LMFDB - Embedded newform 60.7.b.a.29.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [60,7,Mod(29,60)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(60, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 7, names="a")

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

chi := DirichletCharacter("60.29");

S:= CuspForms(chi, 7);

N := Newforms(S);

Level:	$ N $	$=$	$ 60 = 2^{2} \cdot 3 \cdot 5 $
Weight:	$ k $	$=$	$ 7 $
Character orbit:	$[\chi]$	$=$	60.b (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:	$13.8032450172$
Analytic rank:	$0$
Dimension:	$12$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} + 1880 x^{10} + 1266870 x^{8} + 399545800 x^{6} + 62009694600 x^{4} + 4432082624000 x^{2} + 109931031040000 $ x^12 + 1880x^10 + 1266870x^8 + 399545800x^6 + 62009694600x^4 + 4432082624000*x^2 + 109931031040000
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{22}\cdot 3^{8}\cdot 5^{9} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			29.8
Root			$-13.3561i$ of defining polynomial
Character	$\chi$	$=$	60.29
Dual form			60.7.b.a.29.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(7.66273 + 25.8898i) q^{3} +(-37.2664 + 119.316i) q^{5} +46.7246i q^{7} +(-611.565 + 396.774i) q^{9} +O(q^{10})$	\(q+(7.66273 + 25.8898i) q^{3} +(-37.2664 + 119.316i) q^{5} +46.7246i q^{7} +(-611.565 + 396.774i) q^{9} +448.732i q^{11} -2072.30i q^{13} +(-3374.62 - 50.5373i) q^{15} -5987.26 q^{17} +7407.66 q^{19} +(-1209.69 + 358.038i) q^{21} -17175.3 q^{23} +(-12847.4 - 8892.93i) q^{25} +(-14958.7 - 12792.9i) q^{27} +37549.0i q^{29} -17977.2 q^{31} +(-11617.6 + 3438.51i) q^{33} +(-5574.97 - 1741.26i) q^{35} +36228.1i q^{37} +(53651.5 - 15879.5i) q^{39} +12817.7i q^{41} -25097.3i q^{43} +(-24550.4 - 87755.6i) q^{45} +51821.1 q^{47} +115466. q^{49} +(-45878.8 - 155009. i) q^{51} +270680. q^{53} +(-53540.7 - 16722.6i) q^{55} +(56762.9 + 191783. i) q^{57} +218274. i q^{59} +38350.9 q^{61} +(-18539.1 - 28575.1i) q^{63} +(247258. + 77227.2i) q^{65} +259141. i q^{67} +(-131610. - 444666. i) q^{69} +452834. i q^{71} -78457.1i q^{73} +(131790. - 400762. i) q^{75} -20966.8 q^{77} -410751. q^{79} +(216583. - 485306. i) q^{81} -630723. q^{83} +(223124. - 714374. i) q^{85} +(-972136. + 287728. i) q^{87} +145021. i q^{89} +96827.4 q^{91} +(-137754. - 465426. i) q^{93} +(-276057. + 883849. i) q^{95} +1.76304e6i q^{97} +(-178045. - 274429. i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 712 q^{9}+O(q^{10}) $ 12 * q + 712 * q^9	$ 12 q + 712 q^{9} + 2480 q^{15} - 192 q^{19} + 5348 q^{21} + 18660 q^{25} + 40848 q^{31} - 45312 q^{39} + 45340 q^{45} - 242940 q^{49} - 40720 q^{51} - 24240 q^{55} - 99312 q^{61} + 108460 q^{69} + 126640 q^{75} + 626544 q^{79} - 798268 q^{81} - 732720 q^{85} + 1996032 q^{91} + 1632080 q^{99}+O(q^{100}) $ 12 * q + 712 * q^9 + 2480 * q^15 - 192 * q^19 + 5348 * q^21 + 18660 * q^25 + 40848 * q^31 - 45312 * q^39 + 45340 * q^45 - 242940 * q^49 - 40720 * q^51 - 24240 * q^55 - 99312 * q^61 + 108460 * q^69 + 126640 * q^75 + 626544 * q^79 - 798268 * q^81 - 732720 * q^85 + 1996032 * q^91 + 1632080 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/60\mathbb{Z}\right)^\times$.

$n$	$31$	$37$	$41$
$\chi(n)$	$1$	$-1$	$-1$

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			0
$2$		0			0
$3$	7.66273	+	25.8898i	0.283805	+	0.958882i
$3$	7.66273	+	25.8898i	0.283805	+	0.958882i
$4$		0			0
$5$	−37.2664	+	119.316i	−0.298131	+	0.954525i
$5$	−37.2664	+	119.316i	−0.298131	+	0.954525i
$6$		0			0
$7$			46.7246i			0.136223i	0.997678	+	0.0681116i	$0.0216974\pi$
$7$			46.7246i			0.136223i	−0.997678	+	0.0681116i	$0.978303\pi$
$8$		0			0
$9$	−611.565	+	396.774i	−0.838909	+	0.544271i
$10$		0			0
$11$			448.732i			0.337139i	0.985690	+	0.168569i	$0.0539148\pi$
$11$			448.732i			0.337139i	−0.985690	+	0.168569i	$0.946085\pi$
$12$		0			0
$13$		−	2072.30i		−	0.943241i	−0.881802	−	0.471620i	$-0.843669\pi$
$13$		−	2072.30i		−	0.943241i	0.881802	−	0.471620i	$-0.156331\pi$
$14$		0			0
$15$	−3374.62	−	50.5373i	−0.999888	−	0.0149740i
$16$		0			0
$17$	−5987.26			−1.21866			−0.609329	−	0.792918i	$-0.708561\pi$
$17$	−5987.26			−1.21866			−0.609329	+	0.792918i	$0.708561\pi$
$18$		0			0
$19$	7407.66			1.07999			0.539996	−	0.841668i	$-0.318426\pi$
$19$	7407.66			1.07999			0.539996	+	0.841668i	$0.318426\pi$
$20$		0			0
$21$	−1209.69	+	358.038i	−0.130622	+	0.0386608i
$22$		0			0
$23$	−17175.3			−1.41163			−0.705817	−	0.708395i	$-0.749420\pi$
$23$	−17175.3			−1.41163			−0.705817	+	0.708395i	$0.749420\pi$
$24$		0			0
$25$	−12847.4	−	8892.93i	−0.822235	−	0.569148i
$26$		0			0
$27$	−14958.7	−	12792.9i	−0.759978	−	0.649948i
$28$		0			0
$29$			37549.0i			1.53959i	0.638294	+	0.769793i	$0.279641\pi$
$29$			37549.0i			1.53959i	−0.638294	+	0.769793i	$0.720359\pi$
$30$		0			0
$31$	−17977.2			−0.603444			−0.301722	−	0.953396i	$-0.597561\pi$
$31$	−17977.2			−0.603444			−0.301722	+	0.953396i	$0.597561\pi$
$32$		0			0
$33$	−11617.6	+	3438.51i	−0.323276	+	0.0956817i
$34$		0			0
$35$	−5574.97	−	1741.26i	−0.130028	−	0.0406124i
$36$		0			0
$37$			36228.1i			0.715222i	0.933871	+	0.357611i	$0.116409\pi$
$37$			36228.1i			0.715222i	−0.933871	+	0.357611i	$0.883591\pi$
$38$		0			0
$39$	53651.5	−	15879.5i	0.904457	−	0.267696i
$40$		0			0
$41$			12817.7i			0.185977i	0.995667	+	0.0929886i	$0.0296420\pi$
$41$			12817.7i			0.185977i	−0.995667	+	0.0929886i	$0.970358\pi$
$42$		0			0
$43$		−	25097.3i		−	0.315661i	−0.987466	−	0.157831i	$-0.949550\pi$
$43$		−	25097.3i		−	0.315661i	0.987466	−	0.157831i	$-0.0504500\pi$
$44$		0			0
$45$	−24550.4	−	87755.6i	−0.269415	−	0.963024i
$46$		0			0
$47$	51821.1			0.499129			0.249564	−	0.968358i	$-0.419713\pi$
$47$	51821.1			0.499129			0.249564	+	0.968358i	$0.419713\pi$
$48$		0			0
$49$	115466.			0.981443
$50$		0			0
$51$	−45878.8	−	155009.i	−0.345861	−	1.16855i
$52$		0			0
$53$	270680.			1.81815			0.909073	−	0.416638i	$-0.136792\pi$
$53$	270680.			1.81815			0.909073	+	0.416638i	$0.136792\pi$
$54$		0			0
$55$	−53540.7	−	16722.6i	−0.321807	−	0.100512i
$56$		0			0
$57$	56762.9	+	191783.i	0.306507	+	1.03558i
$58$		0			0
$59$			218274.i			1.06279i	0.847126	+	0.531393i	$0.178331\pi$
$59$			218274.i			1.06279i	−0.847126	+	0.531393i	$0.821669\pi$
$60$		0			0
$61$	38350.9			0.168961			0.0844804	−	0.996425i	$-0.473077\pi$
