LMFDB - Embedded newform 624.2.cn.d.353.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [624,2,Mod(305,624)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(624, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([0, 0, 6, 5]))

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

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

chi := DirichletCharacter("624.305");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 624 = 2^{4} \cdot 3 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	624.cn (of order $12$, degree $4$, not minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$4.98266508613$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$4$ over $\Q(\zeta_{12})$
Coefficient field:	16.0.9349208943630483456.9
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 8 x^{15} + 48 x^{14} - 196 x^{13} + 642 x^{12} - 1668 x^{11} + 3580 x^{10} - 6328 x^{9} + \cdots + 25 $ x^16 - 8x^15 + 48x^14 - 196x^13 + 642x^12 - 1668x^11 + 3580x^10 - 6328x^9 + 9297x^8 - 11276x^7 + 11224x^6 - 9024x^5 + 5736x^4 - 2780x^3 + 972x^2 - 220*x + 25
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{2}\cdot 3^{2} $
Twist minimal:	no (minimal twist has level 78)
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			353.1
Root			$0.500000 + 0.410882i$ of defining polynomial
Character	$\chi$	$=$	624.353
Dual form			624.2.cn.d.449.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.45865 - 0.933998i) q^{3} +(-0.428520 - 0.428520i) q^{5} +(0.735180 - 0.196991i) q^{7} +(1.25529 + 2.72474i) q^{9} +O(q^{10})$	\(q+(-1.45865 - 0.933998i) q^{3} +(-0.428520 - 0.428520i) q^{5} +(0.735180 - 0.196991i) q^{7} +(1.25529 + 2.72474i) q^{9} +(4.05922 + 1.08766i) q^{11} +(0.601205 - 3.55507i) q^{13} +(0.224822 + 1.02529i) q^{15} +(-2.62362 + 4.54424i) q^{17} +(-0.882911 - 3.29507i) q^{19} +(-1.25636 - 0.399317i) q^{21} +(-0.933306 - 1.61653i) q^{23} -4.63274i q^{25} +(0.713876 - 5.14688i) q^{27} +(7.53987 - 4.35315i) q^{29} +(2.68240 - 2.68240i) q^{31} +(-4.90508 - 5.37782i) q^{33} +(-0.399453 - 0.230625i) q^{35} +(1.52130 - 5.67758i) q^{37} +(-4.19738 + 4.62407i) q^{39} +(2.29545 - 8.56672i) q^{41} +(-1.68905 - 0.975173i) q^{43} +(0.629688 - 1.70553i) q^{45} +(-5.73474 + 5.73474i) q^{47} +(-5.56049 + 3.21035i) q^{49} +(8.07123 - 4.17798i) q^{51} +9.01501i q^{53} +(-1.27337 - 2.20554i) q^{55} +(-1.78973 + 5.63097i) q^{57} +(-2.23614 - 8.34539i) q^{59} +(4.06531 - 7.04132i) q^{61} +(1.45962 + 1.75590i) q^{63} +(-1.78105 + 1.26579i) q^{65} +(0.101205 + 0.0271179i) q^{67} +(-0.148476 + 3.22966i) q^{69} +(10.0749 - 2.69957i) q^{71} +(5.57806 + 5.57806i) q^{73} +(-4.32697 + 6.75753i) q^{75} +3.19851 q^{77} +13.5805 q^{79} +(-5.84847 + 6.84072i) q^{81} +(-0.996926 - 0.996926i) q^{83} +(3.07156 - 0.823023i) q^{85} +(-15.0638 - 0.692527i) q^{87} +(-6.32442 - 1.69462i) q^{89} +(-0.258323 - 2.73205i) q^{91} +(-6.41802 + 1.40731i) q^{93} +(-1.03366 + 1.79035i) q^{95} +(4.07638 + 15.2132i) q^{97} +(2.13191 + 12.4257i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 8 q^{7}+O(q^{10}) $ 16 * q - 8 * q^7	$ 16 q - 8 q^{7} - 24 q^{13} + 16 q^{19} - 24 q^{21} - 16 q^{31} - 24 q^{33} + 16 q^{37} - 48 q^{39} + 24 q^{45} + 24 q^{49} + 24 q^{55} - 24 q^{57} - 24 q^{61} + 24 q^{63} - 32 q^{67} - 48 q^{69} + 56 q^{73} + 96 q^{79} + 24 q^{81} - 24 q^{85} - 48 q^{87} + 16 q^{91} - 24 q^{93} + 16 q^{97}+O(q^{100}) $ 16 * q - 8 * q^7 - 24 * q^13 + 16 * q^19 - 24 * q^21 - 16 * q^31 - 24 * q^33 + 16 * q^37 - 48 * q^39 + 24 * q^45 + 24 * q^49 + 24 * q^55 - 24 * q^57 - 24 * q^61 + 24 * q^63 - 32 * q^67 - 48 * q^69 + 56 * q^73 + 96 * q^79 + 24 * q^81 - 24 * q^85 - 48 * q^87 + 16 * q^91 - 24 * q^93 + 16 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/624\mathbb{Z}\right)^\times$.

$n$	$79$	$145$	$209$	$469$
$\chi(n)$	$1$	$e\left(\frac{1}{12}\right)$	$-1$	$1$

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
$3$	−1.45865	−	0.933998i	−0.842150	−	0.539244i
$3$	−1.45865	−	0.933998i	−0.842150	−	0.539244i
$4$		0			0
$5$	−0.428520	−	0.428520i	−0.191640	−	0.191640i	0.604765	−	0.796404i	$-0.293267\pi$
$5$	−0.428520	−	0.428520i	−0.191640	−	0.191640i	−0.796404	+	0.604765i	$0.793267\pi$
$6$		0			0
$7$	0.735180	−	0.196991i	0.277872	−	0.0744555i	−0.117192	−	0.993109i	$-0.537389\pi$
$7$	0.735180	−	0.196991i	0.277872	−	0.0744555i	0.395064	+	0.918654i	$0.370723\pi$
$8$		0			0
$9$	1.25529	+	2.72474i	0.418432	+	0.908248i
$10$		0			0
$11$	4.05922	+	1.08766i	1.22390	+	0.327943i	0.812201	−	0.583377i	$-0.198269\pi$
$11$	4.05922	+	1.08766i	1.22390	+	0.327943i	0.411699	+	0.911320i	$0.364936\pi$
$12$		0			0
$13$	0.601205	−	3.55507i	0.166744	−	0.986000i
$13$	0.601205	−	3.55507i	0.166744	−	0.986000i
$14$		0			0
$15$	0.224822	+	1.02529i	0.0580487	+	0.264730i
$16$		0			0
$17$	−2.62362	+	4.54424i	−0.636320	+	1.10214i	0.349914	+	0.936782i	$0.386211\pi$
$17$	−2.62362	+	4.54424i	−0.636320	+	1.10214i	−0.986234	+	0.165357i	$0.947122\pi$
$18$		0			0
$19$	−0.882911	−	3.29507i	−0.202554	−	0.755940i	−0.990181	−	0.139789i	$-0.955358\pi$
$19$	−0.882911	−	3.29507i	−0.202554	−	0.755940i	0.787628	−	0.616151i	$-0.211309\pi$
$20$		0			0
$21$	−1.25636	−	0.399317i	−0.274159	−	0.0871381i
$22$		0			0
$23$	−0.933306	−	1.61653i	−0.194608	−	0.337071i	0.752164	−	0.658976i	$-0.229010\pi$
$23$	−0.933306	−	1.61653i	−0.194608	−	0.337071i	−0.946772	+	0.321905i	$0.895677\pi$
$24$		0			0
$25$		−	4.63274i		−	0.926548i
$26$		0			0
$27$	0.713876	−	5.14688i	0.137386	−	0.990518i
$28$		0			0
$29$	7.53987	−	4.35315i	1.40012	−	0.808359i	0.405715	−	0.914000i	$-0.367023\pi$
$29$	7.53987	−	4.35315i	1.40012	−	0.808359i	0.994404	+	0.105641i	$0.0336893\pi$
$30$		0			0
$31$	2.68240	−	2.68240i	0.481773	−	0.481773i	−0.423925	−	0.905697i	$-0.639348\pi$
$31$	2.68240	−	2.68240i	0.481773	−	0.481773i	0.905697	+	0.423925i	$0.139348\pi$
$32$		0			0
$33$	−4.90508	−	5.37782i	−0.853865	−	0.936158i
$34$		0			0
$35$	−0.399453	−	0.230625i	−0.0675200	−	0.0389827i
$36$		0			0
$37$	1.52130	−	5.67758i	0.250101	−	0.933389i	−0.720650	−	0.693299i	$-0.756156\pi$
$37$	1.52130	−	5.67758i	0.250101	−	0.933389i	0.970751	−	0.240090i	$-0.0771769\pi$
$38$		0			0
$39$	−4.19738	+	4.62407i	−0.672118	+	0.740444i
$40$		0			0
$41$	2.29545	−	8.56672i	0.358488	−	1.33790i	−0.517549	−	0.855654i	$-0.673155\pi$
$41$	2.29545	−	8.56672i	0.358488	−	1.33790i	0.876037	−	0.482243i	$-0.160178\pi$
$42$		0			0
$43$	−1.68905	−	0.975173i	−0.257578	−	0.148712i	0.365651	−	0.930752i	$-0.380846\pi$
$43$	−1.68905	−	0.975173i	−0.257578	−	0.148712i	−0.623229	+	0.782039i	$0.714180\pi$
$44$		0			0
$45$	0.629688	−	1.70553i	0.0938684	−	0.254245i
$46$		0			0
$47$	−5.73474	+	5.73474i	−0.836498	+	0.836498i	−0.988396	−	0.151898i	$-0.951461\pi$
$47$	−5.73474	+	5.73474i	−0.836498	+	0.836498i	0.151898	+	0.988396i	$0.451461\pi$
$48$		0			0
$49$	−5.56049	+	3.21035i	−0.794356	+	0.458622i
$50$		0			0
$51$	8.07123	−	4.17798i	1.13020	−	0.585034i
$52$		0			0
$53$			9.01501i			1.23831i	0.785270	+	0.619153i	$0.212524\pi$
$53$			9.01501i			1.23831i	−0.785270	+	0.619153i	$0.787476\pi$
$54$		0			0
$55$	−1.27337	−	2.20554i	−0.171701	−	0.297395i
$56$		0			0
