LMFDB - Embedded newform 460.2.s.a.449.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [460,2,Mod(9,460)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(460, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([0, 11, 10]))

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

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

chi := DirichletCharacter("460.9");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 460 = 2^{2} \cdot 5 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	460.s (of order $22$, degree $10$, 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:	$3.67311849298$
Analytic rank:	$0$
Dimension:	$120$
Relative dimension:	$12$ over $\Q(\zeta_{22})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{22}]$

Embedding invariants

Embedding label			449.11
Character	$\chi$	$=$	460.449
Dual form			460.2.s.a.209.11

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(2.38576 + 0.343021i) q^{3} +(1.24170 - 1.85962i) q^{5} +(0.826691 - 0.716332i) q^{7} +(2.69572 + 0.791536i) q^{9} +O(q^{10})$	\(q+(2.38576 + 0.343021i) q^{3} +(1.24170 - 1.85962i) q^{5} +(0.826691 - 0.716332i) q^{7} +(2.69572 + 0.791536i) q^{9} +(-1.07086 - 0.688200i) q^{11} +(-0.352835 - 0.305734i) q^{13} +(3.60028 - 4.01069i) q^{15} +(0.504385 - 0.230345i) q^{17} +(-2.60049 + 5.69429i) q^{19} +(2.21801 - 1.42543i) q^{21} +(-1.37139 - 4.59557i) q^{23} +(-1.91638 - 4.61817i) q^{25} +(-0.417601 - 0.190712i) q^{27} +(3.77717 + 8.27084i) q^{29} +(0.476938 + 3.31718i) q^{31} +(-2.31875 - 2.00921i) q^{33} +(-0.305606 - 2.42680i) q^{35} +(-0.601229 + 2.04760i) q^{37} +(-0.736909 - 0.850438i) q^{39} +(-0.622798 + 0.182870i) q^{41} +(-0.451677 - 0.0649413i) q^{43} +(4.81923 - 4.03018i) q^{45} +7.73135i q^{47} +(-0.825917 + 5.74438i) q^{49} +(1.28236 - 0.376534i) q^{51} +(8.34751 - 7.23316i) q^{53} +(-2.60947 + 1.13686i) q^{55} +(-8.15743 + 12.6932i) q^{57} +(-5.65964 + 6.53157i) q^{59} +(-0.781299 - 5.43405i) q^{61} +(2.79554 - 1.27668i) q^{63} +(-1.00666 + 0.276512i) q^{65} +(0.346449 + 0.539086i) q^{67} +(-1.69543 - 11.4344i) q^{69} +(6.97016 - 4.47945i) q^{71} +(-3.75036 - 1.71273i) q^{73} +(-2.98789 - 11.6752i) q^{75} +(-1.37825 + 0.198162i) q^{77} +(2.51187 - 2.89886i) q^{79} +(-8.02146 - 5.15508i) q^{81} +(0.460581 - 1.56860i) q^{83} +(0.197939 - 1.22398i) q^{85} +(6.17435 + 21.0279i) q^{87} +(1.33493 - 9.28465i) q^{89} -0.510693 q^{91} +8.07760i q^{93} +(7.36019 + 11.9065i) q^{95} +(0.295759 + 1.00726i) q^{97} +(-2.34201 - 2.70282i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 120 q + 20 q^{9}+O(q^{10}) $ 120 * q + 20 * q^9	$ 120 q + 20 q^{9} - 4 q^{11} + 9 q^{15} + 8 q^{19} + 14 q^{25} + 10 q^{29} - 18 q^{31} + 10 q^{35} - 60 q^{39} + 2 q^{41} - 2 q^{45} - 28 q^{49} + 24 q^{51} + 6 q^{55} - 36 q^{61} + 39 q^{65} + 118 q^{69} - 76 q^{71} + 83 q^{75} + 64 q^{79} - 160 q^{81} + 38 q^{85} - 48 q^{89} - 80 q^{91} + 21 q^{95} - 142 q^{99}+O(q^{100}) $ 120 * q + 20 * q^9 - 4 * q^11 + 9 * q^15 + 8 * q^19 + 14 * q^25 + 10 * q^29 - 18 * q^31 + 10 * q^35 - 60 * q^39 + 2 * q^41 - 2 * q^45 - 28 * q^49 + 24 * q^51 + 6 * q^55 - 36 * q^61 + 39 * q^65 + 118 * q^69 - 76 * q^71 + 83 * q^75 + 64 * q^79 - 160 * q^81 + 38 * q^85 - 48 * q^89 - 80 * q^91 + 21 * q^95 - 142 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/460\mathbb{Z}\right)^\times$.

$n$	$231$	$277$	$281$
$\chi(n)$	$1$	$-1$	$e\left(\frac{10}{11}\right)$

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
$3$	2.38576	+	0.343021i	1.37742	+	0.198043i	0.790927	−	0.611910i	$-0.209599\pi$
$3$	2.38576	+	0.343021i	1.37742	+	0.198043i	0.586494	+	0.809954i	$0.300508\pi$
$4$		0			0
$5$	1.24170	−	1.85962i	0.555304	−	0.831648i
$5$	1.24170	−	1.85962i	0.555304	−	0.831648i
$6$		0			0
$7$	0.826691	−	0.716332i	0.312460	−	0.270748i	−0.484486	−	0.874799i	$-0.660993\pi$
$7$	0.826691	−	0.716332i	0.312460	−	0.270748i	0.796946	+	0.604051i	$0.206448\pi$
$8$		0			0
$9$	2.69572	+	0.791536i	0.898575	+	0.263845i
$10$		0			0
$11$	−1.07086	−	0.688200i	−0.322876	−	0.207500i	0.369154	−	0.929368i	$-0.379647\pi$
$11$	−1.07086	−	0.688200i	−0.322876	−	0.207500i	−0.692031	+	0.721868i	$0.743284\pi$
$12$		0			0
$13$	−0.352835	−	0.305734i	−0.0978590	−	0.0847953i	0.604557	−	0.796562i	$-0.293350\pi$
$13$	−0.352835	−	0.305734i	−0.0978590	−	0.0847953i	−0.702416	+	0.711766i	$0.747895\pi$
$14$		0			0
$15$	3.60028	−	4.01069i	0.929589	−	1.03555i
$16$		0			0
$17$	0.504385	−	0.230345i	0.122331	−	0.0558669i	−0.353309	−	0.935507i	$-0.614944\pi$
$17$	0.504385	−	0.230345i	0.122331	−	0.0558669i	0.475641	+	0.879640i	$0.342216\pi$
$18$		0			0
$19$	−2.60049	+	5.69429i	−0.596594	+	1.30636i	0.334780	+	0.942296i	$0.391338\pi$
$19$	−2.60049	+	5.69429i	−0.596594	+	1.30636i	−0.931374	+	0.364063i	$0.881389\pi$
$20$		0			0
$21$	2.21801	−	1.42543i	0.484009	−	0.311054i
$22$		0			0
$23$	−1.37139	−	4.59557i	−0.285954	−	0.958243i
$23$	−1.37139	−	4.59557i	−0.285954	−	0.958243i
$24$		0			0
$25$	−1.91638	−	4.61817i	−0.383276	−	0.923634i
$26$		0			0
$27$	−0.417601	−	0.190712i	−0.0803674	−	0.0367025i
$28$		0			0
$29$	3.77717	+	8.27084i	0.701402	+	1.53586i	0.838263	+	0.545266i	$0.183571\pi$
$29$	3.77717	+	8.27084i	0.701402	+	1.53586i	−0.136861	+	0.990590i	$0.543701\pi$
$30$		0			0
$31$	0.476938	+	3.31718i	0.0856606	+	0.595783i	0.986762	+	0.162174i	$0.0518507\pi$
$31$	0.476938	+	3.31718i	0.0856606	+	0.595783i	−0.901101	+	0.433608i	$0.857240\pi$
$32$		0			0
$33$	−2.31875	−	2.00921i	−0.403643	−	0.349759i
$34$		0			0
$35$	−0.305606	−	2.42680i	−0.0516568	−	0.410204i
$36$		0			0
$37$	−0.601229	+	2.04760i	−0.0988415	+	0.336623i	−0.994036	−	0.109052i	$-0.965218\pi$
$37$	−0.601229	+	2.04760i	−0.0988415	+	0.336623i	0.895194	+	0.445676i	$0.147037\pi$
$38$		0			0
$39$	−0.736909	−	0.850438i	−0.118000	−	0.136179i
$40$		0			0
$41$	−0.622798	+	0.182870i	−0.0972647	+	0.0285595i	−0.330003	−	0.943980i	$-0.607050\pi$
$41$	−0.622798	+	0.182870i	−0.0972647	+	0.0285595i	0.232738	+	0.972539i	$0.425232\pi$
$42$		0			0
$43$	−0.451677	−	0.0649413i	−0.0688800	−	0.00990345i	0.107789	−	0.994174i	$-0.465623\pi$
$43$	−0.451677	−	0.0649413i	−0.0688800	−	0.00990345i	−0.176669	+	0.984270i	$0.556532\pi$
$44$		0			0
$45$	4.81923	−	4.03018i	0.718408	−	0.600783i
$46$		0			0
$47$			7.73135i			1.12773i	0.825866	+	0.563867i	$0.190687\pi$
$47$			7.73135i			1.12773i	−0.825866	+	0.563867i	$0.809313\pi$
$48$		0			0
$49$	−0.825917	+	5.74438i	−0.117988	+	0.820626i
$50$		0			0
$51$	1.28236	−	0.376534i	0.179566	−	0.0527253i
$52$		0			0
$53$	8.34751	−	7.23316i	1.14662	−	0.993551i	0.146628	−	0.989192i	$-0.453158\pi$
$53$	8.34751	−	7.23316i	1.14662	−	0.993551i	0.999990	−	0.00435908i	$-0.00138754\pi$
$54$		0			0
$55$	−2.60947	+	1.13686i	−0.351861	+	0.153294i
$56$		0			0
$57$	−8.15743	+	12.6932i	−1.08048	+	1.68126i
$58$		0			0
$59$	−5.65964	+	6.53157i	−0.736822	+	0.850338i	−0.993222	−	0.116233i	$-0.962918\pi$
$59$	−5.65964	+	6.53157i	−0.736822	+	0.850338i	0.256400	+	0.966571i	$0.417464\pi$
$60$		0			0
$61$	−0.781299	−	5.43405i	−0.100035	−	0.695759i	−0.976692	−	0.214644i	$-0.931141\pi$
