LMFDB - Embedded newform 1078.2.c.b.1077.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1078,2,Mod(1077,1078)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1078, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("1078.1077");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1078 = 2 \cdot 7^{2} \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1078.c (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:	$8.60787333789$
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} - 6 x^{15} + 18 x^{14} - 36 x^{13} + 34 x^{12} + 18 x^{11} - 72 x^{10} + 132 x^{9} - 93 x^{8} + \cdots + 1 $ x^16 - 6x^15 + 18x^14 - 36x^13 + 34x^12 + 18x^11 - 72x^10 + 132x^9 - 93x^8 - 102x^7 + 144x^6 - 432x^5 + 502x^4 + 288x^3 + 72x^2 + 12*x + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{12} $
Twist minimal:	no (minimal twist has level 154)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			1077.1
Root			$-0.186243 + 0.0499037i$ of defining polynomial
Character	$\chi$	$=$	1078.1077
Dual form			1078.2.c.b.1077.16

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000i q^{2} -3.12703i q^{3} -1.00000 q^{4} +2.20288i q^{5} -3.12703 q^{6} +1.00000i q^{8} -6.77832 q^{9} +O(q^{10})$	\(q-1.00000i q^{2} -3.12703i q^{3} -1.00000 q^{4} +2.20288i q^{5} -3.12703 q^{6} +1.00000i q^{8} -6.77832 q^{9} +2.20288 q^{10} +(-1.49053 - 2.96282i) q^{11} +3.12703i q^{12} -1.45937 q^{13} +6.88847 q^{15} +1.00000 q^{16} -7.60732 q^{17} +6.77832i q^{18} -0.180645 q^{19} -2.20288i q^{20} +(-2.96282 + 1.49053i) q^{22} +2.28779 q^{23} +3.12703 q^{24} +0.147325 q^{25} +1.45937i q^{26} +11.8149i q^{27} +4.45335i q^{29} -6.88847i q^{30} +8.54897i q^{31} -1.00000i q^{32} +(-9.26484 + 4.66093i) q^{33} +7.60732i q^{34} +6.77832 q^{36} +1.50947 q^{37} +0.180645i q^{38} +4.56350i q^{39} -2.20288 q^{40} -7.10368 q^{41} +1.58174i q^{43} +(1.49053 + 2.96282i) q^{44} -14.9318i q^{45} -2.28779i q^{46} +0.545357i q^{47} -3.12703i q^{48} -0.147325i q^{50} +23.7883i q^{51} +1.45937 q^{52} +4.83444 q^{53} +11.8149 q^{54} +(6.52674 - 3.28346i) q^{55} +0.564883i q^{57} +4.45335 q^{58} -6.18967i q^{59} -6.88847 q^{60} -5.72621 q^{61} +8.54897 q^{62} -1.00000 q^{64} -3.21482i q^{65} +(4.66093 + 9.26484i) q^{66} -2.98176 q^{67} +7.60732 q^{68} -7.15399i q^{69} -7.57488 q^{71} -6.77832i q^{72} -9.67644 q^{73} -1.50947i q^{74} -0.460691i q^{75} +0.180645 q^{76} +4.56350 q^{78} -6.91879i q^{79} +2.20288i q^{80} +16.6107 q^{81} +7.10368i q^{82} -5.84246 q^{83} -16.7580i q^{85} +1.58174 q^{86} +13.9258 q^{87} +(2.96282 - 1.49053i) q^{88} -16.1111i q^{89} -14.9318 q^{90} -2.28779 q^{92} +26.7329 q^{93} +0.545357 q^{94} -0.397940i q^{95} -3.12703 q^{96} +11.3012i q^{97} +(10.1033 + 20.0830i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 16 q^{4} - 32 q^{9}+O(q^{10}) $ 16 * q - 16 * q^4 - 32 * q^9	$ 16 q - 16 q^{4} - 32 q^{9} - 16 q^{11} - 8 q^{15} + 16 q^{16} - 8 q^{22} - 32 q^{23} + 32 q^{36} + 32 q^{37} + 16 q^{44} + 56 q^{53} + 24 q^{58} + 8 q^{60} - 16 q^{64} - 24 q^{67} + 8 q^{71} - 16 q^{78} + 16 q^{81} - 40 q^{86} + 8 q^{88} + 32 q^{92} + 88 q^{93} + 56 q^{99}+O(q^{100}) $ 16 * q - 16 * q^4 - 32 * q^9 - 16 * q^11 - 8 * q^15 + 16 * q^16 - 8 * q^22 - 32 * q^23 + 32 * q^36 + 32 * q^37 + 16 * q^44 + 56 * q^53 + 24 * q^58 + 8 * q^60 - 16 * q^64 - 24 * q^67 + 8 * q^71 - 16 * q^78 + 16 * q^81 - 40 * q^86 + 8 * q^88 + 32 * q^92 + 88 * q^93 + 56 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1078\mathbb{Z}\right)^\times$.

$n$	$199$	$981$
$\chi(n)$	$-1$	$-1$

Coefficient data

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

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

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

$2$		−	1.00000i		−	0.707107i
$2$		−	1.00000i		−	0.707107i
$3$		−	3.12703i		−	1.80539i	−0.430279	−	0.902696i	$-0.641585\pi$
$3$		−	3.12703i		−	1.80539i	0.430279	−	0.902696i	$-0.358415\pi$
$4$	−1.00000			−0.500000
$5$			2.20288i			0.985157i	0.870268	+	0.492579i	$0.163946\pi$
$5$			2.20288i			0.985157i	−0.870268	+	0.492579i	$0.836054\pi$
$6$	−3.12703			−1.27660
$7$		0			0
$7$		0			0
$8$			1.00000i			0.353553i
$9$	−6.77832			−2.25944
$10$	2.20288			0.696611
$11$	−1.49053	−	2.96282i	−0.449412	−	0.893325i
$11$	−1.49053	−	2.96282i	−0.449412	−	0.893325i
$12$			3.12703i			0.902696i
$13$	−1.45937			−0.404757			−0.202378	−	0.979307i	$-0.564867\pi$
$13$	−1.45937			−0.404757			−0.202378	+	0.979307i	$0.564867\pi$
$14$		0			0
$15$	6.88847			1.77860
$16$	1.00000			0.250000
$17$	−7.60732			−1.84505			−0.922523	−	0.385943i	$-0.873876\pi$
$17$	−7.60732			−1.84505			−0.922523	+	0.385943i	$0.873876\pi$
$18$			6.77832i			1.59767i
$19$	−0.180645			−0.0414429			−0.0207214	−	0.999785i	$-0.506596\pi$
$19$	−0.180645			−0.0414429			−0.0207214	+	0.999785i	$0.506596\pi$
$20$		−	2.20288i		−	0.492579i
$21$		0			0
$22$	−2.96282	+	1.49053i	−0.631676	+	0.317782i
$23$	2.28779			0.477037			0.238519	−	0.971138i	$-0.423338\pi$
$23$	2.28779			0.477037			0.238519	+	0.971138i	$0.423338\pi$
$24$	3.12703			0.638302
$25$	0.147325			0.0294651
$26$			1.45937i			0.286206i
$27$			11.8149i			2.27378i
$28$		0			0
$29$			4.45335i			0.826967i	0.910512	+	0.413483i	$0.135688\pi$
$29$			4.45335i			0.826967i	−0.910512	+	0.413483i	$0.864312\pi$
$30$		−	6.88847i		−	1.25766i
$31$			8.54897i			1.53544i	0.640785	+	0.767720i	$0.278609\pi$
$31$			8.54897i			1.53544i	−0.640785	+	0.767720i	$0.721391\pi$
$32$		−	1.00000i		−	0.176777i
$33$	−9.26484	+	4.66093i	−1.61280	+	0.811364i
$34$			7.60732i			1.30464i
$35$		0			0
$36$	6.77832			1.12972
$37$	1.50947			0.248155			0.124078	−	0.992273i	$-0.460403\pi$
$37$	1.50947			0.248155			0.124078	+	0.992273i	$0.460403\pi$
$38$			0.180645i			0.0293045i
$39$			4.56350i			0.730745i
$40$	−2.20288			−0.348306
$41$	−7.10368			−1.10941			−0.554705	−	0.832047i	$-0.687169\pi$
$41$	−7.10368			−1.10941			−0.554705	+	0.832047i	$0.687169\pi$
$42$		0			0
$43$			1.58174i			0.241213i	0.992700	+	0.120606i	$0.0384839\pi$
$43$			1.58174i			0.241213i	−0.992700	+	0.120606i	$0.961516\pi$
$44$	1.49053	+	2.96282i	0.224706	+	0.446662i
$45$		−	14.9318i		−	2.22590i
$46$		−	2.28779i		−	0.337316i
$47$			0.545357i			0.0795486i	0.999209	+	0.0397743i	$0.0126639\pi$
$47$			0.545357i			0.0795486i	−0.999209	+	0.0397743i	$0.987336\pi$
$48$		−	3.12703i		−	0.451348i
$49$		0			0
$50$		−	0.147325i		−	0.0208349i
$51$			23.7883i			3.33103i
$52$	1.45937			0.202378
$53$	4.83444			0.664061			0.332031	−	0.943269i	$-0.392266\pi$
$53$	4.83444			0.664061			0.332031	+	0.943269i	$0.392266\pi$
$54$	11.8149			1.60781
$55$	6.52674	−	3.28346i	0.880065	−	0.442741i
