LMFDB - Embedded newform 980.2.x.l.263.9

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [980,2,Mod(67,980)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("980.67"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(980, base_ring=CyclotomicField(12)) chi = DirichletCharacter(H, H._module([6, 3, 8])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 980 = 2^{2} \cdot 5 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	980.x (of order $12$, degree $4$, not minimal)

Newform invariants

comment:select newform

sage:traces = [72,0,0,0,0,16,0,0,0,-16,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(11)] == traces)

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

Self dual:	no
Analytic conductor:	$7.82533939809$
Analytic rank:	$0$
Dimension:	$72$
Relative dimension:	$18$ over $\Q(\zeta_{12})$
Twist minimal:	no (minimal twist has level 140)
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			263.9
Character	$\chi$	$=$	980.263
Dual form			980.2.x.l.667.9

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.112153 + 1.40976i) q^{2} +(0.643219 + 2.40053i) q^{3} +(-1.97484 - 0.316219i) q^{4} +(1.36213 - 1.77331i) q^{5} +(-3.45630 + 0.637557i) q^{6} +(0.667278 - 2.74859i) q^{8} +(-2.75072 + 1.58813i) q^{9} +(2.34717 + 2.11915i) q^{10} +(4.62887 + 2.67248i) q^{11} +(-0.511166 - 4.94406i) q^{12} +(2.61810 + 2.61810i) q^{13} +(5.13301 + 2.12920i) q^{15} +(3.80001 + 1.24896i) q^{16} +(0.381657 + 1.42436i) q^{17} +(-1.93038 - 4.05597i) q^{18} +(-0.130253 - 0.225604i) q^{19} +(-3.25074 + 3.07127i) q^{20} +(-4.28669 + 6.22586i) q^{22} +(-1.44978 - 0.388469i) q^{23} +(7.02727 - 0.166127i) q^{24} +(-1.28922 - 4.83093i) q^{25} +(-3.98452 + 3.39727i) q^{26} +(-0.309743 - 0.309743i) q^{27} -1.36847i q^{29} +(-3.57734 + 6.99752i) q^{30} +(1.77668 + 1.02577i) q^{31} +(-2.18692 + 5.21703i) q^{32} +(-3.43798 + 12.8307i) q^{33} +(-2.05081 + 0.378297i) q^{34} +(5.93444 - 2.26648i) q^{36} +(-11.2136 - 3.00467i) q^{37} +(0.332656 - 0.158323i) q^{38} +(-4.60081 + 7.96884i) q^{39} +(-3.96517 - 4.92721i) q^{40} +9.70325 q^{41} +(-6.86124 + 6.86124i) q^{43} +(-8.29620 - 6.74146i) q^{44} +(-0.930593 + 7.04110i) q^{45} +(0.710245 - 2.00028i) q^{46} +(-0.357579 + 1.33450i) q^{47} +(-0.553932 + 9.92539i) q^{48} +(6.95504 - 1.27569i) q^{50} +(-3.17373 + 1.83236i) q^{51} +(-4.34245 - 5.99823i) q^{52} +(-2.48296 + 0.665306i) q^{53} +(0.471402 - 0.401925i) q^{54} +(11.0442 - 4.56814i) q^{55} +(0.457788 - 0.457788i) q^{57} +(1.92921 + 0.153478i) q^{58} +(-2.26592 + 3.92468i) q^{59} +(-9.46360 - 5.82799i) q^{60} +(-2.06834 - 3.58246i) q^{61} +(-1.64535 + 2.38965i) q^{62} +(-7.10948 - 3.66814i) q^{64} +(8.20888 - 1.07651i) q^{65} +(-17.7026 - 6.28573i) q^{66} +(6.78396 - 1.81776i) q^{67} +(-0.303302 - 2.93358i) q^{68} -3.73012i q^{69} -7.29096i q^{71} +(2.52962 + 8.62033i) q^{72} +(13.1916 - 3.53467i) q^{73} +(5.49350 - 15.4714i) q^{74} +(10.7675 - 6.20216i) q^{75} +(0.185888 + 0.486722i) q^{76} +(-10.7181 - 7.37977i) q^{78} +(-5.09813 - 8.83021i) q^{79} +(7.39089 - 5.03733i) q^{80} +(-4.22008 + 7.30939i) q^{81} +(-1.08825 + 13.6793i) q^{82} +(-5.83046 + 5.83046i) q^{83} +(3.04570 + 1.26337i) q^{85} +(-8.90318 - 10.4422i) q^{86} +(3.28504 - 0.880224i) q^{87} +(10.4343 - 10.9396i) q^{88} +(6.60960 - 3.81606i) q^{89} +(-9.82189 - 2.10160i) q^{90} +(2.74026 + 1.22561i) q^{92} +(-1.31959 + 4.92476i) q^{93} +(-1.84123 - 0.653770i) q^{94} +(-0.577486 - 0.0763239i) q^{95} +(-13.9303 - 1.89408i) q^{96} +(-11.5761 + 11.5761i) q^{97} -16.9770 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 72 q + 16 q^{6} - 16 q^{10} - 16 q^{12} + 8 q^{13} + 8 q^{16} - 20 q^{17} - 28 q^{18} - 40 q^{20} + 8 q^{22} + 20 q^{25} - 32 q^{26} + 4 q^{30} - 20 q^{37} - 36 q^{40} + 20 q^{45} - 16 q^{46} + 48 q^{48}+ \cdots - 40 q^{97}+O(q^{100}) $ 72 * q + 16 * q^6 - 16 * q^10 - 16 * q^12 + 8 * q^13 + 8 * q^16 - 20 * q^17 - 28 * q^18 - 40 * q^20 + 8 * q^22 + 20 * q^25 - 32 * q^26 + 4 * q^30 - 20 * q^37 - 36 * q^40 + 20 * q^45 - 16 * q^46 + 48 * q^48 + 80 * q^50 + 16 * q^52 + 44 * q^53 - 32 * q^57 + 4 * q^58 - 40 * q^60 - 64 * q^61 - 80 * q^62 - 4 * q^65 + 32 * q^66 + 80 * q^68 - 80 * q^72 + 52 * q^73 - 16 * q^76 - 152 * q^78 - 20 * q^80 + 36 * q^81 + 56 * q^82 - 40 * q^85 - 56 * q^86 + 40 * q^88 + 32 * q^90 - 112 * q^92 - 32 * q^93 + 120 * q^96 - 40 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/980\mathbb{Z}\right)^\times$.

$n$	$101$	$197$	$491$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{3}{4}\right)$	$-1$

