LMFDB - Embedded newform 312.2.bp.a.89.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [312,2,Mod(41,312)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(312, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([0, 0, 6, 1]))

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

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

chi := DirichletCharacter("312.41");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 312 = 2^{3} \cdot 3 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	312.bp (of order $12$, degree $4$, 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:	$2.49133254306$
Analytic rank:	$0$
Dimension:	$56$
Relative dimension:	$14$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			89.1
Character	$\chi$	$=$	312.89
Dual form			312.2.bp.a.305.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.68472 + 0.402146i) q^{3} +(-2.36656 + 2.36656i) q^{5} +(-0.332282 - 1.24009i) q^{7} +(2.67656 - 1.35501i) q^{9} +O(q^{10})$	\(q+(-1.68472 + 0.402146i) q^{3} +(-2.36656 + 2.36656i) q^{5} +(-0.332282 - 1.24009i) q^{7} +(2.67656 - 1.35501i) q^{9} +(1.52674 - 5.69787i) q^{11} +(-3.51077 - 0.821290i) q^{13} +(3.03528 - 4.93869i) q^{15} +(1.04019 - 1.80167i) q^{17} +(1.34634 - 0.360750i) q^{19} +(1.05850 + 1.95558i) q^{21} +(-3.81352 - 6.60522i) q^{23} -6.20118i q^{25} +(-3.96433 + 3.35917i) q^{27} +(-6.87044 + 3.96665i) q^{29} +(1.42567 + 1.42567i) q^{31} +(-0.280749 + 10.2133i) q^{33} +(3.72111 + 2.14839i) q^{35} +(4.28784 + 1.14892i) q^{37} +(6.24493 - 0.0281999i) q^{39} +(0.985195 + 0.263982i) q^{41} +(-8.68002 - 5.01141i) q^{43} +(-3.12752 + 9.54093i) q^{45} +(-2.59357 - 2.59357i) q^{47} +(4.63476 - 2.67588i) q^{49} +(-1.02790 + 3.45361i) q^{51} -7.08357i q^{53} +(9.87121 + 17.0974i) q^{55} +(-2.12313 + 1.14919i) q^{57} +(-1.48170 + 0.397021i) q^{59} +(3.39878 - 5.88685i) q^{61} +(-2.56971 - 2.86893i) q^{63} +(10.2521 - 6.36480i) q^{65} +(-2.22473 + 8.30282i) q^{67} +(9.08098 + 9.59434i) q^{69} +(1.21596 + 4.53804i) q^{71} +(-9.61981 + 9.61981i) q^{73} +(2.49378 + 10.4473i) q^{75} -7.57319 q^{77} -11.7272 q^{79} +(5.32791 - 7.25351i) q^{81} +(0.406364 - 0.406364i) q^{83} +(1.80207 + 6.72543i) q^{85} +(9.97958 - 9.44561i) q^{87} +(1.75705 - 6.55739i) q^{89} +(0.148089 + 4.62658i) q^{91} +(-2.97518 - 1.82853i) q^{93} +(-2.33245 + 4.03992i) q^{95} +(-5.89119 + 1.57854i) q^{97} +(-3.63425 - 17.3194i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 56 q + 4 q^{7}+O(q^{10}) $ 56 * q + 4 * q^7	$ 56 q + 4 q^{7} + 8 q^{13} - 8 q^{15} + 4 q^{19} + 16 q^{21} + 24 q^{27} - 36 q^{31} + 28 q^{33} + 20 q^{37} + 16 q^{39} - 84 q^{43} + 12 q^{45} - 12 q^{49} - 24 q^{55} - 36 q^{57} - 24 q^{61} - 12 q^{63} - 32 q^{67} - 36 q^{69} - 20 q^{73} - 60 q^{75} - 32 q^{79} - 88 q^{85} - 16 q^{87} + 28 q^{91} - 88 q^{93} - 36 q^{97} + 44 q^{99}+O(q^{100}) $ 56 * q + 4 * q^7 + 8 * q^13 - 8 * q^15 + 4 * q^19 + 16 * q^21 + 24 * q^27 - 36 * q^31 + 28 * q^33 + 20 * q^37 + 16 * q^39 - 84 * q^43 + 12 * q^45 - 12 * q^49 - 24 * q^55 - 36 * q^57 - 24 * q^61 - 12 * q^63 - 32 * q^67 - 36 * q^69 - 20 * q^73 - 60 * q^75 - 32 * q^79 - 88 * q^85 - 16 * q^87 + 28 * q^91 - 88 * q^93 - 36 * q^97 + 44 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/312\mathbb{Z}\right)^\times$.

$n$	$79$	$145$	$157$	$209$
$\chi(n)$	$1$	$e\left(\frac{7}{12}\right)$	$1$	$-1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−1.68472	+	0.402146i	−0.972673	+	0.232179i
$3$	−1.68472	+	0.402146i	−0.972673	+	0.232179i
$4$		0			0
$5$	−2.36656	+	2.36656i	−1.05836	+	1.05836i	−0.0601682	+	0.998188i	$0.519164\pi$
$5$	−2.36656	+	2.36656i	−1.05836	+	1.05836i	−0.998188	+	0.0601682i	$0.980836\pi$
$6$		0			0
$7$	−0.332282	−	1.24009i	−0.125591	−	0.468711i	0.874269	−	0.485441i	$-0.161341\pi$
$7$	−0.332282	−	1.24009i	−0.125591	−	0.468711i	−0.999860	+	0.0167303i	$0.994674\pi$
$8$		0			0
$9$	2.67656	−	1.35501i	0.892185	−	0.451669i
$10$		0			0
$11$	1.52674	−	5.69787i	0.460329	−	1.71797i	−0.211600	−	0.977356i	$-0.567867\pi$
$11$	1.52674	−	5.69787i	0.460329	−	1.71797i	0.671929	−	0.740615i	$-0.265466\pi$
$12$		0			0
$13$	−3.51077	−	0.821290i	−0.973712	−	0.227785i
$13$	−3.51077	−	0.821290i	−0.973712	−	0.227785i
$14$		0			0
$15$	3.03528	−	4.93869i	0.783706	−	1.27516i
$16$		0			0
$17$	1.04019	−	1.80167i	0.252284	−	0.436969i	−0.711870	−	0.702311i	$-0.752152\pi$
$17$	1.04019	−	1.80167i	0.252284	−	0.436969i	0.964154	+	0.265342i	$0.0854850\pi$
$18$		0			0
$19$	1.34634	−	0.360750i	0.308871	−	0.0827618i	−0.101054	−	0.994881i	$-0.532221\pi$
$19$	1.34634	−	0.360750i	0.308871	−	0.0827618i	0.409925	+	0.912119i	$0.365555\pi$
$20$		0			0
$21$	1.05850	+	1.95558i	0.230984	+	0.426743i
$22$		0			0
$23$	−3.81352	−	6.60522i	−0.795175	−	1.37728i	−0.922728	−	0.385452i	$-0.874046\pi$
$23$	−3.81352	−	6.60522i	−0.795175	−	1.37728i	0.127553	−	0.991832i	$-0.459288\pi$
$24$		0			0
$25$		−	6.20118i		−	1.24024i
$26$		0			0
$27$	−3.96433	+	3.35917i	−0.762936	+	0.646473i
$28$		0			0
$29$	−6.87044	+	3.96665i	−1.27581	+	0.736588i	−0.976075	−	0.217435i	$-0.930231\pi$
$29$	−6.87044	+	3.96665i	−1.27581	+	0.736588i	−0.299733	+	0.954023i	$0.596898\pi$
$30$		0			0
$31$	1.42567	+	1.42567i	0.256058	+	0.256058i	0.823449	−	0.567391i	$-0.192047\pi$
$31$	1.42567	+	1.42567i	0.256058	+	0.256058i	−0.567391	+	0.823449i	$0.692047\pi$
$32$		0			0
$33$	−0.280749	+	10.2133i	−0.0488721	+	1.77790i
$34$		0			0
$35$	3.72111	+	2.14839i	0.628983	+	0.363143i
$36$		0			0
$37$	4.28784	+	1.14892i	0.704917	+	0.188882i	0.593432	−	0.804884i	$-0.297773\pi$
$37$	4.28784	+	1.14892i	0.704917	+	0.188882i	0.111485	+	0.993766i	$0.464439\pi$
$38$		0			0
$39$	6.24493	−	0.0281999i	0.999990	−	0.00451560i
$40$		0			0
$41$	0.985195	+	0.263982i	0.153862	+	0.0412271i	0.334928	−	0.942244i	$-0.391288\pi$
$41$	0.985195	+	0.263982i	0.153862	+	0.0412271i	−0.181066	+	0.983471i	$0.557955\pi$
$42$		0			0
$43$	−8.68002	−	5.01141i	−1.32369	−	0.764233i	−0.339376	−	0.940651i	$-0.610216\pi$
$43$	−8.68002	−	5.01141i	−1.32369	−	0.764233i	−0.984315	+	0.176418i	$0.943549\pi$
$44$		0			0
$45$	−3.12752	+	9.54093i	−0.466223	+	1.42228i
$46$		0			0
$47$	−2.59357	−	2.59357i	−0.378312	−	0.378312i	0.492181	−	0.870493i	$-0.336200\pi$
$47$	−2.59357	−	2.59357i	−0.378312	−	0.378312i	−0.870493	+	0.492181i	$0.836200\pi$
$48$		0			0
$49$	4.63476	−	2.67588i	0.662109	−	0.382269i
$50$		0			0
$51$	−1.02790	+	3.45361i	−0.143935	+	0.483603i
$52$		0			0
$53$		−	7.08357i		−	0.973003i	−0.873680	−	0.486501i	$-0.838273\pi$
$53$		−	7.08357i		−	0.973003i	0.873680	−	0.486501i	$-0.161727\pi$
$54$		0			0
$55$	9.87121	+	17.0974i	1.33103	+	2.30542i
$56$		0			0
$57$	−2.12313	+	1.14919i	−0.281215	+	0.152214i
$58$		0			0
$59$	−1.48170	+	0.397021i	−0.192901	+	0.0516877i	−0.353976	−	0.935254i	$-0.615171\pi$
$59$	−1.48170	+	0.397021i	−0.192901	+	0.0516877i	0.161075	+	0.986942i	$0.448504\pi$
$60$		0			0
$61$	3.39878	−	5.88685i	0.435169	−	0.753734i	−0.562141	−	0.827042i	$-0.690022\pi$
$61$	3.39878	−	5.88685i	0.435169	−	0.753734i	0.997309	+	0.0733074i	$0.0233554\pi$
