LMFDB - Embedded newform 784.2.j.a.587.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [784,2,Mod(195,784)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(784, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 3, 2]))

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

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

chi := DirichletCharacter("784.195");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 784 = 2^{4} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	784.j (of order $4$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$6.26027151847$
Analytic rank:	$0$
Dimension:	$56$
Relative dimension:	$28$ over $\Q(i)$
Twist minimal:	no (minimal twist has level 112)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			587.11
Character	$\chi$	$=$	784.587
Dual form			784.2.j.a.195.11

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.436725 + 1.34509i) q^{2} +(-2.03150 + 2.03150i) q^{3} +(-1.61854 - 1.17487i) q^{4} +(-2.47931 + 2.47931i) q^{5} +(-1.84535 - 3.61976i) q^{6} +(2.28717 - 1.66399i) q^{8} -5.25398i q^{9} +O(q^{10})$	\(q+(-0.436725 + 1.34509i) q^{2} +(-2.03150 + 2.03150i) q^{3} +(-1.61854 - 1.17487i) q^{4} +(-2.47931 + 2.47931i) q^{5} +(-1.84535 - 3.61976i) q^{6} +(2.28717 - 1.66399i) q^{8} -5.25398i q^{9} +(-2.25212 - 4.41768i) q^{10} +(0.304175 - 0.304175i) q^{11} +(5.67482 - 0.901319i) q^{12} +(-1.52743 - 1.52743i) q^{13} -10.0734i q^{15} +(1.23936 + 3.80316i) q^{16} -2.95292i q^{17} +(7.06708 + 2.29454i) q^{18} +(0.0417673 - 0.0417673i) q^{19} +(6.92574 - 1.10000i) q^{20} +(0.276302 + 0.541984i) q^{22} +1.12990 q^{23} +(-1.26598 + 8.02678i) q^{24} -7.29397i q^{25} +(2.72159 - 1.38746i) q^{26} +(4.57896 + 4.57896i) q^{27} +(-6.00198 + 6.00198i) q^{29} +(13.5497 + 4.39932i) q^{30} +0.0405284 q^{31} +(-5.65685 + 0.00611747i) q^{32} +1.23586i q^{33} +(3.97195 + 1.28961i) q^{34} +(-6.17275 + 8.50379i) q^{36} +(-3.74283 - 3.74283i) q^{37} +(0.0379400 + 0.0744217i) q^{38} +6.20593 q^{39} +(-1.54504 + 9.79615i) q^{40} -1.51601 q^{41} +(0.767367 - 0.767367i) q^{43} +(-0.849686 + 0.134954i) q^{44} +(13.0262 + 13.0262i) q^{45} +(-0.493455 + 1.51982i) q^{46} +3.39052 q^{47} +(-10.2439 - 5.20835i) q^{48} +(9.81105 + 3.18546i) q^{50} +(5.99885 + 5.99885i) q^{51} +(0.677676 + 4.26673i) q^{52} +(3.79626 + 3.79626i) q^{53} +(-8.15886 + 4.15937i) q^{54} +1.50829i q^{55} +0.169701i q^{57} +(-5.45199 - 10.6944i) q^{58} +(10.5724 + 10.5724i) q^{59} +(-11.8350 + 16.3043i) q^{60} +(-6.81551 - 6.81551i) q^{61} +(-0.0176998 + 0.0545144i) q^{62} +(2.46226 - 7.61165i) q^{64} +7.57393 q^{65} +(-1.66235 - 0.539732i) q^{66} +(-6.14636 - 6.14636i) q^{67} +(-3.46930 + 4.77942i) q^{68} +(-2.29539 + 2.29539i) q^{69} +5.84154 q^{71} +(-8.74258 - 12.0167i) q^{72} -3.78781 q^{73} +(6.66905 - 3.39987i) q^{74} +(14.8177 + 14.8177i) q^{75} +(-0.116673 + 0.0185310i) q^{76} +(-2.71029 + 8.34754i) q^{78} +5.64881i q^{79} +(-12.5020 - 6.35645i) q^{80} -2.84236 q^{81} +(0.662080 - 2.03917i) q^{82} +(9.59296 - 9.59296i) q^{83} +(7.32120 + 7.32120i) q^{85} +(0.697051 + 1.36731i) q^{86} -24.3860i q^{87} +(0.189554 - 1.20184i) q^{88} -14.6331 q^{89} +(-23.2104 + 11.8326i) q^{90} +(-1.82879 - 1.32748i) q^{92} +(-0.0823334 + 0.0823334i) q^{93} +(-1.48073 + 4.56056i) q^{94} +0.207108i q^{95} +(11.4795 - 11.5043i) q^{96} -8.20099i q^{97} +(-1.59813 - 1.59813i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 56 q + 4 q^{2} + 8 q^{4} + 4 q^{8}+O(q^{10}) $ 56 * q + 4 * q^2 + 8 * q^4 + 4 * q^8	$ 56 q + 4 q^{2} + 8 q^{4} + 4 q^{8} - 4 q^{11} - 16 q^{16} + 60 q^{18} - 28 q^{22} + 24 q^{23} - 24 q^{29} + 36 q^{30} + 24 q^{32} + 16 q^{36} - 12 q^{37} + 8 q^{39} - 52 q^{44} - 32 q^{46} + 68 q^{51} - 12 q^{53} - 36 q^{58} - 156 q^{60} - 16 q^{64} + 8 q^{65} - 12 q^{67} - 80 q^{71} + 8 q^{72} - 124 q^{74} + 4 q^{78} + 16 q^{81} - 28 q^{85} - 60 q^{88} - 20 q^{92} - 20 q^{93} - 16 q^{99}+O(q^{100}) $ 56 * q + 4 * q^2 + 8 * q^4 + 4 * q^8 - 4 * q^11 - 16 * q^16 + 60 * q^18 - 28 * q^22 + 24 * q^23 - 24 * q^29 + 36 * q^30 + 24 * q^32 + 16 * q^36 - 12 * q^37 + 8 * q^39 - 52 * q^44 - 32 * q^46 + 68 * q^51 - 12 * q^53 - 36 * q^58 - 156 * q^60 - 16 * q^64 + 8 * q^65 - 12 * q^67 - 80 * q^71 + 8 * q^72 - 124 * q^74 + 4 * q^78 + 16 * q^81 - 28 * q^85 - 60 * q^88 - 20 * q^92 - 20 * q^93 - 16 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/784\mathbb{Z}\right)^\times$.

$n$	$197$	$687$	$689$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$-1$	$-1$

