LMFDB - Embedded newform 1710.2.p.d.37.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1710,2,Mod(37,1710)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1710, base_ring=CyclotomicField(4))

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

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

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

chi := DirichletCharacter("1710.37");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1710 = 2 \cdot 3^{2} \cdot 5 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1710.p (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:	$13.6544187456$
Analytic rank:	$0$
Dimension:	$20$
Relative dimension:	$10$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} + 153x^{16} + 6416x^{12} + 78648x^{8} + 19120x^{4} + 16 $ x^20 + 153x^16 + 6416x^12 + 78648x^8 + 19120x^4 + 16
Coefficient ring:	$\Z[a_1, \ldots, a_{19}]$
Coefficient ring index:	$ 2^{10} $
Twist minimal:	no (minimal twist has level 570)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			37.2
Root			$2.19691 - 2.19691i$ of defining polynomial
Character	$\chi$	$=$	1710.37
Dual form			1710.2.p.d.1063.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.707107 + 0.707107i) q^{2} -1.00000i q^{4} +(-1.25884 - 1.84806i) q^{5} +(3.10690 + 3.10690i) q^{7} +(0.707107 + 0.707107i) q^{8} +O(q^{10})$	\(q+(-0.707107 + 0.707107i) q^{2} -1.00000i q^{4} +(-1.25884 - 1.84806i) q^{5} +(3.10690 + 3.10690i) q^{7} +(0.707107 + 0.707107i) q^{8} +(2.19691 + 0.416642i) q^{10} +3.82217 q^{11} +(-0.0891314 - 0.0891314i) q^{13} -4.39382 q^{14} -1.00000 q^{16} +(1.83065 + 1.83065i) q^{17} +(-2.70268 + 3.41987i) q^{19} +(-1.84806 + 1.25884i) q^{20} +(-2.70268 + 2.70268i) q^{22} +(-2.58922 + 2.58922i) q^{23} +(-1.83065 + 4.65282i) q^{25} +0.126051 q^{26} +(3.10690 - 3.10690i) q^{28} -3.60048 q^{29} -3.60048i q^{31} +(0.707107 - 0.707107i) q^{32} -2.58893 q^{34} +(1.83065 - 9.65282i) q^{35} +(7.07188 - 7.07188i) q^{37} +(-0.507128 - 4.32930i) q^{38} +(0.416642 - 2.19691i) q^{40} +11.2134i q^{41} +(7.93755 - 7.93755i) q^{43} -3.82217i q^{44} -3.66171i q^{46} +(0.463170 + 0.463170i) q^{47} +12.3056i q^{49} +(-1.99558 - 4.58450i) q^{50} +(-0.0891314 + 0.0891314i) q^{52} +(3.21910 + 3.21910i) q^{53} +(-4.81150 - 7.06360i) q^{55} +4.39382i q^{56} +(2.54592 - 2.54592i) q^{58} -9.40851 q^{59} +8.21380 q^{61} +(2.54592 + 2.54592i) q^{62} +1.00000i q^{64} +(-0.0525181 + 0.276922i) q^{65} +(-8.78764 + 8.78764i) q^{67} +(1.83065 - 1.83065i) q^{68} +(5.53111 + 8.12004i) q^{70} +1.66657i q^{71} +(-3.64373 + 3.64373i) q^{73} +10.0011i q^{74} +(3.41987 + 2.70268i) q^{76} +(11.8751 + 11.8751i) q^{77} -8.82758 q^{79} +(1.25884 + 1.84806i) q^{80} +(-7.92907 - 7.92907i) q^{82} +(0.347181 - 0.347181i) q^{83} +(1.07866 - 5.68764i) q^{85} +11.2254i q^{86} +(2.70268 + 2.70268i) q^{88} +9.79832 q^{89} -0.553844i q^{91} +(2.58922 + 2.58922i) q^{92} -0.655021 q^{94} +(9.72236 + 0.689653i) q^{95} +(-6.88409 + 6.88409i) q^{97} +(-8.70140 - 8.70140i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q + 4 q^{5} - 4 q^{7}+O(q^{10}) $ 20 * q + 4 * q^5 - 4 * q^7	$ 20 q + 4 q^{5} - 4 q^{7} + 8 q^{11} - 20 q^{16} - 4 q^{17} - 44 q^{23} + 4 q^{25} + 8 q^{26} - 4 q^{28} - 4 q^{35} + 4 q^{38} + 52 q^{43} - 4 q^{47} + 16 q^{55} + 8 q^{58} + 32 q^{61} + 8 q^{62} - 4 q^{68} - 20 q^{73} + 20 q^{76} + 24 q^{77} - 4 q^{80} - 24 q^{82} + 116 q^{83} - 60 q^{85} + 44 q^{92} + 32 q^{95}+O(q^{100}) $ 20 * q + 4 * q^5 - 4 * q^7 + 8 * q^11 - 20 * q^16 - 4 * q^17 - 44 * q^23 + 4 * q^25 + 8 * q^26 - 4 * q^28 - 4 * q^35 + 4 * q^38 + 52 * q^43 - 4 * q^47 + 16 * q^55 + 8 * q^58 + 32 * q^61 + 8 * q^62 - 4 * q^68 - 20 * q^73 + 20 * q^76 + 24 * q^77 - 4 * q^80 - 24 * q^82 + 116 * q^83 - 60 * q^85 + 44 * q^92 + 32 * q^95

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1710\mathbb{Z}\right)^\times$.

$n$	$191$	$1027$	$1351$
$\chi(n)$	$1$	$e\left(\frac{1}{4}\right)$	$-1$

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
$5$	−1.25884	−	1.84806i	−0.562970	−	0.826477i
$5$	−1.25884	−	1.84806i	−0.562970	−	0.826477i
$6$		0			0
$7$	3.10690	+	3.10690i	1.17430	+	1.17430i	0.981175	+	0.193123i	$0.0618615\pi$
$7$	3.10690	+	3.10690i	1.17430	+	1.17430i	0.193123	+	0.981175i	$0.438138\pi$
$8$	0.707107	+	0.707107i	0.250000	+	0.250000i
$9$		0			0
$10$	2.19691	+	0.416642i	0.694724	+	0.131754i
$11$	3.82217			1.15243			0.576214	−	0.817299i	$-0.304530\pi$
$11$	3.82217			1.15243			0.576214	+	0.817299i	$0.304530\pi$
$12$		0			0
$13$	−0.0891314	−	0.0891314i	−0.0247206	−	0.0247206i	0.694638	−	0.719359i	$-0.255564\pi$
$13$	−0.0891314	−	0.0891314i	−0.0247206	−	0.0247206i	−0.719359	+	0.694638i	$0.755564\pi$
$14$	−4.39382			−1.17430
$15$		0			0
$16$	−1.00000			−0.250000
$17$	1.83065	+	1.83065i	0.443998	+	0.443998i	0.893353	−	0.449355i	$-0.148346\pi$
$17$	1.83065	+	1.83065i	0.443998	+	0.443998i	−0.449355	+	0.893353i	$0.648346\pi$
$18$		0			0
$19$	−2.70268	+	3.41987i	−0.620038	+	0.784572i
$19$	−2.70268	+	3.41987i	−0.620038	+	0.784572i
$20$	−1.84806	+	1.25884i	−0.413239	+	0.281485i
$21$		0			0
$22$	−2.70268	+	2.70268i	−0.576214	+	0.576214i
$23$	−2.58922	+	2.58922i	−0.539890	+	0.539890i	−0.923497	−	0.383607i	$-0.874682\pi$
$23$	−2.58922	+	2.58922i	−0.539890	+	0.539890i	0.383607	+	0.923497i	$0.374682\pi$
$24$		0			0
$25$	−1.83065	+	4.65282i	−0.366130	+	0.930564i
$26$	0.126051			0.0247206
$27$		0			0
$28$	3.10690	−	3.10690i	0.587149	−	0.587149i
$29$	−3.60048			−0.668591			−0.334296	−	0.942468i	$-0.608498\pi$
$29$	−3.60048			−0.668591			−0.334296	+	0.942468i	$0.608498\pi$
$30$		0			0
$31$		−	3.60048i		−	0.646664i	−0.946286	−	0.323332i	$-0.895197\pi$
$31$		−	3.60048i		−	0.646664i	0.946286	−	0.323332i	$-0.104803\pi$
$32$	0.707107	−	0.707107i	0.125000	−	0.125000i
$33$		0			0
$34$	−2.58893			−0.443998
$35$	1.83065	−	9.65282i	0.309436	−	1.63162i
$36$		0			0
$37$	7.07188	−	7.07188i	1.16261	−	1.16261i	0.178707	−	0.983902i	$-0.442808\pi$
$37$	7.07188	−	7.07188i	1.16261	−	1.16261i	0.983902	−	0.178707i	$-0.0571915\pi$
$38$	−0.507128	−	4.32930i	−0.0822670	−	0.702305i
$39$		0			0
$40$	0.416642	−	2.19691i	0.0658769	−	0.347362i
$41$			11.2134i			1.75124i	0.483002	+	0.875619i	$0.339546\pi$
$41$			11.2134i			1.75124i	−0.483002	+	0.875619i	$0.660454\pi$
$42$		0			0
$43$	7.93755	−	7.93755i	1.21046	−	1.21046i	0.239591	−	0.970874i	$-0.422987\pi$
$43$	7.93755	−	7.93755i	1.21046	−	1.21046i	0.970874	−	0.239591i	$-0.0770132\pi$
$44$		−	3.82217i		−	0.576214i
$45$		0			0
$46$		−	3.66171i		−	0.539890i
$47$	0.463170	+	0.463170i	0.0675603	+	0.0675603i	0.740080	−	0.672519i	$-0.234788\pi$
$47$	0.463170	+	0.463170i	0.0675603	+	0.0675603i	−0.672519	+	0.740080i	$0.734788\pi$
$48$		0			0
$49$			12.3056i			1.75795i
$50$	−1.99558	−	4.58450i	−0.282217	−	0.648347i
$51$		0			0
$52$	−0.0891314	+	0.0891314i	−0.0123603	+	0.0123603i
$53$	3.21910	+	3.21910i	0.442178	+	0.442178i	0.892743	−	0.450566i	$-0.148778\pi$
$53$	3.21910	+	3.21910i	0.442178	+	0.442178i	−0.450566	+	0.892743i	$0.648778\pi$
$54$		0			0
$55$	−4.81150	−	7.06360i	−0.648782	−	0.952455i
$56$			4.39382i			0.587149i
$57$		0			0
$58$	2.54592	−	2.54592i	0.334296	−	0.334296i
$59$	−9.40851			−1.22488			−0.612442	−	0.790516i	$-0.709813\pi$
