294			−0.149647	+	0.988739i	$0.547814\pi$
$830$	−15.6257	−	6.53343i	−0.542375	−	0.226779i
$831$		0			0
$832$	10.8503	−	10.4251i	0.376168	−	0.361425i
$833$		0			0
$834$		0			0
$835$		−	1.68159i		−	0.0581938i
$836$	25.6425	−	25.3031i	0.886864	−	0.875126i
$837$		0			0
$838$	−8.79019	+	21.0231i	−0.303652	+	0.726229i
$839$	35.7594			1.23455			0.617275	−	0.786747i	$-0.288237\pi$
$839$	35.7594			1.23455			0.617275	+	0.786747i	$0.288237\pi$
$840$		0			0
$841$	25.5374			0.880599
$842$	−3.00045	+	7.17604i	−0.103403	+	0.247303i
$843$		0			0
$844$	27.4582	−	27.0948i	0.945150	−	0.932640i
$845$		−	6.60696i		−	0.227286i
$846$		0			0
$847$		0			0
$848$	−2.11891	−	0.0282327i	−0.0727636	−	0.000969516i
$849$		0			0
$850$	−23.3932	−	9.78119i	−0.802379	−	0.335492i
$851$	−30.1989			−1.03520
$852$		0			0
$853$	−13.3666			−0.457664			−0.228832	−	0.973466i	$-0.573491\pi$
$853$	−13.3666			−0.457664			−0.228832	+	0.973466i	$0.573491\pi$
$854$		0			0
$855$		0			0
$856$	−25.2200	+	10.1524i	−0.862003	+	0.347003i
$857$		−	9.93285i		−	0.339300i	−0.985504	−	0.169650i	$-0.945736\pi$
$857$		−	9.93285i		−	0.339300i	0.985504	−	0.169650i	$-0.0542637\pi$
$858$		0			0
$859$			29.8791i			1.01946i	0.860334	+	0.509731i	$0.170255\pi$
$859$			29.8791i			1.01946i	−0.860334	+	0.509731i	$0.829745\pi$
$860$	−3.89610	−	3.94835i	−0.132856	−	0.134638i
$861$		0			0
$862$	−7.31608	+	17.4975i	−0.249187	+	0.595968i
$863$	−3.56359			−0.121306			−0.0606530	−	0.998159i	$-0.519318\pi$
$863$	−3.56359			−0.121306			−0.0606530	+	0.998159i	$0.519318\pi$
$864$		0			0
$865$	−3.26795			−0.111113
$866$	17.2829	−	41.3347i	0.587297	−	1.40461i
$867$		0			0
$868$		0			0
$869$		−	34.5380i		−	1.17162i
$870$		0			0
$871$		−	5.12162i		−	0.173540i
$872$	37.3212	−	15.0238i	1.26386	−	0.508771i
$873$		0			0
$874$	37.0813	+	15.5045i	1.25430	+	0.524448i
$875$		0			0
$876$		0			0
$877$	−8.69412			−0.293580			−0.146790	−	0.989168i	$-0.546894\pi$
$877$	−8.69412			−0.293580			−0.146790	+	0.989168i	$0.546894\pi$
$878$	25.4181	+	10.6279i	0.857820	+	0.358673i
$879$		0			0
$880$	7.12696	+	0.0949608i	0.240250	+	0.00320113i
$881$			48.2017i			1.62396i	0.583688	+	0.811978i	$0.301609\pi$
$881$			48.2017i			1.62396i	−0.583688	+	0.811978i	$0.698391\pi$
$882$		0			0
$883$		−	6.60661i		−	0.222330i	−0.993802	−	0.111165i	$-0.964542\pi$
$883$		−	6.60661i		−	0.222330i	0.993802	−	0.111165i	$-0.0354582\pi$
$884$	10.6389	−	10.4981i	0.357825	−	0.353089i
$885$		0			0
$886$	3.75474	−	8.98002i	0.126143	−	0.301690i
$887$	−48.1193			−1.61569			−0.807844	−	0.589397i	$-0.799365\pi$
$887$	−48.1193			−1.61569			−0.807844	+	0.589397i	$0.799365\pi$
$888$		0			0
$889$		0			0