$56$		0			0
$57$			0.564883i			0.0748206i
$58$	4.45335			0.584754
$59$		−	6.18967i		−	0.805826i	−0.915238	−	0.402913i	$-0.867998\pi$
$59$		−	6.18967i		−	0.805826i	0.915238	−	0.402913i	$-0.132002\pi$
$60$	−6.88847			−0.889298
$61$	−5.72621			−0.733166			−0.366583	−	0.930385i	$-0.619472\pi$
$61$	−5.72621			−0.733166			−0.366583	+	0.930385i	$0.619472\pi$
$62$	8.54897			1.08572
$63$		0			0
$64$	−1.00000			−0.125000
$65$		−	3.21482i		−	0.398749i
$66$	4.66093	+	9.26484i	0.573721	+	1.14042i
$67$	−2.98176			−0.364280			−0.182140	−	0.983273i	$-0.558302\pi$
$67$	−2.98176			−0.364280			−0.182140	+	0.983273i	$0.558302\pi$
$68$	7.60732			0.922523
$69$		−	7.15399i		−	0.861240i
$70$		0			0
$71$	−7.57488			−0.898973			−0.449486	−	0.893287i	$-0.648393\pi$
$71$	−7.57488			−0.898973			−0.449486	+	0.893287i	$0.648393\pi$
$72$		−	6.77832i		−	0.798833i
$73$	−9.67644			−1.13254			−0.566271	−	0.824219i	$-0.691614\pi$
$73$	−9.67644			−1.13254			−0.566271	+	0.824219i	$0.691614\pi$
$74$		−	1.50947i		−	0.175472i
$75$		−	0.460691i		−	0.0531960i
$76$	0.180645			0.0207214
$77$		0			0
$78$	4.56350			0.516715
$79$		−	6.91879i		−	0.778424i	−0.921148	−	0.389212i	$-0.872747\pi$
$79$		−	6.91879i		−	0.778424i	0.921148	−	0.389212i	$-0.127253\pi$
$80$			2.20288i			0.246289i
$81$	16.6107			1.84563
$82$			7.10368i			0.784471i
$83$	−5.84246			−0.641293			−0.320647	−	0.947199i	$-0.603900\pi$
$83$	−5.84246			−0.641293			−0.320647	+	0.947199i	$0.603900\pi$
$84$		0			0
$85$		−	16.7580i		−	1.81766i
$86$	1.58174			0.170563
$87$	13.9258			1.49300
$88$	2.96282	−	1.49053i	0.315838	−	0.158891i
$89$		−	16.1111i		−	1.70778i	−0.520455	−	0.853889i	$-0.674238\pi$
$89$		−	16.1111i		−	1.70778i	0.520455	−	0.853889i	$-0.325762\pi$
$90$	−14.9318			−1.57395
$91$		0			0
$92$	−2.28779			−0.238519
$93$	26.7329			2.77207
$94$	0.545357			0.0562493
$95$		−	0.397940i		−	0.0408278i
$96$	−3.12703			−0.319151
$97$			11.3012i			1.14746i	0.819045	+	0.573729i	$0.194504\pi$
$97$			11.3012i			1.14746i	−0.819045	+	0.573729i	$0.805496\pi$
$98$		0			0
$99$	10.1033	+	20.0830i	1.01542	+	2.01841i
$100$	−0.147325			−0.0147325
$101$	−0.517716			−0.0515147			−0.0257573	−	0.999668i	$-0.508200\pi$
$101$	−0.517716			−0.0515147			−0.0257573	+	0.999668i	$0.508200\pi$
$102$	23.7883			2.35539
$103$			2.88716i			0.284480i	0.989832	+	0.142240i	$0.0454305\pi$
$103$			2.88716i			0.284480i	−0.989832	+	0.142240i	$0.954570\pi$
$104$		−	1.45937i		−	0.143103i
$105$		0			0
$106$		−	4.83444i		−	0.469562i
$107$		−	5.21959i		−	0.504597i	−0.967649	−	0.252299i	$-0.918814\pi$
$107$		−	5.21959i		−	0.504597i	0.967649	−	0.252299i	$-0.0811865\pi$
$108$		−	11.8149i		−	1.13689i
$109$		−	10.0540i		−	0.963002i	−0.876446	−	0.481501i	$-0.840092\pi$
$109$		−	10.0540i		−	0.963002i	0.876446	−	0.481501i	$-0.159908\pi$
$110$	−3.28346	−	6.52674i	−0.313065	−	0.622300i
$111$		−	4.72016i		−	0.448018i
$112$		0			0
$113$	7.83235			0.736806			0.368403	−	0.929666i	$-0.379905\pi$
$113$	7.83235			0.736806			0.368403	+	0.929666i	$0.379905\pi$
$114$	0.564883			0.0529062
$115$			5.03973i			0.469957i
$116$		−	4.45335i		−	0.413483i
$117$	9.89209			0.914524
$118$	−6.18967			−0.569805
$119$		0			0
$120$			6.88847i			0.628828i
$121$	−6.55664	+	8.83235i	−0.596058	+	0.802941i
$122$			5.72621i			0.518427i
$123$			22.2134i			2.00292i
$124$		−	8.54897i		−	0.767720i
$125$			11.3389i			1.01419i
$126$		0			0
$127$		−	13.4702i		−	1.19529i	−0.801762	−	0.597644i	$-0.796104\pi$
$127$		−	13.4702i		−	1.19529i	0.801762	−	0.597644i	$-0.203896\pi$
$128$			1.00000i			0.0883883i
$129$	4.94614			0.435484
$130$	−3.21482			−0.281958
$131$	−2.62462			−0.229314			−0.114657	−	0.993405i	$-0.536577\pi$
$131$	−2.62462			−0.229314			−0.114657	+	0.993405i	$0.536577\pi$
$132$	9.26484	−	4.66093i	0.806401	−	0.405682i
$133$		0			0
$134$			2.98176i			0.257585i
$135$	−26.0268			−2.24003
$136$		−	7.60732i		−	0.652322i
$137$	−8.72291			−0.745248			−0.372624	−	0.927982i	$-0.621542\pi$
$137$	−8.72291			−0.745248			−0.372624	+	0.927982i	$0.621542\pi$
$138$	−7.15399			−0.608988
$139$	4.09291			0.347156			0.173578	−	0.984820i	$-0.444467\pi$
$139$	4.09291			0.347156			0.173578	+	0.984820i	$0.444467\pi$
$140$		0			0
$141$	1.70535			0.143616
$142$			7.57488i			0.635670i
$143$	2.17524	+	4.32386i	0.181902	+	0.361579i
$144$	−6.77832			−0.564860
$145$	−9.81020			−0.814692
$146$			9.67644i			0.800828i
$147$		0			0
$148$	−1.50947			−0.124078
$149$		−	18.5917i		−	1.52309i	−0.648110	−	0.761547i	$-0.724440\pi$
$149$		−	18.5917i		−	1.52309i	0.648110	−	0.761547i	$-0.275560\pi$
$150$	−0.460691			−0.0376152
$151$			13.2045i			1.07457i	0.843402	+	0.537283i	$0.180549\pi$
$151$			13.2045i			1.07457i	−0.843402	+	0.537283i	$0.819451\pi$
$152$		−	0.180645i		−	0.0146523i
$153$	51.5648			4.16877
$154$		0			0
$155$	−18.8324			−1.51265
$156$		−	4.56350i		−	0.365373i
$157$			5.75901i			0.459619i	0.973236	+	0.229810i	$0.0738104\pi$
$157$			5.75901i			0.459619i	−0.973236	+	0.229810i	$0.926190\pi$
$158$	−6.91879			−0.550429
$159$		−	15.1174i		−	1.19889i
$160$	2.20288			0.174153
$161$		0			0
$162$		−	16.6107i		−	1.30506i
$163$	−5.31289			−0.416137			−0.208069	−	0.978114i	$-0.566718\pi$
$163$	−5.31289			−0.416137			−0.208069	+	0.978114i	$0.566718\pi$
$164$	7.10368			0.554705
$165$	−10.2675	−	20.4093i	−0.799321	−	1.58886i
$166$			5.84246i			0.453463i
$167$	−16.0519			−1.24213			−0.621067	−	0.783757i	$-0.713301\pi$
$167$	−16.0519			−1.24213			−0.621067	+	0.783757i	$0.713301\pi$
$168$		0			0
$169$	−10.8702			−0.836172
$170$	−16.7580			−1.28528
$171$	1.22447			0.0936377
$172$		−	1.58174i		−	0.120606i
$173$	−7.09477			−0.539405			−0.269703	−	0.962944i	$-0.586925\pi$
$173$	−7.09477			−0.539405			−0.269703	+	0.962944i	$0.586925\pi$
$174$		−	13.9258i		−	1.05571i
$175$		0			0
$176$	−1.49053	−	2.96282i	−0.112353	−	0.223331i
$177$	−19.3553			−1.45483
$178$	−16.1111			−1.20758
$179$	−24.9728			−1.86656			−0.933278	−	0.359155i	$-0.883065\pi$
$179$	−24.9728			−1.86656			−0.933278	+	0.359155i	$0.883065\pi$
$180$			14.9318i			1.11295i
$181$		−	19.3579i		−	1.43886i	−0.694566	−	0.719429i	$-0.744404\pi$
$181$		−	19.3579i		−	1.43886i	0.694566	−	0.719429i	$-0.255596\pi$
$182$		0			0
$183$			17.9060i			1.32365i
$184$			2.28779i			0.168658i
$185$			3.32518i			0.244472i
$186$		−	26.7329i		−	1.96015i
$187$	11.3389	+	22.5391i	0.829185	+	1.64822i
$188$		−	0.545357i		−	0.0397743i
$189$		0			0
$190$	−0.397940			−0.0288696
$191$	6.00000			0.434145			0.217072	−	0.976156i	$-0.430349\pi$
$191$	6.00000			0.434145			0.217072	+	0.976156i	$0.430349\pi$
$192$			3.12703i			0.225674i