Coefficient data

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

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

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

$2$	−0.112153	+	1.40976i	−0.0793044	+	0.996850i
$2$	−0.112153	+	1.40976i	−0.0793044	+	0.996850i
$3$	0.643219	+	2.40053i	0.371363	+	1.38594i	0.858587	+	0.512668i	$0.171343\pi$
$3$	0.643219	+	2.40053i	0.371363	+	1.38594i	−0.487224	+	0.873277i	$0.661991\pi$
$4$	−1.97484	−	0.316219i	−0.987422	−	0.158109i
$5$	1.36213	−	1.77331i	0.609162	−	0.793046i
$5$	1.36213	−	1.77331i	0.609162	−	0.793046i
$6$	−3.45630	+	0.637557i	−1.41103	+	0.260282i
$7$		0			0
$7$		0			0
$8$	0.667278	−	2.74859i	0.235918	−	0.971773i
$9$	−2.75072	+	1.58813i	−0.916907	+	0.529377i
$10$	2.34717	+	2.11915i	0.742239	+	0.670135i
$11$	4.62887	+	2.67248i	1.39566	+	0.805782i	0.993934	−	0.109979i	$-0.0350785\pi$
$11$	4.62887	+	2.67248i	1.39566	+	0.805782i	0.401722	+	0.915762i	$0.368412\pi$
$12$	−0.511166	−	4.94406i	−0.147561	−	1.42723i
$13$	2.61810	+	2.61810i	0.726131	+	0.726131i	0.969847	−	0.243716i	$-0.0783664\pi$
$13$	2.61810	+	2.61810i	0.726131	+	0.726131i	−0.243716	+	0.969847i	$0.578366\pi$
$14$		0			0
$15$	5.13301	+	2.12920i	1.32534	+	0.549757i
$16$	3.80001	+	1.24896i	0.950003	+	0.312241i
$17$	0.381657	+	1.42436i	0.0925654	+	0.345459i	0.996639	−	0.0819178i	$-0.0261045\pi$
$17$	0.381657	+	1.42436i	0.0925654	+	0.345459i	−0.904074	+	0.427377i	$0.859438\pi$
$18$	−1.93038	−	4.05597i	−0.454995	−	0.956001i
$19$	−0.130253	−	0.225604i	−0.0298820	−	0.0517572i	0.850698	−	0.525655i	$-0.176180\pi$
$19$	−0.130253	−	0.225604i	−0.0298820	−	0.0517572i	−0.880580	+	0.473898i	$0.842846\pi$
$20$	−3.25074	+	3.07127i	−0.726887	+	0.686757i
$21$		0			0
$22$	−4.28669	+	6.22586i	−0.913926	+	1.32736i
$23$	−1.44978	−	0.388469i	−0.302301	−	0.0810013i	0.104480	−	0.994527i	$-0.466682\pi$
$23$	−1.44978	−	0.388469i	−0.302301	−	0.0810013i	−0.406781	+	0.913526i	$0.633349\pi$
$24$	7.02727	−	0.166127i	1.43443	−	0.0339106i
$25$	−1.28922	−	4.83093i	−0.257844	−	0.966186i
$26$	−3.98452	+	3.39727i	−0.781429	+	0.666259i
$27$	−0.309743	−	0.309743i	−0.0596101	−	0.0596101i
$28$		0			0
$29$		−	1.36847i		−	0.254118i	−0.991895	−	0.127059i	$-0.959446\pi$
$29$		−	1.36847i		−	0.254118i	0.991895	−	0.127059i	$-0.0405537\pi$
$30$	−3.57734	+	6.99752i	−0.653130	+	1.27757i
$31$	1.77668	+	1.02577i	0.319101	+	0.184233i	0.650992	−	0.759085i	$-0.274353\pi$
$31$	1.77668	+	1.02577i	0.319101	+	0.184233i	−0.331891	+	0.943318i	$0.607687\pi$
$32$	−2.18692	+	5.21703i	−0.386597	+	0.922249i
$33$	−3.43798	+	12.8307i	−0.598475	+	2.23354i
$34$	−2.05081	+	0.378297i	−0.351712	+	0.0648775i
$35$		0			0
$36$	5.93444	−	2.26648i	0.989073	−	0.377746i
$37$	−11.2136	−	3.00467i	−1.84350	−	0.493964i	−0.844373	−	0.535756i	$-0.820027\pi$
$37$	−11.2136	−	3.00467i	−1.84350	−	0.493964i	−0.999126	+	0.0417917i	$0.986693\pi$
$38$	0.332656	−	0.158323i	0.0539640	−	0.0256833i
$39$	−4.60081	+	7.96884i	−0.736719	+	1.27604i
$40$	−3.96517	−	4.92721i	−0.626948	−	0.779061i
$41$	9.70325			1.51539			0.757697	−	0.652607i	$-0.226325\pi$
$41$	9.70325			1.51539			0.757697	+	0.652607i	$0.226325\pi$
$42$		0			0
$43$	−6.86124	+	6.86124i	−1.04633	+	1.04633i	−0.0474554	+	0.998873i	$0.515111\pi$
$43$	−6.86124	+	6.86124i	−1.04633	+	1.04633i	−0.998873	+	0.0474554i	$0.984889\pi$
$44$	−8.29620	−	6.74146i	−1.25070	−	1.01631i
$45$	−0.930593	+	7.04110i	−0.138725	+	1.04963i
$46$	0.710245	−	2.00028i	0.104720	−	0.294925i
$47$	−0.357579	+	1.33450i	−0.0521583	+	0.194658i	−0.987089	−	0.160173i	$-0.948795\pi$
$47$	−0.357579	+	1.33450i	−0.0521583	+	0.194658i	0.934931	+	0.354831i	$0.115461\pi$
$48$	−0.553932	+	9.92539i	−0.0799532	+	1.43261i
$49$		0			0
$50$	6.95504	−	1.27569i	0.983592	−	0.180409i
$51$	−3.17373	+	1.83236i	−0.444412	+	0.256581i
$52$	−4.34245	−	5.99823i	−0.602189	−	0.831806i
$53$	−2.48296	+	0.665306i	−0.341060	+	0.0913868i	−0.425284	−	0.905060i	$-0.639826\pi$
$53$	−2.48296	+	0.665306i	−0.341060	+	0.0913868i	0.0842235	+	0.996447i	$0.473159\pi$
$54$	0.471402	−	0.401925i	0.0641497	−	0.0546950i
$55$	11.0442	−	4.56814i	1.48920	−	0.615968i
$56$		0			0
$57$	0.457788	−	0.457788i	0.0606356	−	0.0606356i
$58$	1.92921	+	0.153478i	0.253317	+	0.0201527i
$59$	−2.26592	+	3.92468i	−0.294997	+	0.510950i	−0.974984	−	0.222274i	$-0.928652\pi$
$59$	−2.26592	+	3.92468i	−0.294997	+	0.510950i	0.679987	+	0.733224i	$0.261985\pi$
$60$	−9.46360	−	5.82799i	−1.22175	−	0.752390i
$61$	−2.06834	−	3.58246i	−0.264823	−	0.458687i	0.702694	−	0.711492i	$-0.251980\pi$
$61$	−2.06834	−	3.58246i	−0.264823	−	0.458687i	−0.967517	+	0.252805i	$0.918647\pi$
$62$	−1.64535	+	2.38965i	−0.208959	+	0.303486i
$63$		0			0
$64$	−7.10948	−	3.66814i	−0.888685	−	0.458518i
$65$	8.20888	−	1.07651i	1.01819	−	0.133524i
$66$	−17.7026	−	6.28573i	−2.17904	−	0.773720i
$67$	6.78396	−	1.81776i	0.828792	−	0.222074i	0.180606	−	0.983556i	$-0.442194\pi$
$67$	6.78396	−	1.81776i	0.828792	−	0.222074i	0.648187	+	0.761481i	$0.275528\pi$
$68$	−0.303302	−	2.93358i	−0.0367808	−	0.355749i
$69$		−	3.73012i		−	0.449053i
$70$		0			0
$71$		−	7.29096i		−	0.865278i	−0.901567	−	0.432639i	$-0.857583\pi$
$71$		−	7.29096i		−	0.865278i	0.901567	−	0.432639i	$-0.142417\pi$
$72$	2.52962	+	8.62033i	0.298119	+	1.01592i
$73$	13.1916	−	3.53467i	1.54395	−	0.413701i	0.616414	−	0.787422i	$-0.288585\pi$
$73$	13.1916	−	3.53467i	1.54395	−	0.413701i	0.927541	+	0.373721i	$0.121918\pi$
$74$	5.49350	−	15.4714i	0.638606	−	1.79852i
$75$	10.7675	−	6.20216i	1.24333	−	0.716164i
$76$	0.185888	+	0.486722i	0.0213229	+	0.0558308i
$77$		0			0
$78$	−10.7181	−	7.37977i	−1.21359	−	0.835594i
$79$	−5.09813	−	8.83021i	−0.573584	−	0.993477i	−0.996194	−	0.0871649i	$-0.972219\pi$
$79$	−5.09813	−	8.83021i	−0.573584	−	0.993477i	0.422610	−	0.906312i	$-0.361114\pi$
$80$	7.39089	−	5.03733i	0.826327	−	0.563191i
$81$	−4.22008	+	7.30939i	−0.468897	+	0.812154i
$82$	−1.08825	+	13.6793i	−0.120177	+	1.51062i
$83$	−5.83046	+	5.83046i	−0.639977	+	0.639977i	−0.950550	−	0.310573i	$-0.899479\pi$
$83$	−5.83046	+	5.83046i	−0.639977	+	0.639977i	0.310573	+	0.950550i	$0.399479\pi$
$84$		0			0
$85$	3.04570	+	1.26337i	0.330352	+	0.137032i
$86$	−8.90318	−	10.4422i	−0.960055	−	1.12601i
$87$	3.28504	−	0.880224i	0.352193	−	0.0943699i
$88$	10.4343	−	10.9396i	1.11230	−	1.16616i
$89$	6.60960	−	3.81606i	0.700616	−	0.404501i	−0.106961	−	0.994263i	$-0.534112\pi$
$89$	6.60960	−	3.81606i	0.700616	−	0.404501i	0.807577	+	0.589762i	$0.200779\pi$
$90$	−9.82189	−	2.10160i	−1.03532	−	0.221528i
$91$		0			0
$92$	2.74026	+	1.22561i	0.285691	+	0.127779i
$93$	−1.31959	+	4.92476i	−0.136835	+	0.510674i
$94$	−1.84123	−	0.653770i	−0.189908	−	0.0674313i
$95$	−0.577486	−	0.0763239i	−0.0592488	−	0.00783067i
$96$	−13.9303	−	1.89408i	−1.42175	−	0.193313i
$97$	−11.5761	+	11.5761i	−1.17538	+	1.17538i	−0.194469	+	0.980909i	$0.562298\pi$
$97$	−11.5761	+	11.5761i	−1.17538	+	1.17538i	−0.980909	+	0.194469i	$0.937702\pi$
$98$		0			0
$99$	−16.9770			−1.70625
$100$	1.01838	+	9.94801i	0.101838	+	0.994801i
$101$	1.41999	−	2.45950i	0.141294	−	0.244729i	−0.786690	−	0.617348i	$-0.788207\pi$
$101$	1.41999	−	2.45950i	0.141294	−	0.244729i	0.927984	+	0.372619i	$0.121540\pi$
$102$	−2.22724	−	4.67970i	−0.220529	−	0.463360i
$103$	11.2333	+	3.00994i	1.10685	+	0.296579i	0.765549	−	0.643377i	$-0.222467\pi$
$103$	11.2333	+	3.00994i	1.10685	+	0.296579i	0.341297	+	0.939956i	$0.389134\pi$
$104$	8.94309	−	5.44909i	0.876942	−	0.534327i
$105$		0			0
$106$	−0.659449	−	3.57499i	−0.0640514	−	0.347233i
$107$	0.911342	−	3.40117i	0.0881028	−	0.328804i	−0.907781	−	0.419445i	$-0.862225\pi$
$107$	0.911342	−	3.40117i	0.0881028	−	0.328804i	0.995884	+	0.0906407i	$0.0288915\pi$
$108$	0.513748	+	0.709641i	0.0494354	+	0.0682852i
$109$	−3.15906	−	1.82388i	−0.302583	−	0.174696i	0.341020	−	0.940056i	$-0.389228\pi$
$109$	−3.15906	−	1.82388i	−0.302583	−	0.174696i	−0.643603	+	0.765360i	$0.722561\pi$
$110$	5.20133	+	16.0820i	0.495927	+	1.53336i
$111$		−	28.8511i		−	2.73843i
$112$		0			0
$113$	−8.10112	−	8.10112i	−0.762089	−	0.762089i	0.214611	−	0.976700i	$-0.431152\pi$
$113$	−8.10112	−	8.10112i	−0.762089	−	0.762089i	−0.976700	+	0.214611i	$0.931152\pi$
$114$	0.594029	+	0.696714i	0.0556359	+	0.0652532i
$115$	−2.66366	+	2.04177i	−0.248388	+	0.190396i
$116$	−0.432734	+	2.70251i	−0.0401784	+	0.250921i
$117$	−11.3596	−	3.04378i	−1.05019	−	0.281398i
$118$	−5.27873	−	3.63456i	−0.485946	−	0.334589i
$119$		0			0
$120$	9.27743	−	12.6878i	0.846910	−	1.15823i
$121$	8.78427	+	15.2148i	0.798570	+	1.38316i
$122$	5.28238	−	2.51407i	0.478244	−	0.227613i
$123$	6.24132	+	23.2929i	0.562761	+	2.10025i
$124$	−3.18430	−	2.58755i	−0.285958	−	0.232369i
$125$	−10.3228	−	4.29416i	−0.923299	−	0.384081i
$126$		0			0
$127$	6.08151	+	6.08151i	0.539647	+	0.539647i	0.923425	−	0.383778i	$-0.125377\pi$
$127$	6.08151	+	6.08151i	0.539647	+	0.539647i	−0.383778	+	0.923425i	$0.625377\pi$
$128$	5.96855	−	9.61126i	0.527550	−	0.849524i
$129$	−20.8839	−	12.0573i	−1.83872	−	1.06159i
$130$	0.596961	+	11.6933i	0.0523570	+	1.02557i
$131$	−6.07484	+	3.50731i	−0.530761	+	0.306435i	−0.741326	−	0.671145i	$-0.765803\pi$
$131$	−6.07484	+	3.50731i	−0.530761	+	0.306435i	0.210565	+	0.977580i	$0.432470\pi$
$132$	10.8468	−	24.2515i	0.944091	−	2.11082i
$133$		0			0
$134$	1.80175	+	9.76762i	0.155648	+	0.843794i
$135$	−0.971179	+	0.127360i	−0.0835857	+	0.0109614i
$136$	4.16966	−	0.0985724i	0.357545	−	0.00845252i
$137$	−1.64243	−	6.12964i	−0.140322	−	0.523690i	−0.999919	−	0.0127172i	$-0.995952\pi$
$137$	−1.64243	−	6.12964i	−0.140322	−	0.523690i	0.859597	−	0.510973i	$-0.170715\pi$
$138$	5.25857	+	0.418345i	0.447639	+	0.0356119i
$139$	−3.41676			−0.289806			−0.144903	−	0.989446i	$-0.546287\pi$
$139$	−3.41676			−0.289806			−0.144903	+	0.989446i	$0.546287\pi$
$140$		0			0
$141$	−3.43352			−0.289154
$142$	10.2785	+	0.817706i	0.862553	+	0.0686204i
$143$	5.12203	+	19.1157i	0.428325	+	1.59853i
$144$	−12.4363	+	2.59936i	−1.03636	+	0.216613i
$145$	−2.42671	−	1.86402i	−0.201527	−	0.154799i
$146$	3.50355	+	18.9933i	0.289956	+	1.57190i
$147$		0			0
$148$	21.1949	+	9.47968i	1.74221	+	0.779225i
$149$	11.6025	−	6.69869i	0.950511	−	0.548778i	0.0572715	−	0.998359i	$-0.481760\pi$
$149$	11.6025	−	6.69869i	0.950511	−	0.548778i	0.893240	+	0.449581i	$0.148427\pi$
$150$	7.53594	+	15.8752i	0.615307	+	1.29621i
$151$	1.88244	+	1.08683i	0.153191	+	0.0884446i	0.574636	−	0.818409i	$-0.305144\pi$
$151$	1.88244	+	1.08683i	0.153191	+	0.0884446i	−0.421445	+	0.906854i	$0.638477\pi$