Coefficient data

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

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

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

$2$	−0.436725	+	1.34509i	−0.308811	+	0.951123i
$2$	−0.436725	+	1.34509i	−0.308811	+	0.951123i
$3$	−2.03150	+	2.03150i	−1.17289	+	1.17289i	−0.191368	+	0.981518i	$0.561293\pi$
$3$	−2.03150	+	2.03150i	−1.17289	+	1.17289i	−0.981518	+	0.191368i	$0.938707\pi$
$4$	−1.61854	−	1.17487i	−0.809271	−	0.587435i
$5$	−2.47931	+	2.47931i	−1.10878	+	1.10878i	−0.115471	+	0.993311i	$0.536838\pi$
$5$	−2.47931	+	2.47931i	−1.10878	+	1.10878i	−0.993311	+	0.115471i	$0.963162\pi$
$6$	−1.84535	−	3.61976i	−0.753359	−	1.47776i
$7$		0			0
$7$		0			0
$8$	2.28717	−	1.66399i	0.808635	−	0.588310i
$9$		−	5.25398i		−	1.75133i
$10$	−2.25212	−	4.41768i	−0.712184	−	1.39699i
$11$	0.304175	−	0.304175i	0.0917122	−	0.0917122i	−0.659762	−	0.751474i	$-0.729343\pi$
$11$	0.304175	−	0.304175i	0.0917122	−	0.0917122i	0.751474	+	0.659762i	$0.229343\pi$
$12$	5.67482	−	0.901319i	1.63818	−	0.260188i
$13$	−1.52743	−	1.52743i	−0.423632	−	0.423632i	0.462820	−	0.886452i	$-0.346837\pi$
$13$	−1.52743	−	1.52743i	−0.423632	−	0.423632i	−0.886452	+	0.462820i	$0.846837\pi$
$14$		0			0
$15$		−	10.0734i		−	2.60095i
$16$	1.23936	+	3.80316i	0.309840	+	0.950789i
$17$		−	2.95292i		−	0.716188i	−0.933686	−	0.358094i	$-0.883427\pi$
$17$		−	2.95292i		−	0.716188i	0.933686	−	0.358094i	$-0.116573\pi$
$18$	7.06708	+	2.29454i	1.66573	+	0.540829i
$19$	0.0417673	−	0.0417673i	0.00958208	−	0.00958208i	−0.702300	−	0.711882i	$-0.747843\pi$
$19$	0.0417673	−	0.0417673i	0.00958208	−	0.00958208i	0.711882	+	0.702300i	$0.247843\pi$
$20$	6.92574	−	1.10000i	1.54864	−	0.245968i
$21$		0			0
$22$	0.276302	+	0.541984i	0.0589079	+	0.115551i
$23$	1.12990			0.235600			0.117800	−	0.993037i	$-0.462416\pi$
$23$	1.12990			0.235600			0.117800	+	0.993037i	$0.462416\pi$
$24$	−1.26598	+	8.02678i	−0.258417	+	1.63846i
$25$		−	7.29397i		−	1.45879i
$26$	2.72159	−	1.38746i	0.533748	−	0.272104i
$27$	4.57896	+	4.57896i	0.881221	+	0.881221i
$28$		0			0
$29$	−6.00198	+	6.00198i	−1.11454	+	1.11454i	−0.122010	+	0.992529i	$0.538934\pi$
$29$	−6.00198	+	6.00198i	−1.11454	+	1.11454i	−0.992529	+	0.122010i	$0.961066\pi$
$30$	13.5497	+	4.39932i	2.47382	+	0.803203i
$31$	0.0405284			0.00727912			0.00363956	−	0.999993i	$-0.498841\pi$
$31$	0.0405284			0.00727912			0.00363956	+	0.999993i	$0.498841\pi$
$32$	−5.65685	+	0.00611747i	−0.999999	+	0.00108143i
$33$			1.23586i			0.215136i
$34$	3.97195	+	1.28961i	0.681183	+	0.221167i
$35$		0			0
$36$	−6.17275	+	8.50379i	−1.02879	+	1.41730i
$37$	−3.74283	−	3.74283i	−0.615318	−	0.615318i	0.329009	−	0.944327i	$-0.393285\pi$
$37$	−3.74283	−	3.74283i	−0.615318	−	0.615318i	−0.944327	+	0.329009i	$0.893285\pi$
$38$	0.0379400	+	0.0744217i	0.00615469	+	0.0120728i
$39$	6.20593			0.993744
$40$	−1.54504	+	9.79615i	−0.244293	+	1.54891i
$41$	−1.51601			−0.236761			−0.118380	−	0.992968i	$-0.537770\pi$
$41$	−1.51601			−0.236761			−0.118380	+	0.992968i	$0.537770\pi$
$42$		0			0
$43$	0.767367	−	0.767367i	0.117022	−	0.117022i	−0.646171	−	0.763193i	$-0.723631\pi$
$43$	0.767367	−	0.767367i	0.117022	−	0.117022i	0.763193	+	0.646171i	$0.223631\pi$
$44$	−0.849686	+	0.134954i	−0.128095	+	0.0203451i
$45$	13.0262	+	13.0262i	1.94184	+	1.94184i
$46$	−0.493455	+	1.51982i	−0.0727560	+	0.224085i
$47$	3.39052			0.494558			0.247279	−	0.968944i	$-0.420464\pi$
$47$	3.39052			0.494558			0.247279	+	0.968944i	$0.420464\pi$
$48$	−10.2439	−	5.20835i	−1.47857	−	0.751761i
$49$		0			0
$50$	9.81105	+	3.18546i	1.38749	+	0.450492i
$51$	5.99885	+	5.99885i	0.840007	+	0.840007i
$52$	0.677676	+	4.26673i	0.0939767	+	0.591689i
$53$	3.79626	+	3.79626i	0.521456	+	0.521456i	0.918011	−	0.396555i	$-0.129794\pi$
$53$	3.79626	+	3.79626i	0.521456	+	0.521456i	−0.396555	+	0.918011i	$0.629794\pi$
$54$	−8.15886	+	4.15937i	−1.11028	+	0.566019i
$55$			1.50829i			0.203378i
$56$		0			0
$57$			0.169701i			0.0224774i
$58$	−5.45199	−	10.6944i	−0.715882	−	1.40425i
$59$	10.5724	+	10.5724i	1.37641	+	1.37641i	0.850611	+	0.525796i	$0.176233\pi$
$59$	10.5724	+	10.5724i	1.37641	+	1.37641i	0.525796	+	0.850611i	$0.323767\pi$
$60$	−11.8350	+	16.3043i	−1.52789	+	2.10487i
$61$	−6.81551	−	6.81551i	−0.872637	−	0.872637i	0.120122	−	0.992759i	$-0.461671\pi$
$61$	−6.81551	−	6.81551i	−0.872637	−	0.872637i	−0.992759	+	0.120122i	$0.961671\pi$
$62$	−0.0176998	+	0.0545144i	−0.00224787	+	0.00692334i
$63$		0			0
$64$	2.46226	−	7.61165i	0.307783	−	0.951457i
$65$	7.57393			0.939430
$66$	−1.66235	−	0.539732i	−0.204621	−	0.0664364i
$67$	−6.14636	−	6.14636i	−0.750898	−	0.750898i	0.223749	−	0.974647i	$-0.428170\pi$
$67$	−6.14636	−	6.14636i	−0.750898	−	0.750898i	−0.974647	+	0.223749i	$0.928170\pi$
$68$	−3.46930	+	4.77942i	−0.420714	+	0.579590i
$69$	−2.29539	+	2.29539i	−0.276332	+	0.276332i
$70$		0			0
$71$	5.84154			0.693263			0.346631	−	0.938001i	$-0.387325\pi$
$71$	5.84154			0.693263			0.346631	+	0.938001i	$0.387325\pi$
$72$	−8.74258	−	12.0167i	−1.03032	−	1.41618i
$73$	−3.78781			−0.443330			−0.221665	−	0.975123i	$-0.571149\pi$
$73$	−3.78781			−0.443330			−0.221665	+	0.975123i	$0.571149\pi$
$74$	6.66905	−	3.39987i	0.775261	−	0.395226i
$75$	14.8177	+	14.8177i	1.71100	+	1.71100i
$76$	−0.116673	+	0.0185310i	−0.0133834	+	0.00212565i
$77$		0			0
$78$	−2.71029	+	8.34754i	−0.306879	+	0.945173i
$79$			5.64881i			0.635541i	0.948168	+	0.317771i	$0.102934\pi$
$79$			5.64881i			0.635541i	−0.948168	+	0.317771i	$0.897066\pi$
$80$	−12.5020	−	6.35645i	−1.39776	−	0.710673i
$81$	−2.84236			−0.315818
$82$	0.662080	−	2.03917i	0.0731145	−	0.225189i
$83$	9.59296	−	9.59296i	1.05296	−	1.05296i	0.0544475	−	0.998517i	$-0.482660\pi$
$83$	9.59296	−	9.59296i	1.05296	−	1.05296i	0.998517	−	0.0544475i	$-0.0173397\pi$
$84$		0			0
$85$	7.32120	+	7.32120i	0.794096	+	0.794096i
$86$	0.697051	+	1.36731i	0.0751649	+	0.147441i
$87$		−	24.3860i		−	2.61446i
$88$	0.189554	−	1.20184i	0.0202065	−	0.128117i
$89$	−14.6331			−1.55110			−0.775551	−	0.631285i	$-0.782528\pi$
$89$	−14.6331			−1.55110			−0.775551	+	0.631285i	$0.782528\pi$
$90$	−23.2104	+	11.8326i	−2.44659	+	1.24727i
$91$		0			0
$92$	−1.82879	−	1.32748i	−0.190664	−	0.138400i
$93$	−0.0823334	+	0.0823334i	−0.00853758	+	0.00853758i
$94$	−1.48073	+	4.56056i	−0.152725	+	0.470386i
$95$			0.207108i			0.0212489i
$96$	11.4795	−	11.5043i	1.17162	−	1.17415i
$97$		−	8.20099i		−	0.832684i	−0.909208	−	0.416342i	$-0.863312\pi$
$97$		−	8.20099i		−	0.832684i	0.909208	−	0.416342i	$-0.136688\pi$
$98$		0			0
$99$	−1.59813	−	1.59813i	−0.160618	−	0.160618i
$100$	−8.56947	+	11.8056i	−0.856947	+	1.18056i
$101$	4.03480	−	4.03480i	0.401477	−	0.401477i	−0.477276	−	0.878753i	$-0.658376\pi$
$101$	4.03480	−	4.03480i	0.401477	−	0.401477i	0.878753	+	0.477276i	$0.158376\pi$
$102$	−10.6889	+	5.44916i	−1.05835	+	0.539547i
$103$		−	11.7396i		−	1.15674i	−0.815776	−	0.578368i	$-0.803690\pi$
$103$		−	11.7396i		−	1.15674i	0.815776	−	0.578368i	$-0.196310\pi$
$104$	−6.03510	−	0.951852i	−0.591790	−	0.0933368i
$105$		0			0
$106$	−6.76424	+	3.44839i	−0.657001	+	0.334938i
$107$	11.1261	−	11.1261i	1.07560	−	1.07560i	0.0787045	−	0.996898i	$-0.474922\pi$
$107$	11.1261	−	11.1261i	1.07560	−	1.07560i	0.996898	−	0.0787045i	$-0.0250784\pi$
$108$	−2.03155	−	12.7909i	−0.195486	−	1.23081i
$109$	−3.38071	+	3.38071i	−0.323813	+	0.323813i	−0.850228	−	0.526415i	$-0.823536\pi$
$109$	−3.38071	+	3.38071i	−0.323813	+	0.323813i	0.526415	+	0.850228i	$0.323536\pi$
$110$	−2.02879	−	0.658708i	−0.193437	−	0.0628053i
$111$	15.2071			1.44340
$112$		0			0
$113$	1.99354			0.187536			0.0937681	−	0.995594i	$-0.470109\pi$
$113$	1.99354			0.187536			0.0937681	+	0.995594i	$0.470109\pi$
$114$	−0.228263	−	0.0741125i	−0.0213788	−	0.00694127i
$115$	−2.80137	+	2.80137i	−0.261229	+	0.261229i
$116$	16.7660	−	2.66291i	1.55668	−	0.247245i
$117$	−8.02506	+	8.02506i	−0.741917	+	0.741917i
$118$	−18.8380	+	9.60360i	−1.73418	+	0.884083i
$119$		0			0
$120$	−16.7621	−	23.0396i	−1.53017	−	2.10322i
$121$			10.8150i			0.983178i
$122$	12.1440	−	6.19098i	1.09947	−	0.560505i
$123$	3.07977	−	3.07977i	0.277694	−	0.277694i
$124$	−0.0655969	−	0.0476156i	−0.00589078	−	0.00427601i
$125$	5.68746	+	5.68746i	0.508702	+	0.508702i
$126$		0			0
$127$			9.25046i			0.820846i	0.911895	+	0.410423i	$0.134619\pi$
$127$			9.25046i			0.820846i	−0.911895	+	0.410423i	$0.865381\pi$
$128$	9.16304	+	6.63617i	0.809906	+	0.586560i
$129$			3.11781i			0.274508i
$130$	−3.30772	+	10.1876i	−0.290107	+	0.893514i
$131$	2.42538	−	2.42538i	0.211907	−	0.211907i	−0.593170	−	0.805077i	$-0.702124\pi$
$131$	2.42538	−	2.42538i	0.211907	−	0.211907i	0.805077	+	0.593170i	$0.202124\pi$
$132$	1.45198	−	2.00030i	0.126378	−	0.174103i
$133$		0			0
$134$	10.9517	−	5.58315i	0.946082	−	0.482311i
$135$	−22.7053			−1.95416
$136$	−4.91363	−	6.75382i	−0.421341	−	0.579135i
$137$		−	18.9640i		−	1.62020i	−0.586289	−	0.810102i	$-0.699412\pi$
$137$		−	18.9640i		−	1.62020i	0.586289	−	0.810102i	$-0.300588\pi$
$138$	−2.08505	−	4.08996i	−0.177491	−	0.348160i
$139$	7.19316	+	7.19316i	0.610116	+	0.610116i	0.942976	−	0.332860i	$-0.108014\pi$
$139$	7.19316	+	7.19316i	0.610116	+	0.610116i	−0.332860	+	0.942976i	$0.608014\pi$
$140$		0			0
$141$	−6.88784	+	6.88784i	−0.580061	+	0.580061i
$142$	−2.55115	+	7.85740i	−0.214087	+	0.659378i
$143$	−0.929209			−0.0777044
$144$	19.9817	−	6.51157i	1.66514	−	0.542630i
$145$		−	29.7615i		−	2.47156i
$146$	1.65423	−	5.09495i	0.136905	−	0.421661i
$147$		0			0
$148$	1.66059	+	10.4553i	0.136500	+	0.859419i
$149$	11.0777	+	11.0777i	0.907518	+	0.907518i	0.996071	−	0.0885538i	$-0.0282245\pi$
$149$	11.0777	+	11.0777i	0.907518	+	0.907518i	−0.0885538	+	0.996071i	$0.528225\pi$
$150$	−26.4024	+	13.4599i	−2.15575	+	1.09900i
$151$	14.4175			1.17328			0.586641	−	0.809847i	$-0.300450\pi$
$151$	14.4175			1.17328			0.586641	+	0.809847i	$0.300450\pi$
$152$	0.0260283	−	0.165029i	0.00211118	−	0.0133856i
$153$	−15.5146			−1.25428
$154$		0			0
$155$	−0.100483	+	0.100483i	−0.00807095	+	0.00807095i
$156$	−10.0446	−	7.29116i	−0.804208	−	0.583760i
$157$	−13.3514	−	13.3514i	−1.06556	−	1.06556i	−0.997695	−	0.0678628i	$-0.978382\pi$
$157$	−13.3514	−	13.3514i	−1.06556	−	1.06556i	−0.0678628	−	0.997695i	$-0.521618\pi$
$158$	−7.59817	−	2.46698i	−0.604478	−	0.196262i
$159$	−15.4242			−1.22322
$160$	14.0099	−	14.0403i	1.10758	−	1.10998i
$161$		0			0
$162$	1.24133	−	3.82324i	0.0975282	−	0.300382i
$163$	−6.96142	−	6.96142i	−0.545261	−	0.545261i	0.379806	−	0.925066i	$-0.375991\pi$
$163$	−6.96142	−	6.96142i	−0.545261	−	0.545261i	−0.925066	+	0.379806i	$0.875991\pi$
$164$	2.45373	+	1.78112i	0.191604	+	0.139082i
$165$	−3.06409	−	3.06409i	−0.238539	−	0.238539i
$166$	8.71392	+	17.0929i	0.676332	+	1.32667i
$167$			13.7025i			1.06033i	0.847894	+	0.530165i	$0.177870\pi$
$167$			13.7025i			1.06033i	−0.847894	+	0.530165i	$0.822130\pi$
$168$		0			0
$169$		−	8.33394i		−	0.641072i
$170$	−13.0450	+	6.65034i	−1.00051	+	0.510057i
$171$	−0.219445	−	0.219445i	−0.0167814	−	0.0167814i
$172$	−2.14357	+	0.340459i	−0.163446	+	0.0259598i
$173$	6.98567	+	6.98567i	0.531111	+	0.531111i	0.920903	−	0.389792i	$-0.127453\pi$
$173$	6.98567	+	6.98567i	0.531111	+	0.531111i	−0.389792	+	0.920903i	$0.627453\pi$
$174$	32.8014	+	10.6500i	2.48667	+	0.807373i
$175$		0			0
$176$	1.53381	+	0.779843i	0.115615	+	0.0587829i
$177$	−42.9556			−3.22874
$178$	6.39063	−	19.6828i	0.478998	−	1.47529i
$179$	−6.25277	−	6.25277i	−0.467354	−	0.467354i	0.433702	−	0.901056i	$-0.357207\pi$
$179$	−6.25277	−	6.25277i	−0.467354	−	0.467354i	−0.901056	+	0.433702i	$0.857207\pi$
$180$	−5.77938	−	36.3877i	−0.430770	−	2.71218i
$181$	14.5287	−	14.5287i	1.07991	−	1.07991i	0.0833952	−	0.996517i	$-0.473424\pi$
$181$	14.5287	−	14.5287i	1.07991	−	1.07991i	0.996517	−	0.0833952i	$-0.0265764\pi$