$57$	−1.78973	+	5.63097i	−0.237056	+	0.745841i
$58$		0			0
$59$	−2.23614	−	8.34539i	−0.291121	−	1.08648i	−0.944249	−	0.329231i	$-0.893211\pi$
$59$	−2.23614	−	8.34539i	−0.291121	−	1.08648i	0.653129	−	0.757247i	$-0.273456\pi$
$60$		0			0
$61$	4.06531	−	7.04132i	0.520509	−	0.901548i	−0.479206	−	0.877702i	$-0.659075\pi$
$61$	4.06531	−	7.04132i	0.520509	−	0.901548i	0.999716	−	0.0238462i	$-0.00759119\pi$
$62$		0			0
$63$	1.45962	+	1.75590i	0.183894	+	0.221222i
$64$		0			0
$65$	−1.78105	+	1.26579i	−0.220912	+	0.157002i
$66$		0			0
$67$	0.101205	+	0.0271179i	0.0123642	+	0.00331297i	0.264996	−	0.964250i	$-0.414629\pi$
$67$	0.101205	+	0.0271179i	0.0123642	+	0.00331297i	−0.252632	+	0.967563i	$0.581296\pi$
$68$		0			0
$69$	−0.148476	+	3.22966i	−0.0178745	+	0.388805i
$70$		0			0
$71$	10.0749	−	2.69957i	1.19567	−	0.320380i	0.394548	−	0.918875i	$-0.370901\pi$
$71$	10.0749	−	2.69957i	1.19567	−	0.320380i	0.801126	+	0.598496i	$0.204235\pi$
$72$		0			0
$73$	5.57806	+	5.57806i	0.652863	+	0.652863i	0.953681	−	0.300819i	$-0.0972599\pi$
$73$	5.57806	+	5.57806i	0.652863	+	0.652863i	−0.300819	+	0.953681i	$0.597260\pi$
$74$		0			0
$75$	−4.32697	+	6.75753i	−0.499636	+	0.780292i
$76$		0			0
$77$	3.19851			0.364505
$78$		0			0
$79$	13.5805			1.52793			0.763963	−	0.645260i	$-0.223251\pi$
$79$	13.5805			1.52793			0.763963	+	0.645260i	$0.223251\pi$
$80$		0			0
$81$	−5.84847	+	6.84072i	−0.649830	+	0.760080i
$82$		0			0
$83$	−0.996926	−	0.996926i	−0.109427	−	0.109427i	0.650273	−	0.759700i	$-0.274654\pi$
$83$	−0.996926	−	0.996926i	−0.109427	−	0.109427i	−0.759700	+	0.650273i	$0.774654\pi$
$84$		0			0
$85$	3.07156	−	0.823023i	0.333158	−	0.0892694i
$86$		0			0
$87$	−15.0638	−	0.692527i	−1.61501	−	0.0742467i
$88$		0			0
$89$	−6.32442	−	1.69462i	−0.670388	−	0.179630i	−0.0924582	−	0.995717i	$-0.529472\pi$
$89$	−6.32442	−	1.69462i	−0.670388	−	0.179630i	−0.577929	+	0.816087i	$0.696139\pi$
$90$		0			0
$91$	−0.258323	−	2.73205i	−0.0270796	−	0.286397i
$92$		0			0
$93$	−6.41802	+	1.40731i	−0.665518	+	0.145932i
$94$		0			0
$95$	−1.03366	+	1.79035i	−0.106051	+	0.183686i
$96$		0			0
$97$	4.07638	+	15.2132i	0.413893	+	1.54467i	0.787042	+	0.616900i	$0.211612\pi$
$97$	4.07638	+	15.2132i	0.413893	+	1.54467i	−0.373148	+	0.927772i	$0.621722\pi$
$98$		0			0
$99$	2.13191	+	12.4257i	0.214265	+	1.24883i
$100$		0			0
$101$	−1.63630	−	2.83416i	−0.162818	−	0.282009i	0.773060	−	0.634333i	$-0.218725\pi$
$101$	−1.63630	−	2.83416i	−0.162818	−	0.282009i	−0.935878	+	0.352323i	$0.885392\pi$
$102$		0			0
$103$		−	4.79880i		−	0.472840i	−0.971651	−	0.236420i	$-0.924026\pi$
$103$		−	4.79880i		−	0.472840i	0.971651	−	0.236420i	$-0.0759741\pi$
$104$		0			0
$105$	0.367258	+	0.709488i	0.0358407	+	0.0692390i
$106$		0			0
$107$	−2.70638	+	1.56253i	−0.261635	+	0.151055i	−0.625080	−	0.780560i	$-0.714934\pi$
$107$	−2.70638	+	1.56253i	−0.261635	+	0.151055i	0.363445	+	0.931616i	$0.381600\pi$
$108$		0			0
$109$	−0.913996	+	0.913996i	−0.0875449	+	0.0875449i	−0.749523	−	0.661978i	$-0.769717\pi$
$109$	−0.913996	+	0.913996i	−0.0875449	+	0.0875449i	0.661978	+	0.749523i	$0.269717\pi$
$110$		0			0
$111$	−7.52190	+	6.86069i	−0.713947	+	0.651188i
$112$		0			0
$113$	−6.03730	−	3.48564i	−0.567942	−	0.327901i	0.188385	−	0.982095i	$-0.439675\pi$
$113$	−6.03730	−	3.48564i	−0.567942	−	0.327901i	−0.756327	+	0.654194i	$0.773008\pi$
$114$		0			0
$115$	−0.292776	+	1.09266i	−0.0273015	+	0.101891i
$116$		0			0
$117$	10.4414	−	2.82454i	0.965304	−	0.261128i
$118$		0			0
$119$	−1.03366	+	3.85766i	−0.0947551	+	0.353631i
$120$		0			0
$121$	5.76795	+	3.33013i	0.524359	+	0.302739i
$122$		0			0
$123$	−11.3495	+	10.3519i	−1.02335	+	0.933397i
$124$		0			0
$125$	−4.12782	+	4.12782i	−0.369203	+	0.369203i
$126$		0			0
$127$	1.93554	−	1.11748i	0.171751	−	0.0991607i	−0.411660	−	0.911337i	$-0.635051\pi$
$127$	1.93554	−	1.11748i	0.171751	−	0.0991607i	0.583411	+	0.812177i	$0.301718\pi$
$128$		0			0
$129$	1.55291	+	3.00000i	0.136726	+	0.264135i
$130$		0			0
$131$			22.0856i			1.92963i	0.262938	+	0.964813i	$0.415308\pi$
$131$			22.0856i			1.92963i	−0.262938	+	0.964813i	$0.584692\pi$
$132$		0			0
$133$	−1.29820	−	2.24854i	−0.112568	−	0.194973i
$134$		0			0
$135$	−2.51145	+	1.89963i	−0.216151	+	0.163494i
$136$		0			0
$137$	2.58408	+	9.64392i	0.220773	+	0.823935i	0.984054	+	0.177869i	$0.0569204\pi$
$137$	2.58408	+	9.64392i	0.220773	+	0.823935i	−0.763281	+	0.646066i	$0.776413\pi$
$138$		0			0
$139$	−1.88252	+	3.26061i	−0.159673	+	0.276562i	−0.934751	−	0.355304i	$-0.884377\pi$
$139$	−1.88252	+	3.26061i	−0.159673	+	0.276562i	0.775078	+	0.631866i	$0.217711\pi$
$140$		0			0
$141$	13.7212	−	3.00872i	1.15553	−	0.253380i
$142$		0			0
$143$	6.30715	−	13.7769i	0.527430	−	1.15208i
$144$		0			0
$145$	−5.09639	−	1.36557i	−0.423232	−	0.113405i
$146$		0			0
$147$	11.1093	+	0.510724i	0.916276	+	0.0421238i
$148$		0			0
$149$	−8.42964	+	2.25872i	−0.690583	+	0.185041i	−0.587009	−	0.809581i	$-0.699695\pi$
$149$	−8.42964	+	2.25872i	−0.690583	+	0.185041i	−0.103574	+	0.994622i	$0.533028\pi$
$150$		0			0
$151$	17.3671	+	17.3671i	1.41331	+	1.41331i	0.731885	+	0.681429i	$0.238641\pi$
$151$	17.3671	+	17.3671i	1.41331	+	1.41331i	0.681429	+	0.731885i	$0.261359\pi$
$152$		0			0
$153$	−15.6753	−	1.44433i	−1.26727	−	0.116767i
$154$		0			0
$155$	−2.29892			−0.184654
$156$		0			0
$157$	11.0713			0.883589			0.441794	−	0.897116i	$-0.354342\pi$
$157$	11.0713			0.883589			0.441794	+	0.897116i	$0.354342\pi$
$158$		0			0
$159$	8.42000	−	13.1497i	0.667750	−	1.04284i
$160$		0			0
$161$	−1.00459	−	1.00459i	−0.0791728	−	0.0791728i
$162$		0			0
$163$	5.07638	−	1.36021i	0.397613	−	0.106540i	−0.0544714	−	0.998515i	$-0.517347\pi$
$163$	5.07638	−	1.36021i	0.397613	−	0.106540i	0.452084	+	0.891975i	$0.350681\pi$
$164$		0			0
$165$	−0.202576	+	4.40643i	−0.0157705	+	0.343040i
$166$		0			0
$167$	−15.1927	−	4.07088i	−1.17565	−	0.315014i	−0.382450	−	0.923976i	$-0.624920\pi$
$167$	−15.1927	−	4.07088i	−1.17565	−	0.315014i	−0.793200	+	0.608962i	$0.791586\pi$
$168$		0			0
$169$	−12.2771	−	4.27466i	−0.944393	−	0.328820i
$170$		0			0
$171$	7.86990	−	6.54199i	0.601827	−	0.500278i
$172$		0			0
$173$	2.71186	−	4.69708i	0.206179	−	0.357113i	−0.744329	−	0.667813i	$-0.767230\pi$
$173$	2.71186	−	4.69708i	0.206179	−	0.357113i	0.950508	+	0.310701i	$0.100564\pi$
$174$		0			0
$175$	−0.912608	−	3.40590i	−0.0689867	−	0.257462i
$176$		0			0
$177$	−4.53284	+	14.2615i	−0.340709	+	1.07196i
$178$		0			0
$179$	−5.19042	−	8.99007i	−0.387950	−	0.671949i	0.604224	−	0.796815i	$-0.293483\pi$
$179$	−5.19042	−	8.99007i	−0.387950	−	0.671949i	−0.992174	+	0.124866i	$0.960150\pi$
$180$		0			0
$181$		−	11.1172i		−	0.826335i	−0.910655	−	0.413167i	$-0.864422\pi$
$181$		−	11.1172i		−	0.826335i	0.910655	−	0.413167i	$-0.135578\pi$
$182$		0			0
$183$	−12.5064	+	6.47380i	−0.924501	+	0.478557i
$184$		0			0
$185$	−3.08486	+	1.78105i	−0.226804	+	0.130945i
$186$		0			0
$187$	−15.5924	+	15.5924i	−1.14023	+	1.14023i
$188$		0			0
$189$	−0.489061	−	3.92451i	−0.0355740	−	0.285466i
$190$		0			0
$191$	4.96444	+	2.86622i	0.359214	+	0.207392i	0.668736	−	0.743500i	$-0.266836\pi$