$59$	−9.40851			−1.22488			−0.612442	+	0.790516i	$0.709813\pi$
$60$		0			0
$61$	8.21380			1.05167			0.525834	−	0.850587i	$-0.323753\pi$
$61$	8.21380			1.05167			0.525834	+	0.850587i	$0.323753\pi$
$62$	2.54592	+	2.54592i	0.323332	+	0.323332i
$63$		0			0
$64$			1.00000i			0.125000i
$65$	−0.0525181	+	0.276922i	−0.00651406	+	0.0343480i
$66$		0			0
$67$	−8.78764	+	8.78764i	−1.07358	+	1.07358i	−0.0765120	+	0.997069i	$0.524378\pi$
$67$	−8.78764	+	8.78764i	−1.07358	+	1.07358i	−0.997069	+	0.0765120i	$0.975622\pi$
$68$	1.83065	−	1.83065i	0.221999	−	0.221999i
$69$		0			0
$70$	5.53111	+	8.12004i	0.661094	+	0.970530i
$71$			1.66657i			0.197785i	0.995098	+	0.0988926i	$0.0315300\pi$
$71$			1.66657i			0.197785i	−0.995098	+	0.0988926i	$0.968470\pi$
$72$		0			0
$73$	−3.64373	+	3.64373i	−0.426466	+	0.426466i	−0.887423	−	0.460957i	$-0.847506\pi$
$73$	−3.64373	+	3.64373i	−0.426466	+	0.426466i	0.460957	+	0.887423i	$0.347506\pi$
$74$			10.0011i			1.16261i
$75$		0			0
$76$	3.41987	+	2.70268i	0.392286	+	0.310019i
$77$	11.8751	+	11.8751i	1.35329	+	1.35329i
$78$		0			0
$79$	−8.82758			−0.993180			−0.496590	−	0.867985i	$-0.665415\pi$
$79$	−8.82758			−0.993180			−0.496590	+	0.867985i	$0.665415\pi$
$80$	1.25884	+	1.84806i	0.140742	+	0.206619i
$81$		0			0
$82$	−7.92907	−	7.92907i	−0.875619	−	0.875619i
$83$	0.347181	−	0.347181i	0.0381081	−	0.0381081i	−0.687796	−	0.725904i	$-0.741422\pi$
$83$	0.347181	−	0.347181i	0.0381081	−	0.0381081i	0.725904	+	0.687796i	$0.241422\pi$
$84$		0			0
$85$	1.07866	−	5.68764i	0.116997	−	0.616911i
$86$			11.2254i			1.21046i
$87$		0			0
$88$	2.70268	+	2.70268i	0.288107	+	0.288107i
$89$	9.79832			1.03862			0.519310	−	0.854586i	$-0.326189\pi$
$89$	9.79832			1.03862			0.519310	+	0.854586i	$0.326189\pi$
$90$		0			0
$91$		−	0.553844i		−	0.0580587i
$92$	2.58922	+	2.58922i	0.269945	+	0.269945i
$93$		0			0
$94$	−0.655021			−0.0675603
$95$	9.72236	+	0.689653i	0.997494	+	0.0707569i
$96$		0			0
$97$	−6.88409	+	6.88409i	−0.698973	+	0.698973i	−0.964189	−	0.265216i	$-0.914557\pi$
$97$	−6.88409	+	6.88409i	−0.698973	+	0.698973i	0.265216	+	0.964189i	$0.414557\pi$
$98$	−8.70140	−	8.70140i	−0.878974	−	0.878974i
$99$		0			0
$100$	4.65282	+	1.83065i	0.465282	+	0.183065i
$101$	3.89174			0.387242			0.193621	−	0.981076i	$-0.437977\pi$
$101$	3.89174			0.387242			0.193621	+	0.981076i	$0.437977\pi$
$102$		0			0
$103$	9.40518	+	9.40518i	0.926720	+	0.926720i	0.997492	−	0.0707726i	$-0.0225465\pi$
$103$	9.40518	+	9.40518i	0.926720	+	0.926720i	−0.0707726	+	0.997492i	$0.522546\pi$
$104$		−	0.126051i		−	0.0123603i
$105$		0			0
$106$	−4.55250			−0.442178
$107$	7.00983	−	7.00983i	0.677666	−	0.677666i	−0.281806	−	0.959472i	$-0.590933\pi$
$107$	7.00983	−	7.00983i	0.677666	−	0.677666i	0.959472	+	0.281806i	$0.0909333\pi$
$108$		0			0
$109$	17.7935			1.70431			0.852153	−	0.523293i	$-0.175297\pi$
$109$	17.7935			1.70431			0.852153	+	0.523293i	$0.175297\pi$
$110$	8.39696	+	1.59248i	0.800619	+	0.151837i
$111$		0			0
$112$	−3.10690	−	3.10690i	−0.293574	−	0.293574i
$113$	12.4493	+	12.4493i	1.17114	+	1.17114i	0.981939	+	0.189197i	$0.0605884\pi$
$113$	12.4493	+	12.4493i	1.17114	+	1.17114i	0.189197	+	0.981939i	$0.439412\pi$
$114$		0			0
$115$	8.04445	+	1.52562i	0.750148	+	0.142265i
$116$			3.60048i			0.334296i
$117$		0			0
$118$	6.65282	−	6.65282i	0.612442	−	0.612442i
$119$			11.3753i			1.04277i
$120$		0			0
$121$	3.60898			0.328089
$122$	−5.80803	+	5.80803i	−0.525834	+	0.525834i
$123$		0			0
$124$	−3.60048			−0.323332
$125$	10.9032	−	2.47400i	0.975210	−	0.221281i
$126$		0			0
$127$	0.0636986	−	0.0636986i	0.00565234	−	0.00565234i	−0.704275	−	0.709927i	$-0.748728\pi$
$127$	0.0636986	−	0.0636986i	0.00565234	−	0.00565234i	0.709927	+	0.704275i	$0.248728\pi$
$128$	−0.707107	−	0.707107i	−0.0625000	−	0.0625000i
$129$		0			0
$130$	−0.158678	−	0.232949i	−0.0139170	−	0.0204310i
$131$	−2.44811			−0.213893			−0.106946	−	0.994265i	$-0.534107\pi$
$131$	−2.44811			−0.213893			−0.106946	+	0.994265i	$0.534107\pi$
$132$		0			0
$133$	−19.0221	+	2.22823i	−1.64943	+	0.193212i
$134$		−	12.4276i		−	1.07358i
$135$		0			0
$136$			2.58893i			0.221999i
$137$	−3.02688	−	3.02688i	−0.258604	−	0.258604i	0.565882	−	0.824486i	$-0.308536\pi$
$137$	−3.02688	−	3.02688i	−0.258604	−	0.258604i	−0.824486	+	0.565882i	$0.808536\pi$
$138$		0			0
$139$			3.96170i			0.336027i	0.985785	+	0.168013i	$0.0537352\pi$
$139$			3.96170i			0.336027i	−0.985785	+	0.168013i	$0.946265\pi$
$140$	−9.65282	−	1.83065i	−0.815812	−	0.154718i
$141$		0			0
$142$	−1.17844	−	1.17844i	−0.0988926	−	0.0988926i
$143$	−0.340675	−	0.340675i	−0.0284887	−	0.0284887i
$144$		0			0
$145$	4.53242	+	6.65389i	0.376397	+	0.552576i
$146$		−	5.15301i		−	0.426466i
$147$		0			0
$148$	−7.07188	−	7.07188i	−0.581305	−	0.581305i
$149$			22.3940i			1.83459i	0.398211	+	0.917294i	$0.369631\pi$
$149$			22.3940i			1.83459i	−0.398211	+	0.917294i	$0.630369\pi$
$150$		0			0
$151$			11.2995i			0.919539i	0.888038	+	0.459769i	$0.152068\pi$
$151$			11.2995i			0.919539i	−0.888038	+	0.459769i	$0.847932\pi$
$152$	−4.32930	+	0.507128i	−0.351152	+	0.0411335i
$153$		0			0
$154$	−16.7939			−1.35329
$155$	−6.65389	+	4.53242i	−0.534454	+	0.364053i
$156$		0			0
$157$	−4.57916	−	4.57916i	−0.365457	−	0.365457i	0.500361	−	0.865817i	$-0.333201\pi$
$157$	−4.57916	−	4.57916i	−0.365457	−	0.365457i	−0.865817	+	0.500361i	$0.833201\pi$
$158$	6.24204	−	6.24204i	0.496590	−	0.496590i
$159$		0			0
$160$	−2.19691	−	0.416642i	−0.173681	−	0.0329384i
$161$	−16.0889			−1.26798
$162$		0			0
$163$	7.54592	−	7.54592i	0.591042	−	0.591042i	−0.346871	−	0.937913i	$-0.612756\pi$
$163$	7.54592	−	7.54592i	0.591042	−	0.591042i	0.937913	+	0.346871i	$0.112756\pi$
$164$	11.2134			0.875619
$165$		0			0
$166$			0.490988i			0.0381081i
$167$	15.1275	−	15.1275i	1.17060	−	1.17060i	0.188531	−	0.982067i	$-0.439627\pi$
$167$	15.1275	−	15.1275i	1.17060	−	1.17060i	0.982067	−	0.188531i	$-0.0603726\pi$
$168$		0			0
$169$		−	12.9841i		−	0.998778i
$170$	3.25904	+	4.78449i	0.249957	+	0.366954i
$171$		0			0
$172$	−7.93755	−	7.93755i	−0.605232	−	0.605232i
$173$	−2.32458	−	2.32458i	−0.176735	−	0.176735i	0.613196	−	0.789931i	$-0.289884\pi$
$173$	−2.32458	−	2.32458i	−0.176735	−	0.176735i	−0.789931	+	0.613196i	$0.789884\pi$
$174$		0			0
$175$	−20.1435	+	8.76820i	−1.52270	+	0.662813i
$176$	−3.82217			−0.288107
$177$		0			0
$178$	−6.92846	+	6.92846i	−0.519310	+	0.519310i
$179$	−0.515834			−0.0385553			−0.0192776	−	0.999814i	$-0.506137\pi$
$179$	−0.515834			−0.0385553			−0.0192776	+	0.999814i	$0.506137\pi$
$180$		0			0
$181$			4.86127i			0.361336i	0.983544	+	0.180668i	$0.0578259\pi$
$181$			4.86127i			0.361336i	−0.983544	+	0.180668i	$0.942174\pi$
$182$	0.391627	+	0.391627i	0.0290293	+	0.0290293i
$183$		0			0
$184$	−3.66171			−0.269945
$185$	−21.9716	−	4.16690i	−1.61538	−	0.306356i
$186$		0			0
$187$	6.99705	+	6.99705i	0.511675	+	0.511675i
$188$	0.463170	−	0.463170i	0.0337801	−	0.0337801i
$189$		0			0
$190$	−7.36241	+	6.38709i	−0.534125	+	0.463368i
$191$	15.3369			1.10974			0.554870	−	0.831937i	$-0.312768\pi$
$191$	15.3369			1.10974			0.554870	+	0.831937i	$0.312768\pi$
$192$		0			0
$193$	−17.1600	−	17.1600i	−1.23521	−	1.23521i	−0.961938	−	0.273268i	$-0.911895\pi$
