LMFDB - Embedded newform 912.2.r.a.341.14

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [912,2,Mod(341,912)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(912, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([0, 1, 2, 2]))

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

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

chi := DirichletCharacter("912.341");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 912 = 2^{4} \cdot 3 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	912.r (of order $4$, degree $2$, 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:	$7.28235666434$
Analytic rank:	$0$
Dimension:	$312$
Relative dimension:	$156$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			341.14
Character	$\chi$	$=$	912.341
Dual form			912.2.r.a.797.14

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.36478 - 0.370630i) q^{2} +(0.456392 + 1.67084i) q^{3} +(1.72527 + 1.01166i) q^{4} +(-2.14913 + 2.14913i) q^{5} +(-0.00361275 - 2.44949i) q^{6} -1.36586i q^{7} +(-1.97966 - 2.02013i) q^{8} +(-2.58341 + 1.52512i) q^{9} +(3.72963 - 2.13657i) q^{10} +(4.29065 - 4.29065i) q^{11} +(-0.902922 + 3.34436i) q^{12} +(-1.95516 - 1.95516i) q^{13} +(-0.506229 + 1.86410i) q^{14} +(-4.57170 - 2.61001i) q^{15} +(1.95309 + 3.49076i) q^{16} -4.16497i q^{17} +(4.09105 - 1.12396i) q^{18} +(-2.11627 - 3.81069i) q^{19} +(-5.88201 + 1.53364i) q^{20} +(2.28213 - 0.623368i) q^{21} +(-7.44606 + 4.26557i) q^{22} +6.21545 q^{23} +(2.47181 - 4.22967i) q^{24} -4.23753i q^{25} +(1.94373 + 3.39301i) q^{26} +(-3.72727 - 3.62042i) q^{27} +(1.38179 - 2.35647i) q^{28} +(-4.85406 + 4.85406i) q^{29} +(5.27203 + 5.25650i) q^{30} -5.08846i q^{31} +(-1.37177 - 5.48801i) q^{32} +(9.12722 + 5.21078i) q^{33} +(-1.54366 + 5.68429i) q^{34} +(2.93541 + 2.93541i) q^{35} +(-5.99997 + 0.0176988i) q^{36} +(2.68391 - 2.68391i) q^{37} +(1.47589 + 5.98513i) q^{38} +(2.37444 - 4.15908i) q^{39} +(8.59608 + 0.0869664i) q^{40} -3.35540i q^{41} +(-3.34566 + 0.00493452i) q^{42} +(-4.09025 - 4.09025i) q^{43} +(11.7432 - 3.06185i) q^{44} +(2.27442 - 8.82976i) q^{45} +(-8.48274 - 2.30363i) q^{46} +1.02514i q^{47} +(-4.94113 + 4.85646i) q^{48} +5.13442 q^{49} +(-1.57055 + 5.78330i) q^{50} +(6.95900 - 1.90086i) q^{51} +(-1.39522 - 5.35113i) q^{52} +(2.02254 + 2.02254i) q^{53} +(3.74508 + 6.32253i) q^{54} +18.4424i q^{55} +(-2.75922 + 2.70395i) q^{56} +(5.40121 - 5.27512i) q^{57} +(8.42380 - 4.82568i) q^{58} +(10.4708 + 10.4708i) q^{59} +(-5.24696 - 9.12796i) q^{60} +(-7.60676 + 7.60676i) q^{61} +(-1.88594 + 6.94465i) q^{62} +(2.08310 + 3.52858i) q^{63} +(-0.161855 + 7.99836i) q^{64} +8.40379 q^{65} +(-10.5254 - 10.4944i) q^{66} +(2.86442 + 2.86442i) q^{67} +(4.21353 - 7.18569i) q^{68} +(2.83668 + 10.3850i) q^{69} +(-2.91825 - 5.09415i) q^{70} +1.11068i q^{71} +(8.19522 + 2.19961i) q^{72} -1.67722i q^{73} +(-4.65769 + 2.66822i) q^{74} +(7.08023 - 1.93397i) q^{75} +(0.203990 - 8.71541i) q^{76} +(-5.86044 - 5.86044i) q^{77} +(-4.78208 + 4.79621i) q^{78} +2.48897i q^{79} +(-11.6996 - 3.30466i) q^{80} +(4.34805 - 7.88001i) q^{81} +(-1.24361 + 4.57940i) q^{82} +(-11.5626 - 11.5626i) q^{83} +(4.56793 + 1.23327i) q^{84} +(8.95107 + 8.95107i) q^{85} +(4.06634 + 7.09828i) q^{86} +(-10.3257 - 5.89501i) q^{87} +(-17.1617 - 0.173625i) q^{88} -17.2247i q^{89} +(-6.37666 + 11.2077i) q^{90} +(-2.67048 + 2.67048i) q^{91} +(10.7233 + 6.28792i) q^{92} +(8.50201 - 2.32233i) q^{93} +(0.379948 - 1.39910i) q^{94} +(12.7378 + 3.64154i) q^{95} +(8.54352 - 4.79669i) q^{96} -10.7797i q^{97} +(-7.00738 - 1.90297i) q^{98} +(-4.54079 + 17.6283i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 312 q - 8 q^{4} - 4 q^{6} - 12 q^{19} - 20 q^{24} + 24 q^{28} - 40 q^{30} + 12 q^{36} + 60 q^{42} - 8 q^{43} - 24 q^{45} - 280 q^{49} + 40 q^{54} - 8 q^{58} - 40 q^{61} + 48 q^{63} + 40 q^{64} - 68 q^{66}+ \cdots - 8 q^{99}+O(q^{100}) $ 312 * q - 8 * q^4 - 4 * q^6 - 12 * q^19 - 20 * q^24 + 24 * q^28 - 40 * q^30 + 12 * q^36 + 60 * q^42 - 8 * q^43 - 24 * q^45 - 280 * q^49 + 40 * q^54 - 8 * q^58 - 40 * q^61 + 48 * q^63 + 40 * q^64 - 68 * q^66 + 32 * q^76 - 8 * q^81 - 32 * q^82 + 8 * q^93 + 120 * q^96 - 8 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/912\mathbb{Z}\right)^\times$.

$n$	$97$	$229$	$305$	$799$
$\chi(n)$	$-1$	$e\left(\frac{1}{4}\right)$	$-1$	$1$

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 $

$2$	−1.36478	−	0.370630i	−0.965048	−	0.262075i
$2$	−1.36478	−	0.370630i	−0.965048	−	0.262075i
$3$	0.456392	+	1.67084i	0.263498	+	0.964660i
$3$	0.456392	+	1.67084i	0.263498	+	0.964660i
$4$	1.72527	+	1.01166i	0.862634	+	0.505829i
$5$	−2.14913	+	2.14913i	−0.961120	+	0.961120i	−0.999272	−	0.0381515i	$-0.987853\pi$
$5$	−2.14913	+	2.14913i	−0.961120	+	0.961120i	0.0381515	+	0.999272i	$0.487853\pi$
$6$	−0.00361275	−	2.44949i	−0.00147490	−	0.999999i
$7$		−	1.36586i		−	0.516247i	−0.966112	−	0.258123i	$-0.916896\pi$
$7$		−	1.36586i		−	0.516247i	0.966112	−	0.258123i	$-0.0831041\pi$
$8$	−1.97966	−	2.02013i	−0.699917	−	0.714224i
$9$	−2.58341	+	1.52512i	−0.861138	+	0.508372i
$10$	3.72963	−	2.13657i	1.17941	−	0.675641i
$11$	4.29065	−	4.29065i	1.29368	−	1.29368i	0.361188	−	0.932493i	$-0.382371\pi$
$11$	4.29065	−	4.29065i	1.29368	−	1.29368i	0.932493	−	0.361188i	$-0.117629\pi$
$12$	−0.902922	+	3.34436i	−0.260651	+	0.965433i
$13$	−1.95516	−	1.95516i	−0.542264	−	0.542264i	0.381928	−	0.924192i	$-0.375260\pi$
$13$	−1.95516	−	1.95516i	−0.542264	−	0.542264i	−0.924192	+	0.381928i	$0.875260\pi$
$14$	−0.506229	+	1.86410i	−0.135295	+	0.498203i
$15$	−4.57170	−	2.61001i	−1.18041	−	0.673901i
$16$	1.95309	+	3.49076i	0.488273	+	0.872691i
$17$		−	4.16497i		−	1.01015i	−0.863074	−	0.505077i	$-0.831464\pi$
$17$		−	4.16497i		−	1.01015i	0.863074	−	0.505077i	$-0.168536\pi$
$18$	4.09105	−	1.12396i	0.964270	−	0.264920i
$19$	−2.11627	−	3.81069i	−0.485506	−	0.874233i
$19$	−2.11627	−	3.81069i	−0.485506	−	0.874233i
$20$	−5.88201	+	1.53364i	−1.31526	+	0.342932i
$21$	2.28213	−	0.623368i	0.498003	−	0.136030i
$22$	−7.44606	+	4.26557i	−1.58751	+	0.909422i
$23$	6.21545			1.29601			0.648006	−	0.761636i	$-0.275603\pi$
$23$	6.21545			1.29601			0.648006	+	0.761636i	$0.275603\pi$
$24$	2.47181	−	4.22967i	0.504557	−	0.863379i
$25$		−	4.23753i		−	0.847505i
$26$	1.94373	+	3.39301i	0.381197	+	0.665424i
$27$	−3.72727	−	3.62042i	−0.717314	−	0.696750i
$28$	1.38179	−	2.35647i	0.261133	−	0.445332i
$29$	−4.85406	+	4.85406i	−0.901377	+	0.901377i	−0.995555	−	0.0941787i	$-0.969978\pi$
$29$	−4.85406	+	4.85406i	−0.901377	+	0.901377i	0.0941787	+	0.995555i	$0.469978\pi$
$30$	5.27203	+	5.25650i	0.962537	+	0.959702i
$31$		−	5.08846i		−	0.913915i	−0.889488	−	0.456958i	$-0.848939\pi$
$31$		−	5.08846i		−	0.913915i	0.889488	−	0.456958i	$-0.151061\pi$
$32$	−1.37177	−	5.48801i	−0.242496	−	0.970152i
$33$	9.12722	+	5.21078i	1.58884	+	0.907080i
$34$	−1.54366	+	5.68429i	−0.264736	+	0.974847i
$35$	2.93541	+	2.93541i	0.496175	+	0.496175i
$36$	−5.99997	+	0.0176988i	−0.999996	+	0.00294980i
$37$	2.68391	−	2.68391i	0.441232	−	0.441232i	−0.451194	−	0.892426i	$-0.649002\pi$
$37$	2.68391	−	2.68391i	0.441232	−	0.441232i	0.892426	+	0.451194i	$0.149002\pi$
$38$	1.47589	+	5.98513i	0.239422	+	0.970916i
$39$	2.37444	−	4.15908i	0.380215	−	0.665986i
$40$	8.59608	+	0.0869664i	1.35916	+	0.0137506i
$41$		−	3.35540i		−	0.524026i	−0.965064	−	0.262013i	$-0.915614\pi$
$41$		−	3.35540i		−	0.524026i	0.965064	−	0.262013i	$-0.0843864\pi$
$42$	−3.34566	+	0.00493452i	−0.516246	+	0.000761412i
$43$	−4.09025	−	4.09025i	−0.623758	−	0.623758i	0.322732	−	0.946490i	$-0.395399\pi$
$43$	−4.09025	−	4.09025i	−0.623758	−	0.623758i	−0.946490	+	0.322732i	$0.895399\pi$
$44$	11.7432	−	3.06185i	1.77035	−	0.461591i
$45$	2.27442	−	8.82976i	0.339050	−	1.31626i
$46$	−8.48274	−	2.30363i	−1.25071	−	0.339652i
$47$			1.02514i			0.149532i	0.997201	+	0.0747662i	$0.0238210\pi$
$47$			1.02514i			0.149532i	−0.997201	+	0.0747662i	$0.976179\pi$
$48$	−4.94113	+	4.85646i	−0.713191	+	0.700970i
$49$	5.13442			0.733489
$50$	−1.57055	+	5.78330i	−0.222110	+	0.817883i
$51$	6.95900	−	1.90086i	0.974455	−	0.266174i
$52$	−1.39522	−	5.35113i	−0.193482	−	0.742068i
$53$	2.02254	+	2.02254i	0.277817	+	0.277817i	0.832237	−	0.554420i	$-0.187060\pi$
$53$	2.02254	+	2.02254i	0.277817	+	0.277817i	−0.554420	+	0.832237i	$0.687060\pi$
$54$	3.74508	+	6.32253i	0.509641	+	0.860387i
$55$			18.4424i			2.48677i
$56$	−2.75922	+	2.70395i	−0.368716	+	0.361330i
$57$	5.40121	−	5.27512i	0.715408	−	0.698707i
$58$	8.42380	−	4.82568i	1.10610	−	0.633643i
$59$	10.4708	+	10.4708i	1.36319	+	1.36319i	0.869825	+	0.493361i	$0.164232\pi$
$59$	10.4708	+	10.4708i	1.36319	+	1.36319i	0.493361	+	0.869825i	$0.335768\pi$
$60$	−5.24696	−	9.12796i	−0.677380	−	1.17841i
$61$	−7.60676	+	7.60676i	−0.973945	+	0.973945i	−0.999669	−	0.0257236i	$-0.991811\pi$
$61$	−7.60676	+	7.60676i	−0.973945	+	0.973945i	0.0257236	+	0.999669i	$0.491811\pi$
$62$	−1.88594	+	6.94465i	−0.239514	+	0.881972i
$63$	2.08310	+	3.52858i	0.262445	+	0.444560i
$64$	−0.161855	+	7.99836i	−0.0202319	+	0.999795i