$191$	4.96444	+	2.86622i	0.359214	+	0.207392i	−0.309522	+	0.950892i	$0.600169\pi$
$192$		0			0
$193$	−2.93615	+	10.9578i	−0.211348	+	0.788763i	0.776072	+	0.630645i	$0.217209\pi$
$193$	−2.93615	+	10.9578i	−0.211348	+	0.788763i	−0.987420	+	0.158118i	$0.949457\pi$
$194$		0			0
$195$	3.78016	−	0.182846i	0.270703	−	0.0130938i
$196$		0			0
$197$	1.21210	−	4.52361i	0.0863584	−	0.322294i	−0.909210	−	0.416339i	$-0.863313\pi$
$197$	1.21210	−	4.52361i	0.0863584	−	0.322294i	0.995568	+	0.0940449i	$0.0299797\pi$
$198$		0			0
$199$	−11.1741	−	6.45135i	−0.792108	−	0.457324i	0.0485961	−	0.998819i	$-0.484525\pi$
$199$	−11.1741	−	6.45135i	−0.792108	−	0.457324i	−0.840704	+	0.541495i	$0.817859\pi$
$200$		0			0
$201$	−0.122295	−	0.134081i	−0.00862599	−	0.00945734i
$202$		0			0
$203$	4.68563	−	4.68563i	0.328867	−	0.328867i
$204$		0			0
$205$	−4.65465	+	2.68736i	−0.325095	+	0.187694i
$206$		0			0
$207$	3.23307	−	4.57225i	0.224714	−	0.317793i
$208$		0			0
$209$		−	14.3357i		−	0.991621i
$210$		0			0
$211$	−2.63979	−	4.57225i	−0.181731	−	0.314767i	0.760739	−	0.649057i	$-0.224837\pi$
$211$	−2.63979	−	4.57225i	−0.181731	−	0.314767i	−0.942470	+	0.334291i	$0.891503\pi$
$212$		0			0
$213$	−17.2171	−	5.47225i	−1.17970	−	0.374952i
$214$		0			0
$215$	0.305910	+	1.14167i	0.0208629	+	0.0778613i
$216$		0			0
$217$	1.44364	−	2.50045i	0.0980004	−	0.169742i
$218$		0			0
$219$	−2.92652	−	13.3463i	−0.197756	−	0.901860i
$220$		0			0
$221$	14.5778	+	12.0592i	0.980606	+	0.811187i
$222$		0			0
$223$	3.42925	+	0.918866i	0.229640	+	0.0615318i	0.371804	−	0.928311i	$-0.378739\pi$
$223$	3.42925	+	0.918866i	0.229640	+	0.0615318i	−0.142164	+	0.989843i	$0.545406\pi$
$224$		0			0
$225$	12.6230	−	5.81546i	0.841536	−	0.387697i
$226$		0			0
$227$	−4.85544	+	1.30101i	−0.322267	+	0.0863512i	−0.416326	−	0.909215i	$-0.636682\pi$
$227$	−4.85544	+	1.30101i	−0.322267	+	0.0863512i	0.0940589	+	0.995567i	$0.470016\pi$
$228$		0			0
$229$	11.3889	+	11.3889i	0.752602	+	0.752602i	0.974964	−	0.222362i	$-0.0713767\pi$
$229$	11.3889	+	11.3889i	0.752602	+	0.752602i	−0.222362	+	0.974964i	$0.571377\pi$
$230$		0			0
$231$	−4.66550	−	2.98741i	−0.306967	−	0.196557i
$232$		0			0
$233$	22.3807			1.46621			0.733103	−	0.680117i	$-0.238071\pi$
$233$	22.3807			1.46621			0.733103	+	0.680117i	$0.238071\pi$
$234$		0			0
$235$	4.91490			0.320613
$236$		0			0
$237$	−19.8092	−	12.6842i	−1.28674	−	0.823925i
$238$		0			0
$239$	6.08236	+	6.08236i	0.393435	+	0.393435i	0.875910	−	0.482475i	$-0.160262\pi$
$239$	6.08236	+	6.08236i	0.393435	+	0.393435i	−0.482475	+	0.875910i	$0.660262\pi$
$240$		0			0
$241$	5.93615	−	1.59059i	0.382381	−	0.102459i	−0.0625080	−	0.998044i	$-0.519910\pi$
$241$	5.93615	−	1.59059i	0.382381	−	0.102459i	0.444889	+	0.895586i	$0.353243\pi$
$242$		0			0
$243$	14.9201	−	4.51572i	0.957122	−	0.289684i
$244$		0			0
$245$	3.75848	+	1.00708i	0.240120	+	0.0643401i
$246$		0			0
$247$	−12.2450	+	1.15780i	−0.779132	+	0.0736691i
$248$		0			0
$249$	0.523035	+	2.38529i	0.0331460	+	0.151162i
$250$		0			0
$251$	−6.27808	+	10.8740i	−0.396269	+	0.686358i	−0.993262	−	0.115888i	$-0.963029\pi$
$251$	−6.27808	+	10.8740i	−0.396269	+	0.686358i	0.596993	+	0.802246i	$0.296362\pi$
$252$		0			0
$253$	−2.03025	−	7.57698i	−0.127641	−	0.476361i
$254$		0			0
$255$	−5.24903	−	1.66834i	−0.328707	−	0.104475i
$256$		0			0
$257$	−2.36891	−	4.10307i	−0.147768	−	0.255942i	0.782634	−	0.622482i	$-0.213876\pi$
$257$	−2.36891	−	4.10307i	−0.147768	−	0.255942i	−0.930402	+	0.366540i	$0.880542\pi$
$258$		0			0
$259$		−	4.47373i		−	0.277984i
$260$		0			0
$261$	21.3260	+	15.0797i	1.32004	+	0.933413i
$262$		0			0
$263$	4.90945	−	2.83447i	0.302730	−	0.174781i	−0.340939	−	0.940085i	$-0.610745\pi$
$263$	4.90945	−	2.83447i	0.302730	−	0.174781i	0.643668	+	0.765304i	$0.277412\pi$
$264$		0			0
$265$	3.86311	−	3.86311i	0.237309	−	0.237309i
$266$		0			0
$267$	7.64232	+	8.37886i	0.467702	+	0.512778i
$268$		0			0
$269$	−6.32711	−	3.65296i	−0.385770	−	0.222725i	0.294555	−	0.955634i	$-0.404828\pi$
$269$	−6.32711	−	3.65296i	−0.385770	−	0.222725i	−0.680326	+	0.732910i	$0.738162\pi$
$270$		0			0
$271$	6.34829	−	23.6922i	0.385631	−	1.43920i	−0.451538	−	0.892252i	$-0.649124\pi$
$271$	6.34829	−	23.6922i	0.385631	−	1.43920i	0.837169	−	0.546944i	$-0.184209\pi$
$272$		0			0
$273$	−2.17493	+	4.22637i	−0.131633	+	0.255791i
$274$		0			0
$275$	5.03887	−	18.8053i	0.303855	−	1.13400i
$276$		0			0
$277$	−7.57448	−	4.37313i	−0.455107	−	0.262756i	0.254878	−	0.966973i	$-0.417965\pi$
$277$	−7.57448	−	4.37313i	−0.455107	−	0.262756i	−0.709984	+	0.704217i	$0.751298\pi$
$278$		0			0
$279$	10.6760	+	3.94165i	0.639158	+	0.235980i
$280$		0			0
$281$	−9.49571	+	9.49571i	−0.566467	+	0.566467i	−0.931137	−	0.364670i	$-0.881182\pi$
$281$	−9.49571	+	9.49571i	−0.566467	+	0.566467i	0.364670	+	0.931137i	$0.381182\pi$
$282$		0			0
$283$	−27.2245	+	15.7181i	−1.61833	+	0.934342i	−0.630975	+	0.775803i	$0.717345\pi$
$283$	−27.2245	+	15.7181i	−1.61833	+	0.934342i	−0.987353	+	0.158539i	$0.949322\pi$
$284$		0			0
$285$	3.17992	−	1.64605i	0.188362	−	0.0975034i
$286$		0			0
$287$		−	6.75026i		−	0.398455i
$288$		0			0
$289$	−5.26672	−	9.12222i	−0.309807	−	0.536601i
$290$		0			0
$291$	8.26316	−	25.9981i	0.484395	−	1.52403i
$292$		0			0
$293$	0.542185	+	2.02346i	0.0316748	+	0.118212i	0.979953	−	0.199228i	$-0.0638435\pi$
$293$	0.542185	+	2.02346i	0.0316748	+	0.118212i	−0.948278	+	0.317440i	$0.897177\pi$
$294$		0			0
$295$	−2.61794	+	4.53440i	−0.152422	+	0.264003i
$296$		0			0
$297$	8.49585	−	20.1158i	0.492979	−	1.16724i
$298$		0			0
$299$	−6.30801	+	2.34610i	−0.364801	+	0.135679i
$300$		0			0
$301$	−1.43385	−	0.384200i	−0.0826460	−	0.0221449i
$302$		0			0
$303$	−0.260313	+	5.66234i	−0.0149546	+	0.325293i
$304$		0			0
$305$	−4.75941	+	1.27528i	−0.272523	+	0.0730223i
$306$		0			0
$307$	−1.91340	−	1.91340i	−0.109203	−	0.109203i	0.650394	−	0.759597i	$-0.274604\pi$
$307$	−1.91340	−	1.91340i	−0.109203	−	0.109203i	−0.759597	+	0.650394i	$0.774604\pi$
$308$		0			0
$309$	−4.48207	+	6.99975i	−0.254976	+	0.398202i
$310$		0			0
$311$	7.19354			0.407908			0.203954	−	0.978980i	$-0.434621\pi$
$311$	7.19354			0.407908			0.203954	+	0.978980i	$0.434621\pi$
$312$		0			0
$313$	−14.6520			−0.828180			−0.414090	−	0.910236i	$-0.635900\pi$
$313$	−14.6520			−0.828180			−0.414090	+	0.910236i	$0.635900\pi$
$314$		0			0
$315$	0.126961	−	1.37791i	0.00715345	−	0.0776365i
$316$		0			0
$317$	−3.93077	−	3.93077i	−0.220774	−	0.220774i	0.588050	−	0.808824i	$-0.299896\pi$
$317$	−3.93077	−	3.93077i	−0.220774	−	0.220774i	−0.808824	+	0.588050i	$0.799896\pi$
$318$		0			0
$319$	35.3407	−	9.46952i	1.97870	−	0.530191i
$320$		0			0
$321$	5.40704	+	0.248577i	0.301792	+	0.0138742i
$322$		0			0
$323$	17.2900	+	4.63284i	0.962040	+	0.257778i
$324$		0			0
$325$	−16.4697	−	2.78523i	−0.913577	−	0.154497i
$326$		0			0
$327$	2.18687	−	0.479526i	0.120934	−	0.0265178i
$328$		0			0
$329$	−3.08637	+	5.34576i	−0.170157	+	0.294721i
$330$		0			0
$331$	5.11244	+	19.0799i	0.281005	+	1.04873i	0.951709	+	0.307000i	$0.0993253\pi$
$331$	5.11244	+	19.0799i	0.281005	+	1.04873i	−0.670704	+	0.741725i	$0.734008\pi$
$332$		0			0
$333$	17.3797	−	2.98188i	0.952399	−	0.163406i