$61$	−0.781299	−	5.43405i	−0.100035	−	0.695759i	0.876657	−	0.481115i	$-0.159768\pi$
$62$		0			0
$63$	2.79554	−	1.27668i	0.352204	−	0.160846i
$64$		0			0
$65$	−1.00666	+	0.276512i	−0.124861	+	0.0342970i
$66$		0			0
$67$	0.346449	+	0.539086i	0.0423255	+	0.0658598i	0.861772	−	0.507297i	$-0.169355\pi$
$67$	0.346449	+	0.539086i	0.0423255	+	0.0658598i	−0.819446	+	0.573156i	$0.805719\pi$
$68$		0			0
$69$	−1.69543	−	11.4344i	−0.204106	−	1.37654i
$70$		0			0
$71$	6.97016	−	4.47945i	0.827206	−	0.531613i	−0.0571831	−	0.998364i	$-0.518212\pi$
$71$	6.97016	−	4.47945i	0.827206	−	0.531613i	0.884389	+	0.466751i	$0.154576\pi$
$72$		0			0
$73$	−3.75036	−	1.71273i	−0.438946	−	0.200460i	0.183669	−	0.982988i	$-0.441202\pi$
$73$	−3.75036	−	1.71273i	−0.438946	−	0.200460i	−0.622615	+	0.782528i	$0.713930\pi$
$74$		0			0
$75$	−2.98789	−	11.6752i	−0.345012	−	1.34814i
$76$		0			0
$77$	−1.37825	+	0.198162i	−0.157066	+	0.0225827i
$78$		0			0
$79$	2.51187	−	2.89886i	0.282608	−	0.326147i	−0.596642	−	0.802507i	$-0.703499\pi$
$79$	2.51187	−	2.89886i	0.282608	−	0.326147i	0.879250	+	0.476360i	$0.158044\pi$
$80$		0			0
$81$	−8.02146	−	5.15508i	−0.891274	−	0.572787i
$82$		0			0
$83$	0.460581	−	1.56860i	0.0505554	−	0.172176i	−0.930345	−	0.366684i	$-0.880493\pi$
$83$	0.460581	−	1.56860i	0.0505554	−	0.172176i	0.980901	+	0.194508i	$0.0623112\pi$
$84$		0			0
$85$	0.197939	−	1.22398i	0.0214695	−	0.132760i
$86$		0			0
$87$	6.17435	+	21.0279i	0.661960	+	2.25443i
$88$		0			0
$89$	1.33493	−	9.28465i	0.141502	−	0.984171i	−0.788084	−	0.615567i	$-0.788927\pi$
$89$	1.33493	−	9.28465i	0.141502	−	0.984171i	0.929587	−	0.368604i	$-0.120164\pi$
$90$		0			0
$91$	−0.510693			−0.0535352
$92$		0			0
$93$			8.07760i			0.837608i
$94$		0			0
$95$	7.36019	+	11.9065i	0.755140	+	1.22158i
$96$		0			0
$97$	0.295759	+	1.00726i	0.0300298	+	0.102272i	0.973144	−	0.230196i	$-0.0739368\pi$
$97$	0.295759	+	1.00726i	0.0300298	+	0.102272i	−0.943114	+	0.332468i	$0.892119\pi$
$98$		0			0
$99$	−2.34201	−	2.70282i	−0.235381	−	0.271644i
$100$		0			0
$101$	−7.55519	−	2.21840i	−0.751769	−	0.220739i	−0.116671	−	0.993171i	$-0.537222\pi$
$101$	−7.55519	−	2.21840i	−0.751769	−	0.220739i	−0.635098	+	0.772431i	$0.719040\pi$
$102$		0			0
$103$	−8.00206	+	12.4514i	−0.788466	+	1.22688i	0.181441	+	0.983402i	$0.441924\pi$
$103$	−8.00206	+	12.4514i	−0.788466	+	1.22688i	−0.969907	+	0.243475i	$0.921712\pi$
$104$		0			0
$105$	0.103340	−	5.89460i	0.0100849	−	0.575254i
$106$		0			0
$107$	−7.60780	+	1.09384i	−0.735473	+	0.105745i	−0.499865	−	0.866103i	$-0.666617\pi$
$107$	−7.60780	+	1.09384i	−0.735473	+	0.105745i	−0.235608	+	0.971848i	$0.575708\pi$
$108$		0			0
$109$	−2.29681	−	5.02931i	−0.219995	−	0.481721i	0.767167	−	0.641448i	$-0.221666\pi$
$109$	−2.29681	−	5.02931i	−0.219995	−	0.481721i	−0.987161	+	0.159727i	$0.948939\pi$
$110$		0			0
$111$	−2.13676	+	4.67885i	−0.202812	+	0.444097i
$112$		0			0
$113$	−2.20350	−	3.42872i	−0.207288	−	0.322547i	0.722006	−	0.691887i	$-0.243220\pi$
$113$	−2.20350	−	3.42872i	−0.207288	−	0.322547i	−0.929294	+	0.369340i	$0.879584\pi$
$114$		0			0
$115$	−10.2489	−	3.15605i	−0.955712	−	0.294303i
$116$		0			0
$117$	−0.709148	−	1.10346i	−0.0655608	−	0.102015i
$118$		0			0
$119$	0.251967	−	0.551732i	0.0230978	−	0.0505772i
$120$		0			0
$121$	−3.89644	−	8.53202i	−0.354222	−	0.775638i
$122$		0			0
$123$	−1.54858	+	0.222652i	−0.139630	+	0.0200758i
$124$		0			0
$125$	−10.9676	−	2.17063i	−0.980972	−	0.194147i
$126$		0			0
$127$	−9.90924	+	15.4191i	−0.879302	+	1.36822i	0.0499406	+	0.998752i	$0.484097\pi$
$127$	−9.90924	+	15.4191i	−0.879302	+	1.36822i	−0.929243	+	0.369469i	$0.879540\pi$
$128$		0			0
$129$	−1.05532	−	0.309869i	−0.0929155	−	0.0272825i
$130$		0			0
$131$	12.5089	+	14.4360i	1.09291	+	1.26128i	0.962926	+	0.269766i	$0.0869465\pi$
$131$	12.5089	+	14.4360i	1.09291	+	1.26128i	0.129982	+	0.991516i	$0.458508\pi$
$132$		0			0
$133$	1.92920	+	6.57024i	0.167282	+	0.569712i
$134$		0			0
$135$	−0.873186	+	0.539773i	−0.0751519	+	0.0464563i
$136$		0			0
$137$		−	17.5928i		−	1.50306i	−0.659701	−	0.751528i	$-0.729317\pi$
$137$		−	17.5928i		−	1.50306i	0.659701	−	0.751528i	$-0.270683\pi$
$138$		0			0
$139$	−19.3531			−1.64151			−0.820756	−	0.571279i	$-0.806447\pi$
$139$	−19.3531			−1.64151			−0.820756	+	0.571279i	$0.806447\pi$
$140$		0			0
$141$	−2.65202	+	18.4452i	−0.223340	+	1.55336i
$142$		0			0
$143$	0.167432	+	0.570219i	0.0140013	+	0.0476841i
$144$		0			0
$145$	20.0707	+	3.24578i	1.66678	+	0.269547i
$146$		0			0
$147$	−3.94089	+	13.4214i	−0.325039	+	1.10698i
$148$		0			0
$149$	8.32668	+	5.35123i	0.682148	+	0.438390i	0.835287	−	0.549815i	$-0.185302\pi$
$149$	8.32668	+	5.35123i	0.682148	+	0.438390i	−0.153139	+	0.988205i	$0.548938\pi$
$150$		0			0
$151$	−2.67029	+	3.08168i	−0.217305	+	0.250783i	−0.853927	−	0.520392i	$-0.825786\pi$
$151$	−2.67029	+	3.08168i	−0.217305	+	0.250783i	0.636622	+	0.771176i	$0.280331\pi$
$152$		0			0
$153$	1.54201	−	0.221708i	0.124664	−	0.0179240i
$154$		0			0
$155$	6.76091	+	3.23201i	0.543049	+	0.259601i
$156$		0			0
$157$	−1.51863	−	0.693536i	−0.121200	−	0.0553502i	0.353892	−	0.935286i	$-0.384858\pi$
$157$	−1.51863	−	0.693536i	−0.121200	−	0.0553502i	−0.475092	+	0.879936i	$0.657585\pi$
$158$		0			0
$159$	22.3963	−	14.3932i	1.77614	−	1.14146i
$160$		0			0
$161$	−4.42567	−	2.81675i	−0.348792	−	0.221991i
$162$		0			0
$163$	−9.02688	−	14.0461i	−0.707040	−	1.10017i	−0.990003	−	0.141044i	$-0.954954\pi$
$163$	−9.02688	−	14.0461i	−0.707040	−	1.10017i	0.282964	−	0.959131i	$-0.408682\pi$
$164$		0			0
$165$	−6.61555	+	1.81717i	−0.515020	+	0.141466i
$166$		0			0
$167$	8.90126	−	4.06507i	0.688800	−	0.314564i	−0.0400893	−	0.999196i	$-0.512764\pi$
$167$	8.90126	−	4.06507i	0.688800	−	0.314564i	0.728889	+	0.684632i	$0.240037\pi$
$168$		0			0
$169$	−1.81907	−	12.6519i	−0.139929	−	0.973225i
$170$		0			0
$171$	−11.5175	+	13.2919i	−0.880762	+	1.01645i
$172$		0			0
$173$	9.83643	−	15.3058i	0.747850	−	1.16368i	−0.233670	−	0.972316i	$-0.575074\pi$
$173$	9.83643	−	15.3058i	0.747850	−	1.16368i	0.981520	−	0.191361i	$-0.0612901\pi$
$174$		0			0
$175$	−4.89240	−	2.44504i	−0.369830	−	0.184828i
$176$		0			0
$177$	−15.7430	+	13.6414i	−1.18332	+	1.02535i
$178$		0			0
$179$	−4.02539	+	1.18196i	−0.300872	+	0.0883439i	−0.428684	−	0.903454i	$-0.641023\pi$
$179$	−4.02539	+	1.18196i	−0.300872	+	0.0883439i	0.127812	+	0.991798i	$0.459204\pi$
$180$		0			0
$181$	2.58787	−	17.9991i	0.192355	−	1.33786i	−0.633398	−	0.773827i	$-0.718340\pi$
$181$	2.58787	−	17.9991i	0.192355	−	1.33786i	0.825753	−	0.564032i	$-0.190751\pi$
$182$		0			0
$183$		−	13.2324i		−	0.978165i
$184$		0			0
$185$	3.06121	+	3.66056i	0.225065	+	0.269129i
$186$		0			0
$187$	−0.698650	−	0.100451i	−0.0510903	−	0.00734568i
$188$		0			0
$189$	−0.481840	+	0.141481i	−0.0350487	+	0.0102912i
$190$		0			0
$191$	11.3962	+	13.1519i	0.824602	+	0.951641i	0.999457	−	0.0329527i	$-0.0104911\pi$
$191$	11.3962	+	13.1519i	0.824602	+	0.951641i	−0.174855	+	0.984594i	$0.555946\pi$
$192$		0			0
$193$	−5.46310	+	18.6056i	−0.393242	+	1.33926i	0.490563	+	0.871406i	$0.336791\pi$