$61$	38350.9			0.168961			0.0844804	+	0.996425i	$0.473077\pi$
$62$		0			0
$63$	−18539.1	−	28575.1i	−0.0741424	−	0.114279i
$64$		0			0
$65$	247258.	+	77227.2i	0.900347	+	0.281210i
$66$		0			0
$67$			259141.i			0.861613i	0.902444	+	0.430807i	$0.141771\pi$
$67$			259141.i			0.861613i	−0.902444	+	0.430807i	$0.858229\pi$
$68$		0			0
$69$	−131610.	−	444666.i	−0.400629	−	1.35359i
$70$		0			0
$71$			452834.i			1.26521i	0.774473	+	0.632607i	$0.218015\pi$
$71$			452834.i			1.26521i	−0.774473	+	0.632607i	$0.781985\pi$
$72$		0			0
$73$		−	78457.1i		−	0.201680i	−0.994903	−	0.100840i	$-0.967847\pi$
$73$		−	78457.1i		−	0.201680i	0.994903	−	0.100840i	$-0.0321531\pi$
$74$		0			0
$75$	131790.	−	400762.i	0.312391	−	0.949954i
$76$		0			0
$77$	−20966.8			−0.0459262
$78$		0			0
$79$	−410751.			−0.833100			−0.416550	−	0.909113i	$-0.636761\pi$
$79$	−410751.			−0.833100			−0.416550	+	0.909113i	$0.636761\pi$
$80$		0			0
$81$	216583.	−	485306.i	0.407538	−	0.913188i
$82$		0			0
$83$	−630723.			−1.10307			−0.551536	−	0.834151i	$-0.685958\pi$
$83$	−630723.			−1.10307			−0.551536	+	0.834151i	$0.685958\pi$
$84$		0			0
$85$	223124.	−	714374.i	0.363320	−	1.16324i
$86$		0			0
$87$	−972136.	+	287728.i	−1.47628	+	0.436942i
$88$		0			0
$89$			145021.i			0.205713i	0.994696	+	0.102857i	$0.0327983\pi$
$89$			145021.i			0.205713i	−0.994696	+	0.102857i	$0.967202\pi$
$90$		0			0
$91$	96827.4			0.128491
$92$		0			0
$93$	−137754.	−	465426.i	−0.171260	−	0.578631i
$94$		0			0
$95$	−276057.	+	883849.i	−0.321979	+	1.03088i
$96$		0			0
$97$			1.76304e6i			1.93174i	0.259035	+	0.965868i	$0.416595\pi$
$97$			1.76304e6i			1.93174i	−0.259035	+	0.965868i	$0.583405\pi$
$98$		0			0
$99$	−178045.	−	274429.i	−0.183495	−	0.282829i
$100$		0			0
$101$			1.01993e6i			0.989929i	0.868913	+	0.494965i	$0.164819\pi$
$101$			1.01993e6i			0.989929i	−0.868913	+	0.494965i	$0.835181\pi$
$102$		0			0
$103$		−	1.45111e6i		−	1.32797i	−0.747745	−	0.663986i	$-0.768864\pi$
$103$		−	1.45111e6i		−	1.32797i	0.747745	−	0.663986i	$-0.231136\pi$
$104$		0			0
$105$	2361.34	−	157678.i	0.00203981	−	0.136208i
$106$		0			0
$107$	−1.63492e6			−1.33459			−0.667293	−	0.744796i	$-0.732547\pi$
$107$	−1.63492e6			−1.33459			−0.667293	+	0.744796i	$0.732547\pi$
$108$		0			0
$109$	−1.13216e6			−0.874239			−0.437119	−	0.899403i	$-0.644001\pi$
$109$	−1.13216e6			−0.874239			−0.437119	+	0.899403i	$0.644001\pi$
$110$		0			0
$111$	−937940.	+	277607.i	−0.685813	+	0.202984i
$112$		0			0
$113$	1.63589e6			1.13376			0.566878	−	0.823801i	$-0.308151\pi$
$113$	1.63589e6			1.13376			0.566878	+	0.823801i	$0.308151\pi$
$114$		0			0
$115$	640064.	−	2.04929e6i	0.420852	−	1.34744i
$116$		0			0
$117$	822234.	+	1.26735e6i	0.513379	+	0.791294i
$118$		0			0
$119$		−	279752.i		−	0.166009i
$120$		0			0
$121$	1.57020e6			0.886337
$122$		0			0
$123$	−331849.	+	98218.9i	−0.178330	+	0.0527813i
$124$		0			0
$125$	1.53984e6	−	1.20149e6i	0.788400	−	0.615163i
$126$		0			0
$127$			3.64094e6i			1.77747i	0.458420	+	0.888735i	$0.348415\pi$
$127$			3.64094e6i			1.77747i	−0.458420	+	0.888735i	$0.651585\pi$
$128$		0			0
$129$	649763.	−	192314.i	0.302682	−	0.0895862i
$130$		0			0
$131$		−	3.48422e6i		−	1.54986i	−0.632048	−	0.774930i	$-0.717785\pi$
$131$		−	3.48422e6i		−	1.54986i	0.632048	−	0.774930i	$-0.282215\pi$
$132$		0			0
$133$			346120.i			0.147120i
$134$		0			0
$135$	2.08385e6	−	1.30805e6i	0.846965	−	0.531648i
$136$		0			0
$137$	1.58430e6			0.616136			0.308068	−	0.951364i	$-0.400318\pi$
$137$	1.58430e6			0.616136			0.308068	+	0.951364i	$0.400318\pi$
$138$		0			0
$139$	3.22087e6			1.19930			0.599652	−	0.800261i	$-0.295306\pi$
$139$	3.22087e6			1.19930			0.599652	+	0.800261i	$0.295306\pi$
$140$		0			0
$141$	397091.	+	1.34164e6i	0.141655	+	0.478606i
$142$		0			0
$143$	929907.			0.318003
$144$		0			0
$145$	−4.48018e6	−	1.39932e6i	−1.46957	−	0.458999i
$146$		0			0
$147$	884784.	+	2.98939e6i	0.278538	+	0.941088i
$148$		0			0
$149$		−	774236.i		−	0.234053i	−0.993129	−	0.117027i	$-0.962664\pi$
$149$		−	774236.i		−	0.234053i	0.993129	−	0.117027i	$-0.0373363\pi$
$150$		0			0
$151$	−3.15530e6			−0.916452			−0.458226	−	0.888836i	$-0.651515\pi$
$151$	−3.15530e6			−0.916452			−0.458226	+	0.888836i	$0.651515\pi$
$152$		0			0
$153$	3.66160e6	−	2.37559e6i	1.02234	−	0.663280i
$154$		0			0
$155$	669946.	−	2.14496e6i	0.179906	−	0.576002i
$156$		0			0
$157$			2.89669e6i			0.748519i	0.927324	+	0.374260i	$0.122103\pi$
$157$			2.89669e6i			0.748519i	−0.927324	+	0.374260i	$0.877897\pi$
$158$		0			0
$159$	2.07415e6	+	7.00786e6i	0.515999	+	1.74339i
$160$		0			0
$161$		−	802511.i		−	0.192297i
$162$		0			0
$163$		−	913439.i		−	0.210919i	−0.994424	−	0.105460i	$-0.966369\pi$
$163$		−	913439.i		−	0.210919i	0.994424	−	0.105460i	$-0.0336314\pi$
$164$		0			0
$165$	22677.7	−	1.51430e6i	0.00504833	−	0.337101i
$166$		0			0
$167$	−2.94266e6			−0.631817			−0.315908	−	0.948790i	$-0.602309\pi$
$167$	−2.94266e6			−0.631817			−0.315908	+	0.948790i	$0.602309\pi$
$168$		0			0
$169$	532380.			0.110296
$170$		0			0
$171$	−4.53027e6	+	2.93916e6i	−0.906015	+	0.587808i
$172$		0			0
$173$	−5.80609e6			−1.12136			−0.560681	−	0.828032i	$-0.689461\pi$
$173$	−5.80609e6			−1.12136			−0.560681	+	0.828032i	$0.689461\pi$
$174$		0			0
$175$	415519.	−	600290.i	0.0775312	−	0.112008i
$176$		0			0
$177$	−5.65107e6	+	1.67257e6i	−1.01909	+	0.301624i
$178$		0			0
$179$		−	3.83986e6i		−	0.669508i	−0.942306	−	0.334754i	$-0.891347\pi$
$179$		−	3.83986e6i		−	0.669508i	0.942306	−	0.334754i	$-0.108653\pi$
$180$		0			0
$181$	8.37561e6			1.41247			0.706237	−	0.707975i	$-0.250391\pi$
$181$	8.37561e6			1.41247			0.706237	+	0.707975i	$0.250391\pi$
$182$		0			0
$183$	293873.	+	992898.i	0.0479519	+	0.162014i
$184$		0			0
$185$	−4.32258e6	−	1.35009e6i	−0.682697	−	0.213230i
$186$		0			0
$187$		−	2.68668e6i		−	0.410857i
$188$		0			0
$189$	597744.	−	698937.i	0.0885381	−	0.103527i
$190$		0			0
$191$		−	4.85770e6i		−	0.697156i	−0.937280	−	0.348578i	$-0.886665\pi$
$191$		−	4.85770e6i		−	0.697156i	0.937280	−	0.348578i	$-0.113335\pi$
$192$		0			0
$193$		−	7.86974e6i		−	1.09468i	−0.836909	−	0.547342i	$-0.815640\pi$
$193$		−	7.86974e6i		−	1.09468i	0.836909	−	0.547342i	$-0.184360\pi$
$194$		0			0
$195$	−104729.	+	6.99323e6i	−0.0141241	+	0.943135i
$196$		0			0
$197$	−1.01804e7			−1.33158			−0.665789	−	0.746140i	$-0.731905\pi$