$65$	8.40379			1.04236
$66$	−10.5254	−	10.4944i	−1.29559	−	1.29177i
$67$	2.86442	+	2.86442i	0.349945	+	0.349945i	0.860089	−	0.510144i	$-0.170408\pi$
$67$	2.86442	+	2.86442i	0.349945	+	0.349945i	−0.510144	+	0.860089i	$0.670408\pi$
$68$	4.21353	−	7.18569i	0.510966	−	0.871393i
$69$	2.83668	+	10.3850i	0.341496	+	1.25021i
$70$	−2.91825	−	5.09415i	−0.348798	−	0.608868i
$71$			1.11068i			0.131813i	0.997826	+	0.0659067i	$0.0209940\pi$
$71$			1.11068i			0.131813i	−0.997826	+	0.0659067i	$0.979006\pi$
$72$	8.19522	+	2.19961i	0.965816	+	0.259227i
$73$		−	1.67722i		−	0.196304i	−0.995171	−	0.0981521i	$-0.968707\pi$
$73$		−	1.67722i		−	0.196304i	0.995171	−	0.0981521i	$-0.0312932\pi$
$74$	−4.65769	+	2.66822i	−0.541445	+	0.310174i
$75$	7.08023	−	1.93397i	0.817554	−	0.223316i
$76$	0.203990	−	8.71541i	0.0233993	−	0.999726i
$77$	−5.86044	−	5.86044i	−0.667859	−	0.667859i
$78$	−4.78208	+	4.79621i	−0.541464	+	0.543063i
$79$			2.48897i			0.280030i	0.990149	+	0.140015i	$0.0447152\pi$
$79$			2.48897i			0.280030i	−0.990149	+	0.140015i	$0.955285\pi$
$80$	−11.6996	−	3.30466i	−1.30805	−	0.369472i
$81$	4.34805	−	7.88001i	0.483116	−	0.875556i
$82$	−1.24361	+	4.57940i	−0.137334	+	0.505710i
$83$	−11.5626	−	11.5626i	−1.26916	−	1.26916i	−0.946522	−	0.322639i	$-0.895430\pi$
$83$	−11.5626	−	11.5626i	−1.26916	−	1.26916i	−0.322639	−	0.946522i	$-0.604570\pi$
$84$	4.56793	+	1.23327i	0.498402	+	0.134560i
$85$	8.95107	+	8.95107i	0.970880	+	0.970880i
$86$	4.06634	+	7.09828i	0.438485	+	0.765427i
$87$	−10.3257	−	5.89501i	−1.10703	−	0.632011i
$88$	−17.1617	−	0.173625i	−1.82945	−	0.0185085i
$89$		−	17.2247i		−	1.82581i	−0.408172	−	0.912905i	$-0.633834\pi$
$89$		−	17.2247i		−	1.82581i	0.408172	−	0.912905i	$-0.366166\pi$
$90$	−6.37666	+	11.2077i	−0.672159	+	1.18140i
$91$	−2.67048	+	2.67048i	−0.279942	+	0.279942i
$92$	10.7233	+	6.28792i	1.11798	+	0.655561i
$93$	8.50201	−	2.32233i	0.881617	−	0.240815i
$94$	0.379948	−	1.39910i	0.0391887	−	0.144306i
$95$	12.7378	+	3.64154i	1.30687	+	0.373614i
$96$	8.54352	−	4.79669i	0.871970	−	0.489560i
$97$		−	10.7797i		−	1.09451i	−0.836967	−	0.547254i	$-0.815673\pi$
$97$		−	10.7797i		−	1.09451i	0.836967	−	0.547254i	$-0.184327\pi$
$98$	−7.00738	−	1.90297i	−0.707852	−	0.192229i
$99$	−4.54079	+	17.6283i	−0.456367	+	1.77171i
$100$	4.28693	−	7.31086i	0.428693	−	0.731086i
$101$	13.4359	−	13.4359i	1.33692	−	1.33692i	0.437894	−	0.899027i	$-0.355725\pi$
$101$	13.4359	−	13.4359i	1.33692	−	1.33692i	0.899027	−	0.437894i	$-0.144275\pi$
$102$	−10.2020	+	0.0150470i	−1.01015	+	0.00148988i
$103$	−4.53600			−0.446945			−0.223472	−	0.974710i	$-0.571739\pi$
$103$	−4.53600			−0.446945			−0.223472	+	0.974710i	$0.571739\pi$
$104$	−0.0791173	+	7.82024i	−0.00775809	+	0.766838i
$105$	−3.56491	+	6.24430i	−0.347899	+	0.609382i
$106$	−2.01071	−	3.50994i	−0.195298	−	0.340915i
$107$	−1.05842	−	1.05842i	−0.102321	−	0.102321i	0.654093	−	0.756414i	$-0.273051\pi$
$107$	−1.05842	−	1.05842i	−0.102321	−	0.102321i	−0.756414	+	0.654093i	$0.773051\pi$
$108$	−2.76791	−	10.0169i	−0.266342	−	0.963878i
$109$	5.11383	+	5.11383i	0.489816	+	0.489816i	0.908248	−	0.418432i	$-0.137420\pi$
$109$	5.11383	+	5.11383i	0.489816	+	0.489816i	−0.418432	+	0.908248i	$0.637420\pi$
$110$	6.83529	−	25.1698i	0.651719	−	2.39985i
$111$	5.70930	+	3.25947i	0.541902	+	0.309375i
$112$	4.76790	−	2.66765i	0.450524	−	0.252069i
$113$	5.04950			0.475017			0.237509	−	0.971385i	$-0.423669\pi$
$113$	5.04950			0.475017			0.237509	+	0.971385i	$0.423669\pi$
$114$	−9.32660	+	5.19755i	−0.873516	+	0.486795i
$115$	−13.3578	+	13.3578i	−1.24562	+	1.24562i
$116$	−13.2852	+	3.46390i	−1.23350	+	0.321615i
$117$	8.03283	+	2.06914i	0.742636	+	0.191292i
$118$	−10.4096	−	18.1712i	−0.958282	−	1.67280i
$119$	−5.68877			−0.521489
$120$	3.77788	+	14.4024i	0.344871	+	1.31475i
$121$		−	25.8194i		−	2.34722i
$122$	13.2009	−	7.56228i	1.19515	−	0.684657i
$123$	5.60634	−	1.53138i	0.505507	−	0.138080i
$124$	5.14779	−	8.77896i	0.462285	−	0.788374i
$125$	−1.63866	−	1.63866i	−0.146566	−	0.146566i
$126$	−1.53518	−	5.58781i	−0.136764	−	0.497801i
$127$		−	12.9470i		−	1.14886i	−0.818554	−	0.574429i	$-0.805224\pi$
$127$		−	12.9470i		−	1.14886i	0.818554	−	0.574429i	$-0.194776\pi$
$128$	3.18533	−	10.8560i	0.281546	−	0.959548i
$129$	4.96740	−	8.70092i	0.437355	−	0.766073i
$130$	−11.4694	−	3.11470i	−1.00593	−	0.273177i
$131$	4.56832	+	4.56832i	0.399136	+	0.399136i	0.877928	−	0.478792i	$-0.158925\pi$
$131$	4.56832	+	4.56832i	0.399136	+	0.399136i	−0.478792	+	0.877928i	$0.658925\pi$
$132$	10.4754	+	18.2236i	0.911763	+	1.58616i
$133$	−5.20488	+	2.89053i	−0.451320	+	0.250641i
$134$	−2.84767	−	4.97095i	−0.246001	−	0.429425i
$135$	15.7912	−	0.229641i	1.35909	−	0.0197643i
$136$	−8.41379	+	8.24525i	−0.721476	+	0.707024i
$137$	−10.1075			−0.863542			−0.431771	−	0.901983i	$-0.642111\pi$
$137$	−10.1075			−0.863542			−0.431771	+	0.901983i	$0.642111\pi$
$138$	−0.0224549	−	15.2247i	−0.00191149	−	1.29601i
$139$	4.53118	+	4.53118i	0.384330	+	0.384330i	0.872659	−	0.488329i	$-0.162394\pi$
$139$	4.53118	+	4.53118i	0.384330	+	0.384330i	−0.488329	+	0.872659i	$0.662394\pi$
$140$	2.09473	+	8.03401i	0.177037	+	0.678998i
$141$	−1.71285	+	0.467867i	−0.144248	+	0.0394015i
$142$	0.411651	−	1.51584i	0.0345450	−	0.127206i
$143$	−16.7778			−1.40303
$144$	−10.3695	−	6.03939i	−0.864122	−	0.503283i
$145$		−	20.8640i		−	1.73266i
$146$	−0.621629	+	2.28905i	−0.0514464	+	0.189443i
$147$	2.34331	+	8.57880i	0.193273	+	0.707568i
$148$	7.34566	−	1.91526i	0.603809	−	0.157433i
$149$	−11.4575	+	11.4575i	−0.938635	+	0.938635i	−0.998223	−	0.0595877i	$-0.981021\pi$
$149$	−11.4575	+	11.4575i	−0.938635	+	0.938635i	0.0595877	+	0.998223i	$0.481021\pi$
$150$	−10.3798	+	0.0153091i	−0.847504	+	0.00124999i
$151$	2.95342			0.240346			0.120173	−	0.992753i	$-0.461655\pi$
$151$	2.95342			0.240346			0.120173	+	0.992753i	$0.461655\pi$
$152$	−3.50859	+	11.8190i	−0.284585	+	0.958651i
$153$	6.35206	+	10.7598i	0.513534	+	0.869882i
$154$	5.82617	+	10.1703i	0.469486	+	0.819544i
$155$	10.9358	+	10.9358i	0.878383	+	0.878383i
$156$	8.30412	−	4.77340i	0.664861	−	0.382178i
$157$	0.665933	−	0.665933i	0.0531473	−	0.0531473i	−0.680034	−	0.733181i	$-0.738035\pi$
$157$	0.665933	−	0.665933i	0.0531473	−	0.0531473i	0.733181	+	0.680034i	$0.238035\pi$
$158$	0.922485	−	3.39690i	0.0733889	−	0.270243i
$159$	−2.45627	+	4.30240i	−0.194795	+	0.341203i
$160$	14.7426	+	8.84634i	1.16550	+	0.699365i
$161$		−	8.48944i		−	0.669062i
$162$	−8.85471	+	9.14299i	−0.695691	+	0.718341i
$163$	2.14466	−	2.14466i	0.167983	−	0.167983i	−0.618109	−	0.786092i	$-0.712101\pi$
$163$	2.14466	−	2.14466i	0.167983	−	0.167983i	0.786092	+	0.618109i	$0.212101\pi$
$164$	3.39452	−	5.78897i	0.265068	−	0.452043i
$165$	−30.8142	+	8.41694i	−2.39888	+	0.655258i
$166$	11.4950	+	20.0659i	0.892186	+	1.55742i
$167$		−	23.6874i		−	1.83299i	−0.400046	−	0.916495i	$-0.631006\pi$
$167$		−	23.6874i		−	1.83299i	0.400046	−	0.916495i	$-0.368994\pi$
$168$	−5.77715	−	3.37615i	−0.445716	−	0.260476i
$169$		−	5.35469i		−	0.411899i
$170$	−8.89874	−	15.5338i	−0.682502	−	1.19139i
$171$	11.2790	+	6.61704i	0.862523	+	0.506018i
$172$	−2.91884	−	11.1947i	−0.222559	−	0.853589i
$173$	−4.82567	+	4.82567i	−0.366889	+	0.366889i	−0.866341	−	0.499452i	$-0.833535\pi$
$173$	−4.82567	+	4.82567i	−0.366889	+	0.366889i	0.499452	+	0.866341i	$0.333535\pi$
$174$	11.9075	+	11.8724i	0.902705	+	0.900046i
$175$	−5.78787			−0.437522
$176$	23.3577	+	6.59761i	1.76065	+	0.497314i
$177$	−12.7163	+	22.2739i	−0.955814	+	1.67421i
$178$	−6.38397	+	23.5079i	−0.478499	+	1.76199i
$179$	−12.2681	+	12.2681i	−0.916962	+	0.916962i	−0.996807	−	0.0798449i	$-0.974558\pi$
$179$	−12.2681	+	12.2681i	−0.916962	+	0.916962i	0.0798449	+	0.996807i	$0.474558\pi$
$180$	12.8567	−	12.9328i	0.958281	−	0.963951i
$181$	11.1824	−	11.1824i	0.831185	−	0.831185i	−0.156494	−	0.987679i	$-0.550019\pi$
$181$	11.1824	−	11.1824i	0.831185	−	0.831185i	0.987679	+	0.156494i	$0.0500193\pi$
$182$	4.63438	−	2.65486i	0.343523	−	0.196792i
$183$	−16.1813	−	9.23801i	−1.19616	−	0.682894i
$184$	−12.3045	−	12.5560i	−0.907100	−	0.925642i
$185$			11.5361i			0.848154i
$186$	−12.4641	+	0.0183834i	−0.913914	+	0.00134793i
$187$	−17.8705	−	17.8705i	−1.30682	−	1.30682i
$188$	−1.03709	+	1.76864i	−0.0756379	+	0.128992i
$189$	−4.94499	+	5.09094i	−0.359695	+	0.370311i
$190$	−16.0347	−	9.69093i	−1.16328	−	0.703054i
$191$			10.8481i			0.784939i	0.919765	+	0.392469i	$0.128379\pi$
$191$			10.8481i			0.784939i	−0.919765	+	0.392469i	$0.871621\pi$
$192$	−13.4379	+	3.37995i	−0.969794	+	0.243927i
$193$		−	0.604176i		−	0.0434895i	−0.999764	−	0.0217448i	$-0.993078\pi$
$193$		−	0.604176i		−	0.0434895i	0.999764	−	0.0217448i	$-0.00692212\pi$
$194$	−3.99526	+	14.7119i	−0.286843	+	1.05625i
$195$	3.83542	+	14.0414i	0.274660	+	1.00553i
$196$	8.85825	+	5.19429i	0.632732	+	0.371020i
$197$	−3.01797	+	3.01797i	−0.215022	+	0.215022i	−0.806397	−	0.591375i	$-0.798585\pi$
$197$	−3.01797	+	3.01797i	−0.215022	+	0.215022i	0.591375	+	0.806397i	$0.298585\pi$
$198$	12.7308	−	22.3758i	0.904736	−	1.59018i
