LMFDB - Embedded newform 2070.2.j.i.737.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2070,2,Mod(323,2070)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2070, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 3, 0]))

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

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

chi := DirichletCharacter("2070.323");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 2070 = 2 \cdot 3^{2} \cdot 5 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2070.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:	$16.5290332184$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} + 28x^{14} + 290x^{12} + 1396x^{10} + 3263x^{8} + 3508x^{6} + 1442x^{4} + 128x^{2} + 1 $ x^16 + 28x^14 + 290x^12 + 1396x^10 + 3263x^8 + 3508x^6 + 1442x^4 + 128*x^2 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{6} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			737.5
Root			$1.67137i$ of defining polynomial
Character	$\chi$	$=$	2070.737
Dual form			2070.2.j.i.323.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.707107 - 0.707107i) q^{2} -1.00000i q^{4} +(-1.80260 - 1.32312i) q^{5} +(0.949464 + 0.949464i) q^{7} +(-0.707107 - 0.707107i) q^{8} +O(q^{10})$	\(q+(0.707107 - 0.707107i) q^{2} -1.00000i q^{4} +(-1.80260 - 1.32312i) q^{5} +(0.949464 + 0.949464i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(-2.21021 + 0.339045i) q^{10} -2.64623i q^{11} +(2.00000 - 2.00000i) q^{13} +1.34274 q^{14} -1.00000 q^{16} +(4.94794 - 4.94794i) q^{17} +2.42043i q^{19} +(-1.32312 + 1.80260i) q^{20} +(-1.87117 - 1.87117i) q^{22} +(0.707107 + 0.707107i) q^{23} +(1.49872 + 4.77010i) q^{25} -2.82843i q^{26} +(0.949464 - 0.949464i) q^{28} -0.383781 q^{29} -6.99745 q^{31} +(-0.707107 + 0.707107i) q^{32} -6.99745i q^{34} +(-0.455250 - 2.96775i) q^{35} +(-0.820634 - 0.820634i) q^{37} +(1.71150 + 1.71150i) q^{38} +(0.339045 + 2.21021i) q^{40} -5.41240i q^{41} +(-2.82063 + 2.82063i) q^{43} -2.64623 q^{44} +1.00000 q^{46} +(-2.19098 + 2.19098i) q^{47} -5.19704i q^{49} +(4.43273 + 2.31321i) q^{50} +(-2.00000 - 2.00000i) q^{52} +(-7.11469 - 7.11469i) q^{53} +(-3.50128 + 4.77010i) q^{55} -1.34274i q^{56} +(-0.271374 + 0.271374i) q^{58} -1.93732 q^{59} -8.31936 q^{61} +(-4.94794 + 4.94794i) q^{62} +1.00000i q^{64} +(-6.25143 + 0.958963i) q^{65} +(-2.59724 - 2.59724i) q^{67} +(-4.94794 - 4.94794i) q^{68} +(-2.42043 - 1.77661i) q^{70} -8.76755i q^{71} +(8.26882 - 8.26882i) q^{73} -1.16055 q^{74} +2.42043 q^{76} +(2.51250 - 2.51250i) q^{77} -12.2526i q^{79} +(1.80260 + 1.32312i) q^{80} +(-3.82714 - 3.82714i) q^{82} +(-5.56115 - 5.56115i) q^{83} +(-15.4659 + 2.37245i) q^{85} +3.98898i q^{86} +(-1.87117 + 1.87117i) q^{88} +5.34093 q^{89} +3.79785 q^{91} +(0.707107 - 0.707107i) q^{92} +3.09852i q^{94} +(3.20251 - 4.36306i) q^{95} +(4.46841 + 4.46841i) q^{97} +(-3.67486 - 3.67486i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q+O(q^{10}) $ 16 * q	$ 16 q - 4 q^{10} + 32 q^{13} - 16 q^{16} - 24 q^{25} - 16 q^{31} + 32 q^{37} + 4 q^{40} + 16 q^{46} - 32 q^{52} - 104 q^{55} + 8 q^{58} - 40 q^{61} + 72 q^{67} + 24 q^{70} + 24 q^{73} - 24 q^{76} - 8 q^{82} - 8 q^{85} - 72 q^{97}+O(q^{100}) $ 16 * q - 4 * q^10 + 32 * q^13 - 16 * q^16 - 24 * q^25 - 16 * q^31 + 32 * q^37 + 4 * q^40 + 16 * q^46 - 32 * q^52 - 104 * q^55 + 8 * q^58 - 40 * q^61 + 72 * q^67 + 24 * q^70 + 24 * q^73 - 24 * q^76 - 8 * q^82 - 8 * q^85 - 72 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/2070\mathbb{Z}\right)^\times$.

$n$	$461$	$1657$	$1891$
$\chi(n)$	$-1$	$e\left(\frac{1}{4}\right)$	$1$

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 $

$2$	0.707107	−	0.707107i	0.500000	−	0.500000i
$2$	0.707107	−	0.707107i	0.500000	−	0.500000i
$3$		0			0
$3$		0			0
$4$		−	1.00000i		−	0.500000i
$5$	−1.80260	−	1.32312i	−0.806147	−	0.591716i
$5$	−1.80260	−	1.32312i	−0.806147	−	0.591716i
$6$		0			0
$7$	0.949464	+	0.949464i	0.358864	+	0.358864i	0.863394	−	0.504530i	$-0.168334\pi$
$7$	0.949464	+	0.949464i	0.358864	+	0.358864i	−0.504530	+	0.863394i	$0.668334\pi$
$8$	−0.707107	−	0.707107i	−0.250000	−	0.250000i
$9$		0			0
$10$	−2.21021	+	0.339045i	−0.698931	+	0.107215i
$11$		−	2.64623i		−	0.797870i	−0.916979	−	0.398935i	$-0.869380\pi$
$11$		−	2.64623i		−	0.797870i	0.916979	−	0.398935i	$-0.130620\pi$
$12$		0			0
$13$	2.00000	−	2.00000i	0.554700	−	0.554700i	−0.373094	−	0.927794i	$-0.621703\pi$
$13$	2.00000	−	2.00000i	0.554700	−	0.554700i	0.927794	+	0.373094i	$0.121703\pi$
$14$	1.34274			0.358864
$15$		0			0
$16$	−1.00000			−0.250000
$17$	4.94794	−	4.94794i	1.20005	−	1.20005i	0.225902	−	0.974150i	$-0.427467\pi$
$17$	4.94794	−	4.94794i	1.20005	−	1.20005i	0.974150	−	0.225902i	$-0.0725329\pi$
$18$		0			0
$19$			2.42043i			0.555285i	0.960685	+	0.277642i	$0.0895530\pi$
$19$			2.42043i			0.555285i	−0.960685	+	0.277642i	$0.910447\pi$
$20$	−1.32312	+	1.80260i	−0.295858	+	0.403073i
$21$		0			0
$22$	−1.87117	−	1.87117i	−0.398935	−	0.398935i
$23$	0.707107	+	0.707107i	0.147442	+	0.147442i
$23$	0.707107	+	0.707107i	0.147442	+	0.147442i
$24$		0			0
$25$	1.49872	+	4.77010i	0.299745	+	0.954019i
$26$		−	2.82843i		−	0.554700i
$27$		0			0
$28$	0.949464	−	0.949464i	0.179432	−	0.179432i
$29$	−0.383781			−0.0712664			−0.0356332	−	0.999365i	$-0.511345\pi$
$29$	−0.383781			−0.0712664			−0.0356332	+	0.999365i	$0.511345\pi$
$30$		0			0
$31$	−6.99745			−1.25678			−0.628389	−	0.777899i	$-0.716285\pi$
$31$	−6.99745			−1.25678			−0.628389	+	0.777899i	$0.716285\pi$
$32$	−0.707107	+	0.707107i	−0.125000	+	0.125000i
$33$		0			0
$34$		−	6.99745i		−	1.20005i
$35$	−0.455250	−	2.96775i	−0.0769514	−	0.501642i
$36$		0			0
$37$	−0.820634	−	0.820634i	−0.134911	−	0.134911i	0.636426	−	0.771338i	$-0.280412\pi$
$37$	−0.820634	−	0.820634i	−0.134911	−	0.134911i	−0.771338	+	0.636426i	$0.780412\pi$
$38$	1.71150	+	1.71150i	0.277642	+	0.277642i
$39$		0			0
$40$	0.339045	+	2.21021i	0.0536077	+	0.349466i
$41$		−	5.41240i		−	0.845275i	−0.906299	−	0.422637i	$-0.861104\pi$
$41$		−	5.41240i		−	0.845275i	0.906299	−	0.422637i	$-0.138896\pi$
$42$		0			0
$43$	−2.82063	+	2.82063i	−0.430143	+	0.430143i	−0.888677	−	0.458534i	$-0.848375\pi$
$43$	−2.82063	+	2.82063i	−0.430143	+	0.430143i	0.458534	+	0.888677i	$0.348375\pi$
$44$	−2.64623			−0.398935
$45$		0			0
$46$	1.00000			0.147442
$47$	−2.19098	+	2.19098i	−0.319588	+	0.319588i	−0.848609	−	0.529021i	$-0.822559\pi$
$47$	−2.19098	+	2.19098i	−0.319588	+	0.319588i	0.529021	+	0.848609i	$0.322559\pi$
$48$		0			0
$49$		−	5.19704i		−	0.742434i
$50$	4.43273	+	2.31321i	0.626882	+	0.327137i
$51$		0			0
$52$	−2.00000	−	2.00000i	−0.277350	−	0.277350i
$53$	−7.11469	−	7.11469i	−0.977278	−	0.977278i	0.0224692	−	0.999748i	$-0.492847\pi$
$53$	−7.11469	−	7.11469i	−0.977278	−	0.977278i	−0.999748	+	0.0224692i	$0.992847\pi$
$54$		0			0
$55$	−3.50128	+	4.77010i	−0.472112	+	0.643200i
$56$		−	1.34274i		−	0.179432i
$57$		0			0
$58$	−0.271374	+	0.271374i	−0.0356332	+	0.0356332i
$59$	−1.93732			−0.252218			−0.126109	−	0.992016i	$-0.540249\pi$
$59$	−1.93732			−0.252218			−0.126109	+	0.992016i	$0.540249\pi$