$197$	−1.01804e7			−1.33158			−0.665789	+	0.746140i	$0.731905\pi$
$198$		0			0
$199$	−6.73312e6			−0.854392			−0.427196	−	0.904159i	$-0.640498\pi$
$199$	−6.73312e6			−0.854392			−0.427196	+	0.904159i	$0.640498\pi$
$200$		0			0
$201$	−6.70912e6	+	1.98573e6i	−0.826186	+	0.244530i
$202$		0			0
$203$	−1.75446e6			−0.209727
$204$		0			0
$205$	−1.52936e6	−	477671.i	−0.177520	−	0.0554457i
$206$		0			0
$207$	1.05038e7	−	6.81472e6i	1.18423	−	0.768311i
$208$		0			0
$209$			3.32405e6i			0.364107i
$210$		0			0
$211$	4.09859e6			0.436301			0.218151	−	0.975915i	$-0.429998\pi$
$211$	4.09859e6			0.436301			0.218151	+	0.975915i	$0.429998\pi$
$212$		0			0
$213$	−1.17238e7	+	3.46995e6i	−1.21319	+	0.359074i
$214$		0			0
$215$	2.99449e6	+	935285.i	0.301306	+	0.0941085i
$216$		0			0
$217$		−	839977.i		−	0.0822031i
$218$		0			0
$219$	2.03124e6	−	601196.i	0.193388	−	0.0572379i
$220$		0			0
$221$			1.24074e7i			1.14949i
$222$		0			0
$223$			1.83188e7i			1.65189i	0.563748	+	0.825947i	$0.309359\pi$
$223$			1.83188e7i			1.65189i	−0.563748	+	0.825947i	$0.690641\pi$
$224$		0			0
$225$	1.13855e7	+	341089.i	0.999552	+	0.0299447i
$226$		0			0
$227$	1.59582e7			1.36429			0.682144	−	0.731218i	$-0.261048\pi$
$227$	1.59582e7			1.36429			0.682144	+	0.731218i	$0.261048\pi$
$228$		0			0
$229$	−1.32756e7			−1.10547			−0.552735	−	0.833357i	$-0.686416\pi$
$229$	−1.32756e7			−1.10547			−0.552735	+	0.833357i	$0.686416\pi$
$230$		0			0
$231$	−160663.	−	542827.i	−0.0130341	−	0.0440378i
$232$		0			0
$233$	1.13333e7			0.895960			0.447980	−	0.894044i	$-0.352144\pi$
$233$	1.13333e7			0.895960			0.447980	+	0.894044i	$0.352144\pi$
$234$		0			0
$235$	−1.93119e6	+	6.18306e6i	−0.148806	+	0.476431i
$236$		0			0
$237$	−3.14747e6	−	1.06343e7i	−0.236438	−	0.798844i
$238$		0			0
$239$		−	1.61780e7i		−	1.18503i	−0.805559	−	0.592516i	$-0.798135\pi$
$239$		−	1.61780e7i		−	1.18503i	0.805559	−	0.592516i	$-0.201865\pi$
$240$		0			0
$241$	1.34658e7			0.962014			0.481007	−	0.876717i	$-0.340271\pi$
$241$	1.34658e7			0.962014			0.481007	+	0.876717i	$0.340271\pi$
$242$		0			0
$243$	1.42241e7	+	1.88851e6i	0.991301	+	0.131614i
$244$		0			0
$245$	−4.30300e6	+	1.37769e7i	−0.292599	+	0.936812i
$246$		0			0
$247$		−	1.53509e7i		−	1.01869i
$248$		0			0
$249$	−4.83306e6	−	1.63293e7i	−0.313058	−	1.05772i
$250$		0			0
$251$		−	1.00586e7i		−	0.636088i	−0.948076	−	0.318044i	$-0.896974\pi$
$251$		−	1.00586e7i		−	0.636088i	0.948076	−	0.318044i	$-0.103026\pi$
$252$		0			0
$253$		−	7.70712e6i		−	0.475917i
$254$		0			0
$255$	2.02048e7	+	302580.i	1.21852	+	0.0182482i
$256$		0			0
$257$	2.26371e7			1.33359			0.666794	−	0.745242i	$-0.267666\pi$
$257$	2.26371e7			1.33359			0.666794	+	0.745242i	$0.267666\pi$
$258$		0			0
$259$	−1.69274e6			−0.0974298
$260$		0			0
$261$	−1.48984e7	−	2.29636e7i	−0.837952	−	1.29157i
$262$		0			0
$263$	5.98035e6			0.328745			0.164373	−	0.986398i	$-0.447440\pi$
$263$	5.98035e6			0.328745			0.164373	+	0.986398i	$0.447440\pi$
$264$		0			0
$265$	−1.00873e7	+	3.22964e7i	−0.542046	+	1.73546i
$266$		0			0
$267$	−3.75458e6	+	1.11126e6i	−0.197255	+	0.0583824i
$268$		0			0
$269$			2.69315e7i			1.38358i	0.722099	+	0.691790i	$0.243177\pi$
$269$			2.69315e7i			1.38358i	−0.722099	+	0.691790i	$0.756823\pi$
$270$		0			0
$271$	2.49610e7			1.25416			0.627082	−	0.778953i	$-0.284249\pi$
$271$	2.49610e7			1.25416			0.627082	+	0.778953i	$0.284249\pi$
$272$		0			0
$273$	741962.	+	2.50684e6i	0.0364665	+	0.123208i
$274$		0			0
$275$	3.99054e6	−	5.76505e6i	0.191882	−	0.277208i
$276$		0			0
$277$		−	3.43348e7i		−	1.61546i	−0.589554	−	0.807729i	$-0.700697\pi$
$277$		−	3.43348e7i		−	1.61546i	0.589554	−	0.807729i	$-0.299303\pi$
$278$		0			0
$279$	1.09942e7	−	7.13287e6i	0.506235	−	0.328437i
$280$		0			0
$281$			2.83941e7i			1.27970i	0.768498	+	0.639852i	$0.221004\pi$
$281$			2.83941e7i			1.27970i	−0.768498	+	0.639852i	$0.778996\pi$
$282$		0			0
$283$			2.60334e7i			1.14861i	0.818642	+	0.574304i	$0.194727\pi$
$283$			2.60334e7i			1.14861i	−0.818642	+	0.574304i	$0.805273\pi$
$284$		0			0
$285$	−2.49980e7	−	374363.i	−1.07987	−	0.0161718i
$286$		0			0
$287$	−598903.			−0.0253344
$288$		0			0
$289$	1.17098e7			0.485126
$290$		0			0
$291$	−4.56449e7	+	1.35097e7i	−1.85231	+	0.548236i
$292$		0			0
$293$	−1.71810e7			−0.683040			−0.341520	−	0.939875i	$-0.610942\pi$
$293$	−1.71810e7			−0.683040			−0.341520	+	0.939875i	$0.610942\pi$
$294$		0			0
$295$	−2.60435e7	−	8.13429e6i	−1.01446	−	0.316850i
$296$		0			0
$297$	5.74060e6	−	6.71243e6i	0.219123	−	0.256218i
$298$		0			0
$299$			3.55925e7i			1.33151i
$300$		0			0
$301$	1.17266e6			0.0430004
$302$		0			0
$303$	−2.64057e7	+	7.81541e6i	−0.949225	+	0.280947i
$304$		0			0
$305$	−1.42920e6	+	4.57586e6i	−0.0503726	+	0.161277i
$306$		0			0
$307$		−	4.77788e7i		−	1.65128i	−0.564198	−	0.825640i	$-0.690814\pi$
$307$		−	4.77788e7i		−	1.65128i	0.564198	−	0.825640i	$-0.309186\pi$
$308$		0			0
$309$	3.75690e7	−	1.11195e7i	1.27337	−	0.376885i
$310$		0			0
$311$			1.05727e6i			0.0351482i	0.999846	+	0.0175741i	$0.00559430\pi$
$311$			1.05727e6i			0.0351482i	−0.999846	+	0.0175741i	$0.994406\pi$
$312$		0			0
$313$			634349.i			0.0206869i	0.999947	+	0.0103435i	$0.00329248\pi$
$313$			634349.i			0.0206869i	−0.999947	+	0.0103435i	$0.996708\pi$
$314$		0			0
$315$	4.10034e6	−	1.14711e6i	0.131186	−	0.0367006i
$316$		0			0
$317$	−1.82810e7			−0.573881			−0.286941	−	0.957948i	$-0.592638\pi$
$317$	−1.82810e7			−0.573881			−0.286941	+	0.957948i	$0.592638\pi$
$318$		0			0
$319$	−1.68494e7			−0.519054
$320$		0			0
$321$	−1.25280e7	−	4.23279e7i	−0.378762	−	1.27971i
$322$		0			0
$323$	−4.43516e7			−1.31614
$324$		0			0
$325$	−1.84288e7	+	2.66237e7i	−0.536844	+	0.775566i
$326$		0			0
$327$	−8.67548e6	−	2.93115e7i	−0.248113	−	0.838292i
$328$		0			0
$329$			2.42132e6i			0.0679930i
$330$		0			0
$331$	4.94881e7			1.36464			0.682318	−	0.731056i	$-0.260972\pi$
$331$	4.94881e7			1.36464			0.682318	+	0.731056i	$0.260972\pi$
$332$		0			0
$333$	−1.43744e7	−	2.21559e7i	−0.389274	−	0.600006i
$334$		0			0
$335$	−3.09196e7	−	9.65728e6i	−0.822431	−	0.256874i
$336$		0			0
$337$			2.06094e7i			0.538488i	0.963072	+	0.269244i	$0.0867738\pi$
$337$			2.06094e7i			0.538488i	−0.963072	+	0.269244i	$0.913226\pi$
$338$		0			0
$339$	1.25354e7	+	4.23530e7i	0.321766	+	1.08714i
$340$		0			0