$152$	−0.707009	+	0.207471i	−0.0573460	+	0.0168281i
$153$	−3.31191	−	3.31191i	−0.267752	−	0.267752i
$154$		0			0
$155$	4.23906	−	1.75337i	0.340490	−	0.140834i
$156$	11.6058	−	14.2823i	0.929206	−	1.14350i
$157$	−1.22478	−	4.57093i	−0.0977479	−	0.364800i	0.899674	−	0.436563i	$-0.143804\pi$
$157$	−1.22478	−	4.57093i	−0.0977479	−	0.364800i	−0.997422	+	0.0717625i	$0.977138\pi$
$158$	13.0202	−	6.19679i	1.03584	−	0.492990i
$159$	−3.19417	−	5.53246i	−0.253314	−	0.438753i
$160$	6.27251	+	10.9843i	0.495886	+	0.868388i
$161$		0			0
$162$	−9.83118	−	6.76906i	−0.772410	−	0.531828i
$163$	11.6440	+	3.12000i	0.912029	+	0.244377i	0.684175	−	0.729318i	$-0.260162\pi$
$163$	11.6440	+	3.12000i	0.912029	+	0.244377i	0.227854	+	0.973695i	$0.426829\pi$
$164$	−19.1624	−	3.06835i	−1.49633	−	0.239598i
$165$	18.0698	+	23.5736i	1.40673	+	1.83520i
$166$	−7.56565	−	8.87346i	−0.587208	−	0.688714i
$167$	3.96863	+	3.96863i	0.307102	+	0.307102i	0.843784	−	0.536682i	$-0.180323\pi$
$167$	3.96863	+	3.96863i	0.307102	+	0.307102i	−0.536682	+	0.843784i	$0.680323\pi$
$168$		0			0
$169$			0.708922i			0.0545325i
$170$	−2.12263	+	4.15201i	−0.162798	+	0.318444i
$171$	0.716578	+	0.413717i	0.0547981	+	0.0316377i
$172$	15.7195	−	11.3802i	1.19860	−	0.867733i
$173$	3.11660	−	11.6313i	0.236951	−	0.884312i	−0.740309	−	0.672267i	$-0.765321\pi$
$173$	3.11660	−	11.6313i	0.236951	−	0.884312i	0.977260	−	0.212045i	$-0.0680125\pi$
$174$	0.872475	+	4.72984i	0.0661422	+	0.358568i
$175$		0			0
$176$	14.2519	+	15.9367i	1.07428	+	1.20128i
$177$	−10.8788	−	2.91496i	−0.817700	−	0.219102i
$178$	4.63843	+	9.74593i	0.347665	+	0.730489i
$179$	−0.736556	+	1.27575i	−0.0550528	+	0.0953542i	−0.892238	−	0.451565i	$-0.850866\pi$
$179$	−0.736556	+	1.27575i	−0.0550528	+	0.0953542i	0.837186	+	0.546919i	$0.184199\pi$
$180$	4.06430	−	13.6108i	0.302935	−	1.01449i
$181$	−9.31481			−0.692364			−0.346182	−	0.938167i	$-0.612522\pi$
$181$	−9.31481			−0.692364			−0.346182	+	0.938167i	$0.612522\pi$
$182$		0			0
$183$	7.26941	−	7.26941i	0.537370	−	0.537370i
$184$	−2.03515	+	3.72564i	−0.150033	+	0.274658i
$185$	−20.6025	+	15.7923i	−1.51473	+	1.16108i
$186$	−6.79473	−	2.41263i	−0.498214	−	0.176902i
$187$	−2.03994	+	7.61316i	−0.149175	+	0.556729i
$188$	1.12816	−	2.52236i	0.0822794	−	0.183962i
$189$		0			0
$190$	0.172365	−	0.805557i	0.0125047	−	0.0584412i
$191$	−18.6259	+	10.7537i	−1.34772	+	0.778107i	−0.987926	−	0.154924i	$-0.950487\pi$
$191$	−18.6259	+	10.7537i	−1.34772	+	0.778107i	−0.359795	+	0.933031i	$0.617153\pi$
$192$	4.23252	−	19.4259i	0.305456	−	1.40195i
$193$	3.76974	−	1.01010i	0.271352	−	0.0727085i	−0.120577	−	0.992704i	$-0.538475\pi$
$193$	3.76974	−	1.01010i	0.271352	−	0.0727085i	0.391929	+	0.919995i	$0.371808\pi$
$194$	−15.0212	−	17.6179i	−1.07846	−	1.26489i
$195$	7.86429	+	19.0132i	0.563174	+	1.36156i
$196$		0			0
$197$	−10.8418	+	10.8418i	−0.772443	+	0.772443i	−0.978533	−	0.206090i	$-0.933926\pi$
$197$	−10.8418	+	10.8418i	−0.772443	+	0.772443i	0.206090	+	0.978533i	$0.433926\pi$
$198$	1.90402	−	23.9334i	0.135313	−	1.70088i
$199$	10.3133	−	17.8632i	0.731091	−	1.26629i	−0.225326	−	0.974283i	$-0.572345\pi$
$199$	10.3133	−	17.8632i	0.731091	−	1.26629i	0.956417	−	0.292004i	$-0.0943220\pi$
$200$	−14.1385	+	0.319966i	−0.999744	+	0.0226250i
$201$	8.72715	+	15.1159i	0.615565	+	1.06619i
$202$	3.30804	+	2.27769i	0.232753	+	0.160257i
$203$		0			0
$204$	6.84705	−	2.61502i	0.479389	−	0.183088i
$205$	13.2171	−	17.2068i	0.923120	−	1.20178i
$206$	−5.50314	+	15.4986i	−0.383422	+	1.07984i
$207$	4.60489	−	1.23388i	0.320062	−	0.0857604i
$208$	6.67890	+	13.2187i	0.463099	+	0.916555i
$209$		−	1.39239i		−	0.0963137i
$210$		0			0
$211$			1.55999i			0.107394i	0.998557	+	0.0536969i	$0.0171005\pi$
$211$			1.55999i			0.107394i	−0.998557	+	0.0536969i	$0.982900\pi$
$212$	5.11383	−	0.528718i	0.351219	−	0.0363125i
$213$	17.5021	−	4.68969i	1.19923	−	0.321332i
$214$	4.69263	+	1.66623i	0.320781	+	0.113901i
$215$	2.82119	+	21.5129i	0.192404	+	1.46717i
$216$	−1.05804	+	0.644672i	−0.0719906	+	0.0438644i
$217$		0			0
$218$	2.92554	−	4.24896i	0.198142	−	0.287776i
$219$	16.9701	+	29.3931i	1.14673	+	1.98620i
$220$	−23.2551	+	5.52897i	−1.56786	+	0.372763i
$221$	−2.72991	+	4.72835i	−0.183634	+	0.318063i
$222$	40.6732	+	3.23575i	2.72980	+	0.217169i
$223$	1.29543	−	1.29543i	0.0867482	−	0.0867482i	−0.662401	−	0.749149i	$-0.730463\pi$
$223$	1.29543	−	1.29543i	0.0867482	−	0.0867482i	0.749149	+	0.662401i	$0.230463\pi$
$224$		0			0
$225$	11.2184	+	11.2411i	0.747896	+	0.749407i
$226$	12.3292	−	10.5121i	0.820126	−	0.699252i
$227$	−5.65204	+	1.51446i	−0.375139	+	0.100518i	−0.441462	−	0.897280i	$-0.645540\pi$
$227$	−5.65204	+	1.51446i	−0.375139	+	0.100518i	0.0663228	+	0.997798i	$0.478873\pi$
$228$	−1.04882	+	0.759299i	−0.0694599	+	0.0502858i
$229$	19.0037	−	10.9718i	1.25580	−	0.725035i	0.283542	−	0.958960i	$-0.408490\pi$
$229$	19.0037	−	10.9718i	1.25580	−	0.725035i	0.972255	+	0.233925i	$0.0751571\pi$
$230$	−2.57966	−	3.98412i	−0.170098	−	0.262705i
$231$		0			0
$232$	−3.76135	−	0.913147i	−0.246945	−	0.0599510i
$233$	1.67921	−	6.26689i	0.110009	−	0.410557i	−0.888857	−	0.458185i	$-0.848500\pi$
$233$	1.67921	−	6.26689i	0.110009	−	0.410557i	0.998865	+	0.0476280i	$0.0151662\pi$
$234$	5.56502	−	15.6729i	0.363797	−	1.02457i
$235$	1.87942	+	2.45186i	0.122600	+	0.159942i
$236$	5.71589	−	7.03411i	0.372073	−	0.457881i
$237$	17.9180	−	17.9180i	1.16390	−	1.16390i
$238$		0			0
$239$	−8.09920			−0.523894			−0.261947	−	0.965082i	$-0.584365\pi$
$239$	−8.09920			−0.523894			−0.261947	+	0.965082i	$0.584365\pi$
$240$	16.8462	+	14.5019i	1.08742	+	0.936095i
$241$	−1.66869	+	2.89025i	−0.107489	+	0.186177i	−0.914753	−	0.404015i	$-0.867615\pi$
$241$	−1.66869	+	2.89025i	−0.107489	+	0.186177i	0.807263	+	0.590192i	$0.200948\pi$
$242$	−22.4344	+	10.6773i	−1.44214	+	0.686364i
$243$	−21.5302	−	5.76899i	−1.38116	−	0.370081i
$244$	2.95180	+	7.72885i	0.188969	+	0.494789i
$245$		0			0
$246$	−33.5374	+	6.18638i	−2.13827	+	0.394429i
$247$	0.249640	−	0.931671i	0.0158842	−	0.0592808i
$248$	4.00495	−	4.19889i	0.254315	−	0.266630i
$249$	−17.7465	−	10.2459i	−1.12464	−	0.649309i
$250$	7.21147	−	14.0711i	0.456093	−	0.889932i
$251$		−	1.41618i		−	0.0893882i	−0.999001	−	0.0446941i	$-0.985769\pi$
$251$		−	1.41618i		−	0.0893882i	0.999001	−	0.0446941i	$-0.0142313\pi$
$252$		0			0
$253$	−5.67269	−	5.67269i	−0.356639	−	0.356639i
$254$	−9.25553	+	7.89141i	−0.580744	+	0.495151i
$255$	−1.07370	+	8.12390i	−0.0672378	+	0.508738i
$256$	12.8802	+	9.49216i	0.805011	+	0.593260i
$257$	−7.78950	−	2.08719i	−0.485896	−	0.130195i	0.00755089	−	0.999971i	$-0.497596\pi$
$257$	−7.78950	−	2.08719i	−0.485896	−	0.130195i	−0.493446	+	0.869776i	$0.664263\pi$
$258$	19.3401	−	28.0890i	1.20406	−	1.74874i
$259$		0			0
$260$	−16.5517	−	0.469869i	−1.02649	−	0.0291401i
$261$	2.17330	+	3.76427i	0.134524	+	0.233002i
$262$	−4.26315	−	8.95742i	−0.263378	−	0.553391i
$263$	−4.65739	−	17.3816i	−0.287187	−	1.07180i	−0.947226	−	0.320565i	$-0.896127\pi$
$263$	−4.65739	−	17.3816i	−0.287187	−	1.07180i	0.660040	−	0.751231i	$-0.270539\pi$
$264$	32.9723	+	18.0112i	2.02930	+	1.10851i
$265$	−2.20231	+	5.30927i	−0.135287	+	0.326146i
$266$		0			0
$267$	13.4120	+	13.4120i	0.820799	+	0.820799i
$268$	−13.9721	+	1.44457i	−0.853480	+	0.0882411i
$269$	9.73017	+	5.61772i	0.593259	+	0.342518i	0.766385	−	0.642381i	$-0.222053\pi$
$269$	9.73017	+	5.61772i	0.593259	+	0.342518i	−0.173126	+	0.984900i	$0.555387\pi$
$270$	−0.0706255	−	1.38341i	−0.00429813	−	0.0841918i
$271$	22.0092	−	12.7070i	1.33696	−	0.771896i	0.350607	−	0.936522i	$-0.385975\pi$
$271$	22.0092	−	12.7070i	1.33696	−	0.771896i	0.986356	+	0.164626i	$0.0526418\pi$
$272$	−0.328678	+	5.88927i	−0.0199290	+	0.357090i
$273$		0			0
$274$	8.82552	−	1.62797i	0.533169	−	0.0983494i
$275$	6.94292	−	25.8072i	0.418674	−	1.55623i
$276$	−1.17953	+	7.36640i	−0.0709995	+	0.443405i
$277$	−3.45451	−	12.8924i	−0.207561	−	0.774629i	−0.988654	−	0.150213i	$-0.952004\pi$
$277$	−3.45451	−	12.8924i	−0.207561	−	0.774629i	0.781092	−	0.624415i	$-0.214663\pi$
$278$	0.383202	−	4.81681i	0.0229829	−	0.288893i
$279$	−6.51620			−0.390115
$280$		0			0
$281$	12.5370			0.747894			0.373947	−	0.927450i	$-0.378004\pi$
$281$	12.5370			0.747894			0.373947	+	0.927450i	$0.378004\pi$
$282$	0.385081	−	4.84043i	0.0229312	−	0.288244i
$283$	−7.26346	−	27.1076i	−0.431768	−	1.61138i	−0.748684	−	0.662927i	$-0.769314\pi$
$283$	−7.26346	−	27.1076i	−0.431768	−	1.61138i	0.316916	−	0.948453i	$-0.397353\pi$
$284$	−2.30554	+	14.3985i	−0.136808	+	0.854394i
$285$	−0.188233	−	1.43536i	−0.0111499	−	0.0850236i
$286$	−27.5229	+	5.07694i	−1.62747	+	0.300206i
$287$		0			0
$288$	−2.26970	−	17.8237i	−0.133743	−	1.05027i
$289$	12.8393	−	7.41276i	0.755252	−	0.436045i
$290$	2.89999	−	3.21202i	0.170293	−	0.188616i
$291$	−35.2348	−	20.3428i	−2.06550	−	1.19252i
$292$	−27.1690	+	2.80900i	−1.58994	+	0.164384i
$293$	12.6339	+	12.6339i	0.738078	+	0.738078i	0.972206	−	0.234128i	$-0.0752234\pi$
$293$	12.6339	+	12.6339i	0.738078	+	0.738078i	−0.234128	+	0.972206i	$0.575223\pi$
$294$		0			0
$295$	3.87319	+	9.36408i	0.225506	+	0.545198i
$296$	−15.7412	+	28.8165i	−0.914936	+	1.67493i
$297$	−0.605978	−	2.26154i	−0.0351624	−	0.131228i
$298$	8.14228	+	17.1080i	0.471670	+	0.991038i
$299$	−2.77863	−	4.81273i	−0.160693	−	0.278328i
$300$	−23.2254	+	8.84340i	−1.34092	+	0.510574i
$301$		0			0
$302$	−1.74328	+	2.53189i	−0.100315	+	0.145694i
$303$	6.81745	+	1.82673i	0.391652	+	0.104943i
$304$	−0.213190	−	1.01998i	−0.0122273	−	0.0584999i
$305$	−9.17014	−	1.21198i	−0.525080	−	0.0693977i
$306$	5.04043	−	4.29755i	0.288142	−	0.245675i
$307$	9.69470	+	9.69470i	0.553306	+	0.553306i	0.927393	−	0.374087i	$-0.122044\pi$
$307$	9.69470	+	9.69470i	0.553306	+	0.553306i	−0.374087	+	0.927393i	$0.622044\pi$
$308$		0			0
$309$			28.9018i			1.64417i
$310$	1.99641	+	6.17270i	0.113388	+	0.350586i
$311$	−9.70173	−	5.60130i	−0.550135	−	0.317620i	0.199042	−	0.979991i	$-0.436217\pi$
$311$	−9.70173	−	5.60130i	−0.550135	−	0.317620i	−0.749176	+	0.662371i	$0.769550\pi$
$312$	18.8330	+	17.9632i	1.06621	+	1.01696i
$313$	−0.0595944	+	0.222409i	−0.00336848	+	0.0125713i	−0.967590	−	0.252528i	$-0.918738\pi$
$313$	−0.0595944	+	0.222409i	−0.00336848	+	0.0125713i	0.964221	+	0.265099i	$0.0854047\pi$
$314$	6.58128	−	1.21400i	0.371403	−	0.0685098i
$315$		0			0
$316$	7.27572	+	19.0504i	0.409291	+	1.07167i
$317$	−13.8508	−	3.71131i	−0.777938	−	0.208448i	−0.152063	−	0.988371i	$-0.548592\pi$