$199$			22.8685i			1.62110i	0.585668	+	0.810551i	$0.300832\pi$
$199$			22.8685i			1.62110i	−0.585668	+	0.810551i	$0.699168\pi$
$200$	−8.56036	+	8.38888i	−0.605309	+	0.593183i
$201$	−3.47869	+	6.09328i	−0.245368	+	0.429787i
$202$	−23.3168	+	13.3573i	−1.64057	+	0.939819i
$203$	6.62997	+	6.62997i	0.465333	+	0.465333i
$204$	13.9292	+	3.76065i	0.975236	+	0.263298i
$205$	7.21120	+	7.21120i	0.503652	+	0.503652i
$206$	6.19065	+	1.68118i	0.431323	+	0.117133i
$207$	−16.0571	+	9.47928i	−1.11604	+	0.658856i
$208$	3.00639	−	10.6436i	0.208456	−	0.738002i
$209$	−25.4306	−	7.27019i	−1.75907	−	0.502889i
$210$	7.17965	−	7.20086i	0.495443	−	0.496907i
$211$	−6.50245	−	6.50245i	−0.447647	−	0.447647i	0.446925	−	0.894572i	$-0.352519\pi$
$211$	−6.50245	−	6.50245i	−0.447647	−	0.447647i	−0.894572	+	0.446925i	$0.852519\pi$
$212$	1.44330	+	5.53553i	0.0991261	+	0.380182i
$213$	−1.85577	+	0.506905i	−0.127155	+	0.0347325i
$214$	1.05223	+	1.83679i	0.0719290	+	0.125561i
$215$	17.5810			1.19901
$216$	0.0650293	+	14.6968i	0.00442469	+	0.999990i
$217$	−6.95013			−0.471806
$218$	−5.08393	−	8.87461i	−0.344327	−	0.601064i
$219$	2.80237	−	0.765472i	0.189367	−	0.0517258i
$220$	−18.6574	+	31.8180i	−1.25788	+	2.14517i
$221$	−8.14319	+	8.14319i	−0.547770	+	0.547770i
$222$	−6.58390	−	6.56450i	−0.441882	−	0.440581i
$223$			16.2790i			1.09012i	0.838397	+	0.545060i	$0.183493\pi$
$223$			16.2790i			1.09012i	−0.838397	+	0.545060i	$0.816507\pi$
$224$	−7.49586	+	1.87364i	−0.500838	+	0.125188i
$225$	6.46272	+	10.9473i	0.430848	+	0.729819i
$226$	−6.89148	−	1.87150i	−0.458414	−	0.124490i
$227$	13.4542	−	13.4542i	0.892986	−	0.892986i	−0.101817	−	0.994803i	$-0.532466\pi$
$227$	13.4542	−	13.4542i	0.892986	−	0.892986i	0.994803	+	0.101817i	$0.0324657\pi$
$228$	14.6552	−	3.63681i	0.970561	−	0.240853i
$229$	−6.04923	−	6.04923i	−0.399745	−	0.399745i	0.478398	−	0.878143i	$-0.341218\pi$
$229$	−6.04923	−	6.04923i	−0.399745	−	0.399745i	−0.878143	+	0.478398i	$0.841218\pi$
$230$	23.1813	−	13.2797i	1.52853	−	0.875639i
$231$	7.11720	−	12.4665i	0.468277	−	0.820236i
$232$	19.4153	+	0.196424i	1.27467	+	0.0128959i
$233$	−2.02609			−0.132734			−0.0663669	−	0.997795i	$-0.521141\pi$
$233$	−2.02609			−0.132734			−0.0663669	+	0.997795i	$0.521141\pi$
$234$	−10.1962	−	5.80114i	−0.666546	−	0.379232i
$235$	−2.20316	−	2.20316i	−0.143719	−	0.143719i
$236$	7.47207	+	28.6579i	0.486390	+	1.86547i
$237$	−4.15866	+	1.13594i	−0.270134	+	0.0737874i
$238$	7.76394	+	2.10843i	0.503262	+	0.136669i
$239$		−	19.1610i		−	1.23942i	−0.784829	−	0.619712i	$-0.787249\pi$
$239$		−	19.1610i		−	1.23942i	0.784829	−	0.619712i	$-0.212751\pi$
$240$	0.181968	−	21.0563i	0.0117460	−	1.35918i
$241$			14.9633i			0.963873i	0.876206	+	0.481937i	$0.160066\pi$
$241$			14.9633i			0.963873i	−0.876206	+	0.481937i	$0.839934\pi$
$242$	−9.56945	+	35.2379i	−0.615148	+	2.26518i
$243$	15.1506	+	3.66852i	0.971914	+	0.235336i
$244$	−20.8191	+	5.42824i	−1.33281	+	0.347508i
$245$	−11.0345	+	11.0345i	−0.704972	+	0.704972i
$246$	−8.21902	+	0.0121222i	−0.524026	+	0.000772886i
$247$	−3.31287	+	11.5882i	−0.210793	+	0.737338i
$248$	−10.2794	+	10.0735i	−0.652740	+	0.639665i
$249$	14.0422	−	24.5963i	0.889888	−	1.55873i
$250$	1.62908	+	2.84375i	0.103032	+	0.179854i
$251$	−4.90587	+	4.90587i	−0.309656	+	0.309656i	−0.844776	−	0.535120i	$-0.820266\pi$
$251$	−4.90587	+	4.90587i	−0.309656	+	0.309656i	0.535120	+	0.844776i	$0.320266\pi$
$252$	0.0241741	+	8.19513i	0.00152282	+	0.516245i
$253$	26.6684	−	26.6684i	1.67663	−	1.67663i
$254$	−4.79854	+	17.6698i	−0.301087	+	1.10870i
$255$	−10.8706	+	19.0410i	−0.680744	+	1.19239i
$256$	−8.37086	+	13.6356i	−0.523179	+	0.852223i
$257$	13.8623			0.864709			0.432354	−	0.901704i	$-0.357683\pi$
$257$	13.8623			0.864709			0.432354	+	0.901704i	$0.357683\pi$
$258$	−10.0042	+	10.0338i	−0.622837	+	0.624677i
$259$	−3.66585	−	3.66585i	−0.227785	−	0.227785i
$260$	14.4988	+	8.50177i	0.899177	+	0.527258i
$261$	5.13704	−	19.9431i	0.317975	−	1.23444i
$262$	−4.54161	−	7.92793i	−0.280582	−	0.489789i
$263$	5.12184			0.315826			0.157913	−	0.987453i	$-0.449523\pi$
$263$	5.12184			0.315826			0.157913	+	0.987453i	$0.449523\pi$
$264$	−7.54238	−	28.7538i	−0.464201	−	1.76967i
$265$	−8.69339			−0.534031
$266$	8.17485	−	2.01587i	0.501232	−	0.123601i
$267$	28.7797	−	7.86119i	1.76129	−	0.481097i
$268$	2.04407	+	7.83970i	0.124862	+	0.478886i
$269$	−1.40930	+	1.40930i	−0.0859266	+	0.0859266i	−0.748764	−	0.662837i	$-0.769352\pi$
$269$	−1.40930	+	1.40930i	−0.0859266	+	0.0859266i	0.662837	+	0.748764i	$0.269352\pi$
$270$	−21.6366	−	5.53926i	−1.31676	−	0.337109i
$271$	16.0336			0.973970			0.486985	−	0.873410i	$-0.338097\pi$
$271$	16.0336			0.973970			0.486985	+	0.873410i	$0.338097\pi$
$272$	14.5389	−	8.13458i	0.881552	−	0.493231i
$273$	−5.68073	−	3.24316i	−0.343813	−	0.196285i
$274$	13.7945	+	3.74614i	0.833359	+	0.226313i
$275$	−18.1818	−	18.1818i	−1.09640	−	1.09640i
$276$	−5.61207	+	20.7867i	−0.337807	+	1.25121i
$277$	−13.8062	−	13.8062i	−0.829533	−	0.829533i	0.157919	−	0.987452i	$-0.449521\pi$
$277$	−13.8062	−	13.8062i	−0.829533	−	0.829533i	−0.987452	+	0.157919i	$0.949521\pi$
$278$	−4.50469	−	7.86347i	−0.270173	−	0.471620i
$279$	7.76050	+	13.1456i	0.464609	+	0.787007i
$280$	0.118784	−	11.7411i	0.00709870	−	0.701662i
$281$			11.8357i			0.706057i	0.935612	+	0.353029i	$0.114848\pi$
$281$			11.8357i			0.706057i	−0.935612	+	0.353029i	$0.885152\pi$
$282$	2.51107	−	0.00370358i	0.149532	−	0.000220545i
$283$	−1.30645	−	1.30645i	−0.0776602	−	0.0776602i	0.667210	−	0.744870i	$-0.267488\pi$
$283$	−1.30645	−	1.30645i	−0.0776602	−	0.0776602i	−0.744870	+	0.667210i	$0.767488\pi$
$284$	−1.12363	+	1.91622i	−0.0666750	+	0.113707i
$285$	−0.270988	+	22.9448i	−0.0160519	+	1.35913i
$286$	22.8981	+	6.21837i	1.35399	+	0.367700i
$287$	−4.58302			−0.270527
$288$	11.9137	+	12.0857i	0.702021	+	0.712156i
$289$	−0.347001			−0.0204118
$290$	−7.73283	+	28.4749i	−0.454087	+	1.67210i
$291$	18.0111	−	4.91974i	1.05583	−	0.288401i
$292$	1.69678	−	2.89366i	0.0992965	−	0.169339i
$293$	4.90724	+	4.90724i	0.286684	+	0.286684i	0.835767	−	0.549084i	$-0.185023\pi$
$293$	4.90724	+	4.90724i	0.286684	+	0.286684i	−0.549084	+	0.835767i	$0.685023\pi$
$294$	−0.0185494	−	12.5767i	−0.00108182	−	0.733488i
$295$	−45.0063			−2.62037
$296$	−10.7351	−	0.108607i	−0.623964	−	0.00631263i
$297$	−31.5264	+	0.458468i	−1.82935	+	0.0266030i
$298$	19.8835	−	11.3905i	1.15182	−	0.659835i
$299$	−12.1522	−	12.1522i	−0.702780	−	0.702780i
$300$	14.1718	+	3.82616i	0.818210	+	0.220903i
$301$	−5.58672	+	5.58672i	−0.322013	+	0.322013i
$302$	−4.03078	−	1.09463i	−0.231945	−	0.0629886i
$303$	28.5812	+	16.3172i	1.64195	+	0.937398i
$304$	9.16896	−	14.8300i	0.525876	−	0.850561i
$305$		−	32.6958i		−	1.87216i
$306$	−4.68127	−	17.0391i	−0.267611	−	0.974062i
$307$	9.62847	+	9.62847i	0.549526	+	0.549526i	0.926304	−	0.376778i	$-0.122968\pi$
$307$	9.62847	+	9.62847i	0.549526	+	0.549526i	−0.376778	+	0.926304i	$0.622968\pi$
$308$	−4.18206	−	16.0396i	−0.238295	−	0.913940i
$309$	−2.07019	−	7.57892i	−0.117769	−	0.431150i
$310$	−10.8718	−	18.9781i	−0.617479	−	1.07788i
$311$	−32.9556			−1.86874			−0.934372	−	0.356300i	$-0.884038\pi$
$311$	−32.9556			−1.86874			−0.934372	+	0.356300i	$0.884038\pi$
$312$	−13.1025	+	3.43690i	−0.741782	+	0.194576i
$313$		−	18.7285i		−	1.05860i	−0.848435	−	0.529300i	$-0.822455\pi$
$313$		−	18.7285i		−	1.05860i	0.848435	−	0.529300i	$-0.177545\pi$
$314$	−1.15567	+	0.662040i	−0.0652182	+	0.0373611i
$315$	−12.0602	−	3.10654i	−0.679517	−	0.175034i
$316$	−2.51798	+	4.29413i	−0.141648	+	0.241564i
$317$	−16.6870	+	16.6870i	−0.937235	+	0.937235i	−0.998143	−	0.0609086i	$-0.980600\pi$
$317$	−16.6870	+	16.6870i	−0.937235	+	0.937235i	0.0609086	+	0.998143i	$0.480600\pi$
$318$	4.94687	−	4.96148i	0.277407	−	0.278226i
$319$			41.6542i			2.33219i
$320$	−16.8417	−	17.5374i	−0.941478	−	0.980369i
$321$	1.28540	−	2.25150i	0.0717438	−	0.125667i
$322$	−3.14644	+	11.5862i	−0.175344	+	0.645676i
$323$	−15.8714	+	8.81421i	−0.883111	+	0.490436i
$324$	15.4734	−	9.19638i	0.859634	−	0.510910i
$325$	−8.28505	+	8.28505i	−0.459572	+	0.459572i
$326$	−3.72188	+	2.13212i	−0.206136	+	0.118087i
$327$	−6.21048	+	10.8783i	−0.343440	+	0.601572i
$328$	−6.77836	+	6.64258i	−0.374272	+	0.366775i
$329$	1.40020			0.0771956
$330$	45.1743	−	0.0666277i	2.48676	−	0.00366773i
$331$	0.348257	−	0.348257i	0.0191419	−	0.0191419i	−0.697471	−	0.716613i	$-0.745691\pi$
$331$	0.348257	−	0.348257i	0.0191419	−	0.0191419i	0.716613	+	0.697471i	$0.245691\pi$
$332$	−8.25117	−	31.6460i	−0.452842	−	1.73680i
$333$	−2.84037	+	11.0269i	−0.155652	+	0.604271i
$334$	−8.77927	+	32.3282i	−0.480381	+	1.76892i
$335$	−12.3120			−0.672678
$336$	6.63325	+	6.74890i	0.361873	+	0.368183i
$337$			2.09189i			0.113952i	0.998376	+	0.0569762i	$0.0181459\pi$
$337$			2.09189i			0.113952i	−0.998376	+	0.0569762i	$0.981854\pi$
$338$	−1.98461	+	7.30799i	−0.107948	+	0.397502i
$339$	2.30455	+	8.43691i	0.125166	+	0.458230i
$340$	6.38756	+	24.4984i	0.346414	+	1.32861i
$341$	−21.8328	−	21.8328i	−1.18231	−	1.18231i