$62$		0			0
$63$	−2.56971	−	2.86893i	−0.323752	−	0.361452i
$64$		0			0
$65$	10.2521	−	6.36480i	1.27161	−	0.789456i
$66$		0			0
$67$	−2.22473	+	8.30282i	−0.271794	+	1.01435i	0.686165	+	0.727446i	$0.259293\pi$
$67$	−2.22473	+	8.30282i	−0.271794	+	1.01435i	−0.957959	+	0.286904i	$0.907374\pi$
$68$		0			0
$69$	9.08098	+	9.59434i	1.09322	+	1.15502i
$70$		0			0
$71$	1.21596	+	4.53804i	0.144308	+	0.538566i	0.999785	+	0.0207249i	$0.00659741\pi$
$71$	1.21596	+	4.53804i	0.144308	+	0.538566i	−0.855477	+	0.517841i	$0.826736\pi$
$72$		0			0
$73$	−9.61981	+	9.61981i	−1.12591	+	1.12591i	−0.135079	+	0.990835i	$0.543129\pi$
$73$	−9.61981	+	9.61981i	−1.12591	+	1.12591i	−0.990835	+	0.135079i	$0.956871\pi$
$74$		0			0
$75$	2.49378	+	10.4473i	0.287957	+	1.20634i
$76$		0			0
$77$	−7.57319			−0.863045
$78$		0			0
$79$	−11.7272			−1.31941			−0.659706	−	0.751524i	$-0.729319\pi$
$79$	−11.7272			−1.31941			−0.659706	+	0.751524i	$0.729319\pi$
$80$		0			0
$81$	5.32791	−	7.25351i	0.591990	−	0.805945i
$82$		0			0
$83$	0.406364	−	0.406364i	0.0446042	−	0.0446042i	−0.684453	−	0.729057i	$-0.739959\pi$
$83$	0.406364	−	0.406364i	0.0446042	−	0.0446042i	0.729057	+	0.684453i	$0.239959\pi$
$84$		0			0
$85$	1.80207	+	6.72543i	0.195462	+	0.729475i
$86$		0			0
$87$	9.97958	−	9.44561i	1.06992	−	1.01268i
$88$		0			0
$89$	1.75705	−	6.55739i	0.186247	−	0.695081i	−0.808114	−	0.589026i	$-0.799511\pi$
$89$	1.75705	−	6.55739i	0.186247	−	0.695081i	0.994360	−	0.106055i	$-0.0338220\pi$
$90$		0			0
$91$	0.148089	+	4.62658i	0.0155239	+	0.484997i
$92$		0			0
$93$	−2.97518	−	1.82853i	−0.308512	−	0.189609i
$94$		0			0
$95$	−2.33245	+	4.03992i	−0.239304	+	0.414487i
$96$		0			0
$97$	−5.89119	+	1.57854i	−0.598160	+	0.160276i	−0.545180	−	0.838319i	$-0.683539\pi$
$97$	−5.89119	+	1.57854i	−0.598160	+	0.160276i	−0.0529800	+	0.998596i	$0.516872\pi$
$98$		0			0
$99$	−3.63425	−	17.3194i	−0.365256	−	1.74067i
$100$		0			0
$101$	5.42569	+	9.39757i	0.539876	+	0.935093i	0.998910	+	0.0466743i	$0.0148623\pi$
$101$	5.42569	+	9.39757i	0.539876	+	0.935093i	−0.459034	+	0.888419i	$0.651804\pi$
$102$		0			0
$103$		−	5.53207i		−	0.545091i	−0.962143	−	0.272546i	$-0.912134\pi$
$103$		−	5.53207i		−	0.545091i	0.962143	−	0.272546i	$-0.0878656\pi$
$104$		0			0
$105$	−7.13300	−	2.12299i	−0.696109	−	0.207183i
$106$		0			0
$107$	4.21782	−	2.43516i	0.407752	−	0.235416i	−0.282071	−	0.959393i	$-0.591022\pi$
$107$	4.21782	−	2.43516i	0.407752	−	0.235416i	0.689823	+	0.723978i	$0.257688\pi$
$108$		0			0
$109$	1.33269	+	1.33269i	0.127649	+	0.127649i	0.768045	−	0.640396i	$-0.221230\pi$
$109$	1.33269	+	1.33269i	0.127649	+	0.127649i	−0.640396	+	0.768045i	$0.721230\pi$
$110$		0			0
$111$	−7.68584	−	0.211273i	−0.729508	−	0.0200532i
$112$		0			0
$113$	−8.42921	−	4.86661i	−0.792954	−	0.457812i	0.0480476	−	0.998845i	$-0.484700\pi$
$113$	−8.42921	−	4.86661i	−0.792954	−	0.457812i	−0.841001	+	0.541033i	$0.818033\pi$
$114$		0			0
$115$	24.6565	+	6.60670i	2.29924	+	0.616078i
$116$		0			0
$117$	−10.5096	+	2.55889i	−0.971615	+	0.236569i
$118$		0			0
$119$	−2.57987	−	0.691275i	−0.236496	−	0.0633690i
$120$		0			0
$121$	−20.6085	−	11.8983i	−1.87350	−	1.08166i
$122$		0			0
$123$	−1.76594	−	0.0485432i	−0.159229	−	0.00437699i
$124$		0			0
$125$	2.84267	+	2.84267i	0.254256	+	0.254256i
$126$		0			0
$127$	3.90233	−	2.25301i	0.346276	−	0.199923i	−0.316768	−	0.948503i	$-0.602598\pi$
$127$	3.90233	−	2.25301i	0.346276	−	0.199923i	0.663044	+	0.748581i	$0.269264\pi$
$128$		0			0
$129$	16.6387	+	4.95218i	1.46496	+	0.436015i
$130$		0			0
$131$			6.24622i			0.545735i	0.962052	+	0.272867i	$0.0879721\pi$
$131$			6.24622i			0.545735i	−0.962052	+	0.272867i	$0.912028\pi$
$132$		0			0
$133$	−0.894727	−	1.54971i	−0.0775827	−	0.134377i
$134$		0			0
$135$	1.43214	−	17.3315i	0.123259	−	1.49166i
$136$		0			0
$137$	22.2503	−	5.96195i	1.90097	−	0.509364i	0.904395	−	0.426696i	$-0.140322\pi$
$137$	22.2503	−	5.96195i	1.90097	−	0.509364i	0.996577	−	0.0826685i	$-0.0263443\pi$
$138$		0			0
$139$	9.56760	−	16.5716i	0.811513	−	1.40558i	−0.100292	−	0.994958i	$-0.531978\pi$
$139$	9.56760	−	16.5716i	0.811513	−	1.40558i	0.911805	−	0.410624i	$-0.134689\pi$
$140$		0			0
$141$	5.41244	+	3.32645i	0.455810	+	0.280137i
$142$		0			0
$143$	−10.0396	+	18.7500i	−0.839556	+	1.56795i
$144$		0			0
$145$	6.87198	−	25.6466i	0.570687	−	2.12983i
$146$		0			0
$147$	−6.73217	+	6.37196i	−0.555260	+	0.525550i
$148$		0			0
$149$	−3.46420	−	12.9286i	−0.283798	−	1.05915i	−0.949713	−	0.313122i	$-0.898625\pi$
$149$	−3.46420	−	12.9286i	−0.283798	−	1.05915i	0.665915	−	0.746028i	$-0.268042\pi$
$150$		0			0
$151$	−8.77938	+	8.77938i	−0.714455	+	0.714455i	−0.967464	−	0.253009i	$-0.918580\pi$
$151$	−8.77938	+	8.77938i	−0.714455	+	0.714455i	0.253009	+	0.967464i	$0.418580\pi$
$152$		0			0
$153$	0.342863	−	6.23173i	0.0277188	−	0.503806i
$154$		0			0
$155$	−6.74786			−0.542001
$156$		0			0
$157$	3.27714			0.261544			0.130772	−	0.991412i	$-0.458254\pi$
$157$	3.27714			0.261544			0.130772	+	0.991412i	$0.458254\pi$
$158$		0			0
$159$	2.84863	+	11.9338i	0.225911	+	0.946414i
$160$		0			0
$161$	−6.92392	+	6.92392i	−0.545681	+	0.545681i
$162$		0			0
$163$	−1.17349	−	4.37951i	−0.0919145	−	0.343030i	0.904619	−	0.426221i	$-0.140155\pi$
$163$	−1.17349	−	4.37951i	−0.0919145	−	0.343030i	−0.996534	+	0.0831914i	$0.973489\pi$
$164$		0			0
$165$	−23.5059	−	24.8347i	−1.82993	−	1.93338i
$166$		0			0
$167$	−2.16836	+	8.09242i	−0.167793	+	0.626210i	0.829875	+	0.557949i	$0.188412\pi$
$167$	−2.16836	+	8.09242i	−0.167793	+	0.626210i	−0.997668	+	0.0682609i	$0.978255\pi$
$168$		0			0
$169$	11.6510	+	5.76671i	0.896228	+	0.443593i
$170$		0			0
$171$	3.11473	−	2.78987i	0.238189	−	0.213346i
$172$		0			0
$173$	−7.39731	+	12.8125i	−0.562407	+	0.974118i	0.434878	+	0.900489i	$0.356791\pi$
$173$	−7.39731	+	12.8125i	−0.562407	+	0.974118i	−0.997286	+	0.0736289i	$0.976542\pi$
$174$		0			0
$175$	−7.69004	+	2.06054i	−0.581312	+	0.155762i
$176$		0			0
$177$	2.33659	−	1.26473i	0.175629	−	0.0950629i
$178$		0			0
$179$	0.299519	+	0.518782i	0.0223871	+	0.0387756i	0.877002	−	0.480487i	$-0.159540\pi$
$179$	0.299519	+	0.518782i	0.0223871	+	0.0387756i	−0.854615	+	0.519262i	$0.826207\pi$
$180$		0			0
$181$		−	16.8056i		−	1.24915i	−0.780964	−	0.624576i	$-0.785272\pi$
$181$		−	16.8056i		−	1.24915i	0.780964	−	0.624576i	$-0.214728\pi$
$182$		0			0
$183$	−3.35861	+	11.2845i	−0.248275	+	0.834174i
$184$		0			0
$185$	−12.8664	+	7.42843i	−0.945958	+	0.546149i
$186$		0			0
$187$	−8.67756	−	8.67756i	−0.634566	−	0.634566i
$188$		0			0
$189$	5.48296	+	3.79995i	0.398827	+	0.276406i
$190$		0			0
$191$	4.19095	+	2.41964i	0.303246	+	0.175079i	0.643900	−	0.765109i	$-0.277315\pi$
$191$	4.19095	+	2.41964i	0.303246	+	0.175079i	−0.340654	+	0.940189i	$0.610648\pi$
$192$		0			0
$193$	8.47201	+	2.27007i	0.609828	+	0.163403i	0.550500	−	0.834835i	$-0.314437\pi$
$193$	8.47201	+	2.27007i	0.609828	+	0.163403i	0.0593289	+	0.998238i	$0.481104\pi$
$194$		0			0