$341$		−	8.06694e6i		−	0.203444i
$342$		0			0
$343$			1.08922e7i			0.269919i
$344$		0			0
$345$	5.79603e7	+	867996.i	1.41147	+	0.0211378i
$346$		0			0
$347$	−2.00318e7			−0.479438			−0.239719	−	0.970842i	$-0.577055\pi$
$347$	−2.00318e7			−0.479438			−0.239719	+	0.970842i	$0.577055\pi$
$348$		0			0
$349$	−1.79347e6			−0.0421909			−0.0210955	−	0.999777i	$-0.506715\pi$
$349$	−1.79347e6			−0.0421909			−0.0210955	+	0.999777i	$0.506715\pi$
$350$		0			0
$351$	−2.65108e7	+	3.09988e7i	−0.613058	+	0.716843i
$352$		0			0
$353$	8.48583e7			1.92917			0.964585	−	0.263774i	$-0.0849673\pi$
$353$	8.48583e7			1.92917			0.964585	+	0.263774i	$0.0849673\pi$
$354$		0			0
$355$	−5.40302e7	−	1.68755e7i	−1.20768	−	0.377200i
$356$		0			0
$357$	7.24274e6	−	2.14367e6i	0.159184	−	0.0471143i
$358$		0			0
$359$		−	5.28803e7i		−	1.14291i	−0.820635	−	0.571453i	$-0.806380\pi$
$359$		−	5.28803e7i		−	1.14291i	0.820635	−	0.571453i	$-0.193620\pi$
$360$		0			0
$361$	7.82753e6			0.166381
$362$		0			0
$363$	1.20320e7	+	4.06522e7i	0.251547	+	0.849893i
$364$		0			0
$365$	9.36116e6	+	2.92382e6i	0.192509	+	0.0601273i
$366$		0			0
$367$			2.30840e7i			0.466995i	0.972357	+	0.233498i	$0.0750171\pi$
$367$			2.30840e7i			0.466995i	−0.972357	+	0.233498i	$0.924983\pi$
$368$		0			0
$369$	−5.08574e6	−	7.83888e6i	−0.101222	−	0.156018i
$370$		0			0
$371$			1.26474e7i			0.247674i
$372$		0			0
$373$		−	5.13180e7i		−	0.988879i	−0.869212	−	0.494440i	$-0.835373\pi$
$373$		−	5.13180e7i		−	0.988879i	0.869212	−	0.494440i	$-0.164627\pi$
$374$		0			0
$375$	4.29058e7	+	3.06596e7i	0.813621	+	0.581396i
$376$		0			0
$377$	7.78127e7			1.45220
$378$		0			0
$379$	−1.54962e7			−0.284648			−0.142324	−	0.989820i	$-0.545458\pi$
$379$	−1.54962e7			−0.284648			−0.142324	+	0.989820i	$0.545458\pi$
$380$		0			0
$381$	−9.42633e7	+	2.78996e7i	−1.70438	+	0.504455i
$382$		0			0
$383$	−1.93567e7			−0.344536			−0.172268	−	0.985050i	$-0.555110\pi$
$383$	−1.93567e7			−0.344536			−0.172268	+	0.985050i	$0.555110\pi$
$384$		0			0
$385$	781358.	−	2.50167e6i	0.0136920	−	0.0438377i
$386$		0			0
$387$	9.95793e6	+	1.53486e7i	0.171805	+	0.264811i
$388$		0			0
$389$			6.41643e6i			0.109005i	0.998514	+	0.0545023i	$0.0173572\pi$
$389$			6.41643e6i			0.109005i	−0.998514	+	0.0545023i	$0.982643\pi$
$390$		0			0
$391$	1.02833e8			1.72030
$392$		0			0
$393$	9.02059e7	−	2.66987e7i	1.48613	−	0.439858i
$394$		0			0
$395$	1.53072e7	−	4.90090e7i	0.248373	−	0.795214i
$396$		0			0
$397$			8.10971e7i			1.29609i	0.761604	+	0.648043i	$0.224412\pi$
$397$			8.10971e7i			1.29609i	−0.761604	+	0.648043i	$0.775588\pi$
$398$		0			0
$399$	−8.96098e6	+	2.65222e6i	−0.141071	+	0.0417534i
$400$		0			0
$401$		−	1.16305e8i		−	1.80370i	−0.432047	−	0.901851i	$-0.642208\pi$
$401$		−	1.16305e8i		−	1.80370i	0.432047	−	0.901851i	$-0.357792\pi$
$402$		0			0
$403$			3.72541e7i			0.569193i
$404$		0			0
$405$	4.98333e7	+	4.39273e7i	0.750161	+	0.661255i
$406$		0			0
$407$	−1.62567e7			−0.241129
$408$		0			0
$409$	−4.34494e7			−0.635059			−0.317529	−	0.948248i	$-0.602853\pi$
$409$	−4.34494e7			−0.635059			−0.317529	+	0.948248i	$0.602853\pi$
$410$		0			0
$411$	1.21401e7	+	4.10173e7i	0.174862	+	0.590801i
$412$		0			0
$413$	−1.01988e7			−0.144776
$414$		0			0
$415$	2.35048e7	−	7.52551e7i	0.328861	−	1.05291i
$416$		0			0
$417$	2.46807e7	+	8.33878e7i	0.340368	+	1.14999i
$418$		0			0
$419$		−	1.29244e8i		−	1.75698i	−0.477757	−	0.878492i	$-0.658550\pi$
$419$		−	1.29244e8i		−	1.75698i	0.477757	−	0.878492i	$-0.341450\pi$
$420$		0			0
$421$	8.10725e7			1.08649			0.543247	−	0.839573i	$-0.317195\pi$
$421$	8.10725e7			1.08649			0.543247	+	0.839573i	$0.317195\pi$
$422$		0			0
$423$	−3.16920e7	+	2.05612e7i	−0.418724	+	0.271661i
$424$		0			0
$425$	7.69209e7	+	5.32443e7i	1.00202	+	0.693596i
$426$		0			0
$427$			1.79193e6i			0.0230164i
$428$		0			0
$429$	7.12563e6	+	2.40751e7i	0.0902509	+	0.304928i
$430$		0			0
$431$		−	1.64885e7i		−	0.205944i	−0.994684	−	0.102972i	$-0.967165\pi$
$431$		−	1.64885e7i		−	0.205944i	0.994684	−	0.102972i	$-0.0328352\pi$
$432$		0			0
$433$		−	6.35196e7i		−	0.782428i	−0.920300	−	0.391214i	$-0.872055\pi$
$433$		−	6.35196e7i		−	0.782428i	0.920300	−	0.391214i	$-0.127945\pi$
$434$		0			0
$435$	1.89762e6	−	1.26714e8i	0.0230538	−	1.53941i
$436$		0			0
$437$	−1.27229e8			−1.52455
$438$		0			0
$439$	−1.43748e8			−1.69905			−0.849526	−	0.527546i	$-0.823112\pi$
$439$	−1.43748e8			−1.69905			−0.849526	+	0.527546i	$0.823112\pi$
$440$		0			0
$441$	−7.06149e7	+	4.58138e7i	−0.823342	+	0.534171i
$442$		0			0
$443$	−6.14621e7			−0.706962			−0.353481	−	0.935442i	$-0.615002\pi$
$443$	−6.14621e7			−0.706962			−0.353481	+	0.935442i	$0.615002\pi$
$444$		0			0
$445$	−1.73033e7	−	5.40443e6i	−0.196358	−	0.0613295i
$446$		0			0
$447$	2.00448e7	−	5.93277e6i	0.224429	−	0.0664255i
$448$		0			0
$449$		−	5.12007e7i		−	0.565635i	−0.959174	−	0.282818i	$-0.908731\pi$
$449$		−	5.12007e7i		−	0.565635i	0.959174	−	0.282818i	$-0.0912692\pi$
$450$		0			0
$451$	−5.75173e6			−0.0627002
$452$		0			0
$453$	−2.41782e7	−	8.16901e7i	−0.260094	−	0.878770i
$454$		0			0
$455$	−3.60841e6	+	1.15530e7i	−0.0383073	+	0.122648i
$456$		0			0
$457$			1.05860e8i			1.10913i	0.832140	+	0.554566i	$0.187116\pi$
$457$			1.05860e8i			1.10913i	−0.832140	+	0.554566i	$0.812884\pi$
$458$		0			0
$459$	8.95614e7	+	7.65947e7i	0.926153	+	0.792065i
$460$		0			0
$461$			1.30381e8i			1.33079i	0.746491	+	0.665396i	$0.231737\pi$
$461$			1.30381e8i			1.33079i	−0.746491	+	0.665396i	$0.768263\pi$
$462$		0			0
$463$			2.84090e7i			0.286229i	0.989706	+	0.143115i	$0.0457117\pi$
$463$			2.84090e7i			0.286229i	−0.989706	+	0.143115i	$0.954288\pi$
$464$		0			0
$465$	6.06662e7	+	908519.i	0.603376	+	0.00903598i
$466$		0			0
$467$	−7.48443e7			−0.734866			−0.367433	−	0.930050i	$-0.619763\pi$
$467$	−7.48443e7			−0.734866			−0.367433	+	0.930050i	$0.619763\pi$
$468$		0			0
$469$	−1.21083e7			−0.117372
$470$		0			0
$471$	−7.49947e7	+	2.21966e7i	−0.717741	+	0.212433i
$472$		0			0
$473$	1.12619e7			0.106422
$474$		0			0
$475$	−9.51694e7	−	6.58758e7i	−0.888007	−	0.614675i
$476$		0			0
$477$	−1.65538e8	+	1.07399e8i	−1.52526	+	0.989564i
$478$		0			0
$479$			1.80284e8i			1.64041i	0.572072	+	0.820203i	$0.306140\pi$
$479$			1.80284e8i			1.64041i	−0.572072	+	0.820203i	$0.693860\pi$
$480$		0			0
$481$	7.50756e7			0.674627