$342$	−12.9409	−	13.2111i	−0.699761	−	0.714377i
$343$		−	16.5739i		−	0.894908i
$344$	−0.165516	+	16.3602i	−0.00892400	+	0.882082i
$345$	−28.4152	−	16.2224i	−1.52982	−	0.873383i
$346$	8.37453	−	4.79746i	0.450218	−	0.257913i
$347$	4.58979	−	4.58979i	0.246393	−	0.246393i	−0.573096	−	0.819488i	$-0.694258\pi$
$347$	4.58979	−	4.58979i	0.246393	−	0.246393i	0.819488	+	0.573096i	$0.194258\pi$
$348$	−11.8509	−	20.6166i	−0.635274	−	1.10516i
$349$	−9.01818	+	9.01818i	−0.482732	+	0.482732i	−0.906003	−	0.423271i	$-0.860882\pi$
$349$	−9.01818	+	9.01818i	−0.482732	+	0.482732i	0.423271	+	0.906003i	$0.360882\pi$
$350$	7.89919	+	2.14516i	0.422229	+	0.114663i
$351$	0.208914	+	14.3659i	0.0111510	+	0.766796i
$352$	−29.4329	−	17.6614i	−1.56878	−	0.941355i
$353$		−	2.23654i		−	0.119039i	−0.998227	−	0.0595195i	$-0.981043\pi$
$353$		−	2.23654i		−	0.119039i	0.998227	−	0.0595195i	$-0.0189569\pi$
$354$	25.6103	−	25.6860i	1.36117	−	1.36519i
$355$	−2.38699	−	2.38699i	−0.126688	−	0.126688i
$356$	17.4255	−	29.7171i	0.923549	−	1.57501i
$357$	−2.59631	−	9.50503i	−0.137411	−	0.503060i
$358$	21.2903	−	12.1964i	1.12523	−	0.644600i
$359$	27.2834			1.43996			0.719981	−	0.693993i	$-0.244150\pi$
$359$	27.2834			1.43996			0.719981	+	0.693993i	$0.244150\pi$
$360$	−22.3399	+	12.8853i	−1.17741	+	0.679118i
$361$	−10.0428	+	16.1289i	−0.528568	+	0.848891i
$362$	−19.4062	+	11.1171i	−1.01997	+	0.584300i
$363$	43.1402	−	11.7838i	2.26427	−	0.618488i
$364$	−7.30890	+	1.90567i	−0.383090	+	0.0998845i
$365$	3.60457	+	3.60457i	0.188672	+	0.188672i
$366$	18.6601	+	18.6052i	0.975381	+	0.972508i
$367$	−14.1425			−0.738233			−0.369116	−	0.929383i	$-0.620340\pi$
$367$	−14.1425			−0.738233			−0.369116	+	0.929383i	$0.620340\pi$
$368$	12.1394	+	21.6967i	0.632807	+	1.13102i
$369$	5.11738	+	8.66840i	0.266400	+	0.451259i
$370$	4.27564	−	15.7443i	0.222280	−	0.818509i
$371$	2.76250	−	2.76250i	0.143422	−	0.143422i
$372$	17.0176	+	4.59449i	0.882324	+	0.238213i
$373$	15.1921	−	15.1921i	0.786619	−	0.786619i	−0.194319	−	0.980938i	$-0.562250\pi$
$373$	15.1921	−	15.1921i	0.786619	−	0.786619i	0.980938	+	0.194319i	$0.0622497\pi$
$374$	17.7660	+	31.0126i	0.918657	+	1.60363i
$375$	1.99006	−	3.48580i	0.102766	−	0.180006i
$376$	2.07092	−	2.02944i	0.106800	−	0.104660i
$377$	18.9809			0.977568
$378$	8.63569	−	5.11526i	0.444172	−	0.263101i
$379$	18.3571	−	18.3571i	0.942940	−	0.942940i	−0.0555177	−	0.998458i	$-0.517681\pi$
$379$	18.3571	−	18.3571i	0.942940	−	0.942940i	0.998458	+	0.0555177i	$0.0176809\pi$
$380$	18.2922	+	19.1690i	0.938368	+	0.983347i
$381$	21.6323	−	5.90890i	1.10826	−	0.302722i
$382$	4.02062	−	14.8053i	0.205713	−	0.757503i
$383$	−2.38770			−0.122006			−0.0610030	−	0.998138i	$-0.519430\pi$
$383$	−2.38770			−0.122006			−0.0610030	+	0.998138i	$0.519430\pi$
$384$	19.5925	+	0.367566i	0.999824	+	0.0187573i
$385$	25.1897			1.28379
$386$	−0.223926	+	0.824570i	−0.0113975	+	0.0419695i
$387$	16.8049	+	4.32871i	0.854242	+	0.220040i
$388$	10.9053	−	18.5978i	0.553634	−	0.944159i
$389$	3.65525	−	3.65525i	0.185328	−	0.185328i	−0.608345	−	0.793673i	$-0.708166\pi$
$389$	3.65525	−	3.65525i	0.185328	−	0.185328i	0.793673	+	0.608345i	$0.208166\pi$
$390$	−0.0303608	−	20.5850i	−0.00153738	−	1.04236i
$391$		−	25.8872i		−	1.30917i
$392$	−10.1644	−	10.3722i	−0.513382	−	0.523876i
$393$	−5.54799	+	9.71788i	−0.279859	+	0.490202i
$394$	5.23743	−	3.00033i	0.263858	−	0.151154i
$395$	−5.34911	−	5.34911i	−0.269143	−	0.269143i
$396$	−25.6679	+	25.8198i	−1.28986	+	1.29749i
$397$	8.53433	−	8.53433i	0.428326	−	0.428326i	−0.459732	−	0.888058i	$-0.652054\pi$
$397$	8.53433	−	8.53433i	0.428326	−	0.428326i	0.888058	+	0.459732i	$0.152054\pi$
$398$	8.47573	−	31.2105i	0.424850	−	1.56444i
$399$	−7.20508	−	7.37730i	−0.360705	−	0.369327i
$400$	14.7922	−	8.27628i	0.739610	−	0.413814i
$401$	2.58774			0.129226			0.0646129	−	0.997910i	$-0.479419\pi$
$401$	2.58774			0.129226			0.0646129	+	0.997910i	$0.479419\pi$
$402$	7.00601	−	7.02671i	0.349428	−	0.350460i
$403$	−9.94877	+	9.94877i	−0.495583	+	0.495583i
$404$	36.7730	−	9.58796i	1.82953	−	0.477019i
$405$	7.59065	+	26.2797i	0.377182	+	1.30585i
$406$	−6.59121	−	11.5057i	−0.327116	−	0.571020i
$407$		−	23.0314i		−	1.14163i
$408$	−17.6165	−	10.2950i	−0.872146	−	0.509680i
$409$	20.7173			1.02440			0.512202	−	0.858865i	$-0.328830\pi$
$409$	20.7173			1.02440			0.512202	+	0.858865i	$0.328830\pi$
$410$	−7.16904	−	12.5144i	−0.354054	−	0.618043i
$411$	−4.61298	−	16.8880i	−0.227542	−	0.833024i
$412$	−7.82580	−	4.58888i	−0.385550	−	0.226078i
$413$	14.3017	−	14.3017i	0.703740	−	0.703740i
$414$	25.4277	−	6.98593i	1.24971	−	0.343340i
$415$	49.6991			2.43963
$416$	−8.04792	+	13.4120i	−0.394582	+	0.657576i
$417$	−5.50289	+	9.63888i	−0.269478	+	0.472018i
$418$	32.0127	+	19.3476i	1.56579	+	0.946320i
$419$	17.3354	+	17.3354i	0.846892	+	0.846892i	0.989744	−	0.142852i	$-0.0456273\pi$
$419$	17.3354	+	17.3354i	0.846892	+	0.846892i	−0.142852	+	0.989744i	$0.545627\pi$
$420$	−12.4675	+	7.16662i	−0.608353	+	0.349695i
$421$	4.26050	−	4.26050i	0.207644	−	0.207644i	−0.595621	−	0.803265i	$-0.703094\pi$
$421$	4.26050	−	4.26050i	0.207644	−	0.207644i	0.803265	+	0.595621i	$0.203094\pi$
$422$	6.46443	+	11.2844i	0.314684	+	0.549318i
$423$	−1.56346	−	2.64837i	−0.0760180	−	0.128768i
$424$	0.0818436	−	8.08973i	0.00397468	−	0.392872i
$425$	−17.6492			−0.856111
$426$	2.72059	−	0.00401261i	0.131813	−	0.000194411i
$427$	10.3898	+	10.3898i	0.502796	+	0.502796i
$428$	−0.755297	−	2.89681i	−0.0365086	−	0.140023i
$429$	−7.65727	−	28.0331i	−0.369696	−	1.35345i
$430$	−23.9942	−	6.51604i	−1.15710	−	0.314231i
$431$	−11.0515			−0.532332			−0.266166	−	0.963927i	$-0.585757\pi$
$431$	−11.0515			−0.532332			−0.266166	+	0.963927i	$0.585757\pi$
$432$	5.35832	−	20.0820i	0.257802	−	0.966198i
$433$		−	14.1110i		−	0.678132i	−0.940763	−	0.339066i	$-0.889889\pi$
$433$		−	14.1110i		−	0.678132i	0.940763	−	0.339066i	$-0.110111\pi$
$434$	9.48543	+	2.57593i	0.455315	+	0.123648i
$435$	34.8605	−	9.52217i	1.67143	−	0.456553i
$436$	3.64927	+	13.9962i	0.174768	+	0.670295i
$437$	−13.1536	−	23.6852i	−0.629221	−	1.13302i
$438$	−4.10834	+	0.00605940i	−0.196304	+	0.000289529i
$439$	−29.1791			−1.39264			−0.696320	−	0.717731i	$-0.745181\pi$
$439$	−29.1791			−1.39264			−0.696320	+	0.717731i	$0.745181\pi$
$440$	37.2560	−	36.5097i	1.77611	−	1.74053i
$441$	−13.2643	+	7.83059i	−0.631635	+	0.372885i
$442$	14.1318	−	8.09558i	0.672181	−	0.385068i
$443$	−0.464687	+	0.464687i	−0.0220779	+	0.0220779i	−0.718060	−	0.695982i	$-0.754969\pi$
$443$	−0.464687	+	0.464687i	−0.0220779	+	0.0220779i	0.695982	+	0.718060i	$0.254969\pi$
$444$	6.55259	+	11.3993i	0.310972	+	0.540987i
$445$	37.0180	+	37.0180i	1.75482	+	1.75482i
$446$	6.03347	−	22.2173i	0.285693	−	1.05202i
$447$	−24.3728	−	13.9145i	−1.15279	−	0.658135i
$448$	10.9246	+	0.221072i	0.516141	+	0.0104446i
$449$	29.1562			1.37597			0.687983	−	0.725727i	$-0.258496\pi$
$449$	29.1562			1.37597			0.687983	+	0.725727i	$0.258496\pi$
$450$	−4.76282	−	17.3359i	−0.224521	−	0.817224i
$451$	−14.3969	−	14.3969i	−0.677923	−	0.677923i
$452$	8.71174	+	5.10838i	0.409766	+	0.240278i
$453$	1.34792	+	4.93469i	0.0633306	+	0.231852i
$454$	−23.3486	+	13.3755i	−1.09580	+	0.627745i
$455$		−	11.4784i		−	0.538116i
$456$	−21.3490	−	0.468184i	−0.999760	−	0.0219247i
$457$			41.2315i			1.92873i	0.264579	+	0.964364i	$0.414767\pi$
$457$			41.2315i			1.92873i	−0.264579	+	0.964364i	$0.585233\pi$
$458$	6.01387	+	10.4979i	0.281010	+	0.490536i
$459$	−15.0790	+	15.5240i	−0.703825	+	0.724598i
$460$	−36.5594	+	9.53225i	−1.70459	+	0.444443i
$461$	−13.0305	−	13.0305i	−0.606889	−	0.606889i	0.335243	−	0.942132i	$-0.391182\pi$
$461$	−13.0305	−	13.0305i	−0.606889	−	0.606889i	−0.942132	+	0.335243i	$0.891182\pi$
$462$	−14.3339	+	14.3762i	−0.666873	+	0.668843i
$463$	−13.7891			−0.640832			−0.320416	−	0.947277i	$-0.603823\pi$
$463$	−13.7891			−0.640832			−0.320416	+	0.947277i	$0.603823\pi$
$464$	−26.4248	−	7.46395i	−1.22674	−	0.346505i
$465$	−13.2809	+	23.2629i	−0.615889	+	1.07879i
$466$	2.76518	+	0.750931i	0.128094	+	0.0347862i
$467$	−18.3701	−	18.3701i	−0.850068	−	0.850068i	0.140073	−	0.990141i	$-0.455266\pi$
$467$	−18.3701	−	18.3701i	−0.850068	−	0.850068i	−0.990141	+	0.140073i	$0.955266\pi$
$468$	11.7655	+	11.6963i	0.543861	+	0.540662i
$469$	3.91240	−	3.91240i	0.180658	−	0.180658i
$470$	2.19028	+	3.82340i	0.101030	+	0.176360i
$471$	1.41659	+	0.808742i	0.0652732	+	0.0372648i
$472$	0.423711	−	41.8812i	0.0195029	−	1.92774i
$473$	−35.0997			−1.61389
$474$	6.09669	−	0.00899201i	0.280030	−	0.000413017i
$475$	−16.1479	+	8.96776i	−0.740917	+	0.411469i
$476$	−9.81465	−	5.75510i	−0.449854	−	0.263784i
$477$	−8.30965	−	2.14044i	−0.380473	−	0.0980042i
$478$	−7.10165	+	26.1506i	−0.324822	+	1.19610i
$479$		−	3.55670i		−	0.162510i	−0.996693	−	0.0812549i	$-0.974107\pi$
$479$		−	3.55670i		−	0.162510i	0.996693	−	0.0812549i	$-0.0258928\pi$
$480$	−8.05244	+	28.6699i	−0.367542	+	1.30859i
$481$	−10.4949			−0.478528
$482$	5.54586	−	20.4217i	0.252607	−	0.930183i
$483$	14.1845	−	3.87451i	0.645417	−	0.176296i
