LMFDB - Embedded newform 980.2.x.l.667.13

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [980,2,Mod(67,980)]

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

lf = mfeigenbasis(mf)

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")

//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);

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

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

Self dual:	no
Analytic conductor:	$7.82533939809$
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			667.13
Character	$\chi$	$=$	980.667
Dual form			980.2.x.l.263.13

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.607752 + 1.27696i) q^{2} +(-0.643219 + 2.40053i) q^{3} +(-1.26127 + 1.55216i) q^{4} +(1.36213 + 1.77331i) q^{5} +(-3.45630 + 0.637557i) q^{6} +(-2.74859 - 0.667278i) q^{8} +(-2.75072 - 1.58813i) q^{9} +O(q^{10})$	\(q+(0.607752 + 1.27696i) q^{2} +(-0.643219 + 2.40053i) q^{3} +(-1.26127 + 1.55216i) q^{4} +(1.36213 + 1.77331i) q^{5} +(-3.45630 + 0.637557i) q^{6} +(-2.74859 - 0.667278i) q^{8} +(-2.75072 - 1.58813i) q^{9} +(-1.43661 + 2.81712i) q^{10} +(-4.62887 + 2.67248i) q^{11} +(-2.91471 - 4.02610i) q^{12} +(2.61810 - 2.61810i) q^{13} +(-5.13301 + 2.12920i) q^{15} +(-0.818371 - 3.91539i) q^{16} +(0.381657 - 1.42436i) q^{17} +(0.356228 - 4.47776i) q^{18} +(0.130253 - 0.225604i) q^{19} +(-4.47046 - 0.122393i) q^{20} +(-6.22586 - 4.28669i) q^{22} +(1.44978 - 0.388469i) q^{23} +(3.36976 - 6.16886i) q^{24} +(-1.28922 + 4.83093i) q^{25} +(4.93438 + 1.75207i) q^{26} +(0.309743 - 0.309743i) q^{27} +1.36847i q^{29} +(-5.83851 - 5.26065i) q^{30} +(-1.77668 + 1.02577i) q^{31} +(4.50244 - 3.42462i) 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} +(0.367250 + 0.0292166i) q^{38} +(4.60081 + 7.96884i) q^{39} +(-2.56064 - 5.78300i) q^{40} +9.70325 q^{41} +(6.86124 + 6.86124i) q^{43} +(1.69017 - 10.5554i) q^{44} +(-0.930593 - 7.04110i) q^{45} +(1.37717 + 1.61523i) q^{46} +(0.357579 + 1.33450i) q^{47} +(9.92539 + 0.553932i) q^{48} +(-6.95245 + 1.28972i) q^{50} +(3.17373 + 1.83236i) q^{51} +(0.761554 + 7.36585i) q^{52} +(-2.48296 - 0.665306i) q^{53} +(0.583778 + 0.207284i) q^{54} +(-11.0442 - 4.56814i) q^{55} +(0.457788 + 0.457788i) q^{57} +(-1.74748 + 0.831688i) q^{58} +(2.26592 + 3.92468i) q^{59} +(3.16929 - 10.6527i) q^{60} +(-2.06834 + 3.58246i) q^{61} +(-2.38965 - 1.64535i) q^{62} +(7.10948 + 3.66814i) q^{64} +(8.20888 + 1.07651i) q^{65} +(14.2949 - 12.1881i) q^{66} +(-6.78396 - 1.81776i) q^{67} +(1.72946 + 2.38890i) q^{68} +3.73012i q^{69} -7.29096i q^{71} +(6.50088 + 6.20061i) q^{72} +(13.1916 + 3.53467i) q^{73} +(-10.6519 - 12.4932i) q^{74} +(-10.7675 - 6.20216i) q^{75} +(0.185888 + 0.486722i) q^{76} +(-7.37977 + 10.7181i) q^{78} +(5.09813 - 8.83021i) q^{79} +(5.82845 - 6.78448i) q^{80} +(-4.22008 - 7.30939i) q^{81} +(5.89717 + 12.3907i) q^{82} +(5.83046 + 5.83046i) q^{83} +(3.04570 - 1.26337i) q^{85} +(-4.59162 + 12.9315i) q^{86} +(-3.28504 - 0.880224i) q^{87} +(14.5061 - 4.25680i) q^{88} +(6.60960 + 3.81606i) q^{89} +(8.42567 - 5.46758i) q^{90} +(-1.22561 + 2.74026i) q^{92} +(-1.31959 - 4.92476i) q^{93} +(-1.48680 + 1.26766i) q^{94} +(0.577486 - 0.0763239i) q^{95} +(5.32482 + 13.0110i) q^{96} +(-11.5761 - 11.5761i) q^{97} +16.9770 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 72 q + 16 q^{6}+O(q^{10}) $ 72 * q + 16 * q^6	$ 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}+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