$60$		0			0
$61$	−8.31936			−1.06518			−0.532592	−	0.846372i	$-0.678782\pi$
$61$	−8.31936			−1.06518			−0.532592	+	0.846372i	$0.678782\pi$
$62$	−4.94794	+	4.94794i	−0.628389	+	0.628389i
$63$		0			0
$64$			1.00000i			0.125000i
$65$	−6.25143	+	0.958963i	−0.775395	+	0.118945i
$66$		0			0
$67$	−2.59724	−	2.59724i	−0.317304	−	0.317304i	0.530427	−	0.847731i	$-0.322032\pi$
$67$	−2.59724	−	2.59724i	−0.317304	−	0.317304i	−0.847731	+	0.530427i	$0.822032\pi$
$68$	−4.94794	−	4.94794i	−0.600026	−	0.600026i
$69$		0			0
$70$	−2.42043	−	1.77661i	−0.289297	−	0.212345i
$71$		−	8.76755i		−	1.04052i	−0.854009	−	0.520258i	$-0.825836\pi$
$71$		−	8.76755i		−	1.04052i	0.854009	−	0.520258i	$-0.174164\pi$
$72$		0			0
$73$	8.26882	−	8.26882i	0.967792	−	0.967792i	−0.0317050	−	0.999497i	$-0.510094\pi$
$73$	8.26882	−	8.26882i	0.967792	−	0.967792i	0.999497	+	0.0317050i	$0.0100937\pi$
$74$	−1.16055			−0.134911
$75$		0			0
$76$	2.42043			0.277642
$77$	2.51250	−	2.51250i	0.286326	−	0.286326i
$78$		0			0
$79$		−	12.2526i		−	1.37852i	−0.724514	−	0.689260i	$-0.757936\pi$
$79$		−	12.2526i		−	1.37852i	0.724514	−	0.689260i	$-0.242064\pi$
$80$	1.80260	+	1.32312i	0.201537	+	0.147929i
$81$		0			0
$82$	−3.82714	−	3.82714i	−0.422637	−	0.422637i
$83$	−5.56115	−	5.56115i	−0.610416	−	0.610416i	0.332638	−	0.943054i	$-0.392061\pi$
$83$	−5.56115	−	5.56115i	−0.610416	−	0.610416i	−0.943054	+	0.332638i	$0.892061\pi$
$84$		0			0
$85$	−15.4659	+	2.37245i	−1.67751	+	0.257328i
$86$			3.98898i			0.430143i
$87$		0			0
$88$	−1.87117	+	1.87117i	−0.199467	+	0.199467i
$89$	5.34093			0.566137			0.283069	−	0.959100i	$-0.408648\pi$
$89$	5.34093			0.566137			0.283069	+	0.959100i	$0.408648\pi$
$90$		0			0
$91$	3.79785			0.398123
$92$	0.707107	−	0.707107i	0.0737210	−	0.0737210i
$93$		0			0
$94$			3.09852i			0.319588i
$95$	3.20251	−	4.36306i	0.328571	−	0.447641i
$96$		0			0
$97$	4.46841	+	4.46841i	0.453698	+	0.453698i	0.896580	−	0.442882i	$-0.146044\pi$
$97$	4.46841	+	4.46841i	0.453698	+	0.453698i	−0.442882	+	0.896580i	$0.646044\pi$
$98$	−3.67486	−	3.67486i	−0.371217	−	0.371217i
$99$		0			0
$100$	4.77010	−	1.49872i	0.477010	−	0.149872i
$101$			4.62281i			0.459987i	0.973192	+	0.229993i	$0.0738705\pi$
$101$			4.62281i			0.459987i	−0.973192	+	0.229993i	$0.926130\pi$
$102$		0			0
$103$	−0.949464	+	0.949464i	−0.0935534	+	0.0935534i	−0.752335	−	0.658781i	$-0.771072\pi$
$103$	−0.949464	+	0.949464i	−0.0935534	+	0.0935534i	0.658781	+	0.752335i	$0.271072\pi$
$104$	−2.82843			−0.277350
$105$		0			0
$106$	−10.0617			−0.977278
$107$	−1.18839	+	1.18839i	−0.114886	+	0.114886i	−0.762213	−	0.647326i	$-0.775887\pi$
$107$	−1.18839	+	1.18839i	−0.114886	+	0.114886i	0.647326	+	0.762213i	$0.275887\pi$
$108$		0			0
$109$			13.5138i			1.29439i	0.762324	+	0.647196i	$0.224058\pi$
$109$			13.5138i			1.29439i	−0.762324	+	0.647196i	$0.775942\pi$
$110$	0.897192	+	5.84874i	0.0855439	+	0.557656i
$111$		0			0
$112$	−0.949464	−	0.949464i	−0.0897159	−	0.0897159i
$113$	−3.74814	−	3.74814i	−0.352595	−	0.352595i	0.508479	−	0.861074i	$-0.330208\pi$
$113$	−3.74814	−	3.74814i	−0.352595	−	0.352595i	−0.861074	+	0.508479i	$0.830208\pi$
$114$		0			0
$115$	−0.339045	−	2.21021i	−0.0316161	−	0.206104i
$116$			0.383781i			0.0356332i
$117$		0			0
$118$	−1.36989	+	1.36989i	−0.126109	+	0.126109i
$119$	9.39578			0.861310
$120$		0			0
$121$	3.99745			0.363404
$122$	−5.88267	+	5.88267i	−0.532592	+	0.532592i
$123$		0			0
$124$			6.99745i			0.628389i
$125$	3.60980	−	10.5816i	0.322870	−	0.946443i
$126$		0			0
$127$	−6.79785	−	6.79785i	−0.603212	−	0.603212i	0.337951	−	0.941164i	$-0.390266\pi$
$127$	−6.79785	−	6.79785i	−0.603212	−	0.603212i	−0.941164	+	0.337951i	$0.890266\pi$
$128$	0.707107	+	0.707107i	0.0625000	+	0.0625000i
$129$		0			0
$130$	−3.74234	+	5.09852i	−0.328225	+	0.447170i
$131$			3.08769i			0.269772i	0.990861	+	0.134886i	$0.0430669\pi$
$131$			3.08769i			0.269772i	−0.990861	+	0.134886i	$0.956933\pi$
$132$		0			0
$133$	−2.29811	+	2.29811i	−0.199271	+	0.199271i
$134$	−3.67305			−0.317304
$135$		0			0
$136$	−6.99745			−0.600026
$137$	−2.43544	+	2.43544i	−0.208074	+	0.208074i	−0.803448	−	0.595375i	$-0.797004\pi$
$137$	−2.43544	+	2.43544i	−0.208074	+	0.208074i	0.595375	+	0.803448i	$0.297004\pi$
$138$		0			0
$139$			20.9368i			1.77584i	0.460000	+	0.887919i	$0.347850\pi$
$139$			20.9368i			1.77584i	−0.460000	+	0.887919i	$0.652150\pi$
$140$	−2.96775	+	0.455250i	−0.250821	+	0.0384757i
$141$		0			0
$142$	−6.19959	−	6.19959i	−0.520258	−	0.520258i
$143$	−5.29247	−	5.29247i	−0.442578	−	0.442578i
$144$		0			0
$145$	0.691804	+	0.507788i	0.0574512	+	0.0421695i
$146$		−	11.6939i		−	0.967792i
$147$		0			0
$148$	−0.820634	+	0.820634i	−0.0674557	+	0.0674557i
$149$	13.0494			1.06905			0.534526	−	0.845152i	$-0.320490\pi$
$149$	13.0494			1.06905			0.534526	+	0.845152i	$0.320490\pi$
$150$		0			0
$151$	−11.9394			−0.971613			−0.485806	−	0.874066i	$-0.661474\pi$
$151$	−11.9394			−0.971613			−0.485806	+	0.874066i	$0.661474\pi$
$152$	1.71150	−	1.71150i	0.138821	−	0.138821i
$153$		0			0
$154$		−	3.55322i		−	0.286326i
$155$	12.6136	+	9.25844i	1.01315	+	0.743656i
$156$		0			0
$157$	15.4593	+	15.4593i	1.23379	+	1.23379i	0.962497	+	0.271294i	$0.0874514\pi$
$157$	15.4593	+	15.4593i	1.23379	+	1.23379i	0.271294	+	0.962497i	$0.412549\pi$
$158$	−8.66386	−	8.66386i	−0.689260	−	0.689260i
$159$		0			0
$160$	2.21021	−	0.339045i	0.174733	−	0.0268038i
$161$			1.34274i			0.105823i
$162$		0			0
$163$	−2.19704	+	2.19704i	−0.172085	+	0.172085i	−0.787895	−	0.615810i	$-0.788829\pi$
$163$	−2.19704	+	2.19704i	−0.172085	+	0.172085i	0.615810	+	0.787895i	$0.288829\pi$
$164$	−5.41240			−0.422637
$165$		0			0
$166$	−7.86466			−0.610416
$167$	−2.05166	+	2.05166i	−0.158762	+	0.158762i	−0.782018	−	0.623256i	$-0.785809\pi$
$167$	−2.05166	+	2.05166i	−0.158762	+	0.158762i	0.623256	+	0.782018i	$0.285809\pi$
$168$		0			0
$169$			5.00000i			0.384615i
$170$	−9.25844	+	12.6136i	−0.710090	+	0.967418i
$171$		0			0
$172$	2.82063	+	2.82063i	0.215071	+	0.215071i
$173$	2.75696	+	2.75696i	0.209608	+	0.209608i	0.804101	−	0.594493i	$-0.202647\pi$
$173$	2.75696	+	2.75696i	0.209608	+	0.209608i	−0.594493	+	0.804101i	$0.702647\pi$
$174$		0			0
$175$	−3.10605	+	5.95202i	−0.234795	+	0.449930i
$176$			2.64623i			0.199467i
$177$		0			0
$178$	3.77661	−	3.77661i	0.283069	−	0.283069i
$179$	12.2620			0.916506			0.458253	−	0.888822i	$-0.348475\pi$
$179$	12.2620			0.916506			0.458253	+	0.888822i	$0.348475\pi$
$180$		0			0
$181$	3.77661			0.280713			0.140357	−	0.990101i	$-0.455175\pi$
$181$	3.77661			0.280713			0.140357	+	0.990101i	$0.455175\pi$
$182$	2.68549	−	2.68549i	0.199062	−	0.199062i
$183$		0			0
$184$		−	1.00000i		−	0.0737210i
$185$	0.393479	+	2.56507i	0.0289291	+	0.188588i
$186$		0			0
$187$	−13.0934	−	13.0934i	−0.957485	−	0.957485i
$188$	2.19098	+	2.19098i	0.159794	+	0.159794i
$189$		0			0
$190$	−0.820634	−	5.34967i	−0.0595350	−	0.388106i
$191$		−	17.0094i		−	1.23075i	−0.788233	−	0.615377i	$-0.789004\pi$
$191$		−	17.0094i		−	1.23075i	0.788233	−	0.615377i	$-0.210996\pi$
$192$		0			0