$193$	−17.1600	−	17.1600i	−1.23521	−	1.23521i	−0.273268	−	0.961938i	$-0.588105\pi$
$194$		−	9.73557i		−	0.698973i
$195$		0			0
$196$	12.3056			0.878974
$197$	6.25052	+	6.25052i	0.445331	+	0.445331i	0.893799	−	0.448468i	$-0.148030\pi$
$197$	6.25052	+	6.25052i	0.445331	+	0.445331i	−0.448468	+	0.893799i	$0.648030\pi$
$198$		0			0
$199$			10.4094i			0.737904i	0.929448	+	0.368952i	$0.120283\pi$
$199$			10.4094i			0.737904i	−0.929448	+	0.368952i	$0.879717\pi$
$200$	−4.58450	+	1.99558i	−0.324173	+	0.141109i
$201$		0			0
$202$	−2.75187	+	2.75187i	−0.193621	+	0.193621i
$203$	−11.1863	−	11.1863i	−0.785125	−	0.785125i
$204$		0			0
$205$	20.7230	−	14.1159i	1.44736	−	0.985894i
$206$	−13.3009			−0.926720
$207$		0			0
$208$	0.0891314	+	0.0891314i	0.00618015	+	0.00618015i
$209$	−10.3301	+	13.0713i	−0.714549	+	0.904162i
$210$		0			0
$211$			13.0551i			0.898752i	0.893343	+	0.449376i	$0.148354\pi$
$211$			13.0551i			0.898752i	−0.893343	+	0.449376i	$0.851646\pi$
$212$	3.21910	−	3.21910i	0.221089	−	0.221089i
$213$		0			0
$214$			9.91340i			0.677666i
$215$	−24.6612	−	4.67697i	−1.68188	−	0.318967i
$216$		0			0
$217$	11.1863	−	11.1863i	0.759376	−	0.759376i
$218$	−12.5819	+	12.5819i	−0.852153	+	0.852153i
$219$		0			0
$220$	−7.06360	+	4.81150i	−0.476228	+	0.324391i
$221$		−	0.326337i		−	0.0219518i
$222$		0			0
$223$	−11.5414	−	11.5414i	−0.772872	−	0.772872i	0.205736	−	0.978608i	$-0.434041\pi$
$223$	−11.5414	−	11.5414i	−0.772872	−	0.772872i	−0.978608	+	0.205736i	$0.934041\pi$
$224$	4.39382			0.293574
$225$		0			0
$226$	−17.6060			−1.17114
$227$	16.4312	−	16.4312i	1.09058	−	1.09058i	0.0951099	−	0.995467i	$-0.469680\pi$
$227$	16.4312	−	16.4312i	1.09058	−	1.09058i	0.995467	−	0.0951099i	$-0.0303202\pi$
$228$		0			0
$229$			15.5194i			1.02555i	0.858522	+	0.512777i	$0.171383\pi$
$229$			15.5194i			1.02555i	−0.858522	+	0.512777i	$0.828617\pi$
$230$	−6.76706	+	4.60950i	−0.446207	+	0.303942i
$231$		0			0
$232$	−2.54592	−	2.54592i	−0.167148	−	0.167148i
$233$	1.69112	−	1.69112i	0.110789	−	0.110789i	−0.649539	−	0.760328i	$-0.725038\pi$
$233$	1.69112	−	1.69112i	0.110789	−	0.110789i	0.760328	+	0.649539i	$0.225038\pi$
$234$		0			0
$235$	0.272909	−	1.43902i	0.0178026	−	0.0938714i
$236$			9.40851i			0.612442i
$237$		0			0
$238$	−8.04354	−	8.04354i	−0.521385	−	0.521385i
$239$		−	12.9971i		−	0.840714i	−0.907359	−	0.420357i	$-0.861905\pi$
$239$		−	12.9971i		−	0.840714i	0.907359	−	0.420357i	$-0.138095\pi$
$240$		0			0
$241$			8.64001i			0.556552i	0.960501	+	0.278276i	$0.0897630\pi$
$241$			8.64001i			0.556552i	−0.960501	+	0.278276i	$0.910237\pi$
$242$	−2.55194	+	2.55194i	−0.164045	+	0.164045i
$243$		0			0
$244$		−	8.21380i		−	0.525834i
$245$	22.7416	−	15.4908i	1.45290	−	0.989672i
$246$		0			0
$247$	0.545712	−	0.0639239i	0.0347228	−	0.00406738i
$248$	2.54592	−	2.54592i	0.161666	−	0.161666i
$249$		0			0
$250$	−5.96033	+	9.45910i	−0.376964	+	0.598246i
$251$	−23.6590			−1.49334			−0.746670	−	0.665194i	$-0.768349\pi$
$251$	−23.6590			−1.49334			−0.746670	+	0.665194i	$0.768349\pi$
$252$		0			0
$253$	−9.89644	+	9.89644i	−0.622184	+	0.622184i
$254$			0.0900835i			0.00565234i
$255$		0			0
$256$	1.00000			0.0625000
$257$	8.63732	−	8.63732i	0.538781	−	0.538781i	−0.384390	−	0.923171i	$-0.625588\pi$
$257$	8.63732	−	8.63732i	0.538781	−	0.538781i	0.923171	+	0.384390i	$0.125588\pi$
$258$		0			0
$259$	43.9432			2.73050
$260$	0.276922	+	0.0525181i	0.0171740	+	0.00325703i
$261$		0			0
$262$	1.73108	−	1.73108i	0.106946	−	0.106946i
$263$	−10.9291	+	10.9291i	−0.673915	+	0.673915i	−0.958616	−	0.284701i	$-0.908106\pi$
$263$	−10.9291	+	10.9291i	−0.673915	+	0.673915i	0.284701	+	0.958616i	$0.408106\pi$
$264$		0			0
$265$	1.89676	−	10.0014i	0.116517	−	0.614383i
$266$	11.8751	−	15.0263i	0.728109	−	0.921321i
$267$		0			0
$268$	8.78764	+	8.78764i	0.536790	+	0.536790i
$269$	−13.8523			−0.844591			−0.422296	−	0.906458i	$-0.638776\pi$
$269$	−13.8523			−0.844591			−0.422296	+	0.906458i	$0.638776\pi$
$270$		0			0
$271$	14.8370			0.901284			0.450642	−	0.892705i	$-0.351195\pi$
$271$	14.8370			0.901284			0.450642	+	0.892705i	$0.351195\pi$
$272$	−1.83065	−	1.83065i	−0.110999	−	0.110999i
$273$		0			0
$274$	4.28065			0.258604
$275$	−6.99705	+	17.7839i	−0.421938	+	1.07241i
$276$		0			0
$277$	−8.95723	−	8.95723i	−0.538188	−	0.538188i	0.384808	−	0.922996i	$-0.374268\pi$
$277$	−8.95723	−	8.95723i	−0.538188	−	0.538188i	−0.922996	+	0.384808i	$0.874268\pi$
$278$	−2.80134	−	2.80134i	−0.168013	−	0.168013i
$279$		0			0
$280$	8.12004	−	5.53111i	0.485265	−	0.330547i
$281$		−	6.13940i		−	0.366246i	−0.983090	−	0.183123i	$-0.941379\pi$
$281$		−	6.13940i		−	0.366246i	0.983090	−	0.183123i	$-0.0586207\pi$
$282$		0			0
$283$	−22.7963	+	22.7963i	−1.35510	+	1.35510i	−0.475246	+	0.879853i	$0.657641\pi$
$283$	−22.7963	+	22.7963i	−1.35510	+	1.35510i	−0.879853	+	0.475246i	$0.842359\pi$
$284$	1.66657			0.0988926
$285$		0			0
$286$	0.481788			0.0284887
$287$	−34.8389	+	34.8389i	−2.05647	+	2.05647i
$288$		0			0
$289$		−	10.2974i		−	0.605732i
$290$	−7.90992	−	1.50011i	−0.464486	−	0.0880894i
$291$		0			0
$292$	3.64373	+	3.64373i	0.213233	+	0.213233i
$293$	0.341431	+	0.341431i	0.0199466	+	0.0199466i	0.717010	−	0.697063i	$-0.245510\pi$
$293$	0.341431	+	0.341431i	0.0199466	+	0.0199466i	−0.697063	+	0.717010i	$0.745510\pi$
$294$		0			0
$295$	11.8438	+	17.3875i	0.689572	+	1.01234i
$296$	10.0011			0.581305
$297$		0			0
$298$	−15.8349	−	15.8349i	−0.917294	−	0.917294i
$299$	0.461562			0.0266928
$300$		0			0
$301$	49.3223			2.84289
$302$	−7.98994	−	7.98994i	−0.459769	−	0.459769i
$303$		0			0
$304$	2.70268	−	3.41987i	0.155009	−	0.196143i
$305$	−10.3398	−	15.1796i	−0.592058	−	0.869181i
$306$		0			0
$307$	18.0543	−	18.0543i	1.03041	−	1.03041i	0.0308888	−	0.999523i	$-0.490166\pi$
$307$	18.0543	−	18.0543i	1.03041	−	1.03041i	0.999523	−	0.0308888i	$-0.00983377\pi$
$308$	11.8751	−	11.8751i	0.676646	−	0.676646i
$309$		0			0
$310$	1.50011	−	7.90992i	0.0852005	−	0.449253i
$311$	−5.73086			−0.324967			−0.162484	−	0.986711i	$-0.551951\pi$
$311$	−5.73086			−0.324967			−0.162484	+	0.986711i	$0.551951\pi$
$312$		0			0
$313$	22.1761	−	22.1761i	1.25347	−	1.25347i	0.299312	−	0.954155i	$-0.403243\pi$
$313$	22.1761	−	22.1761i	1.25347	−	1.25347i	0.954155	−	0.299312i	$-0.0967572\pi$
$314$	6.47591			0.365457
$315$		0			0
$316$			8.82758i			0.496590i
$317$	11.0630	−	11.0630i	0.621359	−	0.621359i	−0.324520	−	0.945879i	$-0.605203\pi$
$317$	11.0630	−	11.0630i	0.621359	−	0.621359i	0.945879	+	0.324520i	$0.105203\pi$
$318$		0			0
$319$	−13.7616			−0.770503
$320$	1.84806	−	1.25884i	0.103310	−	0.0703712i
$321$		0			0
$322$	11.3766	−	11.3766i	0.633991	−	0.633991i
$323$	−11.2082	+	1.31292i	−0.623643	+	0.0730527i
$324$		0			0
$325$	0.577881	−	0.251544i	0.0320550	−	0.0139531i
$326$			10.6715i			0.591042i
$327$		0			0
$328$	−7.92907	+	7.92907i	−0.437810	+	0.437810i
$329$			2.87804i			0.158672i
$330$		0			0
$331$			11.7959i			0.648364i	0.945995	+	0.324182i	$0.105089\pi$
$331$			11.7959i			0.648364i	−0.945995	+	0.324182i	$0.894911\pi$
$332$	−0.347181	−	0.347181i	−0.0190540	−	0.0190540i
$333$		0			0
$334$			21.3935i			1.17060i
$335$	27.3023	+	5.17786i	1.49168	+	0.282897i