$193$	−5.46310	+	18.6056i	−0.393242	+	1.33926i	−0.883806	+	0.467854i	$0.845027\pi$
$194$		0			0
$195$	−2.49651	+	0.314384i	−0.178779	+	0.0225135i
$196$		0			0
$197$	10.4016	+	9.01305i	0.741085	+	0.642154i	0.941289	−	0.337601i	$-0.109615\pi$
$197$	10.4016	+	9.01305i	0.741085	+	0.642154i	−0.200205	+	0.979754i	$0.564161\pi$
$198$		0			0
$199$	−1.71343	−	11.9172i	−0.121462	−	0.844785i	−0.955902	−	0.293686i	$-0.905118\pi$
$199$	−1.71343	−	11.9172i	−0.121462	−	0.844785i	0.834440	−	0.551099i	$-0.185791\pi$
$200$		0			0
$201$	0.641628	+	1.40497i	0.0452570	+	0.0990990i
$202$		0			0
$203$	9.04722	+	4.13173i	0.634990	+	0.289990i
$204$		0			0
$205$	−0.433258	+	1.38524i	−0.0302600	+	0.0967492i
$206$		0			0
$207$	−0.0593211	−	13.4739i	−0.00412310	−	0.936501i
$208$		0			0
$209$	6.70358	−	4.30813i	0.463696	−	0.297999i
$210$		0			0
$211$	6.25795	−	13.7030i	0.430815	−	0.943354i	−0.562379	−	0.826880i	$-0.690114\pi$
$211$	6.25795	−	13.7030i	0.430815	−	0.943354i	0.993194	−	0.116474i	$-0.0371591\pi$
$212$		0			0
$213$	18.1657	−	8.29600i	1.24469	−	0.568432i
$214$		0			0
$215$	−0.681612	+	0.759310i	−0.0464855	+	0.0517845i
$216$		0			0
$217$	2.77048	+	2.40064i	0.188073	+	0.162966i
$218$		0			0
$219$	−8.35996	−	5.37262i	−0.564914	−	0.363048i
$220$		0			0
$221$	−0.248389	−	0.0729337i	−0.0167085	−	0.00490605i
$222$		0			0
$223$	7.82877	−	6.78367i	0.524253	−	0.454268i	−0.352082	−	0.935969i	$-0.614526\pi$
$223$	7.82877	−	6.78367i	0.524253	−	0.454268i	0.876336	+	0.481701i	$0.159981\pi$
$224$		0			0
$225$	−1.51058	−	13.9662i	−0.100705	−	0.931080i
$226$		0			0
$227$	27.1026	+	3.89677i	1.79887	+	0.258638i	0.958848	−	0.283921i	$-0.0916354\pi$
$227$	27.1026	+	3.89677i	1.79887	+	0.258638i	0.840018	+	0.542559i	$0.182544\pi$
$228$		0			0
$229$	17.2559			1.14030			0.570150	−	0.821540i	$-0.306885\pi$
$229$	17.2559			1.14030			0.570150	+	0.821540i	$0.306885\pi$
$230$		0			0
$231$	−3.35615			−0.220819
$232$		0			0
$233$	12.6754	+	1.82245i	0.830394	+	0.119393i	0.544386	−	0.838835i	$-0.316763\pi$
$233$	12.6754	+	1.82245i	0.830394	+	0.119393i	0.286008	+	0.958227i	$0.407672\pi$
$234$		0			0
$235$	14.3774	+	9.60000i	0.937877	+	0.626235i
$236$		0			0
$237$	6.98711	−	6.05436i	0.453861	−	0.393273i
$238$		0			0
$239$	15.8373	+	4.65024i	1.02443	+	0.300799i	0.750443	−	0.660935i	$-0.229840\pi$
$239$	15.8373	+	4.65024i	1.02443	+	0.300799i	0.273984	+	0.961734i	$0.411658\pi$
$240$		0			0
$241$	−0.694984	−	0.446639i	−0.0447678	−	0.0287705i	0.518065	−	0.855341i	$-0.326652\pi$
$241$	−0.694984	−	0.446639i	−0.0447678	−	0.0287705i	−0.562833	+	0.826570i	$0.690289\pi$
$242$		0			0
$243$	−16.3281	−	14.1484i	−1.04745	−	0.907621i
$244$		0			0
$245$	9.65683	+	8.66867i	0.616952	+	0.553821i
$246$		0			0
$247$	2.65848	−	1.21409i	0.169155	−	0.0772506i
$248$		0			0
$249$	1.63690	−	3.58431i	0.103734	−	0.227146i
$250$		0			0
$251$	10.3522	−	6.65296i	0.653425	−	0.419931i	−0.171491	−	0.985186i	$-0.554858\pi$
$251$	10.3522	−	6.65296i	0.653425	−	0.419931i	0.824916	+	0.565255i	$0.191222\pi$
$252$		0			0
$253$	−1.69411	+	5.86500i	−0.106508	+	0.368730i
$254$		0			0
$255$	0.892089	−	2.85224i	0.0558648	−	0.178614i
$256$		0			0
$257$	−15.8815	−	7.25283i	−0.990660	−	0.452419i	−0.146907	−	0.989150i	$-0.546932\pi$
$257$	−15.8815	−	7.25283i	−0.990660	−	0.452419i	−0.843753	+	0.536731i	$0.819659\pi$
$258$		0			0
$259$	0.969730	+	2.12341i	0.0602561	+	0.131942i
$260$		0			0
$261$	3.63553	+	25.2857i	0.225034	+	1.56514i
$262$		0			0
$263$	−13.8086	−	11.9652i	−0.851477	−	0.737809i	0.115327	−	0.993328i	$-0.463208\pi$
$263$	−13.8086	−	11.9652i	−0.851477	−	0.737809i	−0.966804	+	0.255519i	$0.917754\pi$
$264$		0			0
$265$	−3.08585	−	24.5046i	−0.189562	−	1.50531i
$266$		0			0
$267$	6.36966	−	21.6931i	0.389817	−	1.32759i
$268$		0			0
$269$	5.83343	+	6.73214i	0.355671	+	0.410466i	0.905185	−	0.425019i	$-0.139732\pi$
$269$	5.83343	+	6.73214i	0.355671	+	0.410466i	−0.549514	+	0.835485i	$0.685187\pi$
$270$		0			0
$271$	2.65142	−	0.778527i	0.161062	−	0.0472922i	−0.200207	−	0.979754i	$-0.564162\pi$
$271$	2.65142	−	0.778527i	0.161062	−	0.0472922i	0.361270	+	0.932461i	$0.382343\pi$
$272$		0			0
$273$	−1.21839	−	0.175178i	−0.0737405	−	0.0106023i
$274$		0			0
$275$	−1.12605	+	6.26426i	−0.0679035	+	0.377749i
$276$		0			0
$277$		−	11.2655i		−	0.676876i	−0.940989	−	0.338438i	$-0.890102\pi$
$277$		−	11.2655i		−	0.676876i	0.940989	−	0.338438i	$-0.109898\pi$
$278$		0			0
$279$	−1.33997	+	9.31971i	−0.0802220	+	0.557957i
$280$		0			0
$281$	26.2861	−	7.71830i	1.56810	−	0.460435i	0.621651	−	0.783295i	$-0.286462\pi$
$281$	26.2861	−	7.71830i	1.56810	−	0.460435i	0.946447	+	0.322860i	$0.104644\pi$
$282$		0			0
$283$	−4.20991	+	3.64791i	−0.250253	+	0.216846i	−0.770949	−	0.636896i	$-0.780218\pi$
$283$	−4.20991	+	3.64791i	−0.250253	+	0.216846i	0.520696	+	0.853742i	$0.325672\pi$
$284$		0			0
$285$	13.4755	+	30.9308i	0.798219	+	1.83218i
$286$		0			0
$287$	−0.383866	+	0.597307i	−0.0226589	+	0.0352579i
$288$		0			0
$289$	−10.9313	+	12.6154i	−0.643017	+	0.742081i
$290$		0			0
$291$	0.360099	+	2.50454i	0.0211094	+	0.146819i
$292$		0			0
$293$	22.3044	−	10.1861i	1.30304	−	0.595076i	0.361620	−	0.932326i	$-0.382224\pi$
$293$	22.3044	−	10.1861i	1.30304	−	0.595076i	0.941415	+	0.337249i	$0.109497\pi$
$294$		0			0
$295$	5.11869	+	18.6350i	0.298022	+	1.08497i
$296$		0			0
$297$	0.315944	+	0.491619i	0.0183329	+	0.0285266i
$298$		0			0
$299$	−0.921147	+	2.04076i	−0.0532713	+	0.118020i
$300$		0			0
$301$	−0.419917	+	0.269864i	−0.0242036	+	0.0155547i
$302$		0			0
$303$	−17.2639	−	7.88418i	−0.991787	−	0.452934i
$304$		0			0
$305$	−11.0754	−	5.29453i	−0.634176	−	0.303164i
$306$		0			0
$307$	4.72513	−	0.679371i	0.269677	−	0.0387738i	−0.00614946	−	0.999981i	$-0.501957\pi$
$307$	4.72513	−	0.679371i	0.269677	−	0.0387738i	0.275827	+	0.961207i	$0.411048\pi$
$308$		0			0
$309$	−23.3621	+	26.9613i	−1.32902	+	1.53378i
$310$		0			0
$311$	−19.8115	−	12.7321i	−1.12341	−	0.721971i	−0.159234	−	0.987241i	$-0.550903\pi$
$311$	−19.8115	−	12.7321i	−1.12341	−	0.721971i	−0.964174	+	0.265270i	$0.914539\pi$
$312$		0			0
$313$	−7.27617	+	24.7804i	−0.411274	+	1.40067i	0.450228	+	0.892914i	$0.351343\pi$
$313$	−7.27617	+	24.7804i	−0.411274	+	1.40067i	−0.861501	+	0.507755i	$0.830475\pi$
$314$		0			0
$315$	1.09707	−	6.78388i	0.0618129	−	0.382228i
$316$		0			0
$317$	2.25070	+	7.66519i	0.126412	+	0.430520i	0.998241	−	0.0592910i	$-0.0188840\pi$
$317$	2.25070	+	7.66519i	0.126412	+	0.430520i	−0.871829	+	0.489811i	$0.837066\pi$
$318$		0			0
$319$	1.64718	−	11.4564i	0.0922241	−	0.641433i
$320$		0			0
$321$	−18.5256			−1.03400
$322$		0			0
$323$			3.47113i			0.193139i
$324$		0			0
$325$	−0.735764	+	2.21536i	−0.0408129	+	0.122886i
$326$		0			0
$327$	−3.75449	−	12.7866i	−0.207624	−	0.707101i
$328$		0			0
$329$	5.53822	+	6.39144i	0.305332	+	0.352372i
$330$		0			0
$331$	22.1435	+	6.50190i	1.21711	+	0.357377i	0.826373	−	0.563123i	$-0.190400\pi$
$331$	22.1435	+	6.50190i	1.21711	+	0.357377i	0.390742	+	0.920500i	$0.372219\pi$
$332$		0			0
$333$	−3.24150	+	5.04387i	−0.177633	+	0.276402i