$193$	17.8964	−	17.8964i	1.28821	−	1.28821i	0.352335	−	0.935874i	$-0.385388\pi$
$193$	17.8964	−	17.8964i	1.28821	−	1.28821i	0.935874	−	0.352335i	$-0.114612\pi$
$194$	6.31929			0.453698
$195$		0			0
$196$	−5.19704			−0.371217
$197$	2.70850	−	2.70850i	0.192972	−	0.192972i	−0.604007	−	0.796979i	$-0.706430\pi$
$197$	2.70850	−	2.70850i	0.192972	−	0.192972i	0.796979	+	0.604007i	$0.206430\pi$
$198$		0			0
$199$		−	7.19448i		−	0.510003i	−0.966941	−	0.255002i	$-0.917924\pi$
$199$		−	7.19448i		−	0.510003i	0.966941	−	0.255002i	$-0.0820760\pi$
$200$	2.31321	−	4.43273i	0.163569	−	0.313441i
$201$		0			0
$202$	3.26882	+	3.26882i	0.229993	+	0.229993i
$203$	−0.364386	−	0.364386i	−0.0255749	−	0.0255749i
$204$		0			0
$205$	−7.16124	+	9.75638i	−0.500163	+	0.681415i
$206$			1.34274i			0.0935534i
$207$		0			0
$208$	−2.00000	+	2.00000i	−0.138675	+	0.138675i
$209$	6.40502			0.443045
$210$		0			0
$211$	−0.0685362			−0.00471823			−0.00235911	−	0.999997i	$-0.500751\pi$
$211$	−0.0685362			−0.00471823			−0.00235911	+	0.999997i	$0.500751\pi$
$212$	−7.11469	+	7.11469i	−0.488639	+	0.488639i
$213$		0			0
$214$			1.68064i			0.114886i
$215$	8.81650	−	1.35244i	0.601280	−	0.0922358i
$216$		0			0
$217$	−6.64382	−	6.64382i	−0.451012	−	0.451012i
$218$	9.55573	+	9.55573i	0.647196	+	0.647196i
$219$		0			0
$220$	4.77010	+	3.50128i	0.321600	+	0.236056i
$221$		−	19.7918i		−	1.33134i
$222$		0			0
$223$	−19.6524	+	19.6524i	−1.31602	+	1.31602i	−0.399129	+	0.916895i	$0.630688\pi$
$223$	−19.6524	+	19.6524i	−1.31602	+	1.31602i	−0.916895	+	0.399129i	$0.869312\pi$
$224$	−1.34274			−0.0897159
$225$		0			0
$226$	−5.30066			−0.352595
$227$	2.83984	−	2.83984i	0.188487	−	0.188487i	−0.606555	−	0.795042i	$-0.707449\pi$
$227$	2.83984	−	2.83984i	0.188487	−	0.188487i	0.795042	+	0.606555i	$0.207449\pi$
$228$		0			0
$229$		−	4.42554i		−	0.292448i	−0.989252	−	0.146224i	$-0.953288\pi$
$229$		−	4.42554i		−	0.292448i	0.989252	−	0.146224i	$-0.0467120\pi$
$230$	−1.80260	−	1.32312i	−0.118860	−	0.0872437i
$231$		0			0
$232$	0.271374	+	0.271374i	0.0178166	+	0.0178166i
$233$	−0.799777	−	0.799777i	−0.0523951	−	0.0523951i	0.680424	−	0.732819i	$-0.261796\pi$
$233$	−0.799777	−	0.799777i	−0.0523951	−	0.0523951i	−0.732819	+	0.680424i	$0.761796\pi$
$234$		0			0
$235$	6.84839	−	1.05054i	0.446740	−	0.0685294i
$236$			1.93732i			0.126109i
$237$		0			0
$238$	6.64382	−	6.64382i	0.430655	−	0.430655i
$239$	17.2078			1.11308			0.556540	−	0.830821i	$-0.312129\pi$
$239$	17.2078			1.11308			0.556540	+	0.830821i	$0.312129\pi$
$240$		0			0
$241$	5.25511			0.338511			0.169256	−	0.985572i	$-0.445864\pi$
$241$	5.25511			0.338511			0.169256	+	0.985572i	$0.445864\pi$
$242$	2.82662	−	2.82662i	0.181702	−	0.181702i
$243$		0			0
$244$			8.31936i			0.532592i
$245$	−6.87629	+	9.36817i	−0.439310	+	0.598511i
$246$		0			0
$247$	4.84086	+	4.84086i	0.308016	+	0.308016i
$248$	4.94794	+	4.94794i	0.314195	+	0.314195i
$249$		0			0
$250$	−4.92978	−	10.0348i	−0.311786	−	0.634657i
$251$		−	16.1381i		−	1.01863i	−0.860581	−	0.509314i	$-0.829899\pi$
$251$		−	16.1381i		−	1.01863i	0.860581	−	0.509314i	$-0.170101\pi$
$252$		0			0
$253$	1.87117	−	1.87117i	0.117639	−	0.117639i
$254$	−9.61362			−0.603212
$255$		0			0
$256$	1.00000			0.0625000
$257$	−21.8720	+	21.8720i	−1.36434	+	1.36434i	−0.496040	+	0.868300i	$0.665213\pi$
$257$	−21.8720	+	21.8720i	−1.36434	+	1.36434i	−0.868300	+	0.496040i	$0.834787\pi$
$258$		0			0
$259$		−	1.55832i		−	0.0968295i
$260$	0.958963	+	6.25143i	0.0594724	+	0.387697i
$261$		0			0
$262$	2.18332	+	2.18332i	0.134886	+	0.134886i
$263$	19.9541	+	19.9541i	1.23042	+	1.23042i	0.963801	+	0.266621i	$0.0859072\pi$
$263$	19.9541	+	19.9541i	1.23042	+	1.23042i	0.266621	+	0.963801i	$0.414093\pi$
$264$		0			0
$265$	3.41136	+	22.2385i	0.209558	+	1.36610i
$266$			3.25002i			0.199271i
$267$		0			0
$268$	−2.59724	+	2.59724i	−0.158652	+	0.158652i
$269$	28.0750			1.71176			0.855881	−	0.517172i	$-0.173015\pi$
$269$	28.0750			1.71176			0.855881	+	0.517172i	$0.173015\pi$
$270$		0			0
$271$	23.6766			1.43825			0.719126	−	0.694880i	$-0.244542\pi$
$271$	23.6766			1.43825			0.719126	+	0.694880i	$0.244542\pi$
$272$	−4.94794	+	4.94794i	−0.300013	+	0.300013i
$273$		0			0
$274$			3.44423i			0.208074i
$275$	12.6228	−	3.96597i	0.761183	−	0.239157i
$276$		0			0
$277$	−6.55577	−	6.55577i	−0.393898	−	0.393898i	0.482176	−	0.876074i	$-0.339846\pi$
$277$	−6.55577	−	6.55577i	−0.393898	−	0.393898i	−0.876074	+	0.482176i	$0.839846\pi$
$278$	14.8046	+	14.8046i	0.887919	+	0.887919i
$279$		0			0
$280$	−1.77661	+	2.42043i	−0.106173	+	0.144648i
$281$		−	20.6150i		−	1.22979i	−0.788610	−	0.614894i	$-0.789199\pi$
$281$		−	20.6150i		−	1.22979i	0.788610	−	0.614894i	$-0.210801\pi$
$282$		0			0
$283$	5.59980	−	5.59980i	0.332873	−	0.332873i	−0.520803	−	0.853677i	$-0.674368\pi$
$283$	5.59980	−	5.59980i	0.332873	−	0.332873i	0.853677	+	0.520803i	$0.174368\pi$
$284$	−8.76755			−0.520258
$285$		0			0
$286$	−7.48468			−0.442578
$287$	5.13888	−	5.13888i	0.303338	−	0.303338i
$288$		0			0
$289$		−	31.9643i		−	1.88025i
$290$	0.848239	−	0.130119i	0.0498103	−	0.00764085i
$291$		0			0
$292$	−8.26882	−	8.26882i	−0.483896	−	0.483896i
$293$	−15.4662	−	15.4662i	−0.903548	−	0.903548i	0.0921935	−	0.995741i	$-0.470612\pi$
$293$	−15.4662	−	15.4662i	−0.903548	−	0.903548i	−0.995741	+	0.0921935i	$0.970612\pi$
$294$		0			0
$295$	3.49221	+	2.56330i	0.203324	+	0.149241i
$296$			1.16055i			0.0674557i
$297$		0			0
$298$	9.22735	−	9.22735i	0.534526	−	0.534526i
$299$	2.82843			0.163572
$300$		0			0
$301$	−5.35618			−0.308725
$302$	−8.44241	+	8.44241i	−0.485806	+	0.485806i
$303$		0			0
$304$		−	2.42043i		−	0.138821i
$305$	14.9965	+	11.0075i	0.858695	+	0.630287i
$306$		0			0
$307$	7.58575	+	7.58575i	0.432942	+	0.432942i	0.889628	−	0.456686i	$-0.150964\pi$
$307$	7.58575	+	7.58575i	0.432942	+	0.432942i	−0.456686	+	0.889628i	$0.650964\pi$
$308$	−2.51250	−	2.51250i	−0.143163	−	0.143163i
$309$		0			0
$310$	15.4659	−	2.37245i	0.878402	−	0.134746i
$311$			3.89765i			0.221015i	0.993875	+	0.110508i	$0.0352477\pi$
$311$			3.89765i			0.221015i	−0.993875	+	0.110508i	$0.964752\pi$
$312$		0			0
$313$	14.9231	−	14.9231i	0.843504	−	0.843504i	−0.145809	−	0.989313i	$-0.546578\pi$
$313$	14.9231	−	14.9231i	0.843504	−	0.843504i	0.989313	+	0.145809i	$0.0465784\pi$
$314$	21.8628			1.23379
$315$		0			0
$316$	−12.2526			−0.689260
$317$	−19.2202	+	19.2202i	−1.07951	+	1.07951i	−0.0829610	+	0.996553i	$0.526438\pi$
$317$	−19.2202	+	19.2202i	−1.07951	+	1.07951i	−0.996553	+	0.0829610i	$0.973562\pi$
$318$		0			0
$319$			1.01558i			0.0568613i
$320$	1.32312	−	1.80260i	0.0739645	−	0.100768i
$321$		0			0
$322$	0.949464	+	0.949464i	0.0529115	+	0.0529115i
$323$	11.9761	+	11.9761i	0.666370	+	0.666370i
$324$		0			0
$325$	12.5376	+	6.54275i	0.695463	+	0.362926i
$326$			3.10708i			0.172085i
$327$		0			0
$328$	−3.82714	+	3.82714i	−0.211319	+	0.211319i
$329$	−4.16052			−0.229377
$330$		0			0
$331$	20.0960			1.10457			0.552287	−	0.833654i	$-0.313755\pi$
$331$	20.0960			1.10457			0.552287	+	0.833654i	$0.313755\pi$
$332$	−5.56115	+	5.56115i	−0.305208	+	0.305208i