$317$	−13.8508	−	3.71131i	−0.777938	−	0.208448i	−0.625876	+	0.779923i	$0.715258\pi$
$318$	8.15768	−	3.88253i	0.457460	−	0.217721i
$319$	3.65719	−	6.33445i	0.204764	−	0.354661i
$320$	−16.1888	+	7.61080i	−0.904979	+	0.425457i
$321$	8.75080			0.488422
$322$		0			0
$323$	0.271631	−	0.271631i	0.0151139	−	0.0151139i
$324$	10.6454	−	13.1004i	0.591408	−	0.727801i
$325$	9.27256	−	16.0232i	0.514349	−	0.888807i
$326$	−5.70437	+	16.0653i	−0.315936	+	0.889776i
$327$	2.34632	−	8.75657i	0.129752	−	0.484239i
$328$	6.47476	−	26.6703i	0.357509	−	1.47262i
$329$		0			0
$330$	−35.2597	+	22.8302i	−1.94098	+	1.25676i
$331$	−14.4821	+	8.36122i	−0.796006	+	0.459574i	−0.842073	−	0.539364i	$-0.818665\pi$
$331$	−14.4821	+	8.36122i	−0.796006	+	0.459574i	0.0460667	+	0.998938i	$0.485331\pi$
$332$	13.3580	−	9.67055i	0.733113	−	0.530740i
$333$	35.6172	−	9.54360i	1.95181	−	0.522986i
$334$	−6.03991	+	5.14972i	−0.330489	+	0.281780i
$335$	6.01718	−	14.5060i	0.328753	−	0.792550i
$336$		0			0
$337$	9.74524	−	9.74524i	0.530857	−	0.530857i	−0.389970	−	0.920827i	$-0.627515\pi$
$337$	9.74524	−	9.74524i	0.530857	−	0.530857i	0.920827	+	0.389970i	$0.127515\pi$
$338$	−0.999409	−	0.0795080i	−0.0543607	−	0.00432467i
$339$	14.2362	−	24.6577i	0.773202	−	1.33923i
$340$	−5.61527	−	3.45806i	−0.304531	−	0.187540i
$341$	5.48268	+	9.49628i	0.296904	+	0.514252i
$342$	−0.663608	+	0.963803i	−0.0358838	+	0.0521165i
$343$		0			0
$344$	14.2804	+	23.4371i	0.769946	+	1.26364i
$345$	−6.61464	−	5.08089i	−0.356120	−	0.273546i
$346$	16.0478	+	5.69815i	0.862736	+	0.306334i
$347$	4.02857	−	1.07945i	0.216265	−	0.0579481i	−0.149060	−	0.988828i	$-0.547625\pi$
$347$	4.02857	−	1.07945i	0.216265	−	0.0579481i	0.365325	+	0.930880i	$0.380958\pi$
$348$	−6.76578	+	0.699513i	−0.362684	+	0.0374978i
$349$		−	30.1290i		−	1.61277i	−0.591393	−	0.806383i	$-0.701422\pi$
$349$		−	30.1290i		−	1.61277i	0.591393	−	0.806383i	$-0.298578\pi$
$350$		0			0
$351$		−	1.62188i		−	0.0865695i
$352$	−24.0654	+	18.3044i	−1.28269	+	0.975629i
$353$	−5.28777	+	1.41685i	−0.281440	+	0.0754116i	−0.396778	−	0.917915i	$-0.629872\pi$
$353$	−5.28777	+	1.41685i	−0.281440	+	0.0754116i	0.115338	+	0.993326i	$0.463205\pi$
$354$	5.32949	−	15.0096i	0.283259	−	0.797749i
$355$	−12.9291	−	9.93121i	−0.686205	−	0.527094i
$356$	−14.2596	+	5.44603i	−0.755759	+	0.288639i
$357$		0			0
$358$	−1.71590	−	1.18145i	−0.0906880	−	0.0624414i
$359$	−11.6607	−	20.1969i	−0.615427	−	1.06595i	−0.990309	−	0.138878i	$-0.955650\pi$
$359$	−11.6607	−	20.1969i	−0.615427	−	1.06595i	0.374883	−	0.927072i	$-0.377683\pi$
$360$	18.7321	+	7.25619i	0.987270	+	0.382435i
$361$	9.46607	−	16.3957i	0.498214	−	0.862932i
$362$	1.04469	−	13.1316i	0.0549076	−	0.690184i
$363$	−30.8733	+	30.8733i	−1.62043	+	1.62043i
$364$		0			0
$365$	11.7005	−	28.2073i	0.612434	−	1.47644i
$366$	9.43282	+	11.0634i	0.493062	+	0.578293i
$367$	−12.4194	+	3.32776i	−0.648285	+	0.173708i	−0.567953	−	0.823061i	$-0.692265\pi$
$367$	−12.4194	+	3.32776i	−0.648285	+	0.173708i	−0.0803318	+	0.996768i	$0.525598\pi$
$368$	−5.02401	−	3.28691i	−0.261895	−	0.171342i
$369$	−26.6910	+	15.4100i	−1.38948	+	0.802214i
$370$	−19.9528	−	30.8157i	−1.03729	−	1.60203i
$371$		0			0
$372$	4.16328	−	9.30835i	0.215856	−	0.482616i
$373$	−3.76324	+	14.0446i	−0.194853	+	0.727202i	0.797452	+	0.603383i	$0.206181\pi$
$373$	−3.76324	+	14.0446i	−0.194853	+	0.727202i	−0.992305	+	0.123819i	$0.960486\pi$
$374$	−10.5039	−	3.72967i	−0.543145	−	0.192856i
$375$	3.66842	−	27.5422i	0.189437	−	1.42228i
$376$	3.42940	+	1.87332i	0.176858	+	0.0966093i
$377$	3.58278	−	3.58278i	0.184523	−	0.184523i
$378$		0			0
$379$	18.3234			0.941208			0.470604	−	0.882344i	$-0.344036\pi$
$379$	18.3234			0.941208			0.470604	+	0.882344i	$0.344036\pi$
$380$	1.11631	+	0.333340i	0.0572655	+	0.0171000i
$381$	−10.6871	+	18.5106i	−0.547516	+	0.948325i
$382$	−13.0711	−	27.4641i	−0.668776	−	1.40518i
$383$	−17.9320	−	4.80487i	−0.916284	−	0.245518i	−0.230288	−	0.973123i	$-0.573967\pi$
$383$	−17.9320	−	4.80487i	−0.916284	−	0.245518i	−0.685996	+	0.727605i	$0.740633\pi$
$384$	26.9112	+	8.14552i	1.37331	+	0.415674i
$385$		0			0
$386$	1.00121	+	5.42771i	0.0509601	+	0.276263i
$387$	7.97682	−	29.7699i	0.405484	−	1.51329i
$388$	26.5216	−	19.2004i	1.34643	−	0.974755i
$389$	28.6326	+	16.5311i	1.45173	+	0.838158i	0.998580	−	0.0532759i	$-0.0169663\pi$
$389$	28.6326	+	16.5311i	1.45173	+	0.838158i	0.453152	+	0.891433i	$0.350300\pi$
$390$	−27.6861	+	8.95437i	−1.40194	+	0.453422i
$391$		−	2.21328i		−	0.111930i
$392$		0			0
$393$	−12.3268	−	12.3268i	−0.621807	−	0.621807i
$394$	−14.0683	−	16.5002i	−0.708752	−	0.831268i
$395$	−22.6030	−	2.98734i	−1.13728	−	0.150309i
$396$	33.5268	+	5.36843i	1.68479	+	0.269774i
$397$	28.7436	+	7.70181i	1.44260	+	0.386543i	0.893443	−	0.449177i	$-0.148283\pi$
$397$	28.7436	+	7.70181i	1.44260	+	0.386543i	0.549155	+	0.835720i	$0.314950\pi$
$398$	24.0261	+	16.5427i	1.20432	+	0.829211i
$399$		0			0
$400$	1.13461	−	19.9678i	0.0567304	−	0.998390i
$401$	−17.1410	−	29.6890i	−0.855979	−	1.48260i	−0.875734	−	0.482794i	$-0.839622\pi$
$401$	−17.1410	−	29.6890i	−0.855979	−	1.48260i	0.0197547	−	0.999805i	$-0.493711\pi$
$402$	−22.2885	+	10.6079i	−1.11165	+	0.529073i
$403$	1.96597	+	7.33709i	0.0979319	+	0.365487i
$404$	−3.58200	+	4.40809i	−0.178211	+	0.219311i
$405$	7.21349	+	17.4398i	0.358441	+	0.866590i
$406$		0			0
$407$	−43.8762	−	43.8762i	−2.17486	−	2.17486i
$408$	2.91863	+	9.94598i	0.144494	+	0.492399i
$409$	−1.83899	−	1.06174i	−0.0909321	−	0.0524997i	0.453844	−	0.891081i	$-0.350052\pi$
$409$	−1.83899	−	1.06174i	−0.0909321	−	0.0524997i	−0.544777	+	0.838581i	$0.683386\pi$
$410$	22.7752	+	20.5627i	1.12478	+	1.01552i
$411$	13.6579	−	7.88540i	0.673695	−	0.388958i
$412$	−21.2321	−	9.49633i	−1.04603	−	0.467851i
$413$		0			0
$414$	1.22302	+	6.63017i	0.0601079	+	0.325855i
$415$	2.39736	+	18.2810i	0.117682	+	0.897380i
$416$	−19.3843	+	7.93312i	−0.950394	+	0.388953i
$417$	−2.19773	−	8.20203i	−0.107623	−	0.401655i
$418$	1.96294	+	0.156161i	0.0960103	+	0.00763810i
$419$	−25.4554			−1.24358			−0.621789	−	0.783185i	$-0.713594\pi$
$419$	−25.4554			−1.24358			−0.621789	+	0.783185i	$0.713594\pi$
$420$		0			0
$421$	6.51083			0.317318			0.158659	−	0.987333i	$-0.449283\pi$
$421$	6.51083			0.317318			0.158659	+	0.987333i	$0.449283\pi$
$422$	−2.19920	−	0.174958i	−0.107056	−	0.00851681i
$423$	−1.13577	−	4.23873i	−0.0552228	−	0.206094i
$424$	0.171832	+	7.26857i	0.00834489	+	0.352993i
$425$	6.38896	−	3.68008i	0.309910	−	0.178510i
$426$	4.64840	+	25.1998i	0.225216	+	1.22093i
$427$		0			0
$428$	−2.87527	+	6.42860i	−0.138982	+	0.310738i
$429$	−42.5931	+	24.5911i	−2.05641	+	1.18727i
$430$	−30.6445	+	1.56445i	−1.47781	+	0.0754445i
$431$	−18.3941	−	10.6198i	−0.886014	−	0.511540i	−0.0133771	−	0.999911i	$-0.504258\pi$
$431$	−18.3941	−	10.6198i	−0.886014	−	0.511540i	−0.872636	+	0.488370i	$0.837592\pi$
$432$	−0.790169	−	1.56389i	−0.0380170	−	0.0752425i
$433$	10.3951	+	10.3951i	0.499557	+	0.499557i	0.911300	−	0.411743i	$-0.135080\pi$
$433$	10.3951	+	10.3951i	0.499557	+	0.499557i	−0.411743	+	0.911300i	$0.635080\pi$
$434$		0			0
$435$	2.91374	−	7.02435i	0.139703	−	0.336792i
$436$	5.66190	+	4.60084i	0.271156	+	0.220340i
$437$	0.101198	+	0.377677i	0.00484097	+	0.0180667i
$438$	−43.3405	+	20.6273i	−2.07089	+	0.985608i
$439$	−2.64749	−	4.58558i	−0.126358	−	0.218858i	0.795905	−	0.605421i	$-0.206995\pi$
$439$	−2.64749	−	4.58558i	−0.126358	−	0.218858i	−0.922263	+	0.386563i	$0.873662\pi$
$440$	−5.18638	−	33.4042i	−0.247251	−	1.59248i
$441$		0			0
$442$	−6.35966	−	4.37882i	−0.302498	−	0.208279i
$443$	28.7891	+	7.71402i	1.36781	+	0.366504i	0.866679	−	0.498867i	$-0.166250\pi$
$443$	28.7891	+	7.71402i	1.36781	+	0.366504i	0.501132	+	0.865371i	$0.332917\pi$
$444$	−9.12327	+	56.9765i	−0.432971	+	2.70398i
$445$	2.23609	−	16.9188i	0.106001	−	0.802028i
$446$	1.68095	+	1.97153i	0.0795955	+	0.0933545i
$447$	23.5433	+	23.5433i	1.11356	+	1.11356i
$448$		0			0
$449$		−	9.50768i		−	0.448695i	−0.974509	−	0.224347i	$-0.927975\pi$
$449$		−	9.50768i		−	0.448695i	0.974509	−	0.224347i	$-0.0720251\pi$
$450$	−17.1054	+	14.5546i	−0.806358	+	0.686109i
$451$	44.9151	+	25.9317i	2.11497	+	1.22108i
$452$	13.4367	+	18.5602i	0.632010	+	0.872997i
$453$	−1.39813	+	5.21791i	−0.0656901	+	0.245159i
$454$	−1.50113	−	8.13787i	−0.0704514	−	0.381929i
$455$		0			0
$456$	−0.952800	−	1.56374i	−0.0446190	−	0.0732290i
$457$	25.8402	+	6.92387i	1.20875	+	0.323885i	0.806273	−	0.591543i	$-0.201481\pi$
$457$	25.8402	+	6.92387i	1.20875	+	0.323885i	0.402482	+	0.915428i	$0.368148\pi$
$458$	13.3362	+	28.0211i	0.623161	+	1.30934i
$459$	0.322971	−	0.559402i	0.0150750	−	0.0261107i
$460$	5.90596	−	3.18987i	0.275367	−	0.148728i
$461$	−4.58670			−0.213624			−0.106812	−	0.994279i	$-0.534064\pi$
$461$	−4.58670			−0.213624			−0.106812	+	0.994279i	$0.534064\pi$
$462$		0			0
$463$	5.55531	−	5.55531i	0.258177	−	0.258177i	−0.566135	−	0.824312i	$-0.691562\pi$
$463$	5.55531	−	5.55531i	0.258177	−	0.258177i	0.824312	+	0.566135i	$0.191562\pi$
$464$	1.70917	−	5.20019i	0.0793460	−	0.241413i
$465$	6.93566	+	9.04818i	0.321634	+	0.419599i
$466$	8.64648	+	3.07013i	0.400540	+	0.142221i
$467$	−8.99874	+	33.5838i	−0.416412	+	1.55407i	0.365578	+	0.930781i	$0.380871\pi$
$467$	−8.99874	+	33.5838i	−0.416412	+	1.55407i	−0.781990	+	0.623291i	$0.785795\pi$
$468$	21.4708	+	9.60310i	0.992490	+	0.443904i
$469$		0			0
$470$	−3.66732	+	2.37454i	−0.169161	+	0.109529i
$471$	10.1848	−	5.88022i	0.469293	−	0.270946i
$472$	9.27534	+	8.84693i	0.426932	+	0.407213i
$473$	−50.0962	+	13.4232i	−2.30343	+	0.617202i
$474$	23.2504	+	27.2696i	1.06793	+	1.25253i
$475$	−0.921955	+	0.920096i	−0.0423022	+	0.0422169i
$476$		0			0
$477$	5.77333	−	5.77333i	0.264343	−	0.264343i
$478$	0.908353	−	11.4179i	0.0415471	−	0.522244i
$479$	−14.8734	+	25.7615i	−0.679583	+	1.17707i	0.295524	+	0.955335i	$0.404506\pi$
$479$	−14.8734	+	25.7615i	−0.679583	+	1.17707i	−0.975107	+	0.221737i	$0.928827\pi$
$480$	−22.3336	+	22.1227i	−1.01938	+	1.00976i
$481$	−21.4917	−	37.2248i	−0.979939	−	1.69730i
$482$	−3.88741	−	2.67660i	−0.177066	−	0.121916i
$483$		0			0
$484$	−12.5364	−	32.8246i	−0.569834	−	1.49203i
$485$	4.75985	+	36.2961i	0.216134	+	1.64812i
$486$	10.5476	−	29.7053i	0.478447	−	1.34746i
$487$	−5.72475	+	1.53394i	−0.259413	+	0.0695095i	−0.386182	−	0.922423i	$-0.626206\pi$
$487$	−5.72475	+	1.53394i	−0.259413	+	0.0695095i	0.126768	+	0.991932i	$0.459539\pi$
$488$	−11.2269	+	3.29451i	−0.508217	+	0.149135i
$489$			29.9586i			1.35477i
$490$		0			0