$193$		−	16.6114i		−	1.19571i	−0.801603	−	0.597857i	$-0.796019\pi$
$193$		−	16.6114i		−	1.19571i	0.801603	−	0.597857i	$-0.203981\pi$
$194$	11.3012			0.811376
$195$	−10.0528			−0.719899
$196$		0			0
$197$			20.6396i			1.47051i	0.677790	+	0.735256i	$0.262938\pi$
$197$			20.6396i			1.47051i	−0.677790	+	0.735256i	$0.737062\pi$
$198$	20.0830	−	10.1033i	1.42723	−	0.718009i
$199$			0.726003i			0.0514650i	0.999669	+	0.0257325i	$0.00819181\pi$
$199$			0.726003i			0.0514650i	−0.999669	+	0.0257325i	$0.991808\pi$
$200$			0.147325i			0.0104175i
$201$			9.32407i			0.657669i
$202$			0.517716i			0.0364264i
$203$		0			0
$204$		−	23.7883i		−	1.66552i
$205$		−	15.6486i		−	1.09294i
$206$	2.88716			0.201158
$207$	−15.5074			−1.07784
$208$	−1.45937			−0.101189
$209$	0.269257	+	0.535220i	0.0186249	+	0.0370219i
$210$		0			0
$211$			10.2878i			0.708241i	0.935200	+	0.354120i	$0.115220\pi$
$211$			10.2878i			0.708241i	−0.935200	+	0.354120i	$0.884780\pi$
$212$	−4.83444			−0.332031
$213$			23.6869i			1.62300i
$214$	−5.21959			−0.356804
$215$	−3.48438			−0.237632
$216$	−11.8149			−0.803904
$217$		0			0
$218$	−10.0540			−0.680945
$219$			30.2585i			2.04468i
$220$	−6.52674	+	3.28346i	−0.440033	+	0.221371i
$221$	11.1019			0.746795
$222$	−4.72016			−0.316796
$223$			0.894768i			0.0599181i	0.999551	+	0.0299590i	$0.00953768\pi$
$223$			0.894768i			0.0599181i	−0.999551	+	0.0299590i	$0.990462\pi$
$224$		0			0
$225$	−0.998618			−0.0665745
$226$		−	7.83235i		−	0.521000i
$227$	13.4848			0.895017			0.447508	−	0.894280i	$-0.352311\pi$
$227$	13.4848			0.895017			0.447508	+	0.894280i	$0.352311\pi$
$228$		−	0.564883i		−	0.0374103i
$229$			4.88550i			0.322843i	0.986886	+	0.161422i	$0.0516079\pi$
$229$			4.88550i			0.322843i	−0.986886	+	0.161422i	$0.948392\pi$
$230$	5.03973			0.332310
$231$		0			0
$232$	−4.45335			−0.292377
$233$			22.6606i			1.48455i	0.670097	+	0.742274i	$0.266253\pi$
$233$			22.6606i			1.48455i	−0.670097	+	0.742274i	$0.733747\pi$
$234$		−	9.89209i		−	0.646666i
$235$	−1.20136			−0.0783678
$236$			6.18967i			0.402913i
$237$	−21.6353			−1.40536
$238$		0			0
$239$		−	25.2410i		−	1.63270i	−0.577556	−	0.816351i	$-0.695993\pi$
$239$		−	25.2410i		−	1.63270i	0.577556	−	0.816351i	$-0.304007\pi$
$240$	6.88847			0.444649
$241$	−14.0669			−0.906128			−0.453064	−	0.891478i	$-0.649669\pi$
$241$	−14.0669			−0.906128			−0.453064	+	0.891478i	$0.649669\pi$
$242$	8.83235	+	6.55664i	0.567765	+	0.421477i
$243$		−	16.4973i		−	1.05830i
$244$	5.72621			0.366583
$245$		0			0
$246$	22.2134			1.41628
$247$	0.263629			0.0167743
$248$	−8.54897			−0.542860
$249$			18.2696i			1.15779i
$250$	11.3389			0.717137
$251$		−	3.03720i		−	0.191706i	−0.995395	−	0.0958532i	$-0.969442\pi$
$251$		−	3.03720i		−	0.191706i	0.995395	−	0.0958532i	$-0.0305579\pi$
$252$		0			0
$253$	−3.41002	−	6.77832i	−0.214386	−	0.426149i
$254$	−13.4702			−0.845196
$255$	−52.4028			−3.28159
$256$	1.00000			0.0625000
$257$		−	25.7683i		−	1.60738i	−0.595045	−	0.803692i	$-0.702866\pi$
$257$		−	25.7683i		−	1.60738i	0.595045	−	0.803692i	$-0.297134\pi$
$258$		−	4.94614i		−	0.307933i
$259$		0			0
$260$			3.21482i			0.199375i
$261$		−	30.1863i		−	1.86848i
$262$			2.62462i			0.162149i
$263$			6.41002i			0.395259i	0.980277	+	0.197629i	$0.0633243\pi$
$263$			6.41002i			0.395259i	−0.980277	+	0.197629i	$0.936676\pi$
$264$	−4.66093	−	9.26484i	−0.286861	−	0.570211i
$265$			10.6497i			0.654205i
$266$		0			0
$267$	−50.3800			−3.08321
$268$	2.98176			0.182140
$269$			2.74152i			0.167153i	0.996501	+	0.0835767i	$0.0266344\pi$
$269$			2.74152i			0.167153i	−0.996501	+	0.0835767i	$0.973366\pi$
$270$			26.0268i			1.58394i
$271$	28.6002			1.73734			0.868670	−	0.495392i	$-0.164976\pi$
$271$	28.6002			1.73734			0.868670	+	0.495392i	$0.164976\pi$
$272$	−7.60732			−0.461261
$273$		0			0
$274$			8.72291i			0.526970i
$275$	−0.219593	−	0.436499i	−0.0132419	−	0.0263219i
$276$			7.15399i			0.430620i
$277$			10.7683i			0.647006i	0.946227	+	0.323503i	$0.104861\pi$
$277$			10.7683i			0.647006i	−0.946227	+	0.323503i	$0.895139\pi$
$278$		−	4.09291i		−	0.245476i
$279$		−	57.9477i		−	3.46924i
$280$		0			0
$281$		−	19.6289i		−	1.17096i	−0.810686	−	0.585481i	$-0.800906\pi$
$281$		−	19.6289i		−	1.17096i	0.810686	−	0.585481i	$-0.199094\pi$
$282$		−	1.70535i		−	0.101552i
$283$	10.6233			0.631487			0.315744	−	0.948845i	$-0.397746\pi$
$283$	10.6233			0.631487			0.315744	+	0.948845i	$0.397746\pi$
$284$	7.57488			0.449486
$285$	−1.24437			−0.0737101
$286$	4.32386	−	2.17524i	0.255675	−	0.128624i
$287$		0			0
$288$			6.77832i			0.399416i
$289$	40.8713			2.40419
$290$			9.81020i			0.576075i
$291$	35.3391			2.07161
$292$	9.67644			0.566271
$293$	0.277651			0.0162206			0.00811028	−	0.999967i	$-0.497418\pi$
$293$	0.277651			0.0162206			0.00811028	+	0.999967i	$0.497418\pi$
$294$		0			0
$295$	13.6351			0.793866
$296$			1.50947i			0.0877362i
$297$	35.0055	−	17.6105i	2.03123	−	1.02186i
$298$	−18.5917			−1.07699
$299$	−3.33874			−0.193084
$300$			0.460691i			0.0265980i
$301$		0			0
$302$	13.2045			0.759833
$303$			1.61891i			0.0930042i
$304$	−0.180645			−0.0103607
$305$		−	12.6141i		−	0.722284i
$306$		−	51.5648i		−	2.94777i
$307$	6.41443			0.366091			0.183045	−	0.983104i	$-0.441404\pi$
$307$	6.41443			0.366091			0.183045	+	0.983104i	$0.441404\pi$
$308$		0			0
$309$	9.02823			0.513598
$310$			18.8324i			1.06961i
$311$		−	11.3024i		−	0.640899i	−0.947266	−	0.320449i	$-0.896166\pi$
$311$		−	11.3024i		−	0.640899i	0.947266	−	0.320449i	$-0.103834\pi$
$312$	−4.56350			−0.258357
$313$			16.4467i			0.929621i	0.885410	+	0.464810i	$0.153877\pi$
$313$			16.4467i			0.929621i	−0.885410	+	0.464810i	$0.846123\pi$
$314$	5.75901			0.325000
$315$		0			0
$316$			6.91879i			0.389212i
$317$	−28.1910			−1.58337			−0.791683	−	0.610932i	$-0.790795\pi$
$317$	−28.1910			−1.58337			−0.791683	+	0.610932i	$0.790795\pi$
$318$	−15.1174			−0.847744
$319$	13.1945	−	6.63786i	0.738750	−	0.371649i
$320$		−	2.20288i		−	0.123145i
$321$	−16.3218			−0.910996
$322$		0			0
$323$	1.37423			0.0764640
$324$	−16.6107			−0.922815
$325$	−0.215002			−0.0119262
$326$			5.31289i			0.294254i
$327$	−31.4393			−1.73860
$328$		−	7.10368i		−	0.392235i
$329$		0			0
$330$	−20.4093	+	10.2675i	−1.12350	+	0.565206i
$331$	19.1126			1.05052			0.525261	−	0.850941i	$-0.323968\pi$
$331$	19.1126			1.05052			0.525261	+	0.850941i	$0.323968\pi$
$332$	5.84246			0.320647
$333$	−10.2317			−0.560692
$334$			16.0519i			0.878322i
$335$		−	6.56846i		−	0.358874i
$336$		0			0
$337$		−	16.0358i		−	0.873525i	−0.899577	−	0.436763i	$-0.856125\pi$
$337$		−	16.0358i		−	0.873525i	0.899577	−	0.436763i	$-0.143875\pi$