$333$		0			0
$334$			2.90148i			0.158762i
$335$	1.24533	+	8.11824i	0.0680396	+	0.443547i
$336$		0			0
$337$	10.6706	+	10.6706i	0.581262	+	0.581262i	0.935250	−	0.353988i	$-0.115175\pi$
$337$	10.6706	+	10.6706i	0.581262	+	0.581262i	−0.353988	+	0.935250i	$0.615175\pi$
$338$	3.53553	+	3.53553i	0.192308	+	0.192308i
$339$		0			0
$340$	2.37245	+	15.4659i	0.128664	+	0.838754i
$341$			18.5169i			1.00275i
$342$		0			0
$343$	11.5806	−	11.5806i	0.625296	−	0.625296i
$344$	3.98898			0.215071
$345$		0			0
$346$	3.89893			0.209608
$347$	−25.3808	+	25.3808i	−1.36251	+	1.36251i	−0.491806	+	0.870705i	$0.663663\pi$
$347$	−25.3808	+	25.3808i	−1.36251	+	1.36251i	−0.870705	+	0.491806i	$0.836337\pi$
$348$		0			0
$349$		−	1.45725i		−	0.0780049i	−0.999239	−	0.0390024i	$-0.987582\pi$
$349$		−	1.45725i		−	0.0780049i	0.999239	−	0.0390024i	$-0.0124180\pi$
$350$	2.01240	+	6.40502i	0.107567	+	0.342363i
$351$		0			0
$352$	1.87117	+	1.87117i	0.0997337	+	0.0997337i
$353$	−6.53153	−	6.53153i	−0.347638	−	0.347638i	0.511591	−	0.859229i	$-0.329056\pi$
$353$	−6.53153	−	6.53153i	−0.347638	−	0.347638i	−0.859229	+	0.511591i	$0.829056\pi$
$354$		0			0
$355$	−11.6005	+	15.8044i	−0.615690	+	0.838809i
$356$		−	5.34093i		−	0.283069i
$357$		0			0
$358$	8.67056	−	8.67056i	0.458253	−	0.458253i
$359$	13.9135			0.734325			0.367162	−	0.930157i	$-0.380329\pi$
$359$	13.9135			0.734325			0.367162	+	0.930157i	$0.380329\pi$
$360$		0			0
$361$	13.1415			0.691659
$362$	2.67047	−	2.67047i	0.140357	−	0.140357i
$363$		0			0
$364$		−	3.79785i		−	0.199062i
$365$	−25.8460	+	3.96475i	−1.35284	+	0.207524i
$366$		0			0
$367$	−5.87837	−	5.87837i	−0.306849	−	0.306849i	0.536837	−	0.843686i	$-0.319619\pi$
$367$	−5.87837	−	5.87837i	−0.306849	−	0.306849i	−0.843686	+	0.536837i	$0.819619\pi$
$368$	−0.707107	−	0.707107i	−0.0368605	−	0.0368605i
$369$		0			0
$370$	2.09201	+	1.53555i	0.108758	+	0.0798292i
$371$		−	13.5103i		−	0.701419i
$372$		0			0
$373$	13.5049	−	13.5049i	0.699257	−	0.699257i	−0.264993	−	0.964250i	$-0.585370\pi$
$373$	13.5049	−	13.5049i	0.699257	−	0.699257i	0.964250	+	0.264993i	$0.0853696\pi$
$374$	−18.5169			−0.957485
$375$		0			0
$376$	3.09852			0.159794
$377$	−0.767563	+	0.767563i	−0.0395315	+	0.0395315i
$378$		0			0
$379$			21.2692i			1.09253i	0.837614	+	0.546263i	$0.183950\pi$
$379$			21.2692i			1.09253i	−0.837614	+	0.546263i	$0.816050\pi$
$380$	−4.36306	−	3.20251i	−0.223820	−	0.164285i
$381$		0			0
$382$	−12.0274	−	12.0274i	−0.615377	−	0.615377i
$383$	−13.5403	−	13.5403i	−0.691879	−	0.691879i	0.270766	−	0.962645i	$-0.412723\pi$
$383$	−13.5403	−	13.5403i	−0.691879	−	0.691879i	−0.962645	+	0.270766i	$0.912723\pi$
$384$		0			0
$385$	−7.85337	+	1.20470i	−0.400245	+	0.0613971i
$386$		−	25.3093i		−	1.28821i
$387$		0			0
$388$	4.46841	−	4.46841i	0.226849	−	0.226849i
$389$	−21.2504			−1.07744			−0.538718	−	0.842486i	$-0.681091\pi$
$389$	−21.2504			−1.07744			−0.538718	+	0.842486i	$0.681091\pi$
$390$		0			0
$391$	6.99745			0.353876
$392$	−3.67486	+	3.67486i	−0.185608	+	0.185608i
$393$		0			0
$394$		−	3.83039i		−	0.192972i
$395$	−16.2116	+	22.0864i	−0.815692	+	1.11129i
$396$		0			0
$397$	−3.48468	−	3.48468i	−0.174891	−	0.174891i	0.614233	−	0.789124i	$-0.289465\pi$
$397$	−3.48468	−	3.48468i	−0.174891	−	0.174891i	−0.789124	+	0.614233i	$0.789465\pi$
$398$	−5.08727	−	5.08727i	−0.255002	−	0.255002i
$399$		0			0
$400$	−1.49872	−	4.77010i	−0.0749362	−	0.238505i
$401$		−	31.1927i		−	1.55769i	−0.627216	−	0.778845i	$-0.715806\pi$
$401$		−	31.1927i		−	1.55769i	0.627216	−	0.778845i	$-0.284194\pi$
$402$		0			0
$403$	−13.9949	+	13.9949i	−0.697135	+	0.697135i
$404$	4.62281			0.229993
$405$		0			0
$406$	−0.515320			−0.0255749
$407$	−2.17159	+	2.17159i	−0.107642	+	0.107642i
$408$		0			0
$409$		−	4.57529i		−	0.226233i	−0.993582	−	0.113117i	$-0.963917\pi$
$409$		−	4.57529i		−	0.226233i	0.993582	−	0.113117i	$-0.0360834\pi$
$410$	1.83505	+	11.9626i	0.0906264	+	0.590789i
$411$		0			0
$412$	0.949464	+	0.949464i	0.0467767	+	0.0467767i
$413$	−1.83942	−	1.83942i	−0.0905118	−	0.0905118i
$414$		0			0
$415$	2.66647	+	17.3826i	0.130892	+	0.853278i
$416$			2.82843i			0.138675i
$417$		0			0
$418$	4.52903	−	4.52903i	0.221522	−	0.221522i
$419$	−9.80817			−0.479160			−0.239580	−	0.970877i	$-0.577010\pi$
$419$	−9.80817			−0.479160			−0.239580	+	0.970877i	$0.577010\pi$
$420$		0			0
$421$	17.0512			0.831026			0.415513	−	0.909587i	$-0.363602\pi$
$421$	17.0512			0.831026			0.415513	+	0.909587i	$0.363602\pi$
$422$	−0.0484624	+	0.0484624i	−0.00235911	+	0.00235911i
$423$		0			0
$424$			10.0617i			0.488639i
$425$	31.0178	+	16.1866i	1.50458	+	0.785164i
$426$		0			0
$427$	−7.89893	−	7.89893i	−0.382256	−	0.382256i
$428$	1.18839	+	1.18839i	0.0574432	+	0.0574432i
$429$		0			0
$430$	5.27788	−	7.19053i	0.254522	−	0.346758i
$431$			2.20380i			0.106153i	0.998590	+	0.0530767i	$0.0169028\pi$
$431$			2.20380i			0.106153i	−0.998590	+	0.0530767i	$0.983097\pi$
$432$		0			0
$433$	11.8571	−	11.8571i	0.569817	−	0.569817i	−0.362260	−	0.932077i	$-0.617995\pi$
$433$	11.8571	−	11.8571i	0.569817	−	0.569817i	0.932077	+	0.362260i	$0.117995\pi$
$434$	−9.39578			−0.451012
$435$		0			0
$436$	13.5138			0.647196
$437$	−1.71150	+	1.71150i	−0.0818722	+	0.0818722i
$438$		0			0
$439$		−	13.0255i		−	0.621675i	−0.950463	−	0.310837i	$-0.899391\pi$
$439$		−	13.0255i		−	0.621675i	0.950463	−	0.310837i	$-0.100609\pi$
$440$	5.84874	−	0.897192i	0.278828	−	0.0427719i
$441$		0			0
$442$	−13.9949	−	13.9949i	−0.665669	−	0.665669i
$443$	16.5990	+	16.5990i	0.788640	+	0.788640i	0.981271	−	0.192631i	$-0.0617021\pi$
$443$	16.5990	+	16.5990i	0.788640	+	0.788640i	−0.192631	+	0.981271i	$0.561702\pi$
$444$		0			0
$445$	−9.62755	−	7.06668i	−0.456390	−	0.334993i
$446$			27.7927i			1.31602i
$447$		0			0
$448$	−0.949464	+	0.949464i	−0.0448579	+	0.0448579i
$449$	−13.8119			−0.651826			−0.325913	−	0.945400i	$-0.605672\pi$
$449$	−13.8119			−0.651826			−0.325913	+	0.945400i	$0.605672\pi$
$450$		0			0
$451$	−14.3225			−0.674419
$452$	−3.74814	+	3.74814i	−0.176297	+	0.176297i
$453$		0			0
$454$		−	4.01614i		−	0.188487i
$455$	−6.84601	−	5.02501i	−0.320946	−	0.235576i
$456$		0			0
$457$	0.0822505	+	0.0822505i	0.00384751	+	0.00384751i	0.709028	−	0.705180i	$-0.249134\pi$
$457$	0.0822505	+	0.0822505i	0.00384751	+	0.00384751i	−0.705180	+	0.709028i	$0.749134\pi$
$458$	−3.12933	−	3.12933i	−0.146224	−	0.146224i
$459$		0			0
$460$	−2.21021	+	0.339045i	−0.103052	+	0.0158080i
$461$			31.1893i			1.45263i	0.687362	+	0.726315i	$0.258769\pi$
$461$			31.1893i			1.45263i	−0.687362	+	0.726315i	$0.741231\pi$
$462$		0			0
$463$	−9.05552	+	9.05552i	−0.420845	+	0.420845i	−0.885495	−	0.464649i	$-0.846180\pi$
$463$	−9.05552	+	9.05552i	−0.420845	+	0.420845i	0.464649	+	0.885495i	$0.346180\pi$
$464$	0.383781			0.0178166
$465$		0			0
$466$	−1.13105			−0.0523951
$467$	9.87526	−	9.87526i	0.456973	−	0.456973i	−0.440688	−	0.897660i	$-0.645265\pi$
$467$	9.87526	−	9.87526i	0.456973	−	0.456973i	0.897660	+	0.440688i	$0.145265\pi$
$468$		0			0
$469$		−	4.93197i		−	0.227737i
$470$	4.09970	−	5.58539i	0.189105	−	0.257635i
$471$		0			0