$491$		−	19.0115i		−	0.857977i	−0.903310	−	0.428989i	$-0.858870\pi$
$491$		−	19.0115i		−	0.857977i	0.903310	−	0.428989i	$-0.141130\pi$
$492$	−4.95997	−	47.9735i	−0.223613	−	2.16281i
$493$	1.94919	−	0.522285i	0.0877872	−	0.0235225i
$494$	1.28543	+	0.456423i	0.0578344	+	0.0205354i
$495$	−23.1248	+	30.1053i	−1.03938	+	1.35313i
$496$	5.47026	+	6.11694i	0.245622	+	0.274659i
$497$		0			0
$498$	16.4346	−	23.8691i	0.736452	−	1.06960i
$499$	16.5605	+	28.6836i	0.741348	+	1.28405i	0.951882	+	0.306466i	$0.0991466\pi$
$499$	16.5605	+	28.6836i	0.741348	+	1.28405i	−0.210534	+	0.977587i	$0.567520\pi$
$500$	19.0280	+	11.7446i	0.850959	+	0.525232i
$501$	−6.97411	+	12.0795i	−0.311580	+	0.539673i
$502$	1.99647	+	0.158829i	0.0891067	+	0.00708888i
$503$	−22.3897	+	22.3897i	−0.998307	+	0.998307i	−0.999999	−	0.00169150i	$-0.999462\pi$
$503$	−22.3897	+	22.3897i	−0.998307	+	0.998307i	0.00169150	+	0.999999i	$0.499462\pi$
$504$		0			0
$505$	−2.42723	−	5.86822i	−0.108010	−	0.261132i
$506$	8.63333	−	7.36091i	0.383798	−	0.327232i
$507$	−1.70179	+	0.455992i	−0.0755790	+	0.0202513i
$508$	−10.0869	−	13.9331i	−0.447536	−	0.618182i
$509$	−9.71677	+	5.60998i	−0.430688	+	0.248658i	−0.699640	−	0.714496i	$-0.746656\pi$
$509$	−9.71677	+	5.60998i	−0.430688	+	0.248658i	0.268952	+	0.963154i	$0.413323\pi$
$510$	−11.3323	−	2.42478i	−0.501804	−	0.107371i
$511$		0			0
$512$	−14.8262	+	17.0934i	−0.655232	+	0.755427i
$513$	−0.0295345	+	0.110224i	−0.00130398	+	0.00486652i
$514$	3.81605	−	10.7472i	0.168319	−	0.474040i
$515$	20.6387	−	15.8201i	0.909449	−	0.697116i
$516$	37.4296	+	30.4152i	1.64775	+	1.33895i
$517$	−5.22162	+	5.22162i	−0.229647	+	0.229647i
$518$		0			0
$519$	29.9259			1.31360
$520$	2.51873	−	23.2812i	0.110454	−	1.02095i
$521$	14.4739	−	25.0695i	0.634111	−	1.09831i	−0.352591	−	0.935777i	$-0.614699\pi$
$521$	14.4739	−	25.0695i	0.634111	−	1.09831i	0.986703	−	0.162536i	$-0.0519673\pi$
$522$	−5.55046	+	2.64166i	−0.242937	+	0.115622i
$523$	−21.7294	−	5.82238i	−0.950161	−	0.254595i	−0.249731	−	0.968315i	$-0.580342\pi$
$523$	−21.7294	−	5.82238i	−0.950161	−	0.254595i	−0.700431	+	0.713720i	$0.747009\pi$
$524$	13.1059	−	5.00541i	0.572535	−	0.218662i
$525$		0			0
$526$	25.0262	−	4.61639i	1.09120	−	0.201284i
$527$	−0.782982	+	2.92213i	−0.0341072	+	0.127290i
$528$	−29.0895	+	44.4629i	−1.26596	+	1.93500i
$529$	−17.9676	−	10.3736i	−0.781201	−	0.451026i
$530$	−7.23780	−	3.70018i	−0.314390	−	0.160726i
$531$		−	14.3943i		−	0.624659i
$532$		0			0
$533$	25.4041	+	25.4041i	1.10037	+	1.10037i
$534$	−20.4118	+	17.4035i	−0.883307	+	0.753121i
$535$	−4.78996	−	6.24892i	−0.207088	−	0.270164i
$536$	−0.469481	−	19.8593i	−0.0202785	−	0.857789i
$537$	−3.53625	−	0.947534i	−0.152600	−	0.0408891i
$538$	−9.01090	+	13.0872i	−0.388488	+	0.564227i
$539$		0			0
$540$	1.95820	+	0.0555894i	0.0842675	+	0.00239219i
$541$	2.92645	+	5.06875i	0.125818	+	0.217923i	0.922052	−	0.387065i	$-0.126511\pi$
$541$	2.92645	+	5.06875i	0.125818	+	0.217923i	−0.796235	+	0.604988i	$0.793178\pi$
$542$	15.4454	+	32.4528i	0.663438	+	1.39397i
$543$	−5.99146	−	22.3604i	−0.257118	−	0.959579i
$544$	−8.26560	−	1.12386i	−0.354384	−	0.0481851i
$545$	−7.53735	+	3.11762i	−0.322864	+	0.133544i
$546$		0			0
$547$	13.8207	+	13.8207i	0.590930	+	0.590930i	0.937883	−	0.346952i	$-0.112783\pi$
$547$	13.8207	+	13.8207i	0.590930	+	0.590930i	−0.346952	+	0.937883i	$0.612783\pi$
$548$	1.30524	+	12.6244i	0.0557570	+	0.539289i
$549$	11.3788	+	6.56957i	0.485637	+	0.280383i
$550$	35.6032	+	12.6822i	1.51813	+	0.540771i
$551$	−0.308732	+	0.178246i	−0.0131524	+	0.00759356i
$552$	−10.2526	−	2.48902i	−0.436378	−	0.105940i
$553$		0			0
$554$	18.5626	−	3.42410i	0.788650	−	0.145476i
$555$	−51.1619	−	39.2989i	−2.17170	−	1.66815i
$556$	6.74757	+	1.08044i	0.286161	+	0.0458210i
$557$	9.09246	+	33.9335i	0.385260	+	1.43781i	0.837757	+	0.546044i	$0.183867\pi$
$557$	9.09246	+	33.9335i	0.385260	+	1.43781i	−0.452496	+	0.891766i	$0.649466\pi$
$558$	0.730815	−	9.18628i	0.0309378	−	0.388886i
$559$	−35.9268			−1.51954
$560$		0			0
$561$	−19.5877			−0.826994
$562$	−1.40607	+	17.6741i	−0.0593113	+	0.745538i
$563$	−7.68371	−	28.6760i	−0.323830	−	1.20855i	−0.915483	−	0.402357i	$-0.868191\pi$
$563$	−7.68371	−	28.6760i	−0.323830	−	1.20855i	0.591653	−	0.806193i	$-0.298475\pi$
$564$	6.78066	+	1.08574i	0.285517	+	0.0457180i
$565$	−25.4005	+	3.33100i	−1.06861	+	0.140136i
$566$	39.0298	−	7.19952i	1.64055	−	0.302619i
$567$		0			0
$568$	−20.0399	−	4.86509i	−0.840854	−	0.204135i
$569$	−27.0392	+	15.6111i	−1.13354	+	0.654451i	−0.944823	−	0.327581i	$-0.893767\pi$
$569$	−27.0392	+	15.6111i	−1.13354	+	0.654451i	−0.188718	+	0.982031i	$0.560433\pi$
$570$	2.04463	−	0.104382i	0.0856401	−	0.00437207i
$571$	−20.8709	−	12.0498i	−0.873420	−	0.504269i	−0.00493696	−	0.999988i	$-0.501571\pi$
$571$	−20.8709	−	12.0498i	−0.873420	−	0.504269i	−0.868483	+	0.495718i	$0.834905\pi$
$572$	−4.07047	−	39.3701i	−0.170195	−	1.64615i
$573$	−37.7950	−	37.7950i	−1.57891	−	1.57891i
$574$		0			0
$575$	−0.00757253	+	7.50463i	−0.000315796	+	0.312965i
$576$	25.3817	−	1.20074i	1.05757	−	0.0500307i
$577$	−0.854134	−	3.18767i	−0.0355581	−	0.132705i	0.945865	−	0.324560i	$-0.105216\pi$
$577$	−0.854134	−	3.18767i	−0.0355581	−	0.132705i	−0.981423	+	0.191855i	$0.938550\pi$
$578$	9.01024	+	18.9317i	0.374777	+	0.787454i
$579$	4.84954	+	8.39964i	0.201540	+	0.349077i
$580$	4.20293	+	4.44853i	0.174517	+	0.184715i
$581$		0			0
$582$	32.6302	−	47.3911i	1.35256	−	1.96442i
$583$	−13.2713	−	3.55603i	−0.549640	−	0.147276i
$584$	−0.912916	−	38.6168i	−0.0377767	−	1.59797i
$585$	−20.8707	+	15.9979i	−0.862898	+	0.661434i
$586$	−19.2276	+	16.3938i	−0.794287	+	0.677221i
$587$	−29.4634	−	29.4634i	−1.21608	−	1.21608i	−0.968992	−	0.247092i	$-0.920525\pi$
$587$	−29.4634	−	29.4634i	−1.21608	−	1.21608i	−0.247092	−	0.968992i	$-0.579475\pi$
$588$		0			0
$589$		−	0.534436i		−	0.0220210i
$590$	−13.6355	+	4.41006i	−0.561364	+	0.181559i
$591$	−32.9995	−	19.0523i	−1.35742	−	0.783707i
$592$	−38.8590	−	25.4231i	−1.59709	−	1.04488i
$593$	−0.0733317	+	0.273678i	−0.00301137	+	0.0112386i	−0.967415	−	0.253195i	$-0.918518\pi$
$593$	−0.0733317	+	0.273678i	−0.00301137	+	0.0112386i	0.964404	+	0.264434i	$0.0851851\pi$
$594$	3.25619	−	0.600644i	0.133603	−	0.0246447i
$595$		0			0
$596$	−25.0313	+	9.55994i	−1.02532	+	0.391591i
$597$	49.5148	+	13.2674i	2.02650	+	0.543000i
$598$	7.09643	−	3.37744i	0.290195	−	0.138114i
$599$	0.792194	−	1.37212i	0.0323682	−	0.0560633i	−0.849388	−	0.527770i	$-0.823028\pi$
$599$	0.792194	−	1.37212i	0.0323682	−	0.0560633i	0.881756	+	0.471706i	$0.156362\pi$
$600$	−9.86225	−	33.7341i	−0.402625	−	1.37719i
$601$	−13.2735			−0.541438			−0.270719	−	0.962658i	$-0.587262\pi$
$601$	−13.2735			−0.541438			−0.270719	+	0.962658i	$0.587262\pi$
$602$		0			0
$603$	−15.7740	+	15.7740i	−0.642365	+	0.642365i
$604$	−3.37384	−	2.74157i	−0.137280	−	0.111553i
$605$	38.9458	+	5.14730i	1.58337	+	0.209267i
$606$	−3.33985	+	9.40609i	−0.135672	+	0.382096i
$607$	8.87912	−	33.1373i	0.360392	−	1.34500i	−0.513168	−	0.858288i	$-0.671528\pi$
$607$	8.87912	−	33.1373i	0.360392	−	1.34500i	0.873561	−	0.486715i	$-0.161805\pi$
$608$	1.46184	−	0.186153i	0.0592853	−	0.00754948i
$609$		0			0
$610$	2.73706	−	12.7918i	0.110820	−	0.517923i
$611$	−4.43005	+	2.55769i	−0.179221	+	0.103473i
$612$	5.49321	+	7.58778i	0.222050	+	0.306718i
$613$	18.6732	−	5.00346i	0.754202	−	0.202088i	0.138821	−	0.990318i	$-0.455669\pi$
$613$	18.6732	−	5.00346i	0.754202	−	0.202088i	0.615381	+	0.788230i	$0.289002\pi$
$614$	−14.7545	+	12.5799i	−0.595443	+	0.507684i
$615$	49.8069	+	20.6601i	2.00841	+	0.833098i
$616$		0			0
$617$	−22.2105	+	22.2105i	−0.894159	+	0.894159i	−0.994912	−	0.100752i	$-0.967875\pi$
$617$	−22.2105	+	22.2105i	−0.894159	+	0.894159i	0.100752	+	0.994912i	$0.467875\pi$
$618$	−40.7446	−	3.24143i	−1.63899	−	0.130390i
$619$	−17.1081	+	29.6322i	−0.687634	+	1.19102i	0.284967	+	0.958537i	$0.408017\pi$
$619$	−17.1081	+	29.6322i	−0.687634	+	1.19102i	−0.972601	+	0.232480i	$0.925316\pi$
$620$	−8.92593	+	2.12216i	−0.358474	+	0.0852281i
$621$	0.328735	+	0.569386i	0.0131917	+	0.0228487i
$622$	8.98456	−	13.0489i	0.360248	−	0.523213i
$623$		0			0
$624$	−27.4359	+	24.5354i	−1.09832	+	0.982203i
$625$	−21.6758	+	12.4563i	−0.867033	+	0.498251i
$626$	−0.306860	−	0.108958i	−0.0122646	−	0.00435483i
$627$	3.34247	−	0.895612i	0.133485	−	0.0357673i
$628$	0.973330	+	9.41417i	0.0388401	+	0.375666i
$629$		−	17.1189i		−	0.682577i
$630$		0			0
$631$		−	26.0102i		−	1.03545i	−0.855548	−	0.517724i	$-0.826779\pi$
$631$		−	26.0102i		−	1.03545i	0.855548	−	0.517724i	$-0.173221\pi$
$632$	−27.6725	+	8.12045i	−1.10075	+	0.323014i
$633$	−3.74479	+	1.00341i	−0.148842	+	0.0398821i
$634$	6.78547	−	19.1101i	0.269485	−	0.758957i
$635$	19.0682	−	2.50058i	0.756697	−	0.0992327i
$636$	4.55852	+	11.9358i	0.180757	+	0.473285i
$637$		0			0
$638$	8.51988	+	5.86619i	0.337305	+	0.232245i
$639$	11.5790	+	20.0554i	0.458058	+	0.793380i
$640$	−8.91378	−	23.6758i	−0.352348	−	0.935869i
$641$	11.4725	−	19.8710i	0.453138	−	0.784858i	−0.545441	−	0.838149i	$-0.683638\pi$
$641$	11.4725	−	19.8710i	0.453138	−	0.784858i	0.998579	+	0.0532913i	$0.0169712\pi$
$642$	−0.981432	+	12.3365i	−0.0387340	+	0.486884i
$643$	17.9293	−	17.9293i	0.707062	−	0.707062i	−0.258855	−	0.965916i	$-0.583345\pi$
$643$	17.9293	−	17.9293i	0.707062	−	0.707062i	0.965916	+	0.258855i	$0.0833450\pi$
$644$		0			0
$645$	−49.8277	+	20.6099i	−1.96197	+	0.811513i
$646$	0.352470	+	0.413398i	0.0138677	+	0.0162649i
$647$	32.2515	−	8.64177i	1.26794	−	0.339743i	0.438697	−	0.898635i	$-0.355440\pi$
$647$	32.2515	−	8.64177i	1.26794	−	0.339743i	0.829240	+	0.558892i	$0.188773\pi$
$648$	17.2745	+	16.4766i	0.678608	+	0.647264i
$649$	−20.9773	+	12.1112i	−0.823429	+	0.475407i
$650$	21.5489	+	14.8691i	0.845217	+	0.583216i
$651$		0			0
$652$	−22.0085	−	9.84357i	−0.861919	−	0.385504i
$653$	8.98773	−	33.5427i	0.351717	−	1.31263i	−0.532849	−	0.846210i	$-0.678879\pi$
$653$	8.98773	−	33.5427i	0.351717	−	1.31263i	0.884566	−	0.466415i	$-0.154455\pi$
$654$	12.0815	+	4.28982i	0.472424	+	0.167745i
$655$	−2.05517	+	15.5499i	−0.0803022	+	0.607587i
$656$	36.8725	+	12.1190i	1.43963	+	0.473168i
$657$	−30.6728	+	30.6728i	−1.19666	+	1.19666i
$658$		0			0
$659$	−48.2178			−1.87830			−0.939149	−	0.343511i	$-0.888384\pi$
$659$	−48.2178			−1.87830			−0.939149	+	0.343511i	$0.888384\pi$
$660$	−28.2306	−	52.2682i	−1.09887	−	2.03454i
$661$	−11.5458	+	19.9978i	−0.449078	+	0.777826i	−0.998326	−	0.0578332i	$-0.981581\pi$