$195$	−14.7123	+	14.8457i	−1.05357	+	1.06312i
$196$		0			0
$197$	19.8579	+	5.32092i	1.41482	+	0.379100i	0.883643	−	0.468162i	$-0.155084\pi$
$197$	19.8579	+	5.32092i	1.41482	+	0.379100i	0.531176	+	0.847261i	$0.321750\pi$
$198$		0			0
$199$	1.29567	+	0.748053i	0.0918473	+	0.0530281i	0.545220	−	0.838293i	$-0.316446\pi$
$199$	1.29567	+	0.748053i	0.0918473	+	0.0530281i	−0.453373	+	0.891321i	$0.649779\pi$
$200$		0			0
$201$	0.409102	−	14.8826i	0.0288558	−	1.04974i
$202$		0			0
$203$	7.20193	+	7.20193i	0.505477	+	0.505477i
$204$		0			0
$205$	−2.95625	+	1.70679i	−0.206473	+	0.119208i
$206$		0			0
$207$	−19.1572	−	12.5119i	−1.33152	−	0.869636i
$208$		0			0
$209$		−	8.22203i		−	0.568729i
$210$		0			0
$211$	−7.74572	−	13.4160i	−0.533237	−	0.923594i	−0.999246	−	0.0388139i	$-0.987642\pi$
$211$	−7.74572	−	13.4160i	−0.533237	−	0.923594i	0.466009	−	0.884780i	$-0.345691\pi$
$212$		0			0
$213$	−3.87351	−	7.15632i	−0.265409	−	0.490343i
$214$		0			0
$215$	32.4016	−	8.68197i	2.20977	−	0.592106i
$216$		0			0
$217$	1.29424	−	2.24169i	0.0878587	−	0.152176i
$218$		0			0
$219$	12.3381	−	20.0752i	0.833732	−	1.35656i
$220$		0			0
$221$	−5.13157	+	5.47093i	−0.345187	+	0.368015i
$222$		0			0
$223$	−4.86321	+	18.1498i	−0.325665	+	1.21540i	0.587977	+	0.808878i	$0.299925\pi$
$223$	−4.86321	+	18.1498i	−0.325665	+	1.21540i	−0.913642	+	0.406520i	$0.866742\pi$
$224$		0			0
$225$	−8.40265	−	16.5978i	−0.560177	−	1.10652i
$226$		0			0
$227$	−0.273750	−	1.02165i	−0.0181694	−	0.0678093i	0.956246	−	0.292564i	$-0.0945085\pi$
$227$	−0.273750	−	1.02165i	−0.0181694	−	0.0678093i	−0.974415	+	0.224755i	$0.927842\pi$
$228$		0			0
$229$	5.97504	−	5.97504i	0.394842	−	0.394842i	−0.481567	−	0.876409i	$-0.659932\pi$
$229$	5.97504	−	5.97504i	0.394842	−	0.394842i	0.876409	+	0.481567i	$0.159932\pi$
$230$		0			0
$231$	12.7587	−	3.04553i	0.839461	−	0.200381i
$232$		0			0
$233$	2.30436			0.150964			0.0754820	−	0.997147i	$-0.475950\pi$
$233$	2.30436			0.150964			0.0754820	+	0.997147i	$0.475950\pi$
$234$		0			0
$235$	12.2757			0.800777
$236$		0			0
$237$	19.7570	−	4.71605i	1.28336	−	0.306340i
$238$		0			0
$239$	−0.0131657	+	0.0131657i	−0.000851621	+	0.000851621i	−0.707532	−	0.706681i	$-0.750192\pi$
$239$	−0.0131657	+	0.0131657i	−0.000851621	+	0.000851621i	0.706681	+	0.707532i	$0.250192\pi$
$240$		0			0
$241$	4.35079	+	16.2374i	0.280259	+	1.04594i	0.952235	+	0.305367i	$0.0987792\pi$
$241$	4.35079	+	16.2374i	0.280259	+	1.04594i	−0.671976	+	0.740573i	$0.734554\pi$
$242$		0			0
$243$	−6.05906	+	14.3627i	−0.388689	+	0.921369i
$244$		0			0
$245$	−4.63580	+	17.3010i	−0.296170	+	1.10532i
$246$		0			0
$247$	−5.02296	+	0.160776i	−0.319603	+	0.0102299i
$248$		0			0
$249$	−0.521191	+	0.848026i	−0.0330291	+	0.0537415i
$250$		0			0
$251$	6.88393	−	11.9233i	0.434510	−	0.752593i	−0.562746	−	0.826630i	$-0.690255\pi$
$251$	6.88393	−	11.9233i	0.434510	−	0.752593i	0.997255	+	0.0740371i	$0.0235883\pi$
$252$		0			0
$253$	−43.4579	+	11.6445i	−2.73218	+	0.732084i
$254$		0			0
$255$	−5.74059	−	10.6058i	−0.359490	−	0.664158i
$256$		0			0
$257$	−5.82331	−	10.0863i	−0.363248	−	0.629164i	0.625245	−	0.780428i	$-0.284999\pi$
$257$	−5.82331	−	10.0863i	−0.363248	−	0.629164i	−0.988493	+	0.151264i	$0.951666\pi$
$258$		0			0
$259$		−	5.69909i		−	0.354124i
$260$		0			0
$261$	−13.0143	+	19.9265i	−0.805563	+	1.23342i
$262$		0			0
$263$	21.2887	−	12.2910i	1.31271	−	0.757896i	0.330170	−	0.943922i	$-0.392894\pi$
$263$	21.2887	−	12.2910i	1.31271	−	0.757896i	0.982545	+	0.186025i	$0.0595606\pi$
$264$		0			0
$265$	16.7637	+	16.7637i	1.02978	+	1.02978i
$266$		0			0
$267$	−0.323100	+	11.7539i	−0.0197734	+	0.719330i
$268$		0			0
$269$	−1.83996	−	1.06230i	−0.112184	−	0.0647697i	0.442858	−	0.896592i	$-0.353965\pi$
$269$	−1.83996	−	1.06230i	−0.112184	−	0.0647697i	−0.555042	+	0.831822i	$0.687298\pi$
$270$		0			0
$271$	2.53449	+	0.679116i	0.153960	+	0.0412533i	0.334976	−	0.942227i	$-0.391272\pi$
$271$	2.53449	+	0.679116i	0.153960	+	0.0412533i	−0.181016	+	0.983480i	$0.557939\pi$
$272$		0			0
$273$	−2.11005	−	7.73493i	−0.127706	−	0.468139i
$274$		0			0
$275$	−35.3335	−	9.46759i	−2.13069	−	0.570917i
$276$		0			0
$277$	17.6137	+	10.1693i	1.05831	+	0.611013i	0.924963	−	0.380057i	$-0.124096\pi$
$277$	17.6137	+	10.1693i	1.05831	+	0.611013i	0.133342	+	0.991070i	$0.457429\pi$
$278$		0			0
$279$	5.74768	+	1.88409i	0.344105	+	0.112798i
$280$		0			0
$281$	21.9749	+	21.9749i	1.31091	+	1.31091i	0.920742	+	0.390172i	$0.127585\pi$
$281$	21.9749	+	21.9749i	1.31091	+	1.31091i	0.390172	+	0.920742i	$0.372415\pi$
$282$		0			0
$283$	−2.14892	+	1.24068i	−0.127740	+	0.0737508i	−0.562508	−	0.826792i	$-0.690164\pi$
$283$	−2.14892	+	1.24068i	−0.127740	+	0.0737508i	0.434768	+	0.900542i	$0.356830\pi$
$284$		0			0
$285$	2.30488	−	7.74412i	0.136529	−	0.458722i
$286$		0			0
$287$		−	1.30945i		−	0.0772944i
$288$		0			0
$289$	6.33600	+	10.9743i	0.372706	+	0.645545i
$290$		0			0
$291$	9.29020	−	5.02852i	0.544601	−	0.294777i
$292$		0			0
$293$	−6.05925	+	1.62357i	−0.353985	+	0.0948500i	−0.431429	−	0.902147i	$-0.641991\pi$
$293$	−6.05925	+	1.62357i	−0.353985	+	0.0948500i	0.0774445	+	0.996997i	$0.475324\pi$
$294$		0			0
$295$	2.56696	−	4.44610i	0.149454	−	0.258862i
$296$		0			0
$297$	13.0876	+	27.7168i	0.759421	+	1.60829i
$298$		0			0
$299$	7.96360	+	26.3214i	0.460547	+	1.52221i
$300$		0			0
$301$	−3.33040	+	12.4292i	−0.191961	+	0.716409i
$302$		0			0
$303$	−12.9200	−	13.6503i	−0.742232	−	0.784192i
$304$		0			0
$305$	5.88817	+	21.9750i	0.337156	+	1.25828i
$306$		0			0
$307$	−3.38970	+	3.38970i	−0.193461	+	0.193461i	−0.797190	−	0.603729i	$-0.793681\pi$
$307$	−3.38970	+	3.38970i	−0.193461	+	0.193461i	0.603729	+	0.797190i	$0.293681\pi$
$308$		0			0
$309$	2.22470	+	9.31999i	0.126559	+	0.530196i
$310$		0			0
$311$	−20.8546			−1.18255			−0.591277	−	0.806469i	$-0.701376\pi$
$311$	−20.8546			−1.18255			−0.591277	+	0.806469i	$0.701376\pi$
$312$		0			0
$313$	−22.0202			−1.24465			−0.622327	−	0.782757i	$-0.713813\pi$
$313$	−22.0202			−1.24465			−0.622327	+	0.782757i	$0.713813\pi$
$314$		0			0
$315$	12.8708	+	0.708139i	0.725190	+	0.0398991i
$316$		0			0
$317$	−12.4092	+	12.4092i	−0.696968	+	0.696968i	−0.963755	−	0.266787i	$-0.914038\pi$
$317$	−12.4092	+	12.4092i	−0.696968	+	0.696968i	0.266787	+	0.963755i	$0.414038\pi$
$318$		0			0
$319$	12.1121	+	45.2029i	0.678146	+	2.53088i
$320$		0			0
$321$	−6.12655	+	5.79874i	−0.341951	+	0.323654i
$322$		0			0
$323$	0.750500	−	2.80090i	0.0417589	−	0.155846i
$324$		0			0
$325$	−5.09297	+	21.7709i	−0.282507	+	1.20763i
$326$		0			0
$327$	−2.78114	−	1.70927i	−0.153798	−	0.0945229i
$328$		0			0
$329$	−2.35447	+	4.07807i	−0.129806	+	0.224831i
$330$		0			0
$331$	10.7039	−	2.86810i	0.588340	−	0.157645i	0.0476456	−	0.998864i	$-0.484828\pi$
$331$	10.7039	−	2.86810i	0.588340	−	0.157645i	0.540694	+	0.841219i	$0.318162\pi$
$332$		0			0
$333$	13.0334	−	2.73490i	0.714229	−	0.149871i
$334$		0			0
$335$	−14.3841	−	24.9140i	−0.785889	−	1.36120i
$336$		0			0
$337$			13.4976i			0.735259i	0.929972	+	0.367630i	$0.119831\pi$