$472$	1.36989	+	1.36989i	0.0630544	+	0.0630544i
$473$	7.46406	+	7.46406i	0.343198	+	0.343198i
$474$		0			0
$475$	−11.5457	+	3.62755i	−0.529752	+	0.166444i
$476$		−	9.39578i		−	0.430655i
$477$		0			0
$478$	12.1677	−	12.1677i	0.556540	−	0.556540i
$479$	21.3913			0.977394			0.488697	−	0.872453i	$-0.337472\pi$
$479$	21.3913			0.977394			0.488697	+	0.872453i	$0.337472\pi$
$480$		0			0
$481$	−3.28253			−0.149671
$482$	3.71592	−	3.71592i	0.169256	−	0.169256i
$483$		0			0
$484$		−	3.99745i		−	0.181702i
$485$	−2.14252	−	13.9670i	−0.0972869	−	0.634208i
$486$		0			0
$487$	25.6336	+	25.6336i	1.16157	+	1.16157i	0.984132	+	0.177437i	$0.0567808\pi$
$487$	25.6336	+	25.6336i	1.16157	+	1.16157i	0.177437	+	0.984132i	$0.443219\pi$
$488$	5.88267	+	5.88267i	0.266296	+	0.266296i
$489$		0			0
$490$	1.76203	+	11.4866i	0.0796003	+	0.518910i
$491$			32.3925i			1.46185i	0.682455	+	0.730927i	$0.260912\pi$
$491$			32.3925i			1.46185i	−0.682455	+	0.730927i	$0.739088\pi$
$492$		0			0
$493$	−1.89893	+	1.89893i	−0.0855234	+	0.0855234i
$494$	6.84601			0.308016
$495$		0			0
$496$	6.99745			0.314195
$497$	8.32447	−	8.32447i	0.373403	−	0.373403i
$498$		0			0
$499$		−	15.0379i		−	0.673189i	−0.941650	−	0.336594i	$-0.890725\pi$
$499$		−	15.0379i		−	0.673189i	0.941650	−	0.336594i	$-0.109275\pi$
$500$	−10.5816	−	3.60980i	−0.473222	−	0.161435i
$501$		0			0
$502$	−11.4114	−	11.4114i	−0.509314	−	0.509314i
$503$	−17.7115	−	17.7115i	−0.789717	−	0.789717i	0.191731	−	0.981448i	$-0.438590\pi$
$503$	−17.7115	−	17.7115i	−0.789717	−	0.789717i	−0.981448	+	0.191731i	$0.938590\pi$
$504$		0			0
$505$	6.11652	−	8.33307i	0.272182	−	0.370817i
$506$		−	2.64623i		−	0.117639i
$507$		0			0
$508$	−6.79785	+	6.79785i	−0.301606	+	0.301606i
$509$	−40.5779			−1.79858			−0.899291	−	0.437351i	$-0.855917\pi$
$509$	−40.5779			−1.79858			−0.899291	+	0.437351i	$0.855917\pi$
$510$		0			0
$511$	15.7019			0.694611
$512$	0.707107	−	0.707107i	0.0312500	−	0.0312500i
$513$		0			0
$514$			30.9317i			1.36434i
$515$	2.96775	−	0.455250i	0.130775	−	0.0200607i
$516$		0			0
$517$	5.79785	+	5.79785i	0.254989	+	0.254989i
$518$	−1.10190	−	1.10190i	−0.0484148	−	0.0484148i
$519$		0			0
$520$	5.09852	+	3.74234i	0.223585	+	0.164112i
$521$		−	17.7938i		−	0.779561i	−0.920908	−	0.389781i	$-0.872551\pi$
$521$		−	17.7938i		−	0.779561i	0.920908	−	0.389781i	$-0.127449\pi$
$522$		0			0
$523$	−13.7300	+	13.7300i	−0.600372	+	0.600372i	−0.940411	−	0.340039i	$-0.889560\pi$
$523$	−13.7300	+	13.7300i	−0.600372	+	0.600372i	0.340039	+	0.940411i	$0.389560\pi$
$524$	3.08769			0.134886
$525$		0			0
$526$	28.2194			1.23042
$527$	−34.6230	+	34.6230i	−1.50820	+	1.50820i
$528$		0			0
$529$			1.00000i			0.0434783i
$530$	18.1372	+	13.3128i	0.787830	+	0.578271i
$531$		0			0
$532$	2.29811	+	2.29811i	0.0996357	+	0.0996357i
$533$	−10.8248	−	10.8248i	−0.468874	−	0.468874i
$534$		0			0
$535$	3.71458	−	0.569813i	0.160595	−	0.0246352i
$536$			3.67305i			0.158652i
$537$		0			0
$538$	19.8520	−	19.8520i	0.855881	−	0.855881i
$539$	−13.7526			−0.592365
$540$		0			0
$541$	22.0000			0.945854			0.472927	−	0.881102i	$-0.343197\pi$
$541$	22.0000			0.945854			0.472927	+	0.881102i	$0.343197\pi$
$542$	16.7419	−	16.7419i	0.719126	−	0.719126i
$543$		0			0
$544$			6.99745i			0.300013i
$545$	17.8804	−	24.3600i	0.765912	−	1.04347i
$546$		0			0
$547$	21.1894	+	21.1894i	0.905992	+	0.905992i	0.995946	−	0.0899537i	$-0.0286719\pi$
$547$	21.1894	+	21.1894i	0.905992	+	0.905992i	−0.0899537	+	0.995946i	$0.528672\pi$
$548$	2.43544	+	2.43544i	0.104037	+	0.104037i
$549$		0			0
$550$	6.12130	−	11.7300i	0.261013	−	0.500170i
$551$		−	0.928915i		−	0.0395731i
$552$		0			0
$553$	11.6334	−	11.6334i	0.494701	−	0.494701i
$554$	−9.27126			−0.393898
$555$		0			0
$556$	20.9368			0.887919
$557$	10.8857	−	10.8857i	0.461240	−	0.461240i	−0.437822	−	0.899062i	$-0.644250\pi$
$557$	10.8857	−	10.8857i	0.461240	−	0.461240i	0.899062	+	0.437822i	$0.144250\pi$
$558$		0			0
$559$			11.2825i			0.477200i
$560$	0.455250	+	2.96775i	0.0192378	+	0.125410i
$561$		0			0
$562$	−14.5770	−	14.5770i	−0.614894	−	0.614894i
$563$	−2.95418	−	2.95418i	−0.124504	−	0.124504i	0.642109	−	0.766613i	$-0.278059\pi$
$563$	−2.95418	−	2.95418i	−0.124504	−	0.124504i	−0.766613	+	0.642109i	$0.778059\pi$
$564$		0			0
$565$	1.79716	+	11.7156i	0.0756072	+	0.492879i
$566$		−	7.91931i		−	0.332873i
$567$		0			0
$568$	−6.19959	+	6.19959i	−0.260129	+	0.260129i
$569$	29.1503			1.22204			0.611022	−	0.791614i	$-0.290759\pi$
$569$	29.1503			1.22204			0.611022	+	0.791614i	$0.290759\pi$
$570$		0			0
$571$	41.2706			1.72712			0.863560	−	0.504246i	$-0.168229\pi$
$571$	41.2706			1.72712			0.863560	+	0.504246i	$0.168229\pi$
$572$	−5.29247	+	5.29247i	−0.221289	+	0.221289i
$573$		0			0
$574$		−	7.26747i		−	0.303338i
$575$	−2.31321	+	4.43273i	−0.0964676	+	0.184857i
$576$		0			0
$577$	−16.0061	−	16.0061i	−0.666341	−	0.666341i	0.290526	−	0.956867i	$-0.406170\pi$
$577$	−16.0061	−	16.0061i	−0.666341	−	0.666341i	−0.956867	+	0.290526i	$0.906170\pi$
$578$	−22.6021	−	22.6021i	−0.940125	−	0.940125i
$579$		0			0
$580$	0.507788	−	0.691804i	0.0210847	−	0.0287256i
$581$		−	10.5602i		−	0.438112i
$582$		0			0
$583$	−18.8271	+	18.8271i	−0.779741	+	0.779741i
$584$	−11.6939			−0.483896
$585$		0			0
$586$	−21.8726			−0.903548
$587$	−18.5920	+	18.5920i	−0.767372	+	0.767372i	−0.977643	−	0.210271i	$-0.932565\pi$
$587$	−18.5920	+	18.5920i	−0.767372	+	0.767372i	0.210271	+	0.977643i	$0.432565\pi$
$588$		0			0
$589$		−	16.9368i		−	0.697870i
$590$	4.28190	−	0.656838i	0.176283	−	0.0270416i
$591$		0			0
$592$	0.820634	+	0.820634i	0.0337278	+	0.0337278i
$593$	−5.19456	−	5.19456i	−0.213315	−	0.213315i	0.592359	−	0.805674i	$-0.298197\pi$
$593$	−5.19456	−	5.19456i	−0.213315	−	0.213315i	−0.805674	+	0.592359i	$0.798197\pi$
$594$		0			0
$595$	−16.9368	−	12.4317i	−0.694342	−	0.509651i
$596$		−	13.0494i		−	0.534526i
$597$		0			0
$598$	2.00000	−	2.00000i	0.0817861	−	0.0817861i
$599$	4.12632			0.168597			0.0842985	−	0.996441i	$-0.473135\pi$
$599$	4.12632			0.168597			0.0842985	+	0.996441i	$0.473135\pi$
$600$		0			0
$601$	18.1364			0.739800			0.369900	−	0.929072i	$-0.379392\pi$
$601$	18.1364			0.739800			0.369900	+	0.929072i	$0.379392\pi$
$602$	−3.78739	+	3.78739i	−0.154363	+	0.154363i
$603$		0			0
$604$			11.9394i			0.485806i
$605$	−7.20579	−	5.28909i	−0.292957	−	0.215032i
$606$		0			0
$607$	7.70794	+	7.70794i	0.312856	+	0.312856i	0.846015	−	0.533159i	$-0.178995\pi$
$607$	7.70794	+	7.70794i	0.312856	+	0.312856i	−0.533159	+	0.846015i	$0.678995\pi$
$608$	−1.71150	−	1.71150i	−0.0694106	−	0.0694106i
$609$		0			0
$610$	18.3876	−	2.82063i	0.744491	−	0.114204i
$611$			8.76393i			0.354551i
$612$		0			0
$613$	14.8073	−	14.8073i	0.598061	−	0.598061i	−0.341735	−	0.939796i	$-0.611015\pi$
$613$	14.8073	−	14.8073i	0.598061	−	0.598061i	0.939796	+	0.341735i	$0.111015\pi$
$614$	10.7279			0.432942
$615$		0			0
$616$	−3.55322			−0.143163
$617$	−8.08164	+	8.08164i	−0.325355	+	0.325355i	−0.850817	−	0.525462i	$-0.823892\pi$
$617$	−8.08164	+	8.08164i	−0.325355	+	0.325355i	0.525462	+	0.850817i	$0.323892\pi$