Display 100 coefficients 10 coefficients

Character values

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

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

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 $

$2$	0.607752	+	1.27696i	0.429746	+	0.902950i
$2$	0.607752	+	1.27696i	0.429746	+	0.902950i
$3$	−0.643219	+	2.40053i	−0.371363	+	1.38594i	0.487224	+	0.873277i	$0.338009\pi$
$3$	−0.643219	+	2.40053i	−0.371363	+	1.38594i	−0.858587	+	0.512668i	$0.828657\pi$
$4$	−1.26127	+	1.55216i	−0.630637	+	0.776078i
$5$	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
$8$	−2.74859	−	0.667278i	−0.971773	−	0.235918i
$9$	−2.75072	−	1.58813i	−0.916907	−	0.529377i
$10$	−1.43661	+	2.81712i	−0.454296	+	0.890851i
$11$	−4.62887	+	2.67248i	−1.39566	+	0.805782i	−0.993934	−	0.109979i	$-0.964921\pi$
$11$	−4.62887	+	2.67248i	−1.39566	+	0.805782i	−0.401722	+	0.915762i	$0.631588\pi$
$12$	−2.91471	−	4.02610i	−0.841405	−	1.16224i
$13$	2.61810	−	2.61810i	0.726131	−	0.726131i	−0.243716	−	0.969847i	$-0.578366\pi$
$13$	2.61810	−	2.61810i	0.726131	−	0.726131i	0.969847	+	0.243716i	$0.0783664\pi$
$14$		0			0
$15$	−5.13301	+	2.12920i	−1.32534	+	0.549757i
$16$	−0.818371	−	3.91539i	−0.204593	−	0.978847i
$17$	0.381657	−	1.42436i	0.0925654	−	0.345459i	−0.904074	−	0.427377i	$-0.859438\pi$
$17$	0.381657	−	1.42436i	0.0925654	−	0.345459i	0.996639	+	0.0819178i	$0.0261045\pi$
$18$	0.356228	−	4.47776i	0.0839638	−	1.05542i
$19$	0.130253	−	0.225604i	0.0298820	−	0.0517572i	−0.850698	−	0.525655i	$-0.823820\pi$
$19$	0.130253	−	0.225604i	0.0298820	−	0.0517572i	0.880580	+	0.473898i	$0.157154\pi$
$20$	−4.47046	−	0.122393i	−0.999625	−	0.0273680i
$21$		0			0
$22$	−6.22586	−	4.28669i	−1.32736	−	0.913926i
$23$	1.44978	−	0.388469i	0.302301	−	0.0810013i	−0.104480	−	0.994527i	$-0.533318\pi$
$23$	1.44978	−	0.388469i	0.302301	−	0.0810013i	0.406781	+	0.913526i	$0.366651\pi$
$24$	3.36976	−	6.16886i	0.687850	−	1.25921i
$25$	−1.28922	+	4.83093i	−0.257844	+	0.966186i
$26$	4.93438	+	1.75207i	0.967712	+	0.343608i
$27$	0.309743	−	0.309743i	0.0596101	−	0.0596101i
$28$		0			0
$29$			1.36847i			0.254118i	0.991895	+	0.127059i	$0.0405537\pi$
$29$			1.36847i			0.254118i	−0.991895	+	0.127059i	$0.959446\pi$
$30$	−5.83851	−	5.26065i	−1.06596	−	0.960459i
$31$	−1.77668	+	1.02577i	−0.319101	+	0.184233i	−0.650992	−	0.759085i	$-0.725647\pi$
$31$	−1.77668	+	1.02577i	−0.319101	+	0.184233i	0.331891	+	0.943318i	$0.392313\pi$
$32$	4.50244	−	3.42462i	0.795927	−	0.605392i
$33$	−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	−0.999126	−	0.0417917i	$-0.986693\pi$
$37$	−11.2136	+	3.00467i	−1.84350	+	0.493964i	−0.844373	+	0.535756i	$0.820027\pi$
$38$	0.367250	+	0.0292166i	0.0595758	+	0.00473956i
$39$	4.60081	+	7.96884i	0.736719	+	1.27604i
$40$	−2.56064	−	5.78300i	−0.404873	−	0.914373i
$41$	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	0.998873	+	0.0474554i	$0.0151112\pi$
$43$	6.86124	+	6.86124i	1.04633	+	1.04633i	0.0474554	+	0.998873i	$0.484889\pi$
$44$	1.69017	−	10.5554i	0.254803	−	1.59129i
$45$	−0.930593	−	7.04110i	−0.138725	−	1.04963i
$46$	1.37717	+	1.61523i	0.203053	+	0.238153i
$47$	0.357579	+	1.33450i	0.0521583	+	0.194658i	0.987089	−	0.160173i	$-0.0512052\pi$
$47$	0.357579	+	1.33450i	0.0521583	+	0.194658i	−0.934931	+	0.354831i	$0.884539\pi$
$48$	9.92539	+	0.553932i	1.43261	+	0.0799532i
$49$		0			0
$50$	−6.95245	+	1.28972i	−0.983226	+	0.182394i
$51$	3.17373	+	1.83236i	0.444412	+	0.256581i
$52$	0.761554	+	7.36585i	0.105609	+	1.02146i
$53$	−2.48296	−	0.665306i	−0.341060	−	0.0913868i	0.0842235	−	0.996447i	$-0.473159\pi$
$53$	−2.48296	−	0.665306i	−0.341060	−	0.0913868i	−0.425284	+	0.905060i	$0.639826\pi$
$54$	0.583778	+	0.207284i	0.0794421	+	0.0282078i
$55$	−11.0442	−	4.56814i	−1.48920	−	0.615968i
$56$		0			0
$57$	0.457788	+	0.457788i	0.0606356	+	0.0606356i
$58$	−1.74748	+	0.831688i	−0.229456	+	0.109206i
$59$	2.26592	+	3.92468i	0.294997	+	0.510950i	0.974984	−	0.222274i	$-0.0713479\pi$
$59$	2.26592	+	3.92468i	0.294997	+	0.510950i	−0.679987	+	0.733224i	$0.738015\pi$
$60$	3.16929	−	10.6527i	0.409154	−	1.37526i
$61$	−2.06834	+	3.58246i	−0.264823	+	0.458687i	−0.967517	−	0.252805i	$-0.918647\pi$
$61$	−2.06834	+	3.58246i	−0.264823	+	0.458687i	0.702694	+	0.711492i	$0.251980\pi$
$62$	−2.38965	−	1.64535i	−0.303486	−	0.208959i
$63$		0			0
$64$	7.10948	+	3.66814i	0.888685	+	0.458518i
$65$	8.20888	+	1.07651i	1.01819	+	0.133524i
$66$	14.2949	−	12.1881i	1.75958	−	1.50025i
$67$	−6.78396	−	1.81776i	−0.828792	−	0.222074i	−0.180606	−	0.983556i	$-0.557806\pi$
$67$	−6.78396	−	1.81776i	−0.828792	−	0.222074i	−0.648187	+	0.761481i	$0.724472\pi$
$68$	1.72946	+	2.38890i	0.209728	+	0.289697i
$69$			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	$-0.142417\pi$
$72$	6.50088	+	6.20061i	0.766136	+	0.730749i
$73$	13.1916	+	3.53467i	1.54395	+	0.413701i	0.927541	−	0.373721i	$-0.121918\pi$
$73$	13.1916	+	3.53467i	1.54395	+	0.413701i	0.616414	+	0.787422i	$0.288585\pi$
$74$	−10.6519	−	12.4932i	−1.23826	−	1.45231i
$75$	−10.7675	−	6.20216i	−1.24333	−	0.716164i
$76$	0.185888	+	0.486722i	0.0213229	+	0.0558308i
$77$		0			0
$78$	−7.37977	+	10.7181i	−0.835594	+	1.21359i
$79$	5.09813	−	8.83021i	0.573584	−	0.993477i	−0.422610	−	0.906312i	$-0.638886\pi$
$79$	5.09813	−	8.83021i	0.573584	−	0.993477i	0.996194	−	0.0871649i	$-0.0277807\pi$
$80$	5.82845	−	6.78448i	0.651641	−	0.758528i
$81$	−4.22008	−	7.30939i	−0.468897	−	0.812154i
$82$	5.89717	+	12.3907i	0.651234	+	1.36832i
$83$	5.83046	+	5.83046i	0.639977	+	0.639977i	0.950550	−	0.310573i	$-0.100521\pi$
$83$	5.83046	+	5.83046i	0.639977	+	0.639977i	−0.310573	+	0.950550i	$0.600521\pi$
$84$		0			0
$85$	3.04570	−	1.26337i	0.330352	−	0.137032i
$86$	−4.59162	+	12.9315i	−0.495127	+	1.39444i
$87$	−3.28504	−	0.880224i	−0.352193	−	0.0943699i
$88$	14.5061	−	4.25680i	1.54636	−	0.453777i
$89$	6.60960	+	3.81606i	0.700616	+	0.404501i	0.807577	−	0.589762i	$-0.200779\pi$
$89$	6.60960	+	3.81606i	0.700616	+	0.404501i	−0.106961	+	0.994263i	$0.534112\pi$
$90$	8.42567	−	5.46758i	0.888143	−	0.576333i
$91$		0			0
$92$	−1.22561	+	2.74026i	−0.127779	+	0.285691i
$93$	−1.31959	−	4.92476i	−0.136835	−	0.510674i
$94$	−1.48680	+	1.26766i	−0.153351	+	0.130750i
$95$	0.577486	−	0.0763239i	0.0592488	−	0.00783067i
$96$	5.32482	+	13.0110i	0.543462	+	1.32793i
$97$	−11.5761	−	11.5761i	−1.17538	−	1.17538i	−0.980909	−	0.194469i	$-0.937702\pi$
$97$	−11.5761	−	11.5761i	−1.17538	−	1.17538i	−0.194469	−	0.980909i	$-0.562298\pi$
$98$		0			0
$99$	16.9770			1.70625
$100$	−5.87229	−	8.09421i	−0.587229	−	0.809421i
$101$	1.41999	+	2.45950i	0.141294	+	0.244729i	0.927984	−	0.372619i	$-0.121540\pi$
$101$	1.41999	+	2.45950i	0.141294	+	0.244729i	−0.786690	+	0.617348i	$0.788207\pi$
$102$	−0.411010	+	5.16636i	−0.0406960	+	0.511546i
$103$	−11.2333	+	3.00994i	−1.10685	+	0.296579i	−0.765549	−	0.643377i	$-0.777533\pi$
$103$	−11.2333	+	3.00994i	−1.10685	+	0.296579i	−0.341297	+	0.939956i	$0.610866\pi$
$104$	−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	$-0.137775\pi$
$107$	−0.911342	−	3.40117i	−0.0881028	−	0.328804i	−0.995884	+	0.0906407i	$0.971109\pi$
$108$	0.0900981	+	0.871441i	0.00866970	+	0.0838544i
$109$	−3.15906	+	1.82388i	−0.302583	+	0.174696i	−0.643603	−	0.765360i	$-0.722561\pi$
$109$	−3.15906	+	1.82388i	−0.302583	+	0.174696i	0.341020	+	0.940056i	$0.389228\pi$
$110$	−0.878797	−	16.8794i	−0.0837900	−	1.60938i
$111$		−	28.8511i		−	2.73843i
$112$		0			0
$113$	−8.10112	+	8.10112i	−0.762089	+	0.762089i	−0.976700	−	0.214611i	$-0.931152\pi$
$113$	−8.10112	+	8.10112i	−0.762089	+	0.762089i	0.214611	+	0.976700i	$0.431152\pi$
$114$	−0.306358	+	0.862801i	−0.0286930	+	0.0808087i
$115$	2.66366	+	2.04177i	0.248388	+	0.190396i
$116$	−2.12407	−	1.72601i	−0.197215	−	0.160256i
$117$	−11.3596	+	3.04378i	−1.05019	+	0.281398i
$118$	−3.63456	+	5.27873i	−0.334589	+	0.485946i
$119$		0			0
$120$	15.5293	−	2.42715i	1.41763	−	0.221567i
$121$	8.78427	−	15.2148i	0.798570	−	1.38316i
$122$	−5.83171	−	0.463942i	−0.527978	−	0.0420033i
$123$	−6.24132	+	23.2929i	−0.562761	+	2.10025i
$124$	0.648733	−	4.05146i	0.0582580	−	0.363832i
$125$	−10.3228	+	4.29416i	−0.923299	+	0.384081i
$126$		0			0
$127$	−6.08151	+	6.08151i	−0.539647	+	0.539647i	−0.923425	−	0.383778i	$-0.874623\pi$
$127$	−6.08151	+	6.08151i	−0.539647	+	0.539647i	0.383778	+	0.923425i	$0.374623\pi$
$128$	−0.363286	+	11.3079i	−0.0321103	+	0.999484i
$129$	−20.8839	+	12.0573i	−1.83872	+	1.06159i
$130$	3.61430	+	11.1367i	0.316995	+	0.976753i
$131$	6.07484	+	3.50731i	0.530761	+	0.306435i	0.741326	−	0.671145i	$-0.234197\pi$
$131$	6.07484	+	3.50731i	0.530761	+	0.306435i	−0.210565	+	0.977580i	$0.567530\pi$
$132$	24.2515	+	10.8468i	2.11082	+	0.944091i
$133$		0			0
$134$	−1.80175	−	9.76762i	−0.155648	−	0.843794i
$135$	0.971179	+	0.127360i	0.0835857	+	0.0109614i
$136$	−1.99946	+	3.66032i	−0.171453	+	0.313870i
$137$	−1.64243	+	6.12964i	−0.140322	+	0.523690i	0.859597	+	0.510973i	$0.170715\pi$
$137$	−1.64243	+	6.12964i	−0.140322	+	0.523690i	−0.999919	+	0.0127172i	$0.995952\pi$
$138$	−4.76323	+	2.26699i	−0.405473	+	0.192979i
$139$	3.41676			0.289806			0.144903	−	0.989446i	$-0.453713\pi$
$139$	3.41676			0.289806			0.144903	+	0.989446i	$0.453713\pi$
$140$		0			0
$141$	−3.43352			−0.289154
$142$	9.31030	−	4.43110i	0.781303	−	0.371849i
$143$	−5.12203	+	19.1157i	−0.428325	+	1.59853i
$144$	−3.96704	+	12.0698i	−0.330586	+	1.00582i
$145$	−2.42671	+	1.86402i	−0.201527	+	0.154799i
$146$	3.50355	+	18.9933i	0.289956	+	1.57190i
$147$		0			0
$148$	9.47968	−	21.1949i	0.779225	−	1.74221i
$149$	11.6025	+	6.69869i	0.950511	+	0.548778i	0.893240	−	0.449581i	$-0.148427\pi$
$149$	11.6025	+	6.69869i	0.950511	+	0.548778i	0.0572715	+	0.998359i	$0.481760\pi$
$150$	1.37595	−	17.5191i	0.112346	−	1.43043i
$151$	−1.88244	+	1.08683i	−0.153191	+	0.0884446i	−0.574636	−	0.818409i	$-0.694856\pi$
$151$	−1.88244	+	1.08683i	−0.153191	+	0.0884446i	0.421445	+	0.906854i	$0.361523\pi$