$334$		0			0
$335$	1.43268	+	0.0251167i	0.0782757	+	0.00137227i
$336$		0			0
$337$	−31.1183	+	4.47413i	−1.69512	+	0.243721i	−0.921068	−	0.389402i	$-0.872682\pi$
$337$	−31.1183	+	4.47413i	−1.69512	+	0.243721i	−0.774051	+	0.633123i	$0.781773\pi$
$338$		0			0
$339$	−4.08092	−	8.93596i	−0.221645	−	0.485335i
$340$		0			0
$341$	1.77215	−	3.88046i	0.0959672	−	0.210139i
$342$		0			0
$343$	7.57184	+	11.7820i	0.408841	+	0.636169i
$344$		0			0
$345$	−23.3688	−	11.0452i	−1.25813	−	0.594652i
$346$		0			0
$347$	−0.925193	−	1.43963i	−0.0496669	−	0.0772833i	0.815532	−	0.578712i	$-0.196444\pi$
$347$	−0.925193	−	1.43963i	−0.0496669	−	0.0772833i	−0.865199	+	0.501429i	$0.832808\pi$
$348$		0			0
$349$	−13.7585	+	30.1268i	−0.736474	+	1.61265i	0.0527961	+	0.998605i	$0.483187\pi$
$349$	−13.7585	+	30.1268i	−0.736474	+	1.61265i	−0.789270	+	0.614047i	$0.789541\pi$
$350$		0			0
$351$	0.0890374	+	0.194965i	0.00475246	+	0.0104064i
$352$		0			0
$353$	−13.3761	+	1.92319i	−0.711936	+	0.102361i	−0.488761	−	0.872418i	$-0.662551\pi$
$353$	−13.3761	+	1.92319i	−0.711936	+	0.102361i	−0.223175	+	0.974778i	$0.571642\pi$
$354$		0			0
$355$	0.324749	−	18.5240i	0.0172359	−	0.983150i
$356$		0			0
$357$	0.790390	−	1.22987i	0.0418319	−	0.0650917i
$358$		0			0
$359$	−9.91940	−	2.91260i	−0.523526	−	0.153721i	0.00928246	−	0.999957i	$-0.497045\pi$
$359$	−9.91940	−	2.91260i	−0.523526	−	0.153721i	−0.532809	+	0.846236i	$0.678863\pi$
$360$		0			0
$361$	−13.2200	−	15.2567i	−0.695790	−	0.802984i
$362$		0			0
$363$	−6.36933	−	21.6919i	−0.334303	−	1.13853i
$364$		0			0
$365$	−7.84183	+	4.84755i	−0.410460	+	0.253732i
$366$		0			0
$367$		−	28.7687i		−	1.50172i	−0.660464	−	0.750858i	$-0.729640\pi$
$367$		−	28.7687i		−	1.50172i	0.660464	−	0.750858i	$-0.270360\pi$
$368$		0			0
$369$	−1.82364			−0.0949349
$370$		0			0
$371$	1.71947	−	11.9592i	0.0892704	−	0.620890i
$372$		0			0
$373$	7.40196	+	25.2088i	0.383259	+	1.30526i	0.894979	+	0.446108i	$0.147190\pi$
$373$	7.40196	+	25.2088i	0.383259	+	1.30526i	−0.511720	+	0.859152i	$0.670992\pi$
$374$		0			0
$375$	−25.4215	−	8.94073i	−1.31276	−	0.461698i
$376$		0			0
$377$	1.19596	−	4.07305i	0.0615949	−	0.209773i
$378$		0			0
$379$	18.6214	+	11.9673i	0.956517	+	0.614716i	0.923032	−	0.384723i	$-0.125703\pi$
$379$	18.6214	+	11.9673i	0.956517	+	0.614716i	0.0334852	+	0.999439i	$0.489339\pi$
$380$		0			0
$381$	−28.9302	+	33.3872i	−1.48214	+	1.71048i
$382$		0			0
$383$	2.63478	−	0.378824i	0.134631	−	0.0193570i	−0.0746700	−	0.997208i	$-0.523790\pi$
$383$	2.63478	−	0.378824i	0.134631	−	0.0193570i	0.209301	+	0.977851i	$0.432881\pi$
$384$		0			0
$385$	−1.34286	+	2.80908i	−0.0684386	+	0.143164i
$386$		0			0
$387$	−1.16619	−	0.532582i	−0.0592809	−	0.0270727i
$388$		0			0
$389$	1.28320	−	0.824665i	0.0650610	−	0.0418122i	−0.507706	−	0.861530i	$-0.669506\pi$
$389$	1.28320	−	0.824665i	0.0650610	−	0.0418122i	0.572767	+	0.819718i	$0.305870\pi$
$390$		0			0
$391$	−1.75028	−	2.00205i	−0.0885152	−	0.101248i
$392$		0			0
$393$	24.8914	+	38.7318i	1.25561	+	1.95376i
$394$		0			0
$395$	−2.27179	−	8.27064i	−0.114306	−	0.416141i
$396$		0			0
$397$	31.1554	−	14.2282i	1.56365	−	0.714093i	0.569485	−	0.822002i	$-0.307143\pi$
$397$	31.1554	−	14.2282i	1.56365	−	0.714093i	0.994161	+	0.107909i	$0.0344155\pi$
$398$		0			0
$399$	2.34888	+	16.3368i	0.117591	+	0.817862i
$400$		0			0
$401$	11.2381	−	12.9694i	0.561202	−	0.647662i	−0.402254	−	0.915528i	$-0.631773\pi$
$401$	11.2381	−	12.9694i	0.561202	−	0.647662i	0.963456	+	0.267866i	$0.0863185\pi$
$402$		0			0
$403$	0.845892	−	1.31623i	0.0421369	−	0.0655663i
$404$		0			0
$405$	−19.5467	+	8.51583i	−0.971284	+	0.423155i
$406$		0			0
$407$	2.05299	−	1.77893i	0.101763	−	0.0881781i
$408$		0			0
$409$	5.19457	−	1.52526i	0.256855	−	0.0754194i	−0.150770	−	0.988569i	$-0.548175\pi$
$409$	5.19457	−	1.52526i	0.256855	−	0.0754194i	0.407625	+	0.913149i	$0.366357\pi$
$410$		0			0
$411$	6.03471	−	41.9723i	0.297670	−	2.07034i
$412$		0			0
$413$			9.45377i			0.465190i
$414$		0			0
$415$	−2.34509	−	2.80423i	−0.115116	−	0.137654i
$416$		0			0
$417$	−46.1720	−	6.63853i	−2.26105	−	0.325090i
$418$		0			0
$419$	−23.7366	+	6.96969i	−1.15961	+	0.340492i	−0.804280	−	0.594250i	$-0.797449\pi$
$419$	−23.7366	+	6.96969i	−1.15961	+	0.340492i	−0.355328	+	0.934742i	$0.615631\pi$
$420$		0			0
$421$	−4.45335	−	5.13944i	−0.217043	−	0.250481i	0.636779	−	0.771047i	$-0.280266\pi$
$421$	−4.45335	−	5.13944i	−0.217043	−	0.250481i	−0.853822	+	0.520566i	$0.825721\pi$
$422$		0			0
$423$	−6.11965	+	20.8416i	−0.297547	+	1.01335i
$424$		0			0
$425$	−2.03037	−	1.88791i	−0.0984872	−	0.0915771i
$426$		0			0
$427$	−4.53848	−	3.93262i	−0.219632	−	0.190313i
$428$		0			0
$429$	0.203855	+	1.41784i	0.00984220	+	0.0684540i
$430$		0			0
$431$	−7.14172	−	15.6382i	−0.344004	−	0.753265i	0.655994	−	0.754766i	$-0.272249\pi$
$431$	−7.14172	−	15.6382i	−0.344004	−	0.753265i	−0.999999	+	0.00150109i	$0.999522\pi$
$432$		0			0
$433$	2.73121	+	1.24730i	0.131254	+	0.0599415i	0.479959	−	0.877291i	$-0.340651\pi$
$433$	2.73121	+	1.24730i	0.131254	+	0.0599415i	−0.348706	+	0.937232i	$0.613379\pi$
$434$		0			0
$435$	46.7706	+	14.6283i	2.24248	+	0.701375i
$436$		0			0
$437$	29.7348	+	4.14169i	1.42241	+	0.198124i
$438$		0			0
$439$	10.4105	−	6.69042i	0.496866	−	0.319316i	−0.268095	−	0.963392i	$-0.586394\pi$
$439$	10.4105	−	6.69042i	0.496866	−	0.319316i	0.764962	+	0.644076i	$0.222758\pi$
$440$		0			0
$441$	−6.77333	+	14.8315i	−0.322539	+	0.706263i
$442$		0			0
$443$	−18.1629	+	8.29471i	−0.862944	+	0.394094i	−0.797180	−	0.603742i	$-0.793676\pi$
$443$	−18.1629	+	8.29471i	−0.862944	+	0.394094i	−0.0657644	+	0.997835i	$0.520949\pi$
$444$		0			0
$445$	−15.6083	−	14.0112i	−0.739907	−	0.664194i
$446$		0			0
$447$	18.0299	+	15.6230i	0.852785	+	0.738942i
$448$		0			0
$449$	−5.41601	−	3.48066i	−0.255597	−	0.164262i	0.406567	−	0.913621i	$-0.366726\pi$
$449$	−5.41601	−	3.48066i	−0.255597	−	0.164262i	−0.662164	+	0.749359i	$0.730362\pi$
$450$		0			0
$451$	0.792781	+	0.232781i	0.0373306	+	0.0109612i
$452$		0			0
$453$	−7.42776	+	6.43619i	−0.348987	+	0.302399i
$454$		0			0
$455$	−0.634126	+	0.949695i	−0.0297283	+	0.0445224i
$456$		0			0
$457$	36.3839	+	5.23121i	1.70197	+	0.244706i	0.923669	−	0.383190i	$-0.125175\pi$
$457$	36.3839	+	5.23121i	1.70197	+	0.244706i	0.778297	+	0.627896i	$0.216084\pi$
$458$		0			0
$459$	−0.254561			−0.0118819
$460$		0			0
$461$	3.21745			0.149852			0.0749259	−	0.997189i	$-0.476128\pi$
$461$	3.21745			0.149852			0.0749259	+	0.997189i	$0.476128\pi$
$462$		0			0
$463$	−34.4791	−	4.95734i	−1.60238	−	0.230387i	−0.717619	−	0.696436i	$-0.754768\pi$
$463$	−34.4791	−	4.95734i	−1.60238	−	0.230387i	−0.884759	+	0.466049i	$0.845677\pi$
$464$		0			0
$465$	15.0213	+	10.0299i	0.696595	+	0.465127i
$466$		0			0
$467$	−24.6959	+	21.3991i	−1.14279	+	0.990232i	−0.142788	+	0.989753i	$0.545607\pi$
$467$	−24.6959	+	21.3991i	−1.14279	+	0.990232i	−1.00000		0.000478367i	$0.999848\pi$
$468$		0			0
$469$	0.672571	+	0.197485i	0.0310564	+	0.00911899i
$470$		0			0
$471$	−3.38520	−	2.17553i	−0.155982	−	0.100243i
$472$		0			0