$182$		0			0
$183$	27.6914			2.04701
$184$	2.58427	−	1.88014i	0.190515	−	0.138606i
$185$	18.5593			1.36451
$186$	−0.0747889	−	0.146703i	−0.00548379	−	0.0107568i
$187$	−0.898204	−	0.898204i	−0.0656832	−	0.0656832i
$188$	−5.48770	−	3.98342i	−0.400232	−	0.290521i
$189$		0			0
$190$	−0.278580	−	0.0904495i	−0.0202103	−	0.00656189i
$191$		−	10.8355i		−	0.784029i	−0.919959	−	0.392014i	$-0.871778\pi$
$191$		−	10.8355i		−	0.784029i	0.919959	−	0.392014i	$-0.128222\pi$
$192$	10.4610	+	20.4652i	0.754957	+	1.47695i
$193$	−9.03679			−0.650483			−0.325241	−	0.945631i	$-0.605446\pi$
$193$	−9.03679			−0.650483			−0.325241	+	0.945631i	$0.605446\pi$
$194$	11.0311	+	3.58158i	0.791985	+	0.257142i
$195$	−15.3864	+	15.3864i	−1.10185	+	1.10185i
$196$		0			0
$197$	−5.48439	−	5.48439i	−0.390747	−	0.390747i	0.484207	−	0.874954i	$-0.339108\pi$
$197$	−5.48439	−	5.48439i	−0.390747	−	0.390747i	−0.874954	+	0.484207i	$0.839108\pi$
$198$	2.84757	−	1.45169i	0.202368	−	0.103167i
$199$			5.70845i			0.404661i	0.979317	+	0.202331i	$0.0648515\pi$
$199$			5.70845i			0.404661i	−0.979317	+	0.202331i	$0.935148\pi$
$200$	−12.1371	−	16.6825i	−0.858223	−	1.17963i
$201$	24.9727			1.76144
$202$	3.66508	+	7.18927i	0.257874	+	0.505835i
$203$		0			0
$204$	−2.66152	−	16.7573i	−0.186344	−	1.17324i
$205$	3.75866	−	3.75866i	0.262516	−	0.262516i
$206$	15.7908	+	5.12698i	1.10020	+	0.357213i
$207$		−	5.93646i		−	0.412613i
$208$	3.91601	−	7.70207i	0.271526	−	0.534042i
$209$		−	0.0254092i		−	0.00175759i
$210$		0			0
$211$	−16.4028	−	16.4028i	−1.12921	−	1.12921i	−0.990305	−	0.138909i	$-0.955640\pi$
$211$	−16.4028	−	16.4028i	−1.12921	−	1.12921i	−0.138909	−	0.990305i	$-0.544360\pi$
$212$	−1.68429	−	10.6045i	−0.115678	−	0.728321i
$213$	−11.8671	+	11.8671i	−0.813119	+	0.813119i
$214$	10.1066	+	19.8247i	0.690872	+	1.35519i
$215$			3.80508i			0.259505i
$216$	18.0922	+	2.85349i	1.23102	+	0.194155i
$217$		0			0
$218$	−3.07092	−	6.02380i	−0.207989	−	0.407983i
$219$	7.69494	−	7.69494i	0.519976	−	0.519976i
$220$	1.77204	−	2.44123i	0.119471	−	0.164588i
$221$	−4.51036	+	4.51036i	−0.303400	+	0.303400i
$222$	−6.64134	+	20.4550i	−0.445737	+	1.37285i
$223$	−2.74928			−0.184105			−0.0920527	−	0.995754i	$-0.529343\pi$
$223$	−2.74928			−0.184105			−0.0920527	+	0.995754i	$0.529343\pi$
$224$		0			0
$225$	−38.3224			−2.55482
$226$	−0.870628	+	2.68149i	−0.0579133	+	0.178370i
$227$	2.82551	−	2.82551i	0.187536	−	0.187536i	−0.607094	−	0.794630i	$-0.707665\pi$
$227$	2.82551	−	2.82551i	0.187536	−	0.187536i	0.794630	+	0.607094i	$0.207665\pi$
$228$	0.199376	−	0.274668i	0.0132040	−	0.0181903i
$229$	1.09528	−	1.09528i	0.0723782	−	0.0723782i	−0.669991	−	0.742369i	$-0.733702\pi$
$229$	1.09528	−	1.09528i	0.0723782	−	0.0723782i	0.742369	+	0.669991i	$0.233702\pi$
$230$	−2.54467	−	4.99153i	−0.167791	−	0.329131i
$231$		0			0
$232$	−3.74028	+	23.7148i	−0.245561	+	1.55695i
$233$		−	13.8787i		−	0.909226i	−0.890689	−	0.454613i	$-0.849778\pi$
$233$		−	13.8787i		−	0.909226i	0.890689	−	0.454613i	$-0.150222\pi$
$234$	−7.28970	−	14.2992i	−0.476542	−	0.934767i
$235$	−8.40616	+	8.40616i	−0.548357	+	0.548357i
$236$	−4.69067	−	29.5330i	−0.305336	−	1.92244i
$237$	−11.4756	−	11.4756i	−0.745418	−	0.745418i
$238$		0			0
$239$			11.0337i			0.713709i	0.934160	+	0.356854i	$0.116151\pi$
$239$			11.0337i			0.713709i	−0.934160	+	0.356854i	$0.883849\pi$
$240$	38.3108	−	12.4846i	2.47295	−	0.805878i
$241$		−	12.8746i		−	0.829324i	−0.909976	−	0.414662i	$-0.863900\pi$
$241$		−	12.8746i		−	0.829324i	0.909976	−	0.414662i	$-0.136100\pi$
$242$	−14.5471	−	4.72316i	−0.935123	−	0.303616i
$243$	−7.96262	+	7.96262i	−0.510802	+	0.510802i
$244$	3.02385	+	19.0385i	0.193582	+	1.21882i
$245$		0			0
$246$	2.79756	+	5.48759i	0.178366	+	0.349876i
$247$	−0.127593			−0.00811855
$248$	0.0926952	−	0.0674389i	0.00588615	−	0.00428238i
$249$			38.9762i			2.47002i
$250$	−10.1340	+	5.16630i	−0.640931	+	0.326745i
$251$	−16.2376	−	16.2376i	−1.02491	−	1.02491i	−0.999682	−	0.0252236i	$-0.991970\pi$
$251$	−16.2376	−	16.2376i	−1.02491	−	1.02491i	−0.0252236	−	0.999682i	$-0.508030\pi$
$252$		0			0
$253$	0.343687	−	0.343687i	0.0216074	−	0.0216074i
$254$	−12.4427	−	4.03991i	−0.780725	−	0.253486i
$255$	−29.7460			−1.86277
$256$	−12.9280	+	9.42695i	−0.807999	+	0.589184i
$257$			5.18858i			0.323655i	0.986819	+	0.161827i	$0.0517387\pi$
$257$			5.18858i			0.323655i	−0.986819	+	0.161827i	$0.948261\pi$
$258$	−4.19374	−	1.36163i	−0.261091	−	0.0847712i
$259$		0			0
$260$	−12.2587	−	8.89838i	−0.760254	−	0.551854i
$261$	31.5343	+	31.5343i	1.95192	+	1.95192i
$262$	2.20313	+	4.32158i	0.136110	+	0.266988i
$263$	−26.4016			−1.62799			−0.813996	−	0.580870i	$-0.802712\pi$
$263$	−26.4016			−1.62799			−0.813996	+	0.580870i	$0.802712\pi$
$264$	2.05647	+	2.82662i	0.126567	+	0.173967i
$265$	−18.8242			−1.15636
$266$		0			0
$267$	29.7271	−	29.7271i	1.81927	−	1.81927i
$268$	2.72697	+	17.1693i	0.166576	+	1.04878i
$269$	3.98468	+	3.98468i	0.242950	+	0.242950i	0.818070	−	0.575119i	$-0.195044\pi$
$269$	3.98468	+	3.98468i	0.242950	+	0.242950i	−0.575119	+	0.818070i	$0.695044\pi$
$270$	9.91599	−	30.5407i	0.603468	−	1.85865i
$271$	10.0223			0.608812			0.304406	−	0.952542i	$-0.401542\pi$
$271$	10.0223			0.608812			0.304406	+	0.952542i	$0.401542\pi$
$272$	11.2304	−	3.65973i	0.680944	−	0.221903i
$273$		0			0
$274$	25.5083	+	8.28206i	1.54101	+	0.500337i
$275$	−2.21864	−	2.21864i	−0.133789	−	0.133789i
$276$	6.41197	−	1.01840i	0.385955	−	0.0613004i
$277$	21.1077	+	21.1077i	1.26824	+	1.26824i	0.946997	+	0.321243i	$0.104101\pi$
$277$	21.1077	+	21.1077i	1.26824	+	1.26824i	0.321243	+	0.946997i	$0.395899\pi$
$278$	−12.8169	+	6.53402i	−0.768706	+	0.391885i
$279$		−	0.212935i		−	0.0127481i
$280$		0			0
$281$			4.50000i			0.268448i	0.990951	+	0.134224i	$0.0428541\pi$
$281$			4.50000i			0.268448i	−0.990951	+	0.134224i	$0.957146\pi$
$282$	−6.25669	−	12.2729i	−0.372580	−	0.730839i
$283$	−1.94851	−	1.94851i	−0.115827	−	0.115827i	0.646818	−	0.762645i	$-0.276099\pi$
$283$	−1.94851	−	1.94851i	−0.115827	−	0.115827i	−0.762645	+	0.646818i	$0.776099\pi$
$284$	−9.45477	−	6.86305i	−0.561038	−	0.407247i
$285$	−0.420741	−	0.420741i	−0.0249225	−	0.0249225i
$286$	0.405809	−	1.24987i	0.0239960	−	0.0739065i
$287$		0			0
$288$	0.0321410	+	29.7210i	0.00189393	+	1.75133i
$289$	8.28027			0.487075
$290$	40.0320	+	12.9976i	2.35076	+	0.763246i
$291$	16.6603	+	16.6603i	0.976644	+	0.976644i
$292$	6.13073	+	4.45019i	0.358774	+	0.260428i
$293$	−6.10508	+	6.10508i	−0.356662	+	0.356662i	−0.862581	−	0.505919i	$-0.831154\pi$
$293$	−6.10508	+	6.10508i	−0.356662	+	0.356662i	0.505919	+	0.862581i	$0.331154\pi$
$294$		0			0
$295$	−52.4244			−3.05227
$296$	−14.7885	−	2.33244i	−0.859566	−	0.135570i
$297$	2.78561			0.161637
$298$	−19.7384	+	10.0626i	−1.14341	+	0.582909i
$299$	−1.72584	−	1.72584i	−0.0998077	−	0.0998077i
$300$	−6.57419	−	41.3919i	−0.379561	−	2.38976i
$301$		0			0
$302$	−6.29649	+	19.3929i	−0.362323	+	1.11594i
$303$			16.3934i			0.941775i
$304$	0.210612	+	0.107083i	0.0120794	+	0.00614163i
$305$	33.7956			1.93513
$306$	6.77560	−	20.8685i	0.387336	−	1.19297i
$307$	−1.15151	+	1.15151i	−0.0657200	+	0.0657200i	−0.739203	−	0.673483i	$-0.764798\pi$
$307$	−1.15151	+	1.15151i	−0.0657200	+	0.0657200i	0.673483	+	0.739203i	$0.264798\pi$
$308$		0			0
$309$	23.8490	+	23.8490i	1.35672	+	1.35672i
$310$	−0.0912749	−	0.179041i	−0.00518407	−	0.0101689i
$311$			8.14834i			0.462050i	0.972948	+	0.231025i	$0.0742079\pi$
$311$			8.14834i			0.462050i	−0.972948	+	0.231025i	$0.925792\pi$
$312$	14.1940	−	10.3266i	0.803577	−	0.584630i
$313$	30.5053			1.72426			0.862130	−	0.506687i	$-0.169130\pi$
$313$	30.5053			1.72426			0.862130	+	0.506687i	$0.169130\pi$
$314$	23.7897	−	12.1280i	1.34253	−	0.684420i
$315$		0			0
$316$	6.63663	−	9.14285i	0.373339	−	0.514325i
$317$	−9.96164	+	9.96164i	−0.559501	+	0.559501i	−0.929165	−	0.369664i	$-0.879473\pi$
$317$	−9.96164	+	9.96164i	−0.559501	+	0.559501i	0.369664	+	0.929165i	$0.379473\pi$
$318$	6.73613	−	20.7469i	0.377743	−	1.16343i
$319$			3.65130i			0.204434i
$320$	12.7669	+	24.9764i	0.713694	+	1.39622i
$321$			45.2054i			2.52312i
$322$		0			0
$323$	−0.123336	−	0.123336i	−0.00686257	−	0.00686257i
$324$	4.60048	+	3.33941i	0.255582	+	0.185523i
$325$	−11.1410	+	11.1410i	−0.617991	+	0.617991i
$326$	12.4040	−	6.32352i	0.686993	−	0.350227i
$327$		−	13.7358i		−	0.759592i
$328$	−3.46737	+	2.52263i	−0.191453	+	0.139289i
$329$		0			0
$330$	5.45964	−	2.78331i	0.300543	−	0.153216i
$331$	14.9522	−	14.9522i	0.821845	−	0.821845i	−0.164527	−	0.986373i	$-0.552610\pi$
$331$	14.9522	−	14.9522i	0.821845	−	0.821845i	0.986373	+	0.164527i	$0.0526098\pi$
$332$	−26.7971	+	4.25613i	−1.47068	+	0.233585i
$333$	−19.6648	+	19.6648i	−1.07762	+	1.07762i
$334$	−18.4311	−	5.98422i	−1.00851	−	0.327442i
$335$	30.4775			1.66516
$336$		0			0
$337$	19.5138			1.06299			0.531493	−	0.847063i	$-0.321631\pi$
$337$	19.5138			1.06299			0.531493	+	0.847063i	$0.321631\pi$
$338$	11.2099	+	3.63964i	0.609739	+	0.197970i
$339$	−4.04987	+	4.04987i	−0.219959	+	0.219959i
$340$	−3.24821	−	20.4511i	−0.176159	−	1.10912i
$341$	0.0123277	−	0.0123277i	0.000667584	−	0.000667584i
$342$	0.391010	−	0.199336i	0.0211434	−	0.0107789i
$343$		0			0
$344$	0.478204	−	3.03199i	0.0257830	−	0.163474i
$345$		−	11.3820i		−	0.612784i
$346$	−12.4472	+	6.34555i	−0.669165	+	0.341139i
$347$	14.0142	−	14.0142i	0.752320	−	0.752320i	−0.222592	−	0.974912i	$-0.571452\pi$
$347$	14.0142	−	14.0142i	0.752320	−	0.752320i	0.974912	+	0.222592i	$0.0714517\pi$
$348$	−28.6504	+	39.4698i	−1.53582	+	2.11580i
$349$	−19.0596	−	19.0596i	−1.02024	−	1.02024i	−0.999791	−	0.0204443i	$-0.993492\pi$
$349$	−19.0596	−	19.0596i	−1.02024	−	1.02024i	−0.0204443	−	0.999791i	$-0.506508\pi$
$350$		0			0
$351$		−	13.9880i		−	0.746626i
$352$	−1.71881	+	1.72253i	−0.0916130	+	0.0918113i
$353$			4.84534i			0.257891i	0.991652	+	0.128946i	$0.0411593\pi$
$353$			4.84534i			0.257891i	−0.991652	+	0.128946i	$0.958841\pi$
$354$	18.7598	−	57.7792i	0.997071	−	3.07093i
$355$	−14.4830	+	14.4830i	−0.768677	+	0.768677i
$356$	23.6842	+	17.1920i	1.25526	+	0.911172i
$357$		0			0
$358$	11.1413	−	5.67981i	0.588835	−	0.300187i
$359$	−22.8441			−1.20566			−0.602832	−	0.797868i	$-0.705961\pi$
$359$	−22.8441			−1.20566			−0.602832	+	0.797868i	$0.705961\pi$
$360$	51.4688	+	8.11762i	2.71264	+	0.427836i
$361$			18.9965i			0.999816i
$362$	13.1974	+	25.8875i	0.693640	+	1.36062i
$363$	−21.9706	−	21.9706i	−1.15316	−	1.15316i
$364$		0			0
$365$	9.39117	−	9.39117i	0.491556	−	0.491556i
$366$	−12.0935	+	37.2475i	−0.632139	+	1.94696i
$367$	−14.0978			−0.735899			−0.367949	−	0.929846i	$-0.619940\pi$
$367$	−14.0978			−0.735899			−0.367949	+	0.929846i	$0.619940\pi$
$368$	1.40035	+	4.29718i	0.0729982	+	0.224006i
$369$			7.96508i			0.414646i
$370$	−8.10531	+	24.9640i	−0.421375	+	1.29781i
$371$		0			0
$372$	0.229991	−	0.0365290i	0.0119245	−	0.00189394i
$373$	−17.8548	−	17.8548i	−0.924488	−	0.924488i	0.0728545	−	0.997343i	$-0.476789\pi$
$373$	−17.8548	−	17.8548i	−0.924488	−	0.924488i	−0.997343	+	0.0728545i	$0.976789\pi$
$374$	1.60043	−	0.815898i	0.0827565	−	0.0421891i
$375$	−23.1081			−1.19330
$376$	7.75469	−	5.64180i	0.399917	−	0.290954i
$377$	18.3351			0.944308
$378$		0			0
$379$	−13.1964	+	13.1964i	−0.677853	+	0.677853i	−0.959514	−	0.281661i	$-0.909115\pi$
$379$	−13.1964	+	13.1964i	−0.677853	+	0.677853i	0.281661	+	0.959514i	$0.409115\pi$
$380$	0.243326	−	0.335214i	0.0124823	−	0.0171961i
$381$	−18.7923	−	18.7923i	−0.962759	−	0.962759i
$382$	14.5747	+	4.73213i	0.745708	+	0.242117i
$383$	−22.5621			−1.15287			−0.576435	−	0.817143i	$-0.695557\pi$
$383$	−22.5621			−1.15287			−0.576435	+	0.817143i	$0.695557\pi$
$384$	−32.0961	+	5.13334i	−1.63790	+	0.261960i
$385$		0			0