$338$			10.8702i			0.591263i
$339$		−	24.4920i		−	1.33022i
$340$			16.7580i			0.908830i
$341$	25.3291	−	12.7425i	1.37165	−	0.690045i
$342$		−	1.22447i		−	0.0662119i
$343$		0			0
$344$	−1.58174			−0.0852816
$345$	15.7594			0.848457
$346$			7.09477i			0.381417i
$347$			9.87094i			0.529900i	0.964262	+	0.264950i	$0.0853554\pi$
$347$			9.87094i			0.529900i	−0.964262	+	0.264950i	$0.914645\pi$
$348$	−13.9258			−0.746500
$349$	31.1871			1.66940			0.834702	−	0.550701i	$-0.185640\pi$
$349$	31.1871			1.66940			0.834702	+	0.550701i	$0.185640\pi$
$350$		0			0
$351$		−	17.2424i		−	0.920330i
$352$	−2.96282	+	1.49053i	−0.157919	+	0.0794455i
$353$		−	25.9682i		−	1.38215i	−0.722783	−	0.691075i	$-0.757138\pi$
$353$		−	25.9682i		−	1.38215i	0.722783	−	0.691075i	$-0.242862\pi$
$354$			19.3553i			1.02872i
$355$		−	16.6865i		−	0.885630i
$356$			16.1111i			0.853889i
$357$		0			0
$358$			24.9728i			1.31985i
$359$		−	4.01067i		−	0.211675i	−0.994383	−	0.105838i	$-0.966248\pi$
$359$		−	4.01067i		−	0.211675i	0.994383	−	0.105838i	$-0.0337524\pi$
$360$	14.9318			0.786976
$361$	−18.9674			−0.998282
$362$	−19.3579			−1.01743
$363$	27.6190	+	20.5028i	1.44962	+	1.07612i
$364$		0			0
$365$		−	21.3160i		−	1.11573i
$366$	17.9060			0.935963
$367$			19.1851i			1.00145i	0.865605	+	0.500727i	$0.166934\pi$
$367$			19.1851i			1.00145i	−0.865605	+	0.500727i	$0.833066\pi$
$368$	2.28779			0.119259
$369$	48.1510			2.50664
$370$	3.32518			0.172868
$371$		0			0
$372$	−26.7329			−1.38604
$373$			21.0289i			1.08884i	0.838814	+	0.544419i	$0.183250\pi$
$373$			21.0289i			1.08884i	−0.838814	+	0.544419i	$0.816750\pi$
$374$	22.5391	−	11.3389i	1.16547	−	0.586322i
$375$	35.4572			1.83100
$376$	−0.545357			−0.0281247
$377$		−	6.49910i		−	0.334721i
$378$		0			0
$379$	20.7525			1.06599			0.532993	−	0.846120i	$-0.321067\pi$
$379$	20.7525			1.06599			0.532993	+	0.846120i	$0.321067\pi$
$380$			0.397940i			0.0204139i
$381$	−42.1218			−2.15796
$382$		−	6.00000i		−	0.306987i
$383$			1.25606i			0.0641816i	0.999485	+	0.0320908i	$0.0102166\pi$
$383$			1.25606i			0.0641816i	−0.999485	+	0.0320908i	$0.989783\pi$
$384$	3.12703			0.159576
$385$		0			0
$386$	−16.6114			−0.845497
$387$		−	10.7215i		−	0.545006i
$388$		−	11.3012i		−	0.573729i
$389$	−16.6479			−0.844080			−0.422040	−	0.906577i	$-0.638686\pi$
$389$	−16.6479			−0.844080			−0.422040	+	0.906577i	$0.638686\pi$
$390$			10.0528i			0.509045i
$391$	−17.4040			−0.880156
$392$		0			0
$393$			8.20726i			0.414001i
$394$	20.6396			1.03981
$395$	15.2412			0.766870
$396$	−10.1033	−	20.0830i	−0.507709	−	1.00921i
$397$		−	14.1742i		−	0.711384i	−0.934603	−	0.355692i	$-0.884245\pi$
$397$		−	14.1742i		−	0.711384i	0.934603	−	0.355692i	$-0.115755\pi$
$398$	0.726003			0.0363912
$399$		0			0
$400$	0.147325			0.00736626
$401$	−4.85270			−0.242332			−0.121166	−	0.992632i	$-0.538663\pi$
$401$	−4.85270			−0.242332			−0.121166	+	0.992632i	$0.538663\pi$
$402$	9.32407			0.465042
$403$		−	12.4761i		−	0.621480i
$404$	0.517716			0.0257573
$405$			36.5913i			1.81824i
$406$		0			0
$407$	−2.24991	−	4.47229i	−0.111524	−	0.221683i
$408$	−23.7883			−1.17770
$409$	10.6280			0.525523			0.262761	−	0.964861i	$-0.415367\pi$
$409$	10.6280			0.525523			0.262761	+	0.964861i	$0.415367\pi$
$410$	−15.6486			−0.772827
$411$			27.2768i			1.34547i
$412$		−	2.88716i		−	0.142240i
$413$		0			0
$414$			15.5074i			0.762146i
$415$		−	12.8702i		−	0.631775i
$416$			1.45937i			0.0715516i
$417$		−	12.7986i		−	0.626752i
$418$	0.535220	−	0.269257i	0.0261785	−	0.0131698i
$419$		−	11.3690i		−	0.555410i	−0.960666	−	0.277705i	$-0.910426\pi$
$419$		−	11.3690i		−	0.555410i	0.960666	−	0.277705i	$-0.0895739\pi$
$420$		0			0
$421$	27.2464			1.32791			0.663955	−	0.747772i	$-0.268877\pi$
$421$	27.2464			1.32791			0.663955	+	0.747772i	$0.268877\pi$
$422$	10.2878			0.500802
$423$		−	3.69661i		−	0.179735i
$424$			4.83444i			0.234781i
$425$	−1.12075			−0.0543644
$426$	23.6869			1.14763
$427$		0			0
$428$			5.21959i			0.252299i
$429$	13.5208	−	6.80203i	0.652793	−	0.328405i
$430$			3.48438i			0.168032i
$431$			15.2210i			0.733169i	0.930385	+	0.366584i	$0.119473\pi$
$431$			15.2210i			0.733169i	−0.930385	+	0.366584i	$0.880527\pi$
$432$			11.8149i			0.568446i
$433$		−	1.85534i		−	0.0891619i	−0.999006	−	0.0445810i	$-0.985805\pi$
$433$		−	1.85534i		−	0.0891619i	0.999006	−	0.0445810i	$-0.0141953\pi$
$434$		0			0
$435$			30.6768i			1.47084i
$436$			10.0540i			0.481501i
$437$	−0.413279			−0.0197698
$438$	30.2585			1.44581
$439$	−32.9404			−1.57216			−0.786079	−	0.618126i	$-0.787892\pi$
$439$	−32.9404			−1.57216			−0.786079	+	0.618126i	$0.787892\pi$
$440$	3.28346	+	6.52674i	0.156533	+	0.311150i
$441$		0			0
$442$		−	11.1019i		−	0.528064i
$443$	−32.8613			−1.56129			−0.780643	−	0.624977i	$-0.785108\pi$
$443$	−32.8613			−1.56129			−0.780643	+	0.624977i	$0.785108\pi$
$444$			4.72016i			0.224009i
$445$	35.4909			1.68243
$446$	0.894768			0.0423685
$447$	−58.1369			−2.74978
$448$		0			0
$449$	3.62716			0.171176			0.0855880	−	0.996331i	$-0.472723\pi$
$449$	3.62716			0.171176			0.0855880	+	0.996331i	$0.472723\pi$
$450$			0.998618i			0.0470753i
$451$	10.5883	+	21.0470i	0.498581	+	0.991063i
$452$	−7.83235			−0.368403
$453$	41.2909			1.94001
$454$		−	13.4848i		−	0.632872i
$455$		0			0
$456$	−0.564883			−0.0264531
$457$			2.73567i			0.127969i	0.997951	+	0.0639846i	$0.0203808\pi$
$457$			2.73567i			0.127969i	−0.997951	+	0.0639846i	$0.979619\pi$
$458$	4.88550			0.228285
$459$		−	89.8799i		−	4.19523i
$460$		−	5.03973i		−	0.234978i
$461$	−20.4439			−0.952169			−0.476084	−	0.879400i	$-0.657944\pi$
$461$	−20.4439			−0.952169			−0.476084	+	0.879400i	$0.657944\pi$
$462$		0			0
$463$	30.1701			1.40212			0.701062	−	0.713100i	$-0.252710\pi$
$463$	30.1701			1.40212			0.701062	+	0.713100i	$0.252710\pi$
$464$			4.45335i			0.206742i
$465$			58.8893i			2.73093i
$466$	22.6606			1.04973
$467$		−	27.1722i		−	1.25738i	−0.777656	−	0.628691i	$-0.783591\pi$
$467$		−	27.1722i		−	1.25738i	0.777656	−	0.628691i	$-0.216409\pi$
$468$	−9.89209			−0.457262
$469$		0			0
$470$			1.20136i			0.0554144i
$471$	18.0086			0.829793
$472$	6.18967			0.284903
$473$	4.68641	−	2.35763i	0.215481	−	0.108404i
$474$			21.6353i			0.993740i
$475$	−0.0266136			−0.00122112
$476$		0			0
$477$	−32.7694			−1.50041
$478$	−25.2410			−1.15449
$479$	−21.6184			−0.987770			−0.493885	−	0.869527i	$-0.664424\pi$
$479$	−21.6184			−0.987770			−0.493885	+	0.869527i	$0.664424\pi$
$480$		−	6.88847i		−	0.314414i
$481$	−2.20288			−0.100443
$482$			14.0669i			0.640730i
$483$		0			0
$484$	6.55664	−	8.83235i	0.298029	−	0.401471i
$485$	−24.8951			−1.13043