$482$		0			0
$483$	2.07768e7	−	6.14942e6i	0.184390	−	0.0545749i
$484$		0			0
$485$	−2.10359e8	−	6.57023e7i	−1.84389	−	0.575911i
$486$		0			0
$487$			1.11747e8i			0.967497i	0.875207	+	0.483748i	$0.160725\pi$
$487$			1.11747e8i			0.967497i	−0.875207	+	0.483748i	$0.839275\pi$
$488$		0			0
$489$	2.36488e7	−	6.99944e6i	0.202247	−	0.0598600i
$490$		0			0
$491$		−	1.05636e8i		−	0.892418i	−0.894929	−	0.446209i	$-0.852774\pi$
$491$		−	1.05636e8i		−	0.892418i	0.894929	−	0.446209i	$-0.147226\pi$
$492$		0			0
$493$		−	2.24816e8i		−	1.87623i
$494$		0			0
$495$	3.93787e7	−	1.10166e7i	0.324673	−	0.0908302i
$496$		0			0
$497$	−2.11585e7			−0.172352
$498$		0			0
$499$	1.60397e8			1.29091			0.645455	−	0.763798i	$-0.276668\pi$
$499$	1.60397e8			1.29091			0.645455	+	0.763798i	$0.276668\pi$
$500$		0			0
$501$	−2.25489e7	−	7.61850e7i	−0.179313	−	0.605838i
$502$		0			0
$503$	5.96577e7			0.468773			0.234386	−	0.972144i	$-0.424692\pi$
$503$	5.96577e7			0.468773			0.234386	+	0.972144i	$0.424692\pi$
$504$		0			0
$505$	−1.21693e8	−	3.80090e7i	−0.944912	−	0.295129i
$506$		0			0
$507$	4.07949e6	+	1.37832e7i	0.0313027	+	0.105761i
$508$		0			0
$509$			2.85507e7i			0.216503i	0.994124	+	0.108251i	$0.0345251\pi$
$509$			2.85507e7i			0.216503i	−0.994124	+	0.108251i	$0.965475\pi$
$510$		0			0
$511$	3.66588e6			0.0274736
$512$		0			0
$513$	−1.10809e8	−	9.47657e7i	−0.820770	−	0.701939i
$514$		0			0
$515$	1.73140e8	+	5.40777e7i	1.26758	+	0.395910i
$516$		0			0
$517$			2.32538e7i			0.168276i
$518$		0			0
$519$	−4.44906e7	−	1.50319e8i	−0.318248	−	1.07525i
$520$		0			0
$521$		−	1.71342e7i		−	0.121158i	−0.998163	−	0.0605788i	$-0.980705\pi$
$521$		−	1.71342e7i		−	0.121158i	0.998163	−	0.0605788i	$-0.0192946\pi$
$522$		0			0
$523$			1.49188e8i			1.04286i	0.853293	+	0.521432i	$0.174602\pi$
$523$			1.49188e8i			1.04286i	−0.853293	+	0.521432i	$0.825398\pi$
$524$		0			0
$525$	1.87254e7	+	6.15783e6i	0.129406	+	0.0425549i
$526$		0			0
$527$	1.07634e8			0.735391
$528$		0			0
$529$	1.46956e8			0.992708
$530$		0			0
$531$	−8.66053e7	−	1.33489e8i	−0.578443	−	0.891581i
$532$		0			0
$533$	2.65622e7			0.175421
$534$		0			0
$535$	6.09278e7	−	1.95072e8i	0.397882	−	1.27389i
$536$		0			0
$537$	9.94132e7	−	2.94238e7i	0.641979	−	0.190010i
$538$		0			0
$539$			5.18132e7i			0.330883i
$540$		0			0
$541$	−8.39377e6			−0.0530109			−0.0265055	−	0.999649i	$-0.508438\pi$
$541$	−8.39377e6			−0.0530109			−0.0265055	+	0.999649i	$0.508438\pi$
$542$		0			0
$543$	6.41801e7	+	2.16843e8i	0.400867	+	1.35440i
$544$		0			0
$545$	4.21917e7	−	1.35085e8i	0.260638	−	0.834483i
$546$		0			0
$547$			8.88362e7i			0.542785i	0.962469	+	0.271393i	$0.0874842\pi$
$547$			8.88362e7i			0.542785i	−0.962469	+	0.271393i	$0.912516\pi$
$548$		0			0
$549$	−2.34541e7	+	1.52166e7i	−0.141743	+	0.0919605i
$550$		0			0
$551$			2.78150e8i			1.66274i
$552$		0			0
$553$		−	1.91921e7i		−	0.113488i
$554$		0			0
$555$	1.83087e6	−	1.22256e8i	0.0107098	−	0.715142i
$556$		0			0
$557$	3.17471e7			0.183713			0.0918563	−	0.995772i	$-0.470720\pi$
$557$	3.17471e7			0.183713			0.0918563	+	0.995772i	$0.470720\pi$
$558$		0			0
$559$	−5.20091e7			−0.297744
$560$		0			0
$561$	6.95576e7	−	2.05873e7i	0.393963	−	0.116603i
$562$		0			0
$563$	1.40188e8			0.785571			0.392786	−	0.919630i	$-0.371511\pi$
$563$	1.40188e8			0.785571			0.392786	+	0.919630i	$0.371511\pi$
$564$		0			0
$565$	−6.09640e7	+	1.95188e8i	−0.338009	+	1.08220i
$566$		0			0
$567$	2.26757e7	+	1.01197e7i	0.124397	+	0.0555162i
$568$		0			0
$569$			1.89176e8i			1.02690i	0.858118	+	0.513452i	$0.171634\pi$
$569$			1.89176e8i			1.02690i	−0.858118	+	0.513452i	$0.828366\pi$
$570$		0			0
$571$	−2.79939e7			−0.150368			−0.0751839	−	0.997170i	$-0.523954\pi$
$571$	−2.79939e7			−0.150368			−0.0751839	+	0.997170i	$0.523954\pi$
$572$		0			0
$573$	1.25765e8	−	3.72232e7i	0.668491	−	0.197856i
$574$		0			0
$575$	2.20659e8	+	1.52739e8i	1.16069	+	0.803428i
$576$		0			0
$577$			5.22774e7i			0.272136i	0.990699	+	0.136068i	$0.0434466\pi$
$577$			5.22774e7i			0.272136i	−0.990699	+	0.136068i	$0.956553\pi$
$578$		0			0
$579$	2.03746e8	−	6.03037e7i	1.04967	−	0.310677i
$580$		0			0
$581$		−	2.94702e7i		−	0.150264i
$582$		0			0
$583$			1.21463e8i			0.612968i
$584$		0			0
$585$	−1.81856e8	+	5.08759e7i	−0.908364	+	0.254123i
$586$		0			0
$587$	2.79365e8			1.38120			0.690601	−	0.723236i	$-0.257346\pi$
$587$	2.79365e8			1.38120			0.690601	+	0.723236i	$0.257346\pi$
$588$		0			0
$589$	−1.33169e8			−0.651714
$590$		0			0
$591$	−7.80097e7	−	2.63569e8i	−0.377908	−	1.27683i
$592$		0			0
$593$	−4.41885e7			−0.211907			−0.105953	−	0.994371i	$-0.533789\pi$
$593$	−4.41885e7			−0.211907			−0.105953	+	0.994371i	$0.533789\pi$
$594$		0			0
$595$	3.33788e7	+	1.04254e7i	0.158460	+	0.0494927i
$596$		0			0
$597$	−5.15941e7	−	1.74319e8i	−0.242481	−	0.819261i
$598$		0			0
$599$		−	9.93133e7i		−	0.462090i	−0.972943	−	0.231045i	$-0.925786\pi$
$599$		−	9.93133e7i		−	0.462090i	0.972943	−	0.231045i	$-0.0742145\pi$
$600$		0			0
$601$	−5.93309e7			−0.273311			−0.136656	−	0.990619i	$-0.543635\pi$
$601$	−5.93309e7			−0.273311			−0.136656	+	0.990619i	$0.543635\pi$
$602$		0			0
$603$	−1.02820e8	−	1.58482e8i	−0.468951	−	0.722816i
$604$		0			0
$605$	−5.85158e7	+	1.87349e8i	−0.264245	+	0.846031i
$606$		0			0
$607$		−	2.86583e8i		−	1.28140i	−0.767792	−	0.640699i	$-0.778645\pi$
$607$		−	2.86583e8i		−	1.28140i	0.767792	−	0.640699i	$-0.221355\pi$
$608$		0			0
$609$	−1.34440e7	−	4.54226e7i	−0.0595217	−	0.201104i
$610$		0			0
$611$		−	1.07389e8i		−	0.470799i
$612$		0			0
$613$		−	1.08241e8i		−	0.469905i	−0.972007	−	0.234952i	$-0.924507\pi$
$613$		−	1.08241e8i		−	0.469905i	0.972007	−	0.234952i	$-0.0754934\pi$
$614$		0			0
$615$	647774.	−	4.32550e7i	0.00278483	−	0.185956i
$616$		0			0
$617$	−1.93425e8			−0.823486			−0.411743	−	0.911300i	$-0.635080\pi$
$617$	−1.93425e8			−0.823486			−0.411743	+	0.911300i	$0.635080\pi$
$618$		0			0
$619$	−9.00769e7			−0.379788			−0.189894	−	0.981805i	$-0.560814\pi$
$619$	−9.00769e7			−0.379788			−0.189894	+	0.981805i	$0.560814\pi$
$620$		0			0
$621$	2.56920e8	+	2.19723e8i	1.07281	+	0.917489i
$622$		0			0
$623$	−6.77606e6			−0.0280229
$624$		0			0
$625$	8.59721e7	+	2.28503e8i	0.352142	+	0.935947i
$626$		0			0
$627$	−8.60591e7	+	2.54713e7i	−0.349136	+	0.103335i
$628$		0			0
$629$		−	2.16907e8i		−	0.871611i