$152$	−0.508552	+	0.533179i	−0.0412490	+	0.0432465i
$153$	−3.31191	+	3.31191i	−0.267752	+	0.267752i
$154$		0			0
$155$	−4.23906	−	1.75337i	−0.340490	−	0.140834i
$156$	−18.1718	−	2.90972i	−1.45491	−	0.232964i
$157$	−1.22478	+	4.57093i	−0.0977479	+	0.364800i	−0.997422	−	0.0717625i	$-0.977138\pi$
$157$	−1.22478	+	4.57093i	−0.0977479	+	0.364800i	0.899674	+	0.436563i	$0.143804\pi$
$158$	14.3743	+	1.14354i	1.14355	+	0.0909755i
$159$	3.19417	−	5.53246i	0.253314	−	0.438753i
$160$	12.2058	+	3.31945i	0.964952	+	0.262425i
$161$		0			0
$162$	6.76906	−	9.83118i	0.531828	−	0.772410i
$163$	−11.6440	+	3.12000i	−0.912029	+	0.244377i	−0.684175	−	0.729318i	$-0.739838\pi$
$163$	−11.6440	+	3.12000i	−0.912029	+	0.244377i	−0.227854	+	0.973695i	$0.573171\pi$
$164$	−12.2385	+	15.0610i	−0.955664	+	1.17606i
$165$	18.0698	−	23.5736i	1.40673	−	1.83520i
$166$	−3.90182	+	10.9888i	−0.302840	+	0.852894i
$167$	−3.96863	+	3.96863i	−0.307102	+	0.307102i	−0.843784	−	0.536682i	$-0.819677\pi$
$167$	−3.96863	+	3.96863i	−0.307102	+	0.307102i	0.536682	+	0.843784i	$0.319677\pi$
$168$		0			0
$169$		−	0.708922i		−	0.0545325i
$170$	3.46430	+	3.12143i	0.265700	+	0.239403i
$171$	−0.716578	+	0.413717i	−0.0547981	+	0.0316377i
$172$	−19.3036	+	1.99580i	−1.47189	+	0.152178i
$173$	3.11660	+	11.6313i	0.236951	+	0.884312i	0.977260	+	0.212045i	$0.0680125\pi$
$173$	3.11660	+	11.6313i	0.236951	+	0.884312i	−0.740309	+	0.672267i	$0.765321\pi$
$174$	−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
$178$	−0.855967	+	10.7594i	−0.0641575	+	0.806454i
$179$	0.736556	+	1.27575i	0.0550528	+	0.0953542i	0.892238	−	0.451565i	$-0.149134\pi$
$179$	0.736556	+	1.27575i	0.0550528	+	0.0953542i	−0.837186	+	0.546919i	$0.815801\pi$
$180$	12.1026	+	7.43634i	0.902076	+	0.554272i
$181$	−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
$184$	−4.24408	+	0.100332i	−0.312878	+	0.00739655i
$185$	−20.6025	−	15.7923i	−1.51473	−	1.16108i
$186$	5.48676	−	4.67810i	0.402309	−	0.343015i
$187$	2.03994	+	7.61316i	0.149175	+	0.556729i
$188$	−2.52236	−	1.12816i	−0.183962	−	0.0822794i
$189$		0			0
$190$	0.448431	+	0.691043i	0.0325326	+	0.0501335i
$191$	18.6259	+	10.7537i	1.34772	+	0.778107i	0.987926	−	0.154924i	$-0.0495134\pi$
$191$	18.6259	+	10.7537i	1.34772	+	0.778107i	0.359795	+	0.933031i	$0.382847\pi$
$192$	−13.3784	+	14.7071i	−0.965505	+	1.06139i
$193$	3.76974	+	1.01010i	0.271352	+	0.0727085i	0.391929	−	0.919995i	$-0.371808\pi$
$193$	3.76974	+	1.01010i	0.271352	+	0.0727085i	−0.120577	+	0.992704i	$0.538475\pi$
$194$	7.74688	−	21.8177i	0.556194	−	1.56642i
$195$	−7.86429	+	19.0132i	−0.563174	+	1.36156i
$196$		0			0
$197$	−10.8418	−	10.8418i	−0.772443	−	0.772443i	0.206090	−	0.978533i	$-0.433926\pi$
$197$	−10.8418	−	10.8418i	−0.772443	−	0.772443i	−0.978533	+	0.206090i	$0.933926\pi$
$198$	10.3178	+	21.6790i	0.733253	+	1.54066i
$199$	−10.3133	−	17.8632i	−0.731091	−	1.26629i	−0.956417	−	0.292004i	$-0.905678\pi$
$199$	−10.3133	−	17.8632i	−0.731091	−	1.26629i	0.225326	−	0.974283i	$-0.427655\pi$
$200$	6.76711	−	12.4180i	0.478507	−	0.878084i
$201$	8.72715	−	15.1159i	0.615565	−	1.06619i
$202$	−2.27769	+	3.30804i	−0.160257	+	0.232753i
$203$		0			0
$204$	−6.84705	+	2.61502i	−0.479389	+	0.183088i
$205$	13.2171	+	17.2068i	0.923120	+	1.20178i
$206$	−10.6706	−	12.5152i	−0.743458	−	0.871973i
$207$	−4.60489	−	1.23388i	−0.320062	−	0.0857604i
$208$	−12.3935	−	8.10831i	−0.859332	−	0.562210i
$209$			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	$0.982900\pi$
$212$	4.16435	−	3.01480i	0.286009	−	0.207057i
$213$	17.5021	+	4.68969i	1.19923	+	0.321332i
$214$	3.78931	−	3.23082i	0.259032	−	0.220854i
$215$	−2.82119	+	21.5129i	−0.192404	+	1.46717i
$216$	−1.05804	+	0.644672i	−0.0719906	+	0.0438644i
$217$		0			0
$218$	−4.24896	−	2.92554i	−0.287776	−	0.198142i
$219$	−16.9701	+	29.3931i	−1.14673	+	1.98620i
$220$	21.0203	−	11.3807i	1.41719	−	0.767284i
$221$	−2.72991	−	4.72835i	−0.183634	−	0.318063i
$222$	36.8419	−	17.5343i	2.47266	−	1.17683i
$223$	−1.29543	−	1.29543i	−0.0867482	−	0.0867482i	0.662401	−	0.749149i	$-0.269537\pi$
$223$	−1.29543	−	1.29543i	−0.0867482	−	0.0867482i	−0.749149	+	0.662401i	$0.769537\pi$
$224$		0			0
$225$	11.2184	−	11.2411i	0.747896	−	0.749407i
$226$	−15.2683	−	5.42137i	−1.01563	−	0.360624i
$227$	5.65204	+	1.51446i	0.375139	+	0.100518i	0.441462	−	0.897280i	$-0.354460\pi$
$227$	5.65204	+	1.51446i	0.375139	+	0.100518i	−0.0663228	+	0.997798i	$0.521127\pi$
$228$	−1.28796	+	0.133162i	−0.0852969	+	0.00881884i
$229$	19.0037	+	10.9718i	1.25580	+	0.725035i	0.972255	−	0.233925i	$-0.0751571\pi$
$229$	19.0037	+	10.9718i	1.25580	+	0.725035i	0.283542	+	0.958960i	$0.408490\pi$
$230$	−0.988416	+	4.64229i	−0.0651742	+	0.306104i
$231$		0			0
$232$	0.913147	−	3.76135i	0.0599510	−	0.246945i
$233$	1.67921	+	6.26689i	0.110009	+	0.410557i	0.998865	−	0.0476280i	$-0.0151662\pi$
$233$	1.67921	+	6.26689i	0.110009	+	0.410557i	−0.888857	+	0.458185i	$0.848500\pi$
$234$	−10.7906	−	12.6559i	−0.705404	−	0.827341i
$235$	−1.87942	+	2.45186i	−0.122600	+	0.159942i
$236$	−8.94966	−	1.43305i	−0.582573	−	0.0932836i
$237$	17.9180	+	17.9180i	1.16390	+	1.16390i
$238$		0			0
$239$	8.09920			0.523894			0.261947	−	0.965082i	$-0.415635\pi$
$239$	8.09920			0.523894			0.261947	+	0.965082i	$0.415635\pi$
$240$	12.5373	+	18.3553i	0.809282	+	1.18483i
$241$	−1.66869	−	2.89025i	−0.107489	−	0.186177i	0.807263	−	0.590192i	$-0.200948\pi$
$241$	−1.66869	−	2.89025i	−0.107489	−	0.186177i	−0.914753	+	0.404015i	$0.867615\pi$
$242$	24.7674	+	1.97037i	1.59211	+	0.126660i
$243$	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
$248$	5.56783	−	1.63387i	0.353558	−	0.103751i
$249$	−17.7465	+	10.2459i	−1.12464	+	0.649309i
$250$	−11.7572	−	10.5721i	−0.743590	−	0.668636i
$251$		−	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
$254$	−11.4619	−	4.06982i	−0.719185	−	0.255363i
$255$	1.07370	+	8.12390i	0.0672378	+	0.508738i
$256$	−14.6605	+	6.40848i	−0.916284	+	0.400530i
$257$	−7.78950	+	2.08719i	−0.485896	+	0.130195i	−0.493446	−	0.869776i	$-0.664263\pi$
$257$	−7.78950	+	2.08719i	−0.485896	+	0.130195i	0.00755089	+	0.999971i	$0.497596\pi$
$258$	−28.0890	−	19.3401i	−1.74874	−	1.20406i
$259$		0			0
$260$	−12.0246	+	11.3837i	−0.745732	+	0.705986i
$261$	2.17330	−	3.76427i	0.134524	−	0.233002i
$262$	−0.786714	+	9.88893i	−0.0486033	+	0.610940i
$263$	4.65739	−	17.3816i	0.287187	−	1.07180i	−0.660040	−	0.751231i	$-0.729461\pi$
$263$	4.65739	−	17.3816i	0.287187	−	1.07180i	0.947226	−	0.320565i	$-0.103873\pi$
$264$	0.887943	+	37.5604i	0.0546491	+	2.31168i
$265$	−2.20231	−	5.30927i	−0.135287	−	0.326146i
$266$		0			0
$267$	−13.4120	+	13.4120i	−0.820799	+	0.820799i
$268$	11.3779	−	8.23707i	0.695014	−	0.503159i
$269$	9.73017	−	5.61772i	0.593259	−	0.342518i	−0.173126	−	0.984900i	$-0.555387\pi$
$269$	9.73017	−	5.61772i	0.593259	−	0.342518i	0.766385	+	0.642381i	$0.222053\pi$
$270$	0.427602	+	1.31756i	0.0260230	+	0.0801843i
$271$	−22.0092	−	12.7070i	−1.33696	−	0.771896i	−0.350607	−	0.936522i	$-0.614025\pi$
$271$	−22.0092	−	12.7070i	−1.33696	−	0.771896i	−0.986356	+	0.164626i	$0.947358\pi$
$272$	−5.88927	−	0.328678i	−0.357090	−	0.0199290i
$273$		0			0
$274$	−8.82552	+	1.62797i	−0.533169	+	0.0983494i
$275$	−6.94292	−	25.8072i	−0.418674	−	1.55623i
$276$	−5.78972	−	4.70470i	−0.348500	−	0.283190i
$277$	−3.45451	+	12.8924i	−0.207561	+	0.774629i	0.781092	+	0.624415i	$0.214663\pi$
$277$	−3.45451	+	12.8924i	−0.207561	+	0.774629i	−0.988654	+	0.150213i	$0.952004\pi$
$278$	2.07654	+	4.36308i	0.124543	+	0.261680i
$279$	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	$0.378004\pi$
$282$	−2.08673	−	4.38448i	−0.124263	−	0.261092i
$283$	7.26346	−	27.1076i	0.431768	−	1.61138i	−0.316916	−	0.948453i	$-0.602647\pi$
$283$	7.26346	−	27.1076i	0.431768	−	1.61138i	0.748684	−	0.662927i	$-0.230686\pi$
$284$	11.3167	+	9.19591i	0.671523	+	0.545677i
$285$	−0.188233	+	1.43536i	−0.0111499	+	0.0850236i
$286$	−27.5229	+	5.07694i	−1.62747	+	0.300206i
$287$		0			0
$288$	−17.8237	+	2.26970i	−1.05027	+	0.133743i
$289$	12.8393	+	7.41276i	0.755252	+	0.436045i
$290$	−3.85513	−	1.96595i	−0.226381	−	0.115445i
$291$	35.2348	−	20.3428i	2.06550	−	1.19252i
$292$	−22.1245	+	16.0172i	−1.29474	+	0.937333i
$293$	12.6339	−	12.6339i	0.738078	−	0.738078i	−0.234128	−	0.972206i	$-0.575223\pi$
$293$	12.6339	−	12.6339i	0.738078	−	0.738078i	0.972206	+	0.234128i	$0.0752234\pi$
$294$		0			0
$295$	−3.87319	+	9.36408i	−0.225506	+	0.545198i
$296$	32.8264	−	0.776030i	1.90800	−	0.0451058i
$297$	−0.605978	+	2.26154i	−0.0351624	+	0.131228i
$298$	−1.50256	+	18.8871i	−0.0870410	+	1.09410i
$299$	2.77863	−	4.81273i	0.160693	−	0.278328i
$300$	23.2075	−	8.89025i	1.33989	−	0.513279i
$301$		0			0
$302$	−2.53189	−	1.74328i	−0.145694	−	0.100315i
$303$	−6.81745	+	1.82673i	−0.391652	+	0.104943i
$304$	−0.989924	−	0.325362i	−0.0567760	−	0.0186608i
$305$	−9.17014	+	1.21198i	−0.525080	+	0.0693977i
$306$	−6.24200	−	2.21637i	−0.356832	−	0.126701i
$307$	−9.69470	+	9.69470i	−0.553306	+	0.553306i	−0.927393	−	0.374087i	$-0.877956\pi$
$307$	−9.69470	+	9.69470i	−0.553306	+	0.553306i	0.374087	+	0.927393i	$0.377956\pi$
$308$		0			0
$309$		−	28.9018i		−	1.64417i
$310$	−0.337305	−	6.47874i	−0.0191577	−	0.367968i
$311$	9.70173	−	5.60130i	0.550135	−	0.317620i	−0.199042	−	0.979991i	$-0.563783\pi$
$311$	9.70173	−	5.60130i	0.550135	−	0.317620i	0.749176	+	0.662371i	$0.230450\pi$
$312$	−7.32831	−	24.9731i	−0.414884	−	1.41382i
$313$	−0.0595944	−	0.222409i	−0.00336848	−	0.0125713i	0.964221	−	0.265099i	$-0.0854047\pi$
$313$	−0.0595944	−	0.222409i	−0.00336848	−	0.0125713i	−0.967590	+	0.252528i	$0.918738\pi$
$314$	−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	−0.625876	−	0.779923i	$-0.715258\pi$
$317$	−13.8508	+	3.71131i	−0.777938	+	0.208448i	−0.152063	+	0.988371i	$0.548592\pi$
$318$	9.00602	+	0.716474i	0.505033	+	0.0401779i
$319$	−3.65719	−	6.33445i	−0.204764	−	0.354661i