$484$	26.1205	−	44.5454i	1.18729	−	2.02479i
$485$	23.1669	+	23.1669i	1.05195	+	1.05195i
$486$	−19.3177	−	10.6220i	−0.876268	−	0.481824i
$487$	22.3950			1.01481			0.507406	−	0.861707i	$-0.330604\pi$
$487$	22.3950			1.01481			0.507406	+	0.861707i	$0.330604\pi$
$488$	30.4255	+	0.307814i	1.37730	+	0.0139341i
$489$	4.56220	+	2.60458i	0.206310	+	0.117783i
$490$	19.1495	−	10.9700i	0.865086	−	0.495576i
$491$	−18.3053	+	18.3053i	−0.826105	+	0.826105i	−0.986975	−	0.160871i	$-0.948570\pi$
$491$	−18.3053	+	18.3053i	−0.826105	+	0.826105i	0.160871	+	0.986975i	$0.448570\pi$
$492$	11.2217	+	3.02967i	0.505912	+	0.136588i
$493$	20.2170	+	20.2170i	0.910530	+	0.910530i
$494$	8.81627	−	14.5875i	0.396663	−	0.656323i
$495$	−28.1267	−	47.6442i	−1.26420	−	2.14145i
$496$	17.7626	−	9.93824i	0.797565	−	0.446240i
$497$	1.51703			0.0680482
$498$	−28.2807	+	28.3642i	−1.26729	+	1.27103i
$499$	−3.22270	+	3.22270i	−0.144268	+	0.144268i	−0.775552	−	0.631284i	$-0.782528\pi$
$499$	−3.22270	+	3.22270i	−0.144268	+	0.144268i	0.631284	+	0.775552i	$0.282528\pi$
$500$	−1.16936	−	4.48488i	−0.0522953	−	0.200570i
$501$	39.5779	−	10.8108i	1.76821	−	0.482989i
$502$	8.51371	−	4.87718i	0.379985	−	0.217679i
$503$	5.47432			0.244088			0.122044	−	0.992525i	$-0.461055\pi$
$503$	5.47432			0.244088			0.122044	+	0.992525i	$0.461055\pi$
$504$	3.00437	−	11.1935i	0.133825	−	0.498600i
$505$			57.7509i			2.56988i
$506$	−46.2806	+	26.5124i	−2.05742	+	1.17862i
$507$	8.94683	−	2.44384i	0.397343	−	0.108535i
$508$	13.0979	−	22.3370i	0.581126	−	0.991044i
$509$	−15.9197	+	15.9197i	−0.705630	+	0.705630i	−0.965613	−	0.259983i	$-0.916283\pi$
$509$	−15.9197	+	15.9197i	−0.705630	+	0.705630i	0.259983	+	0.965613i	$0.416283\pi$
$510$	21.8932	−	21.9579i	0.969447	−	0.972311i
$511$	−2.29086			−0.101341
$512$	16.4782	−	15.5071i	0.728238	−	0.685324i
$513$	−5.90839	+	21.8653i	−0.260862	+	0.965376i
$514$	−18.9191	−	5.13779i	−0.834485	−	0.226618i
$515$	9.74845	−	9.74845i	0.429568	−	0.429568i
$516$	17.3725	−	9.98609i	0.764780	−	0.439613i
$517$	4.39853	+	4.39853i	0.193447	+	0.193447i
$518$	3.64441	+	6.36176i	0.160126	+	0.279520i
$519$	−10.2653	−	5.86053i	−0.450598	−	0.257249i
$520$	−16.6367	−	16.9768i	−0.729567	−	0.744480i
$521$		−	27.2877i		−	1.19550i	−0.801683	−	0.597749i	$-0.796062\pi$
$521$		−	27.2877i		−	1.19550i	0.801683	−	0.597749i	$-0.203938\pi$
$522$	−14.4024	+	25.3140i	−0.630378	+	1.10796i
$523$	−7.79172	+	7.79172i	−0.340708	+	0.340708i	−0.856634	−	0.515925i	$-0.827448\pi$
$523$	−7.79172	+	7.79172i	−0.340708	+	0.340708i	0.515925	+	0.856634i	$0.327448\pi$
$524$	3.25999	+	12.5032i	0.142413	+	0.546203i
$525$	−2.64154	−	9.67061i	−0.115286	−	0.422060i
$526$	−6.99020	−	1.89831i	−0.304787	−	0.0827701i
$527$	−21.1933			−0.923195
$528$	−0.363291	+	42.0381i	−0.0158102	+	1.82947i
$529$	15.6318			0.679645
$530$	11.8646	+	3.22203i	0.515365	+	0.139956i
$531$	−43.0197	−	11.0812i	−1.86690	−	0.480885i
$532$	−11.9040	−	0.278622i	−0.516105	−	0.0120798i
$533$	−6.56036	+	6.56036i	−0.284161	+	0.284161i
$534$	−42.1916	+	0.0622284i	−1.82581	+	0.00269289i
$535$	4.54936			0.196686
$536$	0.115911	−	11.4571i	0.00500660	−	0.494871i
$537$	−26.0971	−	14.8990i	−1.12617	−	0.642939i
$538$	2.44572	−	1.40106i	0.105442	−	0.0604040i
$539$	22.0300	−	22.0300i	0.948901	−	0.948901i
$540$	27.4763	+	15.5791i	1.18239	+	0.670416i
$541$	0.637347	−	0.637347i	0.0274017	−	0.0274017i	−0.693273	−	0.720675i	$-0.743832\pi$
$541$	0.637347	−	0.637347i	0.0274017	−	0.0274017i	0.720675	+	0.693273i	$0.243832\pi$
$542$	−21.8823	−	5.94252i	−0.939927	−	0.255253i
$543$	23.7877	+	13.5805i	1.02083	+	0.582795i
$544$	−22.8574	+	5.71337i	−0.980004	+	0.244959i
$545$	−21.9806			−0.941545
$546$	6.55095	+	6.53165i	0.280355	+	0.279529i
$547$	−7.37532	−	7.37532i	−0.315346	−	0.315346i	0.531631	−	0.846976i	$-0.321579\pi$
$547$	−7.37532	−	7.37532i	−0.315346	−	0.315346i	−0.846976	+	0.531631i	$0.821579\pi$
$548$	−17.4381	−	10.2253i	−0.744920	−	0.436805i
$549$	8.05021	−	31.2526i	0.343575	−	1.33383i
$550$	18.0755	+	31.5529i	0.770740	+	1.34542i
$551$	28.7699	+	8.22484i	1.22564	+	0.350390i
$552$	15.3634	−	26.2893i	0.653911	−	1.11895i
$553$	3.39958			0.144565
$554$	13.7255	+	23.9594i	0.583139	+	1.01794i
$555$	−19.2750	+	5.26500i	−0.818180	+	0.223487i
$556$	3.23349	+	12.4015i	0.137130	+	0.525941i
$557$	5.97386	+	5.97386i	0.253120	+	0.253120i	0.822249	−	0.569128i	$-0.192719\pi$
$557$	5.97386	+	5.97386i	0.253120	+	0.253120i	−0.569128	+	0.822249i	$0.692719\pi$
$558$	−5.71924	−	20.8172i	−0.242115	−	0.881261i
$559$			15.9942i			0.676483i
$560$	−4.51370	+	15.9800i	−0.190739	+	0.675277i
$561$	21.7028	−	38.0146i	0.916291	−	1.60498i
$562$	4.38666	−	16.1531i	0.185040	−	0.681379i
$563$	−28.0386	+	28.0386i	−1.18169	+	1.18169i	−0.202378	+	0.979308i	$0.564867\pi$
$563$	−28.0386	+	28.0386i	−1.18169	+	1.18169i	−0.979308	+	0.202378i	$0.935133\pi$
$564$	−3.42844	−	0.925624i	−0.144363	−	0.0389758i
$565$	−10.8520	+	10.8520i	−0.456549	+	0.456549i
$566$	1.29881	+	2.26723i	0.0545930	+	0.0952986i
$567$	−10.7630	−	5.93882i	−0.452003	−	0.249407i
$568$	2.24372	−	2.19877i	0.0941442	−	0.0922584i
$569$		−	4.55944i		−	0.191142i	−0.995423	−	0.0955708i	$-0.969532\pi$
$569$		−	4.55944i		−	0.191142i	0.995423	−	0.0955708i	$-0.0304676\pi$
$570$	8.87388	−	31.2143i	0.371686	−	1.30742i
$571$	22.8480	+	22.8480i	0.956158	+	0.956158i	0.999078	−	0.0429205i	$-0.0136662\pi$
$571$	22.8480	+	22.8480i	0.956158	+	0.956158i	−0.0429205	+	0.999078i	$0.513666\pi$
$572$	−28.9463	−	16.9735i	−1.21030	−	0.709696i
$573$	−18.1254	+	4.95097i	−0.757199	+	0.206830i
$574$	6.25482	+	1.69860i	0.261071	+	0.0708983i
$575$		−	26.3381i		−	1.09838i
$576$	−11.7803	−	20.9099i	−0.490845	−	0.871247i
$577$	−32.4939			−1.35274			−0.676370	−	0.736562i	$-0.736448\pi$
$577$	−32.4939			−1.35274			−0.676370	+	0.736562i	$0.736448\pi$
$578$	0.473581	+	0.128609i	0.0196984	+	0.00534942i
$579$	1.00948	−	0.275741i	0.0419526	−	0.0114594i
$580$	21.1073	−	35.9960i	0.876432	−	1.49465i
$581$	−15.7929	+	15.7929i	−0.655200	+	0.655200i
$582$	−26.4046	+	0.0389442i	−1.09451	+	0.00161429i
$583$	17.3560			0.718812
$584$	−3.38821	+	3.32034i	−0.140205	+	0.137397i
$585$	−21.7105	+	12.8168i	−0.897617	+	0.529908i
$586$	−4.87855	−	8.51608i	−0.201531	−	0.351796i
$587$	−18.6914	+	18.6914i	−0.771475	+	0.771475i	−0.978364	−	0.206889i	$-0.933666\pi$
$587$	−18.6914	+	18.6914i	−0.771475	+	0.771475i	0.206889	+	0.978364i	$0.433666\pi$
$588$	−4.63599	+	17.1714i	−0.191185	+	0.708135i
$589$	−19.3906	+	10.7686i	−0.798975	+	0.443711i
$590$	61.4239	+	16.6807i	2.52878	+	0.686733i
$591$	−6.41993	−	3.66517i	−0.264080	−	0.150765i
$592$	14.6108	+	4.12697i	0.600501	+	0.169617i
$593$		−	40.4436i		−	1.66082i	−0.557152	−	0.830410i	$-0.688106\pi$
$593$		−	40.4436i		−	1.66082i	0.557152	−	0.830410i	$-0.311894\pi$
$594$	43.1966	+	11.0589i	1.77238	+	0.453753i
$595$	12.2259	−	12.2259i	0.501214	−	0.501214i
$596$	−31.3583	+	8.17617i	−1.28449	+	0.334909i
$597$	−38.2095	+	10.4370i	−1.56381	+	0.427157i
$598$	12.0812	+	21.0891i	0.494035	+	0.862397i
$599$		−	24.6679i		−	1.00790i	−0.863731	−	0.503952i	$-0.831879\pi$
$599$		−	24.6679i		−	1.00790i	0.863731	−	0.503952i	$-0.168121\pi$
$600$	−17.9234	−	10.4744i	−0.731718	−	0.427614i
$601$	4.53043			0.184800			0.0924000	−	0.995722i	$-0.470546\pi$
$601$	4.53043			0.184800			0.0924000	+	0.995722i	$0.470546\pi$
$602$	9.69526	−	5.55405i	0.395149	−	0.226366i
$603$	−11.7685	−	3.03141i	−0.479252	−	0.123448i
$604$	5.09544	+	2.98785i	0.207330	+	0.121574i
$605$	55.4893	+	55.4893i	2.25596	+	2.25596i
$606$	−32.9596	−	32.8625i	−1.33889	−	1.33495i
$607$		−	44.9571i		−	1.82475i	−0.409355	−	0.912375i	$-0.634246\pi$
$607$		−	44.9571i		−	1.82475i	0.409355	−	0.912375i	$-0.365754\pi$
$608$	−18.0101	+	16.8415i	−0.730406	+	0.683013i
$609$	−8.05176	+	14.1035i	−0.326274	+	0.571502i
$610$	−12.1181	+	44.6227i	−0.490646	+	1.80672i
$611$	2.00432	−	2.00432i	0.0810860	−	0.0810860i
$612$	0.0737149	+	24.9897i	0.00297975	+	1.01015i
$613$	−25.4762	−	25.4762i	−1.02897	−	1.02897i	−0.999568	−	0.0294066i	$-0.990638\pi$
$613$	−25.4762	−	25.4762i	−1.02897	−	1.02897i	−0.0294066	−	0.999568i	$-0.509362\pi$
$614$	−9.57218	−	16.7094i	−0.386302	−	0.674336i
$615$	−8.75763	+	15.3399i	−0.353142	+	0.618565i
$616$	−0.237148	+	23.4405i	−0.00955495	+	0.944447i
$617$	18.7215			0.753699			0.376849	−	0.926275i	$-0.377007\pi$
$617$	18.7215			0.753699			0.376849	+	0.926275i	$0.377007\pi$
$618$	0.0163874	+	11.1109i	0.000659199	+	0.446944i
$619$	29.7590	+	29.7590i	1.19612	+	1.19612i	0.975320	+	0.220795i	$0.0708652\pi$
$619$	29.7590	+	29.7590i	1.19612	+	1.19612i	0.220795	+	0.975320i	$0.429135\pi$
$620$	7.80386	+	29.9304i	0.313410	+	1.20203i
$621$	−23.1667	−	22.5025i	−0.929647	−	0.902996i
$622$	44.9773	+	12.2143i	1.80343	+	0.489751i
$623$	−23.5265			−0.942569
$624$	19.1559	+	0.165544i	0.766849	+	0.00662707i
$625$	28.2310			1.12924
$626$	−6.94136	+	25.5604i	−0.277433	+	1.02160i
$627$	0.541016	−	45.8085i	0.0216061	−	1.82941i
$628$	1.82261	−	0.475216i	0.0727301	−	0.0189632i
$629$	−11.1784	−	11.1784i	−0.445712	−	0.445712i