$334$		0			0
$335$	−0.0317479	−	0.0549890i	−0.00173457	−	0.00300437i
$336$		0			0
$337$		−	16.3889i		−	0.892762i	−0.894843	−	0.446381i	$-0.852713\pi$
$337$		−	16.3889i		−	0.892762i	0.894843	−	0.446381i	$-0.147287\pi$
$338$		0			0
$339$	5.55071	+	10.7231i	0.301473	+	0.582401i
$340$		0			0
$341$	13.8060	−	7.97088i	0.747635	−	0.431647i
$342$		0			0
$343$	−7.22288	+	7.22288i	−0.389999	+	0.389999i
$344$		0			0
$345$	1.44760	−	1.32035i	0.0779360	−	0.0710851i
$346$		0			0
$347$	18.7272	+	10.8122i	1.00533	+	0.580427i	0.909821	−	0.415001i	$-0.136219\pi$
$347$	18.7272	+	10.8122i	1.00533	+	0.580427i	0.0955087	+	0.995429i	$0.469552\pi$
$348$		0			0
$349$	−0.503975	+	1.88086i	−0.0269771	+	0.100680i	−0.978102	−	0.208127i	$-0.933263\pi$
$349$	−0.503975	+	1.88086i	−0.0269771	+	0.100680i	0.951125	+	0.308807i	$0.0999298\pi$
$350$		0			0
$351$	−17.8684	−	5.63221i	−0.953742	−	0.300625i
$352$		0			0
$353$	−6.02369	+	22.4807i	−0.320609	+	1.19653i	0.598045	+	0.801463i	$0.295945\pi$
$353$	−6.02369	+	22.4807i	−0.320609	+	1.19653i	−0.918653	+	0.395065i	$0.870722\pi$
$354$		0			0
$355$	−5.47412	−	3.16049i	−0.290536	−	0.167741i
$356$		0			0
$357$	5.11078	−	4.66152i	0.270491	−	0.246714i
$358$		0			0
$359$	−15.8859	+	15.8859i	−0.838428	+	0.838428i	−0.988652	−	0.150224i	$-0.952000\pi$
$359$	−15.8859	+	15.8859i	−0.838428	+	0.838428i	0.150224	+	0.988652i	$0.452000\pi$
$360$		0			0
$361$	6.37655	−	3.68150i	0.335608	−	0.193763i
$362$		0			0
$363$	−5.30306	−	10.2447i	−0.278339	−	0.537709i
$364$		0			0
$365$		−	4.78062i		−	0.250229i
$366$		0			0
$367$	0.300881	+	0.521141i	0.0157059	+	0.0272034i	0.873772	−	0.486337i	$-0.161667\pi$
$367$	0.300881	+	0.521141i	0.0157059	+	0.0272034i	−0.858066	+	0.513540i	$0.828334\pi$
$368$		0			0
$369$	26.2236	−	4.49926i	1.36515	−	0.234222i
$370$		0			0
$371$	1.77587	+	6.62765i	0.0921988	+	0.344091i
$372$		0			0
$373$	−5.70783	+	9.88625i	−0.295540	+	0.511891i	−0.975110	−	0.221720i	$-0.928833\pi$
$373$	−5.70783	+	9.88625i	−0.295540	+	0.511891i	0.679570	+	0.733611i	$0.262166\pi$
$374$		0			0
$375$	9.87640	−	2.16565i	0.510015	−	0.111834i
$376$		0			0
$377$	−10.9427	−	29.4219i	−0.563580	−	1.51531i
$378$		0			0
$379$	−36.2846	−	9.72242i	−1.86381	−	0.499407i	−0.863823	−	0.503795i	$-0.831937\pi$
$379$	−36.2846	−	9.72242i	−1.86381	−	0.499407i	−0.999990	+	0.00438723i	$0.998603\pi$
$380$		0			0
$381$	−3.86699	−	0.177777i	−0.198112	−	0.00910777i
$382$		0			0
$383$	−12.2026	+	3.26967i	−0.623523	+	0.167073i	−0.556729	−	0.830694i	$-0.687944\pi$
$383$	−12.2026	+	3.26967i	−0.623523	+	0.167073i	−0.0667943	+	0.997767i	$0.521277\pi$
$384$		0			0
$385$	−1.37063	−	1.37063i	−0.0698536	−	0.0698536i
$386$		0			0
$387$	0.536843	−	5.82636i	0.0272892	−	0.296170i
$388$		0			0
$389$	−18.8229			−0.954361			−0.477180	−	0.878805i	$-0.658341\pi$
$389$	−18.8229			−0.954361			−0.477180	+	0.878805i	$0.658341\pi$
$390$		0			0
$391$	9.79455			0.495332
$392$		0			0
$393$	20.6279	−	32.2150i	1.04054	−	1.62503i
$394$		0			0
$395$	−5.81951	−	5.81951i	−0.292812	−	0.292812i
$396$		0			0
$397$	11.5273	−	3.08874i	0.578540	−	0.155019i	0.0423297	−	0.999104i	$-0.486522\pi$
$397$	11.5273	−	3.08874i	0.578540	−	0.155019i	0.536210	+	0.844084i	$0.319855\pi$
$398$		0			0
$399$	−0.206525	+	4.49234i	−0.0103392	+	0.224898i
$400$		0			0
$401$	23.3959	+	6.26891i	1.16833	+	0.313054i	0.790290	−	0.612733i	$-0.209930\pi$
$401$	23.3959	+	6.26891i	1.16833	+	0.313054i	0.378045	+	0.925787i	$0.376597\pi$
$402$		0			0
$403$	−7.92345	−	11.1488i	−0.394695	−	0.555361i
$404$		0			0
$405$	5.43757	−	0.425198i	0.270195	−	0.0211282i
$406$		0			0
$407$	12.3506	−	21.3919i	0.612197	−	1.06036i
$408$		0			0
$409$	6.94441	+	25.9169i	0.343379	+	1.28151i	0.894495	+	0.447078i	$0.147535\pi$
$409$	6.94441	+	25.9169i	0.343379	+	1.28151i	−0.551116	+	0.834429i	$0.685798\pi$
$410$		0			0
$411$	5.23814	−	16.4806i	0.258379	−	0.812927i
$412$		0			0
$413$	−3.28793	−	5.69487i	−0.161789	−	0.280226i
$414$		0			0
$415$			0.854405i			0.0419411i
$416$		0			0
$417$	5.79133	−	2.99781i	0.283603	−	0.146804i
$418$		0			0
$419$	9.38488	−	5.41836i	0.458481	−	0.264704i	−0.252924	−	0.967486i	$-0.581392\pi$
$419$	9.38488	−	5.41836i	0.458481	−	0.264704i	0.711405	+	0.702782i	$0.248059\pi$
$420$		0			0
$421$	−22.8984	+	22.8984i	−1.11600	+	1.11600i	−0.123676	+	0.992323i	$0.539468\pi$
$421$	−22.8984	+	22.8984i	−1.11600	+	1.11600i	−0.992323	+	0.123676i	$0.960532\pi$
$422$		0			0
$423$	−22.8245	−	8.42691i	−1.10977	−	0.409731i
$424$		0			0
$425$	21.0523	+	12.1545i	1.02119	+	0.589581i
$426$		0			0
$427$	1.60166	−	5.97746i	0.0775096	−	0.289270i
$428$		0			0
$429$	−22.0675	+	14.2048i	−1.06543	+	0.685812i
$430$		0			0
$431$	−8.68719	+	32.4210i	−0.418447	+	1.56167i	0.359381	+	0.933191i	$0.382988\pi$
$431$	−8.68719	+	32.4210i	−0.418447	+	1.56167i	−0.777829	+	0.628476i	$0.783679\pi$
$432$		0			0
$433$	−20.5735	−	11.8781i	−0.988698	−	0.570825i	−0.0838130	−	0.996482i	$-0.526710\pi$
$433$	−20.5735	−	11.8781i	−0.988698	−	0.570825i	−0.904885	+	0.425657i	$0.860043\pi$
$434$		0			0
$435$	6.15839	+	6.75191i	0.295272	+	0.323729i
$436$		0			0
$437$	−4.50256	+	4.50256i	−0.215387	+	0.215387i
$438$		0			0
$439$	−12.8746	+	7.43317i	−0.614473	+	0.354766i	−0.774714	−	0.632312i	$-0.782106\pi$
$439$	−12.8746	+	7.43317i	−0.614473	+	0.354766i	0.160241	+	0.987078i	$0.448773\pi$
$440$		0			0
$441$	−15.7275	−	11.1210i	−0.748926	−	0.529571i
$442$		0			0
$443$		−	40.3416i		−	1.91669i	−0.285619	−	0.958343i	$-0.592199\pi$
$443$		−	40.3416i		−	1.91669i	0.285619	−	0.958343i	$-0.407801\pi$
$444$		0			0
$445$	1.98396	+	3.43632i	0.0940487	+	0.162897i
$446$		0			0
$447$	14.4055	+	4.57860i	0.681357	+	0.216560i
$448$		0			0
$449$	−1.18156	−	4.40965i	−0.0557613	−	0.208104i	0.932424	−	0.361365i	$-0.117689\pi$
$449$	−1.18156	−	4.40965i	−0.0557613	−	0.208104i	−0.988186	+	0.153261i	$0.951022\pi$
$450$		0			0
$451$	18.6354	−	32.2775i	0.877508	−	1.51989i
$452$		0			0
$453$	−9.11160	−	41.5532i	−0.428100	−	1.95234i
$454$		0			0
$455$	−1.06004	+	1.28143i	−0.0496955	+	0.0600746i
$456$		0			0
$457$	25.3969	+	6.80507i	1.18801	+	0.318328i	0.798101	−	0.602524i	$-0.205838\pi$
$457$	25.3969	+	6.80507i	1.18801	+	0.318328i	0.389914	+	0.920851i	$0.372505\pi$
$458$		0			0
$459$	21.5157	+	16.7475i	1.00427	+	0.781704i
$460$		0			0
$461$	14.5525	−	3.89933i	0.677778	−	0.181610i	0.0965219	−	0.995331i	$-0.469228\pi$
$461$	14.5525	−	3.89933i	0.677778	−	0.181610i	0.581256	+	0.813721i	$0.302562\pi$
$462$		0			0
$463$	12.8578	+	12.8578i	0.597552	+	0.597552i	0.939661	−	0.342108i	$-0.111141\pi$
$463$	12.8578	+	12.8578i	0.597552	+	0.597552i	−0.342108	+	0.939661i	$0.611141\pi$
$464$		0			0
$465$	3.35331	+	2.14719i	0.155506	+	0.0995734i
$466$		0			0
$467$	12.7104			0.588168			0.294084	−	0.955780i	$-0.404985\pi$
$467$	12.7104			0.588168			0.294084	+	0.955780i	$0.404985\pi$
$468$		0			0
$469$	0.0797460			0.00368233
$470$		0			0
$471$	−16.1492	−	10.3406i	−0.744114	−	0.476470i
$472$		0			0
$473$	−5.79555	−	5.79555i	−0.266480	−	0.266480i
$474$		0			0
$475$	−15.2652	+	4.09030i	−0.700415	+	0.187676i
$476$		0			0
$477$	−24.5636	+	11.3165i	−1.12469	+	0.518147i