$890$	4.52153	−	10.8139i	0.151562	−	0.362483i
$891$		0			0
$892$	−25.8227	+	25.4810i	−0.864609	+	0.853165i
$893$		−	62.8488i		−	2.10315i
$894$		0			0
$895$			9.21040i			0.307870i
$896$		0			0
$897$		0			0
$898$	−25.2150	−	10.5429i	−0.841434	−	0.351821i
$899$	1.75121			0.0584062
$900$		0			0
$901$	−2.10493			−0.0701255
$902$	35.3165	+	14.7666i	1.17591	+	0.491674i
$903$		0			0
$904$	−12.7844	−	31.7583i	−0.425204	−	1.05627i
$905$			12.3449i			0.410360i
$906$		0			0
$907$		−	8.03274i		−	0.266723i	−0.991067	−	0.133361i	$-0.957423\pi$
$907$		−	8.03274i		−	0.266723i	0.991067	−	0.133361i	$-0.0425771\pi$
$908$	13.4551	+	13.6355i	0.446522	+	0.452511i
$909$		0			0
$910$		0			0
$911$	−55.0200			−1.82289			−0.911446	−	0.411419i	$-0.865033\pi$
$911$	−55.0200			−1.82289			−0.911446	+	0.411419i	$0.865033\pi$
$912$		0			0
$913$	−43.7707			−1.44860
$914$	−2.63880	+	6.31108i	−0.0872836	+	0.208752i
$915$		0			0
$916$	−6.80362	−	6.89488i	−0.224798	−	0.227813i
$917$		0			0
$918$		0			0
$919$		−	17.0878i		−	0.563674i	−0.959462	−	0.281837i	$-0.909056\pi$
$919$		−	17.0878i		−	0.563674i	0.959462	−	0.281837i	$-0.0909438\pi$
$920$	2.96959	+	7.37686i	0.0979044	+	0.243208i
$921$		0			0
$922$	34.3790	+	14.3746i	1.13221	+	0.473402i
$923$	−6.60771			−0.217495
$924$		0			0
$925$	−33.8431			−1.11275
$926$	49.7143	+	20.7866i	1.63371	+	0.683090i
$927$		0			0
$928$	−4.18965	+	9.65663i	−0.137532	+	0.316995i
$929$			27.9950i			0.918488i	0.888310	+	0.459244i	$0.151880\pi$
$929$			27.9950i			0.918488i	−0.888310	+	0.459244i	$0.848120\pi$
$930$		0			0
$931$		0			0
$932$	−30.7969	+	30.3893i	−1.00879	+	0.995435i
$933$		0			0
$934$	3.48297	−	8.33006i	0.113966	−	0.272568i
$935$	7.07995			0.231539
$936$		0			0
$937$	−50.4480			−1.64806			−0.824031	−	0.566544i	$-0.808280\pi$
$937$	−50.4480			−1.64806			−0.824031	+	0.566544i	$0.808280\pi$
$938$		0			0
$939$		0			0
$940$	8.85110	−	8.73395i	0.288691	−	0.284870i
$941$		−	23.1572i		−	0.754903i	−0.926029	−	0.377451i	$-0.876801\pi$
$941$		−	23.1572i		−	0.754903i	0.926029	−	0.377451i	$-0.123199\pi$
$942$		0			0
$943$			42.7076i			1.39075i
$944$	−0.708823	+	53.1982i	−0.0230702	+	1.73145i
$945$		0			0
$946$	−13.2260	−	5.53007i	−0.430014	−	0.179798i
$947$	−14.5787			−0.473745			−0.236873	−	0.971541i	$-0.576122\pi$
$947$	−14.5787			−0.473745			−0.236873	+	0.971541i	$0.576122\pi$
$948$		0			0
$949$	−5.17374			−0.167947
$950$	41.5561	+	17.3755i	1.34826	+	0.563736i
$951$		0			0
$952$		0			0
$953$			27.8728i			0.902889i	0.892299	+	0.451444i	$0.149091\pi$
$953$			27.8728i			0.902889i	−0.892299	+	0.451444i	$0.850909\pi$
$954$		0			0
$955$			14.8334i			0.479998i
$956$	28.8747	+	29.2620i	0.933875	+	0.946401i