$320$	3.17928	+	17.6038i	0.177727	+	0.984080i
$321$	8.75080			0.488422
$322$		0			0
$323$	−0.271631	−	0.271631i	−0.0151139	−	0.0151139i
$324$	16.6680	+	2.66893i	0.925999	+	0.148274i
$325$	9.27256	+	16.0232i	0.514349	+	0.888807i
$326$	−11.0608	−	12.9728i	−0.612601	−	0.718497i
$327$	−2.34632	−	8.75657i	−0.129752	−	0.484239i
$328$	−26.6703	−	6.47476i	−1.47262	−	0.357509i
$329$		0			0
$330$	41.0846	+	8.74756i	2.26163	+	0.481537i
$331$	14.4821	+	8.36122i	0.796006	+	0.459574i	0.842073	−	0.539364i	$-0.181335\pi$
$331$	14.4821	+	8.36122i	0.796006	+	0.459574i	−0.0460667	+	0.998938i	$0.514669\pi$
$332$	−16.4036	+	1.69597i	−0.900265	+	0.0930782i
$333$	35.6172	+	9.54360i	1.95181	+	0.522986i
$334$	−7.47975	−	2.65586i	−0.409274	−	0.145322i
$335$	−6.01718	−	14.5060i	−0.328753	−	0.792550i
$336$		0			0
$337$	9.74524	+	9.74524i	0.530857	+	0.530857i	0.920827	−	0.389970i	$-0.127515\pi$
$337$	9.74524	+	9.74524i	0.530857	+	0.530857i	−0.389970	+	0.920827i	$0.627515\pi$
$338$	0.905268	−	0.430849i	0.0492401	−	0.0234351i
$339$	−14.2362	−	24.6577i	−0.773202	−	1.33923i
$340$	−1.88051	+	6.32085i	−0.101985	+	0.342796i
$341$	5.48268	−	9.49628i	0.296904	−	0.514252i
$342$	−0.963803	−	0.663608i	−0.0521165	−	0.0358838i
$343$		0			0
$344$	−14.2804	−	23.4371i	−0.769946	−	1.26364i
$345$	−6.61464	+	5.08089i	−0.356120	+	0.273546i
$346$	−12.9586	+	11.0487i	−0.696661	+	0.593984i
$347$	−4.02857	−	1.07945i	−0.216265	−	0.0579481i	0.149060	−	0.988828i	$-0.452375\pi$
$347$	−4.02857	−	1.07945i	−0.216265	−	0.0579481i	−0.365325	+	0.930880i	$0.619042\pi$
$348$	5.50958	−	3.98869i	0.295345	−	0.213816i
$349$			30.1290i			1.61277i	0.591393	+	0.806383i	$0.298578\pi$
$349$			30.1290i			1.61277i	−0.591393	+	0.806383i	$0.701422\pi$
$350$		0			0
$351$		−	1.62188i		−	0.0865695i
$352$	−11.6890	+	27.8848i	−0.623026	+	1.48626i
$353$	−5.28777	−	1.41685i	−0.281440	−	0.0754116i	0.115338	−	0.993326i	$-0.463205\pi$
$353$	−5.28777	−	1.41685i	−0.281440	−	0.0754116i	−0.396778	+	0.917915i	$0.629872\pi$
$354$	−10.3339	−	12.1202i	−0.549241	−	0.644184i
$355$	12.9291	−	9.93121i	0.686205	−	0.527094i
$356$	−14.2596	+	5.44603i	−0.755759	+	0.288639i
$357$		0			0
$358$	−1.18145	+	1.71590i	−0.0624414	+	0.0906880i
$359$	11.6607	−	20.1969i	0.615427	−	1.06595i	−0.374883	−	0.927072i	$-0.622317\pi$
$359$	11.6607	−	20.1969i	0.615427	−	1.06595i	0.990309	−	0.138878i	$-0.0443497\pi$
$360$	−2.14055	+	19.9741i	−0.112817	+	1.05273i
$361$	9.46607	+	16.3957i	0.498214	+	0.862932i
$362$	−5.66109	−	11.8947i	−0.297540	−	0.625170i
$363$	30.8733	+	30.8733i	1.62043	+	1.62043i
$364$		0			0
$365$	11.7005	+	28.2073i	0.612434	+	1.47644i
$366$	4.86477	−	13.7008i	0.254286	−	0.716151i
$367$	12.4194	+	3.32776i	0.648285	+	0.173708i	0.567953	−	0.823061i	$-0.307735\pi$
$367$	12.4194	+	3.32776i	0.648285	+	0.173708i	0.0803318	+	0.996768i	$0.474402\pi$
$368$	−2.70747	−	5.35856i	−0.141136	−	0.279334i
$369$	−26.6910	−	15.4100i	−1.38948	−	0.802214i
$370$	7.64505	−	35.9065i	0.397447	−	1.86669i
$371$		0			0
$372$	9.30835	+	4.16328i	0.482616	+	0.215856i
$373$	−3.76324	−	14.0446i	−0.194853	−	0.727202i	−0.992305	−	0.123819i	$-0.960486\pi$
$373$	−3.76324	−	14.0446i	−0.194853	−	0.727202i	0.797452	−	0.603383i	$-0.206181\pi$
$374$	−8.48195	+	7.23184i	−0.438591	+	0.373950i
$375$	−3.66842	−	27.5422i	−0.189437	−	1.42228i
$376$	−0.0923538	−	3.90661i	−0.00476278	−	0.201468i
$377$	3.58278	+	3.58278i	0.184523	+	0.184523i
$378$		0			0
$379$	−18.3234			−0.941208			−0.470604	−	0.882344i	$-0.655964\pi$
$379$	−18.3234			−0.941208			−0.470604	+	0.882344i	$0.655964\pi$
$380$	−0.609902	+	0.992614i	−0.0312873	+	0.0509200i
$381$	−10.6871	−	18.5106i	−0.547516	−	0.948325i
$382$	−2.41212	+	30.3201i	−0.123415	+	1.55131i
$383$	17.9320	−	4.80487i	0.916284	−	0.245518i	0.230288	−	0.973123i	$-0.426033\pi$
$383$	17.9320	−	4.80487i	0.916284	−	0.245518i	0.685996	+	0.727605i	$0.259367\pi$
$384$	−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
$388$	32.5686	−	3.36726i	1.65342	−	0.170947i
$389$	28.6326	−	16.5311i	1.45173	−	0.838158i	0.453152	−	0.891433i	$-0.350300\pi$
$389$	28.6326	−	16.5311i	1.45173	−	0.838158i	0.998580	+	0.0532759i	$0.0169663\pi$
$390$	−29.0587	+	1.51290i	−1.47145	+	0.0766085i
$391$		−	2.21328i		−	0.111930i
$392$		0			0
$393$	−12.3268	+	12.3268i	−0.621807	+	0.621807i
$394$	7.25543	−	20.4336i	0.365523	−	1.02943i
$395$	22.6030	−	2.98734i	1.13728	−	0.150309i
$396$	−21.4126	+	26.3509i	−1.07602	+	1.32418i
$397$	28.7436	−	7.70181i	1.44260	−	0.386543i	0.549155	−	0.835720i	$-0.314950\pi$
$397$	28.7436	−	7.70181i	1.44260	−	0.386543i	0.893443	+	0.449177i	$0.148283\pi$
$398$	16.5427	−	24.0261i	0.829211	−	1.20432i
$399$		0			0
$400$	19.9700	+	1.09431i	0.998502	+	0.0547154i
$401$	−17.1410	+	29.6890i	−0.855979	+	1.48260i	0.0197547	+	0.999805i	$0.493711\pi$
$401$	−17.1410	+	29.6890i	−0.855979	+	1.48260i	−0.875734	+	0.482794i	$0.839622\pi$
$402$	24.6064	+	1.95756i	1.22725	+	0.0976341i
$403$	−1.96597	+	7.33709i	−0.0979319	+	0.365487i
$404$	−5.60852	−	0.898055i	−0.279034	−	0.0446799i
$405$	7.21349	−	17.4398i	0.358441	−	0.866590i
$406$		0			0
$407$	43.8762	−	43.8762i	2.17486	−	2.17486i
$408$	−7.50060	−	7.15415i	−0.371335	−	0.354183i
$409$	−1.83899	+	1.06174i	−0.0909321	+	0.0524997i	−0.544777	−	0.838581i	$-0.683386\pi$
$409$	−1.83899	+	1.06174i	−0.0909321	+	0.0524997i	0.453844	+	0.891081i	$0.350052\pi$
$410$	−13.9398	+	27.3352i	−0.688438	+	1.34999i
$411$	−13.6579	−	7.88540i	−0.673695	−	0.388958i
$412$	9.49633	−	21.2321i	0.467851	−	1.04603i
$413$		0			0
$414$	−1.22302	−	6.63017i	−0.0601079	−	0.325855i
$415$	−2.39736	+	18.2810i	−0.117682	+	0.897380i
$416$	2.82187	−	20.7539i	0.138353	−	1.01754i
$417$	−2.19773	+	8.20203i	−0.107623	+	0.401655i
$418$	−1.77803	+	0.846228i	−0.0869664	+	0.0413904i
$419$	25.4554			1.24358			0.621789	−	0.783185i	$-0.286406\pi$
$419$	25.4554			1.24358			0.621789	+	0.783185i	$0.286406\pi$
$420$		0			0
$421$	6.51083			0.317318			0.158659	−	0.987333i	$-0.449283\pi$
$421$	6.51083			0.317318			0.158659	+	0.987333i	$0.449283\pi$
$422$	−1.99205	+	0.948084i	−0.0969712	+	0.0461520i
$423$	1.13577	−	4.23873i	0.0552228	−	0.206094i
$424$	6.38068	+	3.48547i	0.309873	+	0.169270i
$425$	6.38896	+	3.68008i	0.309910	+	0.178510i
$426$	4.64840	+	25.1998i	0.225216	+	1.22093i
$427$		0			0
$428$	6.42860	+	2.87527i	0.310738	+	0.138982i
$429$	−42.5931	−	24.5911i	−2.05641	−	1.18727i
$430$	−29.1858	+	9.47197i	−1.40747	+	0.456779i
$431$	18.3941	−	10.6198i	0.886014	−	0.511540i	0.0133771	−	0.999911i	$-0.495742\pi$
$431$	18.3941	−	10.6198i	0.886014	−	0.511540i	0.872636	+	0.488370i	$0.162408\pi$
$432$	−1.46625	−	0.959280i	−0.0705450	−	0.0461534i
$433$	10.3951	−	10.3951i	0.499557	−	0.499557i	−0.411743	−	0.911300i	$-0.635080\pi$
$433$	10.3951	−	10.3951i	0.499557	−	0.499557i	0.911300	+	0.411743i	$0.135080\pi$
$434$		0			0
$435$	−2.91374	−	7.02435i	−0.139703	−	0.336792i
$436$	1.15349	−	7.20377i	0.0552423	−	0.344998i
$437$	0.101198	−	0.377677i	0.00484097	−	0.0180667i
$438$	−47.8476	−	3.80651i	−2.28625	−	0.181882i
$439$	2.64749	−	4.58558i	0.126358	−	0.218858i	−0.795905	−	0.605421i	$-0.793005\pi$
$439$	2.64749	−	4.58558i	0.126358	−	0.218858i	0.922263	+	0.386563i	$0.126338\pi$
$440$	27.3078	+	19.9255i	1.30185	+	0.949911i
$441$		0			0
$442$	4.37882	−	6.35966i	0.208279	−	0.302498i
$443$	−28.7891	+	7.71402i	−1.36781	+	0.366504i	−0.866679	−	0.498867i	$-0.833750\pi$
$443$	−28.7891	+	7.71402i	−1.36781	+	0.366504i	−0.501132	+	0.865371i	$0.667083\pi$
$444$	44.7814	+	36.3892i	2.12523	+	1.72696i
$445$	2.23609	+	16.9188i	0.106001	+	0.802028i
$446$	0.866916	−	2.44151i	0.0410497	−	0.115609i
$447$	−23.5433	+	23.5433i	−1.11356	+	1.11356i
$448$		0			0
$449$			9.50768i			0.448695i	0.974509	+	0.224347i	$0.0720251\pi$
$449$			9.50768i			0.448695i	−0.974509	+	0.224347i	$0.927975\pi$
$450$	21.1725	+	7.49374i	0.998082	+	0.353258i
$451$	−44.9151	+	25.9317i	−2.11497	+	1.22108i
$452$	−2.35645	−	22.7919i	−0.110838	−	1.07204i
$453$	−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	0.402482	−	0.915428i	$-0.368148\pi$
$457$	25.8402	−	6.92387i	1.20875	−	0.323885i	0.806273	+	0.591543i	$0.201481\pi$
$458$	−2.46104	+	30.9351i	−0.114997	+	1.44550i
$459$	−0.322971	−	0.559402i	−0.0150750	−	0.0261107i
$460$	−6.52875	+	1.55919i	−0.304405	+	0.0726976i
$461$	−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	$-0.308438\pi$
$463$	−5.55531	−	5.55531i	−0.258177	−	0.258177i	−0.824312	+	0.566135i	$0.808438\pi$
$464$	5.35808	−	1.11991i	0.248742	−	0.0519906i
$465$	6.93566	−	9.04818i	0.321634	−	0.419599i
$466$	−6.98205	+	5.95300i	−0.323437	+	0.275767i
$467$	8.99874	+	33.5838i	0.416412	+	1.55407i	0.781990	+	0.623291i	$0.214205\pi$
$467$	8.99874	+	33.5838i	0.416412	+	1.55407i	−0.365578	+	0.930781i	$0.619129\pi$
$468$	9.60310	−	21.4708i	0.443904	−	0.992490i
$469$		0			0
$470$	−4.27316	−	0.909822i	−0.197106	−	0.0419670i
$471$	−10.1848	−	5.88022i	−0.469293	−	0.270946i
$472$	−3.60922	−	12.2993i	−0.166128	−	0.566123i
$473$	−50.0962	−	13.4232i	−2.30343	−	0.617202i
$474$	−11.9909	+	33.7703i	−0.550761	+	1.55112i
$475$	0.921955	+	0.920096i	0.0423022	+	0.0422169i
$476$		0			0
$477$	5.77333	+	5.77333i	0.264343	+	0.264343i
$478$	4.92231	+	10.3424i	0.225141	+	0.473050i
$479$	14.8734	+	25.7615i	0.679583	+	1.17707i	0.975107	+	0.221737i	$0.0711726\pi$
$479$	14.8734	+	25.7615i	0.679583	+	1.17707i	−0.295524	+	0.955335i	$0.595494\pi$
$480$	−15.8194	+	27.1652i	−0.722054	+	1.23992i
$481$	−21.4917	+	37.2248i	−0.979939	+	1.69730i
$482$	2.67660	−	3.88741i	0.121916	−	0.177066i
$483$		0			0
$484$	12.5364	+	32.8246i	0.569834	+	1.49203i
$485$	4.75985	−	36.2961i	0.216134	−	1.64812i
$486$	20.4518	+	23.9871i	0.927712	+	1.08808i
$487$	5.72475	+	1.53394i	0.259413	+	0.0695095i	0.386182	−	0.922423i	$-0.373794\pi$
$487$	5.72475	+	1.53394i	0.259413	+	0.0695095i	−0.126768	+	0.991932i	$0.540461\pi$
$488$	8.07550	−	8.46656i	0.365561	−	0.383263i
$489$		−	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	$-0.141130\pi$