$486$	−16.4973			−0.748333
$487$	2.08573			0.0945135			0.0472567	−	0.998883i	$-0.484952\pi$
$487$	2.08573			0.0945135			0.0472567	+	0.998883i	$0.484952\pi$
$488$		−	5.72621i		−	0.259213i
$489$			16.6136i			0.751291i
$490$		0			0
$491$			2.47983i			0.111913i	0.998433	+	0.0559566i	$0.0178208\pi$
$491$			2.47983i			0.111913i	−0.998433	+	0.0559566i	$0.982179\pi$
$492$		−	22.2134i		−	1.00146i
$493$		−	33.8781i		−	1.52579i
$494$		−	0.263629i		−	0.0118612i
$495$	−44.2403	+	22.2563i	−1.98846	+	1.00035i
$496$			8.54897i			0.383860i
$497$		0			0
$498$	18.2696			0.818678
$499$	15.3838			0.688672			0.344336	−	0.938846i	$-0.388104\pi$
$499$	15.3838			0.688672			0.344336	+	0.938846i	$0.388104\pi$
$500$		−	11.3389i		−	0.507093i
$501$			50.1948i			2.24254i
$502$	−3.03720			−0.135557
$503$	−15.5714			−0.694295			−0.347147	−	0.937811i	$-0.612850\pi$
$503$	−15.5714			−0.694295			−0.347147	+	0.937811i	$0.612850\pi$
$504$		0			0
$505$		−	1.14047i		−	0.0507501i
$506$	−6.77832	+	3.41002i	−0.301333	+	0.151594i
$507$			33.9916i			1.50962i
$508$			13.4702i			0.597644i
$509$			30.7550i			1.36319i	0.731729	+	0.681595i	$0.238714\pi$
$509$			30.7550i			1.36319i	−0.731729	+	0.681595i	$0.761286\pi$
$510$			52.4028i			2.32043i
$511$		0			0
$512$		−	1.00000i		−	0.0441942i
$513$		−	2.13431i		−	0.0942321i
$514$	−25.7683			−1.13659
$515$	−6.36006			−0.280258
$516$	−4.94614			−0.217742
$517$	1.61580	−	0.812872i	0.0710627	−	0.0357500i
$518$		0			0
$519$			22.1856i			0.973838i
$520$	3.21482			0.140979
$521$		−	3.69331i		−	0.161807i	−0.996722	−	0.0809035i	$-0.974219\pi$
$521$		−	3.69331i		−	0.161807i	0.996722	−	0.0809035i	$-0.0257806\pi$
$522$	−30.1863			−1.32122
$523$	−29.2014			−1.27689			−0.638444	−	0.769669i	$-0.720421\pi$
$523$	−29.2014			−1.27689			−0.638444	+	0.769669i	$0.720421\pi$
$524$	2.62462			0.114657
$525$		0			0
$526$	6.41002			0.279490
$527$		−	65.0348i		−	2.83296i
$528$	−9.26484	+	4.66093i	−0.403200	+	0.202841i
$529$	−17.7660			−0.772435
$530$	10.6497			0.462593
$531$			41.9556i			1.82072i
$532$		0			0
$533$	10.3669			0.449041
$534$			50.3800i			2.18016i
$535$	11.4981			0.497107
$536$		−	2.98176i		−	0.128793i
$537$			78.0908i			3.36987i
$538$	2.74152			0.118195
$539$		0			0
$540$	26.0268			1.12002
$541$			16.1749i			0.695411i	0.937604	+	0.347706i	$0.113039\pi$
$541$			16.1749i			0.695411i	−0.937604	+	0.347706i	$0.886961\pi$
$542$		−	28.6002i		−	1.22848i
$543$	−60.5326			−2.59770
$544$			7.60732i			0.326161i
$545$	22.1478			0.948708
$546$		0			0
$547$			34.0719i			1.45681i	0.685146	+	0.728405i	$0.259738\pi$
$547$			34.0719i			1.45681i	−0.685146	+	0.728405i	$0.740262\pi$
$548$	8.72291			0.372624
$549$	38.8141			1.65654
$550$	−0.436499	+	0.219593i	−0.0186124	+	0.00936346i
$551$		−	0.804477i		−	0.0342719i
$552$	7.15399			0.304494
$553$		0			0
$554$	10.7683			0.457502
$555$	10.3979			0.441368
$556$	−4.09291			−0.173578
$557$			25.6864i			1.08837i	0.838966	+	0.544185i	$0.183161\pi$
$557$			25.6864i			1.08837i	−0.838966	+	0.544185i	$0.816839\pi$
$558$	−57.9477			−2.45312
$559$		−	2.30834i		−	0.0976325i
$560$		0			0
$561$	70.4806	−	35.4572i	2.97569	−	1.49700i
$562$	−19.6289			−0.827996
$563$	21.9366			0.924516			0.462258	−	0.886746i	$-0.347039\pi$
$563$	21.9366			0.924516			0.462258	+	0.886746i	$0.347039\pi$
$564$	−1.70535			−0.0718082
$565$			17.2537i			0.725870i
$566$		−	10.6233i		−	0.446529i
$567$		0			0
$568$		−	7.57488i		−	0.317835i
$569$		−	2.56697i		−	0.107613i	−0.998551	−	0.0538065i	$-0.982865\pi$
$569$		−	2.56697i		−	0.107613i	0.998551	−	0.0538065i	$-0.0171354\pi$
$570$			1.24437i			0.0521209i
$571$		−	34.3092i		−	1.43579i	−0.696149	−	0.717897i	$-0.745105\pi$
$571$		−	34.3092i		−	1.43579i	0.696149	−	0.717897i	$-0.254895\pi$
$572$	−2.17524	−	4.32386i	−0.0909512	−	0.180790i
$573$		−	18.7622i		−	0.783801i
$574$		0			0
$575$	0.337049			0.0140559
$576$	6.77832			0.282430
$577$		−	20.6988i		−	0.861701i	−0.902423	−	0.430851i	$-0.858214\pi$
$577$		−	20.6988i		−	0.861701i	0.902423	−	0.430851i	$-0.141786\pi$
$578$		−	40.8713i		−	1.70002i
$579$	−51.9443			−2.15873
$580$	9.81020			0.407346
$581$		0			0
$582$		−	35.3391i		−	1.46485i
$583$	−7.20587	−	14.3236i	−0.298437	−	0.593222i
$584$		−	9.67644i		−	0.400414i
$585$			21.7911i			0.900950i
$586$		−	0.277651i		−	0.0114697i
$587$			16.0435i			0.662184i	0.943598	+	0.331092i	$0.107417\pi$
$587$			16.0435i			0.662184i	−0.943598	+	0.331092i	$0.892583\pi$
$588$		0			0
$589$		−	1.54433i		−	0.0636331i
$590$		−	13.6351i		−	0.561348i
$591$	64.5407			2.65485
$592$	1.50947			0.0620388
$593$	35.4872			1.45728			0.728641	−	0.684895i	$-0.240152\pi$
$593$	35.4872			1.45728			0.728641	+	0.684895i	$0.240152\pi$
$594$	−17.6105	−	35.0055i	−0.722568	−	1.43629i
$595$		0			0
$596$			18.5917i			0.761547i
$597$	2.27023			0.0929144
$598$			3.33874i			0.136531i
$599$	0.749386			0.0306191			0.0153095	−	0.999883i	$-0.495127\pi$
$599$	0.749386			0.0306191			0.0153095	+	0.999883i	$0.495127\pi$
$600$	0.460691			0.0188076
$601$	18.5168			0.755317			0.377658	−	0.925945i	$-0.376729\pi$
$601$	18.5168			0.755317			0.377658	+	0.925945i	$0.376729\pi$
$602$		0			0
$603$	20.2114			0.823070
$604$		−	13.2045i		−	0.537283i
$605$	−19.4566	−	14.4435i	−0.791023	−	0.587211i
$606$	1.61891			0.0657639
$607$	36.9910			1.50142			0.750710	−	0.660632i	$-0.229712\pi$
$607$	36.9910			1.50142			0.750710	+	0.660632i	$0.229712\pi$
$608$			0.180645i			0.00732613i
$609$		0			0
$610$	−12.6141			−0.510732
$611$		−	0.795879i		−	0.0321978i
$612$	−51.5648			−2.08439
$613$			3.22552i			0.130277i	0.997876	+	0.0651387i	$0.0207490\pi$
$613$			3.22552i			0.130277i	−0.997876	+	0.0651387i	$0.979251\pi$
$614$		−	6.41443i		−	0.258865i
$615$	−48.9335			−1.97319
$616$		0			0
$617$	−10.8351			−0.436206			−0.218103	−	0.975926i	$-0.569987\pi$
$617$	−10.8351			−0.436206			−0.218103	+	0.975926i	$0.569987\pi$
$618$		−	9.02823i		−	0.363169i
$619$			5.12834i			0.206125i	0.994675	+	0.103063i	$0.0328642\pi$
$619$			5.12834i			0.206125i	−0.994675	+	0.103063i	$0.967136\pi$
$620$	18.8324			0.756325
$621$			27.0301i			1.08468i
$622$	−11.3024			−0.453184
$623$		0			0
$624$			4.56350i			0.182686i
$625$	−24.2417			−0.969667
$626$	16.4467			0.657341
$627$	1.67365	−	0.841976i	0.0668391	−	0.0336253i
$628$		−	5.75901i		−	0.229810i
$629$	−11.4830			−0.457858
$630$		0			0
$631$	−29.9567			−1.19256			−0.596278	−	0.802778i	$-0.703354\pi$
$631$	−29.9567			−1.19256			−0.596278	+	0.802778i	$0.703354\pi$
$632$	6.91879			0.275215
$633$	32.1702			1.27865
$634$			28.1910i			1.11961i
$635$	29.6732			1.17755
$636$			15.1174i			0.599445i
$637$		0			0