$336$		0			0
$337$	10.9001	−	10.9001i	0.593765	−	0.593765i	−0.344881	−	0.938646i	$-0.612081\pi$
$337$	10.9001	−	10.9001i	0.593765	−	0.593765i	0.938646	+	0.344881i	$0.112081\pi$
$338$	9.18115	+	9.18115i	0.499389	+	0.499389i
$339$		0			0
$340$	−5.68764	−	1.07866i	−0.308456	−	0.0584983i
$341$		−	13.7616i		−	0.745234i
$342$		0			0
$343$	−16.4841	+	16.4841i	−0.890057	+	0.890057i
$344$	11.2254			0.605232
$345$		0			0
$346$	3.28746			0.176735
$347$	−15.9014	−	15.9014i	−0.853630	−	0.853630i	0.136948	−	0.990578i	$-0.456271\pi$
$347$	−15.9014	−	15.9014i	−0.853630	−	0.853630i	−0.990578	+	0.136948i	$0.956271\pi$
$348$		0			0
$349$		−	14.0170i		−	0.750311i	−0.926962	−	0.375155i	$-0.877589\pi$
$349$		−	14.0170i		−	0.750311i	0.926962	−	0.375155i	$-0.122411\pi$
$350$	8.04354	−	20.4436i	0.429945	−	1.09276i
$351$		0			0
$352$	2.70268	−	2.70268i	0.144053	−	0.144053i
$353$	1.70112	−	1.70112i	0.0905412	−	0.0905412i	−0.660386	−	0.750927i	$-0.729607\pi$
$353$	1.70112	−	1.70112i	0.0905412	−	0.0905412i	0.750927	+	0.660386i	$0.229607\pi$
$354$		0			0
$355$	3.07992	−	2.09794i	0.163465	−	0.111347i
$356$		−	9.79832i		−	0.519310i
$357$		0			0
$358$	0.364750	−	0.364750i	0.0192776	−	0.0192776i
$359$		−	36.9693i		−	1.95117i	−0.219633	−	0.975583i	$-0.570486\pi$
$359$		−	36.9693i		−	1.95117i	0.219633	−	0.975583i	$-0.429514\pi$
$360$		0			0
$361$	−4.39102	−	18.4856i	−0.231106	−	0.972929i
$362$	−3.43744	−	3.43744i	−0.180668	−	0.180668i
$363$		0			0
$364$	−0.553844			−0.0290293
$365$	11.3207	+	2.14696i	0.592552	+	0.112377i
$366$		0			0
$367$	−11.7866	−	11.7866i	−0.615255	−	0.615255i	0.329055	−	0.944311i	$-0.393270\pi$
$367$	−11.7866	−	11.7866i	−0.615255	−	0.615255i	−0.944311	+	0.329055i	$0.893270\pi$
$368$	2.58922	−	2.58922i	0.134972	−	0.134972i
$369$		0			0
$370$	18.4827	−	12.5898i	0.960871	−	0.654514i
$371$			20.0029i			1.03850i
$372$		0			0
$373$	−9.29229	−	9.29229i	−0.481137	−	0.481137i	0.424358	−	0.905495i	$-0.360500\pi$
$373$	−9.29229	−	9.29229i	−0.481137	−	0.481137i	−0.905495	+	0.424358i	$0.860500\pi$
$374$	−9.89533			−0.511675
$375$		0			0
$376$			0.655021i			0.0337801i
$377$	0.320915	+	0.320915i	0.0165280	+	0.0165280i
$378$		0			0
$379$	−9.08999			−0.466921			−0.233461	−	0.972366i	$-0.575005\pi$
$379$	−9.08999			−0.466921			−0.233461	+	0.972366i	$0.575005\pi$
$380$	0.689653	−	9.72236i	0.0353785	−	0.498747i
$381$		0			0
$382$	−10.8448	+	10.8448i	−0.554870	+	0.554870i
$383$	2.91923	+	2.91923i	0.149166	+	0.149166i	0.777745	−	0.628579i	$-0.216363\pi$
$383$	2.91923	+	2.91923i	0.149166	+	0.149166i	−0.628579	+	0.777745i	$0.716363\pi$
$384$		0			0
$385$	6.99705	−	36.8947i	0.356603	−	1.88033i
$386$	24.2679			1.23521
$387$		0			0
$388$	6.88409	+	6.88409i	0.349487	+	0.349487i
$389$		−	25.2850i		−	1.28200i	−0.767540	−	0.641001i	$-0.778519\pi$
$389$		−	25.2850i		−	1.28200i	0.767540	−	0.641001i	$-0.221481\pi$
$390$		0			0
$391$	−9.47991			−0.479420
$392$	−8.70140	+	8.70140i	−0.439487	+	0.439487i
$393$		0			0
$394$	−8.83957			−0.445331
$395$	11.1125	+	16.3139i	0.559130	+	0.820841i
$396$		0			0
$397$	11.4572	+	11.4572i	0.575020	+	0.575020i	0.933527	−	0.358507i	$-0.116714\pi$
$397$	11.4572	+	11.4572i	0.575020	+	0.575020i	−0.358507	+	0.933527i	$0.616714\pi$
$398$	−7.36057	−	7.36057i	−0.368952	−	0.368952i
$399$		0			0
$400$	1.83065	−	4.65282i	0.0915324	−	0.232641i
$401$			7.22311i			0.360705i	0.983602	+	0.180352i	$0.0577238\pi$
$401$			7.22311i			0.360705i	−0.983602	+	0.180352i	$0.942276\pi$
$402$		0			0
$403$	−0.320915	+	0.320915i	−0.0159859	+	0.0159859i
$404$		−	3.89174i		−	0.193621i
$405$		0			0
$406$	15.8198			0.785125
$407$	27.0299	−	27.0299i	1.33982	−	1.33982i
$408$		0			0
$409$	−17.4019			−0.860470			−0.430235	−	0.902717i	$-0.641569\pi$
$409$	−17.4019			−0.860470			−0.430235	+	0.902717i	$0.641569\pi$
$410$	−4.67197	+	24.6348i	−0.230732	+	1.21663i
$411$		0			0
$412$	9.40518	−	9.40518i	0.463360	−	0.463360i
$413$	−29.2313	−	29.2313i	−1.43838	−	1.43838i
$414$		0			0
$415$	−1.07866	−	0.204566i	−0.0529491	−	0.0100418i
$416$	−0.126051			−0.00618015
$417$		0			0
$418$	−1.93833	−	16.5473i	−0.0948068	−	0.809356i
$419$		−	1.67485i		−	0.0818218i	−0.999163	−	0.0409109i	$-0.986974\pi$
$419$		−	1.67485i		−	0.0818218i	0.999163	−	0.0409109i	$-0.0130260\pi$
$420$		0			0
$421$			26.3045i			1.28200i	0.767540	+	0.641001i	$0.221480\pi$
$421$			26.3045i			1.28200i	−0.767540	+	0.641001i	$0.778520\pi$
$422$	−9.23137	−	9.23137i	−0.449376	−	0.449376i
$423$		0			0
$424$			4.55250i			0.221089i
$425$	−11.8690	+	5.16640i	−0.575729	+	0.250607i
$426$		0			0
$427$	25.5194	+	25.5194i	1.23497	+	1.23497i
$428$	−7.00983	−	7.00983i	−0.338833	−	0.338833i
$429$		0			0
$430$	20.7452	−	14.1310i	1.00042	−	0.681455i
$431$		−	9.18675i		−	0.442510i	−0.975216	−	0.221255i	$-0.928985\pi$
$431$		−	9.18675i		−	0.442510i	0.975216	−	0.221255i	$-0.0710154\pi$
$432$		0			0
$433$	7.28482	+	7.28482i	0.350086	+	0.350086i	0.860142	−	0.510055i	$-0.170375\pi$
$433$	7.28482	+	7.28482i	0.350086	+	0.350086i	−0.510055	+	0.860142i	$0.670375\pi$
$434$			15.8198i			0.759376i
$435$		0			0
$436$		−	17.7935i		−	0.852153i
$437$	−1.85696	−	15.8526i	−0.0888302	−	0.758335i
$438$		0			0
$439$	11.5269			0.550148			0.275074	−	0.961423i	$-0.411298\pi$
$439$	11.5269			0.550148			0.275074	+	0.961423i	$0.411298\pi$
$440$	1.59248	−	8.39696i	0.0759183	−	0.400309i
$441$		0			0
$442$	0.230755	+	0.230755i	0.0109759	+	0.0109759i
$443$	−1.68879	+	1.68879i	−0.0802367	+	0.0802367i	−0.746086	−	0.665849i	$-0.768069\pi$
$443$	−1.68879	+	1.68879i	−0.0802367	+	0.0802367i	0.665849	+	0.746086i	$0.268069\pi$
$444$		0			0
$445$	−12.3345	−	18.1079i	−0.584712	−	0.858396i
$446$	16.3221			0.772872
$447$		0			0
$448$	−3.10690	+	3.10690i	−0.146787	+	0.146787i
$449$	10.9876			0.518538			0.259269	−	0.965805i	$-0.416518\pi$
$449$	10.9876			0.518538			0.259269	+	0.965805i	$0.416518\pi$
$450$		0			0
$451$			42.8595i			2.01818i
$452$	12.4493	−	12.4493i	0.585568	−	0.585568i
$453$		0			0
$454$			23.2372i			1.09058i
$455$	−1.02354	+	0.697201i	−0.0479842	+	0.0326853i
$456$		0			0
$457$	−24.3188	−	24.3188i	−1.13759	−	1.13759i	−0.988882	−	0.148703i	$-0.952490\pi$
$457$	−24.3188	−	24.3188i	−1.13759	−	1.13759i	−0.148703	−	0.988882i	$-0.547510\pi$
$458$	−10.9739	−	10.9739i	−0.512777	−	0.512777i
$459$		0			0
$460$	1.52562	−	8.04445i	0.0711325	−	0.375074i
$461$	−20.8769			−0.972332			−0.486166	−	0.873866i	$-0.661605\pi$
$461$	−20.8769			−0.972332			−0.486166	+	0.873866i	$0.661605\pi$
$462$		0			0
$463$	−16.5161	+	16.5161i	−0.767568	+	0.767568i	−0.977678	−	0.210110i	$-0.932618\pi$
$463$	−16.5161	+	16.5161i	−0.767568	+	0.767568i	0.210110	+	0.977678i	$0.432618\pi$
$464$	3.60048			0.167148
$465$		0			0
$466$			2.39161i			0.110789i
$467$	14.6317	+	14.6317i	0.677074	+	0.677074i	0.959337	−	0.282263i	$-0.0910851\pi$
$467$	14.6317	+	14.6317i	0.677074	+	0.677074i	−0.282263	+	0.959337i	$0.591085\pi$
$468$		0			0
$469$	−54.6046			−2.52141
$470$	0.824566	+	1.21052i	0.0380344	+	0.0558370i
$471$		0			0
$472$	−6.65282	−	6.65282i	−0.306221	−	0.306221i
$473$	30.3387	−	30.3387i	1.39497	−	1.39497i
$474$		0			0
$475$	−10.9644	−	18.8357i	−0.503080	−	0.864240i
$476$	11.3753			0.521385
$477$		0			0
$478$	9.19036	+	9.19036i	0.420357	+	0.420357i