$473$	0.438990	+	0.380387i	0.0201848	+	0.0174902i
$474$		0			0
$475$	31.2807	+	1.09712i	1.43526	+	0.0503393i
$476$		0			0
$477$	28.2279	−	12.8912i	1.29247	−	0.590250i
$478$		0			0
$479$	−10.2470	+	22.4378i	−0.468198	+	1.02521i	0.517343	+	0.855778i	$0.326921\pi$
$479$	−10.2470	+	22.4378i	−0.468198	+	1.02521i	−0.985542	+	0.169433i	$0.945806\pi$
$480$		0			0
$481$	0.838155	−	0.538650i	0.0382166	−	0.0245603i
$482$		0			0
$483$	−9.59240	−	8.23820i	−0.436469	−	0.374851i
$484$		0			0
$485$	2.24037	+	0.700715i	0.101730	+	0.0318179i
$486$		0			0
$487$	−27.7396	−	12.6683i	−1.25700	−	0.574053i	−0.328192	−	0.944611i	$-0.606439\pi$
$487$	−27.7396	−	12.6683i	−1.25700	−	0.574053i	−0.928809	+	0.370558i	$0.879167\pi$
$488$		0			0
$489$	−16.7179	−	36.6071i	−0.756009	−	1.65543i
$490$		0			0
$491$	2.24283	+	15.5993i	0.101218	+	0.703984i	0.975729	+	0.218980i	$0.0702729\pi$
$491$	2.24283	+	15.5993i	0.101218	+	0.703984i	−0.874512	+	0.485004i	$0.838818\pi$
$492$		0			0
$493$	3.81029	+	3.30164i	0.171607	+	0.148698i
$494$		0			0
$495$	−7.93429	+	0.999162i	−0.356620	+	0.0449090i
$496$		0			0
$497$	2.55340	−	8.69607i	0.114536	−	0.390072i
$498$		0			0
$499$	9.15145	+	10.5613i	0.409675	+	0.472790i	0.922664	−	0.385605i	$-0.126007\pi$
$499$	9.15145	+	10.5613i	0.409675	+	0.472790i	−0.512989	+	0.858395i	$0.671462\pi$
$500$		0			0
$501$	22.6307	−	6.64497i	1.01106	−	0.296875i
$502$		0			0
$503$	29.7468	+	4.27695i	1.32635	+	0.190700i	0.768823	−	0.639462i	$-0.220843\pi$
$503$	29.7468	+	4.27695i	1.32635	+	0.190700i	0.557523	+	0.830162i	$0.311752\pi$
$504$		0			0
$505$	−13.5066	+	11.2952i	−0.601038	+	0.502630i
$506$		0			0
$507$		−	30.8085i		−	1.36825i
$508$		0			0
$509$	−0.971127	+	6.75434i	−0.0430445	+	0.299381i	0.956915	+	0.290368i	$0.0937778\pi$
$509$	−0.971127	+	6.75434i	−0.0430445	+	0.299381i	−0.999959	+	0.00901235i	$0.997131\pi$
$510$		0			0
$511$	−4.32727	+	1.27060i	−0.191427	+	0.0562081i
$512$		0			0
$513$	2.17194	−	1.88200i	0.0958934	−	0.0830921i
$514$		0			0
$515$	13.2188	+	30.3417i	0.582491	+	1.33702i
$516$		0			0
$517$	5.32072	−	8.27920i	0.234005	−	0.364119i
$518$		0			0
$519$	28.7176	−	33.1419i	1.26056	−	1.45477i
$520$		0			0
$521$	−3.11438	−	21.6610i	−0.136443	−	0.948984i	−0.936901	−	0.349595i	$-0.886319\pi$
$521$	−3.11438	−	21.6610i	−0.136443	−	0.948984i	0.800458	−	0.599389i	$-0.204590\pi$
$522$		0			0
$523$	−25.7978	+	11.7814i	−1.12806	+	0.515167i	−0.889944	−	0.456071i	$-0.849256\pi$
$523$	−25.7978	+	11.7814i	−1.12806	+	0.515167i	−0.238114	+	0.971237i	$0.576529\pi$
$524$		0			0
$525$	−10.8334	−	7.51148i	−0.472808	−	0.327828i
$526$		0			0
$527$	1.00466	+	1.56328i	0.0437635	+	0.0680974i
$528$		0			0
$529$	−19.2386	+	12.6046i	−0.836460	+	0.548027i
$530$		0			0
$531$	−20.4268	+	13.1275i	−0.886448	+	0.569685i
$532$		0			0
$533$	0.275655	+	0.125887i	0.0119399	+	0.00545278i
$534$		0			0
$535$	−7.41246	+	15.5058i	−0.320468	+	0.670375i
$536$		0			0
$537$	−10.0091	+	1.43909i	−0.431923	+	0.0621012i
$538$		0			0
$539$	4.83772	−	5.58303i	0.208375	−	0.240478i
$540$		0			0
$541$	33.4382	+	21.4894i	1.43762	+	0.923903i	0.999690	+	0.0248953i	$0.00792523\pi$
$541$	33.4382	+	21.4894i	1.43762	+	0.923903i	0.437932	+	0.899008i	$0.355711\pi$
$542$		0			0
$543$	12.3481	−	42.0538i	0.529908	−	1.80470i
$544$		0			0
$545$	−12.2046	−	1.97369i	−0.522786	−	0.0845435i
$546$		0			0
$547$	7.43696	+	25.3280i	0.317982	+	1.08295i	0.951098	+	0.308889i	$0.0999573\pi$
$547$	7.43696	+	25.3280i	0.317982	+	1.08295i	−0.633116	+	0.774057i	$0.718225\pi$
$548$		0			0
$549$	2.19508	−	15.2671i	0.0936839	−	0.651586i
$550$		0			0
$551$	−56.9190			−2.42483
$552$		0			0
$553$		−	4.19580i		−	0.178423i
$554$		0			0
$555$	6.04768	+	9.78328i	0.256710	+	0.415277i
$556$		0			0
$557$	−13.1341	−	44.7306i	−0.556510	−	1.89530i	−0.428549	−	0.903519i	$-0.640975\pi$
$557$	−13.1341	−	44.7306i	−0.556510	−	1.89530i	−0.127961	−	0.991779i	$-0.540843\pi$
$558$		0			0
$559$	0.139513	+	0.161006i	0.00590076	+	0.00680984i
$560$		0			0
$561$	−1.63236	−	0.479303i	−0.0689181	−	0.0202362i
$562$		0			0
$563$	3.86474	−	6.01366i	0.162879	−	0.253445i	−0.750215	−	0.661194i	$-0.770050\pi$
$563$	3.86474	−	6.01366i	0.162879	−	0.253445i	0.913094	+	0.407749i	$0.133686\pi$
$564$		0			0
$565$	−9.11220	−	0.159749i	−0.383353	−	0.00672067i
$566$		0			0
$567$	−10.3240	+	1.48437i	−0.433568	+	0.0623377i
$568$		0			0
$569$	−6.45483	−	14.1341i	−0.270601	−	0.592533i	0.724733	−	0.689030i	$-0.241963\pi$
$569$	−6.45483	−	14.1341i	−0.270601	−	0.592533i	−0.995333	+	0.0964974i	$0.969236\pi$
$570$		0			0
$571$	11.2239	−	24.5769i	0.469705	−	1.02851i	−0.515463	−	0.856912i	$-0.672380\pi$
$571$	11.2239	−	24.5769i	0.469705	−	1.02851i	0.985167	−	0.171598i	$-0.0548929\pi$
$572$		0			0
$573$	22.6773	+	35.2866i	0.947358	+	1.47412i
$574$		0			0
$575$	−18.5950	+	15.1402i	−0.775467	+	0.631388i
$576$		0			0
$577$	15.4474	+	24.0366i	0.643084	+	1.00066i	0.997839	+	0.0656991i	$0.0209277\pi$
$577$	15.4474	+	24.0366i	0.643084	+	1.00066i	−0.354756	+	0.934959i	$0.615436\pi$
$578$		0			0
$579$	−19.4158	+	42.5146i	−0.806892	+	1.76685i
$580$		0			0
$581$	−0.742877	−	1.62667i	−0.0308197	−	0.0674858i
$582$		0			0
$583$	−13.9169	+	2.00094i	−0.576378	+	0.0828707i
$584$		0			0
$585$	−2.93256	−	0.0514115i	−0.121246	−	0.00212560i
$586$		0			0
$587$	−5.43499	+	8.45701i	−0.224326	+	0.349058i	−0.935113	−	0.354349i	$-0.884702\pi$
$587$	−5.43499	+	8.45701i	−0.224326	+	0.349058i	0.710787	+	0.703407i	$0.248339\pi$
$588$		0			0
$589$	−20.1292	−	5.91048i	−0.829411	−	0.243537i
$590$		0			0
$591$	21.7241	+	25.0710i	0.893612	+	1.03128i
$592$		0			0
$593$	−8.24598	−	28.0832i	−0.338622	−	1.15324i	−0.936211	−	0.351438i	$-0.885693\pi$
$593$	−8.24598	−	28.0832i	−0.338622	−	1.15324i	0.597589	−	0.801803i	$-0.296125\pi$
$594$		0			0
$595$	−0.713144	−	1.15365i	−0.0292361	−	0.0472949i
$596$		0			0
$597$		−	29.0193i		−	1.18768i
$598$		0			0
$599$	18.0748			0.738515			0.369258	−	0.929327i	$-0.379612\pi$
$599$	18.0748			0.738515			0.369258	+	0.929327i	$0.379612\pi$
$600$		0			0
$601$	−3.92111	+	27.2719i	−0.159945	+	1.11244i	0.738785	+	0.673942i	$0.235400\pi$
$601$	−3.92111	+	27.2719i	−0.159945	+	1.11244i	−0.898730	+	0.438503i	$0.855509\pi$
$602$		0			0
$603$	0.507226	+	1.72745i	0.0206558	+	0.0703474i
$604$		0			0
$605$	−20.7045	−	3.34828i	−0.841759	−	0.136127i
$606$		0			0
$607$	13.1526	−	44.7937i	0.533848	−	1.81812i	−0.0400586	−	0.999197i	$-0.512754\pi$
$607$	13.1526	−	44.7937i	0.533848	−	1.81812i	0.573906	−	0.818921i	$-0.305427\pi$
$608$		0			0
$609$	20.1673	+	12.9607i	0.817218	+	0.525194i
$610$		0			0
$611$	2.36374	−	2.72790i	0.0956265	−	0.110359i
$612$		0			0
$613$	5.01545	−	0.721113i	0.202572	−	0.0291255i	−0.0402817	−	0.999188i	$-0.512826\pi$
$613$	5.01545	−	0.721113i	0.202572	−	0.0291255i	0.242854	+	0.970063i	$0.421916\pi$
$614$		0			0
$615$	−1.50882	+	3.15623i	−0.0608413	+	0.127272i
$616$		0			0
$617$	−34.3661	−	15.6945i	−1.38353	−	0.631836i	−0.422014	−	0.906589i	$-0.638677\pi$
$617$	−34.3661	−	15.6945i	−1.38353	−	0.631836i	−0.961515	+	0.274753i	$0.911404\pi$
$618$		0			0