$630$	15.3082	+	8.70964i	0.609894	+	0.347000i
$631$			16.7412i			0.666456i	0.942846	+	0.333228i	$0.108138\pi$
$631$			16.7412i			0.666456i	−0.942846	+	0.333228i	$0.891862\pi$
$632$	5.02803	−	4.92732i	0.200004	−	0.195998i
$633$	7.89689	−	13.8322i	0.313873	−	0.549781i
$634$	28.9588	−	16.5894i	1.15010	−	0.658850i
$635$	27.8248	+	27.8248i	1.10419	+	1.10419i
$636$	−8.59028	+	4.93789i	−0.340627	+	0.195800i
$637$	−10.0386	−	10.0386i	−0.397745	−	0.397745i
$638$	15.4383	−	56.8490i	0.611208	−	2.25067i
$639$	−1.69391	−	2.86934i	−0.0670102	−	0.113509i
$640$	16.4854	+	30.1767i	0.651641	+	1.19284i
$641$	9.10882			0.359777			0.179888	−	0.983687i	$-0.442426\pi$
$641$	9.10882			0.359777			0.179888	+	0.983687i	$0.442426\pi$
$642$	−2.58876	+	2.59641i	−0.102170	+	0.102472i
$643$	−11.0484	+	11.0484i	−0.435705	+	0.435705i	−0.890564	−	0.454859i	$-0.849690\pi$
$643$	−11.0484	+	11.0484i	−0.435705	+	0.435705i	0.454859	+	0.890564i	$0.349690\pi$
$644$	8.58842	−	14.6466i	0.338431	−	0.577155i
$645$	8.02382	+	29.3750i	0.315937	+	1.15664i
$646$	24.9279	−	6.14706i	0.980775	−	0.241853i
$647$	−28.3406			−1.11418			−0.557092	−	0.830451i	$-0.688083\pi$
$647$	−28.3406			−1.11418			−0.557092	+	0.830451i	$0.688083\pi$
$648$	−24.5263	+	6.81615i	−0.963485	+	0.267764i
$649$	89.8534			3.52705
$650$	14.3780	−	8.23661i	0.563951	−	0.323066i
$651$	−3.17198	−	11.6126i	−0.124320	−	0.455132i
$652$	5.86979	−	1.53045i	0.229879	−	0.0599370i
$653$	18.7759	+	18.7759i	0.734758	+	0.734758i	0.971558	−	0.236800i	$-0.0760986\pi$
$653$	18.7759	+	18.7759i	0.734758	+	0.734758i	−0.236800	+	0.971558i	$0.576099\pi$
$654$	12.5078	−	12.5447i	0.489093	−	0.490538i
$655$	−19.6358			−0.767236
$656$	11.7129	−	6.55342i	0.457313	−	0.255868i
$657$	2.55796	+	4.33296i	0.0997956	+	0.169045i
$658$	−1.91097	−	0.518956i	−0.0744974	−	0.0202310i
$659$	−3.12908	+	3.12908i	−0.121892	+	0.121892i	−0.765421	−	0.643530i	$-0.777469\pi$
$659$	−3.12908	+	3.12908i	−0.121892	+	0.121892i	0.643530	+	0.765421i	$0.277469\pi$
$660$	−61.6778	−	16.6520i	−2.40081	−	0.648179i
$661$	−17.2327	+	17.2327i	−0.670273	+	0.670273i	−0.957779	−	0.287506i	$-0.907174\pi$
$661$	−17.2327	+	17.2327i	−0.670273	+	0.670273i	0.287506	+	0.957779i	$0.407174\pi$
$662$	−0.604370	+	0.346221i	−0.0234895	+	0.0134563i
$663$	−17.3225	−	9.88949i	−0.672749	−	0.384076i
$664$	−0.467891	+	46.2481i	−0.0181577	+	1.79477i
$665$	4.97383	−	17.3981i	0.192877	−	0.674669i
$666$	7.96340	−	13.9966i	0.308575	−	0.542358i
$667$	−30.1702	+	30.1702i	−1.16819	+	1.16819i
$668$	23.9636	−	40.8672i	0.927180	−	1.58120i
$669$	−27.1996	+	7.42959i	−1.05160	+	0.287244i
$670$	16.8032	+	4.56320i	0.649166	+	0.176292i
$671$			65.2759i			2.51995i
$672$	−6.55161	−	11.6693i	−0.252734	−	0.450152i
$673$			14.8244i			0.571439i	0.958313	+	0.285720i	$0.0922326\pi$
$673$			14.8244i			0.571439i	−0.958313	+	0.285720i	$0.907767\pi$
$674$	0.775315	−	2.85497i	0.0298640	−	0.109969i
$675$	−15.3416	+	15.7944i	−0.590499	+	0.607927i
$676$	5.41712	−	9.23827i	0.208351	−	0.355318i
$677$	20.6014	+	20.6014i	0.791776	+	0.791776i	0.981783	−	0.190007i	$-0.0608509\pi$
$677$	20.6014	+	20.6014i	0.791776	+	0.791776i	−0.190007	+	0.981783i	$0.560851\pi$
$678$	−0.0182426	−	12.3687i	−0.000700603	−	0.475017i
$679$	−14.7235			−0.565036
$680$	0.362213	−	35.8025i	0.0138902	−	1.37296i
$681$	28.6202	+	16.3394i	1.09673	+	0.626128i
$682$	21.7052	+	37.8890i	0.831135	+	1.45084i
$683$	19.0171	+	19.0171i	0.727669	+	0.727669i	0.970155	−	0.242486i	$-0.0779629\pi$
$683$	19.0171	+	19.0171i	0.727669	+	0.727669i	−0.242486	+	0.970155i	$0.577963\pi$
$684$	12.7650	+	22.8266i	0.488083	+	0.872797i
$685$	21.7223	−	21.7223i	0.829968	−	0.829968i
$686$	−6.14279	+	22.6198i	−0.234533	+	0.863629i
$687$	7.34648	−	12.8681i	0.280286	−	0.490950i
$688$	6.28946	−	22.2668i	0.239784	−	0.848912i
$689$		−	7.90877i		−	0.301300i
$690$	32.7681	+	32.6715i	1.24746	+	1.24378i
$691$	28.6146	−	28.6146i	1.08855	−	1.08855i	0.0928722	−	0.995678i	$-0.470395\pi$
$691$	28.6146	−	28.6146i	1.08855	−	1.08855i	0.995678	−	0.0928722i	$-0.0296048\pi$
$692$	−13.2075	+	3.44364i	−0.502074	+	0.130908i
$693$	24.0778	+	6.20209i	0.914639	+	0.235598i
$694$	−7.96518	+	4.56295i	−0.302354	+	0.173207i
$695$	−19.4762			−0.738775
$696$	8.53277	+	32.5294i	0.323434	+	1.23302i
$697$	−13.9752			−0.529347
$698$	15.6503	−	8.96545i	0.592371	−	0.339347i
$699$	−0.924693	−	3.38528i	−0.0349751	−	0.128043i
$700$	−9.98562	−	5.85535i	−0.377421	−	0.221311i
$701$	7.62597	+	7.62597i	0.288029	+	0.288029i	0.836300	−	0.548272i	$-0.184714\pi$
$701$	7.62597	+	7.62597i	0.288029	+	0.288029i	−0.548272	+	0.836300i	$0.684714\pi$
$702$	5.03932	−	19.6838i	0.190197	−	0.742917i
$703$	−15.9074	−	4.54768i	−0.599960	−	0.171519i
$704$	33.6237	+	35.0127i	1.26724	+	1.31959i
$705$	2.67563	−	4.68664i	0.100770	−	0.176509i
$706$	−0.828929	+	3.05239i	−0.0311972	+	0.114878i
$707$	−18.3515	−	18.3515i	−0.690181	−	0.690181i
$708$	−44.4725	+	25.5638i	−1.67138	+	0.960748i
$709$	10.1564	+	10.1564i	0.381430	+	0.381430i	0.871617	−	0.490187i	$-0.163072\pi$
$709$	10.1564	+	10.1564i	0.381430	+	0.381430i	−0.490187	+	0.871617i	$0.663072\pi$
$710$	2.37304	+	4.14242i	0.0890585	+	0.155462i
$711$	−3.79596	−	6.43002i	−0.142360	−	0.241145i
$712$	−34.7961	+	34.0991i	−1.30404	+	1.27792i
$713$		−	31.6271i		−	1.18444i
$714$	0.0205521	+	13.9346i	0.000769144	+	0.521488i
$715$	36.0578	−	36.0578i	1.34848	−	1.34848i
$716$	−33.5769	+	8.75463i	−1.25483	+	0.327176i
$717$	32.0150	−	8.74494i	1.19562	−	0.326586i
$718$	−37.2359	−	10.1120i	−1.38963	−	0.377378i
$719$			1.78004i			0.0663844i	0.999449	+	0.0331922i	$0.0105673\pi$
$719$			1.78004i			0.0663844i	−0.999449	+	0.0331922i	$0.989433\pi$
$720$	35.2648	−	9.30589i	1.31424	−	0.346810i
$721$			6.19554i			0.230734i
$722$	19.6841	−	18.2903i	0.732566	−	0.680696i
$723$	−25.0013	+	6.82914i	−0.929810	+	0.253979i
$724$	30.6055	−	7.97988i	1.13745	−	0.296570i
$725$	20.5692	+	20.5692i	0.763921	+	0.763921i
$726$	−63.2444	+	0.0932792i	−2.34722	+	0.00346192i
$727$		−	20.0942i		−	0.745253i	−0.927981	−	0.372626i	$-0.878457\pi$
$727$		−	20.0942i		−	0.745253i	0.927981	−	0.372626i	$-0.121543\pi$
$728$	10.6814	+	0.108063i	0.395878	+	0.00400509i
$729$	0.785121	+	26.9886i	0.0290786	+	0.999577i
$730$	−3.58350	−	6.25543i	−0.132631	−	0.231524i
$731$	−17.0358	+	17.0358i	−0.630092	+	0.630092i
$732$	−18.5714	−	32.3080i	−0.686419	−	1.19414i
$733$	−7.70945	+	7.70945i	−0.284755	+	0.284755i	−0.835002	−	0.550247i	$-0.814534\pi$
$733$	−7.70945	+	7.70945i	−0.284755	+	0.284755i	0.550247	+	0.835002i	$0.314534\pi$
$734$	19.3015	+	5.24163i	0.712430	+	0.193472i
$735$	−23.4730	−	13.4009i	−0.865816	−	0.494299i
$736$	−8.52615	−	34.1105i	−0.314278	−	1.25733i
$737$	24.5805			0.905433
$738$	−3.77135	−	13.7271i	−0.138825	−	0.505303i
$739$	16.4204	−	16.4204i	0.604033	−	0.604033i	−0.337347	−	0.941380i	$-0.609530\pi$
$739$	16.4204	−	16.4204i	0.604033	−	0.604033i	0.941380	+	0.337347i	$0.109530\pi$
$740$	−11.6706	+	19.9029i	−0.429021	+	0.731646i
$741$	−20.8740	−	0.246530i	−0.766824	−	0.00905650i
$742$	−4.79408	+	2.74635i	−0.175996	+	0.100822i
$743$			52.6090i			1.93004i	0.262181	+	0.965019i	$0.415558\pi$
$743$			52.6090i			1.93004i	−0.262181	+	0.965019i	$0.584442\pi$
$744$	−21.5225	−	12.5777i	−0.789055	−	0.461122i
$745$		−	49.2474i		−	1.80428i
$746$	−26.3646	+	15.1033i	−0.965278	+	0.552972i
$747$	47.5053	+	12.2367i	1.73813	+	0.447717i
$748$	−12.7525	−	48.9101i	−0.466278	−	1.78833i
$749$	−1.44565	+	1.44565i	−0.0528230	+	0.0528230i
$750$	−4.00795	+	4.01979i	−0.146350	+	0.146782i
$751$			27.8184i			1.01511i	0.861620	+	0.507554i	$0.169450\pi$
$751$			27.8184i			1.01511i	−0.861620	+	0.507554i	$0.830550\pi$
$752$	−3.57853	+	2.00220i	−0.130496	+	0.0730126i
$753$	−10.4359	−	5.95792i	−0.380306	−	0.217119i
$754$	−25.9049	−	7.03490i	−0.943400	−	0.256196i
$755$	−6.34728	+	6.34728i	−0.231001	+	0.231001i
$756$	−13.6817	+	3.78058i	−0.497599	+	0.137498i
$757$	−17.3283	−	17.3283i	−0.629809	−	0.629809i	0.318211	−	0.948020i	$-0.396918\pi$
$757$	−17.3283	−	17.3283i	−0.629809	−	0.629809i	−0.948020	+	0.318211i	$0.896918\pi$
$758$	−31.8571	+	18.2498i	−1.15710	+	0.662861i
$759$	56.7298	+	32.3873i	2.05916	+	1.17559i
$760$	−17.8602	−	32.9411i	−0.647859	−	1.19490i
$761$	18.8700			0.684036			0.342018	−	0.939693i	$-0.388890\pi$
$761$	18.8700			0.684036			0.342018	+	0.939693i	$0.388890\pi$
$762$	−31.7135	+	0.0467742i	−1.14886	+	0.00169445i
$763$	6.98478	−	6.98478i	0.252866	−	0.252866i
$764$	−10.9745	+	18.7158i	−0.397045	+	0.677114i
$765$	−36.7757	−	9.47290i	−1.32963	−	0.342493i
$766$	3.25870	+	0.884955i	0.117742	+	0.0319747i
$767$		−	40.9443i		−	1.47841i
$768$	−26.6032	−	7.76320i	−0.959962	−	0.280130i
$769$	−39.6994			−1.43160			−0.715799	−	0.698306i	$-0.753937\pi$
$769$	−39.6994			−1.43160			−0.715799	+	0.698306i	$0.753937\pi$
$770$	−34.3785	−	9.33605i	−1.23891	−	0.336448i
$771$	6.32666	+	23.1617i	0.227849	+	0.834150i
$772$	0.611220	−	1.04237i	0.0219983	−	0.0375155i
$773$	15.1149	+	15.1149i	0.543643	+	0.543643i	0.924595	−	0.380952i	$-0.124404\pi$
$773$	15.1149	+	15.1149i	0.543643	+	0.543643i	−0.380952	+	0.924595i	$0.624404\pi$