$386$	3.94659	−	12.1553i	0.200876	−	0.618689i
$387$	−4.03173	−	4.03173i	−0.204944	−	0.204944i
$388$	−9.63510	+	13.2736i	−0.489148	+	0.673867i
$389$	−11.8822	−	11.8822i	−0.602453	−	0.602453i	0.338510	−	0.940963i	$-0.390077\pi$
$389$	−11.8822	−	11.8822i	−0.602453	−	0.602453i	−0.940963	+	0.338510i	$0.890077\pi$
$390$	−13.9765	−	27.4158i	−0.707728	−	1.38825i
$391$		−	3.33650i		−	0.168734i
$392$		0			0
$393$			9.85432i			0.497085i
$394$	9.77218	−	4.98184i	0.492316	−	0.250981i
$395$	−14.0052	−	14.0052i	−0.704677	−	0.704677i
$396$	0.709045	+	4.46423i	0.0356308	+	0.224336i
$397$	−16.6861	−	16.6861i	−0.837453	−	0.837453i	0.151070	−	0.988523i	$-0.451728\pi$
$397$	−16.6861	−	16.6861i	−0.837453	−	0.837453i	−0.988523	+	0.151070i	$0.951728\pi$
$398$	−7.67838	−	2.49302i	−0.384883	−	0.124964i
$399$		0			0
$400$	27.7401	−	9.03984i	1.38700	−	0.451992i
$401$	9.21243			0.460047			0.230023	−	0.973185i	$-0.426120\pi$
$401$	9.21243			0.460047			0.230023	+	0.973185i	$0.426120\pi$
$402$	−10.9062	+	33.5905i	−0.543951	+	1.67534i
$403$	−0.0619041	−	0.0619041i	−0.00308366	−	0.00308366i
$404$	−11.2709	+	1.79013i	−0.560746	+	0.0890621i
$405$	7.04710	−	7.04710i	0.350173	−	0.350173i
$406$		0			0
$407$	−2.27695			−0.112864
$408$	23.7024	+	3.73833i	1.17344	+	0.185075i
$409$	21.8961			1.08269			0.541347	−	0.840799i	$-0.317915\pi$
$409$	21.8961			1.08269			0.541347	+	0.840799i	$0.317915\pi$
$410$	3.41424	+	6.69724i	0.168617	+	0.330753i
$411$	38.5254	+	38.5254i	1.90032	+	1.90032i
$412$	−13.7925	+	19.0010i	−0.679508	+	0.936114i
$413$		0			0
$414$	7.98508	+	2.59260i	0.392446	+	0.127419i
$415$			47.5679i			2.33501i
$416$	8.64976	+	8.63108i	0.424090	+	0.423173i
$417$	−29.2258			−1.43119
$418$	0.0341776	+	0.0110968i	0.00167168	+	0.000542763i
$419$	−20.3219	+	20.3219i	−0.992790	+	0.992790i	−0.999974	−	0.00718417i	$-0.997713\pi$
$419$	−20.3219	+	20.3219i	−0.992790	+	0.992790i	0.00718417	+	0.999974i	$0.497713\pi$
$420$		0			0
$421$	−23.7959	−	23.7959i	−1.15974	−	1.15974i	−0.984531	−	0.175210i	$-0.943940\pi$
$421$	−23.7959	−	23.7959i	−1.15974	−	1.15974i	−0.175210	−	0.984531i	$-0.556060\pi$
$422$	29.2268	−	14.8997i	1.42274	−	0.725308i
$423$		−	17.8137i		−	0.866133i
$424$	14.9996	+	2.36573i	0.728446	+	0.114890i
$425$	−21.5385			−1.04477
$426$	−10.7797	−	21.1450i	−0.522276	−	1.02448i
$427$		0			0
$428$	−31.0798	+	4.93635i	−1.50230	+	0.238607i
$429$	1.88769	−	1.88769i	0.0911384	−	0.0911384i
$430$	−5.11819	−	1.66178i	−0.246821	−	0.0801379i
$431$		−	14.9611i		−	0.720651i	−0.932827	−	0.360325i	$-0.882666\pi$
$431$		−	14.9611i		−	0.720651i	0.932827	−	0.360325i	$-0.117334\pi$
$432$	−11.7395	+	23.0895i	−0.564818	+	1.11089i
$433$		−	22.5541i		−	1.08388i	−0.840417	−	0.541941i	$-0.817690\pi$
$433$		−	22.5541i		−	1.08388i	0.840417	−	0.541941i	$-0.182310\pi$
$434$		0			0
$435$	60.4605	+	60.4605i	2.89886	+	2.89886i
$436$	9.44371	−	1.49993i	0.452272	−	0.0718334i
$437$	0.0471928	−	0.0471928i	0.00225754	−	0.00225754i
$438$	6.98982	+	13.7110i	0.333987	+	0.655135i
$439$			5.36645i			0.256127i	0.991766	+	0.128063i	$0.0408761\pi$
$439$			5.36645i			0.256127i	−0.991766	+	0.128063i	$0.959124\pi$
$440$	2.50978	+	3.44971i	0.119649	+	0.164458i
$441$		0			0
$442$	−4.09706	−	8.03664i	−0.194877	−	0.382264i
$443$	6.70533	−	6.70533i	0.318580	−	0.318580i	−0.529642	−	0.848221i	$-0.677674\pi$
$443$	6.70533	−	6.70533i	0.318580	−	0.318580i	0.848221	+	0.529642i	$0.177674\pi$
$444$	−24.6134	−	17.8664i	−1.16810	−	0.847902i
$445$	36.2799	−	36.2799i	1.71983	−	1.71983i
$446$	1.20068	−	3.69803i	0.0568538	−	0.175107i
$447$	−45.0085			−2.12883
$448$		0			0
$449$	15.0862			0.711963			0.355981	−	0.934493i	$-0.384147\pi$
$449$	15.0862			0.711963			0.355981	+	0.934493i	$0.384147\pi$
$450$	16.7363	−	51.5471i	0.788958	−	2.42995i
$451$	−0.461132	+	0.461132i	−0.0217139	+	0.0217139i
$452$	−3.22662	−	2.34215i	−0.151768	−	0.110165i
$453$	−29.2892	+	29.2892i	−1.37613	+	1.37613i
$454$	2.56660	+	5.03454i	0.120456	+	0.236283i
$455$		0			0
$456$	0.282381	+	0.388134i	0.0132237	+	0.0181760i
$457$		−	13.2348i		−	0.619099i	−0.950883	−	0.309550i	$-0.899822\pi$
$457$		−	13.2348i		−	0.619099i	0.950883	−	0.309550i	$-0.100178\pi$
$458$	0.994916	+	1.95159i	0.0464894	+	0.0911917i
$459$	13.5213	−	13.5213i	0.631120	−	0.631120i
$460$	7.82538	−	1.24289i	0.364860	−	0.0579500i
$461$	2.15151	+	2.15151i	0.100206	+	0.100206i	0.755432	−	0.655227i	$-0.227427\pi$
$461$	2.15151	+	2.15151i	0.100206	+	0.100206i	−0.655227	+	0.755432i	$0.727427\pi$
$462$		0			0
$463$			16.3798i			0.761232i	0.924733	+	0.380616i	$0.124288\pi$
$463$			16.3798i			0.761232i	−0.924733	+	0.380616i	$0.875712\pi$
$464$	−30.2650	−	15.3878i	−1.40502	−	0.714363i
$465$		−	0.408260i		−	0.0189326i
$466$	18.6682	+	6.06119i	0.864786	+	0.280779i
$467$	27.7614	−	27.7614i	1.28464	−	1.28464i	0.346647	−	0.937995i	$-0.387320\pi$
$467$	27.7614	−	27.7614i	1.28464	−	1.28464i	0.937995	−	0.346647i	$-0.112680\pi$
$468$	22.4173	−	3.56050i	1.03624	−	0.164584i
$469$		0			0
$470$	−7.63587	−	14.9782i	−0.352217	−	0.690894i
$471$	54.2467			2.49956
$472$	41.7732	+	6.58844i	1.92277	+	0.303257i
$473$		−	0.466828i		−	0.0214648i
$474$	20.4474	−	10.4240i	0.939178	−	0.478791i
$475$	−0.304650	−	0.304650i	−0.0139783	−	0.0139783i
$476$		0			0
$477$	19.9455	−	19.9455i	0.913240	−	0.913240i
$478$	−14.8413	−	4.81868i	−0.678825	−	0.220401i
$479$	23.5346			1.07532			0.537662	−	0.843161i	$-0.319308\pi$
$479$	23.5346			1.07532			0.537662	+	0.843161i	$0.319308\pi$
$480$	0.0616239	+	56.9839i	0.00281273	+	2.60095i
$481$			11.4338i			0.521337i
$482$	17.3175	+	5.62265i	0.788789	+	0.256105i
$483$		0			0
$484$	12.7062	−	17.5045i	0.577553	−	0.795657i
$485$	20.3328	+	20.3328i	0.923265	+	0.923265i
$486$	−7.23297	−	14.1879i	−0.328094	−	0.643577i
$487$	10.9787			0.497490			0.248745	−	0.968569i	$-0.419982\pi$
$487$	10.9787			0.497490			0.248745	+	0.968569i	$0.419982\pi$
$488$	−26.9292	−	4.24725i	−1.21903	−	0.192264i
$489$	28.2842			1.27906
$490$		0			0
$491$	5.88999	−	5.88999i	0.265812	−	0.265812i	−0.561598	−	0.827410i	$-0.689813\pi$
$491$	5.88999	−	5.88999i	0.265812	−	0.265812i	0.827410	+	0.561598i	$0.189813\pi$
$492$	−8.60308	+	1.36641i	−0.387857	+	0.0616025i
$493$	17.7233	+	17.7233i	0.798219	+	0.798219i
$494$	0.0557231	−	0.171624i	0.00250710	−	0.00772174i
$495$	7.92452			0.356181
$496$	0.0502292	+	0.154136i	0.00225536	+	0.00692090i
$497$		0			0
$498$	−52.4265	−	17.0219i	−2.34929	−	0.762769i
$499$	9.83776	+	9.83776i	0.440399	+	0.440399i	0.892146	−	0.451747i	$-0.149199\pi$
$499$	9.83776	+	9.83776i	0.440399	+	0.440399i	−0.451747	+	0.892146i	$0.649199\pi$
$500$	−2.52337	−	15.8874i	−0.112848	−	0.710507i
$501$	−27.8366	−	27.8366i	−1.24365	−	1.24365i
$502$	28.9323	−	14.7497i	1.29131	−	0.658309i
$503$		−	2.74125i		−	0.122226i	−0.998131	−	0.0611131i	$-0.980535\pi$
$503$		−	2.74125i		−	0.122226i	0.998131	−	0.0611131i	$-0.0194650\pi$
$504$		0			0
$505$			20.0070i			0.890302i
$506$	0.312194	+	0.612387i	0.0138787	+	0.0272239i
$507$	16.9304	+	16.9304i	0.751905	+	0.751905i
$508$	10.8681	−	14.9723i	0.482194	−	0.664287i
$509$	8.42394	+	8.42394i	0.373385	+	0.373385i	0.868708	−	0.495324i	$-0.164951\pi$
$509$	8.42394	+	8.42394i	0.373385	+	0.373385i	−0.495324	+	0.868708i	$0.664951\pi$
$510$	12.9908	−	40.0111i	0.575244	−	1.77172i
$511$		0			0
$512$	−7.03413	−	21.5063i	−0.310868	−	0.950453i
$513$	0.382502			0.0168879
$514$	−6.97911	−	2.26598i	−0.307835	−	0.0999482i
$515$	29.1061	+	29.1061i	1.28257	+	1.28257i
$516$	3.66303	−	5.04631i	0.161256	−	0.222151i
$517$	1.03131	−	1.03131i	0.0453570	−	0.0453570i
$518$		0			0
$519$	−28.3828			−1.24587
$520$	17.3228	−	12.6030i	0.759656	−	0.552676i
$521$	−33.8649			−1.48365			−0.741824	−	0.670595i	$-0.766039\pi$
$521$	−33.8649			−1.48365			−0.741824	+	0.670595i	$0.766039\pi$
$522$	−56.1883	+	28.6447i	−2.45929	+	1.25374i
$523$	−12.3358	−	12.3358i	−0.539408	−	0.539408i	0.383947	−	0.923355i	$-0.374564\pi$
$523$	−12.3358	−	12.3358i	−0.539408	−	0.539408i	−0.923355	+	0.383947i	$0.874564\pi$
$524$	−6.77509	+	1.07607i	−0.295971	+	0.0470085i
$525$		0			0
$526$	11.5302	−	35.5126i	0.502742	−	1.54842i
$527$		−	0.119677i		−	0.00521322i
$528$	−4.70018	+	1.53168i	−0.204549	+	0.0666577i
$529$	−21.7233			−0.944493
$530$	8.22100	−	25.3203i	0.357098	−	1.09984i
$531$	55.5471	−	55.5471i	2.41054	−	2.41054i
$532$		0			0
$533$	2.31559	+	2.31559i	0.100299	+	0.100299i
$534$	27.0031	+	52.9682i	1.16854	+	2.29216i
$535$			55.1702i			2.38522i
$536$	−24.2853	−	3.83025i	−1.04896	−	0.165442i
$537$	25.4050			1.09631
$538$	−7.09997	+	3.61955i	−0.306102	+	0.156050i
$539$		0			0
$540$	36.7495	+	26.6758i	1.58145	+	1.14794i
$541$	−0.909017	+	0.909017i	−0.0390817	+	0.0390817i	−0.726378	−	0.687296i	$-0.758798\pi$
$541$	−0.909017	+	0.909017i	−0.0390817	+	0.0390817i	0.687296	+	0.726378i	$0.258798\pi$
$542$	−4.37699	+	13.4809i	−0.188008	+	0.579055i
$543$			59.0302i			2.53323i
$544$	0.0180644	+	16.7042i	0.000774504	+	0.716188i
$545$		−	16.7637i		−	0.718076i
$546$		0			0
$547$	−12.1930	−	12.1930i	−0.521335	−	0.521335i	0.396640	−	0.917974i	$-0.370176\pi$
$547$	−12.1930	−	12.1930i	−0.521335	−	0.521335i	−0.917974	+	0.396640i	$0.870176\pi$
$548$	−22.2802	+	30.6940i	−0.951765	+	1.31118i
$549$	−35.8086	+	35.8086i	−1.52827	+	1.52827i
$550$	3.95321	−	2.01534i	0.168566	−	0.0859344i
$551$			0.501373i			0.0213592i
$552$	−1.43043	+	9.06944i	−0.0608830	+	0.386021i
$553$		0			0
$554$	−37.6101	+	19.1735i	−1.59790	+	0.814606i
$555$	−37.7032	+	37.7032i	−1.60041	+	1.60041i
$556$	−3.19140	−	20.0935i	−0.135346	−	0.852152i
$557$	18.4703	−	18.4703i	0.782612	−	0.782612i	−0.197659	−	0.980271i	$-0.563334\pi$
$557$	18.4703	−	18.4703i	0.782612	−	0.782612i	0.980271	+	0.197659i	$0.0633339\pi$
$558$	0.286418	+	0.0929942i	0.0121250	+	0.00393676i
$559$	−2.34419			−0.0991488
$560$		0			0
$561$	3.64940			0.154078
$562$	−6.05292	−	1.96526i	−0.255327	−	0.0828997i
$563$	9.45119	−	9.45119i	0.398320	−	0.398320i	−0.479320	−	0.877640i	$-0.659117\pi$
$563$	9.45119	−	9.45119i	0.398320	−	0.398320i	0.877640	+	0.479320i	$0.159117\pi$
$564$	19.2406	−	3.05594i	0.810175	−	0.128678i
$565$	−4.94260	+	4.94260i	−0.207937	+	0.207937i
$566$	3.47189	−	1.76996i	0.145935	−	0.0743971i
$567$		0			0
$568$	13.3606	−	9.72027i	0.560597	−	0.407853i
$569$		−	45.4239i		−	1.90427i	−0.305677	−	0.952135i	$-0.598883\pi$
$569$		−	45.4239i		−	1.90427i	0.305677	−	0.952135i	$-0.401117\pi$
$570$	0.749683	−	0.382187i	0.0314008	−	0.0160080i
$571$	−26.6515	+	26.6515i	−1.11533	+	1.11533i	−0.122914	+	0.992417i	$0.539224\pi$
$571$	−26.6515	+	26.6515i	−1.11533	+	1.11533i	−0.992417	+	0.122914i	$0.960776\pi$
$572$	1.50396	+	1.09170i	0.0628839	+	0.0456463i
$573$	22.0123	+	22.0123i	0.919577	+	0.919577i
$574$		0			0
$575$		−	8.24144i		−	0.343692i
$576$	−39.9915	−	12.9367i	−1.66631	−	0.539028i
$577$		−	39.8980i		−	1.66098i	−0.557036	−	0.830488i	$-0.688061\pi$
$577$		−	39.8980i		−	1.66098i	0.557036	−	0.830488i	$-0.311939\pi$
$578$	−3.61620	+	11.1377i	−0.150414	+	0.463268i
$579$	18.3582	−	18.3582i	0.762943	−	0.762943i
$580$	−34.9659	+	48.1703i	−1.45188	+	2.00016i
$581$		0			0
$582$	−29.6856	+	15.1337i	−1.23051	+	0.627310i
$583$	2.30945			0.0956478
$584$	−8.66336	+	6.30289i	−0.358492	+	0.260815i
$585$		−	39.7933i		−	1.64525i
$586$	−5.54565	−	10.8781i	−0.229089	−	0.449371i
$587$	9.68509	+	9.68509i	0.399746	+	0.399746i	0.878144	−	0.478397i	$-0.158782\pi$
$587$	9.68509	+	9.68509i	0.399746	+	0.399746i	−0.478397	+	0.878144i	$0.658782\pi$
$588$		0			0
$589$	0.00169276	−	0.00169276i	6.97491e−5	−	6.97491e-5i
$590$	22.8951	−	70.5157i	0.942575	−	2.90308i
$591$	22.2831			0.916604
$592$	9.59587	−	18.8733i	0.394388	−	0.775688i
$593$		−	1.04557i		−	0.0429366i	−0.999770	−	0.0214683i	$-0.993166\pi$
$593$		−	1.04557i		−	0.0429366i	0.999770	−	0.0214683i	$-0.00683410\pi$