$638$	−6.63786	−	13.1945i	−0.262795	−	0.522375i
$639$	51.3450			2.03118
$640$	−2.20288			−0.0870764
$641$	9.22690			0.364441			0.182220	−	0.983258i	$-0.441672\pi$
$641$	9.22690			0.364441			0.182220	+	0.983258i	$0.441672\pi$
$642$			16.3218i			0.644171i
$643$			1.79941i			0.0709616i	0.999370	+	0.0354808i	$0.0112963\pi$
$643$			1.79941i			0.0709616i	−0.999370	+	0.0354808i	$0.988704\pi$
$644$		0			0
$645$			10.8958i			0.429020i
$646$		−	1.37423i		−	0.0540682i
$647$		−	40.7244i		−	1.60104i	−0.599306	−	0.800520i	$-0.704557\pi$
$647$		−	40.7244i		−	1.60104i	0.599306	−	0.800520i	$-0.295443\pi$
$648$			16.6107i			0.652529i
$649$	−18.3389	+	9.22589i	−0.719865	+	0.362148i
$650$			0.215002i			0.00843309i
$651$		0			0
$652$	5.31289			0.208069
$653$	−37.7384			−1.47682			−0.738408	−	0.674354i	$-0.764422\pi$
$653$	−37.7384			−1.47682			−0.738408	+	0.674354i	$0.764422\pi$
$654$			31.4393i			1.22937i
$655$		−	5.78171i		−	0.225910i
$656$	−7.10368			−0.277352
$657$	65.5900			2.55891
$658$		0			0
$659$			32.5997i			1.26991i	0.772551	+	0.634953i	$0.218981\pi$
$659$			32.5997i			1.26991i	−0.772551	+	0.634953i	$0.781019\pi$
$660$	10.2675	+	20.4093i	0.399661	+	0.794432i
$661$			12.6725i			0.492902i	0.969155	+	0.246451i	$0.0792645\pi$
$661$			12.6725i			0.492902i	−0.969155	+	0.246451i	$0.920735\pi$
$662$		−	19.1126i		−	0.742832i
$663$		−	34.7160i		−	1.34826i
$664$		−	5.84246i		−	0.226731i
$665$		0			0
$666$			10.2317i			0.396469i
$667$			10.1883i			0.394494i
$668$	16.0519			0.621067
$669$	2.79797			0.108176
$670$	−6.56846			−0.253762
$671$	8.53508	+	16.9657i	0.329493	+	0.654955i
$672$		0			0
$673$			1.20344i			0.0463893i	0.999731	+	0.0231947i	$0.00738375\pi$
$673$			1.20344i			0.0463893i	−0.999731	+	0.0231947i	$0.992616\pi$
$674$	−16.0358			−0.617676
$675$			1.74064i			0.0669971i
$676$	10.8702			0.418086
$677$	−26.3159			−1.01140			−0.505701	−	0.862709i	$-0.668766\pi$
$677$	−26.3159			−1.01140			−0.505701	+	0.862709i	$0.668766\pi$
$678$	−24.4920			−0.940610
$679$		0			0
$680$	16.7580			0.642640
$681$		−	42.1673i		−	1.61586i
$682$	−12.7425	−	25.3291i	−0.487936	−	0.969901i
$683$	32.9274			1.25993			0.629966	−	0.776623i	$-0.283069\pi$
$683$	32.9274			1.25993			0.629966	+	0.776623i	$0.283069\pi$
$684$	−1.22447			−0.0468189
$685$		−	19.2155i		−	0.734187i
$686$		0			0
$687$	15.2771			0.582858
$688$			1.58174i			0.0603032i
$689$	−7.05524			−0.268783
$690$		−	15.7594i		−	0.599949i
$691$		−	28.2336i		−	1.07406i	−0.843565	−	0.537028i	$-0.819547\pi$
$691$		−	28.2336i		−	1.07406i	0.843565	−	0.537028i	$-0.180453\pi$
$692$	7.09477			0.269703
$693$		0			0
$694$	9.87094			0.374696
$695$			9.01618i			0.342003i
$696$			13.9258i			0.527855i
$697$	54.0400			2.04691
$698$		−	31.1871i		−	1.18045i
$699$	70.8605			2.68019
$700$		0			0
$701$			24.2464i			0.915775i	0.889010	+	0.457888i	$0.151394\pi$
$701$			24.2464i			0.915775i	−0.889010	+	0.457888i	$0.848606\pi$
$702$	−17.2424			−0.650771
$703$	−0.272679			−0.0102843
$704$	1.49053	+	2.96282i	0.0561765	+	0.111666i
$705$			3.75668i			0.141485i
$706$	−25.9682			−0.977327
$707$		0			0
$708$	19.3553			0.727416
$709$	43.2699			1.62504			0.812518	−	0.582936i	$-0.198096\pi$
$709$	43.2699			1.62504			0.812518	+	0.582936i	$0.198096\pi$
$710$	−16.6865			−0.626235
$711$			46.8978i			1.75880i
$712$	16.1111			0.603791
$713$			19.5583i			0.732463i
$714$		0			0
$715$	−9.52494	+	4.79178i	−0.356213	+	0.179203i
$716$	24.9728			0.933278
$717$	−78.9293			−2.94767
$718$	−4.01067			−0.149677
$719$		−	23.0095i		−	0.858110i	−0.903278	−	0.429055i	$-0.858847\pi$
$719$		−	23.0095i		−	0.858110i	0.903278	−	0.429055i	$-0.141153\pi$
$720$		−	14.9318i		−	0.556476i
$721$		0			0
$722$			18.9674i			0.705892i
$723$			43.9876i			1.63592i
$724$			19.3579i			0.719429i
$725$			0.656091i			0.0243666i
$726$	20.5028	−	27.6190i	0.760931	−	1.02504i
$727$			39.3745i			1.46032i	0.683276	+	0.730160i	$0.260555\pi$
$727$			39.3745i			1.46032i	−0.683276	+	0.730160i	$0.739445\pi$
$728$		0			0
$729$	−1.75557			−0.0650210
$730$	−21.3160			−0.788941
$731$		−	12.0328i		−	0.445048i
$732$		−	17.9060i		−	0.661826i
$733$	−8.18529			−0.302331			−0.151165	−	0.988509i	$-0.548303\pi$
$733$	−8.18529			−0.302331			−0.151165	+	0.988509i	$0.548303\pi$
$734$	19.1851			0.708135
$735$		0			0
$736$		−	2.28779i		−	0.0843291i
$737$	4.44441	+	8.83444i	0.163712	+	0.325421i
$738$		−	48.1510i		−	1.77246i
$739$			38.1924i			1.40493i	0.711718	+	0.702466i	$0.247918\pi$
$739$			38.1924i			1.40493i	−0.711718	+	0.702466i	$0.752082\pi$
$740$		−	3.32518i		−	0.122236i
$741$		−	0.824375i		−	0.0302842i
$742$		0			0
$743$			27.3005i			1.00156i	0.865575	+	0.500779i	$0.166953\pi$
$743$			27.3005i			1.00156i	−0.865575	+	0.500779i	$0.833047\pi$
$744$			26.7329i			0.980076i
$745$	40.9553			1.50049
$746$	21.0289			0.769924
$747$	39.6021			1.44896
$748$	−11.3389	−	22.5391i	−0.414592	−	0.824112i
$749$		0			0
$750$		−	35.4572i		−	1.29471i
$751$	−2.23167			−0.0814349			−0.0407175	−	0.999171i	$-0.512964\pi$
$751$	−2.23167			−0.0814349			−0.0407175	+	0.999171i	$0.512964\pi$
$752$			0.545357i			0.0198871i
$753$	−9.49742			−0.346105
$754$	−6.49910			−0.236683
$755$	−29.0879			−1.05862
$756$		0			0
$757$	−16.6709			−0.605913			−0.302956	−	0.953004i	$-0.597974\pi$
$757$	−16.6709			−0.605913			−0.302956	+	0.953004i	$0.597974\pi$
$758$		−	20.7525i		−	0.753766i
$759$	−21.1960	+	10.6632i	−0.769367	+	0.387051i
$760$	0.397940			0.0144348
$761$	45.6321			1.65416			0.827081	−	0.562083i	$-0.190000\pi$
$761$	45.6321			1.65416			0.827081	+	0.562083i	$0.190000\pi$
$762$			42.1218i			1.52591i
$763$		0			0
$764$	−6.00000			−0.217072
$765$			113.591i			4.10689i
$766$	1.25606			0.0453832
$767$			9.03303i			0.326164i
$768$		−	3.12703i		−	0.112837i
$769$	−51.3570			−1.85198			−0.925991	−	0.377546i	$-0.876768\pi$
$769$	−51.3570			−1.85198			−0.925991	+	0.377546i	$0.876768\pi$
$770$		0			0
$771$	−80.5784			−2.90196
$772$			16.6114i			0.597857i
$773$		−	21.8478i		−	0.785812i	−0.919579	−	0.392906i	$-0.871470\pi$
$773$		−	21.8478i		−	0.785812i	0.919579	−	0.392906i	$-0.128530\pi$
$774$	−10.7215			−0.385377
$775$			1.25948i			0.0452418i
$776$	−11.3012			−0.405688
$777$		0			0
$778$			16.6479i			0.596854i
$779$	1.28325			0.0459771
$780$	10.0528			0.359949
$781$	11.2906	+	22.4430i	0.404009	+	0.803075i
$782$			17.4040i			0.622364i
$783$	−52.6160			−1.88034
$784$		0			0
$785$	−12.6864			−0.452797
$786$	8.20726			0.292743
$787$	20.4402			0.728613			0.364307	−	0.931279i	$-0.381306\pi$
$787$	20.4402			0.728613			0.364307	+	0.931279i	$0.381306\pi$
$788$		−	20.6396i		−	0.735256i
$789$	20.0443			0.713597