$618$		0			0
$619$		−	23.4100i		−	0.940926i	−0.882420	−	0.470463i	$-0.844087\pi$
$619$		−	23.4100i		−	0.940926i	0.882420	−	0.470463i	$-0.155913\pi$
$620$	9.25844	−	12.6136i	0.371828	−	0.506574i
$621$		0			0
$622$	2.75605	+	2.75605i	0.110508	+	0.110508i
$623$	5.07102	+	5.07102i	0.203166	+	0.203166i
$624$		0			0
$625$	−20.5077	+	14.2981i	−0.820306	+	0.571924i
$626$		−	21.1045i		−	0.843504i
$627$		0			0
$628$	15.4593	−	15.4593i	0.616895	−	0.616895i
$629$	−8.12089			−0.323801
$630$		0			0
$631$	33.4977			1.33352			0.666761	−	0.745271i	$-0.267680\pi$
$631$	33.4977			1.33352			0.666761	+	0.745271i	$0.267680\pi$
$632$	−8.66386	+	8.66386i	−0.344630	+	0.344630i
$633$		0			0
$634$			27.1815i			1.07951i
$635$	3.25945	+	21.2482i	0.129347	+	0.843208i
$636$		0			0
$637$	−10.3941	−	10.3941i	−0.411828	−	0.411828i
$638$	0.718120	+	0.718120i	0.0284306	+	0.0284306i
$639$		0			0
$640$	−0.339045	−	2.21021i	−0.0134019	−	0.0873664i
$641$		−	6.17292i		−	0.243816i	−0.992541	−	0.121908i	$-0.961099\pi$
$641$		−	6.17292i		−	0.243816i	0.992541	−	0.121908i	$-0.0389012\pi$
$642$		0			0
$643$	21.5947	−	21.5947i	0.851611	−	0.851611i	−0.138720	−	0.990332i	$-0.544299\pi$
$643$	21.5947	−	21.5947i	0.851611	−	0.851611i	0.990332	+	0.138720i	$0.0442989\pi$
$644$	1.34274			0.0529115
$645$		0			0
$646$	16.9368			0.666370
$647$	−16.9863	+	16.9863i	−0.667802	+	0.667802i	−0.957207	−	0.289405i	$-0.906543\pi$
$647$	−16.9863	+	16.9863i	−0.667802	+	0.667802i	0.289405	+	0.957207i	$0.406543\pi$
$648$		0			0
$649$			5.12661i			0.201237i
$650$	13.4919	−	4.23903i	0.529195	−	0.166268i
$651$		0			0
$652$	2.19704	+	2.19704i	0.0860426	+	0.0860426i
$653$	−34.5321	−	34.5321i	−1.35135	−	1.35135i	−0.884159	−	0.467186i	$-0.845268\pi$
$653$	−34.5321	−	34.5321i	−1.35135	−	1.35135i	−0.467186	−	0.884159i	$-0.654732\pi$
$654$		0			0
$655$	4.08537	−	5.56586i	0.159629	−	0.217476i
$656$			5.41240i			0.211319i
$657$		0			0
$658$	−2.94193	+	2.94193i	−0.114688	+	0.114688i
$659$	44.6066			1.73762			0.868812	−	0.495142i	$-0.164884\pi$
$659$	44.6066			1.73762			0.868812	+	0.495142i	$0.164884\pi$
$660$		0			0
$661$	17.6200			0.685339			0.342670	−	0.939456i	$-0.388669\pi$
$661$	17.6200			0.685339			0.342670	+	0.939456i	$0.388669\pi$
$662$	14.2100	−	14.2100i	0.552287	−	0.552287i
$663$		0			0
$664$			7.86466i			0.305208i
$665$	7.18324	−	1.10190i	0.278554	−	0.0427299i
$666$		0			0
$667$	−0.271374	−	0.271374i	−0.0105077	−	0.0105077i
$668$	2.05166	+	2.05166i	0.0793810	+	0.0793810i
$669$		0			0
$670$	6.62104	+	4.85988i	0.255793	+	0.187754i
$671$			22.0150i			0.849878i
$672$		0			0
$673$	3.66545	−	3.66545i	0.141293	−	0.141293i	−0.632922	−	0.774215i	$-0.718145\pi$
$673$	3.66545	−	3.66545i	0.141293	−	0.141293i	0.774215	+	0.632922i	$0.218145\pi$
$674$	15.0904			0.581262
$675$		0			0
$676$	5.00000			0.192308
$677$	−12.1377	+	12.1377i	−0.466490	+	0.466490i	−0.900775	−	0.434285i	$-0.857001\pi$
$677$	−12.1377	+	12.1377i	−0.466490	+	0.466490i	0.434285	+	0.900775i	$0.357001\pi$
$678$		0			0
$679$			8.48519i			0.325632i
$680$	12.6136	+	9.25844i	0.483709	+	0.355045i
$681$		0			0
$682$	13.0934	+	13.0934i	0.501373	+	0.501373i
$683$	27.4988	+	27.4988i	1.05221	+	1.05221i	0.998560	+	0.0536540i	$0.0170868\pi$
$683$	27.4988	+	27.4988i	1.05221	+	1.05221i	0.0536540	+	0.998560i	$0.482913\pi$
$684$		0			0
$685$	7.61249	−	1.16775i	0.290858	−	0.0446174i
$686$		−	16.3775i		−	0.625296i
$687$		0			0
$688$	2.82063	−	2.82063i	0.107536	−	0.107536i
$689$	−28.4588			−1.08419
$690$		0			0
$691$	−5.04300			−0.191845			−0.0959224	−	0.995389i	$-0.530580\pi$
$691$	−5.04300			−0.191845			−0.0959224	+	0.995389i	$0.530580\pi$
$692$	2.75696	−	2.75696i	0.104804	−	0.104804i
$693$		0			0
$694$			35.8938i			1.36251i
$695$	27.7019	−	37.7407i	1.05079	−	1.43159i
$696$		0			0
$697$	−26.7802	−	26.7802i	−1.01437	−	1.01437i
$698$	−1.03043	−	1.03043i	−0.0390024	−	0.0390024i
$699$		0			0
$700$	5.95202	+	3.10605i	0.224965	+	0.117398i
$701$			35.4022i			1.33712i	0.743657	+	0.668561i	$0.233089\pi$
$701$			35.4022i			1.33712i	−0.743657	+	0.668561i	$0.766911\pi$
$702$		0			0
$703$	1.98629	−	1.98629i	0.0749142	−	0.0749142i
$704$	2.64623			0.0997337
$705$		0			0
$706$	−9.23698			−0.347638
$707$	−4.38919	+	4.38919i	−0.165073	+	0.165073i
$708$		0			0
$709$		−	32.8245i		−	1.23275i	−0.787453	−	0.616374i	$-0.788601\pi$
$709$		−	32.8245i		−	1.23275i	0.787453	−	0.616374i	$-0.211399\pi$
$710$	2.97259	+	19.3782i	0.111559	+	0.727249i
$711$		0			0
$712$	−3.77661	−	3.77661i	−0.141534	−	0.141534i
$713$	−4.94794	−	4.94794i	−0.185302	−	0.185302i
$714$		0			0
$715$	2.53764	+	16.5427i	0.0949024	+	0.618664i
$716$		−	12.2620i		−	0.458253i
$717$		0			0
$718$	9.83830	−	9.83830i	0.367162	−	0.367162i
$719$	6.08304			0.226859			0.113430	−	0.993546i	$-0.463816\pi$
$719$	6.08304			0.226859			0.113430	+	0.993546i	$0.463816\pi$
$720$		0			0
$721$	−1.80296			−0.0671458
$722$	9.29246	−	9.29246i	0.345830	−	0.345830i
$723$		0			0
$724$		−	3.77661i		−	0.140357i
$725$	−0.575182	−	1.83067i	−0.0213617	−	0.0679895i
$726$		0			0
$727$	−35.6416	−	35.6416i	−1.32188	−	1.32188i	−0.912257	−	0.409619i	$-0.865662\pi$
$727$	−35.6416	−	35.6416i	−1.32188	−	1.32188i	−0.409619	−	0.912257i	$-0.634338\pi$
$728$	−2.68549	−	2.68549i	−0.0995308	−	0.0995308i
$729$		0			0
$730$	−15.4724	+	21.0794i	−0.572658	+	0.780182i
$731$			27.9127i			1.03239i
$732$		0			0
$733$	−12.6247	+	12.6247i	−0.466303	+	0.466303i	−0.900714	−	0.434412i	$-0.856956\pi$
$733$	−12.6247	+	12.6247i	−0.466303	+	0.466303i	0.434412	+	0.900714i	$0.356956\pi$
$734$	−8.31328			−0.306849
$735$		0			0
$736$	−1.00000			−0.0368605
$737$	−6.87291	+	6.87291i	−0.253167	+	0.253167i
$738$		0			0
$739$		−	26.0758i		−	0.959213i	−0.877484	−	0.479607i	$-0.840779\pi$
$739$		−	26.0758i		−	0.959213i	0.877484	−	0.479607i	$-0.159221\pi$
$740$	2.56507	−	0.393479i	0.0942938	−	0.0144646i
$741$		0			0
$742$	−9.55322	−	9.55322i	−0.350710	−	0.350710i
$743$	37.8958	+	37.8958i	1.39026	+	1.39026i	0.824719	+	0.565543i	$0.191334\pi$
$743$	37.8958	+	37.8958i	1.39026	+	1.39026i	0.565543	+	0.824719i	$0.308666\pi$
$744$		0			0
$745$	−23.5229	−	17.2659i	−0.861813	−	0.632575i
$746$		−	19.0988i		−	0.699257i
$747$		0			0
$748$	−13.0934	+	13.0934i	−0.478743	+	0.478743i
$749$	−2.25667			−0.0824571
$750$		0			0
$751$	−21.0249			−0.767209			−0.383604	−	0.923498i	$-0.625317\pi$
$751$	−21.0249			−0.767209			−0.383604	+	0.923498i	$0.625317\pi$
$752$	2.19098	−	2.19098i	0.0798969	−	0.0798969i
$753$		0			0
$754$			1.08550i			0.0395315i
$755$	21.5219	+	15.7972i	0.783262	+	0.574919i
$756$		0			0
$757$	23.8472	+	23.8472i	0.866743	+	0.866743i	0.992110	−	0.125368i	$-0.0400110\pi$
$757$	23.8472	+	23.8472i	0.866743	+	0.866743i	−0.125368	+	0.992110i	$0.540011\pi$
$758$	15.0396	+	15.0396i	0.546263	+	0.546263i
$759$		0			0
$760$	−5.34967	+	0.820634i	−0.194053	+	0.0297675i
$761$		−	25.7309i		−	0.932744i	−0.884589	−	0.466372i	$-0.845561\pi$
$761$		−	25.7309i		−	0.932744i	0.884589	−	0.466372i	$-0.154439\pi$
$762$		0			0
$763$	−12.8309	+	12.8309i	−0.464510	+	0.464510i
$764$	−17.0094			−0.615377
$765$		0			0