$492$	−28.2822	−	39.0663i	−1.27506	−	1.76124i
$493$	1.94919	+	0.522285i	0.0877872	+	0.0235225i
$494$	1.03799	−	0.885007i	0.0467014	−	0.0398183i
$495$	23.1248	+	30.1053i	1.03938	+	1.35313i
$496$	5.47026	+	6.11694i	0.245622	+	0.274659i
$497$		0			0
$498$	−23.8691	−	16.4346i	−1.06960	−	0.736452i
$499$	−16.5605	+	28.6836i	−0.741348	+	1.28405i	0.210534	+	0.977587i	$0.432480\pi$
$499$	−16.5605	+	28.6836i	−0.741348	+	1.28405i	−0.951882	+	0.306466i	$0.900853\pi$
$500$	6.35469	−	21.4387i	0.284190	−	0.958768i
$501$	−6.97411	−	12.0795i	−0.311580	−	0.539673i
$502$	1.80841	−	0.860684i	0.0807131	−	0.0384142i
$503$	22.3897	+	22.3897i	0.998307	+	0.998307i	0.999999	−	0.00169150i	$-0.000538420\pi$
$503$	22.3897	+	22.3897i	0.998307	+	0.998307i	−0.00169150	+	0.999999i	$0.500538\pi$
$504$		0			0
$505$	−2.42723	+	5.86822i	−0.108010	+	0.261132i
$506$	−10.6914	−	3.79623i	−0.475291	−	0.168763i
$507$	1.70179	+	0.455992i	0.0755790	+	0.0202513i
$508$	−1.76899	−	17.1099i	−0.0784863	−	0.759129i
$509$	−9.71677	−	5.60998i	−0.430688	−	0.248658i	0.268952	−	0.963154i	$-0.413323\pi$
$509$	−9.71677	−	5.60998i	−0.430688	−	0.248658i	−0.699640	+	0.714496i	$0.746656\pi$
$510$	−9.72138	+	6.30839i	−0.430470	+	0.279340i
$511$		0			0
$512$	−17.0934	−	14.8262i	−0.755427	−	0.655232i
$513$	−0.0295345	−	0.110224i	−0.00130398	−	0.00486652i
$514$	−7.39935	−	8.67842i	−0.326371	−	0.382789i
$515$	−20.6387	−	15.8201i	−0.909449	−	0.697116i
$516$	7.62549	−	47.6226i	0.335693	−	2.09647i
$517$	−5.22162	−	5.22162i	−0.229647	−	0.229647i
$518$		0			0
$519$	−29.9259			−1.31360
$520$	−21.8445	−	8.43648i	−0.957945	−	0.369964i
$521$	14.4739	+	25.0695i	0.634111	+	1.09831i	0.986703	+	0.162536i	$0.0519673\pi$
$521$	14.4739	+	25.0695i	0.634111	+	1.09831i	−0.352591	+	0.935777i	$0.614699\pi$
$522$	6.12767	+	0.487486i	0.268201	+	0.0213367i
$523$	21.7294	−	5.82238i	0.950161	−	0.254595i	0.249731	−	0.968315i	$-0.419658\pi$
$523$	21.7294	−	5.82238i	0.950161	−	0.254595i	0.700431	+	0.713720i	$0.252991\pi$
$524$	−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
$528$	−47.4237	+	23.9613i	−2.06385	+	1.04278i
$529$	−17.9676	+	10.3736i	−0.781201	+	0.451026i
$530$	5.44129	−	6.03899i	0.236354	−	0.262317i
$531$		−	14.3943i		−	0.624659i
$532$		0			0
$533$	25.4041	−	25.4041i	1.10037	−	1.10037i
$534$	−25.2778	−	8.97545i	−1.09388	−	0.388406i
$535$	4.78996	−	6.24892i	0.207088	−	0.270164i
$536$	17.4334	+	9.52305i	0.753007	+	0.411333i
$537$	−3.53625	+	0.947534i	−0.152600	+	0.0408891i
$538$	13.0872	+	9.01090i	0.564227	+	0.388488i
$539$		0			0
$540$	−1.42261	+	1.34678i	−0.0612192	+	0.0579564i
$541$	2.92645	−	5.06875i	0.125818	−	0.217923i	−0.796235	−	0.604988i	$-0.793178\pi$
$541$	2.92645	−	5.06875i	0.125818	−	0.217923i	0.922052	+	0.387065i	$0.126511\pi$
$542$	2.85027	−	35.8277i	0.122430	−	1.53893i
$543$	5.99146	−	22.3604i	0.257118	−	0.959579i
$544$	−3.15951	−	7.72015i	−0.135463	−	0.330998i
$545$	−7.53735	−	3.11762i	−0.322864	−	0.133544i
$546$		0			0
$547$	−13.8207	+	13.8207i	−0.590930	+	0.590930i	−0.937883	−	0.346952i	$-0.887217\pi$
$547$	−13.8207	+	13.8207i	−0.590930	+	0.590930i	0.346952	+	0.937883i	$0.387217\pi$
$548$	−7.44259	−	10.2805i	−0.317932	−	0.439160i
$549$	11.3788	−	6.56957i	0.485637	−	0.280383i
$550$	28.7352	−	24.5502i	1.22527	−	1.04682i
$551$	0.308732	+	0.178246i	0.0131524	+	0.00759356i
$552$	2.48902	−	10.2526i	0.105940	−	0.436378i
$553$		0			0
$554$	−18.5626	+	3.42410i	−0.788650	+	0.145476i
$555$	51.1619	−	39.2989i	2.17170	−	1.66815i
$556$	−4.30948	+	5.30335i	−0.182763	+	0.224912i
$557$	9.09246	−	33.9335i	0.385260	−	1.43781i	−0.452496	−	0.891766i	$-0.649466\pi$
$557$	9.09246	−	33.9335i	0.385260	−	1.43781i	0.837757	−	0.546044i	$-0.183867\pi$
$558$	3.96024	+	8.32096i	0.167650	+	0.352254i
$559$	35.9268			1.51954
$560$		0			0
$561$	−19.5877			−0.826994
$562$	7.61938	+	16.0093i	0.321404	+	0.675311i
$563$	7.68371	−	28.6760i	0.323830	−	1.20855i	−0.591653	−	0.806193i	$-0.701525\pi$
$563$	7.68371	−	28.6760i	0.323830	−	1.20855i	0.915483	−	0.402357i	$-0.131809\pi$
$564$	4.33061	−	5.32935i	0.182352	−	0.224406i
$565$	−25.4005	−	3.33100i	−1.06861	−	0.140136i
$566$	39.0298	−	7.19952i	1.64055	−	0.302619i
$567$		0			0
$568$	−4.86509	+	20.0399i	−0.204135	+	0.840854i
$569$	−27.0392	−	15.6111i	−1.13354	−	0.654451i	−0.188718	−	0.982031i	$-0.560433\pi$
$569$	−27.0392	−	15.6111i	−1.13354	−	0.654451i	−0.944823	+	0.327581i	$0.893767\pi$
$570$	−1.94731	+	0.631979i	−0.0815637	+	0.0264707i
$571$	20.8709	−	12.0498i	0.873420	−	0.504269i	0.00493696	−	0.999988i	$-0.498429\pi$
$571$	20.8709	−	12.0498i	0.873420	−	0.504269i	0.868483	+	0.495718i	$0.165095\pi$
$572$	−23.2102	−	32.0603i	−0.970467	−	1.34051i
$573$	−37.7950	+	37.7950i	−1.57891	+	1.57891i
$574$		0			0
$575$	0.00757253	+	7.50463i	0.000315796	+	0.312965i
$576$	−13.7307	−	21.3808i	−0.572113	−	0.890868i
$577$	−0.854134	+	3.18767i	−0.0355581	+	0.132705i	−0.981423	−	0.191855i	$-0.938550\pi$
$577$	−0.854134	+	3.18767i	−0.0355581	+	0.132705i	0.945865	+	0.324560i	$0.105216\pi$
$578$	−1.66273	+	20.9004i	−0.0691606	+	0.869343i
$579$	−4.84954	+	8.39964i	−0.201540	+	0.349077i
$580$	0.167491	−	6.11767i	0.00695468	−	0.254023i
$581$		0			0
$582$	47.3911	+	32.6302i	1.96442	+	1.35256i
$583$	13.2713	−	3.55603i	0.549640	−	0.147276i
$584$	−33.8996	−	18.5178i	−1.40277	−	0.766271i
$585$	−20.8707	−	15.9979i	−0.862898	−	0.661434i
$586$	23.8112	+	8.45474i	0.983634	+	0.349262i
$587$	29.4634	−	29.4634i	1.21608	−	1.21608i	0.247092	−	0.968992i	$-0.420525\pi$
$587$	29.4634	−	29.4634i	1.21608	−	1.21608i	0.968992	−	0.247092i	$-0.0794751\pi$
$588$		0			0
$589$			0.534436i			0.0220210i
$590$	−14.3115	+	0.745107i	−0.589196	+	0.0306756i
$591$	32.9995	−	19.0523i	1.35742	−	0.783707i
$592$	20.9413	+	41.4465i	0.860682	+	1.70344i
$593$	−0.0733317	−	0.273678i	−0.00301137	−	0.0112386i	0.964404	−	0.264434i	$-0.0851851\pi$
$593$	−0.0733317	−	0.273678i	−0.00301137	−	0.0112386i	−0.967415	+	0.253195i	$0.918518\pi$
$594$	−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
$598$	7.83441	+	0.623266i	0.320373	+	0.0254873i
$599$	−0.792194	−	1.37212i	−0.0323682	−	0.0560633i	0.849388	−	0.527770i	$-0.176972\pi$
$599$	−0.792194	−	1.37212i	−0.0323682	−	0.0560633i	−0.881756	+	0.471706i	$0.843638\pi$
$600$	25.4570	+	24.2321i	1.03928	+	0.989272i
$601$	−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
$604$	0.687349	−	4.29262i	0.0279678	−	0.174664i
$605$	38.9458	−	5.14730i	1.58337	−	0.209267i
$606$	−6.47599	−	7.59544i	−0.263069	−	0.308544i
$607$	−8.87912	−	33.1373i	−0.360392	−	1.34500i	−0.873561	−	0.486715i	$-0.838195\pi$
$607$	−8.87912	−	33.1373i	−0.360392	−	1.34500i	0.513168	−	0.858288i	$-0.328472\pi$
$608$	−0.186153	−	1.46184i	−0.00754948	−	0.0592853i
$609$		0			0
$610$	−7.12082	−	10.9734i	−0.288314	−	0.444298i
$611$	4.43005	+	2.55769i	0.179221	+	0.103473i
$612$	−0.963368	−	9.31782i	−0.0389418	−	0.376650i
$613$	18.6732	+	5.00346i	0.754202	+	0.202088i	0.615381	−	0.788230i	$-0.289002\pi$
$613$	18.6732	+	5.00346i	0.754202	+	0.202088i	0.138821	+	0.990318i	$0.455669\pi$
$614$	−18.2718	−	6.48781i	−0.737388	−	0.261827i
$615$	−49.8069	+	20.6601i	−2.00841	+	0.833098i
$616$		0			0
$617$	−22.2105	−	22.2105i	−0.894159	−	0.894159i	0.100752	−	0.994912i	$-0.467875\pi$
$617$	−22.2105	−	22.2105i	−0.894159	−	0.894159i	−0.994912	+	0.100752i	$0.967875\pi$
$618$	36.9066	−	17.5651i	1.48460	−	0.706573i
$619$	17.1081	+	29.6322i	0.687634	+	1.19102i	0.972601	+	0.232480i	$0.0746839\pi$
$619$	17.1081	+	29.6322i	0.687634	+	1.19102i	−0.284967	+	0.958537i	$0.591983\pi$
$620$	8.06813	−	4.36820i	0.324024	−	0.175431i
$621$	0.328735	−	0.569386i	0.0131917	−	0.0228487i
$622$	13.0489	+	8.98456i	0.523213	+	0.360248i
$623$		0			0
$624$	27.4359	−	24.5354i	1.09832	−	0.982203i
$625$	−21.6758	−	12.4563i	−0.867033	−	0.498251i
$626$	0.247790	−	0.211270i	0.00990369	−	0.00844403i
$627$	−3.34247	−	0.895612i	−0.133485	−	0.0357673i
$628$	−5.55001	−	7.66625i	−0.221470	−	0.305917i
$629$			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	$-0.173221\pi$
$632$	−19.9049	+	20.8688i	−0.791773	+	0.830115i
$633$	−3.74479	−	1.00341i	−0.148842	−	0.0398821i
$634$	−13.1571	−	15.4314i	−0.522534	−	0.612860i
$635$	−19.0682	−	2.50058i	−0.756697	−	0.0992327i
$636$	4.55852	+	11.9358i	0.180757	+	0.473285i
$637$		0			0
$638$	5.86619	−	8.51988i	0.232245	−	0.337305i
$639$	−11.5790	+	20.0554i	−0.458058	+	0.793380i
$640$	−20.5472	+	14.7585i	−0.812198	+	0.583383i
$641$	11.4725	+	19.8710i	0.453138	+	0.784858i	0.998579	−	0.0532913i	$-0.0169712\pi$
$641$	11.4725	+	19.8710i	0.453138	+	0.784858i	−0.545441	+	0.838149i	$0.683638\pi$
$642$	5.31832	+	11.1745i	0.209897	+	0.441021i
$643$	−17.9293	−	17.9293i	−0.707062	−	0.707062i	0.258855	−	0.965916i	$-0.416655\pi$
$643$	−17.9293	−	17.9293i	−0.707062	−	0.707062i	−0.965916	+	0.258855i	$0.916655\pi$
$644$		0			0
$645$	−49.8277	−	20.6099i	−1.96197	−	0.811513i
$646$	0.181779	−	0.511947i	0.00715198	−	0.0201423i
$647$	−32.2515	−	8.64177i	−1.26794	−	0.339743i	−0.438697	−	0.898635i	$-0.644560\pi$
$647$	−32.2515	−	8.64177i	−1.26794	−	0.339743i	−0.829240	+	0.558892i	$0.811227\pi$
$648$	6.72186	+	22.9065i	0.264060	+	0.899851i
$649$	−20.9773	−	12.1112i	−0.823429	−	0.475407i
$650$	−14.8256	+	21.5789i	−0.581509	+	0.846392i
$651$		0			0
$652$	9.84357	−	22.0085i	0.385504	−	0.861919i
$653$	8.98773	+	33.5427i	0.351717	+	1.31263i	0.884566	+	0.466415i	$0.154455\pi$
$653$	8.98773	+	33.5427i	0.351717	+	1.31263i	−0.532849	+	0.846210i	$0.678879\pi$
$654$	9.75585	−	8.31798i	0.381484	−	0.325259i
$655$	2.05517	+	15.5499i	0.0803022	+	0.607587i
$656$	−7.94086	−	37.9920i	−0.310038	−	1.48334i
$657$	−30.6728	−	30.6728i	−1.19666	−	1.19666i
$658$		0			0
$659$	48.2178			1.87830			0.939149	−	0.343511i	$-0.111616\pi$
$659$	48.2178			1.87830			0.939149	+	0.343511i	$0.111616\pi$
$660$	13.7990	+	57.7800i	0.537123	+	2.24908i