$661$	−11.5458	+	19.9978i	−0.449078	+	0.777826i	0.549248	+	0.835659i	$0.314914\pi$
$662$	−10.1631	−	21.3540i	−0.395000	−	0.829945i
$663$	−13.1065	−	3.51186i	−0.509012	−	0.136389i
$664$	12.1350	+	19.9161i	0.470930	+	0.772894i
$665$		0			0
$666$	9.45959	+	51.2820i	0.366552	+	1.98714i
$667$	−0.531606	+	1.98398i	−0.0205839	+	0.0768200i
$668$	−6.58247	−	9.09238i	−0.254684	−	0.351795i
$669$	3.94295	+	2.27646i	0.152443	+	0.0880132i
$670$	19.7752	+	10.1097i	0.763982	+	0.390571i
$671$		−	22.1103i		−	0.853560i
$672$		0			0
$673$	−15.6001	−	15.6001i	−0.601340	−	0.601340i	0.339328	−	0.940668i	$-0.389800\pi$
$673$	−15.6001	−	15.6001i	−0.601340	−	0.601340i	−0.940668	+	0.339328i	$0.889800\pi$
$674$	12.6455	+	14.8314i	0.487086	+	0.571285i
$675$	−1.09702	+	1.89568i	−0.0422244	+	0.0729646i
$676$	0.224174	−	1.40001i	0.00862209	−	0.0538465i
$677$	16.9000	+	4.52833i	0.649519	+	0.174038i	0.568511	−	0.822675i	$-0.307520\pi$
$677$	16.9000	+	4.52833i	0.649519	+	0.174038i	0.0810075	+	0.996713i	$0.474186\pi$
$678$	33.1649	+	22.8350i	1.27369	+	0.876973i
$679$		0			0
$680$	5.50481	−	7.52835i	0.211100	−	0.288699i
$681$	−7.27100	−	12.5937i	−0.278625	−	0.482593i
$682$	−14.0024	+	6.66422i	−0.536178	+	0.255186i
$683$	3.51923	+	13.1339i	0.134659	+	0.502556i	0.999999	+	0.00136990i	$0.000436053\pi$
$683$	3.51923	+	13.1339i	0.134659	+	0.502556i	−0.865340	+	0.501186i	$0.832897\pi$
$684$	−1.28430	−	1.04362i	−0.0491066	−	0.0399038i
$685$	−13.1069	−	5.43681i	−0.500789	−	0.207730i
$686$		0			0
$687$	38.5615	+	38.5615i	1.47121	+	1.47121i
$688$	−34.6422	+	17.5033i	−1.32072	+	0.667309i
$689$	−8.24247	−	4.75879i	−0.314013	−	0.181296i
$690$	7.90469	−	8.75520i	0.300926	−	0.333305i
$691$	−12.2266	+	7.05900i	−0.465120	+	0.268537i	−0.714195	−	0.699947i	$-0.753207\pi$
$691$	−12.2266	+	7.05900i	−0.465120	+	0.268537i	0.249075	+	0.968484i	$0.419874\pi$
$692$	−9.83283	+	21.9845i	−0.373788	+	0.835725i
$693$		0			0
$694$	1.06995	+	5.80039i	0.0406148	+	0.220180i
$695$	−4.65407	+	6.05896i	−0.176539	+	0.229830i
$696$	−0.227340	−	9.61658i	−0.00861729	−	0.364515i
$697$	3.70331	+	13.8210i	0.140273	+	0.523506i
$698$	42.4746	+	3.37907i	1.60769	+	0.127900i
$699$	16.1239			0.609863
$700$		0			0
$701$	10.5837			0.399740			0.199870	−	0.979822i	$-0.435948\pi$
$701$	10.5837			0.399740			0.199870	+	0.979822i	$0.435948\pi$
$702$	2.28646	+	0.181899i	0.0862968	+	0.00686534i
$703$	0.782732	+	2.92120i	0.0295213	+	0.110175i
$704$	−23.1058	−	35.9793i	−0.870833	−	1.35602i
$705$	−4.67688	+	6.08867i	−0.176142	+	0.229313i
$706$	−1.40438	−	7.61339i	−0.0528546	−	0.286534i
$707$		0			0
$708$	20.5621	+	9.19667i	0.772772	+	0.345632i
$709$	−13.6491	+	7.88034i	−0.512605	+	0.295952i	−0.733904	−	0.679254i	$-0.762304\pi$
$709$	−13.6491	+	7.88034i	−0.512605	+	0.295952i	0.221299	+	0.975206i	$0.428970\pi$
$710$	15.4507	−	17.1131i	0.579853	−	0.642243i
$711$	28.0471	+	16.1930i	1.05185	+	0.607284i
$712$	−6.07833	−	20.7134i	−0.227795	−	0.776269i
$713$	−2.17733	−	2.17733i	−0.0815415	−	0.0815415i
$714$		0			0
$715$	40.8748	+	16.9550i	1.52863	+	0.634083i
$716$	1.85800	−	2.28650i	0.0694367	−	0.0854505i
$717$	−5.20956	−	19.4423i	−0.194555	−	0.726088i
$718$	29.7805	−	14.1736i	1.11140	−	0.528954i
$719$	−5.20424	−	9.01401i	−0.194085	−	0.336166i	0.752515	−	0.658575i	$-0.228841\pi$
$719$	−5.20424	−	9.01401i	−0.194085	−	0.336166i	−0.946600	+	0.322409i	$0.895507\pi$
$720$	−12.3304	+	25.5940i	−0.459525	+	0.953832i
$721$		0			0
$722$	22.0524	+	15.1837i	0.820704	+	0.565079i
$723$	−8.01145	−	2.14666i	−0.297949	−	0.0798352i
$724$	18.3953	+	2.94552i	0.683655	+	0.109469i
$725$	−6.61097	+	1.76426i	−0.245525	+	0.0655228i
$726$	−40.0614	−	46.9865i	−1.48682	−	1.74383i
$727$	11.4932	+	11.4932i	0.426259	+	0.426259i	0.887352	−	0.461093i	$-0.152542\pi$
$727$	11.4932	+	11.4932i	0.426259	+	0.426259i	−0.461093	+	0.887352i	$0.652542\pi$
$728$		0			0
$729$		−	30.0740i		−	1.11385i
$730$	38.4533	+	19.6585i	1.42322	+	0.727593i
$731$	−12.3915	−	7.15425i	−0.458317	−	0.264610i
$732$	−16.6547	+	12.0572i	−0.615574	+	0.445647i
$733$	5.20693	−	19.4325i	0.192322	−	0.717757i	−0.800621	−	0.599171i	$-0.795497\pi$
$733$	5.20693	−	19.4325i	0.192322	−	0.717757i	0.992944	−	0.118586i	$-0.0378362\pi$
$734$	−3.29846	−	17.8815i	−0.121749	−	0.660019i
$735$		0			0
$736$	5.19722	−	6.71401i	0.191572	−	0.247482i
$737$	36.2600	+	9.71582i	1.33565	+	0.357887i
$738$	−18.7310	−	39.3561i	−0.689496	−	1.44872i
$739$	13.8181	−	23.9337i	0.508308	−	0.880416i	−0.491645	−	0.870796i	$-0.663604\pi$
$739$	13.8181	−	23.9337i	0.508308	−	0.880416i	0.999954	−	0.00962048i	$-0.00306234\pi$
$740$	45.6805	−	24.6725i	1.67925	−	0.906979i
$741$	2.39707			0.0880587
$742$		0			0
$743$	−22.3607	+	22.3607i	−0.820334	+	0.820334i	−0.986156	−	0.165822i	$-0.946972\pi$
$743$	−22.3607	+	22.3607i	−0.820334	+	0.820334i	0.165822	+	0.986156i	$0.446972\pi$
$744$	12.6556	+	6.91318i	0.463977	+	0.253450i
$745$	3.92522	−	29.6992i	0.143809	−	1.08809i
$746$	−19.3775	−	6.88041i	−0.709459	−	0.251910i
$747$	6.77845	−	25.2975i	0.248011	−	0.925588i
$748$	6.43598	−	14.3897i	0.235323	−	0.526140i
$749$		0			0
$750$	38.4165	+	8.26055i	1.40277	+	0.301633i
$751$	20.3290	−	11.7369i	0.741815	−	0.428287i	−0.0809138	−	0.996721i	$-0.525784\pi$
$751$	20.3290	−	11.7369i	0.741815	−	0.428287i	0.822729	+	0.568434i	$0.192451\pi$
$752$	−3.02556	+	4.62453i	−0.110331	+	0.168639i
$753$	3.39957	−	0.910911i	0.123887	−	0.0331955i
$754$	4.64904	+	5.45269i	0.169308	+	0.198575i
$755$	4.49139	−	1.85774i	0.163458	−	0.0676101i
$756$		0			0
$757$	1.19863	−	1.19863i	0.0435649	−	0.0435649i	−0.684989	−	0.728554i	$-0.740193\pi$
$757$	1.19863	−	1.19863i	0.0435649	−	0.0435649i	0.728554	+	0.684989i	$0.240193\pi$
$758$	−2.05503	+	25.8315i	−0.0746420	+	0.938244i
$759$	9.96865	−	17.2662i	0.361839	−	0.626724i
$760$	−0.595127	+	1.53634i	−0.0215875	+	0.0557290i
$761$	14.7741	+	25.5895i	0.535560	+	0.927618i	0.999136	+	0.0415603i	$0.0132329\pi$
$761$	14.7741	+	25.5895i	0.535560	+	0.927618i	−0.463576	+	0.886057i	$0.653434\pi$
$762$	−24.8969	−	17.1422i	−0.901918	−	0.620998i
$763$		0			0
$764$	40.1837	−	15.3469i	1.45379	−	0.555233i
$765$	−10.3843	+	1.36178i	−0.375444	+	0.0492354i
$766$	8.78486	−	24.7410i	0.317410	−	0.893928i
$767$	−16.2076	+	4.34282i	−0.585223	+	0.156810i
$768$	−14.5014	+	37.0247i	−0.523274	+	1.33602i
$769$			39.8461i			1.43689i	0.695584	+	0.718444i	$0.255146\pi$
$769$			39.8461i			1.43689i	−0.695584	+	0.718444i	$0.744854\pi$
$770$		0			0
$771$		−	20.0414i		−	0.721774i
$772$	−7.76406	+	0.802724i	−0.279434	+	0.0288907i
$773$	−16.8262	+	4.50856i	−0.605195	+	0.162162i	−0.548388	−	0.836224i	$-0.684758\pi$
$773$	−16.8262	+	4.50856i	−0.605195	+	0.162162i	−0.0568065	+	0.998385i	$0.518092\pi$
$774$	41.0738	+	14.5842i	1.47637	+	0.524218i
$775$	2.66488	−	9.90546i	0.0957252	−	0.355815i
$776$	24.0935	+	39.5425i	0.864907	+	1.41949i
$777$		0			0
$778$	−26.5161	+	38.5111i	−0.950646	+	1.38069i
$779$	−1.26388	−	2.18910i	−0.0452830	−	0.0784325i
$780$	−9.51842	−	40.0349i	−0.340814	−	1.43348i
$781$	19.4849	−	33.7489i	0.697225	−	1.20763i
$782$	3.12019	+	0.248227i	0.111578	+	0.00887658i
$783$	−0.423873	+	0.423873i	−0.0151480	+	0.0151480i
$784$		0			0
$785$	−9.77396	−	4.05429i	−0.348848	−	0.144704i
$786$	18.7604	−	15.9954i	0.669161	−	0.570537i
$787$	37.2220	−	9.97361i	1.32682	−	0.355521i	0.475292	−	0.879828i	$-0.342342\pi$
$787$	37.2220	−	9.97361i	1.32682	−	0.355521i	0.851529	+	0.524307i	$0.175676\pi$
$788$	24.8391	−	17.9824i	0.884857	−	0.640597i
$789$	38.7293	−	22.3604i	1.37880	−	0.796050i
$790$	6.74643	−	31.5297i	0.240027	−	1.12178i
$791$		0			0
$792$	−11.3283	+	46.6627i	−0.402535	+	1.65809i
$793$	3.96414	−	14.7944i	0.140771	−	0.525364i
$794$	−14.0814	+	39.6577i	−0.499730	+	1.40740i
$795$	−14.1616	−	1.87168i	−0.502261	−	0.0663817i
$796$	−26.0158	+	32.0157i	−0.922107	+	1.13477i
$797$	4.70746	−	4.70746i	0.166747	−	0.166747i	−0.618801	−	0.785548i	$-0.712381\pi$
$797$	4.70746	−	4.70746i	0.166747	−	0.166747i	0.785548	+	0.618801i	$0.212381\pi$
$798$		0			0
$799$	−2.03729			−0.0720742
$800$	28.0225	+	3.83898i	0.990746	+	0.135728i
$801$	−12.1208	+	20.9938i	−0.428267	+	0.741780i
$802$	43.7768	−	20.8349i	1.54581	−	0.735706i
$803$	70.5083	+	18.8926i	2.48818	+	0.666707i
$804$	−12.4548	−	32.6111i	−0.439248	−	1.15011i
$805$		0			0
$806$	−10.5640	+	1.94866i	−0.372102	+	0.0686387i
$807$	−7.22685	+	26.9710i	−0.254397	+	0.949423i
$808$	−5.81261	−	5.54414i	−0.204487	−	0.195042i
$809$	−6.63972	−	3.83344i	−0.233440	−	0.134777i	0.378718	−	0.925512i	$-0.376365\pi$
$809$	−6.63972	−	3.83344i	−0.233440	−	0.134777i	−0.612158	+	0.790735i	$0.709698\pi$
$810$	−25.3949	+	8.21336i	−0.892287	+	0.288588i
$811$		−	6.37079i		−	0.223709i	−0.993725	−	0.111854i	$-0.964321\pi$
$811$		−	6.37079i		−	0.223709i	0.993725	−	0.111854i	$-0.0356790\pi$
$812$		0			0
$813$	44.6603	+	44.6603i	1.56630	+	1.56630i
$814$	66.7758	−	56.9340i	2.34049	−	1.99554i
$815$	21.3933	−	16.3985i	0.749376	−	0.574416i
$816$	−14.3488	+	2.99909i	−0.502307	+	0.104989i
$817$	2.44162	+	0.654230i	0.0854215	+	0.0228886i
$818$	1.70305	−	2.47345i	0.0595456	−	0.0864822i
$819$		0			0
$820$	−31.5427	+	29.8013i	−1.10152	+	1.04071i
$821$	−0.931693	−	1.61374i	−0.0325163	−	0.0563199i	0.849309	−	0.527896i	$-0.177019\pi$
$821$	−0.931693	−	1.61374i	−0.0325163	−	0.0563199i	−0.881826	+	0.471576i	$0.843685\pi$
$822$	9.58473	+	20.1387i	0.334306	+	0.702419i
$823$	12.2331	+	45.6547i	0.426420	+	1.59142i	0.760802	+	0.648984i	$0.224806\pi$
$823$	12.2331	+	45.6547i	0.426420	+	1.59142i	−0.334382	+	0.942437i	$0.608528\pi$
$824$	15.7688	−	28.8671i	0.549332	−	1.00563i
$825$	66.4166	+	0.0670175i	2.31233	+	0.00233325i
$826$		0			0
$827$	−10.7786	−	10.7786i	−0.374809	−	0.374809i	0.494416	−	0.869225i	$-0.335382\pi$
$827$	−10.7786	−	10.7786i	−0.374809	−	0.374809i	−0.869225	+	0.494416i	$0.835382\pi$
$828$	−9.48412	+	0.980561i	−0.329596	+	0.0340769i
$829$	20.7913	+	12.0039i	0.722112	+	0.416911i	0.815529	−	0.578716i	$-0.196446\pi$
$829$	20.7913	+	12.0039i	0.722112	+	0.416911i	−0.0934177	+	0.995627i	$0.529779\pi$
$830$	−26.0407	+	1.32942i	−0.903886	+	0.0461449i
$831$	28.7265	−	16.5853i	0.996512	−	0.575337i
$832$	−9.00978	−	28.2169i	−0.312358	−	0.978246i
$833$		0			0
$834$	11.8094	−	2.17838i	0.408925	−	0.0754312i
$835$	12.4434	−	1.63182i	0.430621	−	0.0564713i
$836$	−0.440300	+	2.74975i	−0.0152281	+	0.0951022i
$837$	−0.232590	−	0.868039i	−0.00803950	−	0.0300038i
$838$	2.85491	−	35.8860i	0.0986213	−	1.23966i
$839$	−21.1523			−0.730259			−0.365130	−	0.930957i	$-0.618975\pi$