$766$	−19.1489			−0.691879
$767$	−3.87464	+	3.87464i	−0.139905	+	0.139905i
$768$		0			0
$769$			1.80807i			0.0652007i	0.999468	+	0.0326003i	$0.0103789\pi$
$769$			1.80807i			0.0652007i	−0.999468	+	0.0326003i	$0.989621\pi$
$770$	−4.70132	+	6.40502i	−0.169424	+	0.230821i
$771$		0			0
$772$	−17.8964	−	17.8964i	−0.644105	−	0.644105i
$773$	10.6612	+	10.6612i	0.383458	+	0.383458i	0.872346	−	0.488888i	$-0.162597\pi$
$773$	10.6612	+	10.6612i	0.383458	+	0.383458i	−0.488888	+	0.872346i	$0.662597\pi$
$774$		0			0
$775$	−10.4872	−	33.3785i	−0.376713	−	1.19899i
$776$		−	6.31929i		−	0.226849i
$777$		0			0
$778$	−15.0263	+	15.0263i	−0.538718	+	0.538718i
$779$	13.1003			0.469368
$780$		0			0
$781$	−23.2010			−0.830196
$782$	4.94794	−	4.94794i	0.176938	−	0.176938i
$783$		0			0
$784$			5.19704i			0.185608i
$785$	−7.41247	−	48.3215i	−0.264562	−	1.72467i
$786$		0			0
$787$	−4.39510	−	4.39510i	−0.156668	−	0.156668i	0.624420	−	0.781089i	$-0.285335\pi$
$787$	−4.39510	−	4.39510i	−0.156668	−	0.156668i	−0.781089	+	0.624420i	$0.785335\pi$
$788$	−2.70850	−	2.70850i	−0.0964862	−	0.0964862i
$789$		0			0
$790$	4.15416	+	27.0808i	0.147798	+	0.963491i
$791$		−	7.11744i		−	0.253067i
$792$		0			0
$793$	−16.6387	+	16.6387i	−0.590858	+	0.590858i
$794$	−4.92808			−0.174891
$795$		0			0
$796$	−7.19448			−0.255002
$797$	−29.1863	+	29.1863i	−1.03383	+	1.03383i	−0.0344254	+	0.999407i	$0.510960\pi$
$797$	−29.1863	+	29.1863i	−1.03383	+	1.03383i	−0.999407	+	0.0344254i	$0.989040\pi$
$798$		0			0
$799$			21.6817i			0.767044i
$800$	−4.43273	−	2.31321i	−0.156721	−	0.0817844i
$801$		0			0
$802$	−22.0566	−	22.0566i	−0.778845	−	0.778845i
$803$	−21.8812	−	21.8812i	−0.772172	−	0.772172i
$804$		0			0
$805$	1.77661	−	2.42043i	0.0626172	−	0.0853089i
$806$			19.7918i			0.697135i
$807$		0			0
$808$	3.26882	−	3.26882i	0.114997	−	0.114997i
$809$	28.8768			1.01525			0.507626	−	0.861577i	$-0.330523\pi$
$809$	28.8768			1.01525			0.507626	+	0.861577i	$0.330523\pi$
$810$		0			0
$811$	−33.9696			−1.19283			−0.596417	−	0.802675i	$-0.703410\pi$
$811$	−33.9696			−1.19283			−0.596417	+	0.802675i	$0.703410\pi$
$812$	−0.364386	+	0.364386i	−0.0127875	+	0.0127875i
$813$		0			0
$814$			3.07109i			0.107642i
$815$	6.86731	−	1.05344i	0.240551	−	0.0369004i
$816$		0			0
$817$	−6.82714	−	6.82714i	−0.238852	−	0.238852i
$818$	−3.23522	−	3.23522i	−0.113117	−	0.113117i
$819$		0			0
$820$	9.75638	+	7.16124i	0.340708	+	0.250081i
$821$		−	43.0419i		−	1.50217i	−0.660204	−	0.751086i	$-0.729530\pi$
$821$		−	43.0419i		−	1.50217i	0.660204	−	0.751086i	$-0.270470\pi$
$822$		0			0
$823$	17.7261	−	17.7261i	0.617892	−	0.617892i	−0.327098	−	0.944990i	$-0.606071\pi$
$823$	17.7261	−	17.7261i	0.617892	−	0.617892i	0.944990	+	0.327098i	$0.106071\pi$
$824$	1.34274			0.0467767
$825$		0			0
$826$	−2.60133			−0.0905118
$827$	9.45223	−	9.45223i	0.328686	−	0.328686i	−0.523401	−	0.852087i	$-0.675337\pi$
$827$	9.45223	−	9.45223i	0.328686	−	0.328686i	0.852087	+	0.523401i	$0.175337\pi$
$828$		0			0
$829$		−	17.1064i		−	0.594131i	−0.954857	−	0.297065i	$-0.903992\pi$
$829$		−	17.1064i		−	0.594131i	0.954857	−	0.297065i	$-0.0960080\pi$
$830$	14.1768	+	10.4059i	0.492085	+	0.361193i
$831$		0			0
$832$	2.00000	+	2.00000i	0.0693375	+	0.0693375i
$833$	−25.7146	−	25.7146i	−0.890959	−	0.890959i
$834$		0			0
$835$	6.41290	−	0.983732i	0.221927	−	0.0340434i
$836$		−	6.40502i		−	0.221522i
$837$		0			0
$838$	−6.93542	+	6.93542i	−0.239580	+	0.239580i
$839$	40.4615			1.39689			0.698444	−	0.715665i	$-0.253876\pi$
$839$	40.4615			1.39689			0.698444	+	0.715665i	$0.253876\pi$
$840$		0			0
$841$	−28.8527			−0.994921
$842$	12.0570	−	12.0570i	0.415513	−	0.415513i
$843$		0			0
$844$			0.0685362i			0.00235911i
$845$	6.61558	−	9.01299i	0.227583	−	0.310056i
$846$		0			0
$847$	3.79543	+	3.79543i	0.130413	+	0.130413i
$848$	7.11469	+	7.11469i	0.244320	+	0.244320i
$849$		0			0
$850$	33.3785	−	10.4872i	1.14487	−	0.359709i
$851$		−	1.16055i		−	0.0397832i
$852$		0			0
$853$	−24.0274	+	24.0274i	−0.822683	+	0.822683i	−0.986492	−	0.163809i	$-0.947622\pi$
$853$	−24.0274	+	24.0274i	−0.822683	+	0.822683i	0.163809	+	0.986492i	$0.447622\pi$
$854$	−11.1708			−0.382256
$855$		0			0
$856$	1.68064			0.0574432
$857$	−18.0066	+	18.0066i	−0.615093	+	0.615093i	−0.944269	−	0.329175i	$-0.893229\pi$
$857$	−18.0066	+	18.0066i	−0.615093	+	0.615093i	0.329175	+	0.944269i	$0.393229\pi$
$858$		0			0
$859$			56.2742i			1.92005i	0.279912	+	0.960026i	$0.409695\pi$
$859$			56.2742i			1.92005i	−0.279912	+	0.960026i	$0.590305\pi$
$860$	−1.35244	−	8.81650i	−0.0461179	−	0.300640i
$861$		0			0
$862$	1.55832	+	1.55832i	0.0530767	+	0.0530767i
$863$	−34.5743	−	34.5743i	−1.17692	−	1.17692i	−0.980524	−	0.196399i	$-0.937075\pi$
$863$	−34.5743	−	34.5743i	−1.17692	−	1.17692i	−0.196399	−	0.980524i	$-0.562925\pi$
$864$		0			0
$865$	−1.32191	−	8.61747i	−0.0449463	−	0.293003i
$866$		−	16.7685i		−	0.569817i
$867$		0			0
$868$	−6.64382	+	6.64382i	−0.225506	+	0.225506i
$869$	−32.4231			−1.09988
$870$		0			0
$871$	−10.3890			−0.352017
$872$	9.55573	−	9.55573i	0.323598	−	0.323598i
$873$		0			0
$874$			2.42043i			0.0818722i
$875$	13.4742	−	6.61943i	0.455510	−	0.223778i
$876$		0			0
$877$	7.46516	+	7.46516i	0.252081	+	0.252081i	0.821823	−	0.569743i	$-0.192957\pi$
$877$	7.46516	+	7.46516i	0.252081	+	0.252081i	−0.569743	+	0.821823i	$0.692957\pi$
$878$	−9.21044	−	9.21044i	−0.310837	−	0.310837i
$879$		0			0
$880$	3.50128	−	4.77010i	0.118028	−	0.160800i
$881$			6.96179i			0.234549i	0.993100	+	0.117274i	$0.0374157\pi$
$881$			6.96179i			0.234549i	−0.993100	+	0.117274i	$0.962584\pi$
$882$		0			0
$883$	11.4066	−	11.4066i	0.383862	−	0.383862i	−0.488629	−	0.872491i	$-0.662503\pi$
$883$	11.4066	−	11.4066i	0.383862	−	0.383862i	0.872491	+	0.488629i	$0.162503\pi$
$884$	−19.7918			−0.665669
$885$		0			0
$886$	23.4745			0.788640
$887$	−4.39479	+	4.39479i	−0.147562	+	0.147562i	−0.777028	−	0.629466i	$-0.783274\pi$
$887$	−4.39479	+	4.39479i	−0.147562	+	0.147562i	0.629466	+	0.777028i	$0.283274\pi$
$888$		0			0
$889$		−	12.9086i		−	0.432942i
$890$	−11.8046	+	1.81081i	−0.395691	+	0.0606986i
$891$		0			0
$892$	19.6524	+	19.6524i	0.658012	+	0.658012i
$893$	−5.30312	−	5.30312i	−0.177462	−	0.177462i
$894$		0			0
$895$	−22.1035	−	16.2241i	−0.738838	−	0.542311i
$896$			1.34274i			0.0448579i
$897$		0			0
$898$	−9.76652	+	9.76652i	−0.325913	+	0.325913i
$899$	2.68549			0.0895661
$900$		0			0
$901$	−70.4062			−2.34557
$902$	−10.1275	+	10.1275i	−0.337209	+	0.337209i
$903$		0			0
$904$			5.30066i			0.176297i
$905$	−6.80771	−	4.99689i	−0.226296	−	0.166102i
$906$		0			0
$907$	−32.6034	−	32.6034i	−1.08258	−	1.08258i	−0.996268	−	0.0863106i	$-0.972492\pi$
$907$	−32.6034	−	32.6034i	−1.08258	−	1.08258i	−0.0863106	−	0.996268i	$-0.527508\pi$
$908$	−2.83984	−	2.83984i	−0.0942434	−	0.0942434i
$909$		0			0
$910$	−8.39407	+	1.28764i	−0.278261	+	0.0426849i
$911$			54.2830i			1.79848i	0.437461	+	0.899238i	$0.355878\pi$
$911$			54.2830i			1.79848i	−0.437461	+	0.899238i	$0.644122\pi$
$912$		0			0
$913$	−14.7161	+	14.7161i	−0.487032	+	0.487032i
$914$	0.116320			0.00384751