$619$	−0.935309	+	0.601086i	−0.0375932	+	0.0241597i	−0.559302	−	0.828964i	$-0.688931\pi$
$619$	−0.935309	+	0.601086i	−0.0375932	+	0.0241597i	0.521709	+	0.853123i	$0.325295\pi$
$620$		0			0
$621$	−0.303738	+	2.18066i	−0.0121886	+	0.0875067i
$622$		0			0
$623$	−5.54732	−	8.63179i	−0.222249	−	0.345826i
$624$		0			0
$625$	−17.6550	+	17.7003i	−0.706200	+	0.708013i
$626$		0			0
$627$	17.4709	−	7.97870i	0.697721	−	0.318639i
$628$		0			0
$629$	0.168403	+	1.17127i	0.00671467	+	0.0467016i
$630$		0			0
$631$	−27.7815	+	32.0615i	−1.10596	+	1.27635i	−0.148147	+	0.988965i	$0.547331\pi$
$631$	−27.7815	+	32.0615i	−1.10596	+	1.27635i	−0.957816	+	0.287384i	$0.907215\pi$
$632$		0			0
$633$	19.6304	−	30.5455i	0.780239	−	1.21408i
$634$		0			0
$635$	16.3694	+	37.5732i	0.649598	+	1.49105i
$636$		0			0
$637$	2.04766	−	1.77431i	0.0811314	−	0.0703007i
$638$		0			0
$639$	22.3353	−	6.55823i	0.883570	−	0.259440i
$640$		0			0
$641$	0.211030	−	1.46775i	0.00833519	−	0.0579725i	−0.985229	−	0.171240i	$-0.945223\pi$
$641$	0.211030	−	1.46775i	0.00833519	−	0.0579725i	0.993565	+	0.113268i	$0.0361317\pi$
$642$		0			0
$643$			43.3776i			1.71064i	0.518097	+	0.855322i	$0.326641\pi$
$643$			43.3776i			1.71064i	−0.518097	+	0.855322i	$0.673359\pi$
$644$		0			0
$645$	−1.88662	+	1.57773i	−0.0742857	+	0.0621229i
$646$		0			0
$647$	−33.7943	−	4.85889i	−1.32859	−	0.191023i	−0.558792	−	0.829308i	$-0.688735\pi$
$647$	−33.7943	−	4.85889i	−1.32859	−	0.191023i	−0.769800	+	0.638286i	$0.779644\pi$
$648$		0			0
$649$	10.5557	−	3.09943i	0.414348	−	0.121663i
$650$		0			0
$651$	5.78625	+	6.67768i	0.226781	+	0.261719i
$652$		0			0
$653$	−1.54126	+	5.24906i	−0.0603143	+	0.205412i	−0.984137	−	0.177408i	$-0.943229\pi$
$653$	−1.54126	+	5.24906i	−0.0603143	+	0.205412i	0.923823	+	0.382820i	$0.125047\pi$
$654$		0			0
$655$	42.3778	−	5.33662i	1.65584	−	0.208519i
$656$		0			0
$657$	−8.75424	−	7.58559i	−0.341535	−	0.295942i
$658$		0			0
$659$	−1.74138	−	12.1116i	−0.0678345	−	0.471799i	−0.995217	−	0.0976856i	$-0.968856\pi$
$659$	−1.74138	−	12.1116i	−0.0678345	−	0.471799i	0.927383	−	0.374114i	$-0.122053\pi$
$660$		0			0
$661$	−16.4813	−	36.0891i	−0.641050	−	1.40370i	−0.899174	−	0.437592i	$-0.855832\pi$
$661$	−16.4813	−	36.0891i	−0.641050	−	1.40370i	0.258124	−	0.966112i	$-0.416896\pi$
$662$		0			0
$663$	−0.567580	−	0.259205i	−0.0220430	−	0.0100667i
$664$		0			0
$665$	14.6136	+	4.57067i	0.566692	+	0.177243i
$666$		0			0
$667$	32.8293	−	28.7008i	1.27116	−	1.11130i
$668$		0			0
$669$	21.0045	−	13.4988i	0.812083	−	0.521894i
$670$		0			0
$671$	−2.90305	+	6.35680i	−0.112071	+	0.245402i
$672$		0			0
$673$	8.25141	−	3.76829i	0.318069	−	0.145257i	−0.249982	−	0.968250i	$-0.580425\pi$
$673$	8.25141	−	3.76829i	0.318069	−	0.145257i	0.568051	+	0.822993i	$0.307698\pi$
$674$		0			0
$675$	−0.0804593	+	2.29403i	−0.00309688	+	0.0882972i
$676$		0			0
$677$	5.72996	+	4.96504i	0.220220	+	0.190822i	0.757983	−	0.652274i	$-0.226185\pi$
$677$	5.72996	+	4.96504i	0.220220	+	0.190822i	−0.537763	+	0.843096i	$0.680730\pi$
$678$		0			0
$679$	0.966036	+	0.620834i	0.0370731	+	0.0238254i
$680$		0			0
$681$	63.3238	+	18.5935i	2.42657	+	0.712506i
$682$		0			0
$683$	14.8203	−	12.8419i	0.567083	−	0.491381i	−0.323483	−	0.946234i	$-0.604854\pi$
$683$	14.8203	−	12.8419i	0.567083	−	0.491381i	0.890566	+	0.454853i	$0.150308\pi$
$684$		0			0
$685$	−32.7160	−	21.8450i	−1.25001	−	0.834653i
$686$		0			0
$687$	41.1684	+	5.91913i	1.57067	+	0.225829i
$688$		0			0
$689$	−5.15672			−0.196455
$690$		0			0
$691$	25.7648			0.980139			0.490070	−	0.871683i	$-0.336971\pi$
$691$	25.7648			0.980139			0.490070	+	0.871683i	$0.336971\pi$
$692$		0			0
$693$	−3.87224	−	0.556744i	−0.147094	−	0.0211489i
$694$		0			0
$695$	−24.0307	+	35.9895i	−0.911537	+	1.36516i
$696$		0			0
$697$	−0.272007	+	0.235695i	−0.0103030	+	0.00892760i
$698$		0			0
$699$	29.6154	+	8.69586i	1.12016	+	0.328908i
$700$		0			0
$701$	40.3378	+	25.9235i	1.52354	+	0.979117i	0.991169	+	0.132604i	$0.0423338\pi$
$701$	40.3378	+	25.9235i	1.52354	+	0.979117i	0.532367	+	0.846514i	$0.321303\pi$
$702$		0			0
$703$	−10.0961	−	8.74835i	−0.380783	−	0.329950i
$704$		0			0
$705$	31.0080	+	27.8351i	1.16783	+	1.04833i
$706$		0			0
$707$	−7.83492	+	3.57809i	−0.294663	+	0.134568i
$708$		0			0
$709$	14.4640	−	31.6717i	0.543206	−	1.18946i	−0.416676	−	0.909055i	$-0.636805\pi$
$709$	14.4640	−	31.6717i	0.543206	−	1.18946i	0.959883	−	0.280401i	$-0.0904676\pi$
$710$		0			0
$711$	9.06587	−	5.82628i	0.339997	−	0.218503i
$712$		0			0
$713$	14.5903	−	6.74094i	0.546410	−	0.252450i
$714$		0			0
$715$	1.26829	+	0.396681i	0.0474314	+	0.0148350i
$716$		0			0
$717$	36.1888	+	16.5269i	1.35150	+	0.617208i
$718$		0			0
$719$	−12.7948	−	28.0167i	−0.477165	−	1.04485i	−0.983233	−	0.182352i	$-0.941629\pi$
$719$	−12.7948	−	28.0167i	−0.477165	−	1.04485i	0.506068	−	0.862494i	$-0.331098\pi$
$720$		0			0
$721$	2.30414	+	16.0256i	0.0858106	+	0.596826i
$722$		0			0
$723$	−1.50486	−	1.30397i	−0.0559664	−	0.0484951i
$724$		0			0
$725$	30.9577	−	33.2936i	1.14974	−	1.23649i
$726$		0			0
$727$	10.9347	−	37.2403i	0.405547	−	1.38117i	−0.463350	−	0.886175i	$-0.653353\pi$
$727$	10.9347	−	37.2403i	0.405547	−	1.38117i	0.868898	−	0.494992i	$-0.164829\pi$
$728$		0			0
$729$	−15.3693	−	17.7372i	−0.569235	−	0.656932i
$730$		0			0
$731$	−0.242778	+	0.0712860i	−0.00897947	+	0.00263661i
$732$		0			0
$733$	−28.8200	−	4.14369i	−1.06449	−	0.153051i	−0.412257	−	0.911068i	$-0.635259\pi$
$733$	−28.8200	−	4.14369i	−1.06449	−	0.153051i	−0.652235	+	0.758017i	$0.726169\pi$
$734$		0			0
$735$	20.0654	+	23.9939i	0.740122	+	0.885028i
$736$		0			0
$737$		−	0.815712i		−	0.0300471i
$738$		0			0
$739$	3.73825	−	26.0001i	0.137514	−	0.956429i	−0.797879	−	0.602818i	$-0.794045\pi$
$739$	3.73825	−	26.0001i	0.137514	−	0.956429i	0.935392	−	0.353611i	$-0.115046\pi$
$740$		0			0
$741$	6.75897	−	1.98461i	0.248297	−	0.0729066i
$742$		0			0
$743$	−18.7074	+	16.2101i	−0.686309	+	0.594690i	−0.926617	−	0.376006i	$-0.877297\pi$
$743$	−18.7074	+	16.2101i	−0.686309	+	0.594690i	0.240308	+	0.970697i	$0.422752\pi$
$744$		0			0
$745$	20.2905	−	8.83986i	0.743385	−	0.323867i
$746$		0			0
$747$	2.48320	−	3.86393i	0.0908555	−	0.141374i
$748$		0			0
$749$	−5.50575	+	6.35397i	−0.201176	+	0.232169i
$750$		0			0
$751$	−2.92226	−	20.3248i	−0.106635	−	0.741662i	−0.971049	−	0.238881i	$-0.923219\pi$
$751$	−2.92226	−	20.3248i	−0.106635	−	0.741662i	0.864414	−	0.502781i	$-0.167690\pi$
$752$		0			0
$753$	26.9800	−	12.3214i	0.983206	−	0.449015i
$754$		0			0
$755$	2.41506	+	8.79224i	0.0878931	+	0.319982i
$756$		0			0
$757$	0.231468	+	0.360172i	0.00841285	+	0.0130907i	0.845434	−	0.534079i	$-0.179342\pi$
$757$	0.231468	+	0.360172i	0.00841285	+	0.0130907i	−0.837022	+	0.547170i	$0.815705\pi$
$758$		0			0
$759$	−6.05356	+	13.4114i	−0.219730	+	0.486803i
$760$		0			0
$761$	−17.5802	+	11.2981i	−0.637283	+	0.409557i	−0.819000	−	0.573794i	$-0.805471\pi$
$761$	−17.5802	+	11.2981i	−0.637283	+	0.409557i	0.181717	+	0.983351i	$0.441835\pi$
$762$		0			0
$763$	−5.50141	−	2.51241i	−0.199164	−	0.0909554i
$764$		0			0