$337$			13.4976i			0.735259i	−0.929972	+	0.367630i	$0.880169\pi$
$338$		0			0
$339$	16.1579	+	4.80909i	0.877579	+	0.261194i
$340$		0			0
$341$	10.2999	−	5.94666i	0.557771	−	0.322029i
$342$		0			0
$343$	−11.2131	−	11.2131i	−0.605448	−	0.605448i
$344$		0			0
$345$	−44.1962	−	1.21489i	−2.37944	−	0.0654077i
$346$		0			0
$347$	9.61214	+	5.54957i	0.516007	+	0.297917i	0.735299	−	0.677742i	$-0.237042\pi$
$347$	9.61214	+	5.54957i	0.516007	+	0.297917i	−0.219293	+	0.975659i	$0.570375\pi$
$348$		0			0
$349$	20.6033	+	5.52063i	1.10287	+	0.295512i	0.763932	−	0.645297i	$-0.223266\pi$
$349$	20.6033	+	5.52063i	1.10287	+	0.295512i	0.338936	+	0.940810i	$0.389933\pi$
$350$		0			0
$351$	16.6767	−	8.53741i	0.890137	−	0.455693i
$352$		0			0
$353$	−17.4311	−	4.67065i	−0.927765	−	0.248594i	−0.236863	−	0.971543i	$-0.576119\pi$
$353$	−17.4311	−	4.67065i	−0.927765	−	0.248594i	−0.690901	+	0.722949i	$0.742786\pi$
$354$		0			0
$355$	−13.6172	−	7.86187i	−0.722724	−	0.417265i
$356$		0			0
$357$	4.62435	+	0.127117i	0.244747	+	0.00672775i
$358$		0			0
$359$	10.6950	+	10.6950i	0.564462	+	0.564462i	0.930572	−	0.366110i	$-0.119311\pi$
$359$	10.6950	+	10.6950i	0.564462	+	0.564462i	−0.366110	+	0.930572i	$0.619311\pi$
$360$		0			0
$361$	−14.7720	+	8.52862i	−0.777474	+	0.448875i
$362$		0			0
$363$	39.5044	+	11.7577i	2.07344	+	0.617118i
$364$		0			0
$365$		−	45.5317i		−	2.38324i
$366$		0			0
$367$	−14.7893	−	25.6158i	−0.771995	−	1.33713i	−0.936468	−	0.350753i	$-0.885926\pi$
$367$	−14.7893	−	25.6158i	−0.771995	−	1.33713i	0.164473	−	0.986382i	$-0.447408\pi$
$368$		0			0
$369$	2.99463	−	0.628384i	0.155894	−	0.0327123i
$370$		0			0
$371$	−8.78428	+	2.35374i	−0.456057	+	0.122200i
$372$		0			0
$373$	9.76737	−	16.9176i	0.505735	−	0.875959i	−0.494243	−	0.869324i	$-0.664555\pi$
$373$	9.76737	−	16.9176i	0.505735	−	0.875959i	0.999978	−	0.00663494i	$-0.00211198\pi$
$374$		0			0
$375$	−5.93227	−	3.64593i	−0.306341	−	0.188275i
$376$		0			0
$377$	27.3783	−	8.28336i	1.41005	−	0.426615i
$378$		0			0
$379$	8.69053	−	32.4335i	0.446402	−	1.66600i	−0.265804	−	0.964027i	$-0.585637\pi$
$379$	8.69053	−	32.4335i	0.446402	−	1.66600i	0.712207	−	0.701970i	$-0.247696\pi$
$380$		0			0
$381$	−5.66829	+	5.36500i	−0.290396	+	0.274857i
$382$		0			0
$383$	1.45165	+	5.41763i	0.0741758	+	0.276828i	0.993045	−	0.117734i	$-0.0375630\pi$
$383$	1.45165	+	5.41763i	0.0741758	+	0.276828i	−0.918869	+	0.394562i	$0.870896\pi$
$384$		0			0
$385$	17.9224	−	17.9224i	0.913409	−	0.913409i
$386$		0			0
$387$	−30.0231	−	1.65183i	−1.52616	−	0.0839675i
$388$		0			0
$389$	14.1875			0.719336			0.359668	−	0.933080i	$-0.382890\pi$
$389$	14.1875			0.719336			0.359668	+	0.933080i	$0.382890\pi$
$390$		0			0
$391$	−15.8672			−0.802439
$392$		0			0
$393$	−2.51190	−	10.5231i	−0.126708	−	0.530822i
$394$		0			0
$395$	27.7531	−	27.7531i	1.39641	−	1.39641i
$396$		0			0
$397$	−10.0364	−	37.4565i	−0.503714	−	1.87989i	−0.474387	−	0.880317i	$-0.657330\pi$
$397$	−10.0364	−	37.4565i	−0.503714	−	1.87989i	−0.0293274	−	0.999570i	$-0.509337\pi$
$398$		0			0
$399$	2.13058	+	2.25102i	0.106662	+	0.112692i
$400$		0			0
$401$	2.47565	−	9.23926i	0.123628	−	0.461387i	−0.876159	−	0.482022i	$-0.839902\pi$
$401$	2.47565	−	9.23926i	0.123628	−	0.461387i	0.999787	+	0.0206358i	$0.00656905\pi$
$402$		0			0
$403$	−3.83431	−	6.17609i	−0.191001	−	0.307653i
$404$		0			0
$405$	4.55704	+	29.7746i	0.226441	+	1.47951i
$406$		0			0
$407$	13.0928	−	22.6774i	0.648987	−	1.12408i
$408$		0			0
$409$	29.7151	−	7.96215i	1.46932	−	0.393703i	0.566622	−	0.823978i	$-0.308250\pi$
$409$	29.7151	−	7.96215i	1.46932	−	0.393703i	0.902698	+	0.430275i	$0.141583\pi$
$410$		0			0
$411$	−35.0879	+	18.9921i	−1.73076	+	0.936811i
$412$		0			0
$413$	0.984685	+	1.70552i	0.0484532	+	0.0839234i
$414$		0			0
$415$			1.92337i			0.0944143i
$416$		0			0
$417$	−9.45452	+	31.7660i	−0.462990	+	1.55559i
$418$		0			0
$419$	−30.1024	+	17.3796i	−1.47060	+	0.849051i	−0.999455	−	0.0330044i	$-0.989492\pi$
$419$	−30.1024	+	17.3796i	−1.47060	+	0.849051i	−0.471145	+	0.882056i	$0.656159\pi$
$420$		0			0
$421$	−2.85119	−	2.85119i	−0.138959	−	0.138959i	0.634206	−	0.773164i	$-0.281327\pi$
$421$	−2.85119	−	2.85119i	−0.138959	−	0.138959i	−0.773164	+	0.634206i	$0.781327\pi$
$422$		0			0
$423$	−10.4562	−	3.42753i	−0.508396	−	0.166652i
$424$		0			0
$425$	−11.1725	−	6.45043i	−0.541944	−	0.312892i
$426$		0			0
$427$	−8.42959	−	2.25870i	−0.407937	−	0.109306i
$428$		0			0
$429$	9.37370	−	35.6259i	0.452567	−	1.72003i
$430$		0			0
$431$	−13.0403	−	3.49414i	−0.628129	−	0.168307i	−0.0693083	−	0.997595i	$-0.522079\pi$
$431$	−13.0403	−	3.49414i	−0.628129	−	0.168307i	−0.558820	+	0.829289i	$0.688746\pi$
$432$		0			0
$433$	−7.21603	−	4.16618i	−0.346781	−	0.200214i	0.316486	−	0.948597i	$-0.397497\pi$
$433$	−7.21603	−	4.16618i	−0.346781	−	0.200214i	−0.663266	+	0.748383i	$0.730830\pi$
$434$		0			0
$435$	−1.26368	+	45.9708i	−0.0605886	+	2.20413i
$436$		0			0
$437$	−7.51713	−	7.51713i	−0.359593	−	0.359593i
$438$		0			0
$439$	18.5522	−	10.7111i	0.885447	−	0.511213i	0.0129962	−	0.999916i	$-0.495863\pi$
$439$	18.5522	−	10.7111i	0.885447	−	0.511213i	0.872450	+	0.488703i	$0.162530\pi$
$440$		0			0
$441$	8.77936	−	13.4423i	0.418065	−	0.640108i
$442$		0			0
$443$			11.8889i			0.564859i	0.959288	+	0.282430i	$0.0911404\pi$
$443$			11.8889i			0.564859i	−0.959288	+	0.282430i	$0.908860\pi$
$444$		0			0
$445$	11.3603	+	19.6766i	0.538529	+	0.932759i
$446$		0			0
$447$	11.0354	+	20.3879i	0.521956	+	0.964315i
$448$		0			0
$449$	−28.5028	+	7.63730i	−1.34513	+	0.360427i	−0.858335	−	0.513089i	$-0.828501\pi$
$449$	−28.5028	+	7.63730i	−1.34513	+	0.360427i	−0.486795	+	0.873516i	$0.661834\pi$
$450$		0			0
$451$	3.00827	−	5.21048i	0.141654	−	0.245352i
$452$		0			0
$453$	11.2602	−	18.3214i	0.529050	−	0.860813i
$454$		0			0
$455$	−11.2995	−	10.5986i	−0.529729	−	0.496870i
$456$		0			0
$457$	0.778148	−	2.90409i	0.0364002	−	0.135848i	−0.945335	−	0.326102i	$-0.894265\pi$
$457$	0.778148	−	2.90409i	0.0364002	−	0.135848i	0.981735	+	0.190255i	$0.0609313\pi$
$458$		0			0
$459$	1.92844	+	10.6366i	0.0900120	+	0.496474i
$460$		0			0
$461$	−6.56519	−	24.5016i	−0.305771	−	1.14115i	−0.932279	−	0.361739i	$-0.882183\pi$
$461$	−6.56519	−	24.5016i	−0.305771	−	1.14115i	0.626508	−	0.779415i	$-0.284484\pi$
$462$		0			0
$463$	24.1905	−	24.1905i	1.12423	−	1.12423i	0.133132	−	0.991098i	$-0.457497\pi$
$463$	24.1905	−	24.1905i	1.12423	−	1.12423i	0.991098	−	0.133132i	$-0.0425034\pi$
$464$		0			0
$465$	11.3683	−	2.71363i	0.527190	−	0.125842i
$466$		0			0
$467$	−33.4165			−1.54633			−0.773166	−	0.634204i	$-0.781328\pi$
$467$	−33.4165			−1.54633			−0.773166	+	0.634204i	$0.781328\pi$
$468$		0			0
$469$	11.0355			0.509572
$470$		0			0
$471$	−5.52105	+	1.31789i	−0.254397	+	0.0607251i
$472$		0			0
$473$	−41.8065	+	41.8065i	−1.92226	+	1.92226i
$474$		0			0
$475$	−2.23708	−	8.34889i	−0.102644	−	0.383073i
$476$		0			0
$477$	−9.59829	−	18.9596i	−0.439475	−	0.868099i
$478$		0			0