$630$		0			0
$631$	1.54497e8			0.614939			0.307469	−	0.951558i	$-0.400518\pi$
$631$	1.54497e8			0.614939			0.307469	+	0.951558i	$0.400518\pi$
$632$		0			0
$633$	3.14064e7	+	1.06112e8i	0.123825	+	0.418362i
$634$		0			0
$635$	−4.34421e8	−	1.35685e8i	−1.69664	−	0.529920i
$636$		0			0
$637$		−	2.39280e8i		−	0.925737i
$638$		0			0
$639$	−1.79673e8	−	2.76938e8i	−0.688620	−	1.06140i
$640$		0			0
$641$			2.72023e8i			1.03284i	0.856337	+	0.516418i	$0.172735\pi$
$641$			2.72023e8i			1.03284i	−0.856337	+	0.516418i	$0.827265\pi$
$642$		0			0
$643$			2.76649e8i			1.04063i	0.853975	+	0.520314i	$0.174185\pi$
$643$			2.76649e8i			1.04063i	−0.853975	+	0.520314i	$0.825815\pi$
$644$		0			0
$645$	−1.26835e6	+	8.46938e7i	−0.00472672	+	0.315626i
$646$		0			0
$647$	−8.70822e7			−0.321526			−0.160763	−	0.986993i	$-0.551396\pi$
$647$	−8.70822e7			−0.321526			−0.160763	+	0.986993i	$0.551396\pi$
$648$		0			0
$649$	−9.79465e7			−0.358306
$650$		0			0
$651$	2.17468e7	−	6.43652e6i	0.0788230	−	0.0233296i
$652$		0			0
$653$	−2.42171e8			−0.869726			−0.434863	−	0.900497i	$-0.643203\pi$
$653$	−2.42171e8			−0.869726			−0.434863	+	0.900497i	$0.643203\pi$
$654$		0			0
$655$	4.15722e8	+	1.29845e8i	1.47938	+	0.462062i
$656$		0			0
$657$	3.11297e7	+	4.79816e7i	0.109769	+	0.169192i
$658$		0			0
$659$			4.98679e8i			1.74247i	0.490869	+	0.871234i	$0.336680\pi$
$659$			4.98679e8i			1.74247i	−0.490869	+	0.871234i	$0.663320\pi$
$660$		0			0
$661$	−1.09071e8			−0.377665			−0.188832	−	0.982009i	$-0.560470\pi$
$661$	−1.09071e8			−0.377665			−0.188832	+	0.982009i	$0.560470\pi$
$662$		0			0
$663$	−3.21226e8	+	9.50747e7i	−1.10222	+	0.326230i
$664$		0			0
$665$	−4.12975e7	−	1.28986e7i	−0.140430	−	0.0438611i
$666$		0			0
$667$		−	6.44916e8i		−	2.17333i
$668$		0			0
$669$	−4.74270e8	+	1.40372e8i	−1.58397	+	0.468816i
$670$		0			0
$671$			1.72093e7i			0.0569633i
$672$		0			0
$673$		−	2.24827e8i		−	0.737571i	−0.929515	−	0.368785i	$-0.879774\pi$
$673$		−	2.24827e8i		−	0.737571i	0.929515	−	0.368785i	$-0.120226\pi$
$674$		0			0
$675$	7.84135e7	+	2.97383e8i	0.254964	+	0.966950i
$676$		0			0
$677$	1.36225e8			0.439027			0.219513	−	0.975609i	$-0.429553\pi$
$677$	1.36225e8			0.439027			0.219513	+	0.975609i	$0.429553\pi$
$678$		0			0
$679$	−8.23774e7			−0.263147
$680$		0			0
$681$	1.22283e8	+	4.13154e8i	0.387192	+	1.30819i
$682$		0			0
$683$	−2.37618e8			−0.745791			−0.372895	−	0.927873i	$-0.621635\pi$
$683$	−2.37618e8			−0.745791			−0.372895	+	0.927873i	$0.621635\pi$
$684$		0			0
$685$	−5.90413e7	+	1.89032e8i	−0.183689	+	0.588117i
$686$		0			0
$687$	−1.01727e8	−	3.43702e8i	−0.313738	−	1.06002i
$688$		0			0
$689$		−	5.60930e8i		−	1.71495i
$690$		0			0
$691$	−4.59119e8			−1.39153			−0.695763	−	0.718271i	$-0.744934\pi$
$691$	−4.59119e8			−1.39153			−0.695763	+	0.718271i	$0.744934\pi$
$692$		0			0
$693$	1.28226e7	−	8.31907e6i	0.0385279	−	0.0249963i
$694$		0			0
$695$	−1.20030e8	+	3.84300e8i	−0.357550	+	1.14476i
$696$		0			0
$697$		−	7.67432e7i		−	0.226643i
$698$		0			0
$699$	8.68440e7	+	2.93417e8i	0.254278	+	0.859119i
$700$		0			0
$701$		−	4.74480e8i		−	1.37741i	−0.725040	−	0.688706i	$-0.758179\pi$
$701$		−	4.74480e8i		−	1.37741i	0.725040	−	0.688706i	$-0.241821\pi$
$702$		0			0
$703$			2.68366e8i			0.772433i
$704$		0			0
$705$	−1.74876e8	−	2.61890e6i	−0.499073	−	0.00747397i
$706$		0			0
$707$	−4.76556e7			−0.134851
$708$		0			0
$709$	4.42288e8			1.24098			0.620492	−	0.784213i	$-0.286933\pi$
$709$	4.42288e8			1.24098			0.620492	+	0.784213i	$0.286933\pi$
$710$		0			0
$711$	2.51201e8	−	1.62975e8i	0.698895	−	0.453432i
$712$		0			0
$713$	3.08764e8			0.851841
$714$		0			0
$715$	−3.46543e7	+	1.10952e8i	−0.0948068	+	0.303542i
$716$		0			0
$717$	4.18844e8	−	1.23967e8i	1.13631	−	0.336318i
$718$		0			0
$719$		−	3.01334e8i		−	0.810703i	−0.914161	−	0.405352i	$-0.867149\pi$
$719$		−	3.01334e8i		−	0.810703i	0.914161	−	0.405352i	$-0.132851\pi$
$720$		0			0
$721$	6.78025e7			0.180901
$722$		0			0
$723$	1.03185e8	+	3.48627e8i	0.273024	+	0.922458i
$724$		0			0
$725$	3.33920e8	−	4.82407e8i	0.876252	−	1.26590i
$726$		0			0
$727$		−	9.93407e7i		−	0.258538i	−0.991610	−	0.129269i	$-0.958737\pi$
$727$		−	9.93407e7i		−	0.258538i	0.991610	−	0.129269i	$-0.0412630\pi$
$728$		0			0
$729$	6.01021e7	+	3.82730e8i	0.155134	+	0.987893i
$730$		0			0
$731$			1.50264e8i			0.384683i
$732$		0			0
$733$			2.97037e8i			0.754221i	0.926168	+	0.377110i	$0.123082\pi$
$733$			2.97037e8i			0.754221i	−0.926168	+	0.377110i	$0.876918\pi$
$734$		0			0
$735$	−3.89653e8	−	5.83534e6i	−0.981333	−	0.0146962i
$736$		0			0
$737$	−1.16285e8			−0.290483
$738$		0			0
$739$	3.04157e8			0.753642			0.376821	−	0.926286i	$-0.377017\pi$
$739$	3.04157e8			0.753642			0.376821	+	0.926286i	$0.377017\pi$
$740$		0			0
$741$	3.97432e8	−	1.17630e8i	0.976805	−	0.289110i
$742$		0			0
$743$	−2.58582e8			−0.630422			−0.315211	−	0.949022i	$-0.602075\pi$
$743$	−2.58582e8			−0.630422			−0.315211	+	0.949022i	$0.602075\pi$
$744$		0			0
$745$	9.23785e7	+	2.88530e7i	0.223410	+	0.0697786i
$746$		0			0
$747$	3.85728e8	−	2.50254e8i	0.925378	−	0.600370i
$748$		0			0
$749$		−	7.63911e7i		−	0.181802i
$750$		0			0
$751$	−6.18305e8			−1.45977			−0.729883	−	0.683572i	$-0.760426\pi$
$751$	−6.18305e8			−1.45977			−0.729883	+	0.683572i	$0.760426\pi$
$752$		0			0
$753$	2.60416e8	−	7.70765e7i	0.609933	−	0.180525i
$754$		0			0
$755$	1.17587e8	−	3.76477e8i	0.273223	−	0.874776i
$756$		0			0
$757$			3.16925e7i			0.0730581i	0.999333	+	0.0365291i	$0.0116301\pi$
$757$			3.16925e7i			0.0730581i	−0.999333	+	0.0365291i	$0.988370\pi$
$758$		0			0
$759$	1.99536e8	−	5.90576e7i	0.456348	−	0.135067i
$760$		0			0
$761$		−	7.25119e8i		−	1.64534i	−0.568520	−	0.822669i	$-0.692484\pi$
$761$		−	7.25119e8i		−	1.64534i	0.568520	−	0.822669i	$-0.307516\pi$
$762$		0			0
$763$		−	5.28999e7i		−	0.119092i
$764$		0			0
$765$	1.46990e8	+	5.25416e8i	0.328324	+	1.17360i
$766$		0			0
$767$	4.52329e8			1.00246
$768$		0			0
$769$	3.41653e7			0.0751288			0.0375644	−	0.999294i	$-0.488040\pi$
$769$	3.41653e7			0.0751288			0.0375644	+	0.999294i	$0.488040\pi$
$770$		0			0
$771$	1.73462e8	+	5.86071e8i	0.378479	+	1.27875i
$772$		0			0
$773$	4.77153e8			1.03304			0.516522	−	0.856274i	$-0.327226\pi$
$773$	4.77153e8			1.03304			0.516522	+	0.856274i	$0.327226\pi$
$774$		0			0