$765$	1.50242	−	3.14285i	0.0543200	−	0.113630i
$766$		0			0
$767$	3.99384	−	0.574228i	0.144209	−	0.0207342i
$768$		0			0
$769$	9.98028	−	11.5179i	0.359898	−	0.415345i	−0.546707	−	0.837324i	$-0.684119\pi$
$769$	9.98028	−	11.5179i	0.359898	−	0.415345i	0.906606	+	0.421979i	$0.138664\pi$
$770$		0			0
$771$	−35.4016	−	22.7512i	−1.27496	−	0.819365i
$772$		0			0
$773$	−13.7014	+	46.6626i	−0.492804	+	1.67834i	0.218811	+	0.975767i	$0.429782\pi$
$773$	−13.7014	+	46.6626i	−0.492804	+	1.67834i	−0.711615	+	0.702569i	$0.752036\pi$
$774$		0			0
$775$	14.4053	−	8.55955i	0.517454	−	0.307468i
$776$		0			0
$777$	1.58517	+	5.39860i	0.0568677	+	0.193674i
$778$		0			0
$779$	0.578268	−	4.02194i	0.0207186	−	0.144101i
$780$		0			0
$781$	−10.5468			−0.377395
$782$		0			0
$783$		−	4.17426i		−	0.149176i
$784$		0			0
$785$	−3.17539	+	1.96292i	−0.113335	+	0.0700595i
$786$		0			0
$787$	6.99901	+	23.8364i	0.249488	+	0.849677i	0.985057	+	0.172228i	$0.0550965\pi$
$787$	6.99901	+	23.8364i	0.249488	+	0.849677i	−0.735569	+	0.677449i	$0.763085\pi$
$788$		0			0
$789$	−28.8398	−	33.2829i	−1.02672	−	1.18490i
$790$		0			0
$791$	−4.27772	−	1.25605i	−0.152098	−	0.0446600i
$792$		0			0
$793$	−1.38570	+	2.15620i	−0.0492078	+	0.0765688i
$794$		0			0
$795$	1.04347	−	59.5207i	0.0370082	−	2.11098i
$796$		0			0
$797$	−29.1439	+	4.19026i	−1.03233	+	0.148426i	−0.637597	−	0.770370i	$-0.720072\pi$
$797$	−29.1439	+	4.19026i	−1.03233	+	0.148426i	−0.394732	+	0.918796i	$0.629162\pi$
$798$		0			0
$799$	1.78088	+	3.89958i	0.0630030	+	0.137957i
$800$		0			0
$801$	10.9477	−	23.9722i	0.386820	−	0.847017i
$802$		0			0
$803$	2.83741	+	4.41509i	0.100130	+	0.155805i
$804$		0			0
$805$	−10.7334	+	4.73252i	−0.378304	+	0.166799i
$806$		0			0
$807$	11.6079	+	18.0623i	0.408618	+	0.635823i
$808$		0			0
$809$	3.33122	−	7.29435i	0.117119	−	0.256456i	−0.841989	−	0.539495i	$-0.818615\pi$
$809$	3.33122	−	7.29435i	0.117119	−	0.256456i	0.959108	+	0.283039i	$0.0913426\pi$
$810$		0			0
$811$	−0.167974	−	0.367813i	−0.00589838	−	0.0129156i	0.906660	−	0.421862i	$-0.138623\pi$
$811$	−0.167974	−	0.367813i	−0.00589838	−	0.0129156i	−0.912558	+	0.408947i	$0.865896\pi$
$812$		0			0
$813$	6.59271	−	0.947889i	0.231217	−	0.0332439i
$814$		0			0
$815$	−37.3290	−	0.654426i	−1.30758	−	0.0229235i
$816$		0			0
$817$	1.54438	−	2.40310i	0.0540309	−	0.0840737i
$818$		0			0
$819$	−1.37669	−	0.404232i	−0.0481054	−	0.0141250i
$820$		0			0
$821$	0.103064	+	0.118943i	0.00359698	+	0.00415113i	0.757545	−	0.652783i	$-0.226399\pi$
$821$	0.103064	+	0.118943i	0.00359698	+	0.00415113i	−0.753948	+	0.656934i	$0.771853\pi$
$822$		0			0
$823$	6.46276	+	22.0101i	0.225278	+	0.767225i	0.992109	+	0.125377i	$0.0400139\pi$
$823$	6.46276	+	22.0101i	0.225278	+	0.767225i	−0.766832	+	0.641848i	$0.778168\pi$
$824$		0			0
$825$	−4.83527	+	14.5588i	−0.168342	+	0.506872i
$826$		0			0
$827$			8.15555i			0.283596i	0.989896	+	0.141798i	$0.0452884\pi$
$827$			8.15555i			0.283596i	−0.989896	+	0.141798i	$0.954712\pi$
$828$		0			0
$829$	33.4974			1.16341			0.581706	−	0.813399i	$-0.302385\pi$
$829$	33.4974			1.16341			0.581706	+	0.813399i	$0.302385\pi$
$830$		0			0
$831$	3.86429	−	26.8767i	0.134051	−	0.932343i
$832$		0			0
$833$	0.906609	+	3.08763i	0.0314121	+	0.106980i
$834$		0			0
$835$	3.49318	−	21.6005i	0.120886	−	0.747518i
$836$		0			0
$837$	0.433456	−	1.47621i	0.0149824	−	0.0510254i
$838$		0			0
$839$	−28.4517	−	18.2848i	−0.982261	−	0.631261i	−0.0521883	−	0.998637i	$-0.516620\pi$
$839$	−28.4517	−	18.2848i	−0.982261	−	0.631261i	−0.930072	+	0.367377i	$0.880256\pi$
$840$		0			0
$841$	−35.1488	+	40.5639i	−1.21203	+	1.39876i
$842$		0			0
$843$	65.3600	−	9.39734i	2.25112	−	0.323662i
$844$		0			0
$845$	−25.7865	−	12.3271i	−0.887084	−	0.424064i
$846$		0			0
$847$	−9.33292	−	4.26220i	−0.320683	−	0.146451i
$848$		0			0
$849$	−11.2952	+	7.25896i	−0.387649	+	0.249127i
$850$		0			0
$851$	10.2344	−	0.0450587i	0.350831	−	0.00154459i
$852$		0			0
$853$	6.63834	+	10.3295i	0.227293	+	0.353674i	0.936104	−	0.351724i	$-0.114405\pi$
$853$	6.63834	+	10.3295i	0.227293	+	0.353674i	−0.708811	+	0.705398i	$0.750768\pi$
$854$		0			0
$855$	10.4166	+	37.9225i	0.356241	+	1.29692i
$856$		0			0
$857$	−20.4169	+	9.32407i	−0.697427	+	0.318504i	−0.732391	−	0.680884i	$-0.761596\pi$
$857$	−20.4169	+	9.32407i	−0.697427	+	0.318504i	0.0349641	+	0.999389i	$0.488868\pi$
$858$		0			0
$859$	1.32996	+	9.25005i	0.0453775	+	0.315607i	0.999850	+	0.0173091i	$0.00550994\pi$
$859$	1.32996	+	9.25005i	0.0453775	+	0.315607i	−0.954473	+	0.298298i	$0.903581\pi$
$860$		0			0
$861$	−1.12070	+	1.29336i	−0.0381934	+	0.0440776i
$862$		0			0
$863$	21.5836	−	33.5848i	0.734715	−	1.14324i	−0.249861	−	0.968282i	$-0.580385\pi$
$863$	21.5836	−	33.5848i	0.734715	−	1.14324i	0.984576	−	0.174957i	$-0.0559787\pi$
$864$		0			0
$865$	−16.2491	−	37.2972i	−0.552485	−	1.26814i
$866$		0			0
$867$	−30.4068	+	26.3476i	−1.03267	+	0.894813i
$868$		0			0
$869$	−4.68486	+	1.37560i	−0.158923	+	0.0466640i
$870$		0			0
$871$	0.0425770	−	0.296130i	0.00144267	−	0.0100340i
$872$		0			0
$873$			2.94941i			0.0998223i
$874$		0			0
$875$	−10.6217	+	6.06200i	−0.359080	+	0.204933i
$876$		0			0
$877$	−43.8489	−	6.30452i	−1.48067	−	0.212889i	−0.645874	−	0.763444i	$-0.723507\pi$
$877$	−43.8489	−	6.30452i	−1.48067	−	0.212889i	−0.834799	+	0.550555i	$0.814416\pi$
$878$		0			0
$879$	56.7070	−	16.6507i	1.91268	−	0.561613i
$880$		0			0
$881$	19.0187	+	21.9487i	0.640755	+	0.739471i	0.979508	−	0.201404i	$-0.0645505\pi$
$881$	19.0187	+	21.9487i	0.640755	+	0.739471i	−0.338753	+	0.940875i	$0.610005\pi$
$882$		0			0
$883$	−1.28604	+	4.37984i	−0.0432786	+	0.147393i	−0.978298	−	0.207204i	$-0.933564\pi$
$883$	−1.28604	+	4.37984i	−0.0432786	+	0.147393i	0.935019	+	0.354597i	$0.115382\pi$
$884$		0			0
$885$	5.81978	+	46.2145i	0.195630	+	1.55348i
$886$		0			0
$887$	42.4141	+	36.7520i	1.42413	+	1.23401i	0.931485	+	0.363781i	$0.118514\pi$
$887$	42.4141	+	36.7520i	1.42413	+	1.23401i	0.492642	+	0.870232i	$0.336031\pi$
$888$		0			0
$889$	2.85330	+	19.8451i	0.0956965	+	0.665584i
$890$		0			0
$891$	5.04214	+	11.0407i	0.168918	+	0.369879i
$892$		0			0
$893$	−44.0246	−	20.1053i	−1.47323	−	0.672800i
$894$		0			0
$895$	−2.80032	+	8.95334i	−0.0936042	+	0.299277i
$896$		0			0
$897$	−2.89766	+	4.55280i	−0.0967502	+	0.152014i
$898$		0			0
$899$	−25.6344	+	16.4742i	−0.854954	+	0.549446i
$900$		0			0
$901$	2.54424	−	5.57111i	0.0847609	−	0.185600i
$902$		0			0
$903$	−1.09439	+	0.499792i	−0.0364190	+	0.0166320i
$904$		0			0
$905$	−30.2581	−	27.1618i	−1.00581	−	0.902890i
$906$		0			0
$907$	−16.7721	−	14.5331i	−0.556908	−	0.482563i	0.330336	−	0.943863i	$-0.392838\pi$
$907$	−16.7721	−	14.5331i	−0.556908	−	0.482563i	−0.887244	+	0.461300i	$0.847383\pi$
$908$		0			0
$909$	−18.6108	−	11.9604i	−0.617280	−	0.396702i
$910$		0			0
$911$	−6.87200	−	2.01780i	−0.227680	−	0.0668527i	0.165903	−	0.986142i	$-0.446946\pi$
$911$	−6.87200	−	2.01780i	−0.227680	−	0.0668527i	−0.393582	+	0.919289i	$0.628764\pi$
$912$		0			0
$913$	−1.57273	+	1.36277i	−0.0520496	+	0.0451012i
$914$		0			0