$478$		0			0
$479$	34.6068	+	9.27288i	1.58123	+	0.423689i	0.939306	−	0.343082i	$-0.111471\pi$
$479$	34.6068	+	9.27288i	1.58123	+	0.423689i	0.641922	+	0.766770i	$0.278137\pi$
$480$		0			0
$481$	−19.2696	−	8.82174i	−0.878619	−	0.402237i
$482$		0			0
$483$	0.527056	+	2.40363i	0.0239819	+	0.109369i
$484$		0			0
$485$	4.77237	−	8.26598i	0.216702	−	0.375339i
$486$		0			0
$487$	1.74173	+	6.50021i	0.0789252	+	0.294553i	0.994095	−	0.108517i	$-0.0346100\pi$
$487$	1.74173	+	6.50021i	0.0789252	+	0.294553i	−0.915169	+	0.403069i	$0.867943\pi$
$488$		0			0
$489$	−8.67507	−	2.75726i	−0.392300	−	0.124688i
$490$		0			0
$491$	−14.9069	−	25.8195i	−0.672740	−	1.16522i	−0.977124	−	0.212670i	$-0.931784\pi$
$491$	−14.9069	−	25.8195i	−0.672740	−	1.16522i	0.304385	−	0.952549i	$-0.401549\pi$
$492$		0			0
$493$			45.6839i			2.05750i
$494$		0			0
$495$	4.41108	−	6.23821i	0.198263	−	0.280387i
$496$		0			0
$497$	6.87509	−	3.96934i	0.308390	−	0.178049i
$498$		0			0
$499$	−25.5487	+	25.5487i	−1.14372	+	1.14372i	−0.155954	+	0.987764i	$0.549845\pi$
$499$	−25.5487	+	25.5487i	−1.14372	+	1.14372i	−0.987764	+	0.155954i	$0.950155\pi$
$500$		0			0
$501$	18.3586	+	20.1280i	0.820203	+	0.899251i
$502$		0			0
$503$	−36.8913	−	21.2992i	−1.64490	−	0.949684i	−0.979055	−	0.203594i	$-0.934738\pi$
$503$	−36.8913	−	21.2992i	−1.64490	−	0.949684i	−0.665845	−	0.746090i	$-0.731929\pi$
$504$		0			0
$505$	−0.513305	+	1.91568i	−0.0228418	+	0.0852466i
$506$		0			0
$507$	13.9154	+	17.7020i	0.618006	+	0.786174i
$508$		0			0
$509$	−4.37237	+	16.3179i	−0.193802	+	0.723279i	0.798772	+	0.601634i	$0.205483\pi$
$509$	−4.37237	+	16.3179i	−0.193802	+	0.723279i	−0.992574	+	0.121645i	$0.961183\pi$
$510$		0			0
$511$	5.19971	+	3.00205i	0.230021	+	0.132803i
$512$		0			0
$513$	−17.5896	+	2.19197i	−0.776600	+	0.0967777i
$514$		0			0
$515$	−2.05638	+	2.05638i	−0.0906150	+	0.0906150i
$516$		0			0
$517$	−29.5160	+	17.0411i	−1.29811	+	0.749466i
$518$		0			0
$519$	−8.34271	+	4.31851i	−0.366204	+	0.189561i
$520$		0			0
$521$			18.8358i			0.825213i	0.910909	+	0.412607i	$0.135382\pi$
$521$			18.8358i			0.825213i	−0.910909	+	0.412607i	$0.864618\pi$
$522$		0			0
$523$	−5.97667	−	10.3519i	−0.261342	−	0.452657i	0.705257	−	0.708952i	$-0.250832\pi$
$523$	−5.97667	−	10.3519i	−0.261342	−	0.452657i	−0.966599	+	0.256295i	$0.917498\pi$
$524$		0			0
$525$	−1.84993	+	5.82037i	−0.0807376	+	0.254022i
$526$		0			0
$527$	5.15186	+	19.2270i	0.224419	+	0.837542i
$528$		0			0
$529$	9.75788	−	16.9011i	0.424256	−	0.734832i
$530$		0			0
$531$	19.9321	−	16.5688i	0.864977	−	0.719027i
$532$		0			0
$533$	−29.0753	−	13.3108i	−1.25939	−	0.576556i
$534$		0			0
$535$	1.82931	+	0.490162i	0.0790879	+	0.0211915i
$536$		0			0
$537$	−0.825725	+	17.9612i	−0.0356327	+	0.775081i
$538$		0			0
$539$	−26.0630	+	6.98357i	−1.12261	+	0.300804i
$540$		0			0
$541$	13.7056	+	13.7056i	0.589250	+	0.589250i	0.937428	−	0.348179i	$-0.113200\pi$
$541$	13.7056	+	13.7056i	0.589250	+	0.589250i	−0.348179	+	0.937428i	$0.613200\pi$
$542$		0			0
$543$	−10.3834	+	16.2160i	−0.445596	+	0.695897i
$544$		0			0
$545$	0.783330			0.0335542
$546$		0			0
$547$	14.6259			0.625359			0.312679	−	0.949859i	$-0.398773\pi$
$547$	14.6259			0.625359			0.312679	+	0.949859i	$0.398773\pi$
$548$		0			0
$549$	24.2890	+	2.23799i	1.03663	+	0.0955152i
$550$		0			0
$551$	−21.0009	−	21.0009i	−0.894670	−	0.894670i
$552$		0			0
$553$	9.98412	−	2.67524i	0.424568	−	0.113763i
$554$		0			0
$555$	6.16322	+	0.283341i	0.261614	+	0.0120271i
$556$		0			0
$557$	1.16825	+	0.313031i	0.0495002	+	0.0132635i	0.283484	−	0.958977i	$-0.408510\pi$
$557$	1.16825	+	0.313031i	0.0495002	+	0.0132635i	−0.233984	+	0.972240i	$0.575176\pi$
$558$		0			0
$559$	−4.48228	+	5.41841i	−0.189580	+	0.229175i
$560$		0			0
$561$	37.3071	−	8.18053i	1.57511	−	0.345382i
$562$		0			0
$563$	−12.2059	+	21.1412i	−0.514416	+	0.890994i	0.485444	+	0.874267i	$0.338658\pi$
$563$	−12.2059	+	21.1412i	−0.514416	+	0.890994i	−0.999860	+	0.0167265i	$0.994676\pi$
$564$		0			0
$565$	1.09344	+	4.08077i	0.0460013	+	0.171679i
$566$		0			0
$567$	−2.95212	+	6.18125i	−0.123977	+	0.259588i
$568$		0			0
$569$	−2.98833	−	5.17593i	−0.125277	−	0.216986i	0.796564	−	0.604554i	$-0.206649\pi$
$569$	−2.98833	−	5.17593i	−0.125277	−	0.216986i	−0.921841	+	0.387568i	$0.873315\pi$
$570$		0			0
$571$			35.8068i			1.49847i	0.662307	+	0.749233i	$0.269578\pi$
$571$			35.8068i			1.49847i	−0.662307	+	0.749233i	$0.730422\pi$
$572$		0			0
$573$	−4.56431	−	8.81758i	−0.190677	−	0.368360i
$574$		0			0
$575$	−7.48898	+	4.32377i	−0.312312	+	0.180314i
$576$		0			0
$577$	13.8142	−	13.8142i	0.575094	−	0.575094i	−0.358453	−	0.933548i	$-0.616696\pi$
$577$	13.8142	−	13.8142i	0.575094	−	0.575094i	0.933548	+	0.358453i	$0.116696\pi$
$578$		0			0
$579$	14.5174	−	13.2413i	0.603323	−	0.550288i
$580$		0			0
$581$	−0.929305	−	0.536534i	−0.0385541	−	0.0222592i
$582$		0			0
$583$	−9.80530	+	36.5939i	−0.406094	+	1.51556i
$584$		0			0
$585$	−5.68470	−	3.26396i	−0.235033	−	0.134948i
$586$		0			0
$587$	−3.99377	+	14.9050i	−0.164841	+	0.615194i	0.833220	+	0.552942i	$0.186495\pi$
$587$	−3.99377	+	14.9050i	−0.164841	+	0.615194i	−0.998060	+	0.0622518i	$0.980172\pi$
$588$		0			0
$589$	−11.2070	−	6.47036i	−0.461776	−	0.266607i
$590$		0			0
$591$	−5.99306	+	5.46625i	−0.246522	+	0.224851i
$592$		0			0
$593$	19.1066	−	19.1066i	0.784613	−	0.784613i	−0.195992	−	0.980605i	$-0.562793\pi$
$593$	19.1066	−	19.1066i	0.784613	−	0.784613i	0.980605	+	0.195992i	$0.0627927\pi$
$594$		0			0
$595$	2.09602	−	1.21014i	0.0859286	−	0.0496109i
$596$		0			0
$597$	10.2734	+	19.8468i	0.420464	+	0.812275i
$598$		0			0
$599$			15.6579i			0.639764i	0.947457	+	0.319882i	$0.103643\pi$
$599$			15.6579i			0.639764i	−0.947457	+	0.319882i	$0.896357\pi$
$600$		0			0
$601$	6.65857	+	11.5330i	0.271609	+	0.470440i	0.969274	−	0.245984i	$-0.0791110\pi$
$601$	6.65857	+	11.5330i	0.271609	+	0.470440i	−0.697665	+	0.716424i	$0.745778\pi$
$602$		0			0
$603$	0.0531532	+	0.309799i	0.00216456	+	0.0126160i
$604$		0			0
$605$	−1.04465	−	3.89870i	−0.0424713	−	0.158505i
$606$		0			0
$607$	6.14650	−	10.6460i	0.249479	−	0.432110i	−0.713903	−	0.700245i	$-0.753074\pi$
$607$	6.14650	−	10.6460i	0.249479	−	0.432110i	0.963381	+	0.268135i	$0.0864074\pi$
$608$		0			0
$609$	−11.2110	+	2.45831i	−0.454295	+	0.0996156i
$610$		0			0
$611$	16.9397	+	23.8352i	0.685306	+	0.964268i
$612$		0			0
$613$	−10.3869	−	2.78315i	−0.419521	−	0.112410i	0.0428820	−	0.999080i	$-0.486346\pi$
$613$	−10.3869	−	2.78315i	−0.419521	−	0.112410i	−0.462403	+	0.886670i	$0.653013\pi$
$614$		0			0
$615$	9.29948	+	0.427523i	0.374991	+	0.0172394i
$616$		0			0
$617$	−12.1675	+	3.26027i	−0.489845	+	0.131254i	−0.495283	−	0.868732i	$-0.664936\pi$
$617$	−12.1675	+	3.26027i	−0.489845	+	0.131254i	0.00543815	+	0.999985i	$0.498269\pi$
$618$		0			0
$619$	5.08096	+	5.08096i	0.204221	+	0.204221i	0.801806	−	0.597585i	$-0.203873\pi$
$619$	5.08096	+	5.08096i	0.204221	+	0.204221i	−0.597585	+	0.801806i	$0.703873\pi$
$620$		0			0
$621$	−8.98637	+	3.64961i	−0.360611	+	0.146454i
$622$		0			0
$623$	−4.98342			−0.199656
$624$		0			0
$625$	−19.6260			−0.785040
$626$		0			0