$479$	4.90851	−	18.3188i	0.224275	−	0.837007i	−0.758418	−	0.651768i	$-0.774027\pi$
$479$	4.90851	−	18.3188i	0.224275	−	0.837007i	0.982693	−	0.185239i	$-0.0593059\pi$
$480$		0			0
$481$	−14.1100	−	7.55516i	−0.643361	−	0.344486i
$482$		0			0
$483$	8.88043	−	14.4493i	0.404073	−	0.657465i
$484$		0			0
$485$	10.2061	−	17.6775i	0.463437	−	0.802696i
$486$		0			0
$487$	−1.74563	+	0.467740i	−0.0791021	+	0.0211953i	−0.298153	−	0.954518i	$-0.596371\pi$
$487$	−1.74563	+	0.467740i	−0.0791021	+	0.0211953i	0.219051	+	0.975713i	$0.429704\pi$
$488$		0			0
$489$	3.73820	+	6.90633i	0.169047	+	0.312315i
$490$		0			0
$491$	−6.52793	−	11.3067i	−0.294601	−	0.510265i	0.680291	−	0.732942i	$-0.261854\pi$
$491$	−6.52793	−	11.3067i	−0.294601	−	0.510265i	−0.974892	+	0.222678i	$0.928520\pi$
$492$		0			0
$493$			16.5043i			0.743317i
$494$		0			0
$495$	49.5880	+	32.3867i	2.22882	+	1.45567i
$496$		0			0
$497$	5.22354	−	3.01581i	0.234308	−	0.135278i
$498$		0			0
$499$	−10.7768	−	10.7768i	−0.482436	−	0.482436i	0.423473	−	0.905909i	$-0.360811\pi$
$499$	−10.7768	−	10.7768i	−0.482436	−	0.482436i	−0.905909	+	0.423473i	$0.860811\pi$
$500$		0			0
$501$	0.398735	−	14.5055i	0.0178142	−	0.648056i
$502$		0			0
$503$	37.3942	+	21.5895i	1.66732	+	0.962630i	0.969072	+	0.246777i	$0.0793714\pi$
$503$	37.3942	+	21.5895i	1.66732	+	0.962630i	0.698251	+	0.715853i	$0.253962\pi$
$504$		0			0
$505$	−35.0801	−	9.39968i	−1.56104	−	0.418280i
$506$		0			0
$507$	−21.9477	−	5.02990i	−0.974730	−	0.223386i
$508$		0			0
$509$	10.6268	+	2.84743i	0.471023	+	0.126210i	0.486520	−	0.873670i	$-0.338266\pi$
$509$	10.6268	+	2.84743i	0.471023	+	0.126210i	−0.0154964	+	0.999880i	$0.504933\pi$
$510$		0			0
$511$	15.1259	+	8.73297i	0.669132	+	0.386324i
$512$		0			0
$513$	−4.12551	+	5.95272i	−0.182146	+	0.262819i
$514$		0			0
$515$	13.0920	+	13.0920i	0.576901	+	0.576901i
$516$		0			0
$517$	−18.7375	+	10.8181i	−0.824076	+	0.475781i
$518$		0			0
$519$	7.30989	−	24.5603i	0.320868	−	1.07808i
$520$		0			0
$521$		−	6.17222i		−	0.270410i	−0.990818	−	0.135205i	$-0.956831\pi$
$521$		−	6.17222i		−	0.270410i	0.990818	−	0.135205i	$-0.0431692\pi$
$522$		0			0
$523$	−0.876655	−	1.51841i	−0.0383334	−	0.0663954i	0.846222	−	0.532830i	$-0.178872\pi$
$523$	−0.876655	−	1.51841i	−0.0383334	−	0.0663954i	−0.884556	+	0.466435i	$0.845538\pi$
$524$		0			0
$525$	12.1269	−	6.56395i	0.529262	−	0.286474i
$526$		0			0
$527$	4.05156	−	1.08561i	0.176489	−	0.0472900i
$528$		0			0
$529$	−17.5859	+	30.4597i	−0.764606	+	1.32434i
$530$		0			0
$531$	−3.42789	+	3.07036i	−0.148758	+	0.133242i
$532$		0			0
$533$	−3.24199	−	1.73591i	−0.140426	−	0.0751907i
$534$		0			0
$535$	−4.21877	+	15.7446i	−0.182393	+	0.680701i
$536$		0			0
$537$	−0.713231	−	0.753551i	−0.0307782	−	0.0325181i
$538$		0			0
$539$	−8.17074	−	30.4936i	−0.351939	−	1.31345i
$540$		0			0
$541$	13.8540	−	13.8540i	0.595630	−	0.595630i	−0.343517	−	0.939147i	$-0.611618\pi$
$541$	13.8540	−	13.8540i	0.595630	−	0.595630i	0.939147	+	0.343517i	$0.111618\pi$
$542$		0			0
$543$	6.75832	+	28.3127i	0.290027	+	1.21502i
$544$		0			0
$545$	−6.30777			−0.270195
$546$		0			0
$547$	−13.1018			−0.560192			−0.280096	−	0.959972i	$-0.590366\pi$
$547$	−13.1018			−0.560192			−0.280096	+	0.959972i	$0.590366\pi$
$548$		0			0
$549$	1.12029	−	20.3619i	0.0478126	−	0.869023i
$550$		0			0
$551$	−7.81896	+	7.81896i	−0.333099	+	0.333099i
$552$		0			0
$553$	3.89673	+	14.5428i	0.165706	+	0.618423i
$554$		0			0
$555$	18.6890	−	17.6890i	0.793303	−	0.750856i
$556$		0			0
$557$	−3.48270	+	12.9976i	−0.147567	+	0.550726i	0.852061	+	0.523442i	$0.175352\pi$
$557$	−3.48270	+	12.9976i	−0.147567	+	0.550726i	−0.999628	+	0.0272837i	$0.991314\pi$
$558$		0			0
$559$	26.3577	+	24.7227i	1.11481	+	1.04566i
$560$		0			0
$561$	18.1089	+	11.1296i	0.764558	+	0.469892i
$562$		0			0
$563$	1.92896	−	3.34105i	0.0812959	−	0.140809i	−0.822511	−	0.568749i	$-0.807427\pi$
$563$	1.92896	−	3.34105i	0.0812959	−	0.140809i	0.903807	+	0.427941i	$0.140761\pi$
$564$		0			0
$565$	31.4653	−	8.43111i	1.32376	−	0.354699i
$566$		0			0
$567$	−10.7654	−	4.19689i	−0.452104	−	0.176253i
$568$		0			0
$569$	−21.1796	−	36.6841i	−0.887895	−	1.53788i	−0.842360	−	0.538916i	$-0.818834\pi$
$569$	−21.1796	−	36.6841i	−0.887895	−	1.53788i	−0.0455351	−	0.998963i	$-0.514499\pi$
$570$		0			0
$571$			17.5465i			0.734300i	0.930162	+	0.367150i	$0.119666\pi$
$571$			17.5465i			0.734300i	−0.930162	+	0.367150i	$0.880334\pi$
$572$		0			0
$573$	−8.03362	−	2.39105i	−0.335609	−	0.0998874i
$574$		0			0
$575$	−40.9602	+	23.6484i	−1.70816	+	0.986205i
$576$		0			0
$577$	−7.37810	−	7.37810i	−0.307154	−	0.307154i	0.536650	−	0.843805i	$-0.319689\pi$
$577$	−7.37810	−	7.37810i	−0.307154	−	0.307154i	−0.843805	+	0.536650i	$0.819689\pi$
$578$		0			0
$579$	−15.1859	−	0.417438i	−0.631103	−	0.0173481i
$580$		0			0
$581$	−0.638956	−	0.368901i	−0.0265084	−	0.0153046i
$582$		0			0
$583$	−40.3612	−	10.8148i	−1.67159	−	0.447902i
$584$		0			0
$585$	18.8159	−	30.9274i	0.777940	−	1.27869i
$586$		0			0
$587$	31.4131	+	8.41711i	1.29656	+	0.347411i	0.840147	−	0.542358i	$-0.182468\pi$
$587$	31.4131	+	8.41711i	1.29656	+	0.347411i	0.456410	+	0.889770i	$0.349135\pi$
$588$		0			0
$589$	2.43375	+	1.40512i	0.100281	+	0.0578971i
$590$		0			0
$591$	−35.5948	−	0.978453i	−1.46418	−	0.0402482i
$592$		0			0
$593$	−2.50934	−	2.50934i	−0.103046	−	0.103046i	0.653704	−	0.756750i	$-0.273214\pi$
$593$	−2.50934	−	2.50934i	−0.103046	−	0.103046i	−0.756750	+	0.653704i	$0.773214\pi$
$594$		0			0
$595$	7.74135	−	4.46947i	0.317365	−	0.183231i
$596$		0			0
$597$	−2.48366	−	0.739212i	−0.101649	−	0.0302539i
$598$		0			0
$599$		−	25.2005i		−	1.02967i	−0.857291	−	0.514833i	$-0.827854\pi$
$599$		−	25.2005i		−	1.02967i	0.857291	−	0.514833i	$-0.172146\pi$
$600$		0			0
$601$	10.3583	+	17.9411i	0.422525	+	0.731834i	0.996186	−	0.0872588i	$-0.0278107\pi$
$601$	10.3583	+	17.9411i	0.422525	+	0.731834i	−0.573661	+	0.819093i	$0.694477\pi$
$602$		0			0
$603$	5.29575	+	25.2375i	0.215660	+	1.02775i
$604$		0			0
$605$	76.9292	−	20.6131i	3.12762	−	0.838042i
$606$		0			0
$607$	−2.69471	+	4.66737i	−0.109375	+	0.189443i	−0.915517	−	0.402279i	$-0.868218\pi$
$607$	−2.69471	+	4.66737i	−0.109375	+	0.189443i	0.806142	+	0.591722i	$0.201552\pi$
$608$		0			0
$609$	−15.0295	−	9.23700i	−0.609025	−	0.374302i
$610$		0			0
$611$	6.97536	+	11.2355i	0.282193	+	0.454540i
$612$		0			0
$613$	4.44016	−	16.5709i	0.179336	−	0.669292i	−0.816436	−	0.577436i	$-0.804053\pi$
$613$	4.44016	−	16.5709i	0.179336	−	0.669292i	0.995772	−	0.0918561i	$-0.0292800\pi$
$614$		0			0
$615$	4.29407	−	4.06431i	0.173154	−	0.163889i
$616$		0			0
$617$	−3.71774	−	13.8748i	−0.149671	−	0.558579i	−0.999503	−	0.0315255i	$-0.989963\pi$
$617$	−3.71774	−	13.8748i	−0.149671	−	0.558579i	0.849832	−	0.527053i	$-0.176703\pi$
$618$		0			0
$619$	−26.5212	+	26.5212i	−1.06598	+	1.06598i	−0.0683140	+	0.997664i	$0.521762\pi$
$619$	−26.5212	+	26.5212i	−1.06598	+	1.06598i	−0.997664	+	0.0683140i	$0.978238\pi$
$620$		0			0
$621$	37.3062	+	13.3750i	1.49704	+	0.536720i
$622$		0			0