$915$	−24.6072	−	16.4306i	−0.813489	−	0.543179i
$916$		0			0
$917$	20.6820	+	2.97362i	0.682980	+	0.0981977i
$918$		0			0
$919$	−30.9993			−1.02257			−0.511286	−	0.859411i	$-0.670831\pi$
$919$	−30.9993			−1.02257			−0.511286	+	0.859411i	$0.670831\pi$
$920$		0			0
$921$	11.5061			0.379138
$922$		0			0
$923$	−3.82884	−	0.550504i	−0.126028	−	0.0181201i
$924$		0			0
$925$	10.6083	−	1.14739i	0.348800	−	0.0377261i
$926$		0			0
$927$	−31.4271	+	27.2317i	−1.03220	+	0.894408i
$928$		0			0
$929$	50.7905	+	14.9134i	1.66638	+	0.489294i	0.972909	−	0.231188i	$-0.0742612\pi$
$929$	50.7905	+	14.9134i	1.66638	+	0.489294i	0.693474	+	0.720482i	$0.256079\pi$
$930$		0			0
$931$	−30.5624	−	19.6412i	−1.00164	−	0.643716i
$932$		0			0
$933$	−42.8982	−	37.1715i	−1.40443	−	1.21694i
$934$		0			0
$935$	−1.05431	+	1.17449i	−0.0344797	+	0.0384101i
$936$		0			0
$937$	−32.1830	+	14.6975i	−1.05137	+	0.480146i	−0.864706	−	0.502278i	$-0.832495\pi$
$937$	−32.1830	+	14.6975i	−1.05137	+	0.480146i	−0.186666	+	0.982423i	$0.559768\pi$
$938$		0			0
$939$	−25.8594	+	56.6242i	−0.843890	+	1.84786i
$940$		0			0
$941$	−20.8031	+	13.3693i	−0.678162	+	0.435828i	−0.833860	−	0.551976i	$-0.813874\pi$
$941$	−20.8031	+	13.3693i	−0.678162	+	0.435828i	0.155698	+	0.987805i	$0.450237\pi$
$942$		0			0
$943$	1.69449	+	2.61133i	0.0551802	+	0.0850365i
$944$		0			0
$945$	−0.335198	+	1.07172i	−0.0109040	+	0.0348629i
$946$		0			0
$947$	10.4549	+	4.77460i	0.339739	+	0.155154i	0.577977	−	0.816053i	$-0.303842\pi$
$947$	10.4549	+	4.77460i	0.339739	+	0.155154i	−0.238238	+	0.971207i	$0.576570\pi$
$948$		0			0
$949$	0.799619	+	1.75092i	0.0259567	+	0.0568373i
$950$		0			0
$951$	2.74032	+	19.0594i	0.0888611	+	0.618042i
$952$		0			0
$953$	−29.0255	−	25.1507i	−0.940227	−	0.814712i	0.0426279	−	0.999091i	$-0.486427\pi$
$953$	−29.0255	−	25.1507i	−0.940227	−	0.814712i	−0.982855	+	0.184379i	$0.940972\pi$
$954$		0			0
$955$	38.6083	−	4.86193i	1.24933	−	0.157328i
$956$		0			0
$957$	7.85954	−	26.7671i	0.254063	−	0.865259i
$958$		0			0
$959$	−12.6023	−	14.5438i	−0.406950	−	0.469645i
$960$		0			0
$961$	18.9681	−	5.56953i	0.611874	−	0.179662i
$962$		0			0
$963$	−21.3743	−	3.07317i	−0.688778	−	0.0990314i
$964$		0			0
$965$	27.8158	+	33.2618i	0.895424	+	1.07074i
$966$		0			0
$967$		−	8.77787i		−	0.282277i	−0.989990	−	0.141139i	$-0.954924\pi$
$967$		−	8.77787i		−	0.282277i	0.989990	−	0.141139i	$-0.0450763\pi$
$968$		0			0
$969$	−1.19067	+	8.28129i	−0.0382498	+	0.266033i
$970$		0			0
$971$	−23.0500	+	6.76810i	−0.739711	+	0.217199i	−0.629816	−	0.776745i	$-0.716870\pi$
$971$	−23.0500	+	6.76810i	−0.739711	+	0.217199i	−0.109895	+	0.993943i	$0.535051\pi$
$972$		0			0
$973$	−15.9991	+	13.8633i	−0.512907	+	0.444436i
$974$		0			0
$975$	−2.51527	+	5.03293i	−0.0805532	+	0.161183i
$976$		0			0
$977$	−28.6748	+	44.6189i	−0.917389	+	1.42749i	−0.0134090	+	0.999910i	$0.504268\pi$
$977$	−28.6748	+	44.6189i	−0.917389	+	1.42749i	−0.903980	+	0.427575i	$0.859368\pi$
$978$		0			0
$979$	−7.81922	+	9.02386i	−0.249903	+	0.288404i
$980$		0			0
$981$	−2.21069	−	15.3757i	−0.0705817	−	0.490907i
$982$		0			0
$983$	−18.4280	+	8.41576i	−0.587760	+	0.268421i	−0.687018	−	0.726641i	$-0.741081\pi$
$983$	−18.4280	+	8.41576i	−0.587760	+	0.268421i	0.0992574	+	0.995062i	$0.468353\pi$
$984$		0			0
$985$	29.6765	−	8.15158i	0.945573	−	0.259731i
$986$		0			0
$987$	11.0205	+	17.1482i	0.350786	+	0.545833i
$988$		0			0
$989$	0.320981	+	2.16477i	0.0102066	+	0.0688358i
$990$		0			0
$991$	−20.0243	+	12.8689i	−0.636094	+	0.408793i	−0.818561	−	0.574419i	$-0.805228\pi$
$991$	−20.0243	+	12.8689i	−0.636094	+	0.408793i	0.182467	+	0.983212i	$0.441592\pi$
$992$		0			0
$993$	50.5988	+	23.1077i	1.60570	+	0.733300i
$994$		0			0
$995$	−24.2889	−	11.6112i	−0.770011	−	0.368099i
$996$		0			0
$997$	24.5769	−	3.53362i	0.778358	−	0.111911i	0.258326	−	0.966058i	$-0.416829\pi$
$997$	24.5769	−	3.53362i	0.778358	−	0.111911i	0.520032	+	0.854147i	$0.325920\pi$
$998$		0			0
$999$	0.641576	−	0.740418i	0.0202986	−	0.0234258i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	460.2.s.a.449.11	yes	120
5.4	even	2	inner	460.2.s.a.449.2	yes	120
23.2	even	11	inner	460.2.s.a.209.2	✓	120
115.94	even	22	inner	460.2.s.a.209.11	yes	120

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
460.2.s.a.209.2	✓	120	23.2	even	11	inner
460.2.s.a.209.11	yes	120	115.94	even	22	inner
460.2.s.a.449.2	yes	120	5.4	even	2	inner
460.2.s.a.449.11	yes	120	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 460 = 2^{2} \cdot 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	460.s (of order \(22\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(2.38576 + 0.343021i) q^{3} +(1.24170 - 1.85962i) q^{5} +(0.826691 - 0.716332i) q^{7} +(2.69572 + 0.791536i) q^{9} +O(q^{10})\)	\(q+(2.38576 + 0.343021i) q^{3} +(1.24170 - 1.85962i) q^{5} +(0.826691 - 0.716332i) q^{7} +(2.69572 + 0.791536i) q^{9} +(-1.07086 - 0.688200i) q^{11} +(-0.352835 - 0.305734i) q^{13} +(3.60028 - 4.01069i) q^{15} +(0.504385 - 0.230345i) q^{17} +(-2.60049 + 5.69429i) q^{19} +(2.21801 - 1.42543i) q^{21} +(-1.37139 - 4.59557i) q^{23} +(-1.91638 - 4.61817i) q^{25} +(-0.417601 - 0.190712i) q^{27} +(3.77717 + 8.27084i) q^{29} +(0.476938 + 3.31718i) q^{31} +(-2.31875 - 2.00921i) q^{33} +(-0.305606 - 2.42680i) q^{35} +(-0.601229 + 2.04760i) q^{37} +(-0.736909 - 0.850438i) q^{39} +(-0.622798 + 0.182870i) q^{41} +(-0.451677 - 0.0649413i) q^{43} +(4.81923 - 4.03018i) q^{45} +7.73135i q^{47} +(-0.825917 + 5.74438i) q^{49} +(1.28236 - 0.376534i) q^{51} +(8.34751 - 7.23316i) q^{53} +(-2.60947 + 1.13686i) q^{55} +(-8.15743 + 12.6932i) q^{57} +(-5.65964 + 6.53157i) q^{59} +(-0.781299 - 5.43405i) q^{61} +(2.79554 - 1.27668i) q^{63} +(-1.00666 + 0.276512i) q^{65} +(0.346449 + 0.539086i) q^{67} +(-1.69543 - 11.4344i) q^{69} +(6.97016 - 4.47945i) q^{71} +(-3.75036 - 1.71273i) q^{73} +(-2.98789 - 11.6752i) q^{75} +(-1.37825 + 0.198162i) q^{77} +(2.51187 - 2.89886i) q^{79} +(-8.02146 - 5.15508i) q^{81} +(0.460581 - 1.56860i) q^{83} +(0.197939 - 1.22398i) q^{85} +(6.17435 + 21.0279i) q^{87} +(1.33493 - 9.28465i) q^{89} -0.510693 q^{91} +8.07760i q^{93} +(7.36019 + 11.9065i) q^{95} +(0.295759 + 1.00726i) q^{97} +(-2.34201 - 2.70282i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 120 q + 20 q^{9}+O(q^{10}) \) 120 * q + 20 * q^9	\( 120 q + 20 q^{9} - 4 q^{11} + 9 q^{15} + 8 q^{19} + 14 q^{25} + 10 q^{29} - 18 q^{31} + 10 q^{35} - 60 q^{39} + 2 q^{41} - 2 q^{45} - 28 q^{49} + 24 q^{51} + 6 q^{55} - 36 q^{61} + 39 q^{65} + 118 q^{69} - 76 q^{71} + 83 q^{75} + 64 q^{79} - 160 q^{81} + 38 q^{85} - 48 q^{89} - 80 q^{91} + 21 q^{95} - 142 q^{99}+O(q^{100}) \) 120 * q + 20 * q^9 - 4 * q^11 + 9 * q^15 + 8 * q^19 + 14 * q^25 + 10 * q^29 - 18 * q^31 + 10 * q^35 - 60 * q^39 + 2 * q^41 - 2 * q^45 - 28 * q^49 + 24 * q^51 + 6 * q^55 - 36 * q^61 + 39 * q^65 + 118 * q^69 - 76 * q^71 + 83 * q^75 + 64 * q^79 - 160 * q^81 + 38 * q^85 - 48 * q^89 - 80 * q^91 + 21 * q^95 - 142 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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