$479$			28.1296i			1.28527i	0.766171	+	0.642636i	$0.222159\pi$
$479$			28.1296i			1.28527i	−0.766171	+	0.642636i	$0.777841\pi$
$480$		0			0
$481$	−1.26065			−0.0574808
$482$	−6.10941	−	6.10941i	−0.278276	−	0.278276i
$483$		0			0
$484$		−	3.60898i		−	0.164045i
$485$	21.3882	+	4.05625i	0.971186	+	0.184185i
$486$		0			0
$487$	−11.6398	+	11.6398i	−0.527451	+	0.527451i	−0.919811	−	0.392361i	$-0.871658\pi$
$487$	−11.6398	+	11.6398i	−0.527451	+	0.527451i	0.392361	+	0.919811i	$0.371658\pi$
$488$	5.80803	+	5.80803i	0.262917	+	0.262917i
$489$		0			0
$490$	−5.12704	+	27.0344i	−0.231616	+	1.22129i
$491$	−5.55189			−0.250553			−0.125277	−	0.992122i	$-0.539982\pi$
$491$	−5.55189			−0.250553			−0.125277	+	0.992122i	$0.539982\pi$
$492$		0			0
$493$	−6.59121	−	6.59121i	−0.296853	−	0.296853i
$494$	−0.340675	+	0.431077i	−0.0153277	+	0.0193951i
$495$		0			0
$496$			3.60048i			0.161666i
$497$	−5.17786	+	5.17786i	−0.232259	+	0.232259i
$498$		0			0
$499$		−	27.8562i		−	1.24701i	−0.781818	−	0.623507i	$-0.785707\pi$
$499$		−	27.8562i		−	1.24701i	0.781818	−	0.623507i	$-0.214293\pi$
$500$	−2.47400	−	10.9032i	−0.110641	−	0.487605i
$501$		0			0
$502$	16.7294	−	16.7294i	0.746670	−	0.746670i
$503$	−20.5340	+	20.5340i	−0.915564	+	0.915564i	−0.996703	−	0.0811388i	$-0.974144\pi$
$503$	−20.5340	+	20.5340i	−0.915564	+	0.915564i	0.0811388	+	0.996703i	$0.474144\pi$
$504$		0			0
$505$	−4.89907	−	7.19216i	−0.218006	−	0.320047i
$506$		−	13.9957i		−	0.622184i
$507$		0			0
$508$	−0.0636986	−	0.0636986i	−0.00282617	−	0.00282617i
$509$	27.6636			1.22617			0.613085	−	0.790017i	$-0.289928\pi$
$509$	27.6636			1.22617			0.613085	+	0.790017i	$0.289928\pi$
$510$		0			0
$511$	−22.6414			−1.00160
$512$	−0.707107	+	0.707107i	−0.0312500	+	0.0312500i
$513$		0			0
$514$			12.2150i			0.538781i
$515$	5.54173	−	29.2209i	0.244198	−	1.28763i
$516$		0			0
$517$	1.77031	+	1.77031i	0.0778583	+	0.0778583i
$518$	−31.0725	+	31.0725i	−1.36525	+	1.36525i
$519$		0			0
$520$	−0.232949	+	0.158678i	−0.0102155	+	0.00695848i
$521$			23.2591i			1.01900i	0.860471	+	0.509500i	$0.170170\pi$
$521$			23.2591i			1.01900i	−0.860471	+	0.509500i	$0.829830\pi$
$522$		0			0
$523$	−8.81162	−	8.81162i	−0.385305	−	0.385305i	0.487704	−	0.873009i	$-0.337835\pi$
$523$	−8.81162	−	8.81162i	−0.385305	−	0.385305i	−0.873009	+	0.487704i	$0.837835\pi$
$524$			2.44811i			0.106946i
$525$		0			0
$526$		−	15.4560i		−	0.673915i
$527$	6.59121	−	6.59121i	0.287117	−	0.287117i
$528$		0			0
$529$			9.59187i			0.417038i
$530$	5.73086	+	8.41329i	0.248933	+	0.365450i
$531$		0			0
$532$	2.22823	+	19.0221i	0.0966059	+	0.824715i
$533$	0.999466	−	0.999466i	0.0432917	−	0.0432917i
$534$		0			0
$535$	−21.7788	−	4.13034i	−0.941581	−	0.178570i
$536$	−12.4276			−0.536790
$537$		0			0
$538$	9.79507	−	9.79507i	0.422296	−	0.422296i
$539$			47.0342i			2.02591i
$540$		0			0
$541$	−16.3738			−0.703966			−0.351983	−	0.936006i	$-0.614493\pi$
$541$	−16.3738			−0.703966			−0.351983	+	0.936006i	$0.614493\pi$
$542$	−10.4913	+	10.4913i	−0.450642	+	0.450642i
$543$		0			0
$544$	2.58893			0.110999
$545$	−22.3991	−	32.8834i	−0.959473	−	1.40857i
$546$		0			0
$547$	20.3289	−	20.3289i	0.869199	−	0.869199i	−0.123185	−	0.992384i	$-0.539311\pi$
$547$	20.3289	−	20.3289i	0.869199	−	0.869199i	0.992384	+	0.123185i	$0.0393108\pi$
$548$	−3.02688	+	3.02688i	−0.129302	+	0.129302i
$549$		0			0
$550$	−7.62743	−	17.5228i	−0.325235	−	0.747173i
$551$	9.73094	−	12.3132i	0.414552	−	0.524558i
$552$		0			0
$553$	−27.4264	−	27.4264i	−1.16629	−	1.16629i
$554$	12.6674			0.538188
$555$		0			0
$556$	3.96170			0.168013
$557$	12.6433	+	12.6433i	0.535713	+	0.535713i	0.922267	−	0.386554i	$-0.126335\pi$
$557$	12.6433	+	12.6433i	0.535713	+	0.535713i	−0.386554	+	0.922267i	$0.626335\pi$
$558$		0			0
$559$	−1.41497			−0.0598468
$560$	−1.83065	+	9.65282i	−0.0773590	+	0.407906i
$561$		0			0
$562$	4.34121	+	4.34121i	0.183123	+	0.183123i
$563$	−20.5997	−	20.5997i	−0.868176	−	0.868176i	0.124095	−	0.992270i	$-0.460397\pi$
$563$	−20.5997	−	20.5997i	−0.868176	−	0.868176i	−0.992270	+	0.124095i	$0.960397\pi$
$564$		0			0
$565$	7.33541	−	38.6789i	0.308603	−	1.62723i
$566$		−	32.2388i		−	1.35510i
$567$		0			0
$568$	−1.17844	+	1.17844i	−0.0494463	+	0.0494463i
$569$	−39.5742			−1.65904			−0.829519	−	0.558478i	$-0.811386\pi$
$569$	−39.5742			−1.65904			−0.829519	+	0.558478i	$0.811386\pi$
$570$		0			0
$571$	−15.5508			−0.650780			−0.325390	−	0.945580i	$-0.605496\pi$
$571$	−15.5508			−0.650780			−0.325390	+	0.945580i	$0.605496\pi$
$572$	−0.340675	+	0.340675i	−0.0142444	+	0.0142444i
$573$		0			0
$574$		−	49.2696i		−	2.05647i
$575$	−7.30722	−	16.7871i	−0.304732	−	0.700072i
$576$		0			0
$577$	2.21358	+	2.21358i	0.0921525	+	0.0921525i	0.751680	−	0.659528i	$-0.229244\pi$
$577$	2.21358	+	2.21358i	0.0921525	+	0.0921525i	−0.659528	+	0.751680i	$0.729244\pi$
$578$	7.28140	+	7.28140i	0.302866	+	0.302866i
$579$		0			0
$580$	6.65389	−	4.53242i	0.276288	−	0.188198i
$581$	2.15731			0.0895004
$582$		0			0
$583$	12.3040	+	12.3040i	0.509578	+	0.509578i
$584$	−5.15301			−0.213233
$585$		0			0
$586$	−0.482856			−0.0199466
$587$	0.773553	+	0.773553i	0.0319279	+	0.0319279i	0.722891	−	0.690963i	$-0.242813\pi$
$587$	0.773553	+	0.773553i	0.0319279	+	0.0319279i	−0.690963	+	0.722891i	$0.742813\pi$
$588$		0			0
$589$	12.3132	+	9.73094i	0.507355	+	0.400956i
$590$	−20.6696	−	3.91998i	−0.850955	−	0.161383i
$591$		0			0
$592$	−7.07188	+	7.07188i	−0.290652	+	0.290652i
$593$	−6.83126	+	6.83126i	−0.280526	+	0.280526i	−0.833319	−	0.552793i	$-0.813562\pi$
$593$	−6.83126	+	6.83126i	−0.280526	+	0.280526i	0.552793	+	0.833319i	$0.313562\pi$
$594$		0			0
$595$	21.0222	−	14.3196i	0.861826	−	0.587048i
$596$	22.3940			0.917294
$597$		0			0
$598$	−0.326373	+	0.326373i	−0.0133464	+	0.0133464i
$599$	4.89411			0.199968			0.0999840	−	0.994989i	$-0.468121\pi$
$599$	4.89411			0.199968			0.0999840	+	0.994989i	$0.468121\pi$
$600$		0			0
$601$		−	18.8596i		−	0.769299i	−0.923063	−	0.384650i	$-0.874322\pi$
$601$		−	18.8596i		−	0.769299i	0.923063	−	0.384650i	$-0.125678\pi$
$602$	−34.8761	+	34.8761i	−1.42145	+	1.42145i
$603$		0			0
$604$	11.2995			0.459769
$605$	−4.54313	−	6.66962i	−0.184705	−	0.271159i
$606$		0			0
$607$	−16.5646	+	16.5646i	−0.672335	+	0.672335i	−0.958254	−	0.285919i	$-0.907701\pi$
$607$	−16.5646	+	16.5646i	−0.672335	+	0.672335i	0.285919	+	0.958254i	$0.407701\pi$
$608$	0.507128	+	4.32930i	0.0205668	+	0.175576i
$609$		0			0
$610$	18.0450	+	3.42221i	0.730619	+	0.138561i
$611$		−	0.0825659i		−	0.00334026i
$612$		0			0
$613$	29.1371	−	29.1371i	1.17684	−	1.17684i	0.196291	−	0.980546i	$-0.437110\pi$
$613$	29.1371	−	29.1371i	1.17684	−	1.17684i	0.980546	−	0.196291i	$-0.0628899\pi$
$614$			25.5326i			1.03041i
$615$		0			0
$616$			16.7939i			0.676646i
$617$	−18.0432	−	18.0432i	−0.726393	−	0.726393i	0.243506	−	0.969899i	$-0.421702\pi$
$617$	−18.0432	−	18.0432i	−0.726393	−	0.726393i	−0.969899	+	0.243506i	$0.921702\pi$
$618$		0			0
$619$			2.38578i			0.0958924i	0.998850	+	0.0479462i	$0.0152676\pi$
$619$			2.38578i			0.0958924i	−0.998850	+	0.0479462i	$0.984732\pi$
$620$	4.53242	+	6.65389i	0.182026	+	0.267227i
$621$		0			0
$622$	4.05233	−	4.05233i	0.162484	−	0.162484i