$661$	−11.5458	−	19.9978i	−0.449078	−	0.777826i	0.549248	−	0.835659i	$-0.314914\pi$
$661$	−11.5458	−	19.9978i	−0.449078	−	0.777826i	−0.998326	+	0.0578332i	$0.981581\pi$
$662$	−1.87548	+	23.5746i	−0.0728926	+	0.916254i
$663$	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
$668$	−1.15440	−	11.1655i	−0.0446649	−	0.432005i
$669$	3.94295	−	2.27646i	0.152443	−	0.0880132i
$670$	14.8667	−	16.4998i	0.574352	−	0.637443i
$671$		−	22.1103i		−	0.853560i
$672$		0			0
$673$	−15.6001	+	15.6001i	−0.601340	+	0.601340i	−0.940668	−	0.339328i	$-0.889800\pi$
$673$	−15.6001	+	15.6001i	−0.601340	+	0.601340i	0.339328	+	0.940668i	$0.389800\pi$
$674$	−6.52163	+	18.3670i	−0.251204	+	0.707471i
$675$	1.09702	+	1.89568i	0.0422244	+	0.0729646i
$676$	1.10036	+	0.894146i	0.0423214	+	0.0343902i
$677$	16.9000	−	4.52833i	0.649519	−	0.174038i	0.0810075	−	0.996713i	$-0.474186\pi$
$677$	16.9000	−	4.52833i	0.649519	−	0.174038i	0.568511	+	0.822675i	$0.307520\pi$
$678$	22.8350	−	33.1649i	0.876973	−	1.27369i
$679$		0			0
$680$	−9.21438	+	1.44016i	−0.353355	+	0.0552275i
$681$	−7.27100	+	12.5937i	−0.278625	+	0.482593i
$682$	15.4585	+	1.22980i	0.591937	+	0.0470915i
$683$	−3.51923	+	13.1339i	−0.134659	+	0.502556i	0.865340	+	0.501186i	$0.167103\pi$
$683$	−3.51923	+	13.1339i	−0.134659	+	0.502556i	−0.999999	+	0.00136990i	$0.999564\pi$
$684$	0.261650	−	1.63405i	0.0100044	−	0.0624795i
$685$	−13.1069	+	5.43681i	−0.500789	+	0.207730i
$686$		0			0
$687$	−38.5615	+	38.5615i	−1.47121	+	1.47121i
$688$	21.2494	−	32.4794i	0.810125	−	1.23827i
$689$	−8.24247	+	4.75879i	−0.314013	+	0.181296i
$690$	−10.5082	−	5.35873i	−0.400039	−	0.204003i
$691$	12.2266	+	7.05900i	0.465120	+	0.268537i	0.714195	−	0.699947i	$-0.246793\pi$
$691$	12.2266	+	7.05900i	0.465120	+	0.268537i	−0.249075	+	0.968484i	$0.580126\pi$
$692$	−21.9845	−	9.83283i	−0.835725	−	0.373788i
$693$		0			0
$694$	−1.06995	−	5.80039i	−0.0406148	−	0.220180i
$695$	4.65407	+	6.05896i	0.176539	+	0.229830i
$696$	8.44187	+	4.61141i	0.319988	+	0.174795i
$697$	3.70331	−	13.8210i	0.140273	−	0.523506i
$698$	−38.4736	+	18.3109i	−1.45625	+	0.693079i
$699$	−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	$0.435948\pi$
$702$	2.07108	−	0.985700i	0.0781679	−	0.0372029i
$703$	−0.782732	+	2.92120i	−0.0295213	+	0.110175i
$704$	−42.7119	+	2.02058i	−1.60976	+	0.0761535i
$705$	−4.67688	−	6.08867i	−0.176142	−	0.229313i
$706$	−1.40438	−	7.61339i	−0.0528546	−	0.286534i
$707$		0			0
$708$	9.19667	−	20.5621i	0.345632	−	0.772772i
$709$	−13.6491	−	7.88034i	−0.512605	−	0.295952i	0.221299	−	0.975206i	$-0.428970\pi$
$709$	−13.6491	−	7.88034i	−0.512605	−	0.295952i	−0.733904	+	0.679254i	$0.762304\pi$
$710$	20.5395	+	10.4743i	0.770833	+	0.393093i
$711$	−28.0471	+	16.1930i	−1.05185	+	0.607284i
$712$	−15.6207	−	14.8992i	−0.585411	−	0.558371i
$713$	−2.17733	+	2.17733i	−0.0815415	+	0.0815415i
$714$		0			0
$715$	−40.8748	+	16.9550i	−1.52863	+	0.634083i
$716$	−2.90917	−	0.465826i	−0.108721	−	0.0174087i
$717$	−5.20956	+	19.4423i	−0.194555	+	0.726088i
$718$	32.8775	+	2.61557i	1.22698	+	0.0976122i
$719$	5.20424	−	9.01401i	0.194085	−	0.336166i	−0.752515	−	0.658575i	$-0.771159\pi$
$719$	5.20424	−	9.01401i	0.194085	−	0.336166i	0.946600	+	0.322409i	$0.104493\pi$
$720$	−26.8071	+	9.40587i	−0.999041	+	0.350536i
$721$		0			0
$722$	−15.1837	+	22.0524i	−0.565079	+	0.820704i
$723$	8.01145	−	2.14666i	0.297949	−	0.0798352i
$724$	11.7485	−	14.4580i	0.436631	−	0.537328i
$725$	−6.61097	−	1.76426i	−0.245525	−	0.0655228i
$726$	−20.6608	+	58.1875i	−0.766794	+	2.15954i
$727$	−11.4932	+	11.4932i	−0.426259	+	0.426259i	−0.887352	−	0.461093i	$-0.847458\pi$
$727$	−11.4932	+	11.4932i	−0.426259	+	0.426259i	0.461093	+	0.887352i	$0.347458\pi$
$728$		0			0
$729$			30.0740i			1.11385i
$730$	−28.9087	+	32.0842i	−1.06996	+	1.18749i
$731$	12.3915	−	7.15425i	0.458317	−	0.264610i
$732$	20.4520	−	2.11453i	0.755926	−	0.0781551i
$733$	5.20693	+	19.4325i	0.192322	+	0.717757i	0.992944	+	0.118586i	$0.0378362\pi$
$733$	5.20693	+	19.4325i	0.192322	+	0.717757i	−0.800621	+	0.599171i	$0.795497\pi$
$734$	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
$738$	3.45657	−	43.4489i	0.127238	−	1.59937i
$739$	−13.8181	−	23.9337i	−0.508308	−	0.880416i	−0.999954	−	0.00962048i	$-0.996938\pi$
$739$	−13.8181	−	23.9337i	−0.508308	−	0.880416i	0.491645	−	0.870796i	$-0.336396\pi$
$740$	50.4976	−	12.0598i	1.85633	−	0.443326i
$741$	2.39707			0.0880587
$742$		0			0
$743$	22.3607	+	22.3607i	0.820334	+	0.820334i	0.986156	−	0.165822i	$-0.0530277\pi$
$743$	22.3607	+	22.3607i	0.820334	+	0.820334i	−0.165822	+	0.986156i	$0.553028\pi$
$744$	0.340816	+	14.4167i	0.0124949	+	0.528541i
$745$	3.92522	+	29.6992i	0.143809	+	1.08809i
$746$	15.6473	−	13.3412i	0.572890	−	0.488455i
$747$	−6.77845	−	25.2975i	−0.248011	−	0.925588i
$748$	−14.3897	−	6.43598i	−0.526140	−	0.235323i
$749$		0			0
$750$	32.9410	−	21.4233i	1.20283	−	0.782268i
$751$	−20.3290	−	11.7369i	−0.741815	−	0.428287i	0.0809138	−	0.996721i	$-0.474216\pi$
$751$	−20.3290	−	11.7369i	−0.741815	−	0.428287i	−0.822729	+	0.568434i	$0.807549\pi$
$752$	4.93247	−	2.49218i	0.179869	−	0.0908805i
$753$	3.39957	+	0.910911i	0.123887	+	0.0331955i
$754$	−2.39764	+	6.75253i	−0.0873170	+	0.245913i
$755$	−4.49139	−	1.85774i	−0.163458	−	0.0676101i
$756$		0			0
$757$	1.19863	+	1.19863i	0.0435649	+	0.0435649i	0.728554	−	0.684989i	$-0.240193\pi$
$757$	1.19863	+	1.19863i	0.0435649	+	0.0435649i	−0.684989	+	0.728554i	$0.740193\pi$
$758$	−11.1361	−	23.3983i	−0.404480	−	0.849864i
$759$	−9.96865	−	17.2662i	−0.361839	−	0.626724i
$760$	−1.63820	−	0.175561i	−0.0594238	−	0.00636825i
$761$	14.7741	−	25.5895i	0.535560	−	0.927618i	−0.463576	−	0.886057i	$-0.653434\pi$
$761$	14.7741	−	25.5895i	0.535560	−	0.927618i	0.999136	−	0.0415603i	$-0.0132329\pi$
$762$	17.1422	−	24.8969i	0.620998	−	0.901918i
$763$		0			0
$764$	−40.1837	+	15.3469i	−1.45379	+	0.555233i
$765$	−10.3843	−	1.36178i	−0.375444	−	0.0492354i
$766$	17.0339	+	19.9784i	0.615459	+	0.721849i
$767$	16.2076	+	4.34282i	0.585223	+	0.156810i
$768$	−5.95379	−	39.3151i	−0.214839	−	1.41866i
$769$		−	39.8461i		−	1.43689i	−0.695584	−	0.718444i	$-0.744854\pi$
$769$		−	39.8461i		−	1.43689i	0.695584	−	0.718444i	$-0.255146\pi$
$770$		0			0
$771$		−	20.0414i		−	0.721774i
$772$	−6.32251	+	4.57721i	−0.227552	+	0.164737i
$773$	−16.8262	−	4.50856i	−0.605195	−	0.162162i	−0.0568065	−	0.998385i	$-0.518092\pi$
$773$	−16.8262	−	4.50856i	−0.605195	−	0.162162i	−0.548388	+	0.836224i	$0.684758\pi$
$774$	33.1672	−	28.2788i	1.19217	−	1.01646i
$775$	−2.66488	−	9.90546i	−0.0957252	−	0.355815i
$776$	24.0935	+	39.5425i	0.864907	+	1.41949i
$777$		0			0
$778$	38.5111	+	26.5161i	1.38069	+	0.950646i
$779$	1.26388	−	2.18910i	0.0452830	−	0.0784325i
$780$	−19.5924	−	36.1875i	−0.701521	−	1.29572i
$781$	19.4849	+	33.7489i	0.697225	+	1.20763i
$782$	2.82628	−	1.34513i	0.101068	−	0.0481016i
$783$	0.423873	+	0.423873i	0.0151480	+	0.0151480i
$784$		0			0
$785$	−9.77396	+	4.05429i	−0.348848	+	0.144704i
$786$	−23.2326	−	8.24928i	−0.828680	−	0.294242i
$787$	−37.2220	−	9.97361i	−1.32682	−	0.355521i	−0.475292	−	0.879828i	$-0.657658\pi$
$787$	−37.2220	−	9.97361i	−1.32682	−	0.355521i	−0.851529	+	0.524307i	$0.824324\pi$
$788$	30.5025	−	3.15365i	1.08661	−	0.112344i
$789$	38.7293	+	22.3604i	1.37880	+	0.796050i
$790$	17.5517	+	27.0476i	0.624462	+	0.962311i
$791$		0			0
$792$	−46.6627	−	11.3283i	−1.65809	−	0.402535i
$793$	3.96414	+	14.7944i	0.140771	+	0.525364i
$794$	27.3039	+	32.0237i	0.968979	+	1.13648i
$795$	14.1616	−	1.87168i	0.502261	−	0.0663817i
$796$	40.7344	+	6.52252i	1.44379	+	0.231185i
$797$	4.70746	+	4.70746i	0.166747	+	0.166747i	0.785548	−	0.618801i	$-0.212381\pi$
$797$	4.70746	+	4.70746i	0.166747	+	0.166747i	−0.618801	+	0.785548i	$0.712381\pi$
$798$		0			0
$799$	2.03729			0.0720742
$800$	10.7394	+	26.1661i	0.379697	+	0.925111i
$801$	−12.1208	−	20.9938i	−0.428267	−	0.741780i
$802$	−48.3293	−	3.84484i	−1.70657	−	0.135766i
$803$	−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
$808$	−2.26180	−	7.70767i	−0.0795700	−	0.271155i
$809$	−6.63972	+	3.83344i	−0.233440	+	0.134777i	−0.612158	−	0.790735i	$-0.709698\pi$
$809$	−6.63972	+	3.83344i	−0.233440	+	0.134777i	0.378718	+	0.925512i	$0.376365\pi$
$810$	26.6540	−	1.38770i	0.936526	−	0.0487587i
$811$		−	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
$814$	82.6942	+	29.3625i	2.89843	+	1.02915i
$815$	−21.3933	−	16.3985i	−0.749376	−	0.574416i
$816$	4.57709	−	13.9259i	0.160230	−	0.487506i
$817$	2.44162	−	0.654230i	0.0854215	−	0.0228886i
$818$	−2.47345	−	1.70305i	−0.0864822	−	0.0595456i
$819$		0			0
$820$	−43.3780	−	1.18761i	−1.51483	−	0.0414732i
$821$	−0.931693	+	1.61374i	−0.0325163	+	0.0563199i	−0.881826	−	0.471576i	$-0.843685\pi$
$821$	−0.931693	+	1.61374i	−0.0325163	+	0.0563199i	0.849309	+	0.527896i	$0.177019\pi$
$822$	1.76875	−	22.2330i	0.0616922	−	0.775466i
$823$	−12.2331	+	45.6547i	−0.426420	+	1.59142i	0.334382	+	0.942437i	$0.391472\pi$
$823$	−12.2331	+	45.6547i	−0.426420	+	1.59142i	−0.760802	+	0.648984i	$0.775194\pi$
$824$	32.8841	−	0.777393i	1.14557	−	0.0270818i
$825$	66.4166	−	0.0670175i	2.31233	−	0.00233325i
$826$		0			0
$827$	10.7786	−	10.7786i	0.374809	−	0.374809i	−0.494416	−	0.869225i	$-0.664618\pi$
$827$	10.7786	−	10.7786i	0.374809	−	0.374809i	0.869225	+	0.494416i	$0.164618\pi$
$828$	7.72320	−	5.59125i	0.268400	−	0.194309i
$829$	20.7913	−	12.0039i	0.722112	−	0.416911i	−0.0934177	−	0.995627i	$-0.529779\pi$
$829$	20.7913	−	12.0039i	0.722112	−	0.416911i	0.815529	+	0.578716i	$0.196446\pi$
$830$	−24.8012	+	8.04899i	−0.860863	+	0.279384i
$831$	−28.7265	−	16.5853i	−0.996512	−	0.575337i
$832$	28.2169	−	9.00978i	0.978246	−	0.312358i
$833$		0			0
$834$	−11.8094	+	2.17838i	−0.408925	+	0.0754312i
$835$	−12.4434	−	1.63182i	−0.430621	−	0.0564713i
$836$	−2.16121	−	1.75619i	−0.0747469	−	0.0607390i
$837$	−0.232590	+	0.868039i	−0.00803950	+	0.0300038i
$838$	15.4706	+	32.5057i	0.534422	+	1.12289i