$594$	−1.21655	+	3.74690i	−0.0499155	+	0.153737i
$595$		0			0
$596$	−4.91485	−	30.9445i	−0.201320	−	1.26754i
$597$	−11.5967	−	11.5967i	−0.474622	−	0.474622i
$598$	3.07512	−	1.56769i	0.125751	−	0.0641077i
$599$	−30.0044			−1.22595			−0.612974	−	0.790103i	$-0.710027\pi$
$599$	−30.0044			−1.22595			−0.612974	+	0.790103i	$0.710027\pi$
$600$	58.5470	+	9.23400i	2.39017	+	0.376977i
$601$	−14.5760			−0.594567			−0.297283	−	0.954789i	$-0.596081\pi$
$601$	−14.5760			−0.594567			−0.297283	+	0.954789i	$0.596081\pi$
$602$		0			0
$603$	−32.2929	+	32.2929i	−1.31507	+	1.31507i
$604$	−23.3354	−	16.9387i	−0.949503	−	0.689227i
$605$	−26.8136	−	26.8136i	−1.09013	−	1.09013i
$606$	−22.0506	−	7.15940i	−0.895744	−	0.290831i
$607$	7.12478			0.289186			0.144593	−	0.989491i	$-0.453813\pi$
$607$	7.12478			0.289186			0.144593	+	0.989491i	$0.453813\pi$
$608$	−0.236016	+	0.236527i	−0.00957172	+	0.00959244i
$609$		0			0
$610$	−14.7594	+	45.4581i	−0.597589	+	1.84055i
$611$	−5.17877	−	5.17877i	−0.209511	−	0.209511i
$612$	25.1110	+	18.2276i	1.01505	+	0.736808i
$613$	−20.6657	−	20.6657i	−0.834680	−	0.834680i	0.153473	−	0.988153i	$-0.450954\pi$
$613$	−20.6657	−	20.6657i	−0.834680	−	0.834680i	−0.988153	+	0.153473i	$0.950954\pi$
$614$	−1.04599	−	2.05177i	−0.0422127	−	0.0828029i
$615$			15.2714i			0.615804i
$616$		0			0
$617$			0.888703i			0.0357778i	0.999840	+	0.0178889i	$0.00569452\pi$
$617$			0.888703i			0.0357778i	−0.999840	+	0.0178889i	$0.994305\pi$
$618$	−42.4945	+	21.6636i	−1.70938	+	0.871438i
$619$	11.8560	+	11.8560i	0.476533	+	0.476533i	0.904021	−	0.427488i	$-0.140601\pi$
$619$	11.8560	+	11.8560i	0.476533	+	0.476533i	−0.427488	+	0.904021i	$0.640601\pi$
$620$	0.280689	−	0.0445813i	0.0112727	−	0.00179043i
$621$	5.17376	+	5.17376i	0.207616	+	0.207616i
$622$	−10.9603	−	3.55858i	−0.439466	−	0.142686i
$623$		0			0
$624$	7.69137	+	23.6021i	0.307901	+	0.944841i
$625$	8.26788			0.330715
$626$	−13.3224	+	41.0324i	−0.532471	+	1.63998i
$627$	0.0516187	+	0.0516187i	0.00206145	+	0.00206145i
$628$	5.92364	+	37.2960i	0.236379	+	1.48827i
$629$	−11.0523	+	11.0523i	−0.440684	+	0.440684i
$630$		0			0
$631$	14.8339			0.590527			0.295264	−	0.955416i	$-0.404593\pi$
$631$	14.8339			0.590527			0.295264	+	0.955416i	$0.404593\pi$
$632$	9.39958	+	12.9198i	0.373895	+	0.513921i
$633$	66.6445			2.64888
$634$	−9.04882	−	17.7498i	−0.359374	−	0.704935i
$635$	−22.9348	−	22.9348i	−0.910139	−	0.910139i
$636$	24.9647	+	18.1214i	0.989915	+	0.718561i
$637$		0			0
$638$	−4.91133	−	1.59461i	−0.194442	−	0.0631314i
$639$		−	30.6913i		−	1.21413i
$640$	−39.1711	+	6.26491i	−1.54838	+	0.247642i
$641$	−6.19324			−0.244618			−0.122309	−	0.992492i	$-0.539030\pi$
$641$	−6.19324			−0.244618			−0.122309	+	0.992492i	$0.539030\pi$
$642$	−60.8054	−	19.7423i	−2.39980	−	0.779168i
$643$	13.4723	−	13.4723i	0.531294	−	0.531294i	−0.389664	−	0.920957i	$-0.627409\pi$
$643$	13.4723	−	13.4723i	0.531294	−	0.531294i	0.920957	+	0.389664i	$0.127409\pi$
$644$		0			0
$645$	−7.73003	−	7.73003i	−0.304369	−	0.304369i
$646$	0.219761	−	0.112034i	0.00864639	−	0.00440791i
$647$		−	30.8102i		−	1.21127i	−0.795741	−	0.605637i	$-0.792918\pi$
$647$		−	30.8102i		−	1.21127i	0.795741	−	0.605637i	$-0.207082\pi$
$648$	−6.50096	+	4.72967i	−0.255382	+	0.185799i
$649$	6.43171			0.252467
$650$	−10.1201	−	19.8512i	−0.396943	−	0.778628i
$651$		0			0
$652$	3.08859	+	19.4461i	0.120958	+	0.761569i
$653$	−27.9329	+	27.9329i	−1.09310	+	1.09310i	−0.0979024	+	0.995196i	$0.531213\pi$
$653$	−27.9329	+	27.9329i	−1.09310	+	1.09310i	−0.995196	+	0.0979024i	$0.968787\pi$
$654$	18.4759	+	5.99877i	0.722466	+	0.234571i
$655$			12.0265i			0.469916i
$656$	−1.87888	−	5.76562i	−0.0733579	−	0.225110i
$657$			19.9011i			0.776415i
$658$		0			0
$659$	−26.1819	−	26.1819i	−1.01990	−	1.01990i	−0.999798	−	0.0201028i	$-0.993601\pi$
$659$	−26.1819	−	26.1819i	−1.01990	−	1.01990i	−0.0201028	−	0.999798i	$-0.506399\pi$
$660$	1.35945	+	8.55926i	0.0529165	+	0.333169i
$661$	−0.872506	+	0.872506i	−0.0339366	+	0.0339366i	−0.723871	−	0.689935i	$-0.757639\pi$
$661$	−0.872506	+	0.872506i	−0.0339366	+	0.0339366i	0.689935	+	0.723871i	$0.257639\pi$
$662$	13.5820	+	26.6420i	0.527881	+	1.03547i
$663$		−	18.3256i		−	0.711707i
$664$	5.97809	−	37.9033i	0.231995	−	1.47093i
$665$		0			0
$666$	−17.8628	−	35.0390i	−0.692170	−	1.35773i
$667$	−6.78162	+	6.78162i	−0.262585	+	0.262585i
$668$	16.0987	−	22.1781i	0.622876	−	0.858095i
$669$	5.58516	−	5.58516i	0.215935	−	0.215935i
$670$	−13.3103	+	40.9950i	−0.514221	+	1.58378i
$671$	−4.14622			−0.160063
$672$		0			0
$673$	−33.2182			−1.28047			−0.640233	−	0.768181i	$-0.721162\pi$
$673$	−33.2182			−1.28047			−0.640233	+	0.768181i	$0.721162\pi$
$674$	−8.52218	+	26.2479i	−0.328262	+	1.01103i
$675$	33.3988	−	33.3988i	1.28552	−	1.28552i
$676$	−9.79130	+	13.4888i	−0.376589	+	0.518801i
$677$	−12.9382	+	12.9382i	−0.497255	+	0.497255i	−0.910582	−	0.413328i	$-0.864366\pi$
$677$	−12.9382	+	12.9382i	−0.497255	+	0.497255i	0.413328	+	0.910582i	$0.364366\pi$
$678$	−3.67877	−	7.21613i	−0.141282	−	0.277134i
$679$		0			0
$680$	28.9272	+	4.56239i	1.10931	+	0.174960i
$681$			11.4800i			0.439916i
$682$	0.0111981	+	0.0219657i	0.000428797	+	0.000841112i
$683$	−4.31164	+	4.31164i	−0.164980	+	0.164980i	−0.784769	−	0.619789i	$-0.787218\pi$
$683$	−4.31164	+	4.31164i	−0.164980	+	0.164980i	0.619789	+	0.784769i	$0.287218\pi$
$684$	0.0973615	+	0.613000i	0.00372271	+	0.0234386i
$685$	47.0177	+	47.0177i	1.79645	+	1.79645i
$686$		0			0
$687$			4.45012i			0.169783i
$688$	3.86946	+	1.96737i	0.147522	+	0.0750054i
$689$		−	11.5970i		−	0.441811i
$690$	15.3098	+	4.97079i	0.582833	+	0.189235i
$691$	−2.26713	+	2.26713i	−0.0862458	+	0.0862458i	−0.748914	−	0.662668i	$-0.769424\pi$
$691$	−2.26713	+	2.26713i	−0.0862458	+	0.0862458i	0.662668	+	0.748914i	$0.269424\pi$
$692$	−3.09935	−	19.5139i	−0.117820	−	0.741806i
$693$		0			0
$694$	12.7300	+	24.9707i	0.483224	+	0.947874i
$695$	−35.6681			−1.35297
$696$	−40.5781	−	55.7749i	−1.53811	−	2.11414i
$697$			4.47665i			0.169565i
$698$	33.9607	−	17.3131i	1.28543	−	0.655309i
$699$	28.1946	+	28.1946i	1.06642	+	1.06642i
$700$		0			0
$701$	25.5995	−	25.5995i	0.966881	−	0.966881i	−0.0325880	−	0.999469i	$-0.510375\pi$
$701$	25.5995	−	25.5995i	0.966881	−	0.966881i	0.999469	+	0.0325880i	$0.0103749\pi$
$702$	18.8152	+	6.10893i	0.710134	+	0.230567i
$703$	−0.312656			−0.0117921
$704$	−1.56632	−	3.06423i	−0.0590328	−	0.115488i
$705$		−	34.1542i		−	1.28632i
$706$	−6.51742	−	2.11608i	−0.245287	−	0.0796398i
$707$		0			0
$708$	69.5254	+	50.4672i	2.61292	+	1.89667i
$709$	−15.4283	−	15.4283i	−0.579420	−	0.579420i	0.355323	−	0.934744i	$-0.384371\pi$
$709$	−15.4283	−	15.4283i	−0.579420	−	0.579420i	−0.934744	+	0.355323i	$0.884371\pi$
$710$	−13.1559	−	25.8060i	−0.493730	−	0.968483i
$711$	29.6788			1.11304
$712$	−33.4683	+	24.3493i	−1.25428	+	0.912529i
$713$	0.0457930			0.00171496
$714$		0			0
$715$	2.30380	−	2.30380i	0.0861572	−	0.0861572i
$716$	2.77418	+	17.4666i	0.103676	+	0.652756i
$717$	−22.4149	−	22.4149i	−0.837100	−	0.837100i
$718$	9.97658	−	30.7274i	0.372323	−	1.14673i
$719$	2.77578			0.103519			0.0517596	−	0.998660i	$-0.483517\pi$
$719$	2.77578			0.103519			0.0517596	+	0.998660i	$0.483517\pi$
$720$	−33.3967	+	65.6850i	−1.24462	+	2.44794i
$721$		0			0
$722$	−25.5520	−	8.29625i	−0.950949	−	0.308755i
$723$	26.1547	+	26.1547i	0.972703	+	0.972703i
$724$	−40.5847	+	6.44599i	−1.50832	+	0.239563i
$725$	43.7782	+	43.7782i	1.62588	+	1.62588i
$726$	39.1475	−	19.9573i	1.45290	−	0.740686i
$727$		−	37.3773i		−	1.38625i	−0.720818	−	0.693124i	$-0.756234\pi$
$727$		−	37.3773i		−	1.38625i	0.720818	−	0.693124i	$-0.243766\pi$
$728$		0			0
$729$		−	40.8792i		−	1.51404i
$730$	8.53062	+	16.7333i	0.315732	+	0.619328i
$731$	−2.26597	−	2.26597i	−0.0838100	−	0.0838100i
$732$	−44.8197	−	32.5338i	−1.65659	−	1.20249i
$733$	13.9401	+	13.9401i	0.514891	+	0.514891i	0.916021	−	0.401130i	$-0.131382\pi$
$733$	13.9401	+	13.9401i	0.514891	+	0.514891i	−0.401130	+	0.916021i	$0.631382\pi$
$734$	6.15686	−	18.9628i	0.227254	−	0.699931i
$735$		0			0
$736$	−6.39167	+	0.00691212i	−0.235600	+	0.000254784i
$737$	−3.73914			−0.137733
$738$	−10.7138	−	3.47855i	−0.394379	−	0.128047i
$739$	−23.1487	−	23.1487i	−0.851538	−	0.851538i	0.138784	−	0.990323i	$-0.455680\pi$
$739$	−23.1487	−	23.1487i	−0.851538	−	0.851538i	−0.990323	+	0.138784i	$0.955680\pi$
$740$	−30.0390	−	21.8048i	−1.10426	−	0.801560i
$741$	0.259205	−	0.259205i	0.00952214	−	0.00952214i
$742$		0			0
$743$	10.8545			0.398211			0.199106	−	0.979978i	$-0.436196\pi$
$743$	10.8545			0.398211			0.199106	+	0.979978i	$0.436196\pi$
$744$	−0.0513081	+	0.325312i	−0.00188105	+	0.0119265i
$745$	−54.9300			−2.01248
$746$	31.8140	−	16.2187i	1.16479	−	0.593810i
$747$	−50.4012	−	50.4012i	−1.84408	−	1.84408i
$748$	0.398508	+	2.50905i	0.0145709	+	0.0917401i
$749$		0			0
$750$	10.0919	−	31.0826i	0.368504	−	1.13497i
$751$		−	38.6761i		−	1.41131i	−0.708556	−	0.705655i	$-0.750653\pi$
$751$		−	38.6761i		−	1.41131i	0.708556	−	0.705655i	$-0.249347\pi$
$752$	4.20207	+	12.8947i	0.153234	+	0.470221i
$753$	65.9732			2.40420
$754$	−8.00742	+	24.6624i	−0.291613	+	0.898153i
$755$	−35.7455	+	35.7455i	−1.30091	+	1.30091i
$756$		0			0
$757$	−25.9813	−	25.9813i	−0.944307	−	0.944307i	0.0542223	−	0.998529i	$-0.482732\pi$
$757$	−25.9813	−	25.9813i	−0.944307	−	0.944307i	−0.998529	+	0.0542223i	$0.982732\pi$
$758$	−11.9872	−	23.5135i	−0.435393	−	0.854050i
$759$			1.39640i			0.0506861i
$760$	0.344627	+	0.473691i	0.0125009	+	0.0171826i
$761$	−19.1517			−0.694248			−0.347124	−	0.937819i	$-0.612842\pi$
$761$	−19.1517			−0.694248			−0.347124	+	0.937819i	$0.612842\pi$
$762$	33.4844	−	17.0703i	1.21301	−	0.618392i
$763$		0			0
$764$	−12.7303	+	17.5377i	−0.460566	+	0.634492i
$765$	38.4655	−	38.4655i	1.39072	−	1.39072i
$766$	9.85344	−	30.3481i	0.356019	−	1.09652i
$767$		−	32.2971i		−	1.16618i
$768$	7.11235	−	45.4140i	0.256645	−	1.63874i
$769$		−	24.3826i		−	0.879260i	−0.898179	−	0.439630i	$-0.855110\pi$
$769$		−	24.3826i		−	0.879260i	0.898179	−	0.439630i	$-0.144890\pi$
$770$		0			0
$771$	−10.5406	−	10.5406i	−0.379610	−	0.379610i
$772$	14.6264	+	10.6171i	0.526417	+	0.382116i
$773$	−6.73822	+	6.73822i	−0.242357	+	0.242357i	−0.817825	−	0.575468i	$-0.804820\pi$
$773$	−6.73822	+	6.73822i	−0.242357	+	0.242357i	0.575468	+	0.817825i	$0.304820\pi$
$774$	7.18381	−	3.66229i	0.258217	−	0.131638i
$775$		−	0.295613i		−	0.0106187i
$776$	−13.6464	−	18.7570i	−0.489876	−	0.673338i
$777$		0			0
$778$	21.1720	−	10.7934i	0.759051	−	0.386963i
$779$	−0.0633197	+	0.0633197i	−0.00226866	+	0.00226866i
$780$	42.9806	−	6.82653i	1.53895	−	0.244429i
$781$	1.77685	−	1.77685i	0.0635807	−	0.0635807i
$782$	4.48789	+	1.45713i	0.160487	+	0.0521069i
$783$	−54.9656			−1.96431
$784$		0			0
$785$	66.2045			2.36294
$786$	−13.2550	−	4.30363i	−0.472789	−	0.153505i
$787$	−9.35245	+	9.35245i	−0.333379	+	0.333379i	−0.853868	−	0.520489i	$-0.825750\pi$
$787$	−9.35245	+	9.35245i	−0.333379	+	0.333379i	0.520489	+	0.853868i	$0.325750\pi$
$788$	2.43327	+	15.3202i	0.0866817	+	0.545759i
$789$	53.6348	−	53.6348i	1.90945	−	1.90945i
$790$	24.9546	−	12.7218i	0.887846	−	0.452622i
$791$		0			0
$792$	−6.31446	−	0.995913i	−0.224375	−	0.0353882i
$793$			20.8204i			0.739353i
$794$	29.7316	−	15.1571i	1.05514	−	0.537906i
$795$	38.2414	−	38.2414i	1.35628	−	1.35628i
$796$	6.70669	−	9.23936i	0.237712	−	0.327481i
$797$	7.68794	+	7.68794i	0.272321	+	0.272321i	0.830034	−	0.557713i	$-0.188321\pi$
$797$	7.68794	+	7.68794i	0.272321	+	0.272321i	−0.557713	+	0.830034i	$0.688321\pi$
$798$		0			0
$799$		−	10.0119i		−	0.354197i
$800$	0.0446206	+	41.2609i	0.00157758	+	1.45879i
$801$			76.8818i			2.71649i
$802$	−4.02330	+	12.3916i	−0.142068	+	0.437561i
$803$	−1.15216	+	1.15216i	−0.0406588	+	0.0406588i