$774$	−21.3307	−	12.1362i	−0.766717	−	0.436225i
$775$	−21.5625			−0.774548
$776$	−21.7763	+	21.3401i	−0.781724	+	0.766065i
$777$	4.45198	−	7.79810i	0.159714	−	0.279755i
$778$	−6.34337	+	3.63388i	−0.227421	+	0.130281i
$779$	−12.7864	+	7.10095i	−0.458121	+	0.254418i
$780$	−7.58797	+	28.1053i	−0.271693	+	1.00633i
$781$	4.76554	+	4.76554i	0.170524	+	0.170524i
$782$	−9.59456	+	35.3304i	−0.343101	+	1.26341i
$783$	35.6662	−	0.518670i	1.27460	−	0.0185358i
$784$	10.0280	+	17.9231i	0.358143	+	0.640109i
$785$			2.86236i			0.102162i
$786$	11.1735	−	11.2066i	0.398547	−	0.399724i
$787$	27.4916	+	27.4916i	0.979969	+	0.979969i	0.999803	−	0.0198344i	$-0.00631391\pi$
$787$	27.4916	+	27.4916i	0.979969	+	0.979969i	−0.0198344	+	0.999803i	$0.506314\pi$
$788$	−8.25997	+	2.15365i	−0.294249	+	0.0767206i
$789$	2.33756	+	8.55777i	0.0832195	+	0.304665i
$790$	5.31784	+	9.28292i	0.189200	+	0.330271i
$791$		−	6.89692i		−	0.245226i
$792$	44.6007	−	25.7251i	1.58482	−	0.914101i
$793$	29.7449			1.05627
$794$	−14.8106	+	8.48444i	−0.525608	+	0.301101i
$795$	−3.96759	−	14.5253i	−0.140716	−	0.515158i
$796$	−23.1351	+	39.4542i	−0.820001	+	1.39842i
$797$	20.3607	−	20.3607i	0.721214	−	0.721214i	−0.247639	−	0.968852i	$-0.579655\pi$
$797$	20.3607	−	20.3607i	0.721214	−	0.721214i	0.968852	+	0.247639i	$0.0796546\pi$
$798$	7.09912	+	12.7388i	0.251306	+	0.450950i
$799$	4.26969			0.151051
$800$	−23.2556	+	5.81290i	−0.822209	+	0.205517i
$801$	26.2696	+	44.4984i	0.928190	+	1.57227i
$802$	−3.53171	−	0.959096i	−0.124709	−	0.0338668i
$803$	−7.19639	−	7.19639i	−0.253955	−	0.253955i
$804$	−12.1660	+	6.99330i	−0.429061	+	0.246635i
$805$	18.2449	+	18.2449i	0.643049	+	0.643049i
$806$	17.2652	−	9.89060i	0.608141	−	0.348382i
$807$	−2.99791	−	1.71152i	−0.105531	−	0.0602484i
$808$	−53.7408	−	0.543695i	−1.89059	−	0.0191271i
$809$	45.2534			1.59103			0.795513	−	0.605936i	$-0.207201\pi$
$809$	45.2534			1.59103			0.795513	+	0.605936i	$0.207201\pi$
$810$	−0.619551	−	38.6794i	−0.0217688	−	1.35906i
$811$	−31.6418	+	31.6418i	−1.11109	+	1.11109i	−0.118091	+	0.993003i	$0.537677\pi$
$811$	−31.6418	+	31.6418i	−1.11109	+	1.11109i	−0.993003	+	0.118091i	$0.962323\pi$
$812$	4.73120	+	18.1457i	0.166033	+	0.636791i
$813$	7.31759	+	26.7895i	0.256639	+	0.939550i
$814$	−8.53614	+	31.4329i	−0.299192	+	1.10172i
$815$			9.21833i			0.322904i
$816$	20.2270	+	20.5797i	0.708088	+	0.720433i
$817$	−6.93062	+	24.2428i	−0.242472	+	0.848148i
$818$	−28.2746	−	7.67844i	−0.988598	−	0.268470i
$819$	2.82616	−	10.9717i	0.0987540	−	0.383383i
$820$	5.14597	+	19.7365i	0.179705	+	0.689229i
$821$	−11.2101	+	11.2101i	−0.391236	+	0.391236i	−0.875128	−	0.483892i	$-0.839223\pi$
$821$	−11.2101	+	11.2101i	−0.391236	+	0.391236i	0.483892	+	0.875128i	$0.339223\pi$
$822$	0.0365159	+	24.7582i	0.00127364	+	0.863541i
$823$		−	35.0901i		−	1.22317i	−0.791180	−	0.611583i	$-0.790533\pi$
$823$		−	35.0901i		−	1.22317i	0.791180	−	0.611583i	$-0.209467\pi$
$824$	8.97975	+	9.16330i	0.312824	+	0.319219i
$825$	22.0808	−	38.6768i	0.768755	−	1.34655i
$826$	−24.8193	+	14.2181i	−0.863575	+	0.494710i
$827$	−10.9816	−	10.9816i	−0.381868	−	0.381868i	0.489907	−	0.871775i	$-0.337031\pi$
$827$	−10.9816	−	10.9816i	−0.381868	−	0.381868i	−0.871775	+	0.489907i	$0.837031\pi$
$828$	−37.2925	+	0.110006i	−1.29601	+	0.00382297i
$829$	−15.3243	−	15.3243i	−0.532235	−	0.532235i	0.389002	−	0.921237i	$-0.372820\pi$
$829$	−15.3243	−	15.3243i	−0.532235	−	0.532235i	−0.921237	+	0.389002i	$0.872820\pi$
$830$	−67.8285	−	18.4200i	−2.35436	−	0.639367i
$831$	16.7669	−	29.3689i	0.581637	−	1.01880i
$832$	15.9545	−	15.3216i	0.553124	−	0.531182i
$833$		−	21.3847i		−	0.740937i
$834$	11.0827	−	11.1154i	0.383763	−	0.384896i
$835$	50.9074	+	50.9074i	1.76172	+	1.76172i
$836$	−36.5196	−	38.2701i	−1.26306	−	1.32360i
$837$	−18.4224	+	18.9661i	−0.636770	+	0.655564i
$838$	−17.2341	−	30.0842i	−0.595342	−	1.03924i
$839$		−	31.3096i		−	1.08093i	−0.841367	−	0.540464i	$-0.818249\pi$
$839$		−	31.3096i		−	1.08093i	0.841367	−	0.540464i	$-0.181751\pi$
$840$	19.6716	−	5.16005i	0.678736	−	0.178039i
$841$		−	18.1238i		−	0.624960i
$842$	−7.39372	+	4.23559i	−0.254804	+	0.145968i
$843$	−19.7755	+	5.40171i	−0.681105	+	0.186045i
$844$	−4.64020	−	17.7967i	−0.159722	−	0.612588i
$845$	11.5079	+	11.5079i	0.395885	+	0.395885i
$846$	1.15222	+	4.19391i	0.0396142	+	0.144190i
$847$	−35.2658			−1.21175
$848$	−3.10999	+	11.0104i	−0.106798	+	0.378099i
$849$	1.58661	−	2.77912i	0.0544524	−	0.0953790i
$850$	24.0873	+	6.54131i	0.826188	+	0.224365i
$851$	16.6817	−	16.6817i	0.571841	−	0.571841i
$852$	−3.71451	−	1.00286i	−0.127257	−	0.0343573i
$853$	−2.61420	−	2.61420i	−0.0895086	−	0.0895086i	0.660935	−	0.750443i	$-0.270160\pi$
$853$	−2.61420	−	2.61420i	−0.0895086	−	0.0895086i	−0.750443	+	0.660935i	$0.770160\pi$
$854$	−10.3290	−	18.0305i	−0.353452	−	0.616993i
$855$	−38.4608	+	10.0191i	−1.31533	+	0.342645i
$856$	−0.0428298	+	4.23346i	−0.00146389	+	0.144697i
$857$			4.87894i			0.166661i	0.996522	+	0.0833307i	$0.0265558\pi$
$857$			4.87894i			0.166661i	−0.996522	+	0.0833307i	$0.973444\pi$
$858$	0.0606142	+	41.0971i	0.00206933	+	1.40303i
$859$	−27.1990	−	27.1990i	−0.928019	−	0.928019i	0.0695591	−	0.997578i	$-0.477841\pi$
$859$	−27.1990	−	27.1990i	−0.928019	−	0.928019i	−0.997578	+	0.0695591i	$0.977841\pi$
$860$	30.3319	+	17.7860i	1.03431	+	0.606496i
$861$	−2.09165	−	7.65749i	−0.0712833	−	0.260966i
$862$	15.0829	+	4.09601i	0.513726	+	0.139511i
$863$	20.0597			0.682839			0.341419	−	0.939911i	$-0.389092\pi$
$863$	20.0597			0.682839			0.341419	+	0.939911i	$0.389092\pi$
$864$	−14.7559	+	25.4217i	−0.502008	+	0.864863i
$865$		−	20.7420i		−	0.705249i
$866$	−5.22996	+	19.2585i	−0.177721	+	0.654430i
$867$	−0.158368	−	0.579783i	−0.00537847	−	0.0196905i
$868$	−11.9908	−	7.03116i	−0.406995	−	0.238653i
$869$	10.6793	+	10.6793i	0.362270	+	0.362270i
$870$	−51.1062	+	0.0753766i	−1.73266	+	0.00255550i
$871$		−	11.2008i		−	0.379525i
$872$	0.206936	−	20.4543i	0.00700772	−	0.692669i
$873$	16.4402	+	27.8483i	0.556417	+	0.942522i
$874$	9.17335	+	37.2003i	0.310293	+	1.25832i
$875$	−2.23818	+	2.23818i	−0.0756642	+	0.0756642i
$876$	5.60924	+	1.51440i	0.189519	+	0.0511670i
$877$	12.2288	+	12.2288i	0.412936	+	0.412936i	0.882760	−	0.469824i	$-0.155683\pi$
$877$	12.2288	+	12.2288i	0.412936	+	0.412936i	−0.469824	+	0.882760i	$0.655683\pi$
$878$	39.8231	+	10.8146i	1.34396	+	0.364976i
$879$	−5.95959	+	10.4388i	−0.201012	+	0.352093i
$880$	−64.3779	+	36.0196i	−2.17018	+	1.21422i
$881$			47.5308i			1.60135i	0.599096	+	0.800677i	$0.295527\pi$
$881$			47.5308i			1.60135i	−0.599096	+	0.800677i	$0.704473\pi$
$882$	21.0052	−	5.77090i	0.707282	−	0.194316i
$883$	26.1275	−	26.1275i	0.879259	−	0.879259i	−0.114199	−	0.993458i	$-0.536430\pi$
$883$	26.1275	−	26.1275i	0.879259	−	0.879259i	0.993458	+	0.114199i	$0.0364302\pi$
$884$	−22.2873	+	5.81105i	−0.749604	+	0.195447i
$885$	−20.5405	−	75.1984i	−0.690462	−	2.52777i
$886$	0.806423	−	0.461970i	0.0270923	−	0.0155202i
$887$		−	28.1577i		−	0.945444i	−0.881212	−	0.472722i	$-0.843272\pi$
$887$		−	28.1577i		−	0.945444i	0.881212	−	0.472722i	$-0.156728\pi$
$888$	−4.71794	−	17.9862i	−0.158324	−	0.603577i
$889$	−17.6838			−0.593095
$890$	−36.8016	−	64.2416i	−1.23359	−	2.15338i
$891$	−15.1544	−	52.4663i	−0.507692	−	1.75769i
$892$	−16.4688	+	28.0856i	−0.551415	+	0.940374i
$893$	3.90650	−	2.16948i	0.130726	−	0.0725988i
$894$	28.1064	+	28.0236i	0.940019	+	0.937250i
$895$		−	52.7316i		−	1.76262i
$896$	−14.8278	−	4.35072i	−0.495363	−	0.145347i
$897$	14.7582	−	25.8506i	0.492763	−	0.863125i
$898$	−39.7919	−	10.8062i	−1.32787	−	0.360606i
$899$	24.6997	+	24.6997i	0.823782	+	0.823782i
$900$	0.0749990	+	25.4250i	0.00249997	+	0.847502i
$901$	8.42381	−	8.42381i	0.280638	−	0.280638i
$902$	14.3127	+	24.9845i	0.476561	+	0.831894i
$903$	−11.8842	−	6.78478i	−0.395483	−	0.225783i
$904$	−9.99632	−	10.2007i	−0.332473	−	0.339269i
$905$			48.0651i			1.59774i
$906$	−0.0106700	−	7.23436i	−0.000354486	−	0.240346i
$907$	−31.9776	+	31.9776i	−1.06180	+	1.06180i	−0.0638369	+	0.997960i	$0.520334\pi$
$907$	−31.9776	+	31.9776i	−1.06180	+	1.06180i	−0.997960	+	0.0638369i	$0.979666\pi$
$908$	36.8231	−	9.60102i	1.22202	−	0.318621i
$909$	−14.2192	+	55.2017i	−0.471620	+	1.83093i
$910$	−4.25424	+	15.6655i	−0.141027	+	0.519308i
$911$	40.3554			1.33704			0.668518	−	0.743696i	$-0.266929\pi$
$911$	40.3554			1.33704			0.668518	+	0.743696i	$0.266929\pi$
$912$	28.9633	+	8.55156i	0.959070	+	0.283170i
$913$	−99.2223			−3.28378
$914$	15.2816	−	56.2721i	0.505471	−	1.86131i
$915$	54.6295	−	14.9221i	1.80600	−	0.493310i
$916$	−4.31678	−	16.5563i	−0.142631	−	0.547036i
$917$	6.23969	−	6.23969i	0.206053	−	0.206053i
$918$	26.3332	−	15.5982i	0.869124	−	0.514816i
$919$			30.4111i			1.00317i	0.865108	+	0.501585i	$0.167250\pi$
$919$			30.4111i			1.00317i	−0.865108	+	0.501585i	$0.832750\pi$
$920$	53.4285	+	0.540535i	1.76149	+	0.0178209i
$921$	−11.6933	+	20.4820i	−0.385307	+	0.674905i
$922$	12.9543	+	22.6132i	0.426626	+	0.744727i
$923$	2.17156	−	2.17156i	0.0714776	−	0.0714776i