$623$	−8.71560			−0.349183
$624$		0			0
$625$	17.5512			0.702050
$626$		0			0
$627$	3.30646	+	13.8518i	0.132047	+	0.553188i
$628$		0			0
$629$	6.53016	−	6.53016i	0.260375	−	0.260375i
$630$		0			0
$631$	−3.01788	−	11.2629i	−0.120140	−	0.448369i	0.879480	−	0.475936i	$-0.157891\pi$
$631$	−3.01788	−	11.2629i	−0.120140	−	0.448369i	−0.999620	+	0.0275672i	$0.991224\pi$
$632$		0			0
$633$	18.4445	+	19.4872i	0.733105	+	0.774548i
$634$		0			0
$635$	−3.90321	+	14.5670i	−0.154894	+	0.578073i
$636$		0			0
$637$	−18.4692	+	5.58791i	−0.731778	+	0.221401i
$638$		0			0
$639$	9.40367	+	10.4987i	0.372003	+	0.415321i
$640$		0			0
$641$	−12.6100	+	21.8411i	−0.498063	+	0.862671i	−0.999998	−	0.00223486i	$-0.999289\pi$
$641$	−12.6100	+	21.8411i	−0.498063	+	0.862671i	0.501934	+	0.864906i	$0.332622\pi$
$642$		0			0
$643$	39.7951	−	10.6631i	1.56937	−	0.420511i	0.633753	−	0.773535i	$-0.281514\pi$
$643$	39.7951	−	10.6631i	1.56937	−	0.420511i	0.935614	+	0.353025i	$0.114847\pi$
$644$		0			0
$645$	−51.0961	+	27.6569i	−2.01191	+	1.08899i
$646$		0			0
$647$	2.88978	+	5.00524i	0.113609	+	0.196776i	0.917223	−	0.398375i	$-0.130426\pi$
$647$	2.88978	+	5.00524i	0.113609	+	0.196776i	−0.803614	+	0.595151i	$0.797092\pi$
$648$		0			0
$649$			9.04868i			0.355192i
$650$		0			0
$651$	−1.27894	+	4.29709i	−0.0501257	+	0.168416i
$652$		0			0
$653$	−5.36540	+	3.09771i	−0.209964	+	0.121223i	−0.601295	−	0.799027i	$-0.705348\pi$
$653$	−5.36540	+	3.09771i	−0.209964	+	0.121223i	0.391330	+	0.920250i	$0.372015\pi$
$654$		0			0
$655$	−14.7820	−	14.7820i	−0.577582	−	0.577582i
$656$		0			0
$657$	−12.7130	+	38.7829i	−0.495983	+	1.51306i
$658$		0			0
$659$	−17.8116	−	10.2836i	−0.693843	−	0.400590i	0.111207	−	0.993797i	$-0.464528\pi$
$659$	−17.8116	−	10.2836i	−0.693843	−	0.400590i	−0.805050	+	0.593207i	$0.797862\pi$
$660$		0			0
$661$	−41.1745	−	11.0327i	−1.60150	−	0.429121i	−0.656007	−	0.754755i	$-0.727756\pi$
$661$	−41.1745	−	11.0327i	−1.60150	−	0.429121i	−0.945496	+	0.325634i	$0.894422\pi$
$662$		0			0
$663$	6.44513	−	11.2806i	0.250308	−	0.438103i
$664$		0			0
$665$	5.78491	+	1.55006i	0.224329	+	0.0601088i
$666$		0			0
$667$	52.4012	+	30.2538i	2.02898	+	1.17143i
$668$		0			0
$669$	0.894287	−	32.5330i	0.0345751	−	1.25780i
$670$		0			0
$671$	−28.3535	−	28.3535i	−1.09457	−	1.09457i
$672$		0			0
$673$	27.9181	−	16.1185i	1.07616	−	0.621323i	0.146304	−	0.989240i	$-0.453262\pi$
$673$	27.9181	−	16.1185i	1.07616	−	0.621323i	0.929859	+	0.367917i	$0.119929\pi$
$674$		0			0
$675$	20.8309	+	24.5836i	0.801780	+	0.946222i
$676$		0			0
$677$		−	37.6671i		−	1.44766i	−0.689977	−	0.723831i	$-0.742379\pi$
$677$		−	37.6671i		−	1.44766i	0.689977	−	0.723831i	$-0.257621\pi$
$678$		0			0
$679$	3.91507	+	6.78110i	0.150247	+	0.260235i
$680$		0			0
$681$	0.872045	+	1.61111i	0.0334168	+	0.0617377i
$682$		0			0
$683$	44.1988	−	11.8430i	1.69122	−	0.453161i	0.720517	−	0.693438i	$-0.243905\pi$
$683$	44.1988	−	11.8430i	1.69122	−	0.453161i	0.970705	+	0.240276i	$0.0772381\pi$
$684$		0			0
$685$	−38.5473	+	66.7659i	−1.47282	+	2.55100i
$686$		0			0
$687$	−7.66342	+	12.4691i	−0.292378	+	0.475726i
$688$		0			0
$689$	−5.81766	+	24.8688i	−0.221635	+	0.947424i
$690$		0			0
$691$	−7.42504	+	27.7106i	−0.282462	+	1.05416i	0.668212	+	0.743971i	$0.267060\pi$
$691$	−7.42504	+	27.7106i	−0.282462	+	1.05416i	−0.950674	+	0.310191i	$0.899607\pi$
$692$		0			0
$693$	−20.2701	+	10.2617i	−0.769996	+	0.389811i
$694$		0			0
$695$	16.5753	+	61.8598i	0.628736	+	2.34648i
$696$		0			0
$697$	1.50040	−	1.50040i	0.0568318	−	0.0568318i
$698$		0			0
$699$	−3.88221	+	0.926692i	−0.146839	+	0.0350507i
$700$		0			0
$701$	8.75126			0.330531			0.165265	−	0.986249i	$-0.447152\pi$
$701$	8.75126			0.330531			0.165265	+	0.986249i	$0.447152\pi$
$702$		0			0
$703$	6.18736			0.233361
$704$		0			0
$705$	−20.6811	+	4.93662i	−0.778894	+	0.185924i
$706$		0			0
$707$	9.85100	−	9.85100i	0.370485	−	0.370485i
$708$		0			0
$709$	−6.73251	−	25.1261i	−0.252845	−	0.943629i	−0.969277	−	0.245972i	$-0.920893\pi$
$709$	−6.73251	−	25.1261i	−0.252845	−	0.943629i	0.716432	−	0.697657i	$-0.245774\pi$
$710$		0			0
$711$	−31.3885	+	15.8904i	−1.17716	+	0.595938i
$712$		0			0
$713$	3.98004	−	14.8537i	0.149054	−	0.556275i
$714$		0			0
$715$	−20.6136	−	68.1323i	−0.770904	−	2.54800i
$716$		0			0
$717$	0.0168860	−	0.0274751i	0.000630620	−	0.00102608i
$718$		0			0
$719$	−17.9675	+	31.1206i	−0.670075	+	1.16060i	0.307807	+	0.951449i	$0.400405\pi$
$719$	−17.9675	+	31.1206i	−0.670075	+	1.16060i	−0.977882	+	0.209155i	$0.932929\pi$
$720$		0			0
$721$	−6.86028	+	1.83821i	−0.255490	+	0.0684584i
$722$		0			0
$723$	−13.8597	−	25.6057i	−0.515446	−	0.952288i
$724$		0			0
$725$	24.5979	+	42.6048i	0.913544	+	1.58230i
$726$		0			0
$727$			29.2791i			1.08590i	0.839764	+	0.542951i	$0.182693\pi$
$727$			29.2791i			1.08590i	−0.839764	+	0.542951i	$0.817307\pi$
$728$		0			0
$729$	4.43189	−	26.6338i	0.164144	−	0.986436i
$730$		0			0
$731$	−18.0578	+	10.4257i	−0.667892	+	0.385608i
$732$		0			0
$733$	0.720934	+	0.720934i	0.0266283	+	0.0266283i	0.720296	−	0.693667i	$-0.244006\pi$
$733$	0.720934	+	0.720934i	0.0266283	+	0.0266283i	−0.693667	+	0.720296i	$0.744006\pi$
$734$		0			0
$735$	0.852469	−	31.0117i	0.0314438	−	1.14388i
$736$		0			0
$737$	43.9118	+	25.3525i	1.61751	+	0.933870i
$738$		0			0
$739$	24.3751	+	6.53128i	0.896652	+	0.240257i	0.677578	−	0.735451i	$-0.263030\pi$
$739$	24.3751	+	6.53128i	0.896652	+	0.240257i	0.219074	+	0.975708i	$0.429696\pi$
$740$		0			0
$741$	8.39762	−	2.29083i	0.308494	−	0.0841557i
$742$		0			0
$743$	−2.74994	−	0.736843i	−0.100885	−	0.0270321i	0.208023	−	0.978124i	$-0.433297\pi$
$743$	−2.74994	−	0.736843i	−0.100885	−	0.0270321i	−0.308909	+	0.951092i	$0.599964\pi$
$744$		0			0
$745$	38.7944	+	22.3980i	1.42132	+	0.820598i
$746$		0			0
$747$	0.537030	−	1.63828i	0.0196489	−	0.0599416i
$748$		0			0
$749$	−4.42133	−	4.42133i	−0.161552	−	0.161552i
$750$		0			0
$751$	−39.7116	+	22.9275i	−1.44910	+	0.836636i	−0.998428	−	0.0560550i	$-0.982148\pi$
$751$	−39.7116	+	22.9275i	−1.44910	+	0.836636i	−0.450669	+	0.892691i	$0.648814\pi$
$752$		0			0
$753$	−6.80257	+	22.8558i	−0.247899	+	0.832911i
$754$		0			0
$755$		−	41.5538i		−	1.51230i
$756$		0			0
$757$	−9.99976	−	17.3201i	−0.363448	−	0.629510i	0.625078	−	0.780562i	$-0.285067\pi$
$757$	−9.99976	−	17.3201i	−0.363448	−	0.629510i	−0.988526	+	0.151052i	$0.951734\pi$
$758$		0			0
$759$	68.5316	−	37.0942i	2.48754	−	1.34643i
$760$		0			0
$761$	−12.2935	+	3.29404i	−0.445640	+	0.119409i	−0.474659	−	0.880170i	$-0.657429\pi$
$761$	−12.2935	+	3.29404i	−0.445640	+	0.119409i	0.0290184	+	0.999579i	$0.490762\pi$
$762$		0			0
$763$	1.20983	−	2.09549i	0.0437988	−	0.0758617i
$764$		0			0
$765$	13.9364	+	15.5592i	0.503870	+	0.562543i
$766$		0			0
$767$	5.52798	−	0.176941i	0.199604	−	0.00638897i
$768$		0			0
$769$	5.98953	−	22.3532i	0.215988	−	0.806078i	−0.769828	−	0.638251i	$-0.779658\pi$
$769$	5.98953	−	22.3532i	0.215988	−	0.806078i	0.985816	−	0.167827i	$-0.0536751\pi$
$770$		0			0