$627$	−13.3895	+	20.9107i	−0.534726	+	0.835093i
$628$		0			0
$629$	21.8090	+	21.8090i	0.869580	+	0.869580i
$630$		0			0
$631$	23.9643	−	6.42121i	0.954002	−	0.255624i	0.251943	−	0.967742i	$-0.418931\pi$
$631$	23.9643	−	6.42121i	0.954002	−	0.255624i	0.702060	+	0.712118i	$0.252264\pi$
$632$		0			0
$633$	−0.419955	+	9.13485i	−0.0166917	+	0.363078i
$634$		0			0
$635$	−1.30828	−	0.350553i	−0.0519175	−	0.0139113i
$636$		0			0
$637$	8.07004	+	21.6980i	0.319747	+	0.859708i
$638$		0			0
$639$	20.0026	+	24.0628i	0.791292	+	0.951912i
$640$		0			0
$641$	−5.92602	+	10.2642i	−0.234064	+	0.405410i	−0.959000	−	0.283406i	$-0.908536\pi$
$641$	−5.92602	+	10.2642i	−0.234064	+	0.405410i	0.724936	+	0.688816i	$0.241869\pi$
$642$		0			0
$643$	7.18682	+	26.8216i	0.283420	+	1.05774i	0.949986	+	0.312293i	$0.101097\pi$
$643$	7.18682	+	26.8216i	0.283420	+	1.05774i	−0.666566	+	0.745446i	$0.732236\pi$
$644$		0			0
$645$	0.620105	−	1.95101i	0.0244166	−	0.0768211i
$646$		0			0
$647$	9.84613	+	17.0540i	0.387091	+	0.670462i	0.992057	−	0.125790i	$-0.0401465\pi$
$647$	9.84613	+	17.0540i	0.387091	+	0.670462i	−0.604966	+	0.796251i	$0.706813\pi$
$648$		0			0
$649$		−	36.3079i		−	1.42521i
$650$		0			0
$651$	−4.44117	+	2.29892i	−0.174063	+	0.0901017i
$652$		0			0
$653$	−42.1003	+	24.3066i	−1.64751	+	0.951191i	−0.669455	+	0.742853i	$0.733472\pi$
$653$	−42.1003	+	24.3066i	−1.64751	+	0.951191i	−0.978057	+	0.208339i	$0.933194\pi$
$654$		0			0
$655$	9.46410	−	9.46410i	0.369793	−	0.369793i
$656$		0			0
$657$	−8.19668	+	22.2009i	−0.319783	+	0.866140i
$658$		0			0
$659$	3.21116	+	1.85397i	0.125089	+	0.0722202i	0.561239	−	0.827654i	$-0.310325\pi$
$659$	3.21116	+	1.85397i	0.125089	+	0.0722202i	−0.436150	+	0.899874i	$0.643658\pi$
$660$		0			0
$661$	1.66416	−	6.21075i	0.0647285	−	0.241570i	−0.925980	−	0.377573i	$-0.876759\pi$
$661$	1.66416	−	6.21075i	0.0647285	−	0.241570i	0.990708	+	0.136003i	$0.0434255\pi$
$662$		0			0
$663$	−10.0006	−	31.2057i	−0.388389	−	1.21193i
$664$		0			0
$665$	−0.407242	+	1.51985i	−0.0157922	+	0.0589371i
$666$		0			0
$667$	−14.0740	−	8.12564i	−0.544948	−	0.314626i
$668$		0			0
$669$	−4.14385	−	4.54322i	−0.160210	−	0.175651i
$670$		0			0
$671$	24.1605	−	24.1605i	0.932708	−	0.932708i
$672$		0			0
$673$	5.14268	−	2.96913i	0.198236	−	0.114451i	−0.397597	−	0.917560i	$-0.630156\pi$
$673$	5.14268	−	2.96913i	0.198236	−	0.114451i	0.595832	+	0.803109i	$0.296822\pi$
$674$		0			0
$675$	−23.8442	−	3.30720i	−0.917763	−	0.127294i
$676$		0			0
$677$			24.5297i			0.942753i	0.881932	+	0.471376i	$0.156243\pi$
$677$			24.5297i			0.942753i	−0.881932	+	0.471376i	$0.843757\pi$
$678$		0			0
$679$	5.99374	+	10.3815i	0.230019	+	0.398404i
$680$		0			0
$681$	8.29751	+	2.63726i	0.317961	+	0.101060i
$682$		0			0
$683$	6.94368	+	25.9142i	0.265693	+	0.991578i	0.961825	+	0.273665i	$0.0882359\pi$
$683$	6.94368	+	25.9142i	0.265693	+	0.991578i	−0.696133	+	0.717913i	$0.745097\pi$
$684$		0			0
$685$	3.02528	−	5.23994i	0.115590	−	0.200208i
$686$		0			0
$687$	−5.97518	−	27.2497i	−0.227967	−	1.03964i
$688$		0			0
$689$	32.0490	+	5.41987i	1.22097	+	0.206481i
$690$		0			0
$691$	10.1788	+	2.72740i	0.387220	+	0.103755i	0.447176	−	0.894446i	$-0.352430\pi$
$691$	10.1788	+	2.72740i	0.387220	+	0.103755i	−0.0599568	+	0.998201i	$0.519096\pi$
$692$		0			0
$693$	4.01508	+	8.71514i	0.152520	+	0.331061i
$694$		0			0
$695$	2.20393	−	0.590542i	0.0835999	−	0.0224005i
$696$		0			0
$697$	32.9068	+	32.9068i	1.24644	+	1.24644i
$698$		0			0
$699$	−32.6455	−	20.9035i	−1.23477	−	0.790643i
$700$		0			0
$701$	−48.3500			−1.82616			−0.913078	−	0.407785i	$-0.866301\pi$
$701$	−48.3500			−1.82616			−0.913078	+	0.407785i	$0.866301\pi$
$702$		0			0
$703$	−20.0512			−0.756245
$704$		0			0
$705$	−7.16910	−	4.59051i	−0.270004	−	0.172888i
$706$		0			0
$707$	−1.76128	−	1.76128i	−0.0662397	−	0.0662397i
$708$		0			0
$709$	28.4274	−	7.61709i	1.06761	−	0.286066i	0.318100	−	0.948057i	$-0.396955\pi$
$709$	28.4274	−	7.61709i	1.06761	−	0.286066i	0.749512	+	0.661991i	$0.230288\pi$
$710$		0			0
$711$	17.0475	+	37.0034i	0.639333	+	1.38774i
$712$		0			0
$713$	−6.83968	−	1.83269i	−0.256148	−	0.0686347i
$714$		0			0
$715$	−8.60641	+	3.20094i	−0.321862	+	0.119708i
$716$		0			0
$717$	−3.19110	−	14.5529i	−0.119174	−	0.543489i
$718$		0			0
$719$	21.4236	−	37.1068i	0.798966	−	1.38385i	−0.121324	−	0.992613i	$-0.538714\pi$
$719$	21.4236	−	37.1068i	0.798966	−	1.38385i	0.920290	−	0.391237i	$-0.127953\pi$
$720$		0			0
$721$	−0.945320	−	3.52798i	−0.0352056	−	0.131389i
$722$		0			0
$723$	−10.1443	−	3.22425i	−0.377272	−	0.119911i
$724$		0			0
$725$	−20.1670	−	34.9303i	−0.748984	−	1.29728i
$726$		0			0
$727$		−	1.92620i		−	0.0714389i	−0.999362	−	0.0357194i	$-0.988628\pi$
$727$		−	1.92620i		−	0.0714389i	0.999362	−	0.0357194i	$-0.0113723\pi$
$728$		0			0
$729$	−25.9808	−	7.34847i	−0.962250	−	0.272166i
$730$		0			0
$731$	8.86283	−	5.11696i	0.327804	−	0.189257i
$732$		0			0
$733$	−22.6065	+	22.6065i	−0.834990	+	0.834990i	−0.988195	−	0.153204i	$-0.951041\pi$
$733$	−22.6065	+	22.6065i	−0.834990	+	0.834990i	0.153204	+	0.988195i	$0.451041\pi$
$734$		0			0
$735$	−4.54168	−	4.97939i	−0.167522	−	0.183668i
$736$		0			0
$737$	0.381319	+	0.220155i	0.0140461	+	0.00810950i
$738$		0			0
$739$	0.376096	−	1.40361i	0.0138349	−	0.0516325i	−0.958663	−	0.284543i	$-0.908158\pi$
$739$	0.376096	−	1.40361i	0.0138349	−	0.0516325i	0.972498	+	0.232910i	$0.0748249\pi$
$740$		0			0
$741$	18.9425	+	9.74800i	0.695871	+	0.358102i
$742$		0			0
$743$	9.58365	−	35.7667i	0.351590	−	1.31215i	−0.533132	−	0.846032i	$-0.678985\pi$
$743$	9.58365	−	35.7667i	0.351590	−	1.31215i	0.884722	−	0.466119i	$-0.154348\pi$
$744$		0			0
$745$	4.58017	+	2.64436i	0.167804	+	0.0968820i
$746$		0			0
$747$	1.46493	−	3.96780i	0.0535991	−	0.145174i
$748$		0			0
$749$	−1.68187	+	1.68187i	−0.0614542	+	0.0614542i
$750$		0			0
$751$	13.2882	−	7.67193i	0.484892	−	0.279953i	−0.237561	−	0.971373i	$-0.576348\pi$
$751$	13.2882	−	7.67193i	0.484892	−	0.279953i	0.722453	+	0.691420i	$0.243015\pi$
$752$		0			0
$753$	19.3138	−	9.99753i	0.703832	−	0.364330i
$754$		0			0
$755$		−	14.8843i		−	0.541694i
$756$		0			0
$757$	−11.2354	−	19.4603i	−0.408357	−	0.707296i	0.586349	−	0.810059i	$-0.300565\pi$
$757$	−11.2354	−	19.4603i	−0.408357	−	0.707296i	−0.994706	+	0.102763i	$0.967232\pi$
$758$		0			0
$759$	−4.11548	+	12.9484i	−0.149382	+	0.469997i
$760$		0			0
$761$	0.210189	+	0.784436i	0.00761934	+	0.0284358i	0.969631	−	0.244573i	$-0.0786478\pi$
$761$	0.210189	+	0.784436i	0.00761934	+	0.0284358i	−0.962012	+	0.273009i	$0.911981\pi$
$762$		0			0
$763$	−0.491903	+	0.852000i	−0.0178081	+	0.0308445i
$764$		0			0
$765$	6.09825	+	7.33609i	0.220483	+	0.265237i
$766$		0			0
$767$	−31.0129	+	2.93235i	−1.11981	+	0.105881i
$768$		0			0
$769$	−12.0810	−	3.23708i	−0.435651	−	0.116732i	0.0343269	−	0.999411i	$-0.489071\pi$
$769$	−12.0810	−	3.23708i	−0.435651	−	0.116732i	−0.469977	+	0.882678i	$0.655738\pi$
$770$		0			0
$771$	−0.376861	+	8.19748i	−0.0135723	+	0.295225i
$772$		0			0
$773$	14.6654	−	3.92957i	0.527476	−	0.141337i	0.0147536	−	0.999891i	$-0.495304\pi$
$773$	14.6654	−	3.92957i	0.527476	−	0.141337i	0.512723	+	0.858554i	$0.328637\pi$