$623$	30.4424	+	30.4424i	1.21965	+	1.21965i
$624$		0			0
$625$	−18.2974	−	17.0354i	−0.731898	−	0.681414i
$626$			31.3617i			1.25347i
$627$		0			0
$628$	−4.57916	+	4.57916i	−0.182728	+	0.182728i
$629$	25.8923			1.03239
$630$		0			0
$631$	−14.5023			−0.577326			−0.288663	−	0.957431i	$-0.593211\pi$
$631$	−14.5023			−0.577326			−0.288663	+	0.957431i	$0.593211\pi$
$632$	−6.24204	−	6.24204i	−0.248295	−	0.248295i
$633$		0			0
$634$			15.6454i			0.621359i
$635$	−0.197905	−	0.0375326i	−0.00785363	−	0.00148943i
$636$		0			0
$637$	1.09682	−	1.09682i	0.0434575	−	0.0434575i
$638$	9.73094	−	9.73094i	0.385252	−	0.385252i
$639$		0			0
$640$	−0.416642	+	2.19691i	−0.0164692	+	0.0868405i
$641$			12.7084i			0.501950i	0.967994	+	0.250975i	$0.0807512\pi$
$641$			12.7084i			0.501950i	−0.967994	+	0.250975i	$0.919249\pi$
$642$		0			0
$643$	−1.79680	+	1.79680i	−0.0708588	+	0.0708588i	−0.741648	−	0.670789i	$-0.765956\pi$
$643$	−1.79680	+	1.79680i	−0.0708588	+	0.0708588i	0.670789	+	0.741648i	$0.265956\pi$
$644$			16.0889i			0.633991i
$645$		0			0
$646$	6.99705	−	8.85380i	0.275295	−	0.348348i
$647$	−7.42896	−	7.42896i	−0.292063	−	0.292063i	0.545832	−	0.837895i	$-0.316214\pi$
$647$	−7.42896	−	7.42896i	−0.292063	−	0.292063i	−0.837895	+	0.545832i	$0.816214\pi$
$648$		0			0
$649$	−35.9609			−1.41159
$650$	−0.230755	+	0.586492i	−0.00905095	+	0.0230041i
$651$		0			0
$652$	−7.54592	−	7.54592i	−0.295521	−	0.295521i
$653$	32.4125	−	32.4125i	1.26840	−	1.26840i	0.321486	−	0.946914i	$-0.395818\pi$
$653$	32.4125	−	32.4125i	1.26840	−	1.26840i	0.946914	−	0.321486i	$-0.104182\pi$
$654$		0			0
$655$	3.08178	+	4.52426i	0.120415	+	0.176777i
$656$		−	11.2134i		−	0.437810i
$657$		0			0
$658$	−2.03508	−	2.03508i	−0.0793358	−	0.0793358i
$659$	−41.3365			−1.61024			−0.805122	−	0.593110i	$-0.797900\pi$
$659$	−41.3365			−1.61024			−0.805122	+	0.593110i	$0.797900\pi$
$660$		0			0
$661$			2.43023i			0.0945250i	0.998883	+	0.0472625i	$0.0150497\pi$
$661$			2.43023i			0.0945250i	−0.998883	+	0.0472625i	$0.984950\pi$
$662$	−8.34099	−	8.34099i	−0.324182	−	0.324182i
$663$		0			0
$664$	0.490988			0.0190540
$665$	28.0637	+	32.3491i	1.08826	+	1.25444i
$666$		0			0
$667$	9.32242	−	9.32242i	0.360966	−	0.360966i
$668$	−15.1275	−	15.1275i	−0.585299	−	0.585299i
$669$		0			0
$670$	−22.9669	+	15.6443i	−0.887290	+	0.604394i
$671$	31.3945			1.21197
$672$		0			0
$673$	19.4040	+	19.4040i	0.747968	+	0.747968i	0.974097	−	0.226129i	$-0.0726071\pi$
$673$	19.4040	+	19.4040i	0.747968	+	0.747968i	−0.226129	+	0.974097i	$0.572607\pi$
$674$			15.4150i			0.593765i
$675$		0			0
$676$	−12.9841			−0.499389
$677$	−18.9654	+	18.9654i	−0.728899	+	0.728899i	−0.970401	−	0.241501i	$-0.922360\pi$
$677$	−18.9654	+	18.9654i	−0.728899	+	0.728899i	0.241501	+	0.970401i	$0.422360\pi$
$678$		0			0
$679$	−42.7763			−1.64160
$680$	4.78449	−	3.25904i	0.183477	−	0.124979i
$681$		0			0
$682$	9.73094	+	9.73094i	0.372617	+	0.372617i
$683$	11.9597	+	11.9597i	0.457626	+	0.457626i	0.897876	−	0.440249i	$-0.145110\pi$
$683$	11.9597	+	11.9597i	0.457626	+	0.457626i	−0.440249	+	0.897876i	$0.645110\pi$
$684$		0			0
$685$	−1.78350	+	9.40420i	−0.0681440	+	0.359316i
$686$		−	23.3120i		−	0.890057i
$687$		0			0
$688$	−7.93755	+	7.93755i	−0.302616	+	0.302616i
$689$		−	0.573846i		−	0.0218618i
$690$		0			0
$691$	3.66130			0.139282			0.0696412	−	0.997572i	$-0.477815\pi$
$691$	3.66130			0.139282			0.0696412	+	0.997572i	$0.477815\pi$
$692$	−2.32458	+	2.32458i	−0.0883674	+	0.0883674i
$693$		0			0
$694$	22.4879			0.853630
$695$	7.32145	−	4.98714i	0.277718	−	0.189173i
$696$		0			0
$697$	−20.5278	+	20.5278i	−0.777546	+	0.777546i
$698$	9.91149	+	9.91149i	0.375155	+	0.375155i
$699$		0			0
$700$	8.76820	+	20.1435i	0.331407	+	0.761352i
$701$	25.2380			0.953225			0.476612	−	0.879113i	$-0.341864\pi$
$701$	25.2380			0.953225			0.476612	+	0.879113i	$0.341864\pi$
$702$		0			0
$703$	5.07186	+	43.2979i	0.191289	+	1.63301i
$704$			3.82217i			0.144053i
$705$		0			0
$706$			2.40574i			0.0905412i
$707$	12.0912	+	12.0912i	0.454737	+	0.454737i
$708$		0			0
$709$		−	7.14208i		−	0.268226i	−0.990966	−	0.134113i	$-0.957181\pi$
$709$		−	7.14208i		−	0.268226i	0.990966	−	0.134113i	$-0.0428186\pi$
$710$	−0.694362	+	3.66130i	−0.0260589	+	0.137406i
$711$		0			0
$712$	6.92846	+	6.92846i	0.259655	+	0.259655i
$713$	9.32242	+	9.32242i	0.349128	+	0.349128i
$714$		0			0
$715$	−0.200733	+	1.05844i	−0.00750699	+	0.0395836i
$716$			0.515834i			0.0192776i
$717$		0			0
$718$	26.1412	+	26.1412i	0.975583	+	0.975583i
$719$		−	30.1848i		−	1.12570i	−0.826558	−	0.562852i	$-0.809704\pi$
$719$		−	30.1848i		−	1.12570i	0.826558	−	0.562852i	$-0.190296\pi$
$720$		0			0
$721$			58.4419i			2.17649i
$722$	16.1762	+	9.96641i	0.602017	+	0.370911i
$723$		0			0
$724$	4.86127			0.180668
$725$	6.59121	−	16.7524i	0.244791	−	0.622167i
$726$		0			0
$727$	10.1806	+	10.1806i	0.377576	+	0.377576i	0.870227	−	0.492651i	$-0.163972\pi$
$727$	10.1806	+	10.1806i	0.377576	+	0.377576i	−0.492651	+	0.870227i	$0.663972\pi$
$728$	0.391627	−	0.391627i	0.0145147	−	0.0145147i
$729$		0			0
$730$	−9.52307	+	6.48681i	−0.352465	+	0.240088i
$731$	29.0617			1.07489
$732$		0			0
$733$	−12.6028	+	12.6028i	−0.465495	+	0.465495i	−0.900451	−	0.434957i	$-0.856764\pi$
$733$	−12.6028	+	12.6028i	−0.465495	+	0.465495i	0.434957	+	0.900451i	$0.356764\pi$
$734$	16.6688			0.615255
$735$		0			0
$736$			3.66171i			0.134972i
$737$	−33.5878	+	33.5878i	−1.23722	+	1.23722i
$738$		0			0
$739$		−	30.9906i		−	1.14001i	−0.821642	−	0.570003i	$-0.806942\pi$
$739$		−	30.9906i		−	1.14001i	0.821642	−	0.570003i	$-0.193058\pi$
$740$	−4.16690	+	21.9716i	−0.153178	+	0.807692i
$741$		0			0
$742$	−14.1442	−	14.1442i	−0.519248	−	0.519248i
$743$	33.1976	+	33.1976i	1.21790	+	1.21790i	0.968366	+	0.249536i	$0.0802779\pi$
$743$	33.1976	+	33.1976i	1.21790	+	1.21790i	0.249536	+	0.968366i	$0.419722\pi$
$744$		0			0
$745$	41.3854	−	28.1904i	1.51625	−	1.03282i
$746$	13.1413			0.481137
$747$		0			0
$748$	6.99705	−	6.99705i	0.255838	−	0.255838i
$749$	43.5577			1.59156
$750$		0			0
$751$		−	11.6085i		−	0.423600i	−0.977313	−	0.211800i	$-0.932067\pi$
$751$		−	11.6085i		−	0.423600i	0.977313	−	0.211800i	$-0.0679325\pi$
$752$	−0.463170	−	0.463170i	−0.0168901	−	0.0168901i
$753$		0			0
$754$	−0.453843			−0.0165280
$755$	20.8821	−	14.2242i	0.759978	−	0.517673i
$756$		0			0
$757$	33.9555	+	33.9555i	1.23413	+	1.23413i	0.962362	+	0.271772i	$0.0876098\pi$
$757$	33.9555	+	33.9555i	1.23413	+	1.23413i	0.271772	+	0.962362i	$0.412390\pi$
$758$	6.42759	−	6.42759i	0.233461	−	0.233461i
$759$		0			0
$760$	6.38709	+	7.36241i	0.231684	+	0.267063i
$761$	1.91340			0.0693607			0.0346803	−	0.999398i	$-0.488959\pi$
$761$	1.91340			0.0693607			0.0346803	+	0.999398i	$0.488959\pi$
$762$		0			0
$763$	55.2825	+	55.2825i	2.00136	+	2.00136i
$764$		−	15.3369i		−	0.554870i
$765$		0			0
$766$	−4.12842			−0.149166
$767$	0.838593	+	0.838593i	0.0302798	+	0.0302798i
$768$		0			0
$769$			17.5747i			0.633760i	0.948466	+	0.316880i	$0.102635\pi$
$769$			17.5747i			0.633760i	−0.948466	+	0.316880i	$0.897365\pi$
$770$	21.1408	+	31.0362i	0.761863	+	1.11847i
$771$		0			0
$772$	−17.1600	+	17.1600i	−0.617603	+	0.617603i