$771$	13.8668	+	14.6507i	0.499401	+	0.527632i
$772$		0			0
$773$	−6.75254	−	25.2008i	−0.242872	−	0.906410i	−0.974441	−	0.224643i	$-0.927878\pi$
$773$	−6.75254	−	25.2008i	−0.242872	−	0.906410i	0.731569	−	0.681767i	$-0.238788\pi$
$774$		0			0
$775$	8.84085	−	8.84085i	0.317573	−	0.317573i
$776$		0			0
$777$	2.29187	+	9.60136i	0.0822203	+	0.344447i
$778$		0			0
$779$	1.42164			0.0509355
$780$		0			0
$781$	27.7136			0.991670
$782$		0			0
$783$	13.9120	−	38.8041i	0.497176	−	1.38675i
$784$		0			0
$785$	−7.75553	+	7.75553i	−0.276807	+	0.276807i
$786$		0			0
$787$	−3.78032	−	14.1083i	−0.134754	−	0.502908i	−0.999999	−	0.00155884i	$-0.999504\pi$
$787$	−3.78032	−	14.1083i	−0.134754	−	0.502908i	0.865245	−	0.501349i	$-0.167163\pi$
$788$		0			0
$789$	−30.9226	+	29.2681i	−1.10087	+	1.04197i
$790$		0			0
$791$	−3.23417	+	12.0701i	−0.114994	+	0.429163i
$792$		0			0
$793$	−16.7671	+	17.8760i	−0.595418	+	0.634795i
$794$		0			0
$795$	−34.9835	−	21.5006i	−1.24074	−	0.762548i
$796$		0			0
$797$	−0.895558	+	1.55115i	−0.0317223	+	0.0549446i	−0.881451	−	0.472276i	$-0.843433\pi$
$797$	−0.895558	+	1.55115i	−0.0317223	+	0.0549446i	0.849728	+	0.527221i	$0.176766\pi$
$798$		0			0
$799$	−7.37058	+	1.97494i	−0.260752	+	0.0698683i
$800$		0			0
$801$	−4.18247	−	19.9320i	−0.147780	−	0.704263i
$802$		0			0
$803$	40.1255	+	69.4993i	1.41600	+	2.45258i
$804$		0			0
$805$		−	32.7717i		−	1.15505i
$806$		0			0
$807$	3.52702	+	1.04975i	0.124157	+	0.0369528i
$808$		0			0
$809$	−3.09499	+	1.78689i	−0.108814	+	0.0628237i	−0.553419	−	0.832903i	$-0.686677\pi$
$809$	−3.09499	+	1.78689i	−0.108814	+	0.0628237i	0.444605	+	0.895727i	$0.353344\pi$
$810$		0			0
$811$	33.8782	+	33.8782i	1.18963	+	1.18963i	0.977171	+	0.212455i	$0.0681458\pi$
$811$	33.8782	+	33.8782i	1.18963	+	1.18963i	0.212455	+	0.977171i	$0.431854\pi$
$812$		0			0
$813$	−4.54301	−	0.124881i	−0.159330	−	0.00437978i
$814$		0			0
$815$	13.1415	+	7.58724i	0.460326	+	0.265769i
$816$		0			0
$817$	−13.4941	−	3.61574i	−0.472099	−	0.126499i
$818$		0			0
$819$	6.66541	+	12.1826i	0.232908	+	0.425695i
$820$		0			0
$821$	−7.99495	−	2.14224i	−0.279026	−	0.0747647i	0.116592	−	0.993180i	$-0.462803\pi$
$821$	−7.99495	−	2.14224i	−0.279026	−	0.0747647i	−0.395618	+	0.918415i	$0.629470\pi$
$822$		0			0
$823$	16.3405	+	9.43421i	0.569595	+	0.328856i	0.756988	−	0.653429i	$-0.226670\pi$
$823$	16.3405	+	9.43421i	0.569595	+	0.328856i	−0.187393	+	0.982285i	$0.560004\pi$
$824$		0			0
$825$	63.3344	+	1.74098i	2.20502	+	0.0606130i
$826$		0			0
$827$	4.13655	+	4.13655i	0.143842	+	0.143842i	0.775361	−	0.631519i	$-0.217568\pi$
$827$	4.13655	+	4.13655i	0.143842	+	0.143842i	−0.631519	+	0.775361i	$0.717568\pi$
$828$		0			0
$829$	20.3605	−	11.7551i	0.707148	−	0.408272i	−0.102856	−	0.994696i	$-0.532798\pi$
$829$	20.3605	−	11.7551i	0.707148	−	0.408272i	0.810004	+	0.586424i	$0.199465\pi$
$830$		0			0
$831$	−33.7637	−	10.0491i	−1.17125	−	0.348599i
$832$		0			0
$833$		−	11.1337i		−	0.385761i
$834$		0			0
$835$	−14.0196	−	24.2827i	−0.485169	−	0.840338i
$836$		0			0
$837$	−10.4409	−	0.862758i	−0.360891	−	0.0298213i
$838$		0			0
$839$	−6.39163	+	1.71263i	−0.220664	+	0.0591266i	−0.367457	−	0.930041i	$-0.619771\pi$
$839$	−6.39163	+	1.71263i	−0.220664	+	0.0591266i	0.146793	+	0.989167i	$0.453105\pi$
$840$		0			0
$841$	16.9686	−	29.3905i	0.585124	−	1.01347i
$842$		0			0
$843$	−45.8587	−	28.1844i	−1.57946	−	0.970724i
$844$		0			0
$845$	−41.2199	+	13.9254i	−1.41801	+	0.479049i
$846$		0			0
$847$	−7.90718	+	29.5100i	−0.271694	+	1.01398i
$848$		0			0
$849$	3.12139	−	2.95438i	0.107126	−	0.101394i
$850$		0			0
$851$	−8.76290	−	32.7036i	−0.300388	−	1.12106i
$852$		0			0
$853$	−19.4996	+	19.4996i	−0.667652	+	0.667652i	−0.957172	−	0.289520i	$-0.906504\pi$
$853$	−19.4996	+	19.4996i	−0.667652	+	0.667652i	0.289520	+	0.957172i	$0.406504\pi$
$854$		0			0
$855$	−0.768809	+	13.9736i	−0.0262927	+	0.477886i
$856$		0			0
$857$	−24.2094			−0.826978			−0.413489	−	0.910509i	$-0.635690\pi$
$857$	−24.2094			−0.826978			−0.413489	+	0.910509i	$0.635690\pi$
$858$		0			0
$859$	−42.1352			−1.43764			−0.718818	−	0.695198i	$-0.755317\pi$
$859$	−42.1352			−1.43764			−0.718818	+	0.695198i	$0.755317\pi$
$860$		0			0
$861$	0.526591	+	2.20606i	0.0179462	+	0.0751822i
$862$		0			0
$863$	−21.6005	+	21.6005i	−0.735291	+	0.735291i	−0.971663	−	0.236372i	$-0.924042\pi$
$863$	−21.6005	+	21.6005i	−0.735291	+	0.735291i	0.236372	+	0.971663i	$0.424042\pi$
$864$		0			0
$865$	−12.8154	−	47.8277i	−0.435737	−	1.62619i
$866$		0			0
$867$	−15.0876	−	15.9406i	−0.512403	−	0.541370i
$868$		0			0
$869$	−17.9044	+	66.8200i	−0.607364	+	2.26671i
$870$		0			0
$871$	14.6295	−	27.3221i	0.495703	−	0.925774i
$872$		0			0
$873$	−13.6292	+	12.2077i	−0.461278	+	0.413167i
$874$		0			0
$875$	2.58061	−	4.46974i	0.0872404	−	0.151105i
$876$		0			0
$877$	−4.03471	+	1.08110i	−0.136242	+	0.0365061i	−0.326296	−	0.945268i	$-0.605801\pi$
$877$	−4.03471	+	1.08110i	−0.136242	+	0.0365061i	0.190053	+	0.981774i	$0.439134\pi$
$878$		0			0
$879$	9.55521	−	5.17196i	0.322289	−	0.174446i
$880$		0			0
$881$	−5.08884	−	8.81413i	−0.171447	−	0.296955i	0.767479	−	0.641074i	$-0.221511\pi$
$881$	−5.08884	−	8.81413i	−0.171447	−	0.296955i	−0.938926	+	0.344119i	$0.888178\pi$
$882$		0			0
$883$			43.9433i			1.47881i	0.673262	+	0.739404i	$0.264893\pi$
$883$			43.9433i			1.47881i	−0.673262	+	0.739404i	$0.735107\pi$
$884$		0			0
$885$	−2.53662	+	8.52273i	−0.0852675	+	0.286488i
$886$		0			0
$887$	19.6015	−	11.3169i	0.658153	−	0.379985i	−0.133420	−	0.991060i	$-0.542596\pi$
$887$	19.6015	−	11.3169i	0.658153	−	0.379985i	0.791573	+	0.611075i	$0.209263\pi$
$888$		0			0
$889$	−4.09062	−	4.09062i	−0.137195	−	0.137195i
$890$		0			0
$891$	−33.1952	−	41.4319i	−1.11208	−	1.38802i
$892$		0			0
$893$	−4.42746	−	2.55619i	−0.148159	−	0.0855398i
$894$		0			0
$895$	−1.93656	−	0.518898i	−0.0647319	−	0.0173449i
$896$		0			0
$897$	−24.0015	−	41.1416i	−0.801386	−	1.37368i
$898$		0			0
$899$	−15.4501	−	4.13985i	−0.515290	−	0.138072i
$900$		0			0
$901$	−12.7622	−	7.36828i	−0.425172	−	0.245473i
$902$		0			0
$903$	0.612421	−	22.2791i	0.0203801	−	0.741401i
$904$		0			0
$905$	39.7714	+	39.7714i	1.32205	+	1.32205i
$906$		0			0
$907$	22.9105	−	13.2274i	0.760732	−	0.439209i	−0.0688263	−	0.997629i	$-0.521925\pi$
$907$	22.9105	−	13.2274i	0.760732	−	0.439209i	0.829559	+	0.558420i	$0.188592\pi$
$908$		0			0
$909$	27.2559	+	17.8013i	0.904022	+	0.590431i
$910$		0			0
$911$		−	4.39151i		−	0.145497i	−0.997350	−	0.0727486i	$-0.976823\pi$
$911$		−	4.39151i		−	0.145497i	0.997350	−	0.0727486i	$-0.0231771\pi$
$912$		0			0
$913$	−1.69500	−	2.93582i	−0.0560962	−	0.0971614i
$914$		0			0
$915$	−18.7571	−	34.6537i	−0.620090	−	1.14562i
$916$		0			0
$917$	7.74589	−	2.07551i	0.255792	−	0.0685392i
$918$		0			0
$919$	−7.06543	+	12.2377i	−0.233067	+	0.403684i	−0.958709	−	0.284388i	$-0.908209\pi$
$919$	−7.06543	+	12.2377i	−0.233067	+	0.403684i	0.725642	+	0.688072i	$0.241543\pi$
$920$		0			0
$921$	4.34754	−	7.07385i	0.143256	−	0.233091i
$922$		0			0