$804$	−40.4193	−	29.3396i	−1.42548	−	1.03473i
$805$		0			0
$806$	0.110302	−	0.0562316i	0.00388522	−	0.00198067i
$807$	−16.1898			−0.569906
$808$	2.51438	−	15.9421i	0.0884557	−	0.560842i
$809$		−	21.0650i		−	0.740607i	−0.928911	−	0.370304i	$-0.879254\pi$
$809$		−	21.0650i		−	0.740607i	0.928911	−	0.370304i	$-0.120746\pi$
$810$	6.40135	+	12.5566i	0.224921	+	0.441195i
$811$	−30.2858	−	30.2858i	−1.06348	−	1.06348i	−0.997844	−	0.0656346i	$-0.979093\pi$
$811$	−30.2858	−	30.2858i	−1.06348	−	1.06348i	−0.0656346	−	0.997844i	$-0.520907\pi$
$812$		0			0
$813$	−20.3603	+	20.3603i	−0.714067	+	0.714067i
$814$	0.994403	−	3.06271i	0.0348538	−	0.107348i
$815$	34.5191			1.20915
$816$	−15.3798	+	30.2493i	−0.538402	+	1.05894i
$817$		−	0.0641018i		−	0.00224264i
$818$	−9.56259	+	29.4523i	−0.334348	+	1.02978i
$819$		0			0
$820$	−10.4995	+	1.66761i	−0.366658	+	0.0582355i
$821$	−17.4598	−	17.4598i	−0.609353	−	0.609353i	0.333424	−	0.942777i	$-0.391796\pi$
$821$	−17.4598	−	17.4598i	−0.609353	−	0.609353i	−0.942777	+	0.333424i	$0.891796\pi$
$822$	−68.6451	+	34.9951i	−2.39427	+	1.22060i
$823$	−7.88133			−0.274726			−0.137363	−	0.990521i	$-0.543863\pi$
$823$	−7.88133			−0.274726			−0.137363	+	0.990521i	$0.543863\pi$
$824$	−19.5346	−	26.8504i	−0.680520	−	0.935378i
$825$	9.01434			0.313839
$826$		0			0
$827$	7.66587	−	7.66587i	0.266569	−	0.266569i	−0.561147	−	0.827716i	$-0.689640\pi$
$827$	7.66587	−	7.66587i	0.266569	−	0.266569i	0.827716	+	0.561147i	$0.189640\pi$
$828$	−6.97457	+	9.60842i	−0.242383	+	0.333916i
$829$	27.0513	+	27.0513i	0.939530	+	0.939530i	0.998273	−	0.0587428i	$-0.0187092\pi$
$829$	27.0513	+	27.0513i	0.939530	+	0.939530i	−0.0587428	+	0.998273i	$0.518709\pi$
$830$	−63.9831	−	20.7741i	−2.22089	−	0.721079i
$831$	−85.7606			−2.97500
$832$	−15.3872	+	7.86532i	−0.533454	+	0.272681i
$833$		0			0
$834$	12.7636	−	39.3114i	0.441969	−	1.36124i
$835$	−33.9727	−	33.9727i	−1.17568	−	1.17568i
$836$	−0.0298525	+	0.0411258i	−0.00103247	+	0.00142237i
$837$	0.185578	+	0.185578i	0.00641451	+	0.00641451i
$838$	−18.4597	−	36.2099i	−0.637681	−	1.25085i
$839$			41.1374i			1.42022i	0.704090	+	0.710111i	$0.251355\pi$
$839$			41.1374i			1.42022i	−0.704090	+	0.710111i	$0.748645\pi$
$840$		0			0
$841$		−	43.0474i		−	1.48439i
$842$	42.3999	−	21.6154i	1.46120	−	0.744916i
$843$	−9.14175	−	9.14175i	−0.314859	−	0.314859i
$844$	7.27745	+	45.8198i	0.250500	+	1.57718i
$845$	20.6624	+	20.6624i	0.710809	+	0.710809i
$846$	23.9611	+	7.77970i	0.823800	+	0.267472i
$847$		0			0
$848$	−9.73283	+	19.1427i	−0.334227	+	0.657362i
$849$	7.91681			0.271704
$850$	9.40640	−	28.9712i	0.322637	−	0.993705i
$851$	−4.22902	−	4.22902i	−0.144969	−	0.144969i
$852$	33.1496	−	5.26509i	1.13569	−	0.180379i
$853$	−31.1520	+	31.1520i	−1.06663	+	1.06663i	−0.0690094	+	0.997616i	$0.521984\pi$
$853$	−31.1520	+	31.1520i	−1.06663	+	1.06663i	−0.997616	+	0.0690094i	$0.978016\pi$
$854$		0			0
$855$	1.08814			0.0372137
$856$	6.93351	−	43.9611i	0.236983	−	1.50256i
$857$	−4.38451			−0.149772			−0.0748861	−	0.997192i	$-0.523859\pi$
$857$	−4.38451			−0.149772			−0.0748861	+	0.997192i	$0.523859\pi$
$858$	1.71471	+	3.36351i	0.0585393	+	0.114828i
$859$	33.9059	+	33.9059i	1.15686	+	1.15686i	0.985148	+	0.171708i	$0.0549285\pi$
$859$	33.9059	+	33.9059i	1.15686	+	1.15686i	0.171708	+	0.985148i	$0.445071\pi$
$860$	4.47048	−	6.15869i	0.152442	−	0.210010i
$861$		0			0
$862$	20.1240	+	6.53389i	0.685428	+	0.222545i
$863$			17.3441i			0.590402i	0.955435	+	0.295201i	$0.0953866\pi$
$863$			17.3441i			0.590402i	−0.955435	+	0.295201i	$0.904613\pi$
$864$	−25.9305	−	25.8745i	−0.882173	−	0.880267i
$865$	−34.6393			−1.17777
$866$	30.3373	+	9.84994i	1.03090	+	0.334715i
$867$	−16.8214	+	16.8214i	−0.571284	+	0.571284i
$868$		0			0
$869$	1.71823	+	1.71823i	0.0582869	+	0.0582869i
$870$	−107.730	+	54.9203i	−3.65237	+	1.86197i
$871$			18.7762i			0.636208i
$872$	−2.10677	+	13.3577i	−0.0713442	+	0.452349i
$873$	−43.0878			−1.45830
$874$	0.0428684	+	0.0840890i	0.00145004	+	0.00284435i
$875$		0			0
$876$	−21.4951	+	3.41403i	−0.726253	+	0.115349i
$877$	5.51050	−	5.51050i	0.186076	−	0.186076i	−0.607921	−	0.793997i	$-0.707996\pi$
$877$	5.51050	−	5.51050i	0.186076	−	0.186076i	0.793997	+	0.607921i	$0.207996\pi$
$878$	−7.21837	−	2.34366i	−0.243608	−	0.0790948i
$879$		−	24.8049i		−	0.836649i
$880$	−5.73626	+	1.86931i	−0.193369	+	0.0630145i
$881$		−	7.64271i		−	0.257489i	−0.991678	−	0.128745i	$-0.958905\pi$
$881$		−	7.64271i		−	0.257489i	0.991678	−	0.128745i	$-0.0410948\pi$
$882$		0			0
$883$	15.7127	+	15.7127i	0.528776	+	0.528776i	0.920207	−	0.391431i	$-0.128020\pi$
$883$	15.7127	+	15.7127i	0.528776	+	0.528776i	−0.391431	+	0.920207i	$0.628020\pi$
$884$	12.5993	−	2.00112i	0.423761	−	0.0673050i
$885$	106.500	−	106.500i	3.57997	−	3.57997i
$886$	6.09089	+	11.9477i	0.204628	+	0.401390i
$887$			21.9363i			0.736549i	0.929717	+	0.368275i	$0.120051\pi$
$887$			21.9363i			0.736549i	−0.929717	+	0.368275i	$0.879949\pi$
$888$	34.7812	−	25.3046i	1.16718	−	0.849165i
$889$		0			0
$890$	32.9555	+	64.6442i	1.10467	+	2.16688i
$891$	−0.864576	+	0.864576i	−0.0289644	+	0.0289644i
$892$	4.44983	+	3.23005i	0.148991	+	0.108150i
$893$	0.141613	−	0.141613i	0.00473890	−	0.00473890i
$894$	19.6564	−	60.5406i	0.657407	−	2.02478i
$895$	31.0051			1.03639
$896$		0			0
$897$	7.01207			0.234126
$898$	−6.58853	+	20.2924i	−0.219862	+	0.677165i
$899$	−0.243250	+	0.243250i	−0.00811286	+	0.00811286i
$900$	62.0264	+	45.0238i	2.06755	+	1.50079i
$901$	11.2100	−	11.2100i	0.373461	−	0.373461i
$902$	−0.418877	−	0.821653i	−0.0139471	−	0.0273581i
$903$		0			0
$904$	4.55955	−	3.31723i	0.151648	−	0.110329i
$905$			72.0425i			2.39477i
$906$	−26.6053	−	52.1880i	−0.883902	−	1.73383i
$907$	−5.23487	+	5.23487i	−0.173821	+	0.173821i	−0.788656	−	0.614835i	$-0.789223\pi$
$907$	−5.23487	+	5.23487i	−0.173821	+	0.173821i	0.614835	+	0.788656i	$0.289223\pi$
$908$	−7.89281	+	1.25360i	−0.261932	+	0.0416021i
$909$	−21.1987	−	21.1987i	−0.703118	−	0.703118i
$910$		0			0
$911$			34.0670i			1.12869i	0.825539	+	0.564344i	$0.190871\pi$
$911$			34.0670i			1.12869i	−0.825539	+	0.564344i	$0.809129\pi$
$912$	−0.645398	+	0.210320i	−0.0213713	+	0.00696439i
$913$		−	5.83588i		−	0.193139i
$914$	17.8021	+	5.77998i	0.588840	+	0.191185i
$915$	−68.6557	+	68.6557i	−2.26969	+	2.26969i
$916$	−3.05957	+	0.485945i	−0.101091	+	0.0160561i
$917$		0			0
$918$	12.2823	+	24.0925i	0.405376	+	0.795170i
$919$	6.96737			0.229832			0.114916	−	0.993375i	$-0.463340\pi$
$919$	6.96737			0.229832			0.114916	+	0.993375i	$0.463340\pi$
$920$	−1.74574	+	11.0687i	−0.0575554	+	0.364923i
$921$		−	4.67857i		−	0.154164i
$922$	−3.83359	+	1.95436i	−0.126253	+	0.0643633i
$923$	−8.92251	−	8.92251i	−0.293688	−	0.293688i
$924$		0			0
$925$	−27.3001	+	27.3001i	−0.897622	+	0.897622i
$926$	−22.0323	−	7.15345i	−0.724025	−	0.235077i
$927$	−61.6796			−2.02582
$928$	33.9156	−	33.9890i	1.11333	−	1.11574i
$929$			30.9563i			1.01564i	0.861462	+	0.507822i	$0.169549\pi$
$929$			30.9563i			1.01564i	−0.861462	+	0.507822i	$0.830451\pi$
$930$	0.549148	+	0.178298i	0.0180073	+	0.00584661i
$931$		0			0
$932$	−16.3057	+	22.4633i	−0.534111	+	0.735810i
$933$	−16.5533	−	16.5533i	−0.541932	−	0.541932i
$934$	25.2175	+	49.4657i	0.825142	+	1.61857i
$935$	4.45385			0.145657
$936$	−5.00101	+	31.7083i	−0.163463	+	1.03642i
$937$	30.2161			0.987116			0.493558	−	0.869713i	$-0.335696\pi$
$937$	30.2161			0.987116			0.493558	+	0.869713i	$0.335696\pi$
$938$		0			0
$939$	−61.9714	+	61.9714i	−2.02236	+	2.02236i
$940$	23.4819	−	3.72958i	0.765894	−	0.121645i
$941$	30.2902	+	30.2902i	0.987431	+	0.987431i	0.999922	−	0.0124906i	$-0.00397599\pi$
$941$	30.2902	+	30.2902i	0.987431	+	0.987431i	−0.0124906	+	0.999922i	$0.503976\pi$
$942$	−23.6909	+	72.9668i	−0.771891	+	2.37739i
$943$	−1.71294			−0.0557809
$944$	−27.1054	+	53.3114i	−0.882207	+	1.73514i
$945$		0			0
$946$	0.627926	+	0.203875i	0.0204156	+	0.00662856i
$947$	17.2108	+	17.2108i	0.559277	+	0.559277i	0.929102	−	0.369825i	$-0.120582\pi$
$947$	17.2108	+	17.2108i	0.559277	+	0.559277i	−0.369825	+	0.929102i	$0.620582\pi$
$948$	5.09138	+	32.0560i	0.165360	+	1.04113i
$949$	5.78560	+	5.78560i	0.187809	+	0.187809i
$950$	0.542830	−	0.276733i	0.0176117	−	0.00897842i
$951$		−	40.4741i		−	1.31246i
$952$		0			0
$953$			33.5515i			1.08684i	0.839461	+	0.543420i	$0.182871\pi$
$953$			33.5515i			1.08684i	−0.839461	+	0.543420i	$0.817129\pi$
$954$	18.1178	+	35.5392i	0.586585	+	1.15062i
$955$	26.8646	+	26.8646i	0.869317	+	0.869317i
$956$	12.9631	−	17.8585i	0.419258	−	0.577584i
$957$	−7.41762	−	7.41762i	−0.239777	−	0.239777i
$958$	−10.2782	+	31.6562i	−0.332072	+	1.02277i
$959$		0			0
$960$	−76.6755	−	24.8034i	−2.47469	−	0.800527i
$961$	−30.9984			−0.999947
$962$	−15.3795	−	4.99343i	−0.495855	−	0.160995i
$963$	−58.4564	−	58.4564i	−1.88373	−	1.88373i
$964$	−15.1260	+	20.8380i	−0.487174	+	0.671148i
$965$	22.4050	−	22.4050i	0.721243	−	0.721243i
$966$		0			0
$967$	27.3461			0.879390			0.439695	−	0.898147i	$-0.355087\pi$
$967$	27.3461			0.879390			0.439695	+	0.898147i	$0.355087\pi$
$968$	17.9960	+	24.7356i	0.578413	+	0.795032i
$969$	0.501112			0.0160980
$970$	−36.2293	+	18.4696i	−1.16325	+	0.593024i
$971$	7.68319	+	7.68319i	0.246565	+	0.246565i	0.819560	−	0.572994i	$-0.194218\pi$
$971$	7.68319	+	7.68319i	0.246565	+	0.246565i	−0.572994	+	0.819560i	$0.694218\pi$
$972$	22.2429	−	3.53279i	0.713441	−	0.113314i
$973$		0			0
$974$	−4.79465	+	14.7673i	−0.153631	+	0.473175i
$975$		−	45.2658i		−	1.44967i
$976$	17.4736	−	34.3673i	0.559316	−	1.10007i
$977$	−16.9769			−0.543138			−0.271569	−	0.962419i	$-0.587542\pi$
$977$	−16.9769			−0.543138			−0.271569	+	0.962419i	$0.587542\pi$
$978$	−12.3524	+	38.0449i	−0.394987	+	1.21654i
$979$	−4.45101	+	4.45101i	−0.142255	+	0.142255i
$980$		0			0
$981$	17.7622	+	17.7622i	0.567103	+	0.567103i
$982$	5.35027	+	10.4949i	0.170734	+	0.334905i
$983$		−	32.9773i		−	1.05181i	−0.850542	−	0.525907i	$-0.823726\pi$
$983$		−	32.9773i		−	1.05181i	0.850542	−	0.525907i	$-0.176274\pi$
$984$	1.91924	−	12.1687i	0.0611830	−	0.387923i
$985$	27.1950			0.866506
$986$	−31.5798	+	16.0993i	−1.00570	+	0.512706i
$987$		0			0
$988$	0.206515	+	0.149905i	0.00657011	+	0.00476912i
$989$	0.867047	−	0.867047i	0.0275705	−	0.0275705i
$990$	−3.46084	+	10.6592i	−0.109993	+	0.338772i
$991$		−	38.8653i		−	1.23460i	−0.786729	−	0.617298i	$-0.788227\pi$
$991$		−	38.8653i		−	1.23460i	0.786729	−	0.617298i	$-0.211773\pi$
$992$	−0.229263		0.000247931i	−0.00727911		7.87182e-6i
$993$			60.7506i			1.92786i
$994$		0			0
$995$	−14.1530	−	14.1530i	−0.448681	−	0.448681i
$996$	45.7920	−	63.0846i	1.45097	−	1.99891i
$997$	12.1577	−	12.1577i	0.385038	−	0.385038i	−0.487875	−	0.872913i	$-0.662228\pi$
$997$	12.1577	−	12.1577i	0.385038	−	0.385038i	0.872913	+	0.487875i	$0.162228\pi$
$998$	−17.5291	+	8.93629i	−0.554873	+	0.282873i
$999$		−	34.2766i		−	1.08446i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	784.2.j.a.587.11		56
7.2	even	3		784.2.w.f.619.14		56
7.3	odd	6		784.2.w.f.411.4		56
7.4	even	3		112.2.v.a.75.4	yes	56
7.5	odd	6		112.2.v.a.59.14	yes	56
7.6	odd	2	inner	784.2.j.a.587.12		56
16.3	odd	4	inner	784.2.j.a.195.12		56
28.11	odd	6		448.2.z.a.271.1		56
28.19	even	6		448.2.z.a.143.1		56
56.5	odd	6		896.2.z.b.31.1		56
56.11	odd	6		896.2.z.a.159.14		56
56.19	even	6		896.2.z.a.31.14		56
56.53	even	6		896.2.z.b.159.1		56
112.3	even	12		784.2.w.f.19.14		56
112.5	odd	12		896.2.z.a.479.14		56
112.11	odd	12		896.2.z.b.607.1		56
112.19	even	12		112.2.v.a.3.4	✓	56
112.51	odd	12		784.2.w.f.227.4		56
112.53	even	12		896.2.z.a.607.14		56
112.61	odd	12		448.2.z.a.367.1		56
112.67	odd	12		112.2.v.a.19.14	yes	56
112.75	even	12		896.2.z.b.479.1		56
112.83	even	4	inner	784.2.j.a.195.11		56
112.109	even	12		448.2.z.a.47.1		56