$790$		−	15.2412i		−	0.542259i
$791$		0			0
$792$	−20.0830	+	10.1033i	−0.713617	+	0.359005i
$793$	8.35667			0.296754
$794$	−14.1742			−0.503025
$795$	33.3019			1.18110
$796$		−	0.726003i		−	0.0257325i
$797$			6.09214i			0.215795i	0.994162	+	0.107897i	$0.0344118\pi$
$797$			6.09214i			0.215795i	−0.994162	+	0.107897i	$0.965588\pi$
$798$		0			0
$799$		−	4.14871i		−	0.146771i
$800$		−	0.147325i		−	0.00520873i
$801$			109.207i			3.85862i
$802$			4.85270i			0.171355i
$803$	14.4230	+	28.6696i	0.508977	+	1.01173i
$804$		−	9.32407i		−	0.328834i
$805$		0			0
$806$	−12.4761			−0.439453
$807$	8.57282			0.301777
$808$		−	0.517716i		−	0.0182132i
$809$		−	34.7780i		−	1.22273i	−0.791349	−	0.611364i	$-0.790621\pi$
$809$		−	34.7780i		−	1.22273i	0.791349	−	0.611364i	$-0.209379\pi$
$810$	36.5913			1.28569
$811$	26.6602			0.936167			0.468083	−	0.883684i	$-0.344945\pi$
$811$	26.6602			0.936167			0.468083	+	0.883684i	$0.344945\pi$
$812$		0			0
$813$		−	89.4337i		−	3.13658i
$814$	−4.47229	+	2.24991i	−0.156754	+	0.0788593i
$815$		−	11.7036i		−	0.409961i
$816$			23.7883i			0.832758i
$817$		−	0.285733i		−	0.00999655i
$818$		−	10.6280i		−	0.371601i
$819$		0			0
$820$			15.6486i			0.546471i
$821$		−	12.7504i		−	0.444993i	−0.974933	−	0.222497i	$-0.928579\pi$
$821$		−	12.7504i		−	0.444993i	0.974933	−	0.222497i	$-0.0714206\pi$
$822$	27.2768			0.951388
$823$	−15.8764			−0.553416			−0.276708	−	0.960954i	$-0.589243\pi$
$823$	−15.8764			−0.553416			−0.276708	+	0.960954i	$0.589243\pi$
$824$	−2.88716			−0.100579
$825$	−1.36494	+	0.686673i	−0.0475213	+	0.0239069i
$826$		0			0
$827$		−	35.9639i		−	1.25059i	−0.780390	−	0.625293i	$-0.784979\pi$
$827$		−	35.9639i		−	1.25059i	0.780390	−	0.625293i	$-0.215021\pi$
$828$	15.5074			0.538919
$829$		−	35.9072i		−	1.24711i	−0.781780	−	0.623555i	$-0.785688\pi$
$829$		−	35.9072i		−	1.24711i	0.781780	−	0.623555i	$-0.214312\pi$
$830$	−12.8702			−0.446732
$831$	33.6729			1.16810
$832$	1.45937			0.0505946
$833$		0			0
$834$	−12.7986			−0.443181
$835$		−	35.3604i		−	1.22370i
$836$	−0.269257	−	0.535220i	−0.00931246	−	0.0185110i
$837$	−101.005			−3.49126
$838$	−11.3690			−0.392735
$839$		−	39.5137i		−	1.36416i	−0.731276	−	0.682081i	$-0.761075\pi$
$839$		−	39.5137i		−	1.36416i	0.731276	−	0.682081i	$-0.238925\pi$
$840$		0			0
$841$	9.16765			0.316126
$842$		−	27.2464i		−	0.938974i
$843$	−61.3802			−2.11405
$844$		−	10.2878i		−	0.354120i
$845$		−	23.9458i		−	0.823761i
$846$	−3.69661			−0.127092
$847$		0			0
$848$	4.83444			0.166015
$849$		−	33.2193i		−	1.14008i
$850$			1.12075i			0.0384414i
$851$	3.45335			0.118379
$852$		−	23.6869i		−	0.811499i
$853$	−8.92246			−0.305499			−0.152750	−	0.988265i	$-0.548813\pi$
$853$	−8.92246			−0.305499			−0.152750	+	0.988265i	$0.548813\pi$
$854$		0			0
$855$			2.69736i			0.0922479i
$856$	5.21959			0.178402
$857$	8.74093			0.298584			0.149292	−	0.988793i	$-0.452300\pi$
$857$	8.74093			0.298584			0.149292	+	0.988793i	$0.452300\pi$
$858$	−6.80203	−	13.5208i	−0.232218	−	0.461594i
$859$		−	29.7711i		−	1.01578i	−0.861423	−	0.507888i	$-0.830426\pi$
$859$		−	29.7711i		−	1.01578i	0.861423	−	0.507888i	$-0.169574\pi$
$860$	3.48438			0.118816
$861$		0			0
$862$	15.2210			0.518428
$863$	22.9728			0.782005			0.391002	−	0.920390i	$-0.372128\pi$
$863$	22.9728			0.782005			0.391002	+	0.920390i	$0.372128\pi$
$864$	11.8149			0.401952
$865$		−	15.6289i		−	0.531399i
$866$	−1.85534			−0.0630470
$867$		−	127.806i		−	4.34051i
$868$		0			0
$869$	−20.4991	+	10.3127i	−0.695386	+	0.349833i
$870$	30.6768			1.04004
$871$	4.35150			0.147445
$872$	10.0540			0.340472
$873$		−	76.6029i		−	2.59261i
$874$			0.413279i			0.0139794i
$875$		0			0
$876$		−	30.2585i		−	1.02234i
$877$			33.2451i			1.12261i	0.827610	+	0.561303i	$0.189700\pi$
$877$			33.2451i			1.12261i	−0.827610	+	0.561303i	$0.810300\pi$
$878$			32.9404i			1.11168i
$879$		−	0.868224i		−	0.0292845i
$880$	6.52674	−	3.28346i	0.220016	−	0.110685i
$881$		−	2.73248i		−	0.0920594i	−0.998940	−	0.0460297i	$-0.985343\pi$
$881$		−	2.73248i		−	0.0920594i	0.998940	−	0.0460297i	$-0.0146569\pi$
$882$		0			0
$883$	−19.7473			−0.664550			−0.332275	−	0.943183i	$-0.607816\pi$
$883$	−19.7473			−0.664550			−0.332275	+	0.943183i	$0.607816\pi$
$884$	−11.1019			−0.373398
$885$		−	42.6373i		−	1.43324i
$886$			32.8613i			1.10400i
$887$	−24.4620			−0.821353			−0.410676	−	0.911781i	$-0.634707\pi$
$887$	−24.4620			−0.821353			−0.410676	+	0.911781i	$0.634707\pi$
$888$	4.72016			0.158398
$889$		0			0
$890$		−	35.4909i		−	1.18966i
$891$	−24.7587	−	49.2145i	−0.829448	−	1.64875i
$892$		−	0.894768i		−	0.0299590i
$893$		−	0.0985163i		−	0.00329672i
$894$			58.1369i			1.94439i
$895$		−	55.0121i		−	1.83885i
$896$		0			0
$897$			10.4403i			0.348593i
$898$		−	3.62716i		−	0.121040i
$899$	−38.0716			−1.26976
$900$	0.998618			0.0332873
$901$	−36.7771			−1.22522
$902$	21.0470	−	10.5883i	0.700787	−	0.352550i
$903$		0			0
$904$			7.83235i			0.260500i
$905$	42.6430			1.41750
$906$		−	41.2909i		−	1.37180i
$907$	−44.6217			−1.48164			−0.740820	−	0.671703i	$-0.765563\pi$
$907$	−44.6217			−1.48164			−0.740820	+	0.671703i	$0.765563\pi$
$908$	−13.4848			−0.447508
$909$	3.50925			0.116394
$910$		0			0
$911$	37.0868			1.22874			0.614370	−	0.789018i	$-0.289410\pi$
$911$	37.0868			1.22874			0.614370	+	0.789018i	$0.289410\pi$
$912$			0.564883i			0.0187052i
$913$	8.70836	+	17.3102i	0.288205	+	0.572883i
$914$	2.73567			0.0904878
$915$	−39.4448			−1.30401
$916$		−	4.88550i		−	0.161422i
$917$		0			0
$918$	−89.8799			−2.96648
$919$		−	50.9873i		−	1.68192i	−0.541100	−	0.840958i	$-0.681992\pi$
$919$		−	50.9873i		−	1.68192i	0.541100	−	0.840958i	$-0.318008\pi$
$920$	−5.03973			−0.166155
$921$		−	20.0581i		−	0.660938i
$922$			20.4439i			0.673285i
$923$	11.0546			0.363865
$924$		0			0
$925$	0.222383			0.00731191
$926$		−	30.1701i		−	0.991451i
$927$		−	19.5701i		−	0.642766i
$928$	4.45335			0.146188
$929$		−	12.1898i		−	0.399934i	−0.979803	−	0.199967i	$-0.935917\pi$
$929$		−	12.1898i		−	0.399934i	0.979803	−	0.199967i	$-0.0640834\pi$
$930$	58.8893			1.93106
$931$		0			0
$932$		−	22.6606i		−	0.742274i
$933$	−35.3429			−1.15707
$934$	−27.1722			−0.889103
$935$	−49.6510	+	24.9783i	−1.62376	+	0.816878i
$936$			9.89209i			0.323333i
$937$	17.0188			0.555979			0.277990	−	0.960584i	$-0.410332\pi$
$937$	17.0188			0.555979			0.277990	+	0.960584i	$0.410332\pi$
$938$		0			0
$939$	51.4292			1.67833
$940$	1.20136			0.0391839
$941$	13.5983			0.443292			0.221646	−	0.975127i	$-0.428857\pi$
$941$	13.5983			0.443292			0.221646	+	0.975127i	$0.428857\pi$
$942$		−	18.0086i		−	0.586752i
$943$	−16.2517			−0.529230