$957$		0			0
$958$	−11.4788	+	27.4533i	−0.370863	+	0.886975i
$959$		0			0
$960$		0			0
$961$	30.1143			0.971430
$962$	7.69569	−	18.4054i	0.248119	−	0.593414i
$963$		0			0
$964$	−15.1020	−	15.3045i	−0.486401	−	0.492925i
$965$			2.91001i			0.0936764i
$966$		0			0
$967$		−	22.2042i		−	0.714038i	−0.934097	−	0.357019i	$-0.883793\pi$
$967$		−	22.2042i		−	0.714038i	0.934097	−	0.357019i	$-0.116207\pi$
$968$	−11.7740	+	4.73969i	−0.378432	+	0.152340i
$969$		0			0
$970$	−9.90125	−	4.13992i	−0.317910	−	0.132925i
$971$	16.1859			0.519430			0.259715	−	0.965685i	$-0.416371\pi$
$971$	16.1859			0.519430			0.259715	+	0.965685i	$0.416371\pi$
$972$		0			0
$973$		0			0
$974$	−20.5937	−	8.61068i	−0.659866	−	0.275904i
$975$		0			0
$976$	−0.552545	+	41.4694i	−0.0176865	+	1.32740i
$977$			28.6168i			0.915531i	0.889073	+	0.457766i	$0.151350\pi$
$977$			28.6168i			0.915531i	−0.889073	+	0.457766i	$0.848650\pi$
$978$		0			0
$979$		−	30.2920i		−	0.968135i
$980$		0			0
$981$		0			0
$982$	10.2674	−	24.5559i	0.327644	−	0.783611i
$983$	47.7843			1.52408			0.762041	−	0.647528i	$-0.224197\pi$
$983$	47.7843			1.52408			0.762041	+	0.647528i	$0.224197\pi$
$984$		0			0
$985$	−5.61904			−0.179038
$986$	−4.03348	+	9.64668i	−0.128452	+	0.307213i
$987$		0			0
$988$	−18.8992	+	18.6490i	−0.601262	+	0.593304i
$989$		−	15.9940i		−	0.508579i
$990$		0			0
$991$			20.4708i			0.650275i	0.945667	+	0.325138i	$0.105411\pi$
$991$			20.4708i			0.650275i	−0.945667	+	0.325138i	$0.894589\pi$
$992$	2.11891	−	4.88382i	0.0672754	−	0.155062i
$993$		0			0
$994$		0			0
$995$	−1.06390			−0.0337278
$996$		0			0
$997$	−34.3491			−1.08785			−0.543924	−	0.839134i	$-0.683062\pi$
$997$	−34.3491			−1.08785			−0.543924	+	0.839134i	$0.683062\pi$
$998$	−10.5149	−	4.39649i	−0.332842	−	0.139168i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1764.2.e.i.1079.8		16
3.2	odd	2	inner	1764.2.e.i.1079.9		16
4.3	odd	2	inner	1764.2.e.i.1079.10		16
7.2	even	3		252.2.be.a.179.15	yes	32
7.4	even	3		252.2.be.a.107.4	yes	32
7.6	odd	2		1764.2.e.h.1079.8		16
12.11	even	2	inner	1764.2.e.i.1079.7		16
21.2	odd	6		252.2.be.a.179.2	yes	32
21.11	odd	6		252.2.be.a.107.13	yes	32
21.20	even	2		1764.2.e.h.1079.9		16
28.11	odd	6		252.2.be.a.107.2	✓	32
28.23	odd	6		252.2.be.a.179.13	yes	32
28.27	even	2		1764.2.e.h.1079.10		16
84.11	even	6		252.2.be.a.107.15	yes	32
84.23	even	6		252.2.be.a.179.4	yes	32
84.83	odd	2		1764.2.e.h.1079.7		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
252.2.be.a.107.2	✓	32	28.11	odd	6
252.2.be.a.107.4	yes	32	7.4	even	3
252.2.be.a.107.13	yes	32	21.11	odd	6
252.2.be.a.107.15	yes	32	84.11	even	6
252.2.be.a.179.2	yes	32	21.2	odd	6
252.2.be.a.179.4	yes	32	84.23	even	6