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
112.2.v.a.3.4	✓	56	112.19	even	12
112.2.v.a.19.14	yes	56	112.67	odd	12
112.2.v.a.59.14	yes	56	7.5	odd	6
112.2.v.a.75.4	yes	56	7.4	even	3
448.2.z.a.47.1		56	112.109	even	12
448.2.z.a.143.1		56	28.19	even	6
448.2.z.a.271.1		56	28.11	odd	6
448.2.z.a.367.1		56	112.61	odd	12
784.2.j.a.195.11		56	112.83	even	4	inner
784.2.j.a.195.12		56	16.3	odd	4	inner
784.2.j.a.587.11		56	1.1	even	1	trivial
784.2.j.a.587.12		56	7.6	odd	2	inner
784.2.w.f.19.14		56	112.3	even	12
784.2.w.f.227.4		56	112.51	odd	12
784.2.w.f.411.4		56	7.3	odd	6
784.2.w.f.619.14		56	7.2	even	3
896.2.z.a.31.14		56	56.19	even	6
896.2.z.a.159.14		56	56.11	odd	6
896.2.z.a.479.14		56	112.5	odd	12
896.2.z.a.607.14		56	112.53	even	12
896.2.z.b.31.1		56	56.5	odd	6
896.2.z.b.159.1		56	56.53	even	6
896.2.z.b.479.1		56	112.75	even	12
896.2.z.b.607.1		56	112.11	odd	12