$839$	21.1523			0.730259			0.365130	−	0.930957i	$-0.381025\pi$
$839$	21.1523			0.730259			0.365130	+	0.930957i	$0.381025\pi$
$840$		0			0
$841$	27.1273			0.935424
$842$	3.95697	+	8.31409i	0.136366	+	0.286523i
$843$	−8.06403	+	30.0954i	−0.277740	+	1.03654i
$844$	−2.42134	−	1.96757i	−0.0833459	−	0.0677266i
$845$	1.25713	−	0.965642i	0.0432468	−	0.0332191i
$846$	6.10298	−	1.12577i	0.209825	−	0.0387047i
$847$		0			0
$848$	−0.572953	+	10.2662i	−0.0196753	+	0.352543i
$849$	60.4005	+	34.8723i	2.07294	+	1.19681i
$850$	−0.816424	+	10.3951i	−0.0280031	+	0.356547i
$851$	−15.0900	+	8.71224i	−0.517280	+	0.298652i
$852$	−29.3541	+	21.2511i	−1.00566	+	0.728049i
$853$	−11.2132	+	11.2132i	−0.383931	+	0.383931i	−0.872516	−	0.488585i	$-0.837513\pi$
$853$	−11.2132	+	11.2132i	−0.383931	+	0.383931i	0.488585	+	0.872516i	$0.337513\pi$
$854$		0			0
$855$	−1.70972	−	0.707177i	−0.0584711	−	0.0241850i
$856$	0.235377	+	9.95655i	0.00804501	+	0.340308i
$857$	−7.32325	+	27.3307i	−0.250157	+	0.933600i	0.720563	+	0.693389i	$0.243883\pi$
$857$	−7.32325	+	27.3307i	−0.250157	+	0.933600i	−0.970721	+	0.240211i	$0.922783\pi$
$858$	5.51596	−	69.3352i	0.188312	−	2.36706i
$859$	−13.9784	+	24.2113i	−0.476936	+	0.826078i	−0.999651	−	0.0264302i	$-0.991586\pi$
$859$	−13.9784	+	24.2113i	−0.476936	+	0.826078i	0.522715	+	0.852508i	$0.324919\pi$
$860$	−29.8331	−	31.5127i	−1.01730	−	1.07457i
$861$		0			0
$862$	24.7402	+	17.0344i	0.842656	+	0.580194i
$863$	−19.5121	+	5.22825i	−0.664199	+	0.177972i	−0.575140	−	0.818055i	$-0.695053\pi$
$863$	−19.5121	+	5.22825i	−0.664199	+	0.177972i	−0.0890588	+	0.996026i	$0.528386\pi$
$864$	0.333850	−	2.45535i	0.0113578	−	0.0835328i
$865$	−16.3807	+	21.3700i	−0.556959	+	0.726602i
$866$	19.5918	+	6.95653i	0.665757	+	0.236392i
$867$	−26.0530	+	26.0530i	−0.884807	+	0.884807i
$868$		0			0
$869$			54.4985i			1.84874i
$870$	7.19902	−	7.98980i	0.244070	−	0.270880i
$871$	−22.5202	+	13.0020i	−0.763067	+	0.440557i
$872$	9.90000	−	2.90514i	0.335256	−	0.0983804i
$873$	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	−0.977697	−	0.210022i	$-0.932646\pi$
$877$	−50.9185	+	13.6436i	−1.71940	+	0.460711i	−0.741699	+	0.670733i	$0.765980\pi$
$878$	7.46464	+	0.593850i	0.251919	+	0.0200415i
$879$	22.2016	+	38.4543i	0.748841	+	1.29703i
$880$	−8.84777	+	46.9808i	−0.298258	+	1.58372i
$881$	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	$-0.129743\pi$
$883$	15.5015	+	15.5015i	0.521668	+	0.521668i	−0.396407	+	0.918075i	$0.629743\pi$
$884$	10.7823	+	1.72650i	0.362648	+	0.0580684i
$885$	−19.9874	−	15.3209i	−0.671869	−	0.515005i
$886$	−27.3472	−	32.0744i	−0.918746	−	1.07756i
$887$	8.94877	+	33.3972i	0.300470	+	1.12137i	0.936775	+	0.349932i	$0.113795\pi$
$887$	8.94877	+	33.3972i	0.300470	+	1.12137i	−0.636305	+	0.771438i	$0.719538\pi$
$888$	−19.2517	+	79.2999i	−0.646045	+	2.66113i
$889$		0			0
$890$	−20.2457	+	13.1378i	−0.678638	+	0.440381i
$891$	39.0683	+	22.5561i	1.30884	+	0.755658i
$892$	3.64459	−	0.376814i	0.122030	−	0.0126167i
$893$	0.347646	+	0.0931514i	0.0116335	+	0.00311719i
$894$	−44.3725	−	15.7555i	−1.48404	−	0.526942i
$895$	−1.25902	+	3.04388i	−0.0420843	+	0.101746i
$896$		0			0
$897$	9.76583	+	9.76583i	0.326072	+	0.326072i
$898$	−12.1410	+	5.77831i	−0.405149	+	0.192825i
$899$	−1.40373	−	2.43133i	−0.0468169	−	0.0810893i
$900$	3.29840	+	31.5909i	0.109947	+	1.05303i
$901$	−1.89527	+	3.28271i	−0.0631408	+	0.109363i
$902$	−60.4111	−	41.5949i	−2.01147	−	1.38496i
$903$		0			0
$904$	27.6723	−	16.8610i	0.920368	−	0.560787i
$905$	−12.6880	−	16.5180i	−0.421762	−	0.549077i
$906$	5.81336	−	4.95656i	0.193136	−	0.164671i
$907$	43.2674	+	11.5935i	1.43667	+	0.384955i	0.891366	−	0.453284i	$-0.149748\pi$
$907$	43.2674	+	11.5935i	1.43667	+	0.384955i	0.545304	+	0.838239i	$0.316414\pi$
$908$	−9.47945	+	6.86269i	−0.314587	+	0.227746i
$909$		−	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	$0.994917\pi$
$912$	1.41778	−	2.16706i	0.0469473	−	0.0717585i
$913$	−42.5702	−	11.4067i	−1.40887	−	0.377505i
$914$	24.5460	+	28.7891i	0.811909	+	0.952257i
$915$	2.98902	−	22.7927i	0.0988140	−	0.753504i
$916$	−40.9987	+	15.6582i	−1.35464	+	0.517362i
$917$		0			0
$918$	0.518050	−	0.752400i	0.0170982	−	0.0248329i
$919$	19.8487	−	34.3789i	0.654747	−	1.13406i	−0.327210	−	0.944952i	$-0.606108\pi$
$919$	19.8487	−	34.3789i	0.654747	−	1.13406i	0.981957	−	0.189104i	$-0.0605583\pi$
$920$	−5.95889	−	7.38938i	−0.196459	−	0.243621i
$921$	−17.0366	−	29.5082i	−0.561374	−	0.972329i
$922$	−2.78758	−	5.85705i	−0.0918040	−	0.192892i
$923$	−19.0885	−	19.0885i	−0.628305	−	0.628305i
$924$		0			0
$925$	−0.0585708	−	58.0457i	−0.00192580	−	1.90853i
$926$	3.71768	−	10.4702i	0.122171	−	0.344072i
$927$	35.6798	+	9.56036i	1.17188	+	0.314003i
$928$	4.68647	+	6.16144i	0.153841	+	0.202259i
$929$	13.3874	+	7.72921i	0.439226	+	0.253587i	0.703269	−	0.710924i	$-0.251723\pi$
$929$	13.3874	+	7.72921i	0.439226	+	0.253587i	−0.264043	+	0.964511i	$0.585056\pi$
$930$	15.7694	+	3.35754i	0.517098	+	0.110098i
$931$		0			0
$932$	−11.8451	−	5.29788i	−0.388000	−	0.173538i
$933$	7.20572	+	26.8921i	0.235905	+	0.880408i
$934$	−37.4163	+	31.9017i	−1.22430	+	1.04385i
$935$	−10.7218	+	13.9875i	−0.350640	+	0.457441i
$936$	33.2538	−	0.786133i	1.08693	−	0.0256956i
$937$	34.3456	+	34.3456i	1.12202	+	1.12202i	0.991437	+	0.130585i	$0.0416856\pi$
$937$	34.3456	+	34.3456i	1.12202	+	1.12202i	0.130585	+	0.991437i	$0.458314\pi$
$938$		0			0
$939$	0.572232			0.0186741
$940$	−1.43521	−	6.00962i	−0.0468114	−	0.196012i
$941$	−9.51809	−	16.4858i	−0.310281	−	0.537422i	0.668142	−	0.744034i	$-0.267090\pi$
$941$	−9.51809	−	16.4858i	−0.310281	−	0.537422i	−0.978423	+	0.206611i	$0.933756\pi$
$942$	1.31897	−	16.5794i	0.0429745	−	0.540186i
$943$	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	$-0.112639\pi$
$947$	−1.46452	−	5.46566i	−0.0475905	−	0.177610i	−0.985630	+	0.168918i	$0.945973\pi$
$948$	−50.4109	+	5.21198i	−1.63727	+	0.169277i
$949$	43.7910	−	25.2827i	1.42152	−	0.820712i
$950$	−0.614610	+	1.73649i	−0.0199406	+	0.0563393i
$951$		−	35.6364i		−	1.15559i
$952$		0			0
$953$	−10.9748	+	10.9748i	−0.355509	+	0.355509i	−0.862154	−	0.506646i	$-0.830885\pi$
$953$	−10.9748	+	10.9748i	−0.355509	+	0.355509i	0.506646	+	0.862154i	$0.330885\pi$
$954$	−3.86358	+	10.8811i	−0.125088	+	0.352288i
$955$	6.30130	+	47.6772i	0.203905	+	1.54280i
$956$	−10.2153	+	12.5712i	−0.330387	+	0.406582i
$957$	17.5584	−	4.70476i	0.567582	−	0.152083i
$958$	−23.8572	+	34.6494i	−0.770790	+	1.11947i
$959$		0			0
$960$	−44.3033	−	3.69113i	−1.42988	−	0.119131i
$961$	−13.3956	+	23.2019i	−0.432116	+	0.748447i
$962$	−60.5964	−	4.82075i	−1.95371	−	0.155427i
$963$	−2.89466	+	10.8030i	−0.0932791	+	0.348122i
$964$	6.59078	+	1.05534i	0.212275	+	0.0339902i
$965$	3.34365	+	8.06078i	0.107636	+	0.259486i
$966$		0			0
$967$	−5.51012	+	5.51012i	−0.177194	+	0.177194i	−0.790131	−	0.612938i	$-0.789988\pi$
$967$	−5.51012	+	5.51012i	−0.177194	+	0.177194i	0.612938	+	0.790131i	$0.289988\pi$
$968$	−34.2968	+	35.9577i	−1.10234	+	1.15572i
$969$	0.826775	−	0.477339i	0.0265598	−	0.0153343i
$970$	49.2417	−	15.9809i	1.58106	−	0.513116i
$971$	42.0895	+	24.3004i	1.35072	+	0.779836i	0.988350	−	0.152200i	$-0.0486358\pi$
$971$	42.0895	+	24.3004i	1.35072	+	0.779836i	0.362366	+	0.932036i	$0.381969\pi$
$972$	−18.2011	+	40.6944i	−0.583800	+	1.30527i
$973$		0			0
$974$	1.52044	+	8.24255i	0.0487180	+	0.264108i
$975$	−44.4284	+	11.9526i	−1.42285	+	0.382790i
$976$	15.7194	+	5.16656i	0.503166	+	0.165377i
$977$	5.89146	−	21.9872i	0.188484	−	0.703433i	−0.805373	−	0.592768i	$-0.798035\pi$
$977$	5.89146	−	21.9872i	0.188484	−	0.703433i	0.993858	−	0.110665i	$-0.0352982\pi$
$978$	38.2561	−	18.2074i	1.22329	−	0.582208i
$979$	−40.7933			−1.30376
$980$		0			0
$981$	11.5863			0.369921
$982$	24.2770	−	11.5543i	0.774711	−	0.368712i
$983$	−3.67375	+	13.7106i	−0.117174	+	0.437301i	−0.999440	−	0.0334503i	$-0.989350\pi$
$983$	−3.67375	+	13.7106i	−0.117174	+	0.437301i	0.882266	+	0.470751i	$0.156017\pi$
$984$	32.6977	−	59.8580i	1.04236	−	1.90820i
$985$	4.45789	−	33.9936i	0.142040	−	1.08313i
$986$	0.517687	+	2.80647i	0.0164865	+	0.0893762i
$987$		0			0
$988$	1.76096	+	0.787612i	0.0560237	+	0.0250573i
$989$	12.6127	+	7.28194i	0.401060	+	0.231552i
$990$	−24.3893	+	47.8261i	−0.775143	+	1.52001i
$991$	−30.8581	+	17.8159i	−0.980240	+	0.565942i	−0.902343	−	0.431019i	$-0.858154\pi$
$991$	−30.8581	+	17.8159i	−0.980240	+	0.565942i	−0.0778976	+	0.996961i	$0.524821\pi$
$992$	−4.48655	+	10.7029i	−0.142448	+	0.339818i
$993$	−29.3865	+	29.3865i	−0.932552	+	0.932552i
$994$		0			0
$995$	17.6288	−	42.6206i	0.558872	−	1.35116i
$996$	6.47990	−	40.4682i	0.205324	−	1.28228i
$997$	3.97096	−	14.8198i	0.125762	−	0.469349i	−0.874104	−	0.485739i	$-0.838551\pi$
$997$	3.97096	−	14.8198i	0.125762	−	0.469349i	0.999866	+	0.0163900i	$0.00521734\pi$
$998$	−46.6925	−	3.71462i	−1.47803	−	0.117584i
$999$	−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.667.13		72
4.3	odd	2	inner	980.2.x.l.667.9		72
5.3	odd	4	inner	980.2.x.l.863.15		72
7.2	even	3		980.2.k.l.687.13		36
7.3	odd	6		980.2.x.k.67.1		72
7.4	even	3	inner	980.2.x.l.67.1		72
7.5	odd	6		140.2.k.a.127.13	yes	36
7.6	odd	2		980.2.x.k.667.13		72
20.3	even	4	inner	980.2.x.l.863.1		72
28.3	even	6		980.2.x.k.67.15		72
28.11	odd	6	inner	980.2.x.l.67.15		72
28.19	even	6		140.2.k.a.127.4	yes	36
28.23	odd	6		980.2.k.l.687.4		36
28.27	even	2		980.2.x.k.667.9		72
35.3	even	12		980.2.x.k.263.9		72
35.12	even	12		700.2.k.b.43.15		36
35.13	even	4		980.2.x.k.863.15		72
35.18	odd	12	inner	980.2.x.l.263.9		72
35.19	odd	6		700.2.k.b.407.6		36
35.23	odd	12		980.2.k.l.883.4		36
35.33	even	12		140.2.k.a.43.4	✓	36
140.3	odd	12		980.2.x.k.263.13		72
140.19	even	6		700.2.k.b.407.15		36
140.23	even	12		980.2.k.l.883.13		36
140.47	odd	12		700.2.k.b.43.6		36
140.83	odd	4		980.2.x.k.863.1		72
140.103	odd	12		140.2.k.a.43.13	yes	36
140.123	even	12	inner	980.2.x.l.263.13		72