$775$	2.30961e8	+	1.59870e8i	0.496173	+	0.343449i
$776$		0			0
$777$	−1.29710e7	−	4.38248e7i	−0.0276511	−	0.0934237i
$778$		0			0
$779$			9.49494e7i			0.200854i
$780$		0			0
$781$	−2.03201e8			−0.426553
$782$		0			0
$783$	4.80361e8	−	5.61682e8i	1.00065	−	1.17005i
$784$		0			0
$785$	−3.45620e8	−	1.07949e8i	−0.714480	−	0.223157i
$786$		0			0
$787$			4.04787e8i			0.830429i	0.909724	+	0.415214i	$0.136293\pi$
$787$			4.04787e8i			0.830429i	−0.909724	+	0.415214i	$0.863707\pi$
$788$		0			0
$789$	4.58259e7	+	1.54830e8i	0.0932996	+	0.315228i
$790$		0			0
$791$			7.64365e7i			0.154444i
$792$		0			0
$793$		−	7.94746e7i		−	0.159371i
$794$		0			0
$795$	−9.13443e8	−	1.36794e7i	−1.81794	−	0.0272250i
$796$		0			0
$797$	7.00656e8			1.38398			0.691990	−	0.721907i	$-0.256734\pi$
$797$	7.00656e8			1.38398			0.691990	+	0.721907i	$0.256734\pi$
$798$		0			0
$799$	−3.10266e8			−0.608267
$800$		0			0
$801$	−5.75406e7	−	8.86900e7i	−0.111964	−	0.172575i
$802$		0			0
$803$	3.52062e7			0.0679943
$804$		0			0
$805$	9.57520e7	+	2.99067e7i	0.183553	+	0.0573299i
$806$		0			0
$807$	−6.97252e8	+	2.06369e8i	−1.32669	+	0.392667i
$808$		0			0
$809$			7.73522e7i			0.146092i	0.997329	+	0.0730461i	$0.0232720\pi$
$809$			7.73522e7i			0.146092i	−0.997329	+	0.0730461i	$0.976728\pi$
$810$		0			0
$811$	−2.60258e8			−0.487913			−0.243956	−	0.969786i	$-0.578445\pi$
$811$	−2.60258e8			−0.487913			−0.243956	+	0.969786i	$0.578445\pi$
$812$		0			0
$813$	1.91270e8	+	6.46236e8i	0.355938	+	1.20260i
$814$		0			0
$815$	1.08988e8	+	3.40406e7i	0.201328	+	0.0628817i
$816$		0			0
$817$		−	1.85912e8i		−	0.340911i
$818$		0			0
$819$	−5.92162e7	+	3.84185e7i	−0.107793	+	0.0699341i
$820$		0			0
$821$			3.85083e8i			0.695865i	0.937520	+	0.347933i	$0.113116\pi$
$821$			3.85083e8i			0.695865i	−0.937520	+	0.347933i	$0.886884\pi$
$822$		0			0
$823$		−	5.06014e8i		−	0.907742i	−0.891067	−	0.453871i	$-0.850043\pi$
$823$		−	5.06014e8i		−	0.907742i	0.891067	−	0.453871i	$-0.149957\pi$
$824$		0			0
$825$	1.79835e8	+	5.91384e7i	0.320266	+	0.105319i
$826$		0			0
$827$	−8.19429e8			−1.44875			−0.724377	−	0.689404i	$-0.757873\pi$
$827$	−8.19429e8			−1.44875			−0.724377	+	0.689404i	$0.757873\pi$
$828$		0			0
$829$	1.12105e9			1.96772			0.983858	−	0.178953i	$-0.0572710\pi$
$829$	1.12105e9			1.96772			0.983858	+	0.178953i	$0.0572710\pi$
$830$		0			0
$831$	8.88922e8	−	2.63099e8i	1.54903	−	0.458475i
$832$		0			0
$833$	−6.91324e8			−1.19604
$834$		0			0
$835$	1.09663e8	−	3.51106e8i	0.188365	−	0.603085i
$836$		0			0
$837$	2.68915e8	+	2.29981e8i	0.458604	+	0.392207i
$838$		0			0
$839$			5.59565e8i			0.947468i	0.880668	+	0.473734i	$0.157094\pi$
$839$			5.59565e8i			0.947468i	−0.880668	+	0.473734i	$0.842906\pi$
$840$		0			0
$841$	−8.15101e8			−1.37032
$842$		0			0
$843$	−7.35119e8	+	2.17577e8i	−1.22708	+	0.363186i
$844$		0			0
$845$	−1.98399e7	+	6.35212e7i	−0.0328828	+	0.105281i
$846$		0			0
$847$			7.33670e7i			0.120740i
$848$		0			0
$849$	−6.74000e8	+	1.99487e8i	−1.10138	+	0.325980i
$850$		0			0
$851$		−	6.22231e8i		−	1.00963i
$852$		0			0
$853$			7.75527e8i			1.24954i	0.780809	+	0.624769i	$0.214807\pi$
$853$			7.75527e8i			1.24954i	−0.780809	+	0.624769i	$0.785193\pi$
$854$		0			0
$855$	−1.81861e8	−	6.50063e8i	−0.290966	−	1.04006i
$856$		0			0
$857$	−5.08412e8			−0.807742			−0.403871	−	0.914816i	$-0.632336\pi$
$857$	−5.08412e8			−0.807742			−0.403871	+	0.914816i	$0.632336\pi$
$858$		0			0
$859$	4.02867e8			0.635597			0.317798	−	0.948158i	$-0.397056\pi$
$859$	4.02867e8			0.635597			0.317798	+	0.948158i	$0.397056\pi$
$860$		0			0
$861$	−4.58924e6	−	1.55055e7i	−0.00719004	−	0.0242927i
$862$		0			0
$863$	−2.50809e8			−0.390222			−0.195111	−	0.980781i	$-0.562507\pi$
$863$	−2.50809e8			−0.390222			−0.195111	+	0.980781i	$0.562507\pi$
$864$		0			0
$865$	2.16372e8	−	6.92758e8i	0.334313	−	1.07037i
$866$		0			0
$867$	8.97288e7	+	3.03164e8i	0.137681	+	0.465179i
$868$		0			0
$869$		−	1.84317e8i		−	0.280870i
$870$		0			0
$871$	5.37019e8			0.812709
$872$		0			0
$873$	−6.99529e8	−	1.07822e9i	−1.05139	−	1.62055i
$874$		0			0
$875$	5.61391e7	+	7.19485e7i	0.0837995	+	0.107398i
$876$		0			0
$877$		−	9.44801e7i		−	0.140069i	−0.997545	−	0.0700344i	$-0.977689\pi$
$877$		−	9.44801e7i		−	0.140069i	0.997545	−	0.0700344i	$-0.0223109\pi$
$878$		0			0
$879$	−1.31654e8	−	4.44813e8i	−0.193850	−	0.654955i
$880$		0			0
$881$			5.66238e8i			0.828079i	0.910259	+	0.414039i	$0.135882\pi$
$881$			5.66238e8i			0.828079i	−0.910259	+	0.414039i	$0.864118\pi$
$882$		0			0
$883$		−	7.41125e8i		−	1.07649i	−0.842789	−	0.538244i	$-0.819088\pi$
$883$		−	7.41125e8i		−	1.07649i	0.842789	−	0.538244i	$-0.180912\pi$
$884$		0			0
$885$	1.10310e7	−	7.36592e8i	0.0159142	−	1.06267i
$886$		0			0
$887$	−7.32272e8			−1.04930			−0.524652	−	0.851317i	$-0.675805\pi$
$887$	−7.32272e8			−1.04930			−0.524652	+	0.851317i	$0.675805\pi$
$888$		0			0
$889$	−1.70121e8			−0.242133
$890$		0			0
$891$	2.17772e8	+	9.71875e7i	0.307871	+	0.137397i
$892$		0			0
$893$	3.83873e8			0.539055
$894$		0			0
$895$	4.58155e8	+	1.43098e8i	0.639062	+	0.199601i
$896$		0			0
$897$	−9.21482e8	+	2.72736e8i	−1.27676	+	0.377889i
$898$		0			0
$899$		−	6.75025e8i		−	0.929053i
$900$		0			0
$901$	−1.62063e9			−2.21570
$902$		0			0
$903$	8.98577e6	+	3.03599e7i	0.0122037	+	0.0412323i
$904$		0			0
$905$	−3.12129e8	+	9.99341e8i	−0.421103	+	1.34824i
$906$		0			0
$907$			7.14826e8i			0.958029i	0.877807	+	0.479014i	$0.159006\pi$
$907$			7.14826e8i			0.958029i	−0.877807	+	0.479014i	$0.840994\pi$
$908$		0			0
$909$	−4.04679e8	−	6.23750e8i	−0.538790	−	0.830461i
$910$		0			0
$911$			1.40325e9i			1.85601i	0.372570	+	0.928004i	$0.378477\pi$
$911$			1.40325e9i			1.85601i	−0.372570	+	0.928004i	$0.621523\pi$
$912$		0			0
$913$		−	2.83025e8i		−	0.371889i
$914$		0			0
$915$	−1.29420e8	−	1.93815e6i	−0.168942	−	0.00253002i
$916$		0			0
$917$	1.62799e8			0.211127
$918$		0			0
$919$	−1.41305e9			−1.82059			−0.910295	−	0.413960i	$-0.864145\pi$
$919$	−1.41305e9			−1.82059			−0.910295	+	0.413960i	$0.864145\pi$
$920$		0			0
$921$	1.23699e9	−	3.66117e8i	1.58338	−	0.468641i
$922$		0			0
$923$	9.38409e8			1.19340
$924$		0			0
$925$	3.22174e8	−	4.65438e8i	0.407067	−	0.588081i
$926$		0			0
$927$	5.75762e8	+	8.87448e8i	0.722776	+	1.11405i
$928$		0			0
$929$			1.19239e9i			1.48721i	0.668621	+	0.743604i	$0.266885\pi$