$924$	24.8909	−	14.3079i	0.818851	−	0.470695i
$925$	−11.3731	−	11.3731i	−0.373946	−	0.373946i
$926$	18.8191	+	5.11064i	0.618433	+	0.167946i
$927$	11.7184	−	6.91792i	0.384881	−	0.227214i
$928$	33.2978	+	19.9805i	1.09305	+	0.655892i
$929$			7.66141i			0.251363i	0.992071	+	0.125681i	$0.0401117\pi$
$929$			7.66141i			0.251363i	−0.992071	+	0.125681i	$0.959888\pi$
$930$	26.7475	−	26.8265i	0.877086	−	0.879677i
$931$	−10.8658	−	19.5657i	−0.356113	−	0.641241i
$932$	−3.49555	−	2.04972i	−0.114501	−	0.0671407i
$933$	−15.0407	−	55.0636i	−0.492410	−	1.80270i
$934$	18.2627	+	31.8798i	0.597575	+	1.04314i
$935$	76.8119			2.51202
$936$	−11.7224	−	20.3236i	−0.383158	−	0.664297i
$937$			25.6467i			0.837841i	0.908023	+	0.418920i	$0.137591\pi$
$937$			25.6467i			0.837841i	−0.908023	+	0.418920i	$0.862409\pi$
$938$	−6.78963	+	3.88952i	−0.221689	+	0.126997i
$939$	31.2924	−	8.54756i	1.02119	−	0.278939i
$940$	−1.57220	−	6.02990i	−0.0512794	−	0.196674i
$941$	25.8382	−	25.8382i	0.842302	−	0.842302i	−0.146856	−	0.989158i	$-0.546915\pi$
$941$	25.8382	−	25.8382i	0.842302	−	0.842302i	0.989158	+	0.146856i	$0.0469152\pi$
$942$	−1.63360	−	1.62879i	−0.0532256	−	0.0530688i
$943$		−	20.8554i		−	0.679144i
$944$	−16.1007	+	57.0017i	−0.524033	+	1.85525i
$945$	−0.313657	−	21.5685i	−0.0102033	−	0.701624i
$946$	47.9035	+	13.0090i	1.55748	+	0.422959i
$947$	13.0865	+	13.0865i	0.425255	+	0.425255i	0.887008	−	0.461753i	$-0.152779\pi$
$947$	13.0865	+	13.0865i	0.425255	+	0.425255i	−0.461753	+	0.887008i	$0.652779\pi$
$948$	−8.32399	−	2.24734i	−0.270351	−	0.0729903i
$949$	−3.27924	+	3.27924i	−0.106449	+	0.106449i
$950$	25.3621	−	6.25414i	0.822856	−	0.202911i
$951$	−35.4971	−	20.2655i	−1.15107	−	0.657153i
$952$	11.2619	+	11.4921i	0.364999	+	0.372460i
$953$			3.44347i			0.111545i	0.998444	+	0.0557724i	$0.0177621\pi$
$953$			3.44347i			0.111545i	−0.998444	+	0.0557724i	$0.982238\pi$
$954$	10.5476	+	6.00105i	0.341490	+	0.194291i
$955$	−23.3139	−	23.3139i	−0.754421	−	0.754421i
$956$	19.3844	−	33.0579i	0.626937	−	1.06917i
$957$	−69.5975	+	19.0106i	−2.24977	+	0.614527i
$958$	−1.31822	+	4.85412i	−0.0425897	+	0.156830i
$959$			13.8054i			0.445801i
$960$	21.6157	−	36.1437i	0.697645	−	1.16653i
$961$	5.10753			0.164759
$962$	14.3233	+	3.88974i	0.461803	+	0.125410i
$963$	4.34854	+	1.12012i	0.140130	+	0.0360954i
$964$	−15.1378	+	25.8157i	−0.487555	+	0.831469i
$965$	1.29845	+	1.29845i	0.0417987	+	0.0417987i
$966$	−20.7948	+	0.0306702i	−0.669061	+	0.000986799i
$967$			37.7558i			1.21414i	0.794647	+	0.607072i	$0.207656\pi$
$967$			37.7558i			1.21414i	−0.794647	+	0.607072i	$0.792344\pi$
$968$	−52.1586	+	51.1138i	−1.67644	+	1.64286i
$969$	−21.9707	−	22.4959i	−0.705802	−	0.722673i
$970$	−23.0314	−	40.2041i	−0.739495	−	1.29088i
$971$	16.5351	+	16.5351i	0.530636	+	0.530636i	0.920762	−	0.390126i	$-0.127569\pi$
$971$	16.5351	+	16.5351i	0.530636	+	0.530636i	−0.390126	+	0.920762i	$0.627569\pi$
$972$	22.4276	+	21.6565i	0.719366	+	0.694631i
$973$	6.18896	−	6.18896i	0.198409	−	0.198409i
$974$	−30.5643	−	8.30024i	−0.979342	−	0.265957i
$975$	−17.6242	−	10.0618i	−0.564427	−	0.322234i
$976$	−41.4101	−	11.6967i	−1.32550	−	0.374402i
$977$	−31.6863			−1.01373			−0.506867	−	0.862024i	$-0.669196\pi$
$977$	−31.6863			−1.01373			−0.506867	+	0.862024i	$0.669196\pi$
$978$	−5.26107	−	5.24558i	−0.168231	−	0.167735i
$979$	−73.9051	−	73.9051i	−2.36202	−	2.36202i
$980$	−30.2007	+	7.87434i	−0.964727	+	0.251537i
$981$	−21.0103	−	5.41195i	−0.670808	−	0.172790i
$982$	31.7672	−	18.1982i	1.01373	−	0.580729i
$983$			24.0948i			0.768503i	0.923228	+	0.384252i	$0.125541\pi$
$983$			24.0948i			0.768503i	−0.923228	+	0.384252i	$0.874459\pi$
$984$	−14.1923	−	8.29393i	−0.452433	−	0.264401i
$985$		−	12.9720i		−	0.413323i
$986$	−20.0988	−	35.0849i	−0.640077	−	1.11733i
$987$	0.639040	+	2.33951i	0.0203409	+	0.0744675i
$988$	−17.4389	+	16.6412i	−0.554804	+	0.529427i
$989$	−25.4228	−	25.4228i	−0.808397	−	0.808397i
$990$	20.7285	+	75.4486i	0.658795	+	2.39792i
$991$			19.0922i			0.606485i	0.952913	+	0.303242i	$0.0980692\pi$
$991$			19.0922i			0.606485i	−0.952913	+	0.303242i	$0.901931\pi$
$992$	−27.9255	+	6.98019i	−0.886637	+	0.221621i
$993$	0.740823	+	0.422940i	0.0235093	+	0.0134216i
$994$	−2.07042	−	0.562257i	−0.0656697	−	0.0178337i
$995$	−49.1473	−	49.1473i	−1.55807	−	1.55807i
$996$	49.1096	−	28.2294i	1.55610	−	0.894482i
$997$	32.3517	+	32.3517i	1.02459	+	1.02459i	0.999690	+	0.0248999i	$0.00792670\pi$
$997$	32.3517	+	32.3517i	1.02459	+	1.02459i	0.0248999	+	0.999690i	$0.492073\pi$
$998$	5.59272	−	3.20386i	0.177034	−	0.101416i
$999$	−19.7205	+	0.286783i	−0.623930	+	0.00907342i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	912.2.r.a.341.14	yes	312
3.2	odd	2	inner	912.2.r.a.341.144	yes	312
16.13	even	4	inner	912.2.r.a.797.13	yes	312
19.18	odd	2	inner	912.2.r.a.341.143	yes	312
48.29	odd	4	inner	912.2.r.a.797.143	yes	312
57.56	even	2	inner	912.2.r.a.341.13	✓	312
304.189	odd	4	inner	912.2.r.a.797.144	yes	312
912.797	even	4	inner	912.2.r.a.797.14	yes	312

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
912.2.r.a.341.13	✓	312	57.56	even	2	inner
912.2.r.a.341.14	yes	312	1.1	even	1	trivial
912.2.r.a.341.143	yes	312	19.18	odd	2	inner
912.2.r.a.341.144	yes	312	3.2	odd	2	inner
912.2.r.a.797.13	yes	312	16.13	even	4	inner
912.2.r.a.797.14	yes	312	912.797	even	4	inner
912.2.r.a.797.143	yes	312	48.29	odd	4	inner
912.2.r.a.797.144	yes	312	304.189	odd	4	inner

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:	\( N \)	\(=\)	\( 912 = 2^{4} \cdot 3 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	912.r (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.36478 - 0.370630i) q^{2} +(0.456392 + 1.67084i) q^{3} +(1.72527 + 1.01166i) q^{4} +(-2.14913 + 2.14913i) q^{5} +(-0.00361275 - 2.44949i) q^{6} -1.36586i q^{7} +(-1.97966 - 2.02013i) q^{8} +(-2.58341 + 1.52512i) q^{9} +(3.72963 - 2.13657i) q^{10} +(4.29065 - 4.29065i) q^{11} +(-0.902922 + 3.34436i) q^{12} +(-1.95516 - 1.95516i) q^{13} +(-0.506229 + 1.86410i) q^{14} +(-4.57170 - 2.61001i) q^{15} +(1.95309 + 3.49076i) q^{16} -4.16497i q^{17} +(4.09105 - 1.12396i) q^{18} +(-2.11627 - 3.81069i) q^{19} +(-5.88201 + 1.53364i) q^{20} +(2.28213 - 0.623368i) q^{21} +(-7.44606 + 4.26557i) q^{22} +6.21545 q^{23} +(2.47181 - 4.22967i) q^{24} -4.23753i q^{25} +(1.94373 + 3.39301i) q^{26} +(-3.72727 - 3.62042i) q^{27} +(1.38179 - 2.35647i) q^{28} +(-4.85406 + 4.85406i) q^{29} +(5.27203 + 5.25650i) q^{30} -5.08846i q^{31} +(-1.37177 - 5.48801i) q^{32} +(9.12722 + 5.21078i) q^{33} +(-1.54366 + 5.68429i) q^{34} +(2.93541 + 2.93541i) q^{35} +(-5.99997 + 0.0176988i) q^{36} +(2.68391 - 2.68391i) q^{37} +(1.47589 + 5.98513i) q^{38} +(2.37444 - 4.15908i) q^{39} +(8.59608 + 0.0869664i) q^{40} -3.35540i q^{41} +(-3.34566 + 0.00493452i) q^{42} +(-4.09025 - 4.09025i) q^{43} +(11.7432 - 3.06185i) q^{44} +(2.27442 - 8.82976i) q^{45} +(-8.48274 - 2.30363i) q^{46} +1.02514i q^{47} +(-4.94113 + 4.85646i) q^{48} +5.13442 q^{49} +(-1.57055 + 5.78330i) q^{50} +(6.95900 - 1.90086i) q^{51} +(-1.39522 - 5.35113i) q^{52} +(2.02254 + 2.02254i) q^{53} +(3.74508 + 6.32253i) q^{54} +18.4424i q^{55} +(-2.75922 + 2.70395i) q^{56} +(5.40121 - 5.27512i) q^{57} +(8.42380 - 4.82568i) q^{58} +(10.4708 + 10.4708i) q^{59} +(-5.24696 - 9.12796i) q^{60} +(-7.60676 + 7.60676i) q^{61} +(-1.88594 + 6.94465i) q^{62} +(2.08310 + 3.52858i) q^{63} +(-0.161855 + 7.99836i) q^{64} +8.40379 q^{65} +(-10.5254 - 10.4944i) q^{66} +(2.86442 + 2.86442i) q^{67} +(4.21353 - 7.18569i) q^{68} +(2.83668 + 10.3850i) q^{69} +(-2.91825 - 5.09415i) q^{70} +1.11068i q^{71} +(8.19522 + 2.19961i) q^{72} -1.67722i q^{73} +(-4.65769 + 2.66822i) q^{74} +(7.08023 - 1.93397i) q^{75} +(0.203990 - 8.71541i) q^{76} +(-5.86044 - 5.86044i) q^{77} +(-4.78208 + 4.79621i) q^{78} +2.48897i q^{79} +(-11.6996 - 3.30466i) q^{80} +(4.34805 - 7.88001i) q^{81} +(-1.24361 + 4.57940i) q^{82} +(-11.5626 - 11.5626i) q^{83} +(4.56793 + 1.23327i) q^{84} +(8.95107 + 8.95107i) q^{85} +(4.06634 + 7.09828i) q^{86} +(-10.3257 - 5.89501i) q^{87} +(-17.1617 - 0.173625i) q^{88} -17.2247i q^{89} +(-6.37666 + 11.2077i) q^{90} +(-2.67048 + 2.67048i) q^{91} +(10.7233 + 6.28792i) q^{92} +(8.50201 - 2.32233i) q^{93} +(0.379948 - 1.39910i) q^{94} +(12.7378 + 3.64154i) q^{95} +(8.54352 - 4.79669i) q^{96} -10.7797i q^{97} +(-7.00738 - 1.90297i) q^{98} +(-4.54079 + 17.6283i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 312 q - 8 q^{4} - 4 q^{6} - 12 q^{19} - 20 q^{24} + 24 q^{28} - 40 q^{30} + 12 q^{36} + 60 q^{42} - 8 q^{43} - 24 q^{45} - 280 q^{49} + 40 q^{54} - 8 q^{58} - 40 q^{61} + 48 q^{63} + 40 q^{64} - 68 q^{66}+ \cdots - 8 q^{99}+O(q^{100}) \) 312 * q - 8 * q^4 - 4 * q^6 - 12 * q^19 - 20 * q^24 + 24 * q^28 - 40 * q^30 + 12 * q^36 + 60 * q^42 - 8 * q^43 - 24 * q^45 - 280 * q^49 + 40 * q^54 - 8 * q^58 - 40 * q^61 + 48 * q^63 + 40 * q^64 - 68 * q^66 + 32 * q^76 - 8 * q^81 - 32 * q^82 + 8 * q^93 + 120 * q^96 - 8 * q^99

Introduction

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