$774$		0			0
$775$	−12.4268	−	12.4268i	−0.446386	−	0.446386i
$776$		0			0
$777$	−4.17845	+	6.52558i	−0.149901	+	0.234104i
$778$		0			0
$779$	−30.2546			−1.08398
$780$		0			0
$781$	43.8325			1.56845
$782$		0			0
$783$	−17.0226	−	41.9144i	−0.608338	−	1.49790i
$784$		0			0
$785$	−4.74428	−	4.74428i	−0.169331	−	0.169331i
$786$		0			0
$787$	26.9442	−	7.21968i	0.960458	−	0.257354i	0.255664	−	0.966766i	$-0.417706\pi$
$787$	26.9442	−	7.21968i	0.960458	−	0.257354i	0.704794	+	0.709412i	$0.251039\pi$
$788$		0			0
$789$	−9.80854	−	0.450926i	−0.349193	−	0.0160534i
$790$		0			0
$791$	−5.12514	−	1.37328i	−0.182229	−	0.0488281i
$792$		0			0
$793$	−22.5883	−	18.6857i	−0.802135	−	0.663550i
$794$		0			0
$795$	−9.24304	+	2.02677i	−0.327817	+	0.0718822i
$796$		0			0
$797$	21.9041	−	37.9390i	0.775883	−	1.34387i	−0.158414	−	0.987373i	$-0.550638\pi$
$797$	21.9041	−	37.9390i	0.775883	−	1.34387i	0.934297	−	0.356496i	$-0.116029\pi$
$798$		0			0
$799$	−11.0143	−	41.1058i	−0.389656	−	1.45422i
$800$		0			0
$801$	−3.32160	−	19.3597i	−0.117363	−	0.684041i
$802$		0			0
$803$	16.5755	+	28.7096i	0.584937	+	1.01314i
$804$		0			0
$805$			0.860973i			0.0303453i
$806$		0			0
$807$	5.81715	+	11.2379i	0.204773	+	0.395592i
$808$		0			0
$809$	−0.336378	+	0.194208i	−0.0118264	+	0.00682798i	−0.505902	−	0.862591i	$-0.668840\pi$
$809$	−0.336378	+	0.194208i	−0.0118264	+	0.00682798i	0.494075	+	0.869419i	$0.335507\pi$
$810$		0			0
$811$	5.70744	−	5.70744i	0.200415	−	0.200415i	−0.599763	−	0.800178i	$-0.704738\pi$
$811$	5.70744	−	5.70744i	0.200415	−	0.200415i	0.800178	+	0.599763i	$0.204738\pi$
$812$		0			0
$813$	−31.3883	+	28.6292i	−1.10084	+	1.00407i
$814$		0			0
$815$	−2.75821	−	1.59245i	−0.0966157	−	0.0557811i
$816$		0			0
$817$	−1.72198	+	6.42652i	−0.0602445	+	0.224835i
$818$		0			0
$819$	7.11987	−	4.13339i	0.248788	−	0.144432i
$820$		0			0
$821$	8.85384	−	33.0430i	0.309001	−	1.15321i	−0.620445	−	0.784250i	$-0.713048\pi$
$821$	8.85384	−	33.0430i	0.309001	−	1.15321i	0.929446	−	0.368958i	$-0.120285\pi$
$822$		0			0
$823$	−32.3186	−	18.6592i	−1.12656	−	0.650418i	−0.183490	−	0.983022i	$-0.558740\pi$
$823$	−32.3186	−	18.6592i	−1.12656	−	0.650418i	−0.943067	+	0.332604i	$0.892073\pi$
$824$		0			0
$825$	−24.9140	+	22.7240i	−0.867396	+	0.791148i
$826$		0			0
$827$	8.16295	−	8.16295i	0.283854	−	0.283854i	−0.550790	−	0.834644i	$-0.685674\pi$
$827$	8.16295	−	8.16295i	0.283854	−	0.283854i	0.834644	+	0.550790i	$0.185674\pi$
$828$		0			0
$829$	28.1823	−	16.2711i	0.978813	−	0.565118i	0.0769017	−	0.997039i	$-0.475497\pi$
$829$	28.1823	−	16.2711i	0.978813	−	0.565118i	0.901912	+	0.431921i	$0.142164\pi$
$830$		0			0
$831$	6.96399	+	13.4534i	0.241578	+	0.466693i
$832$		0			0
$833$		−	33.6909i		−	1.16732i
$834$		0			0
$835$	4.76593	+	8.25484i	0.164932	+	0.285671i
$836$		0			0
$837$	−11.8911	−	15.7209i	−0.411016	−	0.543393i
$838$		0			0
$839$	3.48230	+	12.9961i	0.120222	+	0.448676i	0.999624	−	0.0274036i	$-0.00872393\pi$
$839$	3.48230	+	12.9961i	0.120222	+	0.448676i	−0.879402	+	0.476080i	$0.842057\pi$
$840$		0			0
$841$	23.3998	−	40.5296i	0.806889	−	1.39757i
$842$		0			0
$843$	22.7199	−	4.98190i	0.782513	−	0.171586i
$844$		0			0
$845$	3.42921	+	7.09276i	0.117968	+	0.243998i
$846$		0			0
$847$	4.89648	+	1.31201i	0.168245	+	0.0450812i
$848$		0			0
$849$	54.3915	+	2.50053i	1.86671	+	0.0858180i
$850$		0			0
$851$	−10.5978	+	2.83968i	−0.363290	+	0.0973431i
$852$		0			0
$853$	−8.09779	−	8.09779i	−0.277263	−	0.277263i	0.554752	−	0.832015i	$-0.312813\pi$
$853$	−8.09779	−	8.09779i	−0.277263	−	0.277263i	−0.832015	+	0.554752i	$0.812813\pi$
$854$		0			0
$855$	−6.17578	−	0.569038i	−0.211207	−	0.0194607i
$856$		0			0
$857$	−2.81672			−0.0962173			−0.0481086	−	0.998842i	$-0.515319\pi$
$857$	−2.81672			−0.0962173			−0.0481086	+	0.998842i	$0.515319\pi$
$858$		0			0
$859$	−18.5174			−0.631807			−0.315903	−	0.948791i	$-0.602308\pi$
$859$	−18.5174			−0.631807			−0.315903	+	0.948791i	$0.602308\pi$
$860$		0			0
$861$	−6.30473	+	9.84624i	−0.214865	+	0.335559i
$862$		0			0
$863$	16.9992	+	16.9992i	0.578658	+	0.578658i	0.934534	−	0.355875i	$-0.115817\pi$
$863$	16.9992	+	16.9992i	0.578658	+	0.578658i	−0.355875	+	0.934534i	$0.615817\pi$
$864$		0			0
$865$	−3.17488	+	0.850706i	−0.107949	+	0.0289249i
$866$		0			0
$867$	−0.837863	+	18.2252i	−0.0284553	+	0.618960i
$868$		0			0
$869$	55.1262	+	14.7710i	1.87003	+	0.501073i
$870$		0			0
$871$	0.157251	−	0.343489i	0.00532825	−	0.0116387i
$872$		0			0
$873$	−36.3352	+	30.2042i	−1.22976	+	1.02226i
$874$		0			0
$875$	−2.22155	+	3.84783i	−0.0751020	+	0.130080i
$876$		0			0
$877$	−7.98650	−	29.8060i	−0.269685	−	1.00648i	−0.959320	−	0.282321i	$-0.908896\pi$
$877$	−7.98650	−	29.8060i	−0.269685	−	1.00648i	0.689635	−	0.724157i	$-0.257771\pi$
$878$		0			0
$879$	1.09905	−	3.45791i	0.0370702	−	0.116633i
$880$		0			0
$881$	23.1312	+	40.0644i	0.779310	+	1.34980i	0.932340	+	0.361583i	$0.117764\pi$
$881$	23.1312	+	40.0644i	0.779310	+	1.34980i	−0.153030	+	0.988222i	$0.548903\pi$
$882$		0			0
$883$		−	31.0867i		−	1.04615i	−0.852286	−	0.523076i	$-0.824784\pi$
$883$		−	31.0867i		−	1.04615i	0.852286	−	0.523076i	$-0.175216\pi$
$884$		0			0
$885$	8.05376	−	4.16893i	0.270724	−	0.140137i
$886$		0			0
$887$	31.3930	−	18.1248i	1.05407	−	0.608570i	0.130287	−	0.991476i	$-0.458410\pi$
$887$	31.3930	−	18.1248i	1.05407	−	0.608570i	0.923787	+	0.382907i	$0.125077\pi$
$888$		0			0
$889$	1.20283	−	1.20283i	0.0403418	−	0.0403418i
$890$		0			0
$891$	−31.1806	+	21.4068i	−1.04459	+	0.717154i
$892$		0			0
$893$	23.9596	+	13.8331i	0.801778	+	0.462907i
$894$		0			0
$895$	−1.62822	+	6.07662i	−0.0544255	+	0.203119i
$896$		0			0
$897$	11.3924	+	2.46953i	0.380381	+	0.0824552i
$898$		0			0
$899$	8.54806	−	31.9018i	0.285094	−	1.06398i
$900$		0			0
$901$	−40.9663	−	23.6519i	−1.36479	−	0.787960i
$902$		0			0
$903$	1.73264	+	1.89963i	0.0576588	+	0.0632157i
$904$		0			0
$905$	−4.76394	+	4.76394i	−0.158359	+	0.158359i
$906$		0			0
$907$	47.4882	−	27.4174i	1.57682	−	0.910378i	0.581522	−	0.813531i	$-0.302457\pi$
$907$	47.4882	−	27.4174i	1.57682	−	0.910378i	0.995299	−	0.0968476i	$-0.0308759\pi$
$908$		0			0
$909$	5.66832	−	8.01621i	0.188006	−	0.265881i
$910$		0			0
$911$			12.4963i			0.414022i	0.978339	+	0.207011i	$0.0663737\pi$
$911$			12.4963i			0.414022i	−0.978339	+	0.207011i	$0.933626\pi$
$912$		0			0
$913$	−2.96242	−	5.13106i	−0.0980417	−	0.169813i
$914$		0			0
$915$	8.13340	+	2.58510i	0.268882	+	0.0854607i
$916$		0			0
$917$	4.35066	+	16.2369i	0.143671	+	0.536189i
$918$		0			0
$919$	15.2143	−	26.3520i	0.501874	−	0.869272i	−0.498123	−	0.867106i	$-0.665977\pi$
$919$	15.2143	−	26.3520i	0.501874	−	0.869272i	0.999998	−	0.00216566i	$-0.000689352\pi$
$920$		0			0
$921$	1.00386	+	4.57808i	0.0330783	+	0.150853i
$922$		0			0
$923$	−3.54007	−	37.4401i	−0.116523	−	1.23236i
$924$		0			0
$925$	−26.3028	−	7.04781i	−0.864830	−	0.231730i
$926$		0			0
$927$	13.0755	−	6.02391i	0.429456	−	0.197851i
$928$		0			0
$929$	11.3485	−	3.04082i	0.372332	−	0.0997662i	−0.0678003	−	0.997699i	$-0.521598\pi$
$929$	11.3485	−	3.04082i	0.372332	−	0.0997662i	0.440133	+	0.897933i	$0.354931\pi$