$773$	−28.9882	−	28.9882i	−1.04263	−	1.04263i	−0.999050	−	0.0435843i	$-0.986122\pi$
$773$	−28.9882	−	28.9882i	−1.04263	−	1.04263i	−0.0435843	−	0.999050i	$-0.513878\pi$
$774$		0			0
$775$	16.7524	+	6.59121i	0.601763	+	0.236763i
$776$	−9.73557			−0.349487
$777$		0			0
$778$	17.8792	+	17.8792i	0.641001	+	0.641001i
$779$	−38.3484	−	30.3062i	−1.37397	−	1.08583i
$780$		0			0
$781$			6.36991i			0.227933i
$782$	6.70331	−	6.70331i	0.239710	−	0.239710i
$783$		0			0
$784$		−	12.3056i		−	0.439487i
$785$	−2.69813	+	14.2270i	−0.0963006	+	0.507783i
$786$		0			0
$787$	−1.82074	+	1.82074i	−0.0649024	+	0.0649024i	−0.738813	−	0.673911i	$-0.764613\pi$
$787$	−1.82074	+	1.82074i	−0.0649024	+	0.0649024i	0.673911	+	0.738813i	$0.264613\pi$
$788$	6.25052	−	6.25052i	0.222666	−	0.222666i
$789$		0			0
$790$	−19.3934	−	3.67794i	−0.689986	−	0.130855i
$791$			77.3577i			2.75052i
$792$		0			0
$793$	−0.732107	−	0.732107i	−0.0259979	−	0.0259979i
$794$	−16.2029			−0.575020
$795$		0			0
$796$	10.4094			0.368952
$797$	2.79855	−	2.79855i	0.0991296	−	0.0991296i	−0.655803	−	0.754932i	$-0.727670\pi$
$797$	2.79855	−	2.79855i	0.0991296	−	0.0991296i	0.754932	+	0.655803i	$0.227670\pi$
$798$		0			0
$799$			1.69580i			0.0599932i
$800$	1.99558	+	4.58450i	0.0705543	+	0.162087i
$801$		0			0
$802$	−5.10751	−	5.10751i	−0.180352	−	0.180352i
$803$	−13.9270	+	13.9270i	−0.491471	+	0.491471i
$804$		0			0
$805$	20.2533	+	29.7332i	0.713836	+	1.04796i
$806$		−	0.453843i		−	0.0159859i
$807$		0			0
$808$	2.75187	+	2.75187i	0.0968106	+	0.0968106i
$809$		−	45.2384i		−	1.59050i	−0.606282	−	0.795249i	$-0.707340\pi$
$809$		−	45.2384i		−	1.59050i	0.606282	−	0.795249i	$-0.292660\pi$
$810$		0			0
$811$		−	42.6013i		−	1.49593i	−0.663737	−	0.747966i	$-0.731030\pi$
$811$		−	42.6013i		−	1.49593i	0.663737	−	0.747966i	$-0.268970\pi$
$812$	−11.1863	+	11.1863i	−0.392563	+	0.392563i
$813$		0			0
$814$			38.2261i			1.33982i
$815$	−23.4444	−	4.44621i	−0.821222	−	0.155744i
$816$		0			0
$817$	5.69271	+	48.5980i	0.199163	+	1.70023i
$818$	12.3050	−	12.3050i	0.430235	−	0.430235i
$819$		0			0
$820$	−14.1159	−	20.7230i	−0.492947	−	0.723679i
$821$	−52.7865			−1.84226			−0.921130	−	0.389255i	$-0.872732\pi$
$821$	−52.7865			−1.84226			−0.921130	+	0.389255i	$0.872732\pi$
$822$		0			0
$823$	−24.2470	+	24.2470i	−0.845199	+	0.845199i	−0.989529	−	0.144331i	$-0.953897\pi$
$823$	−24.2470	+	24.2470i	−0.845199	+	0.845199i	0.144331	+	0.989529i	$0.453897\pi$
$824$			13.3009i			0.463360i
$825$		0			0
$826$	41.3393			1.43838
$827$	8.09237	−	8.09237i	0.281399	−	0.281399i	−0.552268	−	0.833667i	$-0.686237\pi$
$827$	8.09237	−	8.09237i	0.281399	−	0.281399i	0.833667	+	0.552268i	$0.186237\pi$
$828$		0			0
$829$	8.26535			0.287067			0.143534	−	0.989645i	$-0.454153\pi$
$829$	8.26535			0.287067			0.143534	+	0.989645i	$0.454153\pi$
$830$	0.907375	−	0.618075i	0.0314955	−	0.0214537i
$831$		0			0
$832$	0.0891314	−	0.0891314i	0.00309007	−	0.00309007i
$833$	−22.5273	+	22.5273i	−0.780525	+	0.780525i
$834$		0			0
$835$	−46.9995	−	8.91341i	−1.62648	−	0.308461i
$836$	13.0713	+	10.3301i	0.452081	+	0.357274i
$837$		0			0
$838$	1.18430	+	1.18430i	0.0409109	+	0.0409109i
$839$	−36.8428			−1.27196			−0.635978	−	0.771707i	$-0.719403\pi$
$839$	−36.8428			−1.27196			−0.635978	+	0.771707i	$0.719403\pi$
$840$		0			0
$841$	−16.0366			−0.552985
$842$	−18.6001	−	18.6001i	−0.641001	−	0.641001i
$843$		0			0
$844$	13.0551			0.449376
$845$	−23.9954	+	16.3449i	−0.825467	+	0.562282i
$846$		0			0
$847$	11.2127	+	11.2127i	0.385275	+	0.385275i
$848$	−3.21910	−	3.21910i	−0.110544	−	0.110544i
$849$		0			0
$850$	4.73942	−	12.0458i	0.162561	−	0.413168i
$851$			36.6213i			1.25536i
$852$		0			0
$853$	25.7405	−	25.7405i	0.881338	−	0.881338i	−0.112333	−	0.993671i	$-0.535832\pi$
$853$	25.7405	−	25.7405i	0.881338	−	0.881338i	0.993671	+	0.112333i	$0.0358324\pi$
$854$	−36.0899			−1.23497
$855$		0			0
$856$	9.91340			0.338833
$857$	4.80004	−	4.80004i	0.163966	−	0.163966i	−0.620355	−	0.784321i	$-0.713011\pi$
$857$	4.80004	−	4.80004i	0.163966	−	0.163966i	0.784321	+	0.620355i	$0.213011\pi$
$858$		0			0
$859$		−	32.4106i		−	1.10584i	−0.833235	−	0.552918i	$-0.813514\pi$
$859$		−	32.4106i		−	1.10584i	0.833235	−	0.552918i	$-0.186486\pi$
$860$	−4.67697	+	24.6612i	−0.159483	+	0.840938i
$861$		0			0
$862$	6.49601	+	6.49601i	0.221255	+	0.221255i
$863$	22.4852	+	22.4852i	0.765406	+	0.765406i	0.977294	−	0.211888i	$-0.0679611\pi$
$863$	22.4852	+	22.4852i	0.765406	+	0.765406i	−0.211888	+	0.977294i	$0.567961\pi$
$864$		0			0
$865$	−1.36969	+	7.22225i	−0.0465709	+	0.245564i
$866$	−10.3023			−0.350086
$867$		0			0
$868$	−11.1863	−	11.1863i	−0.379688	−	0.379688i
$869$	−33.7405			−1.14457
$870$		0			0
$871$	1.56651			0.0530791
$872$	12.5819	+	12.5819i	0.426076	+	0.426076i
$873$		0			0
$874$	12.5226	+	9.89644i	0.423582	+	0.334752i
$875$	41.5615	+	26.1886i	1.40504	+	0.885336i
$876$		0			0
$877$	35.3194	−	35.3194i	1.19265	−	1.19265i	0.216334	−	0.976320i	$-0.430590\pi$
$877$	35.3194	−	35.3194i	1.19265	−	1.19265i	0.976320	−	0.216334i	$-0.0694099\pi$
$878$	−8.15073	+	8.15073i	−0.275074	+	0.275074i
$879$		0			0
$880$	4.81150	+	7.06360i	0.162196	+	0.238114i
$881$	−31.6981			−1.06794			−0.533968	−	0.845505i	$-0.679300\pi$
$881$	−31.6981			−1.06794			−0.533968	+	0.845505i	$0.679300\pi$
$882$		0			0
$883$	5.19260	−	5.19260i	0.174745	−	0.174745i	−0.614316	−	0.789060i	$-0.710568\pi$
$883$	5.19260	−	5.19260i	0.174745	−	0.174745i	0.789060	+	0.614316i	$0.210568\pi$
$884$	−0.326337			−0.0109759
$885$		0			0
$886$		−	2.38830i		−	0.0802367i
$887$	−38.1720	+	38.1720i	−1.28169	+	1.28169i	−0.341986	+	0.939705i	$0.611100\pi$
$887$	−38.1720	+	38.1720i	−1.28169	+	1.28169i	−0.939705	+	0.341986i	$0.888900\pi$
$888$		0			0
$889$	0.395810			0.0132751
$890$	21.5260	+	4.08239i	0.721554	+	0.136842i
$891$		0			0
$892$	−11.5414	+	11.5414i	−0.386436	+	0.386436i
$893$	−2.83578	+	0.332179i	−0.0948958	+	0.0111160i
$894$		0			0
$895$	0.649352	+	0.953293i	0.0217055	+	0.0318651i
$896$		−	4.39382i		−	0.146787i
$897$		0			0
$898$	−7.76942	+	7.76942i	−0.259269	+	0.259269i
$899$			12.9634i			0.432354i
$900$		0			0
$901$			11.7861i			0.392652i
$902$	−30.3062	−	30.3062i	−1.00909	−	1.00909i
$903$		0			0
$904$			17.6060i			0.585568i
$905$	8.98392	−	6.11956i	0.298636	−	0.203421i
$906$		0			0
$907$	2.04159	−	2.04159i	0.0677900	−	0.0677900i	−0.672399	−	0.740189i	$-0.734736\pi$
$907$	2.04159	−	2.04159i	0.0677900	−	0.0677900i	0.740189	+	0.672399i	$0.234736\pi$
$908$	−16.4312	−	16.4312i	−0.545288	−	0.545288i
$909$		0			0
$910$	0.230755	−	1.21675i	0.00764945	−	0.0403347i
$911$		−	52.8342i		−	1.75047i	−0.483695	−	0.875237i	$-0.660705\pi$
$911$		−	52.8342i		−	1.75047i	0.483695	−	0.875237i	$-0.339295\pi$
$912$		0			0
$913$	1.32698	−	1.32698i	0.0439168	−	0.0439168i
$914$	34.3920			1.13759
$915$		0			0
$916$	15.5194			0.512777
$917$	−7.60604	−	7.60604i	−0.251173	−	0.251173i
$918$		0			0
$919$			3.57090i			0.117793i	0.998264	+	0.0588965i	$0.0187582\pi$
$919$			3.57090i			0.117793i	−0.998264	+	0.0588965i	$0.981242\pi$
$920$	4.60950	+	6.76706i	0.151971	+	0.223103i
$921$		0			0
$922$	14.7622	−	14.7622i	0.486166	−	0.486166i
$923$	0.148543	−	0.148543i	0.00488937	−	0.00488937i
$924$		0			0