$915$		0			0
$916$	−4.42554			−0.146224
$917$	−2.93164	+	2.93164i	−0.0968114	+	0.0968114i
$918$		0			0
$919$		−	52.6590i		−	1.73706i	−0.495637	−	0.868530i	$-0.665065\pi$
$919$		−	52.6590i		−	1.73706i	0.495637	−	0.868530i	$-0.334935\pi$
$920$	−1.32312	+	1.80260i	−0.0436219	+	0.0594299i
$921$		0			0
$922$	22.0542	+	22.0542i	0.726315	+	0.726315i
$923$	−17.5351	−	17.5351i	−0.577175	−	0.577175i
$924$		0			0
$925$	2.68460	−	5.14441i	0.0882691	−	0.169147i
$926$			12.8064i			0.420845i
$927$		0			0
$928$	0.271374	−	0.271374i	0.00890830	−	0.00890830i
$929$	13.6515			0.447892			0.223946	−	0.974602i	$-0.428106\pi$
$929$	13.6515			0.447892			0.223946	+	0.974602i	$0.428106\pi$
$930$		0			0
$931$	12.5791			0.412262
$932$	−0.799777	+	0.799777i	−0.0261976	+	0.0261976i
$933$		0			0
$934$		−	13.9657i		−	0.456973i
$935$	6.27805	+	40.9263i	0.205314	+	1.33843i
$936$		0			0
$937$	28.6980	+	28.6980i	0.937522	+	0.937522i	0.998160	−	0.0606375i	$-0.0193134\pi$
$937$	28.6980	+	28.6980i	0.937522	+	0.937522i	−0.0606375	+	0.998160i	$0.519313\pi$
$938$	−3.48743	−	3.48743i	−0.113869	−	0.113869i
$939$		0			0
$940$	−1.05054	−	6.84839i	−0.0342647	−	0.223370i
$941$		−	9.58042i		−	0.312313i	−0.987732	−	0.156156i	$-0.950090\pi$
$941$		−	9.58042i		−	0.312313i	0.987732	−	0.156156i	$-0.0499104\pi$
$942$		0			0
$943$	3.82714	−	3.82714i	0.124629	−	0.124629i
$944$	1.93732			0.0630544
$945$		0			0
$946$	10.5558			0.343198
$947$	21.3347	−	21.3347i	0.693283	−	0.693283i	−0.269670	−	0.962953i	$-0.586915\pi$
$947$	21.3347	−	21.3347i	0.693283	−	0.693283i	0.962953	+	0.269670i	$0.0869145\pi$
$948$		0			0
$949$		−	33.0753i		−	1.07367i
$950$	−5.59896	+	10.7291i	−0.181654	+	0.348098i
$951$		0			0
$952$	−6.64382	−	6.64382i	−0.215327	−	0.215327i
$953$	17.9775	+	17.9775i	0.582349	+	0.582349i	0.935548	−	0.353199i	$-0.114906\pi$
$953$	17.9775	+	17.9775i	0.582349	+	0.582349i	−0.353199	+	0.935548i	$0.614906\pi$
$954$		0			0
$955$	−22.5054	+	30.6610i	−0.728256	+	0.992168i
$956$		−	17.2078i		−	0.556540i
$957$		0			0
$958$	15.1259	−	15.1259i	0.488697	−	0.488697i
$959$	−4.62472			−0.149340
$960$		0			0
$961$	17.9643			0.579492
$962$	−2.32110	+	2.32110i	−0.0748353	+	0.0748353i
$963$		0			0
$964$		−	5.25511i		−	0.169256i
$965$	−55.9390	+	8.58098i	−1.80074	+	0.276232i
$966$		0			0
$967$	14.2356	+	14.2356i	0.457787	+	0.457787i	0.897928	−	0.440142i	$-0.145072\pi$
$967$	14.2356	+	14.2356i	0.457787	+	0.457787i	−0.440142	+	0.897928i	$0.645072\pi$
$968$	−2.82662	−	2.82662i	−0.0908510	−	0.0908510i
$969$		0			0
$970$	−11.3911	−	8.36116i	−0.365747	−	0.268461i
$971$			14.5361i			0.466486i	0.972419	+	0.233243i	$0.0749337\pi$
$971$			14.5361i			0.466486i	−0.972419	+	0.233243i	$0.925066\pi$
$972$		0			0
$973$	−19.8788	+	19.8788i	−0.637284	+	0.637284i
$974$	36.2514			1.16157
$975$		0			0
$976$	8.31936			0.266296
$977$	3.29748	−	3.29748i	0.105496	−	0.105496i	−0.652389	−	0.757884i	$-0.726233\pi$
$977$	3.29748	−	3.29748i	0.105496	−	0.105496i	0.757884	+	0.652389i	$0.226233\pi$
$978$		0			0
$979$		−	14.1334i		−	0.451704i
$980$	9.36817	+	6.87629i	0.299255	+	0.219655i
$981$		0			0
$982$	22.9050	+	22.9050i	0.730927	+	0.730927i
$983$	−16.4632	−	16.4632i	−0.525096	−	0.525096i	0.394010	−	0.919106i	$-0.371087\pi$
$983$	−16.4632	−	16.4632i	−0.525096	−	0.525096i	−0.919106	+	0.394010i	$0.871087\pi$
$984$		0			0
$985$	−8.46599	+	1.29867i	−0.269749	+	0.0413792i
$986$			2.68549i			0.0855234i
$987$		0			0
$988$	4.84086	−	4.84086i	0.154008	−	0.154008i
$989$	−3.98898			−0.126842
$990$		0			0
$991$	−46.1262			−1.46525			−0.732623	−	0.680634i	$-0.761704\pi$
$991$	−46.1262			−1.46525			−0.732623	+	0.680634i	$0.761704\pi$
$992$	4.94794	−	4.94794i	0.157097	−	0.157097i
$993$		0			0
$994$		−	11.7726i		−	0.373403i
$995$	−9.51914	+	12.9688i	−0.301777	+	0.411137i
$996$		0			0
$997$	−2.42727	−	2.42727i	−0.0768724	−	0.0768724i	0.667625	−	0.744498i	$-0.267311\pi$
$997$	−2.42727	−	2.42727i	−0.0768724	−	0.0768724i	−0.744498	+	0.667625i	$0.767311\pi$
$998$	−10.6334	−	10.6334i	−0.336594	−	0.336594i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2070.2.j.i.737.5	yes	16
3.2	odd	2	inner	2070.2.j.i.737.4	yes	16
5.3	odd	4	inner	2070.2.j.i.323.4	✓	16
15.8	even	4	inner	2070.2.j.i.323.5	yes	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2070.2.j.i.323.4	✓	16	5.3	odd	4	inner
2070.2.j.i.323.5	yes	16	15.8	even	4	inner
2070.2.j.i.737.4	yes	16	3.2	odd	2	inner
2070.2.j.i.737.5	yes	16	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 2070 = 2 \cdot 3^{2} \cdot 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2070.j (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.707107 - 0.707107i) q^{2} -1.00000i q^{4} +(-1.80260 - 1.32312i) q^{5} +(0.949464 + 0.949464i) q^{7} +(-0.707107 - 0.707107i) q^{8} +O(q^{10})\)	\(q+(0.707107 - 0.707107i) q^{2} -1.00000i q^{4} +(-1.80260 - 1.32312i) q^{5} +(0.949464 + 0.949464i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(-2.21021 + 0.339045i) q^{10} -2.64623i q^{11} +(2.00000 - 2.00000i) q^{13} +1.34274 q^{14} -1.00000 q^{16} +(4.94794 - 4.94794i) q^{17} +2.42043i q^{19} +(-1.32312 + 1.80260i) q^{20} +(-1.87117 - 1.87117i) q^{22} +(0.707107 + 0.707107i) q^{23} +(1.49872 + 4.77010i) q^{25} -2.82843i q^{26} +(0.949464 - 0.949464i) q^{28} -0.383781 q^{29} -6.99745 q^{31} +(-0.707107 + 0.707107i) q^{32} -6.99745i q^{34} +(-0.455250 - 2.96775i) q^{35} +(-0.820634 - 0.820634i) q^{37} +(1.71150 + 1.71150i) q^{38} +(0.339045 + 2.21021i) q^{40} -5.41240i q^{41} +(-2.82063 + 2.82063i) q^{43} -2.64623 q^{44} +1.00000 q^{46} +(-2.19098 + 2.19098i) q^{47} -5.19704i q^{49} +(4.43273 + 2.31321i) q^{50} +(-2.00000 - 2.00000i) q^{52} +(-7.11469 - 7.11469i) q^{53} +(-3.50128 + 4.77010i) q^{55} -1.34274i q^{56} +(-0.271374 + 0.271374i) q^{58} -1.93732 q^{59} -8.31936 q^{61} +(-4.94794 + 4.94794i) q^{62} +1.00000i q^{64} +(-6.25143 + 0.958963i) q^{65} +(-2.59724 - 2.59724i) q^{67} +(-4.94794 - 4.94794i) q^{68} +(-2.42043 - 1.77661i) q^{70} -8.76755i q^{71} +(8.26882 - 8.26882i) q^{73} -1.16055 q^{74} +2.42043 q^{76} +(2.51250 - 2.51250i) q^{77} -12.2526i q^{79} +(1.80260 + 1.32312i) q^{80} +(-3.82714 - 3.82714i) q^{82} +(-5.56115 - 5.56115i) q^{83} +(-15.4659 + 2.37245i) q^{85} +3.98898i q^{86} +(-1.87117 + 1.87117i) q^{88} +5.34093 q^{89} +3.79785 q^{91} +(0.707107 - 0.707107i) q^{92} +3.09852i q^{94} +(3.20251 - 4.36306i) q^{95} +(4.46841 + 4.46841i) q^{97} +(-3.67486 - 3.67486i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q+O(q^{10}) \) 16 * q	\( 16 q - 4 q^{10} + 32 q^{13} - 16 q^{16} - 24 q^{25} - 16 q^{31} + 32 q^{37} + 4 q^{40} + 16 q^{46} - 32 q^{52} - 104 q^{55} + 8 q^{58} - 40 q^{61} + 72 q^{67} + 24 q^{70} + 24 q^{73} - 24 q^{76} - 8 q^{82} - 8 q^{85} - 72 q^{97}+O(q^{100}) \) 16 * q - 4 * q^10 + 32 * q^13 - 16 * q^16 - 24 * q^25 - 16 * q^31 + 32 * q^37 + 4 * q^40 + 16 * q^46 - 32 * q^52 - 104 * q^55 + 8 * q^58 - 40 * q^61 + 72 * q^67 + 24 * q^70 + 24 * q^73 - 24 * q^76 - 8 * q^82 - 8 * q^85 - 72 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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