$930$		0			0
$931$	15.4877	+	15.4877i	0.507590	+	0.507590i
$932$		0			0
$933$	−10.4928	−	6.71876i	−0.343520	−	0.219962i
$934$		0			0
$935$	13.3633			0.437027
$936$		0			0
$937$	4.30645			0.140686			0.0703429	−	0.997523i	$-0.477591\pi$
$937$	4.30645			0.140686			0.0703429	+	0.997523i	$0.477591\pi$
$938$		0			0
$939$	21.3721	+	13.6849i	0.697451	+	0.446591i
$940$		0			0
$941$	−35.4161	−	35.4161i	−1.15453	−	1.15453i	−0.985634	−	0.168897i	$-0.945980\pi$
$941$	−35.4161	−	35.4161i	−1.15453	−	1.15453i	−0.168897	−	0.985634i	$-0.554020\pi$
$942$		0			0
$943$	−15.9907	+	4.28471i	−0.520730	+	0.139529i
$944$		0			0
$945$	−1.47216	+	1.89130i	−0.0478893	+	0.0615241i
$946$		0			0
$947$	−54.5457	−	14.6155i	−1.77250	−	0.474939i	−0.783314	−	0.621626i	$-0.786472\pi$
$947$	−54.5457	−	14.6155i	−1.77250	−	0.474939i	−0.989183	+	0.146687i	$0.953139\pi$
$948$		0			0
$949$	23.1840	−	16.4769i	0.752584	−	0.534862i
$950$		0			0
$951$	2.06227	+	9.40492i	0.0668736	+	0.304976i
$952$		0			0
$953$	−3.27175	+	5.66683i	−0.105982	+	0.183567i	−0.914139	−	0.405401i	$-0.867132\pi$
$953$	−3.27175	+	5.66683i	−0.105982	+	0.183567i	0.808157	+	0.588967i	$0.200465\pi$
$954$		0			0
$955$	−0.899128	−	3.35559i	−0.0290951	−	0.108584i
$956$		0			0
$957$	−60.3941	−	19.1955i	−1.95226	−	0.620502i
$958$		0			0
$959$	3.79953	+	6.58097i	0.122693	+	0.212511i
$960$		0			0
$961$			16.6095i			0.535790i
$962$		0			0
$963$	−7.65478	−	5.41275i	−0.246672	−	0.174423i
$964$		0			0
$965$	5.95385	−	3.43746i	0.191661	−	0.110656i
$966$		0			0
$967$	10.8941	−	10.8941i	0.350332	−	0.350332i	−0.509901	−	0.860233i	$-0.670318\pi$
$967$	10.8941	−	10.8941i	0.350332	−	0.350332i	0.860233	+	0.509901i	$0.170318\pi$
$968$		0			0
$969$	−20.8929	−	22.9065i	−0.671176	−	0.735862i
$970$		0			0
$971$	2.07268	+	1.19666i	0.0665153	+	0.0384027i	0.532889	−	0.846185i	$-0.321106\pi$
$971$	2.07268	+	1.19666i	0.0665153	+	0.0384027i	−0.466373	+	0.884588i	$0.654440\pi$
$972$		0			0
$973$	−0.741677	+	2.76798i	−0.0237771	+	0.0887372i
$974$		0			0
$975$	21.4221	+	19.4454i	0.686057	+	0.622750i
$976$		0			0
$977$	−8.71475	+	32.5239i	−0.278810	+	1.04053i	0.674436	+	0.738334i	$0.264387\pi$
$977$	−8.71475	+	32.5239i	−0.278810	+	1.04053i	−0.953245	+	0.302198i	$0.902280\pi$
$978$		0			0
$979$	−23.8290	−	13.7577i	−0.761579	−	0.439698i
$980$		0			0
$981$	−3.63774	−	1.34307i	−0.116144	−	0.0428810i
$982$		0			0
$983$	−26.5732	+	26.5732i	−0.847553	+	0.847553i	−0.989827	−	0.142274i	$-0.954558\pi$
$983$	−26.5732	+	26.5732i	−0.847553	+	0.847553i	0.142274	+	0.989827i	$0.454558\pi$
$984$		0			0
$985$	−2.45786	+	1.41905i	−0.0783140	+	0.0452146i
$986$		0			0
$987$	9.49485	−	4.91490i	0.302225	−	0.156443i
$988$		0			0
$989$			3.64054i			0.115762i
$990$		0			0
$991$	10.8598	+	18.8098i	0.344974	+	0.597512i	0.985349	−	0.170550i	$-0.0545545\pi$
$991$	10.8598	+	18.8098i	0.344974	+	0.597512i	−0.640375	+	0.768062i	$0.721221\pi$
$992$		0			0
$993$	10.3633	−	32.6058i	0.328871	−	1.03471i
$994$		0			0
$995$	2.02378	+	7.55283i	0.0641580	+	0.239441i
$996$		0			0
$997$	5.77610	−	10.0045i	0.182931	−	0.316846i	−0.759946	−	0.649986i	$-0.774775\pi$
$997$	5.77610	−	10.0045i	0.182931	−	0.316846i	0.942877	+	0.333140i	$0.108108\pi$
$998$		0			0
$999$	−28.1358	−	11.8831i	−0.890178	−	0.375963i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	624.2.cn.d.353.1		16
3.2	odd	2	inner	624.2.cn.d.353.2		16
4.3	odd	2		78.2.k.a.41.4	yes	16
12.11	even	2		78.2.k.a.41.2	✓	16
13.7	odd	12	inner	624.2.cn.d.449.2		16
39.20	even	12	inner	624.2.cn.d.449.1		16
52.3	odd	6		1014.2.g.c.239.5		16
52.7	even	12		78.2.k.a.59.2	yes	16
52.11	even	12		1014.2.g.c.437.1		16
52.15	even	12		1014.2.g.d.437.5		16
52.23	odd	6		1014.2.g.d.239.1		16
156.11	odd	12		1014.2.g.c.437.5		16
156.23	even	6		1014.2.g.d.239.5		16
156.59	odd	12		78.2.k.a.59.4	yes	16
156.107	even	6		1014.2.g.c.239.1		16
156.119	odd	12		1014.2.g.d.437.1		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
78.2.k.a.41.2	✓	16	12.11	even	2
78.2.k.a.41.4	yes	16	4.3	odd	2
78.2.k.a.59.2	yes	16	52.7	even	12
78.2.k.a.59.4	yes	16	156.59	odd	12
624.2.cn.d.353.1		16	1.1	even	1	trivial
624.2.cn.d.353.2		16	3.2	odd	2	inner
624.2.cn.d.449.1		16	39.20	even	12	inner
624.2.cn.d.449.2		16	13.7	odd	12	inner
1014.2.g.c.239.1		16	156.107	even	6
1014.2.g.c.239.5		16	52.3	odd	6
1014.2.g.c.437.1		16	52.11	even	12
1014.2.g.c.437.5		16	156.11	odd	12
1014.2.g.d.239.1		16	52.23	odd	6
1014.2.g.d.239.5		16	156.23	even	6
1014.2.g.d.437.1		16	156.119	odd	12
1014.2.g.d.437.5		16	52.15	even	12

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:	\( N \)	\(=\)	\( 624 = 2^{4} \cdot 3 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	624.cn (of order \(12\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.45865 - 0.933998i) q^{3} +(-0.428520 - 0.428520i) q^{5} +(0.735180 - 0.196991i) q^{7} +(1.25529 + 2.72474i) q^{9} +O(q^{10})\)	\(q+(-1.45865 - 0.933998i) q^{3} +(-0.428520 - 0.428520i) q^{5} +(0.735180 - 0.196991i) q^{7} +(1.25529 + 2.72474i) q^{9} +(4.05922 + 1.08766i) q^{11} +(0.601205 - 3.55507i) q^{13} +(0.224822 + 1.02529i) q^{15} +(-2.62362 + 4.54424i) q^{17} +(-0.882911 - 3.29507i) q^{19} +(-1.25636 - 0.399317i) q^{21} +(-0.933306 - 1.61653i) q^{23} -4.63274i q^{25} +(0.713876 - 5.14688i) q^{27} +(7.53987 - 4.35315i) q^{29} +(2.68240 - 2.68240i) q^{31} +(-4.90508 - 5.37782i) q^{33} +(-0.399453 - 0.230625i) q^{35} +(1.52130 - 5.67758i) q^{37} +(-4.19738 + 4.62407i) q^{39} +(2.29545 - 8.56672i) q^{41} +(-1.68905 - 0.975173i) q^{43} +(0.629688 - 1.70553i) q^{45} +(-5.73474 + 5.73474i) q^{47} +(-5.56049 + 3.21035i) q^{49} +(8.07123 - 4.17798i) q^{51} +9.01501i q^{53} +(-1.27337 - 2.20554i) q^{55} +(-1.78973 + 5.63097i) q^{57} +(-2.23614 - 8.34539i) q^{59} +(4.06531 - 7.04132i) q^{61} +(1.45962 + 1.75590i) q^{63} +(-1.78105 + 1.26579i) q^{65} +(0.101205 + 0.0271179i) q^{67} +(-0.148476 + 3.22966i) q^{69} +(10.0749 - 2.69957i) q^{71} +(5.57806 + 5.57806i) q^{73} +(-4.32697 + 6.75753i) q^{75} +3.19851 q^{77} +13.5805 q^{79} +(-5.84847 + 6.84072i) q^{81} +(-0.996926 - 0.996926i) q^{83} +(3.07156 - 0.823023i) q^{85} +(-15.0638 - 0.692527i) q^{87} +(-6.32442 - 1.69462i) q^{89} +(-0.258323 - 2.73205i) q^{91} +(-6.41802 + 1.40731i) q^{93} +(-1.03366 + 1.79035i) q^{95} +(4.07638 + 15.2132i) q^{97} +(2.13191 + 12.4257i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 8 q^{7}+O(q^{10}) \) 16 * q - 8 * q^7	\( 16 q - 8 q^{7} - 24 q^{13} + 16 q^{19} - 24 q^{21} - 16 q^{31} - 24 q^{33} + 16 q^{37} - 48 q^{39} + 24 q^{45} + 24 q^{49} + 24 q^{55} - 24 q^{57} - 24 q^{61} + 24 q^{63} - 32 q^{67} - 48 q^{69} + 56 q^{73} + 96 q^{79} + 24 q^{81} - 24 q^{85} - 48 q^{87} + 16 q^{91} - 24 q^{93} + 16 q^{97}+O(q^{100}) \) 16 * q - 8 * q^7 - 24 * q^13 + 16 * q^19 - 24 * q^21 - 16 * q^31 - 24 * q^33 + 16 * q^37 - 48 * q^39 + 24 * q^45 + 24 * q^49 + 24 * q^55 - 24 * q^57 - 24 * q^61 + 24 * q^63 - 32 * q^67 - 48 * q^69 + 56 * q^73 + 96 * q^79 + 24 * q^81 - 24 * q^85 - 48 * q^87 + 16 * q^91 - 24 * q^93 + 16 * q^97

Introduction

L-functions

Modular forms

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