$923$	−0.541920	−	16.9306i	−0.0178375	−	0.557279i
$924$		0			0
$925$	7.12469	−	26.5897i	0.234258	−	0.874264i
$926$		0			0
$927$	−7.49600	−	14.8069i	−0.246201	−	0.486323i
$928$		0			0
$929$	0.181846	+	0.678658i	0.00596617	+	0.0222660i	0.968845	−	0.247669i	$-0.0796645\pi$
$929$	0.181846	+	0.678658i	0.00596617	+	0.0222660i	−0.962879	+	0.269935i	$0.912998\pi$
$930$		0			0
$931$	5.27463	−	5.27463i	0.172869	−	0.172869i
$932$		0			0
$933$	35.1341	−	8.38658i	1.15024	−	0.274564i
$934$		0			0
$935$	41.0719			1.34319
$936$		0			0
$937$	52.7363			1.72282			0.861409	−	0.507912i	$-0.169582\pi$
$937$	52.7363			1.72282			0.861409	+	0.507912i	$0.169582\pi$
$938$		0			0
$939$	37.0978	−	8.85534i	1.21064	−	0.288983i
$940$		0			0
$941$	24.4625	−	24.4625i	0.797454	−	0.797454i	−0.185239	−	0.982693i	$-0.559306\pi$
$941$	24.4625	−	24.4625i	0.797454	−	0.797454i	0.982693	+	0.185239i	$0.0593059\pi$
$942$		0			0
$943$	−2.01341	−	7.51413i	−0.0655655	−	0.244694i
$944$		0			0
$945$	−21.9685	+	3.98295i	−0.714637	+	0.129565i
$946$		0			0
$947$	9.78982	−	36.5361i	0.318126	−	1.18726i	−0.602917	−	0.797804i	$-0.705995\pi$
$947$	9.78982	−	36.5361i	0.318126	−	1.18726i	0.921043	−	0.389460i	$-0.127338\pi$
$948$		0			0
$949$	41.6736	−	25.8723i	1.35278	−	0.839849i
$950$		0			0
$951$	15.9157	−	25.8963i	0.516101	−	0.839744i
$952$		0			0
$953$	13.6532	−	23.6480i	0.442271	−	0.766035i	−0.555587	−	0.831458i	$-0.687506\pi$
$953$	13.6532	−	23.6480i	0.442271	−	0.766035i	0.997858	+	0.0654232i	$0.0208397\pi$
$954$		0			0
$955$	−15.6443	+	4.19189i	−0.506239	+	0.135646i
$956$		0			0
$957$	−38.5836	−	71.2833i	−1.24723	−	2.30426i
$958$		0			0
$959$	−14.7867	−	25.6114i	−0.477489	−	0.827035i
$960$		0			0
$961$		−	26.9349i		−	0.868869i
$962$		0			0
$963$	7.98957	−	12.2330i	0.257460	−	0.394203i
$964$		0			0
$965$	−25.4217	+	14.6772i	−0.818355	+	0.472477i
$966$		0			0
$967$	8.85578	+	8.85578i	0.284783	+	0.284783i	0.835013	−	0.550230i	$-0.185460\pi$
$967$	8.85578	+	8.85578i	0.284783	+	0.284783i	−0.550230	+	0.835013i	$0.685460\pi$
$968$		0			0
$969$	−0.138008	+	5.02055i	−0.00443345	+	0.161283i
$970$		0			0
$971$	34.0062	+	19.6335i	1.09131	+	0.630069i	0.933925	−	0.357468i	$-0.116360\pi$
$971$	34.0062	+	19.6335i	1.09131	+	0.630069i	0.157386	+	0.987537i	$0.449693\pi$
$972$		0			0
$973$	−23.7294	−	6.35828i	−0.760730	−	0.203837i
$974$		0			0
$975$	−0.174873	−	38.7260i	−0.00560041	−	1.24022i
$976$		0			0
$977$	31.3843	+	8.40939i	1.00407	+	0.269040i	0.723150	−	0.690691i	$-0.242693\pi$
$977$	31.3843	+	8.40939i	1.00407	+	0.269040i	0.280921	+	0.959731i	$0.409360\pi$
$978$		0			0
$979$	−34.6806	−	20.0228i	−1.10840	−	0.639932i
$980$		0			0
$981$	5.37282	+	1.76121i	0.171541	+	0.0562313i
$982$		0			0
$983$	−23.9552	−	23.9552i	−0.764054	−	0.764054i	0.212999	−	0.977052i	$-0.431677\pi$
$983$	−23.9552	−	23.9552i	−0.764054	−	0.764054i	−0.977052	+	0.212999i	$0.931677\pi$
$984$		0			0
$985$	−59.5872	+	34.4027i	−1.89861	+	1.09616i
$986$		0			0
$987$	2.32665	−	7.81724i	0.0740580	−	0.248826i
$988$		0			0
$989$			76.4446i			2.43080i
$990$		0			0
$991$	−17.9059	−	31.0140i	−0.568801	−	0.985192i	−0.996685	−	0.0813580i	$-0.974074\pi$
$991$	−17.9059	−	31.0140i	−0.568801	−	0.985192i	0.427884	−	0.903833i	$-0.359259\pi$
$992$		0			0
$993$	−16.8797	+	9.13649i	−0.535661	+	0.289938i
$994$		0			0
$995$	−4.83658	+	1.29596i	−0.153330	+	0.0410846i
$996$		0			0
$997$	−0.138048	+	0.239107i	−0.00437204	+	0.00757259i	−0.868203	−	0.496209i	$-0.834725\pi$
$997$	−0.138048	+	0.239107i	−0.00437204	+	0.00757259i	0.863831	+	0.503782i	$0.168058\pi$
$998$		0			0
$999$	−20.8579	+	9.84889i	−0.659914	+	0.311605i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	312.2.bp.a.89.1	✓	56
3.2	odd	2	inner	312.2.bp.a.89.10	yes	56
4.3	odd	2		624.2.cn.f.401.14		56
12.11	even	2		624.2.cn.f.401.5		56
13.6	odd	12	inner	312.2.bp.a.305.10	yes	56
39.32	even	12	inner	312.2.bp.a.305.1	yes	56
52.19	even	12		624.2.cn.f.305.5		56
156.71	odd	12		624.2.cn.f.305.14		56

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
312.2.bp.a.89.1	✓	56	1.1	even	1	trivial
312.2.bp.a.89.10	yes	56	3.2	odd	2	inner
312.2.bp.a.305.1	yes	56	39.32	even	12	inner
312.2.bp.a.305.10	yes	56	13.6	odd	12	inner
624.2.cn.f.305.5		56	52.19	even	12
624.2.cn.f.305.14		56	156.71	odd	12
624.2.cn.f.401.5		56	12.11	even	2
624.2.cn.f.401.14		56	4.3	odd	2

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:	\( N \)	\(=\)	\( 312 = 2^{3} \cdot 3 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	312.bp (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.68472 + 0.402146i) q^{3} +(-2.36656 + 2.36656i) q^{5} +(-0.332282 - 1.24009i) q^{7} +(2.67656 - 1.35501i) q^{9} +O(q^{10})\)	\(q+(-1.68472 + 0.402146i) q^{3} +(-2.36656 + 2.36656i) q^{5} +(-0.332282 - 1.24009i) q^{7} +(2.67656 - 1.35501i) q^{9} +(1.52674 - 5.69787i) q^{11} +(-3.51077 - 0.821290i) q^{13} +(3.03528 - 4.93869i) q^{15} +(1.04019 - 1.80167i) q^{17} +(1.34634 - 0.360750i) q^{19} +(1.05850 + 1.95558i) q^{21} +(-3.81352 - 6.60522i) q^{23} -6.20118i q^{25} +(-3.96433 + 3.35917i) q^{27} +(-6.87044 + 3.96665i) q^{29} +(1.42567 + 1.42567i) q^{31} +(-0.280749 + 10.2133i) q^{33} +(3.72111 + 2.14839i) q^{35} +(4.28784 + 1.14892i) q^{37} +(6.24493 - 0.0281999i) q^{39} +(0.985195 + 0.263982i) q^{41} +(-8.68002 - 5.01141i) q^{43} +(-3.12752 + 9.54093i) q^{45} +(-2.59357 - 2.59357i) q^{47} +(4.63476 - 2.67588i) q^{49} +(-1.02790 + 3.45361i) q^{51} -7.08357i q^{53} +(9.87121 + 17.0974i) q^{55} +(-2.12313 + 1.14919i) q^{57} +(-1.48170 + 0.397021i) q^{59} +(3.39878 - 5.88685i) q^{61} +(-2.56971 - 2.86893i) q^{63} +(10.2521 - 6.36480i) q^{65} +(-2.22473 + 8.30282i) q^{67} +(9.08098 + 9.59434i) q^{69} +(1.21596 + 4.53804i) q^{71} +(-9.61981 + 9.61981i) q^{73} +(2.49378 + 10.4473i) q^{75} -7.57319 q^{77} -11.7272 q^{79} +(5.32791 - 7.25351i) q^{81} +(0.406364 - 0.406364i) q^{83} +(1.80207 + 6.72543i) q^{85} +(9.97958 - 9.44561i) q^{87} +(1.75705 - 6.55739i) q^{89} +(0.148089 + 4.62658i) q^{91} +(-2.97518 - 1.82853i) q^{93} +(-2.33245 + 4.03992i) q^{95} +(-5.89119 + 1.57854i) q^{97} +(-3.63425 - 17.3194i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 56 q + 4 q^{7}+O(q^{10}) \) 56 * q + 4 * q^7	\( 56 q + 4 q^{7} + 8 q^{13} - 8 q^{15} + 4 q^{19} + 16 q^{21} + 24 q^{27} - 36 q^{31} + 28 q^{33} + 20 q^{37} + 16 q^{39} - 84 q^{43} + 12 q^{45} - 12 q^{49} - 24 q^{55} - 36 q^{57} - 24 q^{61} - 12 q^{63} - 32 q^{67} - 36 q^{69} - 20 q^{73} - 60 q^{75} - 32 q^{79} - 88 q^{85} - 16 q^{87} + 28 q^{91} - 88 q^{93} - 36 q^{97} + 44 q^{99}+O(q^{100}) \) 56 * q + 4 * q^7 + 8 * q^13 - 8 * q^15 + 4 * q^19 + 16 * q^21 + 24 * q^27 - 36 * q^31 + 28 * q^33 + 20 * q^37 + 16 * q^39 - 84 * q^43 + 12 * q^45 - 12 * q^49 - 24 * q^55 - 36 * q^57 - 24 * q^61 - 12 * q^63 - 32 * q^67 - 36 * q^69 - 20 * q^73 - 60 * q^75 - 32 * q^79 - 88 * q^85 - 16 * q^87 + 28 * q^91 - 88 * q^93 - 36 * q^97 + 44 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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