$839$	−21.1523			−0.730259			−0.365130	+	0.930957i	$0.618975\pi$
$840$		0			0
$841$	27.1273			0.935424
$842$	−0.730212	+	9.17870i	−0.0251648	+	0.316319i
$843$	8.06403	+	30.0954i	0.277740	+	1.03654i
$844$	0.493296	−	3.08073i	0.0169800	−	0.106043i
$845$	1.25713	+	0.965642i	0.0432468	+	0.0332191i
$846$	6.10298	−	1.12577i	0.209825	−	0.0387047i
$847$		0			0
$848$	−10.2662	−	0.572953i	−0.352543	−	0.0196753i
$849$	60.4005	−	34.8723i	2.07294	−	1.19681i
$850$	4.47148	+	9.41963i	0.153371	+	0.323091i
$851$	15.0900	+	8.71224i	0.517280	+	0.298652i
$852$	−36.0470	+	3.72689i	−1.23495	+	0.127681i
$853$	−11.2132	−	11.2132i	−0.383931	−	0.383931i	0.488585	−	0.872516i	$-0.337513\pi$
$853$	−11.2132	−	11.2132i	−0.383931	−	0.383931i	−0.872516	+	0.488585i	$0.837513\pi$
$854$		0			0
$855$	1.70972	−	0.707177i	0.0584711	−	0.0241850i
$856$	−8.74031	−	4.77443i	−0.298738	−	0.163187i
$857$	−7.32325	−	27.3307i	−0.250157	−	0.933600i	−0.970721	−	0.240211i	$-0.922783\pi$
$857$	−7.32325	−	27.3307i	−0.250157	−	0.933600i	0.720563	−	0.693389i	$-0.243883\pi$
$858$	−29.8906	−	62.8040i	−1.02045	−	2.14409i
$859$	13.9784	+	24.2113i	0.476936	+	0.826078i	0.999651	−	0.0264302i	$-0.00841397\pi$
$859$	13.9784	+	24.2113i	0.476936	+	0.826078i	−0.522715	+	0.852508i	$0.675081\pi$
$860$	1.23138	−	43.3768i	0.0419898	−	1.47914i
$861$		0			0
$862$	17.0344	−	24.7402i	0.580194	−	0.842656i
$863$	19.5121	+	5.22825i	0.664199	+	0.177972i	0.575140	−	0.818055i	$-0.304947\pi$
$863$	19.5121	+	5.22825i	0.664199	+	0.177972i	0.0890588	+	0.996026i	$0.471614\pi$
$864$	2.29332	−	0.938554i	0.0780204	−	0.0319302i
$865$	−16.3807	−	21.3700i	−0.556959	−	0.726602i
$866$	−15.8204	+	13.4887i	−0.537600	+	0.458366i
$867$	26.0530	+	26.0530i	0.884807	+	0.884807i
$868$		0			0
$869$		−	54.4985i		−	1.84874i
$870$	9.57586	+	4.89547i	0.324652	+	0.165972i
$871$	22.5202	+	13.0020i	0.763067	+	0.440557i
$872$	−7.12108	+	7.46592i	−0.241150	+	0.252828i
$873$	13.4583	−	50.2271i	0.455495	−	1.69993i
$874$	−0.543783	+	0.100307i	−0.0183937	+	0.00339295i
$875$		0			0
$876$	−24.2187	−	63.4131i	−0.818274	−	2.14253i
$877$	−50.9185	−	13.6436i	−1.71940	−	0.460711i	−0.741699	−	0.670733i	$-0.765980\pi$
$877$	−50.9185	−	13.6436i	−1.71940	−	0.460711i	−0.977697	+	0.210022i	$0.932646\pi$
$878$	6.76149	−	3.21803i	0.228189	−	0.108603i
$879$	−22.2016	+	38.4543i	−0.748841	+	1.29703i
$880$	47.6736	−	3.56514i	1.60708	−	0.120181i
$881$	39.2472			1.32227			0.661136	−	0.750266i	$-0.270075\pi$
$881$	39.2472			1.32227			0.661136	+	0.750266i	$0.270075\pi$
$882$		0			0
$883$	−15.5015	+	15.5015i	−0.521668	+	0.521668i	−0.918075	−	0.396407i	$-0.870257\pi$
$883$	−15.5015	+	15.5015i	−0.521668	+	0.521668i	0.396407	+	0.918075i	$0.370257\pi$
$884$	6.88634	−	8.47449i	0.231613	−	0.285028i
$885$	−19.9874	+	15.3209i	−0.671869	+	0.515005i
$886$	−14.1037	+	39.7205i	−0.473823	+	1.33444i
$887$	−8.94877	+	33.3972i	−0.300470	+	1.12137i	0.636305	+	0.771438i	$0.280462\pi$
$887$	−8.94877	+	33.3972i	−0.300470	+	1.12137i	−0.936775	+	0.349932i	$0.886205\pi$
$888$	−79.2999	−	19.2517i	−2.66113	−	0.646045i
$889$		0			0
$890$	23.6006	+	5.04984i	0.791095	+	0.169271i
$891$	−39.0683	+	22.5561i	−1.30884	+	0.755658i
$892$	−2.96790	+	2.14863i	−0.0993728	+	0.0719414i
$893$	0.347646	−	0.0931514i	0.0116335	−	0.00311719i
$894$	−35.8309	+	30.5499i	−1.19836	+	1.02174i
$895$	1.25902	+	3.04388i	0.0420843	+	0.101746i
$896$		0			0
$897$	9.76583	−	9.76583i	0.326072	−	0.326072i
$898$	13.4035	+	1.06632i	0.447282	+	0.0355835i
$899$	1.40373	−	2.43133i	0.0468169	−	0.0810893i
$900$	−18.6000	−	25.7469i	−0.620000	−	0.858230i
$901$	−1.89527	−	3.28271i	−0.0631408	−	0.109363i
$902$	−41.5949	+	60.4111i	−1.38496	+	2.01147i
$903$		0			0
$904$	−27.6723	+	16.8610i	−0.920368	+	0.560787i
$905$	−12.6880	+	16.5180i	−0.421762	+	0.549077i
$906$	−7.19919	−	2.55624i	−0.239177	−	0.0849253i
$907$	−43.2674	+	11.5935i	−1.43667	+	0.384955i	−0.891366	−	0.453284i	$-0.850252\pi$
$907$	−43.2674	+	11.5935i	−1.43667	+	0.384955i	−0.545304	+	0.838239i	$0.683586\pi$
$908$	11.6408	−	1.20354i	0.386313	−	0.0399409i
$909$			9.02052i			0.299192i
$910$		0			0
$911$			0.963995i			0.0319386i	0.999872	+	0.0159693i	$0.00508340\pi$
$911$			0.963995i			0.0319386i	−0.999872	+	0.0159693i	$0.994917\pi$
$912$	2.31136	−	1.16784i	0.0765369	−	0.0386710i
$913$	−42.5702	+	11.4067i	−1.40887	+	0.377505i
$914$	−12.6591	+	35.6520i	−0.418724	+	1.17926i
$915$	−2.98902	−	22.7927i	−0.0988140	−	0.753504i
$916$	−40.9987	+	15.6582i	−1.35464	+	0.517362i
$917$		0			0
$918$	0.752400	+	0.518050i	0.0248329	+	0.0170982i
$919$	−19.8487	−	34.3789i	−0.654747	−	1.13406i	−0.981957	−	0.189104i	$-0.939442\pi$
$919$	−19.8487	−	34.3789i	−0.654747	−	1.13406i	0.327210	−	0.944952i	$-0.393892\pi$
$920$	3.83457	+	8.68374i	0.126422	+	0.286294i
$921$	−17.0366	+	29.5082i	−0.561374	+	0.972329i
$922$	0.514414	−	6.46615i	0.0169413	−	0.212951i
$923$	19.0885	−	19.0885i	0.628305	−	0.628305i
$924$		0			0
$925$	−0.0585708	+	58.0457i	−0.00192580	+	1.90853i
$926$	7.20861	+	8.45470i	0.236890	+	0.277839i
$927$	−35.6798	+	9.56036i	−1.17188	+	0.314003i
$928$	7.13932	+	2.99273i	0.234360	+	0.0982412i
$929$	13.3874	−	7.72921i	0.439226	−	0.253587i	−0.264043	−	0.964511i	$-0.585056\pi$
$929$	13.3874	−	7.72921i	0.439226	−	0.253587i	0.703269	+	0.710924i	$0.251723\pi$
$930$	−13.5336	+	8.76283i	−0.443785	+	0.287344i
$931$		0			0
$932$	−5.29788	+	11.8451i	−0.173538	+	0.388000i
$933$	7.20572	−	26.8921i	0.235905	−	0.880408i
$934$	−46.3358	−	16.4526i	−1.51615	−	0.538345i
$935$	10.7218	+	13.9875i	0.350640	+	0.457441i
$936$	−15.9461	+	29.1917i	−0.521214	+	0.954161i
$937$	34.3456	−	34.3456i	1.12202	−	1.12202i	0.130585	−	0.991437i	$-0.458314\pi$
$937$	34.3456	−	34.3456i	1.12202	−	1.12202i	0.991437	−	0.130585i	$-0.0416856\pi$
$938$		0			0
$939$	−0.572232			−0.0186741
$940$	−2.93623	−	5.43635i	−0.0957691	−	0.177314i
$941$	−9.51809	+	16.4858i	−0.310281	+	0.537422i	−0.978423	−	0.206611i	$-0.933756\pi$
$941$	−9.51809	+	16.4858i	−0.310281	+	0.537422i	0.668142	+	0.744034i	$0.267090\pi$
$942$	7.14744	+	15.0177i	0.232876	+	0.489302i
$943$	−14.0676	−	3.76941i	−0.458105	−	0.122749i
$944$	−13.5123	+	12.0838i	−0.439788	+	0.393294i
$945$		0			0
$946$	−13.3051	−	72.1291i	−0.432586	−	2.34512i
$947$	1.46452	−	5.46566i	0.0475905	−	0.177610i	−0.938040	−	0.346528i	$-0.887361\pi$
$947$	1.46452	−	5.46566i	0.0475905	−	0.177610i	0.985630	+	0.168918i	$0.0540272\pi$
$948$	−41.0511	+	29.7192i	−1.33328	+	0.965233i
$949$	43.7910	+	25.2827i	1.42152	+	0.820712i
$950$	−1.19371	−	1.40293i	−0.0387292	−	0.0455170i
$951$		−	35.6364i		−	1.15559i
$952$		0			0
$953$	−10.9748	−	10.9748i	−0.355509	−	0.355509i	0.506646	−	0.862154i	$-0.330885\pi$
$953$	−10.9748	−	10.9748i	−0.355509	−	0.355509i	−0.862154	+	0.506646i	$0.830885\pi$
$954$	7.49151	+	8.78650i	0.242546	+	0.284474i
$955$	−6.30130	+	47.6772i	−0.203905	+	1.54280i
$956$	15.9947	+	2.56112i	0.517304	+	0.0828325i
$957$	17.5584	+	4.70476i	0.567582	+	0.152083i
$958$	−34.6494	−	23.8572i	−1.11947	−	0.770790i
$959$		0			0
$960$	−28.6829	−	33.9661i	−0.925735	−	1.09625i
$961$	−13.3956	−	23.2019i	−0.432116	−	0.748447i
$962$	54.8884	−	26.1233i	1.76967	−	0.842249i
$963$	2.89466	+	10.8030i	0.0932791	+	0.348122i
$964$	4.20934	−	5.18012i	0.135574	−	0.166840i
$965$	3.34365	−	8.06078i	0.107636	−	0.259486i
$966$		0			0
$967$	5.51012	+	5.51012i	0.177194	+	0.177194i	0.790131	−	0.612938i	$-0.210012\pi$
$967$	5.51012	+	5.51012i	0.177194	+	0.177194i	−0.612938	+	0.790131i	$0.710012\pi$
$968$	47.6808	−	13.9919i	1.53252	−	0.449715i
$969$	0.826775	+	0.477339i	0.0265598	+	0.0153343i
$970$	−51.7027	+	2.63951i	−1.66007	+	0.0847495i
$971$	−42.0895	+	24.3004i	−1.35072	+	0.779836i	−0.988350	−	0.152200i	$-0.951364\pi$
$971$	−42.0895	+	24.3004i	−1.35072	+	0.779836i	−0.362366	+	0.932036i	$0.618031\pi$
$972$	40.6944	+	18.2011i	1.30527	+	0.583800i
$973$		0			0
$974$	−1.52044	−	8.24255i	−0.0487180	−	0.264108i
$975$	44.4284	+	11.9526i	1.42285	+	0.382790i
$976$	−3.38533	−	16.1967i	−0.108362	−	0.518443i
$977$	5.89146	+	21.9872i	0.188484	+	0.703433i	0.993858	+	0.110665i	$0.0352982\pi$
$977$	5.89146	+	21.9872i	0.188484	+	0.703433i	−0.805373	+	0.592768i	$0.798035\pi$
$978$	−42.2344	−	3.35996i	−1.35051	−	0.107440i
$979$	40.7933			1.30376
$980$		0			0
$981$	11.5863			0.369921
$982$	26.8017	+	2.13221i	0.855275	+	0.0680414i
$983$	3.67375	+	13.7106i	0.117174	+	0.437301i	0.999440	−	0.0334503i	$-0.0106495\pi$
$983$	3.67375	+	13.7106i	0.117174	+	0.437301i	−0.882266	+	0.470751i	$0.843983\pi$
$984$	68.1874	−	1.61198i	2.17373	−	0.0513879i
$985$	4.45789	+	33.9936i	0.142040	+	1.08313i
$986$	0.517687	+	2.80647i	0.0164865	+	0.0893762i
$987$		0			0
$988$	−0.787612	+	1.76096i	−0.0250573	+	0.0560237i
$989$	12.6127	−	7.28194i	0.401060	−	0.231552i
$990$	−39.8478	−	35.9768i	−1.26645	−	1.14342i
$991$	30.8581	+	17.8159i	0.980240	+	0.565942i	0.902343	−	0.431019i	$-0.141846\pi$
$991$	30.8581	+	17.8159i	0.980240	+	0.565942i	0.0778976	+	0.996961i	$0.475179\pi$
$992$	−9.23692	+	7.02571i	−0.293272	+	0.223067i
$993$	−29.3865	−	29.3865i	−0.932552	−	0.932552i
$994$		0			0
$995$	−17.6288	−	42.6206i	−0.558872	−	1.35116i
$996$	31.8065	+	25.8458i	1.00783	+	0.818957i
$997$	3.97096	+	14.8198i	0.125762	+	0.469349i	0.999866	−	0.0163900i	$-0.00521734\pi$
$997$	3.97096	+	14.8198i	0.125762	+	0.469349i	−0.874104	+	0.485739i	$0.838551\pi$
$998$	−42.2942	+	20.1293i	−1.33880	+	0.637182i
$999$	2.54265	+	4.40400i	0.0804459	+	0.139336i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	980.2.x.l.263.9		72
4.3	odd	2	inner	980.2.x.l.263.13		72
5.2	odd	4	inner	980.2.x.l.67.1		72
7.2	even	3	inner	980.2.x.l.863.15		72
7.3	odd	6		140.2.k.a.43.4	✓	36
7.4	even	3		980.2.k.l.883.4		36
7.5	odd	6		980.2.x.k.863.15		72
7.6	odd	2		980.2.x.k.263.9		72
20.7	even	4	inner	980.2.x.l.67.15		72
28.3	even	6		140.2.k.a.43.13	yes	36
28.11	odd	6		980.2.k.l.883.13		36
28.19	even	6		980.2.x.k.863.1		72
28.23	odd	6	inner	980.2.x.l.863.1		72
28.27	even	2		980.2.x.k.263.13		72
35.2	odd	12	inner	980.2.x.l.667.13		72
35.3	even	12		700.2.k.b.407.6		36
35.12	even	12		980.2.x.k.667.13		72
35.17	even	12		140.2.k.a.127.13	yes	36
35.24	odd	6		700.2.k.b.43.15		36
35.27	even	4		980.2.x.k.67.1		72
35.32	odd	12		980.2.k.l.687.13		36
140.3	odd	12		700.2.k.b.407.15		36
140.27	odd	4		980.2.x.k.67.15		72
140.47	odd	12		980.2.x.k.667.9		72
140.59	even	6		700.2.k.b.43.6		36
140.67	even	12		980.2.k.l.687.4		36
140.87	odd	12		140.2.k.a.127.4	yes	36
140.107	even	12	inner	980.2.x.l.667.9		72