$944$		−	6.18967i		−	0.201457i
$945$		0			0
$946$	−2.35763	−	4.68641i	−0.0766531	−	0.152368i
$947$	−33.0849			−1.07512			−0.537558	−	0.843227i	$-0.680653\pi$
$947$	−33.0849			−1.07512			−0.537558	+	0.843227i	$0.680653\pi$
$948$	21.6353			0.702681
$949$	14.1215			0.458404
$950$			0.0266136i			0.000863460i
$951$			88.1542i			2.85860i
$952$		0			0
$953$		−	0.427553i		−	0.0138498i	−0.999976	−	0.00692490i	$-0.997796\pi$
$953$		−	0.427553i		−	0.0138498i	0.999976	−	0.00692490i	$-0.00220428\pi$
$954$			32.7694i			1.06095i
$955$			13.2173i			0.427701i
$956$			25.2410i			0.816351i
$957$	−20.7568	−	41.2596i	−0.670971	−	1.33373i
$958$			21.6184i			0.698459i
$959$		0			0
$960$	−6.88847			−0.222324
$961$	−42.0849			−1.35758
$962$			2.20288i			0.0710237i
$963$			35.3801i			1.14011i
$964$	14.0669			0.453064
$965$	36.5928			1.17797
$966$		0			0
$967$		−	6.75935i		−	0.217366i	−0.994076	−	0.108683i	$-0.965337\pi$
$967$		−	6.75935i		−	0.217366i	0.994076	−	0.108683i	$-0.0346634\pi$
$968$	−8.83235	−	6.55664i	−0.283883	−	0.210738i
$969$		−	4.29725i		−	0.138047i
$970$			24.8951i			0.799333i
$971$		−	21.4878i		−	0.689575i	−0.938681	−	0.344787i	$-0.887951\pi$
$971$		−	21.4878i		−	0.689575i	0.938681	−	0.344787i	$-0.112049\pi$
$972$			16.4973i			0.529151i
$973$		0			0
$974$		−	2.08573i		−	0.0668311i
$975$			0.672319i			0.0215314i
$976$	−5.72621			−0.183291
$977$	43.2933			1.38507			0.692537	−	0.721382i	$-0.256493\pi$
$977$	43.2933			1.38507			0.692537	+	0.721382i	$0.256493\pi$
$978$	16.6136			0.531243
$979$	−47.7345	+	24.0141i	−1.52560	+	0.767495i
$980$		0			0
$981$			68.1495i			2.17584i
$982$	2.47983			0.0791346
$983$			20.9608i			0.668545i	0.942476	+	0.334273i	$0.108491\pi$
$983$			20.9608i			0.668545i	−0.942476	+	0.334273i	$0.891509\pi$
$984$	−22.2134			−0.708139
$985$	−45.4666			−1.44868
$986$	−33.8781			−1.07890
$987$		0			0
$988$	−0.263629			−0.00838715
$989$			3.61869i			0.115068i
$990$	22.2563	+	44.2403i	0.707352	+	1.40605i
$991$	38.5404			1.22428			0.612138	−	0.790751i	$-0.290310\pi$
$991$	38.5404			1.22428			0.612138	+	0.790751i	$0.290310\pi$
$992$	8.54897			0.271430
$993$		−	59.7656i		−	1.89660i
$994$		0			0
$995$	−1.59930			−0.0507011
$996$		−	18.2696i		−	0.578893i
$997$	−19.4465			−0.615876			−0.307938	−	0.951406i	$-0.599639\pi$
$997$	−19.4465			−0.615876			−0.307938	+	0.951406i	$0.599639\pi$
$998$		−	15.3838i		−	0.486965i
$999$			17.8343i			0.564252i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1078.2.c.b.1077.1		16
7.2	even	3		1078.2.i.c.1011.4		16
7.3	odd	6		1078.2.i.c.901.8		16
7.4	even	3		154.2.i.a.131.5	yes	16
7.5	odd	6		154.2.i.a.87.1	✓	16
7.6	odd	2	inner	1078.2.c.b.1077.8		16
11.10	odd	2	inner	1078.2.c.b.1077.9		16
21.5	even	6		1386.2.bk.c.703.7		16
21.11	odd	6		1386.2.bk.c.901.3		16
28.11	odd	6		1232.2.bn.b.593.8		16
28.19	even	6		1232.2.bn.b.241.7		16
77.10	even	6		1078.2.i.c.901.4		16
77.32	odd	6		154.2.i.a.131.1	yes	16
77.54	even	6		154.2.i.a.87.5	yes	16
77.65	odd	6		1078.2.i.c.1011.8		16
77.76	even	2	inner	1078.2.c.b.1077.16		16
231.32	even	6		1386.2.bk.c.901.7		16
231.131	odd	6		1386.2.bk.c.703.3		16
308.131	odd	6		1232.2.bn.b.241.8		16
308.263	even	6		1232.2.bn.b.593.7		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
154.2.i.a.87.1	✓	16	7.5	odd	6
154.2.i.a.87.5	yes	16	77.54	even	6
154.2.i.a.131.1	yes	16	77.32	odd	6
154.2.i.a.131.5	yes	16	7.4	even	3
1078.2.c.b.1077.1		16	1.1	even	1	trivial
1078.2.c.b.1077.8		16	7.6	odd	2	inner
1078.2.c.b.1077.9		16	11.10	odd	2	inner
1078.2.c.b.1077.16		16	77.76	even	2	inner
1078.2.i.c.901.4		16	77.10	even	6
1078.2.i.c.901.8		16	7.3	odd	6
1078.2.i.c.1011.4		16	7.2	even	3
1078.2.i.c.1011.8		16	77.65	odd	6
1232.2.bn.b.241.7		16	28.19	even	6
1232.2.bn.b.241.8		16	308.131	odd	6
1232.2.bn.b.593.7		16	308.263	even	6
1232.2.bn.b.593.8		16	28.11	odd	6
1386.2.bk.c.703.3		16	231.131	odd	6
1386.2.bk.c.703.7		16	21.5	even	6
1386.2.bk.c.901.3		16	21.11	odd	6
1386.2.bk.c.901.7		16	231.32	even	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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 1078 = 2 \cdot 7^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1078.c (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-1.00000i q^{2} -3.12703i q^{3} -1.00000 q^{4} +2.20288i q^{5} -3.12703 q^{6} +1.00000i q^{8} -6.77832 q^{9} +O(q^{10})\)	\(q-1.00000i q^{2} -3.12703i q^{3} -1.00000 q^{4} +2.20288i q^{5} -3.12703 q^{6} +1.00000i q^{8} -6.77832 q^{9} +2.20288 q^{10} +(-1.49053 - 2.96282i) q^{11} +3.12703i q^{12} -1.45937 q^{13} +6.88847 q^{15} +1.00000 q^{16} -7.60732 q^{17} +6.77832i q^{18} -0.180645 q^{19} -2.20288i q^{20} +(-2.96282 + 1.49053i) q^{22} +2.28779 q^{23} +3.12703 q^{24} +0.147325 q^{25} +1.45937i q^{26} +11.8149i q^{27} +4.45335i q^{29} -6.88847i q^{30} +8.54897i q^{31} -1.00000i q^{32} +(-9.26484 + 4.66093i) q^{33} +7.60732i q^{34} +6.77832 q^{36} +1.50947 q^{37} +0.180645i q^{38} +4.56350i q^{39} -2.20288 q^{40} -7.10368 q^{41} +1.58174i q^{43} +(1.49053 + 2.96282i) q^{44} -14.9318i q^{45} -2.28779i q^{46} +0.545357i q^{47} -3.12703i q^{48} -0.147325i q^{50} +23.7883i q^{51} +1.45937 q^{52} +4.83444 q^{53} +11.8149 q^{54} +(6.52674 - 3.28346i) q^{55} +0.564883i q^{57} +4.45335 q^{58} -6.18967i q^{59} -6.88847 q^{60} -5.72621 q^{61} +8.54897 q^{62} -1.00000 q^{64} -3.21482i q^{65} +(4.66093 + 9.26484i) q^{66} -2.98176 q^{67} +7.60732 q^{68} -7.15399i q^{69} -7.57488 q^{71} -6.77832i q^{72} -9.67644 q^{73} -1.50947i q^{74} -0.460691i q^{75} +0.180645 q^{76} +4.56350 q^{78} -6.91879i q^{79} +2.20288i q^{80} +16.6107 q^{81} +7.10368i q^{82} -5.84246 q^{83} -16.7580i q^{85} +1.58174 q^{86} +13.9258 q^{87} +(2.96282 - 1.49053i) q^{88} -16.1111i q^{89} -14.9318 q^{90} -2.28779 q^{92} +26.7329 q^{93} +0.545357 q^{94} -0.397940i q^{95} -3.12703 q^{96} +11.3012i q^{97} +(10.1033 + 20.0830i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 16 q^{4} - 32 q^{9}+O(q^{10}) \) 16 * q - 16 * q^4 - 32 * q^9	\( 16 q - 16 q^{4} - 32 q^{9} - 16 q^{11} - 8 q^{15} + 16 q^{16} - 8 q^{22} - 32 q^{23} + 32 q^{36} + 32 q^{37} + 16 q^{44} + 56 q^{53} + 24 q^{58} + 8 q^{60} - 16 q^{64} - 24 q^{67} + 8 q^{71} - 16 q^{78} + 16 q^{81} - 40 q^{86} + 8 q^{88} + 32 q^{92} + 88 q^{93} + 56 q^{99}+O(q^{100}) \) 16 * q - 16 * q^4 - 32 * q^9 - 16 * q^11 - 8 * q^15 + 16 * q^16 - 8 * q^22 - 32 * q^23 + 32 * q^36 + 32 * q^37 + 16 * q^44 + 56 * q^53 + 24 * q^58 + 8 * q^60 - 16 * q^64 - 24 * q^67 + 8 * q^71 - 16 * q^78 + 16 * q^81 - 40 * q^86 + 8 * q^88 + 32 * q^92 + 88 * q^93 + 56 * q^99

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