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 784 = 2^{4} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	784.j (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.436725 + 1.34509i) q^{2} +(-2.03150 + 2.03150i) q^{3} +(-1.61854 - 1.17487i) q^{4} +(-2.47931 + 2.47931i) q^{5} +(-1.84535 - 3.61976i) q^{6} +(2.28717 - 1.66399i) q^{8} -5.25398i q^{9} +O(q^{10})\)	\(q+(-0.436725 + 1.34509i) q^{2} +(-2.03150 + 2.03150i) q^{3} +(-1.61854 - 1.17487i) q^{4} +(-2.47931 + 2.47931i) q^{5} +(-1.84535 - 3.61976i) q^{6} +(2.28717 - 1.66399i) q^{8} -5.25398i q^{9} +(-2.25212 - 4.41768i) q^{10} +(0.304175 - 0.304175i) q^{11} +(5.67482 - 0.901319i) q^{12} +(-1.52743 - 1.52743i) q^{13} -10.0734i q^{15} +(1.23936 + 3.80316i) q^{16} -2.95292i q^{17} +(7.06708 + 2.29454i) q^{18} +(0.0417673 - 0.0417673i) q^{19} +(6.92574 - 1.10000i) q^{20} +(0.276302 + 0.541984i) q^{22} +1.12990 q^{23} +(-1.26598 + 8.02678i) q^{24} -7.29397i q^{25} +(2.72159 - 1.38746i) q^{26} +(4.57896 + 4.57896i) q^{27} +(-6.00198 + 6.00198i) q^{29} +(13.5497 + 4.39932i) q^{30} +0.0405284 q^{31} +(-5.65685 + 0.00611747i) q^{32} +1.23586i q^{33} +(3.97195 + 1.28961i) q^{34} +(-6.17275 + 8.50379i) q^{36} +(-3.74283 - 3.74283i) q^{37} +(0.0379400 + 0.0744217i) q^{38} +6.20593 q^{39} +(-1.54504 + 9.79615i) q^{40} -1.51601 q^{41} +(0.767367 - 0.767367i) q^{43} +(-0.849686 + 0.134954i) q^{44} +(13.0262 + 13.0262i) q^{45} +(-0.493455 + 1.51982i) q^{46} +3.39052 q^{47} +(-10.2439 - 5.20835i) q^{48} +(9.81105 + 3.18546i) q^{50} +(5.99885 + 5.99885i) q^{51} +(0.677676 + 4.26673i) q^{52} +(3.79626 + 3.79626i) q^{53} +(-8.15886 + 4.15937i) q^{54} +1.50829i q^{55} +0.169701i q^{57} +(-5.45199 - 10.6944i) q^{58} +(10.5724 + 10.5724i) q^{59} +(-11.8350 + 16.3043i) q^{60} +(-6.81551 - 6.81551i) q^{61} +(-0.0176998 + 0.0545144i) q^{62} +(2.46226 - 7.61165i) q^{64} +7.57393 q^{65} +(-1.66235 - 0.539732i) q^{66} +(-6.14636 - 6.14636i) q^{67} +(-3.46930 + 4.77942i) q^{68} +(-2.29539 + 2.29539i) q^{69} +5.84154 q^{71} +(-8.74258 - 12.0167i) q^{72} -3.78781 q^{73} +(6.66905 - 3.39987i) q^{74} +(14.8177 + 14.8177i) q^{75} +(-0.116673 + 0.0185310i) q^{76} +(-2.71029 + 8.34754i) q^{78} +5.64881i q^{79} +(-12.5020 - 6.35645i) q^{80} -2.84236 q^{81} +(0.662080 - 2.03917i) q^{82} +(9.59296 - 9.59296i) q^{83} +(7.32120 + 7.32120i) q^{85} +(0.697051 + 1.36731i) q^{86} -24.3860i q^{87} +(0.189554 - 1.20184i) q^{88} -14.6331 q^{89} +(-23.2104 + 11.8326i) q^{90} +(-1.82879 - 1.32748i) q^{92} +(-0.0823334 + 0.0823334i) q^{93} +(-1.48073 + 4.56056i) q^{94} +0.207108i q^{95} +(11.4795 - 11.5043i) q^{96} -8.20099i q^{97} +(-1.59813 - 1.59813i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 56 q + 4 q^{2} + 8 q^{4} + 4 q^{8}+O(q^{10}) \) 56 * q + 4 * q^2 + 8 * q^4 + 4 * q^8	\( 56 q + 4 q^{2} + 8 q^{4} + 4 q^{8} - 4 q^{11} - 16 q^{16} + 60 q^{18} - 28 q^{22} + 24 q^{23} - 24 q^{29} + 36 q^{30} + 24 q^{32} + 16 q^{36} - 12 q^{37} + 8 q^{39} - 52 q^{44} - 32 q^{46} + 68 q^{51} - 12 q^{53} - 36 q^{58} - 156 q^{60} - 16 q^{64} + 8 q^{65} - 12 q^{67} - 80 q^{71} + 8 q^{72} - 124 q^{74} + 4 q^{78} + 16 q^{81} - 28 q^{85} - 60 q^{88} - 20 q^{92} - 20 q^{93} - 16 q^{99}+O(q^{100}) \) 56 * q + 4 * q^2 + 8 * q^4 + 4 * q^8 - 4 * q^11 - 16 * q^16 + 60 * q^18 - 28 * q^22 + 24 * q^23 - 24 * q^29 + 36 * q^30 + 24 * q^32 + 16 * q^36 - 12 * q^37 + 8 * q^39 - 52 * q^44 - 32 * q^46 + 68 * q^51 - 12 * q^53 - 36 * q^58 - 156 * q^60 - 16 * q^64 + 8 * q^65 - 12 * q^67 - 80 * q^71 + 8 * q^72 - 124 * q^74 + 4 * q^78 + 16 * q^81 - 28 * q^85 - 60 * q^88 - 20 * q^92 - 20 * q^93 - 16 * q^99

Introduction

L-functions

Modular forms

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