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
140.2.k.a.43.4	✓	36	7.3	odd	6
140.2.k.a.43.13	yes	36	28.3	even	6
140.2.k.a.127.4	yes	36	140.87	odd	12
140.2.k.a.127.13	yes	36	35.17	even	12
700.2.k.b.43.6		36	140.59	even	6
700.2.k.b.43.15		36	35.24	odd	6
700.2.k.b.407.6		36	35.3	even	12
700.2.k.b.407.15		36	140.3	odd	12
980.2.k.l.687.4		36	140.67	even	12
980.2.k.l.687.13		36	35.32	odd	12
980.2.k.l.883.4		36	7.4	even	3
980.2.k.l.883.13		36	28.11	odd	6
980.2.x.k.67.1		72	35.27	even	4
980.2.x.k.67.15		72	140.27	odd	4
980.2.x.k.263.9		72	7.6	odd	2
980.2.x.k.263.13		72	28.27	even	2
980.2.x.k.667.9		72	140.47	odd	12
980.2.x.k.667.13		72	35.12	even	12
980.2.x.k.863.1		72	28.19	even	6
980.2.x.k.863.15		72	7.5	odd	6
980.2.x.l.67.1		72	5.2	odd	4	inner
980.2.x.l.67.15		72	20.7	even	4	inner
980.2.x.l.263.9		72	1.1	even	1	trivial
980.2.x.l.263.13		72	4.3	odd	2	inner
980.2.x.l.667.9		72	140.107	even	12	inner
980.2.x.l.667.13		72	35.2	odd	12	inner
980.2.x.l.863.1		72	28.23	odd	6	inner
980.2.x.l.863.15		72	7.2	even	3	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 980 = 2^{2} \cdot 5 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	980.x (of order \(12\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.112153 + 1.40976i) q^{2} +(0.643219 + 2.40053i) q^{3} +(-1.97484 - 0.316219i) q^{4} +(1.36213 - 1.77331i) q^{5} +(-3.45630 + 0.637557i) q^{6} +(0.667278 - 2.74859i) q^{8} +(-2.75072 + 1.58813i) q^{9} +(2.34717 + 2.11915i) q^{10} +(4.62887 + 2.67248i) q^{11} +(-0.511166 - 4.94406i) q^{12} +(2.61810 + 2.61810i) q^{13} +(5.13301 + 2.12920i) q^{15} +(3.80001 + 1.24896i) q^{16} +(0.381657 + 1.42436i) q^{17} +(-1.93038 - 4.05597i) q^{18} +(-0.130253 - 0.225604i) q^{19} +(-3.25074 + 3.07127i) q^{20} +(-4.28669 + 6.22586i) q^{22} +(-1.44978 - 0.388469i) q^{23} +(7.02727 - 0.166127i) q^{24} +(-1.28922 - 4.83093i) q^{25} +(-3.98452 + 3.39727i) q^{26} +(-0.309743 - 0.309743i) q^{27} -1.36847i q^{29} +(-3.57734 + 6.99752i) q^{30} +(1.77668 + 1.02577i) q^{31} +(-2.18692 + 5.21703i) q^{32} +(-3.43798 + 12.8307i) q^{33} +(-2.05081 + 0.378297i) q^{34} +(5.93444 - 2.26648i) q^{36} +(-11.2136 - 3.00467i) q^{37} +(0.332656 - 0.158323i) q^{38} +(-4.60081 + 7.96884i) q^{39} +(-3.96517 - 4.92721i) q^{40} +9.70325 q^{41} +(-6.86124 + 6.86124i) q^{43} +(-8.29620 - 6.74146i) q^{44} +(-0.930593 + 7.04110i) q^{45} +(0.710245 - 2.00028i) q^{46} +(-0.357579 + 1.33450i) q^{47} +(-0.553932 + 9.92539i) q^{48} +(6.95504 - 1.27569i) q^{50} +(-3.17373 + 1.83236i) q^{51} +(-4.34245 - 5.99823i) q^{52} +(-2.48296 + 0.665306i) q^{53} +(0.471402 - 0.401925i) q^{54} +(11.0442 - 4.56814i) q^{55} +(0.457788 - 0.457788i) q^{57} +(1.92921 + 0.153478i) q^{58} +(-2.26592 + 3.92468i) q^{59} +(-9.46360 - 5.82799i) q^{60} +(-2.06834 - 3.58246i) q^{61} +(-1.64535 + 2.38965i) q^{62} +(-7.10948 - 3.66814i) q^{64} +(8.20888 - 1.07651i) q^{65} +(-17.7026 - 6.28573i) q^{66} +(6.78396 - 1.81776i) q^{67} +(-0.303302 - 2.93358i) q^{68} -3.73012i q^{69} -7.29096i q^{71} +(2.52962 + 8.62033i) q^{72} +(13.1916 - 3.53467i) q^{73} +(5.49350 - 15.4714i) q^{74} +(10.7675 - 6.20216i) q^{75} +(0.185888 + 0.486722i) q^{76} +(-10.7181 - 7.37977i) q^{78} +(-5.09813 - 8.83021i) q^{79} +(7.39089 - 5.03733i) q^{80} +(-4.22008 + 7.30939i) q^{81} +(-1.08825 + 13.6793i) q^{82} +(-5.83046 + 5.83046i) q^{83} +(3.04570 + 1.26337i) q^{85} +(-8.90318 - 10.4422i) q^{86} +(3.28504 - 0.880224i) q^{87} +(10.4343 - 10.9396i) q^{88} +(6.60960 - 3.81606i) q^{89} +(-9.82189 - 2.10160i) q^{90} +(2.74026 + 1.22561i) q^{92} +(-1.31959 + 4.92476i) q^{93} +(-1.84123 - 0.653770i) q^{94} +(-0.577486 - 0.0763239i) q^{95} +(-13.9303 - 1.89408i) q^{96} +(-11.5761 + 11.5761i) q^{97} -16.9770 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 72 q + 16 q^{6} - 16 q^{10} - 16 q^{12} + 8 q^{13} + 8 q^{16} - 20 q^{17} - 28 q^{18} - 40 q^{20} + 8 q^{22} + 20 q^{25} - 32 q^{26} + 4 q^{30} - 20 q^{37} - 36 q^{40} + 20 q^{45} - 16 q^{46} + 48 q^{48}+ \cdots - 40 q^{97}+O(q^{100}) \) 72 * q + 16 * q^6 - 16 * q^10 - 16 * q^12 + 8 * q^13 + 8 * q^16 - 20 * q^17 - 28 * q^18 - 40 * q^20 + 8 * q^22 + 20 * q^25 - 32 * q^26 + 4 * q^30 - 20 * q^37 - 36 * q^40 + 20 * q^45 - 16 * q^46 + 48 * q^48 + 80 * q^50 + 16 * q^52 + 44 * q^53 - 32 * q^57 + 4 * q^58 - 40 * q^60 - 64 * q^61 - 80 * q^62 - 4 * q^65 + 32 * q^66 + 80 * q^68 - 80 * q^72 + 52 * q^73 - 16 * q^76 - 152 * q^78 - 20 * q^80 + 36 * q^81 + 56 * q^82 - 40 * q^85 - 56 * q^86 + 40 * q^88 + 32 * q^90 - 112 * q^92 - 32 * q^93 + 120 * q^96 - 40 * q^97

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