252.2.be.a.179.13	yes	32	28.23	odd	6
252.2.be.a.179.15	yes	32	7.2	even	3
1764.2.e.h.1079.7		16	84.83	odd	2
1764.2.e.h.1079.8		16	7.6	odd	2
1764.2.e.h.1079.9		16	21.20	even	2
1764.2.e.h.1079.10		16	28.27	even	2
1764.2.e.i.1079.7		16	12.11	even	2	inner
1764.2.e.i.1079.8		16	1.1	even	1	trivial
1764.2.e.i.1079.9		16	3.2	odd	2	inner
1764.2.e.i.1079.10		16	4.3	odd	2	inner

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:	\( N \)	\(=\)	\( 1764 = 2^{2} \cdot 3^{2} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1764.e (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.545545 + 1.30475i) q^{2} +(-1.40476 - 1.42360i) q^{4} +0.698240i q^{5} +(2.62381 - 1.05623i) q^{8} +O(q^{10})\)	\(q+(-0.545545 + 1.30475i) q^{2} +(-1.40476 - 1.42360i) q^{4} +0.698240i q^{5} +(2.62381 - 1.05623i) q^{8} +(-0.911031 - 0.380921i) q^{10} -2.55198 q^{11} +1.88088 q^{13} +(-0.0532920 + 3.99964i) q^{16} +3.97326i q^{17} -7.05819i q^{19} +(0.994017 - 0.980861i) q^{20} +(1.39222 - 3.32971i) q^{22} +4.02656 q^{23} +4.51246 q^{25} +(-1.02610 + 2.45408i) q^{26} -1.86081i q^{29} +0.941102i q^{31} +(-5.18948 - 2.25152i) q^{32} +(-5.18413 - 2.16759i) q^{34} -7.49992 q^{37} +(9.20919 + 3.85056i) q^{38} +(0.737500 + 1.83205i) q^{40} +10.6065i q^{41} -3.97212i q^{43} +(3.58493 + 3.63301i) q^{44} +(-2.19667 + 5.25366i) q^{46} +8.90438 q^{47} +(-2.46175 + 5.88765i) q^{50} +(-2.64218 - 2.67762i) q^{52} +0.529774i q^{53} -1.78190i q^{55} +(2.42790 + 1.01516i) q^{58} +13.3007 q^{59} +10.3683 q^{61} +(-1.22791 - 0.513413i) q^{62} +(5.76877 - 5.54268i) q^{64} +1.31330i q^{65} -2.72300i q^{67} +(5.65635 - 5.58149i) q^{68} -3.51310 q^{71} -2.75071 q^{73} +(4.09155 - 9.78555i) q^{74} +(-10.0481 + 9.91507i) q^{76} +13.5338i q^{79} +(-2.79271 - 0.0372106i) q^{80} +(-13.8389 - 5.78632i) q^{82} +17.1516 q^{83} -2.77429 q^{85} +(5.18264 + 2.16697i) q^{86} +(-6.69592 + 2.69547i) q^{88} +11.8700i q^{89} +(-5.65635 - 5.73222i) q^{92} +(-4.85774 + 11.6180i) q^{94} +4.92831 q^{95} +10.8682 q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q+O(q^{10}) \) 16 * q	\( 16 q + 8 q^{13} - 4 q^{16} - 16 q^{22} - 24 q^{25} - 8 q^{34} - 8 q^{37} + 52 q^{40} + 24 q^{46} + 52 q^{52} + 12 q^{58} + 16 q^{61} + 60 q^{64} + 8 q^{73} + 36 q^{76} - 68 q^{82} - 16 q^{85} - 44 q^{88} - 60 q^{94} - 88 q^{97}+O(q^{100}) \) 16 * q + 8 * q^13 - 4 * q^16 - 16 * q^22 - 24 * q^25 - 8 * q^34 - 8 * q^37 + 52 * q^40 + 24 * q^46 + 52 * q^52 + 12 * q^58 + 16 * q^61 + 60 * q^64 + 8 * q^73 + 36 * q^76 - 68 * q^82 - 16 * q^85 - 44 * q^88 - 60 * q^94 - 88 * q^97

Introduction

L-functions

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