$925$	19.9580	+	45.8503i	0.656216	+	1.50755i
$926$		−	23.3573i		−	0.767568i
$927$		0			0
$928$	−2.54592	+	2.54592i	−0.0835739	+	0.0835739i
$929$		−	14.0100i		−	0.459653i	−0.973232	−	0.229826i	$-0.926184\pi$
$929$		−	14.0100i		−	0.459653i	0.973232	−	0.229826i	$-0.0738159\pi$
$930$		0			0
$931$	−42.0837	−	33.2582i	−1.37924	−	1.08999i
$932$	−1.69112	−	1.69112i	−0.0553946	−	0.0553946i
$933$		0			0
$934$	−20.6923			−0.677074
$935$	4.12281	−	21.7391i	0.134830	−	0.710946i
$936$		0			0
$937$	0.588249	+	0.588249i	0.0192173	+	0.0192173i	0.716650	−	0.697433i	$-0.245674\pi$
$937$	0.588249	+	0.588249i	0.0192173	+	0.0192173i	−0.697433	+	0.716650i	$0.745674\pi$
$938$	38.6113	−	38.6113i	1.26070	−	1.26070i
$939$		0			0
$940$	−1.43902	−	0.272909i	−0.0469357	−	0.00890132i
$941$		−	52.7538i		−	1.71972i	−0.510526	−	0.859862i	$-0.670549\pi$
$941$		−	52.7538i		−	1.71972i	0.510526	−	0.859862i	$-0.329451\pi$
$942$		0			0
$943$	−29.0340	−	29.0340i	−0.945476	−	0.945476i
$944$	9.40851			0.306221
$945$		0			0
$946$			42.9053i			1.39497i
$947$	16.9932	+	16.9932i	0.552205	+	0.552205i	0.927077	−	0.374872i	$-0.122313\pi$
$947$	16.9932	+	16.9932i	0.552205	+	0.552205i	−0.374872	+	0.927077i	$0.622313\pi$
$948$		0			0
$949$	0.649541			0.0210850
$950$	21.0718	+	5.56585i	0.683660	+	0.180580i
$951$		0			0
$952$	−8.04354	+	8.04354i	−0.260693	+	0.260693i
$953$	−15.6870	−	15.6870i	−0.508151	−	0.508151i	0.405807	−	0.913959i	$-0.366990\pi$
$953$	−15.6870	−	15.6870i	−0.508151	−	0.508151i	−0.913959	+	0.405807i	$0.866990\pi$
$954$		0			0
$955$	−19.3067	−	28.3435i	−0.624750	−	0.917174i
$956$	−12.9971			−0.420357
$957$		0			0
$958$	−19.8906	−	19.8906i	−0.642636	−	0.642636i
$959$		−	18.8084i		−	0.607355i
$960$		0			0
$961$	18.0366			0.581825
$962$	0.891416	−	0.891416i	0.0287404	−	0.0287404i
$963$		0			0
$964$	8.64001			0.278276
$965$	−10.1110	+	53.3145i	−0.325486	+	1.71625i
$966$		0			0
$967$	−33.2376	−	33.2376i	−1.06885	−	1.06885i	−0.997448	−	0.0714018i	$-0.977253\pi$
$967$	−33.2376	−	33.2376i	−1.06885	−	1.06885i	−0.0714018	−	0.997448i	$-0.522747\pi$
$968$	2.55194	+	2.55194i	0.0820224	+	0.0820224i
$969$		0			0
$970$	−17.9919	+	12.2555i	−0.577686	+	0.393501i
$971$			35.6664i			1.14459i	0.820048	+	0.572294i	$0.193946\pi$
$971$			35.6664i			1.14459i	−0.820048	+	0.572294i	$0.806054\pi$
$972$		0			0
$973$	−12.3086	+	12.3086i	−0.394595	+	0.394595i
$974$		−	16.4612i		−	0.527451i
$975$		0			0
$976$	−8.21380			−0.262917
$977$	31.4909	−	31.4909i	1.00748	−	1.00748i	0.00751053	−	0.999972i	$-0.497609\pi$
$977$	31.4909	−	31.4909i	1.00748	−	1.00748i	0.999972	−	0.00751053i	$-0.00239070\pi$
$978$		0			0
$979$	37.4508			1.19693
$980$	−15.4908	−	22.7416i	−0.494836	−	0.726452i
$981$		0			0
$982$	3.92578	−	3.92578i	0.125277	−	0.125277i
$983$	5.10301	+	5.10301i	0.162761	+	0.162761i	0.783789	−	0.621028i	$-0.213285\pi$
$983$	5.10301	+	5.10301i	0.162761	+	0.162761i	−0.621028	+	0.783789i	$0.713285\pi$
$984$		0			0
$985$	3.68293	−	19.4197i	0.117348	−	0.618764i
$986$	9.32137			0.296853
$987$		0			0
$988$	−0.0639239	−	0.545712i	−0.00203369	−	0.0173614i
$989$			41.1041i			1.30704i
$990$		0			0
$991$		−	12.3920i		−	0.393644i	−0.980439	−	0.196822i	$-0.936938\pi$
$991$		−	12.3920i		−	0.393644i	0.980439	−	0.196822i	$-0.0630621\pi$
$992$	−2.54592	−	2.54592i	−0.0808331	−	0.0808331i
$993$		0			0
$994$		−	7.32260i		−	0.232259i
$995$	19.2372	−	13.1038i	0.609861	−	0.415418i
$996$		0			0
$997$	−22.8719	−	22.8719i	−0.724359	−	0.724359i	0.245131	−	0.969490i	$-0.421169\pi$
$997$	−22.8719	−	22.8719i	−0.724359	−	0.724359i	−0.969490	+	0.245131i	$0.921169\pi$
$998$	19.6973	+	19.6973i	0.623507	+	0.623507i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1710.2.p.d.37.2		20
3.2	odd	2		570.2.m.a.37.9	yes	20
5.3	odd	4	inner	1710.2.p.d.1063.7		20
15.8	even	4		570.2.m.a.493.4	yes	20
19.18	odd	2	inner	1710.2.p.d.37.7		20
57.56	even	2		570.2.m.a.37.4	✓	20
95.18	even	4	inner	1710.2.p.d.1063.2		20
285.113	odd	4		570.2.m.a.493.9	yes	20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
570.2.m.a.37.4	✓	20	57.56	even	2
570.2.m.a.37.9	yes	20	3.2	odd	2
570.2.m.a.493.4	yes	20	15.8	even	4
570.2.m.a.493.9	yes	20	285.113	odd	4
1710.2.p.d.37.2		20	1.1	even	1	trivial
1710.2.p.d.37.7		20	19.18	odd	2	inner
1710.2.p.d.1063.2		20	95.18	even	4	inner
1710.2.p.d.1063.7		20	5.3	odd	4	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1710 = 2 \cdot 3^{2} \cdot 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1710.p (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.707107 + 0.707107i) q^{2} -1.00000i q^{4} +(-1.25884 - 1.84806i) q^{5} +(3.10690 + 3.10690i) q^{7} +(0.707107 + 0.707107i) q^{8} +O(q^{10})\)	\(q+(-0.707107 + 0.707107i) q^{2} -1.00000i q^{4} +(-1.25884 - 1.84806i) q^{5} +(3.10690 + 3.10690i) q^{7} +(0.707107 + 0.707107i) q^{8} +(2.19691 + 0.416642i) q^{10} +3.82217 q^{11} +(-0.0891314 - 0.0891314i) q^{13} -4.39382 q^{14} -1.00000 q^{16} +(1.83065 + 1.83065i) q^{17} +(-2.70268 + 3.41987i) q^{19} +(-1.84806 + 1.25884i) q^{20} +(-2.70268 + 2.70268i) q^{22} +(-2.58922 + 2.58922i) q^{23} +(-1.83065 + 4.65282i) q^{25} +0.126051 q^{26} +(3.10690 - 3.10690i) q^{28} -3.60048 q^{29} -3.60048i q^{31} +(0.707107 - 0.707107i) q^{32} -2.58893 q^{34} +(1.83065 - 9.65282i) q^{35} +(7.07188 - 7.07188i) q^{37} +(-0.507128 - 4.32930i) q^{38} +(0.416642 - 2.19691i) q^{40} +11.2134i q^{41} +(7.93755 - 7.93755i) q^{43} -3.82217i q^{44} -3.66171i q^{46} +(0.463170 + 0.463170i) q^{47} +12.3056i q^{49} +(-1.99558 - 4.58450i) q^{50} +(-0.0891314 + 0.0891314i) q^{52} +(3.21910 + 3.21910i) q^{53} +(-4.81150 - 7.06360i) q^{55} +4.39382i q^{56} +(2.54592 - 2.54592i) q^{58} -9.40851 q^{59} +8.21380 q^{61} +(2.54592 + 2.54592i) q^{62} +1.00000i q^{64} +(-0.0525181 + 0.276922i) q^{65} +(-8.78764 + 8.78764i) q^{67} +(1.83065 - 1.83065i) q^{68} +(5.53111 + 8.12004i) q^{70} +1.66657i q^{71} +(-3.64373 + 3.64373i) q^{73} +10.0011i q^{74} +(3.41987 + 2.70268i) q^{76} +(11.8751 + 11.8751i) q^{77} -8.82758 q^{79} +(1.25884 + 1.84806i) q^{80} +(-7.92907 - 7.92907i) q^{82} +(0.347181 - 0.347181i) q^{83} +(1.07866 - 5.68764i) q^{85} +11.2254i q^{86} +(2.70268 + 2.70268i) q^{88} +9.79832 q^{89} -0.553844i q^{91} +(2.58922 + 2.58922i) q^{92} -0.655021 q^{94} +(9.72236 + 0.689653i) q^{95} +(-6.88409 + 6.88409i) q^{97} +(-8.70140 - 8.70140i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q + 4 q^{5} - 4 q^{7}+O(q^{10}) \) 20 * q + 4 * q^5 - 4 * q^7	\( 20 q + 4 q^{5} - 4 q^{7} + 8 q^{11} - 20 q^{16} - 4 q^{17} - 44 q^{23} + 4 q^{25} + 8 q^{26} - 4 q^{28} - 4 q^{35} + 4 q^{38} + 52 q^{43} - 4 q^{47} + 16 q^{55} + 8 q^{58} + 32 q^{61} + 8 q^{62} - 4 q^{68} - 20 q^{73} + 20 q^{76} + 24 q^{77} - 4 q^{80} - 24 q^{82} + 116 q^{83} - 60 q^{85} + 44 q^{92} + 32 q^{95}+O(q^{100}) \) 20 * q + 4 * q^5 - 4 * q^7 + 8 * q^11 - 20 * q^16 - 4 * q^17 - 44 * q^23 + 4 * q^25 + 8 * q^26 - 4 * q^28 - 4 * q^35 + 4 * q^38 + 52 * q^43 - 4 * q^47 + 16 * q^55 + 8 * q^58 + 32 * q^61 + 8 * q^62 - 4 * q^68 - 20 * q^73 + 20 * q^76 + 24 * q^77 - 4 * q^80 - 24 * q^82 + 116 * q^83 - 60 * q^85 + 44 * q^92 + 32 * q^95

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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