$929$			1.19239e9i			1.48721i	−0.668621	+	0.743604i	$0.733115\pi$
$930$		0			0
$931$	8.55331e8			1.05995
$932$		0			0
$933$	−2.73724e7	+	8.10155e6i	−0.0337030	+	0.00997523i
$934$		0			0
$935$	3.20562e8	+	1.00123e8i	0.392173	+	0.122489i
$936$		0			0
$937$			1.46631e9i			1.78241i	0.453598	+	0.891206i	$0.350140\pi$
$937$			1.46631e9i			1.78241i	−0.453598	+	0.891206i	$0.649860\pi$
$938$		0			0
$939$	−1.64232e7	+	4.86085e6i	−0.0198363	+	0.00587105i
$940$		0			0
$941$		−	2.75926e8i		−	0.331149i	−0.986197	−	0.165575i	$-0.947052\pi$
$941$		−	2.75926e8i		−	0.331149i	0.986197	−	0.165575i	$-0.0529479\pi$
$942$		0			0
$943$		−	2.20149e8i		−	0.262532i
$944$		0			0
$945$	6.11182e7	+	9.73671e7i	0.0724228	+	0.115376i
$946$		0			0
$947$	2.93474e8			0.345557			0.172778	−	0.984961i	$-0.444726\pi$
$947$	2.93474e8			0.345557			0.172778	+	0.984961i	$0.444726\pi$
$948$		0			0
$949$	−1.62587e8			−0.190233
$950$		0			0
$951$	−1.40082e8	−	4.73292e8i	−0.162870	−	0.550284i
$952$		0			0
$953$	−4.98288e8			−0.575707			−0.287854	−	0.957674i	$-0.592942\pi$
$953$	−4.98288e8			−0.575707			−0.287854	+	0.957674i	$0.592942\pi$
$954$		0			0
$955$	5.79599e8	+	1.81029e8i	0.665453	+	0.207844i
$956$		0			0
$957$	−1.29113e8	−	4.36228e8i	−0.147310	−	0.497712i
$958$		0			0
$959$			7.40258e7i			0.0839320i
$960$		0			0
$961$	−5.64324e8			−0.635856
$962$		0			0
$963$	9.99862e8	−	6.48695e8i	1.11960	−	0.726376i
$964$		0			0
$965$	9.38983e8	+	2.93277e8i	1.04490	+	0.326359i
$966$		0			0
$967$			1.12248e9i			1.24137i	0.784060	+	0.620685i	$0.213145\pi$
$967$			1.12248e9i			1.24137i	−0.784060	+	0.620685i	$0.786855\pi$
$968$		0			0
$969$	−3.39855e8	−	1.14826e9i	−0.373527	−	1.26202i
$970$		0			0
$971$		−	2.83802e8i		−	0.309997i	−0.987915	−	0.154998i	$-0.950463\pi$
$971$		−	2.83802e8i		−	0.309997i	0.987915	−	0.154998i	$-0.0495373\pi$
$972$		0			0
$973$			1.50494e8i			0.163373i
$974$		0			0
$975$	−8.30499e8	−	2.73108e8i	−0.896035	−	0.294660i
$976$		0			0
$977$	−2.06216e8			−0.221125			−0.110562	−	0.993869i	$-0.535265\pi$
$977$	−2.06216e8			−0.221125			−0.110562	+	0.993869i	$0.535265\pi$
$978$		0			0
$979$	−6.50757e7			−0.0693539
$980$		0			0
$981$	6.92392e8	−	4.49213e8i	0.733407	−	0.475823i
$982$		0			0
$983$	1.13092e9			1.19061			0.595306	−	0.803499i	$-0.297031\pi$
$983$	1.13092e9			1.19061			0.595306	+	0.803499i	$0.297031\pi$
$984$		0			0
$985$	3.79387e8	−	1.21468e9i	0.396985	−	1.27102i
$986$		0			0
$987$	−6.26875e7	+	1.85539e7i	−0.0651972	+	0.0192967i
$988$		0			0
$989$			4.31054e8i			0.445598i
$990$		0			0
$991$	−3.33850e8			−0.343029			−0.171514	−	0.985182i	$-0.554866\pi$
$991$	−3.33850e8			−0.343029			−0.171514	+	0.985182i	$0.554866\pi$
$992$		0			0
$993$	3.79214e8	+	1.28124e9i	0.387290	+	1.30852i
$994$		0			0
$995$	2.50919e8	−	8.03366e8i	0.254721	−	0.815538i
$996$		0			0
$997$		−	5.06430e7i		−	0.0511015i	−0.999674	−	0.0255508i	$-0.991866\pi$
$997$		−	5.06430e7i		−	0.0511015i	0.999674	−	0.0255508i	$-0.00813395\pi$
$998$		0			0
$999$	4.63464e8	−	5.41924e8i	0.464857	−	0.543553i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	60.7.b.a.29.8	yes	12
3.2	odd	2	inner	60.7.b.a.29.6	yes	12
4.3	odd	2		240.7.c.e.209.5		12
5.2	odd	4		300.7.g.i.101.11		12
5.3	odd	4		300.7.g.i.101.2		12
5.4	even	2	inner	60.7.b.a.29.5	✓	12
12.11	even	2		240.7.c.e.209.7		12
15.2	even	4		300.7.g.i.101.12		12
15.8	even	4		300.7.g.i.101.1		12
15.14	odd	2	inner	60.7.b.a.29.7	yes	12
20.19	odd	2		240.7.c.e.209.8		12
60.59	even	2		240.7.c.e.209.6		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
60.7.b.a.29.5	✓	12	5.4	even	2	inner
60.7.b.a.29.6	yes	12	3.2	odd	2	inner
60.7.b.a.29.7	yes	12	15.14	odd	2	inner
60.7.b.a.29.8	yes	12	1.1	even	1	trivial
240.7.c.e.209.5		12	4.3	odd	2
240.7.c.e.209.6		12	60.59	even	2
240.7.c.e.209.7		12	12.11	even	2
240.7.c.e.209.8		12	20.19	odd	2
300.7.g.i.101.1		12	15.8	even	4
300.7.g.i.101.2		12	5.3	odd	4
300.7.g.i.101.11		12	5.2	odd	4
300.7.g.i.101.12		12	15.2	even	4

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 60 = 2^{2} \cdot 3 \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 7 \)
Character orbit:	\([\chi]\)	\(=\)	60.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(7.66273 + 25.8898i) q^{3} +(-37.2664 + 119.316i) q^{5} +46.7246i q^{7} +(-611.565 + 396.774i) q^{9} +O(q^{10})\)	\(q+(7.66273 + 25.8898i) q^{3} +(-37.2664 + 119.316i) q^{5} +46.7246i q^{7} +(-611.565 + 396.774i) q^{9} +448.732i q^{11} -2072.30i q^{13} +(-3374.62 - 50.5373i) q^{15} -5987.26 q^{17} +7407.66 q^{19} +(-1209.69 + 358.038i) q^{21} -17175.3 q^{23} +(-12847.4 - 8892.93i) q^{25} +(-14958.7 - 12792.9i) q^{27} +37549.0i q^{29} -17977.2 q^{31} +(-11617.6 + 3438.51i) q^{33} +(-5574.97 - 1741.26i) q^{35} +36228.1i q^{37} +(53651.5 - 15879.5i) q^{39} +12817.7i q^{41} -25097.3i q^{43} +(-24550.4 - 87755.6i) q^{45} +51821.1 q^{47} +115466. q^{49} +(-45878.8 - 155009. i) q^{51} +270680. q^{53} +(-53540.7 - 16722.6i) q^{55} +(56762.9 + 191783. i) q^{57} +218274. i q^{59} +38350.9 q^{61} +(-18539.1 - 28575.1i) q^{63} +(247258. + 77227.2i) q^{65} +259141. i q^{67} +(-131610. - 444666. i) q^{69} +452834. i q^{71} -78457.1i q^{73} +(131790. - 400762. i) q^{75} -20966.8 q^{77} -410751. q^{79} +(216583. - 485306. i) q^{81} -630723. q^{83} +(223124. - 714374. i) q^{85} +(-972136. + 287728. i) q^{87} +145021. i q^{89} +96827.4 q^{91} +(-137754. - 465426. i) q^{93} +(-276057. + 883849. i) q^{95} +1.76304e6i q^{97} +(-178045. - 274429. i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 712 q^{9}+O(q^{10}) \) 12 * q + 712 * q^9	\( 12 q + 712 q^{9} + 2480 q^{15} - 192 q^{19} + 5348 q^{21} + 18660 q^{25} + 40848 q^{31} - 45312 q^{39} + 45340 q^{45} - 242940 q^{49} - 40720 q^{51} - 24240 q^{55} - 99312 q^{61} + 108460 q^{69} + 126640 q^{75} + 626544 q^{79} - 798268 q^{81} - 732720 q^{85} + 1996032 q^{91} + 1632080 q^{99}+O(q^{100}) \) 12 * q + 712 * q^9 + 2480 * q^15 - 192 * q^19 + 5348 * q^21 + 18660 * q^25 + 40848 * q^31 - 45312 * q^39 + 45340 * q^45 - 242940 * q^49 - 40720 * q^51 - 24240 * q^55 - 99312 * q^61 + 108460 * q^69 + 126640 * q^75 + 626544 * q^79 - 798268 * q^81 - 732720 * q^85 + 1996032 * q^91 + 1632080 * q^99

Introduction

L-functions

Modular forms

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Database

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