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
140.2.k.a.43.4	✓	36	35.33	even	12
140.2.k.a.43.13	yes	36	140.103	odd	12
140.2.k.a.127.4	yes	36	28.19	even	6
140.2.k.a.127.13	yes	36	7.5	odd	6
700.2.k.b.43.6		36	140.47	odd	12
700.2.k.b.43.15		36	35.12	even	12
700.2.k.b.407.6		36	35.19	odd	6
700.2.k.b.407.15		36	140.19	even	6
980.2.k.l.687.4		36	28.23	odd	6
980.2.k.l.687.13		36	7.2	even	3
980.2.k.l.883.4		36	35.23	odd	12
980.2.k.l.883.13		36	140.23	even	12
980.2.x.k.67.1		72	7.3	odd	6
980.2.x.k.67.15		72	28.3	even	6
980.2.x.k.263.9		72	35.3	even	12
980.2.x.k.263.13		72	140.3	odd	12
980.2.x.k.667.9		72	28.27	even	2
980.2.x.k.667.13		72	7.6	odd	2
980.2.x.k.863.1		72	140.83	odd	4
980.2.x.k.863.15		72	35.13	even	4
980.2.x.l.67.1		72	7.4	even	3	inner
980.2.x.l.67.15		72	28.11	odd	6	inner
980.2.x.l.263.9		72	35.18	odd	12	inner
980.2.x.l.263.13		72	140.123	even	12	inner
980.2.x.l.667.9		72	4.3	odd	2	inner
980.2.x.l.667.13		72	1.1	even	1	trivial
980.2.x.l.863.1		72	20.3	even	4	inner
980.2.x.l.863.15		72	5.3	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:	\( N \)	\(=\)	\( 980 = 2^{2} \cdot 5 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	980.x (of order \(12\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.607752 + 1.27696i) q^{2} +(-0.643219 + 2.40053i) q^{3} +(-1.26127 + 1.55216i) q^{4} +(1.36213 + 1.77331i) q^{5} +(-3.45630 + 0.637557i) q^{6} +(-2.74859 - 0.667278i) q^{8} +(-2.75072 - 1.58813i) q^{9} +O(q^{10})\)	\(q+(0.607752 + 1.27696i) q^{2} +(-0.643219 + 2.40053i) q^{3} +(-1.26127 + 1.55216i) q^{4} +(1.36213 + 1.77331i) q^{5} +(-3.45630 + 0.637557i) q^{6} +(-2.74859 - 0.667278i) q^{8} +(-2.75072 - 1.58813i) q^{9} +(-1.43661 + 2.81712i) q^{10} +(-4.62887 + 2.67248i) q^{11} +(-2.91471 - 4.02610i) q^{12} +(2.61810 - 2.61810i) q^{13} +(-5.13301 + 2.12920i) q^{15} +(-0.818371 - 3.91539i) q^{16} +(0.381657 - 1.42436i) q^{17} +(0.356228 - 4.47776i) q^{18} +(0.130253 - 0.225604i) q^{19} +(-4.47046 - 0.122393i) q^{20} +(-6.22586 - 4.28669i) q^{22} +(1.44978 - 0.388469i) q^{23} +(3.36976 - 6.16886i) q^{24} +(-1.28922 + 4.83093i) q^{25} +(4.93438 + 1.75207i) q^{26} +(0.309743 - 0.309743i) q^{27} +1.36847i q^{29} +(-5.83851 - 5.26065i) q^{30} +(-1.77668 + 1.02577i) q^{31} +(4.50244 - 3.42462i) 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} +(0.367250 + 0.0292166i) q^{38} +(4.60081 + 7.96884i) q^{39} +(-2.56064 - 5.78300i) q^{40} +9.70325 q^{41} +(6.86124 + 6.86124i) q^{43} +(1.69017 - 10.5554i) q^{44} +(-0.930593 - 7.04110i) q^{45} +(1.37717 + 1.61523i) q^{46} +(0.357579 + 1.33450i) q^{47} +(9.92539 + 0.553932i) q^{48} +(-6.95245 + 1.28972i) q^{50} +(3.17373 + 1.83236i) q^{51} +(0.761554 + 7.36585i) q^{52} +(-2.48296 - 0.665306i) q^{53} +(0.583778 + 0.207284i) q^{54} +(-11.0442 - 4.56814i) q^{55} +(0.457788 + 0.457788i) q^{57} +(-1.74748 + 0.831688i) q^{58} +(2.26592 + 3.92468i) q^{59} +(3.16929 - 10.6527i) q^{60} +(-2.06834 + 3.58246i) q^{61} +(-2.38965 - 1.64535i) q^{62} +(7.10948 + 3.66814i) q^{64} +(8.20888 + 1.07651i) q^{65} +(14.2949 - 12.1881i) q^{66} +(-6.78396 - 1.81776i) q^{67} +(1.72946 + 2.38890i) q^{68} +3.73012i q^{69} -7.29096i q^{71} +(6.50088 + 6.20061i) q^{72} +(13.1916 + 3.53467i) q^{73} +(-10.6519 - 12.4932i) q^{74} +(-10.7675 - 6.20216i) q^{75} +(0.185888 + 0.486722i) q^{76} +(-7.37977 + 10.7181i) q^{78} +(5.09813 - 8.83021i) q^{79} +(5.82845 - 6.78448i) q^{80} +(-4.22008 - 7.30939i) q^{81} +(5.89717 + 12.3907i) q^{82} +(5.83046 + 5.83046i) q^{83} +(3.04570 - 1.26337i) q^{85} +(-4.59162 + 12.9315i) q^{86} +(-3.28504 - 0.880224i) q^{87} +(14.5061 - 4.25680i) q^{88} +(6.60960 + 3.81606i) q^{89} +(8.42567 - 5.46758i) q^{90} +(-1.22561 + 2.74026i) q^{92} +(-1.31959 - 4.92476i) q^{93} +(-1.48680 + 1.26766i) q^{94} +(0.577486 - 0.0763239i) q^{95} +(5.32482 + 13.0110i) q^{96} +(-11.5761 - 11.5761i) q^{97} +16.9770 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 72 q + 16 q^{6}+O(q^{10}) \) 72 * q + 16 * q^6	\( 72 q + 16 q^{6} - 16 q^{10} - 16 q^{12} + 8 q^{13} + 8 q^{16} - 20 q^{17} - 28 q^{18} - 40 q^{20} + 8 q^{22} + 20 q^{25} - 32 q^{26} + 4 q^{30} - 20 q^{37} - 36 q^{40} + 20 q^{45} - 16 q^{46} + 48 q^{48} + 80 q^{50} + 16 q^{52} + 44 q^{53} - 32 q^{57} + 4 q^{58} - 40 q^{60} - 64 q^{61} - 80 q^{62} - 4 q^{65} + 32 q^{66} + 80 q^{68} - 80 q^{72} + 52 q^{73} - 16 q^{76} - 152 q^{78} - 20 q^{80} + 36 q^{81} + 56 q^{82} - 40 q^{85} - 56 q^{86} + 40 q^{88} + 32 q^{90} - 112 q^{92} - 32 q^{93} + 120 q^{96} - 40 q^{97}+O(q^{100}) \) 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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